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MRANSACTIONS
OF THE
POY @. SoOcintTyY
EDINBURGH.
VOL. XXV.
EDINBURGH:
PUBLISHED BY ROBERT GRANT & SON, 54 PRINCES STREET.
AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON.
MDCCCLXIX.
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LAWS
OF THE
ROYAL SOCIETY OF EDINBURGH,
AS REVISED 31st OCTOBER 1869.
VOL. XXV. PART II. C
of : ea : a -
et te ah ee
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LAWS.
[By the Charter of the Society (printed in the Transactions, Vol. VI. p. 5), the Laws cannot
be altered, except at a Meeting held one month after that at which the Motion for
alteration shall have been proposed. |
R
THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and
Honorary Fellows.
Il.
Kvery Ordinary Fellow, within three months after his election, shall pay Two
Guineas as the fee of admission, and Three Guineas as his contribution for the
Session in which he has been elected ; and annually at the commencement of every
Session, Three Guineas into the hands of the Treasurer. This annual contribution
shall continue for ten years after his admission, and it shall be limited to Two
Guineas for fifteen years thereafter.*
Ti.
All Fellows who shall have paid Twenty-five years’ annual contribution shall
be exempted from farther payment.
IV.
The fees of admission of an Ordinary Non-Resident Fellow shall be £26, 5s.,
payable on his admission; and in case of any Non-Resident Fellow coming to
reside at any time in Scotland, he shall, during each year of his residence, pay the
usual annual contribution of £3, 3s., payable by each Resident Fellow ; but after
payment of such annual contribution for eight years, he shallbe exempt from any
farther payment. In the case of any Resident Fellow ceasing to reside in Scot-
* At the Meeting of the Society, on the 5th January 1857, when the reduction of the Contri-.
butions from £3, 3s., to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was
resolved that the existing Members shall share in this reduction, so far as regards their future
annual Contributions.
A modification of this rule, in certain cases, was agreed to 3d January 1831.
Title.
The fees of Ordi-
nary Fellows resid-
ing in Scotland.
Payment to cease
after 25 years.
Fees of Non-Kesi-
dent Ordinary
Fellows.
Case of Fellows
becoming Non-Re-
sident.
Defaulters.
Privileges of
Ordinary Fellows.
Numbers Un-
limited.
Fellows entitled
to Transactions.
Mode of Recom-
mending Ordinary
Fellows.
Honorary Fellows,
British and
Foreign.
x
land, and wishing to continue a Fellow of the Society, it shall be in the power of
the Council to determine on what terms, in the circumstances of each case, the
privilege of remaining a Fellow of the Society shall be continued to such Fellow
while out of Scotland.
V.
Members failing to pay their contributions for three successive years (due
application having been made to them by the Treasurer) shall be reported to the
Council, and, if they see fit, shall be declared from that period to be no longer
Fellows, and the legal means for recovering such arrears shall be employed.
VI.
None but Ordinary Fellows shall bear any office in the Society, or vote in the
choice of Fellows or Office-Bearers, or interfere in the patrimonial interests of the
Society.
Vit
The number of Ordinary Fellows shall be unlimited.
VIII.
The Ordinary Fellows, upon producing an order from the TREASURER, shall be
entitled to receive from the Publisher, gratis, the Parts of the Society’s Trans-
actions which shall be published subsequent to their admission.
IX:
No person shall be proposed as an Ordinary Fellow without a recommenda-
tion subscribed by One Ordinary Fellow, to the purport below.* This recom-
mendation shall be delivered to the Secretary, and by him laid before the Council,
and shall afterwards be printed in the circulars for three Ordinary Meetings of
the Society, previous to the day of the election, and shall lie upon the table during
that time.
X.
Honorary Fellows shall not be ‘subject to any contribution. This class shall
* « A. B., a gentleman well skilled in several branches of Science (or Polite Literature, as the case
“may be), being to my knowledge desirous of becoming a Fellow of the Royal Society of Edin-
“ burgh, I hereby recommend him as deserving ofthat honour, and as likely to prove a useful and
‘“« valuable Member.”
This recommendation to be accompanied by a request of admission signed by the Candidate.
xl
consist of persons eminently distinguished for science or literature. Its number
shall not exceed Fifty-six, of whom Twenty may be British subjects, and Thirty-
six may be subjects of foreign states.
Xi.
Personages of Royal Blood may be elected Honorary Fellows, without regard
to the limitation of numbers specified in Law X.
XII.
Honorary Fellows may be proposed by the Council, or by a recommendation
(in the form given below*) subscribed by three Ordinary Fellows; and in case
the Council shall decline to bring this recommendation before the Society, it shall
be competent for the proposers to bring the same before a General Meeting. The
election shall be by ballot, after the proposal has been communicated viva voce
from the Chair at one meeting, and printed in the circulars for two ordinary
meetings of the Society, previous to the day of election.
XIII.
Royal Personages.
Recommendation
of Honorary Fel-
lows.
Mode of Election.
The election of Ordinary Fellows shall take place at the Ordinary Meetings of Election of Ordi-
the Society. The election shall be by ballot, and shall be determined by a majo-
rity of at least two-thirds of the votes, provided Twenty-four Fellows be present
and vote.
XIV.
The Ordinary Meetings shall be held on the first and third Mondays of every
month from November to June inclusive. Regular Minutes shall be kept of the
proceedings, and the Secretaries shall do the duty alternately, or according to such
agreement as they may find it convenient to make.
XV.
The Society shall from time to time publish its Transactions and Proceedings.
For this purpose the Council shall select and arrange the papers which they shall
* We hereby recommend
for the distinction of being made an Honorary Fellow of this Society, declaring that each of us from
our own knowledge of his services to (Literature or Science, as the case may be) believe him to be
worthy of that honour.
(To be signed by three Ordinary Fellows.)
To the President and Council of Royal Society
of Edinburgh.
VOL. XXV. PART II. d
nary Fellows.
Ordinary Meet-
ings.
The Transactions.
How Published.
xii
deem it expedient to publish in the Zvransactions of the Society, and shall super-
intend the printing of the same.
mV A;
The Transactions shall be published in Parts or Fasciculi at the close of each
' Session, and the expense shall be defrayed by the Society.
The Council.
Retiring Council-
lors.
Election of Office-
Bearers.
Special Meetings ;
how called.
Treasurer’s Duties.
Auditor,
There shall be elected annually, for conducting the publications and regulating
the private business of the Society, a Council, consisting of a President; Six Vice-
Presidents, two at least of whom shall be resident ; Twelve Councillors, a General
Secretary, Two Secretaries to the Ordinary Meetings, a Treasurer, and a Curator
of the Museum and Library.
XVII.
Four Councillors shall go out annually, to be taken according to the order in
which they stand on the list of the Council.
XVIII.
An Extraordinary Meeting for the Election of Office-Bearers shall be held on
the fourth Monday of November annually.
XIX.
Special Meetings of the Society may be called by the Secretary, by direction
of the Council; or on a requisition signed by six or more Ordinary Fellows.
Notice of not less than two days must be given of such Meetings.
XX.
The Treasurer shall receive and disburse the money belonging to the Society,
eranting the necessary receipts, and collecting the money when due.
He shall keep regular accounts of all the cash received and expended, which
shall be made up and balanced annually; and at the Extraordinary Meeting in
November, he shall present the accounts for the preceding year, duly audited. At
this Meeting, the Treasurer shall also lay before the Council a list of all arrears
due above two years, and the Council shall thereupon give such directions as
they may deem necessary for recovery thereof.
AXE
At the Extraordinary Meeting in November, a professional accountant shall
be chosen to audit the Treasurer’s accounts for that year, and to give the necessary
discharge of his intromissions.
Xi
XXII.
The General Secretary shall keep Minutes of the Extraordinary Meetings of General Sratetaays
the Society, and of the Meetings of the Council, in two distinct books. He shall,
under the direction of the Council, conduct the correspondence of the Society, and
superintend its publications. For these purposes, he shall, when necessary, employ
a clerk, to be paid by the Society.
The Secretaries to the Ordinary Meetings shall keep a regular Minute-book, in secretaries to
which a full account of the proceedings of these Meetings shall be entered ; they "ny Metine®
shall specify all the Donations received, and furnish a list of them, and of the
donors’ names, to the Curator of the Library and Museum: they shall likewise
furnish the Treasurer with notes of all admissions of Ordinary Fellows. They
shall assist the General Secretary in superintending the publications, and in his
absence shall take his duty.
XXIII.
The Curator of the Museum and Library shall have the custody and charge of Curator of Museum
all the Books, Manuscripts, objects of Natural History, Scientific Productions, and Speen 2.
other articles of a similar description belonging to the Society ; he shall take an
account of these when received, and keep a regular catalogue of the whole, which
shall lie in the Hall, for the inspection of the Fellows.
XXIV.
All Articles of the above description shall be open to the inspection of the Use of Museu
Fellows at the Hall of the Society, at such times and under such regulations, as “1”
the Council from time to time shall appoint.
OO
A Register shall be kept, in which the names of the Fellows shal! be enrolled Register Book.
at their admission, with the date.
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DIRECTIONS TO THE BINDER FOR PLACING THE PLATES IN THIS VOLUME.
Plate li \ Illustrating Sir David Brewster’s Paper on the Motion, Equilibrium, and
IT. Forms of Liquid Films, : . To face page
Illustrating Mr John Scott’s Paper on the Burning Mirrors of Archi-
eal miedo with some Propositions relating to the Concentration of
Light produced by Reflectors on different forms,
I11.* Ilustrating Professor Sir William Thomson’s Paper on Vortex Motion, .
TY.
Ve
VAR
NEL.
VAN.
re Illustrating Dr W. Carmichael M‘Intosh’s Paper on the Structure of the
XT British Nemerteans, and some New British Annelids,
XII.
DAG
XIV.
XV.
x VI
XVI.
ae Ilustrating Professor Fleeming Jenkin’s Paper on the Practical Appli-
XX cation of Reciprocal Figures to the Calculation of Strains on Frame-
XXL work, 3 ; ; : : ;
XXII.
XXIII. ) Illustrating Dr W. Lauder Lindsay’s Observations on New Lichenicolous
XXIV. } Micro-Fungi, ; : ;
XXYV. ) Illustrating Mr Alexander Buchan’s Paper on the Mean Pressure of the
XXVI. Atmosphere and the ens over the Globe, for the Months
XXVII. and for the Year. Part II., : E
XXVIII Illustrating Professor Alexander Dickson’s Paper on the Development of
XXIX. the Flower of Pinguicula vulgaris, L., with Remarks on the Embryos
XXX. of P. vulgaris, P. ees Gs PE: lusitanica, P. caudata, and Utri-
: cularia minor, . : ; ;
XXXI. Illustrating Mr David Milne-Home’s Paper on the Boulder-Clay of Europe,
VOL. XXV. PART II. é
305
. 441
655
‘ 0, ed
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CONTENTS.
PART I. (1868-69.)
T.—On Polyzomal Curves, otherwise the Curves JU + /V + &c. = 0.
By Professor CayLEY. Communicated by Professor Tarr,
I1.—On the Motion, Equilibrium, and Forms of Liquid Films. By the
late Sir Davin Brewster, K.H., D.C.L., &c. (Plates I.
and II.) Communicated by Francis Deas, Esq., LL.B., .
IlI].—On the Temperature of the Common Fowl (Gallus domesticus).
By the late Dr Joun Davy, F.R.SS. Lond. & Edin.
Communicated by Professor ALLMAN, oe
1V.—On the Burning Mirrors of Archimedes, with some Propositions
relating to the Concentration of Light produced by Reflectors
of diferent forms. By Joun Scort, Esq., Tain. (Plate III.)
Communicated by Professor KELLAND,
V.—On the Connection between Chemical Constitution and Physiological
Action. Part I.—On the Physiological Action of the Salts
of the Ammonium Bases, derived from Strychnia, Bructa,
Thebaia, Codeia, Morphia, and Nicotta. By Dr A. Crum
Brown and Dr Tuomas R. FRASER,
VI.—On the Products of the Destructive Distillation of Animal Sub-
stances. Part V. By THomas ANDERson, M.D., Professor
of Chemistry in the University of Glasgow,
VII.—On Vortex Motion. By Professor Sir W. THomson. (Plate III.*),
PAGE
111
119
151
XVill CONTENTS.
PART II. (1868-69.)
VIII.—On the Rotation of a Rigid a about a, Fited Point. By Pro-
fessor TIT, ; ; /
IX.—On the Structure of the British Nemerteans, and some New
British Annelids. By W. CarmicHareL M‘Intosu, M.D.,
F.L.S., Murthly, Perthshire. Communicated by Professor
TurNER. (Plates IV.-XVL.), : :
X.—Observations on the Temperature of Newly-Born Children. By
T. J. Mactacan, M.D., Dundee. Communicated by Dr J.
MatTtTHEews Duncan,
XI.—On the Practical Application of Reciprocal Figures to the Calcula-
tion of Strains on Framework. By Professor FLEEMING
JENKIN. (Plates XVII.—XXIL),
XII.—An Investigation into some previously undescribed Tetanie Symptoms
produced by Atropia in Cold-Blooded Animals, with a Com-
parison of the Action of Atropia on Cold-Blooded Animals
and on Mammals. By Tuomas R. Fraser, M.D.,
XIT—Hegel and the Metaphysics of the Fluxional Calculus. By W.
Ropertson SmitTH, M.A., Assistant to the Professor of
Natural Philosophy in the University of Edinburgh.
Communicated by Professor Ta1r, é
XIV.— Observations on New Lichenicolous Micro-Fungi. By W.LAvupER
Linpsay, M.D., F.L.S., &e. (Plates XXIII, XXIV),
XV.—On the Thermal Energy of Molecular Vortices. By W. J.
Macquorn RankInE, C.E., LL.D., F.R.SS. L. & E., &c.,
XVI.—On the Alkaloids contained in the Wood of the Bebeceru, or Green-
heart Tree (Nectandra Rodicei, Schomb.) By Doveias
MaciaGaNn, M.D., F.R.S.E., Professor of Medical Juris-
prudence in the University of Edinburgh, and ARTHUR
GamcEE, M.D., F.R.S.E., Lecturer on Physiology in
Surgeon’s Hall, Edinburgh,
PAGE
261
305
435
441
449
491
513
Or
Or
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Or
jan)
-~]
CONTENTS.
XVII.—The Mean Pressure of the Atmosphere and the Prevailing Winds
over the Globe for the Months and for the Year. Part II.
By ALEXANDER Bucnan, M.A., Secretary of the Scottish
Meteorological Society. (Plates XXV. to XXVIL.),
XVIII.—On the Development of the Flower of Pinguicula vulgaris, L. ;
with Remarks on the Embryos of P. vulgaris, P. grandiflora,
P. lusitanica, P. caudata, and Utricularia minor. By
ALEXANDER Dickson, M.D. Edin. & Dublin; Regius Pro-
fessor of Botany in the University of Glasgow. (Plates
XXVIII.-XXX.),
X1IX.—On the Boulder-Clay of Europe. By Davin Mitne Home, Esq.
(Plate XXX1.),
XX.—On the Connection between Chemical Constitution and Physiological
Action. Part IL—On the Physiological Action of the
Anmonium Bases, derived from Atropia and Conia. By Dr
A. Crum Brown and Dr THomas R. FRASER,
Proceedings of Statutory General Meetings, &c.,
List of Members Elected,
List of the present Ordinary Members AGean ly arran dee.
List of the present Ordinary Members in the Order of their Election,
List of Non-Resident Members, elected under the Old Laws,
Honorary Fellows,
» Fellows Deceased and cae Jrom 1867 a 1869,
Public Institutions, de., entitled to receive the Transactions and Prececdings
of the Society,
List of Donations continued aon Vol. XXI V. sD 830.
Indez,
9)
WO, XXV. PART If. of
X1x
PAGE
639
655
_ 693
741
745
T47
750
758
758
760
762
765
781
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ERRATA.
In Professor Tarv’s Paper,
Page 281, line 6, omit the sign of integration.
In Dr Dicxson’s Paper,
Page 641, note, line 1, omit “ only.”
Page 646, line 3, for “ extremities” read “‘ extremity.”
Plate XXIX. fig. 14, for “ pt” read “ pl.”
iy
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TRANSACTIONS.
I.—On Polyzomal Curves, otherwise the Curves
VU +V/V + &. = 0.
By Professor CayLEY. Communicated by Professor Tarr.
(Read 16th December 1867.)
Ir U, V, &c., are rational and integral functions (*)(2, y, z)’, all of the same
degree 7°, in regard to the co-ordinates (7, y, z), then /7 + /V + &c. is a poly-
zome, and the curve /U + W/V + &c. = 0a polyzomal curve. Each of the
curves / VU = 0,7 V = 0, &c. (or say the curves U = 0, V = 0, &c.) is, on account .
of its relation of circumscription to the curve /V + /V + &c. = 0, considered
as a girdle thereto (Coua), and we have thence the term “zome” and the derived
expressions ‘‘polyzome,” “zomal,” &c. If the number of the zomes /{7, V/V,
&c. be = v, then we have a »-zome, and corresponding thereto a v-zomal curve;
the curves U = 0, V = 0, &c., are the zomal curves or zomals thereof. The cases
v = 1, v = 2, are not, for their own sake, worthy of consideration ; it isin general
assumed that vis = 3 at least. It is sometimes convenient to write the general
equation in the form //V + &c. = 0, where /, &c. are constants. The Memoir
contains researches in regard to the general »-zomal curve; the branches thereof,
the order of the curve, its singularities, class, &c.; also in regard to the v-zomal
curve / (6 + L@) + &c. = 0, where the zomal curves 6 + Lo = 0, all pass
through the points of intersection of the same two curves 6 = 0, = 0 of the
orders 7 and r—s respectively ; included herein we have the theory of the depres-
sion of order as arising from the ideal factor or factors of a branch or branches.
A general theorem is given of ‘the decomposition of a tetrazomal curve,” viz..
if the equation of the curve be VJU + /mV +V¥aW + V pT = 0; then if
U, V, W, Tf are in involution, that is, connected by an identical equation
aU + bV + cW + d7 = 0, and if /, m, n, p,. satisfy the condition
“+ = + ad E = 0, the tetrazomal curve breaks up into two trizomal curves,
each expressible by means of any three of the four functions U, V, W, 7; for
VOL. XXV. PART I. a
4 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
example, in the form // U + /m V+ /p' T= 0. If, in this theorem, we take
p = 0, then the original curve is the trizomal /7U + /mV+W/n W = 0, Tis
any function = — - (aU +bV+cW), where, considering /, m, 2 as given, a, b, ¢
n
c
theorem of ‘the variable zomal of a trizomal curve,’’ viz., the equation of the
trizomal VJ U + VW V + /n W = 0, may be expressed by means of any two of
the three functions U, V, W, and ofa function 7’ determined as above, for example
in the form Vl U + Vm’ V + Vn’ T = 0; whehce also it may be expressed in
terms of three new functions 7, determined as above. This theorem, which occu-
pies a prominent position in the whole theory, was suggested to me by Mr Casey’s
theorem, presently referred to, for the construction of a bicircular quartic as the
envelope of a variable circle.
In the »-zomal curve ViU6+Le) + &c.=0, if @= 0 be a conic, 6= 0 a line.
the zomals 6 + L@ = 0, &c. are conics passing through the same two points
9 = 0, 6 = 0, and there is no real loss of generality in taking these to be the circular
points at infinity—that is, in taking the conics to be circles. Doing this, and using
a special notation A° = 0 for the equation of a circle having its centre at a given
point A, and similarly A = 0 for the equation of an evanescent circle, or say of
are quantities subject only to the condition +7 +— -—0, and we have the
the point A, we have the »-zomal curve V/A° + &c. = 0, and the more special
form /7/A + &c.=0. Asregards the last-mentioned curve, //A + &c. = 0, the
point A to which the equation A = 0 belongs, is a focus of the curve, viz., in
the case v = 3, it is an ordinary focus, and in the case v> 3, it is a special kind
of focus, which, if the term were required, might be called a foco-focus; the
Memoir contains an explanation of the general theory of the foci of plane curves.
For v = 3, the equation VJA + /mB + VnC = 0 is really equivalent to the
apparently more general form V/A° + “/mB°.+ /nC° = 0. In fact, this last is
in general a bicircular quartic, and, in regard to it, the before-mentioned theorem
of the variable zomal becomes Mr Casey’s theorem, that ‘‘ the bicircular quartic
(and, as a particular case thereof, the circular cubic) is the envelope of a variable
circle having its centre on a given conic and cutting at right angles a given
circle.” This theorem is a sufficient basis for the complete theory of the tri-
zomal curve /IA° +/“mB° + “nC? =9; and it is thereby very easily seen
that the curve V/A° + /mBY + “nC° = 0 can be represented by an equation
VUN + Vim'B’ + /n/C’=0. But for »> 3 this is not so, and the curve
VIA + &c. = 0 is only a particular form of the curve W/A° + &c. = 0; and the
discussion of this general form is scarcely more difficult than that of the special
form V/A + &c. = 0, included therein. The investigations in relation to the
theory of foci, and in particular to that of the foci of the circular cubic and
bicircular quartic, precede in the Memoir the theories of the trizomal curve
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 3
VIR? +V mB? +WnC’=9, and the tetrazomal curve //A° + /mB°+Vn0°+V pD*
—0, to which the concluding portions relate. I have accordingly divided the
Memoir into four parts, viz., these are—Part I, On Polyzomal Curves in general ;
Part II., Subsidiary Investigations; Part III, On the Theory of Foci; and Part IV.,
On the Trizomal and Tetrazomal Curves where the zomals are circles. There
is, however, some necessary intermixture of the theories treated of, and the
arrangement will appear more in detail from the headings of the several articles.
The paragraphs are numbered continuously through the Memoir. There are
four Annexes, relating to questions which it seemed to me more convenient to
treat of thus separately.
It is right that I should explain the very great extent to which, in the com-
position of the present Memoir, I am indebted to Mr Casey’s researches. His
Paper ‘On the Equations and Properties (1.) of the System of Circles touching
three circles in a plane; (2.) of the System of Spheres touching four spheres in
space; (3.) of the System of Circles touching three circles on a sphere; (4.) on
the System of Conics inscribed in a conic and touching three inscribed conics in
a plane,” was read to the Royal Irish Academy, April 9, 1866, and is published
in their “ Proceedings.” The fundamental theorem for the equation of the pairs
of circles touching three given circles was, previous to the publication of the
paper, mentioned to me by Dr Salmon, and I communicated it to Professor Cre-
mona, suggesting to him the problem solved in his letter of March 3, 1866, as men-
tioned in my paper, “Investigations in connection with Casey’s Equation,”
“Quarterly Math. Journal,” t. viii. 1867, pp. 334-341, and as also appears,
Annex No. IV. of the present Memoir.
In connection with this theorem, I communicated to Mr Casey, in March or
April 1867, the theorem No. 164 of the present Memoir, that for any three given
circles, centres A, B, C, the equation BOVA® + CA VB° + ABVC° = 0 (where
BC, CA, AB, denote the mutual distances of the points A, B, C) belongs to a
Cartesian. Mr Casey, in a letter to me dated 30th April 1867, informed me of
his own mode of viewing the question as follows :—“ The general equation of the
second order (a, 6, ¢, f, g, h) (4, 8, y) =9, where a, 8, y are circles, is a bicircular
quartic. If we take the equation (a, }, ¢, f. g, h) (A, », v)’=0 in tangential co-ordi-
nates (that is, when 4, «, v are perpendiculars let fall from the centres of a, 8, y
on any line), it denotes a conic; denoting this conic by /, and the circle which
cuts a, 8, y orthogonally by J, I proved that, if a variable circle moves with its
centre on F, and if it cuts J orthogonally, its envelope will be the bicircular
quartic whose equation is that written down above;” and among other conse-
quences, he mentions that the foci of / are the double foci of the quartic, and the
points in which J cuts /'single foci of the quartic, and also the theorem which I
had sent him as to the Cartesian, and he refers to his Memoir on Bicircular Quartics
as then nearly finished. An Abstract of the Memoir as read before the Royal Irish
4 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
“Academy, 10th February 1867, and published in their “ Proceedings,” pp. 44, 45,
contains the theorems mentioned in the letter of 50th April, and some other
theorems. It is not necessary that I should particularly explain in what manner
the present Memoir has been, in the course of writing it, added to or altered in
consequence of the information which I have thus had of Mr Casey’s researches;
it is enough to say that I have freely availed myself of such information, and that
there is no question as to Mr Casey’s priority in anything which there may be in
common in his memoir on Bicircular Quartics and in the present Memoir.
Part I. (Nos. 1 to 55).—On Potyzomat Curves IN GENERAL.
Definition and Preliminary Remarks—Art. Nos. 1 to 4.
1. As already mentioned, U, V, &c. denote rational and integral functions
(*) (a, y, 2)”, all of the same degree 7 in the co-ordinates (2, 7, ~), and the equation
VU +V7V + &. = 0
then belongs to a polyzomal curve, viz., if the number of the zomes / U7, VV, &c.,
is = v, then we have av-zomal curve. The radicals, or any of them, may con-
tain rational factors, or be of the form P/Q; but in speaking of the curve asa
v-zomal, it is assumed that any two terms, such as P VO se PNG. involving the
same radical ./Q, are united into a single term, so that the number of distinct
radicals is always = v; in particular (7 being even), it is assumed that there is
only one rational term P. But the ordinary case, and that which is almost ex-
clusively attended to, is that in which the radicals / U7, / V, &c. are distinct irre-
ducible radicals without rational factors.
2. The curves U= V = 0, &c. are said to be the zomal curves, or simply the
zomals of the polyzomal curve /U + /V + &c. = 0; more strictly, the term
zomal would be applied to the functions U, V, &c. It is to be noticed, that al-
though the form /U + /V + &c. = 0 is equally general with the form
/iU + /mV + &c.=0 (in fact, in the former case, the functions U, V, &c., are con-
sidered as implicitly containing the constant factors /, m, &c., which are expressed
in the latter case), yet it is frequently convenient to express these factors, and
thus write the equation in the form //U + ,/m V + &c. For instance, in speak-
ing of any given curves U=0, V = 0, &€., we are apt, disregarding the constant
factors which they may involve, to consider U, V, &c. as given functions; but in
this case the general equation of the polyzomal with the zomals U = 0, V = 0,
&e., is of course J/70 + /m V + &e. = 0.
3. Anticipating in regard to the cases vy = 1, vy = 2, the remark which will be
presently made in regard to the »-zomal, that ./77 + ./V + &c. = 0 is the curve
represented by the rationalised form of this equation, the monozomal curve
/U = 0 is merely the curve U = 0, viz., this is any curve whatever U = 0 of the
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 9)
order 7; and similarly, the bizomal curve ,./7 + ./V = 0 is merely the curve
U— V= 0, viz. this is any curve whatever Q = 0, of the order 7; the zomal
curves U = 0, V = 0, taken separately, are not curves standing in any special
relation to the curve in question Q = 0, but U = 0 may be any curve whatever
of the order 7, and then V = 0 is a curve of the same order 7, in involution with
the two curves OQ = 0, U= 0; we may, in fact, write the equation {2 = 0 under
the bizomal form /7 + ./9 + U=0. Inthe case 7 even, we may, however,
notice the bizomal curve P + ./U = 0 (Ff a rational function of the degree 7);
the rational equation is here Q = U— P” = 0, thatis V=Q + P’, viz., Pisany
curve whatever of the order 47, and U = 0 is a curve of the order 7, touching the
given curve Q = 0 at each of its 37’ intersections with the curve P= 0. I fur-
ther remark that the order of the v-zomal curve ,/V + &c. = 0 is =2’—7; this is
right in the case of the bizomal curve ,/U + ./V = 0, the order being = 7, but
it fails for the monozomal curve ,/U = 0, the order being in this case 7, instead of
#7, as given by the formula. The two unimportant and somewhat exceptional
cases v = 1, y = 2, are thus disposed of, and in all that follows (except in so far
as this is in fact applicable to the cases just referred to), y may be taken to be = 3
at least.
4, It is to be throughout understood that by the curve /U + /V + &c. =0
is meant the curve represented by the rationalised equation—
Norm (SU+V7V + &.) 0
viz. the Norm is obtained by attributing to all but one of the zomes ,/U, ./V, &c.,
each of the two signs +, —, and multiplying together the several resulting
values of the polyzome; in the case of a »-zomal curve, the number of factors is
thus =2’-1 r (whence, as each factor is of the degree 47, the order of the curve
is 2’-! _ 47, = 2’-27,as mentioned above). I expressly mention that, as regards
the polyzomal curve, we are not in any wise concerned with the signs of the
radicals, which signs are and remain essentially indeterminate; the equation
JU + /V + &c. = 0, is a mere symbol for the rationalised equation, Norm
(JU + /V + &¢.) = 0.
The Branches of a Polyzomal Curve—Art. Nos. 5 to 12.
5. But we may in a different point of view attend to the signs of the radicals;
if forall values of the co-ordinates we take the symbol ,/,, » andconsider /U, ./V,
&c. as signifying determinately, say the positive values of /U,./V, &c.; then each
of the several equations + ./U + ./V'+ &c.=0, or, fixing at pleasure one of the
signs, suppose that prefixed to ./V, then each of the several equations
JU + JV + &e. = 0, will belong to a branch of the polyzomal curve: a
v-zomal curve has thus 2’-! branches corresponding to the 2’—! values respec-
VOL. XXV. PART I. B
6 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
tively of the polyzome. The separation of the branches depends on the precise
fixation of the significations of ./U, ./V, &c., and in regard hereto some further
explanation is necessary.
6. When U is real and positive,*./7/ may be taken to be, in the ordinary
sense, the positive value of ./V, and so when U is real and negative, ./{7 may
be taken to be = 7 into the positive value of ./—U/; and the like as regards
JV, &c. The functions U, V, &., are assumed to be real functions of the
co-ordinates ; hence, for any real values of the co-ordinates, U, V, &c. are real
positive or negative quantities, and the significations of /U, ./V, &c. are com-
pletely determined.
7. But the co-ordinates may be imaginary. In this case the functions
U, V, &c. will for any given values of the co-ordinates acquire each of them a
determinate, in general imaginary, value. If for all real values whatever of a, 6,
we select once for all one of the two opposite values of ./a + £7, calling it the
positive value, and representing it by ./a + £7, then, for any particular values of
the co-ordinates, U being = a + Bi, the value of ./U may be taken to be
= /a + Bi; and the like as regards ,/V, &c. ./U, ./V, &c. have thus each
of them a determinate signification for any values whatever, real or ima-
ginary, of the co-ordinates. The co-ordinates of a given point on the curve
JU + /V + &. = 0, will in general satisfy only one of the equations
JU + JV &e. = 0; that is, the point will belong to one (but in general
only one) of the 2” branches of the curve; the entire series of points the
co-ordinates of which satisfy any one of the 2’! equations, will constitute the
branch corresponding to that equation. a ang
8. The signification to be attached to the expression ./a + 87 should agree with
that previously attached to the like symbol in the case of a positive or negative
real quantity; and it should, as far as possible, be subject to the condition of
continuity, viz., as a + @2 passes continuously to a’ + 8%, so ./a + Bi should pass
continuously to ./a’ + 6’7; but (as is known) it is not possible to satisfy univer-
sally this condition of continuity ; viz., if for facility of explanation we consider
(a, 8) as the co-ordinates of a point in a plane, and imagine this point to describe
a closed curve surrounding the origin or point (0, 0), then it is not possible so to
define /a + fi that this quantity, varying continuously as the point moves along
the curve, shall, when the point has made a complete circuit, resume its original
value. The signification to be attached to /a + Bi is thus in some measure
arbitrary, and it would appear that the division of the curve into branches is
affected by a corresponding arbitrariness, but this arbitrariness relates only to the
imaginary branches of the curve: the notion of a real branch is perfectly definite.
9. It would seem that a branch may be impossible for any series whatever of
points real or imaginary. Thus, in the bizomal curve /U + ,/V =0, the
branch ee /V = 0is impossible. In fact, for any point whatever, real or
PROFESSOR CAYLEY ON POLYZOMAL CURVES. fh
imaginary, of the curve, we have U = V, and therefore /U= ./V; the
point thus belongs to the other branch Mi J/V= 0, not to the branch
JU + ./V = 0; the only points belonging to the last-mentioned branch are the
isolated points for which simultaneously JU = 0, J/V= 0; viz., the points of
intersection of the two curves VU = 0, V=0.
10. It is not clear to me whether the case is the same in regard to the branch
Cre ee Vat x/ W =0 of a trizomal curve. In fact, for each point of the
curve /U+ /V + /W=0 we have (U—V—W)’=4 VW, and therefore,
U—V—W=+2A/V /W;; there may very well be points for which the sign
is +; that is, pointsfor which U=V+ W + 2 /V JW, and for these points
we have + /U= /V + \/W;; for real values of the co-ordinates the sign on
the left hand must be + (for otherwise the two sides would have opposite signs),
but there is no apparent reason, or at least no obviously apparent reason, why
this should be so for imaginary values of the co-ordinates, and if the sign be in
fact —, then the point will belong to the branch /U + /V + #/ Wak
11. But the branch in question is clearly impossible for any series of real
points ; so that, leaving it an open question whether the epithet ‘‘ impossible”’ is
to be understood to mean impossible for any series of real points (that is, as a
mere synonym of imaginary), or whether it is to mean impossible for any series
of points, real or imaginary, whatever, I say that in a »-zomal curve some of
the branches are or may be impossible, and that there is at least one impossible
branch, viz. the branch /U + /V + &c. = 0.
12. For the purpose of referring to any branch of a polyzomal curve it will be
convenient to consider /U as signifying determinately + /U, or else — /U;
and the like as regards ,/V, &c., but without any identity or relation between
the signs prefixed to the /% Nap &¢., respectively; the equation
/U + J/V + &e. = 0, so understood, will denote determinately some one (that
is, any one at pleasure) of the equations /U+/V + &. = 0, and it will thus
be the equation of some one (that is, any one at pleasure) of the branches of the
polyzomal curve — all risk of ambiguity which might otherwise exist will be
removed if we speak either of the curve /U7+ ./V, &c. = 0, or else of the
branch JU + /V + &. = 0. Observe that by the foregoing convention, when
only one branch is considered, we avoid the necessity of any employment of
the sign +, or of the sign —; but when two or more branches are consi-
dered in connection with each other, it is necessary to employ the sign —
with one or more of the radicals ./U, ./V, &c.; thus in the trizomal curve
JU + JV + /W = 0, we may have to consider the branches
wi tee WW = 0/0 + SV — /W = 0; viz. either ‘of these
equations apart from the other denotes any one branch at pleasure of the curve,
but when the branch represented by the one equation is fixed, then the branch
represented by the other equation is also fixed.
8 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
The Points common to Two Branches of a Polyzomal Curve—Art. Nos. 13 to 17.
13. I consider the points which are situate simultaneously on two branches
of the »-zomal curve /U + /V + &.= 0. The equations of the two
branches may be taken to be
JU + &. + (./W + &.) = 0,
JU + &. — (./W + &e.) = 0,
viz., fixing the significations of ./U7, ./V, ./W, &c. in such wise that in the
equation of one branch these shall each of them have the sign +, we may take
/U, &e. to be those radicals which, in the equation of the other branch, have the
sign +,and ,/W, &c. to be those radicals which have the sign —. The fore-
going equations break up into the more simple equations
JU + &=—0, /W+ &. = 0,
which are the equations of certain branches of the curves ,./U + &c. = 0, and
/W + &e. = 0, respectively, and conversely each of the intersections of these
two. curves is a point situate simultaneously on some two branches of the
original »-zomal curve /U + ./V + &. = 90. Hence, partitioning in any
manner the »-zome ./U7 + ,/V + &c. into an a-zome, ,/{7 + &c. and a 6-zome
/W + &e. (a + 8 = »), and writing down the equations
JU + & =0, /Wt+ & =0
of an a-zomal curve and a $-zomal curve respectively, each of the intersections
of these two curves is a point situate simultaneously on two branches of the
v-zomal curve; and the points situate simultaneously on two branches of the
v-zomal curve are the points of intersection of the several pairs of an a-zomal
curve and a 6-zomal curve, which can be formed by any bipartition of the »-zome.
14. There are two cases to be considered :—First, when the parts are
1,v—1(»—lis> 1, except in the case »=2, which may be excluded from
consideration), or say when the »-zome is partitioned into a zome and antizome.
Secondly, when the parts a, 8, are each > 1 (this implies vy = 4 atleast), or say
when the »-zome is partitioned into a pair of complementary parazomes.
15. To fix the ideas, take the tetrazomal curve /U+ /V+ /W+ /Tf
— 0, and consider first a point for which /U=0, /V+ /W+ /T=0.
The Norm is the product of (2° =) 8 factors; selecting hereout the factors
JU+ J0+ JW JT,
hed ese fora 8
let the product of these
=U0—-(VV+ Jw JT)
be called /, and the product of the remaining six factors be called G; the
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 9
rationalised equation of the curve is therefore YG = 0. The derived equation is
GdF + FdG = 0; at the point in question /G=0, /V+ /W+ /T=0;
G and dG are each of them finite (that is, they neither vanish nor become
infinite), but we have
F=0,dF=dU—(J/V + JW+ VD AV + JV +dWe JW+ dl + JT), =a,
and the derived equation is thus GdU = 0, or simply dU = 0. It thus appears
that the point in question is an ordinary point on the tetrazomal curve; and,
further, that the tetrazomal curve is at this point touched by the zomal curve
U=0. And similarly, each of the points of intersection of the two curves
JU=9, /V + JW + /T = 9, is an ordinary point on the tetrazomal curve ;
and the tetrazomal curve is at each of these points touched by the zomal curve
ae 0.
16. Consider, secondly, a point for which /7 + /V=0, /W+./T=0;
to form the Norm, taking in this case the two factors
LO TNE ST,
NO ER i ee
i Ot CW eel RY
be called F, and the product of the remaining six factors be called G; the
rationalised equation is /G' = 0, and the derived equation is FdG' + GdF = 0.
At the point in question G and dG are each of them finite (that is, they neither
vanish nor become infinite), but we have
F=0,dF=(/U+ JV) (dU+ JU+dV + JW-(J/W+ /D(dW+ JW+ dT+ JT), =0,
that is, the derived equation becomes identically 0 = 0; the point in question is
thus a singular point, and it is easy to see that it is in fact a node, or ordinary
double point, on the tetrazomal curve. And similarly, each of the points of
intersection of the two curves ./U+./V=09, /W+./7=0 is a node on
the tetrazomal curve.
17. The proofs in the foregoing two examples respectively are quite general,
and we may, in regard toa »-zomal curve, enunciate the results as follows, viz.,
in a »-zomal curve, the points situate simultaneously on two branches are either
the intersections of a zomal curve and its antizomal curve, or else they are the
intersections of a pair of complementary parazomal curves. In the former case,
the points in question are ordinary points on the v-zomal, but they are points of
contact of the »-zomal with the zomal; it may be added, that the intersections of
the zomal and antizomal, each reckoned twice, are all the intersections of the
v-zomal and zomal. In the latter case, the points in question are nodes of the
v-zomal; it may be added, that the »-zomal has not, im general, any nodes other
than the points which are thus the intersections of a pair of complementary para-
zomals, and that it has not 7m general any cusps.
VOL. XXV. PART I. C
let their product
10 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
Singularities of a y-comal Curve—Art. Nos. 18 to 21.
18. It has been already shown that the order of the »-zomal curve is = 2”~?7.
Considering the case where v is = 3 at least, the curve, as we have just seen, has
contacts with each of the zomal curves, and it has also nodes. I proceed to deter-
mine the number of these contacts and nodes respectively.
19. Consider first the zomal curve U = 0, and its antizomal,/V + ./W +c.
= 0, these are curves of the orders 7 and 2”~—*7 respectively, and they inter-
sect therefore in 2”-*7* points. Hence the »-zomal touches the zomal in 2”—*7*
points, and reckoning each of these twice, the number of intersections is = 2”—?7*,
viz., these are all the intersections of the »-zomal with the zomal U = 0. The
number of contacts of the v-zomal with the several zomals / = 0, V = 0, &e., is .
of course = 2”—*7°7y.
20. Considering next a pair of complementary parazomal curves, an a-zomal
and a 6-zomal respectively (a + 6 = v), these are of the orders 2*—°7 and 2°—?7
respectively, and they intersect therefore in 2«**—‘*7” = 2-47" points, nodes of
the v-zomal. This number is independent of the particular partition (a, 6), and
the v-zomal has thus this same number, 2”~—‘7°’, of nodes in respect of each pair
of complementary parazomals ; hence the total number of nodes is = 2”~‘7* into
the number of pairs of complementary parazomals. For the partition (a, 8) the
number of pairs is = [v|”+[a]{6]*, or when a = 8, which of course implies »
even, it is one-half of this; extending the summation from « = 2 to a =v — 2, each
pair is obtained twice, and the number of pairs is thus = 42D) + [a}*(B]*{;
the sum extended from « = 0 to a=» is (1 + 1)’,= 2”, but we thus in-
clude the terms 1, »,»,1, which are together = 2y + 2, hence the correct
value of the sum is = 2” — 2v—2, and the number of pairs is the half
of this = 2”~'—v—1. Hence the number of nodes of the »-zomal curve is
= (2"—1— y —]1)2"~—47".
21. The »-zomal is thus a curve of the order 2”—?7, with (2’—!— v — 1) 2¥—*r*
nodes, but without cusps; the class is therefore
= 2" ro + Ir — 2],
and the deficiency is
=2"~‘*r[ + lr—6] +1.
These are the general expressions, but even when the zomal curves U = 0, V = 0,
&c., are given, then writing the equation of the »-zomal under the form
JiU+ /mV + &c. = 0, the constants /: m: &c., may be so determined as to
give rise to nodes or cusps which do not occur in the general case; the formule
will also undergo modification in the particular cases next referred to.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 11
Special Case where all the Zomals have a Common Point or Points—Art. Nos. 22 to 27.
22. Consider the case where the zomals U = 0, V = 0 have all of them any
number, say &, of common intersections—these may be referred to simply as the
common points. Each common point is a 2”’—?-tuple point on the »-zomal curve :
it is on each zomal an ordinary point, and on each antizomal a 2”—*-tuple point,
and on any a-zomal parazomal a 2*—*-tuple point. Hence, considering first the
intersections of any zomal with its antizomal, the common point reckons as
2¥—3 intersections, and the £ common points reckon as 2”—* & intersections; the
number of the remaining intersections is therefore = 2”—*(7°— k), and the zomal
touches the v-zomal in each of these points. The intersections of the zomal with
the »-zomal are the * common points, each of them a 2”—?-tuple point on
the v-zomal, and therefore reckoning together as 2”—°s intersections; and the
2¥—% (7? — k) points of contact, each reckoning twice, and therefore together
fem2ue (@ — 4%). intersections (2"~*h + 2”~?(r*— ky = 2°97", = 7. 2”—? 4);
the total number of contacts with the zomals U=0, V=0, &c., is thus
= Be (rT —_— k) Vv.
23. Secondly, considering any pair of complementary parazomals, an «-zomal
and a $-zomal, each of the common points, being a 2«—*-tuple point and a
28—?_tuple point on the two curves respectively, counts as 2**+*—4, = 2»—* in-
tersections, and the £ common points count as 2”—‘*&# intersections; the number
of the remaining intersections is therefore = 2”—‘*(7r’ — k), each of which is a
node on the v-zomal curve; and we have thus in all 2”—*(2”—!— »— 1) (7? — &)
nodes.
24. There are, besides, the £ common points, each of them a 2”~—?-tuple point
on the v-zomal, and therefore each reckoning as $2”—?(2”—?— 1), = 2%—5— Qu—-8
double points, or together as (2””—°— 2”—*)k double points. Reserving the term
nde for the above-mentioned nodes or proper double points, and considering,
therefore, the double points (dps.) as made up of the nodes and of the 2”—?-tuple
points, the total number of dps. is thus
274 (Q”—*— y — 1) (7? — &) + (2 —F— 2%),
SDPO ee SS eee (CE ar
or finally this is
= DP CRW 3 v— 1) 7? + (v _ 1)}
so that there is a gain = 2”—*(v — 1)& in the number of dps. arising from the
& common points. There is, of course, in the class a diminution equal to twice
this number, or 2”~*(v — |); and in the deficiency a diminution equal to this
number, or 2’—*(v — 1)k.
25. The zomal curves U = 0, V = 0, &c., may all of them pass through the
same »* points; we have then / = 7’, and the expression for the number of dps.
12 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
is = (2%—*— 2”—*)p”, viz., this is = 4 2¥—? (2”—?— 1)7”. But in this case the dps.
are nothing else than the 7” common points, each of them a 2”—*-tuple point, the
v-zomal curve in fact breaking up into a system of 2”—? curves of the order
r, each passing through the 7” common points. This is easily verified, for if
6 = 0, 6 = 0 are some two curves of the order 7, then, in the present case, the
zomal curves are curves in involution with these curves; that is, they are curves
of the form /6 + /@ = 0, me + m’m = 0, &c., and the equation of the »-zomal
curve is
Jie + lo+ Jme + mot &. = 0.
The rationalised equation is obviously an equation of the degree 2”—? in 6, @,
giving therefore a constant value for the ratio 6: @; calling this g, or writing
0 = Q®, we have oes
Jig+U + Jmq +m’ + &.=0,
viz., the rationalised equation is an equation of the degree 2”—? in q, and gives
therefore 2”—? values of g. And the »-zomal curve thus breaks up into a system
of 2”—? curves each of the form 6 — g@ = 0, that is, each of them in involution
with the curves 6 = 0, 6=0. The equation in g may have a multiple root or
roots, and the system of curves so contain repetitions of the same curve or curves;
an instance of this (in relation to the trizomal curve) will present itself in the
sequel; but I do not at present stop to consider the question.
26. A more important case is when the zomal curves are each of them in
involution with the same two given curves, one of them of the order 7, the other
of an inferior order. Let 6 = 0 be acurve of the order 7, 6 = 0 a curve of an
inferior order 7 —s; L = 0, M = 0, &c., curves of the order s ; then the case in
question is when the zomal curves are of the form 6 + L@=0, 6 + Mo = 0,
&c., the equation of the »-zomal is
Jie + Le) + Jno + Me) + &. =0,
where /, m, &c., are constants. This is the most convenient form for the equation,
and by considering the functions L, M7, &c. as containing implicitly the factors
1-1, m1, &c. respectively, we may take it to includethe form //g + Lo
+ Jie Tee &c. = 0, which last has the advantage of being immediately
applicable to the case where any one or more of the constants /, m, &c. may be = 0.
27. In the case now under consideration we have the 7(7 — s) points of inter-
section of; the curves 6 = 0, @ = 0 as common points of all the zomals. Hence,
putting in the foregoing formula 4 = r(7 — s), we have a »-zomal curve of the
order 2”—?7, having with each zomal 2”—?7s contacts, or with all the zomals
2¥—7sv contacts, having a node at each of the 2”—‘7s intersections (not being
common points 6 = 0, @ = 0) of each pair of complementary parazomals; that
is, together 2”—*(2”-!— v—1)rs nodes, and having, besides, at each of the
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 13
r(r — s) common points, a 2”—?-tuple point, counting as 2?”—°’— 2”—* dps., to-
gether as (2””—°— 2”—*) r(7 — s) dps.; whence, taking account of the nodes, the
total number of dps. is = 2¥-*9[(2”-1— 2) r — (v—1)s]-
Depression of Order of the v-zomal Curve from the Ideal Factor of a Branch or Branches—
Art. Nos. 28 to 37.
28. In the case of the 7(7 — s) common points as thus far considered, the
order of the v-zomal curve has remained throughout = 2”—?7r, but the order admits
of depression, viz., the constants /, m, &c., and those of the functions L, MW, &c.,
may be such that the norm contains the factor @”; the v-zomal curve then con-
tains as part of itself (@’= 0) the curve @ = 0 taken @ times, and this being so,
if we discard the factor in question, and consider the residual curve as being the
v-zomal, the order of the v-zomal will be = 2”—’r — w (r — s).
29. To explain how such a factor * presents itself, consider the polyzome
Jie + Lo) + &c., or, what is the same thing, //7./6 + Lo + &c., belonging
to any particular branch of the curve, we may, it is clear, take ./6 + Zo, &c.
each in a fixed signification as equivalent to ./6 + Le, &c., respectively, and the
particular branch will then be determined by means of the significations attached
to /l, ./m, &c. Expanding the several radicals, the polyzome is
= lye 2? & l ies
Jt{ Je +5 L - L = + &e, 5 + be;
or, what is the same thing, it is
J6( vi i. &e.) so ene tp &e.) 7 sous (” Ji+ &e.) + &e,
which expansion may contain the factor @, or a higher power of @. For in-
stance, if we have ,// + &c. = 0, the expansion will then contain the factor @;
and if we also have L/7 + &c. = 0 (observe this implies as many equations as
there are asyzygetic terms in the whole series of functions Z, JZ, &c.; thus, if
L, M, &e., are each of them of the form aP + 6Q + cR, with the same values
of P, Q, #, but with different values of the co-efficients «, , c, then it implies the
three equations a@,/7 + &.= 0, b,/7 + &. = 0, c,/] + &c. = 0; and so in
other cases), if I say Z./7 + &c. be also = 0, then the expansion will contain
the factor @*, and so on; the most general supposition being, that the expansion
contains as factor a certain power @* of @. Imagine each of the polyzomes
expanded in this manner, and let certain of the expansions contain the factors
@*, b°, &c., respectively. The produce of the expansions is identically equal to
the product of the unexpanded polyzomes—that is, it is equal to the Norm ,
hence, if a + 6 + &c. = wo, the Norm will contain the factor @~.
VOL. XXV. PART I. D
14 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
30. It has been mentioned that the form ./7(6 + Z@) is considered as includ-
ing the form //6 + Lo, that is, when / = 0, the form ./Z@. If in the equa-
tion of the »-zomal curve there is any such term—for instance, if the equation
be /Lo + J/m(o + Mo) + &c. = 0—the radical ./Z@ contains the factor
@’; but if Z contains as factor an odd or an even power of @, then ./Z@ will
contain the factor * where « is either an integer, or an integer +3. Consider
the polyzome /Z@ + /m(6 + Mo) + &c., belonging to any particular branch
of the curve; the radical ./Z@ contains, as just mentioned, the factor @, and if
the remaining terms ./m(6 + Mo) + &c., are such that the expansion contains
as factor the same or any higher power of &, then the expansion of the polyzome
JL + J/m(Q + Mo) + &c., belonging to the particular branch will contain the
factor @*; and similarly we may have branches containing the factors +, 64, &c.,
whence, as before, if » = a + 8 + &c., the Norm will contain the factor ”; the
only difference is, that now a,(, &c., instead of being of necessity all integers,
are each of them an integer, or an integer + 4; of course, in the latter case the
integer may be zero, or the index be = 3. It is clear that » must be an integer,
and it is, in fact, easy to see that the fractional indices occur in pairs; for
observe that « being fractional, the expansion of ./m(@ + Mo) + &c., will con-
tain not «, but a higher power, @«*+2, where a + g isan integer; whence each
of the polyzomes ./Z@ + (/m(6 + Mo) + &c.) will contain the factor
31. Observe that in every case the factor presents itself as a factor of the
expansion of the polyzome corresponding to a particular branch of the curve;
the polyzome itself does not contain the factor @*, and we cannot in anywise say
that the corresponding branch contains as factor the curve @* = 0; but we may,
with great propriety of expression, say that the branch ideally contains the curve
*« = 0; and this being so, the general theorem is, that if we have branches
ideally containing the curves @* = 0, 6° = 0, &c. respectively, then the »-zomal
curve contains not ideally but actually the factor dy = 0 (# =a+6 + &c.), the
order of the v-zomal being thus reduced from 2’-27 to 2°-27 — w(7 — s); and
conversely, that any such reduction in the order of the v-zomal arises from factors
p* = 0, &? = 0, &c., ideally contained in the several branches of the »-zomal.
32. It is worth while to explain the notion of an ideal factor somewhat more
generally; an irrational function, taking the irrationalities thereof in a deter-
minate manner, may be such that, as well the function itself as all its differential
co-efficients up to the order « — 1, vanish when a certain parameter @ contained
in the function is put = 0; this is only saying, in other words, that the function
expanded in ascending powers of @ contains no power lower than ®*; and, in
this case, we say that the irrational function contains ideally the factor @«. The
rationalised expression, or Norm, in virtue of the irrational function (taken deter-
minately as above) thus ideally containing *, will actually contain the factor
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 15
*; and if any other values of the irrational function contain respectively 4, &c.,
then the Norm will contain the factor p< + 4 + &.
33. A branch ideally containing @* = 0 may for shortness be called integral
or fractional, according as the index ¢ is an integer or a fraction; by what precedes
the fractional branches present themselves in pairs. If for a moment we consider
integral branches only, then if the »-zomal contain @= 0, this can happen in one
way only, there must be some one branch ideally containing ® = 0; but if the
v-zomal contain ©’ = 0, then this may happen in two ways,—either there is a
single branch ideally containing 6 = 0, or else there are two branches, each of
them ideally containing @ = 0. And generally, if the »-zomal contain @ = 0,
then forming any partition » =a + 6+ &c. (the parts being integral), this
may arise from there being branches ideally containing @* = 0, 6 = 0, &e.
respectively. The like remarks apply to the case where we attend also to
fractional branches,—thus, if the v-zomal contain @ = 0, this may arise (not
only, as above mentioned, from a branch ideally containing @ = 0, but also) from
a pair of branches, each ideally containing @'= 0. And so in general, if the
v-zomal contain @“ = 0, the partition » = a + 8 + &c. is to be made with the
parts integral or fractional (= } or integer + 3 as above), but with the fractional
terms in pairs; and then the factor @* = 0 may arise from branches ideally con-
taining @* = 0, of = 0, &c. respectively.
34. Any zomal, antizomal, or parazomal of a v-zomal curve, af l.O+L@) + &e.
= 0, is a polyzomal curve (including in the term a monozomal curve) of the
same form as the »-zomal; and may in like manner contain @ = 0, or more gene-
rally, @* = 0, viz., ifo = a + 6 + &c. be any partition of » as above, this will
be the case if the zomal, antizomal, or parazomal has branches ideally contain-
ing @* = 0, @° = 0, &c. respectively. It is to be observed that if a zomal, anti-
zomal, or parazomal contain @ = 0, or any higher power 6” = 0, this does not
in anywise imply that the zomal contains even @'= 0. But if (attending only to
the most simple case)a zomal and its antizomal, or a pair of complementary
parazomals, each contain @ = 0 inseparably (that is, through a single branch
ideally containing @ = 0), then the »-zomal will have two branches, each ideally
containing @ = 0, and it will thus contain @’ = 0. In fact, if in the zomal and
antizomal, or in the complementary parazomals, the branches which ideally con-
tain @ = 0 are
Ji(o + Le) + &.=0, /n(o + N®) + &. = 0
respectively (for a zomal, the + &c. should be omitted, and the first equation be *
written ./7(6 + Lp) = 9), then in the »-zomal there will be the two branches
(Jo + L%) + &.)+(J/n(o + N®) + &e.) = 0,
each ideally containing @ = 0.
16 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
Conversely, if a v-zomal contain 6? = 0 by reason that it has two branches
each ideally containing @ = 0, then either a zomal and its antizomal will each of
them, or else a pair of complementary parazomals will each of them, inseparably
contain @ = 0.
35. Reverting to the case of the v-zomal curve
Ji(o + Le) + J/m(e + MS) + &. = 0,
which does not contain @ = 0, each of the 7(7— s) common points 6 = 0,
® = 0isa 2’—2-tuple point on the v-zomal; each of these counts therefore for
2»—2 intersections of the v-zomal with the curve 6 = 0, and we have thus the com-
plete number 2’—? 7 (7 — s) of intersections of the two curves, viz., the curve
@=0 meets the »-zomal in the 7(7—s) common points, each of them a
2»—2-tuple point on the v-zomal, and in no other point.
36. But if the v-zomal contains @* = 0, then each of the 7 (7 — s) common
points is still a 2’—?-tuple point on the aggregate curve; the ageregate curve
therefore passes 2’—? times through each common point; but among these
passages are included » passages of the curve @ = 0 through the common point.
The residual curve—say the v-zomal—passes therefore only 2’—2 — w times
through the common point; that is, each of the 7(7—s) common points is a
(2»—2 — w) tuple point on the »-zomal. The curve @ = 0 meets the »-zomal in
{2»—2 » — (7 —s)} (r —s) points, viz., these include the 7(7— s) common
points, each of them a (2’—? —o) tuple point on the »-zomal, and therefore
counting together as (2’—? —w) r(#— s) intersections; there remain conse-
quently » s(7 — s) other intersections of the curve 6 = 0 with the v-zomal.
37. In the case where the v-zomal contains the factor @* = 0, then throughout
excluding from consideration the 7(7—s) common points 6 = 0, @ = 0, the
remaining intersections of any zomal with its antizomal are points of contact of
the zomal with the v-zomal, and the »emaining intersections of each pair of com-
plementary parazomals are nodes of the »-zomal, it being understood that if any
zomal, antizomal, or parazomal contain a power of @6=0, such powers of
® = 0 are to be discarded, and only the residual curves attended to. The num-
ber of contacts and of nodes may in any particular case be investigated without
difficulty, and some instances will present themselves in the sequel, but on
account of the different ways in which the factor @* = 0 may present itself,
ideally in a single branch, or in several branches, and the consequent occur-
, rence in the latter case of powers of 6=0 in certain of the zomals, anti-
zomals, or parazomals, the cases to be considered would be very numerous, and
there is no reason to believe that the results could be presented in any moderately
concise form; I therefore abstain from entering on the question.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 17
On the Trizomal Curve and the Tetrazomal Curve—Art. Nos. 38 and 39.
38. The trizomal curve
VOR SV Bl WS 0
has for its rationalised form of equation
U24+ V27+ W2?—2VW —2WU —2UV=0;
or as this may also be written,
Cee OL ea 0
and we may from this rational equation verify the general results applicable to
the case in hand, viz., that the trizomal is a curve of the order 27, and that
U = 0, at each of its rv? intersections with V —~ W= 0
Ve 0; »” » W—U=0
W = 0, a : CV =0
respectively touch the trizomal. There are not, in general, any nodes or cusps,
and the order being = 27, the class is = 27(27 — 1).
39. The tetrazomal curve
J0+ JV+JWt+J/T=0
has for its rationalised form of equation
(U274+V27+4+W? + 7? — 2UV — 2UW — 2UT — 2VW— 2VT — 2WT)8 — 64UV WT = 0,
and we may hereby verify the fundamental properties, viz., that the tetrazomal
is a curve of the order 47, touched by each of the zomals VU = 0, V=0, W=0,
T = 0 in 27’ points, viz. by U = 0 at its intersections with /7 + /W+/T
= 0, that is, V? + W? + T? —2VW —2VT —2WT = 0; and the like as
regards the other zomals), and having 37’ nodes, viz., these are the intersections
of (JU + VV =9, JW+ SJT=09),(J0+ JW=9, JV + ST = 9),
(JU + /T=90,/V + /W = 9), or, what is the same thing, the intersections
of (U—V=0, W—T=0), (U—W =0, V—T= 0), (U— T=0, V—W= 0).
There are not in general any cusps, and the class is thus = 47(4r — 1) — 67’,
= 107r°— 4r.
On the Intersection of two y-Zomals having the same Zomal Curves—Art. Nos. 40 and 41.
40. Without going into any detail, I may notice the question of the intersec-
tion of two »-zomals which have the same zomal curves—say the two trizomals
JU+NV +/W=09, JIU +/mV +/nW = 9, or two similarly related
VOL. XXV. PART I. E
18 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
tetrazomals. For the trizomals, writing the equations under the form
JO+J0+ J/W=9, SINT + Vin J/V+ Jn JW=9,
then, when these equations are considered as existing simultaneously, we may,
without loss of generality, attribute to the radicals ./77, ./V, ./W, the same
values in the two equations respectively; but doing so, we must in the second
equation successively attribute to all but one of the radicals ./7, /m, ./n, each
of its two opposite values. For the intersections of the two curves we have thus
VU: SVN W = Nm — Nnidn — JSi:Ji— dm,
viz., this is one of a system of four equations, obtained from it by changes of sign,
say in the radicals ./jm and ,/n. Each of the four equations gives a set of 7°
points; we have thus the complete number, = 47°, of the points of intersection of
the two curves.
41. But take, in like manner, two tetrazomal curves; writing their equations
in the form Lidl ai ot i
ICRA +L WV tat =0.
Ji JO + Im IV + Jn JW+ VpVTH=0,
then /U, /V,/W, /7 may be considered as having the same values in the
two equations respectively, but we must in the second equation attribute succes-
sively, say to ./m, /n, \/p, each of their two opposite values. For the inter-
sections of the two curves we have
C/a> J) LV + (la Jt) JW + Jp — JT) IT = 6
(afl = lm) EF +(J/n—- Jm) JW + (Jp — J/m) /T=0
viz., this is one of a system of eight similar pairs of equations, obtained therefrom
by changes of sign of the radicals ./m, ./n, /p. The equations represent each
of them a trizomal curve, of the order 27; the two curves intersect therefore in
Ar’ points, and if each of these was a point of intersection of the two tetrazomals,
we should have in all 8 x 47” = 327° intersections. But the tetrazomals are
each of them a curve of the order 47, and they intersect therefore in only 167°
points. The explanation is, that not all the 47° points, but only 27° of them are
intersections of the tetrazomals. In fact, to find a// the intersections of the two
trizomals, it is necessary in their two equations to attribute opposite signs to one
of the radicals ./W, ./7'; we obtain 27° intersections from the equations as they
stand, the remaining 27” intersections from the two equations after we have in the
second equation reversed the sign, say of ,/7. Now, from the two equations as
they stand we can pass back to the two tetrazomal equations, and the first men-
tioned 27” points are thus points of intersection of the two tetrazomal curves —
from the two equations after such reversal of the sign of ./7, we cannot pass
back to the two tetrazomal equations, and the last-mentioned 27° points are thus
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 19
not points of intersection of the two tetrazomal curves. The number of inter-
sections of the two curves is thus 8 x 27’, = 167”, as it should be.
The Theorem of the Decomposition of a Tetrazomal Curve—Art. Nos. 42 to 45.
42. I consider the tetrazomal curve
JIT + JmVit+ JnW+ J/pT=0,
where the zomal curves are in involution,—that is, where we have an identical
relation,
aU +bV+cW+dT=0;
and I proceed to show that if /, m, n, p, satisfy the relation
mn
pa ae
b c
the curve breaks up into two trizomals. In fact, writing the equation under the
form
(J17 + /mV + J/nW) — pT =0,
and substituting for 7’ its value, in terms of U, V, W, this is
(Jd + pa)U + (md + pb)V + (nd + pe) W
+2 4/mnd J/VW+2/nid JWU + 2J/imd JUV = 9;
or, considering the left-hand side as a quadric function of (,/U, /V, ./JV), the
condition for its breaking up into factors is
ld + pa, d Jim, d Jin — 0,
el erties Suet a md
| d Jnl, dJ/nm, nd + pe
that is
p(lbed + meda + ndab + pabe) = 0 ,
or finally, the condition is
: + ~ +e SI f =.
43. Multiplying by Jd + pa, and observing that in virtue of the relation we
have
(id + pa) (md + pb) = lmd? — abe pn
(Id + pa) (nd + pce) = Ind? — sa pm ,
the equation becomes
(Ud + pa) J+ Alm JT + AJ JW) = = ad ae P( Stirs Un JW).
7 ae PROFESSOR CAYLEY ON POLYZOMAL CURVES.
or as this is more conveniently written
‘ ap TT a TT . a at ra as weet ;
(( J+ aD JU + JmV + val) = peas (b Ja - - Jn) ?
an equation breaking up into two equations, which may be represented by
VLO+ JmVt+ J/nw=l, JL0+ Jn,V+ Jn,wW=0,
where
i ee ap sehy a p
Vi = Jl + ay De a a Be
J/m,= JVnm—- La wy i i m= jee? oe
1 bed/ ss 2 bed/ a
Jag = Sat EP ovm\ ? ny = dd Sale
easariss Pp rae,
beds Cm
where, in the expressions for ,/7, &c., the signs of the radicals
J Sm, Jaa) 2
bed Z
may be taken determinately in any way whatever at pleasure; the only effect
of an alteration of sign would in some cases be to interchange the values of
(Jl, /m,, /n,) With those of (./7,, ./m,, /n,). The tetrazomal curve thus
breaks up into two trizomals.
44. It is to be noticed that we have
ty Pane
a) ap\ (1 Pp
=(+ @) (~+7+2 +4);
nN a mp
that is
And similarly we have
The meaning is, that, taking the trizomal curve /] U + /m,V + /n,W = 09,
this regarded as a tetrazomal curve, /l, U + /m,V + /n,W + »/07' = 0, satis-
fies the condition fu + = + 2 + += 0 ; and the like as to the trizomal curve
1,0 + /m,V + Jn, W = 0.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 21.
45. The equation by which the decomposition was effected is, it is clear, one
of twelve equivalent equations ; four of these are
(0+ a vn WY = A 0 \ (We Vents JT) cs
d/l
eS ES PAN 2
bao — Jin )
(0 ik ae age ) ( : y-
4. Hovw— ‘sary
ee ote ty -
aa a JIT — 2 lp 0 v)
(vi itis ilo p+) ( : y b.
ae “(a JmU—bJIP)
and the others may be deduced from these by a cyclical permutation of (U, V, W),
(a, b, c), (2, m, 2), leaving 7, d, p unaltered.
Application to the Trizomal ; the Theorem of the Variable Zomal—Art. Nos. 46 to 51.
46. I take the last equation written under the form
a sa b — — d NZ
(a Jind — > JIV) = Fe (VipU + VinpV + (p+ PVT)?
which, putting therein p = 0, is
(a, Jmol — b JI)? = ar,
which is in fact the trizomal curve,
aJm0~bJI7 + fe ar=o,
viz., the trizomal curve /J17 + /mV + /nW = 0,—if a,b, c be any quantities
connected by the equation .
oe
(the ratios a, b,c thus involving a single arbitrary parameter); and if we take 7
a function such that av + bV +cW+d7= 0; that is, 7 = 0, any one of the
VOL. XXV. PART I. F
22 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
series of curves aU +bV+cW= 0, in involution with the given curves
U=0, V=0, W = 0,—has its equation expressible in the form
aJmU — b JIT + J nr=o;
that is, we have the curve 7’ = 0 (the equation whereof contains a variable para-
meter) as a zomal of the given trizomal curve 70 + ./mV + /nW=0; and
we have thus from the theorem of the decomposition of a tetrazomal deduced
the theorem of the variable zomal of a trizomal. The analytical investigation is
somewhat simplified by assuming p = 0 ab initio, and it may be as well to repeat
it in this form.
47. Starting, then, with the trizomal curve
Ji + JnmV+ JnW =0,
and writing
aU +bV+cW+d7=0
as the definition of 7, the coefficients being connected by
Von ot:
ad a)
the equation gives
lU+mV + 2 /imUV — aW=;
or substituting in this equation for W its value in terms of U, V, T, we have
(an + cl) U + (bn + em) V + 2c /imUV + nT = 0,
which by the given relation between a, b, c, is converted into
ac be es
=f eS or 2c JimUV +dnT=0 ;
that is
ates SEM 10/0
a2m U + b21V — 2ab JimUV = ‘Ce nT ;
viz., this is
Pe OL
(a. /mU —b JiV)? = — Me
or finally
adm —bvI0 +) arso.
48. The result just obtained of course implies that when as above
L
aU +bV +eW +d7=0,5+5 +2 =0,
the trizomal curve ./7U + ./mN + »/nW = 0 can be expressed by means of any
three of the four zomals U, V, W, 7, and we may at once write down the four
forms
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 23
Re ature, WW, 7) 6
( "
z Pere
2’ az’ abe
Bs: ie
io? az ‘ abe
find, fad
abe’ abe’ abe’
the last of which is the original equation ./77 + ./mV + /nW = 9. Itmay be
added that if the first equation be represented by /m,V + /n,W + J/p,T = 9
—that is, if we have
id
amps In Fee m ie Nae ea
Jim = C2” m= b?’ YP =>
and therefore,
- t44 Fa (att Ee ae =) is (ie
or if the second equation be represented by //,U + /n,W + »/p,7 = 0,—that
is, if we have
= i. Maree 1
AE =a 2? Jig= Js, t= a
and therefore
or if the third equation be represented by /7,U + /m,V + /p,T = 0,—that
is, if we have
- [rw i
Ji, = ge, Jims = ete a2? JP = =
and therefore
then the equation of the trizomal may also be expressed in the forms—
es alc ane
oo
<a mea
Fe eee Ee
EY PR mbe _ [med
Ja, a, ab ”
24 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
bs _ [pac nad )( A A 7)=
( . 5 -ve, -NBE, JE )( Jt J7 JW JT)=0
Jl, , : ’ al ty ? Po |
[Pet = _ [aed
RES g Jig, F e ab
Nad = led
Ju Ce ea Jpg > “ab ?
and
( Fie’ lest, “a Ji, — [mee \ (vu JV. JW. JT)=0
pad — ibd
— NJ * , 5] — J» = fe
Jip Meek ae
mad lbp ey
be ’ ac ” VPs»
49, These equations may, however, be expressed in a much more elegant
form. Write
j b . Cc —d
df eee be Se
~ (By8)? — (yu)? (BB)? (aey”)”
where, for shortness, (875) = (8 — y) (y — 8) (0 — 8), &e.; (a, 8, y) being arbitrary
quantities: or, what is the same thing,
a:b:c:d = a(6yd): — b(yéda) : c'(da8) : — d'(aBy) .
Assume
Lim:n = ga(B—y)? : ob(y—a)? : rc'(a—B);
then the equation —— D +2 — = (0) takes the form
e(B—y) ate + o(y—a) (8-8) + r(a—B8) (y—8),
and the four forms of the equation are found to be
( . , ve@=7), Ve(B—2), Je (y-8)) (V2, VOT Je, VAT) =0
Vr (7- 9), - 9 ve(b—4), Jo(a—y )
Je (8-9), Vo(y—%), Vr (a—B)
viz., these are the equivalent forms of the original equation assumed to be
(8 —y) JpaU + (y—4) JSob’V + (¢ — 8) /reW = 9.
50. I remark that the theorem of the variable zomal may be obtained as a
transformation theorem—viz., comparing the equation /7U + /mV + /nw=0
with the equation //z + /my + »/nz = 0; this last belongs to a conic touched
by the three lines z = 0, y = 0, z = 0; the equation of the same conic must,
it is clear, be expressible in a similar form by means of any other three tangents
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 25
thereof, but the equation of any tangent of the conic is ax + by + cz = 0, where
m
i)
ing az + by + cz + dw = 0, we may introduce w = 0 along with any two of the
original zomals « = 0, y = 0, z = 0, or, instead of them, any three functions of
the form w; and then the mere change of 2, y, z,w into U, V, W, T gives the
theorem. But it is as easy to conduct the analysis with (U, V, W, 7) as with
(x, y,%, wv), and, so conducted, it is really the same analysis as that whereby the
theorem is established ante, No. 47.
51. It is worth while to exhibit the equation of the curve
a, b,c are any quantities satisfying the condition i ++ ~ = (0; whence, writ-
JIT + JmVit J/nW = 9,
in a form containing three new zomals. Observe that the equation L of er. - =0
b
is satisfied by a = /dx, b = mx0, c= nO”, if only 06+ 6+ x=); or say, if
6=a—a, p= a—a, x= a—a'. The equation
aA J(a—a)(a—a’\lU + (a —a’) (a —a)mV + (a’—a) (a”—a)nW
+ J/(b—v) O-VU + WV’) G—b)mV + (VU —b) (’—0)nW
+» J/(e=¢) (C—elU + (=e) (’—c)mV + (c’—c) (c’—c)nW = 0
is consequently an equation involving three zomals of the proper form; and we
can determine A, “,v in suchwise as to identify this with the original equation
JIU + J/mV + J/nW, Viz., writing successively V = 0, V= 0, W = 0, we find
(a —a")a+ (V—V’) wt (C—c’)v =0,
(a’—a)r~A + (0’—b) wt (—c) v=0,
(a—a’)rA+ (b—-U) wt (ec—e v=0,
equations which are, as they should be, equivalent to two equations only, and
which give
FM eT amt) Ha ocala pe jl Fe! Rn Ti at lS
bi0\0" GONE COO
Oe” G30 100 b, 0’, b”
and the equation, with these values of , », v substituted therein, is in fact the
equation of the trizomal curve ./W + ./mV + /nW =9 in terms of three
new zomals. It is easy to return to the forms involving one new zomal and any
two of the original three zomals.
Remark as to the Tetrazomal Curve—Art. No. 52.
52. I return for a moment to the case of the tetrazomal curve, in order to
show that there is not, in regard to it in general, any theorem such as that of the
variable zomal. Considering the form /lz + /my + J/nz + /pw = ° (the co-
VOL. XXV. PART I. G
26 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
ordinates 2, y,z,m are of course connected by a linear equation, but nothing
turns upon this), the curve is here a quartic touched twice by each of the lines
a=0, ¥y=0, z=0, w = 0 (viz., each of these is a double tangent of the curve),
and having besides the three nodes (z# = y, z = ®), (v=2% Y=W), (T=, Y = 2).
But a quartic curve with three nodes, or trinodal quartic, has only four double
tangents—that is, besides the lines z = 0, y = 0, z = 0, w = 0, there is no line
ax + By + yz + dw = 0 which is a double tangent of the curve; and writing
U, V, W, T in place of 2, y, 2, vw, then if U, V, W, 7 are connected by a linear
equation (and, @ fortiori, if they are not so connected), there is not any curve
aU +BV+yW +0L=0 which is related to the curve in the same way with
the lines VU = 0, V=0, W =0, T = 0; or say there is not (besides the curves
U=0, V=0, W=0, T=0), any other zomal eU+ BV+yW+ dST=0,
of the tetrazomal curve. The proof does not show that for special forms of
U,V, W,T there may not be zomals, not of the above forma +6V+yW+d7T=0,
but belonging to a separate system. An instance of this will be mentioned in the
sequel.
The Theorem of the Variable Zomal of a Trizomal Curve reswmed—Art. Nos. 53 to 56.
53. I resume the theorem of the variable zomal of the trizomal curve
JIT + /mV + /nW=0. ‘The variable zomal 7 =0 is the curve
aU +bV + cW = 0, where a, b, c are connected by the equation : we ks oa “ =0;
that is, it belongs to a single series of curves selected in a certain manner out of
the double series aU’ + bV + cW = 0 (a double series, as containing the two
variable parameters a: b:c). These are the whole series of curves in involution
with the given curves U = 0, V = 0, W = 0, or being such that the Jacobian
of any three of them is identical with the Jacobian of the three given curves; in
particular, the Jacobian of any one of the curves aU + bV + cW = 0, and of two
of the three given curves, is identical with the Jacobian of the three given curves.
I call to mind that, by the Jacobian of the curves U= 0, V=0, W = 0, is
meant the curve
d(x, y, 2) hg Vy V=eaV
d,W,d,W,d.W
viz., the curve obtained by equating to zero the Jacobian or functional deter-
minant of the functions U, V, W. Some properties of the Jacobian, which are
material as to what follows, are mentioned in the Annex No. I.
For the complete statement of the theorem of the variable zomal, it would
be necessary to interpret geometrically the condition ‘ ee ; a ~ = 0, thereby
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 27
showing how the single series of the variable zomal is selected out of the double
series of the curves aU + bV + cW = 0 in involution with the given curves.
Such a geometrical interpretation of the condition may be sought for as follows.
but it is only in a particular case, as afterwards mentioned, that a convenient
geometrical interpretation is thereby obtained.
54. Consider the fixed line 2 = px + qy + rz = 0, and let it be proposed to
find the locus of the (r— 1)? poles of the line 2 = 0 in regard to the series of curves
aV +bV+cw =), where « As % ae . —(, Take (z,y, z) as the co-ordinates
of any one of the poles in question, then in order that (#, y, z) may belong to one
of the (7 — 1)? poles of the line 2 = px + qy + 7rz =0 in regard to the curve
aU + bV + cW = 0, we must have
d(aU +bV+cW):d,aU +bV+cW): dau +bV+eW) =p:¢:7;
or, what is the same thing—
=ds0r dard, a
and these equations give without difficulty
abet ICV, We OyICW, U, a) :d(U, Voy,
en Sociale “en (aaa 7
whence, substituting in the equation Eat eae Uae have
l m
nN
TVW, a) t 7(W, 0a) * 70 Va"
as the locus of the (r—1)’ poles in question. Each of the Jacobians is a func-
tion of the order 277 — 2, and the order of the locus is thus = 4r—4. As the
given curves U = 0, V = 0, W = 0 belong to the single series of curves, it is clear
that the locus passes through the 3(7 — 1)? points which are the (7 — 1)? poles of
the fixed line in regard to the curves U = 0, V= 0, W= 0 respectively.
55. In the case where the given trizomal is
Jie + Le) + J/m(o + Me) + JVn(o + No=0,
s=r—1, that is, where the zomals 96+ ZOb=0, 0+ MG=0,6+4+ NO=0
are each of them curves of the order 7, passing through the 7 intersections of the
line @ = O with the curve 6 = 0, then, visti this line » = 0 for the fixed line
(2 = 0, we have
J(V,W,2) = J(0 + MS, 0 + No, s)=O{M,N},
if, for shortness, {7, V' = J(M-N,0, ©) + @J(M, N,o&), and the like as to the
other two Jacobians, so that, attaching the analogous significations to {N, ZL} and
{L, M}., the equation of the locus is
l m n
(wy * EN Zy * {za °
where observe that each of the curves {17, M} = 0, {N, LZ} = 0, {L,M} =0 is
28 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
a curve of the order 27 — 3; the order of the locus is thus = 47 — 6, and (as
before) this locus passes through the 3(7 — 1)’ points which are the (7 — 1)’ poles
of the line @ = 0 in regard to the curves 69 + Lb = 0,6 + Mb = 0,0 + Nb = 0
respectively.
56. In the case 7 = 2, the trizomal is
Jio+ Le) + J/m(o+ Me) + Jn(O+ No) =0,
where the zomals are the conics 6 + Lo = 0, 9 + MH = 0, 8 + NS = O, each
passing through the same two points 6 = 0, 6 = 0; the locus of the pole of the
line @ = 0, in regard to the variable zomal, is the conic
l m n
(W,N}* {NZ} 7 {Za ~°>
viz., {M@, N} = 0, {N,L}= 0, {Z,M}=0, are here the lines passing through
the poles of the line @ = 0 in regard to the second and third, the third and first,
and the first and second of the given conics respectively : treating /, m, n as arbi-
trary, the locus is clearly any conic through the poles of the line @ = 0 in regard
to the three conics respectively. The Jacobian of the three given conics is a conic
related in a special manner to the three given conics, and which might be called
the Jacobian conic thereof, and it would be easy to give a complete enunciation of
the theorem for the case in hand. (See as to this, Annex No. I, above referred to.)
But if, in accordance with the plan adopted in the remainder of the memoir, we
at once assume that the points 6 = 0, @ = 0 are the circular points at infinity,
then the theorem can be enunciated under a more simple form—viz., if A° = 0,
B° = 0, C° = 0 are the equations of any three circles, then in the trizomal
VIX + J/mB°+ J/nO°=0,
the variable zomal is any circle whatever of the series of circles cutting at right
angles the orthotomic circle of the three given circles, and having its centre on a
certain conic which passes through the centres of the given circles. Moreover, if
the co-efficients /, m, m are not given in the first instance, but are regarded as
arbitrary, then the last-mentioned conic is any conic whatever through the three
centres, and there belongs to such conic and the series of zomals derived there-
from as above, a trizomal curve ,//A° + ./mB° + ./nC° = 0. This is obviously
the theorem, that ifa variable circle has its centre on a given conic, and cuts at
right angles a given circle, then the envelope of the variable circle is a trizomal
curve .//A° + ./mB° + /nC*, where A®= 0, B°=0, C°=0 are any three
circles, positions of the variable circle, and /, m, 7 are constant quantities depend-
ing on the selected three circles.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 29-
Part IT. (Nos. 57 to 104).—SuBsiD1aRy INVESTIGATIONS.
Preliminary Remarks—Att. Nos. 57 and 58.
57. We have just been led to consider the conics which pass through two
given points. There is no real loss of generality in taking these to be the circular
points at infinity, or say the points /, J/—viz., every theorem which in anywise
explicitly or implicitly relates to these two points, may, without the necessity of
any change in the statement thereof, be understood as a theorem relating instead
to any two points P,Q. I call to mind that a circle is a conic passing through
the two points /, J, and that lines at right angles to each other are lines har-
monically related to the pair of lines from their intersection to the points J, J
respectively, so that when (J, /) are replaced by any two given points whatever,
the expression a circle must be understood to mean a conic passing through the
two given points; and in speaking of lines at right angles to each other, it must
be understood that we mean lines harmonically related to the pair of lines from
their intersection to the two given points respectively. For instance, the theorem
that the Jacobian of any three circles is their orthotomic circle, will mean that
the Jacobian of any three conics which each of them passes through the two given
points is the orthotomic conic through the same two points, that is, the conic such -
that at each of its intersections with any one of the three conics, the two tangents
are harmonically related to the pair of lines from this intersection to the two
given points respectively. Such extended interpretation of any theorem is appli-
cable even to the theorems which involve distances or angles—viz., the terms
“distance” and ‘‘ angle” have a determinate signification when interpreted in
reference (not to the circular points at infinity, but instead thereof) to any two
given points whatever (see as to this my “Sixth Memoir on Quantics,” Nos.
220, et seqg.*) And this being so, the theorem can, without change in the
statement thereof, be understood as referring to the two given points.
58. I say then that any theorem (referring explicitly or implicitly) to the cir-
cular points at infinity Z, J, may be understood as a theorem referring instead
to any two given points. We might of course give the theorems in the first
instance in terms explicitly referring to the two given points—(viz., instead of a
circle, speak of a conic through the two given points, and so in other instances) ;
but, as just explained, this is not really more general, and the theorems would be
given in a less concise and familiar form. It would not, on the face of the inves-
tigations, be apparent that in treating of the polyzomal curves
Ji + 1%) + Jm(@ + Me) + &e. = 0,
(9 = 0 a conic, = 0 a line, as above), that we were really treating of the
* Phil. Transactions, vol. cxlix. (1859), pp. 61-90. See p. 86,
VOL, XXY. PART I, H
30 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
curves the zomals whereof are circles, and therein of the theories of foci and
focofoci as about to be explained. And for these reasons! shall consider the
two points 6 = 0, @ = 0, to be the circular points at infinity J, J, and in the
investigations, &c., make use of the terms circle, right angles, &c., which, in their
ordinary significations, have implicit reference to these two points.
The present Part does not explicitly relate to the theory of polyzomal curves,
but contains a series of researches, partly analytical and partly geometrical, which
will be made use of in the following Parts III. and IV. of the Memoir.
The Circular Points at Infinity ; Rectangular and Circular Co-ordinates—Art. Nos. 59 to 62.
59. The co-ordinates made use of (except in the cases where the general
trilinear co-ordinates (2, 7, ), or any other co-ordinates, are explicitly referred to),
will be either the ordinary rectangular co-ordinates 2, y, or else, as we may term
them, the circular co-ordinates & 7 (= + iy, 2 — iy respectively, 7 = ./ — ] as
usual), but in either case I shall introduce for homogeneity the co-ordinate 2, it
being understood that this co-ordinate is in fact = 1, and that it may be retained
or replaced by this its value, in different investigations or stages of the same
investigation, as may for the time being be most convenient. In more con-
cise terms, we may say that the co-ordinates are either the rectangular co-ordi-
nates x, y, and z ( = 1), or else the circular co-ordinates £, », and z(=1). The
equation of the line infinity is 7 = 0; the points J, J are given by the equations
(a + iy = 0, z = 0) and (« — wy = 0, z = 0), or, what is the same thing, by the
equations (& = 0, z = 0) and (7 = 0, = 0) respectively; or in the rectangular co-
ordinates the co-ordinates of these points are ( — 7, 1, 0) and (2, 1, 0) respectively,
and in the circular co-ordinates they are (1, 0, 0) and (0, 1, 0) respectively. It is
of course, only for points at infinity that the co-ordinate z is = 0 (and observe that
for any such point the z and y or € and 7 co-ordinates may be regarded as finite) ,
for every point whatever not at infinity the co-ordinate z is, as stated above, = 1.
60. Consider a point A, whose co-ordinates (rectangular) are (a, a’, 1) and
(circular) (a, a’, 1), viz. a = a+ ai, a =a—av7; then the equations of the lines
through A to the points J, J, are
x—az+uUy—az)=0, «—az— i(y— az)=0
respectively, or they are
-—az= » n—az=0
respectively. These equations, if (a, a’) or (a, a’) are arbitrary, will, it is clear, be
the equations of any two lines through the points J, J, respectively.
61. We have from either of the equations in (2, y,z)
(«— az? + (y—a’z)? =0,
that is, the distance from each other of any two points (2, y, 1), and (a,@’,1) ina
PROFESSOR CAYLEY ON POLYZOMAL CURVES. dl
line through J or Jis=0. And in particular, if z = 0, then 2 + y’ = 0; that is,
the distance of the point (@,a@’,1) from J or J is in each case = 0.
62. Consider for a moment any three points P,Q, A; the perpendicular dis-
tance of P from QA is = 2 triangle PQA ~ distance QA; if Q be any point on
the line through A to either of the points J, J, and in particular if Q be either of
the points J, J, then the triangle PQA is finite, but the distance QA is = 0: that
is, the perpendicular distance of P from the line through A to either of the points
I, J, that is, from any line through either of these points, is = 00. But, as just
stated, the triangle PQA is finite, or say the triangles P/A, PJA are each finite;
viz., the co-ordinates (rectangular) of P, A being (a, y, z = 1), (a, a’, 1) or (circular)
(E,, 2 = 1), (a, a’, 1), the expressions for the doubles of these triangles respec-
tively are
L,Y, @ 6 “L,Y, @
me ay Ae
a, Gal | a, DEAL
that is, they are (rectangular co-ordinates) e—az + 1(y— a’ z), x—az—i(y—a@e),
or (circular co-ordinates) & — az, » —a’ z.
Representing the double areas by PJA, PJA, respectively, and the squared
distance of the points A, P by A, we have—
A = (a — az)? + (y — a2)?
= (& — az) (n — wz), = PIA, PUA.
Antipoints ; Definition and Fundamental Properties—Art. No. 63.
63. Two pairs of points (A,B) and (4,,B,) which are such that the lines
AB, A,B, bisect each other at right angles in a point O in such wise that
OA = OB =1 0A, =i0OB,, are said to be antipoints, each of the other. In
rectangular co-ordinates, taking the co-ordinates of (4 B,) to be (a,0,1) and
(—a, 0,1), those of (A,, B,) will be (0, a, 1) and (0, — az, 1) respectively, whence
joining the points (A, B) with the points (J, -/), the points A,,B, are given as the
intersections of the lines AJ and BJ, and of the lines AJ and BI respectively.
Or, what is the same thing, in any quadrilateral wherein J, J are opposite angles,
the remaining pairs (A,B) and (A,, B,) are antipoints each of the other.
64. In circular co-ordinates, if the co-ordinates of A are (a, a’, 1), and those of B
are ((@, 6’, 1), then the equations of
ALAJ are §—az=0, 1-—e&z=0
BI, BI ” &—pz= 2 1—6z=0
whence the equations of
A,I,A,J are §—az=0, 4—Bz=0
BLBIT , F—-Pze=0, 4-az=0.
32 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
65. Considering any point P the co-ordinates of which are £,,2 (= 1), let
A,B,A,,B, be its squared distances from the points A,B, A,,B, respectively;
then by what precedes—
A = (& — az) (n— a2),
B = (§ — 2) (n— 8B),
A, = (€ — az) (n — B2),
B, = (§ — Bz) (n — 2),
and thence
A.B=A,.B,;
that is, the product of the squared distances of a point P from any two points
A, B, is equal to the product of the squared distances of the same point P from
the two antipoints A,,.B,. This theorem, which was, I believe, first given by me
in the Educational Times (see reprint, vol. vi. 1866, p. 81), is an important one
in the theory of foci. It is to be further noticed that we have
A+B—A,—B,=(«-8)(/—6)#
= K2,=K,
if K, = (a — a’) (8 — 8’), be the squared distance of the points A, 6, = — squared
distance of points 4,, B,.
Antipoints of a Circle—Art. No. 66.
66. A similar notion to that of two pairs of antipoints is as follows, viz., if
from the centre of a circle perpendicular to its plane and in opposite senses, we
measure off two distances each = 7 into the radius, the extremities of these
distances are antipoints of the circle. It is clear that the antipoints of the circle
and the extremities of any diameter thereof are (in the plane of these four points)
pairs of antipoints. It is to be added that each antipoint is the centre of a sphere
radius zero, or say of a cone sphere, passing through the circle: the circle is thus
the intersection of the two cone spheres having their centres at the two antipoints
respectively.
Antipoints in relation to a Pair of Orthotomie Circles—Art. No. 67.
67. It is a well-known property that if any circle pass through the points
(A, B), and any other circle through the antipoints (4,, B,), then these two circles
cut at right angles. Conversely if a circle pass through the points A, B, then all
the orthotomic circles which have their centres on the line AB pass through the
antipoints 4,,.B,. In particular, if on AZ as diameter we describe a circle and
on A, #, as diameter a circle, then these two circles—being, it is clear, concentric
circles with their radii in the ratio 1:7, and as concentric circles touching each
other at the points (Z,/)—cut each other at right angles; or say they are con-
centric orthotomic circles:
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 33
Forms of the Equation of a Circle—Art. Nos. 68 to 71.
68. Tn rectangular co-ordinates the equation of a circle, co-ordinates of centre
(a, a’, 1) and radius = a’, is
Ao = (a@—az? + (y—a 2)?-a® 2 =0;
and in circular co-ordinates, the co-ordinates of the centre being (a, a’, 1), and
radius=a’ as before, the equation is
A® = (&— az) (n- wz) -—a? 2 =0.
69. I observe in passing, that the origin being at the centre and the radius
being=1, then writing also z=1, the equation of the circle is &;=1, that is the
circular co-ordinates of any point of the circle, expressed by means of a
variable parameter @, are (6, 7 i.
70. Consider a current point P, the co-ordinates of which (rectangular) are
2, y, (=1), and (circular) are &, », 2 (=1), then the foregoing expression
= (wx—az)? + (y—a 2)? —a'?
= (§—az) (n—a@z) —a'?
denotes, it is clear, the square of the tangential distance of the point P from the
circle A° = 0.
71. But there is another interpretation of this same function A°, viz., writing —
therein z = 1, and then
A’ =(x—a)? +(y— a)? + (a1)?,
we see that A’ is the squared distance of P from either of the anti-points of the
circle (points lying, it will be recollected, out of the plane of the circle), and we
have thus the theorem that the square of the tangential distance of any point P
from the circle is equal to the square of its distance from either anti-point of
the circle.
On a System of Sixteen Points—Art. Nos. 72 to 77.
72. Take (A, B, C, D) any four concyclic points, and let the anti-points of
(B, C), (A, D) be (By, OC), (Ap Dy) »
(C, 4), (BD) » (Cy Ae), (Ba De) »
(4, B), (GD) » (As Bs), (Cs, Ds) »
then each of the three new sets (4,, B,, C,, D,), (4,, B,, C,, D,), (Ag, B;, Cz, Ds)
will be a set of four concyclic points.
73. Let O be the centre of the circle through (A, B, C, D), say of the circle O,
and then, the lines BC, AD meeting in R, the lines CA, BD in S, and the lines
AB, CD in T, let each of these points be made the centre of a circle orthotomic
to O, viz., let these new circles be called the circles R, S, T respectively.
As regards the circle #, since its centre lies in BC, the circle passes through
(B,, C,); and since the centre lies in AD, the circle passes through (4,, D,), that
is, the four points (4,, B,, C,, D,) lie in the circle R. Similarly (4,, B,, C,, D,)
lie in the circle S, and (A,, B,, C,, D,) in the circle 7.
VOL. XXV. PART I. I
34 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
74. The points #, S, 7 are conjugate points in relation to the circle O; that
is, ST, TR, RS are the polars of &, S, 7 respectively in regard to this circle; and
they are, consequently, at right angles to the lines OR, OS, OT respectively ; viz.,
the four centres O, #,S,7 are such that the line joining any two of them
cuts at right angles the line joining the other two of them, and we see that the
relation between the four sets is in fact a symmetrical one; this is most easily
seen by consideration of the circular points at infinity J, J, the four sets of
points may be arranged thus :—
A,A oe
By; Ty, Tie, Pas
OL, Us eas
BEDS | TEs RS
a» Ao,
B
in such wise that any four of them in the same vertical line pass through J, and
any four in the same horizontal line pass through / ; and this being so, starting
for instance with (A,, B,, C,,.D,) we have anti-points
of (Bs, C,), (Ag, Ds) are (By, Cy), (Ag, Dy),
» (Cy Ay), (By Dg)» (Cy Ay) (By Dy);
» (Az, Bs), (C;, D,) » (A ? £,), (C , D 7;
and similarly if we start from (4,, B,, C,, D,) or (A,, B,, C,, D,).
75. [return for a moment to the construction of (A,, B,, C,, D,); these are
points on the circle #, and (B,, C,) are the anti-points of (B, C); that is, they are
the intersections of the circle # by the line at right angles to BC from its middle
point, or, what is the same thing, by the perpendicular on BC from O. Similarly
(A,, D,) are the anti-points of (A, D); that is, they are the intersections of the
circle 2 by the perpendicular on AD from O. And the like as to (A,, B,, C,, D,)
and (A,, B,, C,, D,) respectively.
76. Hence, starting with the points A, 6, C, D on the circle O, and constructing
as above the circles P, Q, #, and constructing also the perpendiculars from O on
the six chords AB, AC, &c.,
the perpendiculars on BC, AD meet circle Rin (B,, C,), (A;, D,),
. CA,BD , 4 S 5 (Cz,A2), (By D,),
3 AB OD eee ogee soe) (tebe a
so that the whole system is given by means of the circles P, Q, &, and the six
perpendiculars.
77. If to fix the ideas (A, 6, C, D) are real points taken in order on the real
circle O, then the points #, S, 7 are each of them real; but # and 7 lie outside,
S inside the circle O. The circles R and 7 are consequently real, but the circle
S imaginary, viz., its radius is = 7 into a real quantity; the imaginary points
(A,, B,, C,, D,) are thus given as the intersections of a real circle by a pair of
real lines, and the like as to the imaginary points (4,, 6,,C,, D,); but the
PROFESSOR CAYLEY OF POLYZOMAL CURVES. 35
imaginary points (A,, B,, C,, D,) are only given as the intersections of an imagin-
ary circle (centre real and radius a pure imaginary) by a pair of real lines. The
points (C,, A,) gud anti-points of (C, A) are easily constructed as the intersections
of a real circle by a real line, and the like as to the points (B,, D.) qua anti-points
of (B, D), but the construction for the two pairs of points cannot be effected by
means of the same real circle.
Property in regard to Four Confocal Conics—Art. Nos. 78 to 80.
78. All the conics which pass through the four concyclic points A, B, C, D, have
their axes in fixed directions; but three such conics are the line-pairs (BC, AD),
(CA, BD), and (AB, CD), whence the directions of the axes are those of the bisec-
tors of the angles formed by any one of these pairs of lines; hence, in particular,
considering either axis of a conic through the four points, the lines 4B and CD
are equally inclined on opposite sides to this axis, and this leads to th theorem
that the anti-points (A,, B,) (C,, D,) are in a conic confocal to the given conic
through (A, B, C, D); whence, also, considering any given conic whatever through
(A, B, C, D), the points (A,,.B,, C,, D,), (A,, B,, C,, D,) (A;, B,, C,, D;) lie seve-
rally in three conics, each of them confocal with the given conic.
79. To prove this, consider any two confocal conics, say an ellipse and a hyper- -
bola, and let /' be one of their four intersections; join / with the common centre
O, and let OT, ON be parallel to the tangent and normal respectively of the ellipse
at the point /. OF, OT are in direction conjugate axes of the ellipse, and OF,
ON are in direction conjugate axes of the hyperbola; and if they are also the axes
in magnitude, that is, if the points 7, NV are the intersections of OT with the
ellipse and of ON with the hyperbola respectively, then it is easy to show that
OT? +0N?=0. And this being so, imagine on the ellipse any two points A, B
such that the chord AB is parallel to OT, that is conjugate to OF; AB is bisected
by OF, say in a point K, or we have parallel to O7 the semichords or ordinates
KA=KEB; and we may, perpendicularly to this or parallel to ON, draw through
K in the hyperbolaa chord A,B,, which chord will be bisected in K, or we shall
have KA, = KB,. Hence KA, KA, are in the ellipse and the hyperbola respec-
tively ordinates conjugate to the same diameter O/’, and the semi-diameters con-
jugate to OF being OT, ON respectively, we have KA?(—KB’): KA; (=KB?’)
= OF : ON’, that is, KA7=KB’= — KA = — KB’; or (A,, B,) will be the
anti-points of (A, B).
80. Conversely, if in the ellipse we have the two points (A, B), then drawing
the diameter OF’ conjugate to A, and through its extremity /, the confocal
hyperbola, then the anti-points (A,, B,) will lie on the hyperbola. And similarly,
if on the ellipse we have the two points (C,D), then drawing the diameter
OG conjugate to CD, and through its extremity G a confocal hyperbola, the
36 PROFESSOR CAYLEY ON POLYZOMAL CURVES,
anti-points (C,, D,) will lie on the hyperbola. Suppose (A, B, C, D) are concyclic,
then, as noticed, AB and CD will be equally inclined on opposite sides to the
transverse axis of the ellipse—the conjugate diameters OF, OG will therefore be
equally inclined on opposite sides of the transverse axis—and the points / and @
will therefore be situate symmetrically on opposite sides of the transverse axis,
that is, the points / and @ will respectively determine the same confocal hyper-
bola, and we have thus the required theorem, viz., if (A, B,C, D) are any four
concyclic points on an ellipse, or say on a conic, and if (A,, B,) are the anti-
points of (A, B), and (C,, D,) the anti-points of (C, D), then (A,, B,, C,, D;) will
lie on a conic confocal with the given conic.
System of the Sixteen Points, the Axial Case—Art. Nos. 81 to 85.
81. The theorems hold good when the four points A, B, C, D are ina line; the
anti-points (B,, C,) of (B, C), &c., are in this case situate symmetrically on oppo-
site sides of the line, so that it is evident at sight that we have (A,, B,, C,, D,),
(A,, B,, C,, D,), (A;, B;, C;, D;), each set in a circle; and that the centres
R, S, T of these circles lie in the line. The construction for the general case
becomes, however, indeterminate, and must therefore be varied. If in the general
case we take any circle through (B, C), and any circle through (A, JD), then the
circle # cuts at right angles these two circles, and has, consequently, its centre
# in the radical axis of the two circles; whence, when the four points are ina
line, taking any circle through (4,C), or in particular the circle on BC as
diameter, and any circle through (A, J), or in particular the circle on AD as
diameter,—the radical axis of these two circles intersects the line in the required
centre /, and the circle # is the circle with this centre cutting at right angles
the two circles respectively; the circles S and 7 are, of course, obtained by the
like construction in regard to the combinations (C, A ; B, D) and (A, B; C,D,
respectively. It may be added, that we have
R extremities R BGs. A, D,
S kent and | of diameter S | sicojngt points of involutions GU, 4, B,D,
g of circles TZ Ay B.D
and that (as in the general case) the circles R, S, 7 intersect each pair of them at
right angles; and they are evidently each intersected at right angles by the line
ABCD (or axis of the figure), which replaces the circle O in the general case.
82. If the points 4, B,C, D are taken in order on the line, then the points
Rk, S, T are all real, viz., the point £ is situate, on one side or the other, outside
AD, but the points S and 7’ are each of them situate between B and C; the
circles & and 7 are real, but the circle S has its radius a pure imaginary
quantity.
83. If one of the four points, suppose D, is at infinity on the line, then the
anti-points of (A, D), of (B, D), and of (C, D) are each of them the two points
PROFESSOR CAYLEY ON POLYZOMAL CURVES. Sif
(Z,J). It would at first sight appear that the only conditions for the circles
R, S, T were the conditions of passing through the anti-points of (B, C), of (C, A),
and of (A, B) respectively, and that these circles thus became indeterminate ;
but in fact the definition of the circles is then as follows, viz., # has its centre
at A, and passes through the anti-points of (B,C): (whence squared radius
=AB.AC). And similarly, S has its centre at B,and passes through anti-points
of (C, A), (squared radius = BA.BC); and 7 has its centre at C, and passes
through anti-points of (A, &), (squared radius = C'A . CB); these three circles
cut each other at right angles. As before, 4, B, C being in order on the line, the
circles 2, 7 are real, but the circle S has its radius a pure imaginary quantity.
84. That the circles are as just mentioned appears as follows: taking the
line as axis of z, and a, b,c, d for the « co-ordinates of the four points respectively,
then the co-ordinates of A,, D, are
t(a + d), +4i(a — a);
whence, m being arbitrary, the general equation of a circle through 4,, D, is
a + y® — 2mxz + [m(a + d) — ad] =0 ,
writing herein 0 — this becomes -
2 2
e+ ye 2(« — 7) + G —k? — <)#=0 ;
d
viz., for d = o it is
which is a circle having 4 for its centre, and its radius an arbitrary quantity &.
If the circle passes through the anti-points of B, C, the co-ordinates of these are
4(64+¢),+Mb-o),
and we find
ke = [3(0 + ec) — a}?— 400 -— OF =(@— bla — 0).
85. Reverting to the general case of four points A, B,C,D on a line, the
theorem as to the confocal conics holds good under the form that, drawing
any conic whatever through (4,, B,, C,, D,) the points (4,, B,, C,, D,), and
(A,, B,, C;, D,) lie in confocal conics, these conics have their centre on the line, and
axes in the direction of and perpendicular to the line. When D is at infinity,
the confocal conics become any three concentric circles through (B,,C,), (C,, A.)
and (A,, B,) respectively.
The Involution of Four Circles——Art. Nos. 86 to 91.
86. Consider any four points A, B,C, D, the centres of circles denoted by
these same letters, and let A°, B°, C°, D° signify as usual, viz., if (in orthogonal
VOL. XXV. PART I. K
38 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
co-ordinates) (a, a’, 1) are the co-ordinates of the centre, and a” the radius of the
circle A, then A° stands for (2 — az)? + (y—az) —a”’~, and the like for
B’, C°, D°. Write also
a:b:e:d=BCD: —CDA : DAB: — ABC,
where BCD, &c., are the triangles formed by the points (B,C, D), &c.; the
analytical expressions are
as bsats th] 0, OS bis) Gee, 2 d,d, 1 | — | aa, 1 |
iw fae | 4d, 1 a, @ 4 bo, Y, 1 |
| hs sill a els |. Cy yh Db ¥, yk oat; 4.\)
so that
a +b itetd> =F,
aa + bb + ce + dd = 0,
aa + bb’ + ce + dd = 0;
this being so, it is clear that we have
aA° + bB° + cC°® + dD® =
2[a(a? + a?—a'?) + b(0?+0?—-b) + (2? +07 — 0") + dP +d*- d®)) = KZ,=K,
a constant.
87. I am not aware that in the general case there is any convenient expres-
sion for this constant A ; it is = 0 when the four circles have the same ortho-
tomic circle; in fact, taking as origin the centre of the orthotomic circle, and its
radius to be = 1, we have
a2 + a® — a? = 1, &.,
whence
K= s+ b+¢.44=0;
that is, if the circles 4, B, C, Dhave the same orthotomic circle, then A’, B°, C°, D®,
a, b, ¢, d, signifying as above, we have
aA° + bB° + cC° + dD°= 0,
and, in particular, if the circles reduce themselves to the points 4, 5, C, D re-
spectively, then (writing as usual A, B,C, D in place of A’, B’, C°, D°) if the
four points A, 6, C, D are on a circle, we have
aA + bB +00 +dD=0.
88. This last theorem may be regarded as a particular case of the theorem
aA + bB+cC + dD= Kk? = K,
viz., the four circles reducing themselves to the points A, B, C, D, we can find
for the constant A an expression which will of course vanish when the points
are onacircle. For this purpose, let the lines BC,AD meet in AR, the lines
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 39
CA, BD in S, and the lines Ab, CD in T; we may, to fix the ideas, consider
ABCD as forming a convex quadrilateral, R and 7’ will then be the exterior
centres, S the interior centre; a, b, c,d, may be taken equal to BCD, — CDA,
DAB, — ABC, where the areas BCD, &c., are each taken positively. The
expression aA + bB + cC + dD has the same value, whatever is the position
of the point P (z, y, z = 1); taking this point at #, and writing for a moment
ha = 7 = 0, Ro = y, AD = 3,
then
BCD = (RCD — RED) =}RD (RC — LB) sin k = (y—B)ésin £,
with similar expressions for the other triangles; and we thus have
, . &(y¥—Bd
eco ae ane) 8? Ca acts Bey — wdyly —
4 eG / &. 77(8 — «)8 ame, Yi a nog B)(6 ae
— Py — Ba
that is, replacing a, 6, y, 0, by their values, and writing also z = 1, we have
aA + bB + cC +dD=4sinR. (RB. RC — RA. RD)BC. AD,
where 4sin &.BC.AD is in fact the area of the quadrilateral ABCD ; we have
thus
aA + bB + cO + dD = (RB.RC—RA.RD)O
= (SC .SA —SB.SD)5
' = (TA.TB-—TC.TD)O
where it is to be observed that SA, SC being measured in opposite directions
from S, must be considered, one as positive, the other as negative, and the like as
regards SB, SD. This expression for the value of the constant is due to Mr
Crofton. In the particular case where A, 6, C, D, are on acircle, we have as
before
aA + bB+cC +dD=0.
89. If the four points A, 6, C, D, are on a circle, then, taking as origin the
centre of this circle and its radius as unity, the circular co-ordinates of the four
points will be ;
(<3); 622): 34) Gh)
the corresponding forms of A, &c., being |
A° = (2 — az) (1 aa 2) — W?2, &e.
the expressions for a, b, c,d, observing that we have
1
= Bye (By8), &e.
+0) PROFESSOR CAYLEY ON POLYZOMAL CURVES.
if (By0), &c., denote (8 — y) (y — 9) (6 — B), &c., become
a:b:c:d = a(Byd): — B(yda) : y(da8): — b(aBy),
which are convenient formule for the case in question.
90. If the points A, B, C, D, are on a line, then taking this line for the axis of
a, we may write A°=(# —az) +y*°—a@’2, &c. It is to be remarked here
that we can, without any relation whatever between the radii of the circles, satisfy
the equation
aA® + bB° + cC° + dD° = 0;
in fact this will be the case if we have
a ze 0) + ¢ 2d 0,
aul + bb + ce +dd=0,
a(a? — a’*) + b(b? — b”) + ee? — ce”) + dd? — d”) = 0,
equations which determine the ratios a: b:c:d. In the case where the circles
reduce themselves to the points A, B, C, ), these equations become
a+b +e++d =0,
aa + bb +cc +dd =0,
aa? + bb? + cc? + dd? = 0,
giving
a:b:ce:d = (bed): — (eda): (dab): — (abe);
if for shortness (Jed), &c. stand for (b — c)(e — d)(d — b), &c.; and for these values,
we have
aA + bB + cO0 + dD=0.
91. A very noticeable case is when the four circles are such that the foregoing
values of (a, b, c, d) also satisfy the equation
aA° + bB° + cC° + dD®° = 0;
the condition for this is obviously
aa”? + bb’? + ce’? + dd’ = 0;
or, as it may also be written,
a Up} b”2 2 qd’?
G-)G-da8) ConC-D0Lo Haie=ate =n
On a Locus connected with the foregoing Properties.—Art. No. 92.
92. lf, as above, A, B, C, Dareany four points, and A, B, C, D are the squared
distances of a current point P from the four points respectively, then the locus
of the foci of the conics which pass through the four points is the tetrazomal curve
aJ/A+b/B+c/6+d/D=0.
In fact the sum aA + bB + cC + dD has, it has been seen, a constant value for
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 41
all positions of the point P; taking P to be the other focus, its squared distances
are (k —,/A)’, &c., whence for the first-mentioned focus we have
aA + bB + cC + dD = a(t — JA)? + bE — VB)? + ck — JOY + d(k— JD);
or recollecting that a+b+e¢e+d=0, we have for the locus in question
a/A+b,/B + ¢./C + 4,/D = 90; this locus will be discussed in the sequel.
I remark here, that in the case where the four points are on a circle, then (as
mentioned above), the axes of the several conics are in the same fixed directions ;
there are thus two sets of foci, those on the axis in one direction, and those on
the axis in the other direction; it might therefore be anticipated, and it will
appear, that in this case the tetrazomal breaks up into two trizomal curves.
Formule as to the two Sets (A, B, C, D), and (A,, B,, Cy, D,), each of four Concyclic
Points—Art. Nos. 98 to 98.
93. Consider the four points A, B, C, D ona circle, then taking, as before, their
circular co-ordinates to be (a, a’, 1), (8, 6’, 1), (vy, y, 1), (6, 6 1), the condition that
the points may be on a circle is
eee ncusmecce | == 4)
1, B, B, BR’
Ly 7,97
eect
viz., this equation may be written
(8 — vy) (@— 8): (y— 4) (8 — 8): (@— 8B) (y — 8)
= (8 — 7) (#—8) : (y¥—@’) (8-8) : (a —B) (7'—8) ;
or, if for shortness, we take
nee ke fy fe 8,
b=y—4, g=P—s4, a g =B-8,
ec=a—PB, h=y—6, ¢d=a@—-P, VW=y7-3,
and consequently
af+bg+ch=0, af +Ug +ch =0,
a=g-h, w=g-h,
= h— if, C= h — f,
c=f—g, eé=f—g,
atb+c=0, wv+04+ce=0,
then the equation is
asg:th=arsbg ich .
94. Let a,b,c,d, denote as before (a:b:c:d= BCD:—CDA:DAB:—ABC),
then we have
aye Drees ee hs Bye Ws |hOn On Wilts ell ten ce, L |
Pee ON aL! he ot! 18.8.1)
siya a,a@,1| |6, 8,1 Ae se
VOL. XXV. PART I. L
42 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
and we may write
a= ; ah’ —ah, af —ag, gi —gh,
b = bh’ — Uh, . , bf —Vf, hf —Xf,
c= — 4, of — cf, : 7 Ie —J9:;
d=cl' — cb, ad —aec, ba — Va,
viz., the expressions in the same horizontal line are equal, and a, b, ¢, d are pro-
portional to the expressions in the four lines respectively.
95. I say that we have
of, of, £9
ge a. na ab 9?
viz., this will be the case if
b'a = hyd,
ach = hf'd,
abe = fia,
and selecting the convenient expressions for a, b, c, d, these equations become
be’ (gh’ — gh) = g/h (cb — eb),
ad (hf —Wf)=fh(aé — ac),
ab (ff —f9) = Ji (ba' — ba),
viz, these equations are respectively bgc’h’ = b’g’ch, chaf = cWaf, aft'g' =a'f'bg,
and are consequently satisfied. It thus appears that the equation
Lm An. ‘'p
ah io eae
is transformable into
which is of course one of a system of similar forms.
96. Take (A,, D,) the anti-points of A, D; (B,, C,) the anti-points of (B, C);
or say that the circular co-ordinates of A,, 6,, C,, D, are (a, 0’, 1), (8, 7, 1),
(y, BY, 1), (6, @, 1) respectively; the points A,, B,, C,, D, are, as above mentioned,
on a circle, the condition that this may be so being in fact
1, a, 8, ad
1, B, ¥ By
1ly,B xB |
1, 6, a, da’
= 0,
equivalent to
af :tg: ch = af «0g =ch..
‘97. Let (a,,b,,¢,,d,) be the corresponding quantities to (a, b, c, d), viz.
aeD ee, :d, = BCD, > — C04. DA BA we have
a, ib, .¢,2:d, = 18 9.11: — 1 ee, Le) eee ee ae ee |
y> BG 1 6, a’, J a, é, ; B, y; 1|
cya fee cANt «vil B, 7, 11 y, By 1)
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 43
giving rise to a similar set of forms
ae . ,-aé +h, ag+va,—¢g —Oh,
b, = — ¢b — gh, . 4 ,-fb—gff,—fht+ cf,
= Uet+hg—fert hf, 5s FG RGS
d= gct+hb,—ha+ ac, —ab—ga,
and leading to
CEA ES OE OE a ie
ae ay —— = cg Dy — ae Cy —— wg er ;
ste ice) We solleg Near ig CD ‘ :
so that the equation Taye tes tan les transformable into
1 i 1 1
Gs Gs COD Pans Uhdideee as
we! eg’ M+ af’ 1 ag ji = 0
98. Let A, B, C, D, be, as above, points on a circle; (4,, D,) and (B,, C,) the
anti-points of (A, B), (B, C) respectively. Write
A = (& — az) (m — wz) , A, = (& — az) (4 — 82),
B= (€ — B2)(n— 82) , B, = - 8) (1-72),
C= (E — yz) (n— yz) , ©, = (E — 92) (4 — Bz),
D = (& — 82)(m — dz) , D, = (§ — 82) (4 — 32);
then we have identically
(6—a)(d—a) B =(8—8) (8-6) A+ (B—a) (B —a) D—(B—8) (B—a) A,—(B—a) (8 —3’/) D, ,
(@—a) (8—a’) © =(y~8) (/—¥) A+ (y—2) (/—a') D—(y—8) (¥ — 2’) A, (ya) (¥-8)D, ,
(6—a) (6 —a’) B, =(8—8) (7-8) A+ (B—a) (7 —a’) D—(8—8) (y'— a’) A, —(8B—«) (7'—8) D, .
(6—a) (8 —a) ©, =(y—8) (B'—8) A+(y—a) (8 —a’) D=(y—8) (B —a’) A, —(y—a@) (B'—8) D, ,
or in the foregoing notation
Sf B = 9A + c’D + gcA, + cgD, ,
ff'C =hWVA + WD — WA, — WD, ,
Tf B, = gVA — c’D — GA, + ch’'D,,
Sf C, = 7A — béD + heA, — d7'D,.
Further Properties in relation to the same Sets (A, B, C,D) and (Ay, By, Cy, Dy)—
Art. Nos. 99 to 104.
99. It is be shown that in virtue of these equations, and if moreover
7 culers F
Tad “ = = + f = 0, then it is possible to find 4, 7, m, p,, such that we have
identically
— 1A + mB + nC — pD + 1,A,— m,B,— 1,0, + p,D, = 9.
+4 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
This equation will in fact be identically true if only
— ffl + gfm + hi'n
cem + bln — ff'p
gem — hb'n
com — bhin
+ fh
— ghim, — ghn, —
+ chm, + ben, = 0,
+ gm, — he n, =
+ chim, + bf n, + ff'py = 0.
From the first and second equations eliminating m, or m, , the other of these
quantities disappears of itself, and we thus obtain two equations which must be
equivalent to a single one, viz., we have
béffl + cgafm + bhafn+ ghffp =0,
beffl + gafm + bhafn + ghffp = 0;
which equations may also be written
of uf, £9
aaa Ae. A lth a
of cy af arn
al’ ie a af’ ay? ea
and it thus appears that the equations are equivalent to each other, and to the
assumed relation
l m N P
a b ;
100. Similarly, from the third and fourth equations eliminating m or n, the
other of these quantities disappears of itself, and we find
og ffl, — egafm, + afegn, — cgff'p, =
DW f{fl, — afU him, + bha'f'n, — Uhff'p, = 9,
equations which may be written
ff Digg 4 Se
ae cg af’ ga? sa
ee ei ap pl
ah Gy ae ape =?
where we see that the two equations are equivalent to each other and to the
equation ;
tig ag ee
ay 1 ei dy
It thus appears that the quantities /,, 7, 7, ,, must satisfy this last equation.
It is to be observed that the first and second equations being, as we have seen,
equivalent to a single equation, either of the quantities m,, m, may be assumed
at pleasure, but the other is then determined; the third and fourth equations
then give /,, p,; and oe quantities /,, 72, 2, 7, so obtained, satisfy identically the
: Une ay ge ne
equation oN 1s cae é fae 0.
i
|
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 45
101. Now writing
Tl, = — gem + U'm,) + hn + en) ,
LTP, = — gm — hm.) + b(h’n— g'n,) ,
and
p= cem+t+ Um) + 00n+ cn),
Tl = gK¢m—Wm) + hhn—- gn),
we find
It (40, — 'p) = — (bg + ch) [(em + Vm, )(hin = — gn) + (om — Wm) (Yn + en,)]
= (bg + ch) (Uy + ch’ )(mn, — mn)
= aaff (mn, — mn)
that is,
Gp, — 'p) = aa'(myny — mn)
viz., this equation is satisfied identically by the values of /,, m,, n,, p, determined
as above.
102. Hence if m, n, = mn, we have also /, p, = /p, and we can determine m,, 7,,
so that m,n, shall = mn, viz., in the first or second of the four equations (these
two being equivalent to each other, as already mentioned), writing m, = 9n, and
therefore 7, = 5m we have
1
— fl + gm + hh'n — gh'nd — ghm .= Om
Amel
cem + bon — fi'p + ch'nd + bem ,= Ou:
which are, in fact, the same quadric equation in 0, viz., we have
—fl+g7m+hhn_ _ gh _ _ gh
cm + bln — fp Gb eeuy ey
The final result is that there are two sets of values of /,, m,, 2,, p,, each satisfying
the identity
— IA + mB + nC — pD + /1,A, — mB, —7,C, + p,D, = 0,
and for each of which we have
Y m eet
ee ee AS 0 6p, Hb, mn, = mM :
a, Mice d, WO a ety
103. Consider, in particular, the case where p = 0; the relation
(ae. Geese Sa i
Ls ea eee 8
a @ b s c i; d
here becomes
/ ‘h
‘=— se) oe q
of if
VOL. XXV. PART I. M
46 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
The equation in 0 is
(ccm + bb’n)d + cb’'n® + bem = 0 ,
viz., this is
(c6 + &m)(U'nd + 6) = 0 ,
giving
b bn cm
G@=—= 5 nh, = — — (ee
c 2 c : b
¥
or else
Pema em eC ie cm a got b'n
b'n ? 1 b/ , 1 Py Ps
Since in the present case /,p, = 0, we have either /, = 0, or else p, = 0, and
as might be anticipated, the two values of 6 correspond to these two cases re-
spectively, viz., proceeding to find the values of /,, »,, the completed systems are
b ae 7 ry bn em
= — er = bo (cm — bb n) = = tu nm = ae 5 14=
cm cm n a
é= — ian TS — eS ee ‘m — bb’
Wy? v; ae 7 oP weF ce’m — bbin ) ,
so that for the first system we have
bg ts ea 0, myn, = mn, —/A + mB + nC = —1,A, + mB, + 1,C,,
ae Vi ee
and for the second system
in a ice fa =0,m n= mn, — 1A + mB + nC = —p',D,+m',B, + 7\C, .
1 Cy 1
104. The whole of the foregoing investigation would have assumed a more
simple form if the circular co-ordinates had been taken with reference to the
centre of the circle A6CD as origin, and the radius of this circle been put = 1;
we should then have a’ = _ &c., and consequently
fate 1 5 ye ee oe ee ere! 5 zy ce 4e 5
ae a ae re dae = i ie a = me
but the symmetrical relation of the circles ABCD and A,6,C\D, would not have
been so clearly shown.
I will however give the investigation in this simplified form, for the identity
—lA + mB + 27C = —1.A+4+™,B + 7,C; viz., in this case we have
L_ _ m(8— 9) (8 — 2). 26 =7) G2
a B(y—a)(@—8) y(a—B)(a—y)’
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 47
and the identity to be satisfied is
— 1l(é — az) (7 = ) = —1(§- a2) = 5*)
+ m(& — Bz) (7 = Z) + ms(E—B2) (1 _ 5°)
+ n(& — 72) (> = 2) + m4 (§ — n(n a 3°) ;
ae Sis 1
writing € = az, 7= 3% we find m,, and writing — = az, 7 = : z, we find n,, and
it is then easy to obtain the value of /,, viz., the results are
ee AO ENS 7) AR Nye), YO ial
6 Biy—a)@—8) y@—BP)@—a’ * «—B a ae
and therefore m,”, = mn; it may be added that we have
viz., this is the form assumed by the equation © te = + a = 0.
1 1 2
Part III. (Nos. 105 to 157.)—On THE THEORY oF Foct.
Explanation of the General Theory—Art. Nos. 105 to 110.
105. If from a focus of a conic we draw two tangents to the curve, these pass
respectively through the two circular points at infinity, and we have thence the
generalised definition of a focus as established by PLUCKER, viz., in any curve a
focus is a point such that the lines joining it with the two circular points at
infinity are respectively tangents to the curve; or, what is the same thing, if
from each of the circular points at infinity, say from the points J, J, tangents are
drawn to the curve, the intersections of each tangent from the one point with each
tangent from the other point are the foci of the curve. A curve of the class
has thus in general n° foci. It is to be added that, as in the conic the line join-
ing the points of contact of the two tangents from a focus is the directrix cor-
responding to that focus, so in general the line joining the points of contact of
the tangents from the focus through the points J, J respectively is the directrix
corresponding to the focus in question.
106. A circular point at infinity 7 or J, may be an ordinary or a singular
point on the curve, and the tangent at this point then counts, or, in the case of
a multiple point, the tangents at this point count a certain number of times, say
q times, among the tangents which can be drawn to the curve from the point ;
the number of the remaining tangents is thus = »— gq. In particular, if the
circular point at infinity be an ordinary point, then the tangent counts twice, or
48 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
we have g = 2; if it be a node, each of the tangents count twice, or g = 4; if it
be a cusp, the tangent counts three times, or g = 3. Similarly, if the other
circular point at infinity be an ordinary or a singular point on the curve, the
tangent or tangents there count a certain number of times, say 7 times, among the
tangents to the curve from this point; the number of the remaining tangents is
thus = 2—g. And if as usual we disregard the tangents at the two points J, J
respectively, and attend only to the remaining tangents, the number of the foci
is = (n—g) (n—q).
107. Among the tangents from the point / or J there may bea tangent which,
either from its being a multiple tangent (that is, a tangent having ordinary con-
tact at two or more distinct points), or from being an osculating tangent at one
or more points, counts a certain number of times, say 7", among the tangents from
the point in question. Similarly, if among the tangents from the other point
J or J, there is a tangent which counts 7” times, then the foci are made up as
follows, viz. we have—
Intersections of the two singular tangents counting as 7 foci.
Intersections of the first singular tangent with each
of the ordinary tangents from the other circular
point at infinity, as : ; : (n—g—ryr ,,
Do. for second singular patent : ; (n—q—r)y” ,,
Intersections of the ordinary tangents, . ; (n—q—?r)(n—q—7) ,,
Giving together the : (n—q) (n—q’) foci :
and the like observation applies to the more general case where the tangents from
each of the points /, / include more than one singular tangent.
108. There is yet another case to be considered ; the line infinity may be an
ordinary or a singular tangent to the curve: assuming that it counts s times
among the tangents from either of the circular points at infinity, the numbers
of the remaining tangents are n —q—s, n—gq’—s from the two points /, J
respectively, and the number of foci is = (x — g —s)(n— q—s).
109. In the case of a real curve the two points /, J are related in the same
manner to the curve, and we have therefore 7 = q'; the singular tangents (if any)
from the two points respectively being the same as well in character as in num-
ber. Writing » —¢—s =n —¢qd—s, = p, and not for the present attending to
the case of singular tangents, I shall assume that the number of tangents to the
curve from each of the two points is = py; the number of foci is thus = p*; and
to each focus there corresponds a directrix, viz., this is the line through the points
of contact of the tangents from the focus to the two points J, J respectively.
110. Consider any two foci A, B not in lined with either of the points J, J,
then joining these with the points /, J, and taking A,, B, the intersections of
AI, BJ and of AJ, BI (A,, B, being therefore by a foregoing definition the anti-
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 49
points of (A, B) ), then A,, B, are, it is clear, foci of the curve. We may out of
the p’ foci select, and that in 1.2..p different ways, a system of p foci such that
no two of them lie in lined with either of the points /,/; and this being so,
taking the anti-points of each of the 4+(p — 1) pairs out of the p foci, we have,
inclusively of the p foci, in all p + 2.4p(p—1), that is p* foci, the entire system
of foci.
On the Foci of Conics—Art. Nos. 111 to 117.
111. A conic is a curve of the class 2, and the number of foci is thus = 4.
Taking as foci any two points A, B, the remaining two foci will be the anti-points
A,, B,. In order that a given point A may be a focus, the conic must.touch the
lines AJ, AJ; similarly, in order that a given point B may be a focus, the conic
must touch the lines B/, BJ; the equation of a conic having the given points
A, B for foci contains therefore a single arbitrary parameter.
112. In the case, however, of the parabola the curve touches the line infinity;
there is consequently from each of the points J, J only a single tangent to the
curve, and consequently only one focus: the parabola having a given point A
for its focus is a conic touching the line infinity and the lines AJ, AJ, or say the
three sides of the triangle A/J; its equation contains therefore two arbitrary
parameters.
113. Returning to the general conic, there are certain trizomal forms of the
focal equation, not of any great interest, but which may be mentioned. Using
circular co-ordinates, and taking (a, a’, 1) and (8, 6’, 1) for the co-ordinates of the
given foci A, B respectively, the conic touches the lines €—az=0, ,—a’z=0,
——Bz=0, »—6’z =0; the equation of a conic touching the first three lines is
VIE — az) + Vm(E — B2) + VW n(n — az) = 0,
where /, m, m are arbitrary, and it is easy to obtain, in order that the conic may
touch the fourth line 7 — 6’z = 0, the condition
B— «a
p—a
io
114. In fact, 2 having this value, the equation gives
U(E — a2) + m(E - Be) + 2VIm(E— a) E— B= — Fs (m—D (1-82 + (BK — ap),
and taking over the term i mie — (m—1) (8 — az, =(B— a) (m—Ipz,
this gives
LE ~ Be — (m — 1) (n—B2),
VOL. XXV. PART I. N
50 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
which puts in evidence the tangent 7 — 6’z. It is easy to see that the equation
may be written in any one of the four forms
STE a8) + 7 mE— Be) + nf — B=* (om —0) (1 a2) =0,
J iniz—az) + S1(E— Bz) + a Lea
Foe —l)(,-Bz) =0,
VA 1(n — az) + Vin(n—82) + a a= (m—1)(E-az)=0,
Vig a+ V8) + nf 2" m9 G8) = 0.
viz., in forms containing any three of the four radicals /—az, /£— Gz,
Jn —a’z, Jn —Bz. The conic is thus expressed as a trizomal curve, the
zomals being each a line, viz., they are any three out of the four focal tangents;
the order of the curve, as deduced from the general expression 2” *7, is = 2; so
that there is here no depression of order.
115. But the ordinary form of the focal equation is a more interesting one:
viz., A, B being as usual the squared distances of the current point from the two
given foci respectively, say
A = (& — az) — a2),
B = (§ — 8:)1 — 82),
then 2a being an arbitrary parameter, the equation is
2az + VA + /B = 0,
viz., the equation is here that of a trizomal curve, the zomals being curves of the
second order, that is, the zomals are (z’= 0) the line infinity twice, and the line-pairs
AI, AJ and BI, BJ respectively: the general expression 2” ~ 7 gives therefore the
order = 4; but in the present case there are two branches, viz., the branches
2aze + VA — VB = 0, 202 —-VA + VB = 0,
each ideally containing (z = 0) the line infinity; the curve contains therefore
(<? = 0) the line infinity twice, and omitting this factor the order is = 2, as it
should be.
116. To express the equation by means of the other two foci A,, B,, writing
the equation under the form
A +B + 2/AB — 40222 = 0,
and then if A,, B, are the squared distances of the current point from A,, B,
respectively, we have (ante, No. 65).
AB =A,B,,
A+B—A,—B,=k2,
PROFESSOR CAYLEY ON POLYZOMAL CURVES. ol
where / is the squared distance of the foci A, B,=4a’e’ suppose: whence putting
a(1 —e’) = BD’, the equation becomes
A, + B, + 2/7A,B, — 40? = 0,
that is
VA, + VB, + 2b2 = 0,
which is the required new form. It is hardly necessary to remark that the
equation 2az + VA + VB = 0, putting therein z = 1, and expressing A, B in
rectangular co-ordinates measured along the axes, is the ordinary focal equation
2a =Vla— apt t+Va@tayty
117. I remark that the equation 2a0z + WA + /B = 0, gives rise to
40°? + A— B + 4az/ A = 0, but here A — B = — 4aevz, so that the equation
contains z = 0, and omitting this it becomes (az — ex) + A = 0, a bizomal form,
being a curve of the order = 2, as it should be; this is in fact the ordinary
equation in regard to a focus and its directrix.
Theorem of the Variable Zomal as applied to a Conic—Art. Nos. 118 to 123.
118. The equation 24z + WA° + “B° = 0 is in like manner that of a conic;
in fact, this would be a curve of the order = 4, but there are as before the two
branches 2kz + WA° —VB° = 0, 2hz —VA° + VB = 0, each ideally containing
(z = 0) the line infinity, and the order is thus reduced to be = 2. Each of the
circles A° = 0, B° = 0 is a circle having double contact with the conic (this of
course implies that the centre of the circle is on an axis of the conic). We may
if we please start from the form 2hz + /A + /B = 0, and then by means of
the theorem of the variable zomal introduce into the equation one, two, or three
such circles.
119. It is in this point of view that I will consider the question, viz., adapting
the formula to the case of the ellipse, and starting from the form
Qaz + VW(a— ae + y+ Ve + az + y = 0,
the equation of the variable zomal or circle of double contact may be taken to be
42 (w«@—aczt+y? , (e+acz?+y¥
NS, Ue Ea)
—2 it 1-—¢q s 1+¢
3
where g is an arbitrary parameter ; writing for greater simplicity z = 1, and re-
- ducing, the equation is
(a — qae)? +y? = PA — ¢).
120. Ifq <1, then writing g = sin 0, we obtain the ellipse
2 2
taal,
52 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
as the envelope of the variable circle
(2 — aesind)? + y? = b?cos76 ,
viz., of a circle having its centre on the major axis at a distance = ae sin 0 from
the centre, and its radius = dcos@. (I notice, in passing, that this gives in
practice a very convenient graphical construction of the ellipse.) It may be re-
marked that for 6 = +sin~—'e, the circle becomes
}? 2 a ge
(e+ @-7)) +=
bt
a?
viz., this is the circle of curvature at one or other of the extremities of the major
axis; as @ passes from 0 to + sin—'e we have a series of real circles, which,
by their continued intersection, generate the ellipse; as @ increases from
6 = +sin—'e to + 90°, the circles continue real, but the consecutive circles no
longer intersect in any real point,—and ultimately for @ = + 90°, the circles be-
come evanescent at the two foci respectively.
121. In the case g> 1, we have a real representation of
(w—qae? + y? + BG’ —1),
as the squared distance of the point (z, y) from a point (X, 0, Z) out of the plane
of the figure, viz., putting this
=(@—-XP+¥4+7,
we have
qae= X, Z*7 = bq? — 1),
whence
or what is the same thing,
that is, the locus is the focal hyperbola, viz., a hyperbola in the plane of zz,
having its vertices at the foci, and its foci at the vertices of the ellipse.
122. If instead of the form first considered, we start from the trizomal form
Qbe + Ja? + (y — aciz)? + Ja? + (y + acz? =90,
then we have the zomal or circle of double contact under the form
x? + (y — gaei)’ = a%(1 — 9”) ;
or putting herein g = — itanq, this is,
x? + (y — aetang)* = a*sec’9 ;
so that we have the ellipse as the envelope of a variable circle having its centre
on the minor axis of the ellipse, distance from the centre = aetan®, and radius
_ ee
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 53
=asecp. This is, in fact, Gergonne’s theorem, according to which the ellipse is
the secondary caustic or orthogonal trajectory of rays issuing from a point and -
refracted at a right line into a rarer medium. It is to be remarked that for
tang = + >; the equation of the circle is
a? 2 at
#+(~t0-5)) =
viz., this is the circle of curvature at one or other extremitity of the minor axis;
from @ = 0 to? = + tan’ = , the intersections of the consecutive circles are
1
real, and give the entire real ellipse; from d@ = + tan — 75 to ¢ = + 90°, the
circles are still real, but the intersections of consecutive circles are imagi-
nary.
123. If in the equation of the generating circle we interchange a, y, a, b, the
equation becomes
(x — aeitang)? + 7? = bsec?o ,
which is (as it should be) equivalent to the former equation
(x — aesiné)? + y? = b?cosé ,
the identity being established by means of the equation
, and .. sind=c<tang, tané = ising ,
which is Jacobi’s imaginary transformation in the theory of Elliptic Functions.
Foci of the Corcular Cubic and the Bicircular Quartic—Art. Nos. 124 to 126.
124. For a cubic curve, the class is in general = 6, and the number of the
foci is = 36. But a specially interesting case is that of a circular cubic, viz., a
cubic passing through each of the circular points at infinity. Here, at each of
the circular points at infinity, the tangent at this point reckons twice among
the tangents to the curve from the point; the number of the remaining
tangents is thus = 4, and the number of the foci is = 16. If from any two
points whatever on the curve tangents be drawn to the curve, then the two
pencils of tangents are, and that in four different ways, homologous to each
other, viz., if the tangents of the first pencil are (1, 2, 3, 4), and those of the
second pencil, taken in a proper order, are (1’, 2’, 3’, 4’), then we have (1, 2, 3, 4)
homologous with each of the arrangements (1’, 2’, 3’, 4’), (2’, 1’, 4’, 3’), (8, 4, 1’, 2’),
VOL. XXV. PART I. )
54 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
(4’, 3’, 2’, 1’). And in each case the intersections of the four corresponding tan-
gents lie on a conic passing through the two given points on the curve.*
125. Hence taking the points on the curve to be the circular points at infinity,
we have the sixteen foci lying in fours upon four different circles—that is, we
have four tetrads of concyclic foci. Let any one of these tetrads be A, B, C, D,
then if
Anti-points of (B,C) (A, D) are (B,, C), (4; D,) .
” (C,A) (B,D) 5 (Cy,Ag), (By, De) ;
, (A,B) (GD) + (As, Bs), (C5, Ds)
the four tetrads of concyclic foci are
a By, C;,
It is to be observed that if A, B, C, D are any four points on a circle, then if, as
above, we pair these in any manner, and take the anti-points of each pair, the
four anti-points lie on a circle, and thus the original system 4, B, C, D, of four
points on a circle, leads to the remaining three systems of four points on a circle.
The theory is in fact that already discussed ante, No. 72 et seq.
126. The preceding theory applies without alteration to the bicircular quartic,
viz., the quartic curve which has a node at each of the circular points at infinity.
The class is here = 8, but among the tangents from a node each of the two
tangents at the node is to be reckoned twice, and the number of the remaining
tangents is = 4: the number of foci is = 16. And, by the general theorem that
in a binodal quartic the pencils of tangents from the two nodes respectively are
homologous, the sixteen foci are related to each other precisely in the manner of
the foci of the circular cubic. The latter is in fact a particular case of the
former, viz., the bicircular quartic may break up into the line infinity, and a
circular cubic.
* It may be remarked that if the equation of the first pencil of lines be
(@ — ay) (x — by) (@— cy)(a — dy) = 0,
and that of the second pencil
(z —aw)(z — bw)(e — ew)(2 —dw) = 0,
then the equations of four conics are
rw —yz=0,
(a + d — b—c) az + (be — ad)(aw + yz) + (ad(b +c) — bea + d))yw 3).
(b+ d —c — a)az + (ca — bd)(aw + yz) + (bd(c +a) —ca(b + d) )yw = Oi
(c+ d—a—b)az +(ab — cd)(aw + yz) + (cd(a + b) — able + d))yw =i.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 5d
Centre of the Circular Cubic, and Nodo-Foci, &c. of the Bicircular Quartic—Art. Nos. 127 to 129.
127. The tangents at 7, J have not been recognised as tangents from J, J,
giving by their intersection a focus, but it is necessary in the theory to pay
attention to the tangents in question. It is clear that these tangents are in fact
asymptotes—viz., in the case of the circular cubic they are the two imaginary
asymptotes of the curve, and in the case of a bicircular quartic, the two pairs of
imaginary parallel asymptotes; but it is convenient to speak of them as the
tangents at J, J.
128. In the case of a circular cubic, the tangents at J and J meet in a point
which I call the centre of the curve, viz., this is the intersection of the two
imaginary asymptotes.
129. In the case of a bicircular quartic, the two tangents at / and the two
tangents at J meet in four points, which (although not recognising them as foci)
I call the nodo-foci; these lie in pairs on two lines, diagonals of the quadrilateral
formed by the four tangents (the third diagonal is of course the line //), which
diagonals I call the ‘‘ nodal axes;’’ and the point of intersection of the two nodal
axes is the ‘centre’ of the curve. The nodo-foci are four points, two of them
real, the other two imaginary, viz., they are two pairs of anti-points, the lines
through the two pairs respectively being, of course, the nodal axes; these are con-
sequently real lines bisecting each other at right angles in the centre (with the
relation 1 : 2 between the distances). The centre may also be defined as the inter-
section of the harmonic of // in regard to the tangents at Z, and the harmonic of
this same line in regard to the tangents at J. Speaking of the tangents as
asymptotes, the nodo-foci are the angles of the rhombus formed by the two pairs
of parallel asymptotes ; the nodal axes are the diagonals of this rhombus, and the
centre is the point of intersection of the two diagonals; as such it is also the
intersection of the two lines drawn parallel to and midway between the lines
forming each pair of parallel asymptotes.
Circular Cubie and Bicircuwlar Quartic ; the Axial or Symmetrical Case—Art. No. 130.
130. In a circular cubic or bicircular quartic, the pencil of the tangents from
Z and that of the tangents through J, considered as corresponding to each other
in some one of the four arrangements, may be such that the line // considered
as belonging to the two pencils respectively shall correspond to itself, and when
this is so, the four foci, A, B, C, D, which are the intersections of the correspond-
ing tangents in question, will lie in a line (viz., the conic which exists in the
general case will break up into a line-pair consisting of the line //J and another
line). The line in question may be called the focal axis; it will presently be
shown that in the case of the circular cubic it passes through the centre, and that
in the case of the bicircular quartic it not only passes through the centre, but
56 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
coincides with one or other of the nodal axes, viz., with that passing through the
real or the imaginary nodo-foci; that is, the curve may have on the focal axis two
real or else two imaginary nodo-foci. The focal axis contains, as has been men-
tioned, four foci—the remaining twelve foci are situate symmetrically, six on each
side of the focal axis, the arrangement of the sixteen foci being as mentioned
ante, No. 81 et seqg.; the focal axis is in fact an axis of symmetry of the curve,
and if preferred it may be named the axis of symmetry, transverse axis, or simply
the axis. And the curve (circular cubic, or bicircular quartic) is in this case a
‘‘ symmetrical” or ‘‘ axial” curve.
Circular Cubie and Bicircular Quartic: Singular Forms—Art. Nos. 131 to 140.
131. The circular cubic may have a node oracusp. If this were at one of the
points /, J the curve would be imaginary, and I do not attend to the case; and
for the same reason, for the bicircular quartic I do not attend to the case where
one of the points /,/ is acusp. There remain then for the circular cubic and
for the bicircular quartic the cases where there is a node or a cusp at a real point
of the curve; and for the bicircular quartic the case where each of the points /, J
is a cusp—in general the curve has no other node or cusp, but it may besides
have a node or cusp at a real point thereof.
132. I consider first the case of the bicircular quartic where each of the points
I, Jisacusp. The curve is in this case of necessity symmetrical*—it is in fact a
Cartesian; viz., the Cartesian may be taken by definition to be a quartic curve
having a cusp at each of the circular points at infinity. But in this case, as dis-
tinguished from the general case of the bicircular quartic, there is an essential
degeneration of all the focal properties, and it is necessary to explain what these
become. The centre is evidently the intersection of the cuspidal tangents; the
nodo-foci (so far as they can be said to exist) coalesce with the centre, and they
do not in so coalescing determine any definite directions for the nodal axes;
that is, there are no nodal axes, and the only theorem in regard to the focal
axis or axis of symmetry is, that it passes through the centre. Of the four
tangents through the point /, one has come to coincide with the line //,; and
similarly, of the four tangents through the point J one has come to coincide with
the line //: there remain only three tangents through / and three tangents
through J/, and these by their intersections determine nine foci—viz., three foci
A, B,C on the axis, and besides (B,, C,) the anti-points of (B, C) : (C,, A,) the
anti-points of (C, A) and (A,, B,) the anti-points of (A, £).
* Tt will appear, post Nos. 161-164, that if starting with three given points as the foci of a
bicireular quartic, we impose the condition that the nodes at J, J shall be each of them a cusp, then
either the quartic will be the circle through the three points taken twice, in which case the assumed
focal property of the given three points disappears altogether, or else the three points must be in lined,
or the curve be symmetrical, that is, a Cartesian.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. — OF
133. The remaining seven foci have disappeared, viz., we may consider that
one of them has gone off to infinity on the focal axis, and that three pairs of foci
have come to coincide with the points J, / respectively. The circle O (as in the
general case of a symmetrical quartic) has become a line, the focal axis ; the circles
R, S, T (contrary to what might at first sight appear) continue to be determinate
circles, viz., these have their centres at A, B, Crespectively, and pass through
the points (B,, C,), (C,, A,), and (A,, B,) respectively, see ante, No. 83. But on
each of these circles we have not more than two proper foci, and it is only on the
axis as representing the circle O that we have three proper foci, the axial foci
A, B,C: in regard hereto it is to be remarked that the equation of the curve
can be expressed not only by means of these three foci in the form
JIA +/mB +/nCG = 0; but by means of any two of them in the form
JIA +/mB + & = 0, where X is a constant, or, what is the same thing
(z being introduced for homogeneity in the expressions of A and B respectively),
in the form //A +./mB + Ke = 0.
134. Using for the moment the expression “‘twisted’’ as opposed to sym-
metrical—(viz., the curve is twisted when there is not any axis of symmetry
but the foci lie only on circles)—then the classification is
Circular Cubics, twisted,
» » symmetrical,
Bicircular Quartics, twisted,
Ordinary,
Bicuspidal = Cartesian,
”»>
" symmetrical, {
and each of these kinds may be general, nodal, or cuspidal—viz., for the two last
mentioned kinds there may be a node or a cusp at a real point of the curve.
135. In the case of a node, say the point NV; first if the curve (circular cubic
or bicircular quartic) be twisted—then of the four foci A, 6, C, D we have two,
suppose B and C, coinciding with V; and the sixteen foci are as follows, viz.
B, Oy ALD ware N,N, ALD;
Bin Ay bie tN oaAnti-pts. of (4, D):;
C,,A,, B,D, . Anti-pts. of (WV, A), Anti-pts. of (W, D) ;
Wallis Aor IDS Do. do.
_ viz., we have the points (A, D) each once, the node JW four times, the anti-points of
(A, D) once, and the anti-points of (NV, A) and of (JN, D), each pair twice. But
properly there are only four foci, viz., the points A, D and their anti-points. The
circle O subsists as in the general case, and so does the circle & (BC, AD), viz.,
this has for centre the intersection of the line AD by the tangent at WN to the
circle O, and it passes through the point JV, of course cutting the circle O at right
angles: the circles S and 7 each reduce themselves each to the point V considered
as an evanescent circle, or what is the same thing to the line-pair V/, WJ.
VOL. XXV. PART I. P
58 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
136. The case is nearly the same if the curve be symmetrical, but in the case
of the bicircular quartic excluding the Cartesian: viz., we have on the axis the
foci B, C coinciding at NV, and the other two foci A, D; the sixteen foci are as
above—and the circle # is determined by the proper construction as applied to
the case in hand, viz., the centre £ is the intersection of the axis by the radical
axis of the point WV (considered as an evanescent circle) and the circle on AD as
diameter; that is RV’ = RA.RD. And the circles S and 7 reduce themselves
each to the point VV considered as an evanescent circle.
137. Next if we have a cusp, say the point A: first if the curve (circular
cubic or bicircular quartic) be twisted—then of the four foci A, B, C, D, three,
suppose A, B, C, coincide with KX ; and the sixteen foci are as follows, viz.,
B, 0, A, D «re\| K,K,K,D,
B,,C,,4,D, , K,K, Anti-points of (K, D),
Cj Bae aS Do. do.
Bg, Bg a ng wig Do. do.
viz., we have the point D once, the point A nine times, and the anti-points of
K, D three times. But properly the point J is the only focus. The circle 0 is,
it would appear, any circle through A, D, but possibly the particular circle which
touches the cuspidal tangent may be a better representative of the circle O of the
general case—the circles #, S, 7’'reduce themselves each to the point A considered
as an evanescent point.
138. The like is the case if the curve be symmetrical, but in the case of the
bicircular quartic excluding the Cartesian; the circle 0 is here the axis, which is
in fact the cuspidal tangent.
139. For the Cartesian, if there is a node 1; then of the three foci A, B, C, two,
suppose B and C, coincide with V; the nine foci are A once, N four times, and the
anti-points of NW, A twice: but properly the point A is the only focus. And if
there be a cusp A; then all the three foci A, B, C coincide with A ; and the
nine foci are A nine times; but in fact there is no proper focus.
140. A circular cubic cannot have two nodes unless it break up into a line
and circle; and similarly a bicircular quartic cannot have two nodes (exclusive
of course of the points /, /) unless it break up into two circles; the last-mentioned
case will be considered in the sequel in reference to the problem of tactions.
As to the Analytical Theory for the Circular Cubic and the Bicircular Quartie respectively—
Art. No. 141.
141. It may be remarked in regard to the analytical theory about to be given,
that although the investigation is very similar for the circular cubic and for the
bicircular quartic, yet the former cannot be deduced from the latter case. In
fact if for the bicircular quartic, using a form somewhat more general than that
—— —— ee
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 59
which is ultimately adopted, we suppose that for the two nodes respectively
0, 2=0)fand 3] = 0, 2=0), then if JE +m=0, 12+ mz = 0,
mm + pz=0, my + pz = 0 are the tangents at the two nodes respectively, the
equation will be
(1E + mz) (VE + m’z) (nn + pz) (n'n + p’z) + cen + 28 (aE + bn) + c2* = 0,
and if (in order to make this equation divisible by z, and the curve so to break
up into the line zg = 0 and a cubic) we write / = 0 or m = 0, then the curve will
indeed break up as required, but we shall have, not the general cubic through
the two points (€ = 0, 2 = 0), (7 = 0, 2 = 0), but in each case a nodal cubic,
viz., if 7= 0 there will be a node at the point (, = 0,2= 0), and ifz=0Oa
node at the point (€ = 0, z= 0).
Analytical Theory for the Circular Cubic—Art. Nos. 142 to 144.
142. I consider then the two cases separately; and first the circular cubic.
The equation may be taken to be
En(p& + qn) + cen + 2 (aE + bn + cz?) = 0,
or what is the same thing
En(pé + gn + cz) + 2(aE + bn + cz) = O,
viz. (€, 7, 2) being any co-ordinates whatever, this is the general equation of a
cubic passing through the points (E=0, z=0), (7=0, z=0), and at these points
touched by the lines €=0, » = O respectively. And if (&, 7, 2 = 1) be circular
co-ordinates, then we have the genera] equation of a circular cubic having the
lines € = 0, » = O for its asymptotes, or say the point €=0, 7 =0 for its
centre; the equation of the remaining asymptote is evidently pé + qn + ez = 0;
to make the curve real we must have (p, 7) and (a, 6) conjugate imaginaries,
e and ¢ real.
143. Taking in any case the points /, J to be the points & = 0, e = 0 and
4=0, z=0 respectively, for the equation of a tangent from / write p& = 0z; then
we have
Oy (02 + Qn + ez) + 2(abz + bpn + cpz) = 0,
that is
2? (ad + cp) + n2z(6? + €6 + bp) + 1°.gd = 0,
and the line will be a tangent if only
(0? + cd + bp)? — 49d (ad + cp) = 0,
that is, the four tangents from / are the lines p& = 02, where @ is any root of
this equation. Similarly the four tangents from J are the lines g7 = ¢z, where
@ is any root of the equation
(9? + ep + ag)?— 4po(bp + cq) = 0,
60 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
writing the two reaped under the forms
é
we , |
| ey eee (6, 1)4 rs On 2aq — 4bp, + (9, 1)* =0,
| 3ebp — 6epq, 3 eng an
L 6 Bp? 6a2q?,
the equations have the same invariants ; viz., for the first equation the invariants
are easily found to be
I= 3@ — 4bp — 4aq)? + 72(ce — 2ab)pq,
J = — (? — 4bp — 4aq)8 — 36 (ce — 2ab)pg(e — 4bp — 4aq) — 21607 p*9?
and then by symmetry the other equation has the same invariants. The
absolute invariant /°*+ J” has therefore the same value in the two equations;
that is, the equations are linearly transformable the one into the other, which is
the before-mentioned theorem that the two pencils are homographic.
144. The two equations will be satisfied by 9 = ¢, if only bp = aq; that is, if
b : : ie :
P=7-9= j.3 Putting for convenience ; in place of ¢, the equation of the curve
is then
En (aE + bn + cz) + ke* (aE + bn + cz) = 0.
In this case the pencils of tangents are a& = k6z, bn = kOz, where 0 is deter-
mined by a quartic equation, or taking the corresponding lines (which by their
intersections determine the foci A, B, C, D) to be (a& = k0,2, bn = k0,z), &c., these
four points lie in the line a — 6, = 0, which is a line through the centre of the
curve, or point € = 0, 7 = 0: the formule just obtained belong therefore to the
symmetrical case of the circular cubic. Passing to rectangular co-ordinates, writing
z = 1, and taking y = 0 for the equation of the axis, it is easy to see that the
equation may be written
(2? + v(x —a)+ k(x —b) = 0;
|
|
or, changing the origin and constants,
ay? + («7 — a\«e—b)(@—ec)=0.
Analytical Theory for the Bicireular Quartic—Art. Nos. 145 to 149. |
145. The equation for the bicircular quartic may be taken to be
h(E — a2?) (m? — B22”) + e2?&y + 22(aE + bn) + ce*# = 0,
viz. (& 7, 2) being any co-ordinates whatever, this is the equation of a quartic :
curve eae a node at each of the points (& = 0, 2 = 0) and (7 = 0,2 = 0): the
equations of the two tangents at the one node are —az= 0, €+ az = 0; and |
those of the two tangents at the other node are 7 — 6z = 0,7 + B2 = 0; €=0
is thus the harmonic of the line z = 0 in regard to the tangents at (& = 0, 2 = 0),
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 61
and 7 = 0 is the harmonic of the same line z = 0 in regard to the tangents at
(7 =0,2=0). If(& 1, 2 = 1) be circular co-ordinates, then we have the general
equation of the bicircular quartic having the lines & + az = 0, & — az = 0 for
one pair, and the lines » —8z=0, 7 + 82 =O for the other pair of parallel
asymptotes; and therefore the point € = 0, »=0 for centre, and the lines
BE — an = 0, BE + ay = O for nodal axes. In order that the curve may be real
we must have (a, @), (a, 6) conjugate imaginaries, 4,¢,c real. The points
(2-0, 2 = 0) and (, = 0, ¢ = 0) are as before the points J, J. If « = 0, the
node at J becomes a cusp, and so if 6 = 0, the node at J becomes a cusp; the
form thus includes the case of a bicuspidal or Cartesian curve.
146. To find the tangents from J, writing in the equation of the curve € = 6az,
we have )
ko? (62 — 1)(m? — B?2”) + eadnz + z(audz + bn) + cz? =0;
that is
n? . ka?(d? — 1),
+ mz. ead + b,
+27. — hea? ?(0 — 1) + aad+c=0,
and the condition of tangency is
Ake(g? — 1) {ka?6? (0? — 1) — aad—c} + (c + >) = 08
viz., the tangents from J are € = 0az, where @ is any root of this equation.
Similarly, if we have
2
4k (9? — 1) {ka?B? (p— 1) — bBe — ct + (eg + 3) ==:0),
the tangents from J are , = $8z, where ¢ is any root of this equation.
147. The two equations may be written
24k? a? B? , 247078? , )
— 6kae, — 6k0£,
— 8ka36? — 4ke + ¢? , — 8k'a’p?— 4ke + e, :
pt 0), L@ 1lt=0,
| 6aa + me @ 1) 6kbB + 30 3 (1)
L 24.h2078? + 24ke + ge eA 24h7a28? + 24ke + 6
which equations have the same invariants; in fact for the first equation the
invariants are found to be as follows, viz., if for shortness
CO = — 8ha26? — Ake + &,
then
T = 576k4a'6* + 57648ca26? + 14422(a2a2 + 026%) + 72hkab + 30? ,
J = Cf{576ktatB! + 576 1%c026? + 14442(a2a? + 028%) + 36heae — 07}
— 8641? caba?6? — 216 ke? (a®a? + 6767) — 216h7070? ,
and then by symmetry the other equation has the same invariants. The
VOL. XXV. PART I. Q
62 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
absolute invariant 7° + J* has thus the same value in the two equations, that is,
the equations are linearly transformable the one into the other, which is the
before-mentioned theorem that the pencils are homographic.
148. The equations will be satisfied by = > if only aa = 88, that is, if
a,b =m, ma; or by 0 = — dif only aa = — 0G, that is, if a,b = mB, — ma:
the equation of the curve is these two cases respectively—
(E? — a2) (q? — 82?) + oz?&q + m2z3(BE + an) + ct = 0,
h(E — az”) (9? — 82?) + c2?&q + mz*®(BE — an) text =0.
If to fix the ideas we attend to the first case, then the equation in @ is
24}? 07,37,
— 6kma8,
— 8h?a?B?— Ake + e?, (6, 1)* = @*
6khma8 + 3me,
24h7a78? + 24ke + 6m?
and we may take as corresponding tangents through the two nodes respectively
& = Oaz, » = 082; the foci A, B, C, D, which are the intersections of the pairs of
lines (& = 0,az, 1 = 0,82), &c., lie, it is clear, in the line B — ay = 0, whichis one
of the nodal axes of the curve. Similarly, in the second case, if 6 be determined
by the foregoing equation, we may take as corresponding tangents through the
two nodes respectively —& = 6az, y = — 08z; the foci (A, B, C, D), which are the
intersections of the pairs of lines (& = 6,az, 7 = — 6,82), &c., lie in the line
BE + ayn = 0, which is the other of the nodal axes of the curve. In either case
the foci A, B, C, D lie ina line, that is, we have the curve symmetrical; and,
as we have just seen, the focal axis, or axis of symmetry, is one or other of the
nodal axes.
149. In the case of the Cartesian, or when a=0, 8=0, viz., the equation aa=b@
is satisfied identically, and this seems to show that the Cartesian is symmetrical ;
it is to be observed, however, that for «=0, 8 =0 the foregoing formule fail, and
it is proper to repeat the investigation for the special case in question. Writing
a=0, 0=0 the equation of the curve is
hE? n? + czEq 4 23 (aE + bn) + cz* = 0,
and then, taking = 6@bz for the equation of the tangent from /, we have
a. ke
+ nz. b(e6 + 1)
+27 .abb+c=0.
and the condition of tangency is
4h0? (abd + c)—(ce6 + 1)? =0;
viz , we have here a cubic equation. Similarly, if we have »=0az for the equa-
tion of a tangent from J, then
4k? (abp + c) — (ep + 1)? =0.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 63
Hence 6 being determined by the cubic equation as above, we may take #=80, and
consequently the equations of the corresponding tangents will be €=0bz, »=6az,
viz., the foci A,B,C will be given as the intersections of the pairs of lines
(E=0,bz, 7»=0,az), &c. The foci lie therefore in the line a—by=0; or the curve
is symmetrical, the focal axis, or axis of symmetry, passing through the centre.
On the Property that the Points of Contact of the Tangents from a Pair of Concyclie Foci lie in a
Circle—Art. Nos. 150 to 158.
150. We have seen that the foci form four concyclic sets (A, B, C, D), (A,, B,,
G)),(A,, B,,C,, D,),(A,, B,, C,, D,), that-is, A,B, C,D are in a circle. We
may, if we please, say that any one focusis concyclic—viz., it lies in a circle with
three other foci; but any two foci taken at random are not concyclic; it is only a pair
such as (A, B) taken out of a set of four concyclic foci which are concyclic, viz.,
there exist two other foci lying with them in a circle. The number of such pairs
is, it is clear = 24. Let A, B be any two concyclic foci, I say that the points of
contact of the tangents AJ, AJ, BI, BJ, lie in a circle.
151. Consider the case of the bi-circular quartic, and take as before (& = 0,
z = 0), and (7 = 0, z = 0) for the co-ordinates of the points J, J respectively. Let
the two tangents from the focus A be & — az = 0, 1 —a’z = 0, say for shortness
p = 0, p’ = 0, then the equation of the curve is expressible in the form pp’U =
V**, where U = 0, V =O are each of them circles, viz., UY and V are each of
them quadric functions containing the terms 2’, zy, z&, and &. ‘Taking an inde-
terminate coefficient \, the equation may be written
pp (U + 2aV + pp’) = (V+ app’),
and then \ may be so determined that V+ 2\V + )’pp’ =0, shall be a 0-circle, or
pair of lines through J and J. It is easy to see that we have thus for \ a cubic
equation, that is, there are three values of \, for each of which the function
U + 2\V + ’pp’ assumes the form (¢ — Gz) (» — 6’z), =qq’ suppose : taking any
one of these, and changing the value of V so as that we may have V in place of
V +rpp’, the equation is pp’gq + V*, where V=0 isas before a circle, the equation
shows that the points of contact of the tangents p = 0, 7p = 0,¢g = 0, 7 = 0 lie
in this circle V = 0. The circumstance that \ is determined by a cubic equation
would suggest that the focus g = 0, g = 0 is one of the three foci B, C, D con-
eyclic with A; but this is the very thing which we wish to prove, and the inves-
tigation, though somewhat long, is an interesting one.
152. Starting from the form pp’qq/ = V’, then introducing as before an
arbitrary coefficient A, the equation may be written
pe’ (aq + 20V + rpp') = (V+ App')?,
* This investigation is similar to that in Salmon’s Higher Plane Curves, p. 196, in regard to
the double tangents of a quartic curve.
64 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
and we may determine \ so that gq7/ + 2\V + *pp’ = 0 shall be a pair of lines.
Writing V = Hi —LIn — L’& + M2’, and substituting for pp’ and gq’ their
values (£ —az) (y — a’z) and (€ —Gz) (n — §’2), the equation in question is
(1 + 20H + 2?) En — (B+2aL + a) nz — (8 + 2a’ + 27a’) Ez+ (BB + 20M + 2200’)? =0,
and the required condition is
(1 + 2aH + 2”) (BB + 20M +270’) = (8 + 2aL + da) (R’ + 2ALl’ + a2a’);
or reducing, this is
(2M + 2HBe — 21/6 — 218)
+ 2((a — 8) (@’ — 8) + 4HM — 4LL’)
+22 (2M + 2Haa’ — 21a — 21a’) = 0,
viz., is determined by a quadric equation. Calling its roots ,, and A,, the
foregoing equation, substituting therein successively these values, becomes
(€ — yz)(1—vz)=9, and (€ — dz)(y — d’z) = 0 respectively, say 77’=0 and ss’= 0.
153. We have to show that the four foci (p= 0, p’ = 0), (g = 0, 7 = 0),
(r = 0,7” = 0), (s = 0, s' = 0) are a set of concyclic foci; that is, that the lines
p=, g=90,7 =0, s=0 correspond homographically to the lines p’ = 0,
g = 0,7’ = 0, s’ = 0; or, what is the same thing, that we have
| 1, a, 6,20 | =O
1, 8,8’, BB
Lyre |
ie Rear
or, as it will be convenient to write this equation,
he ee ae
a—By—s a—d B—y
154. We have
_B+2,2+a%a |, B+ 2a, + ro’
. 1+ 2Ha,+A,7 ” ? 1 + 2d, + a,?
3 —B + 2A,0 + A,%u ya Bt 2d! + 22a!
1+ 2H, +2, ” 1+ 2H, +22 ©
The expressions of a — 0, &c., are severally fractions, the denominators of which
disappear from the equation; the numerators are
fora — 38, = a(1 + 2a, + a,?)—(84+ 2aL + a,*),
=o) BoP + 21, (eb f)-
forB—y, = #(1+ 2,H +2?) - 6+ 2a, + aa,?),
= {26H - L) (a - 8};
fory —8 = (6 + 22a, + oa,”) (1 + 2M, + a,?)
— (B + 2Ld, + ad”) (1 + 2Ha, + 22),
(a! — 6) {2H?a8 — 2HL(a + B) + 20? + 4 (a — B)?}
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 65
and it hence easily appears that the equation to be verified is
2H?o8 — 2HL(a + 8) + 207+}4(@-B)? _«-B+2@H-L)r, 2(GH-L)-(a-8B)a,
2H?a/e’ — 2HL (a + B)2L7 +4 —- BP w- B+ 2WH-TL)a,° 2CH-L)-(a-B)a,
155. This is
Gee B ice Chote Dae
B’-C A’ + Bret Cr, + Dry,’
if for shortness
A=2(a-8)(GH-L), A’= 2(e¢ -B)(BH-L) ,
B= -(a—£) » bB=-¢- 6) ;
C=4(eH-L(8-—L, C’'= 4(H-L)(wH-L),
D=-2(e-—fP)\e¢H—L) D= —2(¢-6)wH-TL),
and the equation then is
AB’ — A'B + CA’ — C'A — (a, + 24) (BC — BO) + 2,2, (CD' - C'D - (BD - B'D)).
156. Calculating AB’ — A’B, CA’ — C'A, CD’ — CD, BD’ — BD, these are
at once seen to divide by {(a8’ — a8) H + L (a’— 8’) —L'(a —8’)} ; we have,
moreover,
BO — BC = —4(a — 6)? WH — L) (6H - L’) + 4(0’ — 8)? (aH - L) (BH — L)
a t (aa — PB)H—L (a —6')- L'(a—B)} {(a' -«8)H+ L(a'-B)-L’'(a-8)},
viz., this also contains the same factor; and omitting it, the equation is found to be
t(@ — B)(# — B) — 4(BH — L) (BH — L)}
—2{ (aa! — BB')H — L(a' — B) — L'(a — B)} (A, + Ag)
+{-(@—P)@— #’) + 4(¢H — L) wWH— L’)} aa, = 0;
viz., substituting for A,+ A, and ,A, their values, this is
{(a — 8) («’ — 6’) — 4(8H — L) (eH — L)} (M+ How’ — La’ — La)
—{(aa' — 8G’) T— L(a’ — B)} {(@ — 8) (@ — 8’) + 40M — 421}
+{-(@—®)@—6)+4@¢H —Lh@wH—-TL)} {M+ Hee — Le — Lp} = 0,
which should be identically true. Multiplying by H, and writing in the form
{(a—) («’ — 6) — 4(@H — L) @H — L)} (AM — LL’ + (@H — L) (eH L))
—{(@@H — L) (/H—L) — (@H — L) @H —L’)} ((@— 8) (@ — 8) + 4H — LL)
+{—(«— 6) (@—f’) + 4@H — L) (wH — L/)} (HM — LI’ + (6H — 1) (6'H - io) ai)
we at once see that this is so, and the theorem is thus proved, viz., that the equa-
tion being pp'gq’ = V’, the foci (p = 0, p’= 0) and (¢ = 0, g’= 0) are concyclic.
157. By what precedes, \ being a root of the foregoing quadric equation, we
may write
q¢ + 20AV + pp’ = K? rr’,
VOL. XXV. PART I. R
66 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
where the focus 7 = 0, 7’= 0 is concyclic with the other two foci; but from the
equation of the curve V = /pp'q7, that is we have
gy + 20 Vpp'qy' + pp’ = Kir’,
or, what is the same thing,
av pp + Ja + Kr’ =0,
viz., this is a form of the equation of the curve; substituting for p, p’, g.9q/, 7,7"
their values, writing also
A = (& — az) (n— az),
B= ( — 8) (1 — 82),
C=(€—)(1— 72),
and changing the constants , K (viz. \:1:K =J/1: /m: s/n) the equation is
JIA + J/mB + JVnC = 0,
viz., we have the theorem that for a bicircular quartic if (& — az = 0, 7 — a’z =0),
(E — Bz =0, n — Bz = 0, (E — yz = 0), 1» — y’z = 0) be any three concyclic foci,
then the equation is as just mentioned ; that is, the curve is a trizomal curve, the
zomals being the three given foci regarded as 0-circles. The same theorem holds
in regard to the circular cubic, and a similar demonstration would apply to
this case.
158. It may be noticed that we might, without proving as above that the
two foci (p = 0, p’ = 0), (¢ = 0, g’ = 0) were concyclic, have passed at once
from the form pp'gq = V, to the form App’ + Vqq + KNrr’ =0 (or
JIA = /mB = J/nC = 0), and then by the application of the theorem of the
variable zomal (thereby establishing the existence of a fourth focus concyclic with
the three) have shown that the original two foci were concyclic. But it seemed
the more orderly course to effect the demonstration without the aid furnished by
the reduction of the equation to the trizomal form.
Part IV. (Nos. 159 To 206).—On TRIZOMAL AND TETRAZOMAL CURVES WHERE THE ZOMALS
ARE CIRCLES.
The Trizomal Curve—The Tangents at I, J, éc—Art. Nos. 159 to 165.
159. I consider the trizomal
JiR + /mB’ + ./n° = 0,
where A, B, C being the centres of three given circles, A°, &c. denote as before,
viz., in rectangular and in circular co-ordinates respectively, we have
A® = (@ — a2)? + (y — az)? — a, = (E — 2) (n — wz) — 22,
B’ (a Te bz)? a (y — bz)? — aa => (§ ai Bz) (n = Bz) sz "222,
O° = (@— oe? + (y — ex)? — 2, = (EF — 92) (1 — 2) — CH.
Il
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 67
By what precedes, the curve is of the order = 4, touching each of the given
circles twice, and having a double point, or node, at each of the points J, J; that
is, it is a bicircular quartic: but if for any determinate values of the radicals
Jl, /m, /n, we have
lt + fmt fn = 0,
UN ae! ie 0.
containing (¢ = 0) the line infinity; and the order is here = 3: viz., the curve
here passes through each of the points /, J and through another point at infinity
(that is, there is an asymptote), and is thus a circular cubic.
160. I commence by investigating the equations of the nodal tangents at
the points J, J respectively; using for this purpose the circular co-ordinates
(&, », 2 = 1), it is to be observed that, in the rationalised equation, for finding the
tangents at (£ = 0, z = 0) we have only to attend to the terms of the second
order in (&, 2), and similarly for finding the tangents at (, = 0, 2 = 0) we have
only to attend to the terms of the second order in (7,2). But it is easy to see
that on any term involving @’, 0", or c’ will be of the third order at least in (é, 2),
and similarly of the third order at least in (7, z); hence for finding the tangents
we may reject the terms in question, or, what is the same thing, we may write
a’,b’,c’ each = 0, thus reducing the three circles to their respective centres.
The equation thus becomes
SIE = a2) a — dz) + J/m(E— B) (9 — B2) + Jn E- Q— 72) = 0.
For finding the tangents at (€ = 0, 2 = 0) we have in the rationalised equation to
attend only to the terms of the second order in (&, 2); and it is easy to see that
any term involving «’, @’, 7 will be of the third order at least in (é,2), that is,
we may reduce a’, 8’, y’ each to zero; the irrational equation then becomes
divisible by , and throwing out this factor, it is
SUE — a2) + /mE — B2) + J/nE— yz) = 0,
viz., this equation which evidently belongs to a pair of lines through the point
(€ = 0, 2 = 0) gives the tangents at the point in question; and similarly the
tangents at the point (7 = 0, 2 = 0) are given by the equation
Jin = v2) + rfm(n — Bz) + RG — vz)=0.
161. To complete the solution, attending to the tangents at (& = 0, z = 0),
and putting for shortness
then there is a branch
A= l—-m—n,
w= —-lim —n,
y= —1 —™m ar WO 5
A= F4m?+nv* — 2mn — 2nl — 2lm,
68 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
the rationalised equation is easily found to be
adie
— 2&2z(lka + mpB + nvy)
+ 2(Pa? + mR? + ny? — 2mnBy — 2nlya — 2lmaB) = 0.
And it is to be noticed that in the case of the circular cubic or when
Jl + /m + /n =0, then A=0, so that the equation contains the factor z, and
throwing this out, the equation gives a single line, which is in fact the tangent of
the circular cubic.
162. Returning to the bicircular quartic, we may seek for the condition in
order that the node may be a cusp: the required condition is obviously
A(l?a? + mB? + 247? — 2mnBy — 2nlya — 2linaB) — (law + muB + nvy)? = 0,
or observing that
A—Ww= — 4mn, &e.
A+ w = — 21a, &e.
this is
la? + mB? + ny* + By + wya + B= 0,
or substituting for A, u, v, their values, it is
L(a — B) (a— y) + m(B— 7) (B— a) + n(y— a) (y— 8) = 0,
or as it is more simply written
1 m n
=—— + — + =O.
B-y ya a—
163. If the node at (7 = 0, z = 0) be also a cusp, then we have in like manner
wp A MED Th
B—y ya a —f
Now observing that
ae et |
p;-B; i
7, ¥, 1
y—9) @ 8) = —*) @—- 2s =
(«— 8) (8 —y/) — («—8B) (B—y),
(B—¥) (7 -—@) — @—9'/) (y—-2),
= () suppose: the two equations give
Lim:n = aA(8—y) (B—y) : U(y—4@) (y'— a): Aa —8) (a — 8’);
or if Q is not = 0, then
Lim:n = (B—y) (8-7): (y—@) (x —@) : (a8) (#8).
164. If 2= we 0'
rg
B, B, 1
7,4
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 69
or, what is the same thing, if
,
pins
oon
Om Cua
2 C,
Zi):
the centres A, B, C are in a line; taking it as the axis of x, we have
a=a =a, B=’ =), y=y'=c; and the conditions for the cusps at J, J respectively
reduce themselves to the single condition
l mM n
b—e Cc—a a—b
= (I).
so that this condition being satisfied, the curve
Wi@—a +a] + /mie—ky +y—vAl + Jawa) + fo] = 0
is a Cartesian ; viz., given any three circles with their centres on a line, there are
a singly infinite series of Cartesians, each touched by the three circles respectively ;
the line of centres is the axis of the curve, but the centres 4, B, C are not the
foci, except in the case a’= 0, b= 0, c'= 0, where the circles vanish, The con-
dition for /, m, is satisfied if /: m:n = (b — cc)’: (ec — a)’: (a —b)’; these values
writing /7: /m: /n = 6—c¢:c—a:a—b, give not only /] + /m + /n = 9,
but also a,/] + b,/m + ¢r/n = 0; these are the conditions for a branch contain-
ing (2? = 0) the line infinity twice; the equation
(b—c) n/(a—a2z)? +? — a? + (c—a) J (a—b)? + y? — 02? + (a—b) J (c— 2)? + — C72 =0,
is thus that of a conic, and if a’ = 0, 6" = 0, c’ = 0, then the curve reduces itself
to y° = 0, the axis twice.
165. If Q is not = 0, then we have
L:m:n = (8 — y)(B— 7) = (y— @)(7'— @) = (a — B)(a’ — 6),
viz., J, m, n are as the squared distances BC’, C/A’, AB’, say as f?:97:h’; or
when the centres of the given circles A, B, Care not in a line, then f, g, h being
the distances BC, CA, AB of these centres from each other, we have, touching
each of the given circles twice, the single Cartesian
Tin Be + 9/B° + De Cr 0 ;
which, in the particular case where the radii a’, 6’, c’ are each = 0, becomes
FJ/A+9/B+h,/6 = 0,
viz., this is the circle through the points A, B, C, say the circle A BC, twice.
VOL. XXV. PART I. S
70 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
Investigation of the Foci of a Conic represented by an Equation in Areal Co-ordinates—
Art. Nos. 166 to 169.
166. I premise as follows: Let A, B,C be any given points, and in regard to
the triangle ABC let the areal co-ordinates of a current point P be u, v, w:
that is, writing PBC, &c., for the areas of these triangles, take the co-ordinates
to be
295 = PRO: PCA = PAB ;
or, what is the same thing in the rectangular co-ordinates (z, y, z = 1), if
(a, a, 1), (6,8, 1), ( ¢,1),
be the co-ordinates of A, B, C respectively, take
WIV DW =e, yy, 2) F/B Wee) 1B Hs
!
a | ie, 6, 4 8,64
ed, 7 | |a,a’,1 Jag pans |
7
or in the circular co-ordinates (£ 7,2 = 1), if (a,a’, 1), (8, 6’, 1), (y, 7’, 1) be the
co-ordinates of the three points respectively, then
*
U:v:w=| a z | &, 4-2 le a 2
| 8, B11 y, 7,1) a a, 1
bsitgied a, a, L B, BY, 1
167. For the point / we have (&, 7, z) = (0,1, 0), and hence if its areal co-
ordinates be (w,, %; 2%), we have
Uy iUyi@ =B—-y:y—a:a—B,
and hence also, (w, v, w) referring to the current point P, we find
YW — Wy = (y — a)[(@ — B)(E — az) — (a —B)(n — @2)]
— (@ — B)[(7 — @)(E — az) — (y — a) (n— a2)] = OF — azz) ,
if 2 = (y—a) (@ —B)—(@— B)(y¥ —2) = |a, a’, 1) 5
B, By
% 7,1]
whence
Vy — WyV 2 Wy — Wig i UyY — WY, =F —az:E— Pz :E—yxz,
and in precisely the same manner, if w,’, v,’, 7,’ refer to the point J, then
Wyityiw,=P—-x7:7¥—a@:ae—f’,
and
Vw —Wyv: wou — wu, Wav — Ww, =n — a2:n— Bein— yz.
_ 168. Consider the conic
(a, 6, ¢, f, 9, h)(u, v, w)? = 0,
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 71
where w, v, wv are any trilinear co-ordinates whatever; and take the inverse
co-efficients to be (A, B, C, F,G, H) (A =be —f’, &c.), then for any given
point the co-ordinates of which are (w,, v,, 2,), the equation of the tangents from
this point to the conic is, as is well known,
(A, BC, F, G, Av,w — wor, wy — UW, Uv — vyu)y?=0;
consequently for the conic
GoaeLgh@ga,wyY = 0,
where (#, v, v) are areal co-ordinates referring, as above, to any three given points
A, B, C, the equation of the pair of tangents from the point- J to the conic is
(A, B, Ce G, H)(g — a2, & — Bz, & cane 92) = 0),
and that of the pair of tangents from J is
(A, B, O, F, G, H)(n— wz, — P2,n-—72)?=0,
these two line-pairs intersecting, of course, in the foci of the conic.
169. In particular, if the conic is a conic passing through the points A, B, C,
then taking its equation to be
low + mwu + nu =0,
the inverse co-efficients are as (/?, m?, n?, — 2mn, — 2nl, — 2/m), and we have for
the equations of the two line-pairs
Jie — a2) + J mE — B2) + J/nE— 72) = 9;
Jin — #2) + n(n — B2) + J nln — 72) = 9 -
The Theorem of the Variable Zomal—Art. No. 170.
170. Consider the four circles
A’ = 0, B= 0, C° = 0, D? = 0 (A° = (a — az)? + (y — wz)? — a'?2*, &e.),
which have a common orthotomic circle; so that as before
aA° + bB° + cC° + dD° = 0,
where
DCB OU —iO DA DAB — ABO .
I consider the first three circles as given, and the fourth circle as a variable
circle cutting at right angles the orthotomic circle of the three given circles; this
being so, attending only to the ratios a:b: c, we may write
aabpee = DBO. DCA. DAB.
that is, (a, b, c) are proportional to the areal co-ordinates of the centre of the vari-
able circle in regard to the triangle A BC.
72 PROFESSOR CAYLEY OF POLYZOMAL CURVES.
171. Suppose that the centre of the variable circle is situate on a given conic,
then expressing the equation of this conic in areal co-ordinates in regard to the
triangle A BC, we have between (a, b,c) the equation obtained by substituting
these values for the co-ordinates in the equation of the conic; that is, the equation
of the variable circle is
aA° + bB° + cC°=0,
where (a, b, c) are connected by an equation,
(a, 6,655 9, AG, b, cf =.0.
Hence (A,B,C, F,G, H) being the inverse co-efficients, the equation of the
envelope of the variable circle is
(A, 8, C, F, G, H(A’, B’, Cc’)? = ?
and, in particular, if the conic be a conic passing through the points A, B, C, and
such that its equation in the areal co-ordinates (wu, v, w) in regard to the triangle
ABC is
lw + mwu + nuv =0,
then the equation of the envelope is
(7, m?, n?, — mn, — nl, — Im)(A®, B’, C°)? = 0;
that is, it is
(1, 1,1, — 1,—1, — 1)(/A’, mB’, nC°)? = 0,
or, what is the same thing, it is
SIR + /mB° + ,/n0° = 0.
172. It has been seen that the equations of the nodal tangents at the points
I, J respectively are respectively
JE = az) + Jm(E—82) + Jn(E-y2) =0,
Jin —az)+ Jm(n — B2) Ea Vania —yz)=0,
and that these are the equations of the tangents to the conic low + miu +
nuv = 0 from the points J,.J respectively. We have thus Casey’s theorem for
the generation of the bi-circular quartic as follows :—The envelope of a variable
circle which cuts at right angles the orthotomic circle of three given circles
A° = 0, B’ = 0, C° = 0, and has its centre on the conic /vw + miu + nuv = 0
which passes through the centres of the three given circles is the bicircular
quartic, or trizomal
JiR + JmB° + J/nC*= 0,
which has its nodo-foci coincident with the foci of the conic.
173. To complete the analytical theory, it is proper to express the equation of
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 73
the orthotomic circle by means of the areal co-ordinates (w, v,w). Writing for
shortness a + a” — ad” = 4a, &c., and therefore
A° = a? + y? — 2auz — 2a'yz — a2", &e.,
then if as before
VeVi UW) D2 | | CeOt Z\s5| COLY, e Ws
, / /
b,.6, 1 @, el CANO Nea
Goo el a,a,1 G, Url
and therefore
eiy:2=aut+bt+ew:dutbo+cwiut+vt+u,
the equation of the orthotomic circle is
Z—az,y—az, axn+vy—az|=0
z— bey — Vz, bu + Vy — V2
L— ,u— cz, a+ Cy— Cz
3
viz., throwing out the factor z, this is
ulaxw + ay — az) + vibe + Vy — bz) + Wea + Cy — ez) = 0,
or what is the same thing, it is
(au + bv + ewha + (aut bv + ecw)y— (dust bv +cw)z = 0,
viz.,it is
(au + bv + ewP+ (wu + bv + cw)? — (wu + bv + cw) (U+04w) =),
that is, substituting for a’, b', c their values, it is
ay? 4. by? + ¢/?*
+ (07% 4 c%—(b-cP — — ¢)?) ww
+ (ce? + a’ — (¢ — a)? — (¢ — ’)*) wu
+ (a? + bv’? — (a — b)? — (a — b’)?) w = 0,
and it may be observed that using for a moment a, 6, y to denote the angles at
which the three circles taken in pairs respectively intersect, then we have
26’ c' cosa = 6" + &” — (b—c)’ — (lV — €)’, &c., and the equation of the ortho-
tomic circle thus is
(1, 1, 1, cos a, cos B, cosy) (au, b’v, cw)? = 0.
174. We have in the foregoing enunciation of the theorem made use of the
three given circles A, B, C, but it is clear that these are in fact any three circles
in the series of the variable circle, and that the theorem may be otherwise stated
thus :—
The envelope of a variable circle which has its centre in a given conic, and
cuts at right angles a given circle, is a bi-circular quartic, such that its nodofoci
are the foci of the conic.
VOL. XXV. PART I. T
74 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
Properties depending on the relation between the Conic and Circle—
Art. Nos. 175 to 177.
175. I refer to the conic of the theorem simply as the conic, and to the fixed
circle simply as the circle, or when any ambiguity might otherwise arise, then
as the orthotomic circle. This being so, I consider the effect in regard to the
trizomal curve, of the various special relations which may exist between the
circle and the conic.
If the conic touch the circle, the curve has a node at the point of contact.
If the conic has with the circle a contact of the second order, the curve has a
cusp at the point of contact.
If the centre of the circle lie on an axis of the conic, then the four intersec-
tions lie in pairs symmetrically in regard to this axis, or the curve has this axis
as an axis of symmetry.
If the conic has double contact with the circle (this implies that the centre of
the circle is situate on an axis of the conic) the curve has a node at each
of the points of contact, viz., it breaks up into two circles intersecting in these
two points. The centres of the two circles respectively are the two foci of the
conic, which foci lie on the axis in question. Observe that in the general case
there are at each of the circular points at infinity two tangents, without any cor-
respondence of the tangents of the one pair singly to those of the other pair, and
there are thus four intersections, the four foci of the conic; in the present case,
where the curve is a pair of circles, the two tangents to the same circle corre-
spond to each other, and intersect in the two foci on the axis in question. The
other two foci, or anti-points of these, are each of them the intersection of a
tangent of the one circle by a tangent of the other circle.
If the conic has with the circle a contact of the third order (this implies that
the circle is a circle of maximum or minimum curvature, at the extremity of an
axis of the conic), then the curve has at this point a tacnode, viz., it breaks up into -
two circles touching each other and the conic at the point in question, and having
their centres at the two foci situate on that axis of the conic respectively.
176. If the conic is a parabola, then the curve is a circular cubic having the
four intersections of the parabola and circle for a set of concyclic foci, and having
the focus of the parabola for centre. The like particular cases arise, viz.,
lf the circle touch the parabola, the curve has a node at the point of contact.
If the circle has, with the parabola, a contact of the second order, the curve has
a cusp at the point of contact.
If the centre of the circle is situate on the axis of the parabola, then the four
intersections are situate in pairs symmetrically in regard to this axis, and the
curve has this axis for an axis of symmetry.
If the circle has double contact with the parabola (which, of course, implies
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 75
that the centre lies on the axis), then the curve has a node at each of the points
of contact, viz., the curve breaks up into a line and circle intersecting at the two
points of contact, and the circle has its centre at the focus of the parabola.
If the circle has with the parabola a contact of the third order (this implies
that the circle is the circle of maximum curvature, touching the parabola at its
vertex), then the curve has a tacnode, viz., it breaks up into a line and circle
touching each other and the parabola at the vertex, that is, the line is the tangent
to the parabola at its vertex, and the circle is the circle having the focus of the
parabola for its centre, and passing through the vertex, or what is the same
thing, having its radius = } of the semi-latus rectum of the parabola.
177. If the conic be a circle, then the curve is a bi-circular quartic such that
its four nodo-foci coincide together at the centre of the circle; viz., the curve is a
cartesian having the centre of the conic for its cuspo-focus, that is, for the inter-
section of the cuspidal tangents of the cartesian. The intersections of the conic
with the other circle, or say with the orthotomic circle, are a pair of non-axial
foci of the cartesian; viz., the anti-points of these are two of the axial foci. The
third axial focus is the centre of the orthotomic circle.
Case of Double Contact, Casey's Equation in the Problem of Tactions—Art. No. 178.
178. In the case where the conic has double contact with the orthotomic circle,
then (as we have seen) the envelope of the variable circle is a pair of circles, each
touching the variable circle; or, if we start with three given circles and a conic
through their centres, then the envelope is a pair of circles, each of them touch-
ing each of the three given circles; that is, we have a solution of the problem of
tactions. Multiplying by 2, the equation found ante, No. 173, for the variable
circle, and then for the moment representing it by (a, b, c, f, g, h) (u,v, wy = 0;
then attributing any signs at pleasure to the radicals /a, /b, s/c, the equation
of a conic through the centres of the given circles, and having double contact
with the orthotomic circle, will be
(a, bc, f, g, h) (uw, , w)? —(w Jat v/b+w/c)?=0,
viz.. representing this equation as before by
lew + mwu+ nuv=0,
we have
l:m:n=f—J/be:g —Jca:h — Jab,
that is, substituting for a, b,c, f, g, h their values, and taking, for instance, a, b, c
Ba 20 2. On) 2, we find
i:m:n= 6" -— ec — G— oF —C' —- ¢?
:(c’ — a’)? — (¢ — a)? — ( — a’)?
: (a” — 6”)? — (a — 6)? — (a — BY,
76 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
that is, 7,m, m are as the squares of the tangential distances (direct) of the three
circles taken in pairs, and this being so, the equation of a pair of circles touch-
ing each of the three given circles is //A° + /mB° + /nC° = 0. It is clear
that, instead of taking the three direct tangential distances, we may take one
direct tangential distance and two inverse tangential distances, viz., the tan-
gential distances corresponding to any three centres of similitude which lie in a
line; we have thus in all the equations of four pairs of circles, viz., of the eight
circles which touch the three given circles. This is Casey’s theorem in the
problem of tactions.
The Intersections of the Conic and Orthotomic Circle are a set of four Coneyclie Foci—
Art. No. 179.
179. The conic of centres intersects the orthotomic circle in four points, and
for each of these the radius of the variable circle is = 0, that is, the points in
question are a set of four concyclic foci (A, B, C, D) of the curve. Regarding
the foci as given, the circle which contains them is of course the orthotomic
circle; and there are a singly infinite series of curves, viz., these correspond to
the singly infinite series of conics which can be drawn through the given foci.
As for a given curve there are four sets of concyclic foci, there are four different
constructions for the curve, viz., the orthotomic circle may be any one of the
four circles O, R, S, 7, which contain the four sets of concyclic foci respectively ;
and the conic of centres is a conic through the corresponding set of four concyclic
foci. We have thus four conics, but the foci of each of them coincide with the
nodofoci of the curve, that is, the conics are confocal; that such confocal conics
exist has been shown, ante, Nos. 78 to 80.
Remark as to the Construction of the Symmetrical Curve—Art. Nos. 180 and 181.
180. It is to be observed that in applying as above the theorem of the
variable zomal to the construction of a symmetrical curve, the orthotomic circle
made use of was one of the circles 2, S, 7, not the circle 0, which is in this case the
axis; in fact, we should then have the conic and the orthotomic circle each of
them coinciding with the axis. And the variable circle, gud circle having its
centre on the axis, cuts the axis at right angles whatever the radius may be;
that is, the variable circle is no longer sufficiently determined by the theorem.
The curve may nevertheless be constructed as the envelope of a variable circle
having its centre on the axis; viz., writing A° = (¢—az’?+y—a’e, &e.,
and starting with the form
Jih® + ./mB + ./nC° = 0,
then recurring to the demonstration of the theorem (ante, No. 47), the equation of
the variable circle is aA° + bB° + cC° = 0, where a, b, ¢ are any quantities
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 77
satisfying - + 5 + = = 0, or, what is the same thing, taking g an arbitrary para-
meter, and writing { =1+4, ~ = 1-49, ~ = — 2, the equation of the variable
circle is
IAP pe i BPs FHP 0)
1 1
tg 1—gq
Compare Nos. 118-123 for the like mode of construction of a conic; but it is
proper to consider this in a somewhat different form.
181. Assume that the equation of the variable circle is
Do =@—dyP+7— ad? = 0;
we have therefore identically
aA®° + bB° + cC° + dD° = 0,
viz., this gives
a+b+ece= -—d,
aa+bb+ce = — dd,
a(a? — a’) + b(0? — 0) +e? —¢?) = —d(d’ —d”),
and from these equations we obtain a, b, c equal respectively to given multiples
of d; substituting these values in the equation : -- e + = = 0, d divides out,
and we have an equation involving the parameters of the given circles, and also
d, d’, the parameters of the variable circle; viz., an equation determining d’,
the radius of the variable circle, in terms of d, the co-ordinate of its centre. I
consider in particular the case where the given circles are points; that is, where
the given equation is
RODE Af ME! + /nc = 0.
The equations here are
a +h +¢,.=-d
aa + bb + cc = — dd
aa? + bb? + cc? = — d(d*—d”),
and from these we obtain
a(a—b)(a—c) = —d((d—2) @—¢)-a”)
b(@ — 0) (b—a) = —d((d- 0) (d-a) -d”)
c (¢ —a)(¢ ~d) = —d((d-a) (d—b)-d”),
™
so that the equation : tapes = = 0 becomes
L(a—b) (a—c) m(b—c) (b—a) TC (G—0)
(d—b) (d—e)—d”® ~ d—c) @—ay—d” * —a) (d—b)—d® ~
VOL ex, PART I. U
0,
78 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
or, as this is more conveniently written
l 1 4 ee | seg he !
b—c (d—b) (d—c)—d” * c—a (d—c)(d—a)—d” * a—b (d—a) (d—b)—d”
=),
viz., considering d,d' as the abscissa and ordinate of a point on a curve, and
representing them by 2, y respectively, the equation of this curve is
pn : ee: 4 mone d Bs
b—c (2—b) (a—e)—y® ~ c—a (2@—c) (x—a)—y? * c—a (4—a) (x—b)-7?
which is a certain quartic curve; and we have the original curve
JIA + /mB + ./ne = 0,
as the envelope of a variable circle having for its diameter the double ordinate of
this quartic curve.
. U m n
Write for shortness ——_, —_, —
b—c’ c—a’ a—b
tion of the quartic curve may be written
= LI, M,N respectively, then the equa-
= L [(w—a)? (x—d) (w@—e) — y*(w—a) (2a—b-c) + y*] = 0,
viz., this is
ZL | «(e—a) @—b) @—e)
— y?( 2a? —(a+tb+cer+ (ab + ac + be)) +7
— a (w—a) («@—b)(a—c) + y (ax + be) | oD
or what is the same thing, the equation is
(L+M+N) [ «(z—a) (a—b) (w—c)—y? (20? —(at+b+c)r+ ab +ac+be) a y* |
— (La+Mb+ Ne) (x—a) (x—b) (xe)
+ y*{La+Mb+Ne)x + Lhe+Mca+ Nab} = 0.
In the particular case where L + M+ N = 0, that is, where
l m n
b—e c—a i TB 0,
the quartic curve becomes a cubic, viz., putting for shortness —
_ Lhe + Mca + Nab
~ La+ Mb+ Ne ’
the equation of the cubic is
fe (x—a) (x—b) (x—e)
y eee
viz., this is a cubic curve having three real asymptotes, and a diameter at right
angles to one of the asymptotes, and at the inclinations + 45°, — 45° to the other
two asymptotes respectively—say that it is a “ rectangular” cubic. The relation
PROFESSOR CAYLEY ON POLYZOMAL CURVES. i)
ae “+ —_=0 implies that the curve JIA+ JmB+ JnC =0 is a
C—O a
cartesian, and we have thus the theorem that the envelope of a variable circle
having for diameter the double ordinate of a rectangular cubic is a cartesian.
I remark that using a particular origin, and writing the equation of the rect-
2 : :
angular cubic in the form y* = 2” — 2mx +a + 2 the equation of the vari-
able circle is
92
(ed +P =P — Ind tar
that is
2
a A aN ga he ENO
d
where d is the variable parameter. Forming the derived equation in regard to d,
we have
eas
a ss Mm ~ q??
and thence
e+ y? — oo — =)
a
2
@ ar y? = Aree == IGA (a = m),
dl
that is, the equation of the envelope is (az? + y’ — «a)* = 16 A (w — m) = 0, which
is a known form of the equation of a Cartesian.
Focal Formule for the General Curve—Art. Nos. 182 and 183.
182. Considering any three circles centres A, B,C, and taking A’, &c., to
denote as usual, let the equation of the curve be
JID + /mB° + Vn0° = 0;
then considering a fourth circle, centre D,a position of the variable circle, and
having therefore the same orthotomic circle with the given circles, so that as before
aA® + bB° + cC° + dD°= 0,
the formule No. 47 (changing only U, V, W, T into A’, B°’, C’, D°) are at once
applicable to express the equation of the curve in terms of any three of the four
circles A, B, C, D.
In particular, the circles may reduce themselves to the four points A, B, 0, D,
a set of concyclic foci, and here, the equation being originally given in the form
JIA + J/mB + JnO = 0,
the same formule are applicable to express the equation in terms of any three
of the four foci.
80 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
183. It is to be observed that in this case if the positions of the four foci are
given by means of the circular co-ordinates (« = ) &e. which refer to the
centre of the circle A BCD as origin, and with the radius of this circle taken as
unity, then the values of a, b, c, d (ante, No. 90), are given in the form adapted to
the formulee of No. 49, viz., we have
a:b:c:d = a(Byd): — B yéda): y (da8) : — b (aby) ,
where (673) = (8 — yy — 38 —B), &e- The relation < + + ” = 0, put.
ting therein /:m:n = pa(B—y)*?:cB8(y —a)*:ty(a — 8), (or, what is the
same thing, taking the equation of the curve to be given in the form
(8 —y) JSpaA + (y — a) /cBB + (a —B) /7tyC = 0), becomes
e(B— y)(a—8 + oy —a)(B— 8) +<(@—-B)(y—8=0,
viz., this equation, considering p, 7, t, «, 2, y as given, determines the position of
the fourth focus D, or when A, B, C, D are given, it is the relation which must
exist between p, o,7; and the four forms of the equation are
; sr (8— 9), Ve(B — 8), Ve(y — B)) (aA, /BB, /7C, /0D) = 0,
ve(y—3, . Ned — a), Jo(a—y)
Jo(8 — 8) Ve(a — 8), , /r(6 — @)
| Ve (8 - 7), Ve.7— a), Vr (a — 8),
viz., the curve is represented by means of any one of these four equations involv-
ing each of them three out of the four given foci A, B, C, D.
Case of the Circular Cubic—Art. Nos. 184 and 185.
184. In the case of a circular cubic, we must have
@(8 — y) (a — 8) + «(y —a) (8 —8) + r(a— B) (y — 8) = 0,
a/oe(8 — y) + n/ Boy — a) ate / yz (a — B) iy
which, when the foci A, B,C, D are given, determine the values of p:o:7 in
order that the curve may bea circular cubic. We see at once that there are two
sets of values, and consequently two circular cubics having each of them the
given points A, B,C, D for a set of concyclic foci. The two systems may be
written
Ve:Vo:Vr = Vad — / By: “Ba = Jya:7 78 — V of,
viz., it being understood that »/ad means Ja 4/0, &c., then, according as /3
has one or other of its two opposite values, we have one or other of the two
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 81
systems of values of p:o+: 7. To verify this, observe that writing the equation
under the form
Vag? VB: V7 yr = 0/8 — VaBy: 8/8 — Joby :7¥ V3 — VaBy ,
the second equation is verified ; and that writing them under the form
e:o:r=—(B+y7)(2+d+M:—(vt+ a) (B+HN4+M:-@ +P) y+ H+,
where ee
M = By + cb + ya + 66+ o8 + 76 — 2 J aby »
the second equation is also verified.
185. Ifwe assume fora momenta = cosa +7sin a = e”, &c., viz., if a,b,c, d
be the inclinations to any fixed line of the radii through A, B, C, D respectively,
then we have
mee Gy eet Tee COT ae Ne rete
Mee cya rt et 4, 20-98 _ g-}@-95 iy
and thence
Jag (8 — 7): VBo(y — 0): J yr (a — 8) = cosj(a +d — b— oe) sin} (b— oc)
:cos }(6 + d— c— a) sin} (¢—a)
:cos }(a+d—a-— b)sin} (a— J);
or else = sini (a +d —-b — c) sin} (6 — ¢)
:sin} (b+ d— ¢ —a) sin} (¢ — a)
:sin}(¢c+d—a — 6)sin } (a — D).
Putting in these formule,
t(a—b—c=A, then we have B-— C=}(b- 0),
16—c —a)=B, : C— A=}(c —a),
d(c -a—b)= 0, ‘5 A-— B=}(a — b),
and for either set of values the verification of the relation
rJag(B — 7) + SBoly — @) + r/yr(a— 8) = 0,
will depend on the two identical equations
sin 4 sin(B — C) + sm Bsn (C — A) + smCsm(4 — B) = 0,
cos A sin(B — C) + cos B sin (C — A) + cosCsin(A — B) = 0:
although the foregoing solution for the case of a circular cubic is the most elegant
one, I will presently return to the question and give the solution in a different
form.
Focal Formule for the Symmetrical Curve—Art. No. 186.
186. In the symmetrical case, where the foci A, 6, C, D are on a line, then
if, as usual, a, 6, c,d denote the distances from a fixed point, we have the ex-
VOL. XXV. PART I. x
82 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
pressions of (a, b, c, d) in a form adapted to the formule of No. 49, viz.,
a:b:c¢:d=(b—c)(¢—d)(d—b) :—(e—d)(d—a)(a—c) : (d—a)(a —b)(b—d) : —(a—b) (b—c)(e—a) ,
so that, assuming
l:m:n = ob —c)?: o¢—a)?: ea — bP,
: l
the equation aif - + = 0, becomes
e(b — ea — d) +0¢ — a) (b—d) + x(a — be —d) = 0,
and the equation of the curve may be presented under any one of the four
forms
( +» 4 oe@=o, Seb-4), ree — 2) ) (SK, JB, SC, JD )= 0.
ORD GE Ns <a RIE Oe eater
Jod—b), rJSe(a—d), : , a/r(b—a@) |
|
| _
Neb-—9), Sole—a), Ve(a—2), sd wt
Case of the Symmetrical Circular Cubic—Art. No. 187.
187. For a circular cubic we must have
e(b — e)(a — d) + o(¢ — a)(b — d) + e(a— ble —d) = 0
J/¢(b — ¢) ee oe) ee ee ae
These equations give ./p: /c: ./r = 1:1:1 (values which obviously satisfy the
two equations), or else
Jeinloinsfe=4+a—b—€:b4+d—e—a:e+d—a—b.
In fact, these values obviously satisfy the second equation; and to see that they —
satisfy the first equation, we have only to write them under the form
eie:r = M—4640(a+ d): M—Ace + a)(b + d): U— Ala + Dc + d),
where M = (a+6+c¢+4+d). The first set gives for the curve
(b-—c) /A+(c—-a™)/B+@—d)/C=0,
but this contains the line z = 0 not once only, but twice; it in fact is (y’ = 0),
the axis taken twice; the only proper cubic with the foci A, B, C, D im lined is
therefore
(b-—o(a+d—b—c) K+ (c—alb+d—c—a) /B +(a—d(c+d —a—d) /6 =0,
the equation of which is, of course, expressible in each of the other three forms.
Case of the General Circular Cubit—Art. Nos. 188 to 192.
188. Returning to the general case of the circular cubic, the lines BC, AD
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 83
meet in #, and if we denote by @,, b,, ¢,, d,, the distances from A of the four
points respectively, so that b,c, = a,d, = rad. *#, then observing that a, b, c, d
are proportional to the triangles BCD, CDA, DAB, ABC, with signs such that
a+b+c+d = 0, we find
eee s0.— — 7,(0, —¢,) 2 ¢e(¢, —d,) : —0,(a, —d)) ad On— Cy) 5
m
F 5 l E at =a b
and this being so, the equations —-+ ; + = = ON EE + a/n =.0.,. give
two systems of values of ,/7: ./m: /n , viz., these are
Ree Olea GG ey Aa Dine
and
Sea OCG cal aaa C Rien On
(To verify this, observe that for the first set we have
Lm. 1 (b, — ¢,)? (¢, — a,)? (a, — 6,)?
-+—+-—= 1 | 1 1 + 1 il
a b ¢ —4,(b)— 6) &(4,—4,) — b,(a, — 4)
b, — 4 1 Ge a,’
el eee =a ee es
— dy Vee Gages : 7
a Gy eae a — 1)
— d, Gy — a, NOs C,
eee rs Oi 2 4(f -1)=0:
ceberaT 2e Gale da Na aie
and the like as regards the second set).
189. These values of ./7: ./m:,/n give the equations of the two circular
cubics with the foci (A, B, C, D), the equation of each of them under a fourfold
form, viz., we have
Be Be a Pat Ae, Yo, /0) = 0
C—O SE ace Orth ee,
d—0,, a—ad,, }.-a,, )—G (first curve) ,
Oe Cn CeO, Ay 0,",
and
oh a) HE re] di EMabs, bi +, \(/A, /B, /C, /D) =‘ 0
d,+ ¢,, ; ; Leia, , — a
nie d,—4,, : a, + 6, (second curve).
Di Cah PSA 5. OE eae
190. Similarly CA and BD meet in S, and if we denote by a,, 6,, ¢,, d, the
distances from S of the four points respectively, so that c,a, = b,d, = rad.’
(observe that if as usual A, B, C, D are taken in order on the circle O, then A,C
are on opposite sides of S, and similarly B. D are on opposite sides of S, so that
84 ' PROFESSOR CAYLEY ON POLYZOMAL CURVES.
taking a,, b, positive c,, d, will be negative) we have
a:b:¢:d = 6,(by— dy) : dy (Cy — dy) : — Gy(By — dy) : — By (Cp — %) ,
m
and then the equations — oh =0, /li+J/mt+A/n = 9, are satisfied by
the two sets of values
Re en een ore oe ey gy ee
and ey Sent ee aR eee ee
and we have the equations of the same two cubic curves, each equation under a
fourfold form, viz., these are
, = Cy ty, — dy + ly, — dy + % ) (V/A, /B, SC, /D) = 0
C, — dy, : dy — Wy, — Cy +a,
—b,+d,, G—dads, «| Nei #0; (sk eurnD)
by — Cy, Cy — By; a,—b,,
and
) Cy + dy, — dy + by, — be — ty )(/A, /B, JSC, /D) =0.
te + 5, : : a, + dy, f — a
2 4 dy, OPS ye ke (second curve).
bo iy 5 — fg Oy, — Oy — 04,
191. And again AB and CD meet in 7, and denoting by a@,, },. c,, d, the
distances from 7’ of the four points respectively, so that a,b,= c,d, = rad.*7', we
have
a:b:e:d = 6,(c¢, —d,): — a,(c¢, —d,) : —d,(a, — 6,) :¢,(a, — 8,).
The equations : + - + =0, J1+ /nm+ J/n=0, then give for /7, /m, /n
two sets of values, viz., these are
wll sinfin if = lly = Oy 4 Oy Oy ty — by s
and = by + Cy: — Cy — a3 : dg — 0g;
and we again obtain the equations of the two cubics, each equation under a four-
fold form, viz., these are
- , —¢+d,, —d,+,, ts — bs )(VA, /B, /C,/D) = 9;
—d,+6¢,,
: Sh + 85 (=
—b,+d,, —d, +4, . See
OM, s ee See) a
and !
( Me dy5 1d ey te \(/A, /B, /C, /D) = 9:
Gn en. ; eee as + Cs
Ort g y) Welt akan AL Se Ota
bs + Cy, Cy — Gs; a, — b,,
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 85
192. The three systems have been obtained independently, but they may of
course be derived each from any other of them: to show how this is, recollecting
that we have
RA, DAR, LD sor. Dede s
SA, SB, SC, SD = d,,0;, — ¢;, — ay;
TANT PO, DO ==, debs 0% tha
then to compare
(az, Dy, Cy, Fy), (Mg, Do, Cg, Fa) 5
similar triangles
SBC sgive: 2 Op 6, =) o50:-0
SAD =, —d, : —d,:a,,
and similar triangles
MCAC OIE TG — Ca CE Gy,
RBD — Wy Ot Oy ee
using these equations to determine the ratios of @,, b,, c,,d, we have
GC c
2 2 1 Ea:
>, Or d,a, — dc, — ¢,), + od, = 0;
1
ae aap: i
that is
b, | (+d, > tal ate = Sho;
2 b l b— &
and hence
‘ Bo(— bye, + Oy? + aydy — dy”) + Oy(— Bydy + dy + Me, — dy) = 0,
that is
by (c,? — d,”) + ¢, (a,c, — b,d,) = 0,
but
aye, — dyd, = Eee — d,”),
1
or the equation gives 3, + 2%, =0, orsay}b,:¢,=6,: —d,, and this with
1
aS
Cie Oy fo
2, gives all the ratios, or we have
a,—d, d
2 Ws
My : bg : Cy : dy = 0, (a, — d,) : 0, (6, — ¢,): — dy (a, — d,) : — d,(b, — ¢,).
We have then for example
by — Cy 3 Cy — Ay 3 My — 09d, — Cy 2, — 4, : a, — 4b; &e.,
showing the identity of the forms in (a,, 0,, ¢,, d,) and (2, be, C2, de) -
Transformation to a New Set of Concyclic Foct.—Art. No. 193.
193. Consider the equation
JIA + JmB+ Jn0 =0,
which refers to the foci A,B, C, and taking D the fourth concyclic focus, let
VOL: &XV. PART I. Y
86 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
(A,, D,) be the antipoints of (A, D) and (B,,C,) the antipoints of (B, C); so that
(4,,B,, ¢,, D,) are another set of concyclic foci. We have B,.C,=B. C, and it
appears, ante No. 104, that we can find /,, m,,7,, such that identically
—/A+ mB + 20 = — 1,A,+ m,B,+ 7,0,
and that m,”, = mn. ‘The equation of the curve gives
— (A+ mB + 2C +2 J/mnBO = 0,
we have therefore
— 1,A,+ m,B,+ 2,0+ 2 /m,n,B,C, =0,
that is,
J1,A, + Jm,B, + J/n,C, =0,
viz., this is the equation of the curve expressed in terms of the concyclic foci
An, Bois
The Tetrazomal Curve, Decomposable or Indecomposable—Art. No. 194.
194. I consider the tetrazomal curve
JI? + JmB° + JnC® + JpD? =0,
where the zomals are circles described about any given points A, B, 0, D as
centres.
There is not, in general, any identical equation aA°+ bB°+ cC°+ dD°= 0, but
when such relation exists, and when we have also- BF sel += op Be 0, then the
b d
curve breaks up into two trizomals. When the conditions in question do not
subsist, the curve is indecomposable. But there may exist between /, m, n, p re-
lations in virtue of which a branch or branches ideally contain (z*= 0) the line
infinity a certain number of times, and which thus cause a depression in the order
of the curve. The several cases are as follows :—
Cases of the Indecomposable Curve-—Art. No. 195.
195. I. The general case; /, 1m, n, p not subjected to any condition. The curve
is here of the order = 8; it has a quadruple point at each of the points J, J (and
there is consequently no other point at infinity) ; it is touched four times by each
of the circles A, B,C, D; and it has six nodes, viz., these are the intersections of
the pairs of circles
| JmB? + JnO? = 0, JIA + J/pD?=0,
Lie? fie =4, J mBe + /pD° = OF
Jie + J/mB°= 0, /nC? + JpD°=0;
the number of dps. is 6 + 2.6, = 18, and there are no cusps, hence the class is
= 20, and the deficiency is = 3.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 87
II. We may have
JtI+ Jn + Jnt+ Jp =9;
there is in this case a single branch ideally containing (z = 0) the line infinity ;
the order is = 7. Each of the points J, J is a triple point, there is consequently
one other point at infinity; viz., this is a real point, or the curve has a real
asymptote. There are 6 nodes as before; dps. are 6 + 2.3,= 12; class = 18,
deficiency = 3.
III. We may have
Jit+ J/m=0, Jn + Jp =0;
there are then two branches each ideally containing (z = 0) the line infinity; the
order is = 6. Lach of the points J, J is a double point, and there are therefore
two more points at infinity. These may be real or imaginary; viz., the curve
may have (besides the asymptotes at J, J) two real or imaginary asymptotes.
The circles //A + /mB = 9, /nC + W/pD = 0, each contain (z = 0) the line
infinity, or they reduce themselves to two lines, so that in place of two nodes we
have a single node at the intersection of these lines; number of nodes is = 5.
Hence dps. are 5 + 2.1,= 7. Classis = 16, deficiency = 3.
IV. We may have
a/ Uist De 5) fs Vp =a:b:c:d
there is here a single branch containing (z*= 0) the line infinity twice; the
order is = 6. Each of the points /, J is a double point, and there are therefore
two more points at infinity, that is (besides the asymptotes at J, J), there are
two (real or imaginary) asymptotes. The number of nodes, as in the general
case, is = 6. Hence dps. are6 + 2.1, = 8; class is = 14; deficiency = 2.
I notice the included particular case where the circles reduce themselves to
their centres ; viz., we have here the curve
aJA+b/B+cJ/6+d/D=0,
which (see ante No. 93) is in fact the curve which is the locus of the foci of the
conics which pass through the four points 4, B,C,D. Itis at present assumed that
the four points are not a circle; this case will be considered post No. 199.
If we have BC, AD meeting in R; CA, BD in S, and AB, CD in T, then these
points £, S, 7 are three of the six nodes. In fact, writing down the equations
of the two circles |
bVB4+cVGC=0,a/A4+d/D= 0,
and observing that when the current point is taken at R, we have B:C
= RB’: RO?=(BAD): (CAD) = c?:b’, and similarly A:D = RA®: RD? =
(ABC) : (DBC)’= d’: a’, we see that each of the two circles passes through
88 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
the point R, or this point is a node. Similarly, the points Sand 7 are each of
them a node.
VIE Jl= Nm = VJn= Jp,
there are here three branches, each ideally containing (z = 0) the line infinity;
the order is thus = 5. Each of the points J, J is an ordinary point on the curve;
there are besides at infinity three points, all real, or one real and two imaginary ;
that is (besides the asymptotes at J,J) there are three asymptotes, all real, or
one real and two imaginary. Each of the circles /A + /B = 0, &c., contains
the line infinity, and is thus reduced to a line; the number of nodes is therefore
= 8. Hence also, dps. = 3; class = 14; deficiency = 3.
Cases of the Indecomposable Curve, the Centres being in a Line.—Art. No. 196.
196. There are some peculiarities in the case where the centres A, B, C, D are
on a line; taking as usual (a, b, c,d) for the 2x-co-ordinates or distances of the
four centres from a fixed point on the line, I enumerate the cases as follows :—
I. No relation between /, m, ,p ; corresponds to I. supra.
Il. J/7+ J/m+ /n + Jp = 0; corresponds to II. supra.
Il. Wl + /m = 0,/n + Sp = 0; corresponds to III. supra.
IV. J0+ JS/m+ Jn + Sp =0, al + bm + cro/n + dr/p = 0; corre-
sponds to IV. supra, viz., there is a branch ideally containing (z*= 0) the line
infinity twice. But, observe that whereas in IV. supra, in order that this might
be so, it was necessary to impose on /, m, n, p three conditions giving the definite
systems of values //: /m: /n: /p = a:b:c:4d, in the present case only two
conditions are imposed, so that a single arbitrary parameter is left.
V. Ji = J/m= J/n = ./p; corresponds to V. supra.
VI. Ji + f/m = 0, Jn t+ Sp = 0, 4 fl + da/m + ¢/n + d,/p = 0, OF
what is the same thing, .//: ./m: /n: /p = ¢—d:d—c:b—a:a—b; the
equation is thus (¢c — d)(,/A° — ./B°) — (@— 8)(,/A° — ./B°) = 0. There is
here one branch ideally containing (z* = 0) the line infinity twice, and another
branch ideally containing (z = 0) the line infinity once; order is = 5. Each of
the points J, J is an ordinary point on the curve, the remaining points at infinity
are a node (A° = B°, C° = D°), as presently mentioned, counting as three points,
viz., one branch has for its tangent the line infinity, and the other branch
has for its tangent a line perpendicular to the axis; or what is the same thing,
there is a hyperbolic branch having an asymptote perpendicular to the axis, and
a parabolic branch ultimately perpendicular to the axis. The number of nodes is
= 5, viz., there is the node A° = B°, C° = D° just referred to; and the two pairs
of nodes ((¢ — d) /A° — (a — b),./C° = 0, — (¢—d),/B° + (4 —b),/D° = 0)
and (c — d),/A° + (a—b) /D° = 9, (¢ — d),/B° + (a — b). /G° = 0), each
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 89
pair symmetrically situate in regard to the axis. Hence alsodps. = 5; class = 10;
deficiency = }.
And there is apparently a seventh case, which, however, | exclude from the
present investigation, viz., this would be if we had
bye oa Hd \ WO way Seay 20"
laps Pa Cie Ole es
ee as, eee
Gi ene Oe,
that is, a, b, c, d denoting as before, if we had
me Jus jp—arbr,e¢d, and aa” + bb? + ce? +dd?%=0.
For observe that in this case we have
PATHE =e oCle dD’ = 0, and 24 42s? = 0.
Ae Salcy ie eal
that is, the supposition in question belongs to the decomposable case.
The Decomposable Curve—Art. No. 197.
197. We have next to consider the decomposable case, viz., when we have
aA® + bB° + cC® + dD°® =
see ante, Nos. 87 et seqg.—it there appears that (unless the centres A, B, C, D
are in a line) the condition signifies that the four circles have a common ortho-
tomic circle; and when we have also
foe. mG nee
5 + 8 i ts aA 05
The formule for the decomposition are given ante, Nos. 42 a seg. Writing
therein A°, B°, C°, D® in place of U, V, W, T respectively, it thereby appears
that the tetrazomal curve //A° + /mB° + /nC° + »/pD° = 9, breaks up into
the two trizomal curves
JIA? + Jm,B° ar /n,C° = 0, JT," + J/m,B° ar /n,O c=
where
Fags 2 2 none ae
i Alber cg ag Vi= Jl + yp
pean ee a, a p
Jn, = lm be sag Na Jim, = /m + NES 5 bJ/n,
‘= a p a ta Pp
al ty = Jn + were Clim , NEP = aca 7 oN
and where we have
VOL. XXV. PART I. Z
90 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
Cases of the Decomposable Curve, Centres not in a line—Art. Nos. 198 to 203.
198. I assume, in the first instance, that the centres of the circles are not in
a line; we have the following cases :—
I. No further relation between /, m, n, p; the order of the tetrazomal is = 8
the order of each of the trizomals is = 4, that is each of them is a bicircular
quartic.
I. J+ /m+ J/n+ »/p = 9; the order of the tetrazomal is = 7, that of
one of the trizomals must be = 3.
To verify this, observe that we have
Ji, + Sm, + vn, = Jit J/m +t Jat ths Le peat (cJ/m—bJ/n),
or substituting for ./7 + i + »/n the value — ,/p, this is
=a 3 a —ayi+ J™ (Jin — bin},
and similarly for ./7, + /m, + s/n,, the only change being in the sign of the
radical , hs . But from the two conditions satisfied by /, m, n, p itis easy to
deduce
(aJp— VIP — © ed — bay = 0,
and hence one or other of the two functions
Wi bolt weg eee apie eee ee
that is, one of the trizomal curves is a cubic.
TW. /0 + /p=9, /m+ /n = 9; order of the tetrazomal is = 6; and
hence order of each of the trizomals is = 3. To verify this, observe that here
1s Oe ot Sie
iG +a) +™Gt5)=o
which since a + b +c + d = 0, gives x = — so that properly fixing the sign
of the radical, we may write Ji - Jsh Sin = 0. We have then
Vu= PFS Mt, Jaa + dmg = J b+ 0S
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 91
which last equation, using er = to denote as above, but properly selecting the
signification of +, may be written
Jing + dng = OT 8 in.
Hence
VIF (lia, + Vn) =={ +4 Jit 040) [84 in}
1 1 1 a N/ be
=!491 n+ J yw} mo,
viz., /l, = (/m, + /n,) with a properly selected signification. of the sign =
is = 0; and similarly //, = (./m, + /n,) with a properly selected signification
of the sign + is = 0; that is, each of the trizomals is a cubic.
HOO, TV. Ji: n/m: n/n: /p = a:b:c:d (values which, be it observed,
satisfy of themselves the above assumed equation “+ a a = 0) ; the
order of the tetrazomal is = 6; and the order of each of the trizomals is here
again = 3. We in fact have /7 =a+d, W/m, + /n, = b+, and there-
fore /7, + J/m, + /n, = 9; and similarly //, + /m, + /n, = 9; that is,
each of the trizomals is a cubic.
I attend, in particular, to the case where the four circles reduces themselves
to the points A, B, C, D; these four points are then in a circle; and the curve
under consideration is
aJA+b/B+c/C6d/D=0;
in the general case where the points A, B, C, D are not on a circle, this is, as has
been seen, a sextic curve, the locus of the foci of the conics which pass through
the four given points; in the case where the points are in a circle then the
sextic breaks up into two cubics (viz., observing that the curve under considera-
tion is //A + /mB + /nC + »/pD = 0, where /i: /m: J/n:/p = a:b:0e:4,
these values do of themselves satisfy the condition of decomposability
: + a + “ + ‘ = 0), that is, the locus of the foci of the conics which pass through
four points on a circle is composed of two circular cubics, each of them having
the four points for a set of concyclic foci. It is easy to see why the sextic, thus
defined as a locus of foci, must break up into two cubics; in fact, as we have seen,
the conics which pass through the four concyclic points A, B, C, D have their
axes in two fixed directions; there is consequently a locus of the foci situate on
the axes which are in one of the fixed directions, and a separate locus of the foci
92 PROFESSOR CAYLEY ON POLYZOMAL CURVES. .
situate on the axes which lie in the other of the fixed directions; viz., each of
these loci is a circular cubic.
200. Adopting the notation of No. 188, or writing
RA =, RB=b,, BC =¢, RD=d, ,
(and therefore b,c, = a,d,) we have
a:b:e:d = — d,(0,—¢,) : ¢(a,—d,) : —b,(a,—d,) + a,(6,—¢,).
Moreover
Ji =ard | fi =erd,
aa bed wes bed
fai Wen eS . Jim, =v — Jf,
bed = beb
gape sala Rs Jing = 6 + aie
and we have
bed b,¢ bed
== (a,—d,)? ware =2,7(a,—d,)*, eS = —a,(a,—d,) suppose;
and thence
n/ly = (a,—d,) (b,—4) , Jl = (a,—4,)( b,-4)
n/m, = (4, —A,) (¢,— 4%), n/ ity = (a,—d,)(_ 4 +4)
Jn, = (a,—d,) (a,—4,), n/N = (a,—d,)(—a,—4,),
that is
Jl, : Sm, / ny = b,—¢,:¢,—a,: a,—5,,
nly: n/m: Jing = b,—e, : ¢, +4, : — a,—b,;
agreeing with the formule No. 188.
The tetrazomal curve
—d,(b,—¢) JA + ¢(a,—d,) /B—),(a,—4d,) /C + a,(b,—¢) /D = 0
is thus decomposed into the two trizomals
(b;—¢y) JA + (¢,—4) /B + (a —4,) Wc
(6; —¢y) JA + (¢, +4) /B — (a@,+,) /C
201. Observe that the tetrazomal equation is a consequence of either of the
trizomal equations; taking for instance the first trizomal equation, this gives the
tetrazomal equation, and consequently any combination of the trizomal equation
and the tetrazomal equation is satisfied if only the trizomal equation is satisfied.
0,
OR
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 93
Multiply the trizomal equation by — a, + d, and add it to the tetrazomal equa-
tion ; the resulting equation contains the factor a,, and omitting this, it is
(0,—4) (— JA + /D)+(4—4,) (/B— JC) = 9,
where observe that 6,—c, is the distance BC, and a,—d, the distance AD. But
in like manner multiplying the second trizomal equation by — a, + d,, and adding
it to the original tetrazomal equation, the resulting equation, omitting the factor
@,, is
(0-4 )(— JA + /D )— (-4,)(/B — JC) = 9;
viz., it is in fact the same tetrazomal equation as was obtained by means of the
first trizomal equation.
201. The new tetrazomal equation, say
Ce wks D) + Gy — a) JB /e)= 9,
is thus equivalent to the original tetrazomal equation; observe that it is an
equation of the form .,/7A + ./mB +r/nC + /pD=9 , where
Jb=—-O,-—¢), Jm=4—d,, Jn=(%—4), Jp =%)—-4,
and where consequently /7+./p=90, /m+./n = 9, that is an equation of
the form (198) III., decomposable, as it should be, into the equations of two circular
cubics. Writing
See WE Neo.
>)
a, — dy by — ty
where @ is an arbitrary parameter, the curve is obtained as the locus of the inter-
sections of two similar conics having respectively the foci (A, D) and the foci
(B, C); (see Satmon, /Tigher Plane Curves, p. 174): whence we have the theorem,
that if A, B, C, D are any four points on a circle, the two circular cubics which are
the locus of the foci of the conics which pass through the four points A, B, C, D, are
also the locus of the intersections of the similar conics, which have for their foci
(A, D) and (B, C) respectively; and of the similar conics with the foci (B, D) and
(C, A) respectively; and of the similar conics with the foci (C, D) and (A, B)
respectively. —
202. V. /lI=/m=J/n=A/p. The order of the tetrazomal is = 5, whence
those of the trizomals should be = 3 and = 2 respectively. To verify this observe
that the equation : a ae ap : aF 4 = 0 gives : ar : “ic : TF : =0, and combining
with a+b+c+d=0, these are only satisfied by one of the systems
VOL. XXV. PART I. 2A
94 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
(a+b=0,c+d=0), (a+e=0, b+d=0), (a+d=0, b+c=0). Select-
ing to fix the ideas the first of these, or writing .
(a, b,c, d) = (a, ~ a, c, — Cc),
so that we have identically
a(4° — B°) + c(C° — D’)=0,
an equation which signifies that the radical axis of the ee A, B is also the
radical axis of the circles C, D; then, writing as we may do, / a ae re ae 5)= 5 3
we have
jew a — a
et ee Jmy=1—-,
Jn,
Ny
a A ie Ja, =1-1,=0.
Here ./i, + /m,— Jn, = 0, which gives one of the trizomals a cubic, viz..
this is the trizomal
(1-2) VAP + (1 + 8) JB + 20= 0.
The other trizomal reduces itself to the bizomal ,/A° + ./B°= 0, which regarded
as a trizomal, or written under the form (,/A° + ./B’)’ = 0, is the line A°— B’= 0
twice, viz., this is the radical axis of the circles 4,, B, twice; and the order is
thus=2. By what precedes, the line in question is in fact the common radical
axis of the circles A, B and of the circles C, D.
Cases of the Decomposable Curve, the Centres in a Line—Art. Nos. 203 to 206.
203. We have yet to consider the decomposable case when the centres
A, B,C, D are on a line; the equation aA°+ bB’+ cC°+ dD°=0 here subsists
universally, whatever be the radii w’, b”, ce’, d’. We establish as before the
relation < d -+> 3 Esk pe aie: P _Q. The cases are as follows :—
1. No eae ines between J, m,n, p, order of tetrazomal = 8, of trizomals
4 and 4.
I. J/2+/m+/n + /p =0; order of tetrazomal=7 ; of trizomals — 4 and
3; same as II. supra.
WT. /0+/p=9, /m+/n=0; order of tetrazomal = 6; of trizomals
3 and 3; same as III. supra.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 95
204. 1V. Ji + Jin t+ /n t+ Jp = 9, an/l + bi/m + Cr/n + Aa/p = 0; order
of tetrazomal = 6; this is a remarkable case, the orders of the trizomals are
either 3, 3 or else 4, 2.
To explain how this is, it is to be noticed that in the absence of any special
relation between the radii, the above conditions combined with § ate - ua : Eee ()
give /1: /m: /n:/p=a:b:c:d*; when J, m, n,p have these values, the
case is the same as IV. supra, and the orders of the trizomals are 3,3. But if
the radii of the circles satisfy the condition
a? , b?, c2, d?
Ges Ge. C= dq
then the two conditions satisfy of themselves the remaining condition
af . + ‘ +4 = 0, and the ratios /J: ./m: ./n: »/p instead of being deter-
minate as above, depend on an arbitrary parameter.
We have
NE x8 F, ding= lm 2? bv lage J+ EB esha
and between /, m,n, p only the relations
Ji+ Jn + J/n+ Jp=0, adnt+bj/m+eNn+dJ/p=0.
We find first
V1, + Jim + Vay = VE+ dm + Jn
- “ef Jp ~ Nig (ovn—e Wn) }
=- “2 {Favi- adn — 2 ova—evm}
* Writing a”, y?, 2?, w? in place of Vt Jm, Jn, /p, we have to find 2, y, z, w from the
conditions
e+y +2+w =0,
az + by +cez2+dw=0,
ey kw
ae =F bh AF ¢ + d ?
where the constants are connected by the relation
aa 25 (i) 2h ge 45 abl = 0),
It readily appears that the line represented by the first two equations touches the quadric surface in the
point x: y:¢:w=a:b:e:d, so that these are in general the only values of ./J: /m: Jn: J/p-
In the case next referred to in the text the line lies in the surface, and the values are not determined.
96 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
and then ei he
(d—a) Jl =(b—d)J/m+ (c—d) Vn,
(d—a) Jp = (a—b)J/m+ (a—c) Jn,
whence
@Ji-adp = 7—_0va— Vm):
and we have thus
Jig + Jin, + dig= 2B (2=* — f°) ae),
d Ji \d
And See :
= Vp (b—¢, fad eee ae
(observe that in the case not under consideration b/n — cx/m = 0, and therefore
JI, + /m, + Sn, = 0, Sl, + /m, + /n,= 0). In the present case we have
a:b:c:d=(b—c) (e—d)(d—b):—(c—d) (d—a) (a—b) :—(d—a)(a—b)(b—d): — (a—b) (b—c)(e—a),
and thence
so that only one of the two sums V1, + /m, + Jn,, V1, + Sm, + Jn, is=0,
viz., assuming
we have
Ji + dm, + vn, =0.
And then also
a Jl, + b/m, +eJ/n, =aJs/i+b/mteJ/n
p YE {tale
of (0a wap)
= at =(dd /t — aa,/p) — es = (bb Jn — com) | ;
but we find
dd JI — aa Jp = =" Jn — co Vin)
and thence
alt, + Jin, + evn, = Ph (S=*— J) Gh Ja = ce ni) = 9,
ee
in virtue of J*t ——. Hence /1,: </m,: /n,, =b —¢:¢—a:a—6, or the
corresponding ae is a conic, but the other trizomal is a quartic.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 97
205. V. JT = J/m = Jn = Ap; order of tetrazomal is = 5; orders of tri-
zomals = 3, 2; same as V. supra.
VL Ji + Jp =9, J/mt+ /n=9, 4/1 + bm + n/n + di/p = 9; order
of tetrazomal = 5; orders of trizomals are 3, 2.
We have here
d
a ©. re ax
Jim, = Jia + sf 2 balm,
ms = ya es
Vn, = Ga) era
or writing the values of /m,, s/n, in the form
in= Jat PE im,
Jig = — inet JG vm,
then observing that as before /= a m, if to fix the ideas we assume
be
vi a = /m, the equations are
A ae At and similarly J//, = ae we
Wig = Maree ull, i in
Jn, = — Vm +5 Ws Jing = Nim — 5 VT,
whence
Ji + dm + Ji = 9, NG -— Vn, - vn = 0.
We have moreover
OMG — a NG
dim +ovm=b- 9 fata VE
and thence
all, +oJ/m, +eva=a—AVi+6—ONm=0,
so that ;
RE Jm,: Vm =b —e:e —a:a— b;
VOR, XOsVe BART Ii IE
98 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
the corresponding trizomal is thus a conic, and it has been seen that the other
trizomal is a cubic. |
VIL. Ifwehave|1, 1, 1, 1 |=0, and (1, 1, 1, 1 )( Jim Jn,J/p)=0,
i, O -@er a ee 4
oe Nae oo fe, a
a’”?, W'2, 2, qi”? a”, B?, ¢”, @’2
the tetrazomal has a branch ideally containing (z= 0) the line infinity 3 times;
order is = 5; orders of the trizomals are 3, 2. We have here
VIi:Vm:Vn: Vp =a:b:e:4,
and thence
Jl, =a+d ; J/1, =a+d
— _j; _ |bed — bed
Vm, = b Rie Jin, =» + fe
= bed — bed
a, = 0 tin es Jn, =¢—/—,
which give
Vi, +Vm, + Vn, = 0, Vi, +Vm, + Vn, = 0.
Moreover
aJ/l,+oJ/m,+¢ Jn, = aatd)+bb+ec
bed
a sade
@-« fre
= (296) j=
_——
— af (a-a)— 0-9, |”
and similarly
——_
oe = i be
aJT, +0Jin, + eda, = Af (ad) + 0-0) |
whence in virtue of
ad __ (6—c)?
be ~ (d—a)?’
one of the two expressions is = 0; and the trizomals are thus a conic anda
cubic.
The Decomposable Curve ; Transformation to a different set of Coneyclic Foci—Art. No. 206.
206. Consider the decomposable case of
JIA + /mB + Jn + JpD = 0;
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 99
: : , : 5 y )
viz., the points A, B, C, D lie here in a circle, and we have aur > + - ++ E = 0.
Taking (A,, D,) the anti-points of (A, D); (B,, C,) the anti-points of (B, C);
then A, D, = AD, B, C, = BC (No. 65) and referring to the formule, anie,
Nos. 100 e seq., it appears that we can find /,, m,, n,, p, such that identically
—lA+mB + 70 — pD = —1,A, + m,B, + 1,C, — p,D,,
and moreover that /p = /, p,, mn = m, n, .
The equation of the curve gives
— (A + mB + 20 — pD — 2 JipAD +2./mnBC = 0,
which may consequently be written
— LA, + m,B, + 2,0, — p,D, — 2,/i,p,A,D, + 2./mn,B,C, = 0;
viz., this is . ree
JTA, + /m,B, + /n,C, + /p,D, oy hs
that is, the two trizomals expressed by the original tetrazomal equation involving
the set of concyclic foci (A, B,C, D) are thus expressed by a new tetrazomal
equation involving the different set of concyclic foci (4,, B,, C,, D,); and we
might of course in like manner express the equation in terms of the other two
sets of concyclic foci (A,, B,, C,, D,) and (A,, B,, C,, D,) respectively. It might
have been anticipated that such a transformation existed, for we could as regards
each of the component trizomals separately pass from the original set to a
different set of concyclic foci, and the two trizomal equations thus obtained would,
it might be presumed, be capable of composition into a single tetrazomal equation ;
but the direct transformation of the tetrazomal equation is not on this account
less interesting.
ANNEX I.—On the Theory of the Jacobian.
Consider any three curves U= 0, V= 0, W = 0, of the same order 7, then
writing
dU, dgV, deW
dy U, dyV, dyW
d,U, d,V, d,W
AE CHCOE ETI Rs
NOE d(a, Y, 2) =
2
we have the Jacobian curve J(U, V, W) = 0, of the order 37 — 3.
A fundamental property is that if the curves U = 0, V = 0, W= 0 have any
common point, this is a point on the Jacobian, and not only so, but it is a node,
or double point, that is, for the point in question we have J = 0, and also
Ca 0, 6, = 0, df = 0.
It follows that for the three curves /90+ Lo=0, m9 + MS—0, n0 + Nb=—0
(Q = 0 of the order r—s’, 6=0 of the order r—s, 1 = 0, m= 0, n = 0 each of
100 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
the order s’, L = 0, M=0, N=0 each of the order s) which have in common
the (7 — s’) (7 — s) points of intersection of the curves 6 = 0, 6 = 0, each of these
points is a node on the Jacobian, and hence that the Jacobian must be of the
form
J(10+ Le, m+ Me, no+ Ne) = Ao’? +2bo0a+Ce*= 0,
where obviously the degrees of A, B, C must be 7+ 2s —3, r+s+s’—3, r+2s—3
respectively. In the particular case where s’=0, that is where /, m, m are con-
stants, we have 4 =0; the Jacobian curve then contains as a factor (b=0), and
throwing this out, the curve is BO + CH=0, viz., this is a curve of the order
2r + s—3 passing through each of 7(7 — s) points of intersection of the curves
e=0,f6=0.
In particular, if »=2,s=1, that is, if the curves are the conics
6+ l0e=0,0+ Mb =0, 0+ Nb = 0, passing through the two points of
intersection of the conic 6 = 0 by the line @ = 0, then the Jacobian is a conic
passing through these same two points, viz., its equation is of the form
9+Q26=0. This intersects any one of the given conics, say 9 + Lm = O in the
points 6 = 0, @ = 0, and in two other points 96 + OQ = 0, Q—L=0; at each
of the last-mentioned points, the tangents to the two curves, and the lines drawn
to the two points 6 = 0, @ = 0, form a harmonic pencil.
Although this is, in fact, the known theorem that the Jacobian of three circles
is their orthotomic circle, yet it is, I think, worth while to give a demonstration
of the theorem as above stated in reference to the conics through two given points.
Taking (2 = 0, x = 0)(z = 0, y = 0) for the two given points 6 = 0, @ = 0,
the general equation of a conic through the two points is a quadric equation con-
taining terms in 2”, zz, zy, zy; taking any two such conics
cz + 2fyz + 2gex + 2hay =0,
C2 + 2Fyz + 2Gzx + 2Hxy = 0,
these intersect in the two points (zx = 0, z = 0), (y = 0, z = 0) and in two other
points; let (z, y, z) be co-ordinates of either of the last-mentioned points, and
take (X, Y, Z) as current co-ordinates, the equations of the lines to the fixed
points and of the two tangents are
Xz — Ze =0, Ye-—-W=0,
(hy +92) (Xz— Zz) + (he + fe) (Vz —-Zy) =0,
(Hy + Gz) (Xz — Ze) + (Hx + Fz) (Vz — Zy) =0,
whence the condition for the harmonic relation is
(hy + g2)(Ha + Fz) + (he + fz) (Hy + G2) = 0,
that is
(/G + gf)2 + (AF + fH) yz + (gH + hG)ex + 2hHaey=0,
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 101
but from the equations of the two conics multiplying by 4H, 3h and adding, we
have
4H +10)2 4+ (AF + fA)yz + GA + h@)ea + 2hHay = 0;
viz., the condition is thus reduced to
cH +hO—2(f6+ GF) =0,
so that being satisfied for one of the points in question, it will be satisfied for the
other of them. Now for the three conics
cz" + 2fyz + 29ee + 2hey =0,
C22 + 2fye + 2g’zx + 2h’ay OF
ca + 2f’ye + 2g’ea + 2h’ay = 0,
II
forming the Jacobian, and throwing out the factor z, we may write the equation
in the form
CP 4+ 2Fyz + 2Gee+2Hay =0,
where the values are
OG Re Cet Gg Gioe—se) + 9-( fe — fe), ,
H=gllif’ — Wh) +g WF ~ Mf) +9" — Kf).
2F=h( fe’ —f') + (fre—fe)th'(fe —fo ,
24 =h(cg” — ce’) +N C%"9 — eg) +h’ (eg — cg) ;
and we thence obtain
cH + hO =— (fo — f'9) (ch — ch’) + (fo — fq’) cl’ — ch)
= f+ gF),
viz., the condition is satisfied in regard to the Jacobian and the first of the three
conics; and it is therefore also satisfied in regard to the Jacobian and the other
two conics respectively.
I do not know any general theorem in regard to the Jacobian which gives the
foregoing theorem of the orthotomic circle. It may be remarked that the use in
the Memoir of the theorem of the orthotomic circle is not so great as would at
first sight appear: it fixes the ideas to speak of the orthotomic circle of three
given circles rather than of their Jacobian, but we are concerned with the ortho-
tomic circle less as the circle which cuts at right angles the given circles than as
a circle standing in a known relation to the given circles.
ANNEX IJ.—On Casty’s Theorem for the Circle which touches three given Circles.
The following two problems are identical :—
1. To find a circle touching three given circles.
2. To find a cone-sphere (sphere the radius of which is = 0) passing through
three given points in space.
VOL. XXV. PART I. 2€
102 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
In fact, in the first problem if we use z to denote a given constant (which may
be = 0), then taking a, a’ and 2(z — a’) for the co-ordinates of the centre and for
the radius of one of the given circles; and similarly }, 0’, i(z — 0"); ¢, ¢, uWz—e)
for the other two given circles; and S, S’,i(z — S”) for the required circle; the
equations of the given circles will be
(@— a +y—aP+@—af=0,
(7 — bP + (y— VP + (2— VP =0,
(@—eP+y—¢P +(e—e")*¥=0,
and that of the required circle will be
(a—S)? + (y—S’)? + @—S’)? = 0.
In order that this may touch the given circles, the distances of its centre from
the centres of the given circles must be 7(S’—a’), i(S’—b’), iS’—c’) respectively;
the conditions of contact then are
(S—a)? + (S’-a? + (S’— a’?
(S — b? + (S’— UY)? + (S"— HF = 0,
(S— co)? + (S’—c)? + (S’— ec’? = 0,
0,
|
or we have from these equations to determine S, S’, S’. But taking (a, a’, a’),
(0, 0’, b’), (c, &, ec) for the co-ordinates of three given points in space, and
(S, S’, S") for the co-ordinates of the centre of the cone-sphere through these
points, we have the very same equations for the determination of (S, S’, 8”), and
the identity of the two problems thus appears.
I will presently give the direct analytical solution of this system of equations.
But to obtain a solution in the form required, I remark that the equation of the
cone-sphere in question is nothing else than the relation that exists between the
co-ordinates of any four points on a cone-sphere; to find this, consider any five
points in space, 1, 2, 3, 4,5; and let 12, &c. denote the distances between the
points 1 and 2, &c.; then we have between the distances of the five points the
relation
pa ie Na ch ert alia
Oe ee ae, Le
oT, 0, 335. 08 25
, O25 W ; a4, 35"
a er ay aS
Sal 58+, Bae 6
whence taking 5 to be the centre of the cone-sphere through the points 1, 2, 3, 4,
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 108
—
we have 15 = 25 = 35 = 45 = 0; and the equation becomes
OR 2215, ee 0
211.05, 23°, 24?
1% So 0 2 34”
es, 0
which is the relation between the distances of any four points on a cone-sphere ;
this equation may be written under the irrational form .
OFC Te 4231, 94 4194
Taking (a, a’, a’), (0, 0’, 0"), (¢, ¢, c’), (x, y, ) for the co-ordinates of the four points
respectively, we have
= J(b-cP + U—e) + ees 14 = J/(@—a? + y—a)? + a’) ,
= /(¢—a)? + (—a) + (=a, 24 = f/(a—bP + (y—by + (20,
JMa=b? + (a 0 + (a0 = 34 = J/(z—c)? + (y—ey + @—ey,
NI
oo
eal
.
or the symbols having these significations, we have
23.14 + 31.24+ 12.34 = 0
for the equation of the cone-sphere through the three points; or rather (since the
rational equation is of the order 4 in the co-ordinates (2, y, z)) this is the equation
of the pair of cone-spheres through the three given points; and similarly it is
in the first problem the equation of a pair of circles each touching the three
given circles respectively.
In the first problem the radii of the given circles were u(z—a’), u(z—0’),
i(z—c’) respectively; denoting these radii by a, 6, y, or taking the equations of the
given circles to be
(c—a)? + (y—-aP—a? = 0,
(a— bP + y—by = Be = 0,
Gy + y-—c? —7 = 0,
the symbols then are
= Jb— oF + © cP — (6-7, = JS@—aP + yap —e’,
a Coes ey Chee (y—a)?, 24 = eran by + (y= ne B’,
S (SX) al
fg
and the equation of the pair of circles is as before
14 + 31.24 412.34.= 0;
esl
104 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
where it is to be noticed that 23, 31, 12 are the tangential distances of the circles
2 and 3, 3 and 1, 1 and 2 respectively; viz., if a, 8, y are the radii taken
positively, then these are the direct tangential distances. By taking the radii
positively or negatively at pleasure, we obtain in all four equations—the tangential
distances being all direct as above, or else any one is direct, and the other two are
inverse ; we have thus the four pairs of tangent circles.
The cone-spheres which pass through a given circle are the two spheres which
have their centres in the two anti-points of the given circle; and it is easy to see
that the foregoing investigation gives the following (imaginary) construction of
the tangent circles; viz., given any three circles A, B, Cin the same plane, to
draw the tangent circles. Taking the anti-points of the three circles, then select-
ing any three anti-points (one for each circle) so as to form a triad, we have in
all four complementary pairs of triads. Through a triad, and through the com-
plementary triad draw two circles, these are situate symmetrically on opposite
sides of the plane; and combining each anti-point of the first circle with the
symmetrically situated anti-point of the second circle, we have two pairs of points,
the points of each pair being symmetrically situate in regard to the plane, and
having therefore an anti-circle in this plane; these two anti-circles are a pair of
tangent circles; and the four pairs of complementary triads give in this manner
the four pairs of tangent circles.
I return to the equations
(@ — S)?+ (y —8)?+ @ —8")? =0,
(a — 8)? + (a — 8)? + (a” — 8”)? = 0,
(6 —S8)?+(0¢—S)?+ 0 — 8’)? =0,
( — 8) + (¢— 8+" — 8) =0;
by eliminating (S, S’, S”) from these equations we shall obtain the equation of
the pair of cone-spheres through the points (a, a’, a’), (0, 0’, b’), (¢, ¢, ¢’). Write
«—S,y—S',z—S" = X, Y, Z, then we have
AF 4} Y2 +77 = 0,
and if, for shortness, we put
A=(a—2)? +(@ —y)*?+(@—-2)?, .
B= (0 —2)* a — 9) i — 22,
CHa + PFC 2,
then by means of the equation just obtained the other three equations become
A+2(@-a)XL4+(—-y)V+ (a —2Z]=0,
B+2[@-2) +0 -—y V+ -2Z]=0,
C+2[( —a) X+( —y) V+ (c’ —2)Z] =0.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 105
These last equations give
A:V:Z= rMA+4B4 IC
>: AA+WB+/C
NA+ u4B+4+/C ,
where
A=0e" —Vd+(¢ —Ve -— (—-O'\y,
w=ca—cad+(a—cej —(a—ey,
yp =al’— a+ U—a)ze— "ay,
N= b’e — be’ +(e’ — Da — (e — dz,
w=la—ca +(e’—c)je-—(a-— cz,
y =a’b — ab” + (0’ —a’)x— (b — az,
w= bl —Ue + (¢ —djyy —(¢ — U)a,
we =e — Ca+ (a —cjyy —W— ca,
ab — ab + (6 —ajyy —(U —a)z;
=
and the result of the elimination then is
(a A+,.B +» cy
+(* A+ 4¢B+y/C?
+(VWA+n'B4+ /CP =0.
But substituting for A, B, C their values, and writing, for shortness,
a 4 — bc’ cee bc’ + cal ar, a + ab” z. a’b ;
—j =U’c — be’ + c’a — ca” +’) — ab’,
—k =be —Ue +cev —ca +ab’ —ab,
A =a(l'c’ — b’c) + a’ (bc — be”) + abe’ — Ue) ,
—p = (Uc’ — ’c) (a? + aw? + a”) + (a”—e'd’) (0? +02 +0") + (vb —a'd’) (2? +67 +c) ,
—q = (bc — be’) (a* + a? + a”) + (ca —ca” ) (0? +07+0"?) + (ab —ab’) (PP? +07 +c) ,
—r = (bec —0U'c)(a* + a7 + a”) + (ca —ca ) (0? +07+0"7) + (ab’ —ab’ ) (ce? +67 +0) ,
—l = (ce —b )(a?+a% +a") +(a —c )(0?+07+0"?) + (0 —a )(P+c%+4c%) ,
—m= (¢ —-0U )\(®+a%74+ 0%) 4+ (a -—c )\U407+0%) + (0 -a’ ) (+e? +c%) ,
—n = (ce —b’)(@ +a? +0) 4+ (a’—c’ )(P+b74+0"7) + (0 —a’ ) (@+c7+0%),
we find
AA + 2B + 9C
= — Ua + xy? + 2°)
+ 2a(a? + y? + 27) — 2a(iw + jy + ke) — 2ax+ ny—mze—p,
with similar expressions for \’A + v’B + C, »’A + «’B + »’C, and the re-
sult is
{u(a? + y? + 2”) — 2u(aw + jy + hz) — 2da+ ny — mz— ph?
+ fie? + y? + 2?) — 2y(iae + jy + ke) — na — 2by+ le— gh?
+ {k(a? + y? + 2?) — Qed + jy + ke) + ma— ly—2az—7rh?=0,
VOL. XXV. PART I. 2D
106 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
viz., this is
(a? + y? + 27)? (i? + 7? + kh?)
+ (a? + y? + 2?) {dain + jy + ke + 2(i(ny — mz) + j(lz — na) + (ma — ly)
+ 44? — 2p + jq + kr) + (7? + m? + n?)h
— (le + my + nz)? + A(ia + jy + kez) (pu + gy + 72)
+ 4A(px + qy +72) — 2(p(ny — mz) + g(lz — nv) + 7(mx — ly))
+r? +7+r=0.
viz., this is in the rational form the equation of the pair of cone-spheres. The
function on the left hand side must, it is clear, be save to a numerical factor the
norm of
VO— oF + We + Ue. J a—a?l + Ya? + &=e'P
+ Sea + C= aF + a}. SOO GP + CUP
+ J(a—b? + @—0P + W VP. Je—o? + Y— oP + — eF,”
the numerical factor of the expression in question is in fact =— 4, that is, the
norm is
=— 4074+ 74+ 27 (P+ 7? + 2) + &.;
so that attending only to the highest powers in (a, y, z) we ought to have
Norm {/(b—c)*+ (U —¢/)? + (U’ — "P+ V(c—a)? + (¢ —a')* + (0” — 0")? +N (a—b)* + (a —U) + (a —0")}
= —4(? +7? +h’) .
It is easy to see that the norm is in fact composed of the terms
WW —e{ OF — C—aP — (a HF},
+ 2(¢ —a'? {—(b—e? + (¢—a?— (a— BY},
+ 2(a’—¥)2 {—(b— 0)? — (¢— a}? + (a—BF},
and of the similar terms (a, 0, c), (a, 6, &) and in (a, 0c’), (a, 6, c’); the above
written terms are = — 4 into
W— ¢)? (a—2) (a—0)
+ (¢—a)? 6 —0)(b —a)
+ (a —0')? (ce —a)(a—b),
which is
= a? (b—c)? + 07 (e—a) + &? (a—b)?
+ 20’c' (a —b) (ec—a) + 2ca' (b—c) (a—b) + 2ad’ (ce —4) (b—c)
= {a(b—c) + U(ec—a) + c(a—d)}?
Sie
and the value of the norm is thus = — 4(2? + 7? + £°), as it should be.
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 107
Annex IIL.—On the Norm of (b—c),/A°+ (c— a), /B°+ (a— 6), /C°, when the Centres
are in a Line.
The norm of /U+,/V+,/W is
= (pall eel = —81).(U, Vy We):
whence that of /U+0’ + /V+WVt+/W+W’ is
Sd ee ee ee (Ge VW)
ag Ds I is RE Wa ORs 30
Vel ee I, ee VC, BWP,
where the last term is = 2 into |
oT 7=W)
ROIS (= Ue W
+W(—-U=V4W).
And the norm of /U+0’+U" + /V4+V+V'+J/W+W’+ W’" is obviously
composed in a similar manner.
Now, applying the formula to obtain the norm of
O-0) JF Fotat C—O JP +I+B + (W-)) JE F047,
the expression contains six terms, two of which are at once seen to vanish ; and
writing for shortness (,, ) in place of (1, 1,1, —1,— 1, — 1) the remaining terms
are
(,)(G@—6)%« , (¢e—a)?8, (a—b)*¥ ye
+2 (,;) ((o- c)?a , (¢c—a)*B, (a—b)*y )(@ —c)*a?, (c—a)?b?, (a— b)?c?)
+ 24(,,)((6—¢)?a , (¢—a)?8, (w~—b)?7 )(G—c)? , (c—a)? , (a—0)? )
+ 26(,,) (@—«)?a?, (¢ — a)?0?, (a—b)?c?) (o— 0)? ,(e—a)? , @—bd)? );
the first of these terms requires no reduction ; the second, omitting the factor 2,
is
(b—c)’a | (6—c)?a® — (¢—a)?b? — (a—b)%c? |
+ (c—a)’p (= (—e)?a? + (¢—a)?b? — (a—b)?c? |
; + (a—b)?y [—@—90?a? — (¢c—a)?b? + (@=b)7e?|;
which is
= 2(a — b) (b — c) ¢ — a) [ bc (b — ¢) a+ca(e—a)B+ab(a— b)y | ’
Similarly the third term, omitting the factor 20, is
(b— ca [ (6—c)? —(—a??—-(a— b)? |
+ (c — a)*B[—(@ — 0)? + ¢ — a)? — (a — |
+ (a — by |—-G@- oF —-C-af +(@—d)],
108 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
which is
= 2(a — b) (6 —¢) (c—a) [@—cat (c — a) B+ (a — Dy],
and for the last term, omitting the factor 20, this may be deduced therefrom by
writing (a’, 6’, c*) in place of (a, 8, y), viz., it is
= — 2(a — b)* (b — ce? (ec — a)’.
Hence, restoring the omitted factors, and collecting, we find
Norm {(} — e) Na+ 6+at(c—a)/P +6484 (a — b) Je +o+ x}
= (b—c)*a? + (c—a)*B? + (a—b)'y? — 2(e—a)? (a—b)*By — 2(a—b)? (b—c)*ya—2(b—c)? (c—a)*aB
+ 46(a—b) (b—c) (c—a) [ (b—c)a+(c—a) B+(a—D)y]
+ 4 (a—b) (b—e) (c—a) [ (be (b—c) a +ea (c—a) B+ab (a—D)y]
— 46(a—b) (b—c)? (e—a)*.
Hence, first writing a— az, b—«2,¢—~wz in place of a,b,c; then 7’ for 6, and
(— a”,— b”,— c’”) for (a, 8, y); and finally introducing 2 for homogeneity, we
find
Norm {(b —c) Va — az)? + y? — a2 + (¢ — a) ye (a — b) J} = 27 into
22((b — c)ta”t + (¢ — a8" + (a — byte”
— 2c — a)? (a — b)?b'9c"? — 2(a — b)* (b — ¢)?e”4a”? — 2(b — c)? (¢ — a)Pa’b"?)
—4y? (b — c) (e— a) (a — Dd) a (b— ec) a? + (c—a)l” +a— b)e"?]
—4 (b—c)(c—a)(a—b) { (b—oc) a” be —w(b+c) +2’)
+(¢c—a)b” (ca — zz (¢ + a) + 2")
+(a—b)c” (#ab—z(a + 0) + a?)}
—4y (b—c) (ec—a) (a—b).
so that the equation (6 — c) ./A° + (¢—a) ./B° + (a —b) ./C° = 0, in its
rationalised form, contains (2? = 0) the line infinity twice, and the curve is thus
aconic. If @?=0?= c’= k”, then the expression of the norm is
= 2 into — 4(a — B)? (& — 0)? (¢ — a)? (y — Bh),
viz., when the three circles have each of them the same radius #”, the curve is the
pair of parallel lines y*? — &”z*? = 0; and in particular when s’ = 0, or the
circles reduce themselves each to a point, then the curve is y’ = 0, the axis twice.
ANNEX IV.—On the Trizomal Curves /JiU+ /mV + »./nW = 9, which have a Cusp, or
two Nodes.
The trizomal curve ./7U + ./mV+/nW= 9, has notin general any nodes
or cusps: in the particular case where the zomal curves are circles, we have
PROFESSOR CAYLEY ON POLYZOMAL CURVES. 109
however seen how the ratios / : m:n may be determined so that the curve shall
acquire a node, two nodes, or a cusp; viz., regarding a, b, c as current areal co-
ordinates, we have here a conic : + + + : = 0, the locus of the centres of the
variable circle, and the solution depends on establishing a relation between this
conic and the orthotomic circle or Jacobian of the three given circles. I have in
my paper “ Investigations in connection with Casry’s Equation,” Quart. Math.
Jour. vol. viii. (1867), pp. 334-342, given, after Professor CrEMona, a solution of
the general question to find the number of the curves /7U + /mV +/nW= 9,
which have a cusp, or which have two nodes, and I will here reproduce the
leading points of the investigation. I remark, that although one of the loci
involved in it is the same as that occurring in the case of the three circles (viz.,
we have in each case the Jacobian of the given curves), the other two loci
> and A, which present themselves, seem to have no relation to the conic of
centres which is made use of in the particular case.
We have the curves U= 0, V=0, W=0, each of the same order 7; and
considering a point the co-ordinates whereof are (/, m, ), we regard as corres-
ponding to this point the curve 707+ /mV+ /nW= 0, say for shortness, the
curve Q, being as above a curve of the order 27, having 7” contacts with each of
the given curves V= 0, V=0, W=0. As long as the point (/, m, 2) is arbitrary,
the curve (2 has not any node, and in order that this curve may have a node, it is
necessary that the point (/, m, 7) shall lie on a certain curve A; this being so, the
node will, it is easy to see, lie on the curve J, the Jacobian of the three given
curves; and the curves J and A will correspond to each other point to point,
viz., taking for (J, m, n) any point whatever on the curve A, the curve Q will have
a node at some one point of J; and conversely, in order that the curve Q may
be a curve having a node at a given point of J, the point (/, m, n) must be at
some one point of the curve A. The curve A has, however, nodes and cusps; each
node of A corresponds to two points of J, viz., for (/, m, n) at a node of A, the
curve () is a binodal curve having a node at each of the corresponding points of ./;
each cusp of A corresponds to two coincident points of J, viz. for (/, m, n) at a cusp
of A, the curve Q has anode at the corresponding point of /. The number of the
binodal curves Q is thus equal to the number of the nodes of A, and the number
of the cuspidal curves Q is equal to the number of the cusps of A; and the
question is to find the Pluckerian numbers of the curve A. This Professor
CREMONA accomplished in a very ingenious manner, by bringing the curve A into
connexion with another curve = (viz., = is the locus of-the nodes of those curves
VOL. XXV. PART I. 25
110 PROFESSOR CAYLEY ON POLYZOMAL CURVES.
lU+ mV + nW = 0 which have a node), and the result arrived at is that for the
curve A
’ Order = 3(r—1) (8-2),
Class = 6(r—1)?,
Nodes = $(r—1) (27r*® — 637? + 227 + 16) ,
Cusps = 3(r—1) (7ir—8),
Double tangents = % (r — 1) (1273 — 36r? + 197 + 16),
Inflexions = 12 (r —1) (r- 2);
so that, finally, the number of the cuspidal curves 707 + ./mV + /nW=0,
is = 3 (r — 1) (77 — 8), and the number of the binodal curves of the same form
is = 3 (7 — 1) (277° — 637" + 22r + 16). When the given curves are conics, or
for r = 2, these numbers are = 18 and 36 respectively; but the formule are
not applicable to the case where the conics have a point or points of intersection
in common ; nor, consequently, to the case of the three circles.
ae
te
Gal bug)
Il.—On the Motion, Equilibrium, and Forms of Liquid Films. By the late Sir
Davip Brewster, K.H., D.C.L., &e. (Plates I. and IL) Communicated
by Francis Dzas, Esq., LL.B.
(Read 6th April 1868.)
[This paper was transmitted to the Council by Sir Davin Brewster, on the
8th February 1868, with the following remarks :—“ I have tried in vain to finish
the two most important of my papers on Liquid Films, but the most beautiful
drawings of all the phenomena which its purpose was to describe have been
finished. I think, therefore, that my friend Mr Deas will, by means of these
drawings, produce an interesting paper. The drawings are numerous and large,
but many of them may be reduced in size. As this is the last of my papers, I hope
the Council will not grudge the expense of having them well lithographed.”
In another letter, Sir Davin BREwstTER expresses a wish, that in the event of
the paper being printed in the ‘‘ Transactions,” notice should be taken of the
fact that the drawings were executed by his friend Miss DickENson. |
I. On some Transformations in Films when brought in contact with Surfaces of Glass.*
(1.) Let a film be formed on the rim of a cylindrical wine-glass, at or very near
its margin; cover it immediately with a watch-glass, and holding the latter firmly
in its place, invert the whole, so that the film is placed in a vertical position.
The film will now attach itself to the watch-glass at the lowest point where it is
in contact with the margin of the wine-glass, and will run up the concave surface
of the former. At the same time, the film will leave the margin of the wine-
glass at its upper edge, and retreat into the glass, running down its inner sur-
face. <A film of the form of the segment of a sphere will thus be produced, which,
with the upper portions of the inner surfaces of the watch-glass and wine-glass,
will form a hollow filled with air, as shown in fig. 1. This state of matters will
remain the same, in whatever position we now place the wine-glass, the figure
which has thus been produced being one of equilibrium. The phenomenon
produced arises from the fact, that when the original film is first taken up on
the margin of the wine-glass, a drop of liquid always remains in the bottom of
the glass, and when the glass is inverted, so as to bring the film into the vertical
* The experiments under Head 1, are best performed by using a watch-glass of considerable
concavity, but they will all succeed more or less perfectly by using a piece of perfectly flat glass, or
even by employing the convex instead of the concave surface of the watch-glass, provided we take
care that the surface of the film on the wine-glass does not project in any part above its rim.
VO, XXVE PART T: Zk
112 SIR DAVID BREWSTER ON THE MOTION, EQUILIBRIUM,
position, this drop runs down the inner surface of the glass till, reaching its
lowest point, it brings the film into close contact with the watch-glass; the film
now attaches itself to and spreads itself over the surface of the latter in a similar
way to what takes place when a bubble blown from a pipe is brought into contact
with any smooth surface, whilst the original system of equilibrium being now
disturbed, the upper part of the film is put in motion, and a new system of equi-
librium is formed.
In making this experiment, the rise of the film upon the surface of the watch-
glass is generally so rapid, that it is difficult to watch its progress, but by careful
inspection it may be observed to commence first at a single point; the edge of
attachment of the film to the watch-glass then becomes first elliptical. then cir-
cularly concave, then a straight line, then convex, as seen in fig. 2, where the
lines represent the edge of the film on the watch-glass in its different stages of
progress. The changes which take place in the curvature of the concave spherical
film within the wine-glass during these stages are also very curious. The concave
film may sometimes be produced without inverting the glass, by holding the
watch-glass firmly in position with the thumb, and briskly shaking the glass.
The drop of liquid is thus thrown upon the margin of the film.
(2.) The concave spherical film being thus formed, we can reduce matters to
tk eir original state (¢.¢. reproduce the single original film on the margin of the wine-
glass) by slowly and carefully removing the watch-glass. The experiment is best
made by lifting the watch-glass from its connection with the wine-glass at its
upper margin, keeping the two in close contact at their lower margin. The upper
edge of the concave film will thus again rise in the wine-glass, while its lower
edge will descend along the watch-glass; and when it has reached the point where
the two glasses are in contact, the watch-glass may be removed, and the original
film left on the wine-glass. The edge of the film, as it descends the watch-glass,
exhibits the same series of curves as it did in ascending in the last experiment;
but, of course, in a reversed order. The nature of these curves may be much
more satisfactorily observed in this experiment than in the last, as their progress
is much less rapid. Before entirely removing the watch-glass, we can cause the
film to ascend or descend at pleasure, with any degree of rapidity, by approxi-
mating or separating the two glasses.
In making the first experiment, the drop of fluid which causes the film to
attach itself to the wine-glass generally entirely escapes; consequently, if we
repeat this experiment upon the film as re-formed in the second experiment, it
will seldom succeed, there being no superfluous fiuid to produce the necessary
contact. If, however, we place a drop of fluid, either on the surface of the
reformed film or on the inner surface of the watch-glass, the experiment will
succeed, and may be repeated indefinitely, till the film bursts—a fact which
clearly proves the drop of fluid to be the agent in producing the phenomenon.
AND FORMS OF LIQUID FILMS. 113
These experiments succeed best with freshly-formed films, but they may be
performed even after the colouring matter has formed on the film, though with
less certainty. In re-forming the original film, as above described, the wine-glass
may be held either horizontally, vertically, or even inverted entirely with the
watch-glass held beneath it.
(3.) If, after forming the concave film, as in the first experiment, we raise the
watch-glass from the wine-glass, maintaining the contact between the two only at
one point, and then cause the watch-glass to rotate by this point round the wine-
glass, the concave film will likewise move round the wine-glass; and by continuing
the movement, the concave film may be gradually enlarged, till it passes into the
original single film, adherent to the wine-glass only as in the last experiment, the
curvature of its margin passing through the forms already observed.
(4.) If, having formed the concave film as in the first experiment, we lift the
watch-glass perpendicularly from the margin of the wine-glass, the edges of the
concave film will remain adherent to the wine-glass and watch-glass respectively,
the film being stretched out, while the fluid between the glasses at their previous
line of contact will be drawn into a second film, which unites with the concave
film to form a cylindrical bag attached above to the watch-glass, and below to the
wine-glass.* By continuing to raise the watch-glass, this bag will sometimes
become detached from the watch-glass, and return into the form of the conéave
film ; at other times it will leave the wine-glass entirely, and take the form of a
lens upon the watch-glass. Fig. 3 exhibits the cylindrical bag thus formed, still
attached to both wine-glass and watch-glass.
As seen from the figure, the remainder of the wine-glass is now covered by a
separate film, upon which the cylindrical bag partly rests. This may be
regarded as that part of the original film which, in the first experiment, ran up
and attached itself to the concave surface of the watch-glass, and which, in
the process of perpendicularly lifting the watch-glass, has become restored to its
original position, and which, for the sake of distinctness, we may call the
complementary film. Whether the cylindrical bag will adhere to the watch-
glass or return into the concave film, seems to depend on the relation of the
radius of curvature of the concave film to that of the film covering the remainder
of the glass, and to that of the watch-glass itself. ‘The smaller the concave
film, and the more convex the complementary film, the more readily will the bag
leave the latter, and attach itself to the watch-glass in the form of a lens, while
the less concave the watch-glass, the more difficult it is to produce this result,
till, when we use a perfectly flat glass, it will rarely take place in any case.
When, however, the complementary film is either accidentally or purposely broken,
so that only the concave film remains, the latter will invariably pass into the form
* The experiment succeeds best, by first raising the portion of the watch-glass most distant from
the concave film, and then lifting the whole watch-glass vertically.
\14 SIR DAVID BREWSTER ON THE MOTION, EQUILIBRIUM,
of the lens. The curious bag shape of the film in this latter form of the experiment,
while thus passing from the wine-glass to the watch-glass, is shown in fig. 4.
(5.) The lens, when obtained upon the watch-glass, may be restored to the
wine-glass in the form of the concave film, by merely replacing the watch-glass
so that the lens shall touch the edge of the wine-glass, and it may be taken up and
replaced several times, and that whether the complementary film has remained
on the wine-glass or not.
(6.) If, when the complementary film has remained on the wine-glass after
removing the lens upon the watch-glass, we replace the lens so as to form the
concave film, we can, by lifting the watch-glass, or causing it to rotate, as in the
previous experiments, reproduce the original single film, which in this case consists
of the same film which was taken up as a lens upon the watch-glass.
II. On the Motions and Figures of Equilibriums of Films within Single Hollow Cones.
In the following experiments, a glass cone of the form in the annexed diagram
was used—the perpendicular height of the cone being 3 inches, the diameter
of the base being 1 inch. The aperture at the apex can be opened
or closed at pleasure, by inserting a plug at 7. When this vessel
is dipped in the soap solution (J7N being open), it gives, when
ALB raised, a plane film at CD. This film (as shown in the previous
paper on “ Liquid Films,” vol. xxiv. p. 503, of the “ Transactions”)
does not remain at CD, but at once commences to ascend towards
A 6, with a velocity increasing—/i'stly, with the angle of the cone
itself; and, secondly, with the angle of inclination at which the
cone is held. Arrived at AB, where the cone ends in the cylin-
drical tube, the film becomes stationary.
The motions and disposition of films within the cone may be
well studied, by blowing small bubbles from a quill or small tube,
and inserting them within the vessel. Thus, if a bubble of moderate size be
placed on the side of the cone near its base, it will gradually ascend till its convex °
surface comes in contact with the opposite side of the cone, when it will separate
into two plane films, the lower of which will remain stationary at AB, the upper
a little way up the tube. This movement of the bubble is represented in fig. 5.
Again, having obtained a plane film, a little way up the cone, insert a small
bubble against the side of the cone, touching the under surface of the plane film,
the upper surface of the bubble will unite with the adjacent portion of the plane
film to form a single film, and produce the system shown in fig. 6. Insert now, on
the opposite side, a second bubble of the same size with the first, and we obtain
the system shown in fig. 7, the upper surface of each of the two hollow figures
thus produced being convex, the lower concave, their surface of contact being a
Man
Cc
AND FORMS OF LIQUID FILMS. 115
plane film. The same result is produced, though no plane film is first formed
within the cone, by simply inserting two bubbles of equal size, so as to come in
contact with one another. In a similar manner, three bubbles may be inserted
in place of two, the result is the system shown in fig. 8, where the three bubbles
are united to one another by three plane films meeting in a central vertical
straight line. The system produced by inserting four bubbles in a similar
manner to the last, is a very curious and beautiful one, peculiarly interesting on
account of its analogy to the system already described in the previous paper, as
formed within the wire cube (vide “ Transactions,” vol. xxiv. p.505). This system,
shown in fig. 9, consists of four similar figures, the curvatures of whose sides are
extremely curious, united in their centre, just as in the case of the system within
the wire cube, by a plane quadrilateral film bounded by convex lines. In the
case of the wire cube, it was seen that this plane film could be transposed from
the vertical to the horizontal position, by blowing upon its margin through a
small tube. It is difficult, if possible, to repeat the experiment in this form
upon the similar system within the cone, but the same result may be produced,
i.e. the system may be obtained with the plane film, in the horizontul position,
by means of the following process.
It has been seen that in the case of the systems formed of two and three
bubbles respectively, it is immaterial whether we proceed by first obtaining a
plane film upon which the bubbles are inserted, or by simply inserting the bubbles
upon the sides of the cone without the previous existence of the plane film. But
in the case of the system now under consideration, if we proceed by first inserting
a plane film as a basis upon which to place the four bubbles, and take care that
these are not too large, the result is the system shown in fig. 10, in which it will .
be seen the plane quadrilateral film connecting the four bubbles, instead of being
vertical, is horizontal, consisting in fact of the central portion of the original plane
film which has remained zn situ, the remainder of it having amalgamated with
the films of the bubbles. A beautiful variety of this experiment may be made in
the following manner :—Having obtained the system with the plane film in the
horizontal position, withdraw the plug from J/ JN, so as to allow the system to
rise in the cone (a result which can always be insured by gently sucking out the
air by the mouth from J7N); the system being thus contracted, the sides of the
bubbles are brought in contact with one another, the horizontal film is first con-
tracted to a point, and then (the system being now unstable) passes into the
vertical position. By again blowing air in at JN, the system may be made again
to descend, and the plane film to pass once more into the horizontal position.
It will be remembered that, in the case of the wire cube, a beautiful system
was produced by forming a small cubical film in the centre of the polyhedron
(vide “Transactions,” vol. xxiv. Plate xxxiv. Fig. 4). This, it was seen, could
be produced either by dipping the cube a second time in the solution, or by blow-
VOL. XXV. PART I. 26
116 SIR DAVID BREWSTER ON THE MOTION, EQUILIBRIUM,
ing a small bubble in the centre of the polyhedron. A precisely similar result
may be obtained with the similar system within the cone, and that by either of the
same methods. The result of causing this system to ascend the cone is strikingly
beautiful ; the cube becomes narrowed above, assuming the form of a truncated
pyramid ; and if caused still further to ascend, the horizontal film at its apex
entirely disappears, and a perfect pyramid is produced, resembling that shown
in Plate xxxiv. Fig. 10, of vol. xxiv. of “‘ The Transactions.’’*
At the same instant that this takes place, the four original bubbles become
united above the pyramid in a vertical straight line, but this system being
unstable, the line quickly passes into a vertical plane film.
As the system continues still further to ascend the cone, it generally settles
into one or other of the forms already described, 7.¢., two, three, or four similar
hollow figures united by one or more plane vertical films. At any time before
the pyramid disappears, we can again reduce the system to its original form by
blowing air in at WN. This experiment is best made with a cone whose
vertical angle is more obtuse than that described.
III. On the Motions and Figures of Equilibrium of Films within Double Hollow Cones.
In these experiments a glass vessel was used of the form of that in the
annexed diagram, consisting of two cones united by their bases. The vessel, as
in the last case, can be closed or opened by a plug fitting at
Man MN. When JN is open, and the vessel is dipped into the
soap solution, it gives, when raised, a single plane film at EF.
A) \B When the vessel is dipped so that the liquid rises in it a little
below CD, and ZN is then entirely or nearly closed, we obtain,
on raising the vessel so that the liquid runs out, a convex film
below CD, and a concave one at EF.
If we make the same experiment with the vessel dipped so
5 fa deep that the liquid rises above CD, we obtain a variety of
regular or irregular systems of films, which, when destroyed,
often leave a fine concave film above CY). On opening JX, this concave film
rises to A B, the rings or bands of colour rising to higher orders by the thicken-
ing of the film. This concave film is sometimes formed along with and above the
regular or irregular systems of films, and separate from them.
When a film is formed exactly at CJ, it is fixed, and moves neither towards
ABnor EF; but if it be made slightly to advance towards A B, it will rise to
AB, or if made to advance in the direction of #F, it will fall to HF, and there
become stationary. Regular binary, ternary, or quaternary systems, similar to
those already described as formed within the single cone (the quaternary system
* The so-called cube is of course more or less a truncated pyramid from the first, owing to
the conical form of the vessel used.
AND FORMS OF LIQUID FILMS. 117
having the plane film in its centre, sometimes vertical, sometimes horizontal),
may be produced by simply dipping the vessel in the solution and raising it with
MN closed; but these systems can all be obtained with much greater ease and
certainty by blowing small bubbles within the vessel in the same way as was
done with the single cone. Figs. 11 to 14 exhibit these systems respectively.
The system formed by thus inserting two bubbles of equal.size is shown in
fig. 11 ; that by inserting three such, in fig. 12; that by inserting four, in fig. 13.
This last system is, like that formed within the single cone, united in its centre
by a plane quadrilateral film, which, as in the experiment with the single cone,
may be obtained in the horizontal instead of in the vertical position, by introducing
a plane film at or near CD, before inserting the bubbles, vide fig. 14. All the
preceding experiments with single and double cones may be performed with
cones of any angle, the forms of the curvatures of the figures produced being
modified accordingly.
These experiments may likewise be further varified by using cylindrical tubes
instead of cones. If asystem of three bubbles be adopted, a small bubble inserted
in their centre will take the form of a triangular prism ;* with four, a cube; with
five, a pentagonal prism; with six, a parallelopiped, and so on; or two cubes,
two parallelopipeds, &c., may be inserted one above the other, forming systems
analogous to that in Plate xxxiv. Fig. 5, of vol. xxiv. of ‘“‘ The Transactions.”’
If two cubes be thus inserted into the system formed in the single cone, and the
system be then allowed to rise in the cone, the lower cube will retain more or
less its quadrilateral form, while the upper passes into the pyramid—a state of
things which may be compared to that previously described with the wire
pyramid, and shown in Plate xxxiv. Fig. 11, of vol. xxiv. of “The Transactions.”
When a cylinder is used, the vertical lines of the prism, cube, &c. thus intro-
duced are straight lines, their horizontal lines being outwardly convex.
IV. On some Miscellaneous Experiments on Paraboidal, Conical, and Cylindrical Films.
If the cone previously described be dipped in the solution, so that it is filled
to A B, and WN be then closed, we obtain, on raising the cone, a paraboidal film
at C.D, and a plane film about half way up the cone (fig. 15). The paraboloid,
as the excess of fluid escapes from its apex, becomes first a hemisphere, then the
segment of a sphere, and then bursts.
If two very convex films be placed in contact with one another, they will
become united by a more or less flattened film, which, as already shown in the
previous paper on this subject (Vol. xxiv. p. 503, of the “‘ Transactions”’), will be
plane, convex, or concave, according to the relative convexity of the bubbles
* This figure is best obtained by inserting the small bubble before inserting the third of the
large bubbles,
118 SIR DAVID BREWSTER ON THE MOTION, ETC., OF LIQUID FILMS.
themselves. If we now draw the bubbles gently apart, they will form two
truncated cones united by a small circular film at their apices, which may some-
times be reduced to a mere point before bursting, thus forming two perfect cones,
as shown in fig. 16.
If, instead of bringing the two convex films into direct connection with one
another, we unite them by means of a small bubble placed between them, this
intermediate small bubble will assume the barrel shape shown in figs. 17 and 18.
If we now decrease the distance between the large convex films, the small bubble
will assume the flattened form of fig. 17. If we increase the distance between
the large films by drawing them apart, the small bubble will become elongated,
as in fig. 18. The larger end of the barrel will always be that in connection with
the film of least convexity; in other words, with the film whose radius of
curvature is the greater, and when the system is drawn apart so as to break the
chain of connection, it is to this film (that, namely, of greater convexity) that the
small bubble will always adhere.
The form of the barrel is always that of a more or less perfect cylinder, all of
whose bounding lines are convexly curved.
When the large convex films have their radii exactly equal, the barrel-
shaped cylinder will be perfectly symmetrical, 7.¢., the circles at its upper and
lower ends will be equal. When this is the case, or nearly so, the system can be
drawn apart without suffering disruption till the ends of the cylindrical bubble
become almost mere points.
To make the two large films of exactly equal convexity is of course impossible
practically, but theoretically it would appear that in such a case the small
central bubble ought to part connection with each of the large bubbles simul-
taneously, and fall, resuming its original form of a perfect sphere.
If a cylindrical or conical tube, such as that used in the previous experiments,
be slightly dipped into the solution, and then gradually raised vertically, the film
formed on its lower aperture will remain attached to the surface of the liquid.
The curvatures of the film as we gradually raise the tube are very curious. At
first, while the surface of attachment is large, the film is convexly curved; its
sides then become straight lines; then concave, then, just before parting with the
surface of the liquid, they become slightly convex above, concave below. In
fig. 19 these changes of curvature are shown.
If the liquid into which we dip the tube be shallow and small in quantity
(that, for example, contained in a watch-glass), it will be elevated bodily when
we raise the tube, its whole surface becoming more and more convex as the film
becomes more concave. If we insert a film half way up the tube before making
this experiment, it will sink in the tube whilst the lower film is convex, and
again rise when the lower film begins to become concave.
(pina is)
Ill.—On the Temperature of the Common Fowl (Gallus domesticus). By
JoHN Davy, M.D., F.R.SS. Lond. and Edin.
Read 17th February 1868.
During the last three years I have made a large number of observations on
the temperature of the common fowl under different circumstances, the results of
which I now beg leave to submit to the Society, with the hope that they may be
considered not altogether uninteresting to the physiologist.
The fowls tried were chiefly of the pure Dorking breed. At the time they
appeared to be healthy, and all in good condition. They had all the run of a field
adjoining the poultry yard.
In all the trials the same thermometer was used,—each degree of which, that
of Fahrenheit, was divided into ten parts, and had been warranted correct by the
makers after comparison with a standard. The quantity of mercury in the bulb
of the instrument was so small that in a minute or two, when introduced into
the rectum of the bird, it reached the maximum; and in every instance the rectum
was the part of which the temperature was ascertained, presuming it to be there
the same as that of the interior of the body generally.
Though the temperature of the air was mostly noted down, as well as other
circumstances likely to affect the results, I do not think it necessary to enter into
minute details respecting them, partly for the sake of brevity, and partly from
their not appearing to influence materially the results. I may, however, remark
that the observations were mostly made, whatever the season of the year, be-
tween 10 and 11 a.m., and that in the majority of instances the birds had been
kept in confinement during the night and early morning, and had not been fed
since the day preceding.
1. Of the Average Temperature.
The total number of observations made during the whole period on birds of
different sexes and different ages, varying in age from five weeks to five years.
the majority from six months to two years, amounted to 163; the average
temperature deducible from them was 107°-81.
2. Of the Temperature of the Male and Female. —
The number of males tried was 68, of females 95. The average temperature
from the former was 108°:39; from the latter, 107°36. The highest temperature
observed in any one instance of the males was 110°—this in August, in sultry
weather, when the thermometer in the shade was 81°; the lowest was 106°5,
whilst the highest noticed in the other sex was 109°25, the lowest 105°—this in
a hen on the sixteenth day of her incubation.
VOL. XXV. PART I. 2H
120 DR DAVY ON THE TEMPERATURE OF THE COMMON FOWL.
3. Of the Temperature of the Sexes previous to Maturity.
The term maturity is used as implying the stage at which the female begins
to lay and the male to exercise the generative faculty—in the instance of the
former about the sixth or seventh month, in that of the latter a month or two
earlier.
The number of both sexes tried was 31,—of males, 16 ; of females, 15,—yield-
ing conjointly an average temperature of 108°:5, and separately, in the instance
of the males, 108°-4; in that of the females, 108°-66. The highest male tempera-
ture was 109°-25, the lowest 107°°5; whilst the highest female temperature was
109°°5, the lowest 108”.
4. Of the Temperature of the Mature Mate.
The temperature of the same male was taken during one year monthly, with
the omission of one month. At the beginning the bird was two years old; at the
end, when three years old, it weighed nine pounds and a half. During the whole
time it seemed in vigorous health. The results were the following :—
In October, . , 109°:'5 In May, : ; : 108°°5
November, . : 109°5 June, : : : 109°:5
December, . ; 108°°5 July, , ; : 108°'75
January, . ; 108°:25 August, . . ‘ 110°-00*
February, . : 107°75 September, 4 , 108°°77+
April, : : 108°-25
affording an average temperature of 108°°77.
5. Of the Temperature of the Female whilst Laying.
The number of females tried was 12, varying in age from six or seven months
to four or five years. The average temperature reducible from them was 107°;
the lowest temperature noticed in any one was 105°:5—this in a hen five years
old; the highest, 108°°5.
6. Of the Temperature during Incubation.
Of 14 sitting hens tried, the average temperature was found to be 107°; the
lowest temperature observed was 105°; the highest, 109°'5.
The average weight of the fowls at the beginning of sitting was 5 lbs. 13 oz.;
the average loss at the end of the process was 1 lb. 7 oz. ; the smallest loss in
any one instance was 4 oz.—this in that of the fowl the temperature of which
at the end was 109°:5; the greatest, and the same in two instances, was 1 lb. 80z., _
and of both the temperature was 107°.
* Thermometer in shade, 81°. + Moulting.
DR DAVY ON THE TEMPERATURE OF THE COMMON FOWL. 121
7. Of the Temperature during Moulting.
Of 10 hens undergoing this change the average temperature was 108°:44 ; the
highest in any one instance was 109°'5; the lowest, 107°. It is noteworthy that
the highest degree was observed in the middle stage of the process, when the
surface of the abdomen was nearly destitute of feathers.
Conclusions.
The results, I would beg to remark, are offered merely as approximations
as such they seem to show—
1. That the temperature of the common fowl is 107°°81.
2. That the temperature of the sexes before maturity is comparatively high,
being 108°°5, whilst that of the two sexes at this stage varies very little.
3. That the temperature of the male, on the whole, irrespective of any parti-
cular age, is higher than that of the female, being as 108°:39 to 107°°3.
4. That the temperature of the fully matured male (a single instance)
is 108"°77.
5. That the temperature of the laying hen is 107°-4.
6. That during incubation the temperature falls, and is as low as 107’.
7. And that during moulting it rises to 108°-44.
The variations of temperature, from the highest to the lowest, noticed in the
several instances, are less perhaps than might have been expected. No doubt,
they were connected with peculiarities of circumstance, which very careful
observation might possibly have detected,— circumstances of weather, not only
as to temperature, but also as to moisture of air, degree of exposure, and varying
strength of wind, not to insist on other conditions, such as the quantity of food
taken, the period of fast, amount of exercise, the precise state of health. The
very few observations I have made, tending at all to illustrate modifying circum-
stances in relation to temperature, are the following :—
A hen, seven months old, after having been confined in a basket thirty-six
hours without food, the thermometer part of the time below the freezing point,
was of the temperature 106"5.
Another of the same age, confined without food twenty-six hours, the ther-
mometer during the time between 40° and 50°, was 107°.
An old hen, the leg of which had been broken two or three days previous to
trial, and had ate little since the preceding evening, was 105°.
A fowl labouring under difficulty of breathing of some hours, was 100°.
A male bird, in full vigour, of the temperature 108°°75, was let loose, and
driven till it stopped, after four minutes,—now its temperature was found to
be 109°.
122 DR DAVY ON THE TEMPERATURE OF THE COMMON FOWL.
On the principal results, as given in the summary, I shall comment but little.
Some of them, especially the near equality of the temperature of the sexes before
maturity, and the lowering of the temperature of the female at the period of
laying, may be viewed as physiological problems; others, as the loss of weight
during incubation, with a fall of temperature, and the contrary as to temperature
during the period of moulting, seem in harmony with what might be expected
according to the theory of animal heat. In the one case, there being a loss of
substance of the individual in connection with diminished nutriment, without
apparently a febrile disturbance of health; whilst in the other case, it would seem
there was such a disturbance, with an elevation of temperature, such as is
witnessed in febrile diseases.
The change of temperature that takes place in the chick on quitting the egg is
remarkable, and, as it appears to me, strongly in support of that view of animal
heat, in which respiration and the formation of carbonic acid by the union of
oxygen with carbon, is considered its principal source. In the egg, just before
hatching, the chick is of a temperature rarely exceeding 100°, and that derived
more from the incubating mother than from the organic changes in progress;
but no sooner is the hatching completed, and the young bird freely respires.
than there is a sudden elevation of temperature. In one instance, in which I
had an opportunity of watching a gosling in the hatching act, the temperature °
actually rose, and that suddenly, from about 100° to 106°, after the manner of a
hybernating animal, such as the dormouse, in which in passing from its torpid to
a state of activity without taking food, there has been, as I have noticed, a rise of
temperature from 56° to 99°°5.*
It is also remarkable how soon the young fowl, after becoming tolerably
fledged and capable of securing adequate food, which would seem to be simul-
taneous with the consumption of the internal provisional yolk, its earliest
nourishment, it attains a comparatively high temperature. Thus of 11—7
of them thirty-one days old, 4 thirty-five—the average temperature in the
middle of October was 108°73; the lowest in any one instance 108°, the
highest 109°5: and I have found the temperature of nestlings also comparatively
high,—a young swallow, fully fledged, just after being taken from the nest on
the 28th July, was 108°.
Dr William Edwards, in his very interesting work, “On the Influence of the
Physical Agents on Life,” has come to the conclusion that ‘‘ the power of pro-
ducing heat in warm-blooded animals is at its maximum at birth, and increases
successively until adult age,”—a conclusion which seems to me questionable, and
requiring, if admitted at all, to be received with many restrictions. Some of the —
results I have obtained are opposed to it, and others might be mentioned tending
to invalidate it. oo
* See Physiological Researches (1863), p. 85.
ae OT a aaa Wirans, Royal Soc Edm Vol RXV:
Vine WE,
(7234 1)
1V.—On the Burning Mirrors of Archimedes, with some Propositions relating to
the concentration of Light produced by fefiectors of different forms. By
Joun Scott, Esq., Tain. (Plate III.)
(Read 6th January 1868).
As the reputed fact of ArcuimMEDEs having burned the Roman ships engaged
in the siege of Syracuse, by concentrating on them the solar rays, has not only
been doubted but disbelieved by some of the most eminent scientific men, I shall
briefly give the evidence on both sides.
The burning of the ships of MarceLuus is mentioned by most of the ancient
writers who refer to the machines which ARcHIMEDES employed in the defence of
his native city, and their statements have been repeated by succeeding authors,
without any doubts having been expressed until comparatively recent times.
Our earliest authorities on the subject are Dioporus Sicutus, Lucian, GALEn, Dion,
and Paprus. Ata later period the architect ANTHEMIUS, of Tralles, in a frag-
ment entitled wep: rapadoEwy wxxavyuatov (Wonderful Machines), not only dwells
particularly on the burning mirror of ARCHIMEDES, but adds, besides, that it
was universally admitted in his time that ArcuIMEDEs had destroyed the Roman
fleet by means of burning mirrors. It is also mentioned by Hero, a writer on
military engines—about the middle of the seventh century—and by Evustarutius,
ZONARES, and TzETzEs, who flourished in the twelfth. Thelast two havetransmitted
to us passages extracted from the work of Pappus on the siege of Syracuse, which
was then extant, but has since disappeared. We givethat by Tzerzxs as the more
definite and circumstantial :—‘‘ When Marce..us had placed the ships a bow-shot
off, the old man (ARCHIMEDES) contrived a hexagonal mirror. He placed at
proper distances from the mirror smaller mirrors of the same kind, and which
were moved by means of their hinges and certain square plates of metal. He
placed it in the midst of the solar rays at noon both in summer and winter. The
rays of the sun being reflected by this, a dreadful fire was excited on the ships,
which reduced them to ashes at the distance of a bow-shot.”
In the sixteenth century mirrors similar to that of ARCHIMEDES seem to have
engaged the attention of Leonuarp Diaaes, and of Baron Napier of Merchiston.
At a subsequent period Father KersHer took up the same subject, prosecuting it
with such assiduity that he travelled to Sicily to examine the coast in the vicinity
of Syracuse, and came to the conclusion that ARCHIMEDES might have oppor-
tunities of placing his mirror within 30 yards of the ships. He also mentions
in his “ Magica Catoptrica,” as the result of experiments which he had performed,
that the superimposed rays reflected from five plane mirrors at the distance of
VOL. XXV. PART I. 21
124 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
more than 100 feet, produced a heat which could scarcely be endured. Apparently
convinced of the practicability of the achievement by means of plane mirrors, he
entreats future mathematicians to prosecute the subject. Burron, following in his
steps, completely established the fact that combustible materials can be set on
fire at distances corresponding to the accounts we have of the mirror of ARcHI-
MEDES. ‘This he effected by means of a combination of plane reflectors, consist-
ing of ordinary looking-glasses, 8 inches by 6, attached to a single frame, each
glass, as well as the supporting frame, being capable of motion in every direction.
With forty of these glasses he set on fire tarred beech at a distance of 66 feet. A
plank, smeared with tar and brimstone, was ignited at 126 feet by 98 glasses. A
combination of 128, with a clear sun, inflamed very suddenly a plank of tarred
fir at 150 feet, the conflagration springing up at once over a space of 16 inches
in diameter—the whole reflected image of the sun at that distance. In addition
to these experiments made about the beginning of April, others were exhibited
with the summer sun, by which wood was kindled at 200 and 210 feet, and
silver and other metals were melted at distances varying from 25 to 40 feet.
Let us now consider the evidence on the opposite side of the question. Des-
CARTES and others have treated the whole affair as fabulous, from the belief that
the burning glass must have consisted of a single spherical or parabolic reflector.
But since no mention is made of the kind of specula employed by ARcHIMEDEs,
such objections, after the successful experiments of Burrow, necessarily become
irrelevant. Another and quite different ground of doubt has arisen from the circum-
stance, that Po.ysius, Livy, and PLuTrarcH make no mention of the destruction
of the Roman fieet by means of burning glasses, although they describe somewhat
in detail the ballistee and other military engines constructed by ARCHIMEDES to
resist the assailants. How far the silence of the forementioned writers should be
taken as negative evidence, it is not easy to determine. It seems to indicate, at
least, that the damage effected by the burning mirror was confined to compara-
tively narrow limits; for, if prominent in the defence, we naturally expect that
it would have received special notice. But allowing that the fleet sustained no
serious injury from this source, some fact must be left sufficient to account for
the belief prevalent among ancient authors in favour of the achievement.
Nothing less, I conceive, will suffice than to admit that ARCHIMEDES made an
attempt to destroy the Roman fleet in the manner described. Such an admission,
however, implies that he must have previously tried his combination of reflectors
in private, and was able to ignite combustible substances at considerable dis-
tances. The mere attempt to bring an artillery so singular and subtle to bear on
the fleet is in itself a conclusive proof that an experiment, similar to those
exhibited by Burron in the Jardin-du-Roi at Paris, had been successfully per-
formed 2000 years before within the walls of Syracuse. We can no more suppose
the contrary than believe that any of the nations of modern Europe would send
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 125
into the field of actual warfare a novel piece of ordnance without subjecting it to
a previous trial. Though on this hypothesis the element of success as an engine
of war is questionable, the invention of the mirror as a fact in the history of
science remains entire. Neither should it be forgotten, as perhaps a reason for
the silence of Potysius, Livy, and PLuTarcu, that with the fall of Syracuse and
the death of the illustrous inventor, all definite information relating to the scien-
tific principles of the mirror seems to have perished—a result not improbable,
when we consider that its application to the art of war would induce the original
possessors to retain its construction, as far as possible, a secret in their own
hands. Finally, it is an admitted axiom in estimating historical evidence, that
the silence of one author respecting an event is never considered sufficient to in-
validate a plain and consistent statement of that event made by another. That
our conclusions should be formed in strict accordance with the principle enunci-
ated, may be made apparent by striking and well-ascertained facts, some of which
have been inaccurately recorded, and others altogether omitted by the most
reliable contemporary historians. As an instance of the former, modern authori-
ties maintain that the account given by Livy of the route by which Hannipau
conducted his army across the Alps cannot be reconciled with that by PoLystus,
and an extract from Sir CHARLES LYELt’s “ Principles of Geology ” will show an
historical omission equally inexplicable. Speaking of the first eruption of
Vesuyius, he says, “The younger Puiny, although giving a substantial detail of
so many physical facts, and describing the eruption and earthquake and the
shower of ashes which fell at Stabiz, makes no allusion to the sudden overwhelm-
ing of two large and populous cities, Herculaneum and Pompeii. In explanation
of this omission, it has been suggested that his chief object was simply to give
Tacitus a full account of the particulars of his uncle’s death. It is worthy of re-
mark, however, that had the buried cities never been discovered, the accounts
transmitted to us of their tragical end might well have been discredited by the
majority, so vague and general are the narratives, or so long subsequent to the
event. Tacitus, the friend and contemporary of Piriny, when adverting in
general terms to the convulsions, says merely cities were consumed or buried.
SuErontius, although he alludes to the eruption incidentally, is silent
as to the cities. They are mentioned by Marriau in an epigram as buried in
cinders; but the first historian who alludes to them by name is Dion Cassius,
who flourished about a century and a half after PLiny.”
Returning to Burron’s combination of reflectors—when the focus had to be
changed, a numerous staff of assistants required about half an hour to re-adjust
the mirrors. After all, the superposition of the reflected light would be imperfect,
each operator being liable to mistake the deviation of the image reflected by some
other glass for that of which he had charge. Pryrarp has appended to his trans-
lation of the works of ARCHIMEDES a memoir of his own, in which he calls atten-
126 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
tion to these defects, and to remedy them proposes that a telescope and some-
what complex apparatus be attached to each reflector, that with fewer hands the
adjustment might be rendered more accurate and speedy.
It is obvious that the improvement suggested by PeyRarp is only partial and
its success doubtful. I conceive the Archimedean mirror to have been a compound
reflecting apparatus, free from these defects, capable of being directed by one eye
and guided by a single hand. From Tzerzes we learn that the mirror was hexa-
gonal, that like Burron’s it consisted of a combination of reflectors, and that at
proper distances from the outer mirror were placed other smaller ones of the
same kind. This last peculiarity of the Archimedean mirror has no parallel in
that of Burron; and yet the arrangement of the smaller mirrors, at proper dis-
tances from the larger, indicates that the relation of the two kinds to each other
formed an essential feature of the combination. Although the above passage
conveys no information respecting the nature of the specula, there is such a de-
scription of the connection of the parts as an intelligent observer might carry
away, and yet be unacquainted with the scientific principles involved in the
construction.
In the sequel (Arts 13 and 14) we show how larger and smaller specula, all
of the same kind, can be so connected as to form a single compound reflector
capable of concentrating on a single spot the reflected rays, and of darting them
instantaneously in any direction, when they will produce the effects ascribed to
the mirror of ARcHIMEDES. ‘The results thus being the same, and the construction
of the combination coinciding with the description given by TzeTzEs, we
therefore infer that the real principle of the Archimedean mirror has been
attained, and that the accounts which have come down to us respecting it are in
the main authentic. This will be brought out more fully after the following
general propositions have been considered.
For the historical facts contained in the preceding, I am chiefly indebted to
PrEYRARD’s edition of the “ Works of Archimedes,” and to the article “ Burning
Glasses,’’ in the Encyclopzedia Britannica.
ArticLe 1L—Prop. When the Light emanating from a Luminous Sphere of small angular
diameter falls on a very small Plane Mirror ; to find the Intensity of the reflected Light
at any distance from the Mirror.
Let GH (fig. 1, Plate III.) be the mirror, B the point of reflection, AC the small
luminous sphere, and DE the plane on which the reflected light falls. It follows,
as a consequence of the equality of the angles of incidence and reflection, that the
angle which DE subtends at B is equal to that which AC subtends, DE being
supposed perpendicular to the cone of rays reflected from B.
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 127
Whatever may be the form of the infinitesimal mirror at B, the perpendicular
section of the reflected rays, at all finite distances from B, is a circle.
Let a = the angle ABC = DBE.
7 = radius of the sphere AC.
c = the distance from B, measured along the slant side of the cone of
rays, at which the diameter of the circle of reflected light is equal
to unity.
= the intensity of the light radiating from the sphere at its surface.
Y = intensity of the light at the mirror, on a plane perpendicular to the
axis of the cone of rays falling on B.
..kY = intensity of the reflected light at the mirror, / being a constant less
than unity.
d = distance of the centre of the sphere from B.
d’ = distance of DE from B, measured along the slant side of the cone
of reflected rays.
oA = sectional area of the light incident on small mirror at B.
Area of the circle DE = 7d” sin’ 5 , . ; (1),
rd
ss = 72 : , ‘ , (2),
because c: d’:: 4: radius of the circle DE.
Since the intensity of the light, emanating from the surface of a luminous
sphere and falling on a concentric spherical surface, is inversely as the square of
the distance from its centre,
; a2 il’
Tere Sk te “T= : : : (3).
Wrote sy il v
But Se Ont at Ia Oe Puke ii = sin?é “ 5 ° (4)
= 4¢71’ (5)
Intensity of the reflected light at DE — ——“1°4 ; (6),
area of circle DE
kVoA
= ed? 3 . (7).
4ce°kKVSA
» SS neaar : d : (8).
When the plane on which the reflected light falls is not perpendicular to the
VOL. XXV. PART I. 2K
128 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
axis of the cone of rays, as de (fig. 1), the intensity of the light at e will exceed
the intensity at d from the greater obliquity of the rays at the latter point. But
if the angle DBE be small, and the plane de cut the axis of the cone at a con-
siderable angle, the intensity will be nearly uniform over the whole ellipse de ;
and the centre of the ellipse may be viewed as situated in the axis of the cone,
because the elongated cone approaches nearly to.a cylinder.
kKVéA
.*. intensit ™ area of ellipse DE
intensity on de = ———— ellipse DE
(9).
In the case of the sun’s light the above formule will give pretty accurate
approximations, since « = 32’and¢ = 1074 nearly . : (10).
ArtrcoLe 2.—Prop. When a Cylindrical Beam of Solar Light is reflected from a Plane Mirror ;
to find the Intensity on a Plane Surface perpendicular to the direction of the reflected Beam,
and at any distance from the Mirror.
Since the rays which emanate from any single point in the sun’s disc may be
considered as perfectly parallel, however large the mirror, it follows that those
from the centre of the disc will, after reflection from the mirror, form a perfectly
cylindrical beam of parallel rays, and will cast on the given plane a circle of light
of uniform intensity.
Let ABG (fig. 2} represent this circle, each point in its area is the centre of a
circular image of the sun’s disc reflected from a corresponding point, or infini-
tesimal area, of the mirror.
If O be one of these points, and the circle ADBP the image of the sun’s disc
at the given distance, or, in other words, the base of a cone of rays whose apex is
at the mirror, as shown in fig. 1, Art. 1, the illumination or intensity of the light
at O will be that due to the superposition of all the images of the sun’s disc
whose centres fall within the area ACBPA; for none of the images of the sun’s
disc, whose centres fall without the above area, can extend so far asO. The
point O is therefore illuminated by a portion of the incident beam equal in area
to ACBPA, every increment of which, after reflection, gives rise to a conical
pencil of rays, a part of whose base overspreads the point O.
Let I’ = intensity of the solar light on a plane perpendicular to the direction
of the incident beam.
Let AO=r, FA=p, FO=2, AFO=]0, AOC Sig yand ua. a, au
the sectional areas, at the mirror, of the respective pencils whose light over-
spreads the point O. Whatever may be the form of these small increments, the
base of the cone of light to which they give rise will be a circle at all finite
distances from the mirror, as shown Art. 1.
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 129
. : 5 kY’ KY’
Therefore the intensity of the solar light at O from area w, = <a yED = — !
» hla
ie a ame A
” Pel kY'u,
i — ar
99 39 33
kY'u
” Un ea
. : kY’
Whole intensity at O = —a (+ M+ Us... + Um);
kY’ x area ACBPA
—_ . (1),
3s = (2 x sector AFO—2 triangle AOF +2 x sector AOP),
kV’ ¢ ;
th a 220+ 7(7— 9) —gz sin 8 \ . f : (2),
kY 3 sin 6 :
= = g041°( sin (E22) )— ps sin é } ;
: in 6
because sing = me ,
also 2 = ecosé—7rcos¢,
= ecos 6— r/(7?—¢ sin?é).
When p > 7 in the preceding expressions, and 6 = 0, then ¢ = 0, 2 = p — r, and
; ; kl’
intensity at O=—y x mr’ = Al. : (5).
If, therefore, the circle ADPB falls wholly within the circle ABG, the in-
tensity of the illumination on the circular space, whose centre is F and radius
p— 7, is constant and equal to that of the beam when it leaves the mirror, or the
intensity is the same as if all the rays from the sun’s disc were parallel to one
another.
When p = 7, then, z= 0, and F is the only point whose intensity = Al’.
Next when p < rand 6 = z, then ¢ = z,z =7 — p, and intensity = = x pa
==} 5 (6).
This formula expresses the intensity throughout the circle, whose radius
is T — p.
When z = r + p, the intensity vanishes.
130 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
The preceding limiting cases are also evident from the geometrical considera-
tion of the problem taken in connection with equation 2; and the same principles
can be applied to find the intensity, whatever the shape of the perpendicular
section of the incident beam.
ARTICLE 3.—When there are m mirrors similar to the preceding, the light
from each making an angle of incidence 7, with the perpendicular to the plane
on which it is thrown, the intensity of the central spot in each of the preceding
cases becomes—
In 1st case, nkl’ cos 2, : é é . (1).
12 «
In 2d case, BENE SOE, é ; ' 6 (2).
r
ARTICLE 4.—Prop. A Small Luminous Sphere has its centre in one of the foci of a Prolate
Elliptic Mirror, to find the Intensity on any Small Plane surface situated in the other
Focus.
Let / (fig. 3) represent the luminous sphere.
(& = the angle which the small plane at F makes with FX: the axis of
z coinciding with the axis ofthe mirror, and the plane of xz being
perpendicular to the small plane passing through F; the axis of
y, which is at right angles to the plane of xz, will therefore
coincide with the small plane which passes through F.
oP.
6 = the angle PFZ.
¢ = the angle which the projection of 7 on the plane of zy make with FX.
a = radius of the luminous sphere at /
V = the angle which 7 makes with the normal to the small plane at F.
I = the intensity of the light at the surface of the small sphere.
Since the well-known differential of a volume 7’ sin 6 d@ df dr has for its
perpendicular section, at the surface of the spheroid, 7” sin 6 d@ dp; we may sup-
pose the whole surface of the elliptic mirror to be divided into small areas, each of
which receives from the sphere at f, and reflects to F, a pencil of light, whose
perpendicular section, at any point P of the mirror, is 7” a 6 dé do.
Moreover, the intensity at P Soa to Py = — = (by Art. 1, eur 3),
and after reflection it becomes © P 7”
The cone of rays reflected from the increment of surface at P, in the direction
PF, will have expanded at F into a oe (perpendicular to the radius vector),
rar?
whose radius by similar triangles is >, o 7 and area = pyr
By Art. 1. Equa. 6, the intensity of the light on this circle at F = 7° sin 6 dé
2 Qprd
dp x prt a = ET sin 0 ddd.
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 131
and e sin 6 d0 dp cos V = its intensity at F on the small plane, whose equation
is z cos 8B — asin B = 0, : , (1),
€os-V = “ cos B —* sin B = cos 6 cos 9 — sin B sin @ cos ¢.
Substituting for cos V its value we obtain for the whole intensity at F, on the
small plane,
EL fos 6 cos 6— sin sin 4 cos g) sin 4 dé dg, ; : (2).
Denoting this integral by u,
Uw = fe f (cos sin? + sin 6 sin é cos @ cos g — é sin 8 cos 9) dp + C.
Now cot 6 = tan@ cos¢, when V = 90’, that is, when PF coincides with the plane
denoted by Equation 1,
.. 6 = cot —1(tan 6 cos ¢)
1
sin = (1 + tan? B cos? 9)!
nae tan 6 cos 9
(1 + tan? 6 cos? 9)?
Taking the integral between the limits 9 = 0, and 6 = cot—’ (tan cos ®),
Pol ee 6 (1 + tan? B cos? 9)
i On I + tan? 6 cos? 9
= iB! ; dy : ar sin 6 tan B sm pol
=e { feos 8 dep sin 8 sin g cot—* (tan 6 cos 9) +f Tae Gas Gos
Bee E : 2 seep dey}
mais f feos 6 do — sin B sin g cot—! (tan B cos 9) —fcosB dp + see Gar tate
1
— cot—? (tan 6 cos g) sin cos S do.
= = { tan (cos B tan 9) — sin f sin 9g cot—! (tan 6 cos 9) } + C.
and between the limits ¢ = 0 and ¢ = 90",
u = 575 sin 6 ),
= = (1 —sin @), which is the intensity at F of the light reflected from
that portion of the spheroid bounded by the planes passing through the
co-ordinate axes of + xand + 2, + y and + z, and the small plane produced.
Similarly ao + sin 8) gives the intensity of the light, from that portion
enclosed by the planes passing through the axes — # and + z, + yand + 2, and
the small plane at F produced. Hence the intensity of all the light which can
fall on the side of the small plane towards A (fig. 3).
fills ; j 5 t : (3).
VOL, XXV. PART I. Dale
132 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
Also - sin 6 is the intensity at F due to the light reflected from the part of the
mirror intercepted between the small plane produced, and the co-ordinate plane
of xy.
In the same manner it can be shown, that the intensity of the light concen-
trated at F, on the opposite side of the small surface, and reflected from the
remaining portion of the spheroid, is also equal to Al.
These results are independent of a, the radius of the luminous sphere, and are
equally true for all spheroids which have F for one of their foci, wherever the
other may be situated.
It appears then, in conclusion, that the light emanating from a small luminous
sphere, with its centre in one of the foci of a prolate elliptic mirror, produces at
the other focus a nucleus of radiant light and heat, equal in intensity to the
radiation at the luminous surface diminished by the quantity lost by reflection.
Again, putting 6 = 0 (in Equation 2), we obtain intensity
kI F
=" [fsin costdodo, . (4).
Integrating between g = 0, and 22;
: ; a Sat
intensity = 2n x — fein cos 6 dé ,
= 2kI Jsin 6 cosé dé;
and between 6°, and zero,
= Aisin oy 7 ’ ; : (5).
This expresses the intensity at the focus of the light reflected from a segment of
the spheroid intercepted between the vertex and a plane perpendicular to the
axis; and the intensity produced by a zone intercepted between two planes, per-
endicular to the axis of revolution, is
kI (sin 76 — sin? 6’) ; : : (6).
ARTICLE 5.—The preceding proposition is true, independently of the size and
form of the luminous body in the focus / (figs. 3 and 4).
Since radiant light and heat diminish in the inverse ratio of the square of the
distance, it follows that the quantities received from circular areas of equal angular
magnitudes are equal, whatever their absolute magnitudes, when the intensities
at the radiating surfaces are equal. Taking this principle in connection with the
fact, that a luminous surface appears equally bright when viewed at any angle,
the light emanating from CD, part of the surface of DCE, will therefore have at F
_ the same intensity as if it had proceeded from the small sphere AB (fig. 4). But
the light reflected from P to F can only emanate from some part of the surface
DC, which lies within the cone described by PA, revolving about Pf Hence the
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 133
intensity at F of the light radiating from DC, and reflected at P, is equal to that
which would have resulted from the sphere AB; and the same is true for every
increment of the elliptic mirror. Therefore, the total illumination at F, from the
luminous surface DCE, is equivalent to that from the small sphere AB.
From this and the preceding article, we infer that a zone or segment of an
elliptic reflector may be used as a pyrometer. For if such a zone, contained between
two planes perpendicular to the axis, be placed before an opening in a furnace,
the place of the focus f falling within the heated body, the heat reflected to F
may be reduced, by diminishing the breadth of the zone, until it can be measured
by a Fahrenheit thermometer ; and I, the intensity of the total radiation from
any point f within the furnace, can be determined in degrees of Fahrenheit by
Art. 4, Equa. 6.
Articrz 6.—Prop. When a Parabolic Reflector has its axis directed to the centre of the Sun,
to find the intensity of the converging Rays which fall on a small Plane Disc at the Focus.
Let « = angular diameter of the sun, which is about 32’,
ce = the distance at which the reflected image of the sun expands into a
circle equal to unity in diameter, being about 107°4,
j—— Pi (fig. 5),
Y’ = intensity of the sun’s rays at the earth’s surface,
I = intensity at the surface of the sun,
u, k, 8, 8, p, and V = the same as in proposition (Art. 4).
2
Then aa = area of the circle, which the light reflected at P occupies at F
perpendicular to PF.
The intensity of the light reflected from the increment of surface at P on
this circle by Art. 1, Equa. 6.
: ye emer?
=r’ sind dddg x kl See
27!
uz y sin 6 dé do ;
: 4c7kl’ .
and on the small disc at F, = —— sin 4 dé do cos V.
cos V = cos cos 6 — sin 6 sin é Cos @,
2 7 ?
us = fico 8 cos @ — sin B sin 4 cos 9) sin é dé dg, (1).
Integrating as in Article 4, we obtain for the intensity of the light reflected
from the corresponding sections of the parobolic mirror
kV (l—sin®), . , F ; (2).
and kl’ (1+sin8), . ; (3).
Hence the total intensity at F (fig. 5) on the side of the plane disc towards
134 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
A, resulting from the light reflected from the segment of the paraboloid cut off
by the plane of the disc produced,
= 2PkI'(1 —sinB) + PkI'(1 + sinB)} = 40°’ = KI . (4),
I being the intensity at surface of the sun.
But c = 107 nearly, therefore the numerical value of this equation
= 45796kI’
nearly, which is a degree of concentration several times that of the most powerful
burning glass ever constructed.
Again putting 6 = 0 (in Equation 1),
ail he
“= AOE | fsivscoseas do;
and integrating as in Article 4, Equation 4,
u = Ac7kI’ sin? 6 ; ; : : . (5),
which gives the intensity at the focus of the light reflected from a segment of a
paraboloid, intercepted between the vertex and a plane perpendicular to the
axis; and the intensity produced by a zone, intercepted between two planes
perpendicular to the axis, is
4(?k]' (sin?é— sin?¢’) = AI (sin?6— sin?é’) ; (6).
Equation 5 shows that the concentration at the focus varies as sin’@: it is a
maximum when @ = 90°, and is independent of the parameter of the parabola.
It may therefore be inferred that a reflector employed to detect the heat of the
lunar rays should be as large a segment of a paraboloid as possible; and the
same condition is essential in improving to its utmost limit the space-penetrating
power of the reflecting telescope.
Again, suppose the parabolic mirror to extend to infinity, it can also be shown
that the light concentrated at the focus on the other side of the small disc is
equal to 4c°Al’=£I. What has been proved respecting the intensity at the focus
is approximately true for every point on the plane of the small disc not farther
from F than + , the quantity = being the radius of the sun’s image reflected
from the vertex of the paraboloid, and p the parameter of the generating para-
bola. Thus, in every position in space, when the axis of a parabolic mirror,
whose extent of surface is not less than that cut off by a plane passing through
the focus, is directed to the sun, a circle of radiant light and heat is formed equal
in intensity to the radiation at the solar surface minus the quantity lost by
reflection.
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 135
ARTICLE 7.—The intensity at the focus of a parabolic reflector is independent
both of the form and distance of the luminous body.
Let BAC (fig. 6) represent a section of the parabolic reflector, and GH that of
a luminous surface of uniform intensity; it can be shown, as in the case of the
spheroid (Art. 5), that the concentration at F produced by the only rays which can
fall on it, namely, those emanating from GH parallel to the axis AF, is equal to
the intensity at the luminous surface GH, minus the quantity lost by reflection.
It is evident that the section of the luminous body must not be less than CB.
Arricir 8.—Prop. When the Axis of a Mirror in the form of a Right Cone is directed to the
centre of the Sun, to find the Intensity of the reflected Light on any point in a Plane placed
perpendicular to its Axis.
Let CAD (fig. 7) represent a section of the mirror,
O the point on which we wish to determine the intensity of the
reflected light.
Every small increment of the mirror gives rise to a cone of rays which casts
an ellipse of light on the plane at F, the major axis of which passes through the
point F. The light of all these ellipses, whose centres fall within a certain
distance of the point O, will overspread it and increase the intensity at that
point. |
If P (fig. 8) be the centre of one of these ellipses NOM, considerably magnified,
whose circumference passes through O, then P is a point in the curve within
which must fall the centres of all the ellipses whose light can overspread O.
To find the equation to this curve,
let 19) eel p
FO =¢z
a and 6 = the co-ordinates of P, referred to rectangular axes whose origin
is at O,
6 = the angle PFO.
Now ay’ +0°x’ = a’b’ is the equation to the ellipse NOM, the centre being the
origin.
When referred to the axes OX and OY; by substituting,
y = (y — 8B) cosé— (a — a) sind,
we = (y’—8) siné + (v’—«)cosé,
fan = abe , we obtain
z+a
(a? cos? 6 + b? sin?) (y’— B)? + (a? sin?6 + b?.cos? 4) (x — a)? — 2(a? —b?) (y’— 8’) (av — @) sind cosd = 020?,
Putting z’=0, y’=0, there results the equation to the required curve, which is
.
VOL. XXV. PART I. 2M
136 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
the locus of the centres of all the preceding ellipses whose transverse axes
intersect in F and their circumferences in O,
(a? cos? 6 + 6? sin? 6) 6? + (a? sin” 4 + b? cos? 6) a? — 2 (a? —b?) a8 sind cosé = a*D? (1),
. (a? +0? tan? 6) B? + (a? tan? 6+ 0?) a? —2(a?—b*) a8 tan d = a?b?(1+ tan? 4).
Substituting for tan 6 its value, we obtain
{a?(z+ a)? + b7B?18? + {0287 + b7(z + a)? }a? — 2(a? —b?) (2+ «) a3? = a7b*{(z+a)?+ 87},
UPB 4+0 fe +a(e+a)}? = wb {(e+a)? +B}. : ; (2).
By substituting in this z+a=p cos @, and 8=p, sin 0, we have the polar equation
to the curve, F being the origin,
9
“
a? 2” 9 sin? 6 + b?(¢” sin? 6 + ¢” cos? d— zecos 6)? = a*b? 6,
72 9? sin? 6+ 676? (2 — 2 cos 6)? = ab?” ,
2
and e=zcosdta(l— 7 sin? 6)! ; ; é (3).
It is evident that the form of the curve represented by the Equations 2 and 3
will vary with the relative values of the constants a, b, and z; but in every case
it is symmetrical with respect to the axis FX (fig. 8).
When z=0, the point O is situated on the axis of the mirror, and the curve
becomes the circle p=a.
And if z=), the equation breaks up into two circles whose centres lie in the
line FO, and which touch one another externally at the point F’, their diameters
being a+ 6 and a— 6d respectively.
When the point F falls without the curve, the radius vector becomes a tangent
for the value sin 6= : :
Putting 6=0 in Equation (1), we get for a plane mirror
CP+0a =a'l’,
an ellipse with O for its centre, and equivalent to
ay + Bat = al.
Now, if PHG (figs. 9 and 10) represent the curve, considerably magnified,
expressed by equation 3, in deducing the intensity at O the proposition divides
itself into cases depending on the relative positions of the points F and O (as in
figs. 9 and 10).
Case 1. When the distance FO from the axis (fig. 7) is so small compared
with FB that the distance of any point within the curve similar to PHG from
CB, that part of the mirror where the light which overspreads O is reflected, may
be considered equal to FB.
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 137
Let 7 = angle of incidence on the mirror,
R = perpendicular distance of B from the axis,
7 = perpendicular distance of any point in the curve similar to HPG (fig. 9),
as represented by FQ,
v = FA = FB, because BFA is an isosceles triangle (fig. 7),
wu = intensity at O,
I’ = intensity of the sun’s light at the earth’s surface ;
then 27 = angle BFA,
90°—7z = angle BAF,
a = bsec 22,
7ab = wb’ sec 27 = area of ellipse, semi-axes @ and 3,
z = FO, in this case less than 0.
Since the rays reflected from C and D (fig. 7) fall upon the same point O, the
circumference of the circle described by O in its revolution about the axis is
illuminated by the light reflected from the two annuli described by C and D.
Besides the point O is situated so near the axis, that the perpendicular distances
of C and D from the axis may be considered as equal to one another. Thus, to
find the concentration which results from the converging of the rays to the axis,
we have,
2RI’
Qar:4cR:: 1’: intensity at distance r from F, (= =
the intensities being estimated on planes perpendicular to the rays. Wherefore
the intensity on the plane at F of the reflected light
2RI’ . 2kRI' cos 22
= lex z A es a aa ae
which would give the intensity on the increment at Q (figs. 9 and 10), if the
sun’s rays were perfectly parallel. But instead of this light being confined to the
increment at Q, it is spread over an ellipse whose area = 7’ sec 27, and hence the
intensity at O due to this increment
es 2k RY cos 2% 7 adr dé im 2k RY cos? 22
7 ? x Fb? sec dt ox 02 r de ;
and the same is true for a corresponding increment on the other side of the axis
GH (figs. 9 and 10),
-/] 2k RI’ cos 22 rdr dé
OP Sy | DN Se ae 8
We vi ax 0? sec 22
4k RI’ cos? 27
e = Scare aia | kl drdé (7).
138 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
This, taken between the limits 7 = p, and r = 0; and 6 = z, and @ = 0, gives
the total intensity
4k RI’ cos? 27
a
xb?
e dé.
2 }
Now, from Equa. 3, p = zcos9 + a(1 — ~~ sin 26 ), 2 being less than b,
’ q b g
i 2 3
= HRT cos! 26 f 4 (1 — Fesinta) + #0086 | a0.
0
ab?
Expressed in terms of elliptic functions,
“= ee [ « E, _ @) + z8ind | + C.
Eee RI’ cos? 27
=i ak z (x) : ; : . (8).
But by Art. 1, R cosec 22: ¢:: 6:4, (R cosec 27 being = FB, fig. 7),
R cosee 27
=
2c a
page! A
nn 2esime27,.”
and |
a = bsec 20 = To55; ¢
Substituting in Equation 8, we get
= 8ck I’ sin 27 cos 22 E, (s),
z z
_ 4ckT’ sin 47 Ee (n) . (9).
An expression which may be put in the following form :—If a circle be described
with Fas a centre (figs. 7,8, or 9) and 26 as a diameter, and an ellipse with O for
one of its foci and the same diameter as a major axis; the circumference of the
circle will be to the circumference of the ellipse as the intensity at the axis to the
intensity at O.
When z = 0, then Ez (7) = 7
6
_ 4ck T' sin 47
a
and < r= 4c sia, : (10),
which is the expression for the intensity at the axis, and shows that in the same
conical mirror it is constant at every point in the axis ; whereas, in conical mirrors
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 139
of different inclinations, there are two which produce a maximum effect at the
axis, viz., when 42 = 90° and 270° (in Equa. 10), that is, when BAF (fig. 7)
= 674° or 224°.
When
z = 6 (Kqua. 9), E, (7) = 2,
6
and Use
ee ——— (11).
If% = 4, the maximum intensity at the axis expressed numerically is
w= Achl sin 904. x 107, x FT S2147 .
When & = 3 and 47 = 2° 36’, it can be shown by Equa. 10 that w = 101’ nearly,
a heat sufficient to ignite wood and other combustibles. This can be effected at
a distance of 130 feet with a segment of the reflector 18 inches broad, and having
a mean diameter of 6 feet. ,
Case 2. When the point O is situated at a considerable distance from the axis,
z being much greater than 0, the distances CO and DO will now differ perceptibly
from one another and from FA = FB = » (fig. 7).
Let R and R’ represent the distances of the points C and D respectively from
the axis, then
R = fC sin 27 = (v + 2 cot 22) sin 27,
and
CO= fc—fO=FA+F f— f0 = + acot 2d — zcosec 27 = 4 — ztan?.
Similarly for the point D,
R’ = (v — cot 22) sin 22 ,
and DO = v0 + ¢ tan 2.
The ellipses of light which overspread O reflected from each increment of the
space around C have for their minor and major axes respectively,
b vy —ztan?d v —ztanz
= Se 2 SSS
2c 2 2ccos2z ’
and the corresponding quantities with respect to the space around D are
_v+aztanz a = Ub atant
rh 2¢ : ~ Qecos2t ©
VOL X XV. PART I 2N
b’
140 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
It can be shown, as in Case 1, Equa. 7, that the concentration at O, due to the
light reflected from the space around C, is ,
2
a drdé, and taken between g, and g,,
2h RI’ cos? 27
= rb? ee ay ee 2) a8 ,
2
4k Rl’acos Sere he — =, sin? do,
ab
because (fig. 10)
a = FP = 2 c0s6+a(1— 5 sin’ 6)? ,
pe zc0sd—a(1— 5 _ aie 6)? ,
21 —%=201-% a)
saat G b .
Taking the integral between the required limits sin 6 = ~, and 6 = 0 we obtain
4kRI’ 294
Tra ag ay AE oy tances ~
(A — H), denoting the difference between the asymptote and the infinite hyper-
3
bolic arc whose major axis is unity, and eccentricity 7 a finite quantity, though
A and H are severally infinite. But, if the distance from the centre to the focus
be equal to unity, the transverse axis is : and (A — H), = ; (A — H), which
D
expressed in complete elliptic functions of the second order gives
Ee
—s je ’
(A—P), = Ac
Swe
e being put for ° , the relation between the moduli ¢ and ¢,, being
ale Onlta
10> ee: Fi ae
and ¢’ and é,, denoting the corresponding quantities when 0’ is put for 0.
Substituting in Equation 12, we get for the light reflected from the space
around C,
4kRVa ae +b
pe — E. = EE} 5
Fae
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 141
and similarly the light reflected from the space around D,
_ 4kRTa a2 a
| Be, — 7 Bef -
Hence the total intensity at O is
AkRIacos? 27 (2+b \ 4kR’Va' cos? 27 {ae Z— )
Se — 58 Pi ab? b’ E., Gare.
and substituting for a, 0, a’, 0’, R, and R’
4c(v+z cot 2)kI’sin4i { v + Qe—tanz)z 2cz \
= : . e — = Ez,
r(v—z tan?) UL v—z tané 1 v—ztant
eee ee 2cz |
io a(v + ztanz) v+zetant “% v+z tant Hee Ge),
the values of the moduli in terms of ¢, v, z, and 2 being
i 2 ./2cz(v — 2 tant) _ v—ztant o! _ 2n/2c2(v +z tant). at v+ztanz
mpeer@e—tani)z” ~~ .2ez 7.1 v+(2c+taniz * A AN Ree
Since the value of w will not be altered by substituting for 7 and 2 any two
quantities having the same ratio, it follows that the intensity of the reflected
light is uniform along the line which joins A and O (fig. 7).
ARTICLE 9.—Corollary. The value of 4, the fraction which expresses the
relation between the intensities of the reflected and incident rays, may be found
by means of a conical reflector, thus :—
Let R = distance from the axis of a small zone described by AB (fig. 11).
r = distance from the axis at which the reflected light or heat becomes,
by convergence to its axis, equal in intensity to the incident.
Then PB, Ase eleue,
Up , We
al ==. 4 amd ie = R:
This result, calculated on the assumption that all the rays emanating from
the sun are parallel, will not deviate perceptibly from the truth, except when r
is small compared with R.
The value of & may also be found by using the combination of m plane mirrors.
By Article 3, Equation 2, intensity
_ nkI'e? cost
Se
142 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
but if the direct rays of the sun fall on the same plane with the light reflected by
the combination, the intensity will be
re 2
nkI ae ae.
Bringing the combination nearer the plane on which the light is thrown,
the intensity of the » mirrors can be made equal to the above equation by
diminishing the value of r.
Hence pls Bd = ad Bi ay
7 72
Cas ne (v2 — r?) cost °
As these results are independent of the absolute value of I’, the equality of
temperature may be detected by a Fahrenheit thermometer, or any more delicate
means of indicating equal temperature.
When £ is accurately known, this combination, or the conical reflector, may
obviously be used to ascertain the intensity of the solar beams at different hours
of the day and different periods of the year, and will thereby furnish data for
estimating accurately the heat or light absorbed by the atmosphere. The light
lost by the solar rays in penetrating the atmosphere being known, the intensity
of the radiation at different parts of the solar disc may be found by (Article 6,
Equation 6), if a zone or segment of a parabolic reflector can be constructed having
a focal length of 70 or 80 feet.
ArticLeE 10.—Prop. When two Conical Mirrors have a common Axis, their Surfaces being
either perpendicular or parallel, if the rays incident on the exterior Reflector parallel to
the Axis meet after rejlection the interior one, they will be again reflected parallel to the
Axis in a beam of increased intensity.
Let AB (figs. 12 and 13) be the common axis of two conical reflectors described
by the revolution of the lines MN and CD about the axis AB, CD being either
perpendicular or parallel to MN.
When AB (fig. 12) is directed to the centre of the sun, the rays which fall on
the surface described by MN will make with it the angle
SKN = MKH = KHD = FHC = DCB,
because DCB = SKN, therefore FH is parallel to AB (Euclid, 1-27). The intensity
of the finally reflected beam at H is to that incident at K as the perpen-
dicular distance of K from AB is to the perpendicular distance of H from
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 143
AB. Since every cylindrical annulus of rays incident on the exterior mirror
forms after reflection from the interior a cylindrical annulus of equal thickness,
the intensities must be inversely as the mean radii, the loss from reflection being
neglected, or, if taken into account, equal to 4° times the preceding intensity
nearly.
ArticLE 11.—The preceding annulus of rays may be thrown upon a circular
area whose. diameter is equal to the breadth of the zone, which forms a section
of the annulus. To effect this, we have only so to increase the angle DCB, that
the rays may meet the axis at the required distance, as shown in fig. 14.
In like manner, the parallel rays, from any extent of reflecting surface may
be thrown upon the area whose section is F/ (fig. 15) by constructing one or both
of the conical mirrors of frustums having the required extent of curved surface
and the requisite inclination, the same axis being common to all. But when the
breadths of the annuli are small compared with the distance of the focus F/ from
the reflectors, the diameter of the circular area mentioned must be increased by
the diameter of the sun’s image for that distance.
Cor. When the number of lines CD, DE, EG, &c. (fig. 15), is indefinitely
increased, their lengths being diminished, CDEG becomes part of a parabola.
ArticiE 12.—Prop. If two Parabolic Reflectors have a common Focus, the Solar Rays which
are made to converge by reflection from the eaterior Mirror will again form a beam of
parallel Rays by reflection from the surface of the interior one.
Let MKN and DHC (fig. 16) be sections of two confocal parabolic reflectors
of which AB is the axis of the exterior and CE that of the interior, / being their
common focus.
When AB is directed to a point in the sun’s disc, the rays which fall on the
exterior mirror parallel to the axis AB, in converging to f, will meet the surface
of the interior mirror, and be reflected parallel to its axis fCE, as indicated
by the course of the rays SKHF. Thus the solar beam of light which falls on
the exterior and larger mirror is again reflected into a beam of parallel rays, and
the intensity of the final beam will be greater than that of the incident, as
explained in the preceding article. Moreover, since the axis fE of the interior
mirror may make any angle with AB the axis of the exterior, the final beam
may be thrown in any direction.
VOL. XXV. PART I. 20
144 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
ArticLe 13.—Prop. The Rays which converge to the focus of the exterior Parabolic Mirror
may be thrown by a second reflection on a given circular space, by constructing the interior
reflector in the following manner :—
Let DH and H’D (fig. 17) be parts of parabolas, whose common focus is /, their
axes being respectively /U parallel to RG, and fC’ to QG.
By causing these to revolve about the line fA, a surface will be described, such
that the rays converging to f and falling on DH, will be reflected parallel to /C,
and fall on the plane FF’.
In like manner, the rays converging to fand falling on H’D, will be reflected
parallel to fC’, and will intersect the axis of revolution at G, and fall upon the
plane FF’.
If this surface be substituted for the inner reflector DHC (fig. 16), the rays
reflected from the outer mirror whose axis is directed to the sun, when con-
verging to 7, will meet the inner reflector described by H’QDH, and be reflected
(as indicated in fig. 17) so as to intersect its axis of revolution at G, and fall
upon the plane FF’. And this is true, whatever angle fG makes with the axis of
the exterior reflector.
Cor. When the number of parts in H’QDRH are indefinitely increased, and
their lengths diminished, it evidently becomes the are of a hyperbola whose
foci are f and G.
ARTICLE 14. The convergence of the solar rays upon a given area can also be
effected by combining a number of exterior reflectors, each with its correspond-
ing interior, as indicated in fig. 16, the axes of all the exterior parabolic reflectors
being directed to the centre of the sun’s disc, while the axes of the interior are
directed to the centre of the given spot, on which the light has to be cast.
Neither is it necessary that the respective reflectors should be complete symme-
trical paraboloids: the exterior may consist of a series of large plates, each form-
ing a part of a paraboloid of revolution, witha corresponding plate cut from a
less paraboloid for its inner reflector. If the axes of all the exterior plates be in
the same straight line, such a combination may have a common focus, each
interior having that diameter of its generating parabola, which passes through
the centre of the plate directed to the spot on which the light is required to fall.
The practicability of such a combination is evident, from fig. 16, where K may be
viewed as the centre of one of the exterior plates, and H that of its correspond-
ing interior, having the diameter of its generating parabola, which passes through
H, directed to the plane on which the light is concentrated. The exterior plates
may be joined together to move as one piece, and in like manner the interior.
This combination is capable of casting the finally reflected beam in a direction
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 145
making any angle with the axis of the exterior plates; and by a readjustment of
the inner plates, the distance at which the rays finally meet may be varied at
pleasure.
ARTICLE 15. It is stated that the Archimedean burning mirror was hexagonal.
Let us consider if the combinations we have been illustrating can be made to
conform to that figure. The term hexagonal may have reference either to the
appearance of the mirror as a whole, or to the form of each individual reflector.
Figs. 14 and 15 will correspond to the former; for if the external and internal
conical frustums be each divided into six equal segments, with sufficient space
between the segments to admit of free motion, the combination, viewed at a dis-
tance, will resemble a hexagonal polygon. Assuming the other meaning to be
the correct one, we have only to suppose the form of the parabolic plates, which
constitute the exterior and interior reflectors previously explained, to be hexagonal.
From this would result two advantages:—they could be so formed that the
different six-sided figures would unite together without leaving any interval, and
the section of the beam cast by each on the required spot, approximating to a
circle, would approach more nearly to the maximum effect with a given section
of solar light.
ArticLe 16.—Prop. As the Hxpansion of the Sun’s image is in proportion to the distance
Jrom the Point of Reflection, no greater accuracy is required for the construction of
curved surfaces, capable of producing Combustion at distances of 150, 200, and 300 feet,
than for those of a focal length of only a few inches.
The expansion being about 1 foot in diameter for every 108 feet of focal
distance, it follows that a reflector is sufficiently accurate for a burning glass, if
it can concentrate the rays which fall on each part of its surface from the
centre of the sun’s disc, within a circular area, whose diameter is the same
multiple or part of 1 foot which its focal length is of 108 feet.
The same principle may be exhibited in another and more definite form. Burn-
ing-glasses, which produce at the focus an intensity equal to parabolic ones, may
be constructed of plane reflectors arranged as tangent planes to a paraboloid of
revolution.
kV6A
area of circle DE (
Since the increment of intensity is Art. 1, Kqua.6, fig. 1), if
we take a portion of the surface of the paraboloid subtending an angle at the
focus not greater than the sun’s disc, the denominator of the foregoing frac-
tion may be considered constant; and the intensity at the focus reflected from
such an extent will be
kl’ area of circle DE
area of circle DE a
146 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
But a plane mirror which is a tangent to the paraboloid at the same spot, and of
just sufficient area to reflect the circular beam of light whose section is equal to
the circle DE, will also produce at the focus an intensity equal to AI’ (Art. 2,
Equa. 5); that is, the concentration at the focus is the same, whether a circular
beam of the section mentioned be reflected from the surface of. the paraboloid or
from its tangent plane; and the same will evidently apply to any polygonal beam
capable of being inscribed in the circular.
Hence a burning mirror, scarcely inferior in its effects to a parabolic one, may
be formed of plane hexagonal reflectors, their sizes, of course, depending on the
distance of the focus. For example, as the sun’s image overspreads an area of
1 inch in diameter at a distance of 9 feet, a burning mirror of that focal length
may be formed of plane hexagonal pieces, each side about half an inch; whereas
at 108 feet distance, the sides of the plane hexagonal plates need not be less than
half a foot, and so on in proportion.
Plates of the latter size being greater than those with which Burron performed
his experiments, we infer that his combination, at distances exceeding 100 feet,
would be little inferior in power to a parabolic segment of equal focal length, and
capable of reflecting exactly the same sectional area of the solar beams.
Again, what has been proved true of plane mirrors, tangents to a paraboloid
of revolution, must be equally true of a series of tangential circumscribing conical
frustums. In all these cases, however, it is probable that the advantage in
practice will remain with the parabolic figure, from the light at its focus having
a greater area of maximum intensity.
From these results, as well as from independent calculations, we con-_
clude that refracting burning-glasses may be constructed, by placing at some
distance from an axis a series of acute-angled conical zones, or wedge-shaped
pieces of glass (fig. 18), built up like the compound lens of Brewster,
which will produce combustion at as great distances as Burron’s combination
of reflectors.
ARTICLE 17. That the practibility of the Archimedean mirror may be made
still more apparent, we shall now apply Equations 1 and 2, Article 3, to find the
numerical intensity of the light in the focus of Burron’s combination. This was
attempted by PEyrarp, but his conclusions are vitiated by the false premises from
which he set out. He assumed that the intensity is uniform at every part of
the luminous image reflected by a plane mirror,—a supposition proved incorrect
by Art. 2. In our calculation we shall suppose that each of Burron’s mirrors,
which were 8 inches by 6, produced an effect equivalent to a circular beam of 6
inches diameter, when it leaves the mirror.
Taking 4 = 4, and cos7 = 1, we obtain by substitution, in the equations of
Art. 3, the following results :—
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 147
40 x 3 x 62
On 23d March, heat produced by 40 glasses at 66 ft. French = (S) = taro
9
Do. do. 98 fhe tt. =. oi
3d April, 4 p.m, do. 112 Ay, bao! Ete = ool 1
10th April, after 12 noon, do. 128 ee lO tts == 8:29 1
10th April, 2°30 p.m., do. 148 Ft LOOT, = 9-95.)
11th April, 2°30 p.m., do. 21 “ 20 ft.=21 x 3 ’=10°5 I'(by Art.3, Hq.1)
Do. 2:30PM, do. 12 3 20 tt. = 12) x tr Sam:
In the first experiment, on the 23d March at noon, tarred beech was ignited
with the 40 glasses; but the mirror not being mounted on a stand, acted at a dis-
advantage. On the same day, when 98 glasses ignited a plank smeared with tar
and brimstone, the mirror is said to have been still more disadvantageously
placed. The experiment on the 3d April was at 4 o’clock P.m., with the mirror
mounted, and placed on its stand. The sun being weak, a slight inflammation
was produced on a plank covered with threads of wool.
On the 10th April, with a clear sun, the 128 glasses very suddenly kindled a
plank of tarred fir. At half-past 2 o’clock on the same day, the combination of
148 glasses was tried on a plank of beech tarred in part, and covered in some
places with shreads of wool. The inflammation, which was very sudden, com-
menced on those parts of the wood which were uncovered. Beech previously
charred was the material ignited with 21 glasses, and little combustible materials
were the substances set on fire by 12 glasses, on the 11th April.
An inspection of the results in the preceding table shows that if /= 4 be
correct, wood done over in the manner mentioned can be ignited by a heat
varying from eight to nine times that of the direct mid-day rays of the sun
at Paris in April, and finely divided combustible substances by a heat consider-—
ably less, as proved by the experiment with 12 mirrors. But if we assume
k = 2,which is probably nearer the truth, the heat required to produce the same
effect will vary between ten and eleven times the sun’s mid-day heat. If the
number in the right-hand column of the preceding table be multiplied by 5
it gives the minimum number of plane mirrors capable in each case of producing
ignition—that is, the number of mirrors which come under Equa. 1, Art. 3.
Supposing 4 = 4, we find the numbers, for the first five experiments adduced,
to be respectively 26:6, 18, 16:58, 17:14, and 19:18. The sizes of these mirrors
will, of course, depend on the distance of the focus, and the angle at which they
receive the incident light. When the distance is about 108 feet, each of them
should have an extent sufficient to reflect a beam of solar light, not less than one
foot in diameter, and their dimensions vary in the same ratio for other focal
lengths.
As these minimum combinations have been calculated on the assumption
VOL. XXV. PART I. 2P
148 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES.
that the centre of the luminous circle reflected by each of the mirrors can be
directed with precision to a given point, which in practice is not attainable, their
number, or the size of each, must be somewhat increased, to compensate for
defective adjustment. After making such an allowance, it will appear that at
distances not exceeding 150 feet, between 16 and 20 plane mirrors, each 25 by
14 feet, may be substituted for the numerous combinations of Burron, the adjust-
ment of which required so much time and trouble.
What has been shown respecting the power of the solar rays to produce com-
bustion after one reflection, can easily be extended to the case in which the light
undergoes two reflections, the intensity of the final beam being then reduced to
about one-fourth that of the direct solar rays. To compensate for this diminu-
tion, the exterior reflectors must have about twice the area of Burron’s com-
bination. Taking, for example, the 128 plane mirrors which kindled combustibles
at 150 feet, the reflecting surface of the combination ‘is paren. = 422 square
feet, and the sectional area of solar light, which we supposed it to reflect, was
A x 6? x 128 + 144 = 25 square feet nearly. It seems then, that about 80 feet of
reflecting surface, or an extent capable of reflecting 50 square feet of solar light,
will be more than sufficient to inflame such a material as tarred wood, &c., at
the distance of 150 feet, after having undergone two reflections,—an extent of
surface not too great to be united in one compound mirror, constructed in the
manner explained in the foregoing articles.
Considering the scepticism which has prevailed respecting the Archimedean
achievement in the most favourable circumstances, we are the less surprised to
find that some recent authors, in quoting the passage from TzeTzEs, omit the
statement which refers to the burning of the Roman ships in winter. Instead of
ignoring these winter attacks, let us examine them in the light which Burron’s
experiments supply. That performed with 112 mirrors, at the distance of 138
feet, was at 4 o’clock on the afternoon of the 3d April, at which time the altitude
of the sun in the sky of Paris would nearly correspond to his meridian altitude
at mid-winter in the more southern latitude of Syracuse; and as the difference
between the meridian altitude of the sun at the summer and winter solstice
amounts to above 46°, it must be admitted that this additional fact corroborates
in a striking manner the evidence already adduced.
Having now shown how compound burning mirrors can be constructed corre-
sponding in every respect to the description which TzEeTzzs gives of the one
invented by ARcHIMEDES, and that every statement in the passage is in accord-
ance with well-established facts, we conclude that his narrative is no fiction, but,
on the contrary, a true account of a real mirror, capable of producing all the
effects ascribed to it. While this ancient discovery can be tried, after the lapse
MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 149
of two thousand years, by the light of modern science, and pass with credit
through the ordeal, the pretended discoveries of comparatively modern times,
when subjected to the same test, fall to pieces.
An instance may be given without digressing from the subject of our paper.
THomas DicGes, who republished in 1591 a work by his father, LEonHarp
Diecss, entitled ‘“‘Pantometria,” would make us believe, in the preface to this
edition, that he had seen his father at sundry times fire gunpowder and discharge
ordnance at a distance of half-a-mile or more, by means of the sun’s beams.
Had he been aware that to accomplish such a feat would require at least four
thousand square feet of reflecting surface, we may venture to affirm that he
would not have overstepped so far the Archimedean range.
We may observe, in conclusion, that the experiments of Burron, taken in
connection with the preceding deductions, are calculated to produce a strong
conviction that, in clear and comparatively warm climates, the sun’s rays may be
made, at a small expense, to supersede in some respects the fires employed in
culinary operations. Further, when it is considered with what ease a combina-
tion of plane mirrors, or a series of conical reflecting zones, can be constructed,
capable of producing a heat exceeding that of the most intense furnace (Art. 16),
we infer that the solar beams may also be turned to account by the chemist
and metallurgist. For these purposes, one reflection only is required, as the
reflected light can be made to fall always on the same spot, by directing the
axis of the reflector to the centre of the sun’s disc, and causing it to follow the
sun’s motion in the heavens, by revolving round a fixed axis parallel to that
of the earth.
(ine)
\
V.—On the Connection between Chemical Constitution and Physiological Action.
Part. lL—On the Physiological Action of the Salts of the Ammonium Bases,
derived from Strychnia, Brucia, Thebaia, Codeia, Morphia, and Nicotia. By
Dr A. Crum Brown and Dr Tuomas R. FRasEr.
(Read 6th January 1868, under the title ‘‘ On the Changes produced by direct Chemical Addition on
the Physiological Action of certain Poisons.”)
There can be no reasonable doubt that a relation exists between the physiolo-
gical action of a substance and its chemical composition and constitution, under-
standing by the latter term the mutual relations of the atoms in the substance.
There are numerous indications of such a relation, and attempts have been made
to express it formally in certain cases. Thus it has been long observed, that the
salts of the same base have a common physiological action, and it has been
pointed out by Mr Biake* that, with some exceptions, the salts of isomorphous
bases havea similar action. A corresponding likeness in physiological action may
be traced in salts having the same acid, but beyond these generalisations we
are not aware that any approach has been made to the statement of a law con-
necting the physiological action of a substance with its chemical constitution.
Some observers have endeavoured to connect physiological action with com-
position, looking for the cause of the peculiar action of substances in the presence
or proportion of particular elements. It is a sufficient answer to this to point to
isomeric or polymeric bodies—bodies having identically the same composition—
which differ totally in action, such as acetic acid (C,H,O,), and sugar (C,H,,0,);
glycocoll (C,H,NO,), and nitrite of ethyl (C,H,NO,); or to instance kakodylic
acid, which is inert, although perfectly soluble, and containing more than 54 per
cent. of metallic arsenic. .
Examples such as these clearly show that composition alone is guite insuf-
ficient to explain physiological action, and that constitution must also be taken
into account in every attempt to connect the chemistry of substances with their
action on the animal body.
The most direct way of making such an attempt would obviously be to com-
pare physiological action and chemical constitution in a sufficiently large number
of cases, and by classifying the results to deduce a law; but, unfortunately, the
data which we possess are quite insufficient for this. We know, indeed, the
“structure” of a considerable number of substances; that is, we know the order
. Proceedings of the Royal Society of London, vol. iv. Jan, 28, 1841, p. 285.
VOL. XXV. PART I. 2Q
152. DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
in which the atoms of these substances are related to each other, but something
more than this is implied in the term constitution, as we have used it above. For
this involves not only the “structure,” or the arrangement of the equivalents in
atoms and in mutually united pairs, but also what we may call the potential of
each pair of united equivalents.* For instance, the structural formula of formic
acid is
©-O-9
©)
@)
which indicates—1lst, That the four carbon equivalents form one atom, the four
oxygen equivalents two atoms, and the two hydrogen equivalents two atoms; 2d,
that these equivalents are united in pairs, thus—co, co, co, ch, ho, but it does not
in any way indicate (and we do not know) what is the potential of each of these
pairs—that is, how much energy would be required to separate the equiva-
lents from each other. We know that this potential depends upon the structure,
and we can to a certain extent trace the nature of this dependence, but we cannot
as yet express the potential numerically, or give a rule for finding its value from
the structure, and till we can do this we do not fully know the constitution.
But even the structure of the majority of substances is not at all, or only very
imperfectly known, and this is especially the case with those whose physiological
action has been most fully investigated, such as the natural alkaloids.
Seeing, then, that we could not follow the direct road of induction, it occurred
to us that a by-path might be found, by making use of a method resembling in
its main features a mathematical calculus of jinite variations. This method con-
sists in performing upon a substance a chemical operation which shall introduce
a known change into its constitution, and then examining and comparing the
physiological action of the substance before and after the change. We may
express this in mathematical language thus:—Let C represent the constitution
of the original substance and @ its physiological action. After the operation, C
becomes C + AC and ©, @ + A®. Here AC, o, and @ + A® are known, and by
applying the method to a sufficient number of substances, and by varying AC, we
might hope to determine what function ® is of C. The only reason why this
method is not a strictly mathematical one is, that we cannot express our known
terms AC, @, and @ + A® with sufficient definiteness to make them the subjects
of calculation. But although, on this account, we cannot obtain an accurate
mathematical definition of fin the equation @ = fC, we may be able, in an approxi-
mate manner, to discover the nature of the relation.
In applying this method, we must select a chemical operation which satisfies
* More correctly, ‘“ the exhaustion of the potential energy” of each pair of united equivalents.
See THomson and Tait’s Treatise in Natural Philosophy, § 547.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 133°
the following conditions :—1s¢, That it is unambiguous; that is, that the change
of structure produced by it is susceptible of only one interpretation. 2d, That
the change of sérwctwre produced by the operation is, in all cases investigated, the
same, and the change of constitution (AC)—that is, the change of structure and
potential—as nearly as possible the same. 3d, That the operation is completely
under our control, so that it cannot be either performed or reversed spontaneously,
in ordinary circumstances, within the animal body. 4th, That the substance is
equally suitable for absorption into the system before and after the change (that
is, that @ and @ + A@ are observed under similar conditions); and 5th, That a
decided change of physiological action is, in some cases at least, produced (that
is, that A® is not always = 0).
Chemical operations may be divided into two classes—ls?, operations of sub-
stitution; and 2d, operations of addition or subtraction. In the first, an atom or
group of atoms is replaced by an equivalent atom or group of atoms, without any
change taking place in the active atomicity of any atom or radical in the
substance.
In the case of addition (and by subtraction we mean to express merely the
- Inverse operation to addition), the active atomicity of one or more atoms or
radicals in the compound is increased, and the bonds thus set free, or rendered
active, are saturated by atoms or radicals (the sum of whose active atomicity is
of course an even number), which are thus added to the substance. We shall
apply the name condensation to capability of being added to in whatever way the
addition takes place, and distinguish two kinds of condensation, zntra-atomic and
inter-atomic; in the first of which it is an atom, and in the second a compound
radical, the active atomicity of which is increased. Thus, carbonic oxide, sulphide
of methyl, and protochloride of tin, are examples of intra-atomic condensation;
olefiant gas, the dibasic anhydrous acids, and allylic alcohol, of zuter-atomic con-
densation ; while hydrocyanic acid (if we assume for it the formula @-@)=@ )
shows both.
Many operations of addition and also of substitution satisfy the Ist, 2d.
3d, and 4th of the five conditions mentioned above; but when we examine
them in reference to the 5th condition, we find a marked difference. Operations
of substitution (satisfying the lst, 2d, 3d, and 4th conditions) do not appear
greatly to change the physiological activity of a substance, except, Ist, where the
activity depends on direct local action; or 2d, where the operation removes or
introduces an atom or radical, the compounds of which are as arule active. As
examples of the first exception, we may take sulphuric acid (H,SO,) and caustic
soda (HNaO), both poisonous; while sulphate of soda (Na,SO,) and water (H,O)
are not: as examples of the second, acetate of lead and cyanide of sodium, both
poisonous, acetate of potash and chloride of sodium not. Besides the exceptions
which can be reduced to the two classes just mentioned, there are several isolated
°154 pRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
cases of change of activity produced by replacement, such as the singular inert-
ness of ferrocyanide of potassium and of the analogous double cyanides, as com-
pared with the activity of cyanide of potassium and its analogues.
On the other hand, operations of addition, particularly where the condensation
diminished by the addition is intra-atomic, seem, in many cases, to produce very
decided change both in the kind and in the degree of the physiological activity of
the substance acted on. The following examples will illustrate this statement.
Some are cases of direct and some of indirect addition, and in all of them the
change of structure produced is known, and there is in none of them much risk
of fallacy arising from the change taking place spontaneously in the animal
system. The first column contains the names and formule of the substances
before addition, the second the atoms or groups added, and the third the names
and formulee of the substances produced.
I, if Tis.
Carbonic oxide, CO O Carbonic acid, CO,
Hydrocyanic acid, HCN 2H, + HCl Hydrochlorate of methylamine, CNH,CI.
Arsenious acid, As,O,, [HAsO,] (CH,), Kakodylic acid, AsC,H,0, *
Strychnia, C,,H,,N,O, (CH, (HO)) Methyl-strychnia (hydrate), C,,H,,N,O, ft
Brucia, C,,H,,N,O, (CH, (HO) ) Methyl-brucia (hydrate), C,,H,,N,O; ¢
It will be observed that all the substances in the first column are highly
poisonous, while those in the third column are either quite inert, or possess an
action entirely different in kind from that of the bodies from which they are
derived, and very much less in degree.
A consideration of the hitherto isolated facts collected in the above table
leads not unnaturally to a suspicion that condensation (and in particular zntra-
atomic condensation) is in some way connected with physiological activity, as the
first is, and the second appears to be, diminished or removed by chemical addi-
tion. This suspicion is strengthened when we observe that in a very large pro-
portion of the cases as yet investigated saturated bodies (that is, bodies whose
condensation is 0) are inert, or nearly so.
Kakodylic acid, as already mentioned, is a remarkable example of this, and
the salts of tetrethyl-arsonium § seem to be equally inert. Similarly, the salts of
tetramethyl-stibonium || are not emetic. So that, as far as experiment goes, it |
would seem that the stable compounds of pentatomic arsenic and antimony have
avery different and much less strongly marked action than the compounds in
which these elements are contained as triads, or than those (such as arsenic acid)
* Bunsen, Annalen der Chemie and Pharmacie, vol. xlvi. p. 10 (1848).
{ Sranutscumipr, Poggendorff’s Annalen, vol. eviil. p. 523 (1859).
¢ Ibid. p. 541.
§ Lanpott, Annalen der Chemie und Pharmacie, vol. Ixxxix. p. 331 (1854).
|| Ibid. vol. Ixxxiv. p. 49 (1852).
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 155-
in which, although present as pentads, they are easily reduced by subtraction
to the state of triads.
In reference to this, we cannot avoid referring to a very remarkable passage
in BuNsEN’s admirable paper on kakodylic acid. After describing the experi-
ments by which he proved the inert character of this acid, he says, ‘* Gehen wir
auf den Grund dieser unerwarteten Erscheinung zuriick, so bietet sich dafiir nur
in der Annahme eine Erklirung dar, dass die Verbindungsweise des Arseniks
im Kakody] eine andere ist, als in seinen unorganischen Verbindungen. Indem
es darin aufgehort hat, fiir sich einen Angriffspunkt der Verwandtschaft zu bilden,
hat es zugleich seine Reaction auf den Organismus verloren.”’ (Annalen, vol. xlvi.
1843, p. 11.) While it is plain that Bunsen does not here refer to the different
degree of saturation of the arsenic in arsenious and kakodylic acids, both because
the whole theory of saturation is of a much later date, and because he makes no
distinction between the mode of combination of the arsenic in those compounds
in which kakodyl is monad and arsenic triad, and those in which kakodyl
is triad and arsenic pentad, he points out in an exceedingly clear manner the
striking coincidence of peculiar chemical constitution and peculiar physiological
action in the case of kakodylic acid.
While, however, the cases mentioned incline us to believe that physiological
activity is related to condensation, the occurrence of saturated substances, such
as alcohol, corrosive sublimate, and oxalic acid, having a well marked poisonous
action, and of condensed substances, such as benzoic acid and salicine, which
are comparatively inert, shows that condensation is not the only condition of
physiological activity. There can, at the same time, be little doubt that if the
effect of condensation were discovered and eliminated, the other conditions might
be much more hopefully sought for.
Under these circumstances, we turned our attention, in the first place, to the
effect of chemical addition in altering the physiological action of the natural
alkaloids. Wewere led to do so, partly by a consideration of the ease with
which, by means of iodide of methyl, the nitrogen of nitrile bases can be
rendered stably pentatomic, and partly by the hope, grounded on the obser-
vations of STAHLSCHMIDT in reference to the salts methyl-strychnium and
methyl-brucium, that we should obtain marked changes of physiological
action.
The great majority of natural alkaloids belong to the class of nztrile bases,
that is, they contain one or more atoms of triatomic nitrogen directly united to
carbon by three bonds. This nitrogen atom (or, in the case of poly-acid bases,
atoms) can become pentatomic, as in the formation of salts; thus in the forma-
tion of hydrochlorate of morphia the nitrogen takes up H and Cl, thus becom-
ing pentatomic, united by three bonds to carbon, by one to hydrogen, and by
one to chlorine. But by this change it is not rendered permanently or stably
VOL. XXV. PART I. 2k
156 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
pentatomic; it easily loses the hydrogen and chlorine it has acquired, and returns
to the triatomic state. The action of allalies, or, in many cases, even of alka-
line carbonates, is sufficient to effect this, and reprecipitate the alkaloid. It is
obvious, therefore, that the chemical addition of an acid does not satisfy the
third condition mentioned above, for it is certain that the addition can be per-
formed in the stomach, which is acid, and very probable that it may be reversed
in the blood and other alkaline fluids of the body. But if, instead of an acid, we
make use of such a substance as iodide of methyl, we find that while the
triatomic nitrogen takes up CH, and I, and becomes pentatomic (just as in the
former case it took up H and Cl), it does not lose these newly-acquired atoms
when the substance is treated with alkalies, but remains pentatomic even when
subjected to attacks more violent than any to which it can be exposed in the
animal system. ‘This operation, the addition of iodide of methyl to nitrile bases,
satisfies the first condition, for we know precisely what change of structure is
produced. It satisfies the second, for the change of structure is the same in all
nitrile bases; and the change of potential, as far as can be judged from a very
rough estimate of the heat produced by the change, and from the general character
of the substances produced, is not very different in different cases. It satisfies the
third, as we have seen above; and as the iodides of the compound ammoniums
thus formed from the alkaloids are all tolerably soluble in warm water, and can
easily be transformed into other salts very readily soluble, it satisfies the fourth
condition; and the observations of SranHLscumipT show, and the sequel of this
paper will further prove, that it satisfies the fifth.
It deserves to be noted that this operation. only removes the condensation of
the typical nitrogen (that is, of one atom of nitrogen for each molecule of a
mono-basic acid that the alkaloid can saturate), and leaves any other condensa-
tion which may exist in the substance unaffected; so that even if physiological
action should depend upon condensation, it would be unreasonable to expect
@ + 4@ to be in all cases zero, that is, that the new bodies should be quite
inert.
In the present paper we communicate the results of the application of the
method described to strychnia, brucia, thebaia, codeia, morphia, and nicotia. In
each case we shall first describe the action of the alkaloid itself. then give the
method of preparing the derived substances, and describe their physical char-
acters, and, with some detail, their physiological action. Our investigation of the
physiological action of these substances has been chiefly directed to the deter-
mination of their poisonous activity, and of the most prominent differences
between the nature of their action and that of the alkaloids from which they are
derived. .
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 157
STRYCHNIA.
It is well known that strychnia acts on the living economy in a distinctly
defined and characteristic manner, and that it is one of the most active of poisons.
When administered subcutaneously, doses varying from one-twentieth to one-
fiftieth of a grain rapidly produce in rabbits the most violent tetanic convulsions,
and in a few minutes kill the animal. Few poisons have been more carefully
studied, and it is now almost undoubtedly established that the phenomena pro-
duced by strychnia are due to a localisation of its action on the spinal cord.
Iodide of methyl-strychnium.—Strychnia (C,,H,,N,0,) is a mono-acid nitrile
base, that is, it contains one atom of nitrogen united by three bonds to carbon ;
the structure of the radical or radicals (C,,H,,NO,)” is unknown. How first
demonstrated that strychnia is a nitrile base by subjecting it to the action of
iodide of ethyl, and described, in a paper read before this Society,* the ethyl-
strychnium and amyl-strychnium compounds. STAHLScHMIDT subsequently pre-
pared and described the compounds of methyl-strychnium.; We prepared the
iodide of methyl-strychnium by STaHLscHmipT’s method. Strychnia, in fine
powder, was treated, in a flask, with excess of pure iodide of methyl;{ the
flask was allowed to stand in the cold for some hours, then heated in the water-
bath, the excess of iodide of methyl distilled off, and the iodide of methyl-
strychnium dissolved in boiling water, filtered, and recrystallised.
Iodide of methyl-strychnium (C,,H,,N,0,CH,I) crystallises in brilliant white
scales, tastes distinctly bitter, though not so strongly or persistently so as
strychnia, and when treated with strong sulphuric acid and peroxide of man-
ganese, or bichromate of potash, it gives the colour reaction of strychnia, some-
what obscured by the presence of free iodine. It dissolves in 133 parts of water
at 37° C., and in 385 parts of water at 9° C.
SrautscHmMipT has published a statement to the effect that the methyl-
strychnium compounds are inert. As the sequel will show, we do not confirm
this assertion ; but it is proper to admit that our investigation arose principally
from it. .
We first examined the effects of this substance by subcutaneous administra-
tion. For this purpose, it was reduced to the form of very fine powder, suspended
and dissolved in warm distilled water, and injected into a previously formed
* Transactions, vol. xxi, p. 32 (1854).
} Pocernporrr’s Annalen, vol. cviii. p. 513 (1859).
t As iodide of methyl prepared directly from pyroxylic spirit is apt to become acid, it is
advisable, if such impure iodide of methyl be used, to add a small quantity of an alkali (such as carbonate
of potash), in order to prevent any of the strychnia being converted into a salt, and thus remaining
unacted on by the iodide of methyl.
158 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
cavity in the subcutaneous cellular tissue. In this way, bya series of pro-
gressively increasing doses, it was found that as much as twelve grains could be
given to a rabbit, weighing three pounds and four ounces, without any effect what-
ever. Fifteen grains, however, produced serious symptoms, though followed by
recovery, and death was caused by the exhibition of twenty grains. Short
abstracts of the majority of the experiments will be found in the table at the end
of this paper; we shall, however, give some details of several experiments, in
order to illustrate the mode of action.
ExPERIMENT VIJ.—Two very small incisions were made through the skin, one
in either flank, of a rabbit, weighing three pounds and eight ounces; and by in-
serting an aneurism needle into these incisions, two cavities were formed in the
cellular tissue. Into each of these we injected seven and a-half grains of iodide
of methyl-strychnium (in all fifteen grains), suspended and dissolved in warm
distilled water. No effect was caused until forty-five minutes, when the rabbit
moved about uneasily, the limbs gradually yielded, and it soon lay on its chin
and abdomen. When placed on the side, it remained quiet, without any efforts
to recover anormal posture. Irritation did not cause any spasm nor give the
slightest evidence of any increase in the reflex excitability. In one hour, when
lifted by the ears, it hung in a perfectly flaccid and unresisting condition; the
respirations were sixty-four per minute; and there were no voluntary move-
ments. In one hour and thirteen minutes, a few spontaneous movements
occurred in the limbs, but these, apparently, were merely feeble efforts to change
its position. The external temperature appeared to be somewhat elevated, and
the respirations were sixty-five per minute. In an hour and twenty-two minutes,
a few twitches of the body, and especially of the abdominal muscles, occurred
during the respiratory movements, which were now at the rate of sixty-six per
minute; the eyelids did not contract when the conjunctiva or cornea was touched:
but the animal was still conscious. In two hours, the condition was nearly the
same as at last note, except that faint twitches of the eyelids could be excited by
gentle irritation of their edges. In two hours and fifteen minutes, a number of
very feeble spasmodic-like movements of the limbs occurred along with the
twitches of the body, and these could also be excited by irritation. In two hours
and thirty-five minutes, the condition of the rabbit had greatly improved.
Efforts to rise were frequently made, in the intervals between which it lay
perfectly quiet and flaccid, and the sensibility of the conjunctiva and cornea
appeared to be normal.
The observations were now stopped until the following morning, when the
rabbit was found jumping actively about, and apparently in a perfectly normal —
condition.
ExprerIMent VIII.—We injected ten grains of iodide of methyl-strychnium,
suspended and dissolved in warm distilled water, into each of two subcutaneous
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 159
cavities (twenty grains in all) of a rabbit, weighing three pounds and two and
a-half ounces. Fifty minutes afterwards, the animal was lying flaccid, and ex-
hibited the continuance of life only by slow and laboured respiratory movements.
In one hour, tremulous movements of the body and limbs accompanied the
respirations; and it was extremely difficult to excite even a feeble reflex move-
ment by pretty strong stimulation. In one hour and ten minutes, the rabbit
was dead.
The autopsy was immediately made: the heart was contracting with regularity
and considerable force, at the rate of 160 beats per minute; the intestinal peristalsis
seemed normal; galvanic stimulation of the exposed muscles caused energetic
contractions, and continued to do so until more than thirty minutes after death;
and similar stimulation of the exposed sciatic nerves caused contractions of the
posterior extremities at four minutes after death, but ceased to do so in other five
minutes.
These experiments are sufficient to illustrate the physiological effects that are
produced when iodide of methyl-strychnium is administered to rabbits by sub-
cutaneous injection. We have made similar experiments, with exactly analogous
results, on dogs and cats, the more important details of which are mentioned in
the table at the end of this paper.
The effects of internal administration were examined by passing a gum-elastic
catheter down the cesophagus of a rabbit, and so injecting iodide of methyl-strych-
nium, suspended and dissolved in warm distilled water. It is unnecessary to
give any description of these experiments, at this place, as no effect was produced
by this method of exhibition, although as much as thirty grains was given at one
_ time, and it was inconvenient, as well as unnecessary, to give larger doses. It is
well known that to produce symptoms with a poison in a rabbit, a much larger
quantity is required when it is administered by the stomach than when it is
injected subcutaneously. The contrast between the action of iodide of methyl-
strychnium and strychnia itself was, however, well shown in the rabbit to which
thirty grains of the former had been given without any effect; for one-tenth of a
grain of strychnia, also administered by the stomach, quickly produced violent
tetanic convulsions, and, in a few minutes, killed the animal.
As iodide of methyl-strychnium is a sparingly soluble substance, it appeared
proper, in conformity with our fourth condition, and in order to compare the
actions of strychnia and of methyl-strychnium, that the properties of the sulphate
of the latter, which is extremely soluble, should be examined.
Sulphate of methyl-strychnium ((C,,H,,N,0,CH,),SO,) was prepared by precipita-
ting a hot aqueous solution of the iodide by a hot solution of sulphate of silver,
the slight excess of the latter was precipitated by chloride of sodium, the filtrate
evaporated to dryness, and the sulphate of methyl-strychnium extracted by
means of alcohol. It erystallises in delicate white needles, is very soluble in cold
VOL. XXV. PART I. 25
160 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWFEN
water, tastes like the iodide, and gives the usual strychnia-reaction with oxidising
agents.
As had been anticipated, it is much more active than the iodide. One grain,
dissolved in water, and injected under the skin of a small rabbit, caused its death
in eighteen minutes. Half-a-grain, however, produced no effect. When eight-
tenths of a grain was similarly administered, the following symptoms were pro-
duced, but death did not result.
Experiment X XIII.—Eight-tenths of a grain of sulphate of methyl-strychnium,
dissolved in a few minims of distilled water, was injected into the subcutaneous
tissue over the abdomen of a rabbit, weighing three pounds and three and a-half
ounces. It caused no immediate uneasiness, and the animal was unaffected for
about twenty-five minutes, after which, however, it became restless. In twenty-
eight minutes, movements of the limbs were made with obvious difficulty, and the
rabbit occasionally stumbled. In twenty-nine minutes, the limbs could no longer
support the body, and a position was assumed in which the rabbit lay on the abdo-
men with the chin resting on the table. It was now perfectly flaccid, and remained
on the side when so placed. There was no evidence of exaggeration in the reflex
motor function; indeed, an extremely violent stimulus was required to produce even
a faint reflex movement. In thirty-two minutes, slight quiverings occurred, and
the respirations were laboured, and at the rate of sixty-eight per minute. This
condition continued until one hour after the administration, and during all this
time consciousness seemed unaffected, and sensibility was not lost, as was shown
by stimulation of the conjunctiva or cornea causing movements of the eyelids.
Repeated efforts were, however, now made to recover a normal posture, and the
frequency of the respirations increased. In one hour and eleven minutes, the
head was raised from the table; and in eleven minutes afterwards, the rabbit
succeeded in rising on its feet and maintained itself thus, though at first some-
what unsteadily. In one hour and twenty-two minutes, all the symptoms had
disappeared. The rabbit was perfectly well on the following morning.
‘The sequence of symptoms to a fatal termination, and the post mortem appear-
ances, are well shown in the experiment where one grain was exhibited (Experi-
ment XXV.).
EXPERIMENT XXV.—We dissolved one grain of sulphate of methyl-strych-
nium in fifteen minims of distilled water, and injected this solution into the sub-
cutaneous tissue of a rabbit, weighing two pounds and fourteen ounces. In eleven
minutes, the first symptom, unsteadiness, appeared. In twelve minutes, the rabbit
was lying on the abdomen and chest, with the lower jaw resting on the table. There
were no voluntary movements; strong irritation caused feeble reflex movements
only, and the respirations were shallow and laboured, and at the rate of sixty per
minute. In sixteen minutes, quivering movements of the chest and abdomi-
nal muscles occurred, from which it was nearly impossible to distinguish the
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 161
respiratory movements; and the sensibility of the eyeball was greatly im-
paired. In seventeen minutes, there were no movements, except occasional faint
twitches of the muscles of the body, while irritation of the skin or of the eye-
- ball did not cause any reflex movements. The rabbit was quite dead in eighteen
minutes.
Four minutes after death, the heart was contracting in proper rhythm and
with regularity, at the rate of 164 beats per minute, and the intestinal peristalsis
was well marked; the heart had however ceased to contract in other twenty-four
minutes, but the intestinal peristalsis continued for some time after this. Six
minutes after death, the gluteal muscles were exposed, and exposure caused them
to twitch. The sciatic nerves were at the same time stimulated with galvanism
and mechanical irritation, but no contractions were produced. igor mortis com-
menced about two hours and forty minutes after death.
When sulphate of methyl-strychnium is administered to rabbits by the
stomach, twenty-five grains appears to be about the minimum fatal dose. The
symptoms and mode of death are the same as those that result from subcutaneous
injection.
These experiments clearly prove that the methyl derivatives of strychnia
possess a very different action from strychnia itself. In none of our experiments,
~ not even in the fatal cases, were the symptoms those of strychnia-poisoning; no
starts nor spasms occurred, nor did stimulation give evidence of the slightest
_ increase of reflex excitability. In fact, a condition exactly the reverse of that
produced by strychnia was produced by these compounds. In place of violent
spasmodic contractions and muscular rigidity, the appearances were those of
paralysis, with a perfectly flaccid condition of the muscles. The limbs of the
animal first yielded, its head gradually sank until it rested on the table, by-
and-by, it lay in a perfectly relaxed condition, and when death occurred, it was
due to stoppage of the respiratory movements. In the autopsis, further evi-
dence was obtained to distinguish the effects of the methyl-strychnium com-
pounds from those of strychnia. The heart was found acting with nearly its
normal rapidity; the spinal motor nerves were either paralysed or nearly so;
| and, in place of the almost immediate occurrence of 72gor mortis that follows the
| action of strychnia, the muscles continued flaccid, contractile, and alkaline for
many hours.
These symptoms are sufficient to suggest a close resemblance between the
action of the methyl derivatives of strychnia and that of curare (wourali), a well
_ known and elaborately studied poison. In a recent publication, Professor Scurorr,
of Vienna, has indicated a resemblance of this kind between the nitrate of methyl-
strychnium and curare.* Both substances undoubtedly produce a condition of
* Wochenblatt der Zeitschrift der k. k. Gesellschaft der Aertze in Wien; vi. Band, 1866,
pp. 157-162.
162 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
general paralysis; but the special characteristic of curare-poisoning is, that this
paralysis is the result of an impairment or destruction of the function of the
peripheral terminations (end-organs) of the motor nerves. It is impossible to
demonstrate such an action without undertaking experiments of a special
character. We, accordingly, extended our research for the purpose of examining
this question.
ExrertmMent XXVIII.—The sciatic artery and vein were tied at the knee of a
frog, and one-tenth of a grain of sulphate of methyl-strychnium, dissolved in
distilled water, was injected under the skin of the back. Eight minutes after-
wards, the frog was lying in a perfectly flaccid state, and, in ten minutes, irrita-
tion of any portion of the skin produced energetic movements of the tied limb,
below the points of ligature, but nowhere else. The sciatic nerve of the untied
limb was now exposed, and on stimulating it with a weak, interrupted galvanic
current, movements occurred in the tied limb only; not the slightest effect
occurred in any part to which the poison had access. At the same time, the
muscles were everywhere active, and freely contracted when directly stimulated.
The sciatic nerve was then exposed in the tied limb, above the points of ligature,
and on stimulating it, energetic movements occurred below the knee of that
limb, and there only. The heart was, at this time, acting at the rate of fifty per
minute.
This experiment was repeated with one grain of iodide of methyl-strychnium,
and the same general results were obtained. The evidence that was thus acquired
in favour of an action on the peripheral terminations of the motor nerves was
strengthened by a modification of this method of experiment.
EXPERIMENT XXIX—The right gastrocnemius muscle of a frog was carefully
dissected from its connections, excepting that its origin and insertion, and the nerve-
fibres entering it, were untouched, and that all its blood-vessels were ligatured.
One-tenth of a grain of sulphate of methyl-strychnium, dissolved in five minims of
distilled water, was then injected under the skin of the back. Twenty minutes
afterwards, the animal] being in a perfectly relaxed and motionless condition, the
two sciatic nerves were exposed. Galvanism of the left produced no movement
in the left limb, while galvanism of the right produced energetic movements of
the right limb, which were seen to be due solely to contractions of the right gas-
trocnemius muscle, the other muscle remaining motionless. At the same time,
direct stimulation by galvanism caused contractions as freely in the poisoned
muscles as in the non-poisoned right gastrocnemius.
In an experiment, in which iodide of methyl-strychnium was substituted for
sulphate, the effects were the same. We have, therefore, demonstrated that the
methyl-strychnium derivatives produce paralysis and death by destroying the
function of the motor nerve end-organs, and that their mode of action is, there-
fore, identical with that of curare. This conclusion is an extremely curious and
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 163
interesting one. It is difficult to imagine a more decided modification in the
action of any substance than has been produced by the addition of iodide or
sulphate of methyl to strychnia. The striking characteristic of strychnia-action
is the great and uncontrollable activity of the muscular system ; that of curare,
of iodide, and sulphate of methyl-strychnium, and, as we shall presently see, of
several other similarly modified poisons, is the flaccid and motionless condition
caused by the impossibility of exciting muscular action through the nervous.
system. So opposite are their effects that physiologists look upon curare as a
powerful counteragent to strychnia, while physicians have employed it with
success in the treatment of strychnia-poisoning and of tetanus. It is remarkable
that by so simple a chemical process so thorough a change should be produced in
physiological action.
The experiments we have already described have also shown that this change
in chemical constitution has greatly reduced the poisonous activity of strychnia.
This effect is still more clearly exhibited in the following table :—
eo ® Substance Animal and its Method of
employed. weight. exhibition. Ese: Effect.
VII. |Lodide of methyl-| Rabbit, 3 lbs. 8 oz. | Subeutaneously.|15 ers. (contain-| Paralysis in 50 minutes,
strychnium. ing 10°5 grs.| continuing for more than
of strychnia). | 2 hours, and followed by
recovery.
XIII. | Strychnia (sus-| Do. (same rabbit | Subcutaneously.| 0:05 gr. Tetanus in 15 minutes;
pended in dis- | as in Expt. VII.) death in 30 minutes.
tilled water).
XVII. |Iodide of methyl-| Do., 3lbs.130z. |By stomach. | 30grs. (contain-! No effect.
strychnium. ing 211 grs.
of strychnia).
XIX. Strychnia (as Do., (same rabbit | By stomach. Ol gr. Tetanus in 22 minutes;
hydrochlorate).| asin Ex. XVII.) death in 31 minutes.
XXIII. | Sulphate of me-| Do., 3 lbs. 33 oz. | Subcutaneously.|0'8 gr. (contain-| Paralysis in 29 minutes,
thyl-strych- ing 0.67 gr. of| continuing for 53 minutes,
nium. strychnia). and followed by recovery.
XXXIII. | Sulphate of me-| Do., 3 lbs. 5? oz. | By stomach. 20 ers. (contain-| No effect.
thyl-strych- ing 16:8 grs.
nium. of strychnia).
We have made experiments with nitrate of methyl-strychnium and hydro-
chlorate of ethyl-strychnium, and have found that their action is identical with
that of the iodide or sulphate of methyl-strychnium.
* The numbers in this, and in the other short tables that are appended to the description of the
physiological action of the derivatives of each alkaloid, have reference, in common with the numbers
in the text, to the arrangement in the complete table at the end of the paper.
VOL. XXV. PART I. 2p
164 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
BRUCIA.
Brucia is a poisonous alkaloid derived from some plants belonging to the
genus Strychnos. It possesses a physiological action exactly similar in character
to that of strychnia, but less in degree.
Todide of methyl-brucium (C,,H,,N,0,CH,I +8H,O).—Brucia (C,,H,,N,0, +
4H,O) is, like strychnia, a mono-acid nitrile base: here also the structure of the
group (C,,H,,NO,)” is unknown, but the action of nitric acid on brucia renders it
probable that it contains the radical 6) 0S) The ethyl-brucium compounds
@
were discovered and described by GUNNING,* and the methyl-brucium compounds
by Srautscumipt.t We prepared the iodide of methyl-brucium by adding
excess of iodide of methyl to a saturated solution of brucia in rectified spirit,
allowing the mixture to stand for some hours, evaporating, and recrystallising
from hot water.
It forms thin white scales, and dissolves in 79 parts of water at 37°C, and
in 225 parts of water at 9°C. Its taste resembles that of the corresponding
strychnia compound.
When administered by subcutaneous injection, iodide of methyl-brucium was
reduced to the form of a very fine powder, and suspended and dissolved in
warm distilled water. In a series of experiments, it was found that as much
as twelve grains could be thus given to a rabbit without any effect, that
fifteen grains produced marked symptoms, and that eighteen grains was about
the minimum fatal dose. Its method of action is well shown in the following
experiment.
EXPERIMENT XL.—We injected seven and a-half grains of iodide of methyl-
brucium, suspended and dissolved in warm distilled water, into each of two
cavities (fifteen grains in all) previously formed in the subcutaneous cellular
tissue over the abdomen of a rabbit, weighing four pounds. This did not pro-
duce the slightest effect until two hours and forty-three minutes after the
administration, when the rabbit’s movements became sluggish. Shortly after, a
difficulty was observed in standing, and this posture soon become impossible on
account of the increasing feebleness of the limbs. In three hours and three
minutes, the rabbit subsided on the abdomen and chest, with the lower jaw rest-
ing on the table. The condition was one of perfect quietness, there being no
twitches; and, though frequently tested, the reflex excitability appeared normal.
* Journal fiir praktische Chemie, vol. Ixvii. p. 46.
+ Poaesnporrr’s Annalen, vol. evil. p. 535 (1859).
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 165
It remained on the side when so placed, but unsuccessful resistance was made to
this change of position. In three hours and thirty-eight minutes, the flaccid
state was even more marked, the position was changed without any resistance
on the part of the rabbit, severe pinching only occasionally excited a reflex
movement, but the respiratory movements were at the rate of sixty-eight per
minute. These symptoms continued for other twenty minutes, when some volun-
tary movements were made, and soon after, the flaccid condition had nearly dis-
appeared. On the following morning, the animal appeared to be perfectly well.
In the experiment we next give, a fatal dose was administered.
EXPERIMENT XLI.—We injected, in all, eighteen grains of iodide of methyl-
brucium, suspended and dissolved in warm distilled water, into two subcu-
taneous cavities formed over the abdomen of a rabbit, weighing three pounds
and twelve ounces. No result was observed until twenty-seven minutes, when
uneasiness was manifested by restless movements, and slight quivers were
seen in the muscles of the neck. In thirty minutes, there was great difficulty in
supporting the head, which shook tremulously, and frequently fell on the table,
where it eventually remained at thirty-two minutes. The body was still supported
on the limbs, though by no means steadily. In thirty-seven minutes, it lay on
the table and remained on the side, unresisting and flaccid. The respirations
were, at this time, at the rate of forty-eight per minute, and were occasionally
interrupted by faint quivering movements, but these had no spasmodic char-
acter. In forty-five minutes, the respirations were thirty-six per minute, and
the heart’s contractions 160 per minute. In one hour, the respirations were
twenty-five per minute; and irritation of the conjunctiva did not now cause any
movements of the eyelids. In one hour and seven minutes, the respiratory
movements were irregular and shallow, only about sixteen occurring in the
minute, while the heart was contracting at the rate of 120 per minute. The
limbs were perfectly flaccid and motionless. The respiratory movements gra-
dually became less apparent, a series of feeble quivers occurred in the muscles
of the face, and death immediately afterwards occurred, one hour and thirteen
minutes after the administration.
In the autopsy, the cardiac action was found to be regular and rhythmical,
though only at the rate of seventy-four per minute. In three minutes after
death, galvanism of the sciatic, phrenic, and other nerves, did not produce any
muscular contraction; while it was found by direct galvanism that the muscles
retained their contractibility for many minutes afterwards. Rigor mortis did
not occur until more than one hour after death.
For the purpose of contrasting these symptoms with those that are caused by
brucia itself, we shall describe, very briefly, an experiment in which the rabbit,
that recovered after the administration of fifteen grains of iodide of methyl-
brucium, was rapidly killed by a somewhat large dose of brucia.
166 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
Experiment XLII1.—One-fifth of a grain of brucia was dissolved in ten minims
of very dilute hydrochloric acid, and injected, with Woonp’s syringe, into the
subcutaneous tissue of the rabbit that had, some days previously, been subjected
to an experiment with fifteen grains of iodide of methyl-brucium. In seven
minutes, a constrained position was assumed by the rabbit, and the slightest
touch caused a sudden spasmodic contraction of the four limbs by which the
body was swiftly elevated. In eight minutes, the rabbit sprang to a considerable
height, and fell in a well-marked tetanic convulsion, which lasted about fifteen
seconds. After this, a series of violent tetanic convulsions, of a distinctly
opisthotonic character, followed each other in rapid succession; and at the
termination of one of these, eighteen minutes and thirty seconds after the injec-
tion of the poison, the rabbit died. There was distinct igor mortis thirty
minutes after death.
For internal administration, the iodide of methyl-brucium was also reduced to
a very fine powder, and suspended and dissolved in warm distilled water. It
was then introduced into the stomach, by means of a gum-elastic catheter. In
this way, we performed several experiments, but never succeeded in producing
any effect, although as large a dose as thirty grains was at one time admin-
istered. It is well known that there is considerable difficulty in affecting
a rabbit by a poison introduced into the stomach. That this difficulty was
not due, in the present instance, to any recognised cause peculiar to the
stomach of the rabbit, was shown by an experiment in which we produced
tetanic symptoms and death by introducing two grains of brucia into the stomach
of the rabbit that had previously received thirty grains of iodide of methyl-
brucium without any effect whatever.
Sulphate of methyl-brucium ((C,,H,,N,0,CH,),SO,, dried at 100°C) was pre-
pared by precipitating a hot solution of the iodide by means of sulphate of silver.
It forms a white crystalline mass, readily soluble in water, and, as well as the
iodide, gives the ordinary brucia reaction with nitric acid. It is freely soluble
in cold water.
We examined the effects of this substance by subcutaneous injection and by
introduction into the stomach. For the former purpose, it was dissolved in a
few minims of distilled water, and injected under the skin with a Woop’s
syringe. In a rabbit, one grain could be thus given without any effect, two
grains caused marked effects, which were not, however, fatal; while two grains
and a-half soon killed the animal. The symptoms were the same as those
of the iodide, and, therefore, very different from the exaggerated reflex action,
convulsions, and tetanus, which are caused by brucia itself. They are illustrated
in the following experiments.
EXPERIMENT LIII.—We injected two grains of sulphate of methyl-brucium, dis-
solved in fifteen minims of distilled water, under the skin of a rabbit, weighing two ~
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 167
pounds and thirteen ounces and three-quarters. In ten minutes, the animal had
obviously some difficulty in moving about, and it could not stand steadily. The
limbs soon after yielded, and it lay down on the abdomen, chest, and lower jaw ;
while occasional quivering movements occurred in the muscles of the body.
In thirty-four minutes, it lay unresisting and quiet on the side, and the respira-
tions were at the rate of seventy-four per minute. In forty minutes, the
respirations were at the rate of fifty-four per minute.. It lay in a perfectly
relaxed and quiet condition, and when the skin was severely irritated, only
extremely feeble reflex movements followed. In one hour and two minutes, the
respirations were at the rate of forty-eight per minute; and though irritation of
the cornea or conjunctiva did not cause any movement of the eyelids, reflex
movements could be excited by severe pinching of the skin. This condition of
helpless prostration continued for about thirty minutes, during which some faint
twitches of the body and jerking movements of the limbs occasionally occurred.
Soon after this, however, a marked improvement was observed : the respirations
became fuller and more frequent ; irritation of the eyeball was followed by con-
tractions of the eyelids; and, at last, well-directed efforts were made to recover a
normal position, and these ultimately proved successful at about two hours after
the poison had been injected. The rabbit recovered perfectly.
Experiment L1V.—Two and a-half-grains of sulphate of methyl-brucium was
dissolved in fifteen minims of distilled water, and administered by subcutaneous
injection to a rabbit, weighing three pounds and fourteen ounces and a-half. In
twenty-two minutes, the animal was lying on the abdomen and chest, but the
head was still supported by the muscles of the neck; there was distinct congestion
of the ears and conjunctiva. In thirty-five minutes, the head had fallen on the
table, and the rabbit was perfectly flaccid, and apparently unable to make any
voluntary movements. The respirations were at the rate of eighty-two per
minute. In fifty-three minutes, the number of the respirations had diminished
to twenty-four per minute, while their character was extremely feeble and
shallow. In one hour and two minutes, the respiratory movements occurred at
long intervals, and were accompanied with a faint tremor of the body and limbs;
and it was ascertained that the cardiac contractions were occurring regularly, at.
the rate of 160 beats per minute. In one hour and ten minutes, the respirations
altogether ceased, and death occurred. During the progress of the symptoms,
the reflex excitability was frequently tested, with the result that not the slightest
increase was ever observed.
The autopsy was immediately made: the heart was found contracting at the
rate of 120 per minute; the vermicular action of the intestines was well marked ;
the conductivity of the sciatic nerves was lost three minutes after death ; and idio-
muscular irritability persisted for more than twenty minutes afterwards. Rigor
mortis had not commenced forty minutes after death.
VOL. XXV. PART I. 2U
168 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
For administration by the stomach, we dissolved this substance in warm dis-
tilled water, and introduced the solution through a gum-elastic catheter. We
found that as much as twenty grains could be thus given without any effect, and it
was not considered advisable to increase this dose. Its magnitude is apparent
when we recollect that it contains about seventeen grains of brucia; and we have
already seen that when two grains of this alkaloid is introduced into the stomach
of a rabbit, the most violent tetanic convulsions are quickly produced, and death
soon follows.
The short account we have given of a few of our experiments with iodide and
sulphate of methyl-brucium is sufficient to show that these substances have an
action that is very different from that of brucia itself. Brucia is a violent con-
vulsant poison, and it causes death by either exhaustion or asphyxia; its methyl
derivatives never produce convulsions, nor do they even increase the reflex
activity ; and although they cause death by asphyxia, this asphyxia, in place of
being the result of prolonged and continuous muscular action, due to abnormal
nerve activity, is the result of muscular paralysis, due to partial or complete
absence of normal nerve activity. We have demonstrated the latter effect by the
following experiments, which further show that the influence of the methyl deri-
vatives of brucia is exercised on the terminations of the motor nerves.
Exrertment LVI.—tThe left iliac artery ofa frog, weighing 608 grains, was tied,
after exposing it by removing a portion of the sacrum, and one-fifth of a grain of
sulphate of methyl-brucium, dissolved in ten minims of distilled water, was then
injected into the abdomen. In four minutes, every portion of the frog except the
left leg was paralysed. In five minutes and thirty seconds, weak interrupted
galvanism, applied to any portion of the skin, caused violent movements of the
left leg, and of it alone, every other part of the body remaining motionless. The
heart, as ascertained by its impulse, was contracting thirty times per minute.
In seven minutes, the right sciatic nerve was exposed—the incisions neces-
sary for which excited energetic reflex movements of the left limb—and on gal-
vanising it, strong contractions of the left limb occurred, but no movement
occurred in the right limb. The muscles were everywhere in a normal state,
and freely responded to direct galvanic stimulation; and the heart still con-
tracted at the rate of thirty beats per minute.
In a similar experiment, with half a grain of iodide of methyl-brucium, the
same effects were observed. It is, therefore, apparent that these substances do
not directly influence the action of the heart, of the muscles, of the spinal cord,
or of the sensory (afferent) nerves, but that the paralysis, which they so promi-
nently cause, is the result of an action on the motor nerves. In the above
experiment, the whole course of the sciatic nerve, from the pelvis to the extremity
of the left posterior limb, was protected from the influence of the poison. The
experiment does not, therefore. show if the methyl-brucium compounds have
—
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 169
an elective action for any special portion of the nerve. In the next experi-
ment, a much more limited portion of the nerve was protected from the poisonous
action.
EXPERIMENT LVII.—In a frog, weighing 542 grains, the right gastrocnemius
muscle was exposed; the muscle was separated from all its connections,
excepting its origin and insertion and the nerve-fibres that entered it. One-
sixth of a grain of sulphate of methyl-brucium, dissolved in ten minims of
distilled water, was then injected into the abdomen. In twenty minutes, a
condition of complete paralysis was present everywhere except in the right leg.
The two sciatic nerves were exposed, and on galvanising the left nerve, feeble
movements occurred in the right leg, and there only. When the right nerve was
galvanised, movements occurred in the right leg, which were observed to be solely
due to contractions in the right gastrocnemius muscle.
In this experiment, the terminations of the sciatic nerve in the right gastroc-
nemius muscle were alone protected from the direct influence of sulphate of
methyl-brucium. This substance had access to all the other terminations of the
right sciatic nerve, to the trunk of this nerve, and to all the other nerves of the
body. No manifestation of vitality was obtained anywhere, except in the right
limb, and it was restricted to contractions of one muscle of that limb. As
these contractions could be produced by a stimulus originated in and conducted
along the nerve trunk, it is obvious that the vitality of this portion of the
nerve was not lost. And as the stimulus produced no effect on the termi-
nations of the nerves to which sulphate of methyl-brucium had access, while
it produced an effect on those that were protected from its direct influence,
it is evident that this poison acts on the peripheral terminations of the motor
nerves.
The physiological action of brucia is, therefore, completely changed by the
addition of iodide or sulphate of methyl. It is also apparent that its activity as
a poison is greatly lessened; and the following table, which contains a succinct
statement of some of the previously-mentioned facts, will clearly illustrate
this :—
170
DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
No. of Substance Animal and its Method of ence Effect.
Experiment. employed. weight. exhibition.
XL. |Iodide of methyl-| Rabbit, 4 Ibs. Subcutaneously.|15 grs. (contain-| Paralysis in 3 hours and
brucium. ing 87 grs. of| 3 minutes, continuing
dry brucia). for more than 28 minutes,
and followed by recovery.
XLIII. | Brucia (erystal- | Do. (same rabbit | Subcutaneously.|0-2 gr. (contain- | Tetanus in 8 minutes;
lised). as in Experi- ing 0°17 gr.of | death in 18 minutes 30
ment XL.) dry brucia). seconds.
XLVI. [Iodide of methyl-| Do.,4Ibs.20z. | By stomach. 30 grs. (contain- | No effect.
brucium. ing 17:4 ers.
of dry brucia).
LI. Brucia (crystal- | Do. (same rabbit | By stomach. 2 grs. (contain- | Tetanus in 44 minutes;
lised). as in Experi- ing 1‘7 gr. of | death after 3 hours.
ment XLVI.) dry brucia).
LIII. | Sulphate of me- | Do.,2 Ibs. 133 oz. Subcutaneously.| 2 grs. (contain- | Paralysis in 20 minutes,
thyl-brucium, ing 1:7 gr. of | continuing for about 1
dried. dry brucia). hour and 40 minutes, and
followed by recovery.
LVIII. | Sulphate of me- | Do.,41bs.20z. |By stomach. 20 grs. (contain-| No effect.
thyl-brucium, ing17-2ers. of
dried. dry brucia).
THEBATA.
One of the active principles of opium possesses an action in all respects the
same in character as that of strychnia or brucia. We principally owe our know-
ledge of the method in which thebaia acts to the admirable researches of CLAUDE
BerNARD. ‘This distinguished physiologist has further demonstrated that thebaia
does not possess any soporific property, that it is the most active toxic principle
in opium, and that it ranks first among the alkaloids of this drug that havea ~
convulsant action.* From our experience of its properties, we should assign
to it a lower rank than brucia as a toxic and convulsant substance.
Lodide of methyl-thebaium—tThe close analogy in physiological action that
exists between thebaia (C,,H,,NO,) on the one hand, and strychnia and brucia on
the other, led us to subject this alkaloid to the action of iodide of methyl. The
method adopted was the same as that described for the preparation of iodide of
methyl-brucium, and the reaction takes place as readily. The product crystallises
from alcohol in hard, shining, transparent crystals, which, when air-dried, have
the composition (C,,H,,NO,CH,1). They dissolve in 16-5 parts of water at 37°C.,
and in 63°5 parts of water at 9°C.+ When a hot, saturated, aqueous solution
is allowed to cool, it gelatinises, and the jelly, when left to itself, in some
hours, and, when stirred, in a few minutes, is converted into a mass of minute
silky needles, which when dried in the air, have the same composition as the
crystals obtained from the alcoholic solution.
* Comptes Rendus, vol. lix. 1864, p. 413.
¢ The methyl derivatives of thebaia have not been described. We shall take some other oppor-
tunity of giving details of their chemical relations.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 171
It is much more soluble in water than the iodides of methyl-strychnium
and methyl-brucium, and, on this account, we commenced its administration
in relatively small quantities. We found that doses of one, five, and six grains,
nearly completely dissolved in very dilute spirit, and administered to rabbits by
subcutaneous injection, produced absolutely no effect. When, however, the dose
was increased to ten grains, partial and then complete paralysis was caused,
and death quickly occurred; while serious symptoms were caused by eight
grains, but they did not terminate fatally. We shall give some details of these
two experiments.
EXPERIMENT LXII.—We dissolved eight grains of iodide of methyl-thebaium
in very dilute alcohol, and injected the solution, with Woon’s syringe, into the
subcutaneous cellular tissue of a rabbit, weighing two pounds and twelve ounces.
Symptoms of uneasiness occurred in thirty minutes, and were soon followed by
quivering movements of the head and ears, and, to a slight extent, of the rest of
the body. It was soon apparent that the neck muscles were scarcely able to
support the head, for it frequently fell on the table,but the rabbit did not permit
it to remain there until forty-five minutes after the administration. At this
time, the respirations were at the rate of seventy-eight per minute, and, although
the head was resting on the table, the body of the animal was supported, in a
comparatively normal posture, on the limbs. There were occasional tremulous
movements of the body, but no exaggeration of the reflex function could be dis-
covered. The rabbit remained in this state for about thirty minutes; but soon
after this, the tremulous movements disappeared, the head was raised and
supported normally, and a perfectly natural posture was assumed. Every
symptom had disappeared within two hours after the administration.
EXPERIMENT LXIII.—Ten grains of iodide of methyl-thebaium, reduced to a
very fine powder, was partially dissolved and partially suspended in very
dilute alcohol, and injected under the skin of a rabbit, weighing two pounds
and eleven ounces. There was no obvious effect until ten minutes, when it was
observed that the animal moved with difficulty. Tremulous movements then
occurred, the limbs occasionally yielded, and the head frequently fell. In
twelve minutes, the rabbit lay on the abdomen and chest, with the lower jaw
resting on the table; and the tremulous movements only occurred at intervals.
It could now be lifted without any struggles. In nineteen minutes, the condition
was one of complete flaccidity, the only movements were an occasional gasping
respiration, but common sensibility was still retained. It continued thus, on the
very verge of death, for about four minutes, when a few quivering contractions
occurred in the muscles of the face and neck, and the respirations altogether
ceased. During the course of the symptoms, there was never the slightest
trace of any exaggeration in the reflex activity, nor of spasmodic or convulsive
movements.
VOL, XXV. PART I. 2X
172 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
The autopsy was immediately made. The heart was found contracting, in
normal rhythm, at the rate of eighty-five per minute, and its spontaneous
contractions did not cease until eight minutes; and the intestinal peristalsis
was active. The sciatic nerves were exposed four minutes after death, and
stimulated with weak and strong currents of interrupted galvanism, but no
muscular contractions were thereby caused. The muscles themselves readily
contracted when the poles were applied directly to their surface, and continued
to do so for more than fifteen minutes after death. There was no appearance
of rigor mortis one hour and five minutes after death, and the muscles were, at
this time, alkaline in reaction.
We administered to the rabbit, which had survived the administration of eight
erains of iodide of methyl-thebaium (Experiment LXII.), a fatal dose of the
thebaia from some of which the methyl compound had been prepared. The
striking contrast in the symptoms that were produced will be seen from the
following account of the Experiment.
EXPERIMENT LX VI.—We injected one-fifth of a grain of thebaia, dissolved in
very dilute hydrochloric acid, into the subcutaneous cellular tissue of the rabbit,
which had been subjected to an experiment, some days previously, with eight
grains of iodide of methyl-thebaium. The injection did not appear to cause
much annoyance, as the animal jumped about naturally for forty minutes after it.
Soon after, however, its movements became more constrained and cautious, and
occasional twitches occurred in the muscles of the back. These gradually became
more marked and powerful, and in forty-eight minutes, they assumed the character
of spasmodic starts. In forty-nine minutes, a touch, even when very gentle, of
any portion of the skin excited a violent spasmodic jump, and in fifty-two
minutes, a spontaneous violent opisthotonic convulsion took place, and continued
for forty-five seconds. The rabbit now lay on its side; every respiratory move-
ment provoked a short fit of tetanus, while, occasionally, a violent and prolonged
fit occurred. This condition lasted for two minutes, when, at the termination of
one of the more violent of these fits, death occurred,—fifty-four minutes after the
administration of the poison.
It was found, in the autopsy, that the sciatic nerves retained their motor con_
ductivity for at least fifteen minutes after death. A certain degree of muscular
rigidity was observed at twenty-eight minutes, and rigor mortis was perfectly
established at forty minutes, when all the muscles were acid in reaction, although
the temperature of the abdominal cavity was as high as 95° F.
The internal administration of iodide of methyl-thebaium was effected in the
same way as we have described for the corresponding strychnia and brucia com-
pounds. It was found that, with this substance also, so large a dose as thirty
grains could be introduced into the stomach of a rabbit without any effect. Well-
marked symptoms were produced in the same animal by three, and, on another
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 173
occasion, by three and a-half grains of thebaia similarly administered, but it
recovered after both doses. Four grains was, however, a fatal dose, as will be
seen from the following Experiment.
EXPERIMENT LX XIV.—Four grains of thebaia, almost completely dissolved in
very dilute hydrochloric acid, was introduced, by a gum-elastic catheter, into the
stomach of the rabbit that had received thirty grains of iodide of methyl-thebaium
(Experiment LXXI.) In six minutes, a violent tetanic convulsion occurred ;
after this, the rabbit remained on the side, and convulsion succeeded convulsion
until its death, nineteen minutes after the administration of thebaia. Azgor mortis,
with an acid reaction of the muscles, was completely established at thirty-seven
minutes after death.
Sulphate of methyl-thebaium ((C,,H,,NO,CH,),SO,, dried at 100° C.), was pre-
pared by precipitating an aqueous solution of the iodide by means of sulphate
of silver. It forms a white, indistinctly crystalline mass. It dissolves readily in
water, and gives, with sulphuric acid, the reaction of thebaia.
We found it to be a less active substance than the corresponding derivative of
either strychnia or brucia, as doses of four and of four-and-a-half grains were
not fatal, though they produced symptoms, when injected into the subcutaneous
cellular tissue of rabbits. Five grains appears to be about the smallest quantity
that can produce death when administered to rabbits in this manner. The expe-
riments in which four and a-half and five grains were given are sufficient to illus-
trate the general physiological effects of this substance.
EXPERIMENT LXXVII.—We dissolved four and a-half grains of sulphate of
methyl-thebaium in fifteen minims of distilled water, and injected this solution
into the subcutaneous tissue at the flank of a rabbit, weighing three pounds and
eleven ounces and a-half. In seventeen minutes, the rabbit had some difficulty
in jumping about, for it occasionally stumbled, and rested for a few seconds on
the chest. In twenty-one minutes, it was lying on the abdomen, with the lower
jaw resting on the table; and, occasionally, a series of shivering tremors took
place in the muscles of the back. In thirty minutes, it remained on the side,
when so placed, and was perfectly flaccid. The respirations were at the rate of
sixty per minute. In forty-one minutes, the respirations had diminished in
frequency to forty per minute, and during inspiration the abdominal muscles
contracted in a tremulous manner. In fifty-five minutes, the respirations
had increased in number to seventy-one per minute, and in one hour and
thirty minutes, they appeared to have regained their normal rapidity; but it
was impossible to ascertain this definitely, on account of frequent interrup-
tions by tremulous movements of the abdominal muscles. The rabbit was
still lying on the side in a perfectly flaccid state. In one hour and thirty-two
minutes, however, it suddenly raised the head, rose, and assumed a normal
posture ; but the trembling continued. This trembling, very faint and not at
174 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
all spasmodic, was the last symptom to disappear, which it did about two hours
and thirty minutes after the injection of the poison. We frequently tested the
condition of the reflex activity, and did not find it increased at any period
during the experiment.
Experiment LX XVIII. —Five grains of sulphate of methyl-thebaium was dis-
solved in thirty minims of distilled water, and injected under the skin of a rabbit,
weighing four pounds and half an ounce. Its effects began to be seen in thirteen
minutes, when, after a few restless movements, the rabbit subsided on the abdo-
men and chest. Complete flaccidity soon after occurred; and the respirations be-
came shallow and gasping, and they diminished in frequency until, at twenty-five
minutes after the injection, they were only at the rate of twenty-three per minute.
Occasional, very weak, tremulous movements occurred at this time. In thirty-five
minutes, severe pinching of the skin caused only a feeble reflex movement, while
the contraction of the eyelids, after irritation of the eyeball, was almost imper-
ceptible. ‘The rabbit appeared still to retain consciousness. In fifty minutes, no
movement followed severe pinching of the skin, or irritation of the eyeball, and
the respirations were gasping and infrequent. In fifty minutes, a few twitches
occurred in the muscles of the face, and either immediately before or during
these the rabbit expired.
In the autopsy, which was immediately performed, the heart was seen con-
tracting at the rate of seventy-eight per minute, and the intestinal peristalsis
seemed normal. Four and a-half minutes after death, neither a weak nora
powerful galvanic current could excite any muscular contraction when applied
to the trunk of a sciatic nerve; but idio-muscular irritability was not lost for
many minutes after this. At two hours and thirty minutes after death, the rabbit
was still perfectly flaccid, and there was not the slightest appearance of muscular
rigidity.
We have not observed any symptoms follow the internal administration 0
this substance, as no effect was produced when we introduced twenty grains, dis-
solved in warm water, into the stomach of arabbit. It has been shown by Experi-
ment LXXIV. that four grains of thebaia is a fatal dose when thus exhibited.
The experiments we have narrated contain the most satisfactory proof that the
chemical addition of iodide and sulphate of methyl has produced a complete
change in the physiological action of thebaia. The nature of the change appears
to be identical with that we have described as occurring under similar circum-
stances in strychnia and brucia. Thebaia acts in the same way as these alkaloids;
for it causes increase of the reflex activity, convulsions, and tetanus by an action
on the spinal cord. The action of iodide and sulphate of methyl-thebaium is strik-
ingly different; for they diminish reflex excitability, and produce a condition of
paralysis in which death occurs by asphyxia. This paralysis, as we have seen, is
dependent on an effect on the spinal nerve system.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 175
We will now describe an experiment in which we endeavoured to determine
what portion of this system is affected.
ExpPERIMENT LX XIX.—The sciatic artery and the two principal veins were
tied in the right thigh of a frog, weighing 420 grains, and one-fifth of a grain of
sulphate of methyl-thebaium, dissolved in seven minims of distilled water, was
injected into the abdominal cavity. In six minutes, the animal was flaccid and
motionless, and in other four minutes the respiratory movements of the chest
and abdomen had ceased, while those of the throat continued, and did so for
several minutes longer. In sixteen minutes, galvanic stimulation by an inter-
rupted current, applied to any portion of the skin, caused movements of the right
leg below the points of ligature, but nowhere else. In twenty-one minutes, the
left sciatic nerve was exposed, and on galvanising it, energetic movements
occurred in the right leg, while the left leg and every other part of the body
remained motionless. The heart was now contracting at the rate of thirty-six
beats in the minute. The muscles that had been laid bare in the left leg, by the
dissection necessary for the exposure of the left sciatic nerve, were stimulated by
the direct application of an interrupted galvanic current, and they contracted
powerfully. This condition continued during other two days; on the second
day, even a feeble stimulus applied to the left sciatic nerve was followed by well-
marked contractions of the right leg, below the points of ligature; while it caused
no movements in those parts of the frog that had been directly acted upon by the
poison, although the muscles everywhere contracted when directly stimulated.
We learn from this experiment that sulphate of methyl-thebaium produces
paralysis by destroying the conductivity of the motor nerves, and not by inter-
fering with the function of the spinal cord, or of the sensory (afferent) nerves.
The next experiment was made with.the view to determine what portion of the
motor nerve is paralysed by this substance.
EXPERIMENT LXXX.—The left gastrocnemius muscle was exposed in the
leg of a frog, weighing 604 grains. The blood-vessels that entered it were
ligatured or twisted, and it was carefully separated from all its connections,
excepting that its origin and insertion were untouched, and that the nerve fibres
that entered it were not divided. Immediately after this somewhat tedious
preparation, one-fifth of a grain of sulphate of methyl-thebaium, dissolved in ten
minims of distilled water, was injected in the abdomen. Omitting the details
of the effects that ensued, it is sufficient to mention that, at thirty minutes
after this injection, the sciatic nerve was exposed in each thigh and galvanised,
with the result that in the case of the right nerve movements followed in the left
leg alone, and in the case of the left nerve movements followed in the left
leg, and there only. It was seen that these movements in the left leg were
entirely caused by contractions of the left gastrocnemius muscle, that is, of the
muscle which had been protected from the direct influence of the poison.
VOL. XXV. PART I. ZN,
176 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
We obtained the same results on repeating these experiments with half-grain
doses of iodide of methyl-thebaium.
These experiments demonstrate clearly that the methyl derivatives of thebaia
produce their principal physiological effects by impairing and destroying the
function of the peripheral termination of the motor nerves—an action that is very
different from that:of thebaia itself. They also differ from thebaia in being con-
siderably less potent as poisons. Several of these characters are summarised in
the appended table.
No. of Substance Animal and its Method of
Experiment. employed. weight. exhibition. Diese Effect.
LXII. | Iodideof methyl-| Rabbit, 2 Ibs. 120z.) Subeutaneously. | 8 grs. (contain-| Paralysis in 45 minutes,
thebaium. ing 5°5 grs. of| continuing for about 30
thebaia). minutes, and followed by
recovery.
LXVI. | Thebaia. Do. (same rabbit | Subcutaneously, | 02 gr. Tetanus in 52 minutes,
as in Experiment and death in 54 minutes.
LXIL)
LXXI. | Iodide of methyl-| Do., 4 lbs. 6 oz. | By stomach. 30 grs. (contain-| No effect.
thebaium. ing 20°6 grs.
of thebaia),
LXXIV. | Thebaia. Do. (same rabbit! By stomach. 4 ors. Tetanus in 6 minutes, and
asin Exp. LXXI.)| death in 19 minutes.
LXXVII, | Sulphate of me-| Do., 3 lbs. 11} 0z. | Subeutaneously. | 4*5grs.(contain-| Paralysis in 21 minutes,
thyl-thebaium. ing 3°7 grs. of| continuing for 2 hours
thebaia). and 9 minutes, and fol-
lowed by recovery.
LXXXI. | Sulphate of me-|Do., 4 Ibs,40z. | By stomach. 20 ers. (contain-| No effect.
thyl-thebaium. ing 16°6 grs.
of thebaia).
CODEIA (C,,H,,NO, + H,0).
We have examined the effect of the addition of iodide and sulphate of
methyl to codeia—an opium alkaloid, which, according to CLAUDE BERNARD, is
the second in toxic activity, and possesses distinct convulsant but feeble soporific
properties.*
Lodide of methyl-codeium.—How } obtained by the action of iodide of ethyl on
codeia, iodide of ethyl-codeium, and from it a number of ethyl-codeium com-
pounds, and proved that codeia is a nitrile base. As was to be expected, iodide
of methyl acts even more readily on codeia.{ It is only necessary to heat codeia
with a little alcohol and an excess of iodide of methyl to 100°C. for an hour, in
a sealed tube, to complete the reaction. The excess of iodide of methyl is distilled
off, the alcohol evaporated, and the product crystallised from hot water. It
* Comptes Rendus, vol, lix. (1864) p. 418.
+ Chemical Society’s Quarterly Journal, vol. vi. (18538) p. 134.
{ We shall give details of the chemical relations of the methyl derivatives of codeia on some
other occasion,
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. ar
forms large transparent prisms, soluble in 14:5 parts of water at 37°C., and in
49 parts of water at 9°C. Its solution is not precipitated by caustic potash, and
in all respects, except in the appearance of its crystals, agrees with iodide of
ethyl-codeium.
As iodide of methyl-codeium is tolerably soluble in warm water, we could
administer it by subcutaneous injection in the form of solution. It was found, in
rabbits, that a dose of five grains was quite inert, that one of fifteen grains caused
prolonged and serious symptoms which were recovered from, and that one of
twenty grains produced death in a short time. The following details include
the principal symptoms that appeared when fifteen and twenty grains were thus
administered.
Exprrtmment LXXXIV.—Fifteen grains of iodide of methyl-codeium was
dissolved in some warm distilled water, to which a few drops of rectified spirit
had been added, and the solution was injected into the subcutaneous cellular
tissue of a rabbit, weighing two pounds and fourteen ounces. The rabbit remained
sitting quietly until twenty-two minutes afterwards, but in a few seconds more it
had some difficulty in retaining a sitting posture, and, on standing, the fore-limbs
occasionally yielded, until, at twenty-five minutes, it subsided on the abdomen,
chest, and lower jaw. In thirty minutes, it remained on the side without strug-
-gling; and now, after considerable intervals, faint twitches occurred in the body
and limbs, which, however, had no convulsive character. In thirty-seven minutes,
irritation of the cornea or conjunctiva did not cause any movement in the eyelids,
but the respirations, though weak, shallow, and somewhat jerking, were at the
rate of sixty-seven in the minute. In forty-five minutes, the frequency of the re-
spirations had diminished to sixty in the minute, and there were now no twitches.
The rabbit continued to lie in this flaccid state for about two hours longer ;
at the end of which time, twitches reappeared, at first extremely faint, but,
by-and-by, of considerable strength, and involving the muscles of the abdomen,
chest, neck, and limbs. In four hours and twenty minutes, the rabbit was again
in a perfectly quiet state, the twitches had disappeared, and the common
sensibility was in a normally active condition. Frequent attempts were made,
soon after, to recover a natural position, and success was at Jength attained, four
hours and twenty-five minutes after the injection of the poison. There were no
further symptoms.
EXPERIMENT LXXXV.—We injected twenty grains of iodide of methyl-codeium,
dissolved as in the preceding experiment, into the subcutaneous cellular tissue of
a rabbit, weighing two pounds and twelve ounces and a-half. The animal
began to tremble in thirteen minutes, and the head, after being unsteadily sup-
ported for a short time, fell on the table. In fifteen minutes, the rabbit remained
on the side; the respirations were weak and irregular, and slight starts
occurred occasionally. Severe irritation of the skin was now required to cause
178 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
even an extremely feeble reflex movement. In twenty-four minutes, no move-
ment followed irritation of either the skin or eyeball, and the respirations were
mere gasping jerks. In thirty-two minutes, a series of feeble twitches occurred
in the face-muscles, and then the respirations entirely ceased.
We immediately exposed the sciatic nerves, and examined their condition :
when they were stimulated with galvanism, slight movements followed in the
hind limbs at one minute after death; but no movement could be excited at
one minute and thirty seconds. The heart was found to be contracting in
regular rhythm, at the rate of eighty-two in the minute. Forty-five minutes
after death, the body was perfectly flaccid, and there was not the slightest ap-
pearance of muscular rigidity.
We may best display the marked differences between these physiological
effects and those that are caused by codeia, by describing an experiment in which
the rabbit that survived the administration of fifteen grains of iodide of methyl-
codeium, was quickly killed by the subcutaneous injection of one grain of codeia.
EXPERIMENT LXXXIX.—We dissolved one grain of codeia in some warm
distilled water, to which a few drops of rectified spirit had been added, and in-
jected the solution into the subcutaneous tissue of the rabbit, which was some
days previously the subject of Experiment LXXXIV. In fifteen minutes, faint
twitches occurred in some of the muscles of the back ; and, soon after, a slight touch
excited a violent start. Spontaneous spasmodic starts now followed each other,
until one hour and eleven minutes, when a violent tetanic convulsion of an opis-
thotonic character occurred. For some time before this, it was observed that
the hind limbs trailed slightly when movements were attempted, indicating,
apparently, a slight degree of motor paralysis. The first tetanic convulsion was
followed by trismus, which lasted for a few seconds, and by a succession of slight
spasms; and soon after its occurrence, unsuccessful efforts were made to recover
a normal position. In one hour and thirty minutes, a second violent tetanic con-
vulsion took place, and this presented the character of emprosthotonos rather
than of opisthotonos. Such convulsions now recurred after intervals of a few
minutes, and at the termination of one of them, one hour and forty-five minutes
after the administration of the poison, the rabbit died. In fifteen minutes after
death, strong 7gor mortis was present.
We introduced iodide of methyl-codeium into the stomach of rabbits on two
occasions. In one of these, fifteen grains were thus administered, and in the other,
thirty grains; but no effect was produced by either dose. Codeia itself, how-
ever, is by no means a violent poison when given to rabbits in this manner. We
made a considerable number of experiments, but did not succeed in causing death
even with fifteen grains. In the following experiment we employed ten grains.
EXPERIMENT XCIV.—By means of a gum-elastic catheter, we injected ten
grains of codeia, dissolved in warm distilled water to which a few drops of |
PHYSICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 179
dilute hydrochloric acid had been added, into the stomach of a rabbit, weighing
three pounds and thirteen ounces. In twenty-four minutes, some symptoms
of sleepiness were observed, which chiefly manifested themselves by nodding
movements of the head. In thirty-nine minutes, the reflex excitability seemed
increased, as a slight touch caused a sudden, somewhat spasmodic start. In one
hour, the sleepy condition had so far increased, that the head rested on the table,
and the eyelids were semi-closed. In one hour and twenty minutes, the rabbit
could be placed in almost any position, provided physical rest were allowed; and
it would remain sleeping in these attitudes until roused by sounds or by pretty
violent irritations. It continued in this condition for more than two hours; but
in three hours, the sleepiness was less marked, and on the following morning
the rabbit was in a perfectly natural state.
Sulphate of methyl-codeitum was prepared from the iodide, by precipitating it
by means of sulphate of silver. It forms a white crystalline mass, readily soluble
in cold water.
It is ‘a rather more active poison than the iodide, for we found that ten grains,
exhibited subcutaneously, was sufficient to kill a rabbit. We observed only
slight symptoms with eight grains.
EXPERIMENT XCVI.—Eight grains of sulphate of methyl-codeium was dissolved
in twenty minims of distilled water, and injected under the skin of a rabbit,
weighing four pounds. No distinct effect was observed until thirty minutes,
when some uneasiness was shown by restless movements of the limbs; and, soon
after, a little trembling occurred. Weakness of the limbs was then exhibited by
occasional stumbles, and, in thirty-three minutes, the rabbit fell, and remained rest-
ing on the abdomen, with the lower jaw on the table. There were no starts nor
spasms, and even the trembling had now ceased; while severe irritation of the ©
skin caused merely slight reflex movements. After remaining in this state for
twenty minutes, the symptoms gradually improved, and the rabbit appeared to
be quite well two hours after it had received the poison.
EXPERIMENT XCVII.—Ten grains of the sulphate of methyl-codeium was dis-
solved in distilled water, and injected under the skin of a rabbit, weighing four
pounds and four ounces. In twenty-three minutes, the head and portions of the
body shook in a quivering manner ; and, gradually, the head sank until it rested
on the table. In twenty-five minutes, the legs gave way, and the animal fell;
faint twitches occurred over the body, but otherwise the condition was one of
complete flaccidity. In thirty-five minutes, it remained on the side, without any
resistance. In thirty-eight minutes, the respirations were laboured, and at the
rate of thirty-six per minute; and in other four minutes, they had fallen to twenty
per minute. In forty-one minutes, these movements were extremely shallow and
irregular; and in forty-two minutes, they altogether ceased. In the course of this
experiment, no convulsive symptoms occurred, and no hypnotism was observed.
VOL. XXV. PART I. 22
180 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
In the autopsy, the heart was seen acting, one minute after death, at the rate :
of 160 beats per minute, and the intestinal peristalsis was found to be normal. __
The motor conductivity of the sciatic nerves was retained at three minutes after
death, but it had disappeared in other four minutes; while the idio-muscular
irritability was not lost until more than sixty minutes after death. |
For internal administration, we followed the plan already described. No |
symptom whatever was observed when the large dose of twenty grains was ~
introduced into the stomach of a rabbit. We did not, accordingly, consider it
advisable to continue this method of administration any further. .
As we have already stated, and as the experiments we have narrated clearly _
show, the principal effects that are caused by codeia are convulsions and hypno- :
tism. In our experiments with rabbits, the latter effect was manifested only when
large doses were introduced into the stomach. It was not seen when this alkaloid
was administered by subcutaneous injection, probably because sleep was then
prevented by the spasmodic starts and convulsions that were so prominently
caused. We learn from our experiments that the iodide and sulphate of methyl-
codeium have a very different action from codeia. We have never observed any
hypnotic effect follow their administration, and, in place of convulsions, we have
seen that they produce paralysis. This, indeed, is the only marked symptom that
follows their administration, and it is apparent that it does not depend on an
effect on the muscles, nor on the cerebral lobes. We endeavoured to determine
the exact cause of this paralysis by experiments with localised poisoning on frogs.
EXPERIMENT XCVIII.—Having tied the right sciatic artery and vein of a
frog, weighing 722 grains, one grain of sulphate of methyl-codeium, dissolved in
distilled water, was injected into the abdominal cavity. In fifteen minutes,
voluntary movements had disappeared, and the frog was lying on the abdomen,
in a flaccid state. In thirty minutes, pinching of the skin with a pair of
forceps excited movements in all the limbs, but these were most energetic in
the right posterior extremity. In one hour and thirty minutes, similar stimula-
tion excited no movement except in the right posterior extremity (where the
vessels had been tied). The application of an interrupted galvanic current to the
exposed trunk of the. left sciatic nerve was now followed by active movements
of the right leg, but of no other part; while, at the same time, the muscles in the
poisoned regions freely responded to galvanic stimulation directly applied to them.
In two hours and forty minutes, the condition was the same, and, judging from
the cardiac impulse, the heart was contracting at the rate of thirty-five per minute.
We need not again enter into the reasons for concluding from such an experi-
ment that the paralysis caused by sulphate of methyl-codeium is due to an action
on the motor nerves. As has been already done with the corresponding sub-
stances treated of in the previous portion of this paper, we, in the next place, —
determined what portion of the motor nerve—trunk or periphery—is acted on.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 181
EXPERIMENT XCIX.—In a frog, weighing 694 grains, the left gastrocnemius
muscle was prepared in the manner described in Experiments XXIX., LVIL,
and LXXX., and one grain of sulphate of methyl-codeium, dissolved in distilled
water, was injected into the abdomen by means of a Woop’s syringe. In one
hour after this, a condition of flaccidity being present, the trunks of the two sciatic
nerves were exposed, and stimulated with an interrupted galvanic current. When
the right nerve was thus treated, some contractions followed in the left leg, and
nowhere else; and when the left nerve was thus treated, vigorous contractions
followed in the left leg; and it was observed that the movements of the left leg
were caused by contractions restricted to its gastrocnemius muscle, that is, the
muscle to which the poison had no direct access. At this time, the muscles in
all parts of the body contracted freely when the poles of the battery were applied
to their surfaces, and continued to do so for many hours longer.
We repeated these last experiments with iodide of methyl-codeium, and
obtained the same general results.
We have, therefore, demonstrated that iodide and sulphate of methyl-codeium
produce paralysis, by destroying the function of the peripheral terminations (end-
organs) of the motor nerves—a mode of action that distinguishes them, as
physiological agents, in a most striking manner from codeia. It will also be seen
from the following table, that the poisonous (toxic) activity of the codeia in these
methyl-compounds is considerably diminished.
No. of Substance Animal and its Method of
Experiment. employed. weight. exhibition. Dove: paba
LXXXIV. Iodide of metnyl-) Rabbit, 21bs, 140z.) Subeutaneously.| 15 grs. (contain-| Paralysis in 25 minutes.
codeium. ing 10-2 grs.of| continuing for about 3
dry codeia). hours, and followed by
recovery.
LXXXIX.| Codeia (crystal-| Do. (same rabbit as| Subcutaneously.|1 gr. (contain-| Spontaneous twitches in
lised). in Ex. LXXXIYV.) ing 0:94 gr.| 15 minutes, tetanus in
of dry codeia).| 1 hour and 11 minutes,
and death in 1 hour and
45 minutes.
XCI. |Lodide of methyl-| Do., 2 lbs. 13 oz. | By stomach. 30 gers. (contain-| No effect.
codeium. ing 20°3 grs. of
dry codeia).
XCIV. | Codeia (crystal-| Do. (same rabbit as| By stomach. 10 grs. (contain-| Sleepiness in 24 minutes,
lised), in Ex. XCL.) ing 9°4 gers. of} increase of reflex exci-
dry codeia), tability in 39 minutes,
and followed by recovery
in more than 3 hours.
XCVI. | Sulphate of me-| Do., 4 lbs, Subcutaneously.|8 grs. (contain-| Paralysis in 33 minutes,
thyl-codeium. ing 6°6 gers. of| continuing for more than
dry codeia). 20 minutes, and followed
by recovery.
C. Sulphate of me-|Do., 41bs.130z. | By stomach. 20 grs. (contain-| No effect.
thyl-codeium. ing 16°5 grs. of
dry codeia).
182 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
- MORPHIA.
The most recent and trustworthy investigations show that, among the opium
alkaloids, morphia (C,,H,,NO,+H,O) is next in activity as a soporific to narceia,
that it possesses a less convulsant action than codeia, and that its fatal dose is
one of the largest of those of the active principles of opium. *
Lodide of methyl-morphium (C,,H,,NO,CH,1)—How subjected morphia to
the action of iodide of ethyl and of iodide of methyl, prepared and described a
number of the ethyl-morphium and methyl-morphium compounds, and proved
that morphia is a nitrile base.t We prepared the iodide of methyl-morphium by
How’s method, viz., by treating morphia with alcohol and an excess of iodide of
methyl in a sealed tube, at 100° C., for an hour, distilling off the excess of iodide
of methyl, and recrystallising from hot water.
It forms long, transparent, prismatic needles; and dissolves in 34 parts of
water at 37° C., and in 88°5 parts of water at 9° C.
As it is well known that comparatively large doses of morphia are required
to produce any symptom in such animals as rabbits, we at once commenced the
administration of iodide of methyl-morphium in very large doses. We were
unable to produce any effect whatever when so large a dose as twenty grains was —
injected under the skin of a small rabbit; and, as this could only be adminis-
tered as a fine powder, suspended in warm distilled water, it was extremely
inconvenient to give any larger quantity in a form necessarily so bulky. Eight
grains of morphia was afterwards exhibited, in the same way, to this rabbit, and
it caused the usual symptoms and death. It may be interesting and satisfactory
to give some details of these two experiments.
EXxPEerRtMENT CI.—Twenty grains of iodide of methyl-morphium was reduced
to a fine powder, mixed with two drachms of warm distilled water, and injected
into two previously formed subcutaneous cavities at the flanks of a rabbit, weigh-
ing two pounds and fourteen ounces. The rabbit was carefully observed for four
hours, but no symptom occurred during this time. It was perfectly well on the
following morning.
ExPERIMENT CV.—Eight grains of morphia, suspended in warm distilled water,
was introduced into the subcutaneous cellular tissue of the rabbit that had been
employed,two days previously, in Experiment CI. In one hour and four minutes, an
inclination to sleep was observed, the eyelids closed, and the head sank on the table,
but a slight sound immediately roused the rabbit. In two hours, the soporific
effect was more marked; and the animal remained in almost any position in
which it could be placed, provided the change was made gradually and gently;
* Craupe Bernarp, Comptes Rendus, vol. lix. 1864, p, 413.
+ Chemical Society’s Quarterly Journal, vol. vi, (1853) p. 126.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 183
and, however unnatural the position might seem to be, if it were consistent with
rest, sleep immediately occurred. In three hours, there was some difficulty in
rousing it, and when this was done, it remained awake for afew seconds only. In
six hours, the respirations had fallen to the slow rate of twenty-six in the minute.
This condition lasted, altogether, for about forty-eight hours, when spasms made
their appearance, which, by-and-by, assumed all the characters of epileptiform
convulsions. These epileptic fits frequently recurred, and could be excited, at any
time, by pinching the skin. They consisted of tonic spasms of the limbs and of
the abdominal muscles, followed by twisting of the head to the right, grinding
movements of the lower jaw, and violent opisthotonos. The rabbit was found
dead on the morning of the third day after the administration.
The two subcutaneous cavities into which the morphia had been introduced
were laid open, and a small quantity of unabsorbed morphia was found in both.
The cavities into which iodide of methyl-morphium had been introduced were
also laid open, but none of this substance was found.
We were unsuccessful in producing any symptoms by the internal administra-
tion of iodide of methyl-morphium. Thirty grains was found to be perfectly
inert when exhibited by the stomach, while the same rabbit was decidedly
narcotised with five grains of morphia similarly exhibited. It is interesting, for
the purpose of comparison, to give a short account of these two Experiments.
EXPERIMENT CVI.—We suspended thirty grains of finely-powdered iodide of
methyl-morphium in distilled water, and injected the mixture into the stomach
of a rabbit, weighing three pounds and twelve ounces. It was observed for more
than two hours, but no symptoms could be detected.
EXPERIMENT CVII.— We suspended five grains of finely-powdered morphia in
distilled water, and injected the mixture into the stomach of the rabbit that was
used, two days previously, in Experiment CVI. In one hour and six minutes,
the rabbit was observed to be sleepy, and it soon after laid its head on the table.
This sleepy condition became gradually more marked: in one hour and twenty-
five minutes, the rabbit could be placed in almost any position, and slept thus ;
while about the same time, a condition resembling that of catalepsy was present,
for when we placed the rabbit on the back and raised the fore legs perpendicu-
larly upwards, it remained in this extraordinary attitude for several minutes. In
two hours and forty-one minutes, it was observed that the pupils, which
were small, did not contract on the approach of a bright light, nor did this
stimulus excite any movement of the body; but the common sensibility was not
lost. The condition of cataleptic-like hypnotism lasted, altogether, about three
hours and twenty minutes. Soon after this, some voluntary movements were
made, and the rabbit gradually recovered to a perfectly normal state.
Any conclusion drawn from experiments on such animals as rabbits, with a
substance whose predominating action is a soporific one, are always liable to
VOL. XXV. PART I. OA
184 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
objection. For this reason, we were induced to try the effect of iodide of methyl-
morphium on man. One of us,* who is perfectly susceptible to the action of
morphia, took on one occasion, half a grain of iodide of methyl-morphium, in the
form of powder; but this produced no effect. On another occasion, one grain
was taken, also as a powder; but not the slightest soporific or other action was
caused. The latter dose contained about three-fourths of a grain of morphia, and
this is certainly much above the usual narcotic dose of this substance.
It is important to mention, that although we have failed in causing any
symptoms in warm-blooded animals with this substance, we have found that it
acts with considerable energy on frogs. The nature of this action will be explained
in the description of the effects of sulphate of methyl-morphium.
Sulphate of methyl-morphium ((C,,H,,NO,CH,),SO,), was prepared by pre-
cipitating a solution of the iodide by means of sulphate of silver. It forms a
white crystalline mass, very soluble in water. It gives the ordinary blue colour-
reaction of morphia with persalts of iron.
This salt of methyl-morphium is much more active than the iodide. By
subcutaneous injection, doses of two, three, four, five and eight grains caused
marked symptoms; while a dose of ten grains was sufficient to kill a large
rabbit. The effects of eight and of ten grains are described in the two following
Experiments.
EXPERIMENT CXII.—Eight grains of sulphate of methyl-morphium, dissolved
in distilled water, was injected under the skin, over the two flanks of a rabbit,
weighing three pounds and one ounce. In twelve minutes, it appeared to be
rather sleepy, and disinclined to move. In fourteen minutes, the head fell on
the table, and the animal remained in this position, without any movements,
except those that were necessary for respiration. In twenty-five minutes, the
hypnotism was extremely well-marked; it was possible to place the animal in
any position, and if this were compatible with stability, sound sleep occurred.
A considerable stimulus was now required before the rabbit could be roused from _
sleep. In two hours and twenty minutes, this condition still continued, but the —
observations were now discontinued. On the following morning, the rabbit
appeared to be perfectly well. No convulsive symptoms nor exaggeration of
reflex activity was observed in this Experiment.
EXPERIMENT CXIII.—We dissolved ten grains of sulphate of methyl-morphium
in 200 minims of distilled water,and injected the solution under the skin of a
rabbit, weighing three pounds and eight ounces. In seven minutes, difficulty in
moving about was observed; and, in rapid succession, some stumbles occurred,
the limbs yielded, and the animal lay in a state of flaccidity, on the abdomen,
chest, and lower jaw. It could now be placed without any resistance in almost
* Dr FRASER.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 185
any position. In twenty-four minutes, the respirations were very feeble and
shallow, and at the rate of twenty-four in the minute; the rabbit was perfectly
quiet and flaccid; and severe pinching of the skin excited only feeble refiex
movements. There was not the slightest appearance of muscular rigidity, nor of
starts, spasms, or even quivering movements. In forty-seven minutes, the respir-
ations were extremely weak and jerky, and at the rate of ten per minute, while
the sensibility of the conjunctiva and cornea had greatly diminished. In fifty-six
minutes, the respirations occurred only eight times in the minute, and no move-
ment of the eyelids could be excited by irritating the conjunctiva or cornea.
Exophthalmos was now markedly present. Death occurred in one hour and two
minutes after the administration of the poison.
In the autopsy, the heart was found to be distended, and acting irregularly
and slowly. There was no appearance of 77gor two hours after death.
When administered by the stomach, twenty grains of sulphate of methyl-
morphium produced no effect on a rabbit.
Our experiments with morphia confirmed the observations made by others,
which show that this alkaloid has two prominent actions on rabbits—a convul-
sant and ahypnotic one. We shall now consider how far each of these is modified
by the addition of sulphate of methyl to morphia. The addition of iodide of
methyl appears, no doubt, to have produced a very important change, but as
‘this is rather in the direction of diminishing, or, as our experiments indicate,
altogether destroying, the physiological activity of morphia, the iodide of methy]-
morphium may, in the mean time, be removed from consideration.
It has been proved, in a most satisfactory manner, that sulphate of methy!-
morphium possesses no convulsant action; for neither in the experiments we
have described in detail, nor in any of the others we performed with this substance,
was there any trace of spasmodic action or of exaggeration of the reflex function.
It, however, undoubtedly causes hypnotic symptoms. In small non-fatal doses,
hypnotism was chiefly manifested, and this rendered it somewhat difficult to
judge whether paralysis were present or not. In large non-fatal doses, and in
fatal doses, on the other hand, paralysis appeared to be the chief effect, though
hypnotism was also present. It would, therefore, seem that sulphate of methy]-
morphium agrees with morphia in possessing a hypnotic action, but differs from
it in producing paralysis, and in being free from all convulsant action. It is
obvious that an objection might be urged against the latter part of this statement ;
for both the absence of convulsions and the production of paralysis might be
merely the effects of hypnotism. Though we were ourselves convinced, from
our experiments on rabbits, that such is not the case, we made some experiments
on frogs to determine this more clearly.
EXPERIMENTS CXV. and CXX.—The blood-vessels were tied in one limb near
the knee of two frogs, selected because of their resemblance to each other in weight
186 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
and in activity. One grain of sulphate of methyl-morphium, in solution, was
injected into the abdominal cavity of one of these frogs (a), and three-fourths of
a grain of morphia, dissolved in very dilute sulphuric acid, into the abdominal
cavity of the other (0).
(a). Frog with Sulphate of Methyl-morphium. (b). Frog with Sulphate of Morphia.
In eight minutes, the limbs yielded, and the frog | In sixteen minutes, some slight sprawling occur-
subsided on the abdomen and chest. red, before which the frog was jumping about
In twenty minutes, it was perfectly flaccid, and vigorously.
the respirations had entirely ceased. Pinching | In fifty minutes, pinching of the skin occasioned
of any portion of the’ skin excited energetic a series of clonic spasms, in which both poste-
movements of the leg whose vessels were tied, rior extremities were forcibly and slowly ex-
and feeble movements in various other parts. tended and then withdrawn, somewhat regu-
In thirty minutes, the two sciatic nerves were larly, during three or four minutes, about four
exposed; galvanism applied to their trunks times in the minute. The movements then
caused contractions of the tied limb, below the | _ ceased, but they could be again excited.
ligatures, and nowhere else. The heart was | In one hour, there was marked increase of the
now acting at the rate of forty-two in the reflex excitability, a slight touch causing a
minute, and the idio-muscular irritability was spasmodic start.
normal everywhere. In one hour and thirty-eight minutes, a slight
In twenty-four hours, the frog was still perfectly touch of the skin excited a short tetanic con-
flaccid, the heart was contracting at the rate vulsion.
of thirty per minute, and the muscles of the | In two hours, the same condition existed, and a
poisoned and non-poisoned regions contracted tetanic convulsion could be at any time excited
when directly galvanised. Galvanism of the by aslight touch. During these convulsions,
sciatic nerve of the poisoned leg, however, pro- the muscles in the non-poisoned limb were
duced no movement; but galvanism of the contracted as forcibly as those in the poisoned
sciatic nerve of the non-poisoned leg, even regions,
when applied to a part where the poison had | In twenty-four hours, the frog was found dead,
access, still caused vigorous movements below with all its muscles rigid.
the ligatures,
These experiments prove distinctly that sulphate of methyl-morphium does
not possess, in any degree, the convulsant action of morphia, but that it causes
paralysis in place of convulsions. They also prove that this paralysis is due
to an effect on the motor nerves. We have further determined, by the same
method of experiment as has been already frequently described, that the
peripheral terminations are the parts of the motor nerves which are primarily
affected.
Iodide of methyl-morphium produces the same effects on frogs as sulphate,
only a larger dose is required.
The poisonous activity of sulphate of methyl-morphium does not appear to be
very different from that of a salt of morphia; for we have seen that for rabbits
ten grains is about the minimum fatal dose of the former by subcutaneous
injection, and this contains about eight grains of morphia, which is little above
the fatal dose when subcutaneously exhibited. We have placed these and several
other results, in a form convenient for comparison, in the following table.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 187
No. of Substance Animal and its Method of
apne Dose. Effect.
Experiment. employed. weight. exhibition.
CI. Iodide of methy1-| Rabbit, 2 lbs. 140z.| Subcutaneously. | 20ers. (contain-| No effect.
morphium. ing 133 grs. of
dry morphia),
CY. Morphia. Do. (same rabbit | Subcutaneously. | 8 grs. (contain- | Sleep in 1 hour and 4
as in Experiment ing 7‘Sgrs. of| minutes, epileptic con-
CI.) dry morphia).| vulsions in about 48
hours, and death some
hours afterwards.
CVI. Iodide of methyl-| Do., 3 1bs. 12 0z. | By stomach. 30ers. (contain- | No effect.
morphium. ing 20 grs. of
dry morphia).
CVII. | Morphia. Do. (same rabbit| By stomach. 5 ers. (contain-| Sleep in 1 hour and 6
as in Experiment ing 4°7 grs. of| minutes, and catalepsy
CVI.) dry morphia).| inlhourand 25minutes;
thesesymptoms lasted for
nearly 3 hours and 30
minutes, and were fol-
lowed by recovery.
CXII. | Sulphate of me-|Do.,3 Ibs. 1 oz. | Subeutaneously. | 8 grs. (contain- | Sleep and partial paralysis
thyl-morphium. ing 6°6 grs. of| in 14 minutes, continu-
dry morphia).| ing for more than 2
hours and 16 minutes,
and followed by recovery.
CXIII. | Sulphate of me-| Do., 3 lbs. 8 oz. | Subeutaneously. | 10 grs. (contain-| Paralysisin 8 minutes, and
thy-morphium. ing 8:2 grs. of| doubtful sleepiness in 10
dry morphia), | minutes; the paralysis
became gradually more
complete, andterminated
in death, at 1 hour and 2
minutes after the admini-
stration of the poison.
CXXI. |Sulphate of me- | Do., 4 lbs. 33 oz. | By stomach. 20 grs. (contain-| No effect.
thyl-morphium. ing 16:4 grs. of
dry morphia).
NICOTIA.
The last substance in which we have now to describe the modifications pro-
duced by chemical addition is nicotia. This is a liquid alkaloid of great poisonous
energy, derived from tobacco. It is a di-acid nitrile base, and has the formula
(C,H, ,N,).
Lodide of methyl-nicotiwm.—Von PLANTA and KEKkvuii* investigated the action
of iodide of ethyl on nicotia, and described a number of the ethyl-nicotium salts.
The compounds of methyl-nicotium were investigated and described by STaHL-
scHMIpT.t When excess of iodide of methyl is added to nicotia, a considerable
amount of heat is developed, and it is advisable to immerse the flask in which
the mixture is made in cold water, in order to moderate the action; by this
means the product (iodide of methyl-nicotium (C,,H,,N,(CH,D),) is obtained
nearly colourless, and crystallises almost as soon as it is cold. The crystalline
* Annalen der Chemie und Pharmacie, vol. Ixxxvii, p. 1 (1858).
+ Ibid. vol. xe. p. 222 (1854).
VOL. XXV. PART I. 3B
188 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
powder is washed with a little cold alcohol, and crystallised from hot rectified
spirit. Thus obtained, it forms tolerably large prismatic crystals, perfectly trans-
parent and colourless, and free from the peculiar odour of nicotia. It is ex-
tremely soluble in water, so that for our purpose it was scarcely necessary to
prepare the sulphate. More for the sake of symmetry, however, than because
we expected to find any difference in action, we did so.
A dose of five grains of iodide of methyl-nicotium, exhibited by subcutaneous
injection, produced no effect on a rabbit. Ten grains caused trembling and slight
impairment of motility; and the same symptoms occurred, in a somewhat
exaggerated form, after the administration of fifteen grains: but recovery took
place after both doses. The subcutaneous injection of twenty grains was fol-
lowed, after several hours, by death. In the following account of the experiments
in which fifteen and twenty grains were exhibited, it will be seen that no convul-
sive movements occurred during the progress of the symptoms.
EXPERIMENT CXXVII.— We injected fifteen grains of iodide of methyl-nicotium,
dissolved in ninety minims of distilled water, into the subcutaneous cellular
tissue of a rabbit, weighing three pounds. In eleven minutes, some trembling
occurred, which, however, did not continue long; but it recurred in twenty-
three minutes. In thirty minutes, it was observed that the head was supported
with great difficulty, and shortly after it fell on the table, and the rabbit assumed
a crouching attitude. There was no trembling so long as it was not disturbed;
but whenever this was done, and when attempts were spontaneously made to
assume some different position, the trembling recommenced. It continued in
this condition for about an hour; soon afterwards the head was raised, and the
trembling ceased. The rabbit was jumping about in a perfectly normal state
two hours and three minutes after the administration.
EXPERIMENT CXXVIII—We injected twenty grains of iodide of methyl- —
nicotium, dissolved in ninety minims of distilled water, into the subcutaneous
cellular tissue of a rabbit, weighing about three pounds. In eight minutes, some
trembling. of the fore-legs was observed, which, however, soon ceased, and the
rabbit sat down and remained quiet. In twenty minutes, the head fell upon the —
table, the neck muscle being apparently unable to support it ; and in twenty-eight
minutes, the paralysis had so far extended to the body that the rabbit, being
unable to maintain even a crouching attitude, fell on the side. In one hour, it ©
was in the flaccid condition of the last note, but the respiratory movements were —
few and feeble. In two hours and ten minutes, the respirations consisted of
occasional gasps merely, and death appeared imminent. The observationswere
unfortunately now (4 p.m.) interrupted until the following morning, when
(10°15 a.m.) the rabbit was dead, and in rigor mortis.
In accordance with the plan followed in this investigation, we shall no
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 189
describe the effects that are produced by nicotia itself,—and in order to obtain as
exactly comparable data as possible, a portion of the nicotia used in the prepara-
tion of the iodide of methyl-nicotium employed in Experiments CX XVII. and
CXXVIII. was administered to the rabbit which recovered from fifteen grains of
the latter substance.
EXPERIMENT CXXXII.—One half-minim of nicotia (about 0°5 grain) was dis-
solved in fifteen minims of very dilute sulphuric acid, and the solution was
injected into the subcutaneous cellular tissue of the rabbit employed, a week pre-
viously, in Experiment CXXVII. Symptoms were rapidly produced. In two
minutes, spasmodic contractions occurred in the four limbs, which became
extended, and raised the body ina convulsive manner. In three minutes, violent
tremors occurred, and the whole body was convulsively agitated. In a few
seconds afterwards, the limbs altogether yielded ; the rabbit lay on the abdomen ;
and strong twitches occurred in the muscles of the neck, by which the head was
jerked upwards, and in the limbs, by which the body was partially raised. This
condition continued until ten minutes, when the spasmodic twitches ceased, and
the rabbit fell on the side. It was now perfectly flaccid, with only twenty-five
laboured respirations in the minute. In fourteen minutes, the respiratory
movements were so feeble as to be scarcely visible; and, in fifteen minutes, they
altogether ceased.
In the autopsy, the heart was tound contracting, five minutes after death, at
the rate of 160 per minute, but its contractions were feeble. The vermicular
movements of the intestines appeared to be normal. The trunk of a sciatic nerve
was irritated, ten minutes after death, and energetic movements followed in the
limb to which the nerve was distributed.
Having found, in the case of iodide of methyl-nicotium, that so large doses of
an extremely soluble substance were necessary to affect a rabbit by subcutaneous
injection, we did not consider it advisable to determine how much was required
to produce symptoms when it is exhibited by the stomach. For it may be almost
positively asserted that, in the latter case, a much larger dose would be necessary;
and while the administration of this would be inconvenient, because of its bulki-
ness, and of the difficulty of obtaining a large quantity in a perfectly pure form,
the data obtained by subcutaneous injection are sufficient to prove the principal
change that the addition of iodide of methyl produces in the physiological action
of nicotia—namely, a great diminution in its poisonous activity.
Sulphate of methyl-nicotium (C,,H,,N,(CH,),SO,) was prepared by precipi-
tating a solution of the iodide by means of sulphate of silver. It forms a white,
crystalline mass, extremely soluble in water.
On account of the readiness with which iodide of methyl-nicotium dissolves
in water, it was not to be expected that any change in poisonous activity would
be caused by its conversion into a sulphate; and the following experiment con-
190 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
firms this surmise, by showing that the activity of the sulphate is apparently no
greater than that of the iodide.
EXPERIMENT CXXXIII.—Ten grains of sulphate of methyl-nicotium, dissolved
in ninety minims of distilled water, was injected into the subcutaneous cellular |
tissue of a rabbit, weighing four pounds and three ounces. In ten minutes, some
trembling occurred, accompanied with partial paralysis of the fore-legs. In
twenty minutes, the head fell on the table, and, at intervals, series of tremors
shook the whole body. It continued in this condition, the body being still sup-
ported by the legs, until fifty minutes, when ineffectual attempts were made to
raise the head. These attempts were frequently repeated, and were finally
successful at one hour and ten minutes; but the trembling, though now very
slight, did not altogether cease until one hour and twenty minutes. After this,
the rabbit seemed perfectly well.
In the absence of any very trustworthy or complete investigation into the
mode in which nicotia acts, we cannot ascertain exactly how far its physiological
properties are modified by chemical addition. It would appear, however, that
the convulsive movements which are described as always occurring during
nicotia poisoning, and which were well marked in Experiment CXXXIL. are not
among the symptoms produced by either iodide or sulphate of methyl-nicotium.
The action of these substances is characterised by paralysis, accompanied with
tremors, but unattended with spasms or convulsions. We performed the follow-
ing experiments on frogs, in order to determine if this change were due not
only to the disappearance of convulsive action, but also to the appearance of
a paralysing action on motor nerves, similar to that so prominently possessed by
the methyl derivatives of the other alkaloids examined in this paper.
EXPERIMENT CXXX.—The blood-vessels were tied in the left thigh of a frog,
weighing 430 grains, and one grain of iodide of methyl-nicotium, dissolved in
fifteen minims of distilled water, was then injected into the abdomen. In ten
minutes, the anterior extremities had become so weak that they could not alto-
gether support the thorax, but still the frog jumped about with considerable
activity. In twenty-five minutes, the movements were sluggish, and the jumps
were by no means so active as formerly, while some trailing of the posterior
extremities was observed. The heart was acting at the rate of forty-two in the
minute. In thirty-five minutes, irritation of any portion of the skin was followed
by contractions of all the limbs, but these appeared to be rather more energetic
in the left posterior (non-poisoned) limb than in the others. In forty minutes,
the respirations were feeble, but the frog was sufficiently powerful to turn itself —
when placed on the back. In fifty-five minutes, severe pinching caused only
slight reflex movements, of nearly equal strength, in both posterior extremities. —
In fifty-seven minutes, it was unable to turn when placed on the back, and the
heart’s contractions were at the rate of thirty-seven per minute. In one hourand ~
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 191
thirty-nine minutes, irritation of any portion of the skin was followed by feeble,
but nearly equal, movements of the four limbs. The observations were now
interrupted. On the following morning the frog was jumping about normally.
EXPERIMENT CXXXI.—The blood-vessels were tied at the right knee of a frog,
weighing 630 grains, and three grains of iodide of methyl-nicotium, dissolved in
twenty minims of distilled water, was injected into the abdomen. In twenty-six
minutes, the frog was lying, flaccid, on the abdomen and chest; and when the
skin was irritated, reflex movements of equal strength were caused in the four
limbs. In one hour and sixteen minutes, the flaccid state had become more
marked, and, now, a somewhat stronger irritation was requisite in order to cause
reflex movements, while these appeared to be of greatest strength in the right
posterior (non-poisoned) limb. In two hours and forty-six minutes, the condi-
tion was exactly the same as last noted. The observations were now inter-
rupted ; and on the following morning the frog was found dead, and in rigor.
We obtained similar results with the sulphate.
It would, therefore, appear that though the convulsant effects of nicotia are
not produced by its methyl derivatives, these derivatives do not possess any
paralysing action on motor nerves. The change that is produced in the physio-
logical action of nicotia is not the same as that which we have described in
strychnia, brucia, thebaia, codeia, and morphia. We are inclined to believe, on
account of this difference, that the convulsions of nicotia are not due to the same
cause as in the other alkaloids we have examined.
A great diminution in physiological activity has, however, been produced by
this chemical addition, and this will be at once recognised by referring to the
following table :—
No. of Substance Animal and its Method of
: Dose. liffect.
_+| Experiment. employed. weight. exhibition. Qs -
CXXVII. | Iodide of methyl-| Rabbit, 3 lbs. | Subcutaneously.| 15 grs. (contain-| Trembling in 11 minutes,
nicotium. 5°4 grs. of ni-| and partial paralysis in
cotia). 30 minutes; these con-
tinued for about 49 and
50 minutes respectively,
and a perfect recovery
afterwards occurred.
CXXXII. | Nicotia (as sul- | Do. (same rabbit| Subcutaneously.| 0°5 min. (0.5 gr.| Convulsions in 3 minutes,
phate). as in Experi- nearly), and partial paralysis in
mentCXXVIT.) less than 4 minutes ; fol-
lowed by death, 15 min-
utes after administration.
CXXXIII.| Sulphate of me- | Do., 4 lbs, 3 oz.|Subcutaneously.| 10 grs. (contain-| Trembling in 10 minutes,
thyl-nicotium. ing 5°6 grs. of| slight paralysis in 20
nicotia). ininutes ; perfect recov-
ery in 1 hour and 20 min-
utes after administration.
VOL. XXV. PART I. 30
192 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
Some experiments were made to determine, for our satisfaction, the physio-
logical effects of iodide of methyl. The only bearing of these on the present
investigation is, that no evidence was obtained in support of the extremely impro-
bable hypothesis, that some of the changes produced in the action of the sub-
stances we have described might have been due to addition of the physiological
action of the methyl compounds.
We have thus shown that chemical addition produces some important modi-
fications in the action of those poisons which have been treated of in this com-
munication. The action of strychnia, brucia, thebaia, codeia, morphia, and
nicotia is evidently greatly diminished in degree, and, at the same time, strikingly
changed in character.
The former effect is shown with all these alkaloids, especially when their
action is compared with that of the iodides of their methyl derivatives. As all
these iodides are much less soluble than the salts of the alkaloids themselves,
it might be supposed that the diminution in activity could be explained by
this difference in solubility. Some support is given to this supposition, by
examining the relations between various of the substances included in this
investigation. Thus, it has been demonstrated, on the one hand, that, for rabbits,
the fatal dose of iodide of methyl-strychnium administered subcutaneously, is
about twenty grains, and that of iodide of methyl-thebaium is about ten grains ;
while the former is soluble in 133 parts of distilled water, at a temperature of
37° C., and the latter in 16-5 parts at the same temperature. On the other
hand, the fatal dose for rabbits, of sulphate of methyl-strychnium, is about
four-fifths of a grain, and that of sulphate of methyl-thebaium is about five
grains ; while both substances are freely soluble, and with nearly equal readi-
ness, in cold water. In these examples, the greater activity of strychnia over
thebaia is manifested when a soluble salt of the methyl derivative of strychnia_
is employed ; but when an extremely insoluble salt—the iodide—is employed,
its activity is nearly the same as that of a corresponding preparation of
thebaia; although the latter alkaloid is itself considerably less energetic than
strychnia. It is, therefore, apparent that poisonous activity may be modified by
the degree of solubility,—a well-recognised principle in toxicological physiology.
But while the diminished activity of the iodides of many of these methyl deriva-
tives may be greatly due to the difficulty of dissolving them, this explanation is
inapplicable to iodide of methyl-nicotium,—an extremely soluble substance,—and
it is insufficient to account for the differences of activity between the majority of
the sulphates of the methyl] derivatives and the salts of the alkaloids themselves.
Our investigation has not furnished us with any explanation of the change in
these sulphates. There are several possible explanations, but we shall not —
specially allude to them, as their discussion can only be properly undertaken
after experimental examination of a laborious and difficult nature, and but indi- —
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 193
rectly connected with our present subject. When, however, we compare the
activity of the sulphates of the majority of the ammonium bases considered in
this paper with that of the corresponding iodides, we observe striking differences,
which cannot be explained by differences of solubility alone, but which, we
believe, must be also due to the remarkable stability possessed by these iodides.
Strychnia is a much less soluble substance than iodide of methyl-strychnium,
and yet a rabbit that survived the administration of fifteen grains of iodide
of methyl-strychium, was killed in a few minutes by the administration of one-
twentieth of a grain of strychnia. Before absorption, the strychnia may have
been converted into a more soluble form, and this change may have facilitated its
absorption, and permitted it to be carried by the blood-stream to the tissues it
affects; but the great stability of the iodide of methyl-strychnium prevents its
conversion into a more soluble form, and so impedes greatly the absorption. Just
as in the more familiar case of the salts of lead, the sulphate is inert while the
carbonate is poisonous, although they are both insoluble; and this difference
of physiological action is undoubtedly due to the fact, that the carbonate, on
account of its instability, is readily converted in the stomach into a soluble salt,
while no such change takes place in the case of the sulphate. Stability may
also influence the physiological activity of these iodides, even after their absorp-
tion, by preventing those chemical actions on the tissues by which many of
the effects of poisons are probably caused.
The change in the character of the physiological action is remarkably illus-
trated by strychnia, brucia, and thebaia, whose purely spinal-stimulant action is
converted into a paralysing action on the periphery (end-organs) of motor nerves ;
it is apparent in codeia and morphia, whose convulsant action is also converted into
a paralysing action on motor nerve end-organs, and whose hypnotic action is
apparently altogether destroyed in the case of codeia, and certainly greatly
| diminished in that of morphia; and it is obviously, though less so than with the
others, in the case of nicotia, whose convulsant action is diminished if not alto-
'gether removed. We may conclude from these facts, that when a nitrile base
| possesses a strychnia-like action, the salts of the corresponding ammonium bases
‘have an action identical with that of curare.
|. It is well known that curare and strychnia are derived from plants belong-
‘ing to the same genus, and it is, therefore, interesting to observe such a
irelationship. It may not, however, be altogether superfluous to add, that
istrychnia, brucia, and the other spinal-stimulant alkaloids examined in this
ipaper, have not been converted by chemical addition into curarina,—the
‘active principle of curare. The action of the methyl derivatives of these
|system, but the degrees of their activity are very different. If we confine our
194 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
attention to the salts of the methyl! derivatives of strychnia, brucia, and thebaia,
where the action is uncomplicated, we observe that they form a series in which
the fatal dose varies for each, while this dose in the case of the most active of
the three is considerably above that of curare, and greatly above that of curarina.
Besides, curarina has a characteristic colour reaction that belongs to none of
these bodies; and the latter further prove this dissimilarity by each of them
possessing special colour reactions by which they may be distinguished from each
other.
It is not only of great interest, but probably of some practical value, that five
new compounds should be found having the physiological action of curare. The
ereat difficulty of obtaining this substance has hitherto proved a serious barrier
to its therapeutical employment. Although none of the compounds that we
have shown to act as curare does are so energetic as that substance, three of
them—sulphate of methyl-strychnium, sulphate of methyl-brucium, and sulphate
of methyl-thebaium—are sufficiently so to fulfil all possible therapuetical require-
ments, and even to rank as powerful poisons. Moreover, they may be readily
obtained in a state of perfect purity, and, therefore, of constant strength; and, in
this respect, they possess a great advantage over curare.
The six alkaloids we have examined may be divided into two classes, accord-
ing to the readiness with which they combine with iodide of methyl. The one —
class includes strychnia, brucia, thebaia, and nicotia; and the other, codeia and
morphia; and the combination is much more easy with the former than with the
latter class. Without attaching any general significance to the occurrence, it —
may not be altogether unworthy of being pointed out that in our experience,
therefore, the more active poisons are the more readily acted upon by iodide of
methyl.
It is curious, though not unexpected, that the ordinary colour reactions of
the alkaloids are retained by their methyl derivatives. This may possibly prove
of some importance to the medical jurist ; and as these compounds are not preci- —
pitated by alkalies, nor by the carbonates of the alkalies, some difficulty may be
met with in discovering their presence in cases of poisoning.
195
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION.
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VI.—On the Products of the Destructive Distillation of Animal Substances.
Part V. By THomas ANDERSON, M.D., Professor of Chemistry in the
University of Glasgow.
(Read 20th April 1868.—Sent for publication, November 1868).
In the fourth part of these researches, I described a new base produced by
the action of sodium upon picoline, to which I gave the name of Parapicoline,
because it has the same composition as picoline, although the circumstances
of its formation appeared to show that it had been produced by the combination
of two molecules of that substance, so that its true formula would be C,,H,,N,.
Unfortunately, its high boiling point, and tendency to decompose when distilled,
made it impossible to determine its vapour density, which afforded the only
means of ascertaining whether this hypothesis was correct; and it was only
assumed, because similar cases of polymerisation had been established beyond
a doubt in the case of other classes of organic compounds. In the hope of
obtaining a similar base of lower boiling point, and therefore better adapted
to the necessary experiments, I have submitted pyridine to the action of sodium,
and the results of the inquiry are contained in the following pages.
My earlier experiments were conducted in precisely the same manner as
those with picoline. Dry pyridine was heated to its boiling point along with
small pieces of sodium, amounting to about one-fifth of its weight, in a flask
furnished with a long cohobating tube. As the temperature rose, the pieces of
sodium became covered with a brown coating; purple streaks appeared in the
fluid, which, however, soon disappeared again; and after some hours the whole
fluid was converted into a dark-brown or black mass, which was viscous when hot,
and on cooling solidified into a hard brittle resin. In this a few white powdery
nodules are disseminated, which explode violently when brought in contact
with water. A large portion of the sodium employed remains unacted on, and if
_ the operation has been well performed, is generally found collected into one or
two large pieces, which can be easily separated from the resinous mass. After
| the sodium has been removed as thoroughly as possible, the crude product is
| thrown into water in small successive portions, so as to avoid the risk of explo-
'sions from any particles of sodium which may have remained disseminated
| through it. The water soon becomes alkaline, owing to the presence of caustic
| soda; unchanged pyridine makes itself manifest by its powerful smell, and the
| resin is slowly converted into a thick, viscid oil of dark-brown colour, and nearly,
| or altogether, insoluble in water, which collects at the bottom of the vessel. This
| oil is washed several times with water, dried over calcic-chloride, and distilled.
| The distillation is best effected in a current of hydrogen, and at a temperature
VOL. XXV. PART I. 3 G
206 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE
below the boiling point of the oil. A little unchanged pyridine distils at first,
accompanied by a small quantity of a light oil, insoluble in water, having a pun-
gent smell similar to, and yet appreciably different from, that of pyridine; and
which, as we shall afterwards see, appears to be a mixture of several bases. As
the temperature rises, a thick, heavy, and yellowish oil, having a peculiar smell,
in no degree pungent, but dull, heavy, and somewhat resembling that of soot,
passes over. As the distillation proceeds, crystals make their appearance in the
neck of the retort. Ata certain stage of the process the product becomes nearly
solid, and on cooling, crystals are deposited from the fluid distillate. Towards the
close of the distillation some ammonia and very volatile bases are evolved, obvi-
ously produced by the decomposition of the oil passing over; and adark resinous
mass remains in the retort, which can be forced over by raising the temperature,
in doing which a large part of it is decomposed, and a residue of charcoal is left
in the retort.
The products of the action being obviously complicated, the whole was
cautiously redistilled, and the portion which solidified in the neck of the retort
collected apart, while the fluid portions having been introduced into a freezing
mixture of snow and salt, soon gave an abundant crop of crystals. These
were purified by pressure between folds of filtering paper, and crystallisation
from water or alcohol, in both of which they are soluble, until they have lost the
smell of the oil by which they are accompanied.
After having proceeded some way in the investigation, I found that the same
substances could be obtained with greater certainty by a modification of the pro-
cess just described. It is by no means necessary to heat the sodium and pyridine
together, for the action takes place in the cold; but in this case it is slower, and
the phenomena are somewhat different. The brown appearance on the surface
of the sodium and the purple streaks appear in the fluid at the beginning of the
action, but the pyridine does not become brown, it retains its colour, and the
sodium is covered with a black crust, which, after two or three days, exceeds it in
bulk, is quite brittle, and sometimes shows a tendency to separate into layers. The
pyridine acquires a yellowish tint, and then contains in solution an oil insoluble
in water. When the action is judged to have gone sufficiently far, the sodium
with its crust is removed from the fluid and washed with a small quantity of
pure pyridine, so as to get rid of any of the oily base which may remain attached
to it. The crust is then detached as thoroughly as possible from the sodium and
thrown into water, any sodium still adhering to it burns, and a dark gray, almost
black, powder falls to the bottom of the glass. This is washed first by decanta-
tion, and afterwards on a cloth filter until it is free from soda, and on being
opened out and exposed for some time to the air, it is entirely converted into a
snow-white mass of interlaced acicular crystals identical with those obtained by
the first process.
= ee
DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 207
DIPYRIDINE.
The substance so obtained is a base to which, for reasons that will be imme-
diately apparent, I give the name of dipyridine. It forms white crystals fusing
at 108° Cent., and solidifies on cooling into a crystalline mass. It volatilises slowly
at 100°, and sublimes unchanged at a high temperature, giving long needle-shaped
crystals. It is rather sparingly soluble in cold but readily in boiling water, and
the fluid, on cooling, becomes filled with a mass of interlaced needles. It is readily
soluble in alcohol and ether, and the boiling solutions give acicular crystals on
cooling. It likewise dissolves in pyridine and in volatile oils. From the oily base
along with which it distils in the first process of preparation, it crystallises in
short, thick, four-sided prisms, which are transparent so long as they remain in
the fluid, but soon become opaque when they are removed from it. When well
purified they are inodorous, but in general they have a faint smell, due, apparently,
to a trace of the fluid base adhering to them. Dipyridine is a very stable com-
pound. Itis not decomposed by hydrochloric, sulphuric, or nitric acids. Potash
and ammonia precipitate it from its solutions in acids as a mass of minute crystals.
Its aqueous solution gives no precipitates with solutions of sulphate of magnesia,
zinc, nickel, acetate of lead, or perchloride of iron. With sulphate of copper it
gives a pale bluish-white precipitate, with corrosive sublimate a white amorphous
powder insoluble in boiling water, and with nitrate of silver a white precipitate
insoluble in cold and sparingly in boiling water, from which the compound is
obtained in crystals on cooling. Its most characteristic reactions, however, are
those it gives with the ferro- and ferri-cyanides of potassium. If a few drops of the
ferrocyanide of potassium be added to a not too dilute solution of the dipyridine
hydrochlorate, a pale precipitate makes its appearance, which rapidly changes to
a dirty indigo colour, increasing at the same time in quantity. Ifthe proper
concentration is hit, the precipitate consists entirely of very minute needle-shaped
crystals having a dark indigo colour. They dissolve in boiling water, forming a
very deep and rather dull purple solution, and are again deposited on cooling;
but if the boiling be continued for some time, the compound appears to undergo
some change, for the fluid retains its red colour at ordinary temperatures, though
a great part of the substance is still deposited in crystals. A saturated cold
solution of dipyridine in water gives no precipitate with ferrocyanide of potassium,
but on the addition to the mixture of a drop or two of hydrochloric acid the dark
precipitate instantly makes its appearance, and is deposited in small crystals. The
precipitate is readily soluble in excess of hydrochloric acid. When ferricyanide
of potassium is added to dipyridine hydrochlorate no immediate effect is observed,
but on standing, the interior of the test-tube becomes lined with minute prisms of
sulphur yellow colour and high lustre. If the solution be boiled, it acquires a
dark colour, and partial decomposition takes place.
208 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE
Dipyridine carefully dried in the water bath was found on analysis to give
these results :—
0:2802 gramme dipyridine gave
I 0-7782 ... carbonic acid, and
( O:1497° ... water.
0:3600 gramme dipyridine gave
10 i 0°8367 ... carbonic acid, and
0:1575 ... water.
Experiment. Calculation.
Sxipils i
Carbon, F . 75°74 76:07 75:94 C, 60
Hydrogen, . . 5:94 5°83 633 4H, 5
Nitrogen, , in coe 17°73 N 14
100-00 79
These numbers lead to the formula C,H,N, which is that of pyridine itself.
The platinum compound of the base, which is thrown down as a yellow
crystalline powder, gave the following results :—
L { 0°3345 gramme gave
01175 ... platinum.
u 0:2007 gramme gave
; 0:0685 ... platinum.
IIL. 0:4335 gramme gave
0:1473 =~... ~— platinum.
0'4052 gramme gave
IV. 0°3087 ... carbonic acid, and
0:0905 ... —~water.
Experiment. Calculation.
ie IL. III.
Carbon, : ; eee a8 20:78 21-02 Ch 120
Hydrogen, . é one ah 2°48 2:10 Hs 12
Nitrogen, . : sae hae ae 4:90 Ne 28
Chlorine, . : ae Ae sep 37°30 Cl, 213
Platinum, . : 34:11 34:12 34:03 34:68 Pt 197-4
100-00 570-4
This agrees with the formula (C,H, NHC1),PtCl,, which is identical with that of
the pyridine salt. In order to fix the true constitution of the base, it was necessary
to determine its vapour density, and as its boiling point was beyond the range of
the mercurial thermometer, it was necessary to use a bath of metallic lead and
an air thermometer. The air thermometer was a bulb of the same size as that
used for containing the vapour, and the details of the experiment were as fol-
lows :—
|
|
q
DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES.
Weight of vapour bulb empty,
full of vapour,
Temperature at ‘weighing,
Barometer,
Volume of bulb,
Residual air,
Hence
Weight of bulb and vapour,
air displaced,
Weight of bulb and vapour in vacuo,
bulb,
22-2530
22°4806
B59
753 mm.
197-1 CC
0-2 C.C.
22°4806
0°1552
22-6358
22-5230
0°3828
Residual air,
Weight of vapour,
Weight of air thermometer,
: partly full of mercury,
Barometer 753 — 67:5 . :
Temperature,
Air thermometer full of mercury,
Hence
ieee of mercury partially filling bulb,
completely,
and 26666 — 14127 = 12539.
Now, we have here in the formula
WCE nag ee ta se
We he wil’
W = 26666
w = 12539
H = 753
h = 685°5
a = 0:00366
k = 0:00003
free 175
whence t = 414°4 Cent.
Now 1271 — 05 = 126°5,*
d 126°5 753 1:29366
an 1 4 4144 x 0:00366 * 760 * 1000
0:3825
and |.
0:0003
0°3825
264 = grains.
14391
685°5 mm.
by aC:
26930
14127
26666
= 0:0646,
09
The formula C,,H,,N, requires 5:46. This result is as close as could be expected
under the circumstances, and proves that the base must be formed by the com-
* 0:6 is the volume of the residual air at 414°.
VOL.EXOaVy. PARD Ir
210 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE
bination of two molecules of pyridine, and hence the name of dipyridine which I
have applied to it.
Salts of Dipyridine.—Though dipyridine is not a very powerful base, it gives
a number of salts, most of which crystallise well, though some of them are not
easily obtained of definite composition.
Hydrochlorate of Dipyridine.—This salt is best obtained by adding a slight
excess of hydrochloric acid to the aqueous solution of the base and evaporating
to crystallisation; the crystals, after being pressed and recrystallised from water,
are sufficiently pure for analysis. They are flat needles readily soluble in water,
especially when hot—insoluble in ether. The salt is very apt to retain hydro-
chloric acid, and it is advisable to heat it to 130° for analysis.
0-6104 gramme of the hydrochlorate gave
0:7633 iodide of silver.
Experiment. Calculation.
Carbon, 51:94 Cio 120
Hydrogen, 519 is De 12
Nitrogen, me 12-13 N, 28
Chlorine, 30:93 30°74 Cl, 7
100-00 231
Sulphate of Dipyridine.—Dipyridine is added in slight excess to dilute sul-
phuric acid, and this fluid is evaporated nearly to dryness; on cooling, crystals of
the sulphate are deposited; they are washed with alcohol, in which they are scarcely
soluble, and again crystallised from water. It is thus obtained in needle-shaped
crystals, which deliquesce in moist air. One determination of sulphuric acid
was made of a specimen of this salt dried in vacuo over sulphuric acid, which
gave 26°85 per cent. of SO,.. This would correspond with a salt containing two
molecules of water of crystallisation with the formula C,,H,,N,H,SO, + 2H,0,
which requires 27:39 per cent.
Nitrate of Dipyridine is obtained by adding a slight excess of nitric acid to
solution of dipyridine, evaporating on the water-bath and recrystallising. It
forms pale yellow needles of moderate solubility in water. When exposed for
some time to a temperature of 100°, it acquires an orange colour, but is not
sensibly decomposed. A combustion of this salt gave
0°5162 gramme of the nitrate gave
it, 0:7915 of carbonic acid, and
0:1820 of water.
Experiment. Calculation.
Carbon, 41°81 42°25 Cc. 120
Hydrogen, 3°92 3°92 fa 12
Nitrogen, aie 20°38 Ny, 56
Oxygen, 33°45 O, 96
100-00 284
DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 211
Double Salt mith Chloride of Zinc.—This substance is prepared by adding to
dipyridine a mixture of hydrochloric acid and zinc chloride, and allowing it to
stand for some time, when small prismatic crystals are deposited. Their formation
is materially assisted by the addition of alcohol and ether. The compound may
even be obtained from the crude product, in which the dipyridine is mixed with
the oily base distilling along with it. For this purpose zine chloride, along with
hydrochloric acid and a considerable excess of alcohol and ether, must be added
to the crude product, when, especially on stirring, the zinc salt deposits, and
can be purified by crystallisation from water. This process can even be em-
ployed for separating the two bases. The salt is in long white needles, soluble in
eight times their weight of water, less so in alcohol, and quite insoluble in ether.
On the addition of potassic hydrate in excess it gives the pure base in minute
crystals. A chlorine determination gave
foie gramme zinc salt gave
05755 ... dichloride of zine.
Experiment. Calculation.
— =
, Carbon, ; . oof 32°70 Cio 120
Hydrogen, , one 3°27 lees 12
Nitrogen, ; : 23 762 N, 28
Chlorine, ; é 38°90 38°68 Cl, 142
Zinc, . é 5 ss emo Zn. 65
100:00 367
Double Salt with Nitrate of Silver—This salt is best obtained by mixing hot
solutions of dipyridine hydrochlorate, and silver nitrate, the latter being in
excess, and at once filtering off the precipitated silver chloride. On cooling, the
salt is deposited in brilliant needles, of sparing solubility in water. This com-
_ pound could not be obtained of constant composition, but one specimen gave
35°09 per cent. of silver, while the formula C,,H,,N,(HNO,),(AgNO,), requires
34°61.
Platino-chloride of Dipyridine—The analysis of this salt has been already
given. It is obtained as a crystalline yellow powder of very sparing solubility.
Palladio-chloride of Dipyridine is obtained as an orange precipitate on
mixing the hydrochlorates.
DERIVATIVES OF DIPYRIDINE.
Diethylo-Dipyridine.—The compounds of this base were obtained in the usual
manner. The ethyl-iodide is easily prepared by exposing dry dipyridine with
iodide of ethyl to the temperature of 100° in hermetically sealed tubes. The
action is complete in half an hour. It is obtained in acicular crystals, which are
brilliant and perfectly colourless if they have not been exposed to the air. They
are very soluble in water, much less so in alcohol and in ether.
212 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE
0:3997 gramme ethyl-iodide gave
I 0:5195 ... carbonic acid, and
01530 ... water.
Il 03512 gramme gave
f 0:3513 ... iodide of silver.
Experiment. Calculation.
— SS
Carbon, : : , 85°44 35°74 Cy, 168
Hydrogen, . ; 4°25 4:26 7 20
Nitrogen, . : : a5 5°96 Ne 28
Iodine, : : : 54:05 54:04 i, 254
100-00 470
Corresponding with the formula C,,H,,N,(C,H.I),. Heated with silver chloride
and water this salt was converted into the chloride, which, on the addition of
platinic-chloride gave the platino-chloride in very sparingly soluble small red
needles.
02780 gramme platino-chloride gave
0:0685 ... platinum.
This corresponds with 31:12 per cent., and the formula C,,H,,N,(C,H,Cl),PtCl,
requires 30°44.
The base itself, when separated from the iodide by silver oxide, forms a highly
alkaline solution, having generally a red or purple colour, which, on evaporation,
leaves a dark-coloured uncrystallised residue. It obviously belongs to the class
of ammonium bases, but I have not pursued its investigation further.
Dibromo-Dipyridine.—This base is thrown down when bromine is added to a
solution of dipyridine hydrochlorate, or hydrobromate, as a white powder, insoluble
in water, sparingly soluble in cold, more so in hot alcohol, from which it is depo-
sited in flattened needles on cooling. If too much bromine has been used in its
preparation, these crystals are pink. Its basic properties are extremely feeble,
and it is a somewhat unstable compound; for, on boiling with water, or with
hydrochloric acid, the original base appears to be more or less completely rege-
nerated. An analysis, in which the hydrogen was lost, gave
L ee gramme dibromo-dipyridine gave
04902 ... carbonic acid.
ll -0°3420 gramme gave
O40 7E ee: silver iodide.
Experiment. Calculation.
EE SEE
Carbon, : : ; 37°56 37°97 Cio 120
Hydrogen, : bse 2:53 H, 8
Nitrogen, ‘ : dios 8°87 N, 28
Bromine, : ; : 50:74 50°87 Br, 160
100-00 316
DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 213
Its platinum compound could not be obtained in a state fitted for analysis.
On boiling with hydrochloric acid, and adding platinic-chloride, a yellow precipi-
tate was obtained, which, in one experiment, gave 32°39 per cent. of platinum ;
and in another, in which the boiling was continued longer, 33°53 per cent. was
obtained. Dibromo-dipyridine requires 30°94, and dipyridine itself 34°68; so
that there can be little doubt that the latter has been regenerated.
OILy BASE.
The oily base from which the dipyridine was deposited in crystals, has been
as yet but imperfectly examined. It was purified by redistillation and cooling,
by which it yielded a small additional quantity of dipyridine, and this was re-
peated as long as it gave crystals. The base so obtained is a rather thick, pale-
yellow oil, heavier than water, having a peculiar heavy smell, quite distinct from
that of pyridine. Itis insoluble in water, but dissolves with great ease in alcohol
and ether. It boils at a high temperature, and if distilled rapidly, it undergoes
partial decomposition, yielding a small quantity of what appears to be a mixture
of several bases with pungent smell, and sparingly soluble in water. If, how-
ever, the distillation be carried on very cautiously at a temperature below its
boiling point, it passes over unchanged. It dissolves in acids and forms salts,
most of which, however, are uncrystallisable. and dry up into gummy masses.
It was prepared for analysis by drying over calcic-chloride, distilling and separat-
ing the first part of the distillate which might retain moisture.
0:3420 gramme of the base gave
I. ¢ 09605 ... carbonic acid.
021385) 2.) ) water.
03662 gramme of the base gave
II. ¢ 10140 ... carbonic acid.
0:2300 =... ~ + water.
Experiment. Calculation.
tesa ei le.
Carbon, . ; 76:59 7551 75:94 C, 60
Hydrogen, ; 6:94 6°98 6:33 Hi. 5
Nitrogen, . ' a a 17°73 N 14
100-00 a
These results, it will be seen, correspond with those given by pyridine and di-
pyridine, and they are confirmed by the analysis of a platinum salt, prepared in
the usual way.
heaiets gramme of the platinum salt gave
01015... _ platinum.
This corresponds to 33:94, and calculation for the formula (C,H,NHCl),PtCl,
requires 34:68. It is obvious, therefore, that this is another polymer of the
VOL. XXV. PART I. 31
214 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE
original pyridine; but, unfortunately, there is no means by which its molecular
constitution can be determined. It is impossible to determine its vapour density,
because it undergoes partial decomposition at its boiling point ; and as its salts
do not crystallise, and probably, like the platinum compound, all correspond with
those of the original pyridine, there is no prospect of satisfactory conclusions
being drawn from them. In the absence of experimental evidence, any assump- |
tion may be made regarding the constitution of this base, and at first sight the
most reasonable view of the matter is to suppose it to be the product of afurther
polymerisation, and to be formed by the combination of three or four molecules of
the original pyridine. Its boiling point, which is certainly lower than that of
dipyridine, however, appears to militate against this view; and taking its proper-
ties and those of its compounds into consideration, I am inclined to believe it to
be another dipyridine, and an example of those cases of physical isomerism of
which so many are now known. As there was no means of ascertaining the
constitution of this base, and the properties of its compounds were not encourag-
ing, I have not pursued their investigation further.
Licgut BaAsEs.
It has been stated at the commencement of this paper that when dipyridine
was prepared by the first of the processes there described, that a light basic
oil was obtained at the beginning of the rectification of the crude product. This
oil, which is insoluble in water, was collected, dried, and rectified when it was
found to consist of several bases. ‘The distillate was collected in several frac-
tions, which were analysed, but the quantity was far too small to admit of any
systematic attempt to separatethem. ‘The results, both of the combustion of the
bases themselves and of the platinum determinations in their platinum com-
pounds, seem to show that they are a class of bases isologous with the pyri-
dine series. I give here the results of these analyses :—
O83s a Eee. ... earbonic acid, and
0°3025 gramme of base boiling between 225° and 240° F. gave
I
0:2302 i... ows | WAUEES
0:4120 gramme of base boiling between 270° and 290° F. gave
LN38Or ser ... carbonic acid, and
ONS 230i. oo. ... Water.
0:2711 gramme of base boiling about 291° F. gave
TE Oo Aae sere ... carbonic acid, and
0:1984 Py: ... water.
0:2708 gramme of base boiling between 287° and 291° F, gave
Omiotle “Sere ... carbonic acid, and
O20 92 ea. ... water.
0:2355 gramme of base boiling between 291° and 360° F. gave
06690... ... carbonic acid,
MOTOR ee, ... Water.
IV.
V.
DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 215
i TE Tae IV. Vv.
Carbon, } re7orol 75°36 76:18 74:23 7747
Hydrogen, . . 8-46 8-71 8:13 8°58 8:47
Nitrogen, . - 16:03 15:93 15°69 T7A9 14:06
—— ———— ed ———— oy
10000 100:00 100-00 10000 100-00
It must be distinctly understood that all the substances analysed were
obviously mixtures, and the degrees above given do not denote true boiling
points, but only that the fractions they represent were collected at these points.
It will be observed that all these analyses are characterised by yielding a per-
centage of hydrogen far above that contained in pyridine, or any of its homo-
logues. To render this more obvious, I place here the calculated numbers for
pyridine and picoline, along with those required by bases containing two atoms
of hydrogen more than these compounds :—
C,H.N C,H,N OHN. CHUN
Carbon, . 75°94 77-42 74:04 75°75
Hydrogen, . A 38/3) 7:53 8°64 9:47
Nitrogen, . Sa Meio 15:05 17:32 14-78
100:00 100-00 100:00 100:00
The experimental results above given are manifestly incompatible with the first
two of these formula, but would agree tolerably with a mixture of substances
containing more hydrogen, and this is further confirmed by several platinum
determinations in platinum compounds obtained from these substances. These
results appear to indicate the existence of a series of bases having the general
formula C,H,,_,;N. The further investigation of these substances would be of
interest, but as they are obtained only in minute quantity, and are clearly
secondary products of the action of sodium on pyridine, it is scarcely possible to
obtain them in sufficient quantity for this purpose.
At the beginning of this paper, mention has been made of a black or dark-gray
substance, obtained in the second process for preparing dipyridine. This com-
pound was only obtained towards the close of the investigation, and I have not
had time to examine its properties and relations minutely. It is a black
amorphous powder, quite insoluble in water. When exposed to the air, it is
rapidly converted into a mass of crystals of pure dipyridine. I was at first
_ disposed to consider this substance to be a sodium compound of dipyridine, but I
soon found that this was not the case, and that its properties more nearly corres-
_ponded with a hydrogen compound of that base ; and it seems probable that its
formula will turn out to be C,,H,,N,, in which case it would be related to
216 DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES.
dipyridine in the same manner as ammonium is to ammonia. Should this
view be correct, it seems probable that, on the addition of hydrochloric acid, it
should, like a metal, evolve hydrogen. An experiment was made to ascertain
whether this occurred by introducing a quantity of the compound into a jar over
mercury, and bringing hydrochloric acid in contact with it; but the anticipated
result was not obtained—no hydrogen was evolved, but a brownish precipitate
appeared in the fluid, and the gray powder at once disappeared. I have been
unable to pursue this subject further, but propose to return to it on a future
occasion.
Numerous experiments have been made, in the hope of throwing light on the
nature of the chemical changes occurring during the first process of preparing
dipyridine; but it is obviously of a very complex kind, and some of the products
must be the result of secondary decompositions. My impression is, that sodio-
dipyridine must be first formed, probably C,,H,Na,N,. In this case hydrogen
must be given off during the action, and this is actually the case, as was estab-
lished by direct experiment; but the quantity evolved is trifling compared with
that of the sodium consumed, so that if the action takes place in this way, a
large part of the hydrogen must be converted into some other compounds within
the mixture itself. The light bases already mentioned might account for this,
if it were not that they are produced in very small quantity. Altogether I am
inclined to think that, in the first process, a number of secondary reactions take
place, which greatly complicate matters, and that it is through some modifica-
tion of the second by which an explanation will most probably be obtained. I
am still engaged with the subject, and have already nearly perfected a process
by which some of the products can be obtained with greater certainty and in
larger quantity than by either of those described in this paper, and which I hope
will enable me to subject the constitution and relations of these curious com-
pounds to a more minute examination.
‘
ic
c
Diagram showing stream lines traversing circular ring.
Pe
i
nme
= ace nites ia
— _ < :
Ky
: a
nie
Wee. |
i.
COLA
)\ mn LO ee 1 |
| ne \ |
PY ———
LS —
a a—\.-\4
Soe LN
Ge QUT
VI.—On Vortex Motion. By Sir W. THomson.
(Read 29th April 1867.)
(2 2 1-59 recast and augmented 28th August to 12th November 1868.)
1. The mathematical work of the present paper has been performed to illus-
trate the hypothesis, that space is continuously occupied by an incompressible
frictionless liquid acted on by no force, and that material phenomena of every
kind depend solely on motions created in this liquid. But I take, in the first
place, as subject of investigation, a finite mass of incompressible frictionless* fluid
completely enclosed in a rigid fixed boundary.
2. The containing vessel may be either simply or multiply continuous.; And
I shall frequently consider solids surrounded by the liquid, which also may be
either simply or multiply continuous. It will not be necessary to exclude the sup-
‘ position that any such solid may touch the outer boundary over some finite area,
in which case it is not surrounded by the liquid; but each such solid, whether
surrounded by the liquid or not, and whether moveable or fixed, must be con-
sidered as a part of the whole boundary of the liquid.
3. Let the whole fluid be given at rest, and let no force, except pressure from
the containing vessel, or from the surfaces of solids immersed in it, ever act on any
part of it. Let there be any number of solids, perfectly incompressible, and of the
same density as the fluid; but either perfectly rigid, or more or less flexible, with
perfect or imperfect elasticity. Some of these may at times be supposed to lose
rigidity, and become perfectly liquid; and portions of the liquid may be supposed
to acquire rigidity, and thus to constitute solids. Let the solids act on one
another with any forces, pressures, frictions, or mutual distant actions, subject
only to the law of ‘‘action and reaction.” Let motions originate among them
and in the liquid, either by the natural mutual actions of the solids or by the
arbitrary application of forces to them during some limited time. It is of no
consequence to us whether these forces have reactions on matter outside the con-
taining vessel, so that they might be called “ natural forces” in the present state
of science (which admits action and reaction at a distance); or are applied
arbitrarily by supernatural action without reaction. To avoid circumlocution,
* A frictionless fluid is defined as a mass continuously occupying space, whose contiguous
portions press on one another everywhere exactly in the direction perpendicular to the surface
separating them.
| Heitmuoirz— Ueber Inteyrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen
entsprechen: Crelle (1858); translated by Tarr in Phil, Mag. 1867, i, Riemann—Lehrsdtze aus
der Analysis situs, §c. Crelle (1857). See also § 58, below.
VOL. XXV. PART I. uk
218 SIR W. THOMSON ON VORTEX MOTION.
and, at the same time, to conform to a common usage, we shall call them
impressed forces.
4. From the homogeneousness as to density of the contents of the fixed
bounding vessel, it follows that the centre of inertia of the whole system of liquid
and solids immersed in it remains at rest; in other words, the integral momentum
of the motion is zero. Hence (THomson and Tart’s “ Natural Philosophy,” § 297)
the time integral of the sum of the components of pressure on the containing
vessel, parallel to any fixed line, is equal to the time-integral of the sum of the com-
ponents of zmpressed forces parallel to the same line. This equality exists, of
course, at each instant during the action of the impressed forces, and continues to
exist for the constant values of their time integrals, after they have ceased. Thus,
in the subsequent motion of the solids, and of the fluids compelled to yield to
them, whatever pressure may come to act on the containing vessel, whether from
the fluid or from some of the solids coming in contact with it, the components of
this pressure, parallel to any fixed line, summed for every element of the inner
surface of the vessel, must vanish for every interval of time during which no im-
pressed forces act. If, for example, one of the solids strikes the containing vessel,
there will be an impulsive pressure of the fluid over all the rest of the fixed con-
taining surface, having the sum of its components parallel to any line, equal and
contrary* to the corresponding component of the impulsive pressure of the solid
on the part of this surface which it strikes [see § 8, and consider oblique impulse
of an inner moving solid, on the fixed solid spherical boundary]. But, after the
impressed forces cease to act, and as long as the containing vessel is not touched by
any of the solids, the integral amount of the component of fiuid pressure on it,
parallel to any line, vanishes.
5. If now forces be applied to stop the whole motion of fluid and solids [as
(§ 62) is done, if the solids are brought to rest by forces applied to themselves
only], the time integrals of the sums of the components of these forces, parallel
to any stated lines, may or may not in general be equal and contrary to the time
integrals of the corresponding sums of components of the initiating impressed
forces (§ 3). But we shall see (§§ 19, 21), that if the containing vessel be infinitely
large, and all of the moving solids be infinitely distant from it during the whole
motion, there must be not merely the equality in question between the time
integrals of the components in contrary directions of the initiating and stopping
impressed forces, but there must be (§ 21) completely equilibrating opposition
between the tivo systems.
6. To avoid circumlocution, henceforth I shall use the unqualified term impulse
to signify a system of impulsive forces, to be dealt with as if acting on a rigid body.
Thus the most general impulse may be reduced to an impulsive force, and couple
* T shall use the word contrary to designate merely directional opposition; and reserve the
unqualified word opposite, to signify contrary and in one line.
SIR W. THOMSON ON VORTEX MOTION. 219
in plane perpendicular to it, according to PornsoT; or to two impulsive forces in
lines not meeting, according to his predecessors. Further, I shall designate by
the impulse of the motion at any instant, in our present subject, the system of
impulsive forces on the moveable solids which would generate it from rest; or
any other system which would be equivalent to that one if the solids were all
rigid and rigidly connected with one another, as, for instance, the Pornsor resultant
impulsive force and minimum couple. The line of this resultant impulsive force
will be called the resultant axis of the motion, and the moment of the minimum
couple (whose plane is perpendicular to this line) will be called the rotational
moment of the motion.
7. But, having thus defined the terms I intend to use, I must, to warn against
errors that might be fallen into, remark that the momentum of the whole motions
of solids and liquid is not equal to what I have defined as the impulse, but (§ 4) is
equal to zero; being the force-resultant of ‘‘ the impulse” and the impulsive
pressure exerted on the tiquid by the containing vessel during the generation of the
motion: and that the moment of momentum of the whole motion round the centre
of inertia of the contents of the vessel is not equal to the rotational moment, as 1
have defined it, but is equal to the moment of the couple constituted by “ the
impulse” and the impulsive pressure of the containing vessel on the liquid. It
must be borne in mind that however large, and however distant all round from
the moveable solids, the containing vessel may be, it exercises a finite influence on
the momentum and moment of momentum of the whole motion within it. But if
it is infinitely large, and infinitely distant all round from the solids, it does so by
infinitely slow motion through an infinitely large mass of fluid, and exercises no
finite influence on the finite motion of the solids or of the neighbouring fluid. This
will be readily understood, if for an instant we suppose the rigid containing vessel
to be not fixed, but quite free to move as arigid body without mass. The momentum
of the whole motion will then be not zero, but exactly equal to the force-resultant
of the impulse on the solids; and the moment of momentum of the whole motion
round the centre of inertia will be precisely equal to the resultant impulsive
couple found by transposing the constituent impulsive forces to this point after
the manner of Poinsot. But the finite motion of the immersed solids, and of the
fluid in their neighbourhood which we shall call the jield of motion, will not be
altered by any finite difference, whether the containing vessel be held fixed or
left free, provided it be infinitely distant from them all round. It is, therefore,
essentially indifferent whether we keep it fixed or let it be free. The former
supposition is more convenient in some respects, the latter in others ; but it would
be inconvenient to leave any ambiguity, and I shall adhere (§ 1) to the former in
all that follows.
8. To further illustrate the impulse of the motion, and its resultant impulsive
force and couple, according to the previous definitions, as distinguished from
220 "SIR W. THOMSON ON VORTEX MOTION.
the momentum, and the moment of momentum, of the whole contents of the
vessel, let the vessel be spherical. Its impulsive pressure on the liquid will
always be reducible to a single resultant in a line.through its centre, which (§ 4)
will be equal and contrary to the force-resultant of “the impulse ;” and, therefore,
with it will constitute in general a couple. The resultant, of this couple and the
couple-resultant of the impulse, will be equal to the moment of momentum of the
whole motion round the centre of the sphere (which is the centre of inertia). But
if the vessel be infinitely large, and infinitely distant all round from the moveable
solids, the moment of momentum of the whole motion is irrelevant; and what
is essentially important, is the impulse and its force and couple-resultants, as
defined above.
9. The following way of stating (S§ 10, 12), and proving (§§ 11—15), a funda-
mental proposition in fluid motion will be useful to us for the theory of the
impulse, whether of the moveable solids we have hitherto considered or of vortices.
10. The moment of momentum of every spherical portion of a liquid mass in
motion, relatively to the centre of the sphere, is always zero, if it is so at any one
instant for every spherical portion of the same mass.
11. To prove this, it is first to be remarked, that the moment of momentum
of that part of the liquid which at any instant occupies a certain fixed spherical
space can experience no change, at that instant (or its vate of change vanishes at
that instant), because the fluid pressure on it (§ 1), being perpendicular to its
surface, is everywhere precisely towards its centre. Hence, if the moment of
momentum of the matter in the fixed spherical space varies, it must be by the
moment of momentum of the matter which enters it not balancing exactly that of
the matter which leaves it. We shall see later (§§ 20, 17, 18) that this balancing
is vitiated by the entry of either a moving solid, or of some of the liquid, if any
there is, of which spherical portions possess moment of momentum, into the fixed
spherical space; but it is perfect under the condition of § 10, as will be proved
in § 15.
12. First, I shall prove the following purely mathematical lemmas; using the
ordinary notation wu, v, w for the components of fluid velocity at any point
(@, 'Y, 2).
Lemma (1.) The condition (last clause) of § 10 requires that udx + vdy + wdz
be a complete differential,* at whatever instant and through whatever part of the
fluid the condition holds.
Lemma (2.) Ifwdax + vdy + wdz be a complete differential of a single valued
function of x, y, z, through any finite space of the fluid, at any instant, the con-
dition of § 10 holds through that space at that instant.
* This proposition was, I believe, first proved by Stokes in his paper “ On the Friction of
Fluids in Motion, and the Equilibrium and Motion of Elastic Solids.” Cambridge Philosophical
Transactions,” 14th April 1845.
SIR W. THOMSON ON VORTEX MOTION. 221
13. The following is Sroxes’ proof of Lemma (1):—First, for any motion
whatever, whether subject to the condition of § 10 or not, let L be the component
moment of momentum round OX of an infinitesimal sphere with its centre at O.
Denoting by /// integration through this space, we have
= /{f (wy — v2z)dxdy dz : : : (1).
Now let (Ge) i &c. denote the values at O of the differential coefficients.
We have, by Mactaurin’s theorem,
on Ne
dat Y \ dy dz i ,
and so for v. Hence, remembering that (Z , &c. are constants for the space
0
w=2
through which the integration is performed, we have
fda dy dzwy = =) Sf ay dx dy dz + (=) fy? da dy dz + we =) Sf zy da dy dz.
0 0
The first and third of the triple integrals vanish, because every diameter of a
homogeneous sphere is a principal axis; and if A denote moment of momentum
of the spherical volume round its centre, we have for the second
Lfy? dedydz=A..
Dealing similarly with vz in the expression for 2 we find
=34[(%) -(3 ale . (2).
But L must be zero according to the condition of § 10; and, therefore, as the
centre of the infinitesimal sphere now considered may be taken at any point of
space through which this condition holds at any instant, we must have, through-
out that space,
do _ do _
dy dz |
2 ae du OB x.
and similarly rie ee PUREE Aare 2 EM BY:
dv du _
a dy
which proves Lemma (1.)
14. To prove Lemma (2.), let
_ _ dp _ do
“u= ae v= dy , w= ae . 5 ° . ci (4) 3
and let L denote the component moment of momentum round OX, through any
spherical space with O in centre. We have [ (1) of § 13],
VOL. XXV. PART I. 3.1L
222 SIR W. THOMSON ON VORTEX MOTION.
L=S{f da dy dz (wy — v2) . ) : ; (5),
// denoting integration throughout this space (not now infinitesimal). But by (4)
d d d
yo—u=(y 5-25, )0= Fe (6);
if Hy denote differentiation with reference to , in the system of co-ordinate
2, p, , such that.
y=ecos),z=esiny . ; 5 : (73:
Hence, transforming (5) to this system of co-ordinates, we have
L=fff dx de ed a . : . . : (8).
Now, as the whole space is spherical, with the origin of co-ordinates in its centre,
we may divide it into infinitesimal circular rings with OX for axis, having each
for normal section an infinitesimal rectangle with dz and dp for sides. Inte-
grating first through one of these rings, we have
; 2Qar dg
die dee f a
which vanishes, because ¢ is a single-valued function of the co-ordinates. Hence
L = 0, which proves Lemma (2.).
15. Returning now to the dynamical proposition, stated at the conclusion of
§ 11; for the promised proof, let R denote the radial component velocity of the fluid
across any element, dc, of the spherical surface, situated at (a, y, z); and let
u, v, w be the three components of the resultant velocity at this point; so that
sty o &
Res US ee RO . : : z : { (yr
The volume of fluid leaving the hollow spherical space across de in an infinitesimal
time, di is Rde . dt, and the moment of momentum of this moving mass round
the centre has, for component round OX,
(wy — vz) Rde dt.
Hence, if L denote the component of the moment of momentum of the whole,
mass within the spherical surface at any instant, ¢, we have (§ 11),
= = ff wy — vz) R de, . : : : (10).
Now, using Lemma (1.) of § 12, and the notation of § 14, we have
" WY — Ve — He)
dap ’
SIR W. THOMSON ON VORTEX MOTION. 223
and, by (9),
= ae
dr
where e denotes rate of variation per unit length perpendicular to the spherical
Lr
surface, that is differentiation with reference to 7, the other two co-ordinates being
directional relatively to the centre. Hence, using ordinary polar co-ordinates, 7,
0, ~, we have : oo
Lit yO ae d
; af fF re sinddédp : : : (11).
But the “equation of continuity” for an incompressible liquid (being
du dv dw
de * dy i oy, Ti
gives* vy’ p =—0, for every point within the spherical space; and therefore [THom-
son & Tait, App. B]
=e
9=8,+S8,7r+ 8,7? + &. 7 : p ; @2)
a converging series, where S, denotes a constant, and §,, S,, &c., surface harmo-
nics of the orders indicated.
Hence
d
R= $=8, +28, +37°8,4+&. © . (18)
And it is clear from the synthesis of the most general surface saga by zonal,
sectional, and tesseral harmonics [THomson & Tarr, $781}, that “ a is a surface
harmonic of the same order as §,:} from which [THomson & Tarr, App. B (16)],
_ it follows that,
d? ae ae
da? * dy? +
+ This follows, of course, from the known analytical theorem that the operations yv? and
* By v? we shall always understand
| (y = — 2% a) are commutative, which is proved thus :—
| By differentiation we have
ddp_ dd
dy dz” dz dy’
v(: dp do vi
7 da eB 7) -*9" dy VEO ‘ay ae
| and therefore, since
OY
Vv? “6 ee 7)? = (v 5 v2 9
dz * dy Cn ¢
| p being any function whatever. Hence, if vy? 9 = 0 we have
224 SIR W. THOMSON ON VORTEX MOTION.
d8Sv .
sé sin 6dédp=—0O,
except when 7?’ =7. But this is true also when ¢’ = 7 because
and therefore, as in § 14, the integration for .), from W = 0 to W = 2 = gives zeru.
Hence (11) gives
aL _
a Pals
This and § 11 establish § 10.
16. Lemma (1) of § 11, and § 10 now proved, show that in any motion whatever
of an incompressible liquid, whether with solids immersed in it or not, wda+
cdy +wdz is always a complete differential through any portion of the fluid, for
which it is a complete differential at any instant, to whatever shape and position
of space this portion may be brought in the course of the motion. This is the
ordinary statement of the fundamental proposition of fluid motion referred to in
§ 9, which was first discovered by Lacrancs. (For another proof see § 60.) Ihave
given the preceding demonstration, not so much because it is useful to look at
mathematical structures from many different points of view, but (§ 19) because the
dynamical considerations and the formule I have used are immediately available
for establishing the theory of the impulse (S$ 3 . . . 8), of which a fundamental pro-
position was stated above (§5). To prove this proposition (in § 19) I now proceed.
17. Imagine any spherical surfaces to be described round a moveable solid or
solids immersed in a liquid. The surrounding fluid can only press (§ 1) perpen-
dicularly; and therefore when any motion is (§ 3) generated by impulsive forces
applied to the solids, the moment round any diameter of the momentum of the —
matter within the spherical surface at the first instant, must be exactly equal to
the moment of those impulsive forces round this line. And the moment. round
this line, of the momentum of the matter in the space between any two concentric
spherical surfaces is zero, provided neither cuts any solid, and provided that, if
there are any solids in this space, no impulse acts on them. |
18. Hence, considering what we have defined as ‘“‘the impulse of the motion,”
(§ 6), we see that its moment round any line is equal to the moment of momen-
tum round the same line, of all the motion within any spherical surface having its
centre in this line, and enclosing all the matter to which any constituent of the —
impulse is applied. This will still hold, though there are other solids not in the
neighbourhood, and impulses are applied to them: provided the moments of mo-
mentum of those only which are within S are taken into account, and provided
none of them is cut by S.
19. The statements of § 11, regarding fluid occupying at any instant a fixed
spherical surface, are applicable without change to the fluids and solids occupying
SIR W. THOMSON ON VORTEX MOTION. 225
the space bounded by S, because of our present condition, that no solid is cut by
S. Hence every statement and formula of § 15, as far as equation (11), may be
now applied to the matter within 8; but instead of (12) we now have [THomson
& Tair, § 736], if we denote by T,, T,, &c., another set of surface spherical
harmonics,
g9=S,+8,7 +837? + &e.
$7 toot Ty r—* + &e } ee
for all space between the greatest and smallest spherical surface concentric with
S, and having no solids in it, because through all this space, § 16, and the equa-
tion of continuity prove that 77 ¢ = 0. Hence, instead of (13), we now have
Fe Se Coop Ries Siti, &e, )
dr
2 3 fie
(15).
Hence finally
es ee Pelle dS; .
dt = see ffs E 8; ap — (@ + 1) T; 7a sin 6d bdL 5 (16).
Now if, as assumed in § 5, neither any moveable solids, nor any part of the
_ boundary exist within any finite distance of S allround; §,, 8,, &c., must each
_ be infinitely small: and therefore (16) gives eDi- his proves the proposition
at
asserted in § 5: because a system of forces cannot have zero moment round
_ every line drawn through any finite portion of space, without having force-resul-
— tant and couple-resultant each equal to zero
20. As the rigidity of the solids has not been taken into account, all or any of
them may be liquefied (§ 3) without violating the demonstration of $19. To save
circumlocutions, I now define a vortex as a portion of fluid having any motion
that it could not acquire by fluid pressure transmitted through itself from its
boundary. Often, merely for brevity, I shall use the expression a body to denote
either a solid or a vortex, or a group of solids or vortices.
21. The proposition thus proved may be now stated in terms of the definitions
of § 6, which were not used in § 5, and so becomes simply this:—The impulse of
the motion of a solid or group of solids or vortices and the surrounding liquid remains
constant as long as no disturbance is suffered from the influence of other solids or
vortices, or of the containing vessel.
This implies, of course (§ 6), that the magnitudes of the force-resultant and
_ the rotational moment of the impulse remain constant, and the position of its axis
invariable.
A iy : ere :
* There is no term at because this would give, in the integral of flow across the whole sphe-
rical surface, a finite amount of flow out of or into the space within, implying a generation or
destruction of matter.
VOL, XV. PART I. 3M
226 SIR W. THOMSON ON VORTEX MOTION.
_ 22. In Pornsot’s system of the statics of a rigid body we may pass from the
resultant force and couple along and round the central axis to an equal resultant
force along the parallel line through any point, and a greater couple the resultant
of the former (or minimum) couple, and a couple in the plane of the two parallels,
having its moment equal to the product of their distance intp the resultant force.
So we may pass from the force-resultant and rotational moment of the impulse
along and round its axis, to an equal force-resultant and greater moment of im-
pulse, by transferring the former to any point, Q, not in the axis (§ 6) of the
motion. This greater moment is (§ 18) equal to the moment of momentum round
the point Q, of the motion within any spherical surface described from Q as
centre, which encloses all the vortices or moving solids.
23. Hence a group of solids or vortices which always keep within a spherical
surface of finite radius, or a single body, moving in an infinite liquid, can have
no permanent average motion of translation in any direction oblique to the direc-
tion of the force-resultant of the impulse, if there is a finite force-resultant. For
the matter within a finite spherical surface enclosing the moving bodies or body,
cannot have moment of momentum round the centre increasing to infinity.
24. But there may be motion of translation when the force-resultant of the
impulse vanishes; and there will be, for example, in the case of a solid, shaped
like the screw-propeller of a steamer, immersed in an infinite homogeneous liquid,
and set in motion by a couple in a plane perpendicular to the axis of the screw.
25. And when the force-resultant of the impulse does not vanish, there may be
no motion of translation, or there may even be translation in the direction opposite
to it. Thus, for example, a rigid ring, with cyclic motion, established (§ 63) through
it, will, if left at rest, remain at rest. And if at any time urged by an impulse
in either direction in the line of the force-resultant of the impulse of the cyclic
motion, it will commence and continue moving with an average motion of trans-
lation in that direction ; a motion which will be uniform, and the same as if there
were no cyclic motion, when the ring is symmetrical. If the translatory impulse
is contrary to the cyclic impulse, but less in magnitude, the translation will be
contrary to the whole force-resultant impulse.
If the translatory impulse is equal and opposite to the cyclic impulse,
there will be translation with zero force-resultant impulse—another example of
what is asserted in § 24. In this case, if the ring is plane and symmetrical, or
of any other shape such that the cyclic motion (which, to fix ideas, we have sup-
posed given first, with the ring at rest,) must have had only a force-resultant,
and no rotational moment, we have a solid moving with a uniform motion of
translation through a fluid, and both force and couple resultant of the whole
impulse zero. “@
26. From §§ 21 and 4, we see that, however long the time of application of —
the impressed forces may be—provided only that, during the whole of it, the —
SIR W. THOMSON ON VORTEX MOTION. 224
solid or group of solids has been at an infinite distance from all other solids and
from the containing vessel—the time integrals of the impressed forces parallel
to three fixed axes, and of their moments round these lines, are equal to the six
corresponding components of “‘ the impulse” (§ 6).
27. If two groups, at first so far asunder as to exercise no sensible influence
on one another, come together, the “impulse” of the whole system remains un-
changed by any disturbance each may experience from the other, whether by im-
pacts of the solids, or through motion and pressure of the surrounding fluid; and
(§ 6) it is always reducible to the force-resultant along the central axis, and the
minimum couple-resultant, of the two impulses reckoned as if applied to one
rigid body. The same holds, of course, if one group separates into two so
distant as to no longer exert any sensible influence on one another.
28. Hence whatever is lost of impulse perpendicular to a fixed plane, or of
component rotational movement round a fixed line, by one group through collision
with another, is gained by the other.
29. Two of the moveable solids, or two groups, will be said to be zn collision
when, having been so far asunder as not to disturb one another’s motions sen-
sibly, they are so near as to do so. ‘This disturbance will generally be supposed
to be through fiuid pressure only, but impacts of solids on solids may take place
during a collision.
30. We are now prepared to investigate (§§ 30, 31, 32) the influence of a fixed
solid on the impulse of a moveable solid, or of a vortex, or of a group of solids or
vortices, passing near it, thus—If during such collisions or separations as are con-
sidered in S§ 27, 28, forces are impressed on any one or more of the solids, their
alteration of the whole impulse is (§ 26) to be reckoned by adding to each of its
rectangular components the time integral of the corresponding component of —
these impressed forces. Now, let us suppose such forces to be impressed on any
one of the moveable solids as shall keep it at rest. These forces are zero as long
as no moving solid is within a finite distance. But if a moving solid or vortex,
or group of solids or vortices, passes near the fixed solid, the change of pressure
due to the motion of the fluid will tend to move it, and the impression of force
on it becomes necessary to keep it fixed. Let do be an element of its surface;
(x, y, 2), the co-ordinates of the centre of this element; a, 8, y the inclinations of
the normal at (2, y, z) to the three rectangular axes; and p the fluid pressure
at time ¢, and point (a, y, z). The six components of force and couple required
to hold the body fixed at time #, are
f[do. cosa.p, ffde.cosB.p, ff/de. cosy. p; ;
Ide (y cosy — zcosB)p , [fde(zcosa — xcosy)p , [/do(xcosB — y cos x)p , a):
| If in these expressions we substitute
Spat ’ Hey
228 SIR W. THOMSON ON VORTEX MOTION.
in place of p ( /dt denoting a time integral from any era of reckoning before the
disturbance became sensible, up to time 7, which may be any instant during the
collision, or after it is finished), we have the changes in the corresponding com-
ponents of the impulse up to time ¢, provided there has been no impact of move-
able solid on the fixed solid.
31. Let now the “ velocity potential” (as we shall call it, in conformity witha
German usage which has been adopted by HeLMHoLTZ,) be denoted by ¢; that is
(S$ 16), let » be such a function of (a, y, z, ¢) that
_ do ___ ap _ do
Use oi, Siti , : ; (3).
and let @ (or ?) denote its rate of variation per unit of time at any instant ¢,
for the point (z, y, 2) regarded as fixed.
Also, let g denote the resultant fluid velocity, so that
‘ do* do* dg?
G@=aw+e¢qdwv= f =F ae + oa . : (4).
The ordinary hydro-dynamical formula gives
p=u-$-3¢ . (5) ;
where II denotes the constant pressure in all sensibly quiescent parts of the
fluid.
32. The constant term II disappears from p in each of the integrals (1) of
§ 30, because a solid is equilibrated by equal pressure around. And in the time
integral (2), we have
Sedt =o : : (Oy;
and therefere if (XYZ) (LMN) denote the changes in the force-and couple-com-
ponents of the impulse produced by the collision up to time ¢, we have
X = —ffdecosa (9 + £/q? di), Y= &.,Z= &e., 7)
L = — ffdo (y cos y — 2 cos B) (9 + 4/¢? dt), M = &., N= &c.,
But because the fluid is quiescent in the neighbourhood of the fixed body when
the moving body or group of bodies is infinitely distant from it; it follows that
before the commencement and after the end of the collision we have ¢ = 0 at
every point of the surface of the fixed body. Hence, for every value of ¢ represent-
ing a time after the completion of the collision, the preceding expressions become
X= —-—iffdecosa/gdt, Y= &., Z= &e., |
L = — }ffdo(y cosy — zc0s 8) fe? dt, M = &., N = &.,, (8);
which express that the integral change of impulse experienced by a body or group
of bodies, in passing beside a fixed body without striking it, may be regarded as a
SIR W. THOMSON ON VORTEX MOTION. 229
system of impulsive attractions towards the latter, everywhere in the direction of the
normal, and amounting to 4 /a°dt per unit of area. But it must not be forgotten
that the term ¢ in the expression [§ 31 (5)] for p produces, as shown in § 30 (1),
an influence during the collision, the integral effect of which only disappears
from the expression [§ 32 (7)] for the impulse after the collision 1s completed ; that
is (§ 29) after the moving system has passed away so far as to leave no sensible
fluid motion in the neighbourhood of the fixed body.
33. Hence, and from § 23, we see that when there is no impact of moving
solid against the fixed body, and when the moving solid or group of solids passes
altogether on one side of the fixed body, the direction of the translation will be
deflected, as if there were, on the whole, an attraction towards the fixed body, or
a repulsion from i, according as (§ 25) the translation is in the direction of the
impulse or opposite to it. For, in each case, the impulse is altered by the intro-
duction of an impulse towards the fixed body upon the moving body or bodies as
they pass it; and (§ 23) the translation before and after the collision is always
along the line of the impulse, and is altered in direction accordingly. This will
be easily understood from the diagrams, where, in each case 5 represents the
fixed body, the dotted line ITT’, and arrow-heads I I’, the directions of the force-
resultant of the impulse at successive times, and the full arrow-heads T 1’, the
directions of the translation.
Fig.1 ag Fig. 2 LAT
BAS Fide
Av’ Vr
" i
) N 1!
‘
“A vee
f
ai | van
Pee
Zoe \
All ordinary cases belong to the class illustrated by fig. 1. The case of a
rigid ring, with cyclic motion (§ 25) established round it as core, belongs to the
class illustrated by fig. 2, if the ring be projected through the fluid in the direc-
tion perpendicular to its own plane, and contrary to the cyclic motion through
its centre.
34. When (§ 66) we substitute vortices for the moving solids, we shall see (§ 67)
that the translation is probably always in the direction with the impulse. Hence,
as illustrated by fig. 1, there is always the deflection, as if by attraction, when a
group of vortices pass all on one side of a fixed body. Thisis easily observed, for
a simple Helmholtz ring, by sending smoke rings on a large scale, according to
VOL. XXV. PART I. oN
230 SIR W. THOMSON ON VORTEX MOTION.
Professor Tait’s plan, in such directions as to pass very near a convex fixed sur-
face. An ordinary 12-inch globe, taken off its bearings and hung by a thin cord,
answers very well for the fixed body.
35. The investigation of §§ 30, 31, 32, is clearly applicable to a vortex or a
moving body, or of a group of vortices or moving bodies, which keep always
near one another (§ 23), passing near a projecting part of the fixed boundary,
and being, before and after this collision (§ 29), at a very great distance from
every part of the fixed boundary. Thus,a Helmholtz ring projected so as to pass
near a projecting angle of two walls, shows a deflection of its course, as if caused
by attraction towards the corner.
36. In every case the force-resultant of the impulse is, as we shall presently
see (§ 37), determinate when the flow of the liquid across every element of any
surface completely enclosing the solids or vortices is given ; but not so, from such
data, either the axis (§ 6) or the rotational moment, as we see at once by con-
sidering the case of a solid sphere (which may afterwards be supposed liquefied) set
in motion by a force in any line not through the centre, and a couple in a plane
perpendicular to it. For this line will be the “axis,” and the impulsive couple will
be the rotational moment of the whole motion of the solid and liquid. But the
liquid, on all sides, will move exactly as it would if the impulse were merely
an impulsive force of equal amount in a parallel line through the centre of the
sphere, with therefore this second line for “ axis” and zero for rotational moment.
For illustration of rotational moment remaining latent in a liquid (with or with-
out solids) until made manifest by actions, tending to alter its axis, or showing
effects of centrifugal force due to it; see § 66, and others later.
37. The component impulse in any direction is equal to the corresponding
component momentum of the mass enclosed within the surface S, containing all
the places of application of the impulse, together with that of the impulsive
pressure outwards on this surface. But asthe matter enclosed by S (whether all —
liquid or partly liquid and partly solid) is of uniform density, its momentum will
be equal to its mass multiplied into the velocity of the centre of gravity of the —
space within the surface S supposed to vary so as to enclose always the same
matter, and will therefore depend solely on the normal motion of 8; that is to
say, on the component of the fiuid velocity in the direction of the normal at every
point of 8. And the impulsive fluid pressure, corresponding to the generation of
the actual motion from rest, being the time integral of the pressure during the
instantaneous generation of the motion, is (S§ 31, 32) equal to — ¢, the velocity
potential; which (§ 61) is determinate for every point of S, and of the exterior
space when the normal component of the fluid motion is given for every point of
S. Hence the proposition asserted in § 36. Denoting by de any element of 8;
N the normal component of the fluid velocity; a the inclination to OX, of the
normal drawn outwards through do ; and X the z-component of the impulse; we
SIR W. THOMSON ON VORTEX MOTION. 231
have for the two parts of this quantity considered above, and its whole value, the
following expressions; of which the first is taken in anticipation from § 42—
xz-momentum of matter, within §, = iff Na de (8) of § 42
ax-component of impulsive pressure on §, outwards, = — //p cos ade (1).
X =//(Nx — 9cosa) do . . , ; : ; ; (2).
It is worthy of remark that this expression holds for the impulse of all the solids
or vortices within S, even if there be others in the immediate neighbourhood out-
side: and that therefore its value must be zero if there be no solids or vortices
within S, and N and ¢ are due solely to those outside.
38. If > be the potential of a magnet or group of magnets, some within S and
others outside it, and N the normal component magnetic force, at any point of S,
the preceding expression (2) is equal to the z-component of the magnetic moment
of all the magnets within S, multiplied by 47. For let p be the density of any
continuous distribution of positive and negative matter, having for potential, and
normal component force, ¢ and N respectively, at every point of S. We have
[THomson & Tait, § 491 (c)] ¢ = — a v’? 9, and therefore
1 ag do Va"
fe dx dy dz= — rae (Fe = dy + Ga) de dy dz ; (3).
Now, integrating by parts,* as usual with such expressions, we have
d? d u u
fe Guyuaf[fo FZ aya: —f{f} das dy de =ff (eZ —) dy dz .
Hence, integrating each of the other two terms of (3) once simply, and reducing
as usual [THomson & Tait, App. A (q@)] to a surface integral, we have
il
W[fewuus-a (Nzx—gcosa)do . 4);
which proves the proposition, and also, of course, that if there be no matter
within S, the value of the second member is zero.
39. Hence, considering the magnetic and hydrokinetic analogous systems
with the sole condition that at every point of some particular closed surface, the
magnetic potential is equal to the velocity potential, we conclude that 47 times
the magnetic moment of all the magnetism within any surface, in the magnetic
system, is equal to the force-resultant of the impulse of the solids or vortices
within the corresponding surface in the hydrokinetic system ; and that the direc-
tions of the magnetic axis and of the force-resultant of the impulse are the same.
For the theory of magnetism, it is interesting to remark that indeterminate dis-
tributions of magnetism within the solids, or portions of fluid to which initiating
* The process here described leads merely to the equation obtained by taking the last two equal
members of App. A (1) (THomson & Tarr) for the casea = 1,U = 9, U'= «.
232 SIR W. THOMSON ON VORTEX MOTION.
forces (§3) were applied, or determinate distributions in infinitely thin layers
at their surfaces, may be found, which through all the space external to them
shall produce the same potential as the velocity-potential, and therefore the same
distribution of force as the distribution of velocity through the whole fluid.
But inasmuch as when the magnetic force in the interior of a magnet is
defined in the manner explained in § 48 (2) of my ‘‘ Mathematical Theory of
Magnetism,’’* it is expressible through all space by the differential coefficients of
a potential; and, on the contrary, for the kinetic system w dz + v dy + w dzis
not a complete differential generally through the spaces occupied by the solids,
the agreement between resultant force and resultant flow holds only through the
space exterior to the magnets and solids in the magnetic and kinetic systems
respectively. But if the other definition of resultant force within a magnet,
[‘‘Math. Theory of Magnetism,” § 77, foot-note, and § 78], published in preparation
for a 6th chapter ‘On Electro-magnets” (still in my hands in manuscript, not
quite completed), and which alone can be adopted for spaces occupied by non-mag-
netic matter traversed by electric currents, the magnetic force has not a potential
within such spaces; and we shall see (§68) that determinate distributions of
closed electric currents through spaces corresponding to the solids of the hydro-
kinetic system can be found which shall give for every point of space, whether
traversed by electric currents or not, a resultant magnetic force, agreeing in
magnitude and direction with the velocity, whether of solid or fluid, at the cor-
responding point of the hydrokinetic system. This thorough agreement for all
space renders the electro-magnetic analogue preferable to the magnetic; and,
having begun with the magnetic analogous system only because of its convenience
for the demonstration of § 38, we shall henceforth chiefly use the purely electro-
magnetic analogue.
40. To prove the formula used in anticipation, in § 37 (1) we must now
(S§ 41, 42, 43) find the momentum of the whole matter—fiuid, fluid and solid,
or even solid alone—at any instant within a closed surface S, in terms of the
normal component velocity of the matter at any point of this surface, or, which is
the same, the normal velocity of this surface itself, if we suppose it to vary so
_ as to enclose always the same matter. ;
41. Let V be the volume of the space bounded by any varying closed surface
S. As yet we need not suppose V constant. Let #, y, 2 be the co-ordinates of
of the centre of gravity. We have
Vzst/fl[edydz] . ; : : (5),
where[ _] indicates that the expression within it is to be taken between proper
limits for S. Now as S varies with the time, the area through which //dy dz is —
taken will in general vary; but the increments or decrements which it experiences
* Trans. R.S. Lond., 1851; or “ THomson’s Electrical Papers.” Macmillan. 1869.
SIR W. THOMSON ON VORTEX MOTION. 233
at different parts of the boundary of this area, in the infinitely small time di,
contribute no increments or decrements to //[a°dy dz], as we see most easily by
first supposing S to be a surface everywhere convex outwards. Hence
di Sg [a* dy dz] =f; ie [ee dyd: | = 2 ff ia & PP * dy dz] : (6).
But if N denote the velocity with which the surface moves in the direction of its
outward normal at («, y, %), we have, in the preceding expression
dx
a N seca : : : : (7),
if a be the inclination of the outward normal to OX. Hence
ane = f[fton sec a dy dz].
But the condition as to limits indicated by [ ] are clearly satisfied, if, de
denoting an element of the surface, such that
dy dz = cos ade,
we simply take //dc over the whole surface. Thus we have
Boe =ffon 2 ae (7) ;
42. In any case in which V is constant, this becomes
ie ea) eM ehan ee hic ital ob vit rook
If now the varying surface, S, is the boundary of a portion of the matter—fluid
or solid—of uniform density unity, with er motions we are occupied, the
a-component momentum of this portion is Wee Fi a and, therefore, equation (8) is
the required (§ 40) expression.
| 43. The same formule (7) and (8) are proved more shortly of course by the
_ regular analytical process given by Porsson* and GREEN t+ in dealing with such
| subjects; thus, in short. Let w, v, w be the components of velocity, of any matter,
| compressible or incompressible, at any point (#, y, z) within S; and let ¢ denote
dv dw
| the value at this point of 4 +7 +7, So that
dy
i Obie. dv , dw
pe =C dy + az , > : s (9).
| We have, for the component momentum of the whole matter within S, if of unit
| density at the instant considered,
Sf fede ay ae = =e [ [vz dy dz ~f ffs 7, dedy dz a CLO)
* Théorie de la Chaleur, § 60, + Essay on Electricity and Magnetism.
VOL. XXV. PART I. 30
234 SIR W. THOMSON ON VORTEX MOTION.
But by (9)
ST fa away ds = ff fox au dy ae S]fe (2+ Ow dee dy da
and by simple integrations,
SS fe (G+ + Gp) dedy de = [fa(vdeds + waedy),
Using these in (10), and altering the expression to a surface integral, as in
THomson & Tait, App. A (@), we have
eae y te = {fx (udy dz + vdzdx + w dx dy) — //fcx dx dy dz
=/f[uNds—f{fexdxdydz . . : 3 (11),
which clearly agrees with (7).
When this mass is incompressible, we have c=o by the formula so ill named
the equation ‘ of continuity” (THomson & Tarr, § 191), and we fall upon by )
The proper analytical interpretation of the differential coefficients 5 ” ites
and of the equation of continuity, when, as at the surfaces of separation a fluid
and solids, w, v, w are discontinuous functions, having abruptly varying values,
presents no difficulty.
44. In the theory of the impulse applied to the collision (§ 29) of solids or
vortices moving through a liquid, the force-resultant of the impulse corresponds,
as we have seen, precisely to the resultant momentum of a solid in the ordinary
theory of impact. Some difficulty may be felt in understanding how the zero-
momentum (§ 4) of the whole mass is composed; there being clearly positive
momentum of solids and fluids in the direction of the impulse in some localities
near the place of its application, and negative in others. [Consider, for example,
the simple case of a solid of revolution struck by a single impulse in the line of —
its axis. The fluid moves in the direction of the impulse, before and behind the
body, but in the contrary direction in the space round its-middle.] Three modes
of dividing the whole moving mass present themselves as illustrative of the dis-
tribution of momentum through it; and the following propositions (§ 45) with
reference to them are readily proved (§§ 46, 47, 48).
45. I. Imagine any cylinder of finite periphery, not necessarily circular, com- —
pletely surrounding the vortices (or moving solids), and any other surrounding
none, and consider the infinitely long prisms of variously moving matter at any
instant surrounded by these two cylinders. The component momentum parallel
to the length of the first is equal to the component of the impulse parallel to the
same direction ; and that of the second is zero.
iI. Imagine any two finite spherical surfaces, one sea all the vortices
SIR W. THOMSON ON VORTEX MOTION. 235
or moving solids, and the other none. The resultant-momentum of the whole
matter enclosed by the first is in the direction of the impulse, and is equal to 2
of its value. The resultant-momentum of the whole fluid enclosed by the
second is the same as if it all moved with the same velocity, and in the same
direction, as at its centre.
III. Imagine any two infinite planes at a finite distance from one another
and from the field of motion, but neither cutting any solid or vortex. The com-
ponent perpendicular to them of the momentum of the matter occupying at any
instant the space between them (whether this includes none, some, or all of the
vortices or moving solids) is zero.
46. To prove these propositions :—
I. Consider in either case a finite length of the prism extending to a very
great distance in each direction from the field of motion, and terminated by
plane or curved ends. Then, the motion being, as we may suppose (§ 61) started
from rest by impulsive pressures on the solids [or (§ 66) on the portions of fluid
constituting the vortices]; the impulsive fluid pressure on the cylindrical surface
can generate no momentum parallel to the length; and to generate momentum
in this direction there will be, in case 1, the impressed impulsive forces on the
solids, and the impulsive fluid pressures on the ends; but in case 2 there will
be only the impulsive fluid pressure on the ends. Now, the impulsive fluid
pressures on the ends diminish [§ 50 (15)] according to the inverse square of the
distance from the field of motion, when the prism is prolonged in each direction,
and are therefore infinitely small when the prisms are infinitely long each way.
Whence the proposition I.
47. By using the harmonic expansions § 19, (14), (15), in the several expres-
sions (1), (2), of § 37, (1), (2); and the fundamental theorem
[2:8 do=0,
of the harmonic analysis [THomson & Tart, App. B. (16)]; and putting S, = 0
for one case, and T; = 0 for the other; we prove the two parts of Prop. II., § 45
immediately.
48. To prove Prop. II., § 45, the well-known theory of electric images in a
plane conductor* may be conveniently referred to. It shows that if N, denotes
the normal component force at any point of an infinite plane due to any distribu-
tion, “, of matter in the space lying on one side of the plane, a distribution of
matter over the plane having = N, for surface density at each point exerts the
same force as » through all the space on the other side of the plane, and therefore
that the whole quantity of matter in that surface distribution is equal to the
* Tuomson, Camb. and Dub. Math. Journal, 1849; Liovvitix’s Journal, 1845 and 1847; or
Reprints of Electrical Papers, (Macmillan, 1869.)
236 SIR W. THOMSON ON VORTEX MOTION.
whole quantity of matter in «.* Hence, // dc, denoting integration over the
infinite plane
[If N,de= 0 ‘ ‘ f : ; ; (12).
if the whole quantity of matter in » be zero. Hence, if N be the normal force
due to matter through space on both sides of the plane, ae the whole quan-
tity of matter on each side separately is zero,
(20 en rere
since N is the sum of two parts, for each of which separately (12) holds. This
translated into hydrokinetics, shows that the whole flow of matter across any
infinite plane is zero at every instant when it cuts no solids or vortices. Hence,
and from the uniformity of density which (§ 3), we assume, the centre of gravity
of the matter between any two infinite fixed parallel planes, has no motion in
the direction perpendicular to them at any time when no vortex or moving solid
is cut by either: which is Prop. III. of § 4 in other words.
49. The integral flow of matter across any surface whatever, imagined to
divide the whole volume of the finite fixed containing vessel of § 1 into two parts is
necessarily zero, because of the uniformity of density; and therefore the momen-
tum of all the matter bounded by two parallel planes, extending to the inner
surface of the containing vessel, and the portion of this surface intercepted
between them has always zero for its component perpendicular to these planes,
whether or not moving solids or vortices are cut by either or both these planes.
But it is remarkable that when any moving solid or vortex is cut by a plane, the
integral flow of matter across this plane (if the containing vessel is infinitely
distant on all sides from the field of motion), converges to a generally jinite value,
as the plane is extended to very great distances all round from the field of
motion, which are still infinitely small in comparison with the distances to the
containing vessel; and diminishes from that finite value to zero by another con-
vergence, when the distances to which the plane is extended all round begin to
be comparable with, and ultimately become equal to, the distances of the curve
in which it cuts the containing vessel. Hence we see how it is that the condition
of neither plane cutting any moving solid or vortex is necessary to allow § 46,
III. to be stated without reference to the containing vessel, and are reminded that
* This is verified synthetically with ease, by direct integrations showing (whether by Cartesian
or polar plane co-ordinates), that
eto s*. ae
And taking = of this, we have
2) Ayre pe ee
he oie Oe iy ae 9p. ue.
(a? + y? + 27)§
the synthesis of (12).
SIR WILLIAM THOMSON ON VORTEX MOTION. 237
the equality to zero asserted in this proposition is proved in § 48 to be approxi-
mated to when the planes are extended to distances all round, which, though infi-
nitely short of the distances to the containing vessel, are very great in comparison
with their perpendicular distances from the most distant parts of the field of
motion.
50. The convergencies concerned in § 46, I., III. may be analysed thus. Per-
pendicular to the resultant impulse draw any two planes on the two sides of the
field of motion, with all the moving solids and vortices between them, and divide
a portion of the space between them into finite prismatic portions by cylindrical
(or plane) surfaces perpendicular to them. Suppose now one of these prismatic
portions to include all the moving solids and vortices, and without altering the
prismatic boundary, let the parallel planes be removed in opposite directions to
distances each infinite (or very great) in comparison with distance of the most
distant of the moving solids or vortices. By § 46, I., the momentum of the motion
within this prismatic space is (approximately) equal to the force-resultant, I, of
the impulse, and that of the motion within any one of the others is (approximately)
zero.
But the sum of these (approximately) zero values must, on account of § 46,
II1., be equal to —I, if the portions of the planes containing the ends of the
prismatic spaces be extended to distances very great in comparison with the dis-
tance between the planes. To understand this, we have only to remark that if
denotes the velocity potential at a point distant D from the middle of the field,
and « from a plane through the middle perpendicular to the impulse, we have
(§ 53) approximately,
la
Cee edu ny mane Ui bat yl thetey,
provided D be great in comparison with the radius of the smallest sphere enclos-
ing all the moving solids or vortices. Hence, putting 2 = +a for the two planes
under consideration, denoting by A the area of either end of one of the prismatic
portions, and calling D the proper mean distance for this area, we have (§ 46) for
the momentum of the fluid motion within this prismatic space, provided it con-
tains no moving solids or vortices,
la
— 2 72D:
OR tLe we Ameer Meet 16),
bes
This vanishes when & is an infinitely small fraction (as D
D is at most unity); but
it is finite if p: 3s finite, provided . be not infinitely small. And its integral
value (compare § 48, footnote) converges to — I, when the portion of area in-
a
cluded in the integration is extended till —p 3S infinitely small for all points of its
boundary.
VOL. XV. PART 1. 3 P
238 SIR WILLIAM THOMSON ON VORTEX MOTION.
51. Both as regards the mathematical theory of the convergence of definite
integrals, and as illustrating the distribution of momentum in a fluid, it is inter-
esting to remark that, w denoting component velocity parallel to x, at any point
(z, y, 2), the integral //u dx dy dz, expressing momentum, may, as is readily
proved, have any value from —o to + according to the portions of space
through which it is taken.
52. As a last illustration of the distribution of momentum, let the containing
vessel be spherical of finite radius a.
We have, as in § 19,
g9=8,+ 5,7 +827? + &e.,
(14),
+ T,r-? + T, 7-7? + &e.,
each series converging, provided 7 is less than a, and greater than the radius
of the smallest concentric spherical surface enclosing all the solids or vortices.
Now, by the condition that there be no flow across the fixed containing surface.
we must have
oe - 0, when7 =a : : : : : (15),
which gives
a+1 T; .
S; = ag : 2 i : « ele
and (14) becomes
4 r® T 3 Pr
p= (1425)4+ 3(1455) + & entaany:
But [§ 37 (1) ]if the whole amount of the w-component of impulsive pressure
exerted by the fluid within the spherical surface of radius 7, upon the fluid round
it be denoted by I, we have
F = — f/9 cos bdo : a (2)
6 being the inclination to OX of the radius through dc. Now cos @ is a surface
harmonic of the first order, and therefore all the terms of the harmonic expan-
sion, except the first, disappear in the integral, which consequently becomes
3 d
P= - (1425) [[Treose S . as
_ Aw + By + Cz
r
Now let
ie (20),
this being [THomson & Tair, App. B, §§ i, j] the most general expression for a sur-
face harmonic of the first order. We have cosé =<; and therefore (by spheri-
cal harmonics, or by the elementary analysis of moments of inertia of a uniform
spherical surface),
SIR WILLIAM THOMSON ON VORTEX MOTION. 239
aff, cos 1% = Af fea= Oi:
as
F= (1425). | . | (22):
Whence, if X denote the z-momentum of the fluid at any instant in the space
between concentric spherical surfaces of radius 7 and 7”,
and (19) becomes
3 nf
4A es
If 7 and 7’ be each infinitely small in comparison with a, this expression vanishes,
as it ought to do, in accordance with § 45, I]. But if
Li ee
ss (24),
it becomes X = —3.4cA
fulfilling § 4, by showing in the fluid outside the spherical surface of radius 7” a
momentum equal and opposite to that (§ 45, II.) of the whole matter, whether
fluid or solid, within that surface.
53, Comparing § 47 and § 52, we see that ff X, Y, Z be rectangular com-
ponents of the force-resultant of the impulse, the term T, 7~—? of the harmonic
expansion (14) is as follows :-—
T, po? = ee + Vy + Ze
Ag v8 :
provided all the solids and vortices taken into account are within a spherical
surface whose radius is very small in comparison with the distances of all other
vortices or moving solids, and with the shortest distance to the fixed bounding
surface.
54, HELMHOLTZ, in his splendid paper on Vortex Motion, has made the very
important remark, that a certain fundamental theorem of GREEN’s, which has
been used to demonstrate the determinateness of solutions in hydrokinetics, is
subject to exception when the functions involved have multiple values. This calls
for a serious correction and extension of elementary hydrokinetic theory, to
' which I now proceed.
55. In the general theorem (1) of THomson & Tait, App. A leta=1. It
becomes
dp do’ poe de’ dodg = ff R be
whee de dx * dy dy * dz i) dedy de = | /dsone ff fix dy dz9v 2
=f/ eee ail DO Oe Cian tially mane os ts) es a (1);
which is true without exception if ~ and ¢’ denote any two single-valued functions
of 2, y,2; ///dx dy dz integration through the space enclosed by any finite closed
(25),
240 SIR WILLIAM THOMSON ON VORTEX MOTION.
surface, S; //do integration over the area of this surface; and 0 rate of variation
per unit of length in the normal direction at any point of it. This is GREEN’s
original theorem, with HELMHOLTz’s limitation added (in italics.) The reader may
verify it for himself.
56. But if either ¢ or ¢’ is a many-valued function, and the differential co-
. d 19" ‘ :
efficients “ye tees - » +++» each single-valued, the double equation (1) cannot
be generally true. Its first member is essentially unambiguous; but the process
of integration by which the second member or the third member is found, would
introduce ambiguity if > or if ¢’ is many-valued. In one case the first member,
though not equal to the ambiguous second, would be equal to the third, provided
? is not also many-valued ; and in the other, the first member, though not equal
to the third, would be equal to the second, provided ¢ is not many-valued.
For example, let
Y=—t ary Y/ 9
i ae : (2).
and let S consist of the portions of two planes perpendicular to OZ, intercepted
between two circular cylinders having OZ for axis, and the portions of these
cylinders intercepted between the two planes. The inner cylindrical boundary
excludes from the space bounded by S, the line OZ where ¢’ has an infinite
19’ dy’ , ante
number of values, and -, and a have infinite values. We have
bl Spleen (3)
da a +y?’ dy x? + y? : ; : ;
and at every point of S, dp’ = 0. Then, if ¢ be single-valued, there is no failure
in the process proving the equality between the first and second members of (1),
which becomes
d d
Mf te
ee dzdyde=0. . : ‘ (4).
Compare § 14 (6) to end.
The third member of (1) becomes
[fa tan-? ve [ffi ‘ V'odxdydz . (5),
which is no result of unambiguous integration of the first member through the
space enclosed by 8S, as we see by examining, in this case, the particular mean-
ing of each step of the ordinary process in rectangular co-ordinates for proving
GREEN’s theorem. It is thus seen that we must add to (5) a term
on ff ax dz (2) ;
dy] y=0
SIR WILLIAM THOMSON ON VORTEX MOTION. 241
ek
if in its other terms the value of tan“*~ is reckoned continuously round from
one side of the plane ZOX to the other: or
dg
ies anf fay a(P) _, 5
if the continuity be from one side of ZOY to the other ; to render it really equal
to the first member of (1). Thus, taking for example the first form of the
added term, we now have for the corrected double equation (1) for the case of
= tan?! , ¢ any single valued function, and S the surface, composed of the
two co-axal cylinders and two parallel planes specified above:
dp
= 7)
Ba: da Z da dy dz =0 = an |) da a(e 4. aH i de tan Ya
a2 + y y=0 OG
ff dx dy dz tant! v%— : é (6).
But if we annex to S any barrier stopping circulation round the inner
cylindrical core, all ambiguity becomes impossible, and the double equa-
tion (1) holds. For instance, if the barrier be the portion of the plane ZOX,
intercepted between the co-axal gylinders and parallel planes constituting the
S of § 55, so that //do must now include integration over each side of this
rectangular area; (6) becomes simply the strict application of (1) to the case
in question.
57. The difficulty of the exceptional interpretation of GREEN’s theorem for the
class of cases exemplified in §§ 55 and 56, depends on the fact that /Fds may have
different values when reckoned along the lengths of different curves, drawn within
the space bounded by S, from a point P to a point Q;: ds being an infinitesimal
element of the curve, and F the rate of variation of ¢ per unit of length along it.
Let PCQ, PC’Q be two curves for which the /Fds has different values; and let
both lie wholly within S. If we draw any curve from P to Q; make it first
coincide with PCQ, and then vary it gradually until it coincides with PC’Q; it
must in some of its intermediate forms cut the bounding surface S: for we have
do do do
Hes == da 4 = sates
ers da + ay dy + > dz
throughout the space contained within 8, and pe ea! al are each of them
a” dy’ de
unambiguous by hypothesis; which implies that /Fds has equal values for all
VOL. XXV. PART I. 3Q
242 SIR WILLIAM THOMSON ON VORTEX MOTION.
gradual variations of one curve between P and Q, each lying wholly within S.
Now, in a simply continuous space, a curve joining the points P and Q may be
gradually varied from any curve PCQ to any other PC’Q, and therefore if the
space contained within S be simply continuous, the difficulty depending on the
multiplicity of value of ¢ or ¢’ cannot exist. And however multiply continuous
(§ 58) the space may be, the difficulty may be evaded if we annex to S a
surface or surfaces stopping every aperture or passage on the openness of which ~
its multiple continuity depends; for these annexed surfaces, as each of them
occupies no space, do not disturb the triple integrations (1), and will, therefore,
not alter the values of its first member; but by removing the multiplicity of con-
tinuity, they free each of the integrations by parts, by which its second or third
members are obtained, from all ambiguity. To avoid circumlocution, we shall
call 6 the addition thus made to S; and further, when the space within § is
($58) not merely doubly but triply, or quadruply, or more multiply, continuous,
we shall designate by 8,, 6,; or 6,, 8,, 8,; and so on; the several parts of 6 re-
quired in any case to stop all multiple continuity of the space. These parts of 6
may be quite detached from one another, as when the multiple continuity is that
due to detached rings, or separate single tunnels in a solid. But one part 6, may
cut through part of another, 6,, as when two rings (§ 58, diagram) linked into one
another without touching constitute part of the boundary of the space considered.
And we shall denote by //ds, integration over the surface 8, or over any one of
its parts, 6,, 8,, &c. Let now P and Q be each infinitely near a point B, of 6, but
on the two sides of this surface. Let « denote the value of /Fds along any curve
lying wholly in the space bounded by §, and joining PQ without cutting the
barrier; this value being the same for all such curves, and for all positions of B
to which it may be brought without leaving 8, and without making either P or Q
pass through any part of 8. That is to say, « is a single constant when the space
is not more than doubly continuous; but it denotes one or other of m constants
Ky) Ko, ++ + Ky Which may be all different from one another, when the space is 7-ply
continuous. Lastly, let «’ denote the same element, relatively to ¢’, as « relatively
to >. We find that the first steps of the integrations by parts now introduce,
without ambiguity, the additions
saffds ye, and 3x’ //ds yo : : : (6),
to the second and third numbers of (1): = denoting summation of the integra-
tions for the different constituents 6,, 6,,... of 8; but only a single term when
the space is (§ 58) not more than doubly continuous. GreEEN’s theorem thus
corrected becomes
do dq’ do dy do +) =/f: ff] “ F
Ee + a + ly dy * Eda) ye do pug + xx// dsdo’ wi ovo dx dy dz
= ff ac gdp + xt [fisry iff} 9 Vv" 9 dx dy dz : (7).
SIR WILLIAM THOMSON ON VORTEX MOTION. 243
58. Adopting the terminology of Riemann, as known to me through Heim-
HOLTZ, I shall call a finite position of space n-ply continuous when its bounding
surface is such that there are m irreconcilable paths between anytwo points in
it. To prevent any misunderstanding, I add (1), that by a portion of space I mean
such a portion that any point of it may be travelled to from any other point of
it, without cutting the bounding'surface; (2), that the ‘* paths” spoken of all lie
within the portion of space referred to; and (3), that by irreconcilable paths
between two points P and Q; I mean paths such, that a line drawn first along
one of them cannot be gradually changed till it coincides with the other, being
always kept passing through P and Q, and always wholly within the portion of
space considered. ‘Thus, when all the paths between any two points are recon-
cilable, the space is simply continuous. When there are just two sets of paths,
so that each of one set is irreconcilable with any one of the other set, the space
is doubly continuous; when there are three such sets it is triply continuous, and
soon. To avoid circumlocutions, we shall suppose S to be the boundary of a
hollow space in the interior of a solid mass, so thick that no operations which we
shall consider shall ever make an opening to the space outside it. A tunnel through
this solid opening at each end into the interior space constitutes the whole space
doubly continuous ; and if more tunnels be made, every new one adds one to the
degree of multiple continuity. When one such tunnel has been made, the surface
of the tunnel is continuous with the whole bounding surface of the space con- ©
sidered; and in reckoning degrees of continuity, it is of no consequence whether
the ends of any fresh tunnel be in one part or another of this whole surface.
Thus, if two tunnels be made side by side, a hole anywhere opening from one of
them into the other adds one to the degree of multiple continuity. Any solid
detached from the outer bounding solid, and left, whether fixed or movable in the
interior space, adds to the bounding surface an isolated portion, but does not in-
terfere with the reckoning of multiple continuity. Thus, if we begin with a simply
continuous space bounded outside by the inner surface of the supposed exter-
nal solid, and internally by the boundary of the detached solid in its interior,
and if we drill a hole in this solid we produce double continuity. Two holes,
or two solids in the interior each with one hole (such as two ordinary solid
rings), constitute triple continuity, and so on. A sponge-like solid whose
pores communicate with one another, illustrates a high degree of multiple con-
tinuity, and it is of no consequence whether it is attached to the external
bounding solid or is an isolated solid in the interior. Another type of multiple
continuity, that presented by two rings linked in one another, was referred
to in § 57.
When many rings are linked into one another in various combinations, there
are complicated mutual intersections of the several partial barriers 6,, 6,, . .
required to stop all multiple continuity. But without having any portion of the
244 SIR WILLIAM THOMSON ON VORTEX MOTION.
bounding solid detached, as in that case in which one at least of the two rings is
loose, we have varieties of multiple continuity curiously different from that illus-
trated by a single ordinary straight or bent tunnel, illustrated sufficiently by the
simplest types, which are obtained by boring a tunnel along a line agreeing in
form with the axis of a cord or wire on which a simple knot is tied; and by fixing
the two ends of wire with a knot on it to the bounding solid, so that the surface
of the wire shall become part of the bounding surface of the space considered, the
knot not being pulled tight, and the wire being arranged not to touch itself in
any point; or by placing a knotted wire, with its ends united, in the interior of
the space. No amount of knotting or knitting, however complex, in the cord
whose axis indicates the line of tunnel, complicates in any way the continuity of
the space considered, or alters the simplicity of the barrier surface required to
stop the circulation. But it is otherwise when a knotted or knitted wire forms -
part of the bounding solid. A single simple knot, though giving only double con-
tinuity, requires a curiously self-cutting surface for stopping barrier: which, in
its form of minimum area, is beautifully shown by the liquid film adhering to an
endless wire, like the first figure, dipped in a soap solution and removed. But no
complication of these types, or of combinations of them with one another, eludes —
the statements and formule of § 57.
59. I shall now give a dynamical lemma, for the immediate object of preparing
to apply GrEEN’s corrected theorem (§ 57) to the motion of a liquid through a
multiply continuous space. But later we shall be led by it to very simple
demonstrations of HretmHoitz’s fundamental theorems of vortex motion; and
shall see that it may be used as a substitute for the common equations of
hydrokinetics. ‘
(Lemma). An endless finite tube* of infinitesimal normal section, being given
full of liquid (whether circulating round through it, or at rest) is altered in shape,
* A finite length of tube with its ends done away by uniting them together.
SIR WILLIAM THOMSON ON VORTEX MOTION. 245
Instalment, received Nov.—Dec. 1869 [§ 59 -§ 64 (5)].
length, and normal section, in any way, and with any speed. The average value of
the component velocity of the fluid along the tube, reckoned all round the circuit
(irrespectively of the normal section), varies inversely as the length of the circuit.
59. (a). To prove this, consider first a single particle of unit mass, acted on by
any force, and moving along a smooth guiding curve, which is moved and bent
about quite arbitrarily. Let e be the radius of curvature, and €, y the component
velocities of the guiding curve, towards the centre of curvature, and perpen-
dicular to the plane of curvature, at the point P, through which the moving
particle is passing at any instant. Let ¢ be the component velocity of the particle
itself, along the instantaneous direction of the tangent through P. Thus &, », ¢
are three rectangular components of the velocity of the particle itself. Let Z be
the component in the direction of ¢, of the whole force on P. We have, by
elementary kinetics,
ay dé dy
ae ee ‘ : : (i);*
* This theorem (not hitherto published 2) will be given in the second volume of Tuomson and
Tarr’s “Natural Philosophy.” It may be proved analytically from the general equations of the
motion of a particle along a varying guide-curve (Watron, “‘ Cambridge Mathematical Journal,”
1842, February); or more synthetically, thus—Let 7, m, n be the direction cosines of PT, the
tangent to the guide at the point through which the particle is passing at any instant; (2, y, z)
the co-ordinates of this point, and («, 7, 2) its component velocities parallel to fixed rectangular axes.
We have
C=le+my+nz; and Z = lz + mij + nd,
and from this
we = lé+ mij +nitléie+ nyt nz=Z+le+ my + nz.
But it is readily proved (Tomson and Tart’s “ Natural Philosophy, § 9, to be made more explicit
on this point in a second edition) that the angular velocity with which PT changes direction is equal
to /(? + mr? + n), and, if this be denoted by w, that
t m n
® @ @
are the direction cosines of the line PK, perpendicular to PT in the plane in which PT changes
direction, and on the side towards which it turns. Hence,
dé
yet Ke
if « denote the component velocity of P along PK. Now, if the curve were fixed we should have
o= by the kinematic definition of curvature (Tomson and Tarr, § 5); and the plane in which
PT changes direction would be the plane of curvature. But in the ease actually supposed, there is
also in this plane an additional angular velocity equal to = , and a component angular velocity
ds
in the plane of PT and 7, equal to = ; due to the normal motion of the varying curve. Hence
the whole angular velocity « is the resultant of two components,
Cf dé
g a ds
VOL. XXV. PART II. Bae 3
in the plane of €,
246 SIR WILLIAM THOMSON ON VORTEX MOTION.
: dé d: ee
where e denotes the radius of curvature, and = = rates of variation of € and 7
from point to point along the curve at one time.
59. (b). Now, instead of a single particle of unit mass, let an infinitesimal
portion, », of a liquid, filling the supposed endless tube, be considered. Let o be
the area of the normal section of the tube in the place where p is, and és the length _
along the tube of the space occupied by it, at any instant; so that (as the density
of the fluid is called unity),
b= wos -
Further, let a denote the rate of variation of the fluid pressure along the tube, —
so that
Thus we have, by (1),
ay te a :o = Bs _ dp
a ae . 7. ae : : : : (2).
(c). Now, because the two ends of the arc ds move with the fluid, we have, by
the kinematics of a varying curve,
dés _ dé E ‘
= = a, 8s = BOS acae ; . (3);
eee Eis +6(Ga- 7) a
and, therefore,
Substituting in this for ® its value by (2), we have
ad(fss) _ (dé dn
cg eg a
(56s)
dt
“p +t Os 5
or
= O(4g?—p) . : ’ : : (5),
if g denote the resultant fiuid velocity; and 6, differences for the two ends of the
arc 6s. Integrating this through the length of any finite arc P,P, of the fluid, its:
ends P,, P,, moving with the fluid, we have
PS) = Gapping os
the suffixes denoting the values of the bracketed function, at the points P, and.
and
ay.
— fn.
de it the plane of 7
Hence | Cased dn
e(j “+ 2) +0 Fra as
and the formula (1) of the text is proved.
SIR WILLIAM THOMSON ON VORTEX MOTION. 247
P,, respectively; and =; denoting integration along the arc from P; to P,. Let
now P, be moved forward, or P, backward, till these points coincide, and the
arc P,P, becomes the complete circuit; and let 2 denote integration round the
whole closed circuit. (6) becomes
d>(&€s)
dt
and we conclude that >fés remains constant, however the tube be varied. This
is the proposition to be proved, as the “average velocity’”’ referred to is found
by dividing >(65s) by the length of the tube. |
59. (d). The tube, imagined in the preceding, has had no other effect than exert-
ing, by its inner surface, normal pressure on the contained ring of fluid. Hence
the proposition®* at the beginning of § 59 is applicable to any closed ring of fluid
forming part of an incompressible fluid mass extending in all directions through
any finite or infinite space, and moving in any possible way; and the formule (5)
and (6) are applicable to any infinitesimal or infinite arc of it with two ends not
met. Thus in words—
Prop. (1.) The line-integral of the tangential component velocity round any
closed curve of a moving fluid remains constant through all time.
And, Prop. (2), The rate of augmentation, per unit of time, of the space
integral of the velocity along any terminated arc of the fluid is equal to the
* Equation (6), from which, as we have seen, that proposition follows immediately, may be
proved with greater ease, and not merely for an incompressible fluid, but for any fluid in which the
density is a function of the pressure, by the method of rectilineal rectangular co-ordinates from the
ordinary hydrokinetic equations. These equations are—
Du da Dw da Dw da
Dian ae PED manreyoib: § nedey
if Di denote rate of variation per unit of time, of any function depending on a point or points moving
with the fluid; and z= he es e denoting density. In terms of rectangular rectilineal co-ordinates
we have
Gs = udu + vdy + wez.
Hence
D(&s) Du Dox
br= pi & + up, + &e.
Now
Dé. DS. Déz
Spa, = =). and = bu.
These and the kinetic equations reduce the preceding to
D (fs) da da da
sae Sl ee Oa Ue ae ON che tut) = ae pCa igs
whence, by integration, equation (6) generalised to apply to compressible fluids.
248 SIR WILLIAM THOMSON ON VORTEX MOTION.
excess of the value of 3g” — p, at the end towards which tangential velocity is
reckoned as positive, above its value at the other end.
59. (e). The condition that wu dz +vdy + dz is a complete differential [proved
above (§ 13) to be the criterion of irrotational motion] means simply
That the flow (defined § 60 (a)] is the same in all different mutually recon-
cilable lines from one to another of any two points in the fluid ; or, which is the
same thing,
That the circulation [§ 60 (a)] is zero round every closed curve capable of being
contracted to a point without passing out of a portion of the fluid through which the
criterion holds.
From Proposition (1), just proved, we see that this condition holds through
all time for any portion of a moving fluid for which it holds at any instant; and
thus we have another proof of LAGRANGE’s celebrated theorem (§ 16), giving us a
new view of its dynamical significance, which [see for example § 60 (g)] we shall
find of much importance in the theory of vortex motion.
(f). But itis only ina closed curve, capable of being contracted to a point without
passing out of space occupied by irrotationally moving fluid, that the circulation
is necessarily zero, in irrotational motion. In § 57 we saw that a continuous fluid
mass, occupying doubly or multiply continuous space, may move altogether irro-
tationally, yet so as to have finite circulation in a closed curve PP’QQ’P, provided
PP’Q and PQQ are “ irreconcilable paths” between P and Q. That the circula-
tion must be the same in all mutually reconcilable closed curves (compare § 57),
is an immediate consequence from the now proved [§ 59 (Prop. 2)] equality of
the flows [§ 60 (a@)] in all mutually reconcilable conterminous arcs. For by
leaving one part of a closed curve unchanged, and varying the remaining
arc continuously, no change is produced in the flow, in this part; and, by —
repetitions of the process, a closed curve may be changed to any other recon-
cilable with it.
60. Definitions and elementary propositions (a). The line-integral of the
tangential component velocity along any finite line, straight or curved, in a
moving fluid, is called the flow in that line. If the line is endless (that is, if
it forms a closed curve or polygon), the flow is called circulation. The use of
these terms abbreviates the statements of Propositions (2) and (1) of § 59 to the
following :— :
[$ 59, Prop. (2)]. The rate of augmentation, per unit of time, of the flow
in any terminated line which moves with the fluid, is equal to the excess of the
value of 3q° — p at the end from which, above its value at the end towards which, —
positive flow is reckoned.
[§ 59, Prop. (1)]. The circulation in any closed line moving with the fluid,
remains constant through all time.
(0). If any open finite surface, lying altogether within a fluid, be cut into
SIR WILLIAM THOMSON ON VORTEX MOTION. 249
parts by lines drawn across it, the circulation in the boundary of the whole is
equal to the sum of the circulations in the boundaries of the parts. This is
obvious, as the latter sum consists of an equal positive and negative flow in each
portion of boundary common to two parts, added to the sum of the flows in all
the parts into which the single boundary of the whole is divided.
60. (c). Hence the circulation round the boundaries of infinitesimal areas,
infinitely near one another in one plane, are simply proportional to these
areas.
(d). Proposition. Let any part of the fluid rotate as a solid (that is, without
changing shape); or consider simply the rotation of a solid. The “ circulation”’
in the boundary of any plane figure moving with it is equal to twice the area
enclosed, multiplied by the component angular velocity in that plane (or round
an axis perpendicular to that plane). For, taking 7, @ to denote polar co-ordinates
of any point in the boundary, A the enclosed area, and » the component angular
velocity in the plane, and continuing the notation of § 59, we have
and therefore
> 40
ds
200s = otr” — és = w2r"6d = @ x 2A.
(e). Definition. (For a fluid moving in any manner), the circulation round
the boundary of an infinitesimal plane area, divided by double the area, is called
the component rotation in that plane (or round an axis perpendicular to that
plane) of the neighbouring fluid.
In this statement, the single word “rotation” is used for angular velocity of
rotation: and the definition is justified by (c) and (d); also by § 13 (2) above,
applied to (p) below. It agrees, in virtue of (p), with the definition of rotation
in fluid motion given first of all, I believe, by SroxeEs, and used by HeLmMuoitz
in his memorable “ Vortex Motion,” also in THomson and Tart’s “ Natural
Philosophy,” §§ 182 and 190 (7).
(f). Proposition. If €, n, ¢ be the components of rotation at any point, P, of
| a fluid, round three axes at right angles to one another, and » the component
| round an axis, making with them angles whose cosines are /, m, n,
o= &+nm+ &.
_.To prove this, let a plane perpendicular to the last-mentioned axis cut the other
| three in A, B, C. The circulation in the periphery of the triangle ABC is, by (0),
| equal to the sum of the circuJations in the peripheries PBC, PCA, and PAB.
Hence, calling A and a, 8, y the areas of these four triangles, we have, by (@),
oA = fa+nB+ &%.
VOL. XXV. PART IT. 35
250 SIR WILLIAM THOMSON ON VORTEX MOTION. .
But a, 8, y are the projections of A on the ee of the pairs of the rectangular
axes; and so the proposition is proved.
It follows, of course, that the composition of rotations in a fluid fulfils the
law of the compositions of angular velocities of a solid, of linear velocities, of
forces, &c.
60. (g). Hence, in any infinitesimal part of the fluid, the circulation is zero in
the periphery of every plane area passing through a certain line ;—the resultant
axis of rotation of that part of the fluid. But (a) the circulation remains zero in
every closed line moving with the fluid, for which it is zero at any time. Hence
(h). The axial lines [defined (z)] move with the fluid.
(2). Definition. An axial line through a. fluid moving rotationally, is a line
(straight or curved) whose direction at every point coincides with the resultant
axis of rotation through that point.
(7). Proposition. The resultant rotation of any part of the fluid varies in
simple proportion to the length of an infinitesimal arc of the axial line through |
it, terminated by points moving with the fluid. To prove this, consider any in-
finitesimal plane area, A, moving with the fluid. Let w be the resultant rotation,
and @ the angle between its axis and the perpendicular to the plane of A. This
makes w cos @ the component rotation in the plane of A; and therefore Aw cos @
remains constant. Now, draw axial lines through all points of the boundary of
A, forming a tube whose area of normal section is A cos @. The resultant rota-
tion must vary inversely as this area, and therefore (in consequence of the in-
compressibility of the fluid) directly as the length of an infinitesimal line along
the axis.
(4). Form a surface by axial lines drawn through all points of any curve in
the fluid. The circulation is zero round the boundary of any infinitesimal area
of this surface; and therefore (0) it is zero round the boundary of any finite
area of it.
(2). Let the curve of (£) be closed, and therefore the surface tubular. On this
surface let ABCA, A’B’C’A’ be any two curves closed round the tube, and ADA’
any arc from A to A’.. The circulation in the closed path, ADA’B’C’A’/DACBA,
is zero by (hk). Hence the circulation in ABCA is equal to the circulation in
A'B'C’A’—that is to say,
The circulations are equal in all circuits of a vortex tube.
(m). Definitions. An axial surface is a surface made up of axial lines. A
cortex tube is an axial surface through every point of which a finite endless path,
cutting every axial line it meets, can be drawn. Any such path, passing just
once round, is called a circuit, or the circuit of the tube. The rotation of a vorter
tube is the circulation in its circuit. A vortex shect is (a portion as it were of a
collapsed vortex tube) a surface on the two sides of which the fluid moves with
different tangential component velocities.
SIR WILLIAM THOMSON ON VORTEX MOTION. Zot
60. (z.) Draw any surface cutting a vortex tube, and bounded by it. The
surface integral of the component rotation round the normal has the same value
for all such surfaces; and this common value is what we now call the rotation of
the tube.
(0). In an unbounded infinite fluid, an axial tube must be either finite and
endless or infinitely long in each direction.* In an infinite fluid with a boundary
(for instance, the surface of an enclosed solid), an axial tube may have two ends,
each in the boundary surface; or it may have one end in the boundary surface,
and no other; or it may be infinitely long in each direction, or it may be finite
and endless. In a finite fluid mass, an axial tube may be endless, or may have
one end, but, if so, must have another, both in the boundary surface.
(p). Proposition. Applying the notation of (/), to axes parallel to those of
co-ordinates 2, y, z, and denoting, as formerly, by w, v, 2, the components of the
fluid velocity at (z, y, z), we have—
ab dw dv be du dw =e dv du
f= dy a)» aie Hae)? ae LC TO ae
The proof is obvious, according to the plan of notation, &c., followed in § 13
above.
(q). Hence by (/), (e), and (2)—
dw dv du dw QE iio b> Tf add a
a as {u( = — =) +n (E- ae aed (‘i gen Sf (uae + vdy + wdz).
where //dS denotes integration over any portion of surface bounded by a closed
curve; J(udx + &c.) integration round the whole of this curve; and (/, m, n) the
direction cosines of any point (z, y, ~) in the surface. It is worthy of remark
that the equation of continuity for an incompressible fluid does not enter into the
demonstration of this proposition, and therefore w, v, 7 may be any functions.
whatever of a, y,z. In a purely analytical light, the result has an important
bearing on the theory of the integration of complete or incomplete differentials.
It was first given, with the indication of a more analytical proof than the pre-
ceding, in THomson and Tart’s “ Natural Philosophy,” § 190 (7).
(7). Propositions (2) (7) (”) (0) of the present section (§ 60) are due to HELM-
HOLTZ; and with his ae, for associated rotational and cyclic irrotational
motion in an unbounded fluid, to be given below, constitute his general theory of
vortex motion. (m) and (0) are purely kinematical; (/) and (7) are dynamical.
_ (s). Henceforth I shall call a circuit any closed curve not continuously reducible
to a point, in a multiply continuous space. I shall call diferent circuits, any
* Vortex tubes apparently ending in the fluid, for instance, a portion of fluid bounded by a
figure of revolution, revolving round its axis as a solid, constitute no exception. Each infinitesimal
vortex tube in this case is completed by a strip of vortex sheet and so is endless,
252 SIR WILLIAM THOMSON ON VORTEX MOTION.
two such closed curves if mutually irreconcilable (§ 58); but different mutually
reconcilable closed curves will not be called different circuits.
60. (¢). Thus, (72+1)ply continuous space, is a space for which there are 7, and
only n, different circuits. This is merely the definition of § 58, abbreviated by
the definite use of the word circuit, which I now propose. The general termin-
ology regarding simply and multiply continuous spaces is, as I have found since
§ 58 was written, altogether due to HetmHoLTz; RremaAnn’s suggestion, to which
he refers, having been confined to two-dimensional space. I have deviated some-
what from the form of definition originally given by HELMHOLTZ, involving, as it
does, the difficult conception of a stopping barrier;* and substituted for it the
definition by reconcilable and irreconcilable paths. It is not easy to conceive the
stopping barrier of any one of the first three diagrams of § 58, or to understand
its singleness; but it is easy to see that in each of those three cases, any two
closed curves drawn round the solid wire represented in the diagrams are recon-
cilable, according to the definition of this term given in § 58, and therefore, that
the presence of any such solid adds only one to the degree of continuity of the
space in which it is placed.
(w). If we call a partition, a surface which separates a closed space into two
parts, and, as hitherto, a barrier, any surface edged by the boundary of the space,
HELMHOLTz’s definition of multiple continuity may be stated shortly thus :—
A space is (n+1)ply continuous if n barriers can be drain across it, none of
which is a partition.
(v). HetMHoutz has pointed out the importance in hydrokinetics of many-—
valued functions, such as tan ~, which have no place in the theories of gravi-
tation, electricity, or magnetism, but are required to express electro-magnetic
potentials, and the velocity potentials for the part of the fluid which moves irro-
tationally in vortex motion. It is, therefore, convenient, before going farther,
that we should fix upon a terminology, with reference to functions of that kind, —
which may save us circumlocutions hereafter.
(w). A function ¢ (a, y, z) will be called cyclic if it experiences a constant —
augmentation every time a point P, of which a, y, z are rectangular rectilineal
co-ordinates, is carried from any position round a certain circuit to the same —
position again, without passing through any position for which either = a or
dd
q, becomes infinite. The value of this augmentation will be called the cyclic
* But without this conception we can make no use of the theory of multiple continuity in
hydrokinetics (see §§ 61-63), and Hztmuottz’s definition is, therefore, perhaps preferable after all
to that which I have substituted for it. Mr Crerk Maxwe zt tells me that J. B. Listine has more
recently treated the subject of multiple continuity in a very complete manner in an article entitled
“ Der Census raumlicher Complexe.”—Kdénigl. Ges. Gittingen, 1861. See also Prof. Cayzzy “ On
the Partition of a Close.”’—Phil. Mag. 1861.
SIR WILLIAM THOMSON ON VORTEX MOTION. 253
constant for that particular circuit. The cyclic constant must clearly have the
same value for all circuits mutually reconcilable (§ 58), in space throughout
which the three differential coefficients remain all finite.
60. (z). When the function is cyclic with reference to several different
mutually irreconcilable circuits, it is called polycyclic. When it is cyclic for only
one set of circuits, it is called monocyclic.
EXAMPLE.—The apparent area of a circle as seen from a point (2, y, 2)
anywhere in space, is a monocyclic function of x, y, z, of which the cyclic con-
stant is 47.
The apparent area of a plane curve of the (2n)th degree, consisting of 2
detached closed (that is finite endless) branches (some of which might be enclosed
within others) is an »-cyclic function, of which the » cyclic constants are essen-
tially equal, being each 47.
Algebraic equations among three variables (2, y, ~), may easily be found to
represent tortuous curves, constituting one or more finite, isolated, endless
branches (which may be knotted, as shown in the first three diagrams of § 58,
or linked into one another, as in the fourth and fifth). The integral expressing
what, for brevity, we shall call the apparent area of such a curve, is a cyclic
function, which, if polycyclic, has essentially equal values for all its cyclic con-
stants. By the apparent area of a finite endless curve (tortuous or plane), I mean
the sum of the apparent areas of all barriers edged by it, which we can draw
without making a partition.
It is worthy of notice that every polycyclic function may be reduced to a
sum of monocyclic functions.
(y). Fluid motion is called cyclic unless the circulation is zero in every closed
path through the fluid, when it is called acyclic. Rotational motion is (e) essen-
tially cyclic.
(z). Irrotational motion may [ § 59 (/)] be either acyclic or cyclic. If cyclic
it is monocyclic if there is only one distinct circuit, or polycyclic if there are several
distinct circuits, in which there is circulation. It is purely cyclic if the boundary
of the space occupied by irrotationally moving fluid is at rest. If the boundary
moves and the motion of the fluid is cyclic, it is acyclic compounded mith cyclic.
61. (a). We are now prepared to investigate the most general possible irrota-
tional motion ofa single continuous fluid mass, occupying either simply or multiply
continuous space, with for every point of the boundary a normal component
velocity given arbitrarily, subject only to the condition that the whole volume
remains unaltered. |
(0).” Genesis of acyclic motion. Commencing, as in § 3, with a fluid mass at
rest throughout, let all multiplicity of the continuity of the space occupied by it
be done away with by temporary barrier surfaces, 6,, 8, ... stopping the circuits,
as described in § 57. The bounding surface of the fluid, which ordinarily consists
VOL. XXV. PART Il. : 37
254 SIR WILLIAM THOMSON ON VORTEX MOTION.
of the inner surface of the containing vessel, will thus be temporarily extended to
include each side of each of these barriers. Let now, as in § 3, any possible
motion be arbitrarily given to the bounding surface. The liquid is consequently
set in motion, purely through fluid pressure ; and the motion is [$§ 10-15, or 60, 59] _
throughout irrotational. Hence irrotational motion fulfilling the prescribed sur-
face conditions is possible, and the actual motion is, of course (as the solution of
every real problem is), unambiguous. But from this bare physical principle we
could not even suspect, what the following simple application of GREEN’s equation
proves, that the surface normal velocity at any instant determines the interior
motion irrespectively of the previous history of the motion from rest.
61. (c). Determinacy of irrotational motion in simply continuous space. In § 57
(1), which is mney applicable, as the volume is now simply continuous,
make 9 = 9, and put y’9 = 0, so that 9 may be the velocity potential of an
incompressible fluid. That double naetion becomes the following single equa-
tion—
ho fe dg?
Sf Gtr e + 5 de dy dz= [| done ;
where the surface integration //do must now include each side of each of the
barrier surfaces 6,, 8,..... Hence, if te = 0 for every point of the bounding
surface, we must have
d dg? dg?
SSS (Ge + Ge + Fe) eyo,
dg. do
de ~ ip.
which requires that
that is to say, if there is no motion of the boundary surface in the direction of the
normal, there can be no motion of the irrotational species in the interior ; whence —
it follows that there cannot be two different internal irrotational motions with
the same surface normal component velocities. Thus, as a particular case,
beginning with a fluid at rest, let its boundary be set in motion; and brought
again to rest at any instant, after having been changed in shape to any extent,
through any series of motions. The whole liquid comes to rest at that instant.
A demonstration of this important theorem, which differs essentially from the
preceding, and includes what the preceding does not include, a purely analytical
proof of the possibility of irrotational motion throughout the fluid, fulfilling the
arbitrary surface-condition specified above, was first published in THomson and
Tair’s “ Natural Philosophy,” § 317 (8), and is to be given below, with some
variation and extension. In the meantime, however, we satisfy ourselves as to
the possibility of irrotational motions fulfilling the various surface-conditions with
which we are concerned, because the surface motions are possible and require
the fluid to move, and [§§ 10-15, or § 59] because the fluid cannot acquire
SIR WILLIAM THOMSON ON VORTEX MOTION. 255
rotational motion through fluid pressure from the motion of its boundary; and
we go on, by aid of Green’s extended formula [§ 57 (7)], to prove the determinate-
ness of the interior motion under conditions now to be specified for multiply
continuous space, as we have done by his unaltered formula [§ 57 (1)] for simply
continuous space.
62. Genesis of Cyclic Irrotational Motion.—In the case of motion considered
in § 61, the value of the normal component velocity is not independently arbitrary
over the whole boundary, but has equal arbitrary values, positive and negative,
on the two sides of each of the barriers 6,, 8,, &c. We must now introduce a
fresh restriction in order that, when the barriers are liquefied, the motion of the
fluid may be irrotational throughout the space thus re-opened into multiple
continuity. For although we have secured that the normal component velocity
is equal everywhere on the two sides of each barrier, we have hitherto left the
tangential velocity. unheeded. If they are not equal on the two sides, and in
the same direction, there will be a finite slipping of fluid on fluid across the
surface left by the dissolution of the infinitely thin barrier membrane; constitut-
ing [§ 60 (mm) above], as Hetmuoutz has shown, a “ vortex sheet.” The analytical
expression of the condition of equality between the tangential velocities is that
the variation of the velocity potential in tangential directions shall be equal on
the two sides of each barrier. Hence, by integration, we see that the difference
between the values of the velocity potential on the two sides must be the same
over the whole of each barrier. This condition requires that the initiating pres-
sure be equal over the whole membrane. For, at any time during the instituting
of the motion, let p,, p, be the pressures at two points P,, P, of the fluid, and
moving with the fluid, infinitely near one another on the two sides of one of
the membranes, so that the pressure 7, which must be applied to the membrane
to produce this difference of fluid pressure on the two sides, is equal to p, — p, in
the direction opposed to p,. And let ¢,, 9, be the velocity potentials at P, and
P,, so that if /ds denote integration from P, to P,, along any path P,PP, what-
ever from P, to P,, altogether through the fluid (and therefore cutting none of
the membranes), and ¢ the component of fluid velocity along the tangent at any
point of this curve, we have
oe Mite cenas elt Genk) (0:
Hence, by (6) of § 59,
eee ave re fo) 0),
where q,, g, denote the resultant fluid velocities at P, and P,. Now, the normal
component velocities at P, and P, are necessarily equal; and therefore, if the
components parallel to the tangent plane of the intervening membrane are also
equal, we have
he oD,
256 SIR WILLIAM THOMSON ON VORTEX MOTION.
and the preceding becomes
sid ee ee vires, hoe
But if the tangential component velocities at P, and P, are not only equal, but
in the same direction, g,— 9, must, as we have seen, be constant over the
membrane, and therefore 7 must also be constant.
Suppose now that after pressure has been applied for any time in the manner
described, of uniform value all over the membrane at each instant, it is applied
no longer, and the membrane (having no longer any influence) is done away
with. The fluid mass is left for ever after in a state of motion, which is irrota-
tional throughout, but cyclic. The “circulation” [§ 60(a)], or the cyclic constant
being equal to ¢, — ¢,, for every circuit reconcilable with P,PP,P, is given by the
equation
%—-%,=—fadt . ; ; : : : (4),
/dt denoting a time-integral extended through the whole period during which =
had any finite value.
The same kind of operation may be performed, on each of the 7 barriers
temporarily introduced in § 61 to reduce the (x+1)fold continuity of the space
occupied by the fluid, to simple continuity.
The velocity potential at any point of the fluid will then be a polycyclic func-
tion [§ 60 (z)] equal to the sum of the separate values corresponding to the
pressure separately applied to the several barriers. ‘Thus we see how a state of
irrotational motion, cyclic with reference to every one of the different circuits of
a multiply continuous space, and having arbitrary values for the corresponding
cyclic constants, or circulations, may be generated. But the proof of the
possibility of fluid motion fulfilling such conditions, founded on this planning out
of a genesis of it, leaves us to imagine that it might be different according to the
infinitely varied choice we may make of surfaces for the initial forms of the
barriers, or according to the order and the duration of the applications of
pressure to them in virtue of which these figures may be changed more or less, —
and in various ways, before the initiating pressures all cease; and hitherto
we have seen no reason even to suspect the following proposition to the con-
trary.
63. (Prop.) The motion of a liquid moving irrotationally within an (7+1)ply
continuous space is determinate when the normal velocity at every point of the
boundary, and the values of the circulations in the » circuits, are given.
This is proved by an application of Green’s extended formula (7) of § 57,
showing, as the simple formula (1) of the same section showed us in § 61 for
simply continuous space, that the difference of the velocity potentials of two
motions, each fulfilling this condition, is necessarily zero throughout the whole
SIR WILLIAM THOMSON ON VORTEX MOTION. 257
fluid. Let 9, 9 be the velocity potentials of two motions fulfilling the prescribed
conditions, and let ;
p=e-—¢.
At every point of the boundary (the barriers not included) the prescribed con-
ditions require that }9=2¢’, and therefore »=0. Again, the cyclic constants
for 9’ are equal to those for g; those for {, being their differences, must there-
fore vanish. Hence, if the 9 and 9’ of § 57 (7) be made equal to one another and
to avoid confusion with our present notation we substitute & for each, the second
members of that double equation vanish, and it becomes simply
Tigao lard yoit _ of
HE + Oy dz? diz dy dz ==(() p
which, as before (§ 61), proves that /=0, and therefore 9 —9; and so establishes
our present proposition.
ExampLe (1). The solution ¢= tan“ considered in § 56, fulfils LapLacr’s equa-
tion, V’9=0; and obviously satisfies the surface condition, not merely for the
annular space with rectangular meridional section there considered, but for
the hollow space bounded by the figure of revolution obtained by carrying a
closed curve of any shape round any axis (OZ) not cutting the curve; which, for
brevity, we shall in future call a hollow circular ring. Hence the irrotational
motion possible within a fixed hollow circular ring is such that the velocity poten-
tial is proportional to the angle between the meridian plane through any point,
and a fixed meridian.
EXAMPLE (2). The solid angle, a, subtended at any point (a, y, z), by an
infinitesimal plane area, A, in any fixed position, fulfils LapLace’s equation y?a=0.
This well-known proposition may be proved by taking A at the origin, and per-
pendicular to OX, when we have
—gayem “eee rey 8 oO
for which V’a = 0 is verified.
The solid angle subtended at (z, y, z) by any single closed circuit is the sum
of those subtended at the same point by all parts into which we may divide any
limited surface having this curve for its bounding edge. [Consider particularly
curves such as those represented by the first three diagrams of § 58.] Hence
if we call ¢ the solid angle subtended at (2, y, z) by this surface, LAPLAcE’s equa-
v’¢ is fulfilled. Hence ¢ represents the velocity potential of the irrotational
motion possible for a liquid contained in an infinite fixed closed vessel, within
which is fixed, at an infinite distance from the outer bounding surface, an in-
finitely thin wire bent into the form of the closed curve in question.
VOL. XXV, PART Il. 3U
258 SIR WILLIAM THOMSON ON VORTEX MOTION.
The particular case of this example for which the curve is a circle, presents
us with the simplest specimen of cyclic irrotational motion not confined [as that.
of Example (1) is] to a set of parallel planes. The velocity potential being the
apparent area of a circular disc (or the area of a spherical ellipse) is readily found,
and shown to be expressible readily in terms of a complete elliptic integral of the
third class, and therefore in terms of incomplete elliptic functions of the first
and second classes. The equi-potential surfaces are therefore traceable by aid of
LrecENDRE's tables. But it is to HeLtmMHotrz that we owe the remarkable and
useful discovery, that the equations of the stream lines (or lines perpendicular to
the equi-potential surfaces) are expressible in terms of complete integrals of the
first and second classes. They are therefore easily traceable by aid of LEGENDRE’s
tables. The annexed diagram, of which we shall make much use later, show
these curves as calculated and drawn by Mr Macraruane from HELMHOLTZ’s.
formula, expressed in terms of rectangular co-ordinates. An improved method
of tracing them is described in a note by Mr CLerK MaxweE tt, which he has
kindly allowed me to append to this paper.
EXAMPLE 3. The motion described in Example 2 will remain unchanged out-
side any solid ring formed by solidifying and reducing to rest a portion of the
fluid bounded by stream lines surrounding the infinitely thin wire. Thus we
have a solid thick endless wire or bar forming a ring, or an endless knot as
illustrated in the first three diagrams of § 59, of peculiar sectional figure depend-
ing on the stream lines round the arbitrary curve of Example 2; and the cyclic
irrotational motion which, if placed in an infinite liquid it permits, is that whose
velocity potential is proportional to the solid angle defined geometrically in the
general solution given under Example 2.
64. Kinetic energy of compounded acyclic and polycyclic irrotational motion— —
kinetico-statics. ‘The work done in the operation described in § 62 is calculated
directly by summing the products of the pressure into an infinitesimal area of
the surface, into the space through which the fluid contiguous with this area
moves in the direction of the normal, for all parts of the surface, whether
boundary or internal barrier, where the genetic pressure is applied, and for all
infinitesimal divisions of the whole time from the commencement of the motion.
(a). Let w denote the work done, and /dé time-integration, from the beginning
of motion up to any instant. At any previous instant let p be the pressure,
q the velocity, and @ the velocity potential, of the fluid contiguous to any
element do of the bounding surface, /& the difference of fluid pressures on the two
sides of any element, ds, of one of the internal barriers, and N the normal com-
ponent of the fluid velocity contiguous to either do or ds. The preceding state- _
ment expressed in symbols is
W =/at[—ffpNdo + S/fkNds] . ee
SIR WILLIAM THOMSON ON VORTEX MOTION. 259
> denoting summation for the several barriers if there are more than one.
According to the general hydrokinetic theorem for irrotational motion [§ 59 (6)
compare with § 31 (5)], with 9 expressed in terms of the co-ordinates of a point
moving with the fluid, we have
do ; eS
eee oth eames reser 3 i:
Now, let us suppose the pressure to be impulsive, so that there is infinitely little
change of shape either of the bounding surface or of the barriers during the time /d¢.
This will also imply that 2S is infinitely great in comparison with 4q°; so that
d
LS a . a . c c ° (8).
And according to the notation of § 57 we have
Ne Dcuemecet cis he Uk oy cee hs
Also & is constant over each barrier surface.
Hence (6) becomes
Ww fal fe veda + 3k ffveus | Lote aay
64. (0). The initiating motion of the bounding surface and the pressures on the
barriers may be varied quite arbitrarily from the beginning to the end of the
impulse; so that the history within that: period of the acquisition of the pre-
scribed final velocity may be altogether different, and not even simultaneous, in
different parts of the bounding surface. Thus 4, and &, may be quite different
functions of ¢; provided only /4,dt and /k,dt have the prescribed values, which
we shall denote by &, and &, respectively.
: (c). But, for one example, we may suppose ¢ to have at each instant of /dt
everywhere one and the same proportion of its final value; so that if the latter
denoted by ®, and if we put
BA SS FN: . 4 . . ° ° Gy
m is independent of co-ordinates of position, but may of course be any arbitrary
function of the time. Hence, observing that
as the final value of m is 1, (10) becomes
Wil fPvbde + Skea] . . . . (12).
(d). The second member of this equation doubled agrees with the two equal
260 SIR WILLIAM THOMSON ON VORTEX MOTION.
second members of (7) § 57 with 9 and 9’ each made equal to ®. And the first
member of that equation becomes twice the kinetic energy of the whole motion.
Hence, when 9’=¢, and V’9=0, (7) of § 57 expresses the equation of energy
for the impulsive generation, of the fluid motion corresponding to velocity potential
9, by pressures varying throughout according to the same function of the time ;
the first member being twice the kinetic energy of the motion generated, and the
second twice the work done in the process.
64. (e). As another example, let us suppose the initiating pressures to be so
applied as first to generate a motion corresponding to velocity potential 9, and
after that to change the velocity potential from 9 to 9+’, denoting by ¢ and ¢’
any two functions, such that 9+9’=©’, and each fulfilling Lapiace’s equation:
and let the augmentation from zero to 9, and again from ¢ to 9+¢’ be uniform
through the whole fluid. The work done in the first process, found as
above (12),
Lf [fod do+ x [de ds] as) i ie
if x,, «,, &c., denote the cyclic constants relative to 9, as k,, &,, &c., relatively to
®, and the additional work done in the second process, similarly found, is
4 //o' (209 +09’) do+ zx //(29 +309’) ds] : : (14).
(f). Now, as we have seen (§ 63) that the actual fluid motion depends at
each instant wholly on the normal velocity at each point of the bounding surface
and the values of the cyclic constants, it follows that the work done in generating
it ought to be independent of the order and law, of the acquisition of velocity
at the bounding surface, and of the attainment of the values of the several cyclic
constants. Hence, the the sum of (13) and (14) ought to be equal to (12). But
if, for ® in (12) we substitute 9+’, the difference between its value and that of
the sum of (13) and (14) is found to be
4L//(9d9 —9'00) do+ UK/de'ds—K' [/Beds)] . s : (15);
which, being the half the difference between the two equal second members of
(7) § 57 for the case of
v7e=0 and y7o’=0,
is equal to zero. Hence, the equality of the second members of (7) § 57, con-
stitutes the analytical reconciliation of the equations of energy for different modes
of generation of the same fluid motion.
a eae ap ieeee ee
@RaEt? y
VIIl—On the Rotation of a Rigid Body about a Fixed Point. By Professor Tarr.
(Received October 13th, Read December 21st, 1868.)
Although it is very improbable that there remains to be discovered any new,
and at the same time simple, fact connected with a question which has been
elaborately treated by many of the greatest mathematicians of this and the pre-
ceding century, the employment of a new mathematical method may enable us
to present some of their results in a more intelligible form, and with far less
expenditure of analytical power than has hitherto been deemed necessary ; and
it may give us such an insight into the question, that we shall be able easily to
discover the mutual relations among the various processes which have been
already employed; so far, at least, as these differ in principle, and not merely in the
peculiar co-ordinates assumed for the purpose of simplifying the equations. Such
a method is that of Quaternions, which seems to be expressly fitted for the
symmetrical evolution of truths which are usually obtained by the ordinary Car-
tesian methods only after great labour of calculation, and by modes of attack so
indirect, and at first sight so purposeless, as to bewilder all but a very small
class of readers. Quaternions afford so clear a view of the nature of the question
they are applied to, that even the student, if he have some little knowledge of
them, can often see why a transformation is made, whose object he would have
been unable to discover had the problem. been masked in the unnecessarily arti-
ficial difficulties of Cartesian geometry, or the outrageously repulsive formule of
spherical trigonometry.
By far the most elegant and most easily intelligible representations of the
motion of a solid body yet discovered, are due to Pornsot. With the following
extract from his splendid work, Théorie Nouvelle de la Rotation des Corps (Liou-
ville’s Journal, 1851), I most cordially agree,— though it appears to me that, when
he does condescend to use analytical methods, he is by no means so happy as
others have been, who, trusting to mathematical analysis alone, had not the
benefit of his beautiful geometrical representations. But in perusing the extract,
let the reader bear in mind that a guaternion equation is quite as suggestively in-
telligible, to those who understand it, as any geometrical diagram can possibly be.
In fact, Imight almost say, that it is more readily intelligible than diagrams usually
VOL. XXV. PART II. 3X
262 PROFESSOR TAIT ON THE ROTATION OF A
are; for, in reading a work illustrated by figures, we have generally to go through
a laborious explanation of what the figure is intended to represent before we can
make use of it for further developments. On the other hand, a purely quaternion
formula draws, as it were, its own figure in the reader’s mind, and saves him at
least the trouble just mentioned. In this way every one has his figures drawn
so as best to suit himself, and is not perplexed by having to pick up the prin-
ciples on which they have been drawn for him by another, very probably of a
different mode of thought. Still, such words as the following, when properly
applied, not to quaternions but, to ordinary so-called analysis, must always convey a
much-needed warning :—“ Gardons-nous de croire qu’une science soit faite quand _
on l’a réduite 4 des formules analytiques. Rien ne nous dispense d’étudier les
choses en elles-mémes, et de nous bien rendre compte des idées qui font objet
de nos spéculations. N’oublions point que les résultats de nos calculs ont pres-
que toujours besoin d’étre vérifiés, d’un autre cété, par quelque raisonnement
simple, ou par l’expérience. Que si le calcul seul peut quelquefois nous offrir
une vérité nouvelle, il ne faut pas croire que, sur ce point méme, lesprit n/ait
plus rien a faire: mais, au contraire, il faut songer que, cette vérité étant indé-
pendante des méthodes ou des artifices qui ont pu nous y conduire, il existe
certainement quelque démonstration simple qui pourrait la porter a l’évidence: ce
qui doit étre le grand objet et le dernier résultat de la science mathématique.”
: “Ce n’est qu'une apparente fécondité de cette méthode de pur
led qu’on appelle assez improprement l’analyse. Car si les théorémes sont déja
connus on découvre bien vite les transformations 4 faire pour que les équa-
tions y répondent; mais quand on n’a aucune idée de ces théoremes, on ne trans-
forme guere qu’au hazard, et le plus souvent on n’arrive 4 rien. La vraie analyse
est dans l’examen attentif du probleme a résoudre, et dans ces premiers raison-
nements qu’on fait pour le mettre en équations. ‘Transformer ensuite ces équa-
tions, c’est-a-dire les combiner ensemble, ou en poser d’autres évidentes que Yon
combine avec elles, n’est au fond que de la synthése; 4 moins que Vidée de
chaque transformation ne nous soit donnée par quelque vue nouvelle de l’esprit, —
ou quelque nouveau raisonnement,ce qui nous fait rentrer dans la véritable analyse.
Hors de cette voie lumineuse, il n’y a donc plus d’analyse, mais une obscure
synthése de formules algébriques que l’on pose, pour ainsi dire, lune sur l’autre,
et sans trop prévoir ce que pourra donner cette combinaison. Voila les idées
nettes qu'il faut attacher aux mots: et c’est au fond ce que tout le monde parait
sentir, puisqu’on dit trés-bien une hewreuse transformation, et qu’on ne dit point
un heureux raisonnement, ni une hewreuse analyse.” |
I was led to the following investigations by a desire to simplify, if possible, —
by asymmetrical process, the usual modes of treating the rotation of a rigid body.
The methods ordinarily employed are essentially unsymmetrical, ¢.g. the determi-
nation, by means of three angles, of the position of the body at a given time, when
RIGID BODY ABOUT A FIXED POINT. 263
its angular velocities about its principal axes are given, or can be found. It was
not till after my investigations were nearly completed, and the chief fundamental
equations had been communicated to the British Association at Norwich, that I
became aware of the existence of Professor CayLry’s* admirable Second Report on
Theoretical Dynamics, which contains an immense amount of valuable informa-
tion, especially bearing on the present subject. From this I found that the
notion of attaining symmetry, by seeking the single rotation which would bring
the body from some initial position to its actual position at a given time, which
had been suggested to me by Hamitron’s} beautiful results, is due to EULER;
and I ‘also found that, by the help of certain formule due to RopRicuEs, CAYLEY
has completely solved the question in the ‘‘ Cambridge Mathematical Journal,”
vol. iii. (1843).{ Comparative symmetry, however, is only attained by means of
a brilliant display of analytical power at a great expense of time and bewilder-
ment to the ordinary reader. In the ‘“‘ Philosophical Magazine,” 1848, ii., Cay-
LEY has translated some of his formule into quaternions, and has thus arrived,
though by a very circuitous route, at the fundamental kinematical equation of
the present paper (§ 7 below). He does not give it in its simplest form, and he
remarks that he has “ not ascertained whether it leads to any results of import-
ance.” Under these circumstances, I have had no hesitation in laying this
paper before the Society; for although many of its more important results have
been otherwise obtained, few, with the exception of those due to Hamitton
(which will be given in their turn), have hitherto been arrived at so easily or in
such simple forms.
As symmetry has been the particular object which I have had in view, by far
the greater part of the investigation bears upon the determination of the qua-
ternion, by which the transition can at one step be effected from any initial
position to the actual position of the body at a given time; and a good many
results have been retained, which are of more interest as properties of quater-
nions, than as regards their connection with the physical question. In the kine-
matical part of the paper, to which I proceed as a necessary preliminary, I have
exhibited, for facility of comparison with other works on the subject, the values
of this quaternion in terms of the various sets of co-ordinates usually employed.
This, I need hardly say, does not lead to very simple or elegant results; but the
fault is due, not to quaternions, but to the wanaturalness and want of symmetry
of these common methods of attacking the problem. On the other hand, nothing
can be neater than the set of formule which are suggested directly by quaternions.
* Report on the Progress of the Solution of certain Special Problems of Dynamics.—Brit.
Ass. Report, 1862.
t Proc. R. I. A., 1846. See also §§ 1 and 4 below.
¢ See also Cambridge and Dublin Math. Journal, vol i. (1846).
264 PROFESSOR TAIT ON THE ROTATION OF A
§§ 1-14. Kinematics of a Rigid System with one Point fixed.
1, If ¢ represent the instantaneous axis of a rigid body, its length being
employed to denote the angular velocity about it; then, = being the vector of any
point of the body, drawn to a point in the axis as origin, we obviously have
(using NEwTon’s convenient notation)
ee a Ver es
This formula was given long ago by Hamitton.
2. Every infinitely small displacement of a Rigid System, one point of which
is fixed, takes place about an instantaneous axis.
Let z, 7,, be the vectors of any two points of the system, referred to the fixed
point as origin; then, whatever displacements may occur, we must have (on
account of the rigidity of the system)
) Ta = const., Ta, = const. , Saaz, = const.
Hence, differentiating with respect to ¢,
Sax = 0, Saaz, = 9, Saa, + Sas, = 0 : ; : (2).
The first shows that
a = Ver,
where ¢ is some vector. With this the third gives
6 a Veey = 10;
which must be true for all values of «. Hence we have also
a, =, Vem.
This is consistent with the second of equations (2), so that the existence of the —
instantaneous axis is proved. From the fact of its existence follows at once the
representation of the motion, in every case, by the rolling of a cone fixed in the
rigid system upon another cone fixed in space. The case of finite displacements
will be treated farther on (§ 5 below).
3. To find the instantancous axis, when the vectors, and vector-velocities, of —
any tivo points of the system are given.
Here we have to find ¢ from the two equations
Za Niece aN ear
They give by inspection
Vase, =— Sau, = sSaa,,
or, more symmetrically,
RIGID BODY ABOUT A FIXED POINT. 265
4, If q be any quaternion, the operator
GG igs
turns the vector, quaternion, or system, to which it is applied, about the axis of q
through double the angle of q.
This was one of HamiLTon’s early* discoveries in his new calculus, but it was
independently obtained by Cayuey (only a month or two later)} by the help of
the formule of RopricuEs already referred to. Conversely, when its truth has
been established by an independent process, these formule may be at once
derived from it: not only far more simply, but even in a somewhat improved
form.
The quaternion g may obviously be considered as a mere versor, since its
tensor does not appear in the operatorg( )q”, and a glance at the annexed
figure proves, by the multiplication of versor arcs, the theorem above stated.
(See Tarr’s Quaternions, § 353, or Hamitton’s Lectures, § 282, and Elements,
§ 308 (9).)
5. In quaternions we have, of course, whatever be g and 7,
(qr) a= pogo,
Hence
Tigi vir ds =a Gn,
which shows how to combine any two rotations into a single one.
6. Given the initial and final positions of any two vectors. of a rigid system,
drawn from the fixed point; to find the quaternion operator by which the rotation
can be effected. Let them be a, 8, a,,@,, and let g be the required quaternion,
then
Gi) maaan rGOd > —: 6, <;
or
q@=ag,9e=6q . : : : : (3).
Hence
S(a—-a)q=0, S(P—-B,)¢ =0,
or
Vq || Vi@— #,) (B— By)
* Proc. R. I. A. November 11, 1844. + Phil. Mag. Feb. 1845.
VOL. XXV. PART II. 3 Y
266 PROFESSOR TAIT ON THE ROTATION OF A
as we might at once have seen by the geometry of the question.
Hence
qg=2%+ yV(a—«,)(B—B,).
By the help of this, the first of equations (3) becomes
0 =a(a—m) + y {V(a—%) (B—B,).«~ a, Via — a) (B—B,)}
or
0O=a2+yS(ata,)(B—B,).
[ The second of equations (3) merely gives us a condition which is equivalent
to this, because
S(a + a,)(@—B,) =—S/a - a,)(B + B,)
or
SaB = Sa,8,. |
Thus, finally,
= y(—S(a+«,)(@-B,) + V@ - a) (8—-8B,))
=—y[(@-B,)«+ «,(8—8,)]
where, as was to be expected, the tensor is left indeterminate.
7. Given the instantaneous axis in terms of the time, it is required to find the
single rotation which will bring the body from any initial position to its position at
a given time.
If a be the initial vector of a point of the body, = the value of the same at
time ¢, and g the required quaternion, we have
a= gag L 3 é AP at - ~ (4).
‘Differentiating with respect to ¢, this gives
a = gag — gag! gq ,
= gq. gag — gag. gq ,
= 2V (Vag — . gag).
But e=Vew=YV., eqag —! -
Hence, as gag~! may be any vector whatever in the displaced body, we must
have
sseveg=) 2"! .. .- ves ee
This is the fundamental kinematical relation already referred to. CAayLEy’s*
quaternion form of it (which will be understood by the help of § 13 below) is
~(ip +jq + kr) = 2 32 =.
* Phil. Mag., Sept. 1848.
be.
RIGID BODY ABOUT A FIXED POINT. 267
where
A=1+ art jut ky.
8. The result of § 7 may be stated in even a simpler form than (5), for we
have always, whatever quaternion g may be,
and, therefore, if we suppose the tensor of g, which may have any value what-
ever, to be a constant (unity, for instance), we may write (5) in the form
Se i, ORES, TSO CAE Ne A ANG.
An immediate consequence, which will be of use to us later, is
GiGpre = 2g”. : (7).
9. It may appear to some that the demonstration of § 7, founded on the
differentiation of quaternions, is not very convincing. For such it is easy to put
it in an expanded form in which no process of differentiation of a function of a
quaternion is alluded to—though in principle it is the same proof.
Let g become g+~7 in the indefinitely short interval tr. Then the change of
position of the extremity of
(op = (6050) me
may be expressed either as
Veo .r or as (+7) «@(q+7r) — gag.
Hence
rV.egag-* = (9 + r)a(y + r)~* — gag’,
lig ad tgs) + — alg,
= pate (ta) e+ Keo) - 14 NDE Ka)
= ros (a + ry (Ve-*r. a) grt.
But 7 is the change of q in time 7, and we may therefore write
AG)
Substituting, expanding, and neglecting small quantities of the orders 7? and
upwards, we have
268 PROFESSOR TAIT ON THE ROTATION OF A
V.. eqag- = 29 Vi(Vo 9 e)g
= q((Vq-"¢.4—«aVq'¢)q
= 9(Vq-*¢)q—*. gag * — gag-*.q(Vq-*q)q-*
= Vagq-* . gag—* — gag-* . Vaq-*
= 2V (Vag *. gag")
the same equation as in § 7.
9*, [Inserted Dec. 19th, 1868.] A geometrical investigation may also easily be
given, if for no other purpose than to serve as an instance of the justice of my
introductory remarks on diagrams as compared with quaternion equations.
Let Q, Q’ be the poles, on the unit-sphere, of the versor angles BQE’, BQ'E’,,
whose bounding arcs intersect in E’; and let P, P’ be the poles of these bounding
arcs, A the pole of QQ’B [A coincides with the projection of O, the centre of the
sphere]. Then evidently AP (=q) and AP’ (=q’) are the versor ares, correspond-
ing to the above versor angles. Obviously the point E’ is deduced from a point é —
on the other side of the sphere [whose projection coincides with that of E’], by a
rotation about Q through double of BQE’, or about Q’ through double of BQ’E.
Hence we have obviously
RIGID BODY ABOUT A FIXED POINT, 269
Thus a rigid body may pass from the position g( )q~* to the position
g( )q, whatever be q and 7, by a rotation about OH’. Also, by g( )qg7,Q
remains fixed; but by g'( ) gq’ it moves to R, where <QHR = 2<QEQ =
2<POP’.
Hence if OE’ = — Us = (Ue), the versor arc PP’ may be expressed by either
of the equal quantities
2PP
(Uz) = o'o:
But the actual rotation about ¢ is 2PP’, because Q moves to R. Hence if
we put
g=qt gt + &.,
we have
Teo, — 2 Ps
and thus
pas Te o¢ ot Te . Ts
1 + qq—1dt + &. =(Us) « = cos — Us sin ret
winner 5 ét + &e.
Hence, as in (6), when o¢ is indefinitely small
2¢q = 6.
10. To express q in terms of the usual angles \, 0, >.
Here the vectors 7, 7, & in the original position of the body correspond to
A
OA, OB, OC, respectively, at time ¢. The transposition is effected by—/irst, a
rotation ~ about £; second, a rotation 6 about the new position of the line
VOL. XXV. PART II. oz
270 PROFESSOR TAIT ON THE ROTATION OF A
originally coinciding with 7; third, a rotation } about the final position of the
line at first coinciding with /.
Let 2, 7, & be taken as the initial directions of the three vectors which at time ¢
terminate at A, B, C respectively.
The rotation \ about & has the operator
Wy w
Pat he: ce:
This converts 7 into 7, where
ie 2a
ae =j cos ~—7sin yp.
The body next rotates about 7 through an-angle 6. This has the operator
It converts / into
8
OG {7 ate ae 6 aa © 6 238
C= 0S35 = CoS 5 + 1SiN 5 k cos 5 — 78IN 5
=kcosé+ sin 6(i cos) +7 sin Y).
The body now turns through the angle ¢ about ¢, the operator being
? =p
Caen jee
Hence
poy
Q=Cn
= (cos 3 + ¢sin 5) (cos - +7 sin 3) (cos = + ksin ¥)
= (‘cos $ + ¢sin $Y [cos 5 cos + keos§ sin} + sin § cos 5) ¥ (jeos - ésinyy) aide 3 sin z ¥ (i cos w.+ 7 sin v)]
ty 8
= (cos $ + ¢sin5 $ ) [eos § 3 008 = — ising sin § + 7 sin 3 COs ¥ + Ieeos § sm ¥]
= eos $ cos 5 cos +sin$ sin § sin Y sin @ cos — sin $ sin 5 cosy sin @ sin yy — sin $ cos 5 sin 4 cos @
+ i(- cos & sin 5 sin + sin $ cos $ cos + sin 6 cos - sin ® sin $ cos % cos + sin ¥ cos § sin & sin Osinwp)
+ j (cos F sin § cos-¥ + sin $ cos & cos “¥ sin 6 sinw — sin & sin $ sin 5 cos — sin cos 5 sin ‘5 sin @ cos yr) ‘
+ ie( cos 8 cos § sin & + sin? cos $ cos ¥ cos +sin & sin & sin sino sin + sin ® sin $ cos sin 6 cos Wr)
St ile 0G 4 peep) Od irae es pty
—-w 0
= cos gy «COS FH VSN “Sin 5 + J cos PS ™ in § + Hesin 7 085
which is, of course, essentially unsymmetrical.
RIGID BODY ABOUT A FIXED POINT.
11. To jind the usual equations connecting b, 9, > with the angular velocities
about three rectangular axes fixed in the body.
Having the value of ¢ in last section in terms of the three angles, it may be
useful to employ it, in conjunction with equation (6) of § 8, partly as a verifi-
cation of that equation. Of course, this is an exceedingly roundabout process, and
does not in the least resemble the simple one which is immediately suggested
by quaternions.
whence
or
We have = lice Lag
29 = eq = {w, OA + w, OB+ w,0C} Q,
2g-1g = ¢*{u, OA + o, OB +o, OC},
2g = q (ta, + jo, + ks).
This breaks up into the four (equivalent to three independent) equations
t) 5 O= t) 0
LS cos # + cos 5) = — a, sin 2 sin 5 — a, cos ® ee, sin tt cos 6
) :
25,(sin 25 ¥ sin 5) = a, cos 4 ™ cos 5 —a,sin *F™ cos? +a, 008 *5 A a
d = a 2n0 - Ot) G+ 0 ; aan)
25,(cos > sin 5) = , SID - cos 4 3 +4, cos —> cos 5 —, sin * kd
9 3 s1n. 3
= sin 2+ ae 5) == a, cos *—* sin § = + w, sin es =e sin 3 + a, cos ®t cos 5
From the second and third eliminate ¢—, and we get by inspection
diy pil. 6
cos 5. d= (a, sin + w, Cos 4) COS 5»
or
= w, sin ¢ + w, cos , : : ; 3 (8).
Similarly, by eliminating 6 between the same two equations,
sin : (¢@—1) =a, sin 5 + a, 00S 9 cos 5 — , Sl) g cos 5.
And from the first and last of the group of four
cos : (@+ b) = a, cos — 0 cos ¢sin 5 + , sin gsin 5.
These last two equations give
OPP ancOS tone on ee | (9).
¢ cos 6+ =(— a, cos ? + w, sin ¢) sin 6 + , cos 6.
From the last two we have
psind=—a,coo?to, sng . . . . (10).
(8), (9), (10) are the forms in which the equations are usually given.
Ziel
272 PROFESSOR TAIT ON THE ROTATION OF A
12, The essential want of symmetry, in the system of three angles usually
employed, has led me to try various other systems. None of them, however,
were quite symmetrical, and I therefore introduce only one of them here.
Suppose the position of the body to be determined by the angles y, 4, ¢,
through which it has been made to turn about three rectangular axes which are
fixed in it; and which may be considered as : ‘i w, dt, : As o, dt, : ve o,dt respec- |
tively; @,, ©,, ©, having values in general different from ,, »,, ©,, but easily
deducible from them.
The essential difference between this process and the ordinary one (just
treated), consists in using rotations about each of the three axes fixed in the
body, instead of one about one axis, followed by another about a second, and
then a final rotation about the jist axis instead of the third.
We have first a rotation \ about 7, next 6 about the new position of y, and
finally @ about the final position of 4.
ue Y ° oy
ix( )@~ = is the operator due to the rotation about 7. It converts 7 into
n=jcos) +ksnwy
kcosy —jsiny.
Next, the operator due to the rotation 6 is
and & into
Z at!
ce Oa
and this converts £ cos) —jsin~ into
= isiné + (kcos) — jsiny) cos 6.
a a .
eee See y a) _ @ r) a ~ ae + ,
q=C n i* = (cos$ + sin) (cos 5 + nsin 5 COS 5 Rear an 4
Thus
RIGID BODY ABOUT A FIXED POINT. 273
Substituting the above values of ¢ and 7, multiplying out and arranging, we find
finally
Ph by ab v
MO be
ee roe eg ee 5
PAT SR ee Ce
+ i( cos $ cos 5 sas) rene only OCs
; sell : 0.
ate (cos $ sin 3 cos ¥ = pbb) chika sin. *)
Vidcwn UC paral an a Ra
+ i (cos$ sin 5 sin 5 + sin 5 cos 5 cos 5 ).
The expressions for ,, ,,, 1m terms of ¢, 0, + and their differential co-
efficients are not very simple, and can scarcely be of any use.
We see by the equation of § 11 that
— w, = 28. igg.
If we put
gq=wt iat yy + kz
this gives
— a, = 2(aw — wi + yz — 27)
from which the required expression may be obtained.
I have not examined the question, but I fancy that to deduce the constituents
of the above value of g by means of spherical trigonometry would not be very
easy.
13. To deduce expressions for the direction-cosines of a set of rectangular axes
in any position in terms of rational functions of three quantities only.
Let a, 8, y be unit-vectors in the directions of these axes. Let q be, as in
§ 7, the requisite quaternion operator for turning the co-ordinate axes into the
position of this rectangular system. Then
q=wtut+ytez
where, as in § 8, we may write
Ll=w? +a? + yy? +27.
Then we have
gqt=w-m—y—e,
_ and therefore
a= gig-*=(wi-x2—yk+z) (w—xw— yj — zk)
= (w? + a — y? — 2?)i +2 (we + ay) i +2 (ez -— wy)k,
| where the coefficients of 2, 7, £ are the direction-cosines of a as required. A simi-
| lar process gives by inspection those of 8 and y.
| As given by Cayury, after Ropricuzs, they have a slightly different and
VOL. XXV. PART I. 4a
rr
274 PROFESSOR TAIT ON THE ROTATION OF A
somewhat less simple form—to which, however, they are easily reduced by
putting
The geometrical interpretation of either set is obvious from the nature of
quaternions. For (taking CayLey’s notation) if 6 be the angle of rotation: cos f,
cos g, cos h, the direction-cosines of the axis, we have
gq=wt+a+t+y+2k =cos ; + sin § (é cos f +7 cos g + keos h)
so that
as WIa
x = sin 5 cos f
y = sin 5 cosg
sel
2 =sin=cosh.
2
From these we pass at once to Ropricugs’ subsidiary formule,
me Da be
eee a 2
2 Be She 6
oS Ses an 5 cos f
&e. = &e,
14, In the system of three angles, corresponding to that usually employed in .
astronomy—viz., 9 the longitude of node, ¢ the inclination of orbit, 7 the angle —
from node in plane of orbit—to find the quaternion operator.
ee
Here we relapse into the essential asymmetry of the method of § 10. First,
.
RIGID BODY ABOUT A FIXED POINT. 275
a rotation @ about 7; second, a rotation ¢ about the new position of 4; third, a
rotation + about the final position of what was originally 7. The connection of
this process with that of § 10 is sufficiently obvious.
, |
Herejz(_) jos is the operator for 0, and converts & into
OS Ose eh, 8) 6 Bene)
n= (008 5 + jsin 5) & (cos 5 —jsin5)
=isiné + kcosé.
OG,
Next, the operator for ¢ is
2 w
nr ( ) 4 7?
and converts 7 into
OB= 7 = (cos $ +sin $ (ésin +h c080)) a (cos $ —sin $ (isin + cos 6) )
=—Zsin cos é+j7cosf?+hksin¢ sin é.
Hence we have
= [ cos 5 + sin 3( - isin g cos 0 + joos @ + ksin sin 6) | (cos $ + sin $i sin @ + k eos €)) (cos 5 + jsin 5)
6
= [ cos 5 + sin 5( - ésing cos0 + jos. + k sing sin®) |( cos $ cosy + isin § sing +5 cos $ sing + ksin $ cosg)
6— () Q-
= 03 Fo cos 2 + isin “G7 sin +jsin cos $ + k cos z sin 5
_ As a verification, we have by § 11
OA = gig!
= (w?4+ 27 -y?— 2)i4+2(we+2y)7 +2 (xz—wy)k
= [ cos (6 +7) cos? £ — cos (8 — 7) sin? a + cost sings + [ sin (0 - x) sin? — sin (0 + +) cost? | k
= (cos @ cos rT cos @ — sin@ sin r) 7 + cost sing j + ( — sin@ cos tT cos m — cosO@ sin z)k.
The coefficients of 2, 7, £, in this are the usual expressions for three of the
direction-cosines. The other six may be obtained by the same process.
To express the angular velocities about OA, OB, OC in terms of the three
angles 0, ¢, 7, we have at once
a= 28. 4¢4¢
= 2(aw — wi + yz — 2y)
=— dcosrsing—¢sin r.
_| And the others can be found in a similar manner.
276 PROFESSOR TAIT ON THE ROTATION OF A
§§ 15-60. Kinetics of a Rigid Body with one Point Fixed.
15. Having premised these kinematical theorems, we pass to the consi-
deration of the motion of a rigid mass. It was of course at once obvious to
Hamitton (Proc. R. I. A. 1847), that if « be (as in § 7) the vector of the
portion m of the mass referred to the fixed point, @ the vector-force acting at m,
LAGRANGE’s general equation of motion takes in quaternions the form
>. Va(ma — B) = 0,
or, if we put
) = 3. Vae
so that ~ denotes the vector-couple acting on the body,
>. mVes = J A. 1. ae
This is our sole dynamical equation.
16. Integrating once with respect to 7, we have, putting
y¥ =f dt = . : . : . (12),
SimVetSy. Ue. 5)
where, if we please, we may omit the V, as == is necessarily a vector.
Now, by the kinematical relation in § 1, if ¢ be the vector-instantaneous axis,
we may write (13) as
>. maVer=y : , z : : (14).
17. From these equations Hamirton has deduced, in an extremely simple
way, many known results of great interest. For instance, if ~ vanish, 2.¢., if
there be no applied forces, y is a constant vector, and (operating on (14) or (13).
by S. «)
Sey = 2. m(Ver*=Ime?=—-W . «ww SC
a constant, by the principle of conservation of energy.
Of these equations
2m(Ver)? = — h?
denotes obviously an ellipsoid fixed in the body, and such that ¢ is a radius-vector
of it. The tangent plane to it at the extremity of « is easily seen to be the fixed ©
plane
Sey = —/?.
Hence we have at once Pornsor’s beautiful construction of the motion, by the
rolling of the central ellipsoid on the invariable plane. But this, although
extremely elegant, is not well adapted to assist us in the determination of the
position of the body in space after a given time.
18. In most of the investigations which follow, we shall use the form (14)
RIGID BODY ABOUT A FIXED POINT. 207
as given by Hamitton; and we shall omit for the present the consideration of
whether y is a constant vector or not.
19. Let a be the initial position of 7, g the quaternion by which the body can
be at one step transferred from its initial position to its position at time 7.
Then
== gag
and HamiLTon’s equation (14) becomes
x. mgag . sgeqt=y,
or
x. mg {aS . aq eq — gq eqa*} gq =y.
Let
ge= 2. m(aSag—a?e) . ; ; ‘ ; (16),
_ where ¢ is a self-conjugate linear and vector function, whose constituent vectors
are fixed in the body in its initial position. Then the previous equation may be
written
g(q Dy" =y7,
or
| oq g=T'10-
_ For simplicity let us write
i =
vite "| (17).
gq" 79=C
Then Hamiutow’s dynamical equation becomes simply
sie een Mememnns SANE he i Meng,
| 20. It is easy to see what the new vectors 7 and ¢ represent. For we may
_ write (17) in the form
| Reap
a mo ert salt uit in Hae
oe
_ from which it is obvious that » is that vector in the initial position of the body
_ which, at time ¢, becomes the instantaneous axis in the moving body. When no
| forces act, y is constant, and ¢ is the initial position of the vector which, at time ¢,
| is perpendicular to the invariable plane.
21. The complete solution of the problem is contained in equations (7), (17),
| (18).* Writing them again we have, attending to (17), while introducing » instead
of « into (7),
* To these it is unnecessary to add
Tq = constant ,
as this constancy of Tq is proved by the form of (7). For, had Tq been variable, there must have
| been a quaternion in place of the vector 7. In fact, = (Tq)? = 28.qKq = (Tq) Sn = 0.
VOL. XXV. PART II. 4B
278 PROFESSOR TAIT ON THE ROTATION OF A
. Qn = 29 , : ; : : ‘ (7),
be ee ee ee
We have only to eliminate ¢ and », and we get
al ae aie) er
in which qg is now the only unknown; y, if variable, being supposed known in
terms of g and z. It is hardly conceivable that any simpler, or more easily inter-
pretable, equation for g can be presented until symbols are devised far more com-
prehensive in their meaning than any we yet have.
22. Before entering into considerations as to the integration of this equation,
we may investigate some other consequences of the group of equations in § 21.
Thus, for instance, differentiating (17), we have
Wt w=H+ah,
~ and, eliminating g by means of (7)
gn + Wig = qnt + 29%
whence
C=Vin+ g19;
which gives, in the case when no forces act, the forms
Gaim : , : ' , (20),
and
(as = 9)
gon = — V. non : : : , : (21).
To each of these the term g~'yq, or g~'Wq, must be added on the right, if forces —
act.
23. It is now desirable to examine the formation of the function ¢. By its
definition (16) we have
$e = L.m (aSag — ae) ,
=>— D2 : ma V ae c
Hence i
— Sege = 2. m (TVae)?, _—
so that — Sede is the moment of inertia of the body about the vector e, multiplied
by the square of the tensor of g. Thus the equation
Sege=— hi,
evidently belongs to an ellipsoid, of which the radii-vectores are inversely as the
RIGID BODY ABOUT A FIXED POINT. 279
square roots of the moments of inertia about them ;* so that, if 2, 7, & be taken
as unit vectors in the directions of its axes respectively, we have
Sigv=—A,
S7o7 =— B, (22),
A, B, C, being the principal moments of inertia. Consequently
op =—{AiSie + BjSje + ChShe} . . 3 . (28).
Thus the equation (21) for 7 breaks up, if we put
1 = 10, + Jo, + ko,
into the three following scalar equations
Aw, + (C — B)a,w, = 0,
Ba, + (A — C)a,o, = 0,
Ca, +(B— A)aw, = 0,
which are the same as those of Euter.~ Only, it is to be understood that the
equations just written are not primarily to be considered as equations of rotation.
They rather express, with reference to fixed axes in the initial position of the body,
the motion of the extremity, ,, »,, »,, of the vector corresponding to the instan-
taneous axis in the moving body. If, however, we consider ©,, ,, », as standing
for their values in terms of m, x, y, z (§ 27 below), or any other coordinates
employed to refer the body to fixed axes, they are the equations of motion.
Similar remarks apply to the equation which determines ¢, for if we put
C= ta, + Jag + kay,
| (20) may be reduced to three scalar equations of the form
“+ (G- 5) = 0.
| 24, EuLer’s equations in their usual form are easily deduced from what pre-
| cedes. For, let
ee = 9h (9 *e)9
| whatever be e; that is, let 9 represent with reference to the moving principal
| axes what ¢ represents with reference to the principal axes in the initial position
| of the body, and we have
ge = Gog tga = 9o(nq
=a = gV (2o-Z)q—
* For further information about this equation, see Hamitton, Proc. R. I. A. 1847, and Elements
| of Quaternions, p. 755. Also Tait, Quaternions, § 367.
280 PROFESSOR TAIT ON THE ROTATION OF A
= — ¥V(ndn)q~
= — V. gno(n)q~
= — V.gnq~ 99(q~* #9) 9g
=— V. «ge,
which is the required expression.
But perhaps the simplest mode of obtaining this equation is to start with
Hamitton’s unintegrated equation (11), which for the case of no forces is simply
>. mVao = 0.
But from
a= Vea
we deduce
x= Veo + Via
= ae — Sea + Via A
so that
2. m(VerSex — tw’ + aSia) = 0.
If we look at equation (16), and remember that 9 differs from ¢ simply in having
2 substituted for a, we see that this may be written
Vege + pe = 0,
the equation before obtained. The first mode of arriving at it has been given
because it leads to an interesting set of transformations, for which reason we
append other two. .
By (17)
Y= 914 sae
therefore
0 = gq. g@q + gq — gta" aq,
qéq— = 2V.yVqqr
= Vy o
or
But, by the beginning of this section, and by (14), this is again the equation
lately proved.
Perhaps, however, the following is neater.*
By (14)
ge = 7.
Hence
ge — ge =— Sy; é Ma Vew ae a Vea)
=— 2. maSen
=— Ved. maSea
= — Vege.
* [Inserted Dec, 19,1868.] Ihave lately found that Hamitron, in his Elements of Quaternions
(1866), has obtained this equation in a manner almost identical with that last given.
RIGID BODY ABOUT A FIXED POINT. 281
25. However they are obtained, such equations as those of § 23 were shown
long ago by Evuuer to be integrable as follows.
Putting
2 [a0 0, dt Sl
we have
Ao? = AQ,? + (B— C)s
with other two equations of the same form. Hence
Odi ds
aa a BEC N? Cane A= Pine
(22+ a :) (O24 B s) (02+ G s) :
so that 7 is known in terms of s by an elliptic integral. Thus, finally, 7 or ¢ may
be expressed in terms of ¢; and in some of the succeeding investigations for ¢
we shall suppose this to have been done. It is with this integration, or an
equivalent one, that most writers on the farther development of the subject have
commenced their investigations.
26. By § 16, y is evidently the vector moment of momentum of the rigid
body; and the kinetic energy is, as in § 17,
—4>.maz? =— hSey.
But
Sey =S.g egg yq = SnZ,
so that when no forces act
S212 = Sagn = — 1’.
But, by (17), we have also
TC =lys orii¢n Ty;
so that we have, for the equations of the cones described in the initial position of
the body by » and ¢, that is, for the cones described in the moving body by the
‘Instantaneous axis and by the perpendicular to the invariable plane,
We FSO 17 = 0,
h?(n)? + y*Sn¢n = 0.
This is on the supposition that y and / are constants. If forces act, these
quantities are functions of 7, and the equations of the cones then described in the
body must be found by eliminating ¢ between the respective equations. The
final results to which such a process will lead must, of course, depend entirely
upon the way in which ¢ is involved in these equations, and therefore no general
statement on the subject can be made.
27. Recurring to our equations for the determination of g, and taking first the
case of no forces, we see that, if we assume 7 to have been found (as in § 25) by
means of elliptic integrals, we have to solve the equation
VOL. XXV. PART Il. 4c
282 PROFESSOR TAIT ON THE ROTATION OF A
qni= 2g 3* |
that is, we have to integrate a system of four other differential equations harder ~
than the first.
Putting, as in § 23, n= tw, + joy + kas ,
where ,, ,, , are supposed to be known functions of ¢, and
g=wtiuat+yy t+ kz,
this system is
1 dw dz a) dz
2 W. Kew me
where
W =— 4,2 — ay — a2,
X= aw + wy — a2,
Y= ww+oz— a7,
Z=
O3W + WL — WY.
or, as suggested by Cay ey to bring out the skew symmetry,
X= . ay —a~+ ww,
Y=o-o7 . +a,2%+0,.v,
VS er WL—-WY . + 0,W,
W =— at — ayy — wz
Here, of course, one integral is
uw? + 2 + y* + 2* = constant.
* To get an idea of the nature of this equation, let us integrate it on the supposition that 7 is a
constant vector. By differentiation and substitution, we get
2g = qn = 3n°q.
Hence
¢g= pet a sug ny Hee
Substituting in the given equation we have
Ta(- Q, sin — + Q, cos 3!) = (a cos “2 + Q, sin OLE
Ty. Q, = Qi,
= T7.Q, = Qa
which are virtually the same equation—and thus
Hence
af Ty 2) Ny
(cos 3° + Uysin z)
7Tn
= Q,(Un) = .
And the interpretation of g(_ —_) q~ will obviously then be a rotation about 7 through the angle
tT, together with any other arbitrary rotation whatever. Thus any position whatever may be taker
as the initial one of the body—and Q, (_ _) Q,— brings it to its required position at time t=0 s
RIGID BODY ABOUT A FIXED POINT. 283
It may suffice thus to have alluded to a possible mode of solution, which,
except for very simple values of 7, involves very great difficulties. The quaternion
solution, when » is of constant length and revolves uniformly in a right cone, will
be given later.
28. If, on the other hand, we eliminate , we have to integrate
qo (ah) =24,
so that one integration theoretically suffices. But, in consequence of the present
imperfect development of the quaternion calculus, the only known method of
effecting this is to reduce the quaternion equation to a set of four ordinary differ-
ential equations of the first order. It may be interesting to form these equations.
Put
gaH=wtmtyjy tke,
and
y= 10 +b + ke,
then, by ordinary quaternion multiplication, we easily reduce the given equation
to the following set :—
ga ee ag am CS
where
W = —- 2a — yB — 2€ or pe yf —2B+wAa
X= wa+ y€ — 2B Y =—2€ +244 wh
Y= wB+2A-—xc€ L= «B-yA . +w€
Z= w€+cB —yA W =—- 2A — yB — 2€
and
A= Z| a(ut — 08 — 9 — A) + Qo(ew 4 by +) + Bw Oe — ey) |
1 2 2 2 2
B= =| bw —xv—y — #) + 2y (an + by + 2) + Dw (en — a2) |
‘ .
@= 5 ow — 2 —y — 2) + 22 (ax + by + cz) + 2 (ay — ta) |
W, X, Y, Z are thus homogeneous functions of 7, x, y, z of the third degree.
Perhaps the simplest way of obtaining these equations is to translate the
group of § 21 into », 2, y, z at once—instead of using the equation from which
¢ and » are eliminated.
We thus see that
7=144+78 +E.
One obvious integral of these equations ought to be
wu? + wo 4+ y? + 27 = constant ,
284 PROFESSOR TAIT ON THE ROTATION OF A
which has been assumed all along. In fact, we see at once that
wW+eX+yY + 2Z=0
identically, which leads to the above integral.
These equations appear to be worthy of attention, partly because of the homo-
geneity of the denominators W, X, Y, Z, but particularly as they afford (what does
not appear to have been sought) the means of solving this celebrated problem at
one step, that is, without the previous integration of HuLER’s equations (§ 23).
A set of equations identical with these, but not in a homogeneous form (being
expressed, in fact, in terms of «, A, u,v of § 13, instead of w, 2, y, z), is given by
Cayiey (Camb. and Dub. Math. Journal, vol. i. 1846), and completely integrated
(in the sense of being reduced to quadratures) by assuming EuLeEr’s equations to
have been previously integrated.. (Compare § 27.)
CayLey’s method may be even more easily applied to the above equations
than to his own; and I therefore leave this part of the development to the reader,
who will at once see (as in § 27) that A, B, € correspond to,, ,, , of the 7 type § 23.
29. It may be well to notice, in connection with the formule for direction
cosines in § 13 above, that we may write
A= al (w? + a? — y? — 2) + 20 (wy + we) + 2¢ (az - wy) | :
6 — al 24 (zy — we) + b(w? — a? + y? — 2%) + Qc(yz + wa) | 4
C= a | 20 (az + wy) + 2b (yz-— we) +e(w? -#-— 7 + 2) | :
These expressions may be considerably simplified by the usual assumption,
that one of the fixed unit-vectors (¢ suppose) is perpendicular to the invariable
plane, which amounts to assigning definitely the initial position of one line in the
body ; and which gives the relations
b=0,c=0.
30. When forces act, y is variable, and the quantities a, 6, c will in general
involve all the variables 1, z, y, z, t, so that the equations of last section become
much more complicated. The type, however, remains the same if y involves 7?
only; if it involve g we must differentiate the equation, put in the form
y= 2449 “Dq,
and we thus easily obtain the differential equation of the second order
| V=4V.49.¢7 a7 + OV ga;
if we recollect that, because 7~*¢ is a vector, we have
5.99 = (9"9)’ -
RIGID BODY ABOUT A FIXED POINT. 285
Though remarkably simple, this formula, in the present state of the development
of quaternions, must be looked on as intractable, except in certain very particular
cases.
31. Instead of solving the diferential equation (7) of the group in § 21, having
previously eliminated » from it by means of the other two, we may solve the
second equation of the group,
7 = 9 : é f b J (17),
for g, and treat as known in terms of ¢. {, of course, is to be regarded as found
by the processes of §§ 23, 25. As this mode of attack leads to a determination of
g by aset of three new differential equations, instead of the four of § 27, it may
be useful to consider it briefly, but only for the case of y = constant. Its interest
seems to be derived entirely from the quaternion investigation to which it leads.
32. In consequence of (17), just cited, we may write
q=yit . ; , : ; : (25),
which will be found to satisfy that equation, whatever value is assigned to 0.
But dis really not unrestricted in value; for, if we exhibit it as the sum of
two vectors, thus
One
of which 6, satisfies the equation
7% + 66=0,
or, which is the same thing, the pair
Sé(7¥ + 2)=0 !
Va(y — 7) =9
b\ly — ¢
satisfies both. [This depends on the fact that TC = Ty]. Hence 6 must be de-
prived of its resolved part parallel to y — ¢: or we must have
we see that
SAG es 0: ee OA NY, Bh sar)
33. By differentiation of (25) we have
' Gg = yo + Bf + 8Z.
Substituting in (7) we have
2(y8 + 6% + 82) = yon + 0Zn.
C= Ven,
tm — 20 = xf,
But, § 22,
whence
and the above equation becomes
. 2 (6 ae 60) = yin+ onf . : ; : (27),
VOL. XXV. PART II, 4D
286 PROFESSOR TAIT ON THE ROTATION OF A
of which a particular solution is evidently
26 = oy.
But this must be completed by the addition (to the second member) of a solution
of the equation
yr +7Z=0,
since any such term in the value of 6 would disappear from the differential
equation.
Such a solution is easily found, by putting — ¢ for ¢ in (17), and attending
to § 32, in the form
oe a a
with (as in § 32) the condition
S(7+.04 =) short vyloae-Bus bes ee
Hence, finally,
28 = on ya — ar ||) Ee
which, by taking the scalar, gives
Sy Oa=— Sin: Abiss co -le ot
34, By differentiation of (26) we have
Sly — Ob = Sol = S. dfn.
Substituting the value of 3 from (30) we have
S.(y — Yan + 2S. y%a = 2S. din,
te IS .yLa=—S8. (y+ Lan Sets oe nn
From (29), (81), and (32), we find A by the usual quaternion process in the form
2AS .(y — Oly + Q)V7Z = — Voy — Oly + DS. (y + Dan — 2V . (y + CV yeSen;
QAV2yf = — VytS. (y +.2)8n + (y — 0) (7? + Sy@)Sen . «SS (83),
or
where, in transforming the last term, we must recollect the equation T¢ = Ty.
From this we deduce at once
(yd — AL)V?¥ l= — (yV7l — VoZ. 2S. (y + O80 + [yy — 2) — (y — O21” + Syf)Sen,
2(yA — ALYV? yf= (y — O)(y? + SyZ)S - (y + 280 + 2(7? — 70)(97 + Syf)Sén,
or, finally, remembering that
Wel = So 6 IG 7
AyA — AL) Syf — 7")'= (y — OS. (y + Fon + Ay? — 72) Son.
35. Substituting this in (30), we get, after a slight transformation, consistin;
in omitting the scalar parts of the right hand side, whose sum is zero,
28(Syf — 9”) = (Syf — 97) Vin + $y — ZS. (y + Con — VyGSon.
or
RIGID BODY ABOUT A FIXED POINT. 287
This may easily be put in the simpler form
= Ven VaGee OVS = Oe ee. (BA),
Reduced to scalars, this gives three linear differential equations of the first order,
the coefficients being functions of 7. These can, of course, be reduced to depend
upon one linear differential equation of the third order with coefficients functions
of ¢.
36. As a verification of the preceding work, we may try whether the result is
consistent, as it ought to be, with the condition (assumed throughout).
Constant = (Tq)? = 2776? + 28. ydZ.
This expression gives, by differentiation,
0 =— &Sy% + 2(7? — Syf)Sdd + 48y5Sy0.
Substituting for 6 its value from (34), we have
0 =— BSyf +S. dyfSdn + 2Syd(S. yan — 48. (y + C)én)
=— PSy% +S. dy%Sdn + SydS. yin — SydS. Lon
=— Sof 4+ 8. df{nS. 72d + CS. ayd + yS. Zand}
=— 6Sy% +S. (6S. fn)
which is true, because by (20) |
C= Vea.
37. Another mode of attacking the problem, at first sight entirely different
from that in § 19, but in reality identical with it, is to seek the linear and vector
function which expresses the Homogeneous Strain which the body must undergo
to pass from its initial position to its position at time 7.
Let
a Ke
a being (as in § 19) the initial position of a vector of the body, =a its position at
time 7. In this case x is a linear and vector function. (Tait’s Quaternions,
§ 355.)
Then, obviously, we have, ~, being the vector of some other point, which had
initially the value a, ,
Sea, = 8S. xaxa, = San,
(a particular case of which is
La = Tye = Ta)
and
Van, = V. xaxe, = Vee, .
288 PROFESSOR TAIT ON THE ROTATION OF A
These are necessary properties of the strain-function x, depending on the fact that
in the present application the system is rigid.
38. The kinematical equation
a= Vea
becomes
ye = V. exe,
(the function x being formed from x by the differentiation of its constituents with
respect to #).
HamiLton’s kinetic equation
>.maVer=y,
becomes
> .myaV .exa= y.
This may be written
>. m(xyaS.exa — ea”) = x,
or
a. m(aS.ay’e—x-16.07) = x14,
where x’ is the conjugate of x.
But, because
S. xaxa, = Sam, ,
we have
Saa, =S. ay'xa, ,
whatever be a and a, , so that
f —1
Xx =X
Hence
> -m(aS..ay—1s— y—le. a”) = y—Iy,
or, by § 19,
—1
4 8= xX 17:
39. Thus we have, as the analogues of (17), (17’), the equations
ree ae
Mee =e,
and the former result
ya =V. enya
becomes
ye = V.xnye = xVia0.
This is our equation to determine x, 7 being supposed known. To find 7 ¥
may remark that
Om =i
RIGID BODY ABOUT A FIXED POINT. 289
and
C=x'y-
But
a a
so that
ZR
KG eae ho 0),
Hence ;
Naty les ee
= er = VC OW GSC
or '
$i = — V non.
These are the equations we obtained before. Having found » from the last
we have to find x from the condition
% 1 xa = Vie.
40. We might, however, have eliminated 7 so as to obtain an equation con-
taining x alone, and corresponding to that of § 21. For this purpuse we have
ere CER ey;
so that, finally,
—1 uy
Mee ND ye
or
Ka = Vx taggly,
which may easily be formed from the preceding equation by putting y—'« for a,
and attending to the value of _ given in last section.
41, We have given this process, though really a disguised form of that in
S§ 19, 21, and though the final equations to which it leads are not quite so easily
attacked in the way of integration as those there arrived at, mainly to show how
free a use we can make of symbolic functional operators in quaternions without
risk of error. It would be very interesting, however, to have the problem worked
out afresh from this point of view by the help of the old analytical methods: as
several new forms of long-known equations, and some useful transformations,
would certainly be obtained.
42. As a verification, let us now try to pass from the final equation, in x
alone, of § 40 to that of § 21 in g alone.
We have, obviously, ,
a= q a Ve = Xe
which gives the relation between g and x.
VOL. XXV. PART II. AR
290 PROFESSOR TAIT ON THE ROTATION OF A
[It shows, for instance, that, as
S.Pya =S.ayx’B
while
S.Bya = S. Bgag—1 =S . ag—1Bq ,
we have
xB = 49-87 ,
XB = o(q—*Bq)q-' = 8 ,
and therefore that
x
xX
or
x =x, as above. |
Differentiating, we have
gay" — gag—*4qq-* = xa .
Hence
x xe = gga — agg
= 2V.V(q—3g)a.
Also
g- 4 "7 = 9 G90);
so that the equation of § 40 becomes
2V ..Vg~*g)a = V.g-(q- 199) ,
or, aS a may have any value whatever,
ee, 2V.9q-'G = 9"(q-"99) ;
which, if we put
Ty = constant
as was originally assumed, may be written
: 24 = 99"(9"7)
as in § 21.
43, Let ¢ be the vector joining the opiremnity of ¢ to the intersection of y with
the invariable plane. Then
etay=e.
Operating by S. y, and remembering the condition
eT Sey = — 1,
we have
ay? = — I;
so that
2
en tee.
In the initial position of the body this vector, considered as being drawn from
the fixed point, was }
RIGID BODY ABOUT A FIXED POINT. 291
In the initial position of the body, therefore, this vector passes through the in-
tersection of the ellipsoid
2\ — ON asst
S, (o 4 ia 6997 Be iB ps ONT es ee
Y if
with a second ellipsoid ans
T(97 +5) C=C = Ty.
It therefore lies on the cone
® -1 2\—1 2-1 OK il
78. (o> +5) so-(9 +5) c+ 18.9445) «(97+5) s=0,
2\—1
8.694 +5 a= i).
or
[We might have saved the last seven lines by noticing that
Sye = 0 }
in the present position of the body, involves
Si = 0
in the initial state, which, with the value of ¢ in terms of « above, gives the
result at once. |
44, This cone is seen at once to be normal to the ¢-cone in the initial body,
viz., by § 26,
s.-~=-"e
Deis,
or .
Ie
Ne 14 )¢=0.*
i(o +5)
The vector > constantly changes so as to be perpendicular to ¢. Hence in the
* Tn fact any equation such as
Seve == '(0!,
where ») is a constant self-conjugate linear and vector function, gives
Sede = 0,
whence
y= be
where » represents the normal-vector. For its locus, we have
a= vy 3
and by substitution for e and ./g in the given equation, we have
Swpy= 0.
292 PROFESSOR TAIT ON THE ROTATION OF A
moving body, the vector p, which is always in the plane through the fixed point |
and perpendicular to , belongs to a cone of which y is a normal, and which there-
fore rolls on that plane. But the cone also slides, because the vector p which is”
in contact with the plane is not the instantaneous axis of the body. This con-
struction for the illustration of the motion is also due to Pornsor, and the com-
plete analytical solution of the problem has been given, from this point of view,
by Ruep and Jacosr.* It is easy to see that the angular velocity of the sliding
motion is the constant resolved angular velocity of the body about the fixed line Y;
which has the value
2
5 p20 = 7 .
45. When two of the moments of inertia of the rigid body are equal, 7.¢. when
the symbolical cubic in ¢ or ¢ has two equal roots, all the previous dynamical
work becomes immensely simplified. In fact, if we now take a, B, y as unit-
vectors coinciding with the principal axes of the moving body, we have by (23)
92 =— AaSag — BBSGe — BySye.
But
g =— aSag— BSB — 7Sye,
so that
ge = Be— (A— B) aSag t : : ; : (35),
and thus depends upon the position of the one vector a. We may attempt to
determine the motion without at first introducing the consideration of the
quaternion which has been our principal object of study in this paper.
46. The general equation of § 24
pe =— Vege
becomes, by substituting for 9 from (35),
Bi — (A— B)aSae =—(A— B)VaeSae ‘ : s (36).
Operating by S.a, we have |
Sae = 0 ; ; ; ; 4 . 37).
Omitting, therefore, this term from (36) and operating by S.¢, we have
Se = 0,
whose integral is
-” = constant =—Q?, suppose, ; (38).
But we have always by § 1 a
a= Veu
because a is fixed in the body.
From this we see that P
Sea 16).
* See Caytzy, B. A. Report, 1862.
RIGID BODY ABOUT A FIXED POINT. 293
This, taken in conjunction with (37), gives
Sat + Sea = O,
whose integral is
Sae = constant. =— Qcos®, suppose, : é ‘ (39).
Equation (86) may now be written
Be = —(A—B) Qé cos B,
or
Be =—(A—B)Qa cos B + constant vector.
But we have always, by (14), (see § 24)
Pee
or by, (85), (36), (39),
Be + (A— B)aQ cos 8B = x ; , : (40).
So that the constant vector is y.
Thus we see that a and « are always coplanar with y, and that each remains
constantly at the same inclination to it.
47, Operating on (40) by S.<, S.a, S.y, respectively, we have
— BO? — (A — B)Q* cos? 8 = — H?,
— BQ cosB— (A — B)Q cos B = Say,
— Bh? + (A—B)Say Q cos 8 = 9’,
and these give, in order,
(A cos? B+ B sin? B)Q? = h?,
— AQ cos B = Say,
— (A? cos? 6 + B? sin? 8) Q? = 9’.
The first and third determine 8 and ® in terms of the given constants h
and Ty, and the second gives the value of the constant inclination of a to the
fixed line y.
Introducing — a’, which is unity, as a multiplier of y’ in the third equation,
and adding to its members the squares of the corresponding members of the
second, we have
— BQ)? sin? B = Vay.
| 48. We get equations immediately derivable from these by seeking at once
_ the equations of the fixed and rolling cones, by which the motion may be exhi-
| bited. Thus the locus of ¢ in the body, 7.¢., the rolling cone, has by (14) and (38)
the equation
QT ge = TyT: ,
VOL. XXV. PART II. 4F
294 PROFESSOR TAIT ON THE ROTATION OF A
which may be transformed as follows—
Q? {B? — 2B (A — B) Sta — (A — B)?S%ae} = — 72?
QQ? (B? 7 _ (A? — B?) Sae) =-—y7’,
(BQ? + 7”) 2 — (A? — B?) Q? S2ae = 0,
and finally
e* cos?B + S?ae = 0.
This might have been written down at once by inspection of (38) and (39).
The locus of ¢ in space, 2.¢., the fixed cone, has the equation
S?ye + 2 oe
49. In the preceding solution we began with the very simple equation for «,
which immediately presented itself Let us now apply to the same problem the
general equation of § 21, viz.,
2g = 9¢—* (q~""79) -
Here, of course, we have
ee ee i
Sea = a ee ae I3@ — 3 BSke ,
Hence
which, because
a= gig",
becomes
which is (40) of § 46, as we see by substituting for Say from § 47.
50. Employing this value of ¢ in the kinetic equation
a= Vea,
we have
a= aVye
Hence
1 : 1
a BY” = Be V-7Vre
RIGID BODY ABOUT A FIXED POINT.
295
of which the integral is obviously
a=y Say + woos 52 t + asin 32,
where « and ) are vector constants of integration.
The two last terms must be, together, equal to
y I Vye,
and, as they vanish alternately, the tensors of « and ’ must be equal. Also
unless
Sxa = 0
the tensor of this part of « will vary. Hence
aw =— Uy SaUy + TVaUy. (Ux cos 52 t + Ua sin fe).
Let us, for simplicity, take the usual z, 7, £ of quaternions as coinciding with
Uy, Ux, Ud, and let
— SaUy = cos.
Then
TVaUy = sin B.
Also let
ye
B ——aie
Thus we have
a —icosB + (j cos nt + & sin nt) sin B
whence
, il : : : 5
ao (3 = . 2B cos B [i cos B + (jcos nt + k sin nt) sin B| +
2ai + 2b(j cos nt + & sin nt),
where
ars = cos 6 sin 8
— BS a= cos?B + n=n (sins + = cos?)
dl, For the complete solution of the problem, it remains that we integrate
the equation above, which we may write as
g = [ai + 0(j cos nt + k sin nt)] q
= (ai + ba)g . (Al),
if we put
a =jcos nt + ksin nt.
296 PROFESSOR TAIT ON THE ROTATION OF A
This gives at once the following results, which are necessary in the elimination of
= by differentiation,
a=—1 ) z= Na,
aa mM ) le =— Na,
z=—n'a. ‘
Also, because
Sia = 0,
we have
(ai + ba)? =— (a? + 0”).
Differentiating (41), and simplifying at every step by the above auxiliary equa- .
tions, we have
gG = (a + ba)g
g=—(@ + B)q + bag
Gg =— (a + &)q — bn? aq + bn (am — bi)g
ices (Fh 4 D2) 9 = On? dna) eg a On? = ina) (F% + ») 4 vn( — a +22)9
=— (a? + 0*)G — (bn? — 2bna + ba? + D)aq + Bn?q.
Eliminating +7 from the last equation by means of the second, we have for the
determination of g the linear equation of the fourth order with constant co-
efficients
G+ [22 + 0?) + n? — 2na] 4G + [(a? + 0)? + (a? + 0?) (n? — 2na) — bn? |g =0 (42).
Assume, as a particular integral,
gq — Qe”,
where Q is an arbitrary, but constant, quaternion, and ¢ is the base of NAPIER’S
Logarithms. Then we find for m the equation
m* + [ 2(a? + 07) + n? — 2na | m? + (a? + 0? — na)? = 0;
m? + a? + 0? — na =A arf — min’.
Hence m is imaginary, so we may write
| m = Wr/—1,
ween a+? —na,
2
w=ts5+,| a-5 + 07.
By § 50 this may be written
or
and our equation gives
whence
pots {ie (1-5 cos > ZZ
RIGID BODY ABOUT A FIXED POINT. 297
These values may be called +u,, +-m,, and we have
fy + Mg = 1.
52. The complete solution of the equation (42) is therefore
q = Q, cos wt + Q, sin wt + Q, cos wt + Q, sin wt.
This, however, is far too general for the solution of the original problem, for it
involves sivtcen arbitrary constants instead of four. But it is a mere piece of
ordinary analysis to find twelve of these in terms of the other four.
Thus, let us write
Q,=40,+114+49,7+ KA,
Q, = H, + 1,4 + J,7 + KF,
Q, = H, + 1,7 + J,7 + K,k,
Q, =H, +1it+Jd 7+ Ke.
If these values be substituted in the above expression for g, and the resulting
value of ¢ be used in the equation
i= [ ai + b(j cos nt + k sin nt) |q :
we find, on replacing products of sines and cosines of multiples of ¢ by swms of
sines or cosines, two sets of terms. One of these is of the type
cos (m — (y)t,
which, being equal to
COS fyb,
may be allowed to remain in the equation. ‘The other set is of the type
cos (n + m,)t,
and the terms introducing it must vanish identically.
This consideration gives us the following relations among the sixteen con-
stants above
We ce el ea aida Kag,, Kd.
eee dK, KS;
so that the values of eight are assigned in terms of the remainder.
Next, by equating coefficients of each such distinct term as
4cos ut, ksin wt, &c.,
we obtain sixteen additional equations, of which, however, eight are mere repeti-
tions of the other eight. Rejecting them, we find the remainder to be
VOL. XXV. PART Il. 4G
298 PROFESSOR TAIT ON THE ROTATION OF A
bH, = (a — mw) K, ; bK, = — (a — »,) H,
bl, = (a — wm) I, bJ, =—(a—4,)I,
J, =—(a—m,)I, 61, = (@ — wm) J,
bK, = — (a — w,) H, bH, = (a —.u,)K, .
These are, again, identical in pairs; for each pair containing the same two
constants agrees with the others in giving
or
a? + BF — (wy + fy) @ + My, = 0.
But, by (43), we have
and the condition is satisfied identically.
The final value of the quaternion in the case of the uniform rolling of one
right cone on another is therefore
q = (H, + 1,7 + Jy7 + KA) cos w,t
—(W, —Hz+ Ky = J,k) sin pyt
+ 581K, + Jy — Lj — Hyh) 008 gt
a
5 (J, — Kyi — Hj + 12) singe * |
Putting
gq=wtititt+yjy + kz,
the ordinary differential equations, corresponding to that just solved, are
* The tensor of g has been assumed constant. Accordingly we find by this formula
; se 2 = 2
[H cos mt — I, sinuyé + = D A (x, cos jt — J, sin nt) | + [1 cos w4,¢ + H, sin pt + Z 5 = (3, cos wt + K, sin nt) }
a- 2 2 : a— :
+ [J, cos wt — K, sin pyé — ah cos pt — H, sin ut) | + [K cos w,é + J, sin py, ¢ == (& cos wot + I, sin ut) |
o— 2
re (He aT il ae J? a K,*) [1 + ( b >) ]
=(H: Pee igs yt K,) (a = Za) ‘
RIGID BODY ABOUT A FIXED POINT. 299
w= — ax — by cos nt — bzsin nt,
zc = aw + becosnt — by sin nt,
y = bweos nt + basin nt — az,
2 = bwsin nt + ay — bxcos nt.
By substitution in these the above result may be verified.
538. Consider, as an example of applied forces, a homogeneous solid of revolu-
tion. moving about a fixed point in tts axis, which is not its centre of gravity.
To determine the motion. .
If a, a unit-vector, represent at time ¢ the position of the axis of the solid, we
may choose the tensor of y, a vertical vector, so that the couple due to gravity is
Vay. Hence the equation of motion is §§ 24, 22,
ge + Vege = Vay.
But
ge = Be— (A — B) a Sag ,
so that
Be — (A — B) aSaé — (A — B) Vea Sae = Vay : : : (44).
This, with the kinematical relation
@. == N em . : , : : : (ts
contains the complete solution of the problem.
54, Operating on (44) by S.a, we have
See = (0.
But, by (1), we have
‘ Sc = 0.
Hence
See ‘constant = @Q. . : (45)
_ (that is, the angular velocity about the axis of revolution of the solid is constant)
| and (44) is reduced to the form
Beat Om Vays. 9! 5) a ye) (AB).
| But, by (45) and (1),
i Og.
) or
. = aOretady tal of) Le AN.
Since aa is a vector, we have (as in § 30)
Sore ectamed he Bawah nha ly pottingiieend vl! (AB),
300 PROFESSOR TAIT ON THE ROTATION OF A
so that the substitution in (46) of the value of « from (47) gives
BVa=AQES Vay 3 *.
an extremely simple equation to determine a. It is curious to remark that this
is the equation of motion of a simple pendulum, disturbed by a force constantly
perpendicular to the cone described by the string, and proportional to the rate at
which the area of the surface of the cone is swept out by the suspending cord.
When A =0 it becomes that of the undisturbed motion,* and gives a number of
curious theorems relating to the curvature of the general path of a simple
pendulum. These we need not at present consider; though we may mention
that the corresponding equation for the motion of FoucauLt’s pendulum may be
written in the form :
Va(é+6) = eVa8,
where £ is a vector known in terms of ¢.
55. If we suppose a determined in terms of ¢ from this equation, (46) gives «
in the form
Be = (A—B)Qa — V. y/fadt.
This equation may be obtained, even more simply, from (47).
56. But, without finding either a or ¢, we may deduce various facts connected
with the motion. Thus operating on (46) by S. ¢, we get
Bse = Sl eey = Sye .
which gives
ee — 2Sya +C : : : : 5 (50).
But, by operating on the same equation by S.+¥ and integrating, we have
BSye — (A— B)QSya = C, Z : ; : (51),
which may be written in the form
Sepy = Syge = C, : : : : : (51Y.
By (50) and (51)
ae hip Dogan Ce
so that ¢ is a vector of a fixed sphere, of which however the centre is not at the
fixed point.
* If m be the mass of the pendulum bob, « the vector representing the string, © its tension, and
y’ the acceleration due to gravity
ma = my — Ua,
or, eliminating @,
Vee = Vay,
It is well to observe that this is the equation of motion of a pendulum bob, acted on by no forces,
ie ¥ be the acceleration of the point of suspension.
RIGID BODY ABOUT A FIXED POINT. 301
57. From (49) we have at once, by operating by S. y and integrating,
BS. yae = AQSya + C’ : ' ‘ (52).
Also, operating by 8. Vya,
BS .yaVae = AQS. yaa — (Vay)? : , : (53),
or
B(—Sya — SyaSaau) = AQS. yac + a®y? — Stay
ALO? ~ AQC’
=e Sya + E — 7° —Say,
by (52).
This may be written
iE Sya — Sya(— QQ? — aug’ = A Sy + ne — 9° —Say,
which leads, by integration, to the ordinary expression for Sya in terms of an
elliptic function. It is to be observed, however, that this quantity is not one
which the quaternion calculus directly points out as an object of research; the
propriety of seeking « in the first place being clearly indicated.
58. From the above equations all the ordinary results connected with this
problem may be at once deduced by any one who has a little skill in quaternion
analysis: but the determination of the quaternion which gives the position of the
body at any time does not appear, so far as I have yet examined the question, to
lead to any very simple expressions.
If we could, generally, integrate equation (49), ¢« would be at once given by
(47), and the determination of the motion would be reduced to comparative sim-
plicity. The equation for the direct determination of ¢ may be formed as
follows, but it is not so simple as that for a.
From the equation
Be — (A — B)QOVew = Vay,
we have, by operating by V . <, the result
BVe — (A — B)Q(ae? — eQ) = Qy — aSye,
which gives
_ BVee + (A — B)Q?e — Qy
Tie (A — B)Qe? — Sye ;
The condition
a— Veu
gives, by substituting this value of a,
BYV24(A.— BYO?s—
(A — B)Qe? — Sye
= Bree? — See) — OVey .
VOL. XXV. PART IL. 4H
BVé + (A — B)Q?2 — Cie ROG Sy)
302 PROFESSOR TAIT ON THE ROTATION OF A
59. Processes very similar to these may be applied to the motions of. the
Gyroscope and to Precession and Nutation. I confine myself at present to the —
formation of the equation for the latter question, reserving for another com-
munication the details of the solutions of these three problems; as they involve
some curious and delicate points of quaternion analysis.
60. To form the equation for Precession and Nutation. Let a be the vector,
from the centre of inertia of the earth, to a particle m of its mass: and let ¢ be the
vector of the disturbing body, whose mass is M. The vector-couple produced is
evidently
U(e —«a
MS.mvV. amis .
Vag
= M2. ma
MV ae
T%e (1+ a m=)
38a
Tp - &e.) :
= MS.
=Mz.7,
; . To . :
no farther terms being necessary, since = is always small in the actual cases
g
presented in nature. But, because a is measured from the centre of inertia,
>.me=0.
Also, as in § 19,
de = Pap m(aSag = 7p) :
Thus the vector-couple required is
3M
Referred to co-ordinates moving with the body, @ becomes ¢ as in § 24, and |
§ 24 gives
ts Salone JW bee
p= y= 3M fae dt.
Introducing the value of ¢ from § 53—1.¢., assuming that the earth has two pu
cipal axes of equal moment of inertia, we have
Be — (A — B)aSae = 3M(A — nf 4 ~ dt .
This gives, as in § 54,
See const. — 0 ,
whence
e=>—Qataa, :
RIGID BODY ABOUT A FIXED POINT. 303
so that, finally,
BVaa — AQa = T (A — B)SagVae .
The most striking peculiarity of this equation is that the form of the solution
is entirely changed, not modified as in ordinary cases of disturbed motion, accord-
ing to the nature of the value of e.
Thus, when the right hand side vanishes, we have the equation (49) with the
restriction that the body moves about its centre of inertia (easily seen to be
identical with that at the beginning of § 50); which, in the case of the earth,
would represent the rolling of a cone fixed in the earth on one fixed in space,
the angles of both being exceedingly small.
If ¢ be finite, but constant, we have a case nearly the same as that of the top ©
in §§ 53, 54, the axis on the whole revolving conically about ¢.
But if we assume the expression
e=7(jcos mt + kcos mt)
(which represents a circular orbit described with uniform velocity) « revolves on
the whole conically about the vector 2, perpendicular to the plane in which ¢ lies.
I hope, on a future occasion, to give detailed solutions of these problems,
to a sufficient degree of approximation.
( 305 )
1X.—On the Structure of the British Nemerteans, and some New British Annelids.
By W. CarmicHaEL M'‘Inrosn, M.D., F.L.S., Murthly, Perthshire. Com-
municated by Professor TuRNER. (Plates 1V.-XVI)
(Read 20th April 1868.)
The anatomy of the soft worms variously arranged under the Nemertean
Order has, even in recent times, not been carried out with that completeness
necessary for their thorough elucidation, a state of matters partly due to the
confounding of the structure of one family with another, and predicating of the
series what investigation has but proved in one group. Few British comparative
anatomists have paid much attention to these animals; indeed, Dr GEorGE JoHN-
ston,* Mr Harry Goopsir,t and Dr Tuomas WIL.IAMs,{ are the only three who
have left researches of any moment on the subject. The observations of the first-
mentioned naturalist were made many years ago, with the aid of inferior instru-
ments, and, though conscientious enough, are very meagre and unsatisfactory; and
those of Dr Witu1ams, while also showing the defects just noted, bear evident
traces of imagination. Mr H. Goonpsir’s interpretation of structures was, from
his limited observations, likewise very erroneous. On the Continent, again, the
investigators have been more numerous, and a long list of distinguished names
attest the interest which the subject has received at their hands. I do not deem
it necessary on the present occasion to enumerate the older writers at full length,
since this has already been accomplished very satisfactorily by MM. DE QuaTRE-
FAGESS and KEFERsSTEIN,|| but shall refer to such of their views under the respec-
tive heads as may be required for the complete elucidation of the subject. Of
those, however, who led the way to a more correct appreciation of the structure
of these animals, I may particularise MM. Duck&s,4{ BLancuarp,** and DE QuaTRE-
FAGES,§ in France; EuREeNBERG,}}+ RatTHKe,}{ Max Scuuirze,§§ and KErer-
* Mag. Zool. and Bot. vol. i. 1837; and Catalogue of Worms, 1865.
+ Annals N. Hist. xv. 1845.
t Report Brit. Assoc. 1851.
§ Annales des Soc. Nat. 3™° ser. vi. 1846; and Voyage en Sicilie, vol. ii. par MM. Epwarps,
DE QUATREFAGES, and BLANCHARD.
|| Zeitschrift fiir wiss. Zool. xii, 1863.
{ Annales des Sc. nat. tom. xxi. 1830.
** Annales des Sc. nat. 3me ser xii. 1849.
tt Symbole Physice, 1831.
tt Neueste Schrift. der Naturforsch. in Danzig, 1842.
§§ Beitrige zur Naturg. der Turbellarien, 1851; and Zeitsch. fiir wiss, Zool. iv. 1853, &e.
VOL. XXV. PART II. 41
306 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
STEIN,* in Germany; CERSTED,t in Denmark; Van BENEDEN,+{ in Belgium ;
CLAPAREDE,S in Switzerland ; and DELLE Cutz, || in Italy.
The confusion in regard to the structural characteristics of the order is well
illustrated in the descriptions given in the lately published “ Catalogue of the
British Museum,” and in the first chapter of Dr CopsoLp’s “‘ Entozoa,” where little
else than an array of doubts is produced as a solution of this question. In France,
again, the valuable Lectures of M. Mitnse Epwarps,{ for instance, are chiefly of
interest on the subject of the Nemerteans as stimulants for further investigation.
An examination of the discrepancies existing between the comparatively recent
and excellent researches of MM. bE QuaTREFAGES,** Max ScHULTZE, CLAPAREDE,
Van BENEDEN, and KEFERSTEIN, demonstrate the same necessity for further
elucidation. MM. ne QuatreracEes, VAN BENEDEN, and KEFERSTEIN have, per-
haps, gone more minutely than the others into the question, but all have
confounded the structure, or certain parts of the structure, of the Ommatopleans
with the Borlasians, whether one or both groups have been examined. M. DE
QUATREFAGES investigated the Ommatoplean group more extensively than the
Borlasian; while Prof. KEFERSTEIN paid more attention to the latter; but he has
not entered so minutely into structural detail as the former, though his observa-
tions are, on the whole, more exact. VAN BENEDEN likewise predicated of one
group what he had found in the other, and hence sometimes gave an erroneous
interpretation of the parts. While thus reviewing the labours of these distin-
guished naturalists, it must not be understood that I in the least degree under-
value their investigations ; but rather, that from a more continued series of obser-
vations,structures—about which they were in doubt—have been more clearly
determined, and many additional facts brought to light. Indeed, no one who is
acquainted with the patience and experience necessary for unravelling the anatomy
of these delicate creatures, will wonder at the occurrence of errors of omission or
commission, either in the labours of others or hisown. Ever restless when alive,
prone to rapid dissolution when dead or too much pressed, and comparatively
few of the requisite transparency for examination, it is only by a happy com-
bination of circumstances that the structure of these animals can be successfully
demonstrated.
One of the main objects of this paper is to show the essential differences
between the Ommatopleans and the Borlasians, from the skin even to the micro-
* Zeitschrift fiir wiss. Zool. xii. 1863.
+ Entwurf einer Syst., &c., der Plattwiirmer, 1844.
t{ Memoires des Sc. des Acad. Roy. de Belgique, tom. xxxi. 1861.
§ Recherches Anatomiques, &c., dans les Hebrides, 1861.
|| Mem. sulle Storia, &., vol. ii, Naples, 1825.
{ Lecons sur la Physiol. et Anat, Comparée, tom. 5™°, pp. 460-65.
** Tn his “ General Outline of the Animal Kingdom,’ 3d edit. 1861, Professor Rymer Jones —
strictly follows this author.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 307
scopic structure of the proboscis, as well as to advance our knowledge of the
minute anatomy of these animals and their immediate allies.
I use the terms Ommatopleans and Borlasians provisionally in the mean-
time, because the majority of these soft animals group themselves round two
centres, represented respectively by the common Ommatoplea alba and Borlasia
olivacea. The terms, indeed, are nearly equivalent to Max Scuuttze’s Hnopla
and Anopla, and to Prof. KErerstEIn’s 7remacephalide and Rhochmocephalidw.
I do not think it advisable to call by the name of Borlasia, as the last-mentioned
author has done, a family whose structure is quite different from that of the
animal originally so termed, and hence I have preferred EHRENBERG’sS name,
Ommatoplea, on the one hand, and substituted Borlasia for KererstE1n’s Nemertes,
on the other, both because it ( Borlasia) has the priority, was applied to an animal
similar in structure, and because there are strong claims to perpetuate the name
of the early English zoologist. So comprehensive are the above terms, that
almost in every minute particular all the known British forms, with the exception
of Cephalothrix and another, resolve themselves at once = their respective
heads.
Ommatoplea alba (and variety rosea) may, as above mentioned, be con-
veniently taken as the type of the Ommatoplean group, both from its size and
abundance, and accordingly a systematic examination of its anatomy shall first
engage our attention, the additional observations made on its immediate allies
being appended and contrasted therewith. It is also fair to state, that I could
not have pursued the following inquiries if a liberal and ever-ready supply of
living animals from the St Andrews’ rocks had not been perseveringly forwarded
by a relative, to whom I owe the deepest obligations in this and other depart-
ments of zoology.
Dermal Tissues—The body of the animal, like that of each in the Order, is
universally covered with cilia, some longer ones being present at the proboscidian
aperture and mouth, and others at the tip of the tail. The ciliary motion is most
active at the openings of the cephalic pits. In Tetrastemma variegatum, it is in-
teresting to watch the cilia at the anterior end, especially around the aperture of the
proboscis, as the long cilia bend outwards and inwards with a less rapid motion
than the shorter. Those at the posterior end cause a complete vortex, the longer
cilia often remaining quiescent. The granules in the surrounding water are directed
by the cilia of the sides of the tail towards the tip, where, after coming in contact.
the two opposing currents dash outwards, frequently again to curve round, and
cause their granules to come under the action of the lateral cilia. The whole
appearances very much resemble the currents of water in a vessel after the
application of heat. This action would be of little service to an animal whose
posterior end was quite closed. The cilia, as long known, perform a respiratory
function ; at least there exist no other special organs for the purpose.
308 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
The skin is somewhat opaque, and presents a cellular or cellulo-granular
appearance. In a small living specimen it is represented as atransparent object
in Plate IV. fig. 8, the entire field being definitely covered with glandular cells,
and the reddish pigment grouped here and there in varying and irregular granular
masses. On snipping a portion of skin from an adult living specimen, and
placing it under moderate pressure (Plate IV. fig. 3), it presents the aspect of a
series of ovate or spathulate cells, which contain soft and minutely granular con-
tents, interspersed with large clear masses of mucus (like oil) of a somewhat
similar figure, the latter becoming more numerous as the pressure increases.
There are also numerous pigment and other granules scattered over the field.
Changes, however, rapidly ensue in this delicate texture, as noted by M. DE
QuATREFAGES, both in this group and in Planaria, and the masses of mucus pass
rapidly to the nearest free border and there accumulate, the granular contents of
the cells following a similar course, but not coalescing. Some of these free globules
are shown in Plate IV. fig. 7, @ being the granular masses, and d a group of
mucous globules like oil. The former structures, though very mobile, are less so
than the latter. A transparent gelatinous basis-substance, often of a reticulated
aspect, remains after the extrusion of the foregoing elements from the skin.
When a transverse section is made of an animal hardened in spirit and
mounted in chloride of calcium, the appearance of the dermal textures (Plate IV.
fig. 2) is as follows:—In rapidly prepared and newly mounted specimens, a
structureless film is sometimes observed to separate from the exterior of the skin,
as indicated by the double line at the edge of the figure. Chloride of calcium
would seem to destroy this delicate structure, as after a time it becomes indis-
tinct, and I have not seen it in those hardened in chromic acid. The cellular
cutis (a) is found to have undergone an alteration, being streaked perpendicularly,
an appearance due to the collapsed state of the areolz and cells, whose contents to
a greater or less degree have escaped, and thus given greater prominence to the
hyaline intercellular substance. It is granular throughout, and rather more so
towards the outer and inner edges. In most of the transverse sections, the
pressure of the cover has caused flattening of the skin, so that the increased
cellular appearance of the outer edge is partly due to the fact that the texture
is seen from the surface, and not laterally. Towards the inner edge, the skin in
this state sometimes assumes a crenate aspect, and adjoins a pale and structureless
basis-layer (b), which separates it from the subjacent muscular walls of the body.
In longitudinal sections of the textures, especially in those much hardened or |
slightly exposed to air, spurious annulations are caused by the folding inwards or —
wrinkling of the skin, but such crenations do not affect the muscular layers, and
have no connection with the segmentation of the digestive chamber, or true
annuli. A thin longitudinal section from the surface of the skin shows a series
of meshes with crenated edges, the size of the spaces being variable. In Omma-
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 309
toplea purpurea and O. gracilis the cells of the skin are much smaller than in
O. alba. In 0. gracilis, indeed, the skin resembles microscopic mosaic work,
from the granules and plaits in each space or cell.
The function of this elaborate glandular arrangement is doubtless the secre-
tion of the abundant mucus so characteristic of these animals, and which is often
of a most tenacious description. I have seen a specimen rapidly form a sandy
investment by this means, when placed in a vessel containing a little sand; and
whether the sand particles simply adhered to the gelatinous mucus by accident
or not, the animal took full advantage of the protection. The same habit is exten-
sively followed by the Ommatopleans of our southern shores, apparently to protect
themselves from the increased danger of desiccation. On placing a living speci-
men on a glass slip, and causing it to emit some mucus, the secretion proved to be
a minutely granular fluid, intermingled with a few larger corpuscles. The silky
sheaths formed by Jetrastemma variegatum and others are well-known examples
of this cutaneous secretion. The tube constructed by Polia involuta, VAN Brn.,*
is the densest yet seen, and it has an areolar aspect, from the granules or globules
being set in a hyaline matrix, sometimes at considerable intervals from each other.
Moreover, when viewed in profile, these globules are found to be elevated above the
external surface, like a series of low pale warts. M. BENEDEN says it is simply
tesselated. The tube is attached to the hairs of the abdominal feet of female
crabs (C. maenas) bearing ova, and is evidently of intrinsic importance to the
species, both as a protection against injury and desiccation. That some of the
characters of this group of worms are due to the thick and soft cutaneous layers
is demonstrated by the appearance which they present when such are removed, as
by improper preservation. Two specimens of 0. pulchra, dredged off the Hebrides
by Mr Jerrreys, were in this condition; and as the proboscis had been thrown off
in the one first examined, it appeared like a new type of non-bristled worms,
characterised by the simple arrangement of its digestive system, and its glisten-
ing and elastic investment, so different from the dull, whitish, and non-elastic
covering of an ordinary preparation.+ Another interesting feature in regard to
the skin of the Ommatopleans (in common with the Borlasians), is the reaction
which ensues on testing with litmus-paper. In this group an acid reaction occurs
in O. alba, O. melanocephala, and O. gracilis; while, on the other hand, a reaction
not less distinctly alkaline characterises O. purpurea and O. pulchra.
M. DE QuATREFAGES’ description of the tegumentary structures differs mate-
rially from that just given, a discrepancy arising partly from his confounding the
* Nemertes carcinophilus, Kolliker.
t The comparison of the external tissues of certain remarkable processes, occurring on a new
Annelid from the Gulf of Suez, to the Nemertean skin, as described by M. tp Dr Lion Vaitianr
in the “ Ann. des Sc. nat.” for 1865, is certainly far fetched and unlikely. The processes referred to
are considered buds, but they seem to me to be no more buds or parasites, than the processes on the
long tentacles of our British Mea mirabilis.
MOM exes PART IT; 4K
310 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
structure of Ommatoplea (his Polia) with Borlasia, and partly from incorrect
observations. He refers to the cells or areolee of the integument as “simples
vacuoles ovoides ou arrondies,’’ which refract light, takes no note of their con-
tents, and apparently considers them empty. His separation of the skin into two
layers, the exterior composed of smaller, the interior of larger cells, is not evident
in Ommatoplea. Smaller cells sometimes do occur towards the ciliated surface,
but the entire integument-proper is continuous as a single layer. The only
representative of his ‘“ fibrous’’ layer, which is described as lying within the
former, is our structureless basement-layer. Dr ScuuLtTzs* figures a small por-
tion of the skin of his Tetrastemma obscurum, showing a series of large cells under
the epidermis, with a few granular bodies interspersed, but the view is diagram-
matic. Prof. KErersTein’s observations on the cutaneous and muscular struc-
tures apply almost entirely to our Borlasians.
Muscular Layers of the Body.—A very distinct belt of circular muscular fibres
(Plate IV. fig. 2, c) occurs next the basement-layer of the cutis. They (the fibres)
are compact throughout, and less bulky than the next coat, with which their fila-
ments donot mix. The succeeding layer (d) forms a powerful wall of longitudinal
muscular fibres, which, in transverse sections, is generally somewhat crenated on
its inner border, and fasciculated throughout. ‘The interfascicular substance is
transparent and structureless, and evidently as mobile and contractile as the
fibres themselves. Numerous fibrous bands stretch from the inner surface in
connection with the various contents of the body. The muscular coats in Tetra-
stemma are formed on the same plan as the foregoing. The appearances of these
muscles in transverse section resemble those recently given by Professor Ko.-
LIKER of the muscles in crabs.+ Thus there are only two distinct muscular coats
of non-striated fibres around the body of the Ommatopleans, making an essential
difference in this respect between them and the Borlasians, to which (latter)
previous observers have for the most part confined their investigations.
M. DE QUATREFAGES describes the muscular coats both in Borlasia and Nemertes
(specially instancing Nemertes balmea, our Ommatoplea gracilis), as consisting of
‘external longitudinal and internal transverse’ fibres. In Ommatoplea, as just —
described, it is exactly the reverse, the circular fibres being external, and the
longitudinal internal. He also speaks of another layer, within the internal, as
forming an aponeurosis, apparently referring to the fibrous prolongations from —
the internal or longitudinal coat.{ Thus Sig. DELLE Cutagz, instead of being in
error, as averred by M. DE QUATREFAGES, is correct in stating that the external —
coat is circular, and the internal longitudinal. Physiologically, it is certainly a_
* Beitriige zur Naturges. der Turbellarien, tab. vi. fig. 4.
+ Zeitsch. fur wiss. Zool. bd. xvi. 1866, p. 375 I
+ Vaw Der Hoeven, apparently from following M. pz Quarreraces, makes the same errors —
—Handbuch der Zoologie, vol. 1. p. 212.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 311
better arrangement for such an animal, which has only two muscular coats, to
have the longitudinal fibres internal, for, on the occurrence of rupture, they, as
well as the other tissues, are constricted by the circular; whereas, in the supposed
arrangement of M. pr QuaTREFAGES, the longitudinal are beyond the reach of the
constricting belt. Other organs also in the same animal, such as the proboscidian
sheath and long posterior gland, have their circular fibres exterior to the longi-
tudinal. The actions of this muscular system are very varied, and include swim-
ming or floating on the surface of the water, an action performed, as in the Nudi-
branchiate mollusca, by aid of the mucous exudation, and not, as stated by M. DE
QUATREFAGES, chiefly by the cilia.
Anteriorly the body-wall terminates in a rounded snout—of the usual cuta-
neous textures, presenting in transverse section an areolar and granular appear-
ance, the soft contents of the areole having for the most part escaped. The
aperture for the proboscis lies at the ventral border of such a section. Somewhat
behind this, but yet in front of the ganglia, a remarkable interlacement of fibres
(Plate IV. fig. 1), occupying almost the entire cephalic region, occurs. Powerful
bands of fibres (1) pass below both the buccal cavity and the tube for the pro-
boscis, meet, and cross each other in an oblique manner, forming afterwards, by
their divergence, extensive lateral connections ; indeed, it will be observed, that
towards the inner muscular layer the fibres just mentioned form a broad fan-
shaped arrangement. Some of the fibres (2) pass upwards by the side of the
central canal, and mingle with those descending from this region; while others
(3) curve downwards to the ventral wall. The fibres (4) that meet above the
central canal cross each other obliquely in the middle line, so as to form a firm
arch; and, besides, there are some transverse fibres (5) that cross over the canal,
and spread out on each side. Other bands of fibres (6) slant downwards and in-
wards on each side of the cavity, and meet inferiorly. The arrangement of these
bands and fibres is so intricate, that each seems to blend with the other, and form
a continuous anastomosis of contractile meshes. In addition to these oblique and
radiating fibres, there is a powerful series of longitudinal fibres interwoven with
them in an intricate manner, besides the denser grouping (¢) at the margin (which
indicates the inner muscular coat of the body), and the glandular masses in
the centre. It will be observed that the bands which pass beneath the central
canal are the most powerful, and afford a much greater resistance to the bulging
of the proboscis and its sheath than the superior fibres, so that in extrusion the
organ is mainly directed upwards. This will be understood by referring to Plate
IV. fig. 5, which represents a section of an animal which had protruded a small
portion of its proboscis after chloroforming and immersion in spirit. The inferior
commissure of the ganglion is thus somewhat protected by the arrangement of
the fibres in front of it. The blood-vessel (Plate IV. fig. 1, 7) lies on each side in
a sheltered position, in an angle between two series of fibres; and its calibre
312 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
would not seem to be much interfered with except in extreme protrusion of the
proboscis. All the oblique or transverse fibres are connected with the body-wall
and the inner muscular layer, as are also the longitudinal at the tip of the snout.
This elaborate interlacement provides in the best possible manner for the
varied changes which this region undergoes during protrusion and retraction of
the proboscis, and the ordinary motions ofa tactile and mobile, yet not too yield-
ing snout. The arrangement of the oblique and circular fibres around the longi-
tudinal layer of the central canal also must act the part of a constrictor, and
adapt the cavity to its ever-varying calibre. On the whole, the stroma in this
group, from the greater predominance of granular elements. is Jess dense than in
Borlasia, and the interlacing of the fibres, though not more complex, is more
beautiful, because possessing greater distinctness and regularity.
The posterior end of the body has no such intricate arrangement, but the
muscular fibres blend together at the tip and close in the cavity, with the
exception of the small and sometimes indistinct opening of the great longitu-
dinal digestive chamber. The modes of fracture of these muscular coats in
some of the Ommatopleans in a sick and perishing condition are interesting, the
body being separated into a number of beads from the constriction and rupture
of the body-wall at somewhat regular intervals.
My observations would lead me to follow a different arrangement in the
description of the cavities within the body-wall, from that pursued by MM. bE
(YUATREFAGES, KEFERSTEIN, and VAN BENEDEN, since there exist some differences
as regards interpretation of structures. Instead of speaking ofa ‘‘ general cavity of
the body,” I shall first refer to that chamber in which the proboscis lies, and
which may be termed the cavity of the proboscidian sheath.
Cavity of Proboscidian Sheath—In Ommatoplea alba as well as in Tetrastemma,
this chamber commences just in front of the ganglionic commissures, and con-
tinues without interruption nearly to the posterior end of the worm. It is recog-
nised in the living animal under the lens, or even with the naked eye, as that
forming a pale dorsal streak, and containing a transparent fluid. The commence-
ment of the chamber is shown in Plate VI. fig. 1, where a fold (a) from the tube
of the proboscis becomes attached to the parenchyma of the head, or where, in-
stead of a canal (ab) simply hollowed out in the tissues of the head, free and
dictinct walls to the proboscis become apparent. This reflection is the anterior
boundary of the proboscidian sheath under ordinary circumstances, and it is
against this obstruction that the wave of proboscidian fluid first impinges in the
evolution of the proboscis. The cavity gradually increases in diameter, and
again diminishes towards the posterior end, where it terminates in a distinct cul-
de-sac, a short distance in front of the tail. Its general appearance, when
viewed from above, as a transparent object, is seen in Plate VI. figs. 3 and 8, but
it varies much according to the position, degree of extension or contraction of the
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 313
animal, sometimes almost clasping the elongated proboscis, at others being
attenuated over the doubled organ.
The various transverse sections of the worms also render the relations of the
cavity more apparent. Like the proboscis, its anterior end passes through the
ring formed by the arching of the superior commissure, the inferior commissure,
and the sides of the ganglia. The nervous matter must thus occasionally undergo
very great stretching, or else the proboscis is rarely launched out. This will be
more particularly noticed in the description of the ganglia, and a reference to
Plate IV. fig. 5, will suffice in the present instance. The inferior commissure
separates it entirely from the chamber of the great ciliated esophagus. The rela-
tion of the parts in the ganglionic region is represented in Plate V. fig. 1, o being
the wall of the proboscidian sheath somewhat compressed, so as to show both
longitudinal and circular fibres; for it may be mentioned, that the structure of
the chamber wall is powerfully muscular, as evinced by its ever-varying condition.
At this point, however, the fibres have not attained a great degree of develop-
ment. In a section made further back (as in Plate V. fig. 2, 0), and in the other
transverse sections, this muscularity is more distinctly exhibited, though, of
course, the spirit has shrivelled all the~ parts, especially the muscular. Exter-
nally the wall of the chamber is furnished with a layer of circular, and inter-
nally with a series of longitudinal fibres, both becoming thinner posteriorly.
The comparatively large size of the cavity during life has doubtless caused several
observers to err, by confounding it with the supposed general cavity of the body.
The presence of ova or sperm-sacs has a considerable influence in modifying the
size of the chamber, which in the ripe animal is pressed upwards and towards the
median line, while in the spawned worm it expands freely in all directions. Itis
a mistake, however, to suppose, with M. pr QuUATREFAGES, that no cavity exists pos-
teriorly in the ripe animal, for this chamber holds the same anatomical relations
from the ganglia to the tail as at other seasons, only its calibre is encroached on
posteriorly, and the consequent distention by the proboscis and fluid makes it
more conspicuous in front. The chamber is absent in the aberrant form Pola
involuta, VAN BENEDEN.
In the foregoing cavity the proboscis floats in a clear fluid, rich in large
flattened discs, which have a minutely granular appearance. In the living
animal, these generally have a fusiform outline, from a slight thickening in the
middle (Plate IV. fig. 9, 5). They are accompanied by certain granules and globules,
which are also represented in this figure. The discs vary in size, and adhere to-
gether in a dying animal very easily, from the highly coagulable nature of the
transparent fluid in which they float; and occasionally fibrinous shreds may be
observed attached to them under the same circumstances. The fluid, indeed, is
highly organised, and very different from sea-water, to which Dr T. WILLiAMs
compares it. When the proboscis has been gently protruded under chloroform,
VOL. XXV. PART II. 41
314 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
the discs in the interspace may by-and-by be seen grouping together, so as to
form stellate bodies, resembling miniature solasters, spiked bodies like thorn apples,
flattened structures with pectinate ends, and various other forms. In O. melan-
cephala the discs are comparatively small, some being clear, spindle-shaped bodies,
others granular and rounded. The enormous increase of cells and granular
masses in the proboscidian fluid, after the discarding of a proboscis, is well seen
in this species. In Tetrastemma the discs (Plate IV. fig. 14), though similar in
shape to those of O. alba, are comparatively large ; and ina variety of 7. varicolor,
which I am at present inclined to regard as the Polia sunguirubra of M. DE
QUATREFAGES, they are tinged pinkish or reddish by transmitted light (Plate IV.
fig. 11). They are not all similarly tinted, some being pale, others yellowish, while
many are bright red—the colour in all cases being in the nuclei. Circular bodies
and granules are present, as in Ommatoplea. The skin of this specimen contained
many minute reddish pigment specks, so that to the naked eye it had a delicate
salmon-pink appearance. Reddish granular masses occasionally occur in the
proboscidian chamber of O. alba, and in other species of Tetrastemma, generally
associated with reddish specks in the skin; and it is curious that a cast-off pro-
boscis in 7. algw, and other species, assumes the same hue by transmitted light. —
With the foregoing exceptions, the only changes noticed in the colour of the discs —
were those caused by refraction of the rays of light. After extrusion into the
water, their shape soon alters, and they adhere together, and become translucent.
M. CixstTED* gives a small figure of a transverse section of his Notospermus
Jiaccidus, and characterises the proboscidian cavity as “ canalis in quo penis est,”
indicating by a blank beneath what might have been the digestive.tract. His
interpretation of structures, however, is more distinct in his section explana-
tory of the Family Amphiporina,} in which the digestive cavity is correctly
alluded to.
The reflection of the walls of the proboscis before-mentioned, in front of the
ganglionic commissures, is the only barrier (and a very effectual one) I have —
observed separating the proboscidian chamber from the tissues of the head. In no
species examined has such a cephalic diaphragm as described by M. DE QuATRE-
FAGES been found; but the peculiar ciliated chamber or cesophagus, to be described —
hereafter, takes its place, and leads one to infer that the distinguished naturalist
has misinterpreted the structure. Besides, the head is not a hollow organ,
requiring such definition from the other parts of the body. This author, while ex-
plaining a transverse section through Nemertes Borlasii{ (vel Borlasia Anglie),
shows a canal surrounding the proboscis; but in his description he confounds it
with the general cavity of the body, and figures (fig. 5 same plate) the proboscis as —
* Entwurf einer syst. Hintheilung, &c. der Plattwiirmer, tab. iii. fig. 51.
} Entwurf &c., p. 94, fig. 18 (woodcut).
t Recherches Anat. and Zool. vol, ii, pl. xviii. fig. 4.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 315
occupying the centre of the general cavity posteriorly. This description, no
doubt, refers to a Borlasian; but he states that the same arrangement occurs in
the Ommatopleans, and represents in Polia* a series of transverse fibres as
forming a platform (plancher) at the anterior and upper portion of the general
cavity of the body, indicating its presence in his figures by a dark shading. No
such arrangement of transverse fibres has been seen by me, but the characteristic
ciliated oesophagus occupies this situation, and has probably misled the observer.
The somewhat erroneous views he entertained with respect to the relations of the
corpusculated fluid of the proboscidian chamber may be seen by a glance at one
of his figures,} which depicts in Polka sanguirubra the proboscidian bodies as
floating in what he calls the genital cavity, and in which the genital ceca are
supposed to lie. I cannot corroborate his statement that these discs become
much more numerous at the epoch of reproductive activity. The diminished size
of the chamber may cause a slight crowding anteriorly, but this is not an increase.
He did not recognise the complete muscular sheath for the proboscis and the
proboscidian fluid. Dr Jonnsron likewise confounded the cavity-proper of the
proboscis with the general cavity of the body ; and Dr Wittrams,{ who styled the
canal the oesophageal intestine, stated that it opened externally on the side of the
body, not far from the head, after the manner of the Sipunculide. M. Van
BENEDEN,§ however, alludes to the sheath for the proboscis in Polia obscura, and
compares the fluid and discs therein to pale blood. Professor KEFERSTEIN,]||
again, follows the majority of his predecessors, in so far as he also describes the
proboscidian discs as floating in the general cavity of the body, in which, more-
over, he locates the proboscis (Riissel); thus ignoring the special and complete
muscular sheath just described.
The structure of the proboscidian discs, and the highly organised condition of
the transparent liquid in which they float, point them out as being, in all proba-
bility, concerned in nutrition, as first mentioned by M. pz Quarreraces, though
he likewise associated generation therewith. Some very interesting questions, how-
ever, are raised by their entire absence in the curious Polia involuta, VAN BEn.,
especially to those who, like the late Dr W1nt1Ams, consider the fluid analogous to
the peritoneal or perivisceral fluid in the true Annelids—a fluid, we may remark,
which Professor HuxLey 4 considers as the true blood, while he thinks the red
fluid in the branching vessels analogous to the water vascular system in the
Annuloida. Ifin Polia mvoluta the proboscidian fiuid had been more important
in nutrition than that in the vessels, it certainly would not have given way to
the latter. It is to be remembered, too, that this absence coincides with the
EaOpeciaug. l. pl. xvai, and figs 1; ploxix. + Op. cit. pl. xxii, fig. 1.
t Report, Brit. Assoc. 1851, § Op. cit. p. 26.
| Zeitsch. fiir wiss. Zool. xii. pp. 69 and 71.
{| Notes of Lectures at the Roy. Coll. Surgeons, Med. Times and Gaz., March 7, 1868.
316 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
atrophied condition of the proboscis itself and all its apparatus. It cannot be
affirmed, also, of the Nemerteans, that the fluid in the so-called blood-vessels is —
devoid of corpuscles, for they occur in several species. Again, I think there can be —
no doubt the fluid and discs exercise a very important influence on the reproduction
of the proboscis, a process hereafter to be described, as well as promote the absorp-
tion of the debris of the discarded organ when it happens to be included in the
chamber. But while thus affirming the fluid has a certain influence on, and bears
a certain relation to, the development of the proboscis, it cannot be said to be
indispensable for the appearance of the latter, since there is a small proboscis in
P. involuta, where the fiuid is altogether absent. The views of Dr THomas
Wi.1aMs in regard to this corpusculated liquid, which he termed the “‘chylaqueous
fluid,” are so much at variance with accuracy, that 1 cannot pass them over in
silence. He says—“ In the case of the Borlasiadze, Planiariadee, and Liniadz, the
chylaqueous fiuid is contained in the digestive czeca and diverticula. In some of the
Planariadz, however, I have proved that a space does actually. exist between the
digestive diverticula and the solid structure of the body, mwhich.is lined by a vibra-
tile epithelium, and into which probably the external water is in some way ad-
mitted. By this water, thus situated, the contents of the digestive ceca are
aérated. The fluid oscillating in these ceecal appendages of the stomach is thickly
charged with corpuscles, which, from their regular character, prove this fluid to
have already reached a high standard of organisation. They occur as elliptical
cells in the Borlasia from which the illustration (fig. 25) was taken; the fluid —
abounded also in small orbicular points, constituting the ‘ molecular basis’ of the
digestive product. In this worm, it is this fluid, and not the true blood, that is
aérated ; the latter system is too little developed.”* The above clearly shows
that he was quite unaware that the so-called “ elliptical cells” are always con-
fined within the cavity of the proboscidian sheath, as well as points out the errone-
ous notion he entertained of the true digestive tract, which in all cases can readily
admit salt water (by mouth or anus), if such is required, but certainly not for the
purpose of converting it into ‘‘ a vital organised fluid.” The proboscidian fluid and
discs, as I have previously shown, are very far removed from sea-water.
In the Ommatopleans, the aperture for the extrusion of the proboscis is situ-
ated towards the ventral edge of the tip of the snout, and under favourable
circumstances in the living animal, may be seen as a terminal pore, surrounded
by a closely set series of radiating lines; as, for instance, when the snout is bent
upwards towards the tube of the microscope (Plate IV. fig. 13). It is furnished
with longer cilia even in the young animal; and in the adult these (cilia) form,
when the lips are slightly pouting, a very pretty arrangement (Plate VI. fig. 1, ae),
similar to the analogous opening in Borlasia (Plate X. fig. 1). The striated ring
* Phil. Trans. Part ii. 1852, p. 627, pl. xxxii. fig. 25.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 317
surrounding this orifice in transverse sections of the tip of the snout indicates
the special muscular coat pertaining thereto. The canal proceeds in a straight
line backwards from this aperture to a point in front of the commissures of the
ganglia, where it meets the differentiated walls of the proboscis, as shown in Plate
VI. fig. 1, ab; and the cilia can be traced backwards to this region, but no further.
This canal is simply hollowed out in the tissues of the head, and is quite inde-
pendent of the motions of the proboscis. It is furnished with a series of longi-
tudinal muscular fibres beneath the ciliated mucous surface, and the strong
oblique and circular bands (Plate IV. fig. 1) form a very efficient constricting invest-
ment. When the proboscis is about to be ejected, it commences to fold over like
the turning of the finger of a glove inside out, at the point (Plate VI. fig. 1, a) in
front of the ganglionic commissures, and not at the tip of the snout, a fact which
has escaped previous observers. In withdrawal also, it may be noticed that, to-
wards the conclusion of the process, the last wrinkle of the proboscis glides
within the terminal aperture, and is seen slowly passing backwards till this
point is reached, when the wrinkle ceases, and the organ is once more in its
ordinary condition, any change that afterwards ensues being due to the stretch-
ing of the shortened organ backwards—a process of simple elongation. Thus
the anterior portion structurally and functionally differs from the succeeding, the
walls of the proboscis always intervening between it and the proboscidian fluid.
The attenuated coats of the proboscis curve outwards all round, and become
fixed to the walls of the foregoing canal and other cephalic tissues just in front
_of the ganglia; and so the reflection constitutes the point dappui against which
the wave of proboscidian fluid impinges, when the organ is about to be extruded.
The thin anterior walls of the proboscis unroll, the terminal canal is distended by
a pouch of fluid, and then the organ is rapidly launched forth. To judge from
the description and drawings of M. pz QuaTReEFAGES, the entire force of this liquid
would dash against the posterior part of his nerve-ganglia, and the straitened
border of his hypothetical ‘‘ diaphragm” would not pass further forwards. In
my specimens, the waves of the proboscidian fluid debouch readily into the yield-
ing anterior canal in front of the commissures, and then externally into the loop
of the extruded proboscis. I have never seen the very pretty lozenge-shaped
arrangement of muscular bands in the snout, as figured* by M. pE QUATREFAGES,
and whose function, he says, is to dilate the “‘ oral’’ orifice, and carry the ‘ gullet”’
forwards; but the elaborate stroma, shown in Plate IV. fig. 1, would amply suffice
for this. During the motions of the proboscis, the reflection in front of the ganglia
assumes various postures, and it frequently does stretch obliquely forwards and
outwards from the tube, especially when that is drawn backwards. On the other
hand, when the tube is thrust forwards, the fibres slope forwards and inwards.
Dr Jounston, M. DE QUATREFAGES, and Dr WiLLiAms agreed in considering
* Op. ct. pl xix. fig. 1.
VOL. XXV. PART II. 4M
318 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
the terminal aperture the mouth, and indeed it could not be otherwise, since the
proboscis was regarded by them as the true alimentary organ. My observations,
while leading me to differfrom M. Van BrenrepENn and Professor KEFERSTEIN,
who aver that the Ommatoplean mouth is situated on the under surface behind
the ganglia, as in the Borlasians, coincide with the three former only in so far as
this anterior opening lies close to the real mouth (communicating with the ciliated
sac or oesophagus). Dr Max ScuuurTze, almost alone amongst foreign authors,
seems to have noticed the true position of the mouth in his Tetrastemma obscurum.
The aperture for the proboscis lies just at the ventral border of the snout, while
the mouth forms a slit on the ventral surface immediately behind the former.
In this respect, therefore, there is a marked distinction between the Ommato-
plea and its allies on the one hand, and Borlasia and Cephalothrix on the other,
the mouth in the first group opening quite in front of the ganglia, while in the
other it is situated considerably behind the ganglia. Analogy gives no grounds
for supposing the proboscis to be the alimentary organ.
I shall divide, for convenience of description, the Ommatoplean proboscis
into three regions, viz., the anterior, middle, and posterior. The first (Plate VI.
fig. 3, A) comprehends that somewhat cylindrical portion between the reflection in
front of the ganglionic commissures and the commencement of the stylet-region
—the trompe of M. pE QuaTreraces; the second (B) includes the stylet-region
proper and the well-marked swelling of the great muscular sac—the oesophagus
of M. DE QuAaTREFAGES; and the third (C) is represented by the long posterior
gland—the intestin of M. DE QUATREFAGES.
Anterior Region of Proboscis—From the point of reflection backwards, the
proboscis (trompe, Riissel) gradually increases in diameter until its full size is
attained. The entire organ is proportionally on a larger scale than in Borlasia,
and its anatomy more apparent ; though I doubt, even in this group, if we can
assign it the ideal office of a vertebral column. The general appearance of the
commencement of the organ in O. alba is seen in Plate VI. fig. 3, and in Tétra-
stemma alge, in Plate VIII. fig. 3. At the point of reflection there is sometimes seen
a kind of os, from the slight turning over of the lips of the organ in the early stage of
ejection (Plate VI. fig. 1, a). This figure also represents the longitudinal fibres of
the proboscis as most conspicuous in thisregion. Sometimes the organ assumes a
twisted position under examination, so as to give the fibres a spiral appearance, and
in such a state the structure might fancifully be likened to the spiral arrangement —
of the muscular fibres in the oesophagus of the higher animals, but the condition is _
purely accidental. I fear, however, it has led M. Dz QuaTREFAGEs into an erroneous —
interpretation of the anatomy of the organ in Polia glauca,* which (organ)
is described and figured as having regular spiral belts at its commencement.
* Op. cit. plate xx. fig. 3.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 319
The anterior fibres of the proboscis, as further shown in the various transverse
sections, and in the ruptured organ when extruded, are chiefly longitudinal, and
while the thinness of the coats renders the exact structure of this region in trans-
verse section less distinct, a very definite arrangement is observable as soon as
the tube has attained larger proportions. Dr Jounston, indeed, considered the
organ to be homogeneous ;* and M. DE QuaTREFAGES describes its commencement
in Polia mutabilis as consisting of two longitudinal muscular coats, separated from
each other by a cellular layer, which, he explains, is a provision for enabling these
muscular coats to act independently. He also observes, that no circular fibres
were seen in this species, in P. jiJum, and some others. In very small specimens
of the British examples the transparency of the tissues renders definition of the
coats somewhat obscure, especially after mounting in chloride of calcium, but, so
far as I have observed, the structure is as follows :—Externally, there is a layer
of what appears to be elastic tissue (Plate IV. fig. 4, g, Plate V. fig. 4, g, &c.).
It is more distinctly striated in transverse than in longitudinal sections of the
organ, hence it may be inferred that its fibres are chiefly circular in direction,
as seen on comparing the last-mentioned figures. Towards its free border, also,
certain obscure granular markings observed in the longitudinal section (Plate IV.
fig. 4), show that the direction of the external fibres is different from the others ;
indeed, in some views, the appearance is such as to raise a suspicion of the
presence of the cut ends of a few fine circular muscular fibres, the rest being
nearly homogeneous. Within this is a somewhat narrow belt of longitudinal
muscular fibres (/, same figures), which may be termed the external longitudinal
muscular coat. It consists of pale, unstriped muscular fibres, whose cut ends are
seen in Plate V. fig. +. Intervening between this coat and the other longitudinal
layer is a remarkable stratum, the reticulated or beaded layer (e), in the same
figures, which in transverse sections (Plate V. fig. 4) assumes a regularly monili-
form appearance, from an increase of its constituent substance at certain points.
In longitudinal sections, I was for a time puzzled by the appearance of the cut
ends of fibres in this layer, as if it had been composed of circular fibres; and a
more minute examination showed that such was due to certain intermediate bands
which passed between the thicker or beaded portions. If a thin longitudinal slice
from the organ in O. pulchra is hardened and mounted in chloride of calcium,
numerous well-marked homogeneous longitudinal belts are seen at regular
intervals, from one end of the anterior region of the proboscis to the other, and
between them are many connecting transverse fibres, which pass from each edge
of the belt. The cut ends of the fibres in the longitudinal sections have therefore
been caused by the knife severing the transverse meshes between two longitu-
dinal belts. Thus the tube is surrounded by a complete investment of this
* Catalogue Brit. Museum, p. 285.
320 | DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
homogeneous though complex layer, which, doubtless, has its physiological use
in the varied movements of the organ. The next layer (d, same figures) consists —
of a strong coat of longitudinal fibres, fully twice as thick as the external longitu-
dinal layer, and which may be termed the znner longitudinal muscular coat. In
essential structure it resembles the exterior, differing only in bulk. In sections
prepared by hardening in alcohol, these fibres, in common with others in this
organ, present a much coarser appearance in transverse section than after harden-
ing in chromic acid. It may be mentioned also, that there is a considerable
histological difference between these muscular fibres and those in the higher
animals, such as absence of nuclei and greater homogeneousness. The fifth
layer from without inwards is a strong band of circular fibres (c, same figures),
the circular muscular coat, which forms a counterpoise to the preceding. . Lying
on the inner side of these fibres is a basement-layer of pale translucent texture, best
observed in the longitudinal sections (Plate IV. fig. 4), where it is marked 2. In
transverse sections this coat is apt to be confounded with the inner layer of ©
circular fibres, but the distinction between the two is sufficiently apparent in
longitudinal sections. It has, on the whole, a cheesy or cartilaginous aspect.
Upon this layer rest the peculiar glandular papillee, which arise from a distinct
margin on its inner edge, as indicated at b in the last-mentioned figure, where
some of the basal streaks of the papille are represented. A glance at the other
figures will show the relations and proportions of these organs. In the ordinary
transverse sections of the proboscis they form en masse a somewhat foliated or
frilled arrangement, often more strictly symmetrical than the view here given (Plate
V. fig. 4). In some contracted specimens they block up the entire cavity, or else a —
transparent mucous film which has exuded from them does so. The form of the
glands in the fresh specimen under pressure is seen in O. a/ba in Plate V. fig. 7, and
in Tetrastemma in Plate VY. figs.6 and 11. The largest glands are situated some
distance in front of the stylets, for towards this region they become smaller, and —
finally the fundus is clothed only by minute papille. In typical examples of
Tetrastemma variegatum the glandular papille are leaf-shaped, and somewhat
crenated at the free border, where there is a regularly streaked appearance from the ~
arrangement of the globules. Under pressure they are granular in the interior,
and furnished with numerous globular or wedge-shaped mucous niasses, that
refract the light like oil. Sometimes in O. alba they present a coarsely fringed
appearance, with large granules in their interior; and when the tube has been
turned inside out, they have a villous aspect, the tough mucosity adverted to
above projecting in strings from the papillze under the slightest pressure. I have 4
generally observed also, towards the first portion of the protruded organ, fine
motionless processes like cilia projecting from the apices of the glands, and they
are probably homologous with the minute spikes which occur on the glands of
the posterior region after rupture from pressure.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 321
The foregoing description of the structure of this region differs much from that
given by M. pE QuaTrReFaGEs, almost the only author who has entered into the
minute anatomy of the Ommatoplean proboscis. He states, like Mr H. Goopsir,*
that externally the tube is furnished with a series of transverse muscular bridles,
which maintain it in position within the body of the worm, and he gives a section
of the parts in Nemertes balmea, which bears out his description very well; but
he did not observe that if such bridles exist, they would have to pass through
the muscular sheath in which the proboscis glides, before reaching the body-wall
of the animal. Apparently he has not made out the two diverse structures. His
minute anatomy of the proboscis is chiefly taken from the examination of
Borlasia Anglic, and hence cannot apply in any degree to the Ommatopleans,
though he considered it the type of both. He makes out only two muscular layers
in the wall of this organ, and though in his section from B. Anglic he indicates
‘traces de fibres transversales,” by a few lines crossing these longitudinal coats,
he distinctly observes that they are not apparent in the smaller species. These
longitudinal coats are separated, says he, by a transparent homogeneous tissue,
which forms a great number of bridles of very elastic fleshy columns, making, in
other words, an elastic cellular layer; and he figures this in the before-men-
tioned section, adding that this lax cellular coat will give the two longitudinal
muscular coats that independence of action necessary for the proper perform-
ance of their functions. No such cellular layer has been seen in the British
species, but between the two longitudinal coats there is found the remarkable
reticulated layer. He mentions a transparent homogeneous coat within his longi-
tudinal muscular layer, corresponding to the mucous coat of the higher animals,
and adds that the papillee of the latter are all covered with vibratile cilia. M.
DE QUATREFAGES thus describes only four coats, viz., mucous, internal longitu-
dinal, elastic cellular, and external longitudinal; and if the stays or bridles
which he notes as connecting the tube to the body-wall be taken into account,
it may be surmised that the muscular sheath for the proboscis is included in
his reckoning. No cilia are present in this organ. Professor KEFERSTEIN does
not enter into the structure of this region in Ommatoplea.
Middie Region —tThe elongated chamber just described terminates posteriorly
in a sort of cul-de-sac, into which three small apertures converge—one at each
side from the lateral stylet-sacs, and a central one in the pit of the cavity con-
nected with the peculiar reservoir which succeeds.
The walls of the proboscis undergo a considerable change in this region,
especially in regard to the deeper layers. Externally there is the investing
coat continued from the anterior region on to the commencement of the reservoir
(Plate IX. fig. 11), and which has acrenated border in the contracted state of the
* Ann. Nat. Hist. xv. 1845.
VOL. XXV. PART II. 4N
322 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
parts, with transverse markings or rugee; but such an appearance does not of
necessity mean that it is composed of circular fibres, for the contraction of the
longitudinal layer underneath would cause even a very feebly elastic coat to
assume similar markings. The thin subjacent layer of longitudinal fibres is
likewise continued to a similar extent on the reservoir-region, and assists in
connecting the divisions. These two layers lie exterior to the stylet-sacs.
The structure of the pit or termination of the anterior chamber (7, Plate LX.
fig. 3) merits special notice, since it has certain important functions to per-
form. The large glands of the inner wall gradually diminish in size until the
floor is covered only by small, densely arranged, and minutely granular pro-
cesses, so that the whole forms a somewhat sharply defined border, which in
the ordinary state of the parts knuckles backwards all round the central
stylet in the manner shown in the figure, becomes firmly bound together so
as to constitute asphincter for the aperture, and gently bending outwards and
backwards, is lost in the obscurity of the parts, caused by the external circlet
of glands—somewhat behind the anterior termination of the wedge-shaped
investment of the sac at the base of the stylet. This floor of the chamber ©
is composed of a series of muscular fibres, whose direction, in the ordinary —
state of the parts, is outwards and backwards, as shown in the drawing,
but which assume various aspects during the motions of the organ. Thus
the floor passes from the conical form with the apex directed backwards to that
of a transverse platform; and in the everted condition forms a cone whose apex
is directed forwards (Plate VI. fig. 2). In the latter position the secure binding
of the fibres which knuckle round the central aperture just permits the stylet to
project, but no more. The whole arrangement constitutes a large muscular pit with —
very powerful and mobile walls, capable of many and varied alterations of form.
In firm contraction of the region the floor or pit of the cavity is pouted forwards
(Plate XII. fig. 9), causing a radiated or slanting appearance of the fibres. A firm
constriction of the tube just in front of the stylet-region often takes place, separat-
ing the pit of the organ from the more glandular region in front, and causing a
double swelling of the parts. Just in front of the stylet-sacs lie some coarse
granular glands, which, however, are less conspicuous than in O. gracilis and
others. Professor KEFERSTEIN* speaks of this region as having only a longitudinal
muscular coat (though the crenated border of the anterior chamber is continued
thereon in his figure), and as possessing much pigmentary and granular matter. ©
The latter is not well marked in Ommatoplea alba or Tetrastemma, as the
entire apparatus is either translucent or white; but in certain species, as will
hereafter be shown, an increase in the granular matter occurs. The longitudinal
fibres of the last-mentioned author end at the posterior border of the stylet-region.
The Lateral Stylet-Sacs—poches styligénes, QuaTreF., Taschen, Ker., &c.
* Op. cit.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 329
(v, Plate LX. fig. 3)—occupy the exterior portion (covered only by the elastic coat
and external longitudinal fibres) of the somewhat solid wall of the section imme-
diately succeeding the foregoing cavity, and in some views cause a distinct bulg-
ing. They are conspicuous by their aqueous translucency, as well as by the
nail-shaped stylets in their interior, though the exact position of their long axes
is rather difficult to determine. In ordinary views, when the animal is examined
as a transparent object under pressure, their long diameter is antero-posterior, or
slightly oblique; but when the worm has been killed and hardened in alcohol,
their long diameter is often found to be transverse (Plate V. fig. 5). Each sac is
somewhat ovoid in outline, has a thin, transparent, contractile investment (suffi-
ciently tough to prevent the points of the stylets piercing it during the motion of
the worm), which lies immediately under the superficial layers of the section, and
a duct passing from its central region to communicate with the pit of the anterior
chamber of the proboscis. The direction of this duct under ordinary circumstances
(2.e. when the animal is viewed from above asatransparent object) is forwards and
inwards, but, like other structures pertaining to this mobile organ, it is liable to
many alterations, and is occasionally much stretched and attenuated. It is also
slightly narrowed on approaching the sac, and has at its junction therewith a
series of protecting fibres (Plate VI. fig. 9, a). MM. pe QuatTREeraces and Max
Scuutrze do not notice the duct at all, and M. CLaparkpe’s figure* shows it dis-
torted from pressure in Tetrastemma, but M. KEFrEersTEIn’s representation is more
accurate. Each sac contains a variable number of the characteristic nail-shaped
stylets (8), from three to five, more or less—in different stages of development, as
well as certain clear fluid vesicles (€), globules and granules, and is quite filled by
a transparent fluid. The relations of the sac and its contents are shown in the
various figures. In Tetrastemma alge I have seen, besides the ordinary stylets,
a group of minute crystalline spinets, which had no connection with the clear
vesicle of the sac. The stylets very much resemble a lath-nail, and are formed
of a translucent calcareous secretion ; indeed, they appear like spikes of the purest
glass. The head is bulged, rounded at the edges, and somewhat flattened on the
top, from which an elongated conical spike proceeds to a sharp apex. The per-
fect spike or spikes in these sacs are usually about the size of the central stylet,
and there are often three or four that can scarcely be distinguished from each
other. Besides the perfect spikes, there are some with heads not fully developed,
but complete in other respects; others again present the form of simple spikes of
various lengths devoid of any head. In some instances the centre both of the
head and point of the stylet is granular, while the superficial portion is of the
usual homogeneous aspect. These stylets are secreted by the sac, yet I do not
think they are always developed originally in one of the contained globules, as
Dr ScHULTZE says; and this would not signify much, since the entire cavity must
* Recherches Anat. sur les Annélides, &c. plate v. fig. 6.
324 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
act as a secreting chamber, else the large ones could receive no increase after
they had outgrown the capacities of the globules. They seem to be formed by
gradual increase of layer upon layer of the calcareous glassy secretion, as is well
shown in some specimens mounted in chloride of calcium, where they have
assumed a stratified or laminated appearance. Sometimes a process (Plate IV.
fig. 10), probably a remnant of the globule, passes from the head down the shaft
of the spike for a short distance, as indicated by Dr Scuuttze in Tetrastemma,*
though seldom to such an extent in the adult stylet. The knob on the head
figured by this author must be rare, and probably represents a casual globule.
The stylets are dissolved in weak acetic acid, as first noted by M. DE QUATREFAGES,
and are roughened or corroded by strong liquor potassee.
In a large animal an interesting arrangement of the stylet-sacs occurred on one
side, for there were two of nearly equal size, which communicated with each
other at one end, so that an interchange of fluid and granular contents took
place. Only one had a duct of communication with the anterior chamber of the
proboscis. The opposite side had a single sac of the usual formation, containing
two large and perfect stylets, and a shorter without a head. On the abnormal
side the outer sac (in this view) had two fully formed stylets, a larger and a
smaller clear globule, besides some other minute globules and granules; the
inner, which possessed the duct of communication, had one stylet as large as
the preceding, and fully formed; another somewhat less, but also having a head;
a third slender spike of greater length than the latter, but headless; and a
fourth, rather more than half the length of the last mentioned. No globule
existed in the inner sac. It is interesting to notice the different degrees of per-
fection of these spikes in relation to what Dr ScHuLTzE avers as to their develop-
ment, viz., that they are the products of the smaller contained vesicles. In the
one there were two large globules, and two perfect stylets, yet no trace of a de-
veloping spike; in the other there were three completely formed stylets, yet
each varied in length; while the long spike without a head was fully as long as
the largest in that sac—head included. The stylets in the outer sac were quite
as large as the central stylet. Thus at present, though I have often seen spikes
inside, and connected with the fluid vesicles, I cannot support Dr ScHULTZE’S
notion that the spikes must be developed therein. M. CLaparEDE says he has
never seen the spikes inside those vesicles,} but I observe, in a more recent publi-
cation,{ he figures a developing stylet in a globule in Prosorhochmus Claparedit.
In a specimen that had often been under the microscope, I found on one
occasion a pair of stylets, apparently from the lateral sac of one side, advanced
nearly to the ganglionic portion of the proboscis. One lateral pouch, as it
* Beitrage zur Naturges der Turb. tab. vi. fig. 10, a.
+ Recherches Anat., &. p. 79. ;
{ Beobachtungen itiber Anat. und Entwicklung, &c., 1863.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 325
happened, was thus emptied, while the other retained its three stylets. The
loose stylets were very slowly moved forwards, scarcely any progress being made
during an hour’s observation. At this time the sac from which they had been.
liberated contained numerous granules, but no circular or ovoid vesicle. Twenty-
four hours after, the stylets had disappeared. The sac is now observed to be
much less than its fellow of the opposite side, and somewhat shrivelled and
undefined ; but it contains a small ovoid vesicle, which is traversed by a minute
slender spike, whose long diameter exceeds that of the globule, and therefore it
cannot be supposed to be within it. In addition, there is a free spike about a
third the length of the larger one. The former has assumed the shape of a stylet
without a head ; the latter is as yet nearly cylindrical (Plate VI. fig. 4). What-
ever the function of these stylets in the lateral sacs may be, there can be no doubt
they have nothing to do with the supply of the central apparatus, for that fur-
nishes its own stylet.
The middle or stylet-region is likewise the seat of other structures of import-
ance, viz., the central stylet and its basal sac, the ejaculatory duct or canal of com-
munication with the reservoir, and the circlet of granular glands. It is of the
same vitreous translucency posteriorly as the succeeding region, while both the
anterior chamber and the posterior region are of an opaque white in the fresh
specimen. Externally there is the investing layer (Plate IX. fig. 3, 7), continued
from the anterior chamber, and which passes backwards to the next region.
Beneath this lies a series of very powerful and conspicuous longitudinal muscular
fibres (7, same plate), apparently to some extent continuous with the more bulky
longitudinal layer of the preceding region, but few of which pass on to the
next. Internally oblique and radiating fibres occur, the former slanting forwards
and outwards from the setting of the central stylet, and forming a kind of mus-
cular sling, well marked in O. melanocephala (Plate VI. fig. 7). This layer is dis-
tinctly separated at its posterior border from the succeeding region or reservoir
by a pale boundary-line under pressure, so that the parts have a somewhat
jointed appearance. In transverse section, the complicated structure of this
part is well observed (Plate V. fig. 5). The longitudinal fibres form a thick belt
exteriorly, and send gradually diminishing bundles inwards towards the central
point. ‘This peculiar appearance in transverse section must be due to some
difference in the arrangement of the ultimate fibres, as such sections of other
muscles usually show a much coarser, more fasciculated, and less granular aspect.
There can be no mistake as to the true structure and arrangement of these fibres,
since I have cut them both obliquely and transversely in the same specimen.
The last-mentioned transverse section also shows a complicated arrangement
round the central stylet-apparatus; exteriorly there is a firm setting, next a layer
which seems to be closely united with the coat of the ejaculatory duct in front,
and other two more immediately connected with the granular sac itself. Some of
VOL. XV. PART Il. 40
326 DR W. CARMICHAEL M‘SINTOSH ON THE STRUCTURE OF THE
these appearances may have been due to the action of the chemicals in mount-
ing, but they were very distinct. The ejaculatory duct has a single ring or coat
surrounding it. The exact arrangement of the fibres of this region is difficult to
unravel, but some evidently curve across the region, while those at the sides
bend backwards, the latter in some views simulating the walls of a cavity. In
Tetrastemma vermiculus (as a living transparent object) the region has its deep
mass formed of fibres which curve outwards and forwards from the central set-
ting (Plate IX. fig. 12). Through this region the ejaculatory duct (js) passes to
the point where it opens into the muscular space behind the constrictor of the
central aperture in the floor of the anterior chamber. The aperture of the duct
pw) is generally obscured by the central stylet-apparatus, unless the observer sees
it at the moment of contraction of the powerful muscular walls of the reservoir,
when the mucous or villous lining is driven forward so as to render the channel
more apparent, and a vigorous jet of the minutely granular fluid is propelled
into the muscular sac, and then through the stylet-aperture into the floor of the
anterior chamber. Closer observation, even when such convulsive contractions
are absent, occasionally shows the minutely granular fluid passing onwards to
the anterior chamber; and when the ejaculatory duct is not obscured by the
glands, the dancing granules of this peculiar fluid are seen therein. Moreover,
when the large compound cells (Plate V. fig. 3) have been detached under pres-
sure, and squeezed forwards into the reservoir and along the duct, the calibre of
the opening into the muscular sac may be ascertained with tolerable accuracy,
and, so far as I could see, is such that only a single file of cells at atime can
be transmitted. The duct has a bent-conical form, a shape that avoids inter-
ference with the basal sac of the stylet, which occupies the centre of the region ;
and its posterior end (that opening into the reservoir) is capable of a certain
amount of constriction, as indicated in one of M. CLapareEpe’s figures, but I have
rarely met with the organ in this position. In the latter state the inner or
convex side of the duct is glandular, while the outer or concave side is not.
A layer of longitudinal fibres, continued from the reservoir posteriorly, consti-
tutes the proper wall of the tube, and is represented in transverse section
in Plate V. fig. 3. Internally the tube has a mucous lining, which anteriorly
is for the most part quite free from glandular papille; a few small glands,
however, are generally observed towards its posterior end. Its wall is not very
dilatable, the cavity becoming elongated, but not much increased in diameter,
even under violent expansive force. It can be firmly closed by the contrac-
tion of the region surrounding it, so as to be marked by a mere central streak —
(Plate XII. fig. 9, »). The villous lining of the reservoir is often pushed forwards
along the duct during violent contractions. The whole structure of the channel,
and its relations to surrounding parts, show that it is formed, not for transmitting —
fluids from before backwards, but entirely in the opposite direction. The mobile
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 327
muscular space (e, various figures) into which this duct opens, forms a kind of sac
that is occasionally distended with the cells and granules, before they reach,
through the central pore, the pit of the anterior chamber.
The cavity or reservoir (0, Plate IX. fig. 3, and other figures), from which the
duct proceeds, is a somewhat globular or ovoid chamber, with its long diameter
for the most part directed transversely ; or it may be compared to the bowl of a
short and wide wine-glass, the stem being formed by the peculiar channel of
communication with the long posterior chamber. It is liable to much variation
in shape, from the contractility of its inner wall, independently of the action of
the massive exterior muscular investment. Extreme contraction of the region
transforms the globular cavity into amere transverse slit. Its inner surface is
provided with a series of glands, the larger and more distinct having minutely
eranular contents (Plate IX. fig. 3, +), and easily distinguished from those of the
anterior chamber or long posterior gland. Towards the opening of the ejaculatory
duct the glands are smaller than in the swollen part of the reservoir, and they
again decrease in size before the organ narrows to its posterior channel of com-
munication. In this comparatively large chamber the dancing granules, hereafter
to be described, have free scope for the display of their movements, and not only
do they move themselves, but they cause such large bodies as the compound gland-
cells from the posterior chamber, when they happen to be present, to revolve and
jerk also, a state of matters that has probably helped to mislead M. pg QuaTRE-
FAGES as to the ciliation of the organ. Such, however, is very distinct from
ciliary motion. The reservoir diminishes posteriorly, so as to form in the con-
tracted state of the parts a very narrow duct (?), which by-and-by expands, and
becomes continuous with the long glandular posterior chamber, the whole form-
ing an hour-glass contraction, as represented in the various figures.
Before, however, proceeding with the description of the posterior chamber, it
may be as well to complete the narration of the structure of the two translucent
regions in which the foregoing duct and cavity lie.
In addition to the ejaculatory duct of the reservoir, the anterior division
possesses also the central stylet and its peculiar arrangements, with the external
circlet of granular glands. The former projects straight forward in the usual
state of the parts, and is generally about the same size as the largest stylet in the
lateral pouches, with which it likewise agrees in structure and composition
(Plate IX. fig. 3, &c.). Its point under examination seems generally: to project
into the pit of the anterior chamber, though the thick muscular floor occasion-
ally closes round it. The base of the stylet is fixed to the granular sac (A) ;
the arrangement being not inaptly likened by Dr JoHNnsTon to an awl, the anterior
or smaller end of the sac sending its investing substance over the head of the
stylet, and grasping part of the spike. The basal sac (or awl-handle) is narrowed
anteriorly, gradually widens backwards, is then marked by a constriction, and
328 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
again is terminated by a wider portion, which may represent the butt of the awl. —
This structure is shorter in proportion to the stylet, and has its constriction
placed further backwards than in Tetrastemma alge. The entire sac is opaque
white, and coarsely granular from an early age, the granules disappearing with
effervescence under the action of weak acetic acid, and rendered paler (in some
cases dissolved) by liquor potassee. These granules would not seem to be simply
inclosed in the structure, as if in an ordinary sac, but they adhere together and
form a consistent whole, as proved, amongst other things, by their not falling out
of the fragment when the anterior part is cast off with the stylet, as will be here- _
after described. I have also seen the stylet and its granular basal sac thrown
off together in a discarded proboscis in the proboscidian chamber of O. melano-
cephala and other species. This peculiar body or sac is set in a firm wedge of
translucent yet compact muscular substance (marked 6 in the various figures)
which often has its posterior border curved in a saddle-shaped manner, projecting
backwards in the middle, and with a curve on each side directed forwards. The —
anterior part of this wedge proceeds about as far forwards as the shoulder of the
first swelling of the awl-handle, and there becomes lost on the coat of the latter.
Though this generally appears like a wedge of translucent and structureless car-
tilage, the addition of liquor potassee and acetic acid shows distinct strize, chiefly —
of atransverse character when viewed under pressure, and therefore of a radiating —
nature with regard to the central granular sac. In front of the wedge-shaped
division hes the muscular cavity (e, Plate IX. fig. 3), into which the ejaculatory —
duct opens (at py’). This cavity is formed by the knuckling outwards of the floor
of the anterior chamber all round, and it is furnished with a distinct inner mus-
cular coat. The walls are thus very mobile, and I have seen them form an hour-
glass contraction in the middle, quite distinct from the narrowing between the
sac (whose greatest diameter is in front) and the firm wedge behind. Its anterior
border can be projected to the tip of the central stylet; while in the extruded
state of the parts (e, Plate VI. fig. 2) it forms, when seen from above, a com-
pressed process at each side of the basal sac of the central stylet ; more correctly,
however, and if viewed from the front, it has the shape of a muscular umbrella,
which slopes all round the anterior portion of the basal sac. M. CLAPAREDE does
not mention this arrangement at all, and M. p—E QuaTREFAGES seems to have |
mistaken it for a pair of glands, which, he explains, probably secrete poison for
cankering the wounds inflicted by the stylet, a supposition unsupported by any |
anatomical basis as regards this spot. Prof. KerersTEIn’s anatomy of the region
also requires correction, since he does not distinguish the separation between this
cavity and the floor of the anterior chamber; thus in his representation* of the
extruded proboscis, the central stylet projects smoothly into the water, and the
ejaculatory duct opens directly into the latter at a short distance from the stylet. —
* Op. cit. tab. v. fig. 3.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 329
A very interesting condition was found in two specimens of Tetrastemma vari-
color, which directly bears on the physiology of this region. In each a fragment
of the granular sac, with the central stylet attached, lay towards the anterior end
of the first region of the proboscis ; and since injury would scarcely have caused
a result so systematic, it is evident the stylet had been thrown off by the animal.
In both instances the central stylet-apparatus was complete, only in one the
anterior part of the basal sac appeared paler, and there was a slight irregularity in
its outline, similar to that in fig. 14, Plate V. In each, the lateral stylet-sacs had
their full complement of stylets, one or two of which equalled the central stylet in
size. There appears to be only one explanation of this state of matters, viz., the
fact that the central stylet can be thrown off, and somewhat rapidly regenerated;
for it is unlikely that in each case it found its way there from without, and it is still
less likely to have been driven in by an enemy. Former experience in regard to the
stylets from the lateral sacs shows that such bodies take some time to gain the
exterior of the worm, and hence our surprise is Jessened at the perfection of the
new structures while the old have not yet escaped from the proboscis. Besides,
the structure of the parts in O. pulchra will by-and-by throw still farther light
on this subject.
Lastly, across this region passes the belt of granular glands (7, various
figures), which have the form of lobules, with their long axes parallel to that of
the proboscis, and are situated beneath the two external layers of the part. The
granules are proportionally larger in Tetrastemma. I have not found any struc-
tural guide to their function, though they are invariably present in the Omma-
topleans. A curious appearance was noticed in a small specimen of Tetrastemma
varicolor, which had its stylet-region in front of the granular glands covered by
an external coating of large cells, with a nucleus and faintly granular contents;
such, however, may have been due to an abnormality.
The structure of the next division—that of the great Reservoir—has now to
be examined (0, Plate IX. fig. 3). On reaching the point previously mentioned
(a, Plate IX. fig. 11), the elastic coat and the external longitudinal muscular
fibres of the proboscis for the most part cease. Before this occurs, however, the
muscular fibres (+) peculiar to the*region arise, sweep backwards in a beautiful
fan-like manner over the reservoir, loop round and meet those from the opposite
side, and leave only a small space in the centre posteriorly, through which the
channel of communication with the third region passes. When viewed as a trans-
parent object under pressure, or in longitudinal section, the direction of these
fibres is backwards and inwards. This great muscular mass does not receive
accessions from the outer wall, but the whole of the loops come from the front.
_ By the varied crossings of these fibres, a felted aspect is produced under examina-
tion in some species, such as O. purpurea and O. alba (Plate IX. fig. 11), and is
doubtless present in all. In addition, there are circular and longitudinal fibres
VoL. XXV. PART II. 4p
330 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
within the former, and to whose presence the independent wrinkles of the inner
structures are due. The longitudinal layer (70) is innermost, and forms a kind
of spindle-shaped arrangement; the anterior fibres—commencing with the ejacu-
latory duct (of which they form the special wall)—soon spread out to cover the
dilated cavity of the reservoir, then become narrowed as they surround the channel
of conmunication, and proceeding backwards, merge into the longitudinal coat
of the posterior chamber. In some positions, these fibres assume a crossed or
spiral aspect in the channel of communication; but, as in the case of the gan-—
glionic region of the proboscis, this is purely accidental. The margins of the reser-
voir and the channel of communication are marked under pressure by the ends of
muscular fasciculi, especially posteriorly; an appearance due to the doubling of the
looped fibres, but also partly to the presence of the thin circular coat, which lies
without the longitudinal. By the contraction of these various fibres, the chamber of
the reservoir is squeezed with great force in every direction, like a thick caoutchoue —
ball or globular syringe in the hand. Its transverse diameter is lessened, and
still more, its antero-posterior, while ajet of the minutely granular fluid is squirted
into the anterior chamber; and, in spasmodic efforts, even a prolapsus of its glan-
dular lining occurs. In contraction, the entire region is much shortened, and
the mass of the looping muscle increased posteriorly. Not only does the peculiar
looping of the fibres cause most powerful squeezing of the cavity, but the posterior
aperture has a tendency to be closed, and slightly carried forwards, the anterior
being less subject to interference. The closing of the posterior aperture (channel —
of communication) is also greatly assisted by the circular fibres which are situated —
outside the longitudinal. The varying conditions of the reservoir may be under-
stood by comparing Plate IX. fig. 3 with Plate XII. fig. 9, the former show-—
ing the organ in its ordinary state, the latter in a somewhat contracted con-—
dition. ’
The peculiar looping of the fibres of the reservoir causes a transverse section
through its posterior part (Plate IX. fig. 10) to assume a finely radiated spiral
arrangement, the whole reminding one strongly of Dr Prerricrew’s beautiful
diagrams of the arrangement of the muscular fibres of the heart ; and in this case ~
- no better structure could have been devised for the complete and forcible evacua-
tion of the chamber. Professor KrrerstTErn describes only oblique and longitu-
dinal muscular fibres in this region.
Posterior Region.—Behind the translucent region just described, the opaque
white long posterior chamber (C) (éntestin, QuaTREF., Drusentheils of the Germans)
occurs. It communicates with the reservoir in front, as previously mentioned,
but its posterior end is cecal. The contractile nature of the parts renders com-
parison uncertain, but it is generally not much shorter than the anterior chamber
in the perfect animal. Sometimes, indeed, it exceeds the latter chamber in
length, the simpler structure of its walls giving greater extensibility. In young
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 331
specimens and in regenerating organs, again, it assumes a nearly globular form in
contraction. Externally, it is covered by a very delicate investing layer. Within
this lies a series of powerful circular muscular fibres, which towards the taper-.,
ing posterior end become indistinct, and finally disappear altogether, after the
czecal tip is reached (Plate VII. fig. 4). The next coat is formed of an equally
strong series of longitudinal fibres, the anterior or primary ones being continuous
with the longitudinal layer of the reservoir, as previously mentioned. These run
throughout the entire length of the posterior chamber, becoming proportionally
more developed as the central cavity diminishes towards the cecal end, and
finally merging into the muscular ribands which terminate the organ. The
mucous layer with its glands lies within the latter, though in several views, both
in the living animal and in transverse sections, I fancied some sub-mucous circular
fibres were present ; they are at any rate insignificant, and the two chief layers
explain all the motions which ensue in this division. This mucous layer in con-
traction of the organ forms many rounded folds, which are especially distinct in
O. gracilis (Plate IX. fig. 16). A transverse section of the chamber is repre-
sented in Plate IX. fig. 14, and the great increase of the glandular mucous layer
in contraction is conspicuous. The two muscular coats are about equal in thick-
ness. From the commencement of the region behind the translucent reservoir
almost, but not quite, to its czecal tip, its entire inner surface is covered with a
series of glandular papillee, which differ materially in structure from those of the
previous regions. Viewed as a transparent object under moderate pressure
(Plate V. fig. 9), the field is found to be covered with globular glands containing
clear rounded vesicles in their interior. In contraction, and when the wall is less
compressed, the glands have an enlarged and coarse appearance, only the
external wall of each being visible. When the pressure has been increased, these
glands, especially towards the posterior end (where, from their lessened numbers,
‘a clearer view can be obtained), alter their shape apparently by bursting (fig. 10,
same plate), and seem like a double ring of a minutely hirsute aspect, while the
contained globules are scattered over the membrane. If the organ has been rup-
tured and partly inverted, the free edge of the laceration and the shrivelled
glands have the appearance shown in fig. 8, same plate. ‘The globules from the
glandular papille (fig. 3) and glands whose contents have been evacuated (and
which are minutely hirsute) readily pass forwards to the reservoir, and roll through
the ejaculatory duct under pressure. The function of the vast array of glands in
this chamber would seem to be the formation and elaboration of the remarkable |
fluid with the dancing granules previously alluded to. This secretion is produced
in considerable quantities, and towards the posterior portion frequently distends
the organ into a translucent pouch (Plate VII. fig. 4, @), wherein the moving
granules are in full action, and even the experienced are apt to err in regard to
the nature of the movements, so like are they to those caused by ciliary currents.
332 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
Under a high power (700-1000 diam.), the moving bodies appear as mere specks
or points, and they retain this remarkable motion for upwards of twenty-four
hours after extrusion from the cavity into the surrounding salt water. There is
thus a peculiar fluid rich in these granules secreted by the posterior chamber or
gland; and continued observation, and the whole anatomy of the parts, show that
this fluid passes forwards into the reservoir, where it is probably mixed with a
small quantity of another secretion from the glandular walls-.of the latter, and
then propelled with force through the ejaculatory duct into the anterior chamber.
What its peculiar function in the anterior chamber, or when discharged into the
surrounding medium in the extruded state of the parts, may be, can only be con-
jectured at present; but from the elaborate structure of the parts concerned in
its economy its action would seem to be important. I have no observations in
support of the view that this granular fluid is poisonous. It cannot pass into a
wound at any rate until the stylet is withdrawn; and if it really acts as a poison
to animals when introduced into their tissues, it might reasonably be supposed
to affect them injuriously when discharged into the water around them. Whether
the fluid has any influence on the secretion of the stylets in the lateral sacs, or in —
the central apparatus, Iam unable to say; but, as already mentioned, a minutely
granular fluid has been seen in the former, and a large though imperfect stylet
in the posterior chamber of 0. pulchra. MM. ve QuATREFAGES, VAN BENEDEN, and
others, state that the proboscis and the foregoing apparatus are used in attacking
prey ; but, we may ask, Do the Borlasians use their feeble and unarmed structure
for the same purpose? So far as I have seen, the proboscis is a somewhat pre-
carious aggressive weapon, since it frequently adheres to the attacking body, and
is thrown off. It is true we may assign, with an air of probability, an aggressive
function to the central stylet; but we cannot do so with the very same organs
in the lateral sacs; for, being developed in a free condition within almost closed —
cavities, they are quite useless as offensive weapons.
In extrusion of the proboscis (Plate VI. fig. 2), the entire spike of the stylet |
projects, the floor of the anterior chamber forms all round a thick and powerful
umbrella-shaped cushion (whose independent structure has escaped Prof. KEFER-
STEIN), the lateral stylet-sacs are under cover, and the region of the reservoir is —
shortened and widened. The position of the muscular chamber (e), which forms —
a second small umbrella round the apex of the basal sac of the central stylet, has
already been mentioned. The separation between the longitudinal fibres of the —
stylet-region proper (v) and the looping fibres (7) of the reservoir is well marked
in this condition. It will also be observed that the stylet-region is widened 7
by the forcible wedging forwards of the reservoir. '
The walls of the posterior chamber, after forming the cul-de-sac, are continued —
backwards in the form of one or two long translucent muscular ribands of extreme
flexibility and contractility (), fig. 4, Plate VIII.), and which are attached to the
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 339
walls of the proboscidian sheath, rather behind the middle of the animal, the
fibres spreading out in a fan-shaped manner, and mingling with those of the tube.
The motions of these muscular bands is most interesting, now jerking into nume-
rous graceful folds or coils, by a sudden contraction, like the stalk of a Vorticella,
now shortening more gradually—the curves being thickened here and there by
the bulging of the fibrille. They are simply muscular fasciculi, with very fine
longitudinal lines—the marks of the fibrillee, and seem to restrain the irregular
protrusion of the proboscis and assist in its retraction. This muscular arrange-
ment is also the wltimum moriens, showing contractions when all other signs of
life have fled. In a young Tetrastemma variegatum, in which the riband had
been ruptured from its attachment, the fibres (Plate VI. fig. 6, 1) had assumed
a clavate aspect from contraction, and only very faint longitudinal markings were
visible.
Before reviewing the statements of previous investigators with regard to the
general structure of the foregoing parts, a description of the peculiarities of the
regions in other species of Ommatoplea will be narrated.
In Ommatoplea melanocephala (Jounst.), the proboscis is somewhat larger in
proportion than in 0. alba ; and, while the type of structure is adhered to, there
are several important differences in detail. The stylet-region (Plate VI. fig. 7) is
peculiar in having the lateral stylet-sacs carried considerably forwards, so that
they lie quite in front of the central apparatus, and the floor of the anterior
region has consequently to form a deep pit to reach the spike of the stylet. In
this figure the organ is shown comparatively free from pressure, and the encroach-
ments of the lateral sacs on the cavity may thus be correctly estimated. The
basal sac of the central stylet is proportionally large, while its wedge-shaped
setting is comparatively meagre. The powerful series of oblique or radiating
fibres which pass outwards and forwards from the latter, in the usual position of
the organ under pressure, are very distinctly shown, and, as it appears, sling the
apparatus. The points of the stylets (central and lateral) are rather blunt, and
their shape, on the whole, resembles that found in Tetrastemma alge. Some of
the looped muscular fibres of the reservoir seemed to pass inwards beyond the
exterior ring in front, so that a continuous series of fibres would thus be formed,
as in certain viscera* (bladder, &c.) of the higher animals, and the chamber
environed with the exception of the anterior and posterior openings. The circlet
of granular glands is much developed in this species, and often renders the subjacent
parts obscure.
The remarks and figures of M. DE QuaTREFAGES fF relating to this species (his
- Polia coronata) require amendment. He mentions that it is the only exception
* Vide the admirable Researches of Dr Pettigrew, Philos. Trans. part ii. 1867.
+ Recherches Anat. &c, p. 166.
VOL. XXV. PART II. 4Q
334 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
he has met with to the uniform arrangement of the stylet-apparatus, as, in
addition to the forward position of the lateral stylet-sacs, the central stylet and
its surroundings are placed in his second cesophageal cavity—that is, in our
reservoir; and his figure* bears out his description, representing, moreover, the
organ as placed at the commencement of the posterior channel. ‘The species is
easily identified by the position of the lateral stylet-sacs and other peculiarities,
and there is certainly no such abnormality of the central apparatus or alteration
of type as noted and figured by this naturalist.
In a very pretty new species—dredged in Lochmaddy—of a salmon hue,
striped down the back with two brown and a white central streak, having also a
transverse brown bar at the posterior part of the head, and only two eyes,+ the
stylets were similar in shape to those of 0. melanocephala, but decidedly smaller.
This shows that while distinctions in size and shape are valuable specifically,
they should not be too much relied on.
The anterior chamber in O. gracilis (Plate VII. fig. 1) is very short in pro-
portion to the great elongation of the animal, the stylet-region being found only
a short distance behind the ganglia; indeed, in this respect, it is not far removed
from Polia involuta, VAN BENEDEN. ‘The floor of the anterior chamber has
generally a bilobed aspect under examination, and hence differs considerably from
that of 0. alba. On each side of the floor in front of the stylet-sacs the end of the —
proboscis has not the massive muscular structure usually found in this position,
but internally has a somewhat opaque mobile lobulated glandular arrangement,
which, when the organ is everted, projects as two semi-opaque whitish papille
(one on each side), the stylet-sacs being sometimes prolapsed into their interior.
The central stylet and its apparatus do not easily project in this condition. The —
stylet-region proper, consisting of that part from the floor of the anterior chamber
to the border of the reservoir, is somewhat opaque, on account of the glandular
nature of the walls anteriorly, and the layer of granular glands posteriorly. The
latter are placed far back, and in developing specimens form an opaque granular
mass on each side of the ejaculatory duct, sometimes entirely filling up the angle
(at a, same fig.), and consist of a dense grouping of minute clear granules, and
occasionally coarser particles in lobulated glands, which are apparently homo-
logous with the granular glands of other species. The lateral stylet-sacs have
very long ducts, and each encloses from seven to ten stylets of a characteristic
shape, besides other contents. The central stylet is appended to a basal sac of
great length, the sac indeed resembling the outline of some long bone, such as
the radius, the stylet being articulated to the head, while the distal extremity of
the bone is represented by the swollen posterior end of the sac. The latter has’
* Op. cit. pl. xi. fig. 8.
+ The Nareda superba of Srimpson has likewise two eyes, but has no longitudinal stripes.—
Synopsis Mar. Invert. of G. Manan, N. Brunswick, p. 28, fig. 17, 1853.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 335
the usual granular contents, but the exterior firm setting, so characteristically
wedge-shaped in other species, does not proceed half-way forwards, the slender
anterior portion having only a thin covering for its support, as indicated in the
figure. While in ordinary views the stylet and sac seem straight, both have a
decided curve when seen laterally (Plate VI. fig. 12). Just in front of the point
where the clear setting of the sac becomes indistinct, the ejaculatory duct opens into
the peculiarly elongated muscular cavity (e), which extends forwards to the cir-
cular opening in the floor of the anterior chamber. This channel shows a distinct
inner layer of longitudinal fibres, which, however, seem to act only in company
with the external oblique fibres surrounding them. The presence of this special
inner coat demonstrates that it is not the mere doubling of the floor of the
anterior chamber that forms this cavity, as indeed certain appearances, previously
observed, had led me to suspect. The central and lateral stylets have the same
shape, and the majority agree in size. In its usual position the stylet has the
form of a spear-head (Plate VI. fig. 13), being sharp-pointed, then dilating gra-
dually till near the posterior end, where a slight diminution occurs, and then a
marked constriction, just in front of the somewhat small head. If minutely
examined, both central and lateral stylets, show a small secondary swelling or
ring above the head (Plate VII. fig. 9). The ejaculatory duct is comparatively
large and boldly marked, comprising at its posterior end almost the entire region
of the reservoir, a slight demarcation, however, marking off the dilated pos-
terior end into a portion pertaining to the reservoir, and another to the duct.
The widened posterior end is covered with small glands, which are continued
along the tube to its opening into the long muscular chamber behind the floor.
One peculiarity in the elongated reservoir is the comparative thinness of the
looped fibres towards the anterior end, and the thickness of the longitudinal
layer, which seems to afford compensation for the diminished strength of the
exterior coat. This deviation from the usual structure is doubtless in connection
with the enlarged posterior end of the ejaculatory duct, and the gradual con-
tinuation of the cavity of the reservoir into it. The bulk of the looped fibres is
grouped posteriorly, and in action would seem to compress the reservoir, so as to
_ throw its contents forward to the gaping aperture of the duct. On this account
also the posterior channel of communication is long. The external layer, con-
tinued from the preceding division, passes about half-way backwards over the
reservoir. Another peculiarity is the presence of numerous clear cells and
granules amongst the looped fibres, most distinctly seen at the posterior part of
the chamber. Some of the cells contain nuclei, and others do not. The glandu-
lar papillee in the interior of the reservoir are large and prominent. The very
great length of the posterior chamber as compared with the anterior is re-
markable.
M. DE QUATREFAGES seems to have devoted considerable attention to the ana-
336 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
tomy of the foregoing species (his Nemertes balmea), and his deviations from
accuracy, therefore, surprise us. He represents* the stylet-region as having the
lateral sacs placed rather behind the long central granular sac, each of the former
having a carunculated gland attached to its posterior end, while the latter has
two longer structures of the same description. None of these carunculated
appendages have been seen by me, since it can scarcely be supposed he refers to
the opaque granular condition of the angle (at a, fig. 1, Plate VII.), previously
described. His description of the contents of the lateral stylet-sacs is erroneous ;
for though the position of the stylets is of no moment, the assertion} (and cor-
responding figure) that each has a developing sac attached to its extremity is
very wide of the correct account. The outline of the stylets given by this author —
is inaccurate, since no constriction is represented in front of the head, and no
mention is made of their curvature. The other objections to his views are noticed
elsewhere.
The proboscis in the long purple species, O. purpurea, while approaching that of
O. gracilis in slenderness and in tenuity of the posterior region, is yet more closely
allied to O. alba in the structure of its comparatively short stylet-region proper.
The floor of the anterior chamber in this species is furnished with very minute
glands. Notwithstanding the great length of the worm, there is no corresponding
elongation of the stylets, and the granular basal sac of the central apparatus is
likewise short (A, fig. 2, Plate VII.) The lateral stylet-sacs are small, and somewhat
rounded, and their ducts are sometimes spindle-shaped, from marked constrictions
situated respectively at the sac and opening into the floor of the anterior cham-
ber. The stylets are at once distinguished by their short, stout form and peculiar
longitudinal markings, which resemble the longitudinal streaks in polished
mahogany (Plate V. fig. 12), and are due to irregularities in the outline. The —
granular sac of the central stylet (Plate V. fig. 13, A) has only a slight constric-
tion in the middle, so that the lateral line, from the apex of the spike to the base
of the sac, is nearly straight. The opening of the ejaculatory duct into the cavity
behind the floor of the anterior chamber is wide. The reservoir is much elon-
gated, and it may be observed that its fibres, as pressed between glasses, are not
seen in a looping series down the sides of the cavity, but form a densely felted —
arrangement on each side. When freed from pressure these fibres are observed to —
cover the reservoir with most elaborate crossings, from the diverse directions which
they pursue. In the same region the longitudinal fibres are much developed
anteriorly, though they are only well seen on stretching the parts, otherwise the |
felted arrangement of the looping fibres obscures them. The glands of the reservoir
are smaller and less distinct than in 0. gracilis, especially anteriorly. The channel
* Op. cit. pl. x. fig. 3.
+ “Quelquefois, surtout chez le Némerte balmée, on apergoit méme un commencement de la tige
du stylet.”—Op. cit. p. 166.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 337
of communication with the posterior chamber is somewhat short and wide, and in
marked contrast with the same part in the latter form. The long posterior
chamber has its inner surface thrown into more prominent ruge than in most
species, so that they sometimes appear like large papillze covered with the glands-
proper of the cavity. These plaits are not mere wrinkles and folds caused by the
contraction of the elongated organ, but are present under severe pressure ;
indeed, they are characteristic and original processes of the chamber (Plate IX.
fig. 16). The granules of the peculiar fluid therein are also very distinct. It
may be mentioned here, that after prolonged confinement the integrity of the
proboscis in this and other species is affected, the stylets degenerating, and even
disappearing altogether, both from the central and lateral structures. Not only is
this the case in the adults themselves, but under the same circumstances the
more advanced young in the interior of Prosorhochmus Claparéedi undergo a like
degeneration. In a specimen of the former species where this had occurred, the
wave of granular fluid driven forward by the contraction of the reservoir distended
the muscular cavity in front of the granular basal sac of the central apparatus
(which in this instance was devoid of a stylet), and as the aperture into the
anterior chamber permitted only a limited discharge at a time, the fluid rushed
into the centre of the granular sac, and distended it and its wedge-shaped setting
with every impulse. The absence of proper nutriment and free aeration—for the
salt water was but rarely changed during the year—are sufficient causes for the
above-mentioned degeneration.
In O. pulchra (Jounst.) the anterior region of the proboscis has a decidedly
pinkish hue, and numerous small clear globules at its commencement, as well as
over the reservoir. The large glandular papillae in the anterior chamber have
their marginal globules less distinctly marked than in O. alba or Tetrastemma, and
hence the structure has a smoother or finer appearance. The lateral stylet-sacs
(Plate VII. fig. 3, vy) are very large, and each contains, in well-developed specimens,
from five to nine stylets, a large circular globule, and a granular orange pigment-
_ mass, besides a fluid rich in moving granules, similar to the secretion from the
long posterior chamber. It is, however, in the apparatus of the central stylet
that the greatest deviation from the typical structure occurs. The basal sac of
the stylet (Plate VI. fig. 11, A) is small, elliptical rather than ovoid, and its
granules are very minute. In addition to the ordinary stylet (a) fixed to its
anterior end, another stylet (>) projects into its posterior portion, enclosed in a
_ kind of sheath, and whose point extends forwards almost to the butt of the an-
terior stylet. This reserve-stylet is not in all cases fully formed, but apparently
awaits the rejection of its progenitor for complete development. The head of the
reserve-stylet projects into a large cavity formed by a peculiar disposition of the
fibres composing the setting of the basal sac and the region behind. Instead of
the usual wedge-shaped structure, radiating fibres pass outwards from the sides
VOL. XXV. PART II. 4R
338 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
of the sac, curve backwards, and arch over a large cavity (Plate VII. fig. 3, oy)
filled with a clear fluid, part of the floor being formed by the anterior fibres of the
reservoir. In certain states of contraction the central (reserve) stylet may be
seen pressed backwards, so that its butt rests on the latter—a position quite
easily attained on account of the yielding nature of the cavity and tissues which
lie immediately behind and around it. Some granular streaks, probably due to
the granular glands, are also observed passing from the central sac along the
arch of the fibres. The granular glands themselves are distinct enough if the
specimen is not too much pressed. The peculiar cavity behind the central granu-
lar sac might be supposed to assist in the rapid formation of the reserve-stylet,
yet it cannot be absolutely necessary for its development, since the stylet is as
readily replaced in front of the sac in 0. alba, and others, where no such space —
exists. Physiologically the cavity may also act as an elastic buffer or cushion ©
when the stylet is driven into any structure, if such ever occurs. The ejaculatory
duct is large, and being surrounded by a yielding region, is more mobile than in
the typical forms. The clear globules interspersed amongst the looped fibres of
the reservoir are numerous, so that under pressure the cavity seems covered with
them; and if pressure is severe, they escape into the reservoir, and pass for-
wards into the ejaculatory duct. Posteriorly these looped fibres have a laminated
appearance. During examination the walls of the reservoir were frequently con-
tracted in the manner shown in the drawing (Plate VII. fig. 3), thus indicating
very clearly the presence of circular fibres. The entire region had more trans-
lucent walls and greater mobility than in O. a/ba, and the coats were somewhat
diminished in total bulk posteriorly, so that the channel of communication was
short. The glands are large transparent structures, with clear globules in their
interior, and in general aspect differ from any hitherto observed. Those of the
posterior chamber of the organ were longer than in 0. alba and Tetrastemma.
In one specimen several stylets lay in the cul-de-sac of the latter chamber, show-
ing that they had passed along the ejaculatory duct, or else had been formed in
the cavity.
The muscular and other structures of the anterior region of the proboscis of
O. pulchra present, in transverse section, a slight variation from the common
type, as seen in O. alba. The beaded layer (Plate VIL. fig. 10, e) is very distinctly
marked, and the external angle of the somewhat lozenge-shaped enlargements
(longitudinal bands) is connected with the outer layer (g), while a process from
the opposite angle passes inwards towards the circular coat (c), so as to cut the
great longitudinal layer (d) into a number of separate fascicles, which, in the
specimen represented, amount to fourteen. The changes which ensue in the various
layers, when the organ is completely everted, are portrayed in the figure; and
the characteristic appearance of the beaded layer (¢) is to be noted, as well as th
swollen segments of the usually thin external longitudinal Jayer (/).
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 339
Dr Jounstron* observes of this species, that “the structure of the stomach ”
(proboscis) “is like that of its congeners, excepting in there being five or six
spines on each side of it, instead of three, which is the usual number.” He does
not refer at all to the remarkable arrangement of the central stylets, though an
incomplete woodcut in one of his early papers} shows that it had not entirely
escaped the notice of his accomplished artist.
The general arrangement of the proboscis in Tetrastemma algw agrees with
that in O. alba, though there are some minor differences in the details of the
stylet-region. If under examination the ejaculatory duct is placed on the left of
the central stylet-apparatus, an explanation is obtained of the mistake into which
M. Cuaparépet had fallen in his description of the region in Tetrastemma vari-
color, Girst. (the figure, however, appears to me to be very like that of 7. alge).
The central stylet and its sac have been slightly pressed backwards so that the
radiating fibres which sling them have been brought out distinctly, and some-
times a faint line of demarcation is seen on the right side (in such a position)
simulating the presence of a separation; but numerous fibres are prolonged past
this, and, moreover, a slight contraction or change of position obliterates this
line, while the curved or radiating fibres are rendered more distinct. On the left
side the only boundary line to the supposed distinct coat around the wedge-
shaped setting is the wall of the ejaculatory duct.. The basal sac of the central
stylet in 7. alge (to continue the description) has rather more shape than in
0. melanocephala, and is proportionally more elongated. I thought I could detect
a slight difference between this species and 7’. variegatum, for the stylet in 7.
alge is generally shorter in proportion to the length of the sac than in 7. varie-
gatum. Considerable variations exist in the size of the several stylets in 7.
alge, independently of the size of the animal, a fact, perhaps, the less to be
wondered at when the reproduction of the tube is remembered; but the greater
size is generally diagnostic when compared with other species. In a developing
or recently repaired central apparatus (Plate V. fig. 14) the basal sac is thinned
off anteriorly from contraction of the parietes, and the difference in size between
this central stylet and one from the lateral stylet-sac (Plate V. fig. 15) of the same
animal is marked. In Tetrastemma variegatum the structure of the stylet-region,
while agreeing generally with O. alba, is yet more particularly allied to 7. alge.
The stylets are on the whole more slender than in the latter, and the central longer
in proportion to its basal sac. In 7. vermiculus the structure is similar to the
two former (Plate IX. fig. 12). The shape of the basal sac of the central apparatus
in 7. varicolor is characteristic (Plate VI. fig. 5), the stylet being more slender
than in the other two species, larger in proportion to the sac, and the lateral lines
_ of the latter nearly straight. The proportionally large size of the glands in the
| * Catalogue of Worms, &c. p. 292. t+ Mag. Zool. and Bot. vol. i. p. 531, fig. 4.
{ Recherches Anat, sur les Annel, Turb., &. p. 81, plate v. fig. 6.
340 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
reservoir in Tetrastemma is well illustrated in this species, where they form
very prominent structures with granular contents, and more nearly allied to
those in the posterior chamber than in O. alba. In transverse section the micro-
scopic structure of the organ in the foregoing species agrees with that in Omma-
toplea.
In Polia involuta, VAN BENEDEN, the proboscis and its apparatus are reduced
toaminimum. ‘The anterior region (Plate VII. fig. 5, a) is very short, and has
in general a somewhat conical outline, the base of the cone being formed by the —
floor of the chamber. Its walls are proportionally thick and muscular, and
internally have a minutely granular aspect, a condition probably due to indica-
tions of papillee. Posteriorly it terminates in the usual floor, into which, how-
ever, only one aperture leads, viz., that of the central stylet. The next, or stylet- _
region proper, while still retaining the Ommatoplean type, differs much from that
of any other British species. Instead of the usual well-defined arrangement of longi-
tudinal and radiating fibres, the entire muscular structure is obscured by numerous
granular or cellulo-granular bodies (ry), which give a characteristic appearance to
the somewhat conical reyion. There is no trace of lateral stylet-sacs. The central
stylet is minute, and furnished with an elongated and faintly granular basal sac,
which is fixed in the usual transparent muscular setting, the mobile muscular
chamber into which the ejaculatory duct opens being situated immediately in front. —
Though the whole apparatus is very minute, I have seen the stylet thrust forwards
by the contraction of the fibres of its basal setting, so that its point projected
into the floor of the anterior chamber of the proboscis. The ejaculatory duct is
large, and, owing to its central position in ordinary examinations, causes the
stylet-region proper to appear bifid posteriorly ; but this is due only to the greater
translucency of the duct, which, for the time being, renders the denser granular
masses at the sides more conspicuous. The region of the reservoir is fairly
developed, the walls being striated with transparent muscular fibres in the usual
manner, and the granular glands lining the inner surface. The walls might be
seen now and then contracting with force, and driving the contents forwards
into the ejaculatory duct and muscular chamber behind the floor of the first
region. The posterior channel of the reservoir led into a posterior chamber of —
comparatively small dimensions, but having thicker walls than usually found in —
this region, and terminating in a cul-de-sac and rounded end, a short distance —
behind the cesophageal apparatus. This chamber had a cellulo-granular lining —
internally, and in some specimens the posterior end was observed under pressure
to be distended with a transparent fluid containing a few compound cells of
similar aspect to those found in other species. This posterior region is kept in
position by fibres from the strong bands at the posterior part of the cesophageal
apparatus.
All that M. Van BENEDEN says with regard to the structure of this organ is
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 341
that it is very short, and bears an ‘‘isolated” stylet, while his enlarged drawing*
is incomplete.
M. bE QuaTREFAGES considered the posterior chamber of the Ommatoplean
proboscis the intestine-proper, but there is no support for this view; and, indeed,
his minute anatomy of the organ is somewhat inaccurate. I have not observed
that the dilatations and contractions of the channels of the reservoir (his ceso-
phagus) vary in the manner he refers to in different species. He describes two
bulgings of this “oesophagus,” a large lozenge-shaped one at its commencement,
and another corresponding to our reservoir, these dilatations being connected by
a straight channel. The former may refer to the mobile muscular chamber
behind the stylet-aperture in the floor of the anterior region, but his descriptions
and drawings are indistinct. He aptly likens the two central divisions (stylet-
region) to crystal; but he says he required the action of hydrochloric and acetic
acids to distinguish fibres, which, he observes, have a transverse direction, and
he especially notes that he could not see any longitudinal fibres. I have always .
been able to see these fibres in the fresh and living animals without any addition
to the sea-water in which they happened to float; and, moreover, the presence
of longitudinal, looped, and other fibres previously described show how much
more complex the structure is than this author imagined. He correctly reports
the absence of vibratile cilia from this region; but he again errs by affirming that
they occur in the posterior chamber. His figures of the stylets are different from
any seen by me, since they exhibit a bulging and then a contraction in front of
the head. The basal sac is termed the “body” of the central stylet, and he narrates
how in Nemertes balmea (our O. gracilis) this body has an exterior coat com-
posed of the same structure as the point. Nothing more than the usual firm
muscular setting is really present (see p. 335). Again, the statement that the
“body” acquires greater solidity is not borne out in fact, for the granular con-
tents of the sac are homogeneous throughout. He speaks of a pouch containing
a granular glandular substance in which the stylet and its “ body” are placed in
this species, and thinks it probably secretes the latter (body); and, though he
has not seen it in Polia, he considers its existence likely. The author has
evidently fallen into confusion here, for the granular sac (or so-called “ body’’) is
fixed in a clear setting of the firm muscular substance. He next describes and
figures other two cavities, which are said to exist at the borders of the “ stylet-
pouch,” semi-opaque and glandular in J. balmea, very transparent in Polia; and
he considers that these two glandular organs secrete a poisonous fluid for use in
offence and defence, which fluid is poured into the pit in front of the stylet-region.
Entomostraca, moreover, were killed instantaneously by wounds of the stylet, an
effect which could not be due to mechanical injury only, but to the presence of an
* Mémoires I’Acad. Roy. &c. pl. iii. fig 6-
VOL. XXV. PART II. 4s
342 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
active poison. It is true he was not able to distinguish these glands or their
cavities in many species, so that if they existed they must have been confounded
with the neighbouring tissues by reason of their transparency. Such glands have
never occurred in any of the British species, and the opaque granular substance
really present in O. gracilis (NV. balmea, QuatTREF.) totally differs in structure and
function from his representations. The folding downwards of the floor of the
anterior chamber and the presence of the muscular space behind this have pro-
bably caused the error—an opinion shared by Prof. Krererstern; and, indeed, it
may be remarked, that the time and opportunities necessary for a correct appre-
ciation of these complex structures make those best acquainted with them least
surprised at such mistakes. The two muscular bands, also, which M. Dz
QUATREFAGES figures and describes as for the probable purpose of carrying forward
the stylet-apparatus, and compressing his hypothetical poison-glands, have not
been seen, and the explanation of the parts already given renders such useless.
With regard to the observation, that the lateral stylet-sacs are free in NV. balmea,
but placed in the thick walls of the oesophagus in Polza, I can only state that the
type of structure is the same in all, and that they occupy corresponding positions in
the species referred to. It is probable also that the finding of only a single lateral
stylet-sac in Polia quadrioculata and P. humilis was accidental, and not by any
means a characteristic of such species (Zetrastemma). I have also very little doubt
that the presence of the toothed cartilaginous plate, which he describes as occupy-
ing the usual place of the central stylet in Cerebratulus spectabilis, has been due
to some mistake or confusion in his notes. Indeed, the author himself does not
speak with certainty on the subject, since he states that he regrets he had mislaid
his drawing of the actual relations of this organ to the other parts. The remark, —
that in Polia vermiculus one sac was placed on the dorsal and the other on the
ventral surface, is of no consequence when the ever-changing condition of this very
mobile organ is remembered. This author further describes the “ intestin” (our
posterior chamber) as having the same coats entering into its composition as the
anterior region, though, he adds, the muscular layers are proportionally thinner.
As already stated, the structure of the walls of the two regions is essentially
different, just as their functions disagree. He is correct in averring that the
cavity ends in a cul-de-sac; but wrong in saying it is ciliated, and that the
terminal ribands are attached “a la paroi abdominale.’ His distinguished
countryman, M. Mitne Epwarps,* is also in error in regard to both of these
points. Lastly, M. pE QuATREFAGES is only certain of the muscularity of these
ribands in Polia coronata (O. melanocephala), and he gives a curious figure (which —
cannot be verified in the British examples) of their termination in this species— —
as a series of arborescent fibres.
* Legons sur la Physiol. et Anat. Comp. tome v. p. 464, 1859.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 348
Dr Jounston’s* description of the stylet-region is as follows :—“ First, we
perceive on each side a small circular spot or cavity, in each of which are three ©
spines with their sharp points directed outwards; beneath these there is a cup-
shaped organ encircled above with a faintly plaited membrane, and armed in the
centre with a strong spine, which can be compared to nothing more aptly than a
cobbler’s awl in miniature, the part representing the handle being very dark, and
the point transparent and crystalline. This apparatus is placed within the intes-
tine, is visible only when this is compressed, and is, as I believe, stomachial,
having some distant analogy with the proper digestive organs of Laplysia and
Bulla.” His anatomy is thus imperfect, and he, moreover, considered that the
“intestine,” as he termed the organ, proceeded to the tip of the body and termi-
nated in a distinct anus.
Dr Witttams} observes with regard to the proboscis (his alimentary organ),
“‘ The extremity of this organ is armed with several styleted jaws, which, from
their construction, seem only designed to fix the suctorial end by perforating the
alimentary object. When the proboscis is withdrawn into the interior of the
body, fitting admirably into a short cesophagus, these sharp instruments are
packed and folded upon themselves,” the sides of the tubes closing round them.
The correct examination of a single extruded organ would have at. once dispelled
such notions. His supposition—that the glands in the interior of this structure
furnished an important secretion for the digestive process, which secretion was
exuded into the ‘‘ cesophagus” (apparently, judging from his figure,t the pro-
boscidian sheath), and thence into the great alimentary organ—rests upon no
facts. He is also wrong in stating that the outlet of this organ is situated not
far from the cephalic end of the body; but his remark, that there is no open
communication between the cesophageal tube (proboscidian sheath) and the
‘alimentary czecum”’ is correct. |
Dr Max S. Scuurrze, in his account of Tetrastemma obscurum,§ gives no
definite description of the ending of the proboscis, and figures the central stylet
as projecting freely into the cavity. He indicates the presence of the muscular
space behind this, but confounds its structure with the wedge-shaped setting of
the basal sac, the whole forming, he says, a quadrangular mass. He falls into
the same error as M. DE QuaTREFAGES and others, in describing the terminal
ribands of the organ as attached to the wall of the body. His figure|| of the
exserted stylet-region is incomplete in detail, for he omitted to notice the ducts
of the lateral stylet-sacs, though he regarded the latter as the producers of the
* Mag. of Zool. and Bot, vol. i. p. 530, 1887, copied into “ Catalogue” Brit. Mus. pp. 285-6
1865.
t Report Brit. Assoc. 1851.
t Op. cit. pl. xi. fig. 64.
§ Beitrige zur Naturges der Turb. 1851, p. 62, tab. vi. figs. 2-10.
| Op. cit. tab, vi. fig. 3,
344 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
stylets for the central organ. He first indicated, however, the connection between
' the developing spikes and the clear globules in the lateral sacs, showing that they
are sometimes seen in their interior. Finally, he has not discriminated the
structure of the reservoir-region, and its relation to the neighbouring parts; and,
indeed, his anatomy of the animal, from the limited nature of his observations, is
somewhat imperfect.
M. CLAPAREDE,* in his remarks on Tetrastemma varicolor, describes the sac of
the central stylet as set in a pale space of a triangular form, and he leaves the
stylet-apparatus to hang therein, apparently by its anterior end. He has evi-
dently mistaken the translucent wedge-shaped setting of the sac for a cavity,
and the triangular muscular structure shown exterior to this has no existence as
figured (vide p. 339). He has correctly observed the presence of a duct to the
lateral sac, though his figure is somewhat distorted from pressure, and repre-
sents the duct by far too wide. He is, moreover, of the opinion that these
chambers are not for the sake of furnishing new stylets for the central organ, as
Dr ScHULTZE avers, but for the lodgment of those discarded from the latter; a
view quite as erroneous as the other. Each supplies its own stylets. He did not
observe any connection between the clear globule in the lateral sacs and the
developing spikes. His representation of the muscular fibres of the stylet-region
is faulty. In mentioning the cavity of our reservoir, he properly describes the
presence of a liquid containing minute granules in suspension (but not in motion),
and that it (reservoir) communicates with the “‘ trompe” by means of an efferent
canal: but he fell into the error of regarding the long posterior chamber as a
““muscle retracteur.”” His figure is inaccurate in other respects, such as in the
mode of opening of the ejaculatory duct, and in the absence of the muscular space
behind the stylet-aperture in the floor of the anterior chamber. He regards the
reservoir as a poison-gland, which squirts its contents along the ejaculatory duct
into the wounds inflicted by the stylet. This author is scarcely correct in saying —
that M. pre QuaTreraceEs had in reality figured this poison-gland without the
efferent canal in Polia mandilla; for the French naturalist figures and describes —
the part as one of the bulgings of his cesophagus, and which, therefore, commu-
nicated both with the ‘“trompe” and “intestin.”” In a still more recent publi-
cation} M. CLaparEDE exhibits the structure of this region in KEFERSTEIN’S
Prosorhochmus Clapareédit, a viviparous species, but he gives no details of muscular
structure. The central stylet and its sac are placed in the middle of a continuous
and apparently homogeneous oblong body, the wedge-shaped enclosure of the
basal sac and the muscular cavity in front being confounded. The opening of
the ejaculatory duct of his poison-gland (reservoir) has the same position as im
his previous figure, viz., at some distance from the stylet, and passing directly
* Recherches Anat. sur les Annélides, Turb. &c. 1861, p. 81, pl. v. fig. 6.
+ Beobach. iiber Anat. und Entwicklung. wirb. Thiere, &c. 1863, p. 23, tab. iv. fig. 10-12.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 345
into the floor of the anterior chamber. He now refers to the posterior chamber,
which, he says, occupies the centre of the muscle of the organ, a modified but
scarcely satisfactory description. The external granular glands show certain
peculiarities when contrasted with other species, viz., complete separation, large
number and minute size of the divisions or lobules—modifications that I have not
been able to verify.
M. Van BENEDEN’s brief remark on the proboscis in Polia involuta has already
been adverted to. It may also be stated, however, that, in addition to the in-
completeness of his figure, he represents certain lines,* which indicate a sheath (one
of his culs-de-sac) around the proboscis—a state that has not been seen in our
examples. The structure of the stylet-region, as observed by him in Polia obscura
(Tetrastemma varicolor ?), is erroneous. He represents no ducts to the lateral
stylet-sacs; no ejaculatory duct. The division of the reservoir has a cavity in
the centre, but is likewise furnished with two hypothetical oval vesicles or cavi-
ties, and the muscular structure, the floor or ending of the anterior chamber, and
other important points, are absent. The statement, that the lateral stylet-sacs
contained stylets of a smaller size than the central, and of a different form at
the base, shows the learned author did not possess good opportunities for
examining these creatures. He follows Dr Scuutrze in calling the lateral sacs _
pouches of replacement, and therefore is not aware of the true physiology of the
parts. While he states that the proboscis is enclosed in a separate sheath, he
distinctly adds, that its muscular retractor is attached to the skin of the animal
posteriorly; and that there may be no misunderstanding on the question, he
again repeats the statement when drawing up his conclusions, by erroneously
averring that the internal surface of the proboscis is ciliated, and that it is fixed
to the bottom of the digestive tube by a retractor muscle, as in the stomach of
the Bryozoa.t
Prof. Kersrstst’s{ remarks, so far as they go, upon this region in Polia man-
dilla, are decidedly in advance of his predecessors. He, however, does not men-
tion the minute glands on the floor of the anterior chamber, and shows the
central aperture for the stylet in the same by far too large, so that in extrusion
the muscular space (€ in our figures) becomes obliterated. The muscular setting
of the granular sac is also continued too far forwards in his figure. He indicates
no oblique fibres from the pit of the anterior region (as shown in Plate IX.
fig. 3), and the thick coat of the reservoir is described as composed of longitudinal
fibres. The external granular glands are not distinctly described ; and the dis-
proportion between the central and lateral stylets is so great, that I fear some
* Mém. de l’Acad. Roy. des Sc. de Belgique, tom, xxxii. pl. iii. fig. 7.
T Op. cit. p. 44. Unfortunately this author has not lettered his plates, so that I have often
been at a loss as to his interpretation of structures of which no mention is made in the text.
{ Zeitsch. fiir wiss. Zool. Bd. xii. p. 72, taf. v. fig. 4. ‘
VOL. XXV. PART II. 4T
346 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
slip has occurred in their delineation. Lastly, his crenated border (external
elastic coat) does not pass the constriction between the stylet-region and the
reservoir-region, whereas, as already shown, both this and the longitudinal coat
are continued some distance on the latter division.
Reproduction of Proboscis.—So far as 1 am aware, no author has alluded to
the reproduction of this organ. The process was first observed in Ommatoplea
melanocephala, but it has since been seen in O. gracilis, Tetrastemma alge, and
others. In a specimen of the former (O. melanocephala), from which three days
before the proboscis had been removed, there existed a pale conical papilla,
which projected a short distance behind the ganglionic commissures. Two days
after considerable progress had been made, and the organ proceeded backwards —
as a slender rod tapered posteriorly (Plate VIII. fig. 1, @). There was a distinct
exterior coat from one end to the other, and an inner terminating at the com-
mencement of the posterior narrow portion. The former had a crenated edge in
contraction. The organ gradually increases in size and complexity, but continues
quite free posteriorly for a considerable time, until, indeed, the stylets are well
developed. At a further stage of growth (Plate VIII. fig. 2), the walls are defined
almost as in the complete structure, but of course are much more delicate and
_ plastic; and the extreme contractility and elasticity of the entire organ are most
interesting, and raise a doubt as to the identity of its muscular fibres with those
of the higher invertebrates, since it so much surpasses them in mobility. The floor
of the anterior chamber ends in the usual pit, which is swollen on account of the
shortening of the organ. The walls of the muscular cavity behind the floor of the
anterior region are not well defined, though the space itself is large, and con-
tains a granular fluid. There is no central stylet, and the basal sac is repre-
sented by a somewhat triangular group of the usual granules, round which the —
radiating fibres are placed. The wedge-shaped setting within the latter (fibres) —
is mobile and translucent. A somewhat indistinct streak (/) in the central line
indicates the canal for the central stylet, and now and then this became bulged
by projected fluid. The lateral stylet-sacs, from the bulging of the chamber in
this instance, seem pressed backwards, but in reality they have their distinc- —
tive position. Each contained a stylet or two, a few granules, and a clear
globule.
The reservoir at this stage had assumed its characteristic shape, though its —
glands were barely visible. The shortening and bulging of the anterior and pos-
terior chambers have annihilated the usual prominent appearance of this part,
and the last has encroached very much on the cavity posteriorly. The glands
were formed in the posterior chamber, though their contents were not elaborated,
and the cavity terminated in the usual czl-de-sac. A few rounded papille at the
posterior end indicated the early condition of the muscular retractor or riband.
It is clear that at some time or other the latter becomes attached to the wall o :
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 347
the proboscidian sheath, and that, too, in a definite manner, since no great devia-
tion in a series of specimens is met with.
In the developing organ of O. gracilis, a very good analysis of the somewhat
complicated structure is obtained, so that doubtful anatomical points are cleared
up satisfactorily. The sac at the base of the central stylet is sometimes seen to
be composed of granules in rounded masses; and they are all grouped posteriorly
at an early stage, and thus present a similar form to that seen in other species
which have no such elongated sac in the complete state. It is curious to witness
the accuracy with which the stylets are reproduced in this and other species.
There is never any confusion, but each invariably produces them of their respec-
tive sizes and curves as infallibly as if they had been struck out of the same
mould. Yet these bodies are not in any way organically connected with the
tissues of the proboscis, but only spring from a secretion poured into the lateral
sacs, or from the central apparatus. In the concentric arrangement of their con-
stituent substance, and some other particulars, these spicula are analogous to
those of the sponges, whose microscopic anatomy has been so excellently investi-
gated by Dr BowrrsBanx.* Indeed, the morphology of the stylets of the Omma-
topleans offers elements for deeper reflection than even the hooks and bristles of
the higher annelids, which are often so diagnostic of genus and species.
Besides the developing organ, the proboscidian chamber contains (unless in
cases where the organ has been violently expelled) the cast-off proboscis; and it
is a curious sight to observe a fully-developed organ floating freely in the chamber,
and still endowed with contractile power, while the new proboscis has advanced
to the stage of the advent of stylets. The discarded organ soon becomes opaque,
appearing reddish by transmitted light, and the stylets leave their positions. As
there is no mode of exit after the new proboscis has begun to develop, the aborted
one can only (not to speak of rupture) be removed by disintegration and absorp-
tion; and hence in the proboscidian chambers of such animals there is a vast
increase of cells, granules, and granular debris.
Digestive System.—Though no such transverse muscular plate, as described by
M. DE QUATREFAGES, occurs at the anterior part of the body of the worm, yet there
exists a very distinct and comparatively large ciliated cesophageal chamber or sac,
as first described by Sig. DeLLe Cu1Asz, apparently in a Borlasian.+ The figures of
the supposed transverse plate given by the former, indeed, show some degree of
doubt, since in the large figure} both wavy and longitudinal fibres are represented,
while in the small figure there are only transverse fibres. I fear the wavy longi-
tudinal lines owe their presence to those actually existing in the oesophageal sac.
Dr Jounston’s figure§ of O. melanocephala indicates this structure, to which he thus
* Monograph of the British Spongiade, Ray Society, vol. i. p. 5, et seg.
+ Mémiorie sulla, &c. vol. ii. 1835. t Op. cit. pl. xix. fig. 1, m.
Op. cit. pl. u. a fig. 5.*
348 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
refers under the head of O. pulchra :—‘‘ Immediately under the hearts” (ganglia) —
we observe a large, somewhat muscular, viscus, apparently hollow, and lying
in the course of the intestine, but seemingly unconnected with it. Of its office —
and nature I can form no opinion; but I may remark, that in all the species a
greater duskiness in its site shows that a similar organ exists in all.” Prof. KErEr-
STEIN’s notice* of the organ in Wrstedia pallida is very brief; and he has
abstained from figuring its relations, though affirming that its opening (constitut-
ing the mouth) is on the ventral surface behind the ganglia, as in the Borlasians.
M. Van BENEDEN,} while indicating an outline of the structure in Polia capitata,
makes no reference thereto in his descriptions. The same omission is made by
M. CLAPAREDE with regard to his figure of Prosorhochmus Claparédii, Ker. {
In every specimen of Ommatoplea and Tetrastemma the great cesophageal
organ above-mentioned has been easily observed (Plate VIII. fig. 3, 7) as an elon-
gated sac, slightly narrowed posteriorly, and usually thrown into various longi-
tudinal wrinkles. In ordinary views from above, it is seen to narrow somewhat
abruptly behind the ganglionic commissure, and to pass forwards beneath the
inferior one, to open at the tip of the snout just at its ventral border, as a short —
longitudinal slit. I have seen the sac turned inside out here, and projecting —
beyond the head in an animal which had been subjected to chloroform. Both
apertures may frequently be observed at once,—that for the proboscis being cir-
cular, while the mouth forms a short longitudinal slit beneath the former. The
observations on this point have been often repeated, out of deference to the dis-
tinguished foreign authors who hold different views, but I have never seen any
other aperture in the British Ommatopleans, and it were hard for such to exist
in the free portion of the cesophageal tube behind the ganglia. Moreover, as
shown in Plate IV. fig. 1, the narrow anterior part of the glandular cesophagus
lies close to the chamber for the proboscis, when the latter is in this region. The
two organs, proboscis and cesophagus, become more evidently separated from
each other in most sections, just in front of the ganglia, and the interposition of
the broad inferior commissure soon renders the distinction more evident; there-—
after they have the tunnel of the proboscis as a partywall, together with that
portion of the fibrous stroma of the extra-proboscidian region in which the median
blood-vessel is situated. The cesophagus, moreover, occupies a special chamber,
bounded by a series of well-marked fibres (Plate V. fig. 2, £), which pass down-
wards from the upper wall by the side of the proboscidian sheath, and unite in
the median line below it. The anterior narrow portion is generally translucent;
and just behind the commissure a pursed arrangement is often seen, which is”
followed by the more opaque portion with its longitudinal rugee. The pursed
arrangement is very similar to that which is caused by tying the mouth of a
* Op. cut. p. 10: + Mém. l’Acad. Belgique, pl. iv. fig. 13.
t Beobachtungen iiber, &c. pl. v. fig. 10. ph.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 349
leathern bottle, and is due to the narrowing of the sac in front. The pale portion
immediately behind the ganglia shows cilia in active motion very distinctly, but
I have never seen anything like an aperture; indeed, the great and peculiar
stretching of this pale portion, as it is dragged backwards from the region in front
of the ganglia during the motions of the animal under pressure, at once demon-
strates the fallacy of supposing it connected with any post-ganglionic aperture,
as in Borlasia. The wall of the sac evidently contains some contractile fibres,
which cause it to dimple inwards here and there during its motions; and in
anterior transverse sections the cut ends of longitudinal muscular fibres are
shown very distinctly, though they are finer than those of the proboscis. Poste-
riorly, the organ opens into the digestive cavity; but the communication is not
actually seen in ordinary views, from the folding together of the walls, and I
have not been so fortunate as to observe the animals feeding. In Polia involuta,
Van BENEDEN, the cesophagus is short and nearly globular under moderate pres-
sure, being also conspicuously tied posteriorly by strong transverse bands. In
this species the posterior aperture is very apparent.
The relations of the oesophagus to surrounding organs may be observed in the
sections (Plate IV. fig. 5, and Plate V. fig. 2, at 7). The walls increase in thick-
ness after passing the narrowed portion in front, form considerable parietes, and
again slightly diminish posteriorly. In transverse sections of specimens hardened
in spirit, and mounted in the usual manner, the structure has a streaked and
fibrillated aspect, or marked by a series of vertical striz, and minutely granular,
an appearance due to the position of the glandular follicles with respect to the
inner surface, and the change caused by the preparation. It will also be
observed that in these sections the organ is thrown into numerous characteristic
longitudinal folds. In life considerable differences in appearance are observed,
according to the degree of pressure—as, for instance, between the flattened fol-
licles of the organ in a small Yetrastemma, and the thicker structure in a good-
sized 0. alba (Plate VIL. fig. 7). In the latter, the inner edge (@) of the glandular
tube has a somewhat translucent and well-defined border, garnished with mode-
rately long and most vigorous cilia, whose activity is in strong contrast with the
motion of the same organs on the epidermis, and which seem to play an im-
portant part in the economy of the tube. Under the microscope the fresh speci-
men is always thrown into numerous wrinkles, and is crossed by pale streaks—
the ciliated edges of the folds (2). The entire organ is studded internally with a
series of granular glands or follicles, and numerous brownish pigment-granules.
The glands taper towards the free ciliated edge of the ruge.
In 0. melanocephala the organ is curiously narrowed posteriorly; and in
O. pulchra the granular glands are distinct and large. In 7. varicolor the
glandular appearance in a small specimen under pressure is somewhat finer and
more translucent, but the structure is essentially the same as in Ommatoplea.
VOL. XXV. PART II. 4uU
350 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
This ciliated glandular structure is physiologically and homologically an
organ of great interest. It is entirely Ommatoplean in the condition just described,
since what is shown here in the complete form is only indicated in Borlasia by
the turning inwards of the margins at the junction of the two regions of the ali-
mentary canal. The granular glands and cells which coat the latter in Omma-
toplea arise (in the case of the cells, at least) on the sides considerably in front of —
the posterior end of the cesophageal region—in some cases, indeed, almost touch-
ing the ganglia (Plate VIII. fig. 3), and besides, the first region has been demon-
strated to occupy a special pouch in which it rolls. The rich ciliation of this
cesophageal region, and the somewhat indistinct ciliary movements seen in the
posterior division of the alimentary chamber, are points of importance when con-
trasted with the arrangement in Bor/lasia, and show that from structure to struc-
ture the essential differences between the groups meet the inquirer at every step. —
In Vortex, again, the homologue of this region is seen in the “ Schlund”’ of the
German authors.
The Digestive Cavity-Proper —The detailed description of the general cavity
of the worm (all within the muscles) given by M. DE QuaTREFAGES, shows that he
had no clear conception of this structure, for, after explaining the hypothetical
transverse diaphragm, to which we have already alluded, he goes on to say,*—
‘** Le reste de la cavité générale occupe tout le corps proprement dit; mais les
cloisons verticales auxquelles sont suspendus les organes générateurs le parta-
gent entrois chambres distinctes, lune médiane, qui renferme le tube digestif
dans une portion de son éntendue; les deux autres latérales, dans lequelles
flottent les ovaires ou les testicles, et qui 4 l’époque de la reproduction se rem-
plissent d’ceufs ou de zoospermes.”’ In his figures} the scalloped shaded portion,
which he terms “ ovaires ou testicles,” is, as Prof. KEFERSTEIN has pointed out, the
glandular wall of the digestive cavity. Iam ata loss to understand how M. DE _
QuATREFAGES did not correct his error on contrasting his figures of the male and —
female elements in his Nemertes balmea (O. gracilis), for the very same organ is
made in the one case ovary, and its gland-cells developing ova, and in the other
respectively testicle and sperm-cells. Dr Jounston{ recognised the structure as i
‘“a close series of vesicles or cells, formed, in the true Nemertes, apparently by
the folds of a membrane.”” The czeca, he adds, are always full of some opaque
matter, which varies “in intensity at least according to the nature of the
animal’s food.” He thought the structure was connected with the digestive sys-
tem, though not in communication with the proboscis (his alimentary organ).
Dr Wittrams§ had also an inexact idea of this cavity, for he speaks of it as a
great spongy mass, or ‘“‘great alimentary caecum,” which commences anteriorl}
* Op! Cit sp. Lode + Op. cit. eg. pl. xviii. fig. 1, and pl. xix. fig. 1.
+ Mag. Zool. and Bot. vol. i. p. 532. § Report Brit. Assoc. 1851, pp. 244-6,
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 35m
immediately behind the hearts (ganglia), under the character of a czecal end,
and as ‘‘a perfectly closed sac, containing a milky fluid.” The walls of this
cavity, he says, act upon the exuded food, after its passage through the walls of
the “oesophagus.” He is correct in denying the ovarian character of the organ,
and in showing that the so-called ova consisted only of oil-globules. He has also
some reason for considering the transverse segmentation of the organ as an indi-
cation of annuli.* Dr Max Scuutrze}+ described it as a straight canal in Tetra-
stemma obscurum, ciliated on its inner surface, and opening anteriorly and pos-
teriorly, and figures { the cells in its walls as altered by extrusion into the water.
M. CraparkgpE, in the before-mentioned figure of Prosorhochmus, shades the
region, but makes no mention of it in his description.
The digestive cavity is a somewhat moniliform or lamellated canal, in so far
as its surface is increased by the numerous diverticula. Its appearance under
pressure is well seen in Tetvustemma (Plate VIII. fig. 3) as a lobulated glandular
organ, usually of a pale flesh or slightly pinkish hue, extending from a short dis-
tance behind the ganglia to the tip of the tail, and forming (in the individual in
which the reproductive elements are not developed) a lining to the body-wall,
except where interrupted by the proboscidian sheath. In the ripe animal, how-
ever, the gradual enlargement of the ova or sperm-sacs pushes in the yielding
- organ, so that it occupies a more median position, and has its ventral portion in-
creased in bulk. It is also well to bear in mind that the body of the adult worm
is only rounded in contraction, and partly so when the ova or spermatozoa are
_ minature, but at other times it is flattened, and very mobile; thus, what is space
in the transverse section is often filled up in the living animal by the collapsing
| and contraction of the yielding tissues in the neighbourhood. Anteriorly the
| only opening leading into this chamber is that of the posterior end of the rugose
| cesophagus; posteriorly it terminates in an anal pore, less easily seen than the
| similar structure in Borlasia, from the absence of the strongly ciliated internal
| line. In intimate structure the walls of this cavity resemble the anterior or
| esophageal portion, only the gland-cells are larger and more numerous, and
| the fatty elements in greater abundance, so that although the type of struc-
ture remains, there are considerable differences in microscopic appearances.
1 was for a long time in doubt about the ciliation of this chamber in
Ommatoplea, since I have seldom been able to see cilia satisfactorily in the
uninjured 0. alba, though in the latter, O. purpurea, Tetrastemma, and especially
| in Polia involuta, VAN BENEDEN, peculiar motions of the cells were apparent.
When a specimen is kept for some time under pressure, a few moving granules
are observed at some particular point; these continue to increase in number,
and sometimes a few cells accompany them, the group gradually enlarging and
* Philos, Transact. 1858. + Op. cit. p. 64. t Op. cit. taf. 1. fig. 35.
352 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
revolving with great velocity. Such motions are doubtless due to the ciliation of —
the chamber. On making a transverse section of the living animal (O. alba), I
have seen the inner margin of the digestive cavity cause motion in the surround-
ing particles, but the cilia were indistinct, and the appearances very different from
the richly ciliated tube of Borlasia, or its own cesophageal portion anteriorly. It
is thus much more feebly ciliated than the others.
In the walls of this complex cavity are a vast series of gland-cells, which,
with M. Van BEnepeEn, I consider as having some analogy with the liver of the
higher forms, notwithstanding the adverse opinion of Prof. KerzrstTe1n, who, how-
ever, probably refers more particularly to the Porlasians. Microscopically the
cells consist of a delicate membrane containing a number of fatty globules (Plate
X. fig. 6), the average size of the cell being ,4,th of an inch. Under pressure,
and when highly magnified (700 diam.), it is seen to consist of a number of
granular fatty bodies (Plate X. fig. 7). After extrusion from a living specimen
into salt water, a remarkable motion occasionally ensues in the contents of the
cell before breaking up, a condition which causes the observer to fancy the entire
organ ciliated. The contained bodies jerk about within the cell, and soon a
number of very minute granules appear, having burst from the larger bodies, in
which their presence is indicated by obscure markings. The peculiar motions would
seem to be due to the action of the water, and ultimately the minute contained |
bodies are all set free. The various appearances of the bodies from the cells are
shown in Plate X. fig. 8, some being granular, others presenting faint con-
centric lines like starch-globules (though probably fatty), while three oil-globules
are indicated on the right. The deep port-wine oil-globule is somewhat sparingly
scattered throughout the wall of the tract, the yellowish red being abundant, and
the pale globule still more plentiful. These cells have a similar structure in
Tetrastemma, and often escape under pressure posteriorly. The quantity of deep
yellow oil in this organ in 7. alge is unusually great. The foregoing glandular
structure undergoes partial absorption at the period of reproductive activity, so-
that after spawning the animal is much flattened; but by-and-by it regains its
plumpness, and often becomes of a greyish hue, apparently from the increased
development of this tissue, which is exuded as a pale, salmon-coloured, semi-fluid —
substance on rupture of the body-wall. In O. gracilis the posterior division of
the digestive system has a somewhat regularly ramified arrangement, when —
viewed from the ventral surface, and this is especially evident some time after
spawning, when the animal has regained its condition. The colour of the region
is of a deep green by transmitted light, whereas the cesophageal division is
brownish. The lamelle of this region in O. pulchra form simple tapering papille
under pressure. In Polia involuta, V. BEN., the cavity is greatly developed,
both as regards the rest of the body and its individual structures; and it also
presents a firmer and more consistent aspect than usual on transverse section.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 309
The absence of the proboscidian sheath and its contents leaves the central space
almost entirely at its disposal.
In O. alba and rosea Mr E. Ray LanxkestTER* found many Gregarinee, but they
were rare in the specimens from St Andrews. In TJetrastemma varicolor a few
eregariniform parasites (Plate IV. fig. 12) occurred in the digestive cavity towards
the tail.
Another parasitic structure was found in January in a large male specimen of
Ommatoplea alba in the form of an ovum enveloped in a granular lobulated
mass—lying close behind the ganglion of one side (Plate XIV. fig. 9, y), to the
exterior of the proboscidian sheath, and altogether unconnected with the ceso-
phagus. Externally there was a distinct hyaline capsule or cyst, to which
certain fragments of the fibro-granular lobulated covering adhered. The embryo
was furnished with a very conspicuous opaque granular mass, and two discs;
while the general stroma was cellulo-granular, here and there closely streaked
by minute lines, apparently from its external investment. No motion of the
included animal was observable, except an alteration of the size and aspect of the
pores and discs after a period of eight or nine hours. There was no doubt as to
this being a Trematode-larva in its capsule, and by rupturing the latter a
complete view of the embryo was obtained (Plate XIV. fig. 10). The oral sucker
(c) was considerably smaller than the ventral (0), and this formed a marked
feature in the general aspect of the animal. The cesophageal bulb (@) appears as
a distinct swelling close behind the margin of the oral disc, and from the tube
behind the former the alimentary czeca (¢, ¢) branched off and became lost in the
cellular tissues posteriorly. The opaque mass of cells and granules (at @) corre-
sponded to those observed in the Trematode-larva of the Carcinus menas,+
though, from the immature condition of this example, these and other structures
were much less definite. There were also two large circular granular bodies
(generative organs) (f and g); but only a trace of the excretory tubes existed in
front near the oral sucker.
Microscopically, the alimentary organ has scarcely the regular and firm
_ glandular appearance of the same structure in Borlasia, but is more friable and
cellular. Its analogy with that of the higher annelids is also borne out; for,
although the biliary matter is not arranged as a distinct organ exterior to the
alimentary, it is incorporated therewith, and probably has a similar function.
The fluid, however, which bathes the liver in the higher forms (if we suppose that
inside the sheath for the proboscis to be the homologue of the former), is here
separated by the muscular walls of its special tube. The large size of the pro-
boscis in the Ommatopleans renders this system very obscure from the dorsal
aspect, and it is only when the ventral surface is upturned that a correct know-
* Jour. Micros, Sc. 1865. + Jour. Micros. Se. vol. v. N.S., pl. viii. fig. 5, &.
VOL. XXV. PART II. 4x
354 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
ledge of its relations is obtained. I have not been able to see O. alba feed
in captivity, and have not found any food in the alimentary cavities of those
examined. It isa curious fact, that in this group the digestive system lies quite
beneath the nervous system anteriorly, whereas the proboscis passes through the
nervous collar.
Circulatory System.—The circulatory system is composed of three great longi-
tudinal trunks—one central and two lateral—besides the cephalic arch and
anastomotic vessels. Commencing with the great central trunk posteriorly
(Plate VI. fig. 8, p) in Ommatoplea, it is found that the vessel, which in this region
is about twice the diameter of the lateral, arises from the point of junction of the
two last-mentioned, just within the posterior border of the worm. It travels —
forward beneath the proboscidian chamber in a very undulated manner—as ©
usually seen—to the region behind the ganglionic commissures, where it bifurcates
(Plate VI. fig. 3, g), a branch passing to either side to join the lateral trunk (7),
which bends inwards to meet it. From this point of junction also a single ©
vascular arch (cephalic) proceeds forwards into the tissues of the snout (/, same —
figure, and in Plate IV. fig. 6, the latter showing the vessels in transverse section),
the pillars of the arch thus meeting the lateral and the anastomotic vessels of |
each side. From the same point of union each lateral trunk passes backwards
under the nerve-cord of its side to the tail, where it meets its fellow of the opposite
side, and gives origin to the single central vessel with which the circuit com- —
menced. The lateral vessels appear to diminish slightly posteriorily. The
median vessel does not actually touch the wall of the proboscidian sheath, though ~
transverse sections usually show a close apposition, but is situated in a layer of
transparent elastic tissue which intervenes between this organ and the digestive
tract. At the ganglionic region the vessels which go to form the cephalic arch
pass below the commissures, and unite in front beneath the channel of the
snout. In O. purpurea there are three main longitudinal trunks as in O. alba;
but it can be observed that the lateral communicate with the central, as in Borlasia.,
by transverse branches, which, however, are proportionally smaller. Whether
such anastomoses occur in the pale Ommatopleans is thus an open question;
but they are distinct enough in this species. Two lateral trunks only could
be discovered in Polia involuta, VAN BENEDEN (Plate VIII. fig. 5, 7), which :
trunks unite by a very short loop just in front of the commissures. This loop (2)
is distinguished from the ordinary arrangement by its not extending forwards
into the tissues of the snout. The lateral vessels are not so clear or well defined
as in O. alba and Tetrastemma, and are observed to have internal transverse
bands or partial septa in front; while the contained fiuid has a few clear granules,
as in O. purpurea and others. ‘The contractions in the lateral vessels are very
vigorous, and even a minute central vessel could not have been passed over if a
trace of such had existed.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 300
The course of the circulation, so far as I can see, is as follows:—Posteriorly
a gentle contraction from behind forwards drives the contained fluid along the
great central vessel to the front, where it is forced through the anastomotic into the
lateral vessels and the cephalic arch. The lateral trunk may be seen to swell
with the wave, and the fluid then passes to the posterior end to enter the median
as before-mentioned. In addition to the stream poured into the lateral trunks,
another passes into the cephalic arch by the vessel on each side, and the counter-
currents must meet and commingle, returning again during the diastole of the
central vessel. I have not made out any branches in the British species except
in O. purpurea ; but this is a somewhat difficult task, on account of the trans-
parency of the circulating medium and channels.
In many species the fluid contained in these vessels is transparent and homo-
geneous. M. DE QuaTREFAGES, however, found corpuscles in his Polia bembix,
Prof. KEFERSTEIN small oval discs in the reddish blood of his Borlasia splendida,*
and I have seen in Ommatoplea purpurea minute granular corpuscules, but both
they and the fluid are colourless. Minute colourless globules also occur in the
blood of O. pulchra.
: Such, in the Ommatopleans, is a brief outline of the circulation, which,
although resembling that of M. pr QuaTREFAGES, in so far as each describes three
main trunks, differs considerably in detail. The first point to be noticed in the
descriptions of this author is the statement that the lateral trunks pass through
the cephalic diaphragm—a structure which has not been seen. He is slightly in
error also when he states that the median vessel lies immediately under the sub-
| cutaneous muscles. The arrangement shown in his two sections of Borlasia
| angliee cannot apply to this group. I have not been able to verify the elaborate
| curves which this author gives} each anastomotic division of the central vessel
anteriorly, and which may be described as first forming a loop behind the gan-
glion, with its curve directed outwards, and a second inversely curved round its
| anterior border—in its passage outwards to join the lateral, which is scarcely
| bent inwards at all, but occupies a space where no vessel occurs in the British
‘forms. The mere shortening of the anastomotic will not retrieve this anatomical
}error. The cephalic arch is also placed otherwise than “immediatement au-
|dessous des couches sous-cutanées,” as already described (Plate IV. fig. 1).
_He mentions the presence of distinct walls to these vessels, which, however, he
learned from Borlasia angliw, and in this I concur (Plate IV. figs. 1 and 6).
| The walls are highly contractile, and in the latter figure the vessels have been
|cut across just before they complete the cephalic arch; they are observed to be
| surrounded by a ring of finely granular texture. M. DE QuatTReEFaGEs likewise
* This species has since been found in the Channel Islands, It is the Cerebratulus spectabilis
| of M. pe QUATREFAGES,
t Op. cit. pl. xviii. fig. 1. and pl. xix. fig. 1; also in his recent Hist. Nat. des Annelés, pl. iv.
2 and 3.
a
| figs.
306 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
states, that though fixed in front the vessels are elsewhere free, and only con-
nected here and there to the body-wall by ligamentous bridles; and in one of his
plates* figures the ova between the lateral vessels and the wall of the body.
All our transverse sections show that such could hardly occur, for the vessels
occupy a secure position beneath the nerve-trunks; and while the ovaries or
sperm-sacs sometimes press the vessels downwards towards the ventral surface,
and increase the distance between them and the nerve-trunks, they never actually
intervene between the latter and the body-wall in the perfect worm.
Many of the older authors confounded the ganglia with hearts, such as
EHRENBERG, HuscHKE, DELLE CuiAse, DucEs, Cirstep, and more recently our
countrymen, Drs Witu1ams and Jounston, The latter mentions that the only
blood-vessel he has seen is one ‘“‘ winding down the middle, along the surface of
the alimentary canal,” but he can neither trace its origin nor termination. Dr
Max ScHuLTzE} seems to have mistaken the edge of the proboscidian sheath
under pressure for the blood-system, which he figures as two long straight trunks
on each side of the digestive tract. The true blood-vessels he describes as the
water-vascular system, but shows neither beginning nor ending, though numerous
large branches are represented as issuing from them throughout their course.
Prof. KererstEtn} does not distinguish with sufficient clearness the different blood-
systems of the Ommatopleans and the Borlasians; and, indeed, applies the
definition of the former to the latter; but so far as they go his descriptions and
representations of the arrangement in this group are good. He, moreover, shows
an elaborate series of minute transverse anastomosing vessels in his Borlasia
splendida, whose structure therefore differs from that usually exhibited by the
British Ommatopleans. M. CLAPparEDE,§ though his publication is more recent, is
less correct than the latter author, for he figures the dorsal vessel as passing above
the ganglionic commissure before giving off the anastomotic to join the lateral, —
and thus a somewhat stiff square is formed in the cephalic region, while the lateral
vessels have to pass to the outside and front of the ganglia before meeting the ©
anastomotic. The vessel appears also to be placed on the dorsum of the proboscis.
Nervous System.—In the living animal two carmine, pinkish, or reddish color-
ations are observed on the snout some distance behind the tip: these mark the
position of the cephalic ganglia or nervous centres. As previously mentioned not
a few authors, misled by their colour, pronounced them to be hearts. The aspect
of the ganglia under pressure is indicated in Plate VI. figs. 1 and 3,2; and in
large specimens they are pear-shaped under a lens. Hach ganglion consists of
two divisions—a superior, shaped somewhat like an almond, and an inferior,
continuous with the great nerve-trunks. The first-mentioned portion is chiefly
* Op. cit. pl. xxi. fig. 3. Polia sanguirubra. t Op. cit. p. 64, pl. vi. fig. 2.
t Zeitsch. fiir wiss. Zool. pp. 85-87, taf. v. & vi. | § Beobach. iiber, &c., taf. v. fig. 10.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 307
cellular, being composed of minutely granular nerve-cells, and is connected with
its fellow of the opposite side by the long or superior commissure (Plate V. fig. 1, /),
which passes over the proboscis. In ordinary circumstances, this commissure is
less than half as broad as the inferior, but it is considerably longer. It is a simple
ribbon of transverse fibres. As observed in the living animal, these fibres pass
on to the superior lobe, where they diverge, some turning slightly forwards, but
the majority passing obliquely backwards to the pale central part of the lobe.
The only remark made by M. DE QuaTREFAGES with regard to the physiology of
this band is, that it removes the somewhat surprising state of matters of having
a brain composed of two lateral masses, and only one (‘‘ sub-cesophageal’’) com-
missure. ‘To me, however, this band seems of more importance, since, during the
enormous distention which takes place in the extrusion of the proboscis, it is the
superior commissure which is stretched to an extreme degree of tenuity. The
proboscis, as mentioned, passes through a complete ring of nervous texture, and,
during extrusion, forces this outwards in all directions, but chiefly superiorly,
the inferior commissure, indeed, being little altered. Nearly half the circum-
ference of the proboscis projects above the level of the ganglion (Plate IV. fig. 5),
and the superior commissure must be correspondingly elongated ; hence, if this
is purely a nervous band, we have a very interesting example of the elasticity of
such texture. It may possess elastic as well as nervous fibres, but such are not
distinguishable. The inferior commissure consists of a thick mass of nerve-fibres,
the majority of which sweep backwards to form the lateral nerve-trunks; thus
it becomes an isthmus between these cords. A few of the anterior fibres are
connected with the central region of the former division of the ganglion.
In long species, such as O. gracilis and O. purpurea, the ganglia are not cor-
respondingly lengthened, but are rather rounded. In Yetrastemma the arrange-
ment of these organs is very similar to that in O. alba, so that a special descrip-
tion need not at present be given, further than by referring to Plate VIII. fig. 7,
which represents the ganglia in a small specimen of 7’. varicolor, where the inferior
commissure is shorter and broader, and the lobes more elongated. This is also
the case in Prosorhochinus. In the aberrant form, Polia involuta, VAN BENED.,
the ganglia are strictly Ommatoplean in shape, and the lateral nerves, which are
not shown by the discoverer of the species, comparatively large. M. BENEDEN’s
figure of the anterior branches of the ganglia is erroneous. The lateral nerves
_ lie quite within the longitudinal muscular coat.
Carefully made transverse sections show how incomplete is the impression
conveyed by the examination of the parts in a compressed, though living animal.
Instead of forming a fiattened organ, whose greatest transverse diameter is across
the plane of the body, each ganglion has its longest (transverse) diameter nearly
perpendicular to the latter (Plate IV. fig 5, and Plate V. fig. 1). The nerve-cells
do not appear to be confined to the superior portion, but occur in the inferior also
VOL. XXV. PART II. ay
358 DR W. CARMICHAEL M*INTOSH ON THE STRUCTURE OF THE
(Plate VI. fig. 1), where they are seen on each side of the origin of the great nerve-
trunks. In the fresh specimen the sheath of the ganglion is moderately resistant;
for under pressure the nerve-cells from the softer interior do not pass through this, |
but escape by travelling along a portion of the great lateral trunk, and rushing out
at its torn end, or pass along other branches, such as the superior and inferior com- —
missures, and the anterior nerves, or through accidental punctures. The nerve-
cells are of a yellowish tinge, and minutely granular (Plate VIL. fig, 11), and rapidly
alter their appearance after escape into the water. Many contain a larger reddish
granule or granules, to which the colour of the organ is partly due; but I cannot
say I saw all the numerous larger pigment-granules so located, although they
might have been. In the fresh as well as in the prepared condition (Plate IV.
fig. 5), the entire ganglion is dotted with minute pigment-specks and granules,
which are also continued along the great nerve-trunk for a considerable distance.
The superior commissure is faintly tinged with colouring matter, but the inferior
more so; both are paler than the masses of the ganglia. The colour of the ganglion
is not destroyed by sulphuric ether, but is rendered paler by acetic acid.
M. DE QUATREFAGES mentions that in a large Borlasia (angliw ?) he found the
cephalic ganglia surrounded by a sheath forming a sort of dura mater, but he
could see none in the smaller species. In the Ommatopleans, the muscular and
other structures of the head form a somewhat condensed capsule round the ganglia,
independently of the delicate sheath-proper of the nervous matter. The longi-
tudinal fibres of the former, indeed, form powerful bands between the ganglia
and the inner muscular layer of the body-wall. M. DE QUATREFAGES mentions
the occurrence of ventricles in the interior of these organs (ganglia), and figures
them in Polia berea; such have never appeared in any British form, though,
under pressure, collections of oil closely resemble the drawing given by this
author. Ihave also never been able to see so many branches proceeding from
the ganglia (as he shows)* to the eyes, cephalic fosse, “mouth,” and other
tissues from the anterior borders,.in addition to the great trunks and other twigs
posteriorly. The arrangement in the British Ommatopleans is represented in
Plate VI. fig. 1, and consists of the following, viz., three very distinct branches
on each side of the superior lobe anteriorly; two about equal in size; and a third
much smaller, to the outer side. Traces of a fourth branch are also present. The
outline of the ganglion throughout the rest of its extent is quite smooth. Various
branches from these trunks proceed in the direction of the eyes; but the nature
of the cephalic tissues renders it very difficult to trace such an object as a pale
nerve-branch with certainty. Dr M. Scuutrzr} gives a tolerably correct view of
the ganglia and nerve-trunks in Tetrastemma obscurum; no branches, however,
occur on the trunks in his figure. This author, in a later publication,{ founded
* Op. cit. e.g. pl. xv. fig. 14; pl. xvin. fig. 1; pl. xix. fig. 1; and the whole of pl. xxiv.
+ Beitrige zur Naturges, Turb., 1851. + Zeitsch. fiir wiss. Zool, iv. 1852.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 359
one of the chief distinctions of his Enopla and Anopla (Tremacephalide and
Rhochmocephalidze) on the structure of the ganglia. Prof. KererstErn figures
only two branches, proceeding from the anterior part of each superior lobe to
the eyes in his Borlasia splendida, but he represents a kind of mesh-work,
formed by three or four trunks between the side of the lobe and the cephalic
sac, and a pair of nerves from the inferior commissure. No equivalent arrange-
ment to the two latter series has been seen in our species. M. CLAPAREDE*
figures the proboscis as passing beneath the great or inferior nervous commis-
sure in Prosorhochmus Claparedii, and the central blood-vessel as placed above
both.
The great nerve-trunks (n, in the various transverse sections), springing from
the inferior lobes of the cephalic ganglia, pass backwards in this group within
the inner (longitudinal) muscular layer of the body-wall to the posterior end of
the worm, where they terminate near the tip. They are surrounded by a coat
of the usual delicate fibroid stroma of the parts. The branches given off by
these trunks are generally pale and indistinct, but by the use of dilute acetic
acid in O. alba, and in others without such aid, they can be satisfactorily observed.
They are easily seen, for instance, in 0. pulchra, the reddish hue which tinges
them at their commencement shining through the translucent integuments. An
elaborate plexus of branches from the lateral trunks has also been noticed in the
same species. In this form also there remains, even after continued pressure, a
peculiar narrowing of the great trunks immediately behind the ganglia, which,
if not an original condition, may be due either to comparative immunity from
pressure, or a tougher investment. The same constriction is seen in O. purpurea.
In transverse section the nerves present a delicately granular appearance from
the ends of the cut fibres. No one who has seized on such specimens as O. gra-
cilis in semi-contraction (though unwrinkled), and drawn them out to treble the
length and upwards, can doubt the peculiar elasticity that must pertain to the
lateral nerves in these animals. +
The nerve-trunks were said by M. pE QuatREFaGESs to lie “‘ between the external
longitudinal and internal transverse muscular fibres” of the body-wall ; a descrip-
tion which may in some respects apply to the Borlasians, but is inapplicable to
the present group. Frey and Levckartt mention that the lateral trunks lie
to the inside of the muscular coats; but while indicating the different arrange-
* Beobachtungen, &c. pl. v. figs. 10 and 12.
+ The arrangement of the nervous system in the curious foreign Turbellarian, described under
the names of Bipalium, Stimpson and Gruse, Sphyrocephalus, Scamarpa, and Dunlopea, Perceva
Waicut, presents a considerable variation from the foregoing, just as the external form of the head
and the digestive system do. Scumarpa represents the cephalic ganglia as quite separated from
each other, except by connecting cords, and the great nerve-trunks placed close together in the
median line, with an intervening ganglion at regular distances.
{ Beitrage zur Kenntniss Wirb. Thiere, p. 72.
360 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
ments of the “ brain” in Tetrastemma and Borlasia, they do not explain the dis-
tinction in regard to the position of the nerve-trunks in these species. Prof. KErer-
STEIN likewise did not observe this essential distinction between the two groups,
but considered Cerebratulus the type of the whole. He describes an otolite or
two in the middle of the ganglion in a young @rstedia pallida, but I fear such
are only pigment-granules and cells, or collections of oil. HE. GRArrFre,* again, in
some brief remarks on a Tetrastemma from Nice, states that he found a small
cluster of otolite-capsules between the eyes, each capsule containing a crowd of
minute otolites. If such were not pigment-cells or structures pertaining to the
cephalic sacs, the Mediterranean form shows a most interesting advance on the
British in this respect, as well as in having lenses to its eyes. Unfortunately,
the author has not figured the structures.
The only British Ommatoplean, so far as I have seen, which shows a special
structure in its eye-specks, is O. pulchra. In this species the pigment is grouped
within a distinct capsule (Plate VII. fig. 8, from a dead, and therefore slightly
injured specimen). The eyes in the living animal have a clear patch in the centre,
from the projection of the lens-like capsule. In O. gracilis and others, a few of the
eye-specks are frequently connected together by bridges of the pigmentary sub-
stance. Though a pale portion is sometimes seen in the specks of the former, I
have not satisfactorily made out a lenticular structure. In Tetrastemma vermi-—
culus, which has frequently been sent me from St Andrews, the eyes of each side
are connected by a longitudinal patch of dark pigment, so that in contraction
the animal seems only to have two large crescentic eyes, of a very characteristic —
appearance.
Cephalic Sacs and Furrows.—Midway between the tip of the snout and the
anterior border of the ganglion in O. a/ba, a furrow runs inwards and slightly
forwards on the dorsum, ceasing, however, before the middle line is reached; and
on the ventral surface a similar though shorter furrow exists, the two meeting in
a dimple, furnished with longer cilia, on the side (where the cilia are more active and
powerful than usual), which depression leads into the cephalic sac. A short distance
behind the ganglia two other superficial furrows occur, each slanting backwards and
inwards to meet its fellow of the opposite side in the middle line. These furrows —
are also continued inferiorly, but with a slightly different direction, so that they
meet under the ganglia. The two sets of furrows are very distinctly marked in a
flattened head as lateral notches. From the dimple mentioned in connection with —
the anterior furrows, a thick-walled ciliated duct on each side leads into a con-
siderable ovoid, pyriform, or almond-shaped glandular mass, which lies in front —
of and rather exterior to the ganglion of the side (Plate VI. fig. 1, m); and from
what is seen in translucent species, such as Tetrastemma vermiculus, it would
appear to end in a cul-de-sac, the walls, moreover, under pressure are marked
* Beobach. iiber Rad, und Wiirmer in Nizza, Ziirich, 1858.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 361
with transverse ruge. Towards its first part the duct is surrounded by a
minutely granular glandular structure, which usually has a somewhat triangular
figure. Several glandular masses lie behind, one tothe outer, and another to the
inner side in this position. The glandular substance around and behind the posterior
part of the ciliated external duct contains numerous granules and finely granular
circular cells. From the posterior end of the outer mass in such a view, a structure
that appears to be a pale duct passes obliquely towards the superior lobe of the
ganglion, crossing this for some distance in a direction inwards and backwards.
Traces of a cavity are apparent at its commencement, and, besides, it is distin-
guished from the adjoining nerve-trunks under pressure by not being continuous
with the ganglion at its edge. In transverse sections of the snout, each sac is seen
to occupy a position to the outside of the cephalic blood-vessel, and somewhat above
it (Plate IV. fig. 1, m), and to have a special space in the muscular stroma of the
head. In large specimens the sacs contain many reddish pigment-granules, and
occasionally a large cell filled with coarse granules. Behind the foregoing glan-
dular apparatus lie the coiled ciliated ducts (m’), which are sometimes pale and
irregularly bulged from included fluid, or else collapsed and minutely granular in
aspect. In some specimens of O. alba the commencement of the duct is tinged
of a faint reddish hue. There seems to be no ground for the supposition that
the sacs are connected with other organs. In O. melanocephala they are less
dilated than in O. alba. The coils of the ciliated duct in O. gracilis are most
elaborate, and can be traced for a long distance backwards by the side of the
nerve-trunk. In O. purpurea* the external apertures are not so evident as in
O. alba and Tetrastemma, because the furrows are less distinct when viewed as
transparent objects. They are best seen when the ventral surface is upturned,
and occur in the angle of the furrow some distance from the margin of the head
in this position. The ciliated pit leading inwards is short. Like other parts of
the animal, there is a considerable variation in O. pulchra from the typical form
in the shape and position of these sacs as well as in regard to the furrows. The
latter species has numerous short longitudinal or accessory furrows on the
front of the ventral grooves, and in this respect is allied to the Borlasia
splendida of Prof. Kererste1n. Instead of lying in front of the ganglia (in the
ordinary position under examination), the sacs are situated laterally and pos-
teriorly, forming somewhat elongated pyriform organs, which adapt themselves
to the curves of the ganglia. Each sac is filled with rounded granular cells,
reddish pigment and other granules, has a ciliated duct anteriorly, which opens
at the constriction or lateral dimple of the head just in front of the ganglia, and
posteriorly ends in a ciliated tube which by-and-by bifurcates and extends for a
* IT have a strong suspicion that this is the same species as the Borlasia camillea of M. pr
Quarreracss, which he places next B. anglie, an association, if I am correct, founded on erroneous
principles,
VOL. XXV. PART II. 47
362 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
considerable distance backwards by the side of the lateral nerve-trunk. Besides.
these sacs there is in the snout of this worm a series of well-marked glandular
organs in front of the ganglia, one of which lies on each side of the blood-vessel,
and is connected with a large lobulated mass in the middle line. In structure
these glands are allied to the foregoing, having in their interior rounded
granular cells, pigment, and other granules. What in some views appeared
to be a duct passed from the posterior end of the external lobule towards the
cephalic sacs. Traces of similar glandular masses were seen in other species (¢.g.
O. alba) near the middle line of the snout, behind the cephalic sacs, and else-
where. In Tetrastemma the sacs agree essentially in structure with those of
O. alba, and in such translucent specimens as 7’. varicolor the ciliated posterior —
ducts are easily traced.
The slight furrows just described on the head in this group have been noticed
by few investigators, and only Prof. Kererstern* and M. CLAPAREDE} mention the
occurrence of the sacs; the former using the term Settenorgane for their signifi- —
cation, but his notice is very brief. He figures and describes his B. splendida as
furnished with sacs at the side of the ganglia, but without the ciliated ducts
posteriorly; while in B. mandilla the latter reach no further back than the
ganglia. The former species has a curious series of oblique furrows on the side
just behind the snout, which are evidently homologous with those described in
O. pulchra. M. CLAPAREDE again figures on each side of the eyes in the young
of Prosorhochmus Claparedii a blind sac, apparently unconnected with the ciliated
pits above-mentioned; moreover, in the drawing of the adult animal (fig. 10)
there is on each sidea ciliated duct, but no sac. M. DE QuATREFAGES only noticed
traces of these structures in the Ommatopleans; for he describes bridles or bands
as passing outwards to the “ fossettes céphaliques.” In his Polia bembix he
represents a large nerve passing from the anterior part of each lateral nerve-
column, not far behind the ganglion, and which, after a course directed obliquely —
forwards, ends in a swollen granular manner at the cephalic fossa. A similar
arrangement occurred in P. humilis; but in this instance the nerve arose from —
the superior lobe of the ganglion, passed obliquely forwards and outwards, and
ended in several branches at the fossa. In Cerebratulus crassus and Nemertes
peronea, again, he figures the nerve as springing from the posterior part of the
superior lobe. He does not seem surprised that the nerve-trunks to these fosse
should spring from sites so diverse as the front and back of the superior lobe and
the lateral trunk. The disposition of an important nerve-branch in species of
the same genus, or even in allied genera, is seldom so varied. The structure
appears to have been misinterpreted in Ommatoplea, the sac having been over-
looked, and the process or duct, which sometimes crosses to the origin of th
great nerve-trunk and ganglion of its side, assumed to be a nerve-branch. M.
* Zeitsch. fiir wiss. Zool. xii. 1863, pp. 81 and 82. t Beobach. iiber, &c. pl. v. fig. 12. :
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 363
Van BENEDEN, though he noticed the sac in Borlasia, does not mention more than
“ fossettes céphaliques” in this group.
Organs of Reproduction.—The sexes are separate, and the generative products
developed between the inner muscular layer of each lateral region of the body
and the glandular digestive chamber, and enclosed in special cavities (Plate XI.
fig. 2) formed by transparent membranous sacs (¢), which are connected with the
inner muscular layer of the body-wall. In the matured specimen the ova are
observed to extend from the cesophagus almost to the tip of the tail, each ovary
containing from one to seven ova, which, when fully developed, are seen with
the naked eye through the attenuated parietes of the body. They attain a
comparatively large size before leaving the body of the parent; and it is curious
that they are not much less in bulk in small specimens, though few in number.
The female in the ripe state has a greyish-white appearance, with the dorsal tube
for the proboscis extending nearly from end to end, though its diameter is lessened
posteriorly from the encroachments of the ovaries. The sperm-sacs in the male
generally have a pyriform or flask-shaped aspect, especially in the early con-
dition, being attached to the body-wall by a narrow tubular neck, which at the
proper period doubtless gives transit to the contents of the sac. In the early
condition the latter is finely granular, then cellulo-granular; and in the mature
state it has a finely fibrous or streaked appearance from the spermatozoa. Some-
times both granules and spermatozoa occur in the same sac, and then the former
are often observed to be somewhat regularly arranged (Plate VII. fig. 12). The
spermatozoa in O. alba (Plate VIII. fig. 13) have a slight curve of the body, which
gently widens from the tip and ends in a perceptibly larger rounded knob, from
which the long tail proceeds. The mature males are easily distinguished from
the females by their whitish or pinkish aspect, and their bodies are less bulged.
The spermatozoa of O. gracilis (Plate IX. fig. 8) are most active wriggling struc-
tures, of a more slender shape than in O. alba or Tetrastemma (Plate VIII. fig. 14),
appearing under a power of 1000 diameters as simple rods, slightly larger
towards the end from which the elongated and very fine tail proceeds. The
sperm-sacs are very numerous in Polia imvoluta; but the tenuity of the sperma-
tozoa (Plate IX. fig. 9) renders their exact structure somewhat obscure. The
body of the spermatozoon is elongated, gently curved, and slightly thickened at
the end from which the tail proceeds. It is very common, moreover, to observe
one or more minute clear globules attached to the body of the spermatozoon, so
that the structure seems to have a tail at both ends, or a large flattened head.
These appearances have misled even so experienced an observer as M. Van
BENEDEN, who figures* these organs as possessed of a somewhat globular body,
with a tail at each pole. But, independently of the strange exception which
such a condition would make in Nemertean physiology, the frequent occurrence
* Recherches, &c. Mém. |’Acad. Belg. t. xxxii. pl. iii. fig. 11.
364 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
of more than one globule on these thread-like organisms, and the comparative
steadiness of the body of the spermatozoon, contrasted with the lashing of the
tail, might have raised a doubt in the mind of the distinguished foreign author.
The spermatozoa in Tetrastemma vermiculus (Plate VIII. fig. 12), though minute,
are amongst the most active of the group. These structures are slender at one
end, and slightly dilate towards the opposite, which is furnished with a very long
tail. Just in front of the posterior end there is in certain views a somewhat
abrupt swelling of the body, as if from an adhering globule, but none were
observed without the enlargement. The ova and spermatozoa in O. alba would
seem to attain full development in February, March, and April; but the breeding-
season of other Ommatopleans ranges from the latter month to November. When
fully developed, the mode of depositing the ova and spermatozoa may be illus-
trated by the following account :—Two specimens, male and female, of O. gracilis
were taken from a deep vessel, and subjected to examination in a large glass cell.
‘In a very few minutes after the male had been placed on the bottom of the cell
tiny jets or jet-like wreaths of sperm-fluid were observed to issue from the sides
of the body, rather past the middle, and gradually increased in number, both in
front and behind. The body of the animal was soon enveloped in a wavy cloud
of the milky substance, whose borders were slowly commingling with the sur-
rounding water, while the numerous coiling jets, like so many miniature wreaths
of white smoke from the sides of the worm, were constantly adding to the central
mass. This operation lasted only a few minutes, and thereafter the animal
crawled about the vessel. The female specimen was now observed to protrude ~
her snout from the mass of sand and mucus in which she was coiled, and crawl-
ing to the side of the vessel, deposited in a few minutes a group of ova, about
three inches distant from the white edges of the sperm-cloud, and she retired —
again under the mass of sand and mucus. The change of water probably caused
the male to eject his matured spermatozoa, and some sympathetic influence,
it may be the diffusion of the latter, induced the female at once to evacuate
her generative organs, so as to afford the ova the benefit of the male element. —
A very few ova were found on examination to remain in the body of the female, —
and they differed in no respect from those deposited in the vessel. The aper-
tures by which the respective elements passed out in these specimens were
readily observed as pale specks, each furnished with a central opening, round
which ciliation for the time being was well marked. These openings, as in
Borlasia, occur a little above the lateral nerve-trunk on each side, and even in —
specimens of O. alba not fully ripened, pressure forces the contents of the
generative sacs in the same direction, although no aperture is visible.
Specimens of O. alba, which had been in confinement for seven months,
deposited their ova about the middle of February; and that this is not later than
in the free examples, the receipt of many mature specimens from St Andrews at
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 365
the end of March proves. The actual number of ova was not counted; but in one
instance the ova of a single specimen covered a circular space of more than half
an inch in diameter. Occasionally, in a crowded vessel, they are found above
the water-line, adhering to the glass in an irregular mass; but they are not con-
nected together by other than accidental mucus, and easily fall asunder. There
is, therefore, a marked difference in regard to the deposition of the ova between
this group and Borlasia; for in the latter they have a totally different shape, and
a special investment of tough mucus. The only exception, so far as I have yet
found, in regard to the deposition of the ova in a free condition, occurs in the
aberrant form Polia involuta, VAN Ben. The bulk of the worm considerably
diminishes after spawning, and the body assumes a flattened form, especially
marked in large examples. That impregnation of the ova (in O. alba) takes place
only after deposition, is proved by segregating a female ready to spawn, for then
it is found that no further change ensues in the egg. Hence the large size of the
male organs, as in fishes and other animals that shed their secretion into the
surrounding water.
It isa mistake to describe, as Dr Jounsron, M. DE QuATREFAGES, and Drs
Frey and Leucxart have done, the ova as occurring in a free condition between
the body-wall, and the Darm or digestive cavity. They are always contained in
ovisacs. M. pE QuATREFAGEs observes that he found at the reproductive season a
milky liquid, containing corpuscles of conglomerated globules, in the generative
ceeca ; and the succeeding descriptions and illustrations make it clear, as already
stated, that he refers to the walls of the digestive cavity, and the special elements
contained therein. Thus it is no wonder he had some difficulty in distinguishing
the sexes in the early condition of the generative products, since the cells would
be identical in every specimen. He indeed gives a tolerable figure of a cell from
the wall of the digestive cavity, as one of the true stages in the growth of the
spermatozoa ;* and again refers (Plate XXII. fig. 2) to the glandular wall of the
said cavity as representing generative ceca. The spermatozoa, therefore, which
he shows, had either been discharged externally, or procured from a specimen in
such a condition as to leave no room for doubt. His figure} of the spermatozoa of
N. balmea is incorrect, for the body is too short and thick. He considered that it
was only after the granular corpuscles fell out of the ceca into the lateral cavities
that they assumed their special characteristics as sperm-cells. He thus failed to
make out the correct anatomy of the parts and the physiology of the process. Dr
Wiuui1ams{ states that the ‘‘ segmental organs” in Lineus, Borlasia, and Nemertes
correspond in number with the transverse divisions of his great “ alimentary
czecum”’ (digestive cavity), and that there is only one British species (Polia
quadrioculata) in which it is possible to demonstrate the segmental organs in situ
* Op. cit. pl. xxi. fig. 4, and still more plainly in pl. xxii. fig. 2.
WiOpacit. pl: xix fie. 6. + Philos. Transact. 1858, p, 131.
VOL. XXV. PART II. DA
366 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
as transparent objects. It is almost unnecessary to contradict the last statement,
since small specimens of most of the species are more or less translucent. This
author also maintains that the group agrees in the structure of its generative
organs with the type of the lateral ovarian pouches of the Hirudinei, differing
from the latter, however, in having the sexes separate. MM. Van Brenepen
and KEFERSTEIN give a correct account of the position of the ova and sperm-sacs
in the body of the species examined by them; but the term “biliary ceca”
used by the former is objectionable, as tending to confound the generative and
digestive systems.
M. DE QUATREFAGES makes no mention as to how the ova are extruded,
though he points out that (irstEp and DucéEs were wrong in averring that they
escaped through the walls of the body. Mirsrep’s observation, however, is cor-
rect, as subsequently proved by MM. Benepen and KerersTein. Frey and
Leuckarr erroneously conjectured that the ripe ova were shed from the posterior
end of the body, ‘‘ as in Arenicola.”
The unimpregnated ova in 0. alba (Plate VIII. fig. 8) are pure white, and mea-
sure about ~4,d of an inch in diameter, the pale spot just before deposition being
about =4,;th of aninch. The ovum has two coats—an external hyaline investment
(a), which becomes considerably firmer after extrusion, and an inner membranous —
sheath (b) of greater delicacy enveloping the vitellus (c). With the exception of
the pale spot the ovum is uniformly granular, the granules on gaining freedom
showing very active molecular motion in the surrounding water. Ata particular
point there is a very distinct process (micropyle?) (7), as if from the remains
of a tube that led through the outer coat. In a few hours after deposition and
impregnation the pale spot disappears, the yolk divides into two masses, and
shortly afterwards into four. On the second day they are almost all in the ©
mulberry-stage. In seven or eight days the contained embryo is observed to —
- revolve within the capsule by aid of its cilia, and the majority are extruded from _
the 12th to the 14th day. The young animal is furnished with two eyes before
bursting the egg (Plate VIII. fig. 11), and the coarse granular matter and globules ©
of the digestive tract are apparent. In such a condition the wall of the ovum is”
readily ruptured, and in several instances the posterior end of the animal emerged ~
first. No sooner did the young get over their labours of extrusion than they
‘glided rapidly off, head first, in a manner that showed no training was necessary —
to enable them to progress. Probably the action of the cilia may have some
influence in determining their course. In these young animals, which are just —
visible to the naked eye as minute specks, the proboscis is marked by a paler
space (Plate IX. fig. 1), that has on each side of it a dense mass of the granules |
of the digestive canal. To the outside of the latter are two pale stripes, broader
in front, caused by the nervous ganglia and trunks. Two longer cilia mark the
posterior end. A further stage of development (after an interval of about eight
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 367
days) is shown in Plate IX. fig. 2, under somewhat less pressure. It will now
be observed that there are four eyes, the anterior pair of which are largest, and
correspond to the first pair. Occasionally a few have an additional pigment-
speck or two on one side of the posterior pair. The anterior pair are nearer each
other than the posterior, differing in this respect from those of the young Tetras-
. temma, whose eyes are equidistant in both pairs.* The two ganglia (4) are large,
pale, distinctly outlined, connected by the two commissures, and give off the
lateral nerves (n), which approach each other very closely at their posterior
termination. The oesophageal sac (7) behind the ganglia is well defined; and
two pale streaks mark the cephalic sacs (m). The proboscis has its anterior
opening, and the first region (a) its glands, the posterior border being marked by
a transverse line (0), after which follows an indistinct stylet and reservoir-region.
No stylets are visible until much crushed, and then in one specimen two slender
spikes, probably from the lateral sacs, were seen. The posterior region of the
proboscis bends forwards, and becomes lost atc. Shortly after this the lateral
stylet-pouches become very evident in some, opening by a short and wide tube
into the floor of the anterior chamber, and either containing granules or small
stylets, while the central apparatus has no stylet (Plate VII. fig. 6). The speci-
men had really only granules in its sacs; but to save multiplication of figures
one of them was deleted, and filled in with correct drawings of stylets from
another example. There is no trace of a central stylet, but the central sac is
filled with coarse granules, and they moved with the muscular setting around
them, for at this time the latter showed distinct contractions. The muscular
space (e) behind the floor of the anterior chamber shows traces of an inner and
special lining, which forms a transverse boundary in front. The basal sac is irre-
gular in outline at present, and the shape less defined than in the adult, but, as
development advances, the form of the ‘‘awl-handle” becomes more characteristic.
The lateral stylet-sacs in a few days afterwards were generally furnished with
stylets, but these organs were not so sharp and smoothly finished as in the older
examples. When the central stylet appears, the granules of the basal sac have a
more definite shape than represented in the figure. An outline of the two kinds
of stylets is shown in fig. 6, Plate VIII., from the same specimen, and the dispro-
portion between them is evident, thus confirming the previous statement, that
each apparatus furnishes its own stylets. The central stylet (a) is generally more
slender and acute, as well as longer than the lateral (0), which have a more
globular head than in.the adult. As the specimen increases in age, the dispro-
portion between the two sets of stylets lessens—one or more of the lateral being
equal to the central in size. The long posterior chamber of the proboscis now
contains the peculiar fluid with moving granules, and the reservoir sometimes con-
* It is curious that in the young of Planaria also four eyes should be a common arrangement :
indeed, they are present in some species before the embryo leaves the egg.
5368 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
tracted with force, so as to propel the granules, and even the glandular lining of
the cavity itself, forwards to the front of the basal sac. The superficial granular —
glands of the stylet-region are also well developed.
Some weeks afterwards (and there was no difficulty in preserving them for
this period, even without a change of water) four eyes were observed in the ma-
jority. The head of the worm is distinctly marked in crawling, and the cuticle
richly ciliated, a few longer cilia occurring at the snout and tail. Ciliation is also
very active in the cephalic pits, whose openings are circular; and there is, moreover,
a slight constriction at this point between the two pairsof eyes. The dermal
tissues are well seen, and the ganglia are still relatively large. Every structure
pertaining to the proboscis now shows considerable advancement; and it may be
noted that the posterior glandular organ is wider and shorter in proportion than in
the adult. In each lateral stylet-sac (Plate IX. fig. 13) there are at least three well-
developed stylets, whose heads still appear somewhat more globular than in the —
perfect animal, besides a headless fragment or two. and one or two clear globules.
The normal position of these organs in the lateral pouches seems to be transverse.
The stylet on the central apparatus is completely formed, and likewise has a
somewhat globular head. The muscular cavity (e) is kept in constant jerking
contractions under pressure, while the posterior part (@) is quite still. The other
structures, such as the cells of the digestive cavity, had made corresponding
advancement, but no blood-vessels were apparent. It may be mentioned, in
passing, that the cuticular tissues of these domesticated examples become less
transparent than in the wild forms brought from the rocks, and the examination
of the internal organs is consequently interfered with. In these young animals
also (under pressure) the proboscis generally escaped by rupture at the posterior
end, as in Tetrastemma variegatum, probably by passing through the anus. In
the adult protrusion rarely occurs posteriorly, but almost invariably anteriorly.
The ova of O. gracilis (Plate VIII. fig. 9) are much smaller than those of 0. alba,
and when first deposited adhere together slightly, so that they may be pushed en
masse, but they afterwards lie flatly on the bottom of the vessel. Each likewise
possesses two coats. The vitellus is of a dull yellow hue. Though there is no
doubt the spermatozoa in this, as in other species, rapidly diffuse themselves
throughout a large bulk of water, yet they were applied directly to the ova by
means of a pipette. In about four hours many were adhering to the exterior of
the hyaline coat, others were within this, while a few seemed to have penetrated —
both capsules (Plate VIII. fig. 10). In six hours cleavage had proceeded much
farther, so as to cause many to have the usual mulberry-aspect. In 0. pulchra the
contents of the ovaries are of a beautiful rose-red colour, with a clear spot in the
centre. Each ovisac in the middle of the body contains from twelve to twenty ova,
therefore it is unlikely that this is a viviparous species, unless only a single ovum
happened to be detained in an ovisac here and there, impregnated and developed.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 369
Numerous specimens of Polia involuta, VAN BEN., were sent from St Andrews
in April, loaded with ova, and their development could easily be followed out.
The newly deposited eggs (Plate XIV. fig. 1), are somewhat ovoid, about 545th of
an inch in their long and 45th to ,},>th in their short diameter, and appear to
possess only a single investment. They are not simply enclosed in a sheath, as
M. Van BENEDEN says, but the animal, during deposition, envelopes them and its
body in a tough hyaline mucus, afterwards withdrawing itself therefrom, as in
Borlasia, so that the whole forms a tunnel of mucus, with the ova in its
walls. The spiral condition of some of the masses was due to the coiled condi-
tion of the animal during deposition. After extrusion the ova pass through the
usual stages, and the embryo in each is sometimes ciliated on the tenth day
(Plate XIV. fig. 2), although entire dependence cannot be placed on this date,
since development occurs within as well as without the body of the parent. In
a short time the young are extruded either with a pair of eye-specks, or without
them, and furnished with a very long anterior, and a shorter posterior ciliary tuft
or whip (Plate XIV. fig. 6). Moreover, numerous adult specimens are found
towards the end of April to contain ova with ciliated young, showing that im-
pregnation, as may easily be understood, can take place through the genital
pores. In many of the ova the embryo had two reddish eyes, and some were
extruded from the body of the parent in a free state, so that they sailed about
actively through the water as ciliated pyriform bodies. The ciliation of the
oesophageal region in those with the eyes was very distinct ; indeed, after the other
and apparently more delicate tissues of the animal had become disintegrated, this
region was left in active ciliation—dissected out, as it were, by rapid decay.
This somewhat globular cesophageal region has probably been mistaken by M.
Van BeneDEN for a mouth. The same author fell into the error of supposing
that a form having a smooth outline was developed within its progenitor with
the long ciliary tuft, the former representing the scolev, and the latter the
proglottis; in short, as he says, a case of digenesis, and not a metamorphosis. But
his figure* represents the so-called proglottis as furnished with two eyes exactly
in the same manner as the scolex, yet he neither mentions having seen the one
form inside the other, nor figures this interesting condition. No such mode of
development has ever been seen by me, either in the case of those ova deposited in
the unimpregnated condition, or in those developed within the body of the parent ;
but the same gradual changes ensue in the young of this animal as in Tetras-
temma, and, as will afterwards be seen, also in Cephalothrix.
Many of the parent-specimens having developing young in their interior are
feeble, and almost in a decaying condition inside their sheaths, so that their inert
bodies seem but the nidi for the growth of their progeny, each of which, pro-
* Op. cit. pl. ii. fig. 28.
VOL. XXV. PART II. oB
370 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
vided with two boldly marked eyes, and other differentiated tissues, revolves
rapidly within its capsule. This evolution of the ova in these decaying adults is
a feature analogous to the elaboration of the respective generative products in
the headless fragments of male and female specimens of Lineus longissimus and
others—the last efforts of the parental tissues being devoted to the reproduction
of the species.
In Tetrastemma variegatum the ova are found in the body of the adult in
June and August, and are deposited freely in the vessel. The same changes
ensue in the egg as in the other forms, and the young are found in swarms beside
the adults in the beginning of July and September. These young forms (Plate
‘IX. fig. 15) are so mobile, that one scarce sees the body of the same shape for
two consecutive seconds. The surface is coated with long cilia, by whose aid
they are piloted through the water like infusorial animalcules ; while, in addi-
tion, they are furnished with a single long tuft anteriorly, as described by M.
Van BENEDEN, in the young of his Polia involuta. The cutaneous textures are
not distinguishable as separate layers, and the entire body has a cellular appear-
ance, probably from the individual elements of the digestive cavity and the cuti-
cular areole. No eyes are visible. About a week afterwards considerable
progress had been made in size, but the cilia had become shorter in proportion to
the bulk of the animal; and though the anterior and posterior ends showed a
few conspicuous cilia, the long tuft was absent. There are now four eyes. In
another week the stylet-region of the proboscis is nearly complete, the lateral
often appearing before the central stylets. The usual mode by which the proboscis
escapes under pressure is by rupture peranum. ‘Thus there is a slight divergence
in the development of this species, whose young move freely as eyeless organisms,
each provided with a long ciliary tuft; while in O. alba two well-marked eyes
appear in the young in ovo.
Dr ScuuLrze* first observed that his Tetrastemma obscurum was viviparous.
He likewise stated that, in the development of the proboscis, the lateral stylets
appear before the central, and as the animal grows older, he figures it with two
loose stylets lying in the pit of the proboscis—an arrangement, as he supposes,
for the supply of the central apparatus. I have also seen a loose stylet or two
lying in the anterior chamber of the proboscis, but this occurred both when there
was, and when there was not, a stylet on the central apparatus. The physiology
of the region, as previously explained, demonstrates that there is no connection
between the lateral and central stylets, save perhaps in the composition of the fluid —
with which both are bathed. Prof. Kererste1n} again details the development of
Prosorhochmus Claparediui—a species in which the young animals attain considerable ~
advancement before extrusion, for they are found with four eyes, a well-developed
* Op. cit. p. 65, tab. v. figs. 7, 8, and 9. + Op. cit. pp. 89 and 90, taf. vi. figs, 2 and 3.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 371
proboscis, and other organs, before they leave the body of the parent, and on being
set free have the same general form as the latter. The larger examples are often
doubled within the body of the parent, and apparently invested by the stretched
covering of the ovisac, or in large cavities produced by the coalescing of many
ovisacs; at any rate, it is clear that to describe them (as Prof. KEFERsTEIN and
M. CLapaREDE* have done) as simply within the body-cavity of the worm, is want-
ing in structural accuracy. It is certainly a curious sight to see these large young
animals moving within the body of the adult, apparently without causing the
latter any inconvenience. Such, then, appears to be a further stage of the type of
development seen in certain species (¢.g., Polia involuta, VAN BENEDEN), in which,
after deposition of the majority, a few ova are left in the body of the parent for
subsequent evolution. It remains, however, to be proved whether all the ova in
Prosorhochmus are so developed (in which case they must be very few), or whether
part are deposited at one or different periods or stages, and the rest evolved in
the body of the parent. By the examination of this species, I have been enabled
to confirm many of the excellent observations of Prof. KerersTeIn and M.
CLAPAREDE; but, on the other hand, the determination of the actual position of
the mouth in the same animal shows that it does not deviate from the typical
Ommatopleans, and that the organ is situated not behind the ganglia, as asserted.
but, like the others previously described, quite in front of the commissures.
The mouth, moreover, is the most distinct of any I have examined.
It appears to me that such viviparous species do not form a group swé generis.
but are connected by insensible gradations with the true oviparous forms. Doubt-
less, in the majority, some of the ova only are retained in the ovisacs, impreg-
nated by the ubiquitous spermatozoa through the genital pores, developed in the
sacs, and space afforded for the growth of the young animals by the stretching
or rupturing of the membranous walls of the latter. It is a very interesting fact
in connection with this subject, that Prof. Kerersrein+} has lately discovered a
Hermaphrodite Nemertean (Borlasia hermaphroditica) at St Malo, in which the
anterior sacs were found full of mature spermatozoa, and the. posterior distended
with developing ova. This can only be explained in one of two ways—either
that the species is truly a hermaphrodite one, or that the spermatozoa are passed
from the body of a male (in apposition) into certain sacs of the female through
the genital pores, there to remain until the other contents of the female generative
organs are evacuated.
BORLASIA.
Cuticular Tissues.—The skin in this group, for which Borlasia olivacea may
be taken as the type, is allied in structure to that of Ommatoplea, though
in the living animal its condition is frequently rendered obscure by the much
* Beobachtungen iiber Anat., &., p. 23.
t Ann, Nat. Hist., 4th ser. vol. i. 1868, p. 229; and Archiv fiir Naturges. 1868.
3712 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
greater development of pigment. The body is everywhere covered with cilia,
which are most active in the lateral fissures, but longest on the papille of
the snout. They may be seen in active motion under a lens in good light.
Sometimes the motion of the cilia in the lateral fissures is suspended, and again
set agoing, without evident cause. Dr WILLIAms first asserts that the cilia are
confined to the dorsal half of the body,* and then seems to contradict himself by
saying farther on that the whole body is ciliated.+ The latter, as above-men-
tioned, is the correct view. k
In the living animal the cutis has a cellular aspect (Plate IX. fig. 4), the cells
or areolee measuring +,)9th of an inch or more, and most distinctly seen towards
the tip of the tail in the adult. Sometimes a number of minute clear granules are
observed overlying the larger cells, as shown at the lower third of the figure. The
pigment-cells and granules reach their greatest development anteriorly, and some
of the former contain very dark brownish black pigment in circumscribed masses.
The dorsal pigment has in general a longitudinally streaked appearance (Plate
IX. fig. 5), a state probably due to the peculiar arrangement of the fibres of the
external muscular layer hereafter to be described. In some pale red specimens
the coloration is observed to be due to a uniform impregnation of the cutis, and
the tint is much deeper than that of the ganglia, which are thus rendered
conspicuous by their pallor. Occasionally one or two pigment-cells of exception-
ally large size are present anteriorly (Plate IX. fig. 6), and there were three clear
granules in the larger of the two figured. The cuticular cells are finer in Borlasia
lactea, Mont. MS., and the body is not clouded by the granular pigmentary
matter. The superficial arrangement in Meckelia annulata (Plate IX. fig. 7) is
similar, though the cells or areolz are smaller, and the pigment-granules do not ©
form themselves into streaks.
There are three tactile papillz on the snout, one of which, from its situation,
falls to be described with the opening of the canal for the proboscis. The other
two are placed on each side of the central (Plate X. fig. 1), but are not always so
prominent. Each is furnished with a series of cilia of greater length than those
on the general surface, and which extend from the erected papilla in a radiating
or fan-shaped manner. They are probably of great tactile service to the worm.
Prof. KErERsTEIN refers to a “transverse” tactile papilla on the snout of his
Cephalothrix longissima, which differs from those usually seen in Borlasia, and
resembles a slight pouting of the lining membrane of the canal for the proboscis.
Under pressure granular masses and globules of mucus resembling oil are ex-
truded from the skin, as in Ommatoplea, and often congregate round the borders of
fresh transverse sections. But, while in Ommatoplea there are only the ciliated and
structureless epidermis, a single layer of cutis-cells and the basement-layer, before
* Report Brit. Assoc. 1851, p. 171. t Op. cit. p. 243.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 373
the circular (external) muscular fibres are reached, in Borlasia the structure of the
dermal layer is more complicated. Fine tranverse sections of B. olivacea demon-
strate that underneath the ciliated epidermis (c, Plate XI. fig. 8), a somewhat
thick layer (¢d) composed of granular cells and globules in areole, occurs. From
the facility with which these contents escape, the drawings show the parts in a
slightly altered condition. Beneath this lies a pale structureless basement-layer
(d’), the presence of which in Cerebratulus had misled Prof. KrrersTer into the
idea that it was a layer of circular muscular fibres ; but an attentive examination
of that genus, as well as the present, demonstrates that, while one may be
deceived if only transverse sections are made, no doubt can exist in longitudinal
sections. This point may readily be settled without reference to the more
explicit, because larger, condition of the parts in the great Lineus longissimus.
A thick compound layer is next encountered in B. olivacea, consisting externally
of pigment-granules and cuticular globules (d”), and internally of a series of
powerful longitudinal muscular fibres (¢). Under a low power, indeed, this com-
pound layer in transverse section appears as one, the pigment and other cells,
and the cut ends of the muscular fibres, presenting a similar aspect. The amount
of pigment varies of course in different specimens, and is always much more
developed dorsally than ventrally. Towards the anterior end of the animal this
layer of the cutis (d”) becomes thicker, and its reticulations more distinctly
marked. Fine longitudinal sections of the snout from above downwards show
superficially a series of very beautiful reticulations of a somewhat regular aspect,
the chief interstitial bands having a longitudinal direction. ‘Towards the tip of
the snout the texture becomes denser in transverse section (Plate X. fig. 4), and
the pigmentary matter increases, especially just within the pale external layer of
the cutis. A section still further back (Plate XII. fig. 2) exhibits a less dense
arrangement, and the pigment is now for the most part grouped into a dorsal and
ventral band. The general stroma consists of radiating and longitudinal fibres,
the cut ends and granular matter being often situated in the axils of the radiating
series. The pigment anteriorly attains its greatest density immediately beneath
the pale external layer of the cutis, diminishing in quantity from this point
inwards. The snouts of these mobile animals resemble in structure the elaborate
arrangements which are sometimes met with in certain organs (such as the
tongue) in the higher animals, where extensive and delicate motions are combined
with great tactile power.
In Cerebratulus bilineatus,* the arrangement of the two white median dorsal
stripes is characteristic, for the pigment is strictly confined to the region cor-
responding to d” and ¢ in Borlasia; and in transverse section they appear as
two patches with an intervening pale space, bounded anteriorly by the basement-
* Gordius tenia, DALYELL, Pow. Creat. vol. ii.
VOL. XXV. PART II. DC
374 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
layer of the pale exterior coat, and internally by the circular muscular fibres. In
transverse section the cutis of Meckelia annulata contains rather small cells
(Plate XIV. fig. 11), which retain much of their ordinary shape after mounting.
The characteristic opaque white dorsal and lateral pigment-stripes pass through-
out the entire thickness of this tissue, while the white touches on the sides that
apparently correspond with the openings of some of the ovaries or sperm-sacs do
not traverse the entire thickness, but lie towards its inner border.
The skin in many of the Borlasians, ¢.g., Zineus longissimus, Borlasia olivacea,
B. octoculata, B. lactea, Micrura (Stylus) purpurea and M. fasciolata, gives a
marked acid reaction when tested with litmus-paper.
Muscular Coats——The longitudinal muscular coat (¢), which is incorporated
with the former cutaneous layer at its commencement, is thick and powerful,
and has a well-marked fasciculated aspect in transverse section. At the sides of
the mouth, where this coat attains great development, and forms a strong lateral —
support, there is a very pretty radiated or somewhat arborescent arrangement of
the interfascicular substance on transverse section (Plate XI. fig. 1, 2). Sucha
condition would permit great stretching in all directions without actual separation
of the muscular bundles, and is thus eminently adapted for the functions of the
parts. The intimate connection of the outer fibres of this layer with the adjoin-
ing coat is well brought out in some superficial longitudinal sections of the body, —
which show the outer bundles of fibres quite separated from each other by rows
of pigment and other cells and granules,—the whole having a curiously streaked
appearance. Anteriorly this longitudinal layer becomes lost in the tissues of the
snout. The next coat (¢’) consists of a series of circular muscular fibres of con-
siderable thickness, and it is between this and the former that the nerve-trunks
are situated. It passes by the sides of the ganglia, and appears to merge into
the wall of the passage for the proboscis in front of these organs. In Cerebra-
tulus bilineatus this coat is decidedly thicker than usual, a condition which may —
be connected with the somewhat rounder form of the body generally in the species.
Within the last-mentioned coat is a layer (e’).of longitudinal muscular fibres,
similar in structure to the corresponding stratum in Ommatoplea. Like the —
former the fibres pass the ganglia to become connected with the muscular channel
for the proboscis in the snout.
Certain peculiarities are observable in the dermal tissues of the large Lineus
longissimus (Borlasia anglize, QUATREF.), and since this species has been taken as”
the type of the Nemerteans by M. pE Quatreraces and others, it is necessary to
enter somewhat minutely into the anatomy of the parts, as shown in the trans-
verse and longitudinal sections (Plate XI. figs. 6 and 7). The external cuticular
layer (d) is proportionally thinner than in the common species. The pigmentary -
layer \d’, d’) is divided by a definite black band (2), and is distinctly separated
from the first or external longitudinal muscular layer. by a curious translucent
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 315
stratum (3, 3), which in transverse section (fig. 6) has a transversely barred
arrangement with linear interruptions, which divide it into numerous and some-
what regular elongated spaces. In longitudinal section, again (fig. 7), this
stratum has a wavy aspect, or, if much contracted, presents a series of moniliform
streaks. That this layer, however elastic, is not muscular, a glance at the
position of the parts in fig. 7 at once demonstrates. It belongs entirely to the
cuticular elements, and with the interior pigmentary layer corresponds to the
region d” in B. olivacea, which, in the larger species, attains much greater per-
fection, and becomes distinctly separated from the longitudinal muscular fibres.
The only peculiarities in the muscular coats consist in the very evident transverse
streaking of the external longitudinal layer (fig. 7, ¢), and in the presence of
certain parasitic (?) cellular masses in it and the next outer layer. These masses
lie in definite spaces, and consist of groups of rounded cells filled with granules.
In the contracted state of the animal, as after preservation in spirit, the fibres of
the circular coat in longitudinal sections are grouped in a wavy manner (¢, fig. 7),
apparently from the extreme shortening of the parts.
In the arrangement of the muscular system of the body-wall the curious
specimen from Balta is distinguished from all other British forms yet encoun-
tered. Externally (Plate X. fig. 2, d’), beneath the basement-layer of the cutis
(which in the fragmentary specimen was almost absent), there is a layer of cir-
cular fibres (¢’).. Within the latter is a very powerful layer of longitudinal fibres
(é), which (layer), however, is not continuous, as in Ommatoplea and Borlasia,
but has at least one very distinct point of separation. Upon approaching the
middle line of the dorsum in transverse section, this longitudinal coat becomes
thinned off, so as to end on each side of the centre in a blunt point. In addition,
there is a somewhat triangular portion (ea) cut off by interfascicular substance
and fibres. The dorsal curve of the proboscidian sheath is closely applied to this
central point of separation, apparently receiving therefrom a few fibres, which
retain it in position, while other fibres pass downwards to join the circular layer
(ja), which here encloses the space for the digestive tract. The separation of the
great longitudinal layer of the body-wall is marked externally by a distinct
median line, which is rendered more conspicuous by the occurrence of the trans-
verse strize of the dorsum on each side of it. There is also a slightly marked
fissure of this muscular coat inferiorly. This arrangement therefore conforms to
the Meckelian type, as seen in MW. annulata, in which there are two muscular coats,
with intermediate lateral nerve-trunks. The deviations from the ordinary aspect
in the Zetlandic specimen may prove to be accidental.
The elaborate system of muscles in the body-wall of these worms enables them
to perform the most varied and complex motions, so that they have not inaptly
been compared to a piece of living caoutchouc. When irritated, the larger species,
such as Borlasia lactea, Mont., and the true B. octoculata, suddenly contract in a
376 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
spiral manner like a cork-screw or the stalk of a Vorticella, or twist their bodies
into a rope of various strands. The great Lineus longissimus may now and then
be observed in its native pools extended between the Fuci of opposite sides in
numerous loops, each several yards in length, and so intricately arranged, that —
they can scarcely be unravelled by other than the animal itself. The extreme
stretching which the body undergoes before it snaps—as in attempting to secure
a specimen in an intricate and inaccessible pool—and the extraordinary shorten-
ing on immersion in spirit, are only well-marked conditions into which the animal
throws its yielding textures at will. A Micrura, again, from the deep water of
St Andrews’ Bay, swims freely on its edge like a fresh-water Nephelis, or its own
ally O. pulchra, lashing the water with alternate strokes of its muscular and flat-
tened posterior extremity. Sir J. G. Datye.t likewise noticed this edge-motion
in his great “ Gordius” fragilis, but he was not sure whether it was a natural —
condition, or caused by the confined vessel. Meckelia annulata forms in captivity
a beautiful silky sheath by its cutaneous secretions, within which it lies in com-
parative security, until, tempted perhaps by love of change, it searches for a fresh
site, whereon to manufacture a new chamber for its protection. In unhealthy —
and slowly dying animals the skin becomes raised into pale bullze, not only from
corrugation, but from degeneration of the cutaneous textures.
The posterior end of the body in Micrura(Stylus) requires special mention, since
there is superadded a peculiar elongated and contractile style. This appendage
seems to be formed by a prolongation of the cutaneous and part of the muscular
(longitudinal and circular) textures of the body-wall of the animal. The entire
organ in contraction has a granular appearance, the coarsest granules, and occa-
sionally a few circular masses of brownish pigment, being at the tip. Within
these coats is a central chamber, which undergoes various alterations in size, and
contains a transparent fluid. This cavity is not connected with the digestive
tract, which opens by a terminal pore at the base of the process, nor can pro-
boscidian discs be seen therein. I have not as yet ascertained with what system.
it communicates, but its connection with the circulatory appears most probable.
The style is richly ciliated externally, and undergoes many and varied motions,
now forming a verrucose knob, now stretched to an extreme degree of tenuity,
and apparently assisted in the latter action by the fixing of the tip, whose warty
formations seem to perform the functions of suckers, for the animal may be
observed crawling about with a loose style, then the tip of the latter suddenly
becomes fixed upon the clean and smooth glass, and the whole organ is elongated
accordingly. The fixed portion at the tip is usually more dilated than the suc-
ceeding part of the style. +
In Cephalothriz, rst. (including Astemma), the dermal tissues, and indeed
the entire body-wall, deviate from the ordinary structure in Ommatoplea, Bor
lasia, and Meckelia; and while the minute anatomy of this genus bears out th
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 3/7
distinctions—based on external characters, and the form of the nerve-ganglia—
given by Prof. KerersTEIN, its independent position can be more satisfactorily
demonstrated. Externally (Plate X. fig. 3) there is the usual ciliated coating,
whose action is most vigorous in the cephalic region. The cutaneous textures are
exceedingly transparent, the pigment, if present, being only developed at the
snout in front of the ganglia as a rose-pink or reddish shading within the super-
ficial cuticular layer of the parts. The cutis (d), composed of the usual granular
cells and gelatinous matter in areole, has along its inner margin a trace of a trans-
lucent homogeneous basement-layer. A very thin layer of circular fibres (¢’) comes
next, the exact structure of which is best demonstrated in the fresh animals, after
the addition of a little dilute acetic acid. The fibres are also evident in fine longi-
tudinal sections, but are not satisfactorily seen in transverse sections on account
of their tenuity. Beneath this lies a very powerful longitudinal muscular coat
(e’), the cut ends of the fibres having the usual fasciculated appearance, the inner
being somewhat coarser than the outer. At each side a distinct increase occurs at
the region of the nerve, where the coat is separated into two portions by a septum
of fibres from the circular coat, the nerve lying in the line of demarcation. This
arrangement is quite characteristic, and the position of the nerve-trunk probably
points to the compound nature of the great longitudinal layer, viz., as analogous
to the two longitudinal layers in Borlasia, the circular muscular coat cutting off
only the lateral portions (¢), instead of dividing it completely. This genus shows
the mobility of the race even in a greater degree than the others. In crawling
about the long yielding snout is used as an exploratory or boring organ, which it
stretches hither and thither with ceaseless energy, and by its aid is able to push
aside its own mobile body in any direction; while through any narrow loop of
mucus the latter is drawn like a thread of semi-fluid, yet coherent substance.
These animals also progress readily on the surface of the water. When tested with
blue litmus-paper the skin of Cephalothrix gives a most vivid red stain.
DELLE Cut14Je’s* description of the structure of the body-wall, if applied to the
Ommatopleans, is correct enough, viz., that there is an external layer of circular
fibres and an internal longitudinal coat; hence the criticism of M. Dz QUATREFAGES
requires qualification. The Polia siphunculus, D. Cu., however, seems to have
been a Borlasian, judging from the large triangular slit which lies at a consider-
able distance behind the snout. H. Raruxe} gives Borlasia striata two coats,—an
epidermis, and a corium,—combining under the latter both the pale and the pig-
mentary layers of the skin. He has omitted to notice the external longitudinal
muscular layer, and mentions only an outer circular and an inner longitudinal
muscular coat. It is somewhat difficult to comprehend the views held by M. bE
QUATREFAGES with regard to the same structures, since his descriptions and
* Memorie sulla storia, &c., vol. ii, 1825.
+ Neueste Schriften der Naturforschenden, &c. p. 95, 1842.
VOL. XXV. PART II. 5D
378 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
figures do not seem to coincide with each other. He divides the skin into three
coats, viz., the ciliated epidermis, cutis, and the fibrous coat. Moreover, the cutis
has two layers—an outer, formed of a homogeneous transparent substance, pre-
senting in its mass a number of cells or simple rounded vacuoles refracting the
light, and an inner, of large elongated cells in a double row; but in his figure* —
the muscular elements occupy a bulk so insignificant that some error appears —
to have been committed, especially as the third layer of the skin is stated to be
a transverse fibrous one. It is at all events difficult to see how the enlarged
transverse section just noted agrees with his figures iv. and v., pl. 18. Two mus-
cular coats only are described by this author—an external longitudinal and an
internal circular—the internal longitudinal being omitted, or rather considered as
an aponeurotic layer. He also commits a serious error in affirming that the
structure of the dermal tissues in Ommatoplea corresponds with that in Borlasia
anglie. Frey and Leucxart likewise describe only two muscular coats—an outer
longitudinal and an internal circular. Prof. Krrersrein,} while representing
the cutaneous textures of Cerebratulus (a Borlasian) with greater accuracy, also
falls into the mistake of applying what he found in this animal to all the Nemer- —
teans. He describes the skin as composed of two coats,—a cuticula covered with
cilia, and an inner thick, finely granular coat which contains the pigment,—a
definition which is scarcely comprehensive enough for the nature of the parts in —
such as Lineus longissimus. He mentions the occurrence of crystals of the form
of arragonite in the pigmentary layer of Cephalothriz ocellata, but such have not
been seen in the British forms, except under the action of chemicals, or after the
evaporation of the salt water. His statement, that in Cerebratulus marginatus
there are four muscular coats—an external circular under the pigment-layer of
the cutis, a longitudinal, a circular, and lastly an internal longitudinal—has
already been noticed. No more than three muscular coats are present in the
Borlasians. Lastly, Dr ANTON ScHNEIDER, in his remarks on the muscles of —
worms, and their importance in the system,{ states that in Nemertes the follow-
ing layers occur :—Circular, longitudinal, and circular, besides radiating muscles
—a description that is unsatisfactory as regards the British species.
Cavity of the Proboscidian Sheath.—This forms a shut sac, as in Ommatoplea,
from the bridge of the ganglionic commissure to the posterior end of the worm.
The long proboscis glides smoothly in this chamber, whose walls are united with
it and other tissues just in front of the commissure. The other contents are the
clear proboscidian fluid and its discs. The latter are circular granular bodies,
similar to, though smaller than, those of Ommatoplea, and when seen on the
edge present a fusiform outline, having a swollen middle and two tapering ends
There are also a few small granules and granular cells. ‘The muscular wall of
*Opcut (pl, XX, ee le + Op. cit. pp. 66-68.
{ Miiller’s Archiv fiir Anat. 1864, p. 595.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 379
this chamber and other points agree so closely, both structurally and function-
ally, with the same parts in Ommatoplea, that it is unnecessary to describe
farther than refer to the aspect of the parts in the living animal (Plate X. fig.
1, 0); and to the various transverse sections, in which the wall of the chamber is
lettered 0, and the cavity ao. Sometimes near its diminished posterior end the
latter shows a series of moniliform spaces, from internal bridles, and often does
not quite reach the tip of the tail either in this group or in Cephalothriz. In
Meckelia annulata the proboscidian sheath is not continued to the tip of the tail
either, and it is an interesting fact that this absence coincides, as in the last-men-
tioned genus, with greatly enlarged lateral vessels. In Cephalothrix the chamber
presents certain peculiarities, being subdivided by transverse bands of contractile
tissue throughout its entire length, so that during the motions of the worm the
anterior region is occasionally thrown into a series of moniliform spaces. These
contractile septa (though imperfect in the middle), doubtless prove of much ser-
vice during rupture—an occurrence so liable in this lengthened animal. More-
over, the wall of the chamber is thin, and the circular muscular fibres of the
body not much developed; hence the advantages afforded by these safeguards
against the inconvenient bulging of the chamber during the motions of the worm.
The transparent liquid of the cavity in this genus (Cephalothrix) contains flask-
shaped bodies and minute clear corpuscles.
Prof. KEFERSTEIN* seems to have had no definite idea of this chamber as a
cavity with special muscular walls, but speaks of the peculiar discs as floating
in the body-cavity (Leibeshohle)— an error of some importance. In his two trans-
verse sections of Cerebratulus marginatus, he appears to have confounded the
wall of the tunnel with that of the proboscis. He is thus less correct than his
predecessors Frey and Levcxart,} who noticed the sheath of the proboscis and
its contents.
Terminal Aperture in the Snout for the Proboscis.—A channel, ciliated for some
distance, leads inwards from the terminal pore to the reflection of the proboscis
just in front of the commissures. This channel, shortly after its commencement
(Plate X. fig. 4, a), is surrounded by an elaborate series of muscular loops
(indicated at 2), which, while keeping it closed under ordinary circumstances,
permit of rapid and easy dilatation. Immediately within these is a series of
longitudinal muscular fibres, which attain a more distinct development some-
what posterior to this point (a, Plate XII. fig. 2). A very beautiful group of
circular and diverging fibres lies to the outside of the first-mentioned series (2, in
the last-mentioned figure), crossing each other in a striking manner superiorly
and inferiorly, as well as less distinctly at intermediate points, and forming with
the longitudinal and other fibres the intricate stoma of the snout. The terminal
* Op cit. pp. 68 and 69. + Beitrige zur Kenntniss, &c. p. 70.
380 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
pore is furnished with a prominent papilla, covered with a fan-shaped brush of
cilia, the whole being only occasionally extruded, and no doubt assisting the
papillae previously mentioned in the tactile functions of the snout. This central
papilla is sometimes bilobed, and each of the divisions supplied with cilia. In
spirit-preparations of large examples of Lineus longissimus the proboscidian
aperture is distinguished by a slight slit on the inferior surface immediately
behind the tip of the snout. | :
Proboscis.—The proboscis (Plate X. fig. 1, @) commences as a somewhat
slender tube just in front of the commissures, gradually enlarges, continues for a
considerable distance of nearly equal calibre, and then, diminishing, terminates
posteriorly in a long muscular ribbon (, sometimes bifid), which, curving
forwards in the ordinary state of the parts, becomes attached to the wall of the —
proboscidian tunnel. Its cavity is continued in front into the canal of the snout,
and posteriorly terminates in a cul-de-sac at the commencement of the muscular
ribbon. It differs from the Ommatoplean organ in certain respects, such as the
absence of the stylets, its more slender proportions, and the shape of the glandular
papillee on its internal surface. Experience, indeed, generally enables the observer
to distinguish by external characters the proboscis of a Borlasian from that of an
Ommatoplean in spirit-preparations, by the abrupt diminution of the calibre at
the posterior portion in the latter, caused by the presence of the stylet-region and
swollen reservoir; but even where the organ is incomplete, a transverse section
at once puts the question beyond doubt. This was illustrated in a well-preserved
though shrunken fragmentary specimen brought by Mr Gwyn JErrreys, the
distinguished conchologist, from North Unst, Shetland. At first sight it looked
like a Borlasian organ, on account of the absence of the stylet and posterior
regions, and from its large size I thought it would demonstrate the structure in
that family favourably, but a transverse section gave a true Ommatoplean
anatomy, with the characteristic beaded and other layers; and an examination of
the animal itself at once confirmed its relationship. In the living animal the organ
is proportionally longer than in Ommatoplea, and when cast off becomes thrown
into numerous screw-like coils. Thus do the two great groups of soft worms q
differ in essential characters; and we are taught how unsafe is that classification, —
é.g., such as SCHMARDA’Ss,* which proceeds on other than anatomical grounds.
A transverse section of the proboscis of a Borlasian (M/zcrura) from St Andrews
is represented in Plate XII: fig. 1. Externally there is a coat (a) similar to that |
in Ommatoplea, apparently composed of homogeneous elastic tissue, yet showing —
some granular markings towards its outer border. This coat is tougher than any
of.the others, and often retains its integrity after they have ruptured. A powerful
longitudinal muscular layer (0) lies within the former, its cut fibres in transverse
* Neue Turbel. Rotat. und Anneliden, vol. i. pt. 1, 1859.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. o8l
section having the same histological characters as in Ommatoplea. At opposite
or nearly opposite poles of the circle, however, a remarkable interposition severs
the continuity of the layer (as seen at g,g’). At one pole, two symmetrical
bundles of fibres spring from the succeeding circular layer, and, slanting out-
wards, cross each other in such a manner as to disconnect the longitudinal coat
just mentioned, and for a portion of its circumference wedge it between two
bands of circular fibres. The outer or oblique bands of circular fibres become
lost in the external coat of the organ. The longitudinal layer (0) is thus
diminished to a blunt point on each side of the crossing of these peculiar fibres,
and a region is formed externally which is occupied by a special and somewhat
lozenge-shaped group of longitudinal fibres, through which the dotted line g
passes. The longitudinal layer, especially near the wedge-shaped ends (where
the fibres are often grouped in a thicker mass in these preparations, is marked in
the centre by a faint linear streak, as if composed of two layers, but this does not
continue all round, and is not apparent in every specimen, nor in B. olivacea.
At the other pole there is a variation in this arrangement, for it is found that an
elongated portion (g’) is cut off without apparent crossing, the ends of the great
longitudinal coat (>) being widely apart. It generally happens that towards this
side the bulging of the contracted organ occurs, and, it may be, such forces the
edges of the longitudinal coat apart, and aids in causing the above appearances;
but it would not account for them all. In contraction this coat is sometimes
thrown into a silky belt of regularly waved fibres. Within the longitudinal layer
is an equally powerful belt of circular fibres (c) which, at opposite poles in the
transverse sections, gives off the peculiar oblique bands previously mentioned.
A basement-layer (d), better marked in this species than in the common form
(B. olivacea), is situated on the inner surface of the latter. There is also present
in this species an incomplete belt of longitudinal fibres (¢) within the basement-
layer, and which is not evident in the species just mentioned. Attached to the
inner surface of the basement-layer, or in the latter case partly to the incomplete
longitudinal layer, is the glandular mucous coat (/), which, from lengthened
preservation, has in this case become somewhat altered. The glandular bodies
are scattered chiefly towards its inner or free surface. In fresh preparations, 7. ¢.,
in those made from the organ immediately after extrusion from the living animal,
a very pretty radiated arrangement of this coat is constantly observed, as if a
series of explosions had occurred in the mucous substance so as to scatter the
globules and gelatinous bands in a fan-shaped manner. Indeed, the aspect
resembles thick and graceful tufts of grass with large spikes, for the granular
glands are mostly at the tips of the streaks of mucus, a state doubtless due to
their passage outwards under compression. Prof. KrererstTeIn* figures this in
* ‘Op. cit, tat. v. fig. 16.
VOL. XXV. PART II. Sm
382 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
Borlasia splendida, but he does not refer thereto in his descriptions. In the fresh _
specimen it is found that the glandular papille are much smaller than in Omma- —
toplea, and widely different in shape (Plate VI. fig. 10, and Plate X. fig. 5), the
former representing them in the extruded proboscis, the latter as viewed from
without. Under ordinary circumstances they appear to have an ovoid shape,
and to vary from ;,/55th to zo5th of an inch in size. Under pressure they
become either flattened circular bodies or assume an elongated and slightly
barred aspect; and, after escape into the surrounding water, the contents are
club-shaped or rounded (Plate XIII. fig. 9).
The usual crossing occurs at one of the poles of the circular section of the
proboscis in Lineus longissimus (Plate XIV. fig. 8), but the separated piece at the
opposite pole is somewhat larger than in B. olivacea. Like the latter, it also has no
inner longitudinal fibres grouped exterior to the mucous layer. In the remarkable
form* dredged in 50 fathoms off Balta by Mr Jerrreys—and the structure of whose
body-wall coincided with the Meckelian type rather than the Borlasian—the
proboscis proceeded backwards from the tip of the snout in the usual manner, but
instead of the posterior end diminishing insensibly into the long muscular ribbon,
the organ divided into two nearly equal trunks (Plate XIV. fig. 12), each about as —
large as the entire portion, and terminated in a somewhat abrupt and swollen
end, from which the long muscular ribbon proceeded. The wall of this peculiar
proboscis, so far as I could make out from the single and rather unfavourable
example, had the following structure :—Externally there was a circular layer
which showed a few granules on the outer margin in transverse section; within
this lay a powerful and apparently continuous longitudinal muscular coat, from —
whose inner surface the granular papillary mucous lining projected. The inner
or free margin of the latter was comparatively smooth, a result probably due —
to the minuteness of the papillze. Each of the forked portions had the same struc-
ture as the anterior region, and the thick longitudinal coat, after bending inwards
at the posterior end of the swollen termination, became continuous with the
muscular ribbon. The proboscis thus differed from the ordinary Meckelian form
in the bifurcation, and in having no distinct circular coat within the longitudinal.
It had no closer analogy with the Borlasian or other type.
In Micrura (Stylus), a true Borlasian, the organ is furnished with somewhat
slender papillee, which, under pressure, became lanceolate and pedicled, fusiform,
or rounded with granular contents. When viewed laterally. the rounded or —
flattened papille that formerly seemed granular appear to be composed of a series
of minute rods set closely together. In some of the elongated structures, how- —
ever, under pressure, the striz are longitudinal. When extruded from the organ
into the water the elongated bodies in the papillee cling together in some instances
like fibrille, and their appearance in the prepared specimens is quite charac-
* See p. 375.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 383
teristic, the inner or free surface of the coat being covered with a vast number
of these elongated glandular structures. These are the baccillary bodies described
by Dr Max. MU.uer,* but I have never observed in the British species any of the
urticating organs mentioned by this author. The minute structure of the wall
of the proboscis agrees with that in Borlasia, only the lozenge-shaped portion
(g, Plate XII. fig. 1) in some specimens was longer than in B. olivacea, from the
more gradual slanting of the fibres to the exterior.
In Cephalothriz the papille of the proboscis are acicular, and they are longest
towards the anterior part of the organ (Plate XI. fig. 9). In transverse section
the walls present a simpler structure than in Borlasia; and, though in the living
animal an external circular and internal longitudinal muscular coat are apparent,
the tissues become so confused after mounting, that I have not yet satisfactorily
unravelled them.
Under the action of powerful ‘irritants, such as alcohol, the animal detaches,
in its spasms, both the anterior and posterior connections of the proboscis at
once, so that the extruded organ remains in its ordinary condition when expelled.
and is not turned inside out. In Cephalothrixz, again, it sometimes ruptures near
the ganglia, and is drawn backwards by the ribbon of attachment and its own
elasticity; and the animal seems to be unaffected by the injury, which regeneration
soon repairs. I have never seen the worm use the proboscis for any purpose:
and though M. Van BENEDEN has observed it extruded in his Cerebratulus @rstedit
(which is only DaLYEL’s Gordius tenia), and threatening its prey, I fear it could
not do much harm. The life-like vermicular motions of this muscular tube, both
in situ and when cast off, have misled Mr Breartie} and others, so that they
have described the organ as a young animal, and the possessor as viviparous, or
else have considered the expelled portion a parasite. This is at once apparent
on examining Mr Breartie’s specimen of the supposed young animal in the British
Museum.{ The proboscis is reproduced in the same manner as in Ommatoplea ;
and the discarded organ, if not ejected, may be seen floating in the proboscidian
eavity amidst much granular debris. Sir J. Dauye.u§ states that the usual
colour of the proboscis in Lineus longissismus is vivid red; our specimens have
generally had white or faintly pinkish organs.
M. Van BENEDEN|| does not mention the tissues to which the muscular
retractor of the proboscis is attached in his Nemertes communis, and speaks of it as
suspended freely in the cavity of the body, like the digestive tube of the Bryozoa.
A further remark with regard to the organ in Cerebratulus Mrstedia (G. tenia,
* Observat. Anat. de Vermibus quibusdam Maritimis, Berolini, 1852.
{+ Ann. Nat. Hist., 1859.
¢ Dr Bairp, in describing Serpentaria Berryi, n. sp., also alludes to the very common practice
of ejecting the proboscis-(not the alimentary canal) after immersion in spirit, It is a habit common
to all the Nemerteans.— Proceed. Zool, Soc. Feb. 12, 1866.
§ Pow. Creat. vol. ii. || Op. cit. p. 10.
384 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
-DALYELL) makes his error still more apparent, for he says, “‘ Toute la trompe se
meut librement dans la cavité intestinale.’* Prof. KrrERSTEIN gives a small —
figure} of a transverse section of the organ in Cerebratulus marginatus turned
inside out; but, though he indicates the lozenge-shaped space formed by the
crossing of the fibres, it is misplaced on one side, and the entire figure is too
indistinct for reference.
Digestive System.—The mouth in Borlasia olivacea is a longitudinal fissure
on the ventral surface, situated a short distance behind the ganglia, and varying ©
in size according to the motions of the animal, and the degree of contraction or
relaxation. Its ordinary appearance under examination is represented in Plate X. —
fig. 1, w. Certain broad pale lines radiate from the lips of the fissure (which lines
in dark specimens are generally pale), an arrangement which led Dr G. Jounston
into the error of considering it a nerve-ganglion and branches. These radiating —
lines or folds are due to the same structural cause as those in the ciliated ceso-
phageal region of Ommatoplea—viz., prominent longitudinal rugze of the thick
glandular texture of the organ, which, in this case, permit great dilatation of the
parts during ingestion. The number of these ruge varies, as may be observed
by a comparison of the figures. In Borlasia lactea, Mont. MS., the mouth is
situated very far back, leaving a long space between it and the ganglia. In
Cerebratulus, again, the aperture is a longitudinal slit, somewhat less marked
than in Borlasia. The mouth leads into a great ciliated cesophageal chamber (7),
which commences anteriorly as a cul-de-sac behind the ganglia and cephalic sacs, —
and nearly closing in by its anterior wall the vascular lacunz there, while it may
be said to terminate posteriorly at a distinct incurving of its wall, by becoming
continuous with the digestive cavity-proper. In the transverse section (Plate XI.
fig. 1), the anterior part of this chamber is seen under favourable circumstances, ©
as a thickly folded glandular mass (7), with the ventral slit (z) leading quite
freely into it. The cavity has not yet attained its full size, and the mouth is
severed at its anterior border. Superiorly, a large space is occupied by the pro-
boscidian sheath (a), and the great lacunee (s,s), and indications of some other
vascular meshes are seen at the sides. The lips of the mouth (w) curve inwards, ©
and gradually merge into the ciliated glandular texture of the cavity. A little”
further back the glandular substance becomes confined to the inner surface of
the body-wall (though actually not closely applied thereto), leaving a large
central space. In full perfection the chamber and glandular texture are seen in
Plate XIII. fig. 6. The minute structure of the wall of this portion of the
digestive cavity is similar to that of the ciliated cesophageal region in Omma-
toplea, being composed of a thick layer of granular gland-cells and basement-
substance, raised here and there into prominent ruge, and richly ciliated on the
E Op. tit. pe le + Op. cit. taf. vii. fig. 5.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 385
inner surface. The turning in of the borders of the region is an interesting cir-
cumstance, and demonstrates the distinction between it and the succeeding
region, even from the earliest condition of the worm, without for the moment
regarding the other cardinal facts relating to the peculiar arrangement of the
circulating channels on the walls, the thicker texture of the latter, and the total
absence of the gregariniform parasites. Moreover, it is only in this region that
the ciliated character of the digestive cavity is apparent, probably because the
greater firmness of the walls keeps the chamber somewhat distended. In certain
lateral views of the animal, the distinction between the cesophageal and the suc-
ceeding region is very evident.
Though in the various drawings of transverse sections of Borlasia this chamber
(cesophageal) is seen in its normal condition, it is well to remember that
it undergoes very marked alterations in size, according to the condition of the
proboscidian cavity in its vicinity, for the proboscis most readily distends the
latter in this region, and bulges it so much that the walls of the former are
pressed flatly together at the ventral surface. In the contracted condition of
the worm, as after immersion in spirit, the communication between the cesopha-
geal and the succeeding portion of the digestive system is almost obliterated by
firm closure.
The second or great division of the alimentary tube extends from the point
of inflection previously mentioned to the posterior end of the worm, as a ciliated
chamber with glandular and sacculated walls; but the cilia, with the exception
of a streak near the tip of the tail, are only favourably seen on making a trans-
verse section of the living animal, though they are actually longer and more
active than those on the cuticular surface. In pale species, such as Borlasia
lactea, Mont. MS., the digestive canal is very distinctly divided, for the posterior
region is not only more opaque than the oesophageal, on account of the greater
development of its glandular elements, but its borders are crenate from the sac-
culations. The posterior aperture or anus is situated slightly in front of the tip
of the tail, and is well guarded by the muscular structures surrounding it, as
may be observed before granular matter escapes, for it requires the impulse of
numerous waves of fluid before yielding under pressure. In some favourable
specimens masses of cells and debris may be seen revolving within the dilated
anus before extrusion. In various examples a distinct anal papilla (Plate XII.
fig. 7), furnished with a tuft of longer cilia, is seen projecting posteriorly.
In transverse section (Plate XII. fig. 3), the encroachment made on the
cavity by the ovaries, during the period of their activity, is well shown, and also
the gregariniform parasites, which often occur so abundantly in these worms.
The parasites were first alluded to and figured by Dr G. Jonnston,* afterwards
* Magaz. Zool. and Botany, vol. i. p. 584, pl. xviii. fig. 1 **.
VOL. XXV. PART II. Bea
386 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE -
by Frey and Leuckart,* Koiiker,+ Max Scauttze,{ Van BEeNnepEN,§ KErer-
STEIN,|| and lately they and certain ova in this species by the author; so that
the subject need not be further alluded to here, save to observe that they are
strictly confined to the region behind the streaked cesophageal division of the
digestive tract, that they hang freely into the cavity, and that the ova mentioned
in the last paper probably may not be connected with this particular species of
parasite. The occurrence of these ova, however, in specimens so widely different
in habitat as St Andrews and South Devon, shows that there is some constancy
in their presence. ‘The parasites occur in young specimens scarcely a quarter of —
an inch in length, and vary in size. When the animal has regained its condition
in its native haunts after spawning, the granular cells of the digestive chamber
become largely developed, so that in transverse section the body is rounder, and
the entire central region filled up by the mass, with the exception of an irregular
fissure in the centre; whereas considerable atrophy of these elements occurs
during long confinement, or the exigencies of reproduction. Towards the poste-
rior end of the worm, the tract becomes considerably diminished in size, and, in
the living animal, more evidently ciliated when viewed from above. The minute
structure of the wall of the cavity (Plate XII. fig. 10) has a considerable resem-
blance under pressure to that of the ciliated cesophageal region in Ommatoplea,
having a basement-substance, in which are imbedded a vast array of granular
olands, and with the inner surface richly ciliated. The contents of the glands
(Plate XIII. fig. 7) consist of granular cells and globules, which readily escape
from the free border of the organ, and are often ejected per anum.
In Cephalothrizx the lips of the oral aperture are frequently pouted out-
wards in the form of a short funnel, so that the animal resembles an elongated ©
Distoma, and the ciliation of the entire canal is more apparent than in Bor-
lasia. Some circular fibres around the mouth are evident in this genus, and
probably exist also in Borlasia. The general arrangement in transverse section
is seen in fig. 3, Plate X., and the same gregariniform parasites before mentioned, —
as well as an Opalina, likewise occur. In minute structure, the first or ceso-
phageal portion has a much more lax and cellular aspect than the succeeding
densely granular region; and from the translucency of the animal, the distinc-
tions in this respect are more exaggerated than in Borlasia. In one specimen
sent from St Andrews in April, the digestive chamber was coloured of a fine pea-
green instead of the usual pale pinkish hue—a state due to the uniform tinting of
the cellular elements.
- It may now be proper to refer to the presence of another parasitic animal
which was found in several specimens of Borlasia olivacea from St Andrews in
* Beitrage zur Kenntniss, &c. + Zeitsch. f. wiss. Zool. bd. i. pp. 1 and 2, taf. i. fig 4.
t Beitraige zur Naturges. Turb., &c. § Op. cit. \|Op. cit. p. 70.
{ Quart. Jour. Micros. Se. &c., April 1867.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 387
November. The animals infested by this parasite present a remarkable aspect,
the posterior half of the dorsum appearing under the lens to be honey-combed
and tracked by pale channels in every direction, as if a microscopic Zomicus
typographus had been at work in their bodies. Under the microscope the vast
net-work of pale channels have a minutely granular appearance, and numerous
small, opaque, ovoid granular bodies likewise occurred. Upon rupturing the body
of the worm, a large number of the peculiar structures (Plate XII. fig. 4) slid out
of their investments, and sailed about in the surrounding water, generally,
though not always, with the upper end in the figure first. They differed totally
from the gregarinz above-mentioned, many of which, however, were present in
the same hosts. Externally, they are coated with long cilia, whose activity in
the free state is of somewhat short duration, for after a time the animals remain
quiet, and they drop off. The body is distinctly segmented, and tapers slightly
towards the posterior end; while the surface is marked by very fine longitudinal
lines, as in Opalina, though in a much more minute degree. Anteriorly, there is
a conical portion (a), composed of three rather indistinctly-marked segments.
Two well-marked annuli (6) succeed, the posterior part of the last being nar-
rowed, so as to cause an evident constriction of the body-wall in many positions.
Behind these are six nearly equal divisions (c), each of which often appears
double, that is, has a broad anterior and a narrow posterior belt, as indicated in
the figure. The posterior region (d) consisted of three indistinct segments. The
body was minutely granular throughout, and an internal cavity was apparent
from the fourth segment to the last; commencing in the former by a rounded end,
and terminating just within the border of the latter. No aperture was observed
at either end. The opaque ovoid granular bodies (Plate XII. fig. 6), scattered pro-
fusely throughout the infected portions of the Borlasian, were evidently young
stages in the development of this species, and they too were ciliated. Upon subject-
ing them to gentle pressure (Plate XII. fig. 5), transverse segmentation was appa-
rent, the number of segments varying according to the degree of advancement. The
parasites were very delicate structures; and in the free state soon broke up into
cells and granules, after discarding their cilia as above-mentioned. Transverse
section of the affected animals showed that they occurred both in the skin and in
walls of the digestive tract; their ravages in the pigmentary layer of the former
tissue causing the curious appearances which led to their detection. Itis a some-
what difficult point to determine whether the skin, muscles of the body-wall, and
the digestive canal, constitute the common area of this creature’s depredations ;
or if it was piercing the former on its way to the surface, or again passing
towards the alimentary cavity to be voided per anum. The differently seg-
mented condition of the full-grown specimens, and their internal structure,
exhibit a higher type of organisation than the ordinary Opalina and Pachyder-
mon, which again are more elevated than the Gregarinee. ‘The ease with which
388 DR W. CARMICHAEL MINTOSH ON TIIE STRUCTURE OF THE
so soft and delicate an organism bores through and tunnels the tissues of its host
is wonderful. *
The Borlasize readily feed upon fragments of mussel (as first noticed by Sir J-
G. DALYELL). When a specimen has come in contact with a suitable portion,
the mouth is enormously dilated, and the bolus, even though of considerable size,
rapidly swallowed. The snout of the animal during this process is curved back-
wards, doubtless to afford assistance by its tactile properties, but there is no
extrusion of the proboscis. They also feed on dead specimens of Nereis pelagica,
ejecting the bristles and indigestible portions afterwards per anum. A specimen
measuring about three inches in length boldly seized the head of a large Nephthys,
upwards of four inches long, and partially ingulfed its prey. The danger of
putting rare specimens, such as Micrure, together in a vessel is great, as the
larger generally makes a meal of the smaller. While thus predatory and vora-
cious, they are in turn tolerant of much injury; for instance, one specimen had
its head and anterior portion seized and held in the stomach of a Sagartia troglo-
dytes for ten minutes, yet the worm subsequently got free, and crawled about as if
nothing had happened. After being put in spirit, they occasionally turn their
bodies inside out, and expose the inner surface of the digestive cavity. In Cepha-
lothrix the contents of the latter are easily observed, and often consist of frag-
ments of its fellows of the same species.
EHRENBERG and DE QUATREFAGES considered the mouth to be the genital
orifice, the former observing that a large quantity of mucus was discharged
therefrom. Mr H. Goopsir} thought the canal common to the respiratory, diges-
tive, and generative systems. ‘ In Serpentaria,” says he, “ it acts almost as an
organ of digestion, while in Nemertes there is a trumpet-shaped exsertile pro-
boscis, which, contrary to the opinion of RaTHKE and other naturalists, and
according to the opinion already expressed by EHRENBERG, is the intestinal canal.”
He agreed with EHRENBERG in supposing that the ova escaped into this chamber.
His views were rather erroneous, such as supposing that the first region of these
worms was composed of a single annulus; but the succeeding or terminal of
many, each about an 4th of an inch in length; moreover, that each of the
separated annuli contained all the elements of the perfect or original animal,
viz.,a male and female generative apparatus, the cavity common to the generative,
digestive, and respiratory functions, and a small dorsal vessel analogous to the
intestinal canal of Nemertes. Serpentaria, therefore, he explains, ‘‘is a com-
* Since the foregoing was communicated to the Society, I find that Prof. KErerstEIN, in a
recent paper, gives a drawing of a parasite very similar to the above, but he does not say more about
it than simply mention, under the explanation of the plate, that it is an enigmatical body from the
stomach of a Leptoplana tremellaris. Beitrage zur Anat. u Entwicklungeschichte Seeplanarien von
St. Malo (Der K. Gesellsch. der Wissensch. vorgel. am 4. Januar 1868), p. 37, taf. ii. fig. 8. It is
probable that the same parasite, as in the case of the Gregarine, may have a wide distribution.
+ Annals Nat. Hist. xv. 1845.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 3389
posite animal, each perfect individual consisting of numerous and apparently
still unformed or imperfectly formed individuals.” Modern researches do not
support any of these suppositions. Of the other British zoologists who have
examined these animals, Dr Witt1ams,* while admitting the digestive nature of
this chamber, misinterpreted its true relations. He considered the organ as a
closed sac filled with a milky fluid, and having many diverticula, into which the
nutritive matter passed by exudation from the proboscis. He appears thus to
have drawn up his description from an Ommatoplean, which possessed no large
slit leading into the chamber. He denied the existence of the proper anus.
While thus deviating from the true structure of the parts, he was correct at least
in viewing the chamber as digestive, and quite independent of the generative
system placed to its exterior. Sir J. G. DALYELL,} whose untiring scrutiny of the
habits of such animals is worthy of all praise, saw a Borlasian (his Gordius
gesserensis) feeding by the ventral slit, which he therefore correctly termed the
mouth. Dr JoHNsToN, in his Catalogue, observes—“ There is another and much
larger aperture in front, behind and underneath the head. Long mistaken for
the mouth, this has been usually described of late as genital, but the orifice is
doubtful.” M. Van BENEDEN does not demonstrate that the so-called biliary
elements are simply constituents of the wall of the digestive cavity, and not
special czeca attached to the sides of the canal. In Cerebratulus tenia (his
C. Grstedii) he states that the digestive canal is divided into three compart-
ments—the first short, and corresponding to the cesophagus ; the second twice or
thrice the length of the former, and representing the stomach; the third extend-
ing to the posterior extremity of the worm and constricted at regular intervals, and
corresponding to the intestine. I have not as yet noticed this in the British
examples, which agree with the typical Borlasian form in the structure of the
chamber, although the external aperture or mouth is somewhat smaller. Prof.
KEFERSTEIN’S} description of the cavity as applied to Borlasia, though brief, is
good, and his criticism of VaN BENEDEN’S view, in regard to the “liver” in the
same group, fair.
Nervous System.—The cerebral ganglia or central organs form two large and
conspicuous pale red masses situated a short distance behind the snout of the
worm (Plate X. fig.1). They differ in shape, as seen under slight pressure, from
the same organs in Ommatoplea, each half being narrower and more elongated,
so as to cause the entire arrangement to have the appearance of a horse-shoe
magnet. In some specimens, instead of being more deeply tinted than the rest
of the cephalic tissues, they are paler, on account of the deep red coloration of the
latter; while, in others, they can scarcely be distinguished under the dense
blackish-green coating of cutaneous pigment. They are surrounded by the usual
* Rept. Brit. Assoc, 1851. t Powers of the Creator, vol. ii. p. 73.
t Zeitsch. f. wiss. Zool. xii. p. 70. |
VOL. XXV. PART II. 5G
390 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
fibres of the cephalic region, besides the sheath-proper of the ganglia. The inferior
commissure, often of a deep red hue, is well marked, and placed quite at the
front. The anterior curves of the ganglia do not bulge so much forwards on each
side as in Ommatoplea, and thus the anterior margin of the system forms a
nearly uniform transverse line. The superior commissure is smaller and less
distinct; indeed, it is with difficulty seen in the living animal as a transparent
preparation. Each ganglion is composed of a superior and an inferior lobe; and
in minute structure of the nervous matter agrees with that in Ommatoplea. On
making a transverse section through the ganglionic mass just behind the com-
missure, the superior lobe is found to be more rounded than the inferior, and
to communicate with its fellow of the opposite side by the superior commissure.
The inferior is somewhat ovoid, and the great commissure joins it with its fellow;
while posteriorly each gives off the great nerve-trunk. In front the two lobes
are soldered together, but towards the posterior part a section is now and then
found, which shows the posterior end of the upper lobe separated from the
inferior. This severing of the end of the upper lobe is not to be confounded with
the free rounded sac which lies close behind, as demonstrated in a section in
which the knife has cut the left ganglion somewhat further back than the
right, and so indicated this separation on that side. The presence of the trumpet-
shaped mouths of the ducts of the cephalic sacs in such a section shows that
these bodies are posterior and not yet reached by the instrument. Longitudinal
sections of the head of the worm exhibit the positions of the ganglia and the
cephalic sacs with great clearness, each of the former often presenting different
appearances on the respective sides from obliquity of section, but the posterior
borders are always distinctly separated from the sacs.
In all the sections of the ganglia a peculiar change occurs after mounting in
chloride of calcium, the oily matter of the tissue collecting in curious streaks and —
circles, and apparently at some parts resisting the penetration of the fluid.
Considerable difficulty is experienced in making out the anterior branches of
the ganglia, from the opacity of the snout; but three or four trunks of note are
occasionally apparent—two large branches superiorly, and one or two smaller
beneath. Some twigs seemed to proceed in the direction of the eye-specks, but
their ultimate distribution could not be traced.
The great nerve-trunks (Plate X. fig. 1, n) leave the posterior end of the
inferior lobe as in Ommatoplea, proceed along each side of the body, and termi-
nate a little within the tip of the tail. Their calibre slightly diminishes as they
course backwards; and their position is nearer the ventral than the dorsal sur-
face. Branches no doubt exist, but only faint traces of such are seen in the —
longitudinal sections, for the opacity of the textures in the living animal prevents:
their being satisfactorily made out. The trunks are imbedded in a fibro-granular
matrix of the same reddish hue, and have, in addition, the proper sheath of the —
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 391
nerve. In some pale species they are marked externally as two pinkish dorsal
streaks. These trunks, as already indicated, have a very different position from the
Ommatoplean nerves, being situated outside the circular muscular coat, and
between it and the great longitudinal. Two muscular coats (circular and internal
longitudinal) thus intervene between the nerves and the body-cavity and its con-
tents, whereas in Ommatoplea the nerves are within all the muscular layers.
In Meckelia annulata, the nerve-trunks are not placed as in Cerebratulus tenia,
which conforms to the Borlasian type, but lie between the external circular and
internal longitudinal muscular coats. This arrangement is characteristic of the
Meckelian type.
In Cephalothrix, the peculiarity of the ganglia (as first pointed out by Prof.
KEFERSTEIN) is the advance of the almond-shaped upper lobes, so that the supe-
rior commissure is quite in front of the inferior (Plate XIII. fig. 1). The lateral
nerves are placed between an isolated longitudinal fasciculus and the great longi-
tudinal muscular coat of the worm.
In regard to the innervation of the body by the lateral trunks, it is interesting to
observe the very long time during which detached fragments of the body survive in
several of the long Borlasians, such as Cerebratulus teenia, DALYELL, and the great
Lineus longissimus. A specimen of the latter, for instance, sent from St Andrews
in September, broke into pieces on the journey; yet six months afterwards most
of the fragments were alive, although the sea-water had not been changed more
than once. The head and anterior portion of the worm, which scarcely measured
two inches at first, had now grown a body and tail that when crawling measured
at least seven inches, and of course capable of much greater extension, so that it
looked like an independent animal; and this was accomplished without the aid
of any food, except perhaps what it might have acquired from the fragments of
its own body in the neighbourhood. Some of the latter measured about a foot in
length, and all lay coiled in various ways, with the ends puckered, and in most
eases fixed by a whitish cicatrix, which was firmer at one end than the other,
and occasionally tapered. A similar power of regeneration was observed in the
anterior end of Borlasia, Cerebratulus, Micrura, and Cephalothrix, when only a
fragment of the body was left behind the mouth; and in Borlasia octoculata, a
very fragile species, reproduction of a complete head upon each of the fragments
ensues, if not with rapidity, at least with certainty.* One of the most: remark-
able features, to continue the case of LZ. longissimus as a type, was the gradual
development and elaboration of the products of the generative organs (in this
case the male elements) in the headless fragments, so that when in February
they were placed in clean sea-water, some gave exit to milky clouds of perfect
spermatozoa. This would seem in these animals to be the main aim of such a
provision, since their very length and softness, if not fragility, apparently court
* Proced, Linn. Soc., June 1868.
392 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
disseverance. The formation of a complete individual, and the prolonged reten-
tion of certain functions by the headless fragments, under circumstances so
adverse as the above, may give us some idea of the powers of regeneration and
vitality possessed by these worms in their native haunts.
Mr H. Goopstr criticises M. DE QuaTREFAGES’ description of the nervous
system in Serpentaria and Nemertes, and denies its existence altogether, averring
that microscopically the so-called nerve-trunks showed no nervous elements at
all, but were the testicles of the worms. I fear, however, this worthy naturalist
depended rather upon analogy than actual observation in this case. He accounts
for the nervous fibres seen by Ratuxe* (the first who correctly described the
Borlasian ganglia) passing out from the cerebral ganglia to the narrow furrows
on each side of the head, by supposing them to be seminal tubes on their way to —
the furrows (his seminal apertures). M. DE QuaTREFAGEs confined his examina-
tions chiefly to Ommatoplean ganglia. FREY and LevcKkart,+ again, confound the
cephalic sacs with the posterior part of the ganglia. M. Van BeNnEDEN| makes a
curious remark in regard to his Nemertes Quatrefagu—viz., that the “ collier -
cesophagien”’ is peculiar for its red colour, which hue, he says, is less marked in —
the other species of Nemertes. This colour, he explains, is not due, as believed —
for a long time, to the nerve-ganglia, but to the vessels which surround them,
and it can easily be understood how the ganglia were confounded with the nerve-
trunks. Nothing akin to this has ever come under my observation, and the
minute anatomy of the region is adverse to the view. M.Gruse§ had previously
made the same remark in describing Nemertes purpurea, JOHNST., a species which
(judging from the descriptions) seems to differ very materially from Omma-
toplea purpurea, and is apparently a Borlasian form, but I have not as yet seen
any British representative. Prof. KrrersTEIN is scarcely accurate in affirming that
the ganglia in this group are larger than those of the Ommatopleans. In his —
figure of the parts viewed from the dorsum (Taf. vii. fig. 1), the cephalic sacs are
not discriminated. :
Lateral Fissures.—On each side of the head in Borlasia is situated an exten- —
sive fissure (Plate X. fig. 1, and Plate XII. fig. 2, 6), which commences as a
shallow groove at the anterior border of the snout, and terminates, as a reddish
pit, somewhat abruptly, just beyond the entrance to the cephalic sac. A distinct
narrowing of the anterior region occurs behind the fissures in B. olivacea, thus —
marking off the cephalic boundary. There is nothing special in the anatomy of ©
these fissures, for they are formed by a simple extension of the cutaneous ele- |
ments superiorly and inferiorly, as represented in the transverse section (Plate |
XIL. fig.2). Their entire surface is covered with very active cilia, which, as before
mentioned, I have often seen cease abruptly, and again begin to play vigorously. |
* Neueste Schriften, &c. + Beitrige zur Kenntniss wirb. Thiere, p. 73, taf. 1. fig. 19.
t Op. cit. p. 16. § Archiv fiir Naturges. 1855, p. 150.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 393
The vapour of chloroform, if applied in sufficient quantity, causes them to cease
entirely, but they again commence vibration on the partial recovery of the animal.
Mr H. Goopsir thought that the fissures were the apertures of the male gener-
ative system, a supposition, as mentioned, scarcely requiring refutation. Prof.
KEFERSTEIN gives a very good summary of the views of previous observers, but,
while agreeing with none, he advances no new interpretation of these structures.
He concludes by criticising M. Van BENEDEN’s statements, with which he dis-
agrees, but he has scarcely reviewed them at sufficient length. M. Van BENEDEN
observes that the cephalic fissures are furnished posteriorly with a pit leading into
a ciliated funnel, and that the lateral vessels when they approach the ganglia
swell out into vesicules (‘‘ils se renflent la en vesicules’”’), which similate the
ganglia, and which lead their contents to the exterior by the ciliated funnel just
mentioned.* He considers that the central point of this apparatus lies imme-
diately beneath the ganglia on each side; and he has seen, under compression,
the pit of the lateral slit adjoin a large canal, which terminated exteriorly by a
sort of funnel, and this led into a pouch behind the nerve-ganglia. He did not
see any vibratile movement within the vesicle; and states his conviction that this
apparatus is similar to that in the Trematoda and Cestoidea. Thus, as Prof.
KEFERSTEIN says, he has nearly retrograded to the time of HuscuKe, who regarded
these fissures as connected with the lateral nerves, which he took for canals. In
his enlarged figure, however, he represents the position of the cephalic sacs
fairly, but he has a large blood-vessel running to the exterior of the nerves, and
extending to the tip of the snout ; this, of course, is quite at variance with a true
interpretation of the structures in Borlasia.
The cephalic fissures, as characteristic of the Borlasians, are absent in Aleckelia
annulata, their places being supplied by two pale curved grooves on the dorsum
and two continuous transverse furrows on the ventral surface of the snout. The
furrows are richly ciliated. In the remarkable form from Balta, the snout is
surmounted by two curious frilled processes (Plate XIV. fig. 12, 6), which termi-
nate posteriorly in a long filament. Whether the latter, however, is a structure
Sut generis, or only some normal constituent of the body (such as a nerve) in a
peculiar position, the state of the specimen forbids our determining.
Cephalic Sacs.—At the posterior end of each lateral fissure, a funnel-shaped
tube (m’, Plate X. fig. 1) leads into-a large globular structure (m), often of a
pinkish or reddish hue, and the apparent homologue of the cephalic sac in Omma-
toplea. This globular sac lies over the origin of the great nerve-trunk on each
side, and abuts so closely on the posterior prominence of the upper lobe of the
ganglion, as to have led some observers into the error of supposing it only a con-
tinuation of the ganglionic texture. Very carefully made preparations and
examinations of the adult animal, as well as observations on the young at various
* Mém. de l’Acad. Roy. des Sc. de Belgique. + Op. cit. pl. i. fig. 5.
VOL. XXY. PART Il. oH
394 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
stages, remove all doubt on this subject, and show that these globular bodies
belong neither to the nervous nor the circulatory system. The funnel-shaped
duct (m’) is richly ciliated, and the cilia may be traced to the sac, wherein they
are continued as a linear streak along its exterior border, but its general mass is
not ciliated. The ciliated curve along the external border is well seen in young —
specimens, but the exact superficial extent of the ciliation is difficult to deter-
mine. In favourable examples the walls are observed to be furnished with finely
granular cells, which have a clear and distinct nucleus. These cells are most
evident on the inner and posterior curves, the outer curve being pale. The sacs
project posteriorly into two large cavities (Plate XI. fig. 1, s,s) on each side of the
proboscidian tunnel, and are thus laved by the circulating fluid, which rushes
forwards from the walls of the digestive cavity; but there is nothing to support
M. Van BENEDEN’S views* as to their continuity with the circulatory system.
Their relations to the ganglia have been adverted to previously, and are well
shown in some horizontal sections, where one sac has been severed considerably
lower than the other. Just in front of the external border of the curved dorsal
groove on the snout of J/eckelia annulata is an ovoid body apparently homolo-
gous with the foregoing; but I have not yet been able to trace its anatomy, on
account of the opacity of the cutaneous tissues in this animal.
The functions of these bodies would seem to be excretory. Their gradual
advance in position and proportional diminution in size in the developing animal
would seem to indicate that their function is more important in the young than
in the adult. They are quite absent in Cephalothrix.
Prof. KEFERSTEIN does not enter into structural detail with regard to these
organs in this group, but states they lie at the posterior end of the lateral
fissures.
Eyes.—These are simply masses of black pigment, arranged on the sides of
the snout with greater or less regularity, and without any special optical struc-_
ture. The textures of the head and nerve-fibres themselves are so unfavourable -
for observation that I have had difficulty in making out nerve-branches thereto.
A more definite structure is observed in the Ommatopleans, both as regards
nervous elements and complexity of organisation. Some Borlasians have no
eyes (a remark, however, which does not apply to Lineus longissimus), or have
them only temporarily in their young state, like the developing oysters and
Terebratule ; while all the Ommatopleans possess them. It is a curious fact
that in transverse sections of the snout (such as Plate X. fig. 4) considerable
pigment-specks are seen towards the ventral surface.
* Op. cit. p. 12.—“ En avant, ces vaisseaux aboutissent au-dessous des ganglions cérébraux, et
si nous ne nous trompons, ils se renflent la en vésicules qui semblent appartenir aux ganglions mémes
et qui conduisent leur contenu 4 l’extérieur par un court canal excréteur aboutissant au fond de]
fossette latérale.”
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 395
Circulatory System.—Vhe circulation in Borlasia diverges considerably from
that in Ommatoplea, the vessels differing in definition, size, coiling, and contents.
The main vessels indeed somewhat resemble long cavities, with contractile walls,
within which floats a transparent fluid with corpuscles. I have referred to this
system as the circulatory, but the current is driven by the contraction of the
vessels now backwards, now forwards, so that it is rather a kind of oscillation.
There are three great longitudinal trunks—confining the description at pre-
sent to the region behind the oesophageal division of the digestive tract—a dorsal
(p) and two ventral, 7, 7 in the various transverse sections, and in Plate XIII. fig. 2.
These three vessels in Borlasia were first mentioned by RatuKke.* The dorsal is
a large trunk situated immediately to the outside and to the ventral surface of
the proboscidian sheath; while the ventral, also considerable trunks, lie on a
lower plane, and nearer the middle line than the nerves. Indeed, when the three
trunks are distended in B. olivacea and B. octoculata, they occupy nearly the
entire breadth of the worm under gentle pressure. These vessels are frequently
swollen in various ways, sometimes being irregularly moniliform from dilatations,
crenate, or simply distended as long pale spaces. The three trunks are inti-
mately connected by an array of simple and rather large transverse anastomos-
ing branches (y, Plate XIII. fig. 2), some of which are forked. These transverse
vessels have special contractile walls, and are not mere random channels, as may
be seen in the longitudinal sections of the worms (Plate XI. fig. 7, 4). They are
subject to the various changes of form noted in the larger trunks. The great
longitudinal trunks are further connected by meeting at the tip of the tail (Plate
XIII. fig. 2). The dorsal vessel generally contracts from behind forwards, and
this causes the corpuscular fluid, not only to rush to the front, but also to flow
through the transverse branches into the lateral trunks. The latter propel their
contents in both directions.
At the posterior end of the cesopbageal division of the alimentary canal the
three great vessels, for the most part, lose their individuality, and, so far as I have
observed, form an elaborate meshwork of vascular spaces (w, wu, Plate X. fig. 1)
around this organ, again meeting in the lacune (s, s) in front of the cavity, and
bathing the bulbs of the cephalic sacs which lie therein. These lacune or chan-
nels pass forwards to unite at the ganglionic commissures, and the granules of
the contained fluid may be seen rushing forwards in the one and backwards in
the other. In addition to the smaller meshes surrounding the cesophageal region,
two larger spaces are seen on each side of the proboscidian sheath in transverse
section, which may be held as the continuations of the dorsal vessel. The reticula-
tions formed by this system are seen under favourable conditions in the living
animal (¢.g., as represented in Plate X. fig. 1), as well as in numerous transverse
* Neueste Schriften, &e. Danzig, 1842.
396 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
sections. I have not been able to see any blood-vessel in the tissues of the head
in Borlasia. A distended pale portion may often be noticed in the central line
between the snout and the ganglionic commissures, as if the animal had gulped
water by the aperture for the proboscis, so as to distend the channel, but this has
no connection with the circulatory system. Transverse section demonstrates
that there is no other channel in the snout in front of the ganglia than that just
referred to.
In long pale species, such as Lineus lactea,* Mont. MS., the intervention of
an elongated region between the posterior end of the ganglia and the anterior
border of the cesophageal region renders a special modification of the circulatory
channels necessary. Accordingly, it is found that after the fluid collects in the
spaces in front of the alimentary organ, it is conveyed by two long channels for-
wards to the ganglia, where the same ending occurs as in the other species.
These channels seem to be simple elongations of the ordinary lacune, and are
represented in transverse section in Plate XII. fig. 8; thus forming an inter-
mediate link between Borlasia olivacea and the still more elongated post-
ganglionic region in Cephalothriz.
In Meckelia annulata there are two great longitudinal vascular trunks (Plate
XIV. fig. 11, 7), which lie within the inner or longitudinal muscular coat
opposite the nerve-trunks, and they are peculiar on account of their large size
and the granular nature of their contained fluid. They form a coarse network
in the cesophageal region as in Borlasia, and are continued forwards just within
the border of the snout to meet in a vascular arch.
Whatever special function the cesophageal region may perform in regard to —
digestion, it is clear that the circulatory fluid bathing its outer wall is placed in |
a favourable condition for oxygenation, as the mouth now and then must give
entrance and exit to sea-water, under the influence of the powerful ciliary cur-
rents caused by the entire surface of this division. Besides, it is evident that
during the varied actions of the oral aperture (e.g., during feeding) the circula-
tion would sometimes be much interfered with if such a rete mirabile did not
exist.
In Cephalothrix I can only make out two great longitudinal vessels, whose
positions are seen in the transverse section (Plate X. fig. 3, 7), viz., nearly oppo-
site the nerve-trunks (), from which they are separated by the chief longitudi- —
nal muscular coat. There is thus in this system also a deviation from the
ordinary Borlasian type. The size of the vessels is proportionally larger than in —
the latter, and their transparent fluid contains a number of minute corpuscles. —
In the living animal each lateral vessel may be observed to contract regularly
and swiftly from before backwards, sending a wave of fluid towards its posterior —
* T am indebted to Mr Parrirt for living specimens of this species from Devonshire.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 397
end, at which the contraction ceases. A reversed movement by-and-by takes
place, the contents being propelled towards the snout. Anteriorly the two ves-
sels course forwards by the side of the cesophageal portion of the alimentary
canal without sub-division, pass along the sides of the proboscidian sheath in
special cavities (v), as in Lineus lactea, in front of the former, and reach the
ganglia, where they communicate. I have not actually seen a junction pos-
teriorly, but analogy would lead us to suppose such to exist. There appeared to
be little regularity or rhythm in the movement of the fluid in these vessels, both
of which were occasionally seen contracting from before backwards at the same
time. Generally, however, the contractions were alternate.
In the fragmentary specimen from Balta, transverse section of the anterior
region (Plate X. fig. 2) showed a large ovoid and probably vascular tube (7°) placed
at the inner border of the great longitudinal muscular coat on each side, while the
nerve-trunk (72) lay outside the latter. The cavity was partly filled in the prepa-
ration with minute granular cells. This agrees with the arrangement in Meckelia.
Both Dr G. Jonnston and Dr WILLIAMs mistook the ganglia for hearts, and
the inferior commissure for a connecting vascular trunk. The blood, says the
latter author, derived from the cutaneous system of capillaries, is poured by a
dorsal vessel into one of the chambers of the heart (the dorsal). From the
latter it is sent into the ventral cavity, and thence distributed over the integu-
mentary and intestinal systems. He, moreover, says the blood is red, and always
devoid of corpuscles. Such remarks are not based on correct observations. .
BLANCHARD,* in his examination of Cerebratulus liguricus, describes the nervous
centres as lodged in a cavity into which the vascular trunks open, and this can
only refer to the post-ganglionic lacune, though such do not by any means sur-
round the ganglia. I have not seen any vascular space surrounding the
“trompe”’ in front of the commissures, as described and figured by this author ;
and the fiuid of the proboscidian cavity could only have been seen there during
the ejection of the proboscis. He shows several longitudinal vessels in Nemertes,
which are not present in the British forms. I cannot agree with M. Van
BENEDEN’S+ views of the circulation in Borlasia, for he describes the lateral ves-
sels as swelling out into vesicles when they approach the ganglia, and their con-
tents conducted to the exterior by a ciliated funnel. The erroneous nature of
this supposition has already been noticed under ‘ Cephalic sacs.’ He also men-
tions that each lateral trunk posteriorly communicates only with that of the
opposite side, and concludes doubtfully thus:—“Le long des parois du tube
digestif, on voit en outre plusieurs vaisseaux, mais dont les aboutissants sont
difficiles a décourvir.’”’ Another deviation from accuracy is apparent from his
remark (under Cerebratulus cerstedii) that “En arriére un gros vaisseau treés-
* Ann. des Sc. Nat. 3™¢ ser, tom viii, pl. ix. fig. 5. + Op. cit. p. 12, &e.
VoL. XXV. PART II. 51
398 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
large, 4 parois trés-contractiles, qui parait et disparait par intervalles, occupe la
ligne médiane et semble s’ouvrir au bout de la queue.” A reference to his
figure* and its explanation at once makes it apparent that he has mistaken the
proboscidian sheath for a blood-vessel. Prof. KEFERSTETN again does not enter into
detail with regard to the circulation in Borlasia, and his figures and descriptions
apply to Ommatoplea, with two exceptions,} which represent transverse sections
of Cerebratulus marginatus. In that through the anterior part of the body five
circular vessels at least are transversely cut in the meshes round the cesophageal
region, and, moreover, they are connected together by a pink band in the figure,
as if from a connecting trunk. I fear the author has been misled by the carmine ~
used in the preparation, for in the British examples of Cerebratulus a true
Borlasian arrangement is found. ;
Generation and Development.—The sexes are separate, as in Ommatoplea,
and the ova and spermatozoa developed in their respective sacs between the
inner muscular layer of the body and the digestive cavity. The glandular ele-
ments in the walls of the latter indeed undergo a certain amount of atrophy
during the period of reproductive perfection, as observed in the transverse —
section through a specimen just before spawning (Plate XII. fig. 3).
In Borlasia olivacea the spermatozoa (Plate X. fig. 9) have the aspect of slender
rods, with a scarcely perceptible enlargement at the end from which the filiform tail
proceeds. When a mass is taken from a living animal, they often adhere to a point
by one end, and, spreading around this in a radiating manner, lash the surrounding
water with their tails. The spermatozoa of B. octoculata (Plate XI. fig. 5) are more
minute than the former, and somewhat resemble an awl-handle in shape, with
the filament projecting from the butt, which is thus frequently agitated, while
the tapered end is comparatively still. In Lineus longissimus the outline of the
body of the spermatozoon (Plate XI. fig. 4) is less regular than in Borlasia, and
it seems slightly crenated or moniliform. A very long filament proceeds from
the body at the larger end. In Micrura fasciolata there is likewise a slight
constriction in the middle of the spermatozoon, and the tail proceeds from the —
larger extremity.
The ova are few and large in B. olivacea, smaller and more numerous in
B. octoculata. Both ova and spermatozoa escape by pores on each side a little
above the nerve-trunks, these apertures being often indicated by pale specks
along the sides of the worm, and occasionally, as in Meckelia annulata, they
are boldly marked by white spots. In this species also the rudimentary condi-
tion of the generative organs may be seen in transverse section as a series of
small globular or pyriform sacs, filled with granules and globules, and situated
above the lateral vessel on each side of the body. Thus far there is a certain
* Op. cit. pl. ii. fig. 4. + Zeitsch. f w. Zool. xu taf. vii. figs. 3 and 4.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 399
resemblance between Ommatoplea and Borlasia (to take, for example, B. olwvacea),
but the moment the ova pass from the animal, and the condition in which they
do so, a decided divergence occurs. Instead of being deposited as free circular
bodies, the products are here placed within a flask-shaped membrane, with one
end narrowed to a fine point, and the whole enclosed in a tough covering of
gelatinous mucus, which is fixed either to stone or glass, in the form of a bulky
cord, as noticed by GErstepD.* When a female specimen is about to deposit ova,
she seeks the water-line, or a space above it, and quietly settles along the vessel.
By-and-by a copious exudation of tough translucent mucus takes place, which
envelopes the entire animal. In this mucus, which when fresh is crowded with
small ovoid granular corpuscles from the cutis, the ova are deposited in the flask-
shaped capsules, each of the latter corresponding to an ovary, and containing all
its ova, viz., from one to seven. Hence, by the nature of the parts, the ova are
arranged in a somewhat irregular double row along each side, the extremities
of the cord—corresponding on the one hand to the head and cesophageal portion
of the digestive tract, and on the other to the extreme tip of the tail—being free
from ova. In some instances, the posterior end of the animal was curiously
frilled and grooved on the ventral surface during deposition. When newly depo-
posited the mucus is softer and less tenacious than it afterwards becomes, and the
same may be said of the membranous flasks. ‘The solidifying of the mucus is
analogous to what takes place, under similar circumstances, in the egg-capsules
of certain mollusca, e.g., Bucconum undatum and others. If one end of the
animal be disturbed from its original site on the glass before the ova are all
deposited, four rows will be found there instead of two, for sufficiently obvious
reasons. The ova of B. olivacea are of two shades, viz., white and pale-
brownish ; and though the dark-greenish examples often lay white eggs, they do
not seem to do so always. Each ovum measures from th to ~oth of an inch
in diameter. The deposition takes place in January and February in those
long confined; but some specimens sent from the St Andrews rocks towards the
end of April likewise deposited ova, so that some latitude in regard to date is
necessary. The American examples deposited their ova in January, and those
from Cuxhaven in March; but the Nemeries communis of M. VAN BENEDEN only
did so in September. It is often observed that impurity of the water causes
recently captured animals to lay their ova rapidly, as if from a kind of abortion.
The development of the ova in Borlasia obscura—a species apparently identi-
eal with our B. olivacea—has been described by E. Desor} up to the period of
the extrusion of the young from the capsules; and Max ScHu.rze{ and Kroun§
have also investigated the subject, especially the former, so that I shall only
dwell on such points as have not been elucidated. Our British forms seem to
* Entwurf einer Syst., &c., p. 25. t Boston Jour. Nat. Hist. vol. vi. No. 1, 1850.
t Zeitch. fiir wiss. Zool. bd. iv. 1853, § Archiv fiir Anat. 1858.
400 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
offer great facilities for such investigations, and I have had no difficulty in rearing
the Borlasiz at a long distance from the sea.
The ova on deposition in the flask-shaped capsules are uniformly granular
and opaque ; and when broken up, are seen to be composed of a granular oily
matter, which forms streaks and rounded masses, and is not cellular, as described
by E. Desor. The clear, semi-transparent spot mentioned by the latter as
occurring in the ova after deposition is seldom visible, though the germinal
vesicle (a) and dot (>) are apparent enough in the centre of a pale oleaginous
space, while they are yet in the body of the female (Plate XIII. fig. 8). The
cleavage of the vitellus generally commences on the second day, when in some
it is found divided into two and in others into four parts. As first pointed out _
by Max Scuutrze, Desor committed an error when he stated that the irregularity
of the divisions of the vitellus distinguished this species from other animals.
The divisions proceed regularly and somewhat rapidly; for ova which presented
four lobes at 9 a.m. were found at 1 p.m. broken up into a number of rounded
masses, so that the ovum had a nodulated or mulberry-aspect. No clear spot
was observed in the centre of these secondary masses. During the next four or
five days the changes which ensue in the ova consist chiefly of sub-divisions of
the vitellus, which daily become finer. There is now a pale spot in the ovum,
and a few free granules and cells in the flask, as noticed by DEsor. The ova
eradually become smoother in the outline from sub-division of the vitellus, and
then only a few nodules appear here and there on the otherwise even cir-
cumferences. EK. DEsor found the ova ciliated on the twelfth and fourteenth
days, Max ScuvuLrTze on the eleventh and twelfth, and I have struck the average
amongst the British examples on the latter date. The ova, again, which had
been left entirely above the water-line did not develop so quickly. At first the
ciliation does not cause the mass to revolve, but subsequently this motion takes
place with vigour. They continue in this condition for about a month, and then
a further change ensues in the contents of the flasks (Plate XIII. fig. 4); and the
latter drawing will explain E. Drsor’s discovery, as well as enable us to correct a
slight inaccuracy into which he has fallen. The opaque ciliated mass previously
noticed by-and-by shows a double outline under pressure, caused by the develop- ~
ment of the young Borlasian within the ciliated coating; indeed, at an advanced
stage, as in the middle of the flask represented in Plate XIII. fig. 4, the embryo
seems as if shrouded in a layer of fatty cells and oil-globules (b), within which it
distinctly moves. In such a condition the animal readily escapes from its invest-
ment, and at the upper part of the same flask a free example (a) is seen. E. DESoR
commits an error in his excellent description, when he states that the cells in the
interior of the embryo are the “residue of the vitellus destined for the support
of the animal ;”’ they are nothing else than the cells in the developing wall of
the alimentary canal. The large dark ciliated mass (c) at the lower part of the
a
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 401
flask, and the scattered cells and granules, are portions of the discarded external
covering of the embryo; and it is to be observed that the cilia on this texture
are, if anything, longer than those on the free young animal, though their motion
is less vigorous. The “ cells’ of which this rejected covering is made up are
entirely of a fatty nature (Plate XI. fig. 10)—in short, an ageregation of fatty
granules, with an oil-globule or two, and capable of changing form accordingly.
It is a fact that this debris after a time quite disappears from the flask, and
therefore it probably acts as nourishment for the young (being swallowed by the
mouth, as in the case of the embryo of Purpura lapillus) just as the yolk-sac,
by a different mode, does in other animals. In escaping from the flask, the
young animals, in many cases, seem to have thrust themselves along the narrow
apex, dilating it and bursting through. Fora considerable time afterwards they
crawl about in swarms amongst the gelatinous mucus, so that the latter has a
curious aspect, being filled, in addition, with the transparent flasks from which
they have escaped, and a few undeveloped ova. Moreover, it is a common prac-
tice for the adult animals to crawl through these masses, and several are gene-
rally coiled in proximity. The number of undeveloped ova is extremely small,
showing how easy it is to rear these animals, even with very limited supplies of
fresh sea-water.
The foregoing development is thus much less complicated than the remark-
able evolution of the Nemertean worm, called Alardus caudatus, Buscu., from
Pylidium gyrans, as described by J. Mutter.* This form would seem to be allied
to Sir J. Datye’s Stylus (Micrura), since it is furnished with a process poste-
riorly ; and the author states that most examples are eyeless. Leuckart and
PAGENSTECHER} have also recorded another species of Pylidium, and the develop-
ment of the Borlasian worm therein; and they remark that the mouth of the
worm is in connection with that of the Pylidium—indeed the organ in the latter
opens into it—a statement verified in the same volume of the “ Archiv” by
KROHN.
The young Borlasians, at the stage previously mentioned, are visible to the
naked eye as small elongated worms, somewhat tapered at both ends, pale, or
rather translucent in front, and opaque-whitish posteriorly (Plate XIII. fig. 5), and
in structure now closely approach the adult. The whole surface of the body is
richly ciliated, the cilia being especially active in the cephalic fissures, and still
more so at the openings of the cephalic sacs. The ganglia are indicated by a
paler space (A) on each side, but their actual outline is indistinct. There are in
all cases at least two well-marked eyes. The cephalic sacs (m) are large and
well defined, indeed very much larger proportionally than they are in the adult:
and from their present position with respect to the ganglia, demonstrate the true
* Archiv fiir Anat. &c. 1854, p. 75, taf. 4. + Archiv fiir Anat. 1858.
VOL. XXV. PART II. dK
402 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE - a
form of the latter, as well as the error into which those authors have fallen who
have confounded the sacs in the adult animals with posterior ganglionic enlarge-
ments. The sacs open by their ducts at the posterior part of the cephalic fissures
(b), and the ciliary action can be traced inwards from these points. The cesopha-
geal division (7) of the digestive canal is distinguished by its pallor, more evident
ciliation, and the well-defined border of the succeeding opaque region (j’). The
proboscis (a) is marked by a central streak of papillee, and, after tapering poste-
riorly, it curves forwards, and disappears. The proboscidian sheath (0) is observed —
to be banded here and there anteriorly by transverse bridles ; and a clear line is
occasionally visible on each side of the opaque alimentary tube, as if from circu-
latory undulation. An anal papilla (Plate XII. fig. 7), with a ciliated line con-
necting it with the digestive cavity, is also apparent.
Shortly after reaching the degree of advancement shown in Plate XIII. fig. 5,
the young Borlasians leave the gelatinous masses, and congregate at the water-
line. Hundreds now perish from want of sufficient food, which in their
native haunts is doubtless both abundant and suitable, while in the artificial cir-
cumstances and confined vessel it is denied them. Two and a half months after-
wards the young animals are found still of the same whitish hue, and possessing
only two eyes, rarely with an additional pigmentary fragment. The proboscis
has much increased in size; indeed, at this time it has attained a comparatively
larger development than the digestive cavity, which is in active use, since the
young animal is entirely dependent on its own exertions for a supply of food.
The oesophageal region is very distinctly marked, though its dimensions are
proportionally small when contrasted with the length of the head; at present
it is not a quarter the length of the latter, whereas in the adult it is several
times longer. Its space is also considerably encroached on by the large cephalic
sacs.
At a further stage of development the animal is much elongated, yet still
possesses only two eyes. In this condition it has, doubtless, been mistaken for
the representative of a different genus, and is probably that referred to by Dr
JoHNSTON, under the name of Cephalothria ( Vermiculus lineatus, DALYELL).
M. DE QUATREFAGES observes that the reproductive organs are digitate in
Borlasia anglie, and figures them after this manner ;* but such is scarcely a cor-
rect definition; neither have any cilia been detected in connection with thes
structures. Indeed, he has probably mistaken the digestive canal and its saccu-
lations for the reproductive system, as he mentions that out of season the ceca
are filled with a fluid more or less opaline. M. Van BrENEDEN remarks that
the ovisacs contain from one to a hundred ova in his Nemertes communis; bw
although deposited in a membranous sheath in September, no change had ensued
* Op. cit. p. 182; pli xx. fig: 8.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 403
in November. His figure of the spermatozoa of this species* is not correct, as
no tails are present, and he describes them as simple rods. He makes the interest-
ing statement,} that in the same animal he found the embryos in some ova covered
with vibratile cilia while yet in the body of the parent, while others were only
fecundated during or after deposition. The development of the curious form
described by Mr Atex. Acassiz,{ which, commencing with an oral and anal
circlet of cilia, gradually looses these and two short antennze which subsequently
appear, and assumes the form of Nareda (GiRaRp) with two eyes, shows that the
type of growth is different from that of any British species yet observed. The
opening of the mouth (to all appearance) behind the ganglia points to some affinity
with the Borlasians; but the absence of so important an organ as the proboscis,
which very soon becomes conspicuous in all the young British forms, again leaves
us in doubt as to its actual position. The young Nemertean described by Dr
Buscu,§ under the name Alardus caudatus, would seem to have some relation to
Stylus (Micrura), since_it possesses a very distinct tail. The apparent segmen-
tation of the latter, however, is characteristic.
In Cephalothria (Astemma) the ova and spermatozoa are developed in a dense
series of sacs (that give the animal a transversely barred aspect), which com-
mence a short distance behind the mouth and continue nearly to the tip of the tail.
The males are distinguished by their somewhat paler aspect when their reproduc-
tive organs are fully developed, viz., towards the end of January and during the
subsequent spring months. The spermatozoa (Plate XI. fig. 3) consist of short
flattened spindles with rounded instead of pointed ends, that to which the tail is
attached being somewhat smaller than the other. In swimming about the two
ends appear as clear dots. Though the animal is extremely elongated, the bodies
or “heads” of the spermatozoa are comparatively short. The body of the female,
with matured ova, presents a duskier or slightly fawn-coloured aspect, the ova,
under slight pressure in the living animal, being arranged in dense transverse rows
in each ovary. The total number of ova produced by a single female must be very
great. In transverse sections they are seen to occupy a large ovoid space on each
side of the alimentary canal, upwards of twenty ova—very prettily arranged in a
concentric manner—occurring in a single thin slice. The space of the digestive
canal in these preparations had thus assumed the form of the letter x, the walls
approaching each other in the middle, but diverging superiorly and inferiorly ;
while a wedge-shaped fold from the dorsum below the proboscis, and another from
the ventral surface, completed the resemblance. This was the more marked, if the
* Op. cit. pl. i. fig. 18.
+ Op. cit. p. 138.—* La vésicule germinative ayant disparu, le vitellus s’organise, et, avant la
ponte, nous avons trouvé des embryons couverts de cils vibratiles.”
t Ann. Nat. Hist., 3d Ser. vol. xix. 1867, pp. 208-214, pl. v. figs. 3-17.
5 § Beobacht. iiber Anat. u. Entwickelung einiger Wirbellos. Seeth. Berlin, 1851, p, 111, taf. xi.
g. 8.
404 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
proboscis had been ejected. The ova are deposited from the beginning of February
till June; sometimes adhering together in irregular masses by their edges ora _
little accidental mucus, at others scattered about the vessel in detached groups.
In several instances, however, they were deposited in a translucent sheath of
mucus. On deposition they have the aspect shown in Plate XIII. fig. 3, being of
a granular structure throughout, with a clear spot and globule, and measuring
about ;i,th of an inch in diameter. The ova pass rapidly through the usual
stages, and on the 11th of February the embryos were revolving rapidly in the
egg by aid of their cilia, and in some cases hatched. The extruded animal (Plate
XIV. fig. 3), under moderate pressure, has a globular form, but assumes various
shapes when freed—the ordinary one being that of an apple—the long ciliary
process representing the stalk, while the body slightly tapers towards the
posterior end. It revolves rapidly between the glasses. The body is opaque and
granular, with the exception of the margin, which is somewhat paler, from the
slight differentiation of the cutaneous textures. lxternally, it is coated with
long cilia, by aid of which it executes rapid motions, and a tuft anteriorly had
the form of a long whip-like process, as during the progress of the animal it
appeared like a single mobile thread. The body is sometimes pitted at the origin
of the latter, while a slight papilla projects at the posterior end. When fixed
between the glasses the cilia were soon pitched off, and the animal resolved itself
into a number of cells and granules (Plate XII. fig. 11). In two days the animal
is found somewhat elongated (Plate XIV. fig. 4), and the mouth (a) becomes more
evident as a strongly ciliated slit placed nearly in the centre of the body, which, —
with the above-mentioned exception, is still uniformly granular. A longer tuft
of cilia at the anus is now more distinctly seen. Two days later considerable
increase has occurred in the length of the body (Plate XIV. fig. 5), and from the —
more anterior position of the mouth, it is apparent that the chief increment has —
taken place in the posterior region. The outline is now pear-shaped, the snout
being much less tapered than the tail. The cutaneous textures are more distinctly
marked, and the cells, with their refracting contents, very apparent; there is also —
a corresponding advance in the growth of the granules of the alimentary canal,
its ciliation, and the posterior sacculations. The whip-like tuft of cilia on the
snout is somewhat shorter, and there now exist a few longer cilia on the side of
the head, the posterior group of which (c) are evidently the precursors of the long
ciliary tuft, which by-and-by appears. ‘There is as yet no trace of eye-specks. A
few cylindrical papillze are observed on the snout and tail, and one or two along
the sides, which processes do not seem to result from pressure. In a day or two
afterwards some are furnished with one and others with two eye-specks. More-
over, the tuft of cilia on the snout is gradually diminishing in length, while the
lateral cilia (c) before-mentioned are becoming longer. During a period stretch-
ing from March to the beginning of June, the various vessels swarmed with
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 405
successive broods of young (from different individuals), which as minute white
specks darted about most actively. They did not crawl along the bottom, but,
like the young of Phyllodoce and other Annelids, swam freely throughout the
water after the manner of Infusorize, or danced to and fro Jike Ephemeree in the
air. Externally at this further stage of advancement they have still a coating
of very long cilia (Plate XIV. fig. 7), which serve as natatory organs, the tuft (c)
on each side being about thrice as long as the rest, while the long anterior
whip has disappeared. There are two large well-defined black eyes, no doubt
provided by nature for the exigencies of the youthful state, just as the young
of certain molluscs and Balani are similarly furnished. The mouth (a), the
cesophageal, and succeeding region of the digestive cavity are all richly ciliated.
The whole animal is soft and delicate, and none of my specimens survived this
stage.
We have thus in Cephalothriz a certain resemblance to the development of
M. Van BENEDEN’S Polia involuta, already described (see p. 369), and the phases of
the growth of the present species likewise corroborate everything that has been
advanced in contradistinction to the interpretations of the Belgian author. His
views in regard to the scolex and proglottis receive no support from the foregoing
observations, for all the changes that occur are only the gradual and very per-
ceptible shedding of certain cilia, and the general advance of organisation as
shown by the differentiation of tissues and the appearance of pigment in the eye-
specks. The shedding of the long anterior tuft of cilia by the young Cephalothrix
has its analogue in the loss of the ciliated ring by the young Phyllodoce and others,
in the casting of the temporary bristles noticed by Buscu and LeucKkart* in the
young of a Nerine, and by M. DE QuaTREFAGES in the young stages of Hermella.}
I think there can be no doubt that the remarkable tuft of cilia which occurs in
the young Cephalothrix on each side of the snout, and which attains its full
development after the long anterior tuft has ceased to be conspicuous, is con-
nected homologically with the entrance to the cephalic sacs in the Ommatopleans
and the fissures in the Borlasians, as well as with the ciliated ring of Phyllodoce
above-mentioned. It is an embryonic type of a structure which disappears
entirely in the adult form. The delicacy of the young at the period of the full
development of the eye-specks is an interesting feature; but it prevented my
observing their growth into perfect animals.
Thus, so far as development goes, Cephalothriz is nearly allied to the Omma-
topleans, especially to Tetrastemma variegatum, Polia involuta, and probably to
others of the group not yet investigated; while, in the structure of its digestive
system, circulatory apparatus, and the unarmed proboscis with its bridled sheath,
it leans rather towards the Borlasians. Prof. KEFrEeRsTEIN in his proposed classi-
* Ann. Nat. Hist. 2d ser. vol. xvi. p. 259, pl. vii.
+ Annales des Sc. Nat. 3d ser. tom. x. 1848.
VOL. XXV. PART II. 5 L
406 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
fication of the Order* rightly places the genus in a special Family, called Gymno-
cephalide, whose chief characteristics as described by him are:—Absence of
cephalic fissures; brain like that of Polia, but the superior ganglion covers the
inferior much less, and is advanced in front of it. He bases his statement of
the relationship to the Ommatopleans, as it appears to me, on somewhat
questionable grounds, for the ganglia are by no means closely allied in form and
structure to those of that group.
ANNELIDA.
In the following part of the paper I purpose making a few remarks on the
structure of some recent additions to the Annelidan fauna of Britain, as well as
of a few species believed to be new to science. Many of them have been known
to me for years, and, indeed, were figured and described in my MS. long before
the appearance of M. pe QuaTReFacEs’s “ Annelés” and Dr A. J. MALMGREN’s
‘Catalogue of Northern Annelids;’’ but the publication of these and other recent
works on the subject has occasionally anticipated me in nomenclature—a kind
of loss, however, which I esteem rather lightly, since so much yet remains to be
done in the minute structure of the entire class.
Amphinome vagans, Lnacu(?)—Two genera have hitherto represented the
British Amphinomea, viz., Huphrosyne and Spinther, and this species introduces
with certainty a third. Two very minute specimens (4th of an inch in length),
from St Magnus Bay, occurred in an extensive collection made last year (1867)
by Mr Gwyn Jerrreys, while dredging in the Shetland seas. The segments
numbered in the one twenty-three, and in the other twenty-seven. The head
agrees with that of Hipponde, Aup. and Ep.,} with which genus I at first thought
it most closely allied, but the feet are biramous. In these specimens also no
caruncle can be observed, the head forming a smooth rounded eminence, from
which a subulate antenna projects. No eyes are present. There are two
antennee in front of the median at the anterior border of the snout, and two
others at a distance behind. The bristles (Plate XV. fig. 1) of the superior and
inferior lobes of the feet agree in structure, and consist (1) of a somewhat stout
kind (6, c), which has serrations on one side, and thus not observable in all
positions ; and (2) of various modifications of a peculiar bifid bristle, some of
which (a), especially towards the posterior end of the body, show a swollen
part below the bifurcation, with a short and simple limb, and a longer process
serrated on one side, while others have the serrated limb extremely elongated
and tapered to a fine point, and with little or no swelling at the bifurcation. —
The inferior cirrus is very small. A large specimen from the Channel Islands —
‘seems to belong to the same or a closely allied species, but there are sixty-seven
* Zeitsch. fiir wiss. Zool. xii. 1863.
+ Hist. Nat. du litt., &c. tom. ii. p. 128, pl. 11 B. fig. 10.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 407
segments and four distinct eyes. The head in the latter is pale, somewhat horse-
shoe-shaped, with two short conical tentacles in front, and two longer ones a
little behind—opposite the swollen part of the snout. A curved line separates
the anterior from the posterior region of the head, the former being flattened, the
latter more elevated, and furnished with four reddish eyes, the anterior pair of
which are about twice the size of the posterior. A little behind the anterior
pair a filiform tentacle projects upwards in the middle line, and close behind this a
wrinkled ridge (caruncle) extends to the anterior border of the third bristled
segment. The sulci between the first three bristled segments are somewhat less
marked, and the slope of the bristles more oblique, but the rest are very distinctly
separated; indeed, the body has a somewhat moniliform aspect. The branchial
tuft springs from a point behind, and rather below the dorsal fascicle, and consists
of about four pale finger-like processes, which arise from a common basis ; they
commence on the second segment, and continue almost to the tip of the tail. In
this example, the swelling below the tip of the bristles, corresponding to fig. 1, a,
was not very evident, and the serrations of the extremely elongated distal por-
tion widely separated ; and, indeed, I was at one time disposed to regard the
animal as specifically different. The bristles of these animals are extremely
fragile, and the majority are broken during the efforts to decipher their structure.
The crop commences at the posterior third of the fourth bristled segment, and
extends to the posterior border of the sixth; it is truncated anteriorly and pos-
teriorly, and swollen in the middle. The commencement is marked by two
brownish specks. The published descriptions of the species of Amphinome make
it somewhat difficult to determine them with accuracy, and I am by no means
certain at present that Savicny refers to this form under the above-mentioned
name. I had provisionally termed the two minute eyeless specimens from the
_ Shetlands Hipponoe jefreysu,* but I think they may more correctly be grouped
with the example last described. The Hurythoe borealis of Sars} is a very
closely allied form.
Letmonice jilicornis, Kinsere.{—Three British species of the family Aphro-
ditaceze are recorded in the Catalogue of the British Museum, and one since the
publication of the latter by Dr Batrp; but I agree with Dr MALMGREN in con-
sidering A. borealis, JounsTon, only the young of A. aculeata, and the Lwtma-
tonice kinbergt, described by Dr Batrp,§ as L. filicornis of KinBERG,|| a species
which abounds on our north-western and northern shores, just as Hermione
hystrix does on our southern coasts. KrinpereG does not show the recurved fang
towards the extremity of the ventral bristles—an error probably due to the
inaccuracy of his artist. The dorsal bristles are very large and powerful, and
* Ann. Nat. Hist. Oct. 1868. + Christ, vid. Selsk. Forh. 1861, p. 56.
¢ Kongliga svenska Fregatten Eugen., &c,, 1851-1853, p. 7, taf. iii. fig. 7.
§ Dr Bairp is now of the same opinion. || Proc. Linnean Soe. vol. viii. p. 180.
408 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
taper towards both ends, especially the terminal. The recurved fangs of the
latter are not always readily seen until the bristle is turned round.
Lepidonotus pellucidus, Euters.*—Amongst the Lepidonoti dredged in Loch- —
maddy, North Uist, in 1865, this peculiar species occurred. The head has two
rounded and prominent lobes in front, that do not form the acute angles seen in
the common species. The eyes of each side are placed close together, while the
pairs are widely separated, and situated far back. Exuers’s description and
figures of the bristles need improvement. These structures throughout are pale
and translucent, the superior fascicle of the foot having a series of slightly curved
bristles (Plate XV. fig. 2, a), whose rows of secondary spines (about eight in
number) are very wide apart inferiorly, while the tip of the bristle is notched, as
if from a minute claw. Those of the ventral bundle are equally peculiar (0, same
figure), having a short but well-marked claw at the tip, with a small spike adjoin-
ing. The terminal portion is somewhat flattened, and marked by oblique rows of
secondary spikes, while it gradually widens inferiorly, and terminates in an
abruptly dilated shoulder, furnished with a projecting series of secondary pro-
cesses. The latter appeared to be similar to the spikes of the dorsal bristles, and
the intervening angle was filled with debris. Dr Ex ters does not discriminate
the bifid nature of the inferior bristles.+
Polynée longisetis, GRuBE,{ a species described as British by Mr E. Ray
LANKESTER,§ under the name of Harmothée malmgreni, though unfortunately,
owing to the engraver, its bristles have not been figured with anything like
recognisable accuracy, has been found after storms at St Andrews. It is
distinguished at once from ZL. cirratus (Harmothée imbricata) by the paler
and more resplendent bristles which flank its sides, by the structure and
ereater pellucidity of its scales, and by the structure of its dorsal cirri.
The dorsal bristles are almost identical, except in length, with those of
H. imbricata ; while the ventral, though formed on the same plan, characteris- —
tically exceed those of the latter in the length of the terminal spiked portion
(Plate XV. fig. 3). The dorsal cirri (Plate XV. fig. 3, a) present scarcely any
swelling below the tip, are pale throughout, and have only a few pale warts, so
that the entire organ is much smoother than in the common species. P. longisetis
exhibits a very close affinity with Lenilla glabra, MALMGREN. ||
Halosydna gelatinosa, Sars, a species first found on the shores of Norway by —
this celebrated naturalist, and afterwards by Kinsere** and Loven,}+ is abundant
* Die Borstenwiirmer, &c, p. 105, taf. ii. fig. 5, 7-13, and taf. iv. fig. 1-3.
+ M. Craparnps probably refers 1o this species (in his recent work ‘‘ Les Annélides Chétopodes —
du Golfe de Naples”), under the name of Hermadion fragile.
§ Archiv fiir Naturges. xxix. 1863. t Linnean Trans. vol. xxv. p. 375, tab, 51, fig, 28.
|| Nordiska Hafs-Annulater, 1865, p. 73, tab. 9, fig. 5.
{ Beskrivelser og Jattagelser, &c. p. 62, pl. ix. fig. 25.
** Kongliga svenska Fregatten Eugenies, &c. p. 19, taf. v. fig. 26.
tt} Cited by Matmeren, op. cit. p. 82.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 409
in the stomachs of cod captured off St Andrews Bay, and a few specimens also
occur at low water under stones. In the scale of the living animal a series of
radiating lines are observed to stretch outwards from the point of attachment.
The dorsal tuft of bristles is not conspicuous, and consists of a series of delicate
translucent bristles, with faint serrations at the tip. The bristles of the ventral
bundle are characteristic (Plate XV. fig. 6, 6a, 66), being pale, elongated, and
flattened out at the tip in varying degrees. The claw at the extremity of the
broad examples is short and strong, while the inferior division is slender. The
oblique transverse lines from the rows of spines are also very distinctly marked.
Sthenelais dendrolepis, Cuar.* was dredged in 90 fathoms, off North Unst,
Shetland, by Mr Jerrreys.—It has rather the aspect of S. boa, Jounston, than
Sigalion mathilde, Aup. and Ep., but it can at once be observed that its bristles
are more elongated than in either of these species. The form of the anterior
scales also approaches that in S. boa, being somewhat quadrate, with one end
‘rounded; but instead of having the simple papillee which characterise the margin
of the scales in the latter, the new species has peculiar pinnate processes (Plate
XII. fig. 12); the whole having a tree-like figure, while the shape of the pinnze
and the contour of the process in general readily distinguish it again from the
pinnate appendages on the scales of S. mathilde. The process in the latter has
aless robust form, its pinnee are hyaline cylindrical processes; whereas in the
present species they are lanceolate and granular lamellz, with a narrowed
papillary tip. The specific differences are likewise very apparent in the form of
the feet and their appendages, the superior lobe being somewhat leaf-shaped or
ovate, with a simple terminal process superiorly, and shorter than in S. mathilde;
the inferior lobe again has the spine-papilla much more prominent than in the
last-mentioned species. While the bristles of S. mathilde are proportionally
more slender than in S. boa, here they exceed both in length, especially as regards
the terminal process. There is a general resemblance in all the three species as
regards the superior fascicle, but the inferior groups differ very characteristically.
In the new species the superior bristles of the series with the jointed tips (which
adjoin the short tapering-spiked forms) have the terminal portion of the shaft
covered with whorls of somewhat sparse spikes (Plate XV. fig. 5), which (spikes)
are much more numerous than in either of the others before mentioned; while
the stouter series next these (Plate XV. fig. 4) have the same portion of the shaft
closely and transversely rowed with minute spikes. The spikes on the terminal
portion of the shaft of the inferior bristles are likewise more distinct, and the
terminal clawed portion longer.
* Les Annélides Chétopodes du Golfe de Naples, p. 99, pl. iv. fig. 4, and pl. v. fig. 1. I had
described this new species under the name of 8. buskii, but the unavoidable delay in the publication
of the present paper gives M. CrapareEpe’s title the priority, if, as I am inclined to think, it refers
to the same species.
VOL. XXV. PART Il. 5M
410 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
Sthenelais limicola, EnHuters.*—Another species of Sthenelais, brought in
numbers by Mr Jerrreys from the Shetland seas, seems to be identical with Dr —
EHLERS’s species from Quarnero, in the Adriatic. The anterior scales are furnished,
towards the outer margin, with peculiar processes, which, so far as regards our
examples, are uncharacteristically represented by the German naturalist. The —
processes are irregular, either simple, bifid, or divided into several pieces, and the
margin of the scale is generally folded back under examination, so as to render
them indistinct. In the first scale the processes are papillary and undivided. -The
dorsal lobe of the foot has four or five elongated papillary processes superiorly,
and a peculiar broad and curved lobule projects upwards from the inferior lobe. —
The inferior bristles have their terminal clawed portions shorter than in S.
mathilde, and those corresponding to figs. 4 and 5, Plate XV. (\S. dendrolepis), have
only two or three spines at the terminal portion of the shaft. Dr EuLErs’s figures
of the bristles are not good, whether as applied to this or any other species of
Sthenelais—no compound claw, for instance, appearing on the terminal process:
The animal also possesses four eyes, instead of the two mentioned by the foregoing
author, the anterior pair being hidden from ordinary observation in two sulci under
the squamous processes at the base of the median tentacle. This may be the
Aphrodita arcta of Sir J. DaLyELL,} a species likewise brought from Shetland.
Notophyllum polynoides, HirstED.—A specimen was procured from the deep-
sea fishing, off St Andrews Bay. The feet are described by Dr Matmeren,{ as
having the dorsal lamellz of an elliptico-subrectangular or unequally reniform
shape; and in this the new or regenerated plates were somewhat reniform, espe-
cially posteriorly, while the older inclined to an elliptico-subrectangular form.
The new lobes are even at the edges, but the older are slightly frilled or waved—
an appearance intensified by the coloured border of rich blackish-brown, which
glistens in the play of light with a purplish-red iridescence. They are also
characteristically marked with small groups of white grains. The structure of
the bristles is represented in (Plate XV. fig. 9), and consists of a long smooth —
shaft, which terminates in the swollen end and jointed tip, seen laterally in 9a,
and in profilein 9. The terminal portion is finely serrated, and on each side of
its base the shaft of the bristle sends off a series of short spikes, which are inclined —
towards the serrated edge of the terminal division.
Ophiodr omus vittatus, Sars.§—Dredged rather abundantly on a bottom of
tenacious grey clay and mud in Lochmaddy, in from four to eight fathoms, and —
rarely met with there under immersed stones at extreme low-water. Length, 27
inches; head small, distinct, furnished with five tentacles—two lateral on each
side, and a median; the inferior or external lateral being furnished with a thick
* Die Borstenwiirmer, &c. 1864, p. 120, taf. iv. fig. 4—7, and taf. v.
+ Pow. Creat. vol. ii. p. 170, pl. xxiv. fig. 14. t Nord. Hafs-Annulater, p. 93.
§ Forhandlinger i Videnskabs-Selskabet, 1861, pp, 87, 88.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 411
basal joint, anda more slender distal portion. Eyes four, the anterior pair being
larger as well as more distant from each other than the posterior pair. The
colour need not be referred to further here, than by simply mentioning that the
dorsum is of various shades of lustrous brown, banded at intervals with belts of
pale iridescent blue; while the under surface is of a deep, dark madder-brown.
The body dilates behind the head, attains its maximum about the anterior third,
and then tapers towards the tail. It is proportionally thicker than in its allies
(such as Castalia and Psamathe), and garnished at each side with long resplendent
bristle-tufts, that glance with the varied hues of the rainbow, the effect being
heightened by the two long hair-like cirri that stretch beyond them. The tail
terminates in two long slender styles, which are shorter, however, than the cirri
of the fourth foot from behind. Through the mouth is protruded a large pro-
boscis, which is unfurnished with jaws or tentacular processes; and this assumes
various forms after immersion of the living animal in spirit, or when killed by
the salt water being impure in any degree,—sometimes being cylindrical, or pre-
senting a constriction between the swollen base and distal rim.
The first four segments after the head bear modified limbs, each consisting of
two long cirri. As soon as the foot attains its perfect condition, it is found to be
distinctly biramous, thus at once demonstrating its distinction from all the
Hesionea except Scumarna’s Cirrosyllis (Pseudosyllis, QuaTREF.) and GirsrEp’s
Castalia. The superior lobe, as observed in a fine spirit-preparation, consists of
the long superior cirrus, which has 4 soft articulation at its base; an inferior
cirriform branch, from the upper and basal part of which spring a series of elon-
gated, slender, and tapering bristles, simple throughout. After attaining some
thickness, the shaft (Plate XV. fig. 8) is observed to be striated longitudinally,
and to have minute transverse touches, which, however, attain a larger develop-
ment in the next series. The inferior branch of the foot also consists of two por-
tions, a ventral cirrus, and a bristle-bearing process, from the posterior suface of
which the somewhat stiff fan of jointed bristles emerges. In such forms the
bristles of the anterior feet have shorter tips, while those of the posterior feet
have more elongated terminal processes. Besides, in each foot in this species
the terminal pieces vary in length, the shorter occurring superiorly and inferiorly,
or at the edges of the fan. When highly magnified (Plate XV. fig. 7), the claw
at the tip of the terminal piece is seen to be somewhat faintly marked, from the
blocking of its curvature by a process beneath, and the serratures of the edge
of the process very fine, indeed scarcely distinguishable near the end. The
shaft of the bristle is obliquely striated towards the articulation, longitudinally
throughout the rest of its extent, except as usual at the pale diminished base
(where the striz become indistinct), and marked by a close series of transverse
Specks or touches. The tip of this division of the foot ends in a cirriform pro-
longation. The jointed bristles of the inferior branch of the foot differ, as we
412 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
might expect, from any other allied British form, such as Psamathe fusca, Joust.,
and Castalia punctata, MiLu., each of which possesses similarly jointed bristles,
and has the serrated terminal portion peculiarly clawed. In Psamathe the larger
size, the structure of the shaft, and the coarser serratures of the terminal portion
(Plate XVI. fig. 2), distinguish it from Castalia; while the latter again (Plate —
XVI. fig. 1) has a much broader and proportionally longer terminal process than
the present form. The distinction in this respect between the Periboea and
Podarke of Dr Exters* and the latter is very apparent. Dr Gruse’s genus
Oxydromus,+ with which the foregoing has certain affinities, has also an unarmed
proboscis, but the feet are uniramous.
I may also remark that two very distinct species, or rather genera, have been
included—on the one hand, by Dr Jounsron in Britain, and on the other, by
several continental authors—under the name of Psamathe punctata. Some of —
the most recent foreign publications—such as the work of Dr Enuers and that of
Dr Matmcren—do not sufficiently recognise the distinctions between the two.
M. DE QUATREFAGES,| however, correctly separates them into genera, yet he places
the synonym Castalia punctata, “ Girst.” under both. Dr Maumeren,§ while
correctly including the Halimede venusta of RatTuKE || under Castalia punctata,
MUutt., falls into the error of comprising Dr JonHNnsTon’s species under the same
head—a slip which would not have happened if this excellent observer had seen a
specimen. Dr JouHnston’s species, for which, notwithstanding Dr EnLErs’s views,
the original name of Psamathe fusca4 may be retained, has a uniramous foot, with
the terminal portion of the bristles characteristically marked shortly after its com-—
mencement by a series of larger serrations, which gradually rise toa maximum, and
similarly diminish, before arriving at the middle of the process, into fine serrations .
that disappear before the clawed tip is reached (Plate XVI. fig. 2). All the bristles
of the foot are not so boldly marked as this example, but in each there is a ten-
dency to have ashorter terminal piece, with coarser serrations, than in those of its
immediate allies, and the clawed portion at the tip is very distinctly seen, so that
the bristle can be distinguished specifically at aglance. Theshaft has also coarser :
transverse markings, and its distal end is somewhat less clavate than in C. punctata.
The Psamathe cirrata of Prof. Kurerstern,** also described by M. CLaPaREDE,}}
seems to me to be allied in the closest manner to P. fusca, if, indeed, it is not
identical therewith. M. pE QuaTREFAGcEs, however,{{ considers the annelids
* Die Borstenwiirmer, &c. pp. 190 and 199, taf. viii.
} Troscuet’s Archiv fiir Naturges. 1855, p. 98.
t Annelés, vol. ii. 1865, pp. 100-102 and 106.
§ Annulata Polycheta Spetsbergie, &c. 1867, p. 31.
|| Beitrige zur Fauna Norwegens, &c. (Nov. Act. Acad. C. L. C. Nat. Cur. &c.), p. 168,
tab. vii. fig. 1-4.
{ Loud. Mag. Nat, Hist. vol. ix. p, 15, 1836.
** Zeitsch. fiir wiss. Zool. bd. xii. p. 107, taf. ix. figs, 32-86.
tt Beobach. iiber Anat. &c. p. 55, taf. xiv. figs. 1-7. tf Op. cit. vol. ii. p. 41;
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 413
described by the two foregoing authors as distinct species (which I hardly think
is the case), and classes them under the genus Kefersteimia. They also appear to
me to be in all respects much more nearly allied to the Hesionea than the Syllidea.
The Castalia punctata, MULL., again, has a biramous foot, whose compound bristles
(Plate XVI. fig. 1) have on the whole a longer terminal portion, with finer
serrations than in P. fusca. I have found it on various parts of the British coast.
Autolytus pictus, KuLERS.*—I agree with Dr R. Greerr,t} who, in his remarks on
Autolytus prolifer, observes that the above species (the Procerwa picia of EHLERS)
is, in truth, an Autolytus. It was first found in Britain under a stone in a
rock-pool at Paible, North Uist, and again, in greater numbers, at St Andrews.
Its length is about an inch. The dorsum is very prettily marked by a pale
central band, with numerous and rather regular transverse branches, which,
uniting with a pale lateral belt on each side, cut the sepia-brown pigment-
masses into oblong spaces. The latter are minutely striated under the lens by
fine pale lines, and the intervals dotted by almost microscopic pale grains. The
first twelve or thirteen segments are darker in hue dorsally, and the intersecting
lines paler; and in some the oblongs are decidedly paler in this region. Below
the pale lateral belt, and just above the feet, a dark-brown band runs from end
to end, intersected only here and there opposite the pale transverse belts by
narrow pale lines. A dark patch of brown is placed behind the median tentacle,
and from the latter two characteristic diverging pale lines proceed backwards.
The under surface is of a pale whitish or flesh colour. These markings were
well seen in specimens preserved for upwards of a year in spirit. The head is
rather small, and appears at first sight to be supplied with two eyes only, which
are situated laterally, and somewhat in front of the great median tentacle, but a
careful examination shows two clear lens-like structures on each side, the larger
towards the front of the pigment-mass, and the smaller behind. There is thus
some difference between our description and that of Dr Eu ers, since he shows
a posterior pair of eyes considerably behind the median tentacle, and quite
separated from the compound group in front. This ocular region is richly
ciliated, and so is the dark pigmentary portion on the sides immediately behind.
The median tentacle had its place supplied in a few instances by two of equal
length, but this is simply an abnormality. The segments (upwards of 100 in
number) behind the three or four anterior rings are furnished with a rather
short dorsal cirrus, a few simple spines, and a fascicle of bristles (Plate XV. fig.
11), which possess a short terminal piece, with a bidentate apex. I have not
seen any with a tridentate terminal portion, as shown by Dr Enters. Towards
the tail there is only a single conspicuous spine in each bundle of bristles, and,
finally, a larger and smaller spine form the sole appendages to the feet. Here,
* Die Borstenwiirmer, &c. p. 256, taf. xi.
+ Archiv fiir Naturges, 1866, and Annals N. Hist. March, 1868.
VOL. XXV. PART Il, ON
414 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
also, aS in many of the Syllidea, the terminal joint of the bristles undergoes
various changes throughout the course of the body, being very short anteriorly,
then lengthening, and again diminishing in size towards the tail. The latter is
terminated by two short curved styles. Dr Enters found his specimens at
Martinsica. M. pE QuaTREFAGES groups this species under his Myrianida, as
M, picta.*
Pionosyllis malmgreni, n. 8.—This species, dredged in the Minch, off Loch-
maddy, and also procured at the latter under a littoral stone, seems to belong to
Dr MALMGREN’s genus Pionosyllis,} but is distinct from the species described by —
him. The elongated terminal portion of the bristles (Plate XVI. fig. 10) is pecu-
liar, from the somewhat rapid widening below the bidentate apex. Faint serra-
tions are observed on the terminal or articulating end of the shaft. The present
is distinguished from Matmeren’s species, P. compacta, by the following par-
ticulars:—A shorter terminal portion to the bristles; the absence of the elon-
gated simple bristles in the non-budding animal; the greater length of the
palpi; and in the much more elongated condition of the tentacula and cirri,
which, moreover, are distinctly moniliform. In a specimen having a two-eyed
bud posteriorly, the latter had, besides the ordinary kind, a tuft of slender —
simple bristles, which did not reach beyond the others.
Under the title Syl/is armillaris, Dr JouNsTON seems to have included two
very distinct species, the S. armillaris, Mitu—a form occurring very abun-
dantly between tide-marks, and having a single claw to the tip of the terminal
piece of the bristle, and another annelid equally common in the laminarian
region and deep water, whose membranous tubes occur in hundreds on the blades ~
of Laminaria saccharina, tossed on shore by storms. The latter is probably the
species referred to by Mr Gosse} under the name of Syllis tubifex, though various
characteristics, such as the single tooth of the proboscis, and the exact structure
of the bristles, are omitted. The palpi are of considerable length, joined at the
base in front of the snout, and richly ciliated, besides having in front some
motionless microscopic spinules. The processes of the head and the two next
segments are most distinctly moniliform, as well as longest, and the succeeding
cirri show the crenations in a diminishing degree. All have the microscopic
spinules. ‘The proboscis has a denticulated edge, though a third of the circum-
ference is only minutely crenated, and it is furnished with a single pyramidal
tooth. This region is usually thrown into prominent wrinkles. Several elon-
gated papilla are present in front of the anterior edge of the proboscis—some
apparently directed forwards, others backwards. The proventriculus is studded
with minutely granular glands. Segments about fifty-six in number. Th
bristles, which are similar to those represented in Plate XV. fig. 21, have a short:
* Annelés, vol. 1. p. 63. t Annulata Polycheta, &. p. 39.
+ Ann, Nat. Hist. 2d ser. vol. xvi. p. 31. y
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 415
bidentate apicial portion. The colours of this species are very beautiful, and it
is brilliantly phosphorescent. It appears to fall under Dr MatmcGren’s genus
Eusyllis, and to be most nearly allied to, though not identical with, his #. moni-
licornis. Another new British species, characterised by indistinctly articulated
tentacles and cirri, four very large and unusually distinct eyes, very short
bidentate apicial portions to the compound bristles, and the presence of long
simple hairs, seems to be the #. blomstrandi of the same author. It was dredged
in the Minch in 1865.
Syllis krohnit, HALERS,* var.?—Found under a stone in a rock-pool at Paible,
North Uist, in a tube of sand. In this animal every alternate dorsal cirrus is a
third larger, more opaque, speckled with white dots, and, instead of passing
transversely outwards like the others, curves upwards in a very graceful fashion,
and is often coiled at the tip. The others are smaller, paler, also speckled with
white dots, and longer than the diameter of the body. The ventral cirrus is very
small. The bristles (Plate XVI. fig. 14) have a stout terminal portion, with an
entire claw at the apex, and the edge is serrated. The curves of the terminal
portion of the shaft are peculiar, and, in this respect, allied to MALMGREN’s Syllis
borealis,} from which, however, the animal is readily distinguished by the charac-
ters of the dorsal cirri, and the more elongated condition of the cephalic lobes.
Unless we are to mistrust the descriptions and figures of the dorsal cirri given
by Dr Enters, the British form varies very considerably from the typical one.
In no state were the alternate cirri club-shaped, and those of the third and fourth
segments were small and nearly equal; whereas he shows them furnished with
a clavated pair, and all much more distinctly annulated than in the British
example.
Syllis cornuta, RatHKe.{—A Syllis, dredged off the Hebrides by Mr Jerrreys,
presents certain characteristics which point to its identity with the above-men-
tioned species of H. Ratuxe; and since it is doubtful (from the description at least)
whether Dr Jonnston’s remarks§ apply to this animal or not, I shall briefiy
allude to its structure. The body, composed of fully 100 segments, is about an
inch in length, and of a highly iridescent aspect, from the close plaiting of the
fine muscular fibres. All the tentacles and cirri are moniliform. Each foot has
a dorsal cirrus, divided usually into twelve segments, a bristle-papilla, and a short
lingulate inferior lobe. The bristle-bundle is chiefly composed of the form 0
(Plate XVI. fig 15), which at first sight resemble simple bristles, as their articu-
lating processes are usually hidden amongst the others. They have, however, a
most minute bidentate tip. Some (a) again have an extremely elongated ter-
minal process. Dr MatmGRen’s figure|| represents the dorsal cirrus as furnished
* Die Borstenwiirner, p. 234, taf. x. { Annulat. Polycheta Spetzbergie, &c. 1867.
{ Beitrage zur Fauna Norwegens, p. 164, taf. vii. fig. 12.
§ Catalogue, &. p. 192. || Annulat. Polycheta, &. p. 43, taf. vil. fig. 46 c.
416 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
with at least double the number of annulations described above, and the bristles
are not characterised by the minute bidentate apex; moreover, only a linear or
profile view of the elongated kind is exhibited, so that the characters required
some further elucidation.
A species allied to the Syllis macrocera, GruBE,* was found under a littoral
stone at Lochmaddy. It had about the same number of segments as the fore-
going, smooth cirri, and a very short apicial piece to the bristles. It was of a —
dull orange-yellow colour, with the head about as long as broad, the central
tentacle longer than the lateral, and all extending beyond the lobes. The bristles —
(Plate XV. fig. 12) of the several fascicles do not vary to the same degree as in
such as S. armillaris, MULL., and each has a blunt claw at the apex, with a
rough edge, for the notches are irregular. The articular portion of the shaft
ends bluntly. 7
Spherosyllis hystrix, CLAPAREDE.}|—Two forms of this species were found at
North Uist in 1865, the one in the littoral region at Lochmaddy, and the other
in the Minch. The littoral form (apparently that described by M. CLAPAREDE)
was marked down the centre of its pale body by a moniliform yellow band
(intestine). The body tapered anteriorly, and ended in a small snout formed by
the united palpi. Eyes four, placed close together in pairs, the anterior only
furnished with lenses. Segments thirty-two. The tuberculated dorsal cirri with
their swollen bases were well marked. At the eleventh segment a series of flask-
shaped bodies (buds)—two in each segment—commenced, and continued almost
to the tail. These bodies were of a pale rose-pink hue, with a reddish spot in
the centre, where the oil-globules were massed. They were nearly equal in size
throughout, had the usual processes at the ends, and were all thrown off when
the animal was placed in spirit. The tail terminated in two swollen cirri. The
bristle-bearing papillee were distinctly tuberculated, and furnished throughout —
with compound bristles (Plate XV. fig. 10, 0), which had a delicate and rather
elongated apicial portion with a simple claw at the tip, and a stout simple bristle
(fig. 10, a) slightly bent towards the attenuated extremity. In addition, from
the ninth segment backwards nearly to the tail, each foot was provided with a
tuft of long filiform bristles, which stretched far beyond the others. It seemed
an inactive animal, and lay rolling on the bottom of the vessel; and the numerous —
parasitic organisms on the bristles would likewise indicate a sluggish habit. In
the other form (from the Minch) there were none of the last-mentioned filiform
bristles, and the compound series, moreover, had a more elongated apicial piece
(Plate XVI. fig. 9). The eyes also were in one specimen six, two larger ones
posteriorly on each side, quite separated from each other, and two small round :
* Quatrer. Annelés, vol. ii. p. 28.
+ Beobach, &c. p, 45, taf. xiii. figs. 36, 37, and Glanures Zootomiques, &c. p. 86, pl. vi.
fig. 1. “a
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 417
specks in front. In the second specimen the two anterior eyes were absent.
Segments about thirty
ee ocophiilus kefersteint, n. s.—On both the eastern and western shores of
North Uist a species of Prof. Gruse’s genus Staurocephalus* occurred under
stones near low-water mark. Body of an orange hue, paler towards head and
tail; length about an inch. Eyes two, black, situated near the posterior border
of the head. The latter conical, the snout forming a somewhat blunt apex.
Tentacles four, the anterior, arising from the infero-lateral region of the head, by
much the largest, and having a short jointed process at the tip; the posterior
pair, springing from the outer side of each eye, are annulated and much less.
The large anterior pair can be coiled and twisted very prettily. The feet, instead
of being furnished with a dorsal and ventral cirrus, as in most of the species,
have only a small ovate dorsal and ventral process (Plate XVI. fig. 11, fand g) as
their representatives, and they are scarcely more prominent than the bristle-
papille ; thus it approaches S. eruceformis, Mcrn.; from which, however, it
differs in the structure of the bristles and other respects. The superior fascicle
of bristles consists of two series, a stout bifid kind (Plate XVI. fig. 11 6) with
the long limb of the fork flattened and slightly clawed at the tip, the shorter trun-
cate and rounded. The second series (fig. 11 @) are more slender, elongated, finely
tapered, and definitely curved, with a limited number of slight serrations on the
distal and convex side of the curve. The bristles of the inferior fascicle again
are all compound and of one kind, the terminal portion being somewhat elon-
gated, clawed at the tip, and without evident serrations on its edge. In regard
to the length of the terminal piece, these bristles present a gradational arrange-
ment, the longest terminal portions being superior, the shortest inferior. The
extreme bristles of a single foot are shown in figs. 11 ¢ and 11 d; and it will be
observed that the swollen terminal portion of the shaft has a few serrations. The
tail is terminated by two styles of moderate length, which, like the processes of
the feet, are much shorter than in S. ciliatus. Matmeren,} alludes to a drawing
of a species of “ Prionognathus,” apparently different from the latter, which had
been sent him by A. Borck from Norway; but he gives no description.
scoticus, n. s.—At least three species of the Family Lwinbrinereide
have been hitherto described as frequenting the British shores, viz., Lysidice ninetta,
Aup. and Ep., Lumbrinereis tricolor, Mont., and L. latreillii, Aup. and Ep. The
two latter, however, have in all probability been sometimes confounded with the
L. fragilis of MULLER, a species abounding on our northern and southern coasts.
A fourth and very well-marked form, which I have designated by the above name,
was dredged amongst tenacious grey clay in 6 to 9 fathoms in Lochmaddy, and
subsequently in several parts of the Hebridean seas by Mr Gwyn Jerrreys. The
* Prionognathus, Kererstein, Zeitsch. fiir wiss. Zool. vol. xii. p. 99, taf. viii. figs. 13-19.
} Annulat. Polychet. &c. 1667, p. 62.
_ VOL. XXV. PART II. DO
418 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
head is of an acutely conical form, with two distinct eye-specks at its posterior
border, close to the first transverse sulcus. Its body is much more slender than
that of ZL. fragilis, and at once attracts notice by its characteristically marked
segments, which, with the exception of a few anteriorly, assume quite a monili-
form appearance. In the structure of its feet it differs from all the foregoing
species. Each foot is furnished with a small branchial lobe (Plate XVI. fig. 17 a)
in which a single vascular loop is observed; and thus it would appear to fall
under the genus Notocirrus, ScuMARDA,* though the possession of the eyes is
exceptional. The tip of a stout spine or two (0) projects beyond the foot amongst
the bristles. The latter (c) have simple shafts with a broad spear-tip, which
tapers to a fine point, and is faintly serrated along part of the edge.
Hyalinecia sicula, QUATREF. (?)—This is a small representative of the Onu-
phidide, dredged in 90 fathoms off North Unst, Shetland, by Mr Gwyn JErrreys,
F.R.S. It is characterised in spirit by two parallel bands of brown which course
along the lustrous dorsum from a transverse belt of the same colour immediately
behind the head, and by a brown spot between each foot from the fifth backwards.
There are three elongated tentacula (a median and two lateral), and two shorter
in front, as in 7. tubscola, Mutt. The small black eyes are situated at the outer
side of the base of the long lateral. All the tentacles have a crenated base. The
antennz are similar to those of H. tubicola, or perhaps slightly longer. In the
structure of the bristles of the anterior feet, however, a very diagnostic feature
occurs; for instead of the large unjointed winged hooks, which are found in the
latter and in Nothria conchilega, Sars, there are peculiar jointed structures (Plate
XVI. fig. 3); and the bristles (fig. 3c) are slender, and furnished with a very
narrow wing, whereas in both of the other species they are shaped like a Valentin’s
knife. Posteriorly the jointed hooks are supplanted by two simple ones (fig. 3 0),
which are stouter and slightly curved. Some of these occasionally present no
wing at the tip. The bristles in this region are also shorter, and some are
characteristically curved at the point. None of the peculiar brush-shaped bristles
common in the two species above-mentioned occurred in this animal. No tube
accompanied it; but I have since found that this species inhabits a tube com-
posed of gravel and shell-fragments, and thus differs very considerably in its
habitation from /7. tubicola, while the length and form of the tube also distinguish
it at once from that of Nothria conchilega. The foregoing animal has certain close
affinities with the Onuphis sicula of M. DE QuATREFAGES,} but differs from the
description of that author in so far as the bases of the tentacles do not occupy the
whole surface of the head, which in the Sicilian species is very small. The body
is rounded in the latter, flattened in the British; and the bristles of the former —
are said by M. DE QuATREFAGES to present a great resemblance to those of
* Neue wirb. Thiere, &c. tom. 1. i. p. 114. t Annelés, vol. i. p. 352.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 419
O. tubicola, a statement at variance with the characteristics of the present
species. The persistent brown stripes and spots also had not been seen by M. pr
QUATREFAGES
———- jeffreysii, 0. s—This curious form, which I have been unable to
identify with any known species, occurred amongst the annelids dredged by Mr
JEFFREYS off the Hebrides in 1866, and again amongst those from Shetland in
1867. The length is about 13 inch, and the outline of the body somewhat fusi-
form, the greatest diameter being at the anterior third. The head is small, fur-
nished with two short thick tentacles, which give it a bilobed aspect, and is gene-
rally retracted within the papillose anterior region in the preparations. The
mouth opens on the ventral surface just behind the snout. The structure of the
skin and the arrangement of the rugose annulations resemble the same parts in
Travisia, Scalibregma, Eumenia, and their allies; but the animal essentially
differs from each of the foregoing in having no trace of branchial filament
or appendage. The tail has several elongated processes around the anus.. The
ventral surface is in some cases marked by an elevated median line. There are
about thirty segments, each of which has three rings. A double row of isolated
papillze runs along each side from the snout to the tail, the summit of each process
giving exit to a fascicle of bristles composed of two kinds, viz., numerous long,
simple, hair-like bristles, tapering to a very fine point, and a shorter forked series
(Plate XVI. fig. 5). The only other case in which I have up to this time met
with such bristles, is in a remarkable fragment of the posterior end of a small
yellow annelid from Lochmaddy, which may have some relation to Montacu’s
Nereis pinnigera. The foot had an elongated unjointed dorsal, and a shorter
ventral lobe, and possessed two fascicles of bristles, each of which consists of long
simple bristles, and a few of the forked kind mentioned above.
There is much in the foregoing description that agrees with Humenia crassa,
(Hrst., but the absence of the branchial filaments is diagnostic. Dr Bartrp had
received this species from the same source, and kindly sent it, with other rare
and doubtful specimens, for my examination. He likewise recognised the absence
of the branchie, and his preparation was labelled ‘‘ &. ebranchiata(?).” The
Vermiculus crassus of DALYELL* had no bristles, and cannot easily be recognised
from the description or figure.
Chloreemide.—Two examples of this family have been recorded as British,
viz., Trophonia plumosa and Siphonostoma uncinata, both of which abound in Scot-
land. Another species of Trophonia, dredged by Mr Jerrreys in the Hebridean
and Zetlandic seas, is recognised specifically by the absence of hooks in the
inferior rows, and the substitution of the jointed bristles. It agrees with the
T. glauca of MatMGREN ;+ but this author does not specially point out the essen-
*Opxcit. p. 8, pl. x. fig. 11. + Annulat. Polychet. &c. p. 82.
420 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
tial change in regard to the inferior appendages of the feet. As contrasted with
the common species, the joints or transverse markings of the bristles are much
more boldly indicated in this form, especially in those from the inferior fascicles —
(Plate XV. fig. 13 6). The latter bristles (inferior) are shorter than the superior,
and both, as usual, have larger joints than the anterior series. A second repre-
sentative of the family (Siphonostoma buski, n. s.), from the Minch, off Lochmaddy,
North Uist, is remarkable for its deep-red colour throughout, a hue so unusual
in the group. The two long tentacles or palpi are pale, but the branchial fila-
ments are deep red. The surface of the body is furnished with minute papille, —
which have the enlarged terminal portion furnished with a knob at the tip. The
hooks (Plate XVI. fig. 4) differ very much from those of S. wncinata, in so far as
the shaft is much longer and less robust, and the terminal claw more elongated,
and abruptly curved. When the latter breaks off, it separates obliquely at a, a
little above the articulation, leaving the short spike through which the dotted
line passes. A bristle is shown in fig. 4a, and a fragment more highly magnified
in Plate XV. fig. 13 a.
Maldanide.—Two species of this family (Clymene, QuaTREF.) are mentioned
as British by the authors of the Catalogue, both of which are of doubtful identity,
and apparently referable to the common Clymene lumbricalis, Fasr.* (Nicomache
lumbricalis, Mern.), though this is by no means certain. Mr E. R. LANKESTER, in
his list of the Annelids collected at Guernsey} in 1865, notices a third species—
viz., the Clymene amphistoma of Savicny. The explorations of the coast line in the
Hebrides, and dredging in the surrounding seas by Mr Jerrreys and myself, as
well as the cruise to the Shetland Islands last summer by the former experienced ©
investigator of our seas, have considerably augmented the number of the British
representatives. One of the most remarkable species is the ARhodine Lovent,
MautMGREN,t which combines an entire anal funnel, with a pointed snout, and has
its characteristic hooks (Plate XV. fig. 16) in a double instead of a single row, thus
materially differing from the others pertaining to the family. The outlines of the
hooks of the British species differ insome details from those represented by Dr —
MALMGREN—a discrepancy in all probably due to the inaccuracy of his artist. The
Awtothea catenata, Mern.,§ was dredged recently by Mr Jerrreys, off St Magnus
Bay, Shetland, in 80 to 100 fathoms. Besides having an infundibuliform anal —
funnel, with alternate longer and shorter filaments, the base of the cup is marked
exteriorly on the ventral surface by a continuation of the median line. There are
about forty processes on the margin of the funnel, a smaller one, and sometimes two,
occurring between the longer filiform divisions. The base of the funnel is surrounded ©
* Faun. Greenland. p. 374. + Annals Nat. Hist. May, 1866.
t Nordiska Hafs-Annulater, &c. 1865, p. 189; and Annulat. Polycheta, &c. p. 99, tab. x.
fig. 61
§ Annulat. Polychet. p. 99, tab. x. fig, 59.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 42]
by a distinct cup or fold exteriorly. The anal nipple, moreover, is roughened by
small papillz. The bristles are slightly winged below the tip, and under a power of
700 diameters show minute serrations at the margins of the wings. Instead of
hooks, the first bristle-bearing segment has three very stout spines gently
curved at the tip, and the second and third four of the same character. They
have a distinct shoulder, and the chitinous substance is strongly striated longi-
tudinally. Only a small portion of the tip is usually seen beyond the skin. The
hooks in the segments which immediately follow have the processes above the
ereat tooth somewhat fewer (four to five), but the rest have six; and in those of
the last row, in front of the anal funnel, the denticles are even more numerous
towards the crown. The great tooth comes off somewhat stiffly at the base, and
its upper curve is not sinuous. Dr Maumcren does not notice the peculiar spines
anteriorly, but simply mentions that the hooks are fewer in those segments, and
omits several characteristics described above. There are no hooks on the soft
lobulated processes which succeed the last bristle-bearing segment, with its con-
spicuous transverse pad. The frontal lobes form two very prominent laminee.
Another species, the Praxilla preetermissa, MALMGREN,* is not uncommon on
our western and northern coasts, inhabiting sandy mud at a depth varying from
four to eight fathoms. Ina large specimen the teeth of the anal funnel are 27
in number. The hooks are characteristic, having about six teeth above the
large fang, and a well-marked interval between the latter and the origin of the
spinous tufts. The first three segments have simple and strong spines with the
apex slightly curved. There are also a few shallow crenations on the margins of
the cephalic lobes. A somewhat rarer species is Praxilla gracilis, Sars,+ two
specimens of which appeared in the rich collection brought by Mr JEFrrRrys
from the Shetlands. The hooks of the first three bristled segments differ from
the others, and are spines with the apices more curved than in Axiothea, so as
to resemble a hook furnished with the large fang only. A third species of
Prazilla from the same region (North Unst, St Magnus Bay, and the Outer
Haaf), while agreeing in several particulars with P. pretermissa, has its funnel-
teeth much more filiform and distinct—in one instance 14in number. The hooks
(Plate XVI. fig. 13) have the large fang short and powerful, with the spinous
filaments arising close underneath, and a numerous array (seven to eight) of
diminishing teeth superiorly, the whole forming a very elevated crown, indeed it is
the most elevated of the series in this respect. The curves of the hook, especially
the posterior, are characteristic. The bristles are also peculiar, for instead of the
usual winged margin, the whole shaft is flattened out towards the translucent
tip, very minutely serrated: at the edges, and tapered to a delicate point. The
shaft below the flattened portion is, as usual, finely striated longitudinally.
* Nordiska Hafs-Annulater, p. 191. + Fauna litt. Norveg. ii. p. 15, tab. 2, figs. 18-22.
VOL. XXV. PART II. DP
422 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
This may be Matmeren’s P. artica,* but as he only says as to its characteristics
that it is similar to P. pretermissa, with the exception of having six teeth on the
crown of the hook, we are left quite in doubt as to his species.
The anterior portion of a specimen of Clymene ebiensis, Aub. and Ep.,+ also
came from Shetland. Itis recognised by the pointed snout, the somewhat swollen
anterior segments, and the absence of the usual frontal flattening. The shape of
the hooks (Plate XVI. fig. 12) is peculiar, the chief fang being short, and the
crown somewhat flattened. There are five or six teeth above the former. The
curves of the organ and its coarse strize are also characteristic. I could not find
in this specimen either spines or hooks in the first three segments. The figure
of the hooks given in the “‘Regne Animal” is quite unfit for identification. The
species is also allied to Prof. GruBe’s Clymene leiopygos,t from Cherso, though his
drawing of the hooks is widely different.
The Ammochares ottonis, GRUBE,S has been found searadonslgs at St Andrews,
in the stomachs of cod, at Lochmaddy under stones near low water, and dredged
by Mr Jerrreys in Shetland and the Minch. The bristles are rendered hirsute
by microscopic spines, as shown by Dr Matmaren;|| but the hooks of the rasp-
like belts have a much more characteristic shape than represented by this author's
artist, since they are figured without any shoulder, and with the curve at the
back of the beak too prominent. Their exact condition is shown in Plate XV. fig.
14. There are three tufts of longer and more delicate bristles in the British
specimens on the first region, instead of two, as shown by Drs Gruse and
MaLMGREN; but one may have been overlooked from its minuteness. I am
inclined to believe, judging from MaumGren’s paper, that the A. assimilis of Sars
is the same species as the above. Dr Carrinaton of Eccles describes this species4,
under the name of Ops digitata.
Of the family of the Ampharetea, MALMGREN, several representatives new to
Britain have occurred. One species, the A mphicteis gunneri, Sars, though unnoticed
in the recent Catalogue of the British Museum, had been found by Mr Gosss at
Ilfracombe, and described by him under the name of Crossostoma midus.** Dr
-MatmeGrentt mentions another form, the A. swndevalli, which is characterised by —
having nineteen hook-bearing processes posteriorly, whereas the former has but —
fifteen; the bristles also have the winged portion striate, and the upper part of
each hook widest, while in A. gunneri the corresponding region of the bristle is
smooth, and the hook widest in the middle. Our common Hebridean and Zet-
landic Amphicteis has certain of the characters ascribed to each of these species,
* Annulat. Poly. Spetz. &. p. 100. + Cuv. Reg. An. iii. pl. xxii. fig. 4.
+ Archiv fiir Naturges, 1860, p. 91, taf. iv. fig. 3.
§ Archiv fiir Naturges. 1846, p. 163, taf. v. fig. 2 a, b, ¢.
|| Annulat, Polycheta, &c. tab. xi. fig. 65 D. Proc. Lit. & Phil. Soc. Manchester, 1865.
** Ann, Nat. Hist. vol. xvi. 1855, p. 310, pl. vin. figs. 7-12.
++ Nordiska Hafs-Annul. taf. xix. fig. 46 D.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 423
for the bristles agree with those of A. swndevalli in having the winged portion
striate, while the hooks are widest in the middle (Plate XIV. fig. 14), and there
are but fifteen hook-bearing processes posteriorly. A boreal form, not uncommon
in the Scotch seas, is Ampharete artica, MALMGREN, the hooks in this species
being furnished with a large number of teeth (Plate XIV. fig. 13). The former
examples possess frontal bristles, but two species in Mr Jerrreys’ Hebridean and
Zetlandic collections have none. The first is the Sabellides sexcirrata, Sars.*
wherein the hooks have for the most part five teeth, though some of the larger
have six (Plate XVI. fig. 16 @ and 16 6). Occasionally one occurs in the centre
of the row with only four large teeth. The other species was in a very imperfect
state, but seems to be an Amage, Marn., having about fourteen bristle-bundles on
each side, somewhat club-shaped smooth tentacles, and the ventral bars very
distinctly marked. The hooks (Plate XIII. fig. 10 and 10 q@) have four or five
teeth, and differ so much from A. euricula, MeRN., that in all probability the
animal is distinct.
_ The descriptions of the British Terebelle given in the Catalogue of the British
Museum stand very much in need of revision, it. being difficult, indeed, in some
cases to understand what species is meant. Thus 7. conchilega could not be
identified from the characteristics there noted. The 7. nebulosa of Dr Jounston
is not that of Montagu, but a very different form, with 24 pairs of bristle-bundles
(he says 23), and well-marked hooks, with the chief fang very long and several
smaller processes above it. It may be remarked in passing, that in such a profile
view all the small hooks on the crown are not seen, and hence the armature is
greater than at first sight appears. This species attains a very large size on our
western shores. Dr MatmGren} proposes for it the name of Amphitrite John-
stont, but Sir J. Datyett had long previously called it 7. jigulus.t The true
T. nebulosa is described in the Catalogue under 7. tuberculata, DALYELL, and
Montacu’s name, at any rate, must stand instead of Matmcren’s recent title,
T. debilis. The hook of this species has two very distinct fangs and a greatly
elongated base.
In addition to the twelve species mentioned in the Catalogue no less than
eight new British forms require notice. In Terebella (Nicolzea) zostericola, GiRst.,
‘a very abundant species, the hooks (Plate XV. fig. 15) are furnished with a single
fang above the large one, and in some cases with a trace of a second. Pista
eristata, MULLER, a species with a single pair of whorled branchive, was first got at
Lochmaddy, and since at various parts of the coast; its hooks are characterised
by the singular form represented in Plate XV. fig. 20, with three or four prongs
above the chief fang, and a powerful process for the ligament at the posterior end
* Fauna litt. Norveg, ii. p. 23. + Nord, Hafs-Ann, p. 377.
{ Pow. Creat. vol. ii. p. 191, pl. xxvii. figs. 1 and 2.
424 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
of the enlarged base. This animal is quite different from the 7. maculata of Sir
J. DALYELL, which may be a species having a speckled aspect in spirit, a single
pair of branchize, and hooks of the form shown in Plate XIV. fig, 15. The
Grymea bairdi, Mern., a form nearly allied to Thelepus circinnatus, Fase.
(Venusia punctata, Jounst.), was dredged in 90 fathoms off St Magnus Bay,
Shetland, by Mr Jerrreys. It is at once distinguished from the latter by the
much greater prominence of the bristle-papillze, and the greater length and lustre
of the bristles themselves throughout the entire body. The hooks resemble those
of the common species (7. circinnatus) very much, but the process for the liga-
ment is not so near the tip of the upper curve as in the latter, and the organs are
proportionally smaller. The tube is composed of fine grains of muddy sand, in-
stead of the coarser and stronger structure of 7. circinnatus.
Amongst the Polycirridea from the same region is a very interesting form,
called by Dr Matmcren Lysilla lovenit, and distinguished by the largely dilated
cephalic lobe, furnished with numerous clavated grooved tentacles along its
margin, and a cluster of tangled filiform processes inferiorly at each side. The
whole of the anterior dorsal region is densely tuberculated with papillee, which,
from the intervening lines, assume a transverse arrangement. On the ventral
surface, which is thrown in contraction into two prominent longitudinal folds with
a central depression, the swollen portions are covered with somewhat larger
tubercles than the dorsum, but the depressed central region forms a nearly
smooth line of demarcation. There are six pairs of foot-papille in front, each —
having a short tuft of simple slender bristles, whose tips in the preparation are
entirely within the summit. From the same source as the latter there is also the
anterior fragment of another curious and new example of the same sub-family.
| Polycirrus tribullata, 0. s., which has neither bristles nor hooks. The head and
tip have the usual tentacles. The body has no ventral plates, but only a raised
central line. There are three pairs of well-marked circular truncated papille —
(on the sixth, seventh, and eighth segments), each consisting of a raised ring
externally, with an elevation in the centre. Two minute papille were visible in —
front of the first flattened process, but only a trace of an elevation occurred on
the lateral region of the succeeding segments, which were two-ringed. The
cuticle has a minutely granular aspect. The remarkable lateral processes may —
act as suckers. ‘'I'wo species, which come under Dr MauMGREN’s recently con-—
stituted genus Lreutho, are not uncommon in Britain. They are distinguished
from other Polycirridea by having thirteen pairs of bristle-bundles. The first,
which seems closely allied to £. smitti, Mern., has hooks (Plate XV. fig. 17), —
which possess only two fangs, and a very much produced and characteristically —
striated basal process. The hooks of the other species (Plate XV. figs. 18 and 19)
are much smaller than the foregoing, and so exactly resemble the figure by
MauMGRrEN from a specimen of P. aurantiacus, GRUBE—forwarded by Prof. GRUBE-
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 425
himself—that one may be allowed to have some doubt as to the correctness of pre-
vious descriptions with regard to the number of the bristle-bundles. The last of the
group is T’richobranchus glacialis, a species which Dr MatMGREN has only described
from aspirit-preparation.* This form was dredged in six to eight fathoms in Loch-
maddy, in 1865, as well as got under a stone amongst sandy mud at low water.
Length about 3ths of an inch when moderately extended. Of a general blood-red
hue, or dark-red anteriorly, paler posteriorly. In shape the body is irregularly
fusiform, ending anteriorly in rich red lips, with a translucent projecting collar
at each side, leaving the dorsal and ventral edges free. From the dorsum, slightly
posterior to the fissure thus left, spring a tangled series of tentacles, which are
easily differentiated into three groups, even in the spirit-preparation. The most
conspicuous, long, thick cylindrical processes, varying from four to six in number,
arise distinctly behind the others, from the dorsal edge posterior to the cephalic frill,
and are distinguished by a bright-red central vessel, as well as by the frequency
with which they are thrown into spiral curves. They are capable of great exten-
sion, and seem more especially homologous with the branchie of the Terebellee.
In front of the latter series is a dense mass of short, pale-pink, thread-like ten-
tacles, while a number of larger, clavated, red-streaked ones, arising from the
border of the lip, are in the centre of these. The latter become grooved in con-
traction. In fine specimens, the varying habit of these three groups of tentacles
is very marked. Four annulations occurred on the ventral, and three on the
dorsal aspect (the first not being visible after immersion in spirit), before the
bristles appeared. These are ranged on fifteen prominent papille, and during
life are frequently directed forwards. The arrangement of the bristles in the
fascicles is peculiar, for they are grouped in pairs—a large and small one alter- |
nately—to the number of six (twelve bristles). The latter (Plate XVI. fig. 8)
are proportionally strong, and taper from a little above the base to a slightly
bent apex. For about a third of the distal portion, there is a very narrow wing
or border at each side, which has minute strie directed forwards and outwards.
A row of hooks runs in a transverse manner on the ventral surface from each
bristle-papilla, the anterior rows being closer to the papilla than the posterior.
These hooks (Plate XVI. figs. 6 and 7) have an elongated and slightly-curved
form like those of Terebellides, the head possessing a strong beak, behind which
are a series of small processes or fangs. There is a distinct narrowing or neck
below the head, and the hook gradually tapers from the succeeding shoulder
backwards. This form of hook is confined to the somewhat prominent pads of
the bristle-bearing segments. A series of elevated mamillee succeed the latter,
each being furnished with a row of short hooks, which differ entirely from the
foregoing (Plate XVI. fig. 7a). Each has a short and wide basal process, a
* Nord. Hafs-Annulat. p. 395, tab. xxiv. fig. 65.
VOL. XXV. PART II. 5Q
426 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
characteristic notch between this and the large beak, and numerous curved fangs
of smaller size above the latter. The fangs above the larger beak are not simply
arranged in a linear manner, but, as it were, form a spined knob, with the points
curved obliquely downwards. The ventral surface of the annelid is marked by
a central blood-vessel, and in spirit thrown into prominent transverse ruge. In
my specimens the posterior part of the body tapered to a blunt tail, terminated
by two soft papillee; but these represented the ordinary processes, and probably
the tail was absent. The peritoneal bodies are of a pale-red colour, and, as usual
in such animals, very large. Dr Matmeren describes the posterior hooks as
bidentate, but does not figure them. If this remark is accurate, then the foregoing
differs specifically.
EXPLANATION OF THE PLATES.
The following letters have been employed as far as possible in designating similar organs in
Ommatoplea and allies.
a. Proboscis A. First region of proboscis.
ac. Reflection of proboscis in front of ganglia, B. Second do. do.
b, Epidermis. C. Third do. do.
ab, Channel in snout for proboscis, €. Globule in lateral stylet-sac.
c. Cutis. 8. Stylets in do.
d. Circular muscular coat. 6. Duct of lateral stylet-sac.
e. Longitudinal muscular coat. «. Muscular chamber behind the floor of the
jf. Superior commissure of ganglia. anterior region of proboscis.
g. Inferior commissure of ganglia. n- Floor of anterior chamber of proboscis.
=>
h. Superior lobe of ganglion. Muscular setting of granular basal appara-
Inferior lobe of do. tus.
j- Esophageal apparatus. a. Granular basal sac.
j. Digestive canal-proper. #&. Hyjaculatory duct.
k. General stroma of snout. “. Aperture of ejaculatory duct into chamber «.
1. Cephalic vessel. m. External granular glands,
m. Cephalic sac. e- Reservoir.
m’. Duct of do. o. Glands of reservoir.
n. Great lateral nerve-trunk. ry. Looping muscular fibres of the walls of re-
o. Proboscidian sheath. servoir,
p- Dorsal blood-vessel. vo. Longitudinal muscular fibres of the walls of
gq. Anastomotic branch. reservoir.
r. Lateral blood-vessel. g. Duct of communication with the posterior
ov. Ova in situ. chamber,
v. Lateral stylet-sacs. %X, Wall of posterior chamber.
z. Anus. a). Muscular ribbons.
Letters used to designate similar parts in Borlasia and Cephalothria.
a. Proboscis. d’. Basement-layer.
ao. Tube for proboscis in snout. d’, Pigment-layer in B. olivacea.
b. Cephalic fissures. e. External (longitudinal) layer.
c. Ciliated epidermis. é. Circular muscular layer.
d. External layer of cutis. e”. Inner (longitudinal) muscular layer.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 427
jf. Superior ganglionic commissure. r. Lateral blood-vessel.
g. Inferior do. do. s. Lacunz behind ganglia.
h. Ganglia. u. Vascular meshes around the cesophageal
h’. Superior lobe of ganglion. region.
h’. Inferior lobe of do. v. Larger vascular cavity at each side of the
j. Csophageal region. sheath for the proboscis in front.
j. Alimentary cavity-proper. w. Mouth.
k, General stroma of cephalic region. y. Constriction marking the junction of the ceso-
m. Cephalic sacs. phageal region with the digestive cavity-
m’, Ducts of cephalic sacs. proper.
n. Great lateral nerves. z. Anus.
o. Proboscidian sheath. : ov. Ovaries and their remains.
p. Dorsal blood-vessel. a}. Muscular ribbons of proboscis.
Puate IV.
Fig. 1. Transverse section, a short distance behind the tip of the snout of Ommatoplea alba, in front
Fig. 1.
of the ganglia, somewhat flattened from pressure. 1, 2, 3, 4, 5, 6, the various bands of
fibres described in the text; ¢, longitudinal muscular fibres ; /, section of cephalic blood-
vessel; m, section of cephalic sac. x 210 diameters.
. Transverse section of the body-wall of .O. alba, after hardening in spirit and mounting in
chloride of calcium; a, cutis, with its cells and areolee, somewhat compressed; 2, struc-
tureless basement-layer; c, circular muscular coat; d, longitudinal muscular coat;
e, delicate fibres proceeding from the latter to the viscera. x 700 diameters.
. View of a portion of skin snipped from a living specimen, and submitted to moderate pres-
sure. x 350 diameters.
. Longitudinal section of the anterior region of the proboscis of O. alba. The same letters
are used as in fig. 4, Pl. V. x 90 diameters,
. Transverse section through the anterior part of the cephalic ganglia, in a specimen which
had been chloroformed and then immersed in strong alcohol, so as to protrude a small
portion of the proboscis. The inferior commissure (g) is not much stretched, but the
superior (/) is almost imperceptible ; j, esophagus. x 55 diameters. In this and other
drawings, accuracy has been preferred to symmetry.
. Section of the snout in front of fig. 1, showing the channel for the proboscis (a), and the
cephalic blood-vessels (7), just before they complete the arch. x 210 diameters.
. Elements as they escape from the fresh skin of the same animal; a, granular cells; , mu-
cous or gelatinous masses, having the appearance of oil-globules. x 350 diameters.
. Skin of O. alba, as seen near the tail of a small living specimen, under slight compression.
x 350 diameters.
. Corpuscles of the proboscidian fluid; a, minute nucleated cells and granules; 0, spindle-
shaped corpuscles. x 500 diameters.
. Stylet, from a lateral sac of the same species, showing a ‘“‘ wing” at base (from remains of
globule), and an abnormal point. x 210 diameters.
. Dises of proboscidian fluid, from a specimen of Tetrastemma varicolor. x 850 diameters.
. Small gregariniform parasite, from the digestive cavity of Tetrastemma variegatum. x 210
diameters.
. Proboscidian aperture in snout of O, alba. x 210 diameters.
. Discs of proboscidian fluid from Tetrastemma variegatum. x 350 diameters.
PuatTEe V.
Transverse section through the cephalic ganglia of O. alba, in the line of the commissures,
the superior of which, from the flattening of the preparation, is shown very plainly ;
a, proboscis; d, circular muscular fibres of the body-wall; %, muscular and glandular
stroma of the region. x 90 diameters,
Fig.
2)
ae
. Isolated gland-cells from the posterior chamber of the proboscis. x 350 diameters.
. Transverse section through the anterior region of the proboscis in a large O. alba, after
. Transverse section through the stylet-region of the proboscis of the same species, in the
. Glandular papillz from the proboscis of Tetrastemmua vermiculus, seen on the free edge of
. Glandular papille in the anterior region of the proboscis of O. alba, seen in the ordinary
. Portion of the everted inner surface of the posterior chamber of the proboscis of the same
. Portion of the glandular surface of the posterior chamber of the proboscis in its normal
. Portion of the inner surface of the same chamber, viewed in situ under pressure. The
. Lanceolate and pedicled papillee from the anterior part of the proboscis of 7. vermiculus.
. Central stylet of Ommatoplea purpurea. x 700 diameters. :
. Central stylet and basal apparatus of the same species. x 350 diameters.
. Developing or recently repaired central stylet-apparatus in 7. alge. x 700 diameters.
. Stylet from a lateral sac of the same animal. x 700 diameters.
. Head of O. alba. x 210 diameters.
. Proboscis of the same species, gently but completely extruded under chloroform, so as to
. View of the nervous and circulatory systems in the anterior end of O. alba.
. Abnormal stylet-region in the same species ; a, perfect stylet-sac of the left side; }, shrivelled
. Stylet-region of the proboscis of 7. varicolor, with the reservoir somewhat contracted. x 210
. Extremity of the posterior chamber of the proboscis in 7. variegatum, apparently after
. Stylet-region in Ommatoplea melanocephala. x 90 diameters.
. Circulation, &c., in the posterior end of O, alba; a fragment of the same drawing from which
. Isolated lateral stylet-sac of O. alba ; a, a few fibres which probably act as constrictors of
. Tip of the snout of Borlasia olivacea, with proboscis partly protruded. x 210 diameters.
. Central stylet-apparatus in Ommatoplea pulchra ; a, central stylet; b, reserve-stylet im situ.
DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
Transverse section through the body of the same animal some distance behind the ganglia.
The sheath for the proboscis now separates the latter from the esophagus, which has —
attained a considerable size. The lateral nerve-trunks have nearly reached their proper
position, viz., to the inner side of the internal muscular layer of the body-wall; s, granular —
masses at the sides of the esophagus. x 55 diameters.
hardening in spirit and mounting in chloride of calcium; «, central cavity; b, the papillary
glandular layer; c, internal circular muscular coat; d, inner longitudinal layer; e¢, pecu-
liar reticulated or beaded layer; /, external longitudinal muscular layer; g, external
layer; h, basement-layer. x90 diameters.
line of the lateral sacs. x 350 diameters.
the everted organ. x 700 diameters.
condition of the organ under pressure. x 210 diameters.
species. The glands have for the most part burst and become minutely hirsute. x 350
diameters,
condition. x 350 diameters.
papille are hirsute, and their contents scattered over the surface of the organ. x 350
diameters,
x 800 diameters.
Puate VI.
render the central stylet prominent. x 55 diameters.
sac of the right side. x 210 diameters.
diameters.
rupture of the muscular ribands from the sheath of the organ. x 350 diameters.
fig. 3 was cut.
the aperture of the duct. The laminated arrangement of the calcareous layers of the
stylets is indicated in this figure. x 850 diameters.
x 210 diameters. d
Central stylet and its basal granular apparatus in O. gracilis, turned round so as to demon-—
strate the curvature of both. x 100 diameters.
Isolated central stylet of the foregomg. x 420 diameters.
Fig.
earl:
a 12:
Fig.
Fig.
mo Ne
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 429
Prate VII.
. Stylet-region of the proboscis of O. gracilis. |x 210 diameters.
. Stylet-region of the proboscis of O. purpurea. x 210 diameters.
. Stylet-region of the proboscis of O pulchra. x 90 diameters.
. Extremity of the posterior region of the proboscis of O. alba distended with fluid; a, a group
of the peculiar dancing granules. x 90 diameters.
. Stylet-region of the proboscis of Polia involuta, VAN BENEDEN. x ‘700 diameters.
. Stylet-region of the proboscis of a young O. alba, illustrating the first appearance of the
stylets, and the development of the parts. The organ is drawn as it bulged from a wound
in the body-wall of the animal. x 700 diameters.
. Fragment of the esophagus from a living animal; a, mner edge of ciliated fold; J, sulcus
between two folds. x 350 diameters.
. Eye of Ommatoplea pulchra. x 210 diameters.
. Central stylet and portion of basal apparatus in a large O. gracilis. x 850 diameters.
. Transverse section of an everted proboscis in a small specimen of O. pulchra. The papillose
mucous surface has been injured in the manipulation. x 90 diameters.
Nerve-cells from a cephalic ganglion of O. alba. x 400 diameters.
Portion of a sperm-sac in Yetrastemma varicolor, showing a streaked and granular aspect,
from the varying nature of the contents. x 350 diameters.
Pirate VIII.
. Aspect of the developing proboscis in O. melanocephala, about the fifth day after the removal
of the original organ. x 55 diameters.
. Stylet-region of a developing proboscis in the same species; /, canal, which by-and-by is
occupied by the central stylet. The organ is contracted. x 350 diameters.
. Anterior region of Tetrastemma alge, showing the arrangement of the digestive system.
Enlarged.
. Termination of the posterior chamber of the proboscis (C) in O. alba, with muscular ribands.
x 210 diameters.
. Head and anterior portion of Polia involuta, V. Bren.; f, powerful transverse band of fibres
which retains the posterior part of the esophagus in situ. x 180 diameters,
. The central (a) and lateral stylets (b) from a young O. albu, on the first appearance of the
former. x 700 diameters.
. Cephalic ganglia of Tetrastemma varicolor. x 210 diameters.
. Unimpregnated ovum of O. alba ; a, outer coat; b, inner coat; c, vitellus; d, “ micropyle,”
or cicatrix-like arrangement. x 90 diameters.
. Ovum of O. gracilis after impregnation; a, outer coat; /, mner coat; ¢, vitellus. x 90
diameters.
. The inner coat and vitellus of an ovum (of O. gracilis) at the same stage of development,
with the relations of the spermatozoa. x 210 diameters.
. Ovum of O. alba, just before the extrusion of the embryo, x 90 diameters.
. Spermatozoa of Tetrastemma vermiculus. x 1000 diameters.
. Spermatozoa of O. alba. x 800 diameters.
. Spermatozoa of 7. variegatum. x 400 diameters.
Puate IX,
. Young OQ. alba, on extrusion from the egg, somewhat compressed, x 55 diameters.
. Young O. alba eight days older than the preceding; 0, stylet-region; c, point where the
posterior chamber of the proboscis becomes lost, after curving forwards. x 90 diameters.
. Structure of the stylet- and reservoir-regions in 0. alba. Considerably magnified,
. View of the cutis in a living specimen of Borlasia olivacea as a transparent object. x 210
diameters.
. Streaked arrangement of the cutis of B. olivacea, from the dorsum, x 210 diameters.
. Pigment-cells from the anterior part of the dorsum of the same species. x 350 diameters.
. View of the skin of a living Meckelia annulata. x 350 diameters.
. Spermatozoa of Ommatoplea gracilis. x 700 diameters.
. Spermatozoa of Polia involuta. x 950 diameters.
VOL. XXV. PART II. DR
430
DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
Fig, 10. Transverse section through the contracted reservoir-region of O. alba, showing the complex _
Salas
Be
oal3y
. 14,
2) ar
Gs
Fig.
Fig.
ile
spiral arrangement of the fibres. x 55 diameters.
Superficial structure of the reservoir- and stylet-regions in the same species.
Central stylet and basal apparatus with radiating fibres in Tetrastemma vermiculus. x 360
diameters.
Stylet-region of a young QO. alba, some weeks older than that represented in fig. 2.
x 350 diameters.
Transverse section through the posterior chamber of the proboscis in a large example of
O. alba. The circular and longitudinal muscular and the mucous coats are well shown.
x 90 diameters.
Young Tetrastemma variegatum, shortly after extrusion from the egg, and somewhat com-
pressed, so as to show its cellulo-granular structure. x 350 diameters.
Portion of the long posterior chamber of the proboscis of O. purpurea, showing the charac-
teristic plaits of the mucous surface. x 90 diameters.
Pruate X.
Enlarged view of the anterior end of B. olivacea as a transparent object.
2, Transverse section through the curious example (probably a variety of Meckelia) from
© OnaTIo
GS Om
co ©
Balta; d, external layer of cutis ; d’, basement-layer; ¢, longitudinal muscular layer ;
ea, dorsal sub-divisions of the latter coat in the central line; ¢’, circular muscular coat ;
j, section of the cesophageal region of the digestive tract ; ja, distinct band of muscular
fibres enclosing the latter ;. x, lateral nerve ; 0, sheath for proboscis; 7, vascular spaces.
x 55 diameters, '
. Transverse section through the body of Cephalothriz filiformis. The proboscis is coiled in
its sheath. x 90 diameters.
. Transverse section just behind the tip of the snout of Borlasia olivacea. The grouping of
the pigment (3) readily enables the observer to distinguish the dorsal from the ventral
surface ; 2, powerful series of fibres arching over the channel leading to proboscis, and
which radiate into the surrounding stroma (x). x 56 diameters.
. Portions of the inner surface of the proboscis of the same species, showing the glandular
papillz, slightly compressed. x 700 diameters.
. Gland-cells from the wall of the digestive cavity of Ommatoplea alba. x 400 diameters.
. One of the same slightly compressed glands. x 700 diameters.
. Contents of the same gland-cells, with oil-globules. x 700 diameters.
. Spermatozoa of Borlasia olivacea. x 700 diameters.
Pruate XI.
. Transverse section through Borlasia olivacea, just at the commencement of the cesophageal
region; 2, radiated or slightly arborescent arrangement of the external longitudinal
muscular coat at the sides of the mouth. The thick folds of the cesophagus are seen
almost at the termination of the anterior cul-de-sac. x 90 diameters.
. Arrangement of the ova in the ovisacs of Tetrastemma vermiculus ; a, proboscis ; 0, probos-
cidian sheath. Only a fragment of the body is represented. x 24 diameters.
. Spermatozoa of Cephalothrix filiformis. x 900 diameters.
. Spermatozoa of Lineus longissimus. x 900 diameters.
. Spermatozoa of Borlasia octoculata. x 800 diameters.
. Transverse section through the body-wall of Lineus longissimus at a somewhat narrow por-
tion ; d, external cuticular layer ; d’, pigmentary layer divided into two strata by a defi-
nite black band (2); 8, curious translucent stratum, cut into somewhat regular spaces.
Other letters as usual. x 210 diameters.
. Longitudinal section of the tissues of the body-wall in the same species; 4, 4, sections of the
transverse connecting trunks between the lateral and dorsal vessels ; 5, granular stroma
within the inner longitudinal muscular coat, supporting the former and various other
tissues. x 90 diameters.
. Transverse section of the body-wall of Borlasia olivacea. x 350 diameters.
. Proboscis of Cephalothrix filiformis, slightly everted, so as to exhibit the acicular papille.
x 850 diameters.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 431
Fig. 10. Aggregations of fatty granules from the discarded coating of the embryo of B. olivacea.
x 210 diameters.
Pruate XII.
. Transverse section through the proboscis of a Borlasian (Micrura) from St Andrews; a,
external coat; }, great longitudinal muscular layer; c¢, belt of circular muscular fibres ;
d, basement-layer ; e, incomplete series of longitudinal fibres which do not occur in the
common species; /, glandular mucous coat; g, peculiar lozenge-shaped portion of longi-
tudinal fibres, formed by the splitting and crossing of two bands from the circular muscu-
lar coat; g, separated segment at the other pole of the circle. x 90 diameters.
. Transverse section of the snout of Borlasia olivaceu, somewhat behind that shown in fig. 4.
Pl. X., and through the anterior part of the cephalic fissures. The channel for the
proboscis has become more central in position. ‘he superior pigmentary belt (3) is
somewhat narrower, and an inferior (4) has now appeared. The central channel has
a layer of longitudinal muscular fibres internally, and a powerful series of oblique and
circular fibres (2, 2) form a very efficient exterior investment. x 55 diameters.
. Transverse section of a specimen of B. olivacea, in which the ova are well developed.
The shrunken condition of the walls of the digestive cavity (j’), with the numerous array
of gregariniform parasites, is in strong contrast with the state of the animal after spawn-
ing. The specimen had been in spirit for a considerable time before dissection, x 55
diameters.
. Parasitic ciliated animal from the tissues of the same species. The letters, a, b, c, and d,
correspond with the groups of segments described in the text. x 350 diameters.
. The foregoing parasite in an earlier state of development. x 350 diameters.
. The last-mentioned specimen subjected to slight pressure, so as to exhibit the seyments.
x 350 diameters.
Posterior end of a young B. olivacea, showing the anal papilla. x 210 diameters.
. Transverse section through the post-ganglionic region of Lineus lactea, Mont. MS., show-
ing the long vascular lacune (s, s) in front of the esophageal region. The slice of the
proboscis has fallen out of its sheath (0). x 90 diameters.
. Stylet-region in Tetrastemma varicgatum, somewhat contracted, and with the floor of the
anterior chamber pouted forwards. The latter condition is more easily seen in Zetras-
temma than in O. alba. x 210 diameters.
. Fragment of the wall of the digestive chamber-proper, from the living Borlasia olivacea.
The cilia mark the inner surface. x 850 diameters.
. Cells from the digestive cavity of a young Cephalothriz filiformis. x 700 diameters.
. One of the pinnate processes of the scale of Sthenelais dendrolepis, Cuar. x 90 diameters.
PuatE XIII.
. Highly magnified view of the anterior end of Cephalothrix filiformis (Astemma) ; 6, b, bridles
of sheath for proboscis.
. Arrangement of the vessels at the posterior extremity of Borlasia olivacea. Magnified.
. Ovum of Cephalothrix filiformis immediately after deposition, x 350 diameters.
. Flask from the mucous cord of B. olivacea, with two young animals somewhat compressed; «,
embryo forced from its ciliated cellulo-granular fatty coating, the bulk of which lies at « ;
b, embryo still within the ciliated coating. x 55 diameters.
. Young B. olivacea immediately after leaving the flask-shaped capsule; 4, opening of the
cephalic sac of the right side. The other letters as in the adult. x 90 diameters.
. Transverse section through the middle of B. olivacea after the second or great region of the
digestive cavity has attained its full size. ‘The difference between such a view and the
indistinct mass formed by the Ommatoplean digestive cavity, after section, is character-
istic. x 56 diameters.
. Cellular elements of the wall of the digestive chamber of the same species. x 700
diameters.
Pale oily region with germinal vesicle (a), and germinal dot (}), in an ovum removed from
the body of the female B. olivacea. x 3650 diameters.
. Elements of the glandular papille of the proboscis of B. olivacea, after their escape into the
surrounding water. x 700 diameters.
432 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE
Seba .
Fig. 10. iB eeai en di
ee ooks of Amaye. x 700 diameters,
‘ Puate XIV.
Fig. 1. Ovum of Polia involuta, Van Bzn., immediately after deposition. x 350 diameters.
... 2, Ovum of the same species about the 10th day, showing the ciliated embryo revolving therein,
x 350 diameters.
3. Young of Cephalothrix filiformis shortly after extrusion from the egg. x 350 diameters.
4, A young specimen of Cephalothrix, two days older than that shown in fig. 3; a, mouth; 4,
granules of digestive cavity. x 2i0 diameters.
5. A specimen about three days older than the foregoing (fig. 4). x 210 diameters.
6. Young Polia involutd, extruded from the body of the adult under pressure. It has the same
appearance when originating in a free ovum. x 350 diameters.
7. Young (©. filiformis, after shedding the long anterior whip of cilia, but having the lateral
tufts (c) and eyes; a, mouth; 0, granules of digestive cavity. x 210 diameters.
8. Transverse section through the proboscis of Lineus longissimus. x 55 diameters.
9. Magnified view of the ganglionic region of a large Ommatoplea alba, in which a parasitic
ovum (7) lay imbedded in a granular lobulated mass (7).
. 10. Parasite extruded from capsule; a, opaque cellular and granular mass ; }, ventral disc; ¢,
oral disc; d, cesophageal bulb; e, alimentary ceca; f and g, large circular granular
bodies.
... 11. Transverse section through the body of a large Meckelia annulata. x 55 diameters.
. 12. Head and proboscis (a) of a remarkable variety of Meckelia, brought from Shetland (Balta)
by Mr Gwyn Jeffreys; b, curiously frilled arrangement of the enlarged homologue of the
superior lip of the cephalic fissure; w, prolapsus of textures from mouth. Magnified
under a lens,
... 18. Hook of Ampharete artica, Mern. x 700 diameters. >
... 14. Hook of Amphicteis gunneri. x '700 diameters.
. 15, Hook of Terebella, from the Hebrides. x '700 diameters.
Piate XV.
Fig. 1. Bristles of Amphinome vagans ; a, bristle from the inferior lobe of foot; }, c, bristles of the ©
superior lobe. x 700 diameters.
2 a. Dorsal bristle of Lepidonotus pellucidus, Haters. x 700 diameters.
2 b. Ventral bristle of the same species. x 700 diameters.
3. Ventral bristle of Polynée longisetis, GRuBE. x 350 diameters.
3 a. Tip of the dorsal cirrus of the same species. x 55 diameters.
| Two of the characteristic bristles (with jointed tips) of Sthenelais dendrolepis, Cur.
}. x 350 diameters,
6.
6 a. } Ventral bristles of Halosydna gelatinosa, Sars. x 180 diameters.
6 b.
7. Ventral bristle of Ophiodromus vittatus, Sars., with short terminal process. x 700 _
diameters.
8. Fragment of a bristle from the dorsal lobe of the same animal. x 700 diameters.
9. Bristle of Notophyllum polynoides, CErst. x 420 diameters,
9 a. Lateral view of the end of the shaft and its processes in the same bristle. x 700 diameters.
9. Profile view of the same. x 700 diameters. ~_
. 10. Bristles of the littoral form of Spherosyllis hystrix, CLAPAREDE ; a, simple spine ; /, jointed
bristle. x 700 diameters.
. LL, Jointed bristles of Autolytus pictus, Enters. x 700 diameters.
... 12. Bristle of Syllis, resembling S. macrocera, GRuBE. x 7U0 diameters.
. 13a. Fragment of the frontal bristle (of Siphonostoma buskii) represented in fig. 4 a, Pl. XVI.
x 360 diameters.
. 13. Piece of a corresponding bristle from Trophonia glauca, MALMGREN. x 300 diameters, —
... 14. Hook from the rasp-like surface of Ammochares ottonis, GRuBE. x 900 diameters.
. 15. Hook of Terebella zostericola, rst. x 700 diameters.
zo.
BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 433
16. Hook of Rhodine loveni, Mern. x 700 diameters.
. 17. Hook of a species allied to Hreutho smitti, Mern. x 900 diameters.
: : Hooks of a form closely resembling Polycirrus aurantiacus, GRUBE. x 900 diameters.
. 20. Hook of Pista cristata, Mttuer. x 700 diameters.
. 21. Bristles of Syllis tubifex (%), GossE ; a, a, from middle of body; 6, spine; c, bristle from
Fig.
the third foot. x 280 diameters.
Puate XVI.
1. Ventral bristle of Castalia punctata, Mitt. x 700 diameters.
2. Bristle of Psamathe fusca, Jounst. x 700 diameters.
3. Jointed hook from the anterior segments of Hyalinecia sicula, QuatREF. x 700 diameters.
3 6. Simple hook from the posterior region of the same. x 700 diameters.
3c. Bristle of the foregoing species. x 700 diameters.
4. Hook of Siphonostoma buskii, n.sp. x 3850 diameters,
4 «. Bristle from the frontal series of the same species. x 90 diameters.
5. Forked bristle of Ewmenia jefireysii, n. sp. x 700 diameters.
6. Hook from the bristle-bearing segments of Trichobranchus glacialis, Mern. x 90 diameters.
7. The same. x 700 diameters.
7 a. Hooks from the posterior segments of the same annelid. x 700 diameters,
8. Bristle of 7. glacialis. x 350 diameters. _
9. Bristle of Spherosyllis from the Minch. x 700 diameters.
... 10. Bristle of Pionosyllis malmgreni, n. sp. x 700 diameters.
... 11. Foot of Staurocephalus kefersteini, n. sp.; f, superior cirrus ; g, inferior cirrus. x 210
diameters.
eek a:
... 11. { The varieties of the bristles in the same species, as described in the text. x 700
Beil ¢. _ diameters.
fee Lila.
. 12. Hook of Clymene ebiensis, Aup. & Ep. x 350 diameters.
... 13. Hook of Prazilla (artica? Mern). x 350 diameters.
. 14. Bristle of Syilis krohnii, Huters. x 700 diameters.
ong HOMee
soe EGR
} Bristles of Syilis cornuta, Ravuxe, x 700 diameters.
oot ss fe \ Hooks of Sabellides sexcirrata, Sars. x 700 diameters.
. 17. Foot of Notocirrus scoticus, nu. sp.; a, branchial lobe; 6, spine; c, bristles. x 350
diameters.
Or
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VOL. XXV. PART II.
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X.—Observations on the Temperature of Newly-Born Children. By T. J.
Maciacan, M.D., Dundee. Communicated by Dr J. MatrHews Duncan.
(Read 5th April 1869.)
The observations which form the basis of this paper were made on newly-
born children with the object of determining whether their temperature differed
from that of the adult, and if so, how and to what extent. They were made
during a recent residence in the Edinburgh Maternity Hospital, with the full
sanction of the attending physician, Dr Cuarues Bett. The thermometers* used _
were CASELLA’s straight self-registering. The rectum was the part chosen for the
insertion of the instrument. The utmost expedition was used in ligaturing the
cord, and separating the child from its mother. This being effected, the bulb of
the thermometer was at once introduced into the rectum, and the child was
wrapped in flannel, and committed to the charge of a nurse, who held the instru-
ment steadily 7m situ. In five minutes it was removed, and the temperature
noted. The observations were repeated every fifteen minutes during the first
hour, every thirty minutes during the second and third hours, and then every
hour up till the sixth hour after birth ; after that at wider intervals up to twenty-
four hours; and then only twice a day between ten and eleven in the morning,
and between six and seven in the evening.
By the adoption of the above method, the first observation was made whilst
the child yet retained the temperature imparted by the mother, whilst any subse-
quent change could not fail to be noted in consequence of the frequency with
which the observations were repeated.
In order that the peculiarities of the child’s temperature may be made as clear
as possible, the facts observed shall be treated of under three different heads.
We will consider (a) the temperature at the time of birth; (0), the range noted
. during the first twenty-four hours of extra-uterine life; (c), that of the next
five days.
(a). The temperature of the child at birth is the same as that of the mother.
If hers be high during the second stage of labour, that of the infant at birth will
show a corresponding elevation; if normal, so also will the child’s be. The mean
range of the maternal temperature at the time of delivery was found to be
* The instruments were verified by the maker by a standard which is in perfect accordance with
that of the Royal Kew Observatory.
VOL. XXV. PART II. 57
436 DR T. J. MACLAGAN ON THE
99°'154; that of the child at birth, 99°872, The highest was 103°5 for the
mother, and 104° for the child; the lowest 97° and 98°:1. As the former case
was altogether abnormal, it ought perhaps to be excluded in striking the average.
By doing so, we get a mean range for the mother of 98°6, and for the child of
99°-3—a difference of “7 in favour of the child. This slightly higher range on
the part of the child is fully accounted for by the fact that the infant’s tempera-
ture was taken in the rectum, whilst the mother’s was taken in the axilla.
From observations made on the adult with the object of determining the point
in question, I found the temperature of the former locality to be from half a
degree to a degree above that of the latter. Making allowance for this, the
range of the mother and child may be regarded as the same. The case with the
high range, in virtue of its abormality, serves well to illustrate the close con-
nection which exists between the two. In it the mother’s temperature towards
the end of labour rose five degrees above the normal standard; the child’s at
birth was found to have undergone a similar elevation.
(b.) The range of the first few hours after birth is altogether peculiar. When
the child is separated from the parent, and commences its new mode of existence,
a marked change takes place. The temperature acquired from the mother is no
longer sustained. The thermometer introduced into the rectum shows a fall
which varies in different cases both in rapidity and extent, but which is never
altogether awanting.
In children born at the full time, the average period after birth at which the
temperature reached its lowest point was two hours. The average extent of the
fall was five degrees below the normal standard of the adult; the greatest was to
90°'8, the least to 96°—-the average being to 93°4. The mean time which elapsed
before the temperature again rose to what might be regarded as its normal range
was 22-25 hours after birth; the shortest was two hours; the longest forty-
four. In one sickly child it was four days before the depression was recovered
from. Ina seven months’ child the temperature fell to 90°:2, more than eight
degrees below the adult standard of health; and during the thirteen days on
which it was under observation the highest point reached was 94°:6, the mean
range being 92°°3.
(c.) So much for the first twenty-four hours. The observations made after
that time were made only morning and evening. I have selected sixteen cases,
in which no disturbing element intervened at all likely to affect the normal
range, and find that the mean range for the first five days immediately succeed-
ing the time at which the normal standard was attained was in the morning
97°43, and in the evening 98°06, the average being 97°74—that is, more than
half a degree below the normal standard of the adult. As the temperature of
these cases was invariably taken in the rectum (in which we have seen that the
range is higher than in the axilla), it may be inferred that the child’s tempera-—
+
TEMPERATURE OF NEWLY-BORN CHILDREN. 437
ture during the first few days of its existence is a degree lower than that of the
adult. It must also be mentioned, however, that all these observations were
made during the winter, and that possibly the external atmosphere may have a
ereater effect on the temperature of the child than on that of the adult. I have
never had the opportunity to repeat them during the warm weather of summer.
How are these pecularities to be accounted for? Why should the child’s
temperature fall so rapidly, and to such an extent, immediately after birth ?
And why should it, on recovering from this temporary depression, still be lower
than that of the adult?
(a.) That the child at birth should have the same temperature as the mother
is what would naturally be expected. Considering the close connection which
exists between them, and the manner in which the child is nourished by the
mother, it could not well be otherwise. The circumstance calls for no explana-
tion whatever.
(b.) With regard to the peculiar range of the first few hours of the child’s sepa-
rate existence, it is quite different ; and we have now to inquire why it is that the
child’s temperature should fall so rapidly, and to such an extent, immediately after
birth. It is probable that the sudden change from the high temperature of the
womb to the low temperature of the external air exercises to some extent a chilling
influence on the child—an influence which it can the less resist, and with the
more difficulty recover from, in consequence of the peculiarities of its circulatory
system allowing of the passage of so much venous blood into the arterial circu-
lation. That, however, is not of itself sufficient to account for a fall so sudden,
so great, and of so short duration; for assuredly, if that were the sole cause,
recovery from a very low range so produced would be a much slower process
than itis. There must be some other and more powerful agent at work; and
this we have in the first necessary act of the child’s independent existence—
respiration. I believe that the passage of air into the lungs has at first a
refrigerating influence, and is the chief, if not the sole, agent in producing the
_ great and sudden fall which takes place immediately after birth. This explana-
tion is to a certain extent borne out by what was observed in one case in which
the child was apparently still-born, and in which considerable difficulty was
experienced in inducing the respiratory act. The temperature in the rectum
half an hour after birth (immediately after respiration was established) was
98°3 ; in the next half-hour it fell to 92°-6. The state of the child at birth was
such that attention was directed solely to the respiration, and until that was
right the temperature wasnot taken. Just before delivery, however, the mother’s
stood at 100°, so that the child’s may with propriety be supposed to have been
100°-7 in the rectum. In ordinary cases, in which breathing commenced at once,
the mean fall during the first half hour was in full-grown healthy children 5°-2,
and during the second half hour 1°4. In this case it was during the first half
x
438 . DR T. J. MACLAGAN ON THE
hour 2°-4, and during the second half hour (after respiration was established)
5°-7. In all other cases in which a comparison could be made the fall was much
greater during the first half hour than during the second; in this one the reverse
was the case; and the only explanation of this circumstance is to be found in
the tardy establishment of the respiratory act. So far as one case can do so,
this one shows that it is not until the child breathes that the temperature falls
to any great extent; though the diminished range may also be partly explained by
the cooling influence of the external air on the blood in the very active cutaneous
circulation.
But the question naturally arises, Why should the respiratory act, which in
the adult has a heat-producing effect, have an opposite result in the infant? The
answer involves a brief consideration of the whole question of the production of
animal heat. To the various theories which have at different times been advanced
to account for this I shall not allude further than to say, that all have given —
place to that which ascribes it to chemical action—to the changes which are con-
stantly going on in the blood in all parts of the capillary system—general and
pulmonic. As these changes take place in organs and parts which are dependent __
for the proper performance of their functions on the integrity of the nervous
system, it follows that the amount of heat produced is apt to be modified by the |
operation of that system. Medicine abounds in illustrative cases in which a part
of the body, a limb for instance, in consequence of being deprived of its nervous
supply by disease or accident, has a lower temperature than it had when that _
supply remained intact. :
Sir B. C. Bropre (I quote from Kirxss’ “ Physiology’) “found that if
artificial respiration was kept up in animals killed by decapitation, division of
the medulla oblongata, destruction of the brain, or poisoning with worara poison, |
the action of the heart continued, and the blood underwent the usual changes in
the lungs, as shown by the analysis of the air respired, but that the heat of the
body was not maintained; on the contrary, being cooled by the air forced into
the lungs, it became cold more rapidly than the body of an animal in which
artificial respiration was not kept up.”
Absence of the due nervous influence is, I believe, the true explanation of the
rapid and transient lowering of the child’s temperature during the first few hours
of extra-uterine life. It is, indeed, unlikely that the child should have its con-
nection with the mother severed, and commence its new and independent
existence with patent foramen ovale, unclosed ductus arteriosus, and lungs
hitherto untried, and from the first maintain the temperature imparted to it by
the parent; but, as already explained, the existence of this peculiar state of the
organs of circulation is inadequate to account for a fall so very rapid and of so
short duration. Closure of the foramen ovale and ductus arteriosus cannot
explain the speedy return to the normal range, for these passages are not —
EO
TEMPERATURE OF NEWLY-BORN CHILDREN. 439
obliterated for some considerable time after birth; respiration goes on as from
the beginning, and why should it after a few hours cease to exert the same
lowering influence which it exercised at first? It seems to me that the only
feasible explanation is to suppose that the hitherto unexercised influence of
the nervous system over the respiratory function is not at once called into
vigorous and efficient action— that though the influence required for inducing the
muscles of respiration to act is in full force from the beginning, there is still
awanting, or only partially supplied, that more delicate and less easily explained
agency without which, even though the blood may undergo the usual changes,
the due amount of heat is not generated; and that coincidently with the estab-
lishment of this influence does the temperature of the child rise to its normal
range. This explanation is quite in harmony with the fact that in delicate and
premature children the fall is greater than in vigorous ones and those born at the
full time, in whom also the normal standard is more rapidly reached, in conse-
quence probably of the more speedy establishment of the due nervous influence.
(c). During the five days immediately succeeding that on which the tempera-
ture rose to a height which might be regarded as normal, we have seen that
the range was one degree below that of the adult, after due allowance had been
made for the difference resulting from the manner in which the thermometer was
applied.
This lower range of the early period of extra-uterine life admits, I think, of
a very ready explanation.
As a general rule, the degree of heat produced bears adefinite relation to the
activity of the respiration: in birds, in which respiration is very active, the
temperature is high; in reptiles, with a sluggish respiration, there is a low
temperature.
Anything which interferes with the proper oxygenation of the venous blood.
or with the due supply of the purified fluid to the tissues, has a lowering effect on
the temperature. Such agencies are constantly at work in the newly-born child.
The patent condition of the foramen ovale and ductus arteriosus permit of so free
a commingling of the venous and arterial blood, that a lower temperature than
exists after the closure of these passages must result; for, in the first place, less
blood goes to the lungs at each contraction of the right ventricle, and so less heat
is produced there; and, in the second place, the blood which goes to the tissues
is less pure, and consequently less of an interchange takes place in the capillaries
of the systemic circulation.
How long the child’s temperature continues lower than that of the adult I am
not prepared to say, as my observations were limited to the first week of extra-
uterine life, but should think it probable that the adult standard of health is not
maintained till the foramen ovale and ductus arteriosus are closed, or nearly so.
This, however, is a mere hypothesis, and must remain so, as the time of closure of
VOL. XXV. PART II. aU
440 DR MACLAGAN ON THE TEMPERATURE OF NEW-BORN CHILDREN.
these orifices cannot be accurately ascertained. Their obliteration is extremely
rare before the completion of the first week of separate existence; but cases are
on record in which the foramen ovale, and others in which the ductus arteriosus
has been found obliterated before birth; whilst there are recorded several in
which the foramen ovale was patulous for many years.
The natural vigour of the child seems to exercise some influence on the extent
and duration of the fall which takes place after birth.
I made some calculations with the object of finding out whether the weight
of the child at birth or the weight of the placenta bore any fixed relationship to
the child’s range of temperature, but failed to establish any necessary connection.
The only conclusion to which I came was, that those children which gave the
most decided indications of being in a vigorous healthy state were also those in
whom the temperature fell least, and in whom it soonest again rose to the
normal standard. In a feeble seven months’ child the range fell to 90°:2, and
only once rose as high as 94°-6, during the thirteen days that it was under
observation. In another case, a vigorous healthy child, born at the full time, the
lowest point was 96°, and in two hours after birth the standard of health was
reached.
It is very probable that the vigour of a healthy child, and the higher range
which it shows, are both merely evidences of a better developed state of the
organs generally, and especially of the nervous and circulatory systems, on the
integrity of which the production of a due amount of heat is dependent.
TPMT UMNO AVM
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XI.—On the Practical Application of Reciprocal Figures to the Calculation of
Strains on Framework. By Professor FLEEMING JENKIN. (Plates XVII. to
XXIL)
(Read 15th March 1869.)
The theory of reciprocal figures used as diagrams of forces was first com-
_ pletely stated by Professor T. CLerK MAxweE LL, in a paper published in the
“ Philosophical Magazine,” April 1864. The following definition of reciprocal
plane figures, and their application to statics, are there given as follows :—
“Two plane figures are reciprocal when they consist of an equal number of
lines, so that corresponding lines in the two figures are parallel, and correspond-
ing lines which converge to a point in one figure form a closed polygon in the
other.”
“Tf forces represented in magnitude by two lines of a ee be made to act
between the extremities of the corresponding lines of the reciprocal figure, then
the points of the reciprocal figure will all be in equilibrium under the action of
these forces.” .
The demonstration of this statement is given. The conditions under
which stresses are determinate, and some examples of reciprocal figures, are
also given in the pave which leaves nothing to be desired by the mathe-
matician.
Few engineers would, however, suspect that the two paragraphs quoted put
at their disposal a remarkably simple and accurate method of calculating the
stresses in framework; and the author’s attention was drawn to the method
chiefly by the circumstance that it was independently discovered by a practical
draughtsman, Mr Taytor, working in the office of the well-known contractor, Mr
J. B. Cocurane. The object of the present paper is to explain how the principles
above enunciated are to be applied to the calculation of the stresses in roofs and
bridges of the usual forms.
The construction of a reciprocal figure for any frame requires the exercise of
a little discrimination, and the method employed can be best explained by
examples; those frames only being considered which are so braced as to be
stiff, but have not more members than is sufficient for this purpose.
The simplest example is that of a triangle loaded in the middle, and supported
at the two ends.
At each point three forces are acting. Thus we have at point 1 the upward
VOL. XXV. PART II. OX
442 PROF. F. JENKIN ON THE PRACTICAL APPLICATION OF RECIPROCAL
reaction of the support, the push due to the compressed member A, and the pull
due to the extended member ©. The directions
of the three triplets of forces are shown by
arrows.
In the reciprocal figure lines parallel to each
triplet of forces must make a triangle, and the
Fig. 1. whole figure must consist of six lines. Begin
with the joint 1, and draw one triangle mnqg with the sides _ S
P, A, C, such that they are parallel to P, A, C in fig. 1; while the
line P is equal on any convenient scale to the known force due to ; ; !
the upward reaction at the point of support. Then PAC, fig. 2,
is the simple polygon of forces acting at 1. i eae /
Next beginning at point m, and using the line A to express “
the upward push at 2 (fig. 1) draw the triangle mno, which re- i
presents the polygon of forces at joint 2. We next find that mqgo 0
represents the polygon of forces at joint 3, and that the fig. 2. iG
is the reciprocal of fig. 1.
The reciprocal figure is thus built up of a series of the well-known polygons
of forces acting at each joint, but so arranged that the line representing the elas-
tic force exerted by each member does not require to be drawn twice, but forms
part of two polygons, in which, however, it represents forces acting in opposite
directions.
Thus the line mg in fig. 2 forms part of the triangle gnm, in which it repre-
sents a pull from m to q, acting at point 1, and it also forms part of the triangle
mgo, in which it represents a pull from g to m, acting at joint 3. It is in
choosing the form of the component polygons, and in their arrangement, that a
certain discrimination is required.
To aid in the construction of the figures, we may observe that the lines repre-
senting the external forces acting on a rigid frame in equilibrium must in the
reciprocal figure form a closed polygon, and when these lines are parallel, as when
weights only are applied, this polygon becomes infinitely thin, and is represented
by a single straight line, subdivided into parts proportional to the forces. Thus,
in figs. 1 and 2, the three vertical forces are represented by the lines no, og, and
gn, which represent respectively the solid weight, acting from x to 0, the up-
ward reaction P acting from o to g and P from qg tom. This line (on), subdivided
in the ratio of the loads, may be conveniently termed the line of loads, and
reappears in all reciprocal figures of framework under parallel forces.
The reciprocal figures corresponding to the ordinary Warren girder will now —
be described in Plate XVII. fig. 1. The load is supposed to be applied at the —
bottom joints, and will just be assumed as equal to 10 tons at each of the eight
joints. These weights are represented by short vertical lines in fig. 1.
FIGURES TO THE CALCULATION OF STRAINS ON FRAMEWORK. 443
Fig. la is the reciprocal figure of Frame I., thus uniformly loaded and sup-
ported at Xand Y. The line zy is the vertical line of loads, equal to 80 tons
in all, and equally subdivided, because the load at each joint is equal. From each
of these subdivisions horizontal lines are ruled, and the lines IJKLMNO in
the reciprocal figure are drawn parallel to the lines similarly lettered in the
frame. The lengths of each of the lines in the reciprocal figure measure the
stresses on the members in the frame. The figure can be drawn in five minutes ;
whereas the algebraic computation of the stresses, though offering no mathe-
matical difficulty, is singularly apt, from mere complexity of notation, to result
in error.
The figure and the direction of each stress will be easily understood
when decomposed into its component polygons. The triangle PIA corresponds
to the polygon of forces at X, in which the direction of all the forces is that
in which the pen moves, starting from Z towards z. The polygon of forces
acting on joint 1, beginning with the forces determined by the previous poly-
gon, and proceeding in the direction-in which the forces act on the joint 1.
esa, J.
| The polygon at joint 2 is shown separately at fig. 16, being AIJB; the
polygon at joint 3 is also shown separately, the directions of the forces being in-
dicated by arrows. The complete fig. 1a is built up of separate polygons similar
to these two; the origin or starting-point on each being indicated by a small
circle in fig. 1.
Each line in fig. 1a serves as a part of two component polygons, but it
_ would be passed over in opposite directions in the two polygons by a pencil fol-
lowing the directions of the forces in the two polygons. This fact is of assistance
in drawing the reciprocal figures, making it easy to find the starting-point or
origin of each new polygon, since the lines representing forces already known
must be traversed in the opposite direction to those forces; thus the polygon at
joint 4 will include the force due to Band L. These have already formed part
of polygons 2 and 3; but in these the direction of the forces was from the joint
4, and hence in the new polygon the direction will be to the joint 4, and the
polygon will begin at Z, running BLMC.
It must be observed that the lines ABCD all begin at Z, ending at the inter-
section of I and J, K and L, M and N respectively. The stress on the two centre
diagonals is nil, and with the uniform load the second half of the reciprocal
figure is exactly symmetrical with the first half. The stress on d is equal to
that on D.
When the load is not uniform (fig. 2), the weights supported on the two piers
are not equal; in other words, the forces P and P, are not equal, and the line of
loads must be subdivided at Z into two portions, P and P, (fig. 2a), equal to the
loads borne by the piers. The divisions 1, 3, 5, 7, 9, 11, 18, 15, are made equal
444 PROF. F. JENKIN ON THE PRACTICAL APPLICATION OF RECIPROCAL
to the various loads on the several joints, these unequal loads being, as before, -
indicated by vertical lines in fig. 2. The two halves of the reciprocal figures are
now no longer symmetrical, but it is as easily drawn as the simpler case. Two of
the component polygons are shown, as in the previous case. The direction of the
stress on each member is found by going round each separate polygon, beginning
with some strain the direction of which is known. Thus at joint 7 the polygon
is ¢,7, d, P,, O, and knowing that the direction of the weight 7 is down, we find at
once that P, and O must both be pulled upwards. Care must be taken as before
to measure ABCDEFGH from the origin Z in each case. As soon as the values
of P and P, have been determined, the most complicated arrangement of loads
presents no more difficulty than the very simplest, the typical form being identical
in all cases, and easily remembered.
In figs. 3 and 3a the reciprocal figure for the same frame with a single load
at the centre is shown. The strains on a, b, c are represented by the lines wa, xb, xe ;
the strains on A, B,C by the lines zA, zB, zC. This will be clear from an
inspection of the component polygons.
In figs. 4 and 4a the reciprocal figure for a single weight hung at any joint is
shown, and will readily be understood from the explanations already given.
If the frame were inverted, and the loads applied at the top, the strains would
remain the same in amount, but be altered in direction in the diagonals; the
reciprocal figures would be identical in form with those already given, but would
lie on the other side of the line of loads, as if simply turned over through 180°
on that line as a hinge.
Yeah by. A : If the loads in Frame I. were applied at the
7 <= 7. top joints instead of along the bottom, the
; ae Ms strains and the reciprocal figure would be modi-
; fied, the component polygons for the bottom
joints being of the annexed type, fig. 3, and the
component polygons for the top joint of the annexed type, fig. 4. P, is also
placed above P, so that the upper and lower halves of the figure change places.
It is not, however, necessary to recollect these
Fig. 3,
—« 8 Y changes of arrangement, since the known reaction
| ead * at one pier and the first polygon of forces deter-
oe mine at once the general arrangement of the
Prine figure.
In the example just given the members of the frame are simply sufficient in
number to make the frame stiff; such a frame is incapable of being self-strained,
that is to say, any member might be lengthened or shortened without throwing
a strain on the other members. When this condition is fulfilled the stresses on a
frame under the action of known external pressure determinate; but when more
members are used than suffice to render the frame stiff, the stresses are indeter-
FIGURES TO THE CALCULATION OF STRAINS ON FRAMEWORK. 445
minate, and the frame may be self-strained. In these cases, therefore, the
reciprocal figure is useless to determine the stresses.
Such a frame as this shown in Plate XVIII. fig. 5; in which, if the diagonals
and verticals were all adapted to resist tension and compression, the stresses could
not be determined by the use of reciprocal figures or any ordinary method of
computation. If, however, the verticals be alone suited to resist the compression,
the diagonals being fit to sustain tension only, the stresses become determinate,
half the diagonals being with any given load wholly inoperative. The reciprocal
figure can be used to discover which are the active members, as they may be
called, and what are the strains upon them.
Fig. 5a shows the reciprocal figure for a uniform load.
The inactive members in Frame IJ. are not numbered. The component poly-
gons of fig. 5a are shown in figs. 5@,506. These figures require no explanation
beyond that already given for frame }.
Fig. 6 shows the active and inactive members of Frame II. partially loaded.
The active members have arrows on them, showing the direction of the stresses.
Fig. 6a is the reciprocal of fig. 6, and figs. 6a and 6@ show the component
polygons as before.
It must be remembered that in fig. 6a, as in fig. 5a, that the lines represent-
ing the stresses on B, C, D, E, F, G, H, I, all start from Z.
In fig. 7 we have a third frame not unfrequently used in roof work. Fig. 7a is
the reciprocal of fig. 7, and is thus constructed. XY is the line of loads subdivided
at Zin the ratio of the loads borne by the two piers. It is further subdivided into
the parts 1,2,5,4,5,6,7, the loads directly borne by each joint. The lines A, B, C, D
and F are in fig. 7a all drawn parallel to the top members of the same name in
fig. 7, and start from points in the line of loads determined by the subdivision
into partial loads. The lines a, b, ¢, d, ¢, fall radiate from Z, and these two sets of
lines are joined by the zigzag line g, h, 7,7, &, 1, m,n, 0, each of course parallel to the
corresponding member in fig. 7. The figure, although a little complex at first
sight, is extremely easily and rapidly constructed. In building it up out of
successive polygons we should as usual begin with the reaction of one pier; start-
ing at Z we draw the line ZX, return along load 1 directly borne by the pier, and
complete the first polygon by drawing Aa. The second polygon is A, 2, 6, H, g, and
the remaining component polygons corresponding to each joint can easily be
traced in like manner. It will be observed that all the members except
A, B, C, D, E, F are in tension.
Fig. 8 and fig. 8a (Plate XIX.) show a slightly different frame with the corre-
sponding reciprocal figure when uniformly loaded. 4h, 7,/,% are in compression
instead of in tension, as in Frame III.
VOL. XXV. PART II. Dat
446 PROF. F. JENKIN ON THE PRACTICAL APPLICATION OF RECIPROCAL
Figs. 9 and 9a show Frame IV. and its reciprocal figure when not uniformly
loaded.
The reciprocal figure now begins to appear very complicated, but it is drawn
on precisely the same plan as fig. 8a; but the lines of loads being no longer equally
subdivided, the reciprocal figure no longer presents two symmetrical parts.
Figs. 10 and 10a with 11 and lla show frames commonly used as roofs, with
reciprocal figures. They are only simplified cases of the roof already described.
Fig. ila may be compared with fig. 76 in Ranxrne’s “ Applied Mechanics.”’
The series of figures 75 in the same work are true elementary reciprocal figures.
Figs. 12 and 12a show a simple roof uniformly loaded, which is drawn in
order to render more intelligible the comparatively complex case in figs. 13 and
13a. Fig. 13 shows the roof under a series of external forces which are no longer
parallel, but represented by the inclined lines 1, 2, 3, which have been some-
what arbitrarily chosen as corresponding to a possible distribution of stresses
produced by the lateral and vertical pressure of wind. These external forces are
met by the two reactions P and P, at the piers, calculated on the hypothesis
that each pier or wall takes half of the horizontal strain.
Fig. 13a is the curiously distorted reciprocal figure which results from these
assumptions. It is drawn by precisely the same rule as the comparatively simple
figs. 12a and 7a. In each the lines a, b, ¢, Jd radiate from a centre Z, which
divides the lines P and P, representing the reactions on the piers. In each the
members A, B, C, D diverge from points separating the successive loads on the
joints 1, 2,3; but in fig. 13a the line of loads 1, 2,3 with the lines P and P,
representing the reactions at the piers, build up a polygon enclosing a space,
whereas in figs. 7a and 12a this polygon was represented by two straight lines
superimposed.
Again, if the zig-zag line corresponding to the diagonals be traced, it will be
found to run in an essentially similar manner in figs. 12 aand 13a; thus I joins d
and ¢ in both, the end of the line d having been determined by its intersection
with D, both starting from Z and X. Looked at by the light of fig. 12 a, fig.
13 a becomes readily intelligible, and serves to show how the theory of reciprocal
figures can be applied to the most complex conditions of stress which are con-
ceivable, without any greater essential complication than occurs in the simplest
examples.
As a final example, the reciprocal figure is given of a braced suspension bridge
or arch uniformly loaded, figs. 14 and 14a. The strains are drawn on the hypo-
thesis that the direction and magnitude of the resultant thrust are known. This —
thrust can be determined by Professor J. CLERK MaxweEtw’s method for calcu-
lating the equilibrium of Frames, published at the same time as his account of
reciprocal figures.
In conclusion, a few words may be said of the advantage of the diagrams of
FIGURES TO THE CALCULATION OF STRAINS ON FRAMEWORK. 447
forces, now explained as reciprocal figures, over the ordinary methods of calcula-
tion used by engineers.
The graphic method of calculation hitherto employed has been to draw a
separate polygon of forces for each joint. To do this it was necessary at each
joint to start afresh, setting out the known forces, and from them determining
the unknown forces. In thus continually measuring and setting out new lines
considerably greater accumulations of error, and more frequent errors, are pro-
bable, than when each line when determined by an intersection is used where it
lies, and if the successive polygons are drawn to any considerable scale, they lap
over one another on the drawing in an awkward and complex manner. Moreover,
it is impossible to complete the diagram of the reciprocal figure without taking
every line into account; and the closing of the diagram by the final line is an
almost perfect check on the accuracy of the delineation.
When compared with algebraic methods, the simplicity and rapidity of exe-
cution of the graphic method is very striking ; and algebraic methods applied to
frames such as the Warren girders, in which there are numerous similar pieces.
are found to result in frequent clerical errors, owing to the cumbrous notation
which is necessary, and especially owing to the necessary distinction between
odd and even diagonals. If this is the case when the loads are uniform or
symmetrical, the advantage is much more strikingly in favour of the graphic
method when the loads are not symmetrical, and when they are inclined, as in
fig. 13, or in such cases as the framed arch and suspension bridge. In fine, the
diagram once drawn acts as a sort of graphic formula for the strain on every part
of the bridge or roof, and it is a formula which can hardly be misapplied.
In conclusion, the author begs to acknowledge with thanks the assistance of
his students, Mr T. H. Cunnincuam and Mr A. M‘CuLtocn, in preparing the
diagrams; and takes the opportunity of repeating, that the merit of discovering
the method is entirely due to Professor MaxweLt and Mr Taytor, the object of
the present paper being to put the theory in such a form as should be intelligible
to the engineer and mechanician.
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( 449 )
XIl.—An Investigation into some previously undescribed Tetanic Symptoms
produced by Atropia in Cold-Blooded Animals, with a Comparison of the
Action of Atropia on Cold-Blooded Animals and on Mammals. By Tuomas R.
Fraser, M.D.
(Read 21st December 1868.)
Authorities on the action of medicinal substances agree in including convul-
sions among the effects on man of belladonna, and of its active principle,
atropia.* Similar effects are described as occurring when large doses of these
substances are administered to dogs, rabbits, and other mammals, and to various
birds. The recent remarkable progress of our knowledge of the exact and ulti-
mate physiological action of many medicinal substances is greatly due to investi-
gations that have been made on animals of a lower type of organisation ; and,
accordingly, numerous observers have instituted experiments with atropia on
such animals, and especially on frogs. Hitherto, however, convulsions and
tetanus have not been described among the effects of atropia-poisoning in cold-
blooded animals. +
While making a series of experiments, in April 1868, to determine the
minimum fatal dose of atropia for frogs, I was somewhat surprised to find that
symptoms of greatly increased reflex excitability occasionally occurred at a
certain stage in the poisoning. Believing that a careful examination of these
symptoms might probably serve to throw some light on the causation of several
of the complicated effects of a substance that has long occupied an important
position as a therapeutic agent, I have made a number of experiments (A), to
determine accurately the character of these convulsive effects; (B), to ascertain
the dose necessary for their production; (C), to differentiate, as far as possible,
* Curistison, “A Treatise on Poisons,” 1845, p. 836; Trousszav and Pipoux, “ Traité de
Thérapeutique et de Matiére Médicale,” tome ii. 1862, p, 55; Pereira, “ The Elements of Materia
Medica and Therapeutics,” vol. ii. part i. 1855, p. 549; Srizxu#, “Therapeutics and Materia
Medica,” vol, i. 1868, p.770; GusBieER, “ Commentaires Thérapeutiques du Codex Médicamentarius,”
1868, p. 602; Tu. and A. Husemann, “ Handbuch der Toxikologie,” Erste Halfte, 1862, p. 465 ;
Tarpizv, “ Etude Médico-Légale et Clinique sur ’Empoisonnement,” 1867, p. 750; Tayzor, “The
Principles and Practice of Medical Jurisprudence,” 1865, p. 358; Scurorr, “ Lehrbuch der
Pharmacologie,” 1868, p. 508.
{ Since this was written, I have communicated with Dr Jouw Hartey, of London (the author
of several important papers on the physiological action and therapeutical employment of bella-
donna), and have had the satisfaction of learning that he also has observed tetanus, and other
symptoms of abnormal reflex activity, in frogs during protracted atropia-poisoning.
2d March 1869.—I quote the following reference to these symptoms from a work which Dr
Hartey has published since this paper was communicated :—“ The action of atropia leaves the frog
in an excessively nervous state; the least disturbance causes great agitation, with increase of the
respiratory movements, and a touch often throws the animal into a tetanic convulsion,”—7he
Old Vegetable Neurotics, 1869, p. 240.
VOL. XXV. PART IIL. DZ
450 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
the structures on whose affection they depend; and (D), to harmonise these
effects with analogous ones in warm-blooded animals, and explain their
appearance in certain special circumstances only, in both frogs and mammals.
This investigation is limited to the consideration of these objects. Only those
effects of atropia that are directly connected with the convulsive symptoms will,
therefore, be considered.
SECTION A.
Soon after a small fatal dose, or one rather Jess than fatal, of a salt
of atropia is administered to a frog, a slight degree of weakness occurs in the
anterior extremities; the respiratory movements of the chest cease, those of the
throat continuing; and the motor power becomes gradually more and more
impaired, until at length no voluntary or respiratory movements occur, and the
animal lies on the abdomen and chest in a perfectly flaccid state. If the condi-
tion of the heart be now examined, it will be observed that the cardiac impulse
is scarcely perceptible, and that the contractions are reduced to a very few in the
minute. At this time, the application of various stimuli shows that the func-
tions of the afferent and efferent nerves and of the spinal cord are retained,
though in a greatly impaired condition.
Several hours afterwards—it may be not until the following day—the action
of the poison is still further advanced; for the afferent and efferent nerves are
completely paralysed, while but an occasional and scarcely perceptible cardiac
impulse can be discovered, the only signs of vitality being this imperfect cardiac
action, and the retained irritability of the striped muscles. This condition may
last for many hours, or for several days. Previous observers have apparently
mistaken it for one of death, and have therefore failed to observe the symptoms
that subsequently appear, and to which, more particularly, I wish to draw
attention.
The first of these symptoms is usually caused by a change that occurs in the
flaccid condition of the animal; the anterior extremities becoming gradually
more and more flexed, until they assume a state of rigid and continuous
contraction, with the webs pressed either against each other, or against the
opposite elbows—-tonic spasm of the muscles of the chest helping to keep the
anterior extremities in this position. At this time, a touch of any portion of the
skin increases the spasm of the anterior extremities and of the chest muscles,
and causes some slight spasmodic movements in the posterior extremities. After
a varying interval, the respiratory movements reappear, the cardiac action
improves greatly in strength and in frequency, and the posterior extremities
assume an extended position, with the webs more or less stretched. I1f the skin
be now touched, a violent attack of tetanus occurs (at this time usually opistho-
tonic), which may last for from two to ten seconds, and which is succeeded by a
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 451
series of clonic spasms. During the first attacks of tetanus the posterior ex-
tremities are often more or less abducted, and immediately after each attack
they become flaccid; but the anterior extremities almost always remain rigidly
flexed. Ata somewhat later period tetanus of a still more violent character,
and of longer duration, may be excited, and the attacks are now almost in-
variably emprosthotonic. During them, the posterior extremities are rigidly
extended; while at their conclusion, not only do the anterior extremities remain
flexed, but the head continues bent downwards by tonic spasm of the muscles of
the abdomen, chest, and neck.
A series of such attacks may be produced by repeated touches of the skin; but
when a number are excited in quick succession, the convulsions become shorter,
and rather less violent, though they reacquire all their former violence after a
period of rest.
During the convulsive stage, and especially at its latter portion, the animal
may execute various movements; but from the difficulty with which these are
performed, even when they do not themselves excite spasms and convulsions, it
is apparent that the power of voluntary movement is still considerably impaired.
The period during which this tetanic condition remains was found to vary
greatly in different experiments; and, as might have been anticipated, the larger,
within certain limits, the dose of atropia administered, the longer the continuance
of this condition. It has been observed to continue in some experiments for only
a few hours; in others, for several days; and, in one experiment, for even so
long as seventeen days.
This great protraction of the stage of tetanus occurred in an experiment in
which a small fatal dose of the sulphate was administered, and this experiment
will now be described, as it admirably illustrates the usual sequence of the
phenomena.
Experiment XIX.*—A solution of 0°45 grain of sulphate of atropia, in eight
minims of distilled water, was injected, by means of a Woop’s hypodermic
syringe,+ into the abdominal cavity of a healthy male frog, weighing 455 grains.
For some minutes afterwards, the frog jumped about very actively; but in about
eight minutes its movements were slow and sluggish, and some weakness
occurred in the anterior extremities, and in ten minutes it was unable to jump
with normal activity, and when undisturbed lay quietly on the abdomen and
chest. A few minutes later, the respiratory movements of the abdominal and
chest muscles ceased, those of the throat muscles, however, continuing, and the
head rested on the lower jaw. In twenty-one minutes, the frog was placed on the
back, and it then made some feeble voluntary movements of the limbs, which
* The numbers of the experiments of which detailed descriptions are given in this section have
reference to the arrangement in Table I. at the end of the section.
+ This instrument was employed in all the experiments in this investigation.
452 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
were insufficient to change its condition, though apparently designed to do so.
There were now no respiratory movements whatever, and the heart’s action, as
ascertained by its impulse, was reduced to twenty-four feeble beats in the
minute. In thirty-one minutes, the frog was in a perfectly flaccid condition ; it
was obviously unable to perform any voluntary movements, and merely feeble
reflex twitches could be excited by strong stimulation. In two hours, reflex
movements could still be excited, but the rate of the cardiac contractions had
diminished to nineteen per minute. In six hours, however, the nerve-paralysis
was more complete; stimulation did not excite any reflex movement; and even
direct galvanic excitation of an exposed sciatic nerve failed to produce any mus-
cular contraction, although the muscles themselves readily contracted when the
poles were applied to their surfaces. The colour of the frog’s skin was now
much darker than before the exhibition of atropia.
At the earlier portion of the following day—eighteen hours after the adminis-
tration of the poison—the frog was in the same state as last noted, except that
the heart’s action was still more feeble, the contractions being distinctly vermi-
cular, and at the rate of only fifteen beats per minute. Twenty-four hours after
the administration, however, an extremely faint twitch of the foot could be
excited by galvanism of a sciatic nerve; though a strong current passed through
the cord caused no movement beyond that resulting from direct stimulation of
several of the muscles of the back, and it was impossible to excite any reflex
contraction.
On the third day—forty-four hours after the administration—the frog was
lying in the same flaccid condition. The heart’s impulse was extremely feeble,
and the beats occurred only ten times in the minute. |
On the fourth day—sixty-eight hours after the administration—a change of
position had occurred, for the anterior extremities were flexed, and formed an arch-
like prop on which the raised head and thorax were supported. Reflex movements
were now more easily excited, though still very sluggish and feeble; and when
such movements occurred the muscles continued in a contracted state for several
seconds before they again slowly relaxed. This peculiarity in the contractions
was most marked in the muscles of the thorax, anterior extremities, and head.
A respiratory movement of the throat occasionally took place; and the rate of
the heart’s beats was increased to twelve in the minute.
On the fifth day—ninety-two hours after the administration—the frog was
lying on the side with the anterior extremities strongly flexed, the webs being m
close contact with the opposite elbows, while the posterior extremities were
normally flexed. At frequent intervals, the contraction of the muscles of the
anterior extremities and of the front of the thorax relaxed somewhat, and,
apparently taking advantage of the intervals, the frog made slight voluntary
movements, which always excited short attacks of emprosthotonic tetanus. These —
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 458
attacks ceased first in the posterior extremities, continuing for several seconds
longer in the anterior extremities and thorax. During the intervals the anterior
extremities were constantly flexed by tonic spasm in their muscles, and in those
passing to them from the thorax (especially in the pectoralis major). If the skin
were touched, or if the frog were otherwise gently stimulated, an attack of empros-
thotonic tetanus followed, during which the flexion of the anterior extremities was
rendered more rigid, and the posterior extremities were extended and consider-
ably abducted. These attacks of tetanus lasted for about five seconds, when the
posterior extremities became flaccid; but the increased spasm of the anterior
extremities and of the chest muscles continued for about sixty seconds longer.
When the frog was not suffering from general tetanus there were occasional
respiratory movements of the throat and chest. It was now impossible to observe
any cardiac impulse, because of the constant spasm of the chest muscles.
On the sixth day—one hundred and sixteen hours after the administration—
the frog was lying on the back with the anterior extremities rigidly retained in
the position already described; but the head was bent forwards (downwards) by
spasm of the anterior abdominal and chest muscles, and the posterior extremities
were loosely extended, with the webs slightly stretched. The respiratory move-
ments of the throat were frequent, but those of the thorax but rarely occurred.
If a posterior web were now touched, a pretty powerful attack of tetanus followed,
during which the body was curved in the form of an arch, with the head bent for-
wards, while the anterior extremities were strongly clasped against the chest,
and the posterior rigidly extended in a straight line. This was general for about
six seconds, when the posterior extremities became flaccid; but the increased
spasm of the muscles of the anterior extremities and of the anterior surfaces of
the abdomen, chest, and throat continued for twelve seconds longer. Still more
powerful and prolonged tetanus could be excited by stimulating the skin of the
head; and these attacks lasted for eight seconds in the posterior extremities, and
for two minutes in the anterior extremities and in the muscles of the anterior
surface of the chest. So powerful was the tetanus at this stage that it was possible
to lift the frog by the feet and hold it horizontally for eight seconds, with either
the back or front of the animal uppermost. The faintest voluntary movements
almost invariably excited a tetanic convulsion, and, indeed, such attacks could
be produced even by excitations through the organs of vision, as by the sudden
approach of any object.
The frog remained in this remarkable condition, without any notable change,
until the fourteenth day.
At this time—three hundred and ten hours after the administration—it still
continued in the position last described, but, although violent tetanus could still
be excited, this did not occur so invariably as before. Frequently, indeed,
excitation produced only slow and stiff movements of the posterior extremities,
VOL. XXV. PART II. OA
454 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
with violent convulsive spasms of the anterior extremities and of the trunk.
Moreover, to excite general tetanus, stimuli of a rather more severe, though still
slight, character were now required.
With this modification in the constancy and readiness with which tetanus could
be excited, and with a slight diminution in the period during which an attack
lasted, the condition of the frog remained unchanged until the twentieth day.
At this time—four hundred and fifty hours after the administration—the frog
had assumed a most extraordinary and ungainly attitude. It lay on the right
side, with the head bent downwards, by strong tonic spasm of the muscles of the
front of the abdomen, chest, and neck; with the anterior extremities rigidly
clasped against the thorax (the webs being, as before, pressed against the oppo-
site elbows) ; and with the right posterior extremity extended, and the left drawn
forwards and slightly flexed. The disagreeable appearance resulting from this
attitude was greatly increased by the emaciation of the frog, which had gradually
increased for several days, until it had so far advanced that the frog now weighed
only 385 grains—its weight before the sulphate of atropia was given having been
455 grains. At this time, excitation usually produced merely stiff and slow
movements of the posterior extremities, and increase of the tonic spasm of the
muscles in the other regions. Occasionally, however, a short attack of empros-
thotonic tetanus could still be excited.
For other two days the frog remained in this condition; but on the twenty-third
day—five hundred and twenty-six hours after the administration—general tetanus
could not be excited by any stimulus, however strong. Stimulation only slightly
increased the tonic spasm of the muscles of the throat, anterior extremities, chest,
and abdomen, and caused slow and feeble movements of the posterior extremities.
On the following day—the twenty-fourth of the experiment—the frog was
found dead and in rigor; the emprosthotonic curve of the body and the rigid
flexion of the anterior extremities being retained in death.
In this experiment the tetanic stage lasted for seventeen days, which in this
investigation is the longest period during which it has been observed to continue.
During eight days the attacks were extremely violent and prolonged; during six
days neither could they be invariably excited, nor did they continue for quite so
long a period as before; and during the three days that immediately preceded
the death of the animal they could but rarely be produced.
Loss of weight is by no means an invariable occurrence after a long continu-
ance of the tetanic stage. Indeed, Iam inclined to think that an opposite effect,
namely, augmentation of weight, more commonly occurs. The latter is caused
by general anasarca, and is sometimes very considerable. :
Allusion has been made in the general description of these remarkable
phenomena to the stage of complete paralysis having continued for several days.
In the following experiment its duration was five days.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 455
Experiment XXXIII—I injected into the abdomen of an active male frog,
weighing 251 grains, a solution of 0:3 grain of sulphate of atropia, in five minims
of distilled water. Flaccidity and motionlessness occurred rather more rapidly
than in the previous experiment; and eight hours after the injection it was found
that the conductivity of the sciatic nerves was completely suspended —the muscles,
however, freely contracting when directly galvanised—and that the heart’s action
was extremely feeble, and at the rate of only nineteen beats in the minute.
On the following day—twenty-two hours after the administration—the heart’s
impulse was even less apparent, and contractions occurred only seven times in
the minute; while galvanism of the sciatic and brachial nerves was not followed
by any muscular contraction, although idio-muscular contractility was apparently
unaffected.
The frog remained in this state of complete nerve-paralysis for other four
days. The cardiac action, however, improved during the latter portion of this
period, and on the sixth and seventh days the contractions occurred sixteen and
nineteen times respectively in the minute.
On the seventh day—at about one hundred and forty-six hours after the
administration—a change occurred. ‘The frog still lay on the abdomen and chest,
with the posterior extremities flaccidly extended; but the anterior extremities
were now slightly arched, there were infrequent respiratory movements of the
throat, and a slight touch of the skin excited a feeble, momentary, and sudden
movement of the whole body.
On the eighth day—one hundred and sixty-eight hours after the adminis-
tration—excitation produced a violent attack of tetanus, which was slightly
opisthotonic in character, and was succeeded, after lasting for eight seconds, by
a series of quivering movements of the posterior extremities. It was not neces-
sary, however, to apply excitation, in order to produce tetanic convulsions, for
they also frequently occurred when voluntary movements were attempted. At
one hundred and seventy hours, the tetanus was emprosthotonic.
On the ninth day—one hundred and ninety hours after the administration—the
tetanic condition was exactly the same as at the latter part of the previous day,
and the frog remained extended horizontally for five seconds when lifted in that
position by the ankles. The heart was now contracting at the rate of twenty-
two beats in the minute.
On the tenth day—two hundred and sixteen hours after the administration—
the frog was lying on the lower jaw, chest, and abdomen, the anterior extremities
being extended at right angles to the body, while the posterior were stretched
backwards. Excitation now caused a feebler and stiffer movement of the
limbs; and however powerful the excitation, it was impossible to cause tetanic
convulsions.
On the eleventh day—two hundred and thirty-eight hours after the adminis-
456 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
tration—only feeble movements could be excited, and there was now a slight
degree of continuous general stiffness. The heart’s action was at the rate of
twenty-two beats in the minute, but the respiratory movements were feeble and
very infrequent.
- On the twelfth day—two hundred and sixty hours after the administration—
the stiffness was more marked, no reflex movements whatever could be excited,
and it was found that the sciatic nerves were completely paralysed, and that the
muscles responded but faintly to direct galvanic stimulation. The heart’s action
was at the rate of only eleven beats in the minute.
On the thirteenth day, the frog was dead, and in rigor.
The dose of atropia administered in this experiment was exceptionally large,
when compared with the weight of the frog; but the frog was a small one, and
had been kept in the laboratory for many months—conditions which appear to
favour a certain amount of tolerance. With a frog recently obtained from its
natural habitat so large a dose, however, would most probably have proved fatal
before tetanus occurred. The stage of complete paralysis of motor nerves lasted
altogether about five days and ten hours.
Each of these two experiments has been distinguished by an exceptional cir-
cumstance: Experiment XIX. by the long continuance of the stage of tetanus,
and Experiment XXXIII. by the long continuance of the stage of complete para-
lysis of the motor nerves. In the experiment which will now be described the
duration of the phenomena was such as more frequently occurred.
Eaperiment XXIU.—A solution of 0:4 grain of sulphate of atropia, in four
minims of distilled water, was injected under the skin at the left flank of a frog,
weighing 386 grains. As usual, after such a dose, in the course of an hour the
frog was flaccid, and unable to perform any voluntary movements.
On the following day—eighteen hours after the administration—the frog was
lying motionless on the abdomen and lower jaw. It was ascertained by galvanic
stimulation that the conductivity of the sciatic nerves was suspended, while the
contractility of the voluntary muscles was apparently unaffected. At twenty-
two hours after the administration, however, a weak stimulus produced feeble
reflex movements. The heart’s impulse was now barely perceptible, and con-
tractions occurred but eight times in the minute.
On the third day—fifty hours after the administration—the frog was still
lying on the abdomen, but the chest and head were slightly raised by continuous
flexion of the anterior extremities. The reflex function was in a more active
state, for a slight stimulus applied to the skin of the head caused an increase in
the flexion of the anterior extremities, by which the head was still further
raised, and a sudden extreme abduction of the two posterior extremities. Irregu-
lar respiratory movements of the throat were now observed.
On the fourth day—seventy-three hours after the administration—a faint
ee aes eS ee Se
——<—
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 457
touch of the skin of the head was followed by an attack of opisthotonic tetanus,
lasting for four seconds; and during it the anterior extremities were rigidly
arched, while the posterior were extended straight backwards. When the
stimulus was applied to any other region, the only effect was an increase in the
tonic spasm of the anterior extremities, and a sudden somewhat spasmodic
flexion of the posterior.
On the fifth day—ninety-five hours after the administration—the frog was
lying on the back with the anterior extremities rigidly flexed, the webs being
pressed against each other, and with the posterior extremities stiffly extended.
A slight touch of the skin of any region was immediately followed by a sudden
and violent attack of emprosthotonic tetanus. These convulsions were usually
general for ten seconds; but the tetanic spasm continued in the anterior extre-
mities for several seconds longer than elsewhere. The respiratory movements
had now become more frequent and regular.
During the two following days the frog remained in this condition.
On the eighth day—one hundred and sixty-four hours after the administra-
tion—it was more difficult to excite general tetanus, somewhat irregular convul-
sions most commonly occurring. When the skin of an ankle was touched, tetanus
occurred in that limb and in the two anterior extremities for five seconds; but
merely spasms, without extension, occurred in the opposite posterior extremity.
General tetanus could be excited only when the irritation was applied
to the head. The cardiac impulse had now greatly improved in character,
while the rate of contraction had increased to twenty-two beats in the
minute.
After this a daily improvement was apparent. On the twelfth day the frog
had resumed a normal sitting posture, the anterior extremities being, however,
still slightly arched; and on the sixteenth day the tonic spasm of the chest
muscles and of the anterior extremities had completely disappeared, while slow,
voluntary movements could be cautiously performed: but during all this time
it was possible to excite a short attack of general tetanus, though severe or
frequently repeated stimulation had to be employed.
On the seventeenth day—three hundred and eighty-two hours after the
administration—stimulation, even when severe, excited mere stiff reflex move-
ments of the two posterior extremities, and comparatively slight and short
tetanus of the two anterior.
The complete disappearance, however, of the exaggerated activity of the
reflex function was but slowly effected, and did not occur until about the twenty-
fourth day, or five hundred and fifty hours after the administration. For several
days after this, the frog was in a somewhat torpid state, moving about very
sluggishly, and obviously preferring to remain quiet; but ultimately it recovered
perfectly.
WOL, XXV. PART Ir. 6B
458 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
The total duration of the symptoms was considerably shorter in a few of the
experiments, of which the following is an example :—
Experiment XV11.—Three-twentieths of a grain of sulphate of atropia was
dissolved in four minims of distilled water, and injected under the skin at the
left flank of a male frog, weighing 156 grains; but during some vigorous move-
ments of the frog, which succeeded this injection, a small quantity of the solution
escaped from the subcutaneous tissue. In a few minutes, the frog was lying on
the abdomen ; chest, and lower jaw in a flaccid state; but even in three hours the
conductivity of the motor nerves was found to be retained. The observations
were now interrupted until the following day.
At this time—twenty-four hours after the administration—the frog was lying
as last described; but the conductivity of the motor nerves was found to be com-
pletely suspended, while idio-muscular contractility was apparently unaffected. The
heart’s contractions were very feeble, and occurred twenty-six times in the minute.
On the third day—fifty hours after the administration—the state of flaccid
paralysis had disappeared, and the frog was sitting in a nearly normal posture,
except that the anterior extremities were unnaturally and somewhat rigidly
flexed. On touching any part of the body, a violent attack of opisthotonic tetanus
occurred, during which the animal was turned on the back. Such attacks could
be excited at any time, at short intervals, during the next three hours, at the end
of which period the observations were interrupted. They were general for five
seconds; but the tetanic contraction continued in the anterior extremities for
five seconds longer than elsewhere. In the intervals between them the frog
turned itself from the back, and executed feeble and slow voluntary movements.
The heart’s contractions were of fair strength, and at the rate of forty-six in the
minute; and the respiratory movements of the chest and throat were of nearly
normal frequency.
On the fourth day—seventy-four hours after the administration—the frog
seemed to have perfectly recovered: it moved and jumped about freely, and no
trace of exaggerated activity of the reflex function could be discovered.
The description that has been given, and the illustrative experiments that have
been narrated, are sufficient to indicate the usual characters and sequence of the
phenomena with such a dose of atropia as produces tetanus. Experiments have,
however, been made in which the functions of the cerebro-spinal nervous system
were not observed to be completely suspended in the stage of the poisoning,
antecedent to the appearance of tetanus. Only impairment of these functions
was observed ; but, as the state of flaccidity often lasts for several days, it is
obviously impossible to make observations so continuously during its existence,
as to authorise the assertion that total suspension did not occur. At the same
time, there is no reason for supposing that complete paralysis is a necessary
antecedent to tetanus. 7
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 459
It has also happened that in one or two experiments symptoms of exaggerated
activity of the reflex function occurred, without being observed to assume the
violence of tetanus. The following is an example of such an experiment :—
Laperiment X.—I\ injected under the skin, at the left flank of a male frog,
weighing 231 grains, one-fifth of a grain of sulphate of atropia, dissolved in four
minims of distilled water. In ten minutes, the frog was resting flaccidly on the
abdomen and chest. In two hours, all voluntary and respiratory movements had
ceased, but stimulation still excited feeble reflex contractions; and the heart was
contracting at the rate of twenty beats in the minute.
On the second day—twenty hours after the administration—the frog had
resumed a natural position, the thorax and head being supported by the anterior
extremities, while the posterior extremities were normally flexed; and the throat
and chest respirations were frequent. When the skin was touched, or when any
object was rapidly approached to the eyes, a sudden, spasmodic, and momentary
contraction occurred simultaneously in the four extremities ; but it was impossible
to excite a tetanic convulsion even by severe stimulation. These spasmodic starts
—for they were only such—were often preceded by a “‘ croak,” and when suddenly
and unexpectedly excited, were sufficiently strong \to raise the body upwards
for about a second. During the following day, these symptoms continued ; but on
the fourth day the only symptom was a slight degree of stiffness when the frog
jumped.
On the fifth day the frog was perfectly well.
It is almost superfluous to allude to the resemblance in frogs between the
tetanic symptoms of atropia and those of strychnia. There are, however, certain
peculiarities connected with the tetanus caused by atropia—altogether apart from
the remarkable circumstance of this tetanus being preceded by more or less com-
plete paralysis—that distinguish it from the tetanus caused by strychnia. After
poisoning by atropia, the symptoms of exaggerated excitability of the reflex func-
tion, as has been shown, are extremely slight on their first appearance, and they
acquire their greatest violence only after some considerable time. When these con-
vulsant effects have become fully developed, the state of the animal is one of nearly
constant tonic spasm—this tonic spasm being rarely general, but almost always
restricted to certain regions,—so that the attacks of tetanus are of the nature rather
of exacerbations of existing spasm than of successive and independent convulsions.
Strychnia tetanus, on the other hand, becomes fully developed with great rapidity;
and, during the stage of remission, the animal is usually in a perfectly flaccid state.*
* Although this is ‘‘ usually” the case, continuous tonic spasm of the anterior extremities may
be produced by strychnia also, if an extremely small dose be given. I have found that a dose
equivalent to about the 7;;,,;th of the weight of a male frog (or of a female in whom the abdomen
is not greatly enlarged by distended oviducts) will almost invariably cause continuous spasm and
arch-like flexion of the anterior extremities; and Tarprev (op. cif. p. 983) describes the same effect
in an experiment with a minute dose of strychnia.
460 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
Further, in atropia-poisoning, the attacks of tetanus can seldom be excited by the
very slight stimuli that are sufficient to do so in strychnia-poisoning.
The tetanus of atropia, also, is characterised by various irregularities. Some
of these have already been described; such as the continuous spasm of the muscles
of the throat, of the front of the thorax and abdomen, and of the anterior extre-
mities, either only accompanying a condition in which tetanus in the posterior
extremities may be excited, or also persisting after this condition has ceased: and
of the others, it is sufficient to mention the occurrence of tonic spasm of one
group of muscles in one limb, and of another group in another; of contractions of
unequal force in the muscles at the opposite sides of the thorax and neck, causing
lateral curvature during a tetanic convulsion; and of tetanus in the posterior
extremities, with only slight increase of reflex excitability in the anterior.
The last of these irregularities was observed in the following among other
experiments :—
Experiment XXIX.—A solution of four-tenths of a grain of sulphate of atropia,
in four minims of distilled water, was injected under the skin, at the right flank _
of a female frog, weighing 361 grains, whose oviducts were greatly distended.
On the following day, the frog was lying on the abdomen, chest, and lower
jaw, with the posterior extremities flexed, and the anterior extended at right
angles to the body. When the skin was stimulated, some feeble movements
followed in the toes of both posterior extremities; but no reflex contraction
could elsewhere be excited.
On the third day—fifty-two hours after the administration—the posture of
the frog was the same as on the previous day; but the paralysis was now more
complete, for no reflex movement whatever could be excited, and it was found,
on examination, that the motor conductivity of the sciatic nerves had dis-
appeared.
On the fourth day—seventy-two hours after the administration—the condi-
tion of flaccidity was no longer present. The anterior extremities were now |
slightly flexed, so as to raise the head and chest; and now and then a feeble __
voluntary movement, and a barely perceptible respiration, occurred. These
movements generally excited an attack of violent tetanus in the posterior
extremities, and a comparatively feeble spasmodic extension of the anterior,
during which the latter assumed a more perpendicular direction than before.
Feeble irritation caused similar attacks. They usually lasted for eight seconds
in the posterior extremities, and for only three in the anterior.
During the fifth and sixth days, the frog continued to suffer from tetanus, .
and the character of the symptoms was exactly the same as on the fourth day.
Neither abnormal flexion nor tonic spasm occurred in the anterior extremities,
and such convulsive movements as appeared in them were always much less
violent, and of shorter duration, than in the posterior extremities.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 461
On the seventh day, the posture of the frog was quite normal; voluntary
movements took place with considerable activity; and although some exaggera-
tion of the reflex function was still present, it was exhibited principally by stiff
spasmodic movements of the posterior extremities, and general tetanus could
not be excited.
The frog recovered completely in a few days.
The absence of rigid and continuous flexion of the anterior extremities, which
is illustrated by this experiment, has been an invariable occurrence in frogs
with distended oviducts. With this exception alone, so far as my experience
has shown, rigid and continuous flexion of the anterior extremities is a con-
stant, prominent, and early symptom of the motor-stimulant action of atropia.
When the dose of atropia exhibited is not a fatal one, the animal usually
recovers completely and rapidly. In one experiment, however, this was not the
case. The symmetrical tonic spasm of the two anterior extremities passed into
unsymmetrical tonic spasm, which persisted for several months after the disap-
pearance of every other symptom. This sequela will be best described by a short
narration of the experiment.
Experiment XX VIII.—I injected three-tenths of a grain of sulphate of atropia,
dissolved in four minims of distilled water, into the abdominal cavity of an active
and perfectly healthy male frog, weighing 275 grains. The usual paralytic effects
followed. During the second and third days, the motor-nerve conductivity was
completely suspended; but on the fourth day it reappeared, though in an
extremely imperfect form, galvanism of a nerve trunk producing only faint
twitches.
On the fifth day, the frog was lying on the abdomen with the head and chest
raised on the anterior extremities, which had become symmetrically flexed, the
webs being rigidly and continuously pressed against the opposite elbows. Slight
irritation now excited a short attack of opisthotonic tetanus.
On the sixth day, the attacks of tetanus were somewhat more violent, but
they were still opisthotonic.
On the seventh, eighth, ninth, and tenth days, the attacks of tetanus were
very violent, and emprosthotonic in character.
On the eleventh day, the violence and duration of the tetanic convulsions had
somewhat diminished.
On the twelfth, thirteenth, and fourteenth days, the frog still retained the
strongly flexed symmetrical posture of the anterior extremities; but irritation
now excited merely a sudden momentary extension of the posterior extremities,
and an increase of the tonic spasm of the anterior.
On the fifteenth day, the frog had assumed a nearly normal sitting posture.
The anterior extremities were, however, still rigidly flexed, and the frog could
move about only by a vigorous use of the posterior extremities. Irritation now
VOL. XXV. PART II. 6 Cc
462 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
caused merely a slight increase of the flexion of the anterior extremities, and
perfectly normal movements in the posterior.
On the sixteenth day, it was observed that the posture of the anterior
extremities was somewhat unsymmetrical; the right being rather more flexed
than before, while the left was extended backwards so as to be nearly parallel
with the left side of the body.
For several days afterwards, the only change was an increase in the rigidity
and tonic spasm of the anterior extremities; until, on the twenty-first day, they
had assumed the following positions:—The right anterior extremity was in
extreme flexion, the upper-arm being at a right angle to the body, with the fore-
arm below it, while the hand was everted at the wrist, and had its dorsal surface
closely pressed against the anterior surface of the shoulder; the left anterior
extremity was extended backwards (towards the posterior extremities), the arm
being in close contact with the left side of the thorax, with the fore-arm slightly
flexed, inverted, and pressed against the abdomen, while the web was firmly
applied, by its palmar surface, against the lower part of the anterior surface of the
abdomen. JEoth anterior extremities were rigidly maintained in these postures,
and the frog had no control over them. Changes of position were effected by the
use of the posterior extremities alone; and, while irritation produced normal
reflex contractions in the posterior extremities, it produced only extremely faint
movements in the anterior without changing their unsymmetrical postures.
When the frog was placed in water, vigorous swimming movements of the
posterior extremities occurred, but the anterior remained motionless.
This sequela first appeared seventy-four days before this description was
written; and at this time, there is neither the slightest abatement in the rigidity,
nor any other change in the character of the distortion.
Although the physiological action of atropia has been frequently and elabor-
ately studied, these very striking and remarkable convulsive phenomena have
hitherto escaped attention. I have, therefore, thought it necessary to enter with
considerable detail into the description of these effects, so as to indicate with
accuracy their usual character, and to point out the principal irregularities that
have been observed. I have likewise shown their relations to some of the other
effects that are produced by this substance.
The following Table contains a succinct account of a number of experiments
on frogs with sulphate of atropia, in which the progress of the symptoms was
not interfered with, either by ligature of blood-vessels before the administration
or by division of nerve-structures before or after the atropia-effects were initiated.
The latter classes of experiments will be described in a subsequent portion of
this paper.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 463
TABLE I.—SuMMARY OF EXPERIMENTS ON FROGS WITH SULPHATE OF ATROPIA, IN WHICH THE
EFFECTS WERE NOT MATERIALLY INTERFERED WITH BY OPERATIONS OR OTHERWISE,
: Relation
Number Ea Grate, of Dose Region
of Weicht to of Effect. |
Experiment.| \» Fe Dose. | Weight Injection.
On enee of Frog.
i, 413 | 0:05 | go> | Under skin of | No obvious effect.
left flank.
ie 275 | 0:05 | s3y> | Into abdomi-| None observed in 6 hours.
nal cavity.
III. 333 | O11 | ga3, | Under skin of | No obvious effect.
left thigh.
IV. 294 | O1 | sgia Do. Slight incomplete paralysis 1st day; and per-
fect recovery 2d day.
V. 298 | 0:2 | roa Do. Incomplete paralysis 1st day; exaggerated reflex
movements 2d day ; tetanus 3d day; and re-
covery 4th day.
VIi.* 275 | 02 | zA,— | Into abdomi-| Incomplete paralysis 1st day; tetanus 2d to
nal cavity. oth days; stiff spasmodic reflex movements
6th to 8th days; and perfect recovery 10th
day.
VII. 273 | 02 | ass5 Do. Incomplete paralysis 1st day ; exaggerated re-
flex movements 2d to 5th days ; and recovery
6th day.
WATT. 376 | 03 | rss Do. Incomplete paralysis Ist to 3d days; tonic
spasm and tetanus of anterior extremities and
chest muscles, with only slightly exaggerated
reflex movements of posterior extremities 4th
to 10th days ; and perfect recovery 12th day.
1X. 250 | 02 | seh5 Do. Incomplete paralysis lst day; tetanus 2d to 6th
days; stiff spasmodic reflex movements 7th
and 8th days; and perfect recovery 9th day.
Xx. 231 | 0-2 | y¥s5 | Under skin of} Incomplete paralysis 1st day; exaggerated re-
left flank. flex movements 2d and 3d days; and perfect |
recovery 5th day.
XI. 346 | 0°3 | zys3 | Into abdomi-| Incomplete paralysis 1st to 8th days; and
nal cavity. death, with commencing rigor, 9th day. |
XII. 230 | 02 | ass Do. Incomplete paralysis 1st and 2d days; slight
tetunus 3d day; stiff spasmodic reflex move-
ments 4th to 6th days; and recovery 7th day.
XIII. 340 | 03 gies Under skin of | Incomplete paralysis 1st day ; tetanus 2d day ;
right flank. stiff spasmodic reflex movements 3d day;
and perfect recovery 5th day.
incomplete paralysis 3d day; tetanus 4th
to 6th days ; stiff reflex movements 7th day ;
|
| XIV. 447 | 04 | svar Do. Incomplete paralysis 1st day ; spasms 2d day ;
| | and recovery 8th day.
* The same frog was used in this experiment as in Experiment II. The second dose (0:2 gr.)
was administered 21 hours after the first, and when the frog appeared to be in normal health. The
influence of the first dose might, however, have been still partially present; and the exceptional
severity of the symptoms described as being caused by a dose equivalent to only the ;,;th of the
weight of the frog may thus be accounted for. If this view be correct, the dose of Experiment VI.
should be about 0°25 grain, or the ;~5,th of the weight of the frog.
464 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
TABLE I.—SuMMARY oF EXPERIMENTS ON FroGsS—continued.
In Grains. Relation
Number of Dose Region
of Weicht to of Effect.
Experiment. of Pog Dose. | Weight Injection.
as of Frog
XV. 432 | 0-4 | zosz | Under skin of| Complete paralysis Ist and 2d days; tetanus
right flank, 3d to 8th days; stiff spasmodic movements
9th day; and perfect recovery 10th day.
XVI. 372 | 0°35 | rss Do. Complete paralysis 1st and 2d days; tetanus
3d to 6th days; stiff spasmodic movements
7th to 9th days; and recovery 10th day.
xVIL 156 | 0:15 | yj45 | Under skin of| Incomplete paralysis 1st day; complete par-
left flank. alysis 2d day; tetanus 3d day; and perfect
recovery 4th day.
XVIII. | 508 | 0°5 | yj; | Into abdomi-} Complete paralysis 1st to 4th days ; incomplete
nal cavity. paralysis 5th day; tetanus 6th to 8th days;
stiff reflex movements 9th to 11th days; and
perfect recovery 12th day.
XIX, 4556 0°48 | a4 Do. Complete paralysis in 6 hours and at earlier
part of 2d day; incomplete paralysis, 2d to
4th days ; tetanus 5th to 22d days ; stiff spas-
modic movements 23d day; and death, with
| commencing rigor, 24th day.
|i ¢ pecan 404 | 0-4 | goka | Under skin of | Complete paralysis, 1st and 2d days; tetanus
left flank, 3d to 9th days; stiff spasmodic movements
10th and 11th days; and recovery 12th
day.
XX, 3800 | 0:3 | ror Do. Incomplete paralysis 1st day; slightly exagger-
ated reflex movements 2d day; and death 3d
day.
XXII. 400 | 04 | asb0 Do. Incomplete paralysis 1st day; complete par-
alysis 2d day ; tetanus 3d to 6th days ; irregu-
lar tetanus, with twisting of body to left, 7th
and 8th days; stiff spasmodic movements,
also with twisting of body to left, 9th to 13th
days; dead, with rigor, 14th day,
Do Complete paralysis 1st and earlier part of 2d
day ; exaggerated reflex movements 3d day ; |
tetanus 4th to 16th days; stiff spasmodic
movements 17th to 21st day; stiffmovements
22d to 24th days; and perfect recovery 27th
day.
XXIV. | 482 | 05 sia | Under skin of iasera hed paralysis lst and 2d days; com-
both flanks. | plete paralysis 3d day; exaggerated reflex
movements 4th day; tetanus 5th to 7th days ;
stiff spasmodic movements 8th and 9th days ;
and death, with rigor, 10th day.
XXV. | 337 | 0:85 | 52, | Under skin of| Incomplete paralysis 1st to 5th days; and death,
left flank. with commencing rigor, 6th day.
XXXVI. | 234 | 0:25 | 53; Do. Incomplete paralysis 1st to 3d days; tetanus 4th
to 12th days; stiff spasmodic movements 13th
and 14th days; and perfect recovery 15th)
day. :
XXVII. | 465 | 0°5 pat Do. Incomplete paralysis 1st day; tetanus 2d to
4th days; and death, with commencing rigor, }
5th day. Ia
XXIII. | 3886 | 0-4
©|
a
oy
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS.
465
TABLE I.—SumMMARyY or EXPERIMENTS oN FRoGS—continued.
Number
of
Experiment.
XXVIII.
XXIX.
XXX.
XXXI.
XXXII,
XXXII.
XXXIV.
XXXV.
XXXVI.
XXXVII.
XXXVIII.
|
| ox XTX.
| ih,
XLI,
XLII.
XLII.
In Grains.
Weight
of rae Dose.
275 0:3
361 0°4
270 0:3
305 0:4
340 0-4
251 0:3
410 0°5
403 0:5
638 0-8
396 0-5
147 0:2
214 0°3
322 0-5
254 0-4
259 0-5
340 1:
Relation
of Dose
to
Weight
of Frog.
dx.
917
Region
of
Injection.
Into abdomi-
nal cavity.
Under skin of
Into abdomi-
nal cavity.
Under skin of
right flank.
Under skin of
both flanks.
Into abdomi-
nal cavity.
Under skin of
both flanks.
Do.
Under skin of
left flank.
Under skin of
left thigh.
Into abdomi-
nal cavity.
Do.
Under skin of
both flanks.
Into abdomi-
nal cavity.
Under skin of
left flank.
Do.
Effect.
right flank, |
Incomplete paralysis 1st day ; complete paraly-
sis 2d and 8d days; incomplete paralysis
again on 4th day; tetanus 5th to 11th days;
stiff spasmodic reflex movements 12th to 14th
days ; stiff reflex movements 15th day; and
unsymmetrical continuous rigidity of the an-
terior extremities 16th day, remaining for
more than 74 days afterwards,
Incomplete paralysis 1st and 2d days ; complete
paralysis 3d day; tetanus 4th to 6th days;
stiff spasmodic movements 7th and 8th days;
and perfect recovery 10th day.
Incomplete paralysis 1st to 5th days; and death,
with commencing rigor, 6th day.
Incomplete paralysis Ist day; slightly exagger-
ated reflex movements 2d day; and death 3d
day.
Incomplete paralysis 1st day; exaggerated re-
flex movements 2d day; tetanus 3d and 4th
days ; stiff spasmodic movements 5th day;
and perfect recovery 7th day.
Complete paralysis 1st to 6th days; slightly ex-
aggerated reflex movements 7th day ; tetanus
8th and 9th days; stiff reflex movements 10th
and 11th days; complete paralysis 12th day ;
and, death, with commencing rigor, 13th day.
Complete paralysis 1st day; and death, with
rigor, 2d day.
Do. do.
Incomplete paralysis 1st day and earlier part of
2d; exaggerated reflex movement latter part
of 2d day ; tetanus 3d day ; stiff reflex move-
ments 4th day ; and death 5th day.
Complete paralysis 1st and 2d days; incom-
plete paralysis 3d day; tetanus 4th to 6th
days ; exaggerated reflex movements 7th day ;
and death 8th day.
Incomplete paralysis 1st day; exaggerated re-
flex movements 2d day; fetanus 3d to 10th
days ; stiff spasmodic movements 11th to 13th
days; and perfect recovery, 15th day.
Complete paralysis, lst and 2d days; and death,
with commencing rigor, 3d day.
Complete paralysis 1st day; and death, with
rigor, 2d day.
Complete paralysis 1st to 3d days; incomplete
paralysis 4th and 5th days; and death, with
commencing rigor, 6th day.
Complete paralysis lst day; and death, with
commencing rigor, 2d day.
Do. do.
VOL. XXYV. PART II.
6D
466 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
Some experiments were made with acetate of atropia also. I have not con-
sidered it necessary to describe these in detail, or to include them in the above
Table, as the symptoms were the same as those observed with corresponding
doses of the sulphate.
It appeared of interest to examine if analogous symptoms were produced
in other cold-blooded animals, and, with this view, a number of experiments were
made with 77zton cristatus—a species of water-newt, which abounds in many of
the lochs in the neighbourhood of Edinburgh.
It was found that sulphate of atropia produces in this animal the same
general paralytic and convulsant effects as in the frog. After the subcutaneous
administration of doses that were somewhat smaller than the minimum fatal, a
condition of partial but marked paralysis was, in the first place, produced; and
this was succeeded, in less than twenty-four hours, by a condition of slight impair-
ment of the power of voluntary movement with decided increase of refiex
excitability, which condition persisted, in many of the experiments, for more than
fourteen days. The reflex excitability manifested itself by sudden starts, when
the skin was gently touched; and by tetanic spasm, lasting for from fifteen to
forty seconds, when the irritation was more prolonged and powerful, as when
produced by a series of taps with the handle of a scalpel. The appearance of this
tetanus was somewhat peculiar, and its characters varied considerably. Fre-
quently, the trunk of the body was curved laterally, with the tail curled in three
or four coils, and the head twisted round to such an extent that the snout was in
contact with the outside coil of the tail; at other times, the body was curved in
an opisthotonic spasm, with the tail elevated either in a straight oblique line or
in coils, and with the head raised; while, not unfrequently, the trunk of the
body was irregularly contorted, with the head and tail in one or other of the
above positions.
SECTION B.
The experiments that have been made are sufficiently numerous to show what
dose is required to produce these extraordinary convulsive phenomena. Tetanus,
or, at least, a state of greatly exaggerated reflex excitability, may be looked for
with great confidence, when a dose of the sulphate or acetate of atropia, equiva-
lent to about the ;,4,5th of the weight of the frog, is administered by injection,
either under the skin or into the abdominal cavity. If the latter region be
selected, it is necessary to puncture the abdominal parietes at a point as far
removed from the heart as possible, in order to prevent a powerful local action
on that organ; at the same time, taking care to avoid injuring the lungs. It
is also important to dissolve the atropia-salt in only a few minims of water—from
four to eight is quite a sufficient quantity. Not only is the danger of affecting
the heart by local contact thereby diminished when the exhibition is by the
-
: 4
Pp
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 467
abdominal cavity, but the small bulk of such a solution is also an advantage
when atropia is exhibited by injection under the skin. In the latter case, the
energetic movements that nearly invariably occur when the frog is set free, are
very apt to press some of the solution out of the subcutaneous tissue; and
even with this precaution I have found it difficult to prevent all loss.
It appears from the experiments contained in Table I. that tetanus is also
pretty constantly produced by doses somewhat greater or less than the z,)yoth
of the weight of the frog; indeed, by the majority of the doses included between
the -4,th and the ;,);jth. The larger doses usually produce the most violent
tetanic symptoms, and they may be given with considerable confidence to very
small animals, and to such as have been kept in a laboratory for several months.
The smaller doses seem best adapted for large frogs, and for such as have been
recently obtained from their natural habitats. If a dose be employed smaller
than those above indicated, impairment of the functions of the cerebro-spinal
nervous system and of the heart may be caused, but general tetanus will seldom
follow, although spasms, generally restricted to certain regions, may occasionally
appear. The tetanic state resulting from the largest doses usually terminates in
death, that from the smallest in recovery.
In the above Table, the smallest dose of sulphate of atropia that produced
tetanus is equivalent to the ;,,th of the weight of a frog of 298 grains (Experi-
ment v.), the largest to the -4;th of the weight of a frog of 147 grains (Experi-
ment xxxviil.)
Without attaching undue weight to an experience which is insufficient to
justify generalisation on such a subject, it may be mentioned that tetanic symp-
toms were usually produced most readily, and continued for longest periods,
in the experiments that were made in winter, when the temperature of the
laboratory was low.
SECTION C.
It is by no means an easy matter to ascertain what structures are concerned
in the production of the convulsant effects of atropia, for the protracted intervals
that often elapse between the administration of the poison and the appearance of
tetanus, and the difference in the duration and severity of the tetanic symptoms
that follow even the most carefully calculated doses, render the inquiry an unusually
difficult one, and frequently necessitate a patient repetition of the experiments.
It is obvious, at the outset, that experimental investigation is required. It cannot
be maintained that these remarkable convulsant and tetanic effects are merely
secondary results of certain degrees of the primary paralysing action of atropia
on the cerebro-spinal system and on the heart. Against such a supposition it
were easy to bring a mass of opposing evidence, derived from the physiological
effects of other active substances. It is well known that after the administration
468 DR T. R. FRASER ON SOME UNDECSRIBED TETANIC SYMPTOMS
of curara (wourali) frogs may remain for lengthened periods in a state of absolute
motor paralysis, with the cardiac action greatly impaired, and nevertheless per-
fectly recover without the occurrence of the slightest degree of abnormal activity
of the reflex function. Professor VuLPIAN has recently shown that iodide of phos-
phethylamine may likewise produce in frogs complete temporary paralysis, yet
this is not succeeded by any spasmodic symptoms.* In many experiments, also,
which I have made with physostigma—one of which is described in a paper com-
municated to this Society|—complete motor paralysis and great diminution of the
cardiac action were produced, yet the animal gradually recovered therefrom, with-
out any symptom of exaggeration in the reflex activity having been observed.
Similar evidence may be accumulated from many other sources; but it is sufficient
to mention an interesting experiment by VuLPian, which has a direct bearing on
the question. That eminent physiologist ligatured the aorta at its origin from
the heart ofa frog, so as completely to stop the arterial circulation. In the course
of a few hours, the excitability of the spinal cord was suspended, and, soon after,
the conductivity of the motor nerves was considerably impaired. The frog pre-
sented all the phenomena of death ; for although the heart still continued to con-
tract, it was unable to propel any blood. The ligature was then removed, and the
circulation became re-established. By-and-by, respiratory movements reappeared;
in one or two hours, reflex contractions could be readily excited, while voluntary
movements were freely executed; and, soon after, the animal regained all its
suspended functions. Yet, although the recovery was established by gradual stages,
no symptoms of exaggerated activity of the reflex function were observed. |
It is unnecessary to discuss this hypothesis further, especially as sufficient
evidence will be adduced, in this and the following Section, to demonstrate that the
convulsant effects of atropia are caused by a direct action on the nervous system.
In the attempt to differentiate the structures on whose affection these effects
depend, I have considered the possibilities of their being dependent on the muscles,
on the efferent (motor) nerves, on the afferent (sensory) nerves, on the spinal cord,
or on the encephalon.
In the first series of experiments, the atropia was prevented from reaching
certain limited regions of the body, while it had access to all other regions.
Experiment XLIV.—The blood-vessels were ligatured at the upper third of
the right thigh of an active male frog, weighing 272 grains; and immediately
afterwards a solution containing one-fourth of a grain of sulphate of atropia,
in four minims of distilled water, was injected under the skin of the left flank.
In the course of two hours voluntary movements had ceased, and a state of
motionless flaccidity was produced.
* Archives de Physiologie Normale et Pathologique, 1868, p. 472.
+ Transactions of the Royal Society of Edinburgh, vol. xxiv. part iii. p. 743.
{ Legons sur la Physiologie Générale et Comparée du Systéme Nerveux. Paris, 1866, p. 457.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 469
On the following day—twenty-two hours after the administration—this state
of flaccidity was present everywhere, except in the right (non-poisoned) leg, which
was extended somewhat stiffly. The skin of this leg, below its upper third, was
also paler than that of any other part of the body, and, occasionally, spasmodic
contractions occurred spontaneously in the right foot, the rest of the body remain-
ing motionless. When the skin of any region—poisoned or non-poisoned—was
touched, a sudden and violent tetanic convulsion occurred in the right (non-
poisoned) leg, continuing in it sometimes for four seconds, and at others for from
six to eight seconds; while at the same time merely feeble twitches occurred in
the left leg and in the two anterior extremities. After several such attacks had
been excited in rapid succession, a repetition of the excitation still caused well-
marked tetanus of the right leg, but it did not cause any movement whatever
in the poisoned regions. The heart was now contracting only twelve times in the
minute, and the respirations were very infrequent.
On the third day—fifty hours after the administration—the anterior extre-
mities had become flexed, so as slightly to raise the head; there was some
improvement in the character of the respiratory movements; and tetanic con-
vulsions, which frequently lasted for ten seconds, could be excited in the right
(non-poisoned) leg, while merely clonic spasms appeared in the other extremities.
On the fourth day—seventy-two hours after the administration—a slight
irritation of the skin was followed by a general tetanic convulsion, during which,
however, the right (non-poisoned) leg was very slightly affected. A weak inter-
rupted galvanic current applied to the right sciatic nerve, below the ligatures,
excited only some faint movements in that limb, while it excited a violent attack
of tetanus in the rest of the body (poisoned regions).
For several days afterwards, tetanic convulsions could still be excited; but
now the right posterior extremity took no part whatever in these—the stoppage
of the circulation having obviously destroyed the vitality of its structures.
Experiment XLV.—Immediately after ligaturing the right sciatic artery and
veins of a frog, weighing 322 grains, I injected a solution of three-tenths of a grain
of sulphate of atropia, in four minims of distilled water, under the skin of the
left flank.
On the second day—at forty-five hours after the administration—faint reflex
movements could everywhere be excited by gentle stimulation of the skin; but
these movements were most marked in the right (non-poisoned) posterior extremity.
On the third day—at forty-five hours after the administration—the reflex
movements rarely occurred anywhere but in the right posterior extremity. On
the same day, at fifty-one hours, the right (non-poisoned) posterior extremity
became extended in violent tetanus when stimulation was applied to any portion
of the skin, while everywhere else only feeble reflex movements occurred.
On the fourth day—seventy-three hours after the administration—stimulation
VOL. XXV. PART IL. 6E
470 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
excited severe and prolonged general tetanus, which affected both posterior extre-
mities equally. ;
On the fifth day, the right posterior extremity was continuously rigid; but
for other three days tetanic convulsions could be excited, in which the whole of
the body except the right (non-poisoned) posterior extremity was involved.
Experiment XLVI.—The right sciatic artery and veins were ligatured in a
frog, weighing 315 grains, and immediately afterwards three-tenths of a grain of |
sulphate of atropia, dissolved in four minims of distilled water, was injected under ;
the skin of the left flank. :
On the third day, rigid incurvation of the anterior extremities, and stiff exten-
sion of the right posterior extremity, had occurred. A faint touch of the skin of
any region caused a violent attack of tetanus; in which the right (non-poisoned)
posterior extremity was rigidly extended with the web stretched, for five seconds,
while the left was almost unaffected, merely becoming momentarily extended at
the commencement of the attack.
On the fourth day, some rigor had appeared in the right posterior extremity ;
but general tetanus could be excited in all the other regions of the body.
Haperiment XLVII.—I tied the left sciatic artery and veins of a frog, weighing
211 grains, and then injected a solution of one-fifth of a grain of sulphate of
atropia, in six minims of distilled water, under the skin of the right flank.
On the second day—twenty-two hours after the administration—general
tetanic convulsions could readily be excited by touching the skin in any region;
and both posterior extremities—poisoned as well as non-poisoned—were equally
involved in the convulsions.
On the third’ day —forty-seven hours after the administration—the left (non-
poisoned) posterior extremity was somewhat rigid, and took no part in the
convulsions.
In the next experiment both the posterior extremities were protected from the
direct influence of the sulphate of atropia.
Experiment XLVIII.—By excising the sacrum, I exposed the sacral nerves
and blood-vessels within the abdomen of a male frog, weighing 210 grains, and
then by passing a strong thread below these nerves, I firmly ligatured the
abdomen, including all its blood-vessels, but excluding the sacral nerves. After
this operative procedure, the frog retained an apparently normal control over the
movements of the posterior extremities. Three minutes afterwards, I injected
eleven-hundredths of a grain of sulphate of atropia, dissolved in four minims of
distilled water, under the skin at the left side of the thorax.
On the following day—at twenty-one hours after the administration—the
frog was lying on the abdomen, with the anterior extremities flexed inwards and
supporting the head and chest, and with the posterior extremities normally flexed.
A slight touch of any portion of the skin was followed by ordinary reflex move-
eee ee ee ee ee ere
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 471
ments of all the extremities; but a somewhat severe excitation of the head, as by
a smart tap, was followed by pretty strong spasm of the anterior extremities, and
of the chest muscles, and by violent tetanus of the two posterior extremities, the
latter lasting for four seconds.
On the same day—at twenty-five hours after the administration—stimulation
caused increase of the tonic spasm of the muscles anterior to the ligature, and,
simultaneously, sudden and rigid contraction of the muscles posterior to it—in
fact, a general tetanic convulsion—the latter lasting for seven seconds. These
convulsions could readily be excited by moderate stimulation of the skin of any
region—below the ligature (non-poisoned regions) as well as above it.
On the third day—at forty-four hours after the administration—it was impos-
- sible to excite tetanic spasm in the non-poisoned regions. At forty-six hours, the
posterior extremities were slightly rigid, and soon afterwards stimulation of the
sacral nerves did not produce in them any movement whatever; but violent
spasm could still be excited in the anterior extremities, and in the other poisoned
regions. *
The evidence contained in these experiments is sufficient to exclude the
muscles and the afferent and the efferent nerves from being held to be directly
concerned in the production of the spasmodic and convulsive symptoms of atropia.
In each experiment, certain regions of considerable extent were protected from the
direct influence of the poison, and yet freely participated in the spasmodic and
tetanic effects, thereby proving that these effects were not caused by a direct action
of atropia on either muscles or efferent nerves. The evidence that excludes the
afferent nerves is quite as satisfactory ; for in each experiment an excitation of
the skin of the non-poisoned region readily produced spasms and general tetanus,
thereby proving that a direct action on the afferent nerves is not required for the
production of these symptoms.
We are now obliged to look for the cause of these effects to a direct action of
atropia on the central nerve-organs. The predominance of cerebral symptoms
during atropia-poisoning in animals of a higher development, suggested the
possibility of the tetanic symptoms being caused in frogs by an influence origi-
nating in the cerebral lobes, or, more probably, in the ganglia at the summit of
the medulla. Accordingly, on several occasions, the spinal cord of a frog in the
stage of tetanus was divided immediately below the brachial enlargement, with
results such as are described in the following experiment.
Eaperiment XLIX.—A solution of fifteen-hundredths of a grain of sulphate
of atropia, in four minims of distilled water, was injected under the skin at the
left flank of a frog, weighing 152 grains. The stage of paralysis continued until
* The experiments in this series were all performed in winter, when the low temperature of the
laboratory was favourable to a long-continued retention of nerve-irritability in parts cut off from the
circulation.
472 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
the end of the third day ; and on the fourth day the frog had entered the tetanic
stage—a slight touch of the skin being followed by opisthotonic tetanus lasting
for four seconds.
On the sixth day, at 1.50 p.m.,a touch of the left ankle caused a violent
attack of emprosthotonic tetanus, during which both posterior extremities were
rigidly extended for three seconds. At 1.51, a touch of the right ankle caused a
similar tetanic convulsion, which lasted in both posterior extemities for three
seconds.
On the same day (sixth), at 2.10 p.w., the spinal cord was divided imme-
diately below the brachial enlargement; and, it is important to note, extremely
little blood was lost by this operation (about a drop only). At 2.21 p.m, a touch
of the right ankle caused rigid tetanic extension of both posterior extremities for
two seconds.. At 2.22, a touch of the left ankle caused similar extension for
three seconds. The anterior portion of the body took no part whatever in these
convulsions; but when the skin at the head or anywhere anterior to the section
of the cord was touched, the regions supplied by the anterior segment of the
divided cord were at once thrown into a state of tetanus. These latter attacks
lasted for about four seconds; and during them the regions supplied by the
posterior segment of the divided cord were unaffected.
On the seventh day, a touch of either ankle caused violent tetanus of both
posterior extremities and of the muscles at the lower part of the flanks, lasting
for five seconds; and immediately after the tetanic contraction had ceased, a
series of clonic spasms occurred in these regions for other fifteen seconds. A
touch of the skin anterior to the position of the section of the cord was followed
by violent tetanus of the anterior portion of the frog, lasting for about eight
seconds.
This condition of independently excitable tetanus of the anterior and posterior
secments continued, with but little change in the character of the excited attacks,
until the nineteenth day of the experiment. There were, however, in this pro-
longed period, some differences in the duration of the tetanic convulsions:
for, on the eighth day, after slight stimulation, the posterior extremities were
rigidly extended for six seconds, and were then affected with clonic spasms for
seventy seconds; on the eleventh day, the rigid extension lasted for four
seconds, and the succeeding clonic spasms for twelve; on the fourteenth day,
the rigid extension lasted for four seconds, and the clonic spasms for only two;
and on the eighteenth day, the rigid extension lasted for four seconds, but in
place of a series of clonic spasms, it was succeeded by merely two or three faint
twitches.
On the nineteenth day, tetanus of the posterior extremities was caused only —
when the stimulation was severe; and there was now no evidence of increased
reflex excitability in the anterior part of the frog.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 473
The observations were now stopped.
In performing this experiment, care must be taken to avoid injuring important
blood-vessels, as any considerable loss of blood would completely vitiate the
results. This is at once apparent, if we compare the experiments contained in
Table IJ. with those in Table III.
TABLE Il—Summary or EXPERIMENTS IN WHICH THE SPINAL CORD WAS DIVIDED DURING
ATROPIA-TETANUS, without any material loss of blood.
Tn Grains. Relation i
oe ; of Pees Effects before the Division oe Effects after the Division
Experiment. vy oe Dose. ite of the Cord. IDenetloyi. of the Cord.
XLIX. | 152 | 0:15 | ,3,,; | Incomplete paralysis 1st | 6th day. | Tetanus in both seg-
to 3d days; tetanus 4th ments 6th to 17th days,
to 6th days, and in posterior segment
alone 17th to 19th days.
L. 294 | 0:3 siz | Incomplete paralysis 1st | 4th day. | Tetanus in both seg-
and 2d days; tetanus 3d ments 4th to 7th days.
and 4th days. Frog was killed on 7th
day.
LI. 358 | 0-4 giz | Complete paralysis 1st | 5th day.| Tetanus in ~ both seg-
and 2d days; incom- ments 5th and 6th days.
plete paralysis 3d day; Frog was killed on 6th
tetanus 4th and dth day.
days.
TABLE ITI.—Summary or EXprrIMENTS IN WHICH THE SPINAL CORD WAS DIVIDED DURING
ATROPIA-TETANUS, with considerable loss of blood.
In Grains. Relation :
paber Wei se we Effects before the Division ne Effects after the Division of
Bxperimont.| of a Dose. | Weight of the Cord. Wii aa the Cord, and oss Lof Blood.
Ps of Frog
LIl. 272 | 0-25 | ,A,, | Incomplete paralysis 1st | 7th day. | Tetanus ceased in 15
to 3d days; tetanus 4th minutes, and rigor mor-
to 7th days. tis was present on 8th
day.
LITT. 288 | 0:3 zéy | Complete paralysis 1st | 5th day. eae of posterior seg-
and 2d days; incomplete ment ceased in 10 min.,
paralysis 3d day; teta- but tonic spasm con-
nus 4th and dth days. tinued in the anterior
segment for 24 hours
longer.
LIV. 310 | 0:35 | gt, | Incomplete paralysis 1st | 6th day.| Tetanus ceased in both
to 4th days; tetanus segments in 5 minutes.”
4th to 6th days.
_ * In this experiment a large quantity of blood was rapidly lost, as the apex of the heart.was
excised immediately after the cord had been divided,
VOL. XXY. PART II.
OF
474 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
I performed the following experiment to ascertain how far the mere division
of the cord affects reflex excitability.
Experiment LV.—In a healthy male frog the reflex excitability was tested in
various ways, and found to be normal. The spinal cord was then divided imme-
diately below the brachial enlargement, with the loss of only one or two drops of
blood. Except that some general quivering occurred at the time of the division,
and for a few minutes afterwards, the frog remained quietly in a normal posture,
and showed no symptoms of exaggerated reflex activity until the second day.
On the second day—at twenty-one hours after the division of the cord—
slight stimulation of an ankle was followed by a series of feeble twitches of
various muscles in both legs, lasting for three seconds. These twitches were
so slight that they caused no movements of either posterior extremity, and during
their occurrence both posterior extremities remained normally flexed. Similar
series of twitches were produced other three times by stimulating each ankle
alternately at intervals of a minute; but when the same stimulation was repeated
for the fifth time, no effect whatever followed.
On the third day, the posture of the frog was still perfectly normal; but stimu-
lation of an ankle excited merely a feeble twitch in both posterior extremities.
On the fourth and fifth days, stimulation of a more energetic character was
required to excite similar feeble twitches in the posterior extremities; but such _
series of twitches as appeared on the second day could not be caused by even
powerful excitation.
The experiment was now terminated.
It is therefore apparent that, in Experiments XLIX., L., and LI., the tetanic
symptoms that were present in the posterior extremities after division of the
spinal cord were not caused by the division. 3
We have thus obtained most satisfactory evidence in favour of the con-
clusion that these convulsive symptoms are due to a direct action of atropia on
the spinal cord.
Moreover, the results of some further experiments made to test this conclusion
are entirely confirmatory thereof. Two of these may be briefly described.
Experiment LV1.—Immediately after dividing the left sciatic nerve in the
thigh of a frog, weighing 360 grains, I injected a solution of seven-twentieths of
a grain of sulphate of atropia, in four minims of distilled water, under the skin
of the right flank.
On the third day, the frog was lying on the abdomen, with the anterior
extremities rigidly arched, with the right posterior extremity stiffly extended,
and with the left posterior extremity flexed and somewhat flaccid. A touch
anywhere, except in the left posterior extremity below the middle of the thigh,
excited a violent tetanic convulsion, in which the left leg took no part. Galvanic —
stimulation, when applied to the cut end of the distal portion of the left sciatic —
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 475
nerve, caused normal contractions of the left leg ; but when applied to the cut end
of its central portion, excited a violent tetanic paroxysm in which the left leg
took no part.
Experiment LVII. differed from Experiment LVI. mainly in the nerve divi-
sion having been postponed until the tetanic stage was entered into. Before
the right sciatic nerve was divided, excitation caused a violent attack of tetanus.
during which the right posterior extremity was rigidly extended for eight
seconds. After the right sciatic nerve was divided, the right leg took no part in
the tetanic convulsions. Galvanic stimulation also of the cut end of the distal
portion of the nerve caused merely normal movements of the right leg.
The symptoms of increased reflex excitability that occur so prominently in frogs
after the exhibition of certain pretty well-defined doses of atropia, are therefore
caused by a direct action of this poison on the spinal cord.
Having reached this stage in the investigation, we are naturally tempted to
proceed a step farther, and to inquire what is the nature of the action on the
spinal cord, by which atropia produces convulsive and tetanic symptoms’? At
first sight, the solution of this question might appear to be an easy one. Inves-
tigation has shown that atropia is a powerful agent in influencing the condition
of at least certain portions of the vascular system, although there is a difference
of opinion among investigators as to the nature of the influence. The probabi-
lities are, however, in favour of the view of Mruriot, that when large doses are
given, atropia first diminishes the calibre, and increases the vermicular contrac-
tion, of the blood-vessels; and, subsequently, increases their calibre by para-
lysing the contractile walls.* It may be supposed that the latter effect—
dilatation of blood-vessels—is the cause of the tetanic symptoms; for such
dilatation might operate either by permitting the augmented blood-supply that
many suppose to be essential for abnormal activity, or by causing irritation of the
cord directly, by congestion, or even rupture of its blood-vessels.+
The plausibility of this view is strengthened by the opinion of so eminent a
physiologist as Brown-S£quarp, who maintains that vascular dilatation is one
of the primary causes of the tetanic effects of strychnia;{ and by the post
mortem appearances of engorgement of the vessels of the spinal cord, after poison-
ing by atropia, which several observers have drawn attention to in mammals,§
and which I have frequently observed in frogs also.
There are, however, several grave objections to the adoption of a theory of the
* De la Méthode Physiologique en Thérapeutique et de ses applications a ]’étude de la Belladone.
Paris, 1868, p. 51, &e.
t Mevriot, op. cit. p. 98.
{ Lectures on the Diagnosis and Treatment of the Principal Forms of Paralysis of the Lower
Extremities. Philadelphia, 1861, pp. 51 and 112.
§ RosenBEerGeR, quoted by Tarpiev, op. cit. p.'752; Scurorr, Lehrbuch der Pharmacologie.
Wien, 1868, p. 508.
476 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
vascular causation of atropia-tetanus, founded on the above arguments. It is true
that the demonstration appears to be perfect of great dilatation of the blood-vessels
of the skin, muscles, abdominal and thoracic viscera, and several other structures
occurring at an advanced stage of atropia poisoning—probably, indeed, this
dilatation is contemporaneous with the tetanus—but we have yet to wait for the
demonstration of a dilatation of the blood-vessels of the spinal cord during the
life of the animal. It is even difficult to believe that the analogous tetanic
symptoms of strychnia are due to vascular engorgement, for a frog may be bled as
perfectly as possible, and still the subsequent direct application of strychnia to
the spinal cord will cause tetanus.* Farther, the discovery of vascular engorge-
ment after death from tetanus is insufficient to prove that the production of the
tetanus is in any way dependent on that engorgement. It might be urged, with
equal reason, that the tetanus is the cause of the spinal engorgement, the
mechanical effect of the muscular contractions tending to force the blood into
those regions where this effect cannot operate. Besides, there are no good grounds
for assuming that an engorged state of the vessels of the cord will necessarily
increase reflex excitability or originate tetanic convulsions.
It is obvious that this question can be solved by direct proof only. An
apparent approach to such a solution might appear to be contained in the results
of the Experiments in Table III. Tetanus and convulsions rapidly disappeared
after copious bleeding. If, however, the blood be freely and abundantly
abstracted from a frog in a normal condition, the reflex excitability will be quickly
impaired, and, very soon afterwards, it will altogether disappear.
While, however, we cannot at present accept the view that the tetanic effects
of atropia are produced by dilatation of the blood-vessels of the spinal cord,
such a method of production is not disproved by any known fact. The question
of the exact nature of the causation of atropia-tetanus—in common with similar
questions in relation, probably, to every active substance—is, therefore, still open
for future research. Meanwhile, by restricting actions to certain organs and struc-_
tures, we gain an essential advance towards the solution of such problems.
SECTION D.
In this section an attempt will be made to show that the convulsive and
tetanic symptoms that have been described in frogs are represented among the
symptoms of atropia-poisoning in rabbits, dogs, and other mammals; and that, in
both cases, the causation and special characters of these symptoms, as well as
the peculiarities of their occurrence, are the results of exactly the same actions.
* MM. Martin-Macron et Buisson, “ Action Comparée de l’Extrait de Noix Vomique et du
Carare,’” Journal de la Physiologie de ’Homme et des Animaux, 1859, p. 487; Dr A. J. Spence,
“On the Mode of Action of Strychnia,” Edinburgh Medical Journal, July 1866, p. 50.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 477
There can be little doubt that, in many cases, the convulsions that appear
during poisoning by atropia in man, dogs, rabbits, and other mammals, are
due chiefly to asphyxia, caused by impairment of the functions of the cerebro-
spinal nervous system. These convulsions are, however, due also to a special
and primary stimulant action of atropia on the spinal cord. ‘The latter method
of production has been recognised by observers who were fully alive to the possi-
bility of such symptoms being produced by asphyxia alone.* Several experiments
in dogs have satisfied me—so far as evidence short of direct demonstration can
do so—that this is the case; for, after the administration of doses that were
about the minimum fatal, I have, on several occasions, observed a condition of
combined unconsciousness, partial paralysis, and exaggerated reflex activity con-
tinue for more than twenty-four hours, while, during a considerable portion of
this time, the respirations were of fair character.
The remarkable position that the convulsive symptoms occupy in frogs—
occurring subsequently to either a partial and short, or a complete and protracted
paralysis of the cerebro-spinal nervous system—at first sight appears to lend but
little support to the assertions that atropia has a primary spinal-stimulant action
in mammals, and that atropia-convulsions are caused by the same action in both
frogs and mammals. It is, however, necessary to remember, that in atropia the
amount of spinal-stimulant is in all animals less than the amount of paralysing
action, and that paralysis, compared with spinal-stimulation, is more rapidly pro-
duced by atropia in frogs than in mammals.
The first of these propositions—that the amount of spinal-stimulant is in
all animals less than the amount of paralysing action—is founded on the fact,
that the principal symptoms produced by an aggregate of various doses are those
of paralysis. Thus, in frogs, the smallest doses that affect motricity cause slight
paralysis without any obvious symptom of spinal-stimulation (Experiment IV.
Table 1.); somewhat larger doses cause more decided paralysis, with slight symp-
toms of spinal-stimulation (Experiments V. and VII. Table I.); still larger doses
cause complete paralysis, and violent symptoms of spinal-stimulation (Experi-
ments XV. XVI. XVIT. XVIII. XIX. XX. XXI., &c. Table I.); and doses so large
as to produce death rapidly, cause complete paralysis without any manifestation
of a spinal-stimulant action (Experiments XLII. XLIII., &c. Table I.) In
mammals, the symptoms are in like manner confirmatory of the proposition. We
may safely refer to almost every investigation in which different doses of atropia
have been administered to animals of the same species; but the following short
account of two experiments, which are described with minute detail in an inge-
* Mevrior, loc. cit. p.98,&c. Brown-Séauarp, “ Lectures on the Diagnosis and Treatment of
Functional Nervous Affections,” 1868, p.66. Both authors account for the increased excitability of
the spinal cord by dilatation of blood-vessels—a method of causation which, I believe, cannot be
established by any evidence that we at present possess.
VOL. XXV. PART II. 6 &
478 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
nious and elaborate paper by Dr LemMaTTRE, contains ample evidence in support
of the proposition. Both experiments were performed on dogs, and in both a
solution of sulphate of atropia was injected into a jugular vein. In the first
experiment, the dose was one decigramme (= 1°54 grain). In six minutes, para-
lytic symptoms occurred, which gradually became well-marked and severe; and
in two hours and forty minutes, “une convulsion réflexe”’ followed pinching of
the skin. This is the only synuptom of a spinal-stimulant action that is mentioned,
although the details of the experiment are described with great minuteness.
This dog recovered.* In the second experiment, the dose was five decigrammes
(=7°'7 grains). In about five minutes, paralytic symptoms were observed; and
in about one hour and ten minutes, some spasms occurred. The paralytic symp-
toms became very obvious soon after their first appearance, while the spinal-
stimulant reached more gradually such an intensity as to cause frequent tetanic
convulsions. This dog died six hours after the administration.+
The second proposition—that the paralysis, compared with the spinal-stimu-
lation, is produced in frogs more rapidly than it is in mammals—may likewise
be established by an appeal to observation. The experiments described in Table
I. show that in frogs complete paralysis (and, therefore, absolute suspension of
reflex activity) may be caused by doses of atropia considerably below the
minimum fatal. On the other hand, it is well known that in mammals even fatal
doses do not completely suspend reflex activity before death. Indeed, it is not to
be expected that they should do so, for an amount of paralysis considerably short
of complete suspension of reflex activity would undoubtedly cause such an embar-
rassment of respiration as to produce death by asphyxia.{ Hence, it is neces-
sary to employ artificial respiration, in order to produce complete paralysis of
motor nerves with even so powerful a paralysing agent as curara (wourali).§
It has been amply demonstrated in Section C. that large doses of atropia com-
pletely suspend the conductivity of motor nerves.|| This one method, among seve-
* “Recherches Expérimentales et Cliniques sur les Alcaloides de la famille des Solanées.”
Archives Générales de Médicine, 1865, vol. ii. p. 175.
+ Op. cit. p. 177. I have in my possession notes of many experiments supporting this
proposition, but have preferred to quote evidence obtained from an investigation in which this marked
difference between the effects of different doses is not specially alluded to.
t That this difficulty in causing complete paralysis does not occur with frogs, is due to their
endowment with the function of cutaneous respiration. In this animal, reflex activity may be so
far impaired by the action of a poison, that pulmonary respiration is rendered impossible, and yet
asphyxia may not take place to such an extent as to bring the circulation to a stand-still, and the
poison may thus be allowed sufficient time to produce on the living nerve-structures its complete
physiological effects.
§ Vutrran, op. cit. p. 196.
|| This action has already been demonstrated by Botkin, Vircnow’s Archiv, Bd. 24, 1862,
p. 84; by Vow Bzzozp and Brorsaum, Untersuchungen aus dem Physiologischen Laboratorium in
Wiirzburg, 1*s Heft, 1867, p. 13; and by Mzurior, op. cit. p. 90. The last author attempted to
prove that it is the result of a local action on the nerves by imbibition, and not of poisoning through
the blood; but his arguments seem insufficient to establish this view. I hope to refer more fully to
this objection on some future opportunity.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. A79
ral, by which it produces paralysis, is, therefore, sufficient to account for the greater
readiness with which complete paralysis is produced in frogs than in mammals.
It is thus seen why atropia produces paralysis so much more rapidly and
completely in frogs than in mammals, and also why in both frogs and mammals
spinal-stimulant effects are obviously manifested only when atropia is adminis-
tered in doses that are near the minimum fatal—that is, in doses containing the
largest amount of spinal-stimulant action consistent with the production of a
prolonged duration of symptoms.
When a dose of atropia near the minimum fatal is given to a frog, paralysis
is caused with such rapidity and completeness, that the spinal-stimulant action
is at first prevented from exhibiting itself; but when a similar dose is given
to a mammal, paralysis is caused so slowly and incompletely that a sufficient
amount of reflex activity remains to allow the spinal-stimulation to manifest
itself by exaggerated reflex movements and convulsive spasms. In the frog, the
spinal-stimulation is, in the first stage, concealed by the impossibility of its effects
being manifested, and the first symptoms are, therefore, those of paralysis; but,
as this paralysis is being recovered from, the spinal-stimulation becomes appa-
rent. In the mammal, the spinal-stimulation is merely impaired by the partial
paralysis; and during the whole course of the poisoning, the symptoms are,
therefore, those of a paralysing combined with a spinal-stimulant action, the
former merely lessening the violence, without concealing the effects of the latter.
This combined action, and the variety produced by it on the symptoms
in frogs and mammals, may be graphically illustrated by two curves, one of
which represents the paralysing, and the other the spinal-stimulant action.
The forms of these curves are to a great extent arbitrary, and they must of
necessity be so until we possess some exact method of estimating degrees of
action, and thereby obtaining ordinates that may have some pretension to
accuracy. Thus, in the curve op,p, &c., of Diagram 1, the motor nerve paralysis
is complete, so far as our methods of examination can show, at pc; but between
pe and p, there is aconsiderable interval, during which the degree of action may
or may not have been constant. What is termed complete paralysis does not
represent the maximum of action, for we know that the paralysis may go on
to permanent suspension of motility, or death, as well as return to normal
activity. As, therefore, the ordinates are but roughly determined, these curves
are in no sense accurate delineations of the paralytic and spinal-stimulant
actions. They may, however, serve the useful purpose of exhibiting clearly the
relations between the effects of these two actions. For the sake of simplicity, the
best marked paralytic action of large doses of atropia—that on the motor nerves
—will alone be considered.
Diagram | is a delineation, on this plan, of Experiment XVI. of Table I. In
480 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
this experiment, seven-twentieths of a grain of sulphate of atropia, administered
to a frog, weighing 372 grains, produced complete paralysis of the motor nerves
on the first and second days; tetanus on the third (slight), fourth, fifth, and sixth
days; and stiff spasmodic movements on the seventh and eighth days. Complete
recovery had taken place on the tenth day.
Diagram 1.*
In the diagram, the curve of paralysis, op,p,p,, &c., rises abruptly from the
line of normality, AB. The symptoms are those of paralysis only, until the curve
of spinal-stimulation, os,s,s,, &c., cuts that of paralysis between ¢, and ¢,, after
the descent of the latter from the line of complete paralysis, CD. Tetanus
then becomes the predominant symptom. At first, its violence is considerably
checked by the coexisting paralysis; but as the ordinates of the paralytic curve
diminish in length, while those of the tetanic curve increase, the tetanic symp-
toms gradually acquire greater prominence and force, until they reach their
maximum intensity between 7, and ¢,. They then, in their turn, also diminish.
This diagram further shows how a paralytic and a spinal-stimulant (tetanic)
action may be coexistent, while the effects of only one of these are apparent.
Between o and ¢,, the symptoms are those of paralysis alone, because the spinal-
stimulant action is altogether masked by the complete paralysis ; between 7, and
t,, tetanic symptoms appear, because the paralysis is incomplete, and reflex
movements are therefore permitted to occur; and between ¢, and ¢,, the spinal-
stimulant action, being but slightly checked by paralysis, manifests itself by
violent tetanic convulsions.
The effects of this combined action on a mammal are graphically repre-
sented in Diagram 2. The experiment (Experiment LVIII.) I have selected —
is one in which eight grains of sulphate of atropia in solution was injected
under the skin of a dog, weighing fifteen pounds. Slight paralysis was
observed at twenty minutes, and feeble spasms occurred at forty minutes; they
together reached their maximum intensities at about seventy minutes; and the
* AB, line of normality, each division of which, of,, t,t,, t,f,, &¢., represents a period of
twenty-four hours; CD, line of complete paralysis ; op,p,p,, &¢., curve of paralysis ; 05,5983, &¢.,
curve of spinal-stimulation (tetanus, &c.); ¢,p,, t,, &c., ordinates whose length roughly represents
the amount of the paralytic action ; ¢,s,, ¢,s,, &e., ordinates whose length roughly represents the
amount of spinal-stimulant action.
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 481
spasms ceased at one hundred minutes, while the paralysis continued until about
one hundred and twenty minutes. The dog recovered perfectly.
Diagram 2.*
In this diagram, the curve of paralysis, op,p,, &c., leaves the line of normality,
AB, before the curve of spinal-stimulation, the first symptoms being those of
paralysis. As the curve op,p,, &c., never attains the level of the line of com-
plete paralysis, CD, the paralytic action is never sufficiently great to prevent the
manifestation of the considerable spinal-stimulant action present. Although the
ordinates ¢,s,, ¢,s,, and ¢,s,, are considerably longer than the ordinates ¢,s, and
t,s,, the effects of spinal-stimulation are not proportionally greater at ¢,,¢,, and
t, than at ¢, and ¢,, for the ordinates of the paralytic curves also are longer at the
former than at the latter times, reaching their highest point at about the same
time as those of the spinal-stimulant curve, and the spinal-stimulant action is,
accordingly, more masked about the time of its greatest intensity than at times
somewhat anterior and subsequent thereto. These curves, therefore, admirably
represent the effects that were observed, the convulsive symptoms having been
of nearly uniform intensity throughout the whole time of their occurrence.
It has been taken for granted that the paralytic and spinal-stimulant actions
coexist in frogs after the administration of large doses of atropia. Some
evidence in support of this view may with propriety be given at this place.
Experiment LIX.—In a frog, weighing 270 grains, the abdominal aorta was
ligatured immediately above its bifurcation into the two iliacs, and one-fifth of
a grain of sulphate of atropia, dissolved in four minims of distilled water, was
then injected under the skin at the right side of the thorax. Great impairment
of motility and other symptoms of atropia action had occurred in one hour, when
the observations were interrupted.
On the following day—twenty-three hours after the administration—the frog
was lying on the abdomen, chest, and lower jaw, the anterior extremities being
perfectly flaccid, while the posterior were extended with the webs stretched. A
slight touch of the head caused a sudden attack of tetanus in the two pos-
terior extremities, which lasted for three seconds; but it was impossible to
* AB, line of normality, each division of which, ot,, t,t,, t)t,, &c., represents a period of ten
minutes ; CD, line of complete paralysis; op,p.p,, &c., curve of paralysis ; 0s,s,s,, &¢., curve of
spinal-stimulation (tetanus, &c.); #,9,, t,p,, &ec., ordinates whose length roughly represents the
amount of the paralytic action ; ¢,s,, t,s,, &e., ordinates whose length roughly represents the amount
of the spinal-stimulant action.
VOL. XXV. PART II. 6H
482 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
excite any movement whatever in the anterior extremities, or in any other
part of the poisoned region. At twenty-eight hours, the position of the frog
was the same as that last described, there being perfect fiaccidity and complete
motionlessness in the poisoned region, while the posterior extremities (non-
poisoned region) were rigidly extended. A touch of the skin anywhere now
excited violent tetanus of the posterior extremities, lasting for five seconds; but
no movement occurred elsewhere, and the anterior extremities were perfectly
flaccid. To test the condition of motor conductivity in the poisoned region, the
right brachial nerve was exposed, and subjected to galvanic stimulation; no
movement of the right anterior extremity was thereby produced, but tetanus of
the two posterior extremities invariably followed each stimulation.
On the third day, the frog was lying on the abdomen, but the chest and head
were now raised by the anterior extremities, which had become rigidly flexed.
On stimulating the skin, an attack of general opisthotonic tetanus occurred,
involving the poisoned as well as the non-poisoned regions.
In this experiment, the spinal-stimulant action would have been completely
masked by the paralytic, if the posterior extremities had not been protected from
the direct influence of the poison. Yet even when this is done, evidence of the
spinal-stimulant action will only exceptionally be obtained at so early a stage.
Atropia causes paralysis by an action not only on the motor nerves, but also on
the sensory (afferent) and on some portion of the reflex apparatus in the spinal
cord. In this experiment, two of these causes of paralysis (suspension of the
function of the sensory nerves, and suspension of that of some portion of the
reflex apparatus in the spinal cord) ceased before the third (suspension of the
function of motor nerves); for the conductivity of the poisoned motor nerves was
still completely suspended when the poisoned spinal cord and sensory nerves had
regained their functions. Usually the return to normality occurs much more
simultaneously in these different structures. It is still more difficult to obtain
evidence in frogs of a spinal-stimulant action occurring soon after the adminis-
tration of large fatal doses. Complete paralysis is so rapidly produced that no
opportunity is given to the spinal-stimulant action to manifest itself. The evi-
dence in support of an early stimulation of the cord is, however, readily obtained
in mammals; for the paralytic effects are never so great as to prevent the mani-
festation of the spinal-stimulant action.
The two already mentioned propositions—namely, that in atropia the amount
of paralysing is, in all mammals, greater than the amount of spinal-stimulant
action, and that atropia-paralysis is more readily produced in frogs than im
mammals—are also sufficient to explain why different effects are produced in
frogs and mammals by different doses of atropia.
When a large fatal dose of atropia is administered to a frog, the predominating
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 483
paralysis is so rapidly and completely produced that no spinal-stimulant symptom
can be exhibited. Death results either from an extreme degree of the paralytic
action, or, possibly, from some other effect of atropia. In neither case, however,
does the paralytic action diminish sufficiently (if it diminish at all) to permit any
effects of spinal-stimulation to appear, for death occurs during a high intensity
of the paralytic action. Diagram 3 represents an experiment (XLII. of Table L)
in which a large fatal dose of sulphate of atropia was administered to a frog.
The reflex activity was destroyed in a few minutes, and the conductivity of the
-motor nerves was completely suspended in one hour and forty minutes. Death
occurred during the complete paralysis.
Diagram 3.*
As the curve of paralysis, op,p,, &c., rises rapidly to the line of complete
paralysis, CD, and crossing, terminates above it (at the time of the occurrence of
death), while the curve of spinal-stimulation, os,s,, &c., rises with comparative
slowness, it is obvious that no spinal-stimulant effect can possibly be manifested.
In frogs, the only symptoms of a fatal dose of atropia are, accordingly, those of
paralysis, notwithstanding that such a dose exerts a large amount of spinal-stimu-
lant action, which is represented in the diagram by the curve 0s,s,s,,, &c.
In mammals, fatal doses of atropia invariably produce spasms and convulsions.
We at once see why this should be so, if we bear in mind that mammals are less
susceptible than frogs to a paralytic action. I have delineated in Diagram 4 the
symptoms that were observed in an experiment (Experiment LX.) in which a
solution, containing fifteen grains of sulphate of atropia, was injected under the
skin of a dog, weighing nine pounds. Partial, but distinct, paralysis was first
observed in eleven minutes, and spasms, with increased reflex excitability, in
sixteen minutes. They both gradually increased in severity—the paralytic action
causing inability to stand in twenty-two minutes, and the spinal-stimulant pro-
ducing the first of a series of frequently recurring tetanic convulsions in nineteen
minutes; and death took place one hour and eighteen minutes after the adminis-
tration.
* AB, line of normality, each division of which, of,, t,f,, tgt,,, &ic., represents a period of forty
minutes ; CD, line of complete paralysis; op,p,p,,, &c., curve of paralysis ; 0s,s,8,., &c., curve of
spinal-stimulation (tetanus, &c.)
484 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
In this diagram (Diagram 4), the curve of paralysis, op,p,p,, &c., does not at
any time rise to the level of the line of complete paralysis, CD; whereas in the
Diagram 4.*
diagram representing the effects of a fatal dose in a frog (Diagram 3), the curve
of paralysis very quickly reaches this line.+ Accordingly, in this experiment,
the spinal-stimulant action, which was considerable, was not prevented from
manifesting itself, and spasms and tetanus coexisted with paralysis up to the time
at which death occurred.
When a dose of atropia considerably below the minimum fatal, and just suffi-
ciently large to produce obvious effects on motility, is administered to a frog, the
effects are such as have been roughly delineated in the next diagram.
Diagram 5.f
In a mammal the effect of such a dose would be represented by a diagram,
in which the differences between the ordinates of the paralytic and spinal-
stimulant curves are less than in the above.
The symptoms being but slight in both cases, the ordinates of the curves are
very short; and as the amount of paralytic action in atropia is greater than the
amount of spinal-stimulant, the area enclosed by the curve op,ps, &c., and the
* AB, line of normality, each division of which, ot,, ¢,t,, tof,, &c., represents a period of ten
minutes ; CD, line of complete paralysis; op,pop3, &¢., curve of paralysis; os,s,8,, &c., curve of
spinal-stimulation (tetanus, &c.); ¢,,, t)P>, &e., ordinates whose length roughly represents the
amount of the paralytic action; f,s,, 1583, &c., ordinates whose length roughly represents the amount
of the spinal-stimulant action.
+ It is probable that a stage of tetanus occurring subsequently to a stage of paralysis has never
been observed in mammals, after the administration of atropia, because a sufficiently large dose can-
not be administered without causing death while the paralytic effects are being developed. It is,
however, possible that separate paralytic and tetanic stages might be produced in mammals, if
artificial respiration were employed after the administration of a very large dose.
+
hours; CD, line of complete paralysis; op,p.P19, &¢., curve of paralysis; s,5,5;,, &e., curve of
spinal-stimulation (tetanus, &c.); t,p,, tgp, wve., ordinates whose length roughly represents the
amount of the paralytic action; ¢,s,, t,S, &c., ordinates whose length roughly represents the amount
of the spinal-stimulant action.
+ AB, line of normality, each division of which, of,, t,t,, tgtj,, &¢., represents a period of four 4
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 485
abscissa o¢,, is greater than the area enclosed by the curve s,s,, &c., and the
abscissa ¢,t,,. The symptoms are, accordingly, those of paralysis; the spinal-
stimulant action being so slight that its effects are not perceived. With small
doses of atropia, spinal-stimulant effects are more likely to be observed in
mammals than in frogs. Ifthe minimum dose that produces paralytic effects be
determined, and then a series of doses gradually increasing from this be ad-
ministered, it will be found that in frogs a considerable increase may be effected
before any spinal-stimulant symptom is produced; but that in mammals an
extremely slight increase will cause spasmodic symptoms to make their appear-
ance. The explanation of this also is to be found in the propositions.
It has thus been shown that the tetanic symptoms produced by atropia in frogs
are represented, though in a somewhat diferent form, in animals of a higher
development. Atropia, therefore, forms no exception to the general Jaw that
poisons affect the same structures in the same way, in whatever animals these
structures occur.
It has also been shown that the differences in the symptoms that are produced by
different doses in animals of the same species may be explained by the paralysing
action of atropia being greater than the spinal-stimulant.
Paralysis, combined with spinal-stimulation, forms, therefore, the leading
characteristic of the action of large doses of atropia on the cerebro-spinal nervous
system, and unless this combination be taken into account, which it has not
hitherto been, the symptoms that are produced by such doses cannot be rationally
explained. In the antecedent portion of this paper, and especially in section C,
this combined action on the nervous system has been demonstrated by a process
of physiological analysis. I now propose to add to this some further proof,
derived from what may be termed a process of physiological synthesis.
So long as we are unable to separate from one another those elements or
groups of elements in atropia that produce its different effects—allowing that it
is legitimate to suppose that such elements or groups of elements exist—a strict
synthetical method cannot be applied to the investigation of its effects; but an
imperfect synthetical method may be applied, in which we imitate these effects by
combining various substances of clearly defined action. For this purpose I have
selected strychnia, as the best known and most typical of the spinal-stimulants,
and sulphate of methyl-strychnium, as one of the simplest and, for such pur-
poses, certainly one of the most convenient of the paralysers of motor nerves.*
It was found that a dose of strychnia, in the form of a salt, equivalent to
* This action of sulphate of methyl-strychnium has been demonstrated by Dr A. Crum Brown
and the author in a paper read before this Society, and published in the Transactions, vol. xxv.
part 1. pp. 151-203. I prefer this substance to curara, because of its strength being constant; and
on this ground I would recommend it to physiologists and physicians.
VOL. XXY. PART II. 61
486 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
about the z5g/55ath of the weight of the frog, was sufficient to produce in it violent
tetanic symptoms, which lasted for many hours, and terminated in recovery.
When such a dose is given to a male frog, or to a female whose abdomen is not
greatly enlarged by distended oviducts, it is of interest to note that the anterior
extremities become incurved at the commencement of the tetanic symptoms, and
continue so until these disappear; thus imitating a symptom produced by atropia
that has been fully describedin this paper (Section A.)
It was also found that doses of sulphate of methyl-strychnium, varying from
the so/goth to the z,dooth of the weight of the frog, were sufficient to produce
complete and prolonged paralysis of the motor nerves, without causing death.
Guided by these results, I then administered to frogs combined doses of
strychnia and sulphate of methyl-strychnium. After making several experi-
ments, I at length discovered that the remarkable combination of paralytic and
tetanic symptoms that has been described in Section A. of this paper could be
exactly imitated by administering to frogs a mixture of strychnia with sulphate
of methyl-strychnium in a certain proportion.
The following experiment is sufficient to confirm this statement :—
Experiment LXI.—One minim of a mixture of two minims of liquor strychnize
(B.P.) in eighteen minims of distilled water (equivalent to ~983 ths of a grain of
strychnia), was added to three minims of a solution of one-tenth of a grain of
sulphate of methyl-strychnium, in ten minims of distilled water (equivalent to
three-hundredths of a grain of sulphate of methyl-strychnium), and the four
minims of solution thus obtained was injected under the skin at the right flank
of a male frog, weighing 355 grains. In two minutes, some sprawling was
observed; in three minutes, the frog was unable to jump, and the respiratory
movements of the chest had ceased; in twelve minutes, only extremely feeble
and sluggish reflex movements could be excited by pinching the skin ; in fourteen
minutes, the lower jaw rested on the table, the respiratory movements of
the throat ceased, and the frog was perfectly flaccid; and in thirty-five
minutes, it was impossible to cause any reflex movement whatever even by
severe excitation of the skin. During all this time, there was not the faintest
strychnic symptom. The reflex activity was frequently tested. At the com-
mencement of the experiment, it was perfectly normal; and as the symptoms
advanced, the only change observed was a gradually increasing feebleness. At
forty minutes, it was found, by exposing a sciatic nerve, and subjecting it to
galvanic stimulation, that motor-nerve conductivity was completely suspended.
At this time, the cardiac impulse was good, and the heart’s contractions occurred
twenty-eight times in the minute.
On the second day—twenty hours after the administration—the frog was
lying on the abdomen with the thorax raised and supported by the anterior ex-
tremities, which were rigidly incurved, and there were infrequent respiratory
PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 487
movements. A slight touch of the skin caused a violent attack of emprostho-
tonic tetanus, which lasted for seven seconds, and was succeeded by a series of
clonic spasms in the posterior extremities and the abdominal muscles. During
the tetanus, the posterior extremities were stiffly extended, with their webs
stretched, while the anterior were rigidly incurved. Tetanic convulsions could
be excited at any time by repetitions of the excitation, and they sometimes
occurred spontaneously. In the intervals between them, the anterior extremi-
ties continued rigidly flexed.
During the third; fourth, and fifth days, the frog remained in this state,
except that, on the fifth day, the convulsions were less powerful and prolonged.
On the sixth, seventh, and eighth days, excitation caused merely sudden spas-
modic movements; but the anterior extremities were still rigidly flexed inwards.
On the ninth and tenth days, the frog was in a normal position; voluntary
movements were freely executed ; but there was still a slight increase in the
activity of the reflex function.
On the twelfth day, the symptoms had completely disappeared.
This experiment, therefore, proves that combined doses of strychnia and
sulphate of methyl-strychnium may produce symptoms that in every detail
imitate the most obvious of the effects of atropia on the cerebro-spinal nervous
system of frogs. By comparing the diagramatic representation of this experi-
ment with that of Experiment XVI. (p. 480), it will be seen how close are the
resemblances.
Diagram 6.*
It is therefore possible, by combining a paralysing with a convulsant sub-
stance, to produce in frogs paralytic and tetanic effects, which in their relative
and general characters are undistinguishable from the paralytic and tetanic effects
of atropia.
The next step was to administer these substances simultaneously to a
mammal.
It has been shown in a paper communicated to this Society by Dr A. Crum
* AB, line of normality, each division of which, ot,,t,t,,tots, &c., represents a period of
twenty-four hours ; CD, line of complete paralysis ; op,p,p,, &c., curve of paralysis ; 03,5), &c., curve
of spinal-stimulation ; ¢,p,,t,p,, &¢., ordinates whose length roughly represents the amount of the
paralytic action ; ¢,s,,,s,, &c., ordinates whose length roughly represents the amount of the spinal-
stimulant action.
488 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS
Brown and myself, that four-fifths of a grain of sulphate of methyl-strychnium
is about the minimum fatal dose for a full-grown rabbit* The amount of
strychnia that should be combined with this dose, in conformity with the ratio
of the last experiment, is about two-hundredths of a grain (or 2°66 minims of
liquor strychnie).
Experiment LXII.—2°66 minims of liquor strychnice (containing 0°02 grain of
strychnia) was mixed with a solution of four-fifths of a grain of sulphate of methyl-
strychnia, in twenty-five minims of distilled water, and this solution was injected
under the skin at the right flank of a rabbit, weighing three pounds and four
ounces. The first symptoms occurred in seven minutes, and consisted of a slight
degree of exaggeration in the starts that were caused by irritating the nostrils of
the animal. In nine minutes, a series of spontaneous spasms occurred in the ante-
rior extremities; and it was now obvious that the motor power of the posterior
extremities was slightly diminished. In nine minutes and thirty seconds, a
further series of spontaneous spasms occurred, but the spasms now involved the
whole body. In ten minutes, the rabbit lay down on the abdomen and chest;
and after remaining quietly in this position for a minute, it was again affected
with spasms, during which it fell over on the side. In twelve minutes and ten
seconds, there was an attack of opisthotonic tetanus, which lasted for only ten
seconds, and was immediately succeeded by a second attack, and, on its termina-
tion, by a third, both also of short continuance. The rabbit was still lying on
the side, and appeared unable to change its position. At frequent intervals, a
series of feeble spasms now succeeded each other; and at the termination of one
of these death occurred, fourteen minutes after the administration.
The symptoms of paralysis and of spinal-stimulation observed in this experi-
ment do not, in their relation to each other, exactly resemble those of atropia.
Indeed, it was not anticipated that they would do so; but it was anticipated
rather that the paralytic phenomena would be less marked, and that the spinal-
stimulant would, consequently, acquire a greater prominence than with atropia.
In the mixture of strychnia and sulphate of methyl-strychnium, the paralysis is
produced by an action on the motor nerves alone, which action affects frogs
much more rapidly and powerfully than mammals; whereas in atropia, it is
produced not only by an action on the motor nerves, but also by actions on the
sensory nerves, and, probably, on a portion of the spinal cord, and the additional
actions seem to affect frogs and mammals nearly equally. Therefore, while
frogs are more readily and completely paralysed than mammals by both atropia
and sulphate of methyl-strychnium, mammals are less readily paralysed by the
latter than by the former substance. Accordingly, the effects of the combination
of sulphate of methyl-strychnium and of strychnia more closely resemble those
of atropia in frogs than in mammals.
* Loc. cit. pp. 160 and 196.
PRODUCED BY ATROPIA IN COLD BLOODED-ANIMALS. 489
At the same time, the last experiment is in all respects a satisfactory one, for
it clearly demonstrates that such a combination of a paralysing with a spinal-
stimulant substance as produces in frogs paralysis followed by convulsions, will
produce in mammals paralysis coexisting with convulsions, and impeding their
manifestation. So that by a process of what may be termed physiological
synthesis, further evidence has been obtained in support of the conclusions, that
the effects of large doses of atropia on the cerebro-spinal nervous system (mental
phenomena excluded) are due to combined spinal-stimulant and paralysing actions
of that substance, and that the differences in the relations of these effects to each
other, which are seen in different species of animals, may be explained by this com-
bination acting on special varieties of organisation.
It is generally admitted that atropia produces both paralytic and convulsive
symptoms in mammals, but no satisfactory attempt has hitherto been made to
define the relations of these symptoms to each other. This investigation has
shown in what manner the paralysing is related to the convulsant action both in
mammals and in frogs; and it has also accounted for the differences in the mani-
festation of these actions after different doses of atropia. It may, without pre- -
sumption, be asserted, that it throws a new light on the causation of some of
the symptoms of atropia, and also of many other substances, whose action, like
that of atropia, produces a combination of paralytic and convulsive symptoms.
The principal results that have been obtained may be thus summarised :—
1. Atropia produces in frogs well-marked convulsive and tetanic symptoms,
which, when present in an extreme degree, form a separate stage in the poisoning,
succeeding that of paralysis.
2. Tetanic symptoms follow the subcutaneous administration of a dose of
sulphate of atropia, equivalent to the ;,oth of the weight of the frog, and of
doses a little greater or less than this.
3. These symptoms are due to a direct action of atropia on the medulla
(oblongata and spinalis).
4. The differences between the paralytic and convulsive synptoms that occur
in frogs and those that occur in mammals may be explained by the greater sus-
ceptibility of the former to the action of a paralysing agent, and by the amount
of paralysing being greater in atropia than the amount of convulsant action.
5. The different symptoms that are produced by different doses of atropia in
animals of the same species may be explained by its paralysing being greater
than its convulsant action.
6. The paralysing and convulsant actions of atropia can be imitated in both
frogs and mammals by a combination of a paralysing with a convulsant sub-
stance.
VOL. XXV. PART II. 6k
( 491 )
XIII.— Hegel and the Metaphysics of the Fluxional Calculus. By W. RoBertson
SmiTH, M.A., Assistant to the Professor of Natural Philosophy in the
University of Edinburgh. Communicated by Professor Tarr.
(Read 17th May 1869.)
It is now many years since Dr WHEwELL drew the attention of the Cambridge
Philosophical Society to the courageous, if somewhat Quixotic, attempts of HEGEL
to cast discredit on Newron’s law of gravitation, and on the mathematical
demonstrations of KEPLEr’s laws given in the “ Principia.” At the time when
WHEWELL wrote, it would probably have been difficult to find in Britain any one
ready to maintain the cause of HEGEL in this matter, or even to hint that the
astounding arguments of the Naturphilosophie flowed from any deeper source
than self-complacent ignorance.
The present state of matters is different. The philosophy of Hecrt is now for
the first time beginning to have a direct and powerful influence on British specula-
tion. Men are beginning to study HeceL; and an author whose works con-
fessedly demand the labour of years, if they are to be fully understood, can hardly
be studied at all except by devoted disciples. A man whose determination to
master HecEL’s philosophy survives the repelling impression which the obscurity
and arrogance of the philosopher are sure to produce at first, is very likely to be
carried away by the calm assumption of omniscience which runs through HrcE.’s
writings. It isnot, therefore, surprising that Dr Stirtine extends his admira-
tion to HecEw’s physical positions; and if he does not venture to say that HzcEL’s
proof of KePier’s laws is right, at least feels sure that it would repay the attention
of mathematicians.
It would not, perhaps, be impossible to rob Dr Srrruine of even this sorry
consolation; but there is the less occasion for retracing any part of the ground
gone over by WHEWELL, in so much as “The Secret of Hegel” calls attention
to another point, in which Hees. criticises Newton, and in which Dr StirLING
has no hesitation in pronouncing HeceEt’s findings “ perfectly safe from assault,”
and Newton guilty of an obvious mathematical blunder.
Such a statement, proceeding from the most powerful of our living metaphy-
sicians, and recently reiterated in the newspaper press, as a sort of challenge to
mathematicians, seems to call for some remark from a mathematical point of
view. Itis true that a confirmed Hegelian is not likely to be influenced by any
reasoning that we can offer. “The judgment of a pure mathematician,” we are
VOL. XXV. PART II. 61L
492 MR W. ROBERTSON SMITH ON HEGEL
told, “‘has really been so peculiarly trained that, perhaps, any such will never
prove decisive as regards any Hegelian element.” We are told, too, that HEGEL’s
‘‘most important note” on the mathematical infinite “‘ has remained hitherto
absolutely sealed,” for C. Franrz, who does take up the subject ‘as in opposition
to, is to be assumed ignorant of, the views of Heget, which plainly, so far as they
go, are inexpugnable”’ (!)
Now I do not profess to be able to treat this question from the stand-point of
Hecet’s own philosophy. I have no desire to criticise Hraex’s doctrine of the
Infinite, in so far as it forms an integral part of his system. But the note to
which Dr StTiRL1NG calls attention is itself a critical note, in which HEGEL proposes
‘to consider in detail the most remarkable attempts to justify the use of the
mathematical notion of the Infinite, and get rid of the difficulties by which the
method feels itself burdened” (HEGEL’s Werke, iii. 286).* What HEGEL seeks to
show is, ‘‘ that the mathematical Infinite is at bottom the true Infinite” (p. 283);
imperfectly conceived, however, by the mathematicians, who have therefore
never been able to put the higher calculus on a basis thoroughly free from con-
fusion, or evenerror. Thus, not to speak of Fermat, Lerpnirz, EuLER, and others,
whose views HeceL takes up more or less fully, we are told that Newron ©
himself, although his fundamental thought was quite in harmony with HEGEL’s
views, was not so far master of his own thought as to be able fairly to deduce
the practical rules of his method. In the actual application of the new instru-
ment, NewTon clung “‘ to the formal and superficial principle of omission because
of relative smallness.”’ He thus fell into real errors; and even so fundamental :
a problem as the determination of the fluxion of a product was solved in a manner
analytically unsound. Now these, I maintain, are assertions that can fairly be
examined by one who does not profess to have mastered HEGEL’s system. They
even afford a fair test whether that system is really so complete in all its parts,
and so light-giving in its applications, as we are told to believe. If NewrTon
is really confused and in error, it must be possible to make this clear by an
argument based on NEwron’s own principles. For if to the mathematician
NewrTon’s method is perfectly clear and self-contained, and if its errors can only
be observed from an entirely different point of view, we have not one truth, but
two truths, mutually destructive. And this surely Dr StirL1ne will not assert.
It is possible, however, to go further than this. To the subject of the calculus
HEGEL devotes two notes. The first of these alone is taken up by Dr Srir.ine.
And in this note Hrecet adds to the destructive criticism of which we have been
speaking only a very general account of the principles on which he would base
the calculus. These general principles are, as HEGEL says, “‘ abstract’’ (we would
rather say vague), “and therefore in themselves also easy” (p. 327). The real
* Here and elsewhere I adopt, as far as possible, the language of Dr Stirxine’s own translations
from Heaet, which may be viewed as authoritative.
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 493
difficulty lies ‘‘in the concrete side,” in the deduction from these generalities of
the practical rules of the method. To this subject Heart devotes his second
note, professing to point out a purely analytical method whereby, without any
application of the doctrine of limits, everything necessary for practice can be
deduced. If we can demonstrate that the analytical method is radically unsound,
producing results mathematically false, it will surely be vain to appeal in defence
to any “deficiency in the judgment of a pure mathematician.”
The plan that suggests itself is therefore the following :—/irst, to consider
the real character of NewrTon’s method, and to show what may, I think, be made
quite clear to an unprejudiced mind, that that great man really did know what
he was doing; and, in the second place, to show that Hecrt having refused to be
instructed by NeEwTon’s real knowledge, but having acutely enough caught sight
of something like the ghost of an idea, which he could not for want of solid
knowledge really make his own, was first ensnared by the plausible but fallacious
method of Lacranceg, and then, in attempting to improve that method, lost any
elimpse of the truth that he had before, and was swamped in hopeless absurdity.
The ingenuity of a great deal that Hrcet has said on this subject I do not wish
to dispute. No doubt he,
“ with as delicate a hand,
Could twist as tough a rope of sand”
as any man that ever lived. But the question is, after all, one of plain truth and
error; and however much we may admire the chivalry with which HEGEL rushes
into an unequal encounter with so gigantic an antagonist as NEwrTon, it will
never do to
“ Coin a formal lie on’t
To make the knight o’ercome the giant.”
We must begin, then, by examining the principles on which NewrTon based his
doctrine of Fluxions. In doing this, it is not necessary to inquire how far
NEWTON’S own views varied during his life. Hrcrt knows Newron’s method
from the Principia only, and a quotation from the second Lemma of the Second
Book (Werke, iii. 305) shows that it was the current text of the Principia (that
of the second edition) which he had before him. In fact, HncEt’s acquaintance
with Newton’s writings was clearly of the most superficial character, embracing
apparently little if anything beyond the section on Prime and Ultimate Ratios,
and the Lemma just referred to. These facts make all merely bibliographical
inquiries superfluous in dealing with HEGEt’s objections. I may refer, however,
to a paper by Professor p—E Morea, in the “ Philosophical Magazine” for 1852,
on the “ Karly History of Infinitesimals in England,” in which it is shown “ that
NEwTon never varied in his meaning of #;” or, in other words, that Newron
“held to the conception of the velocity or fluxion,” although he at first ‘‘ used
the infinitely small increment” (only of the first order, however), “as a means of
494 MR W. ROBERTSON SMITH ON HEGEL
determining it.” What follows will, I hope, serve to show that these facts imply
that Newton had all along a firm grasp of the principle of his method, and that
his frequent employment of abbreviated practical processes was really based on
a consciousness of the strength of his method, according to the general principle
of mathematicians, who never hesitate to apply the boldest symbolical methods
in detail, when they feel confident of the starting-point in the use of these
symbols. This, in fact, is a point that metaphysicians have never properly
attended to. One is disposed to cap Dr Stiruine’s wish that some great analyst
would study Hece, by expressing a hope that some metaphysician of real ability
may pay sufficient attention to what are technically called the ‘‘ Symbolical
Methods” of mathematics, to enable him to appreciate BooLr’s profound preface
to his treatise on “ Differential Equations.” This exercise would at least make
it clear that metaphysical criticism on mathematics is still—I speak without any
desire to be disrespectful—in the circle-squaring stage, 7.e., still treats as the real
questions for discussion points that mathematicians have long seen to be merely
special cases of general principles, and therefore to be no longer possessed of
independent interest.
To return from this digression. NEwTon saw that there were two ways in
which quantities might be conceived as generated. The first of these is that
which the usual processes of arithmetic have made familiar to everybody, viz.,
the addition of discrete units. The theory of numbers thus viewed is contained
in the arithmetic of integers, to which may be added the doctrine of arithmetical
fractions as an extension of the method, reached by supposing the unit itself to
change in value. NEwrTon was especially attentive to the importance of the
doctrine of decimal fractions, in which the change of unit is so regulated as to
give the greatest possible increase of power that the arithmetical conception of
quantity admits of; and the opening pages of his “‘ Geometria Analytica” are
expressly directed to show that these advantages may be made available in literal
as well as in numerical calculations. [See also the treatise ‘‘ De Analysi per
Equationes Numero Terminorum Infinitas.” ]
NEWTON saw, however, that arithmetic in its most perfect form could give full
mastery over quantity, only on the supposition that quantity, as it comes before
us in the universe, is always produced by the synthesis of ultimate units, or, in
other words, of indivisibles. And this, says NEwTon, is contrary to what Evciip
has proved concerning incommensurables in the tenth book of the Elements
(Prine. lib. i. sec. i. schol.)
Instead, therefore, of endeavouring to eke out this view of quantity by arbi-
trary assumptions, NewTon resolved to turn to Nature herself, and inquire how
quantity is really generated in the objective universe. ‘‘ Lineae,” he writes
‘‘ describuntur ac describendo generantur non per appositiones partium sed per
motum continuum punctorum; superficies per motum linearum; solida per
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 495
motum superficierum; anguli per rotationenem laterum; tempora per fluxum
continuum et sic in ceteris. Hae Geneses in rerum natura locum vere habent et
in motu corporum quotidie cernuntur.” (Introd. ad Quad. Curv.)
In a word, NewrTon’s fundamental position is, that the arithmetical concep-
tion of quantity is not that with which nature herself presents us, and is not,
therefore, universally applicable. On the other hand, every quantity that has
objective reality [.¢., is an object of real intuition] is generated by continuous
motion, with definite (constant or variable) velocity within definite limits of
time. The metaphysical nature of time and motion NeEwron has nothing to do
with. Itis enough for him that mathematical time, conceived as an independent
variable flowing uniformly, is clearly the ¢rwe time made known to us in nature
(Principia; Schol. to the Defs.), and that the existence of a definite velocity at
each point of a motion is in like manner an undoubted physical fact.
By means of these profound yet simple considerations, NEwron is at once able
to revolutionise the whole theory of quantity, and to substitute for the relation
of unit and sum that of velocity and quantity generated, or, in NEwTon’s own
language, of fluxion and fluent. It must be remembered that we have said
nothing of space, so that fluent is not limited to extensive quantity, while velocity,
or as we should rather say rate, has a correspondingly wide application. Thus,
any fluxion may itself be treated as a fluent quantity, and its fluxion sought, the
only independent variable being time, which is thus a fluent which has no variable
fluxion.
This conception of time, as the one absolute and independent variable, is
undoubtedly one of the most splendid and fruitful in the history of human
thought, and well deserves the attention of metaphysicians. Only let it be said
that no criticism of NrEwron’s time, which starts from the arithmetical view of
quantity, and urges the old objections about infinite divisibility, and so forth, is
competent ; for the arithmetical theory is a product of abstract reflection, and so
stands on a lower platform than the pure objective notion of NrewTon.
There is no difficulty in comprehending the mathematical power which the
conception of fluxions at once puts in Nrewron’s hands, if we remember that it
is not in any sense an extension of the theory of numbers that he is seeking. It
is true that the calculus has revolutionised algebra as well as geometry; but it
has done so by transforming algebra from the abstract science of numbers to a
physical science—the science of pure time. In Newron’s own mind, however,
this conception was probably not explicitly present. What he did see was, that
all difficulties in geometry (and to Newmov, as to the old geometers, geometrical
magnitude is the type and exponent of all magnitude whatsoever, when viewed
with respect to its generation) are reducible to the general form :—‘‘ Given the
fluent as a function of time to determine the fluxion and vice versd.”
The one class of problems that can be thoroughly treated without explicit
VOL. XXV. PART II. 6M
496 MR W. ROBERTSON SMITH ON HEGEL
reference to a generation by flux, is that which has for its geometrical type
systems of straight lines; and thus geometers were tempted to introduce the
fiction of indivisibles, in order to reduce higher problems to this type.
But these higher problems are not simply complicated cases of the rectilineal
type; on the contrary, that type is produced -by one of the two essentially distinct
elements (generated and generating quantity), which usually appear side by side,
ceasing to be explicitly manifest.
Take, for example, NEwron’s own instance at the beginning of the “De
Quadratura.” Suppose the abscissa AB of a curve to flow uniformly, in which
case it may be taken as the graphic representation of the independent variable,
i.e., of time, while the ordinate BC is of course a func-
tion of the abscissa. Then NewrTon shows that the
reason why the determination of the tangent at C
is a difficult problem, is that the ratio of the ordinate
BC to the sub-tangent VB is the graphical represen-
tation of the fluxion of the ordinate. In fact, the
meaning of the tangent is, that it is the direction in which the curve is flowing at
the point C; and all attempts to give it another explanation without reference
to motion simply ignore the real gist of the problem, and of course end in diffi-
culties that can be escaped only by violent assumptions. It is only in the straight
line where the fluxion of the ordinate is constant, or the tangent sinks into the
curve, that the conception of vate can be dispensed with.
Before we go farther, it is proper to remark that in criticising NEwron, HEGEL
coolly ignores the whole foundation of the doctrine of fluxions as here developed.
‘The thought,” says he (Werke, ili. 302; Sriruine, ii. 354), “cannot be more
correctly determined than NewrTon has given it; that is, the conceptions of move-
ment and velocity (whence fluxion) being withdrawn as burdening the thought
with inessential forms and interfering with due abstraction” —~.¢., because HEGEL
thought that the calculus should be based, after the manner of LAGRANGE, on
purely analytical considerations, it never enters his head that if NewTon thought
otherwise there might be some deeper ground for this course than a want of
insight into his own method. On the contrary, HEGEL comments in the most
edifying manner on the “early still naive period of the calculus” in which
‘‘mathematicians sought to express, in words and propositions, results of the
newly invented calculus, and to present them in geometrical delineations,”
assigning to the “ definitions and propositions so presented a real sense per sé,”
in which sense they were “‘applied in proof of the main positions concerned.” If
there is any meaning at all in these statements, which are the gist of a somewhat
lengthy discussion (Werke, iii. 324; Srrrurne, ii. 375), that meaning must be
that NrewTon and others first differentiated a function, then sought a geometrical
construction to suit, and finally invented a physical proposition to correspond.
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 497
Purely analytical considerations without any physical basis were held, HEGEL
thinks, to furnish in this way physical laws. In support of this view, Hrece,
triumphantly refers to “the Newtonian proof of his fundamental proposition in
the theory of gravitation compared with ScuubErt’s ‘ Astronomy,’ where it is
admitted that .. . in the point, which is the nerve of the proof, the truth is not
as NEwTon assumes it’’[!] And so upheld by the dictum of this forgotten
astronomer, HEGEL goes on to inveigh against the mere jugglery by which
NewTon, already knowing KepeEr’s results, avails himself of the “‘ mist of the
infinitely little” to bring out apparent mathematical proofs of these results. One
does not know whether the singular perversity of this accusation against NEwTon’s
moral character, or the incredible ignorance of the argument by which it is
supported, is most to be wondered at; for, not only do the reasonings of the
‘« Principia” rest throughout on the experimental laws of motion on which
NeEwrTon’s first proposition is expressly based, but the proof itself depends not
on the interpretation of an analytical process, but on the essentially physical or,
more definitely, kinematical considerations above developed. Nay, so little is it
the case, that the “mist of the infinitely little” is needed to give a show of
plausibility to NEwron’s process, that the whole gist of the proof lies in the one
conception of quantity generated at a definite though variable rate, and that thus,
without any change in the spirit of the proof, by simply introducing explicitly a
theorem about moments of velocity which the demonstration in the “ Principia”’
implies, the law of equal areas can be deduced without even that apparent use of
the infinitely little which, as NewTon himself warns his readers, is always merely
apparent (THomson and Tarv’s “ Natural Philosophy,” § 234). In one word,
NEwrTon’s proofs are always physical throughout, and really belong to the essence
of the thing to be proved; while Hecet first shuts his eyes to the real import of
the fluxional method, insisting that it mus tbe made purely analytical, and then
rails at Newron for using the method to do work for which, if it had been purely
algebraic, it would not have been fit. A Hegelian calculus, as we shall see,
would certainly have been of little service to physics; but the doctrine of fluxions
is itself a part of physics, and absolutely indispensable in some form or other to
the right understanding of physical problems.
We have still, however, to see how it is that Newron’s system comes to have
anything at all to do with the infinitely little which, as he himself says (Introd.
ad Quad. Curv. § 11), it is the peculiar merit of that system to render unessential.
The reason is simply, as we are told in the scholium at the end of the first section
of the “ Principia,”’ that he was anxious to provide for ease of conception, and
also to introduce all legitimate abbreviations in his arguments. When Newton
is called upon to justify his method, he always refers to the simple fact that a
velocity definite, yet never for the shortest space of time uniform, is a notion
really furnished by nature, and that the true measure of that velocity is to be
498 MR W. ROBERTSON SMITH ON HEGEL
got by allowing the motion at any point to become uniform for a unit of time.
But if one wishes, as HEGEL would say, to substitute for this notion a convenient
“Vorstellung” to assist the imagination, NEwron is ready, by means of the
doctrine of prime and ultimate ratios, to point out a way in which we may avail
ourselves of the method of indivisibles, always remembering that this method
shall have merely a symbolic value, and so must be used with caution.
If two quantities have the same fluxion at any moment, they begin at that
moment to increase at the same rate. It does not follow from this that the two
quantities shall receive equal increments in any space of time however small,
unless during that time the rates of flow remain constant. But NewrTon shows
that in a very large class of cases, which he takes up one by one in the first
section of the ‘‘ Principia,” not only may we, by taking the time of flow small
enough, make the difference of the increments generated in that time as small as
we please, but if we enlarge both increments on the same scale up to any given
size, we may make the differences of the increased increments as small as we
please, while the time of flow has still a definite value. Since, then, the ratio of
the increments is always nearer to unity the less the time of flow, and may be
brought as near to unity as we please by taking the time short enough, but still
finite, the ratio must ultimately be unity—ze., that quantity which, varying
according to a definite rule, always represents at any given time the ratio of the
increments, may still be constructed when the time is made zero, and is now
equal to unity, or is equal to the ratio at which the increments start, which
Newton calls their prime or ultimate ratio.
The practical application of this reasoning is, of course, that in virtue of it, we
may in certain cases with strict accuracy treat the increments of two variables
(of a curve, for example, and its tangent) as equal, if, before closing our reason-
ing, we proceed to take the limit. Thus, if any one finds that it assists his
imagination to deal with magnitudes as if they were composed of indivisibles,
instead of confining himself to fluxions, NEwTon provides in the method of prime
ratios a criterion by which the applicability of the process may be judged. ‘The
details by which it is shown in the “ Principia,” that the limit of the ratio of the
increments is equal to the ratio of the fluxions whenever the fluents may be
geometrically represented as curves of continuous curvature, involve no new
principle in geometry. Everything is as plainly and undeniably reduced to
ordinary geometrical intuition as anything in Evciip, when we once bring with
us the fundamental kinematical ideas of velocity and acceleration. It is obvious,
: 0 , ,
moreover, that to Newron the fraction o? as above explained, means simply the
ratio of the rates at which two quantities are flowing at the moment at which
they pass together through the point from which we have agreed to reckon their
magnitude backwards and forwards. Except where such rates can be assigned
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 499
‘ ; 5 22, 20
possessing a definite ratio, NewTon does not pretend to recognise o as a mathe-
matical reality.
This outline of NEwron’s principles is, of course, very meagre. It will
probably, however, suffice to enable us to estimate the real value of HEGEL's
criticisms.
Hrcet highly approves of NeEwron’s statement of what he means by
prime and ultimate ratios, viz., that he always deals not with indivisible
but with vanishing divisibles. This is very satisfactory so far, but the
next paragraph makes one doubt whether HreceL knew what he was ap-
proving.
“Newton,” we are told, “‘ only explained what he means by his terms, with-
out showing that such a notion has internal truth.” *
This is an accusation constantly recurring in various forms. Its source is, of
course, that determination which we have already noticed in HEGEL to pay no
regard to considerations of velocity and motion. Now it is quite true that
Newton does not condescend to offer any explanation of his ‘‘ notion” to the
man who has failed to familiarise himself by actual intuition with the nature of
velocity, and acceleration, and the genesis of quantities by flux. But these
notions are just as truly capable of being constructed by pure intuition as those
of ordinary geometry, and so NEwron’s definitions enjoy fully the advantage
which Kant ascribes to mathematical definitions in general. They cannot err,
because they simply unfold a construction by means of which the notion is
actually produced.
If HEGEL, however, shut his eyes to Newron’s notion, he has got one of his
own, which he is sure is just what Newron wanted. I do not intend to attempt
to take up anything but the concrete applications of this notion; but perhaps it
may be well to give here part of HEGEL’s abstract statement of what he con-
ceives to be the mathematical infinite. ‘“ Das unendliche Quantum. . . ist nicht
mehr irgend ein endliches Quantum, nicht eine Grossebestimmtheit, die ein
Daseyn als Quantum hatte sondern es ist einfach, und daher nur als Moment; es
ist eine Grossebestimmtheit in qualitativer Form; seine Unendlichkeit ist als eine
qualitative Bestimmtheit zu seyn” (iii. 289; Srrruine, ii. 341). Now, says HEGEL,
this is clearly what Newron needs. His vanishing magnitudes have ceased to
exist as quanta, and exist only as sides of a relation; but farther, the relation
itself, in so far as itis a quantum, vanishes. “ The limit of a quantitative rela-
tion is that in which it both is and is not, or, more accurately, that in
which the quantum has disappeared, and there remains the relation only
* Dr Srirnuine (ii. 355) seems to have read “ Nach dem damaligen Stande der wissenschaft-
lichen Methode wurde nun erklart.” In the collected edition of the “ Werke,” ii, 303, I read
*‘ wurde nur erklart,” which seems to give a more intelligible sense.
VOL. XXV. PART II. 6N
500 MR W. ROBERTSON SMITH ON HEGEL
as qualitative relation of quantity.” This sentence must mean that in the
equation
oy _¥
Lt 5 3
the left hand side vanishes as quantum in the same sense in which dz and dy
vanish, or, as Hrce often puts it, es is “infinite,” just as truly as dy and dz.
Now, we are told again and again that the ‘‘ infinity” of the dx and dy does not
lie in their being infinitely small, but in their having ceased to be any
determinate magnitude, and only representing the qualitative principle of a
magnitude. To this statement NEwron would probably not have objected, as
his whole use of infinitely small quantities is, as we have seen, merely to help
the imagination, and scientific strictness is given to his method from another
side. But certainly he would never have dreamed of admitting that y
is also indeterminate ; for both numerator and denominator of this fraction are in
their nature definite quantities. That the fraction can be expressed as : is to
NEwTOoN by no means the essential point. On the contrary, he argues distinctly
that : must have a definite value, just because this is the form in which certain
processes present to us a quantity which, from kinematical grounds, we know
to be definite. To Hxrcrt, however, the fascinating element is just this
5 which for his ends would be quite spoiled by being evaluated. That would
reduce it to a mere quantum; but, in the meantime, it is “‘a qualitative relation
of quantity,” which is a far finer thing. Not unnaturally, however, Hecex has
now to ask himself, what is to be the practical use of this Lt a , Which certainly
“ expresses a certain value which lies in the function of variable magnitude.” In
asking this question, he still supposes himself to be criticising Newron and the
mathematicians, and accordingly proceeds, with much severity of manner, to
knock down the indeterminate oH which he has just set up (p. 318). To apply
the conception of limit in the concrete we must determine the limit. This is
done by TAyLor’s theorem, from which if y = /(z) we get
by __
ap PT geet, &e.,
and then letting dv and dy vanish “es p;—not as it should have been = a
This, of course, is sadly inconsistent; for instead of our fine qualitative deter-
mination, here is a stubborn quantum turning up. Now, says HxcsEx, the
—— re ae
SS Ce a oe e) eee
/
= =
«
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 501
mathematicians try to get over this by saying that pis not really = HE but is
only a definite value, to which ; comes as near as you please. Of course,
if this is so, it is as evident as anything can be that the difference between p and
O is not a quantitative one. But, adds the philosopher, naively enough, that
d. d
doesn’t help one over = = 4. Suppose now that we were to say = really = p (a
definite quantity), as, in fact, mathematicians do say, then it is obvious that dx
couldn’t have been = 0. Or if, finally, it is conceded that = = 0 (which Heeger
seems to think most likely, since dy and dz vanish together), then what can
p be?
Now, can any one say that the man who devised this argument knew what
he was doing? When did any mathematician suppose that after evaluation
Oe. 2 - Sm ase
9 is indeterminate? Or had HrceL never read NewrTon’s first lemma, with its
“fiunt ultimo equales”? Or, again, if Hecrn allows that there is no quantita-
tive difference between p and oe why does he assume a qualitative one? Or, above
all, why try to explain Newron’s doctrine without ever deigning more than a
contemptuous glance at the one central point of the whole? Hxcet boasts that
half an hour would suffice to learn the calculus. Certainly he might have
employed a good many hours in unlearning his false conceptions of it.
HEGEL has next something to say about the way in which mathematicians
have developed the details of the calculus. Since none of them had a clear
notion of the matter in hand, their proofs, we are told, are very weak. They
always fall back into methods merely approximate, subjecting infinitely small
quantities to the laws of finite quanta, and yet rejecting them as relatively unim-
portant, in despite of these laws. Of course, adds HEGEL, we need not look for
the rigour of demonstration of the old geometry, for the analysis of the infinite
is of a nature essentially higher than that geometry. However, mathema-
ticians have sought this rigour, and they have all failed.—Of course, it would
be easy for any one to point out numerous mathematicians who have failed; but
let us simply ask whether Newton has done so. HeceEt unhesitatingly affirms
that he has, and Dr Srirtive is jubilant at the discovery.
The error is supposed to lie in the deduction in Prin. ii. Lem. 2, of the
fluxion of a product. The statement of Newton is as follows:—If A,B be two
quantities increasing continuously, and their moments or rates of change a and 8,
the moment or change of the rectangle ABis aB + JA. By moment Newron
does not mean the increment actually received in any time, however short, but the
502 MR W. ROBERTSON SMITH ON HEGEL
nascent principle of the fluent quantity—a notion, of course, made clear by the pre-
vious discussion of prime and ultimate ratios. The moments, in fact, are any quan-
tities proportional to the rates at which A and B are flowing—the products of the
fluxions of A and B by an arbitrary increment of time. If moments, then, are
called increments, the meaning is increments which would be received if the rate
of flow remained constant, and the ratio of two moments is simply the ratio of
the fluxions, and therefore equal to the limit of the ratio of the actual incre-
ments, while it is quite independent of the magnitude of the separate moments.
Now, says Newton, when A and B are diminished by half their moments, the
rectangle is AB — 4 aB —36A + 446; and when A and B are increased by half
their moments, it is AB + }¢B + 406A + 4a; and so to the increments @ and }
in the sides corresponds an increment @B + 0A in the rectangle. This demon-
stration is certainly very curt, and intended only for those who have mastered
Nrewton’s fundamental notions, and may therefore be saved the tedium of a long
reductio ad absurdum. More at length, the proof would be of this kind. The
fluxion of the rectangle must, since the flow is continuous, be a definite quantity,
depending only on the magnitudes and fluxions of the sides at each moment.
Thus the fluxion of AB will be unchanged, if we suppose that from the values
A —4a, B —40 the sides flow with uniform velocity, equal to A and B, until
they attain the values A+ 4a, B +40. In this case the increments a and 6
will represent exactly upon the same scale the fluxions A and B. Meantime, the
rectangle has been flowing with a constantly increasing velocity, which at the
moment when the value AB was reached, was the velocity Newton is seeking to
determine. The whole increment of the rectangle is a@B + 0A, which therefore
represents the, average velocity of the rectangle on the same scale as a,b repre-
sent the uniform velocities of the sides. Clearly the average velocity with which
the increment is described is greater than the velocity at the beginning of the
motion, and less than that at the end, and therefore, since the velocity is continuous,
is strictly the velocity at some intermediate point. But this point can be none
other than that at which the rectangle = AB, for were it any other point, we
could take a and } small enough to throw this point out, and there would still be
another point at which the fluxion of the rectangle must = aB + 0A. But thisis
contrary to the intuitive fact that the velocity is continuously increasing. To the
mathematician, however, this round-about process is unnecessary. He sees at
once that if the average velocity is independent of the duration of flow, and
depends solely on a certain point being included within the flow considered, the
velocity at that point must be strictly the average velocity, for in the limit the
two coincide.
Now, Hece., of course, did not see this, because he would not admit the
kinematical reality of fluxions. He, therefore, supposes that NEwron wants to
find the diferential of AB—a way of stating the problem which Newton would
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 503
have rejected as misleading. The differential can be nothing else than (A + dA)
(B +dB)— AB. But Newton writes instead of this (A + 4dA) (B + 3dB)
— (B— 4dA) (B — 4. dB), thereby making an error in so elementary a process as
the multiplication of two binomials !—But where is HeceEw’s justification for
saying that what Newvon is seeking is (A+ dA) (B + dB) — AB? NeEwron says
nothing about differentials at all; his a is, as we have seen, not the infinitely
small increment of A, but an arbitrary multiple of the fluxion of A, which need
aB + bA
a
not be infinitely small. NerwrTon’s is, if you please,
?
_ pp AA) B+ aB)— AB
= lt an
but even this, which is very different from what Hrcet writes, is simply a
different, by no means a more fundamental, view of the problem than NEwrTon’s.
Dr Sririine tells us that HEGEL’s expression 7s what NewrTon’s says his is,
“ the excess of the increase by a whole dA and dB.” But what NEwTon says is
only that when the sides are increased from A — 4a and B — } 4, through incre-
ments @ and 0 the rectangle increases by aB + DA. That this is true surely
cannot be denied. In fact (A + a) (B + 6)— AB would have represented not
the velocity at value AB, but the average velocity of the rectangle during the
interval between values AB and (A + @) (B + 0), and therefore the real velocity at
a point between these limits which NEwTon was not wanting. We know, in fact,
that it would have been the velocity when the sides are = A + 5 and B + ss
Instead, therefore, of NEwron rejecting a quantity on the ground of relative
smallness, we find that Hrcet has gratuitously introduced such a quantity.
Of course, the Hegelian will reply to all this, that our method is “ rendered
impure by the concrete adjunct of motion.” And here, of course, we can say
nothing, except that the fluxional calculus is essentially kinematical, and that to
~ construct it apart from motion is as likely a task as to make a geometry without
lines. To make bricks without straw is a light task compared with that which
HEGEL has set himself.
Happily unconscious of these difficulties, HrGEL goes on to moralise with
much satisfaction upon NewrTon’s melancholy self-deception, in palming on him-
self such a proof.
After this specimen of HecGeEL’s analytical subtilty, it is perhaps sufficient to
confront the assertion which immediately follows (Werke, ili. 313; STIRLING, ii.
364), that NewTon, in finding fluxions by the method of expansions, uses a process
analogous to his method of solving approximately numerical equations, con-
stantly ‘‘ neglecting what is relatively unimportant,” with the explicit words of
the De Quadratura (Introd. § 5)—“‘ Errores quam minimi in rebus mathematicis
non sunt contemnendi.” Theterms omitted are, of course, always terms which we
VOL. XXV. PART II. 6 0
504 MR W. ROBERTSON SMITH ON HEGEL
know to become not relatively but absolutely zero in proceeding to the limit.
The motive for using such expressions as ‘‘ minuatur quantitas o in infinitum,”
instead of simply saying, let o = zero, is merely to show that o becomes zero not
by a discontinuous process, as subtraction, but by a continuous flow. Nay, cries
HecEeL, for in the 3d Problem of Book ii. of the “‘ Principia,”” Newton fell into an
error, by “ throwing out, as LAGRANGE has shown, the very term which—for the
problem in hand—was wanted. Newtown had erred from adhering to the formal
and superficial principle of omission from relative smallness.” This error, by the
way, is only in the first edition of the “ Principia,” which HEGEL, one may safely
affirm, had never seen. The whole statement here is taken from LAGRANGE, and
applies much better to LAGRANGE’s analytical way of putting NewTon’s argument,
than to that argument in its geometrical form.
NEwTOov, in fact, investigating the law of resistance, that a body under gravity
may describe a given path, seeks a geometrical expression for the moment of the
sagitta—a small quantity of the third order. It is clear, therefore, that no such
expression can be exact unless account is taken of every small quantity of an
order not higher than the third in the geometrical construction involved, for such
quantities will not vanish in the limit, or are not “relatively small,” in a mathe-
matical sense. The principle of the problem, then, presents no difficulty on
Newton’s method; and the true account of the error is, that by a mere slip in
the details of a complicated process, NeEwTon failed to see that he was omitting
a term (or better, a line) not small relatively to the moment of the sagitta.
HeGeEL, however, conceives that so far as this goes Newton was all right. The
error, according to him, lies in neglecting a term which, though “relatively small,”
‘« possessed the qualitative value sought.” ‘In mechanic, a particular import is
attached to the terms of the series in which the function of a motion is developed,
so that the first term, or the first function, relates to the moment of velocity, the
second to the accelerating force, and the third to the resistance of forces.” The
terms are thus to be regarded as ‘“‘ qualitative moments of a whole of the
notion ;”” and, of course, in a problem about resistances Newron needed the
third term.—Now here we have, jivstly, a laxness in the use of terms so gross,
as to make it hardly possible to criticise our author fairly. Luckily, we can see
that HrGex is leaning entirely on Lacranee, and that “ the series in which the
function of a motion is developed,” must therefore mean the series which expresses
space in ascending powers of time. And this enables us to ask, secondly, What
reason HxrceEu has for supposing that it is in this series that we are to find the
basis for a truly philosophical view of kinetics? It was HEGEL’s misfortune to live
at a time when, among other fruits of the “ Aufklirung,” Lagrance’s “ formal
and superficial” method of treating physics was in great repute; and surely it
was a cruel fate that the great enemy of the Aufklirung should, through a
defective mathematical education, be made a willing captive to a mathematical
SS Beh Val ais, ei dl he 2 pk thd
Sa EA Sebi
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 505
‘ Aufklarung,” which has, from its intrinsic weakness, fallen as fast as it rose. In
details, it is true, HEGEL is keen enough in detecting the unsatisfactory character
of LAGRANGE’s stand-point [see, for example, a note at this very point]; but that
the whole method was artificial he could not see, not for want of mental power, but
because, having never studied the subject, he knew nothing whatever about it—
had not even mastered its technicalities. Then, again, if it is true that successive
differential coefficients have a qualitative difference, how can that be brought out
except in virtue of the relations established in mathematics between quantity
and quality, relations which are not reached by pure analysis, but only in
NEWTON’S way, 7.¢., by intuition? And would not these relations be violated,
and all mathematics rendered absurd, if the term that is qualitatively important
could be quantitatively negligible? And, last of all, let me challenge HzcEL to
bring forward any proof on his own principles, that the third term relates to the
resistance of forces; or for that matter, to show that this statement has any real
meaning whatever.
But most men, I imagine, have now had enough of Heeet’s criticisms—
criticisms which simply show that the “ half hour” which he had devoted to the
calculus had not sufficed to give him any just idea of that great method. It is
certainly much to be regretted that so ableaman did not study mathematics
thoroughly, for such a course might have proved useful to the theory of mathe-
matics, and could not have failed to be profitable to himself. As it is, he has
only given us criticisms such as we have seen, and an attempt to which we now
proceed to establish the calculus on a new and very inadequate basis.
The point which we have always found HrGet urging is, that mathematical
functions, when they become quantitatively indefinite or ‘“ infinite,” may still have
areal qualitative value. Passing over the fact that this is not the technical
sense of infinite in mathematics, we may grant that there is a kind of meaning,
however vague, that may be attached to the view. Thus an incommensurable is
infinite in the Hegelian sense, not because it can be expressed arithmetically only
by an infinite series, but because it is essentially not a sum of units, but, as
HEGEL vaguely says, a “relation.” For relation we should say function, and
then we should be able to read in HerceEL’s words some meaning like this.
Algebraic and geometrical functions are qualitatively different from mere arith-
metical functions. ‘They imply an entirely different way of looking at quantity,
expressing, in fact, steps in time or space [or in kinematics, both in time and
space]. So, again, the differential coefficient which takes the form : ceases to be
intelligible on the mere arithmetical view, but gives us a real result of a different
quality, when we understand it as equivalent to a proposition about the rates of
the vanishing quantities. But then Hecer does not seem to have seen that 3 has
areal quantitative value, expressing accurately a definite quantity of a different
506 MR W. ROBERTSON SMITH ON HEGEL
quality. And further, there was in HEGEL a rigid determination not to see the
real qualitative difference between the continuous quantity of the higher analysis
and of actual nature, and the discrete quantity of arithmetical abstraction.* He
thus fell into the delusion, that a writer like LAGRANGE who, from the extreme
nominalistic stand-point of the eighteenth century, seeks to make analysis a
merely formal instrument, in no way expressing the essence of things, and who,
for example, boasts that in his Mécanique Analytique one will find no such
unnecessary incumbrances as figures—HEGEL, I say, imagined that such a writer
had really reached a higher generality than Newron, when he had only reached
an untenable extremity of one-sided abstraction, and hence, without a moment’s
hesitation, resolved that by simply treating the successive differential coefficients
as the successive derived functions obtained by explanding y in terms of a, we
shall be quit “ of the formal categories of the infinite, and of infinite approxima-
tion, and of the equally empty category of continuous magnitude”? (iil. 320).
The differential calculus, then, is a special branch of mathematics which has
to deal (by purely arithmetical methods) with qualitative forms of quantity,
7 é., says HEGEL, with relations of powers. A power, it should be said, means
with HEGEL a quantity raised to a higher power than the first, and the link
between the clauses of the foregoing sentence is as follows :—“In the equation
= a the relation of y to z is an ordinary quantity, and a common fraction,
just like 5 so that the function is only formally one of variable magnitudes. On
2 ;
the contrary, if a — oe has no determinate quotient, and, in fact, 2 has no ratio
to y, but only toy’. Now the relation of a magnitude to a power is not a quantum,
but qualitative.” It is needless to say that the man who could make “no con-
stant ratio” identical with “no ratio,’ and who did not see that ,/px has a
definite value for each value of 2, or who did not see that p is a quantum, though
not of the same dimensions as y’ (which probably was what confused HEGEL), is
hardly fit to construct a new theory of the calculus. But let us pass on.
The subject matter of the calculus is then, we are to believe, equations in
which one variable appears as a function of a second, one of these at least occur-
ring in a power higher than the first. In such a case the variation of the variables
is qualitatively determined, and therefore continuous. It would be vain to ask
why; but since we are told that in the equation s = ct there is no scope for differ-
entiation, 5 not being qualitative, we may at least conclude that Hzce does not
regard uniform motion as continuous!
So far as the principle goes it is quite sufficient, continues HEGEL, to consider
* Heeger absolutely identifies analysis with arithmetical process—“ Auf analytische d. i. ganz
arithmetische Weise” (iii, 328). Had Hrexzn ever studied the treatment of incommensurables in
ordinary algebra? If algebra is “ ganz arithmetisch,” the whole doctrine of indices is false.
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 507
the equation x = y”; the advance to more complicated functions is quite mechanical.
Now both y and 2 are really numbers, and so may be expressed as sums. _[This,
of course, is a very bold assumption, as HEGEL says nothing of the possible case
of incommensurables.] The simple and yet comprehensive way of representing «
as a sum is to write it as binomial. Now expand 2” as a binomial function, and
we have a series of terms which are ‘‘ wholly functions of the potentiation and
the power.” The differential calculus seeks the relation between these terms and
the original components of z. As we are not concerned with the sum, but merely
with the relation of the terms of the expansion, it would be best simply to
expand (# +7)", and to define the particular “ Potenzenbestimmung” got by con-
sidering the second term of this series as the first derived potence-function of y.
In short, the true mathematical commencement in this part of analysis is no more
than the discovery of the functions determined by the expansion of a power.
We see at once that this is simply an excessively clumsy adaptation of the
method of Lagrange, which is based on the proposition that f (x + 72) can always
be expanded in a series of ascending integral powers of 7, and then defines the
successive fluxions [or derived functions] of 7x with reference to the series.
HEGEL adds to LAGRANGE nothing but confusion, and a degree of vagueness which
is quite pitiable; and, of course, his method has the same fundamental fallacy as
that of LAGRANGE, in so much as /(# +7) cannot always be expanded as LAGRANGE
proposes, or what comes to the same thing, the details of the calculus cannot be
deduced by processes purely arithmetical from the definition (for it is no more)
n n—1
= =nx . Ido not, therefore, think it needful to go into details on this part
of Hecret’s method. The really important point is the use to be made of these
magical “ Potenzenbestimmungen,” which, according to HeceEt, depends on the
discovery of concrete relations which can be referred to these abstract analytical
forms. HeceEt proceeds as follows :—
There is always a fall of one dimension in passing to the first derived function.
Hence the calculus is useful in cases where we have a similar fall in the powers.
We are also to remember that, by differentiating an equation, we get not an
equation but a relation. Whenever, then, we wish to investigate relations con-
nected with any equation, but of a lower dimension, we have room for the cal-
culus. A case in point is the investigation of the relations between the tangent,
subtangent, and ordinate, for example, in a curve of the second degree. These
relations are linear, while the equation contains squares. They depend, there-
fore, on the first derived function (pp. 341, 342, 344).
That such a statement is mere guess work is clear, if we observe that
by a linear relation HrGreL means indifferently the ratio of two straight lines,
or a ratio involving only first powers of w andy. Or, again, since the value
of the radius of curvature is also on HeGeEL’s principles linear, why does
VOL. XXV. PART II. 6 P
508 MR W. ROBERTSON SMITH ON HEGEL
it involve the second derived function? Let us, however, follow our philo-
sopher further. ‘Suppose we have 2az — a” = y’, and take the derived function,
we get a ratio a— ax: y,—a linear ratio representing the proportion of two
lines. The real point is to show that these two lines are the ordinate and sub-
tangent.” This is very plausible, no doubt; but let us try a cubic equation, say
2ax—a2’=y’. Now the resulting ratio, to put it in HEGEL’s way, is 2(a — 2): 3y’.
Is this a linear ratio? Yet it still represents the ratio of the ordinate and sub-
tangent. Clearly Hecren does not know that when 2 and y become definite
; ; E) . "heg ’ :
co-ordinates of a point on the curve the ratio a ceases to be a linear function
of variables in any proper sense, and is simply a determinate fraction. This
mistake augurs ill for the validity of Hrcet’s proof, that the two lines, whose
ratio is the ratio of the derived functions, are really ordinate and subtangent.
But he has Lacrance luckily to help him, who, he says, has entered on the truly
scientific way. We get, therefore, a wordy and loose description, which would be
utterly unintelligible to any one who did not know the thing before, of the way
in which LaGRANGE proves that the line g = fv — af’x + pf lies nearer to the
curve y = fz in the neighbourhood of the point (z, y) than any other straight line
through that point. HrceEw’s confusion is not diminished by the fact, that
LAGRANGE deduces this proposition from a general theorem about the contact of
curves, and originally writes the straight line as g= Fp. This piece of tactics so
puzzles the philosopher that, after all his invective against the differentiation of
linear functions, he allows Lacrance, without rebuke, to write fv = F’a.
In other respects, however, we have great improvements on LaGRaNcE. It
is absurd to write g = a@ + bp* as the equation of the line to be compared with
the tangent, g = pb being quite general. That the line g = dp would not neces-
sarily pass through the given point of the curve at all is, of course, a trifling
consideration !
A still greater improvement regards the process by which LacrancE shows
that we can always find a point (with abscissa 2 + 7), at which g=fx—afax + pf«
shall be nearer the curve than any other assigned straight line. At this point
Hece begins to dread (not unjustly) that the conception of limit, or rather “ das
beriichtigte Increment,” is to be employed. However “this apparently only
relative smallness contains absolutely nothing empirical, z.¢., dependent on the
quantum as such; it is qualitatively determined through the nature of the
formula, when the difference of the moment on which the magnitude to be compared
depends, is a difference of powers. Since this difference depends on 2 and 2”, and
i, as a proper fraction, is necessarily greater than 2’, it is really not in place to say
anything about taking 7 of any size we please, and any such statement is quite
* HEGEL uses p = ag + b, but I keep Lacrancr’s own letters throughout,
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 509
superfluous” (p. 347). One word in explanation of these. LaGrange takes an
abscissa (2 + 2), and gets
fleri=ferife+ Sf @+)),
and
F+t) = Fot+ilo + i FE’ (x@+J);
or for the straight line given above,
== fot @ .
Thus the difference of the ordinates of the curve and straight line with abscissa
2
a+tis > f’'(@+ 7). For any other straight line the difference may be written mz.
Now, the ratio of these increments is it ee J) , which may always be made less
12
than unity by taking 7< Peas . HEGEL, however, asserts that - fF (@+j) < mt,
whenever 7 is a proper fraction, which is an obvious analytical absurdity, and,
in fact, is equivalent to saying that it is impossible to draw a chord to a
curve, the difference of the abscissze of whose points of section is less than unity,
since for the chord through (za, y) cutting the curve again at (v+7),mi=0. In
the face of this absurdity, it is scarcely necessary to add, that Hecen having
resolved to simplify matters, as we saw, by getting his derived functions from
the expansion of (# + 7)", has no right even to form for every curve the expan-
sions on which LaGrance’s proof depends.
I shall, in passing from the subject of geometry, merely enunciate a simple
deduction from HEGEL’s result in an intelligible form. ‘‘ At any point of a curve
there are an infinite number of tangents, which may be got by uniting that point
with any other point on the curve whose abscissa is not different by a quantity
greater than unity.” I present this proposition, which is entirely due to HEGEL,
and in the development of which my share has been “ purely mechanical,”’ for
the admiration of all Hegelians whatsoever.
HEGEL’s account of the application of the calculus to mechanic is much briefer,
and presents less interest after what WHEWELL has written on a connected point.
I cull only one or two illustrative points. For the purposes of the calculus,
HecEL classes motion as uniform, uniformly accelerated, and motion returning
into itself, alternately uniformly accelerated and retarded. Variable acceleration,
which in the form of harmonic motion is by far the most common in nature, is
quite ignored.
Again, criticising the assertion that = represents the velocity at any point of
a course, he tells us that it is “ schiefe Metaphysik” to speak of the velocity at
the end of a part of time. ‘‘ This end must still be a part of time; if it were not,
5210 MR W. ROBERTSON SMITH ON HEGEL
there would be rest, and no motion; velocity can be measured only by the space
passed through in a definite time” (p. 352).—An appeal to Atrwoov’s machine
would probably be too ‘‘empirical” for our philosopher, but the law of energy
might surely convince HEGEL of the reality of a variable velocity dependent on
potential energy lost or gained. It is clear, at least, that HecxEt lacked the first
elements of physical notions, and these were not likely to be supplied by the
method of LacrancEe to which he adheres, beginning with s=/¢, and deducing
every other consideration by differentiation.
The following criticism on a remark of LAGRANGE is splendid :—“ We find,
_ says LAGRANGE, the motion represented by s=a?@’ in the actual fall of bodies. The
next simplest motion would be s=cé’, but nature shows no such motion, and we
do not know what ccould mean.”’ [The ground of this is, of course, to be found
in the law of the conservation of energy.| “If so, we have at least a motion
whose equation is s’=at’,—KeEpLer’s law of planetary motion; and here the
: . Lat ; ;
investigation of the first derived function sa , &c., the direct treatment of this
equation by differentiation, the development of the laws of that absolute move-
ment from this starting point, must certainly be a most interesting task, in which
analysis would appear in the brightest splendour ”[!]. That ¢ and s in KEpLer’s
law are not variables, but constants determined for each planet ; that the equation
has no analogy whatsoever with the equation of motion; that its differentiation
would be meaningless unless space were filled with planets; and that then it
would have nothing to do with “the determinations of that absolute motion,”
are considerations that never entered HEGEL’s head.
It is rather hard that, from a metaphysical stand-point, a man is still allowed
to write about things he has not studied; and more than this, that men so able as
Dr SrirLine should be found imploring great mathematicians to come and read
such utter nonsense as naturally results from the attempt. Certainly Hecrn’s
fame is not likely to rise higher the more his notes on the calculus are studied ;
for these notes show quite clearly—irst, substantial ignorance of the subject in
hand, bolstered up by some hasty glances at the “literature of the subject;”
secondly, great disingenuousness in criticising NEwTon, without having ever given
his views a careful study; thirdly, almost incredible confusion of mind, in so far
as he seems to have thought that he knew his own meaning when he really had
no meaning at all; and dastly, to add nothing more, such a degree of self-compla-
cent arrogance as led him to fancy the results of his “ half-hour” more valuable
than the fruit of the whole life of men like NEwron.
This paper has already grown to such a length that it seems better to say
nothing of HEGEL’s remarks on integration in the closing pages of his second note
on the calculus, or of the third note, in which he treats “some other forms con-
nected with the qualitative determination of quantity.” The subject, in fact, has
AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 511
a purely adventitious interest, and no one will care to linger longer over such a
mass of confusion, both as to language and thought, than is absolutely necessary
in self-defence. And the preceding pages may perhaps suffice to show that he who
would exchange Newton’s clear ideas, based on nature’s own showings, and
alike removed from shallow empiricism and self-conceited dogmatism, for the
vague pomposities of a HEGEL, exchanges
xpicea XaAkelwy, ExaTouBor évveaBolar.
VOL. XXV. PART IT.
( 513°)
XIV.— Observations on New Lichenicolous Micro-Fungi. By W.LAupER Linpsay,
M.D., F.L.S., &c. (Plates XXIII.—XXIV.)
(Read 19th April 1869.)
In the course of my studies on the Microscopic Anatomy of Lichens, during
the last fifteen years, I have frequently met with various more or less minute
Parasites—mostly black and punctiform or papilleeform—sometimes disciform or
maculeeform—affecting either the thallus or apothecia of lichens, or both thallus
and apothecia. They grow equally on foliaceous and crustaceous lichens,
especially of the following genera:—Parmeiia; Physcia; Umbilicaria; Solorina;
Peltidea ; Nephromium; Sticta ; Stereocaulon; Usnea; Neuropogon; Cladonia;
Beomyces; Squamaria; Placodium; Lecanora; Pertusaria; Thelotrema ;
Lecidea ; Graphis ; Endocarpon ; Verrucaria.
Most of these Parasites occur on lichens in my own Herbarium, collected by
myself in 1856; or on lichens sent me for examination and determination by
various British lichenologists between 1856 and 1858. They were examined, and
described with figures in my Herbarium Note-books, between 1856 and 1859;
in most cases without the assignation of names. I have not hitherto published
their descriptions, or assigned names, for a variety of reasons, and especially on
account of the difficulties which appear to me* to surround the determination
of what, to any single observer, seem to be (so-called) ‘new species.”” Hence the
parasites in question have been accumulating in my Herbarium, and their descrip-
tions in my Note-books, for twelve years or upwards; and they now form a large
and interesting, though obscure and puzzling, group of microscopic plants. I
cannot, however, quote them in a Memoir I have in preparation on the Spermo-
gonia and Pycnidia of the lower lichens (with which Spermogonia and Pycnidia
the said parasites are frequently apt to be confounded) without placing their
description—and, in certain cases at least, their names—on record in a form con-
venient for future reference. Nor can I otherwise contrast with them various
groups of Lichenicolous Micro-Lichens,} Micro-Fungi, or Micro-Algze, which have
been described by other authors, or having been observed are yet to be described by
myself. Inasmuch, moreover, as the said descriptions and names have not been,
so far as I am aware, published by other authors—-whether fungologists or
* Vide Author’s ‘ Contributions to New Zealand Botany,” 1868, p. 22; “ Otago Lichens and
Fungi,” Transactions of Royal Society of Edinburgh, vol. xxiv, p. 407; “Parasitic (lichenicolous) Micro-
Lichens,” Quart. Jour. of Micro. Science, January 1869; “ Polymorphism in Fructification of
Lichens,” Quart. Jour. of Micro. Science, January 1868,
{ E.g. “Enumeration of Micro-Lichens parasitic on other Lichens,’’ Quart. Jour. of Micro.
Science, January 1869.
VOL. XXV. PART II. OR
514 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
lichenologists—I can no longer hesitate in contributing to botanical science the
following observations on the structure and place in classification of the Micro-
Parasites referred to.
In the earlier years of my lichenological studies, I examined microscopically,
with the greatest minuteness, large numbers of lichens for different collectors, from
various parts of Britain and Ireland. I gave much more attention to the con-
tents of other Herbaria than to those of my own; and to this circumstance, along
with my reluctance to describe and name “ new species”—a hesitancy to ‘“‘ rush
into print” with accounts of mere novelties, real or supposed—I owe the fact
that many of my own gatherings in different parts of the world—many of the
original observations recorded in my MSS.—have been published to science, with
the stamp and éclat of novelty, by other—mostly continental—lichenologists.
This, however, I do not regard as subject for regret. Much more important than
the mere discovery and nomenclature of so-called ‘‘ new species” —only a small
proportion of which has any claim to permanent rank as species—is, I think, the
proper classification of existing material, so as to render additions to our know-
ledge capable at once of estimation at their proper value, and of absorption and
assimilation in their proper place. So far as regards descriptive or systematic
lichenology, my own aim has always been and still is to arrange on a simple
plan of classification the data already accumulated, so that they may be readily
accessible and intelligible to the student. My own studies in lichenology are and
have been preferentially biological; regarding as I do questions affecting (¢.g.) the
physiology and anatomy, affinities and uses, of lichens as of higher interest than
the mere collection and nomenclature of varieties or species’!
The lichenicolous parasites above-mentioned are partly of the character of
true lichens, partly of true fungi; while many partake of, or possess, the characters
both of lichens and fungi, and can be appropriately referred only to the inter-
mediate group of fungo-lichens.* In the present communication I confine myself
to the two last-named groups—to Parasites which are either true fungi or fungo-
lichens. All of them require for proper examination the microscope, and most —
of them are distinguishable only under the lens. Very few, such as Coniothectum —
sometimes, are sufficiently large to be visible to the naked eye. All are rendered
more conspicuous by moisture, which frequently converts punctiform into papille-
form perithecia, and flat surfaces into convex ones.
In determining the genera under which to arrange the parasites hereinafter.
to be described, I have availed myself of the opinion, kindly accorded, of two of
the most competent British Fungologists, who have at various times examined
certain of the said parasites at my request, viz., Rev. M. J. BerKevey, F.L.S.,
and FRep. Currey, F.R.S. While agreeing with these distinguished fungologists
* Vide Author’s “ Otago Lichens and Fungi,” p. 434, and Arthonia melaspermella, Journal
of Linnean Society (Botany), vol. ix. p. 269.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 515
in many, I do not profess to agree with them in all, respects. When they claim
parasites as indubitable fwngz, I have no hesitation in accepting their determina-
tions, as I have done (e.y.) in the case of various organisms referred by Mr CurREY
to Torula, Conivthecium, and Spheria. While agreeing with Mr BERKELEY as to
the close alliance between the fungi and lichens,* I cannot subscribe to his views
of the place in classification to be assigned to various members of the group of
fungo-lichens.+
Many of the lichenicolous parasites hereinafter described belong to the Torw-
lacei—to the genera Torula and Coniothectum. The majority of the remainder,
which are confessedly most heterogeneous, I arrange provisionally under the
genus Microthelia, adopting this genus only in the sense elsewhere and already
explained.{ The parasites in question are, in a manner at least, hereinafter
systematically described in detail, their variations especially being made the
subject of exposition. But here it is desirable to make certain preliminary
general observations regarding the more prominent of their features
1. Genus Torula. §
What I hereinafter describe as 7’. lichenicola varies considerably in its internal
characters. In particular the spores are not always simple. Nevertheless all
the forms described appear to me to be referable to asingle type or species.
Externally, 7. lichenicola shows little diversity of form. It is black, punctiform,
and superficial, resembling in this respect, and apt to be confounded with,
(a). Spermogonia and of many lichens, especially when intermixed
(6). Pycnidia therewith.
(c). Many minute parasitic lichens belonging to such genera as Verrucaria
and Endoccocus. ||
(d). Many minute parasitic fungo-lichens belonging to the provisional genus
Microthelia.
* In various letters Mr Berxerey has expressed himself as follows :—“ So convinced am I of
the near relation of lichens and fungi that in the portion of my ‘ Introduction to Cryptogamic
Botany,’ which is printed, I make one division, Mycetales, to include Fungales and Lichenales”
(July 1856). . . . “One or two Verrucarie are so near Spheri@ that it is almost impossible to
draw the line” (Dec. 1856). . . . “It is quite impossible to distinguish some lichens from fungi,
and I consider the whole series as a division of fungals” (Feb. 1869). I hold quite as decided an
opinion as to the impossibility of distinguishing many lichens from many fungi; or, in other words,
of referring members of the group of fungo-lichens to the group of fungi rather than to the lichens!
But I regard any classification, which arranges lichens as a co-division with fungi of a group of
Jungals, as imperfect, artificial, and arbitrary, excluding as it does the equally close alliance that
subsists between lichens and Alga.
+ His views and my objections are fully given in a subsequent part of the present memoir
(pp. 528-580).
¢ “Otago Lich. and Fungi,” p. 436; Arthonia melaspermella, p. 279.
§ As determined by Mr Currey, who wrote me in February 1866 as to “a curious species of
Torula” (contained in my Herbarium) “ which I do not recognise as having seen before. It is ramose,
with bluish or greenish-black joints, the cells of which measure from 00003 to 0 0005 inch.”
|| £.g. those described in Korper’s “ Parerga,” p. 452, et seq.
516 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
(e). Many minute parasitic fungi, belonging especially to the genus Spheria.
(f). Certain members of the pseudo-genus (of lichens) Pyrenothea.
(g). Granules of coal dust, or other morganic foreign bodies.
From all of these the Toruwia is readily distinguished on microscopical examination,
more especially by the presence of its peculiar spore-chains or filaments. There is
no complete perithecium; but the basa] cellular tissue, from which spring the spore-
filaments, and which is generally sub-immersed in the host, is indistinguishable
from that which constitutes the envelope or perithecium in many lichens, fungi,*
or fungo-lichens, and their spermogonia or pycnidia. The cellular tissue in
question is most frequently of an indigo colour, or bluish or bluish-black, though
sometimes also it is brownish; not varying, however, in colour to so great an
extent as do the spores. The free surface, which is granular or powdery, consists
of spores separated from their filaments, and of the apices of the spore-filaments,
which are closely aggregated, just as are the sterigmata or basidia in lichen or
fungus-spermogonia, and pycnidia. In the young state, these filaments are
simple hyaline tubes, resembling the simple paraphyses of many lichens, broader
or thicker at the distal or free end, tapering into a thread-like pedicle at the lower,
basal or proximal extremity. Gradually, however, articulations appear, beginning
first at the distal end; and colour is added, the filament increasing in volume.
The filaments then resemble the articulated paraphyses of many lichens, e@y.,
Lecidea lenticularis, Fr. Usually in maturity four or six articulations are formed,
and gradually thrown off one after another from the distal end as free spores.
Sometimes only one or two articulations are developed. The spore-filaments
necessarily vary considerably in length, but less so in breadth. Some filaments
appear to be abortive, and maintain throughout the simple or non-articulated,
colourless character; not even increasing in length. These sterile filaments are
intermixed with the fertile ones—just as sterile sterigmata—in this case gene-
rally elongated and ramose, and exceptionally articulated or pseudo-articulated,
frequently accompany the fertile ones in the spermogonia of many lichens.t
Occasionally there is atrophy of certain articulations, which then assume the
character of threads connecting the normal spores. The distal half of the spore-
filament is generally coloured, though the colour is sometimes faint or excep-
tionally absent. Where colour exists, it is always deepest at the distal or free
end—in the terminal articulation. This colour is most frequently bluish (indigo
or with a blackish shade); but sometimes it consists of various shades of olive
or brown. The colour of the spore-filament is that also of the articulations of
which it is composed. The colour of the spores is much more variable than their
* E.g. Dichena rugosa, Fr.
+ Vide author’s “Memoir on Spermogones and Pyenides,” Trans. Royal Society of Edinburgh,
vol. xxil, plates iv. v. vi. vii. vill. Xi. xii,
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 517
dimensions or form. The proximal articulation is frequently colourless, while
the terminal one is deeply coloured. In size the articulations always vary on the
same filament—the oldest or terminal one being the largest—the younger being
at least narrower in proportion to their youth. Thus the terminal spore is
frequently twice as large as the proximal one, the increase in dimension relating
to breadth rather than length. In maturity, and when free—thrown off from
their filaments—there is much less difference in the form and size of the spores.
In form they are generally oblong, with flattened ends, unless in the terminal spore,
which has its free or upper end rounded, even while attached to the filament.
Occasionally the corners of all the free articulations or spores are similarly
rounded. Sometimes the spores are oval or ellipsoid. Their length is generally
‘ about 00025”. In structure they are usually simple, with or without double con-
tour; sometimes, though rarely, granular; occasionally also having a central sep-
tum, or faint indications of the existence of one or more septa; more frequently
containing one or more (two to three) spherical nuclei. Where there are two nuclei,
they are generally arranged near the poles or extremities of the spores, to which
they sometimes then give a sub-physcioid aspect, that which occupies the distal
end of a spore being always the larger. This bi-nuclear character may attach to
all the spores in a given specimen; and then, as well as in other cases, the spores
in question resemble many lichen-sporidia. Sometimes chains or groups of spores
of equal size and uniform character occur in numbers of four to eight, apparently
the result of agglutination after maturity, and gaining the free state. In some
cases the concatenate condition might be supposed to arise from simple absorp-
tion or disappearance of the pedicle of the filament; but in such a case the
constituent articulations would probably retain, even in age, their differences in
size. The site of Torula lichenicola is the thallus or apothecia (or both) of various
lichens, mostly crustaceous, and belonging to the Lecanorw or Lecidew. It is
much more common in Lecanora subfusca than in any other species in my own
experience; and it is so markedly more common on Jrish specimens of that
Lecanora—mostly from the vicinity of Cork—as to give rise to the supposition
that there may be some connection between the greater frequency of the parasite
in Ireland and the (alleged) greater moistness of the climate of that country.
There is, moreover, a frequent connection between the growth of the parasite and
degeneration of the thallus or apothecia of the host; sometimes at least, obviously
as productive of degeneration, ¢.g., when the Torula overspreads the disk of
L. subfusca, rendering it as black as that of Z. atra. On the thallus of lichens it
may be scattered generally over the surface; or only over particular parts thereof,
é.g., the periphery, or it may occupy only the areole or verrucee. On the apothecia
it may occur only on the disk, or both on the exciple and disk. The apothecia
affected by the parasite are frequently degenerate or deformed; the disk has
sometimes disappeared, and the whole apothecium has acquired an irregularly
VOL. XXV. PART II. 6s
~
518 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
verruceeform character. But in this case the degeneration appears to be quite
unconnected with the growth of the parasite, which equally affects the thallus
and apothecia, whether healthy or diseased, normal or deformed. The parasite
may be scattered ; or closely aggregated, becoming confluent and maculeform;
or it may be copiously studded over the apothecia, and sparingly on the thallus
of the same species, or vice versa, though the former arrangement is the more
common. Generally there is a marked contrast of colour between the parasite
and the whitish or greyish thallus, brownish or reddish disk of the apothecia,
which it so frequently affects. Necessarily the Torula is most conspicuous by
reason of this contrast, where the thallus and disk of the host are pale—whitish
in the one case, and brownish in the other. Its structure is essentially the same
on whatever lichen it be parasitic. In one case I found it occupying the cavity
of spermogonia (in Lecanora varia).*
2. Genus Coniothecium.
There are various points of resemblance between Coniothecium lichenicolum
and Yorula lichenicola. In both cases the parasite is black, and is conspicuous
from contrast of its colour to that of the pale (or whitish) thallus on which it
so frequently occurs. In the Coniothecowm the basal cellular tissue is the same.
There is no complete perithecium; the granular or powdery surface consists of the
free spores, which possess deep and dirty colours, mostly brown, though some-
times blackish or olive. In the young state only is the Coniothecium papilleeform
or verrucarioid, in which condition it may be confounded externally with Torwla,
or with the various organisms with which the Zorula may itself be confounded.
But there is a greater number of points of difference between these two common
lichenicolous parasites. While Torula mostly affects corticolous lichens in the
fertile state, Coniothecium affects only saxicolous Lecanore in the sterile, and
frequently isidioid or other degenerate or hypertrophic, condition. In maturity,
moreover, Conzothecitum is much larger, and more conspicuous—visible for the
most part to the naked eye. It is largish and flattish, discoid or lecidioid,
resembling some forms of the pseudo-genus (of lichens) Spz/oma, as well as the
parasitic Spilomatic fungi—Spilomium Graphideorum, and Gassicurtia silacea.
It varies considerably in size, surface, and outline; in the old state frequently
resembling soot-spots. It is apt to be confounded witli the apothecia, especially
when they are sub-degenerate, of various saxicolous Lecidew; and the character
of the spores is sometimes such as to assist in this confusion. These spores are
typically, in the young state, spherical and single; but they gradually acquire a
sub-cubical form, and are associated in groups—sometimes most irregular in out-
line—of two, three, or four, the form of the constituent spores then undergoing
* Vide p. 520, and foot note ft.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 519
change from mutual pressure. Their colour is usually in maturity and age a deep
blackish-brown ; but in the young state they may be pale, or even colourless;
while in older conditions they may be olive, with a blackish tinge. When aggre-
gated in groups of two, if the form of the constituent spores remains compara-
tively regular, they may be indistinguishable from some figure-8-shaped lichen or
fungus-sporidia. Hence, in one case, among the parasites hereinafter described
(the Mangerton plant),* it is difficult to determine whether it is Coniothecium
lichenicolum or a separate parasite. Sometimes the spores are concatenate,
as in Torula ; but they are at once distinguished from those of Torula by their
breadth being greater than their length, as well as by their sub-cubical form.
When in aggregates of four, the spore-groups resemble wool-pack-like or Sarcina-
like cubes. When in threes, as well as sometimes in twos or fours, they are very
unlike spores, and are apt to be mistaken for fragments of cellular tissue, such
as that which constitutes the perithecium of many of the lower lichens and
fungi Whether simple or aggregate, the spores always exhibit double contour,
presenting the aspect of being thick-walled. The Coniothecituwm may be scattered,
as it generally is, or grouped; very rarely it is closely aggregated or even con-
fluent. The thallus, which it affects, is frequently so altered—apart, however,
from the growth of the parasite—that, in the absence of apothecia, it is impossible
to determine the species to which it is referable. It appears generally, if not
always, to belong to Lecanora, and, at least frequently, to the species ¢artarea,
parella, and glaucoma.
3. Genus Microthelia.
The parasites, which I have provisionally grouped in this pseudo-genus,{ are
confessedly most diverse in character, though they possess certain characters in
common. For the reasons elsewhere set forth,§ I think there is an advantage
in considering them as a group until their characters are more fully known and
understood. Their common or general characters are the following :—
Most of them are microscopic, like Torula; black, papillzeform or punctiform.
The papillzeform or verrucarioid condition is always rendered more distinct by
moisture. Sometimes they are flattened and discoid, lecidioid or arthonioid (e¢.g.,
the parasites on Lichen dactylinus, Lecidea pachycarpa, and L. albo-atra). Some-
times they are maculeeform ad initio (e.g., the parasites affecting Squamaria crassa
and S. saxicola); at other times the macule are produced by the confluence or
aggregation of minute papillz (as in the parasite affecting Parmelia perlata).
* (b) P. 540,
t I have seen true Lichen-sporidia by cohesion acquiring characters closely resembling those
concatenate and woolpack-like forms of the spores of Coniotheciwm lichenicolum (pl. xxiii. fig. 28), ¢.g.,
in Lecidea dubia, T. and B., Leight. Exs. No. 88. In several other cases, I have met with Lichen-
sporidia cohering in such manner as to resemble cellular tissue, ¢.g., in Verrucaria subalbicans,
Leight, Exs, No. 200.
t Vide p. 515, and foot note +. § “ Otago Lich. and Fungi,” p. 436.
520 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
Their size varies in the same species, but mostly with age. As to site, they affect
the thallus or apothecia, or both; sometimes the under as well as upper surface of
the apothecia. They are, like Torwla, more frequent on fertile than sterile lichens.
As in Torula and Coniothecium, they are conspicuous where the colour of their
host is pale. As in these parasites also, they may be few or numerous, scattered
or aggregated, discrete or confluent; in the latter case becoming maculeform.
Externally, they frequently resemble Torula and Coniothecium, or the organisms
with which they are apt to be confounded; as well as certain young lichen-
apothecia, belonging to the Lecidew, e.g., Abrothallus Smithit and oxysporus.
Generally only the base is immersed in the host, but sometimes the body of the
perithecium is immersed, only the apex or ostiole projecting above, or being visible
on, the surface of the host. The envelope or perithecium is in all cases the same,
consisting of brown cellular tissue; frequently, if not generally, the cells being sub-
hexagonal. The Microthelic are sometimes associated with, if not productive of,
deformities or degenerations of the thallus or apothecia of the lichens on which
they grow (¢.g., M. Stereocaulicola, M. Beeomycearia, and the parasite which
affects Sguamaria saxicola as Torula does Lecanora subfusca).
Their internal structure varies considerably. Some of them are verrucarioid,
in so far as they possess sporidiiferous asci, with or without paraphyses. Where
paraphyses exist, they are either very delicate, filiform, more or less indistinct,
without thickened or coloured tips; or they appear as a mere striated jelly. The
asci are frequently saccate, as in Arthonia; short and broad, not tapering below
into a pedicle. |
In another group, no asci, paraphyses, sterigmata, nor basidia, were visible, so
that it was impossible to determine whether the contained reproductive corpuscles
are to be considered sporidia, spores, stylospores, or conidio-spores. Probably
in the majority of cases they are really sporidia contained in asci.
In a third series, the perithecia are quite sterile, containing no reproductive
structure. Some of these parasites may prove to be mere pycnidia analogous to
Phoma, Septoria, Diplodia, and Spheropsis. At least one of the parasites grouped
under Microthelia possesses pycnidia in addition to sporidiiferous perithecia, viz.,
that affecting Thelotrema lepadinum.
In certain exceptional cases, the same perithecium contained not only
sporidiiferous asci, but stylospores and basidia; and in one instance ramose
filaments, resembling the hypertrophied sterigmata of many lichen-spermogonia*
(eg. the parasites accompanying Verrucaria epidermidis v. analepta, and
Lecanora pyracea). Parallel phenomena are the occurrence of sporidia and
spermatia in the same perithecia in Verrucaria atomaria and Spheria Lindsay-
ana, as seen by myself, and in a certain section of the Verrucarie as described
* Vide p. 516, and foot note +.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 521
by GrpeLui.* This observation is one obviously of much interest in regard to the
physiology of reproduction, and of the reproductive organs, in lichens. I doubt
not that careful observation will yet multiply the number of instances in which
different forms of reproductive corpuscles exist in the same peritheciwm or organ.
It may be provisionally convenient to classify the parasites grouped under
Microthelia, according to the character of their contained reproductive corpuscles,
as follows (omitting any specific mention of those whose reproductive structure
is imperfect, and which are, therefore, for the present indeterminable) :—
Sporidia, or reproductive corpuscles—
1. Simple. For the most part spherical and brown.
Microthelia atricola. Parasites on (c.) Graphis scripta,
Spilomium Graphideorum. (d.) Pertusaria.
Gassicurtia silacea. Parasites accompanying
Parasites on (a.) Opegrapha atra.
(a.) Lecidea rupestris. (b.) Abrothallus Smithi.
(0.) L. sanguinaria v. affinis. (c.) Pyrenothea verrucosa.
2. 1-septate (=bilocular).
A. Brown, in maturity; frequently or generally soleaforim.
Microthelia Stereocaulicola. Parasites on
rugulosaria. (c.) Squamaria crassa.
Stictaria. (d.) Endocarpon microsticticum.
parietinaria. (e.) Usnea barbata v. florida.
Parasites on (f.) Lecanora pyracea.
(a.) Lecidea pachycarpa. Parasite accompanying
(b.) Thelotrema lepadinum. Verrucaria fusiformis.
B. Colourless or yellowish; sometimes szmple.
Microthelia Cookei. Parasites on
Parasites on (c.) Lecidea Hookeri; colourless.
(a.) Lecanora cenisia; brownish- (d.) Verrucaria Garovaglii; colourless.
yellow. Parasites accompanying
(b.) L. polytropa v. intricata; Verrucaria epidermidis v. analepta;
sometimes simple; colourless colourless.
or yellowish.
* So long ago as July 1856, Mr Berxetey wrote me—‘ You are aware, probably, that in a
species of Tympanis, Mr Broome and myself have seen on the same hymenium the spores of a Diplodiu
and true asc. TuLasne doubts Mr Broome and myself having seen stylospores on the paraphyses
of a lichen. Nothing, however, was more clear and free from illusion. Almost in the same breath
TuLAsveE calls in question the correctness of Hooker and Bazineton’s observation. He should not do
this. I sent Turasnz the very section we had seen the stylospores of the lichen in, but he could see
nothing. Unfortunately, there were but two or three scattered apothecia on the roots of Ammophila,
sent for a fungus by Gaxpiner. I have in vain tried to get more from the same locality.” (Vide
also my “ Monogr. Abrothallus,” p. 55; Ny tanper’s “ Prodromus,” p. 55; BerKexey’s “ Brit.
Fungology,” p. &7, plate i. fig. 18.)
In December of the same year Mr BerkeLEy again wrote me (in regard probably to Abro
thallus Smithii)—“ In American specimens of your plant I sometimes find asci, sometimes naked
spores, which have the same relation to the asci that the stylospores of Diplodia to the asci of the
Spheria to which they belong. Whether the production in question is a lichen or fungus is a knotty
point. It grows on living burk, and therefore should be a lichen !”
VOL. XXV. PART II. 6T
522 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
3. 1 to 3-septate, mostly 3-septate and brown; sometime colourless.
Microthelia vesicularia; 1—3 septate. Parasites on
Umbilicariz; 1- sometimes (a.) Physcia ciliaris.
2-septate. (b.) Lecidea lurida.
Nepromiaria; colourless. Parasites accompanying
Beomycearia, (a.) Lecidea ferruginea v. sinapisperma.,
(b.) Verrucaria Taylori,
Any such classification, however, is obviously artificial and defective; for not
only in the same species, but in the same individual, the sporidia frequently vary
much in character—in size, form, colour, and structure. In particular, they are
frequently both simple and compound, colourless or coloured, of regular or
irregular outline—according to the stage of growth. The “character” selected as
the basis of classification must, therefore, be that which is presumed to prevail
in maturity, and in normal conditions of growth. But what is prevalent or
normal in one district or set of circumstances is not so in another, especially if
the district or circumstances in or under which one systematist works are very
diverse from those of others. There is, therefore, in such cases no precise or
permanent basis of classification; whence it follows that the classification itself
must be faulty. These remarks apply to too many modern “ classifications” of
lichens, based on the characters of the sporidia alone, or on any single ‘‘ characters”
or combination thereof !
In the group of parasites hereinafter described under Microthelia, the Iodine-
reaction, which by fungologists is considered /ichenoid, denoting the presence of
lichenine in the lichen-tissues, is generally absent. In the parasite accompany-
ing Verrucaria epidermidis v. analepta, however, the asci give a blue reaction with
iodine; in Microthelia Stictaria they become deep violet; in M. Umbilicaric the
asci and hymenial gelatine assume various shades of violet; while in J.
Nephronuaria the hymenial gelatine becomes violet. These exceptional reactions,
however, neither prove nor disprove in themselves that the parasites, in which
they occur, are lichens or fungi ; for, as I have elsewhere* sufficiently shown, this
so-called lichenoid reaction occurs in indubitable fungi ; while there are many
true lichens destitute of any colour-reaction—indicative of the presence of starch,
or its varieties or allies—with iodine.
Lodine-reaction is a subject of so great (supposed) importance in relation to
the differential diagnosis between lichens and fungi: and as a “character” it
bears so intimately on the place in classification to be assigned to the group of
fungo-lichens, and to the members of the provisional genus M/icrothelia, as adopted
or established by me, that it requires here some additional consideration. Asa
ground for regarding it as a diagnostic ‘‘ character,” it appears to me necessary,
* Arthonia melaspermella, p. 283; “Otago Lich, and Fungi,” p. 423; “Parasitic Micro-
lichens.”
:
4
!
q
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. a23
in the first place, that we should possess some trustworthy information as to the
chemstry of the reaction, and as to the nature of those substances which, in
lichens and fungi respectively, yield colour-reactions with iodine. As regards
the lichens, I have carefully studied the most recent and approved standard works
in chemistry; and the result is, that I find a discrepancy and confusion of asser-
tion and opinion among chemists, nearly as great as that which exists between
lichenologists and fungologists in regard to the application of the test, or of its
colour-reaction, as a botanical ‘“ character.”
So far as I have been able to ascertain, the substances occurring in lichens,
which give colour-reactions with iodine, of the class which is now under review,
are the following :—
I. Starch or its modifications.
A. Lichenine, Syn. Lichen starch, Lichenic acid. Formule, C,H,,0,. C,,H,,0,,
(GrEecory).* Has been examined by chemists as it occurs in Cetraria Islandica
and aculeata, Sticta pulmonaria, Ramalina fraxinea, Usnea barbata, Physcia
parietina.
Chemical characters.—Isomeric with starch. In C. Jslandica does not occur
in granules; but is uniformly distributed through the tissues in a soluble con-
dition. Pure lichenine is merely coloured yellow by iodine; but a green or blue
is often produced from admixture of starch (Wart).+ A colourles jelly ‘‘ some-
times assumes a dlue, and sometimes a greenish tint,” with iodine (Gorup
BESsANEZ).{ Gives with iodine a greenish-brown colour (KaNne).§ ‘Its solu-
tion is not coloured by iodine; but the jelly is rendered blue by that test”
(GreGoRY). Other authors describe the reaction with iodine as blue, and this is
the reaction (generally) assumed by lichenologists as the basis of theirlodine-
testings.
B. Jnuline, Syn. Dahline, Alantine, Menyanthine, Datiscine|| (GrEGoRy).
Formule, C,,H,,0,, (GREGoRY), C,,H,,0,, (PARNELL). Has been examined as it
oceurs in Cetraria Islandica in association with lichenine.
Chemical Characters.—Also isomeric with starch. Occurs in white, crystal-
line grains. Sparingly soluble in cold, very soluble in hot, water. Iodine colours
it slightly brown (GreEGoRY). Insoluble in alcohol. Not blue, but yellow, with
iodine (MILLER).
C. Starch. Formula, C,,H,,0,,. Has been examined as it occurs in Rama-
hina fastigiata (in large quantity); and Cladonia macilenta, digitata, and uncialis
(Watt). It does not quite clearly appear whether this is ordinary starch in its
* « Handbook of Organic Chemistry,” 4th edition (1856).
+ “Dictionary of Chemistry,” 5 vols. (1860-68).
¢ Quoted in ‘‘ Chambers’s Encyclopedia,’ 10 vols. (1860-68).
§ “Elements of Chemistry,” 2d. ed. (1849).
|| Mrzxer (‘‘ Elements of Chemistry,” 2d ed., 1862, p. 597”) gives Datiscine (=C,,H,,0,,),
as the colorific principle of Datisca cannabina—not as a starch !
524 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
ordinary form. ‘There is asubstance in lichens that gives a beautiful and deep blue
reaction with iodine; and if chemists are correct in asserting that such a reaction
is indicative of the presence of free starch in its ordinary form, while lichenine
and inuline give yellow or brown colours to the reagent, we must admit that
common starch not only occurs in the lichen-tissues, but that it is sometimes
associated with, and at other times substituted for, lichenine and inuline.
Il. Gum, or its modifications.
Gum has been examined as it exists in Lecanora parella. Gives a greenish-
blue with iodine (ScHuNcK). Ordinary gum (= Arabin) is not altered in colour
by iodine; but the modification thereof known as Bassorin gives blue and red
reactions (MILLER, p. 109).
Were we to accept as a trustworthy basis for our conclusions the foregoing
assertions of chemists, we would deduce that in lichens occur several forms or
modifications of starch and gum that give reactions with iodine, variously blue,
red, or brown, or admixtures of these shades, especially green. But it is impos-
sible to accept as proper bases, on which to found diagnostic characters, state-
ments so contradictory. The conclusion to be drawn is rather that chemists are
yet ignorant in great measure of the composition and character of the muci-
laginous and other components of lichens; and that at present they probably
confound substances of somewhat dissimilar character. Thus the character of
the iodine-reaction leads to the suspicion that what ScuuncK describes as a gum,
may be in reality a starch!
It by no means follows that the same reagent should produce the same colour-
reaction in the same species of lichen, whether it is applied by the chemist in
the laboratory to the separated amylaceous or mucilaginous principles, or by the
lichenologist in his library to microscopical sections or preparations of the
hymenium or other tissues. On the contrary, what we know of other colour-
developments in lichens would lead us here to expect a certain difference in
result; and, in point of fact, there 7s such a difference. And, further, differences
of result in the same species, when iodine is applied as a test in microscopico-
botanical diagnosis, arise in the hands of different experimenters from circum- —
stances sometimes apparently most trivial, ¢.g., the strength or character of the
iodine solution, the age or other conditions of development of the specimen
operated on. I need not, however, further pursue or illustrate the subject here,
having pointed out in detail elsewhere the sources of fallacy and the causes of
difference in the colour-reactions of lichens as supposed botanical characters.*
The substances or tissues in lichens, which yield colour-reactions with iodine,
are chiefly—(i.) The hymenial gelatine or mucilage, which has hitherto been
* “On Chemical Reaction as a Specific Character in Lichens,” Journ. of Linn. Soc. vol. xi.
(Botany), p. 86; and “ Experiments on Colour-reaction as a Specific Character in Lichens,” Trans.
Botanical Society of Edinburgh, vol. x.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 525
generally assumed to be, but on insufficient grounds, lichenine; (2.) The asci;
(3.) The sporidia; (4.) The medullary or other tissues of the thallus. Excep-
tionally colour-reaction may occur in other tissues. I have, for instance, met
with a blue reaction from iodine in the interior structure of the spermogonia
of Abrothallus oxysporus (Birnam, June 1856). The commonest iodine-reaction,
that with which lichenologists have to do as a botanical character, is that of the
hymenial gelatine,* in which are imbedded the asci and paraphyses; and of the
asci themselves, on which the reaction is generally the most intense. Typically
this reaction is a beautiful Prusszan-blue; that is to say, it has been generally
regarded by continental lichenologists as what NyLanpER calls a “ Nota
lichenosa,”—a diagnostic “character” of lichens as contra-distinguished from
fungi. But this blue is not always exhibited in different specimens of the same
species, nor even in the same specimen at different times; it may, moreover, be
faintt or fugacious. Ina large number of lichens, instead of blue, the colour-
reaction with iodine is violet, red, brown, or yellow; while in another large group
there is no colour-reaction! Thus, in the genus Verrucaria, as defined by
NYLANDER (in his “Lich. Scand.” p. 266), iodine developes in the hymenial
gelatine of
(a.) One section—the supposed typical or lichenic reaction.
(6.) In another section—a wine red.
(¢.) In a third section—a faint bluish or reddish tinge.
(d.) In a fourth section—no reaction. t
To which it may be here added, that some Verrucarie have no paraphyses, while
in others they are distinct; but, are always (where they exist) more or less
graceful, delicate, and filiform. Further, different tissue-constituents of the same
lichen, or different parts of the same organ, give frequently different colour-
results with the same reagent.
These irregularities in colour-reaction may be conveniently and sufficiently
illustrated by the following selection of quotations from the record of my micro-
scopical examination of the lichens contained in the published Fasciculi of Sco =RER
(Switzerland), NyLanper (France), and LeicuTon (England). The advantage of
using published Fasciculi is, that a standard of comparison is secured accessible
* The term, “ gelatine” or “ mucilage,” is here used, and by lichenologists generally, in a popular,
not in a strictly chemical, sense; for it has already been shown that the so-called “gelatine” may
really be a form of starch or gum, ora mixture of forms of either or both! Compare Arthoniu
melaspermella, p. 283.
+ It is faint or obscure in the following, and in many other, true lichens :—
Collema turgidum, Scher. Exs. 433. Asci.
Stereocaulon condensatum, Scher. Exs. 509. Asci.
Calicium stigonellum, Leight. Exs. 226. Asci.
Lecidea Wahlenbergiana v. truncigena, Ach., Leight. Exs. 123. Hymenium, mere trace.
t In his “ Prodromus” he describes some species as possessing a yellow reaction, e.g. V. xylina
(p. 191).
Ole XOX Ve PART 11. 6uU
526 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
to other lichenologists ; and I doubt not that, if they take the trouble to make
similar microscopico-botanical testings, they will meet with many marked
instances in which their own results will differ both from mine and from those
recorded by authors, like NyLANnDER, who have given prominence in their works
to chemical reaction as a botanical character.* This arises from the circum-
stance, already mentioned, that the same species, under different circumstances,
yields different colour-results with the same reagent. The following list could
have been largely extended had I introduced quotations from similar records
relating to the contents of my own Herbarium or of that at Kew. But such
plenitude of illustration is, for present purposes at least, quite unnecessary.
Omitting all instances of b/we-reaction with iodine, whether’ distinct or faint, the
other results of iodine-testing may be roughly classified as follows :—
I. No reaction.
Thelopsis rubella, Nyl. Exs. 96. According to Nytanper (Prod. 196), its hymenial
gelatine becomes red.
Nephromium cellulosum, Ach, Hermite Island, Cape Horn. According to NYLANDER
(Syn. 318), hymenial gelatine becomes blue.
Urceolaria actinostoma, Scher, Exs. 578.
Strigula Babingtonti, Leight. Exs, 35.
Lecidea spheroides, Smrf., accompanying Opegrapha atra in my copy of LetcHrTon’s
Exs. 245. According to NyLanper (Scand. 204), hymenial gelatine gives in different
forms of the plant various shades of violet, or wine-red.
L. foveolaris, Scher, Exs. 293.
LL, Lightfootii, Ach. v. commutata, Scher. Exs. 581. Apothecia here degenerate.
Calicium turbinatum, Scher. Exs. 6.
Verrucaria chlorotica, Ach., Nyl. Exs. 96.
V. eleina, Scher. Exs, 590.
V. biformis, Scher. Exs. 109 (= V. chlorotiea, Ach.)
V. levata, Leight. Exs. 198.
V. rupestris, accompanying V. pyrenophora in my copy of Letcuton’s Exs. 245.
Melaspilea arthonioides, Nyl. Exs. According to Nytanper (Prod. 159), hymenial
gelatine becomes wine-red or bluish.
Il. Reaction violet, red, or brown.
Lecidea luteola, Leight, Exs. 150. Hymenium deep violet, with reddish tinge.
LL. Wahlenbergiana, Ach., Leight. Exs. 123. Hymenium very faint purple.
Li. cupularis, Ach., Leight. Exs. 122. Hymenial gelatine and asci deep brownish-red ;
hypothecium (only) blue.
L. abietina, Ach., Leight. Exs. 124. Same reactions as in L. cupuluris.
L. lurida, Nyl. Exs. 131. Some tissues rose-red, others purple. Scher. Exs. 157,
asci pale blue or wine-red; Hepp Exs. 121, asci wine-red.
L. exilis, Hepp Exs. 473. Asci violet.
LL. premnea, Ach. (saxicolous), Leight. Exs. 185. Asci lilac or lake-coloured.
L, atro-alba v. concentrica, Leight. Exs. 17. Hymenial gelatine violet. According to
Nyanper (Scand. 283), it becomes deep blue.
L. expansa, Nyl., Leight. Exs. 186. Hymenium indistinct blue, with a lilac tinge.
L. coarctata, Leight. Exs. 177. sci faint blue; contained protoplasm orange-red.
* The majority of lichenological systematists give no attention to chemico-botanical characters, —
e.g., Massatoneo, Kérzer, Tu. M. Fries and Mupp; while Nyzanper, on the contrary, gives them
decided prominence, e.g., in his “ Lich. Scand.”
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. O24
Lvcanora aivra v. verrucoso-areolata, Scher. Exs. 538. Hymenium pale rose-coloured.
Asci give no blue. According to Nytanper (Scand. 192), the hymenial gelatine of
Verrucaria verrucoso-arcolata becomes yellowish-red.
Physcia stellaris v. ambigua, Scher. Exs. 351. Asci-tips pale brown.
Squamaria crassa, Ach., Leight. Exs. 5. Hymenium dirty palish blue or violet.
Opegrapha dendritica, Scher, Exs, 585. Hymenial gelatine pale lilac.
O. vulgata, Ach. v. vulgata, Leight. Exs. 194. Asci violet.
Arthonia cinnabarina, Wallr., accompanying Opegrapha atra in my copy of Leiguton’s
Exs. 245. Some asci very pale purple.
Verrucaria rimosicola, Leight. Exs, 253. Hymenial gelatine violet ; asei not blue.
V. subalbicans, Leight. Exs. 200. Hymenium violet or lilac; hypothecium pale blue.
V. epigwa, Ach. (apparently), accompanying Sguamaria saxicola, in my copy of Leicu-
ton’s Exs.145. Hymenial gelatine palish purple or violet; asci not blue. Accord-
ing to NyLanper (Scand, 276), hymenial gelatine becomes blue.
V. gemmifera, Tayl. Glenfarg, April 1858. Hymenium pale rose-red; no blue tinge.
On the other hand, I found a very marked Uichenic reaction—a beautiful and
more or less deep blue—with iodine in certain plants, generally regarded by
fungologists as fungi; but now classed by lichenologists as lichens, on the sole
ground apparently of this supposed diagnostic reaction. In Xylographa parallelu
v. pallens, Ny. Exs., the asci and hymenial gelatine gave a beautiful blue. In
X. flexella, Ny\. Exs., they gave a deep blue; and in Agyriwin rufum, Nyl. Exs., the
hymenium became blue.* Ihave elsewhere} cited instances of what are still
regarded, alike by lichenologists and fungologists, as fung?, giving so-called lichenic
reactions with iodine. Sphweria ventosaria, which Mr Currey considers “a true
Spheria,” gave me in its hymenium a violet or carmine with iodine; while ina
plant lately submitted to Mr Berxe ey, and by him regarded as a “ Peziza of the
tribe Patellea,” the asci sometimes give a b/we, sometimes no reaction with iodine.
This Peziza (which appears to be new, and for which, if it is so, I propose the
specific name lichenotdes), is associated with Lecidea parasema and disciforimis on
the bark of fir trees, Morchone, Braemar, collected by myself in August 1856. The
apothecia are apparently sub-stipitate; this appearance being produced by the dis-
integration of the fibres of the bark on which they are seated. They vary greatly
in form and size, being variously angular or oblong, or irregularly subspherical.
The margins are involute to various degrees. ‘They are always black ; frequently
wavy both in surface and outline, and generally thin. The paraphyses are very
delicate, filiform, wavy, without coloured tips. The asci are long and sublinear
or clavate, springing in groups or tufts from the hypothecium. The sporidia are
innumerable in each ascus; atomic, subellipsoid or subspherical. The protoplasm,
which is gradually developed into sporidia, closely occupies the cavity of the asci,
separated only by a very narrow margin or double contour. Externally the
Peziza has much of the character of a Patellaria, e.g., P. atrata (as described in
* In BerKeey’s “ British Fungology” (1860) p. 375, both Agyrium and Xylographa tigure
among fungi, the latter having rank as a subgenus under Stictis. A. rufum aud X. parallelu are
mentioned; but not X. flexella (unless it be as Peziza flewella, Fr., p. 871), which, however, appears
associated with X. parallela in NytanpeEr’s “ Prodromus,” p. 148, as a lichen.
} ‘Parasitic Micro-lichens;” Arthonia melaspermella, p. 284.
o28 - DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
my ‘Otago Lich. and Fungi,” p. 427). It has also certain resemblances to a
Hysterium, e.g., H. pulicare, P. The asci and sporidia are similar to those of
what, now regarded as a lichen, was by Fries the elder considered a Peziza,
viz., Lecidea (Peziza) resine, Fr. (= Biatorella, Mudd, p. 191).* From that
Lecidea or Peziza, P. lichenoides differs only in the colour of its apothecium.
The asci of Abrothallus Smithi, which NyLanvER regards as a fungus, and
BERKELEY} as a lichen, though they generally give no colour-reaction with iodine, +
have, in one instance at least, yielded in my hands the lichenic blue, less distinct,
however, than in A. oxysporus. In the latter species, on the other hand, which is
equally by fungologists and lichenologists admitted to be a lichen, while iodine
generally developes a vivid and beautiful blue in the asci, this reaction is some-
times either obscure or absent; and the same remark applies to many true lichens,
which generally exhibit the typical iodine-reaction:
Spheria (Stereocaulicola), Th. Fries, and Leptosphwria (Lopadiicola), Th. Fries
(Lich. Spitsb. p. 34), give in their hymenium a yellow iodine-reaction. But, accord-
ing to the same careful observer, F'r1Es the younger (in his ‘‘ Lich. Spitsbergenses,”’
where he has recorded the iodine-reactions of most or many of the lichens therein
described), the same reaction§ is exhibited by the following true lichens :—
Leptogium \acerum and tenuissimum ; ) Lecothecium asperellum; protoplasm of asci.
Collema pulposum ; Pannaria arctophila ; sporidia.
hymenium, except the sporidia; i Lecidea pezizoidea ; sporidia and paraphyses.
L. scotinum ; sporidia. Endocarpon pulvinatum ; protoplasm of asc.
Sphcerophoron fragile; medullary tissue (of Microglena sphinctrinoides ; sporidia.
thallus.) Staurothele clopima; sporidia and protoplasm of
Gyrophora cylindrica; sporidia, asc.
Leeanora flavida; sporidia and protoplasm of Thelidium pyrenophorum ; sporidia.
the asci. Verrucaria extrema; do.
L. mastrucata ; hymenium. Arthapyrenia couspurcans ; protoplasm of asci.
L. ealcarea; do.
Some of the parasites, which I have grouped meanwhile under M/zcrothelia,
were lately submitted to Mr BerKELey, in the hope that he might claim a portion
at least as fungi proper. But only one of them, what I have described as MW.
Nephromiaria, he refers to Sphwria and the fungi. The remainder he considers
lichens belonging to the genera Verrucaria, Celidium, and Abrothallus. To Verru-
caria he refers M. Umbilicarie and M. Beomycearia; to Abrothallus the parasite
* Quoad the asci and sporidia it also resembles Lecanora cervina, Pers., Lecidea morio, Sch.,
L. fossarum, Duf. of Nytanver’s Exs., and LZ. pruinosa, Sm.
+ “I think,” writes Mr Berxezey, in Feb. 1869, “TuLasne is quite right in making Phacopsis,
Abrothallus, Celidium, and Scutula lichens.”
+ Vide my “Monograph of Abrothallus,” Quart. Journ, of Micro. Science, Jany. 1857. Nyan-
DER (Prod, 55) remarks, ‘* Nullam enim mihi obtulit notam lichenosam.” But what constitutes a “ Nota
lichenosa?” What diagnostic is there characteristic of a lichen as contradistinguished from a
Fungus 2? For my own part, I know of none /
§ I have never myself met with in lichens a yellow iodine-reaction, which I did or could not
regard as the natural (unchanged) colour of the reagent itself.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 529
which affects Lecanora polytropa v. intricata ; to Celidium, M. Stereocaulicola and
the parasites on Sguamaria crassa and S. saxicola.
Some of the parasites formerly grouped by me under Microthelia and the
fungo-lichens have been transferred to the fungi proper, ¢.g., Spheria ventosaria,
by Mr Currey. And it is most likely that other members of that provisional
genus or group will from time to time be claimed as true fungi. But I find it
impossible to perceive the validity of the claim, or the grounds of distinction. To
me it appears that Sphwria is quite as nondescript or heterogeneous a genus as
Microthelia, and that it passes into Verrucaria by connecting links that defy
differential definitions! In the “‘ Treasury of Botany,” Mr Brerxeey says that the
only distinction between Verrucaria and Spheria consists in the presence of
thalline gonidia ; but, as | have elsewhere* shown, no gonidia can be present
in the large group of parasitic athalline lichens, in which the apothecia—with or
without spermogonia or pycnidia—constitute the plant. In the same work he
describes Endothia as distinguished from Verrucaria by its ‘naked spores.” He
also apparently regards it as consisting merely of the pycnidia or spermogonia
of different lichens (Treasury, p. 1211); but he elsewhere describes “ asci’’ (Brit.
Fungology, p. 384)! I am utterly at a loss to reconcile or understand these
diverse and puzzling statements. Moreover, if we may judge from NyLanpEr’s
description of S. homostegia (Prod. 56), which is flat and maculeform, the
Spheeric are not necessarily papilleeform or verrucarioid. Some of them are thus
arthonioid; and there are a few parasitic athalline Arthonie which have quite
the facies of Sphweria homostegia, e.g., A. varians, Dav. (Nyx. Scand. 260).
Mr Berxerey regards M. Umbilicaric and M. Beeomycearia (in my specimens)
as having a “distinct crust;” or, in other words, a proper thallus. This I quite
fail to discover, on repeated examination; the perithecia appearing to me to be
indubitably seated directly on an alien (lichen) thallus. No doubt, AZ. Umbili-
caricee and M. Beomycearia may be referred to the Verrucarie ; but only in the
same sense in which the whole group of the Microthelie may be so transferred,
constituting, with Lndococcus or other pseudo-genera, an athalline (parasitic) sec-
tion. We have already seen that the botanical ‘‘ characters” of Verrucaria are
in great measure negative; while there can be no doubt, as a genus, it is
already much too (confusingly) large and heterogeneous.
None of my Microthelie have the essential characters of TULASNE’s genus Celi-
diwmn (as defined in his Mémoire, p. 120, pl. xiv. figs. 9-13, or in my ‘‘ Otago Lich.
and Fungi,” p. 448). According to TuLasnz, the perithecia are aggregated so as
to form maculee, in the centre of which are seated spermogonia, the spermatia
being linear and very slender. In the typical species C. Stictarwm, Tul.(Mém.
p. 122), the iodine-reaction is lichenic; the hymenium becoming bluish, reddish,
* Arthonia melaspermella, p. 282.
VOL. XXV. PART II. ; 6 Xx
530 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
brownish, or yellowish; but there is no such reaction in the Microtheliw, which
Mr Berxexey refers to Celidium. Nor can I conceive any proper ground for
assigning the parasite of Lecanora polytropa v. intricata to Abrothallus, which is
itself a provisional and pseudo-genus.
Indeed, I am utterly at a loss to comprehend the principles of Mr BERKELEY’s
classification in the parasites above referred to; and I am led to regard his opinion
as another of the many illustrations that may be cited of the diversity between
lichenologists and fungologists regarding the nature and affinities of a large and
important group of parasites, which have been fully studied by neither class of
observers, and are yet, therefore, most imperfectly known. And further, his
(quite recent) opinion I accept, as strongly confirmatory of the propriety of estab-
lishing a provisional group of Fungo-lichens, and of resting contented with placing
therein such doubtful organisms as the Microthelic, which I have hereinafter
and elsewhere described,* instead of engaging in fruitless and interminable dis-
cussion as to whether they are /wngz or lichens.
When they become more generally studied and more thoroughly known, it
may prove that some of the A/icrothelie in question are not parasitic or athalline,
really possessing a proper thallus; or they may occur—as not a few true lichens
do—both in the thalline and athalline state. .
Only in certain cases, in describing the parasites, which form the subject of
the present communication, have I ventured to assign names, viz., in the cases of
those which may be considered typical or representative. In other cases—by
reason of their resemblances to certain types or to each other, of the imperfec-
tions of their structure, or for other causes—I have deemed it preferable for the
present not to assign names, either generic or specific, though all these doubtful
parasites are grouped provisionally, for convenience in future study and reference,
under the pseudo-genus Aicrothelia. I have little doubt that when the parasites
in question, as well as the parasitic Micro-lichens and Micro-fungi that have been
described by other authors, are more thoroughly studied and known, the same
type or species will be held to include several of those which at present appear
distinct. There will be not only a certain reduction, but abolition, of genera
and species, of which there is at present a most confusing redundancy.f
Description of Illustrative Specvmens.
I. Torula lichenicola.
A. Parasitic on thallus or apothecia (or both) of Lecanora subfusca, Ach.
1. Scotch forms.
(a) Corticolous ; Craig Choinich, Braemar, Aug. 1856, W. L. L.—Parasitic both on
thallus and apothecia in one specimen of ordinary form of the Lecanora. The
* « Otago Lich, and Fungi,” pp. 436-442.
++ An excellent illustration is to be found in the group of * Parasitie Micro-lichens,” (antea citat.)
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 531
disk of the apothecium is, however, chiefly affected. Here the parasite is so
abundant and so closely aggregated, that it renders the usually smooth disk
quite black, and rough-granular or warted; the apothecia then resembling,
especially in colour, those of LZ. atra. The spores are sometimes 1-septate or
3-nuclear, resembling many lichen-sporidia.
(>) Corticolous: on birch bark, Corramulzie Linn, Braemar, Aug. 16856, W. L. L.
—Parasitic on both thallus and apothecia. As in the last case, the disk of the
apothecia is frequently quite black and roughened from the growth of the
Torula. .
(c) Corticolous: Morchone, Braemar, Aug. 1856, W. L. L.—On thallus only.
(d) Corticolous: on firs, base of Ben Lawers, on banks of Loch Tay, June 1856,
W. L. L.—Equally on thallus and apothecia. Sometimes, as in cases « and },
the disk is blackened with the parasite, and resembles that of Z. atra. Spores
bluish.
(e) Corticolous: on ash, roadside, Loch Tay, June 1856, W. L. L.—Copiously
and generally studded over thallus; much more abundant than the spermo-
gonia of the Lecanora ; very distinct, black, punctiform bodies; spores generally
2-nuclear, brown.
(f) Both corticolous and saxicolous: Kyles of Bute, Aug. 1852, W. L. L._—On
thallus; spores indigo-blue; simple (no contained nuclei); narrow, and fre-
quently longer than usual.
(g) Corticolous: on firs and other trees, Caerlaverock road, Dumfries, Aug. 1856,
. L. L.—Seattered on thallus of var. albella, Pers. Spores large and more
numerous than usual; frequently exhibit 2 polar nuclei; that which occupies
the upper and broader end of each spore in the spore-chain being generally the
larger ; or there is only one nucleus at the superior or distal end of the spore.
(h) Corticolous: near Dunglass, Cockburnspath, June 1856, Dr Murray Lindsay.
—Variety of the Lecanora. Torula intermixed on thallus with spermogonia,
which have not the usual characters of those of L. swbfusca. Spores bluish.
Terminal articulation of the spore-chain, as usual, darkest in colour, with a
rounded apex. The other spores, when separated, have squarish or truncated
ends, and an oblong form. Occasionally the mature spore contains one or two
nuclei. Sometimes the spore-filament developes only one (terminal) articula-
tion; at other times there is no articulation at all—the filament being sterile
or abortive—then resembling the paraphysis of a lichen,
(i) Corticolous: woods of Blackhall, Strichen, Aberdeenshire, July 1865, Layton.
—Copiously scattered over the warts or areole of the subverrucose and areolate
thallus, but sparingly studding the apothecia.
(k) Corticolous: on alder; Pease Dean, Berwickshire, 1856, James Hardy.—
Thallus sub-tartareous ; many apothecia degenerate; disks eroded. Parasite
abundant, both on disk and exciple'of apothecia, and on thalline areole.
Spores with polar nuclei, somewhat resembling certain physcioid sporidia in
lichens.
(2) Corticolous: Penmanshiel, Berwickshire, February 1857, Hardy.
2. Irish forms.
(a) Corticolous: near Cork, March 1858, Isaac Carroll. Associated with Physciu
candelaria, Ach.—Thallus subtartareous, made up of numerous closely-aggre-
gated verruceform areole ; apothecia mostly degenerate ; disk has disappeared,
and the apothecia have assumed the appearance of irregular warts. Parasite
is copiously studded over both thallus and apothecia, which have alike a black-
punctate character. The Torula has its usual black, punctiform character.
The basal cellular tissue is bluish, bluish-black, or brownish, resembling in
this respect the varying colour of the spores. Lach spore-filament usually
developes four or five articulations, which are oblong and simple, broader above
than below. The terminal ones, the largest, are about *00025” long, and
‘000111” broad.
(b) Corticolous: on old keeches, Castle Bernard, Cork, Carroll, Associated with
Stigmatidium crassum, Dub.—On both thallus and apothecia (disk and exciple
532 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
alike). Parasite very minute, punctiform, black; basal cellular tissue deep
indigo-blue. Spore-filaments about :001” long, and -000111” broad. Spores
pale olive to bluish-black—about 00025” long, and -000111” broad.
(c) Corticolous: Rathconnac, Co. Cork, Mar. 1858, Carroll.—On thalline areol
and apothecia. Parasite resembles granules of a black powder dusted over
thallus, its blackness contrasting strongly with the brown disk of the apo-
thecium and white thallus of the ZLecanora. Basal cellular tissue, like the
spores, bluish-black or indigo colour. Spore-filament, before separation of the
spores, ‘00066” long. It frequently throws off only two articulations from its
tip; the lower or basal—that is, the longer—portion showing no division.
Sometimes there are three articulations or spores; rarely more. The mature
spores are 00025” long, and -00014” broad.
(2) Corticolous: Great Island, Cork, Mar. 1858, Carroll.—On periphery of
thallus. Spores pale olive or brown; oval, ellipsoid, or oblong; 00016” long,
and 000090” broad.
(ec) Corticolous: Carrigaloe, Cork Harbour, Mar. 1858, Carroll. Associated with
Physcia pulverulenta, Schreb.—Both on apothecia and thallus, on the latter
somewhat inconspicuous; apothecia degenerate; margin eroded; disk black-
punctate with the parasite, which is very numerous and crowded. The
Torula is here larger than is usual, Basal cellular tissue indigo-blue. Spores
brown ; 00025” to -00033” long, and 00016” broad—usually simple. Asso-
ciated with the sporiferous filaments are numerous sterile or non-articulated—
probably abortive—colourless, very delicate and linear filaments, which re-
semble the paraphyses of many lichens. Sometimes they exhibit a faint appear-
ance of septa, A parallel to these sterile filaments is to be found in the sterile _
hypertrophied sterigmata in the spermogonia of many lichens.*
(f) Corticolous: Upper Lakes, Killarney, Mar. 1858, Carroll. —Disk of apo-
thecia destroyed, and the apothecia converted into an uniform dark purple,
sterile, degenerate mass.
(g) Corticolous: Ardrum, Carroll.—Basal cellular tissue deep indigo. Spore-
filaments 001338” long, ‘000111” broad; spores -00025” long, ‘000111” broad;
olive or bluish-brown ; oblong, with rounded ends; simple, or frequently with
two polar spherical nuclei; sometimes with double contour.
(2) Kerry: Taylor in Herb. Mackay.—On apothecia ; disks of which become syb-
convex and deformed, and frequently as black as those of LZ. atra, from growth
of the parasite.
3. English or other forms.
Betton, 1805,in Herb. Kew. All disks of the Lecanora entirely blackened by growth
of the parasite, so that the lichen is apt to be mistaken for L. atra.
Korzer (“ Parerga,” p. 470) describes his Pharcidia congesta as very frequently para-
sitic on the apothecia of Z. subfusca and L. intumescens, Rebent., in Germany. It
possesses 8-spored asci; the sporidia clavate-oblong, sub-baccillar, 1-3-septate,
hyaline. Lecidea parasitica, Flk., and Arthonia varians, Dav., are also occasionally
parasitic either on the thallus or apothecia (or both) of LZ. subfusca.t
B. Parasitic on thallus of Lecidea canescens, Ach.
Corticolous: Aghada, Cork Harbour, Carroll_—On portions of thallus free of apothecia.
Basal cellular tissue bluish-black. Spores pale indigo-blue or olive ; terminal or larger
ones 00041” long; ‘00016” broad ; others 00025” long, and 00011” to -00016” broad.
C. Parasitic on thallus of Lecidea parasema, Ach.
On a specimen in Herb, Kew, from Ireland (sub nom. Opegrapha gemmata, Ach.) Apothecia
of the Zecidea confluent and somewhat irregular in form and surface ; colour bluish or
greenish ; sporidia normal. The parasite presents very numerous individuals, closely
aggregated, occupying the site of, and otherwise externally resembling, spermogonia ;
very minute (microscopic), black, punctiform, superficial on, or more or less immersed
in, thallus of the Lecidea. Spore-filaments about 0025” long, and -00016” broad,
* Vide ‘‘ Mem. Spermog.” Plates IV. V. VI. VIII. XI. XII.
t+ Vide Paper on “ Parasitic Micro-Lichens.”
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. D990
varying, however, both in length and breadth. Spores also variable in dimension ;
simple; oblong, with rounded ends when mature; colourless in the young state,
gradually acquiring an olive tint with maturescence ; terminal articulation, as usual,
deepest in colour. Spore-filaments consist frequently of six articulations—some of
which, however, are sometimes atrophied, assuming the aspect of linear threads or
ribbons connecting the normal spores.
D. Parasitic on the apothecia of Lecidea ferruginea, Huds.
(a) Corticolous: Craig Rossie, Dunning, Perthshire, April 1858, W. L. L.
(b) Corticolous: on silver fir: Ardrum, near Cork, Mar. 1858, Carroll.
E. Parasitic on thallus of Lecidea anomala, Ach.
(a) On ash and other trees, associated with Lecanora subfusca and Pertusaria com-
munis; near Dunglass, Cockburnspath, Berwickshire, Dr Murray Lindsay,
June 1856.- The parasite here is associated with, and apt to be mistaken for,
spermogonia. Terminal spores blackish; rounded at upper end; sometimes
containing enclosed nuclei.
(b) Dunglass; thallus of the Zecidea white and granulate. Torula intermixed with
spermogonia,
F. Parasitic on thallus of Lecanora varia, Ach.
Sub Parmelia in Lziguton’s Exs. No, 176; on fir bark, Twyford Churchyard, Shropshire.
Intermixed with spermogonia, with which the parasitic perithecia are apt to be con-
founded. In the same perithecia, moreover, the spore-filaments of the Torula are
associated with the sterigmata of the Zecanora, taking here the place of the sterile
hypertrophied sterigmata of lichen-spermogonia,*
G. Closely associated with, but not parasitic on, various corticolous Lichens.
(a) On or with Arthonia melaspermella, Nyl.; corticolous; Weybridge, Surrey,
Currey. In the “Journal of the Linnean Society” (Botany, vol. ix. pp, 271 and
286, tab. 6, figs. 2 c, 3 c, and 6), I have erroneously described and figured the
parasite as the Pycnides of the Arthonia. Mere the articulations of the spore-
filament are bluish. It is impossible to determine whether or not there is a
proper thallus of the Arthonia, on which the Torula occurs.
(6) With Opegrapha atra, Pers.; in Scu#rer’s Exs. No. 634; right hand specimen
in my copy. Spores brown ; smaller than is usual.
(ce) With Verrucaria epidermidis, Ach., Malham, Yorkshire, Oct. 1857, Dr Carrington.
—Spore-filaments of two or three articulations only. Terminal spores :00025”
long, very narrow and granular.
In the foregoing cases (6 to G) the parasite has the same essential characters
that it exhibits when frequenting its much commoner host—especially in Ireland
—Lecanora subfusca.
It is probable that the Torula, which is described as destroying the apothecia
of Biatorina fraudans, Helb., in Spitzbergen (TH. Fries in “ Lichenes Spitsber-
genses,”’ p. 35), as well as that referred to in NyYLANDER’s “Synopsis” (p. 58),
is Torula lichenicola. But of neither Fries’ nor NyLanpEr’s plants have I seen
specimens. 7’ lichenicola has a suspiciously close resemblance to what NYLANDER
describes in his “ Prodromus” (p. 86), as the Pycnides of Spheria epicymatia—
a parasite, which, he says, is common on Lecanora subfusca, but which I have
never found. In the same work (and same page) he mentions Torula moni-
lioides, Bon. ; but I have no means of knowing whether this is 7. monilioides,
Cd., or Bispora monilioides, Cd., of BrrKELEy’s “ British Fungology” (pp. 326
and 327); or 7. lichenicola ; or some plant—fungus or lichen—different from
either.
* Vide p. 532 and foot note.*
VOL. XXV. PART II. 6 Y
534 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
IL. Coniothecium lichenicoluin.
A, Parasitic on thallus of Lecanora tartarea, L.
(a) Morchone, Braemar, Aug. 1856, W. L. L.—On isidioid, sterile states of the
thallus of the Lecanora. Spores deep brown; sometimes spherical and simple ;
frequently 8-shaped (didymous) ; frequently also in moniliform chains, as in
Torula lichenicola, or in groups of four or three,
B, Parasitic on thallus of LZ. parella, Ach.
(a) Blackeairn Hill, near Newburgh, Fifeshire, May 1858, W. L. L.—On sterile
forms of thallus of the Lecanora. Parasite more irregular in surface and out-
line, more crowded, and more frequently confluent than is usual. Occurs in
groups on different parts of the thallus of the host. Spores sometimes 8-shaped
(didymous), 00025” broad, 0005” long; more generally single or simple and
spherical, about -00016” in diameter,
(b) Morchone, Braemar, Aug. 1856, W. L. L.—On sterile states of thallus, spar-
ingly scattered, sometimes only about periphery of thallus. Parasite has
sometimes an apothecioid aspect, its black mass being girt with an obscure
thalline ring. Occasionally it appears as if seated in thalline verruce, and is
so small as to resemble spermogonia. At other times it resembles the smaller
urceolate apothecia of Lecanora cinerea ; and if the thallus of L. parella were
more generally covered with the parasite, it might, at first sight, be confounded
with a form of L. cinerea,
(c) Glen Dee, Braemar, Aug. 1856, W. L. L.—On isidioid states of thallus.
Parasite mostly large and flattish, with very ragged outline in the old state,
resembling spots of soot; in young state, is regularly papillar. Has a close
resemblance to Spilomium Graphideorum, Nyl., in size and irregularity of out-
line and surface.
C. Parasitic on Isidiwm corallinum, Ach.
(a) Old Wall, Craigie Hill, Perth, May 1856, W. L. L.—The surface of the thallus
shows little distinction between the constituent isidia, which are so closely
aggregated as to form a general white subcretaceous mass, sometimes obscurely
divided into areole. Parasite occupies generally the centre of these areole
where they occur, or is studded generally over surface of thallus, as black,
round, convex masses, varying in size. Spores in all cases show double
contour; in age acquire an irregular or corrugate outline; colour generally
brown, or blackish-brown, graduating into olive; sometimes very pale or almost
colourless in young state.
It appears to be the same parasite which occurs on Isidium corallinum im
Moveror and Nestter’s Exsic. No. 74; which Jsidiwm is there probably refer-
able to Lecanora parella. The parasite resembles black apothecia, which have
been doubtless by lichenologists of the pre-microscope era mistaken for the
“fruit” of the Lsidiwm or Lecanora.
The columns of [sidium corallinum have apices that are frequently coloured
more darkly than the body of the isidia; which coloured apices were often
mistaken by the earlier lichenologists for apothecia or “ fruit” of different kinds,
and which often have aclose resemblance to some forms of spermogonia. The
plant consists, when typically developed, of a series of minute, round, perpen-
dicular columns, which become by close appression sometimes subangulose,
and may even lose their individuality, coalescing into a general subcretaceous
mass, }” to 1” thick. Where such coalescence does not take place, there is seen
on cross section, either natural or artificial—a honeycomb-like arrangement of
columns—similar to the basaltic columns of Staffa or the Giant’s Causeway on
a microscopic scale. Where the apices are not cut off by natural cross section
or erosion, they are discrete and papilleform, resembling, on a small scale, the
young ramuscles of Sphcrophoron, as these are figured in my “Observations —
on New Zealand Lichens” (PI. Ixii. fig. 5).* The colour of the isidia varies
considerably ; sometimes, especially in specimens long preserved in the
* Transactions of Linnean Society of London, vol. xxv.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 535
Herbarium, they are flesh-coloured; more generally they are grey. The
colour is always deepest at the apex, gradually disappearing below, where
the bodies of the columns coalesce into a chalky mass. The tips of the
papille, which form the upper or free extremities of the columns, are generally
brown; but this tint varies in depth or distinctness, being frequently very
obscure.
D. Parasitic on thallus of Lecanora atra, Ach.
Saxicolous: Pentland Hills, Edinburgh, Aug. 1855, W. L L.—No part of this parasite
gives a blue reaction with iodine.
E. Parasitic on thallus of Diplotomma caleareum, Weis.
Clapham, Yorkshire, Dr Carrington, Oct. 1857.— What appears to be the Coniothecium is
seated on the thalline areol, where they are at all distinct. It is black, generally
round, sometimes irregular in form, e.., becoming sub-arthonioid; generally flat;
seldom, and only in young state, verrucarioid or papilleform; sometimes confluent ;
superficial, the base only immersed. The parasite is sometimes indistinguishable from
the apothecia of its host, save as to the inferior size of the Coniothecium; its size, how-
ever, is variable; it generally wants the thalline margin—which is, however, sometimes
comparatively distinct, girding the apothecia. Here the Coniotheciwm exhibits no
reproductive structure.
The same Diplotomma is in England the seat of the parasitic Microthelia rimosicola,
Leight. (Munpp, “‘ Brit. Lich.,” p. 308, plate v. fig. 129), which has 8-spored asci, and
oblong, 3-septate, brown sporidia, My note-book records, on the Yorkshire plant, the
presence of Pycnidia, containing stylospores.
F. Parasitic on thallus of Lecanora cinerea, UL.
Kerry, Taylor (in Fl. Hibern., sub-nom, Spiloma spherale).—Thallus of Lecanora sterile.
The parasite is scattered about the periphery of the alien thallus, much more abundantly
than the spermogonia of the Zecanora usually are. In the young state the Coniothecium
is immersed, and then frequently resembles closely some forms of the spermogonia of
LL. cinerea ; but gradually it becomes emergent and epithalline, resembling, according
to its size and form—whether flattish or sub-globose—the black apothecial disks of a
sessile Calicium or a Lecidea. It contains no reproductive structure, exhibiting under
the microscope only its deep-brown, basal, cellular tissue.
G. Parasitic on sterile conditions (which are variously isidioid or variolarioid) of the thallus of
several Lecanore.
It is in general impossible to determine in these cases what is the species of Lecanora.
Sometimes only it appears to be Z. glaucoma, L. parella, or L. tartarea. In no case is
the isidioid condition so marked as to bring the thallus under the category (C) of Isidium
corallinum.*
(a) Scuir-na-gillean, Skye, Aug. 1856, W. L. L.—Black papille of parasite
very variable in size; generally very distinct. Spores of a sooty-brown
colour.
(b) Saxicolous: Moors east of Reykjavik, Iceland, June 1860, W. L. L.—Here,
again, no distinct reproductive structure is visible. The parasite is large, black,
and conspicuous by contrast of colour on the whitish or grey thallus, having
somewhat the characters of the apothecia of a Lecidea of the parasema or contiguiu
group; much more irregular in form, however, and variable in size; consist-
ing, moreover, apparently of aggregations, or glomeruli, of irregular papille ;
semi-immersed in the thalline areolx, but projecting by an irregular, rough,
granular surface above their level.
(ec) Morchone, Braemar, Aug. 1856, W. L. L.—Abundant and in fine condition.
(d) North Wales, Rev. H. Davies (sub-nom, I[sidiwm microsticticum, E. B. and
Lich, Brit.) in Herb. Kew.—Parasite seated on, and partly in, small thalline
papillz ; in which latter case it possesses a pale thalline border; small, black,
* IT have recently (August 1869) found Coniothecium frequent on the sterile saxicolous thalli
of Lecanore, both in the northern and southern Highlands, ¢.g., Helmsdale, Sutherlandshire, and
St Mary’s Loch district, Selkirkshire. In these districts the thalli in question are most probably
referable to Lecanora parella or glaucoma, or both. On similar sterile thalli the parasite is common
throughout Scotland, and probably throughout Britain.
536 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
lecidioid, convex, scabrous—studded over the thallus of the host. Spores
brown; very irregular; concatenate, or Sarcinate, in groups of 4-woolpack-
like masses, similar to those of Surcina ventriculi, Goodsir.
(c) Kinnoull Hill, Perth, May 1856, W. L. L.— Associated with Sguwamaria
gelida, . Parasite occurs on an areolate, white, crustaceous thallus, sterile
of apothecia, referable, doubtless, to some Lecanora. The Coniothecium has
quite the aspect of some species of Microthelia, e.g., M. rimosicola, Leight.
Spores chestnut-brown; have the appearance of portions of cellular tissue,*
composed of irregular, subcubical cellules,
(7) Barmouth, N. Wales, June 1836, Leighton (sub-nom. Spiloma).—Referred
by Mr Cooke to “ Sporidesmium sp.” in my Herbarium.
H. Not parasitic on, though closely associated with, various saxicolous lichens.
Roadside between Sligachan and Portree, Skye, Aug. 1856, W. L. L.
Some at least of the parasites which I have referred to Coniotheciwm licheni-
colum have apparently been mentioned, if not also described, by various of
the earlier lichenologists, under most diverse names. Specimen (d) has the
characters of /sidiwm nucrosticticum of ** English Botany” and the “ Lichenographia
Britannica ;” (+) has quite the appearance externally of Spiloma nigrum, Leight.
and “English Botany,”+ and of Spilomium Graphideorum, Nyl.t A plant from
Clapham, Yorkshire, Dr Carrington, is apparently—partly at least—Sclerococcum
sphorale, Fr.; § and Cyphelium (or Acolium) corallinum, Herp Exs. No. 531,
and Korser’s “ Parerga,” pp. 299 and 465. Coniothecium lichenicolum agrees
also with Variolaria conspurcata, Eng). Bot., tab. 1993 (at least) with the char-
acters of the plate.
Coniothecium lichenicolum has a close resemblance to some forms of Sporides-
muum; and it is quite likely that there is a lichenicolous Sporidesmium, hitherto
undescribed, for which the specific name Jlichenicolum would be appropriate. —
I have not, however, at present sufficient data for determining this. What
appears to me to be Con. lichenicolum, occurring on the white, crustaceous, sterile
thallus of a Lecanora from Barmouth, N. Wales, Leighton, June 1856—in my
Herbarium—was (as already stated) labelled by Mr Cooks “ Sporidesmium sp.”
Two of the lichens of the earlier lichenologists have been transferred by fungo-
logists to the genus Sporidesmium, viz , 1. Lepraria nigra, Engl. Bot., t. 2409, of
Ist edition, which is the Coniothecium effusum, Cd., and the Sporidesmium
* Vide p. 519 and foot note.*
+ P. 45, tab. 1984, 2d ed., 1843.
t The specimen of S. Graphideorum, Nyl., contained in my copy of his ‘ Herb. Lich. Paris,” No.
72 (from Fontainebleau, on a white, mealy thallus—of some Graphis—coating a very rugged bark,
and associated with a Hysteriwm), has the external characters, on a large scale, of a Spiloma. Spiloma
nigrum, var. variolosum, Turn. & Borr. in Leieuton’s Exsic. No. 259, closely resembles it, though
LeicHTon’s plant is more crowded and more irregular in outline. The French Spilomium is quite
visible to the naked eye; variable in size; very black; irregular in outline, though generally
round; sometimes confluent; surface usually more or less convex and rough, as in Coniothecium,
from the projecting powdery or granular spore-masses. The spores are spherical or oval; generally
with double contour; simple; deep brown; about -00025” in diameter ; sometimes slightly irregular
in outline; cohering frequently in rouleaux like blood-corpuscles.
§ = Spiloma spherale, Ach., but not Buellia saxatilis, Scher. (NyLaNpDER, ‘“ Prod.” p. 140), ac-
cording to Tu. Frigs (“L. Aret.” p. 116).
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. Dot
Lepraria, Berk. and Broome, of BERKELEY’s “ Brit. Fungology,” p. 327; and 2.
Spiloma melanopum, Eng). Bot. t. 2358 of Ist edition, which is the Sporidesmium
melanopum, Berk. and Broome, of BERKELEY’s “ Brit. Fungol.” p. 327.
IIL. Spheria ventosaria, Linds. “ Obs. on Otago Lichens and Fungi,” p. 439 ;*
“ Obs. on Greenland Lichens.’+
Parasitic on the thallus of what appears to be Lecidea grossa, Ach., Ingleby,
Cleveland, Yorkshire, Mudd; inmy Herbarium. Occurs as minute, black papille,
intermixed with the apothecia of the Lecidea. Externally the parasite has the
character, as it has the position, of certain verrucarioid spermogonia, ¢.g., in the
genus Lecidea; and it has also the facies of Endococcus or Microthelia. No
distinct asci are visible; but the hymenial gelatine showed a beautiful carmine
or violet colour with rodine, just as many true lichens do. Sporidia minute, pale
brown, oblong, with rounded ends, with or without double contour, according to
age; l-septate—septum indistinct in young state. Mr Currey regards it as “a
true Spheria. ... There are certainly thece filled with very numerous, brown,
1-septate sporidia, 0:0003”. . . . The perithecia are so minute and so scattered, that
it is extremely difficult to detach them for examination.” He refers the parasite
to S. ventosaria; but the perithecia are very different from those common in
the same parasite on Lecanora ventosa.
IV. Microthelia.
1. M. Cookei. Parasitic on thallus of Lecanora crenulata, Dicks., Barrack wall,
Chichester, W. C. Cooke, March 1866. The parasite occurs on the thicker,
whiter portions of the thallus, as black, papilleeform, scattered conceptacles. The
hymenium gives no blue with iodine; its constituents are very indistinct, unless
under the action of iodine or other colouring matter. Hypothecium is colourless.
Paraphyses appear rather like a mass of striated jelly than as distinct, filiform
threads—resembling in this respect those of Pertusaria. Apices not coloured.
Asci polysporous, saccate, bulging irregularly, 0018” long, 00045” broad. Sporidia
very small, 00022” long, 00009” broad; colourless; oblong-ellipsoid ; 1-septate,
sometimes simple.
M. Cookei externally resembles MM. rimosicola of Mupn’s Exsic. No. 301;
but the asci in the latter are 8-spored. It differs from all the MZccrotheliw men-
tioned in Mupp’s “ Manual of British Lichens,” in having colourless sporidia;
but in other points it resembles JZ. pygmea, Korb., which is also polysporous.
2. M. Stereocaulicola. Parasitic on thallus of Stereocaulon paschale, L., Glen
Derrie, Braemar, Croall, July 1854.
The free ends of some of the podetia of the Stereocaulon are the seat of
bullose-looking deformities or expansions, which are compound solid verruce,
made up of an aggregation of minute wartlets, of the same colour as the normal
* Transactions of the Royal Society of Edinburgh, vol. xxiv.
+ Transactions of the Linnean Society, vol. xxvii. (1869).
VOL. XXV. PART II. 6 Z
538 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
podetium and its squamules. These thalline deformities closely resemble those
which are occupied by spermogonia in the same Séereocaulon and in S. denudatum,
Flk., as they are figured in my ‘‘ Memoir on Spermogones” (plate v. figs. 33 and
36). Moreover, the parasite closely resembles the spermogonia in question in its
conceptacles forming brown or black verrucarioid papilla; sometimes visible as
mere points, the body immersed in the wartlets of the thalline deformities of the
Stereocaulon—one or two in each wartlet—the apex alone projecting. Asci not
blue with iodine, ‘0023” long, -00066” broad. No distinct paraphyses. Sporidia,
0005” long, ‘00033” broad; obovate; colourless when young, becoming olive or
brown with age; 1-septate.
Tu. Frres* has described, without naming, a Spheria as parasitic on the thallus
of S. alpinum, Laur., in Spitzbergen ; whose sporidia, however, distinguish it from |
the Microthelia. The hymenium of the Spheria—which may appropriately bear
the specific name Stereocaulicola—becomes yellow with iodine. The sporidia are
blackish, four in each ascus, oblong-elongate, 3-5-septate, becoming submuri-
form by longitudinal division of the loculi. Korser (in his “ Parerga,” p. 455),
describes Scutula Stereocaulorum, Anzi, as parasitic on Stereocaulon alpinum and
S. fastigiatum in the Alps of Northern Italy. But its sporidia are smallish,
narrowly ellipsoid, subcymbiform, 1-septate, and colourless. Also his Polycoccum
Sauteri (“ Parerga,” p. 470) as occurring on the protothallus and thallus of S. con-
densatum, Hffm. Sporidia small, dacryoid, 1-septate, brownish.
One or more species of Sirosiphon (an alga belonging to the family Siro-
siphoniacee, of the Palmellacec or Protophyta, according to RasENHorsT (FI. Europ.
Algar. Aq. dulcis, &c. p. 289), are parasitic on some species of Stereocaulon. Thus
Sirosiphon saxicola, Neg. (perhaps the SS. crustacea, Ag., of RABENHORST, op. cit.
p. 289), is parasitic on Stereocaulon denudatum in Scandinavia (Ny. ‘ Scand.”
p. 65); while a Szvosiphon, not named, and which may be also S. sazicola, grows
on the podetia of Stereocaulon vulcani, Bor., and was mistaken for cephalodia by
Fries (Nyt. “ Lich. Exotic.” p. 252). The parasite occurs as blackish pulvinuli,
which are quite different in anatomical constitution from cephalodia; the latter
always exhibiting on section the structure of—1. The cortical; 2. Gonimic; and
3. Medullary, tissues of the lichen-thallus.
3. M. Umbilicarie. Parasitic on the sterile thallus of Umbilicaria pustulata,
Hiffm.; collected in Norway as commercial ‘‘ Pustulatous moss.” The parasite is
copiously studded over both the bullae and interspaces of the thallus, as black,
papilleeform conceptacles, varying somewhat in size and form; semi-immersed ;
comparatively conspicuous on the gray, cracked thallus of the host. Paraphyses
very delicate and indistinct, as in Verrucaria. Asci very faint violet with iodine;
while the hymenial gelatine shows more distinctly the same tint with the same
*
‘“* Lichenes Spitsbergenses,” p. 386. Vide also author’s ‘“ Observations on Greenland
Lichens.”
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 539
reagent. Large quantity of oil globules intermixed with the hymenial consti-
tuents. Contents of young asci colourless, gradually assuming a brown tint as
the protoplasm becomes distinctly partitioned into sporidia. Latter are, in
maturity and when free, deep brown, generally 1- sometimes 2-septate; oval
or broadly ellipsoid. It is possible the parasite on U. pustulata may prove
referable to what KorBeEr describes in his “ Parerga’”’ (pp. 40 and 469) as Ticho-
thecium grossum, which affects the thallus of U. arctica, Ach. The latter species
of Umbilicaria is the seat also of Dothidea lichenum, Smrf., which Tu. Frtes
(Lich. Arct. p. 166) suggests may be KorBer’s 7. grossum. I have not met with
any description of SomMERFELT’s plant. Its name, D. lichenum, is apt to be con-
founded with that of MassaLoneo’s D. lichenicola (‘ Richerche,” p. 45, fig. 81),
which affects the apothecia of Pachyspora viridescens, Mass.; has 1-septate
sporidia, that, however, are colourless, elliptic-oblong, and slightly curved; and
is apparently, therefore, a different plant.
4. M. Nephromiaria. Parasitic on thallus, and (back or under side of old)
apothecia of Nephromium cellulosum, Ach.; Hermite Island, Cape Horn, Dr
Hooker, Antarctic Expedition, 1839-48.
Parasite occurs as very minute, black, punctiform or papilleform, semi-
immersed conceptacles, dotted over the thalline ruge, or on the back of the old
apothecia. It is sparingly scattered about the centre of the thallus, more
plentifully on the thalline underside of the apothecia. The black apex is the cnly
part that is superficial, the body being immersed. According to their size, and the
form of the ostioles, the perithecia resemble those of many lichen-spermogonia, or
of some of the smaller Verrucarie. They vary in size, and are sometimes con-
fluent, though generally scattered. The asci are sac-shaped like those of Arthonia,
bulging broadly, not blue with iodine. Hymenial gelatine wzolet under iodine.
Paraphyses indistinct, and as in Verrucaria. Sporidia 3-septate, colourless,
fusiform; eight in each ascus.
The asci and sporidia agree with those of what I described in my ‘“ Memoir
on Spermogones” (p. 135) as Lecidea Alectorie; and as the plants otherwise
appear essentially the same, I merge the two in a single type, and abolish both
the generic and specific* designations as inappropriate. MM. Nephromiaria also
resembles externally M. Cargilliana ;+ but the simple, spherical, brown sporidia of
the latter sufficiently distinguish it.
Also having 3-septate sporidia in sac-shaped asci is a parasite which covers
copiously, with its punctiform perithecia, some of the lacinize of Physcia ciliaris,
L., in ScH2ZRER’s Exs. No. 388 (sub-nom. Parmelia ciliaris: the lower of two
Specimens in my copy =ed. alt. immut., 1840). The body of the perithecium is
* What was originally designated Alecforia, is now known as Newropogon, Taylori (Nyt.
ey, p. 273).
Tt ‘‘ Otago Lichens and Fungi,” p. 441, pl xxx. figs. 31-34.
540 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
immersed in the thallus of the host, only the black apex being visible on the
surface. The whole length of some laciniz is dotted over with the parasite, while
others are unaffected. My notes, made in 1857, do not record, unfortunately,
the colour, size, or form of the sporidia.
5. M. rugulosaria. Parasitic on apothecia of Placodium rugulosum, Ny).
(“ Chil.” p. 193 ;) Tasmania, Stuart, in Herb. Kew; saxicolous.
The apothecia, which are of a deep orange-red, are abundantly studded over
with the very minute, black, punctiform, or papilleeform conceptacles of the
parasite. The latter are prominent under the lens, especially when the apothecia
are moistened, from the striking contrast of colour. They are semi-immersed in
the epithecium of the Placodium. Paraphyses very delicate and _ filiform.
Asci as long as the paraphyses; ‘0016’ long, -0005" broad; 8-spored. Sporidia
0004" long, ‘00016" broad; 1-septate; soleaform ;* brown. Both asci and sporidia
resemble those of tlhe microspermous and microsporous forms of Abrothallus
Smithit.
(a) Having similar sporidia—brown, soleaform, -0005" long, -00016" broad—is
a similar parasite (which may prove referable to MW. rugulosaria, or to the same
type to which it may hereafter itself be referred) that affects the thallus of
Thelotrema lepadinum, Ach.; on Holly, Ireland, Carroll. Its perithecia are
black and sub-verrucarioid, resembling those of Verrucaria fusiformis or epider-
midis. These sporidiiferous perithecia are accompanied by others containing
stylospores, like some of those of Lecidea abietina ; narrowly ellipsoid; -00033’
long, ‘000111" broad; pale yellow, Both forms of perithecia are probably refer-
able to the same parasite.
The thallus of 7. lepadinum is also affected by Nesolechia Nitschkit, Korb. (Par.
p. 462), which has minute, oblong-sub-bacillar, simple, hyaline sporidia; and
by Stenocbye eusporum, Nyl.
(b) Another Irish specimen, sent me as a Spheria, by CaRRo.t, in August
1856, from Mangerton, County Kerry, on a tartareous, white, much areolate,
sterile thallus (which cannot be referred to its proper species), has figure-8-
shaped, l-septate, deep brown or olive sporidia or spores; ‘00033’ long, and
00025" broad. The perithecia are largish and verrucarioid; very black; vary-
ing greatly in size and form; in the young state papilleform, in age flattened
and lecidioid ; they are scattered on the thalline areola, and are very conspicuous
on the whitish or cream-coloured thallus.
The plant has externally the facies of Coniothectwm lichenicolum, to which it
may really belong.+ Mr Cooxe, who examined it, describes the contained repro-
ductive corpuscles, which may be either sporidia or spores, as ‘‘ Toruloid spores.”
* Frequently erroneously written soleform. Soleaform sporidia are necessarily 1-septate. Vide
definition of the term in “ Otago Lich. and Fungi,” foot note, p. 447.
t Vide p. 519.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 541
Both thallus (of the host) and disks of the parasite closely resemble those of
Barmouth (North Wales) specimens of C. lichenicolwm.
(c) Lecanora cenisia, Ach. (which = var. atrynea, Ach., of Lecanora subfusca,
Ach. according to NyLANDER) from Ayton, Cleveland, Yorkshire, Mudd, in my
Herbarium, bears on its apothecia a minute punctiform parasite, containing solea-
form sporidia; here, however, of a pale, brownish-yellow hue.
(d) On thallus of Lecidea pachycarpa, Duf., Ireland, Admiral Jones, June
1858. Parasite is small, black, and Lecidioid, resembling certain lichen-spermo-
gonia of the flat, discoid type. Hymenium gives no blue with iodine. Paraphyses
filiform, indistinct, wavy, not coloured at tips; asci -0040" long, :00083" broad ;
sporidia colourless when young, gradually acquiring an olive or brown tint with
age; soleaform; 00066" to 0010" long, -00033" broad.
It is impossible to confound the perithecia or sporidia of the parasite with the
apothecia or sporidia of the Lecidea. The apothecia in question are very large
and conspicuous; while the sporidia of the Lecidea are also very large—-0040"
long, and -00133" broad; 7-septate, colourless, oval-oblong. The asci of the
Lecidea are, moreover, 1-spored, 0050" long, :0014" broad, becoming pale blue
with iodine. Its paraphyses are indistinct ; obscured about their irregular tips
by much granular, greenish pigment-matter, and throughout the length of their
bodies by the same colouring matter (in quantity), and by oil globules.
6. M. Stictaria. Parasitic on thallus of Sticta Freycinetiz, Dél., Campbell's
Island, Dr Hooker, Antarctic Expedition (sub-nom. S. scrobiculata). The con-
ceptacles of the parasite are small, black, and superficial, easily detached. Asci
8-spored, small, subsaccate, deep violet with iodine. This is, at least, an unusual
reaction if the plant is a fungus; while it does not appear to possess other
characters of a lichen! Sporidia brown, soleaform (1-septate),* resembling those
of M. rugulosaria, but much smaller.
7. M. parietinaria. Parasitic on thallus of Physcia parietina, L., Cottishall,
in Herb. Kew; on a single fragment of the Physcia. Parasite occurs as minute,
black perithecia, variously punctiform or papilleeform according very much to
size; partly immersed; much crowded on the thallus of the host; variously
resembling lichen-spermogonia (¢.g. of some Leczdec), or the smaller Verrucarie.
Asci not seen; sporidia brown, 1-septate, -0005” long, 00016" broad; soleaform
as in M. Stictaria and M. rugulosaria ; nearly of same size as those of latter,
but larger considerably than those of former. JZ. purietinaria must not be con-
founded with Phacopsis varia, Tul. (Mém., p. 125, tab. 14, figs. 1-3; Celidium,
Korb., Parerga, p. 456), which has 3-septate, ellipsoid, colourless sporidia,
according to TULASNE; but oblong and becoming brown, according to Korper.
8. M. Beomycearia. Parasitic on sterile thallus of Beomyces rufus, DC., Bal-
* Frequently erroneously written soleform. Soleaform sporidia are necessarily 1-septate. Vide
definition of the term in “ Otago Lich. and Fungi,” foot note, p. 447.
VOL. XXV. PART II. (ee
542 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
thayock Woods, Perth, June 1856, W. L.L. Thallus consists of a series of
minute, irregular pulvinuli, of a buff colour, on which the black perithecia of the
parasite are conspicuous by contrast. This contrast is rendered greater, however,
by the circumstance that the patches of thallus occupied by the parasite are
lighter in colour than the rest of its surface. The parasitic perithecia are
extremely minute and punctiform, so closely scattered as to give the thallus the
appearance of being covered with granules of coal-dust. Sometimes they are so
numerous and so closely aggregated as to become confluent in very irregular
patches. Under moisture, the single perithecia assume a papilleeform character.
The Microthelia cannot be confounded with the young apothecia of the Beomyces,
which are brown, and much larger in almost all stages of growth. Sporidia
of the Microthelia dark brown, oval; 3-septate; frequently or generally con-
stricted at or opposite the septa. The thallus of the same Bwomyces, as well
as that of B. roseus, Pers., is affected by Nesolechia ericetorum, Fw. (Kors.,
Parerga, p. 461), whose sporidia are minute, ellipsoid, sub-bacillar, simple,
and hyaline. On B. rufus also occur Lecidea parasitica, Flk., L. scabrosa.
Ach., ZL. inquinans, Tul., and LZ. arenicola, Nyl., as well as Thelocarpon epithal-
linum, Leight. *
9. MW. atricola. Parasitic on thallus of Lecanora atra, Ach., on red sandstone,
Derriquin, County Kerry, Taylor in Herb. Moore, Dublin; associated with
Lecanora periclea, Ach. (= var. of ZL. sophodes, Ach.). The parasite has the
facies of a Verrucaria or Endococcus ; its perithecia being minute, distinct, black
cones, with sometimes a flattish or depressed apex; becoming occasionally
irregular in form; seated on, scarcely 7m, the thallus of the host. Asci -0020°
long, ‘00066’ broad ; crowded with innumerable sporidia. Sporidia spherical,
simple, deep brown, about -000083" in diameter; resembling those of many
Calicia.
L. atra, on the Continent,+ is occasionally the seat of another parasitic fungus,
Gassicurtia silacea, Fée (NYLANDER, Prod. p. 91; Lich. Parisienses, No. 150),
which either affects the thallus or apothecia, sometimes occupying the place of the
latter. The parasite consists of black filaments, forming in the aggregate brush-like
masses, similar to the apothecium of Sphwrophoron in some of its old stages of
growth; it has a Spilomatic or glomeruliform facies. In the only authentic
specimen I have examined (in NYLANDER’s Herb. Lich. Paris., No. 150; on stones in
Forest of Fontainebleau), the thallus is sterile, consisting of a series of cushion-
like areole, more or less scattered, seldom closely aggregated. Some of these
white tartareous verrucee are occupied by the parasite, which is very black,
irregular in form, and easily distinguishable under the lens from the apothecia of the —
Lecanora ; surface generally more or lesssubgranular. The spores are deep brown;
* Vide Paper on ‘ Parasitic Micro-Lichens”’ (antea citat.).
+ And in New Zealand ; Linpsay, ‘* Obs. on N. Z. Lichens,” p. 540.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 343
spherical, ‘00033’ in diameter, generally with double contour—rough or granulate
- externally—resembling, in some respects, those of Sphwrophoron ; than which,
however, they are much larger. Sometimes in age they become oval and
unequally figure-8-shaped, as if in process of fission. What appear to be the nuclei
of the spores also occur abundantly, as much smaller spherical corpuscles,
00016’ to 00020’ in diameter, pale yellow, gradually becoming olive and brown,
exhibiting like the spores themselves double contour. NyLANpER describes (Prod.
91) its spores as black and spherical, and thinks the plant should be referred to
the genus Spilomium * (Uredinee).
10. M. vesicularia. Parasitic on thallus of Lecidea vesicularis, Ach., Switzer-
land; in Herb. Kew. Occurs as small but distinct black papillee, closely aggregated;
superficial; scarcely immersed ; externally resembling those of M. pygmea. It
resembles that species further in its asci being polysporous; but the sporidia are
1-3-septate, according to age; most usually the latter in maturity. The smaller
ones, when 1-septate, resemble those of M/. pygmwa. Hymenium gives no blue
with iodine. Asci -0027" long, and -00083" broad. Sporidia :00033’ to :00050"
long, 00016" broad, but variable in size ; fusiform or oval; brown. ~
Also having brown, minute sporidia, which are here, however, oval or
ellipsoid, and are sometimes concatenate, is a parasite that affects the sterile
thallus of what appears to be a Pertusaria, in Balthayock Woods, Perth, June
1856, W. L. L. No part of the hymenium gives blue reaction with iodine. The
thallus of Pertusaria communis is the seat of a parasitic fungus, Spilomiwm
Pertusariicolum, Nyl. (Enum. Génér. p. 91, and Synopsis, p. 144), which is conidio-
sporous, the spores being oblong and blackish. The same thallus is affected by
Lecidea parasitica, Flk., Sphinctrina turbinata, Pers., and var. microcephala, Ny}.,
Trachylia stigonella, Ach., Pseudographis elatina, Ach., and Opegrapha anomea,
Nyl.+
My Herbarium contains a number of other lichenicolous parasites, having
(more or less) characters resembling those of the Microthelice above described. But
I cannot at present venture to assign names, or a specific place in classification,
on account of the imperfections of their reproductive structure, the doubtful
nature of their habitats, or other difficulties as regards their determination or
description. The following are illustrations of this heterogeneous group of
parasites :—
1. Associated with Verrucaria epidermidis, Ach., var. analepta, Ach. ; banks
of Crinan Canal, Argyleshire; on birch; Aug. 1856, W. L. L.—It has quite
the thallus and aspect of a Verrucaria (e.g. gemmata); and it is impossible
to determine whether the thallus is that of V. epidermidis or other Verrucaria,
or belongs to the plant now to be described. Intermixed with the apothecia of
* A genus not mentioned in Berxsxey’s “ British Fungology” (1860),
t Vide Paper on * Parasitic Micro-Lichens” (untea citat.),
544 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
V. epidermidis are certain other perithecia—scattered, round, minute, punctiform
—somewhat prominent. Instead of paraphyses of ordinary character, the para-
site possesses long, delicate, branching filaments, like those of many lichen-sper-
mogonia. Asci are frequently grouped and ribbon-shaped; giving a faint blue-
reaction with iodine; 8-spored. Sporidia ellipsoid, colourless, 1-septate, exactly
like those of Verrucaria gemmata. The same hymenium, which contains spori-
diiferous asci and ramose paraphyses, contains also stylospores, oval or ellipsoid,
‘00066’ long; borne on long filiform basidia, resembling paraphyses; sometimes
l1-septate; occasionally exhibiting 3 nuclei, central largest.
2. Associated with Physcia obscura, Fr., var. leprosa, Hepp; Morchone, Brae-
mar; corticolous; Aug. 1856, W. L. L. (Mem. Spermog. p. 247.)—Black and
punctiform, but exhibiting no reproductive structure.
3. Associated with Lecidea ferruginea, Huds., var. sinapisperma, DC.; on
dead mosses, grasses, twigs of shrubs, &c.; Hepp Exsic. No. 200 (sub-nom.
Placodium sinapispermum, DC.)—Scattered over the decayed vegetation on which
the apothecia of the Lecidea occur, and apparently partly intermixed with them,
are very minute, black specks, which are perithecia, containing brown, 3-septate,
ellipsoid, largish sporidia or spores.
4. On thallus of Lecanora polytropa, Ehrh., var. intricata, Schrad., Penman-
shiel, Berwickshire; Hardy, Novem. 1856; saxicolous.—Parasite occurs on thalline
areolee as punctiform and black conceptacles, very minute, sometimes papille-
form and Verrucarioid, varying in size; full of corpuscles, which may be either
sporidia or stylospores (for neither asci nor basidia were observed), these re-
productive corpuscles being very variable in size and shape—spherical to
figure-8-shaped, simple to l-septate, and colourless. The parasite is certainly
not the Thelidium epipolytropum of Muvp (Brit. Lich. p. 298). I have also met
with what appears to be the latter, externally resembling Verrucarioid spermo-
gonia, and containing ellipsoid, 1-septate sporidia, with pale yellow loculi, but
having no distinct paraphyses; while Mupp describes the paraphyses as distinct
in his plant.
5. On apothecia (disk) of Physcia chrysophthalma, L., var. Dickieana, Linds.
(Nyl. and Mudd, Brit. Lich. p. 112; sub-nom. var. of Physcia villosa, Dub., in Linds.
Mem. Spermog., plate xiii. fig. 14); Belfast, Prof. Dickie Parasite consists of
small, round, brown, quite superficial papillae or points, easily removable. Its
envelope is composed of dark brown or bluish-brown cellular tissue, but the
conceptacle contains no sporidia, stylospores, nor spermatia.
6. On thallus of Zecidea albo-atra, Fr.; shore of Great Island, Cork, Carroll,
Sept. 1858.—Parasite is studded over areolate thallus as black papillee, generally
crowded; varying in size; frequently flattened and irregular in form; semi-
immersed ; sometimes confluent, and then very difform.
7. With Verrucaria fusiformis, Leight.; Douglas, near Cork; on ash; Carroll,
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 545
Mar. 1858.—Perithecia are black and punctiform, containing in great numbers
corpuscles that are ‘00025’ long, and 000066" broad; simple, or sometimes faintly
l-septate, brown, linear or ellipsoid-oblong, frequently somewhat constricted
centrally. Neither asci nor basidia were visible, and the corpuscles above
described may therefore be either sporidia or stylospores.
8. The horizontal squamules (and, to a less extent, the scales of the podetia
from base to apex) of a specimen of Cladonia bellidijiora, Ach., collected on Kelly's
Green, Ireland, by Dr Moorz, Aug. 1853, in Herb. Carrol), (Linds. Mem. Spermog.
p. 163), bear, copiously scattered, a parasite, which has certain of the characters of
NyLanpeEr’s Lecidea Cladoniaria* (Enum. Génér., Suppl. p. 339). His description,
however, is imperfect, ¢.g., as regards the sporidia, which, he hints, may some-
times be normally d7own. In the Irish plant, the sporidia are eight in each ascus,
arranged in one series; ellipsoid, simple, and colourless, 00033" long, -000111’
broad; asci elongated, 00166” long, 00033” broad; paraphyses with discrete
tips, but colourless, and not thickened. With apothecia, having externally the
characters partly of those of Abrothallus Smithi, partly of A. oxysporus, are
associated Pycnidia, containing stylospores precisely of the characters of the
sporidia as respects size, form, colour, and structure, ‘00033” long, ‘00014’ broad.
Externally, however, these pycnidia are always brown. In my “Memoir on
Spermogones and Pycnides,” I have described them as spermogones ; but their con-
tained corpuscles have rather the characters of stylospores.+_ The apothecia have
a convex surface in maturity; seldom sessile, and equally seldom altogether
immersed; the body or bulk being generally immersed, and the surface nearly on
the same level as the thallus of the host. They are discoid; black throughout ;
and their section resembles that of a double convex lens. In the young state they
appear as minute, black papillee, emergent from the thallus; in which condition
they are apt to be confounded with the pycnidia.
In my “Memoir on Spermogones,” I have mentioned this parasite under the head
of NyLANDER’s Lecidea Cladoniaria; to which I have also provisionally referred a
commoner parasite on Cladonia uncialis, Hffm. (p. 285, plate vii. figs. 14-16).
But the stylospores of the latter parasite are not the same as those of the para-
site on C. bellidiflora; and, indeed, the two parasites seem distinct in several
essential respects. Nor does NYLANDER mention either spermogonia or pycnidia as
possessed by his plant. While, then, it is possible that one or other of the parasites
in question is referable to NYLANDER’s plant, it is equally likely they are hitherto
undescribed. Should this prove to be the case, I propose for that which affects
* It may also be compared with his Lecidea oxysporella (Prod. 145), which grows on the thallus
of C. digituta on the Spliigen; and with Lecidea Cetraricola, Linds. (“ Lichenicolous Micro-Lichens,”
Quart. Journal of Microscopical Science, Jan. 1869).
t I have pointed out the anatomical or morphological distinction between stylospores and sj er-
matia in my paper on “ Polymorphism in the Fructification of Lichens ” (antea citat.).
VOL. XXV. PART II.
Ly
(
B
546 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
C. bellidiflora—as an appropriate name—A brothallus Moorei,* in honour of the
distinguished Director of the Botanic Garden of Glasnevin, Dublin, who has made
so many important contributions to the Irish flora—cryptogamic as well as
phenogamic.
The protothallus of various Cladonie is affected by Nesolechia punctum, Mass.
(Korper, Parerga, p. 461), the sporidia of which are minute, linear-fusiform,
simple, and hyaline.
9. On thallus of Squamaria crassa, Huds.; Crosshaven, Cork Harbour, Sullivan.
Parasite occurs as deep bluish-black round macul, surrounded frequently by a
black ring; both conspicuous on the buff-coloured thallus of the host; seated on a
sort of thalline papillze; body immersed. Paraphyses Verrucarioid—very delicate,
wavy, filiform, indistinct—not knobbed nor coloured at tips; asci :0028" long, and
00066" broad. Sporidia brown, soleaform, ‘00050" to 00066" long, :00025” broad ;
while in the asci always have the broadest and shortest end upwards.
This parasite is obviously different from the Spheria squamarioides and S.
gelidaria of Mupp. (Brit. Lich. p. 130), which affect the thallus of Squamaria
gelida, L.
Nor does it appear to be any of these parasites which copiously affects the
apothecia of 8. saxicola, Poll., in a specimen which I collected near Jerkin, Nor-
way (4600 feet), in August 1857. I have not in this case, however, been able to
detect reproductive structure. In its young state the parasite appears as black
spots on the epithecium. These gradually increase in number, and at length
coalesce till they cover the whole disk; which covering leads apparently to the
degeneration and consequent shrivelling of the whole apothecium. Its outline
becomes most irregular; both exciple and disk acquire a very black granular
surface, while the whole apothecium decreases in thickness. At a later stage it
appears as a very black shapeless granular mass, frequently crowded or confluent,
conspicuous on the pale stramineous thallus.
NyYLANDER (Scand. p. 133), describes a parasitic Sphwria as affecting, in some
parts of Scandinavia, Squamaria saxicola and S.chrysoleuca, Sm. Itis black, puncti-
form, immersed in the thallus; spores fusiform, colourless; possessed of spermo-
gonia, which are also black and punctiform, containing minute straight spermatia.
Korper (Parerga, p. 458) deseribes Conida clemens, Tul. (Mém. p. 124, sub
Phacopsis) as parasitic on the apothecia of Sqguwamaria chrysoleuca and saxicola ;
the sporidia being small, irregularly oblong, l-septate, and hyaline. Also Cerei-
dospora Ulothii (Parerga, p. 466), as affecting the thallus of S. saxicola ; sporidia
fusiform or cymbiform, 1-septate, and hyaline. S. sazicola is also affected with
Lecidea micraspis, Smrf., and Thelidium epipolytropum, Mudd.+
* In my MS. Notes on Moore's Irish Lichens—made in 1858—I named this parasite pro-
visionally Abroth. Cladoniarum, but any such specific designation is apt to lead to confusion with
Nyvanpver’s Lecidea Ciadoniaria.
+ Vide Paper on “ Parasitic Micro-Lichens” (anteu citat.).
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 547
10. On or with Lecanora varia, Ach., var. symmicta, Ach. ; on rotten stumps of
Pinus sylvestris, Blaeberry Hill, Perth, April 1858, W. L. L. Conceptacles, ex-
ternally resembling spermogonia, contain deep brown, oval or ellipsoid, apparently
simple, sporidia, 0005" long, 00033" broad.
11. On Lecidea rupestris, Scop. (sub-nom. Biatora rupestris, var. calva, Dicks.),
on limestone rocks, in Hepp’s Exsic. No. 134. Parasite consists of very small,
black, punctiform perithecia, scattered among the apothecia of the Lecidea, ex-
ternally resembling spermogonia, but containing very deep brown, oval sporidia ;
simple, or 1-septate, or both; the colour rendering it impossible to determine their
structure. NYLANDER arranges LZ. rupestris as a variety under Lecanora cerina ;
a classification to which I cannot subscribe.
12. Accompanying Pyrenothea verrucosa ; on old oak, Castle Bernard, near Cork,
Carroll. Parasite is seated on some of the thalline verruce, associated and apt
to be confounded with spermogonia; sporidia spherical, brown, -00025" in
diameter.
13. On thallus of Endocarpon microsticticum, Leight. (which appears to be
only a var. of Lecanora cervina, Pers.; having quite the aspect of the common
var. smaragdula, Whinb.); Barmouth, North Wales, Leighton, 1856. Hymenium
gives no blue with iodine. Asci sublinear, -00020” to 000233” long, -00033” to
0005” broad. Sporidia deep brown or olive according to age, 1-septate, oval,
0005” long, 00025” broad, arranged either in a single row, or in a double series,
in each ascus.
Endocarpon rufescens, Ach. is the seat of Spharia Hookeri, Ny. (Prod. p.
139 and 175; Linps. Otago Lich. and Fungi, p. 438), which has broadly fusiform,
3-septate sporidia (NyL. Prod. 139), becoming sometimes 5-septate or polysep-
tate and muriform (Mupp, Brit. Lich. p. 271, plate v. fig. 112), in all cases brown
—sometimes constricted centrally or opposite each septum.
Lecidea Endocarpicola. On the thallus of Endocarpon hepaticum, Ach.—on
walls, Lower Glanmire Road, Cork, Carroll—there is a parasitic Lecidea associated
with the apothecia and spermogonia of the Hndocarpon, having many of the cha-
racters of Z. aromatica, Turn. (which, however, is not known to occur in the
athalline condition). The paraphyses have deep brown or bluish-black apices,
which are irregularly knobbed; their bodies constitute, however, a mere striated
indistinct mass. Hymenial gelatine and asci become deep indigo-blue under
iodine; latter are 00233" long, and -00050" broad. Sporidia very variable in
size, length from 00033" to -00083", and in breadth from :000083’ to -000133’;
ellipsoid-oblong or linear-oblong; simple in young state, normally 3-septate in
maturity.
14. On thallus of Usnea barbata, Fr., var. florida, L.; Rio Janeiro, Henry Paul,
1851. Parasite is seated on some of the thalline tubercles usually occupied by the
spermogonia. Sporidia brown, l-septate; very different from the simple, colour-
048 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
less, oval sporidia of the Usnea. No hymenial tissue, asci, nor paraphyses can be
made out, even under iodine; which, however, produces in some places only a
blue reaction in the medullary tissue of the Usnea. The structure of the spermo-
gones of the Usnea is described and figured in my “‘ Memoir on Spermogones”
(p. 122, plate iv. figs. 2-5). This parasite has certain points of resemblance, espe-
cially as regards the sporidia, to Phymatopsis dubia, Linds., and Abrothallus Usnee,
Rabenh., as I have described and figured them in my ‘ Otago Lichens and Fungi”
(p. 442, et seq., plate xxx. figs. 36-41).
15. Onsterile thallus of Parmelia perlata, L.; India, M. C. Cooke, 1866; ordinary
a-ciliate form of the Parmelia as it occurs, from Britain, Norway, New Zealand,
and the Canary Islands, in my Herbarium. In what appears to be its highest
stage of growth, the parasite occurs as sub-rotund or sub-difform, raised, sub-
convex, black maculze, with a granulate irregular surface. In the young state it
is developed as punctiform or papilleeform bodies, sometimes girt with a ragged
thalline margin. In the young state the body is wholly immersed in the thallus
of the host or nearly so, while in age it emerges and becomes epithalline. In
none of its stages of growth does the parasite show sporidia or other reproductive
structure.
16. Associated with Verrucaria Taylori, Carr., and Opegrapha vulgata, Ach.;
corticolous; Dunscombes Wood, Cork, Carroll. Perithecia contain sporidia that
are brown, 3-septate, bulging opposite each septum; 00083” long, and -00033"
broad.
17. On thallus of Lecidea Hookeri, Scheer. (sub-nom. L. spherica, Scheer.) in
his Exsic. No. 526. The thalline squamules are dotted over with small, black,
prominent papille, externally resembling spermogonia, but containing sac-shaped
asci, and 1l-septate, colourless, ellipsoid sporidia, somewhat resembling those of
some forms of Verrucaria epidermidis. The same thallus bears the parasitic
Spheeria Hookert, Nyl. (Prod. 175 and 139; Linps. “Otago Lich. and Fungi,” p.
438)* with verrucarioid perithecia, and deep brown, 3-septate sporidia, ‘001’
* Two specimens of §. Hookeri (sub-nom, Verrucaria), which I examined in the Kew Herbarium,
had the following characters :—
1. Summit of Ben Lawers, Thallus Parmelioid, pale yellowish-white. Perithecia are quit
those of a Verrucaria ; seldom, however, forming regular cones or papillze; more usually flattened and
irregular as to form and size. None of the hymenial elements give blue with iodine. Sporidia
broadly ellipsoid, tapering suddenly at the tips ; 3-septate; becoming by longitudinal sub-division of
the loculi sub-muriform ; deep brown; ‘001” long, 0005” broad.
2. Gemmi, Switzerland. Perithecia much larger and ostioles more distinct; immersed or semi-
immersed ; bursting through the cortical layer of thallus, with—at least usually at first, in their
young state—stellate fissuring. Thallus here again Parmelioid and simple; usually buff-coloured,
sometimes pale green. The plant has an Endocarpoid facies.
In both cases the perithecia occur by themselves on a thallus, which appears to belong to them.
It seems to me that it is the same plant that occurs sometimes with a proper thallus (Verrucaria),
and at other times as an athalline parasite (Sphewria); that it has equal claims to rank as a Spheria
or Verrucaria ; and that it matters little whether it is classed among the Spherie or Verrucarie—
fungi or lichens—provided only fungologists and lichenologists would come to some common under-
standing regarding it !
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 549
long, and :0004" broad. The Zecidea itself (in my copy, original edition, 1847)
has simple, ellipsoid, colourless sporidia; while those of the true L. Hooker,
according to NYLANDER (Prod. p. 139), are brown and 1-septate.
18. On thallus of Lecidea sangunaria, Ach., var. affinis, Scher. (Exsic. No.
629, on left hand specimen in my copy, orig. ed. 1852). Intermixed with the
spermogonia, and indistinguishable therefrom ; but the parasitic perithecia con-
tain round, brown spores.
19. On thalline scales of Lecanora coarctata, Ach., var. involuta, Tayl. (sub-
nom. LZ. znvoluta, Tayl., Fl. Hibern., p. 134); Dunkerron, Taylor in Herb. Moore. ;
on grey sandstone; associated with Z. varia. Parasite occurs as minute black
cones, externally resembling spermogonia, but exhibiting no reproductive structure.
20. On thallus of an isidioid form of Lecanora parella, Ach. (sub-nom. Lichen
dactylinus, Ach.), collected by Dr Scorr, 1802; in Herb. Kew, where it was ex-
amined by Dawson TurNER. Associated with spermogonia, and externally
resembling them. Parasite is black and discoid; immersed, and bursting through
cortical layer of thallus of host.
21. On thallus of Verrucaria Garovaglii, Mont. (sub-nom. Thelotrema Scheereri)
Hepp, Exsic. No. 100; which I regard as a mere form of V. pallida, Ach. Parasite
may be externally confounded either with the sporidiiferous perithecia or spermo-
gonia of the Verrucaria; but its sporidia are oblong-ovoid, colourless, and 1-
septate.
22. On thallus of Graphis scripta, Ach., var. horizontalis, Leight. Exsic. No.
244 (sub-nom. G. serpentina, var.); Abdon, Shropshire. Intermixed with apo-
thecia and pycnidia, and externally resembling the latter; occurring here and
there as minute black cones, full of minute brown spherical sporidia.
23. Associated with Opegrapha atra, Pers., var., and Lecidea canescens. Aghada:
corticolous ; Carroll. Possesses no distinct paaicplnyses Sporidia simple, pale
brown, -00066" long, :00033” broad—contained in asci.
24. Associated with Lecanora pyracea, Ach. (sub-nom. Beatora rupestiis, var.
irrubata) in Leighton’s Exsic. No. 213, are conceptacles externally resembling
pycnidia or spermogonia, which contain not only stylospores but sporidiiferous
asci; in which, further, the stylospores and sporidia have the same characters.
The perithecia occur as small, brown, punctiform bodies seated on the thalline scales
of the Lecanora. Stylospores are oblong-ellipsoid—normally 1-septate; granular
or occupied by two or more nuclear globules or cellules in the young and older
States; borne on long, filiform basidia. Sporidia also 1-septate, and having
otherwise precisely the characters of the stylospores; asci 8-spored. There is no
possibility of confounding the internal structure of what appears to be a fungus
with that of the ordinary spermogonia of the Lecanora, which possess arthro-
sterigmata, and very short rod-shaped spermatia. The existence in this fungus of
stylospores and sporidia within the same perithecium—springing from the same
VOL. XXV. PART II. Tc
550 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
hymenium—is most interesting in both an anatomical and physiological point of
view. Ihave met with the same phenomenon in several other fungi, ¢.g., that
described in this paper as associated with Verrucaria epidermidis. Parallel
phenomena are the co-existence of sporidia and spermatia or stylospores in the
same perithecia in Spheria Inndsayana, Curr. (Linps. “‘ Otago Lich. and Fungi,”
p. 425, plate xxx. fig. 7); of sporidia and spermatia in Verrucaria atomaria,
Ach. (Linps. ‘‘On Polymorphism in the Fructification of Lichens,” in Quart. Journal
of Microscopical Science, Jan. 1868); and of spermatia in the ordinary sporidii-
ferous perithecia of Verrucaria, by GipeLLi (Annals of Nat. History, April 1866,
p. 270).
25. Associated with Lecidea luwrida, Ach., in Herb. Kew; “sea rocks near
Bangor, July 1802.” Thallus exhibits a number of spermogonia scattered about
the margins of its lobes as deep brown points, the body of the conceptacle be-
ing immersed in the thallus. Intermixed are the externally similar, but more
conoid, perithecia of the parasite, whose hymenium gives no blue with iodine. Asci
apparently polysporous; -0020" long, ‘00066’ broad. Sporidia fusiform or ellipsoid,
dark bottle-green or brown, irregularly 3-septate in maturity ; -0005" to 00066"
long, 00014" broad.
On the same sheet, and associated with ZL. /urida, are fastened specimens of
what appears to be the same lichen, labelled “No. 19, on rocks by the sea, Miss
Hutchins,” from Ireland doubtless. In both, the apothecia are distinctly Lecan-
orine in the young state, possessing a thalline margin, and thus differing alto-
gether from the Lecidea. But their apothecia resemble those of L. luwrida in
the old state, when the disk becomes sub-convex, and the thalline border dis-
appears, or is covered by the swollen disk. The disk in the Lecanorine apothecia
is usually of a lighter red than in LZ. Jurida. In Miss Hurcuins’ plant the thallus
is much paler than in Bangor specimens. The colour of the thallus obviously
varies, just as it does in Physcia aquila, with its degree of exposure to light; being
palest when the plant grows in the shaded crevices of rocks. In the Irish plant
the paryphyses are subdiscrete, with brown tips; the asci 8-spored, -00166" long,
0005" broad; the sporidia ellipsoid, colourless, apparently 1-septate, -00033°
long, 00014" broad. Probably the lichen in both the Bangor and Irish speci-
mens is Lecidea sublurida, Nyl. (Mupp. Brit. Lich. p. 172), which Mupp places in
the genus Thalloidima, Mass.
26. Several parasitic fungi, or fungoid growths of the most diverse character, —
affect the apothecia of Abrothallus Siithii, Tul. or are associated with its
pycnidia. But their apparent frequency in that lichen probably depends simply
on the greater amount of attention I gave to the examination of the pseudo-
genus Abrothallus while preparing my ‘‘ Monograph” thereof* in 1856.
* Quarterly Journal of Microscopical Science, vol. v. 1857.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. ODL
(a) Ben Lawers. Intermixed with the pycnidia of the Adrothallus, and
externally indistinguishable therefrom, is a minute papilleeform parasite, which
consists of an envelope of dark-brown, hexagonal, cellular tissue, enclosing
myriads of dark-brown spherical spores, which are frequently irregular or jagged
in outline, like blood-corpuscles in a condition of shrivelling from exosmosis.
(0) Var. Welwitzschit, Tul.; Amulree Road, Dunkeld. Black perithecia— exter-
nally resembling pycnidia, with which they are associated—contain nothing
but spherical oil globules, or corpuscles closely resembling them.
(c) Craigie Hill, Perth As in (a) and (6), intermixed with pycnidia, and like
them papilleeform or punctiform. They contain—
1. Largish, spherical corpuscles, with pale brownish-yellow subgranular proto-
plasm, resembling the sporidia of certain lichens, ¢.g. some forms of Lecanora
cinerea. Sometimes the protoplasm becomes distinctly circumscribed and
separated from the cell-wall by a varying hyaline interspace. This protoplasm
gradually acquires a nuclear character and a central position, and then divides
into two or four (sometimes three) equal subspherical segments, after the manner
of some of the larger forms of gonidia. In age, both cell-wall and outline of
nucleus, or its segments, become irregular, as if from shrivelling.
2. Corpuscles resembling shrivelled sporidia; most irregular in form, colour-
less, generally with double contour, and containing one or more largish, distinct
subspherical nuclei, and frequently also fine granular protoplasm. These cor-
puscles are often found attached to each other in groups of two or more.
3. Most irregular, ribbon-like tubules, marked by subspherical nuclei, which
are sometimes of an iodine colour. In some cases these would appear to be mere
chains of degenerate sporidia. Sometimes only two or three constitute the
pseudo-tubule, whose septa (the walls of the sporidia) have disappeared. But
at other times the outline of the sporidia remains; there isa pedicle formed by
the base of the shrivelled ascus; the nuclei are polar and distinct, sometimes
yellowish; or they are connected by a central canal, as in the sporidia of Physcia
parietina.
A solitary black conceptacle, externally resembling an apothecium of the
Abrothallus, picked off the bluish, curled squamules of the host (Parmelia saxa-
tis), consists of an envelope of dark-brown, honeycomb-like cellular tissue ;
rootlets being sent downwards into the tissues of the thallus of the Parmelia,
penetrating through its cortical and gonidic layers to the medullary tissue. It
contains—(1.) A parenchymaof colourless hexagonal cells, associated with mycelioid
tubes—also hyaline, but short and thickish, and intermixed with much oily
matter in the form of globules; (2.) Largish, spherical, colourless, sporoid
corpuscles, full of a nucleiform, cellular, or granular protoplasm.
On one of the true apothecia of A. Smzthiz, from Craigie, I found a large, dark-
brown, 3-septate sporidium, with bulgings opposite the loculi. Its size and form
Dd2 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
are so different from those of the sporidia of the Abrothallus (as figured in my
‘‘ Monograph,” pl. iv.) that it is more probably referable to some Sphwria or
fungus—not necessarily immediately associated with the Abrothallus, for in the
course of microscopic studies on lichens, I have frequently met with alien spori-
dia—sporidia belonging to other and topographically distant lichens or fungi.
Thus, in a specimen of var. Welmitzschu in Leicuron’s Exsic. No. 191, 1 found
a number of dark-brown figure-8-shaped sporidia on and among the thalline
rhizinee of Parmelia saxatilis. They had not the usual soleaform character of
the sporidia of A. Smthuv and its varieties; nevertheless they probably belonged,
in this case, to the parasitic Abrothallus.
(dq) Var. Welwitzschii (LEIicHTon’s Exsic. No. 191). A specimen of the
deformed thallus of P. saxatilis, without apothecia of the Abrothallus, bears
bodies externally similar—like some degenerate forms of the apothecia of A.
Smithu. Their envelope is of hexagonal cellular tissue, containing bodies like some
forms of gonidia in process of segmentation—large spherical cells with delicate
hyaline wall, enclosing centrally four bluish corpuscles, evidently resulting from
segmentation into four of a central spherical nucleus.
(e) A specimen of A. Smitha (from Glen Dee, Braemar; on boulders, August
1856, W. L. L.), bears a Spheerioid parasite on its apothecia. In another specimen
of the same Abrothallus, from Glenbeg, between Spittal of Glenshee and Braemar
(on a roadside wall), August 1856, a similar parasite, occurring on the thallus of P.
saxatilis, resembles externally the apothecia of the Abrothallus, and is apt to be
confounded therewith. It contains a mass of minute globular brown spores,
intermixed with a few partially disintegrated sporidia of the Abrothallus.
(f) Associated with A. oxysporus, Tul., and with the pycnidia of A. Smithii
(on an old wall, top of Craig-y-Barns, Dunkeld, June 1856, W. L. L.), on thallus
of P. saxatilis. Parasite punctiform, black, containing masses of hyaline Toruloid
spore-filaments, with myriads of very minute, also colourless, globular cells,
generally aggregated in irregular masses; associated with a few sporidia, partially
degenerate, both of A. oxysporus and A. Smithit.
Those parasitic fungi, accompanying Abrothallus Smithii, that are Verrucarioid
externally, are apt to be confounded not only with the pycnidia of the Abro-
thallus, but with young states of the apothecia of both A. Smith and A.
oxysporus.
27. In my copy of ScH#rRER’s Exsic. No 503, Calicium disseminatum, Fr.,
patelleforme, Sch., has not the sporidia of the Caliciwm, which are, according to
NYLANDER (Syn. 146), blackish, oblong, and sometimes subspherical; but ellip-
soid, colourless ones, ‘00033’ long, 00013” broad, contained in asci ‘00133’ long, —
00033” broad. There are no distinct paraphyses, and the plant may be regarded
as either Verrucaria or Microthelia—lichen or fungus.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
553
EXPLANATION OF PLATES XXIII, XXIV.
PuatTE
Figs. 1 to 18. Torula lichenicola.
1 to 12. On Lecanora subfusca.
1. Craig Choinich, Braemar,
(a) Portion of thallus, with apo-
thecia, of the Lecanora.
(b) Sections of said thallus and
apothecia—magnified.
(c) One of its apothecia—magnified.
(d) Spore-filaments and spores of
Torula.*
. Ben Lawers. Spore-filaments and
spores of Torula.
Loch Tay. Do.
Kyles of Bute. Do.
Caerlaverock road, Dumfries. Spores.
Dunglass, Berwickshire. Spore-fila-
ments and spores.
Pease Dean, Berwickshire.
Near Cork.
(a) Portion of thallus of the Leca-
nora with apothecia.
(b) Section of said thallus and apo-
thecia.
(c) Spore-filaments and spores of
Torula.
Castle Bernard, Co. Cork. Spore-fila-
ments and spores.
Rathconnae, Co. Cork.
(a) Portion of thallus, with apo-
thecia, of the Lecanora.
(b) Section of said thallus and an
apothecium.
Great Island, Cork.
(a) Portion of thallus of the Leca-
nora with apothecia.
(b) Spores.
Carrigaloe, Cork.
(a) Portion of thallus of Leca-
Spores.
OT Arp ww
so
10.
jibe
12.
nora.
(b) Section of do.
13. On Lecidea canescens. Aghada, Cork.
(a) Portion of thallus of the Lecidea with
apothecia.
(bc) Sections of said thallus and an
apothecium.
14. On Lecidea parasema. Ireland. Spore-
filaments and spores of the Torula.
15. Accompanying Opegrapha atra, Scherer’s
Exsic. No. 634. Spore-filaments and
spores.
16. Accompanying Verrucaria epidermidis,
var.; Malham, Yorkshire. Spore-fila-
ments and spores.
XXIII.
17. In spermogonia of Lecanora varia,
Leighton’s Exsie. No. 176.
(a) Portion of thalline scales bearing
spermogonia.
(b) Section of said spermogonia.
(c) Normal spermatia and sterigmata
of the Lecanora.
(d) Associated Torula.
(e) Spore-filaments and spores of do.
18. Torula lichenicola on Lecanora subfusca.
Ardrum, Co. Cork. Spore-filaments
and spores.
Coniothectwm lichenicolum.
On Lecanora parella. Morchone, Braemar.
(a) Portion of thallus of Lecanora,
showing the parasite on its
areolee.
(6) The Coniothecitum, magnified
and sectioned.
Isidium corallinum. Craigie, Perth.
(a) Section, logitudinal.
(b) Portions (terminal) of some of the Isidia,
variously magnified.
(c) Portion of the plant viewed from above,
showing the brown-tipped apices of
the Isidia.
Fig. 21. Parasite on I. corallinwm (sub-nom. Lichen
dactylinus, Ach.), in Herb. Kew.
(a) Section of disk.
(b) Sporidia.
Figs. 22 to 28. Coniotheciwm lichenicolum.
22. On I. corallinwm. Oraigie, Perth.
(a) Portion of thallus of the Isidiwm.
(b) Do. magnified.
(c) Sections of parasite.
23. Diplotomma calcareum. Clapham, York-
shire.
(a) Portion of thallus of the Diplo-
tomma.
(b) Do. magnified.
(c) Sections of the parasite.
Coniothectum lichenicolum.
Perth. Spores.
Do. Scuir-na-gillean, Skye. Spores.
Do. Sligachan, Skye. Spores.
Do. Mangerton, Co. Kerry.
(a) Portion of thallus of host.
Fig. 19.
Fig. 20.
24. Kinnoull,
25.
26.
27.
(b) Sections of the parasite, variously
magnified.
(c) Spores.
Do. NorthWales; Davies, in Herb. Kew.
(a) Sections of the parasite.
(b) Spores.
28.
* The magnifying power is that which I have uniformly adopted in my drawings of microscopical structure
in Lichens, viz., 425 diameters linear (under Objective No. 8, and Eye-piece No. 3) of a Nachet’s microscope
made for me in 1851 (vide ‘‘ Otago Lich. and Fungi,” foot note, p. 410).
VOL. XXV. PART Ii.
rey)
554
Fig. 29, Microthelia Cookei, on Lecanora crenulata.
Chichester.
(a) Section of hymenium, showing asci and
paraphyses.
(6) Sporidia.
Fig. 30. M. Stereocaulicola, on Stereocaulon paschale.
Glen Derrie, Braemar.
(a) Portions of the podetia of Stereocaulon
paschale, showing the deformities occu-
pied by the parasite; variously mag-
nified.
(6) One of the conglomerate wartlets iso-
lated.
(c) Sections of the parasite.
(ad) Ascus, with young sporidia.
(e) Mature sporidium.
Fig. 31. M. Umbilicarie, on Umbilicaria pustulata.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
Fig. 32.
Fig. 33.
Fig. 34.
Fig. 35.
Piate XXIV.
Fig. 1. Microthelia Nephromiaria, on Nephromiwm
cellulosum. Hermite Island.
(a) Old apothecium of the Nephromium ;
under side—bearing the parasite.
(b) Sections of the parasite.
(c) Section of hymenium, showing an ascus
and paraphyses.
(d) Sporidium, mature.
M. Nephromiaria, on Neuropogon Taylori.
Kerguelen’s Land.
(a) Ascus.
(b) Mature sporidia.
M. Umbilicarie. Norway.
(a) Section of hymenium, showing asci and
paraphyses.
(b) Young, and (c) Mature, ascus.
(d) Oil globules.
(e) Reaction of iodine on hymenial gelatine.
(f) Mature sporidia.
(Vide Plate xxiii. fig. 31.)
MM. Stictaria, on Sticta Freycinetii. Campbell’s
Island.
(a) Ascus, showing reaction with iodine.
(b) Sporidia, mature and young.
Parasite on Lecidea pachycarpa.
Sporidia, young and mature.
Microthelia Beomycearia, on Beomyces rufus.
Balthayock.
(a) Portion of thallus of the Beomyces,
showing—(1) its own young apothecia ;
and (2) the parasite.
(b) Portion of same thallus, further mag-
nified, showing young apothecia.
(c) Sections of said apothecia.
(d) Sections of parasite,
(e) Sporidia.
M. atricola, on Lecanora atra.
Co. Kerry,
(a) Perithecia, magnified ; one sectioned.
(b) Sporidia.
Parasite on Pertusaria.
Sporidia.
Gassicurtia silacea.
Exsic. No. 150.
(a) Portion of thallus of Lecanora atra,
showing the parasite on its areole.
(b) Two of said areole, further magnified.
(c) Sections of the said areole and of their
parasite.
d) Spores.
Fig.10. Microthelia vesicularia, on Lecidea vesicu-
laris. Switzerland. Sporida.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5. Treland.
Fig. 6.
Fig. 7.
Derriquin,
Fig. 8. Balthayock, Perth.
Fig. 9. Fontainebleau, Nyl.
Fig. 11.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
12.
is
St
16.
. Parasite on Lecidea albo-atra. Great Island,
. Parasite on Sguamaria crassa. Crosshaven,
Cork,
(a) Thallus bearing apothecia and the para-
site.
(b) Section of an apothecium and of the
parasite.
(c) Section of hymenium, showing ascus and
paraphyses,
. Parasite on Squamaria saxicola.
. Lecidea Endocarpicola, on Endocarpon hepa-
. Abrothallus Moore, on Cladonia bellidifiora,
, Associated with Verrucaria Taylort. Dun
Norway.
(a) Portion of thallus of the Umbilicaria,
magnified.
(b) Sections of the parasite.
(Vide also Plate xxiv. fig. 3.)
M. rugulosaria, on Placodium rugulosum.
Tasmania. Sporidia.
M. parietinaria, on Physcia parietina.
tishall. Sporidia.
Parasite on Thelotrema lepadinum.
(a) Sporidium.
(b) Stylospores.
Parasite on Lecanora cenisea.
land. Sporidia.
Cot-
Treland.
Ayton, Cleve-
Spilomium Graphideorum. Fontainebleau,
Nyl. Exsic. No. 72.
(a) Portion of thallus of Graphis, bearing
the parasite.
(6) Sections of the latter.
(c) Spores.
Parasite on Lecanora polytropa, var. intricata.
Penmanshiel.
(a) Portion of thallus of the Lecanora, with
apothecia and the parasite.
(b) Sections of young apothecia.
(c) Sections of mature apothecium and of the
parasite.
(d) Sporida or stylospores.
Cork.
(a) Portion of the thallus of the Lecidea with
apothecia and the parasite.
(b) Sections of (1) said apothecia and (2)
parasite.
(d) Mature sporidia.
Jerkin,
Norway.
(a) Portion of thallus bearing apothecia and
the parasite.
(b) Sections of said apothecia and para-
site.
Parasite on Endocarpon microsticticum.
Barmouth, N. Wales, .
(a) Section of hymenium, showing asci and
paraphyses.
(6) Mature sporidia.
ticum, Glanmire Road, Cork.
(a) Ascus under iodine, with young sporidia. —
b) Paraphyses, isolated.
Sporidia, mature and young.
Ach. Kelly’s Green, Ireland.
(a) Ascus.
(6) Mature sporidia.
(c) Stylospores.
combes Wood, Cork. Sporidium.
DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI.
Fig. 20. Associated with Verrucaria fusiformis. Dou-
glas, Cork. Sporidia. é
Fig. 21. Associated with Graphis scripta. Leighton’s
Exsic. No. 244. Sporidia.
Fig. 22. Microthelia Collemaria, on Collemamuscicolum,
Ach. On walls, Ingleby, Cleveland, York-
shire, Mupp, 1857. (Compare Parasite
(Spheria or Microthelia) on C. melenum,
Ach., in Linps. “ Otago Lich. and Fungi,”
p. 442; and “Mem. Spermog.” p. 272.)
(a) Section of hymenium, showing an ascus
and paraphyses ; with the reaction of
iodine on the hymenial gelatine.
(b) Mature sporidia.
Parasite on Usnea barbata, var. florida.
Janeiro. Sporidia.
Parasite on Urceolaria. Glenarm, Co. Antrim.
Spores or stylospores.
Associated with Opegrapha atra, Leighton’s
Exsic. No. 245. Sporidia.
Associated with Opegrapha atra, Scherer’s
Exsic. No. 634. Ascus and sporidia.
Spheria Hookeri, on Lecidea spherica.
Scher. (Exsic. No. 526). Sporidia ;
(a) One of them preparing to germinate.
S. Hookeri (sub-nom. Verrucaria), in Herb.
Kew.
(a) Specimen from the summit of Ben
Lawers ; perithecia magnified and sec-
tioned.
Fig. 23. Rio
Fig. 24,
Fig. 25.
Fig. 26.
Fig. 27.
Fig. 28.
Fig. 29.
Fig. 30.
Fig. 31.
Fig. 32.
Fig. 33.
Fig. 34.
Fig. 35.
555
(b) Specimen from the Gemmi, Switzerland ;
Sporidia.
Accompanying Hndocarpon rufescens, Ach.
Scherer’s Exsic. No. 465. Ascus with
young sporidia. (Perhaps Hndocarpon
cinerewm, Pers. 2)
Associated with Physcia astroidea, Fr., var.
Clementi, Turn. Sporidia. (Perithecia
verrucarioid.)
Associated with Umbilicaria hyperborea,
Hffm., Scherer’s Exsic. No. 151. Sporidia.
Parasite on Lecidea sanguinaria, var. affinis.
Scher. Exsic. No. 629.
(a) Sporidium,
(6) Spores.
Associated with Abrothallus Smithi, Tul.
Craigie Hill, Perth.
(a) Perithecium of dark-brown hexagonien-
chyma; parasitic on thallus of Par-
melia saxatilis,
(6) Mycelium ; (1) spores, and (2) oil globules.
(c) Spores,
Associated with Abrothallus oxysporus, Tul.
Craig-y-Barns, Dunkeld. Toruloid spore-
filaments and spores.
Associated with Lecidea lurida, Ach.
Herb, Kew. Sporidia.
(a) On seaside rocks, Ireland, Miss Hutchins.
(6) Seaside rocks, Bangor, July 1802.
In
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A
XV.—On the Thermal Energy of Molecular Vortices. By W. J. Macquorn
RanxIne, C.E., LL.D., F.R.SS. L. & E., &e.
(Read 31st May 1869.)
§ 1. Object of this Paper.—In a paper on the Mechanical Action of Heat,
which I sent to the Royal Society of Edinburgh in December 1849, and which
was read in February 1850, it was shown, that if sensible or thermometric heat
consists in the motion of molecular vortices supposed to be arranged in a par-
ticular way, and combined in a particular way with oscillatory movements, the
principles of thermodynamics, and various relations between heat and elasticity,
are arrived at by applying the laws of dynamics to that hypothesis.* The object
of the present paper is to show how the general equation of thermodynamics, and
other propositions, are deduced from the hypothesis of molecular vortices, when
freed from all special suppositions as to the figure and arrangement of the vor-
tices, and the properties of the matter that moves in them, and reduced to the
following form :—That thermometric heat consists in a motion of the particles of
bodies in circulating streams, with a velocity either constant or fluctuating periodi-
cally. This, of course, implies that the forces acting amongst those particles are
capable of transmitting that motion.
§ 2. Steady und Periodical Component Motions.—A vortex, in the most
general sense of the word, is a stream or current which circulates within a limited
space. Conceive a closed vessel of any figure and volume to be filled with
vortices, or circulating streams, the mean velocity of circulation in each such
stream being the same; and let the velocities of the moving particles be either
constant or periodic. How complex soever those motions may be, they may be
resolved into the following component motions ;—a motion of steady circulation
with the uniform velocity already mentioned as the mean velocity; and a motion
consisting in periodical fluctuations of velocity. Those two component motions
may be called respectively the steady circulation and the disturbance.
§ 3. Mean Pressure due to Centrifugal Force.—Let an elementary circu-
lating stream—that is, a circulating stream of indefinitely small sectional area—
be supposed to flow round and round in an endless tube with the uniform velocity
mw; let p denote the density of the stream ; do the sectional area. Consider two
cross sections of the stream at which the directions of motion of the particles are
* Transactions of the Royal Society of Edinburgh, 1850, vol. xx.
VOL. XXV. PART II. 7E
558 PROFESSOR RANKINE ON THE THERMAL ENERGY
contrary; and consider what resultant forces are exerted by the stream on the
two parts into which those two cross sections divide the tube. The mass of
matter which flows through each cross section of the tube in an unit of time is
pwde ;
and in each unit of time a mass of matter of that amount has its velocity reversed.
The force required in order to produce that reversal of velocity is of the following
amount in absolute units,
2 pw de ;
and such is the amount of each of the pair of inward pressures which the tube
exerts on the stream, and of each of the pair of equal and opposite outward
pressures exerted by the stream on the tube, tending to pull it to pieces. It may
be called the centrifugal tension of an elementary stream.
The velocity of the particles flowing in the stream may undergo periodical
fluctuations, positive and negative alternately ; these will cause periodical varia-
tions in the centrifugal tension; but the mean value of that tension will continue
to be that given by the formula.
The mean intensity of the centrifugal tension, in a direction tangential to the
stream, is found by dividing the amount given in the preceding expression
by the collective area, 2dco, of the two cross sections, giving the following result,
pu.
Suppose now that the stream is cut by an oblique sectional plane, making the
angle 6 with a transverse section. Then the area of that oblique section is
ereater than that of a transverse section in the ratio of 1:cos@; and the amount
of the component tension in a direction normal to the oblique section is less than
that of the total centrifugal tension in the ration of cos 0:1; whence it follows,
that the mean intensity of the component centrifugal tension in a direction
making an angle @ with a tangent to the stream is
pw? cos” 6.
Next, suppose a vessel of any invariable volume and figure to be filled with
vortices or circulating streams, the velocity of steady circulation being w, and the
mean density p. ‘The centrifugal force will cause a pressure to be exerted in all
directions against the inside of the vessel. To determine the mean intensity of
that pressure, irrespectively of periodical variations, conceive the contents of the
vessel to be divided into two parts by an imaginary plane, and consider what
will be the mean intensity of the force with which the circulating streams tend
to drive asunder the portions of matter at the two sides of that plane. The
. ———
:
;
4
:
.
OF MOLECULAR VORTICES. 559
plane will cut the streams that flow across it, some normally, others obliquely ;
and the tangents to those streams will have all possible directions relatively to a
normal to the plane, subject to the condition, in the case of isotropic action,
that the mean value of cos’@ must be the same for all positions of the plane.
But the sum of the mean values of cos’@ for three planes at right angles to each
other must be = 1; therefore the mean value of cos’@ is = ta and finally, the
mean intensity of the centrifugal pressure is given in absolute units per unit ot
area, by the equation,
aye
ee : 2 : : : : (1.)
§ 4. Energy of Steady Circulation compared with Centrifugal Pressure.—
The actual energy} of the steady circulation in an unit of volume, is expressed
in absolute units of work, as follows :—
wr
oe aOR aa OE Nie. oll pain Q)s
which, being compared with equation (1), gives the following result :—
as =e 2 ' . , ° . (3);
that is to say, the intensity of the centrifugal pressure on the unit of area is tivo-
thirds of the energy of the steady circulation in an unit of volume. This is one ot
the propositions of the paper of 1849-50, p. 151, eq. v.; but it is now shown to be
true, not merely, as in the former paper, for molecular vortices arranged in a
particular way, but for molecular vortices arranged in any way whatsoever,
provided their action is isotropic, and their mean velocity uniform.
A similar proposition has been proved by Warerston, Ciausius, CLERK
MAXweELL, and others, for the pressure produced by the impulse of small particles
flying about in all directions within a closed vessel, and rebounding from its
sides.
§ 5. Vortices with Heterotropic Action.—It is conceivable that in solid bodies,
molecular vortices may be so arranged as to produce centrifugal pressures of
different intensities in different directions. In such cases, it is to be recollected
that the sum of the mean values of cos’@ for the obliquities of any set of lines to
any three planes at right angles to each other is = 1; whence it follows, that if
Pp, p’, and p” be the mean intensities of the centrifugal pressures in any three
orthogonal directions, we have
p+p +p" = pw ; : , : (4);
* There is a well-known integration by which it is easily proved, that for a number of
; — ’ deal
directions equally distributed round a point, the mean value of cos”@ is 3°
+ Called by Tomson and Tarr the “ Kinetic Energy.”
560 PROFESSOR RANKINE ON THE THERMAL ENERGY
that is to say, the sum of the mean intensities of the three centrifugal pressures
in any three orthogonal directions ts equal to twice the energy of the steady circula-
tion in an unit of volume. This proposition was not in the paper of 1849-50.
which was confined to an isotropic arrangement of vortices.
§ 6. Energy of the Periodical Disturbances.—In the paper of 1849-50, p. 152,
equation x., the energy of the periodical disturbances was taken into account by
multiplying the energy of the steady circulation by a factor & greater than unity;
thus giving for the total energy in an unit of volume the following expression,
vr
2
€
4
xe)
kpu?
Q >
in which v* denotes the mean of the squares of the resultant velocities of the
particles with their combined motions. The values of the factor 4, being the
ratio which the total energy of the molecular motions bears to the energy of the
steady circulation, are to be deduced in each case from the results of experiments
on specific heat.
Thus the energy of the disturbances in an unit of volume is expressed by
(1) °F = 5(e-1)p 5 =, nee
It may now be observed, in addition, that the energy of the disturbances may,
and indeed must, be at times partly potential as well as actual; in other words,
partly due to displacement as well as to fluctuation of velocity.
Let + wu be the greatest fluctuation of velocity; then a particle of the mass
2
unity has the energy = due to that fluctuation, in addition to the energy due
to the steady circulation. It is only at the instants of greatest disturbance of
velocity that the energy is all actual: at every other instant the energy is partly
potential. Hence v? = kw? may be taken to denote, not the square of an actual
velocity common to all the particles, but the value to which the square of the
velocity of the particles would rise, if all the energy of the disturbances, actual
and potential, were expended in increasing the velocity of steady circulation.
§ 7. Total Energy of Thermal Motions.—The total energy of the motion, com-
pounded of steady circulation and periodical disturbances, in an unit of volume,
is expressed, as in the paper of 1849-50, by the following equation, which also
shows its relation to the centrifugal pressure,
kpw? 8k
a eee
in which (to recapitulate the notation) p is the mean density; w the velocity of
steady circulation; the centrifugal pressure p is expressed in absolute units of
OF MOLECULAR VORTICES. 561
force on the unit of area; and the proportion 4, in which the total energy of
thermal motions exceeds the energy of steady circulation, is a quantity whose
values and laws are left to be deduced from the results of experiment.
§$ 8. Determination of Centrifugal Pressures——The external pressure exerted
by any substance, as we find it in nature, is a complex quantity, being com-
pounded of the centrifugal pressure already mentioned, and of forces which may
be classed together under the name of cohesion. To enable us to distinguish
those components of the total pressure from each other, we have the principle,
that the centrifugal pressure varies as the density simply; whereas pressure or
tension, or siress (to use a general term), arising from cohesive forces, must
vary as some function of the density of a higher order than the first power.
The perfectly gaseous state is an ideal state in which the substance exerts
no external pressure except that which varies as the density simply; that is,
centrifugal pressure. It is impossible to obtain a substance absolutely in the
state of perfect gas; but the cohesive stress diminishes with increase of tempera-
ture and diminution of density in such a manner, that it is possible, as is well
known, to obtain substances approaching very nearly to the perfectly gaseous
state, such as atmospheric air and various other gases; and the actual pressures
of such nearly perfect gases may be used, either as approximate values of the
pressures in the ideal state of perfect gas, or as data for calculating the latter
kind of pressures by the method of limits. We thus have the means of determin-
ing, to a close approximation, the centrifugal pressure of a given substance at a
given temperature and density; the well-known formula being
ee Og ey Ore!) | kt UCP):
p Po To
in which 7, is the absolute temperature of melting ice; + the actual absolute
temperature; and Fs the value of the quotient 5 at the temperature of melting
0
ice, for the particular substance in question.
§ 9. Temperature and Specific Heat.—It is shown in the paper of 1849-50,
that temperature, according to the hypothesis of molecular vortices, is a function
of the quotient found by dividing the energy of the steady circulation in an unit of
mass by a constant depending on the nature of the substance; which constant
may be defined, as the value which the energy of steady circulation in an unit
of mass of the given substance assumes at a standard temperature, such as that
of melting ice. The energy of the steady circulation in an unit of mass is
whence it appears, that the principle stated as to absolute temperature is
VOL. XXV. PART II. 7F
562 PROFESSOR RANKINE ON THE THERMAL ENERGY
expressed by equation (7), already given in§ 8. The total energy of the thermal
motions in an unit of mass is expressed by dividing equation (6) of § 7 by the
density p; hence that quantity of energy (denoted for shortness by Q) is given
in terms of the absolute temperature by the following equation,
we Shep oR Dye.
Q= S. = se = ==> i oh T) . . . - (8).
The real specific heat of a substance, as defined in the previous paper, when
expressed in units of work per degree, is
dQ okp, 3p oT , dk
Je = dr 2 oT 20,7) Ot
(9).
in which ¢ is the real specific heat, in terms of the minimum specific heat of liquid
water, and J, JouLe’s equivalent, or the dynamical value of the ordinary thermal
unit.
There is one part of the specific heat which is necessarily constant for a given
substance in all conditions; and that is the part which expresses the rate of
increase with the temperature, of the energy of the steady circulation alone in an
unit of mass, viZ.,
Q ii Le: Po
AG: )= oan = == 2o5T : (10).
The part of the specific heat which depends on periodical disturbances is
expressed as follows :—
d ((k—1 3(k—1 Op yt . dk
dr {! k ey a 25 aa Bs ne dr j ; Op
It is only by experiment that it can be ascertained whether this part of the
specific heat is constant or variable. Experiment has proved that it is constant
for the perfectly gaseous state, and nearly, if not exactly constant, for other con-
ditions; but that its values for the same substance in the solid, liquid, and
gaseous conditions are often different.*
The apparent specific heat contains other terms, depending on the expenditure
of energy in performing external and internal work, according to principles of
thermodynamics which are now well known.
§ 10. Examples of the Proportion in which the Total Energy of the Thermal
Motions exceeds the Energy of the Steady Circulation.—In the perfectly gaseous
* According to the nomenclature used by Crausius, the phrase “ real specific heat” is applied
to that part only of the specific heat which is necessarily constant for a given substance in all
conditions. Hence, if that nomenclature were adapted to the hypothesis of molecular vortices, the
term real specific heat would be applied to the coefficient given in equation (10) only, and that given
in equation (11) would be considered as part of the apparent specific heat.
OF MOLECULAR VORTICES. 563
state, the coefficient given in equation (9) is the specific heat at constant volume;
and as that quantity is known to be constant at all temperatures, the second
term of the right hand side of the equation disappears, and it is reduced simply
to the following—
3kp
Jc = u . 2 . 5 . 5 Wy .
2PoTo ee
The specific heat, in dynamical units per degree, of a perfect gas under
constant pressure, is expressed as follows :—
Jd = Jo+ Pe _ he (#41). PDA aiid
PoT. ~~ PoTo \ 2
and the ratio in which the latter coefficient is greater than the former is,
therefore,
rou
Dy
Bir array
(14);
whence we have the following formule for deducing the proportion 4, borne by
the total energy of the thermal motions to the energy of the steady circulation,
from the ratio — as determined by experiment,
2
eo) (15).
is
This method is applicable only to substances that are nearly in the perfectly
gaseous state.
There is another method, applicable to the same class of substances, which is
expressed as follows :—
2
= “Peet PES PAE AE UTS OPE ie
This second method may be applied to liquids and solids also, under the follow-
aN
: Poo
state; and the specific heat ¢ must be nearly constant.
The ratio which the energy of periodical disturbances in an unit of volume
bears to the centrifugal pressure may be interesting in connection with hypo-
thetical views of the constitution of matter. It is expressed as follows :—
ing conditions; the quantity is to be calculated as for the perfectly gaseous
ss lea oulkys, kadai aati daa avg
564 PROFESSOR RANKINE ON THE THERMAL ENERGY
The following are some examples of the results of calculations by for-
mulee (15) and (17) :—
Substance, — k 5(H =)
Atmospheric air, .. : 1-408 1634 0-951
Nitrogen, ; ; 1-409 1630 0:945
Oxygen,. . . . 1400 1667 1-000
Hydrogen, ; : : 1-413 1614 0921
Steam-gas, . - : 1:297 2°242 1863
§ 11. General Equation of Thermodynamics.—In the paper of 1849-50, pp.
158 to 164, the general equation of thermodynamics (equation 6 of that paper-
p. 161) is deduced from the hypothesis of molecular vortices, on the supposition
of a special form and arrangement of the vortices. In a subsequent paper, ‘On
the Centrifugal Theory of Elasticity,” read to the Royal Society of Edinburgh in
December 1851 (‘ Transactions,” vol. xx. pp. 433 to 436), the same general
equation (being equation 25 of the latter paper, p. 436) is deduced from the
hypothesis of molecular vortices, without any special supposition as to the form
and arrangement of the vortices, but with certain assumptions as to the laws of
the elasticity of the matter which moves in them. In a paper read to the British
Association in 1865, and published in the “ Philosophical Magazine” for October
of that year, a further generalisation is effected; and it is shown that the general
equation of thermodynamics follows from the supposition, that sensible heat con-
sists in any kind of steady molecular motion within limited spaces, without any
assumption either as to the figures of vortices, or as to the special properties of
the matter that moves in them. The object of this section of the present paper
is to show how the same general equation is deducible from the hypothesis of
molecular vortices, as stated at the commencement of the paper; that is, freed
from all special suppositions except that of a steady circulation, combined with
periodical disturbances of speed, whose energy may bear any proportion, constant
or variable, to that of the steady circulation.
The forces by which an elementary circulating stream, whether flowing with
a steady or with a fluctuating speed, is kept in a given state of motion, and of a
definite figure and dimensions, are equivalent in their action to a tension exerted
at each cross-section of the stream, of an amount which, at a given cross-section,
and at a given instant, is expressed in absolute units of force by the product of
the mass which flows along the stream in a second into the velocity of flow at
that cross-section and instant. The mean value of the tension is the product of
the same mass into the mean velocity; that is, into the velocity of steady circu-
lation. Hence the mean centrifugal tension, as this force may be called, is pro-
portional to the square of the velocity of steady circulation, and therefore to the
absolute temperature; and the work done by the forces to which the virtual
OF MOLECULAR VORTICES. 565
tension is equivalent, during a change of the figure and dimensions of all the
elementary circulating streams in a given body, may therefore be expressed by
multiplying the absolute temperature by the change in the value of a function,
to be afterwards determined, of the dimensions, figure, and temperature. If to
that function be added a function which is the integral of the increment of the
energy of steady circulation divided by the absolute temperature, the sum is
what I have elsewhere called the thermodynamic function. Let it be denoted by
¢; and let dQ denote the quantity of energy which must be communicated to
the body, in order to produce the increment d. ¢ in the thermodynamic function
at the mean absolute temperature 7 ; then we have
PE ENS” ae een a ei
and this, when the proper value has been assigned to the thermodynamic
function, is the general equation of thermodynamics. The process of finding the
value of the thermodynamic function is well known; but a summary of it will
be given here for the sake of completeness :—
Let dx, dy, dz, &c., denote changes in the dimensions of unity of mass of the
body, of the nature of strain, such as dilatations and distortions; and let
X, Y, Z, &c., denote the forces, of the nature of elastic stress, which the body exerts
in the respective directions of such changes; so that while the thermodynamic
function undergoes the change d¢, the external work done by unity of mass of
the body is
Xda+Ydy + Zda+ &e.;
Then, by the principle of the conservation of energy, it is necessary that the
following expression should be a complete differential :—
tdh — Xda — &e.;
whence it follows, that the thermodynamic function ¢ is the integral of the
following set of partial differential equations :*
Eee ee es Oe,
Ge dr dy de> de de?
that is to say, the thermodynamic function has the following value :-—
dX
9= Wr) + “dat f O dy + &e.;
dr
in which all the integrals are taken at constant temperature.
For a perfect gas at constant volume, we have dQ, = Je dr, in which Jc is the
* See Philos. Mag. for December 1865.
VOL. XXV. PART II. 7G
566 PROF. RANKINE ON THE THERMAL ENERGY OF MOLECULAR VORTICES.
dynamical value of the specific heat of the gas at constant volume; and conse-
quently, (7) = Jc hyp. log. 7; and the same is the value for any substance
which, at the temperature 7, is capable of approaching indefinitely near to the
perfectly gaseous condition. There is some reason for believing that all substances
may have that property;* but to provide for the possibility, pointed out by
Cuausius (“PoacenporFr’s Annalen,” vol. xcvi. p. 73), of the existence of substances
which at certain temperatures are incapable of approaching indefinitely near to
the perfectly gaseous condition, we may make (as that author does),
(7) = Jc hyp. log. t — x(7);
where x (r) is a function of the temperature, which becomes = 0 at all tempe-
ratures at which an indefinitely close approximation to the perfectly gaseous
state is possible; thus giving, for the complete value of the thermodynamic
function,
gh = Jc hyp. log. t + x(7) +f[S da + [2 dy + &ce. : (19).
That expression may be abbreviated as follows :—Let U be the potential energy
of the elastic stress of unity of mass of the body at constant temperature; then
g = Jchyp. log. 7 + y(r) + _ - . : (20);
and the corresponding form of the general equation of thermodynamics is as
follows :—
dQ = Je+7xX (th dr+rd . = ee
§ 12. Conclusion—In conclusion, then, it appears that the special supposi-
tions as to matters of detail, introduced into the hypothesis of molecular vortices
in the paper of 1849-50, are not essential to the deduction from that hypothesis
of the principles of thermodynamics, but that such matters of detail may be left
open to be determined by future investigations.
* See Phil. Mag. December 1865.
© S67)" )
XVI.—On the Alkaloids contained in the Wood of the Bebeeruor Greenheart Tree
(Nectandra Rodici, Schomb.). By Dovatas Mactagan, M.D., F.R.S.E.,
Professor of Medical Jurisprudence in the University of Edinburgh, and
ARTHUR GAMGEE, M.D., F.R.S.E., Lecturer on Physiology in Surgeon’s Hall,
Edinburgh.
(Read 8d May 1869.)
In a paper read before the Royal Society of Edinburgh in April 1848,* Dr
MacuaGan described the general properties of the alkaloid, whose presence had
been indicated in the bark of the bebeeru or greenheart tree, by Dr Rope of
Demerara, and described the mode cf. preparation of its sulphate for medicinal
use. The fact that bebeerine appeared to possess marked antiperiodic pro-
perties,} rendered its careful chemical study desirable, and accordingly the alka-
loid, purified as far as possible, was subjected to analysis by Drs Maciacan and
Trmuey.{ It resulted from this research that bebeerine is an uncrystallisable
base, very soluble in alcohol, less so in ether, and very sparingly so in water. It
forms with acids salts which are all uncrystallisable. With perchloride of
gold, mercury, copper, and platinum, it gives precipitates which are soluble to a
certain extent in water and alcohol, but which are deposited in a non-crystalline
form when the solution cools. To this base the author assigned the formula
C,,H,,N,0,(C=6). Von Pianta* subsequently attempts to purify further the
alkaloid, and assigned to it the formula C,,H,,0,N(C=6) or C,,H,,0,N(C=12.)
In consequence of the apparent impossibility to obtain bebeerine in a crystal-
line form, it is impossible to state whether the substances examined by Maciacan
and TILLEY, or by Von Puanta, were absolutely pure; and there is no evidence
to show that the product obtained by the latter chemist was purer than that
examined by the former investigators. Since the time when these papers were
published, sulphate of bebeerine has found its way into medical practice, and
the experience of many appears to show that it is possessed of no insignificant
tonic and antiperiodic properties. The sulphate of bebeerine, as it occurs in the
market, has been, we believe, almost entirely manufactured by Messrs MAcFARLANE
& Co. of Edinburgh.
Experimenting with various portions of the bebeeru tree, one of the members
* Transactions of the Royal Society of Edinburgh, vol. xv. part. ii.
+ Mactaean, Edinburgh Medical and Surgical Journal, April 1845.
+ London and Edinburgh Philosophical Magazine, series ni. vol. xxvil. p. 253.
VOL. XXV. PART II. 7H
568 DRS MACLAGAN AND A. GAMGEE ON THE. ALKALOIDS CONTAINED
of that firm discovered that, on subjecting the wood to a process similar to that
which had been used in the separation of bebeerine from the bark, a product was
obtained which did not apparently differ from bebeerine in its physical properties.
He requested us to undertake for ourselves the examination of the product which
he had obtained from the wood. ,
The substance handed to us for examination had been prepared by subjecting
the wood of the bebeeru tree to a process substantially identical with that recom-
' mended in the “ British Pharmacopceia” for the extraction of the sulphate of
bebeerine from the bark. The product did not differ in appearance from the
latter substance as it occurs in commerce, 7.é., it was in the form of shining
yellowish-brown scales, soluble in water, and possessed of an intensely bitter
taste, not differing perceptibly from that of sulphate of bebeerine.
In the first place, a portion of this substance was dried in the water-bath, and :
then the amount of sulphuric acid determined.
(1.) 2°001 grms. of substance yielded 0:5300 grms. of cnigliate of barium. ]
(2) 2.001 germs. of substance yielded 0:483 grms. of sulphate of barium. |
The mean of these two results gives to amount of sulphuric acid (calculated
as H,SO,) as 10°69 per cent. This would indicate that the substance examined
consisted of sulphate of bebeerine, mixed with other substances; or that it was
composed of the sulphate of one or more alkaloids, having a higher molecular
weight than bebeerine.
One hundred grammes of the powdered but undried sulphate were dissolved
in two litres and a half of distilled water. An insignificant quantity of a brownish
powder was left undissolved. The fluid was filtered through calico, and precipi-
tated carefully with solution of ammonia. The bulky precipitate was collected
on calico, carefully washed, and dried on the water-bath. When dry, it was
boiled for some time with chloroform. The latter fluid soon acquired a deep
brownish-yellow colour. The residue was treated three successive times with
chloroform. At the end of that time, the chloroform appeared to exert no action
upon the tolerably abundant residue. When dried, the chloroform extract
weighed 60°55 grammes; it had a brownish-yellow colour, and broke witha
resinoid fracture. When powdered, it possessed a very pretty yellow colour.
We shall, in the first place, state the result of our examination of this sub-
stance before proceeding to that of the bodies which were left undissolved by the
chloroform.
I. Examination of Nectandria, a new Base soluble in Chloroform.
The chloroformic extract, to which we have referred, left no ash when ignited
on platinum. It was very freely soluble in rectified spirit; less soluble in absolute
alcohol. It was not perceptibly dissolved by cold distilled water. When boiled
with water, it very readily fused at a temperature below 100°C.; and the boiling
IN THE WOOD OF THE BEBEERU OR GREENHEART TREE. 569
solution, when filtered, deposited a small quantity of yellow powder, which was
found to be amorphous when examined under the microscope. 49 grammes of
the solution in boiling water yielded 0:07 grammes of dry residue; or 100 parts
yielded 0-142 parts of solid residue. The powder was found to be entirely soluble
in dilute acid; the solution possessed a yellow colour, and an intensely bitter
taste. The residue, dissolved in water, and treated with solution of ammonia, or
of any of the fixed alkalies, yielded a bulky yellowish precipitate. When evapo-
rated to dryness, and redissolved in water, a perfectly neutral solution was
obtained. This was abundantly precipitated by tetrachloride of platinum, the
precipitate being quite amorphous, and not fusible when heated to 100°C. 0°709
grammes of this hydrochlorate yielded 0-268 grammes of chloride of silver; 100
parts, therefore, contained 9:361 per cent. of chlorine. Oil of vitriol added to the
base did not blacken it, but merely caused it to assume a faint rose tint. When
binoxide of manganese was added to the acid solution thus obtained, a most
splendid rich green colour was developed, which, on exposure to the air, passed
into a violet of great beauty, scarcely distinguishable from that procured when
strychnia is similarly treated.. This reaction is one of very great delicacy. On
adding sulphuric acid and binoxide of manganese to a fragment of the alkaloid
placed in a tube, and afterwards diluting the fluid sufficiently by means of oil of
vitriol, we observed its effects on the spectrum. In the case of the green fluid
first spoken of, the violet end of the spectrum was cut off, and when a sufficiently
thick stratum was examined none but the red rays passed. No definite absorption
band was, however, present.
After assuming the violet tint, besides a cutting off of the violet end of the
spectrum, a very well-marked absorption band, situated between C and D, is
noticed, as is shown in the annexed diagram.
A Br c D E
| 1 2 3 : ip |
Pee tvsoluntbushnn mili i WA) EE ee AIRE nial Hil HM hit fe byididdt I|
The reaction above described was possessed equally by all compounds of the
alkaloid under examination.
On heating the alkaloid on a platinum spoon, it first melts, and then burns
with the evolution of fumes which are both pungent and fragrant. ‘These are
identical with the fumes evolved under the same circumstances by bebeerine.
A comparison of the properties which we have described with those of pure
bebeerine, established in the clearest manner the difference between the two.
The chief of these differences are—
ene
Ig a
pean
570 DRS MACLAGAN AND A. GAMGEE ON THE ALKALOIDS CONTAINED
lst, The ready fusibility in hot water of the base from the wood.
2d, The beautiful and most delicate reaction with binoxide of manganese and
sulphuric acid, which is not possessed by bebeerine.
3d, The much smaller solubility of the new base in ether. With regard to
this point it may be stated, that, in a paper previously quoted, one of us had
stated the solubility of bebeerine in ether to be 1 in 13. The ether used had a
specific gravity of 730.
On repeating, however, our observations with perfectly pure ether, of density
0-715, and pure bebeerine, which had been prepared from the bark exhibited by
the firm of MacrarLaANnE & Co. in the Great Exhibition, we ascertained the
solubility to be smaller.
100 parts of this ether dissolved, at 14° C., 0:96 parts of pure bebeerine.
Under the same circumstances, 100 parts of this ether dissolved 0:201 parts
of the base from the wood. After being boiled in contact with the base for ten
minutes, being filtered and evaporated, 100 parts of ether was found to have
dissolved 07188 parts of our new base. These numbers are, however, higher than
the truth. After the two latter determinations, it was found that the substance
which had been used retained chloroform with great tenacity, and could only be
freed from it by very prolonged heating and exhaustion im vacuo. The base,
when purified by a process to be mentioned below, and thoroughly dried, was
again treated with ether.
1. After standing for many days in contact with it, ether of density 715 had
dissolved only 0:04 parts of alkaloid.
2. After standing for twenty-four hours only, in contact with the same sample
of base, 100 parts of the same ether had dissolved only 0-021 parts of the base.
We have mentioned that the base which we obtained from the wood possessed
a fine yellow colour. This colour is not, however, essential to it.
On treating the yellow solution of the hydrochlorate of the base with animal
charcoal, the solution is almost completely decolorised ; and when treated with
solution of ammonia a precipitate is obtained, which, after being drained and
allowed to dry (without the application of heat), either in the air or zn vacuo,
occurs in the form ofan almost purely white powder. When heated in the water-
bath, it soon acquires the fawn colour which it possessed before the treatment
with charcoal.
On dissolving the white powder in alcohol, and evaporating the solution, a
translucent residue of yellowish tint is obtained. All-attempts to obtain this
base in a crystalline form have failed. Obtained by evaporation from alcohol,
chloroform, or ether, like bebeerine, it never presents the slightest crystalline
form.
We have ascertained the composition of this base, to which we now assign
the name of Nectandria, by the analysis of two different samples, one of which
IN THE WOOD OF THE BEBEERU OR GREENHEART TREE. 571
was quite white, the other possessed of a light fawn colour. We must remark,
that this alkaloid is excessively difficult to burn. In the two first analyses
quoted, the substance was burned in the manner now usual with oxide of copper
and oxygen gas, taking great care to have a sufficient quantity of copper
turnings in the anterior part of the tube. In the third analysis, we used the
method proposed by GrnrL, one of RocunepErR’s pupils, and which consists in
mixing the substance intimately with fused and powdered bichromate of potash
and powdered oxide of copper, and filling up the tube as usual with granulated
oxide of copper. Operating with the greatest precaution, the combination was,
however, not completed until a very considerable quantity of oxygen gas had been
passed through the tube.
I. 0:225 germs. of substance gave 0:139 germs. of water and 0°583 grms. of
carbonic acid.
If. 0:317 grms. of substance gave 0:194 grms. of water and 0°816 grms of
carbonic acid.
III. 0272 grms. of substance gave 0158 grms. of water and 0°6945 grms. of
carbonic acid.
Nitrogen was determined by Witt and VaRRENPTRAPP’S method. The ammonia
evolved was collected in standard sulphuric acid.
04015 grms. of substance yielded ammonia, which required for neutralisation
13 cubic cents. of normal sulphuric acid (1 C.C. corresponded to 0°0177 ammonia,
or 0°014 grms. of nitrogen).
These numbers lead to the following per-centage composition :—
I. Il. Ill. Mean.
Carbon, ‘ : - (0:26 70°19 69°63 70:02
Hydrogen, : ; 6:86 6°81 6°43 6°73
Nitrogen, : : 4:53 4:53 4°53 4:53
Oxygen, : : 18°35 18:47 19°31 18-72
The double compound, with tetrachloride of platinum, was employed in the
determination of the atomic weight of the base.
(1.) 0:2985 grms. of the salt gave 0-053 grms, of platinum = 17-72 per cent. of platinum.
(2.) 0:259 9 ) 0046 39 29 = lag fev ” 93
(3.) 0°1735 “ 33 00295 __,, m = 17:0 i a
(4.) 0:288 ¥ es 0-052 BS a — 18:05 - ,
(5.) 0°329 ‘, =f 0:06 9 a = 18:23 = 99
The mean of these five determinations gives the per-centage composition of
platinum in the double salt as 17°72, from which we deduce 348-08 as the atomic
weight of the alkaloid. From the above numbers, we deduce for our new
alkaloid, Nectandria, the formula—
C,oH,3NO,(C=6.)
Crile N O (C=12')
VOL. XXV. PART II. (ey
572 DRS MACLAGAN AND A. GAMGEE ON THE ALKALOIDS CONTAINED
This gives by calculation—
Found.
Carbon, . : : 70°38 70:02
Hydrogen, : : 6-74 6:70
Nitrogen, . ; ' 4:10 4:53
Oxygen, - : : 18-79 18°71
100:00 100-00
According to this formula, the compound with tetrachloride of platinum
should contain ; é } : : : 18°07 per cent. of platinum,
Mean of five determinations, . Lt-F2 2 a
According to this formula, the hydrochlorate
of the base should contain é : : 9°60 _ per cent of chlorine.
Actually found, y : ' : 9°361 Me
Below the formula of bebeerine, as ascertained by Von PLANTA, is placed side
by side with that of nectandria, as ascertained by ourselves—
Bebeerine, : E : C,H Oe
Nectandria, : 3 : Cts, aN.
II. ELxamination of a new Base insoluble in Chloroform.
In a previous part of this paper it has been stated, that the precipitate pro-
duced by ammonia in a solution of the mixed sulphates obtained from the wood
of the bebeeru tree, was by treatment with chloroform subdivided into two portions,
of which one, Nectandria, has been already examined.
After the treatment with chloroform, 16:7 grammes of a greyish solid matter
remained. This matter was nitrogenous, soluble in dilute acids; its alcoholic
solution had a very marked alkaline reaction; its solution in hydrochloric acid was
abundantly precipitated by tetrachloride of platinum. On boiling the base with
water, the latter soon acquired a rich yellow colour, and possessed a very bitter taste;
the solution had a strongly alkaline reaction. On allowing the hot solution to cool,
a yellow powder subsided. When examined with a power of 300 diameters, this
powder was seen to be uniformly composed of nodules, and clustres of nodules.
On repeatedly dissolving the powder in boiling water, and examining the deposit
which subsided on cooling, the same forms were visible. From the portion of
residue insoluble in chloroform, we obtained 5°65 grammes of this yellow sub-
stance, which our observations prove to be a powerful base.
It was entirely soluble in water.
1. 100 grammes of the boiling solution, on being evaporated, gave 2:11 grammes _
of solid. residue.
2. 100 grammes of the solution which had cooled, and had deposited the yellow
nodules, yielded 1:77 grammes of solid residue. P
From these determinations, it would appear that one part of this yellow base
IN THE WOOD OF THE BEBEERU OR GREENHEART TREE, 573
is soluble in 56°81 parts of cold water, and in 473 parts of boiling water. The
aqueous solution possessed a powerfully alkaline reaction. When boiled with a
solution of chloride of ammonium, ammonia was evolved abundantly ; when
treated with solution of nitrate of silver, a white precipitate fell, which became
black on boiling.
Sulphuric acid dissolved the yellow base with the production of a dirty
brownish-yellow colour. When binoxide of manganese was added to the acid
solution, a magnificent green colour was produced, which, on exposure to air,
changed to a rich purple, and ultimately assumed a dirty red tint. This reaction
was compared with, and found to be identical with that manifested by nec-
tandria, although, from the very remarkable differences in the action of solvents
upon them, the one alkaloid could not be contaminated with the other. The
yellow base is rich in nitrogen; and when heated on platinum it melts, and
evolves the same fumes as bebeerine and nectandria.
When dissolved in hydrochloric acid, and treated with tetrachloride of
platinum, a yellow precipitate falls, which on the fluid being heated to boiling
point fuses, and is then perceptibly dissolved. <A portion resists solution, and is
converted into a brown substance. On cooling, the solution deposits a yellow
powder, which is not amorphous, but displays, under a power of 300 diameters,
clusters of nodules similar to those of the alkaloid itself, as it is deposited from
its aqueous solution. The platinum was determined.
I. 0551 germs. of the double salt gave 0-111 grms. of platinum =20-1 of
platinum per cent.
II. 0345 germs. of the double salt gave 0:071 grms. of platinum =20-57 of
platinum per cent.
We reserve the further examination of this base for a future memoir; as far
as our examination goes, it however appears to show, that this is best charac-
terised and most clearly separated of all the products obtained from the bebeeru
tree.
III. Hxamination of the Substance Insoluble in Chloroform and in Boiling Water.
After treatment with chloroform and with boiling water, there still remains a
considerable residue. It appears, from the observations which we have hitherto
made upon it, that this residue possesses all the characters of a non-crystalline
vegetable base, or of a mixture of such bases. It is soluble in alcohol, and almost
completely insoluble in ether and chloroform. Its alcoholic solution possesses
an alkaline reaction. The substance is capable of neutralising acids, and forms
with platinum tetrachloride, a compound which is fusible in boiling water.
It is our intention to prosecute further the chemical characters of the alkaloids
of the wood of the bebeeru tree, and more particularly to direct our attention
to their therapeutical properties.
i)
a
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CHARTS SHEWING (I) BY ISOBARIC LINES THE MEAN PRESSURE oF THEATMOSPHERE AND (2) BY ARROWS THE PREVAILING WINDS over THE GLOBE cach MONTH FROM DECEMBER To MAY.
(alms marked thus O- Variable Winds taos *
PLATE XXVv,
= DECEMBER ~ |
JANUARY | he | f fee}
| | | f
i i 1 i
= = SSS 7 ; = 5 es 160 70 20 LeagmdcI) Wertct 80 Geax 6O ah x 7 Tr as 77 = - rt (00 Wert af BO Greardh 60 4 0 2 10 69 BO Lefimds 100 Fart of 120 lem 140
iso
as ——
4 aoe ; Pai a - 3 f Sime
alfa Se ico A lL] 3 | (ieee
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CHARTS SHEWING (1) BY ISOBARIC LINES THE MEAN PRESSURE oF THEATMOSPHERE AND (2) BY ARROWS THE PREVAILING WINDS over THE GLOBE cach MONTH From JUNE To NOVEMBER.
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CHART SHEWING (I) BY ISOBARIC LINES THE MEAN PRESSURE oF THEATMOSPHERE AnD (2) BY ARROWS THE PREVAILING WINDS ror THE YEAR.
Trans. Roy: Soc.Edin. YolXXV. Calins marked thus O Variable Winds this * PLATE XXVIL
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To WOLeapesie100 Wer af 80 Grearics 60
CHARTS SHEWING BY ARROWS THE LEAST FREQUENT WINDS wick PREVAIL IN JANUARY AND JULY. THE ISOBARIC LINES ARE ALSO GIVEN FOR THESE MONTHS.
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W. & A.K. JOHNSTON. EDINBURGH
—
QEsBA
XVII.— The Mean Pressure of the Atmosphere and the Prevailing Winds over the
Globe, for the Months and for the Year. Part Il. By ALEXANDER Bucuay, M.A.,
Secretary of the Scottish Meteorological Society. (Plates XXV. to XXVIL)
(Read 19th April 1869.)
Cuarts, showing by Jsobaric Lines the mean pressure of the atmosphere over
the globe during the months of the year, may be justly regarded as furnishing
the key to all questions of meteorological inquiry; for without the information
conveyed by such charts it is impossible to discuss satisfactorily those questions
which relate to prevailing winds, the varying temperature, and the rainfall
throughout the year in the different countries of the world. It is to meet this
desideratum that the Charts of Mean Atmospheric Pressure of the globe which
are given with this paper are offered as the first approximate solution of this
great physical problem.
Since Part I.* was read in March 1868, valuable additional information has
been obtained from Australia, New Zealand, Tasmania, Africa, South America,
the west coast of North America, Iceland, Norway, and Sweden, and from
several isolated stations in different parts of Europe and Asia. The period for
the British Islands and a large portion of Europe has been extended so as to
include the eleven years from 1857 to 1867.
In this Part the complete set of Charts for the twelve months and for the
year are given, together with the data from which the Charts have been con-
structed.
As regards Pressure, the stations were selected with the view of representing
as well as possible the geographical distribution of the pressure. The first place
was assigned to those stations at which the barometric observations were known
to be, or presumably were, of the best quality; and in drawing the isobaric
curves, the greatest weight was given to means deduced from these observations.
Since it is the mean pressure at sea-level which is here inquired into, and since
the manner of the geographical distribution of the pressure doubtless varies at
different heights, stations at low elevations were preferred to those at greater
heights. The pressures at a few elevated places, such as Great St Bernard and
Dodabetta, are given in the Tables; but they were not made use of in drawing
the curves,—their value consisting in the light they tend to throw on the
_ movements of the upper currents of the atmosphere.
In an inquiry into the comparative distribution of atmospheric pressure, it i:
* Proceedings of the Society, vol. vi. p. 303.
VOL. XXV. PART II. 7
576 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
evident that the first requisite, as regards time, is, that the means be deduced
from observations made in the same years. In the tropics, where there is great
regularity in the mean pressure of the same month from year to year, observa-
tions in the same years are of less importance; but in extra-tropical regions,
where the mean pressure of the same month varies considerably frem year to
year, it is of the utmost importance to obtain observations for the same years.
This has been the guiding principle in selecting the years from which the means
of the different places in Table I. have been calculated. Thus, in the British
Islands, the means are uniformly given for the eleven years from 1857 to 1867,
and the means of many European stations are given for the same years; and in
the United States of America the means are for the six years from 1854 to 1859.
It will be observed, that the means for two or more series of years are given
for several places, such as Christiania, Upsal, Toronto, Hobart Town, Algiers,
&c. At Christiania, the average for 1861-68 is that for most other Norwegian
stations, and that for 1857-67 is the average adopted for the British Islands.
For Upsala, the average for 1857-67 is given together with the average for
1859-66, the average of the other stations in Sweden. By the comparisons
which may be instituted between these means, a closer approximation to the
course of the isobaric curves over this portion of north-western Europe is ob-
tained. Similar comparisons may be made from the data given in Table I. for
different regions of the world, and thus the disadvantages, arising from the
necessary use of averages of different terms of years, for different places in the
same or in neighbouring regions, may, to some extent, be obviated.
In addition to these two classes of averages, the averages deduced from long
series of years are given for many places, such as London, 89 years; Turin, 74
years ; Bologna, 45 years ; Brussels, 38 years; Christiania, 31 years; Toronto, 27
years; Stykkisholm, 23 years; Hobart Town, 28 years, &c. A comparison of these
with the other averages will give some indication of the true mean pressure of
the atmosphere for different regions of the globe. But for a general survey of
the geographical distribution of the mass of the earth’s atmosphere through the
months of the year, the data, from which the isobaric lines of the charts have
been drawn, may be regarded as sufficient. The closer approximations to the
true mean pressure of the atmosphere, to be obtained from the accumulated
observations of future years, will give the data for more detailed representations
of the pressure of the atmosphere over different regions of the earth. Ifthe
isobaric curves could be drawn true for every 0:025 inch, the disturbing influence
of the Mediterranean, Black and Caspian Seas, and American Lakes; and of the
Pyrenees, Alps, Dovrefeld, Himalayas, and other mountain ranges, would be
more apparent.
In every case, where possible, the means in the Table are the arithmetic
means of the observations, reduced to-32° Fahr. only,—no corrections being
AND THE PREVAILING WINDS OVER THE GLOBE. 577
applied for daily range or for height. For places, for which the means were
obtained corrected for daily range, “red.” (meaning reduced to mean daily
pressure), is entered in Table I. in the column of Houwrs of Observation. Those
stations for which the means are reduced to sea-level are printed in ztalics.
The next step was to apply to the figures in Table I. corrections (1) for daily
range and (2) for height. So far as possible, that hour, or those hours, of
observation were selected when the pressure of the atmosphere is nearly the
mean of the day. For places for which this could not be done, a collection of
Mean Hourly Variations of the Barometer was made from a considerable number
of stations in different parts of the world. From these, approximate corrections
for daily range were deduced, and applied to the monthly means of the stations.
For reducing to sea-level, a table was prepared from the Formula and Table
XVL, given in Guyor’s Meteorological and Physical Tables, D, p. 89. This table,
calculated for each 5° Fahr. of the temperature of the air, from — 40° to 90°,
was used in all cases where the height did not exceed 800 feet. For higher
situations, the reduction was made by means of Dippr’s method, as detailed in
Guyot’s Tables, D, p. 60. ,
The means,* so corrected, were then entered on large polar projections of the
northern hemisphere, from which the dsobars were drawn for every tenth of an
English inch of pressure. The isobars for the southern hemisphere were drawn on
charts of MERcarTor’s Projection. The whole was ultimately transferred to charts
of the projection on Plates XXV. to XXVII. The isobars, indicating a pressure of
30 inches, which is nearly the average pressure, and upwards, are represented on
the charts by heavy lines, and lower pressures are represented by light lines.
For many of the means I have been indebted to the labours and writings of
Dove, Buys Batiot, Seccur, Cart JeLtinck, Moun, JAMES, QUETELET, and
Kuprrer. For the means of single stations and groups of stations, I have
received most valuable assistance from Meteorologists in all parts of the world,
for which I beg to return them my grateful thanks.
DISTRIBUTION OF ATMOSPHERIC PreEssuRE, in December, January, and February.
—In these months, the highest pressures are grouped over the land portions of
the northern hemisphere, and the larger the extent of the land the greater is
the pressure. The area of high barometer (30 inches and upwards) embraces
nearly all Asia; all Europe, south of the North and Baltic Seas; the North Atlantic,
between 15° and 45° lat.; the West Indies; North America, except the north and
north-west; and the North Pacific, between 8° and 24° lat. There are also two
regions of high pressure of comparatively small extent—the one in the South
Atlantic, and the other in the South Pacific.
* The original observations are given in Table I. in preference to the corrected means deduced
from them.
578 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
The regions of low pressure are the northern portions of the North Atlantic and
of the North Pacific, including portions of the continents adjoining; the belt of low
pressure in the equatorial regions, towards which the trade winds blow; and the
remarkable depression in the Antarctic regions, which probably is subject to
little variation throughout the year.
In March, pressure diminishes over Asia, the middle and south of Europe,
and the United States of America. Everywhere else, except in the tropics, it is
rising. ‘This rise of pressure is most apparent in the temperate regions of the
southern hemisphere. In the north of the Atlantic it is rapidly rising, the
average pressure in Iceland now being 29°609 inches, thus showing an increase of
0-34 inch as compared with January.
In April, the heavy lines showing a pressure above the average have now all
but left Asia, Europe, and the United States, and the isobars of 30 inches bound
a belt of high pressure which completely encircles the globe in the south tem-
perate zone. Pressure continues to rise in the north of the Atlantic, and to the
north of North America, and it is probable that a space of high pressure (at least
30 inches) surrounds the North Pole. In this month pressure is more equally dis-
tributed over the globe than in any other month; for, excepting the Antarctic
Ocean, it scarcely rises anywhere above 30:1 inches, or falls below 29°8 inches.
In May, in the north of Europe, in Greenland, and in the north of America,
atmospheric pressure attains the maximum of the year. Pressure continues to
increase over the south temperate zone, and the zsobar of 30:1 inches now nearly
extends round the globe. At this time the highest pressure in the southern
hemisphere occurs in the south-east of Australia, where, at Deniliquin, it is
30°185 inches. Pressure is rapidly falling over Asia and the United States.
In June, July, and August, pressure falls in the central regions of Asia to
about 295 inches. In this season this great diminution of pressure, which may
be regarded as absolutely determining the summer climates of Asia, reaches its
lowest point. Pressure falls also in the interior of North America, where at
Utah, Great Salt Lake, it is only about 29:7 inches. The annual maximum of the
south temperate zone is attained in these months. The isobar of 30:1 inches
goes completely round the globe, and a still higher pressure prevails over the
south of Africa, and over those parts of the ocean immediately to the west and
east of it. In these months the arrangement of the isobars may be regarded as
being, generally speaking, reversed from that of December, January, and
February, and on this account a comparison of these two groups of months is
very instructive.
From this period, pressures increase over the continents of the northern
hemisphere, and diminish over the south temperate zone, till the distribution of
pressure is regained, which has been already shown to prevail during the winter
months. Jn September and October, an interesting feature of these lines is a very
“ee
————— ==
—*"
AND THE FREVAILING WINDS OVER THE GLOBE. O79
rapid diminution of the pressure indicated as taking place in the north of the
Atlantic and adjoining regions. This is the season of the year when the first
great decrease of temperature takes place, which is accompanied by heavy rains
and furious storms. The increase of pressure in Sweden in October, taken in con-
nection with the simultaneous decrease in Greenland, Iceland, north of Norway,
and the British Islands, is interesting, as bearing on the transference of masses of
the atmosphere from one region to another.
In November, pressure rises considerably over the continents of the northern
hemisphere, and falls in the south temperate zone; and the belt of low pressure
in the equatorial regions may be regarded as now passing completely round the
elobe. This belt, towards which the trades on each side of the equator blow,
does not occur in the summer months in the Indian Ocean; but, on the contrary,
there is a continuous diminution of pressure northwards, from Australia and
Mauritius to the interior of Asia. It will be seen that in November, as compared
with October, the isobars have advanced a little northwards from the British Isles
to Iceland, and eastwards from Baffin’s Bay to Iceland, thus indicating a general
increase of pressure over the north of the Atlantic and regions adjoining.
Coincident with this increase of pressure, there occurs a diminution of pressure
to the south-east of it, including Austria, Italy, and countries adjoining the
Mediterranean; and in the Atlantic to the south of it, from about latitude 45° to
15° N. Probably these extensive oscillations of the pressure are parts of one
general movement of the atmosphere, which in one of its manifestations has been
long known to meteorologists under the name of the great November wave, but
of which no very satisfactory account has yet been given.
In addition to these changes in the monthly distribution of the pressure, it is
probable that a system of low pressures traverses the continent of Africa, follow-
ing the sun’s course ; but since the grounds of this supposition have been recently
laid before the Society, in a paper on ‘‘ The Determination of Heights, chiefly in
the Interior of Continents, by Observations of Atmospheric Pressure,” * it is not
necessary to reproduce them here. The probable pressure for the months is
shown on the separate charts.
PrevalLinc Winps.—It will be seen that every one of the charts shows con-
siderable disturbance of the equilibrium of the atmosphere at the surface of the
earth. If the pressure was equal in all parts of the globe, we should have the
physical conditions of a stagnant atmosphere. But such is not the case. From
the different pressures which the charts show in different regions, it might be
expected, from the laws of aérial fluids, that movements of the atmosphere
would set in, giving rise to the prevailing winds of these regions.
* Proceedings of the Roy. Soc, Edin. vol. vi. p. 465.
VOL. XXV. PART I, 7L
580 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
To ascertain what relation may subsist between mean atmospheric pressure
and prevailing winds, Table II. has beemprepared, which shows the mean number
of days in each month winds from N., N.E., E., 8.E., 8., S.W., W., and N.W. have
been observed to blow. In tropical and subtropical regions, a period of one or
two years is sufficient to indicate the average direction, or the prevailing winds
of the locality, owing to the steadiness with which the wind blows in these
regions; but in temperate and polar regions a considerable number of years is
indispensable. The direction of the winds has been generally obtained, or
calculated, for the same years as the atmospheric pressure; but where such obser-
vations could not be obtained, care was taken to include in the list only those
places for which a sufficient number of years was available, so as to give a good
average. As regards the stations in British North America, the shortness of the
time during which, in each case, the observations were made, is to a great extent
compensated for by the number of places at which observations have been made,
and the comparative steadiness of the winds in these high latitudes of America.
Valuable assistance was obtained from Professor Corrin’s elaborate “ Treatise on
the Winds of the Northern Hemisphere,” though many averages given in this work
could not be adopted, being based on an insufficient number of years,—a remark
which applies extensively to averages of observations of the wind hitherto
published.
In selecting stations, a preference was given to those which are situated in
comparatively level localities, with the view of obtaining as close an approxima-
tion as possible to the true direction of the wind. To this there are, however,
several exceptions, such as the stations in Norway and in Greenland, these places
being given to illustrate the effect of mountain ranges in changing the mean
direction of the wind. Stations at no great elevation above the sea were selected
in different regions, it being evident that winds observed at great elevations are
not suited to an inquiry into the movements of the atmosphere in relation to
sea-level pressures.
It will be observed that the time, or the duration of the prevalence of each wind
(N., N.E., E., &c.), is the only element taken into account in this inquiry. The
element of force has, for several reasons, been neglected :—(1.) The force of the
wind has been less generally observed than the direction; and at very many
places where the force has been observed, the observations, from the manner in
which they have been made, do not give the materials for arriving at absolute
results. (2.) It is well known that the velocity of the wind is retarded by the
land as it passes across it; thus, for example, an anemometer on the west coast
of the British Islés registers considerably more wind than one erected at an inland
or eastern situation. Also, more wind is registered in rising above the surface
of the earth. The effect of local situation on the velocity of the different winds
is very great. Hence, whilst the amount of these disturbing influences are
AND THE PREVAILING WINDS OVER THE GLOBE. 581
unknown, to attempt to determine the velocity of any general movement of
the atmosphere from the observed velocity of the wind at Observatories could
lead to no satisfactory result as regards the present inquiry. In the broad
results aimed at in this comparison of atmospheric pressure and prevailing
winds, it cannot affect the conclusions arrived at to assume, as is here done,
that the mean velocities of winds from different directions are equal to each
other.
From the figures given in Table II. the mean direction of the wind has been
calculated in the usual way. This direction is represented in the charts by
arrows flying in the direction of the wind. In cases where the winds do not pre-
ponderate from one quarter, but are nearly equally distributed over different
points of the compass, an asterisk (*) is entered on the charts, which thus repre-
sents variable winds ; when calms preponderate, a circle with a dot in the centre
(©) is used. When two maximum directions are strongly indicated, or when the
smaller one is very decidedly marked, instead of resolving the two into one
intermediate, which would in many cases represent a wind which scarcely ever
occurs at the time, the greater of the two is represented by the ordinary arrow,
and the smaller in the more marked cases by a less arrow placed beside it. By
this means an important feature in climate is represented.
Thus two distinct sets of facts are exhibited on the charts, viz., lines showing
the mean pressure of the atmosphere, and arrows showing the prevailing winds at
the earth’s surface, each being independently arrived at by the summing and averag-
ing of observed facts. What relation is there between these two classes of facts ?
I Winbs within, or near, a space of Low Pressure.—Of this class, the best
example is the low pressure which prevails in the north of the Atlantic and adjoining
regions in the winter months. This region of low pressure is bounded to the
S.W. by the high pressure of North America; to the S. by the high pressure in
the Atlantic, about 30° lat. N.; to the S.E. by the high pressure in the interior of
Asia. In January, the difference between the average pressure of Iceland and the
interior of Asia is fully an inch.
It is seen from the charts, that in Baffin’s Bay and east of the Rocky Moun-
tains, as far south as 40° lat., the winds are N.N.W., N.W., and W.N.W. Cross-
ing the Atlantic, winds in the British Islands, in France, and the north of
Germany, are from W.S.W. to S.W.; in Denmark, 8.8S.W.; near Bergen, in
Norway, S.; and at Christiansund and Hammerfest, S.S.E. The relation of
these winds to the isobaric lines is the same as that which is illustrated by the
winds in storms, in their relation to the isobaric lines of these storms. This has
been already stated in a Paper by the author, published in the ‘“‘ Transactions of
the Society,” vol. xxiv. Part i. p. 201, in the following words :—‘‘ The wind in
storms neither blows round the centre of least pressure in circles, or as tangents to
the concentric isobaric curves, nor does it blow directly towards that centre. It
582 MR ALEX BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
takes a direction intermediate, approaching, however, more nearly to the direc-
tion and course of the circular curves than of the radii to the centre.” Or,
according to Dr Buys Ba tor, the angle is not a right angle, but from about
60° to 80°. This relation is usually called “ Buys Batiot’s Law or THE WINDs.”
Another well-marked depression is the low summer pressure in the interior
of Asia; with reference to which, it is seen from the charts that the winds of
Eastern Europe and Western Asia are from N.W. to W.N.W. and W.; at Ceylon,
S.W.; at Shanghai, 8.E.; and on the Sea of Okotsk, N.E.; whilst in the interior,
calms generally prevail.
The behaviour of the winds, as regards the low pressure of North America,
is exactly similar to that of the winds in Asia at this season. In all these cases
the wind appears to flow round and in upon the space where pressures are
low. Even in those instances where the depression over a limited space is com-
paratively small, such as in Australia during the summer months, the winds
observe the same course with respect to it.
A well-known and remarkable diminution of pressure is that of the Antarctic
regions; and though, except in Tasmania and the south of New Zealand, obser-
vations are wanting at particular points for a sufficiently long time to give good
averages, yet the concurrent testimony of sailors and the inhabitants of these
regions all go to show that, at least on the outskirts of the region, winds are
chiefly N.W. or W.N.W.—that is, they appear to flow in upon the space of low
pressure. The low pressure in the equatorial regions, towards which the trades
blow, is an illustration of the same principle.
Winns within. or near, a space of High Pressure—The most prominent illus-
tration of this is the high pressure in the interior of Asia in winter. It is seen
from a single glance at the charts that the winds flow owt of this space in every
direction. The same outflow is seen with respect to the less strongly marked,
but still very distinct space of high pressure in North America; owing to the
large number of stations available here, this principle is amply illustrated.
The next most noteworthy area of high pressure occurs in summer between
Africa and North America, out of which also the charts show the winds blowing
in all directions towards and round upon the surrounding low pressures.
The following mean pressures, in inches, at 32° and sea-level, occur in Australia
in June :—At Brisbane, Queensland, 30:062 ; Sydney, 30°116; Melbourne, 30:173;
Adelaide, 30°132; Freemantle, 30:121; and at Deniliquin, in the interior, on a
branch of the Murray River, 30:217. Hence a higher pressure occurs at this season
(winter) in the interior, and it may be inferred that it is greatest in the southern
portion of the interior. The prevailing winds are these :—At Brisbane, 8.S.W.;
Sydney, W. by N.W.; Melbourne, N.; Adelaide, N.E. by N.; Freemantle, N.E.
by E.; in other words, the winds blow out from this space of high pressure.
‘Lhis behaviour of the winds with respect to spaces of high pressure differs in
AND THE PREVAILING WINDS OVER THE GLOBE. 083
no respect from what occurs on particular days on which the isobaric lines present
the same conditions of pressure. Mr Francis GAuTon first drew attention to this
peculiarity, under the name of Anticyclones, by which name he intended to convey
the idea that in cases of high pressure occurring over a limited area, the course of
the winds is exactly the reverse of what is seen to prevail in cyclones in which
the winds blow round and in upon a space of low pressure.
The outflow of the air from a region of high pressure, and the zzflow upon a
region of low pressure, appears to be reducible to a single principle, viz., the
principle of gravitation. Given as observed facts the differences of pressure, it
might almost be predicted, before calculating the averages, what the prevailing
winds are. Indeed, so predominating is the influence of gravitation that it may be
regarded as the sole force immediately concerned in determining the movements of
the atmosphere. If there be any other force or forces which set the winds in mo-
tion, their influence must be altogether insignificant as compared with gravitation.
The effect of a mountain range interposed in the course of one of these great
atmospheric currents is interesting. Of this, the best example is furnished by the
mountain range of the Scandinavian peninsula, in its effect on the prevailing winds
in winter. It will be observed that this mountain range lies between the low
pressure about Iceland, and the high pressure in the interior of Asia.
The following are the mean directions of the wind at different places in Norway
in January, deduced from Table II., to which are added the winds at other points,
courteously sent by Professor Moun :—Christiania, N.E.; Sandosund, N.N.E.;
Lindesnes, N.E.; Mandal, N.E. by E. ; Lister, E.; Skudesnes, 8.S.E. ; Udsire and
Bergen, S.; Christiansund, 8.8.E.; Villa, S.E.; Hammerfest, 8.E. by S.; and
Vardo,S.W. Thus at Christiania, Sandosund, and Lindesnes, which lie on the east
side of the south spur of the mountain range, the prevailing winds are N.E. or
N.N.E.; at Mandal, at the extreme south point of Norway, the wind is N.E. by E.,
and calms also largely prevail; and at Lister, a little to the west, the wind is
E.; along the whole west coast from Skudesnes to Hammerfest, near the North
Cape, winds are chiefly S., 8.S.E., or S.E.; while at Vardo, to the east of the north
spur of the mountain range, the prevailing winds are S.W. These directions are
very much the directions water should take in flowing past and round a rock
lying in the bed of the current; the Scandinavian mountains being in this case
the obstacle which diverts the winds from what may called their normal course
in flowing towards and round the low pressure in the north of the Atlantic.
On the other hand, in July it is seen from the Chart (Plate XXVI.) that the
lowest pressures occur in the interior of Asia, towards which there is an extensive
aérial current from W.S.W., W., and N.W. over Europe and Western Asia. Here
also the influence of the mountain system of Norway is very perceptible. The
following are the prevailing winds in July:—Christiansund, N.W. by N.; Bergen,
N.; Skudesnes, N.W.; Lindesnes, W.; Mandal, W. by S.W.; Sandosund, S.W. ;
VOL. XXV. PART II. 7M
584 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
Christiania, S. Thus, this part of the great atmospheric current flows round the
southern region of Norway, being N. at Bergen, thence in succession N.W. and
W., and on rounding the coast becomes diverted intoa SW. and S. wind. The
extraordinary deflection of the isothermal lines in the different months, as they
cross Norway and Sweden, is doubtless to no inconsiderable extent occasioned by
the opposite prevailing winds, which arise from the obstruction presented by
the mountain range to the prevailing atmospheric currents of the seasons.
The prevailing winds at Upernivik, Jacobshavn, and Godthaab, in the west of
Greenland, appear to point to another principle. It will be seen from the Charts
and the Table that the prevailing winds in the winter months at these stations
are N.E. and E. instead of N. and N.N.W., which, from the analogy of the winds
at other places, they might have been supposed to be. They are thus diverted a
few points from their proper course in the direction of E., or, roughly speaking,
into a direction which is perpendicular to the line of the coast; in other words,
they follow the course of the ravines. The daily observations at the Greenland
stations have been published by the Danish Academy of Sciences, from which
the averages have been calculated. A large proportion of these winds are very
light, being frequently marked 0 by the observers ; that is, they were too light
to be represented by the scale for wind force in use (0 to 4.) Since the west coast
of Greenland is bounded immediately to the east by a steep high mountain range
covered with snow, it is probable that the direction of these winds is still further
modified by the same causes which give rise to the well-known class of breezes
peculiar to mountain districts, of which the Vent du Mont Blanc is an example.
These breezes are caused by the cooling of the air in immediate contact with
the high ground, which, thus acquiring greater density, flows down their slopes,
and thence diffuses itself over the low ground as a surface wind of inconsiderable
depth. The Greenland stations are in those very situations which expose them
to this wind. It is in favour of this supposition that these easterly winds occur
oftenest, and blow with greatest force in the afternoon, it being at this time of the
day that the difference is greatest between the temperature of the low grounds
and that of the snow-covered mountains; just as sea and land breezes are
strongest at those hours of the day, when the difference of temperature is greatest
between the sea and land.
It will be observed that at St Helena the mean direction of the wind varies little
from month to month,—being almost uniformly from S.E. or §.; and it will also
be observed that the relative distribution of the pressure in neighbouring regions
varies little from month to month. The result is one mean annual direction of
nearly S.E. by S. At Mauritius there occurs a little variation from month to
month. Thus, whilst in June, July, and August, the mean direction is about
S.E. by E., in December, January, and February, it is nearly due E.; in other
words, during the summer season the wind shifts a few points from S.E. by E. in
AND THE PREVAILING WINDS OVER THE GLOBE. 585
the direction of N. This northing of the winds at Mauritius is exactly what
should be expected to result from the proximity to the low pressures which
prevail in South Africa at this season. This change in the mean direction
of the wind being small, the mean annual direction may be regarded as E.S.H.
Such slight variation, however, is limited to very few regions, for on examin-
ing the number of days each wind (N., N.E., E., &c.) has on the mean of the
year prevailed at the different stations in Table II., it will be observed that in
almost every instance there are two maximum directions, the one being con-
siderably greater than the other. These maximum directions may arise in two
ways— 1st, At places such as Colombo, Ceylon, where the wind during summer is
S.W., and during winter chiefly N.E., the two annual maximum directions are
S.W. and N.E.; in like manner the maximum directions at all places in monsoon
regions are occasioned. 2d, At Greenwich two maximum directions, from about
S.W. and N.E., appear in the means of every month, from which it is evident that
the wind at this place blows oftener, and remains longer, in these two directions
than in any other. In cases where the less maximum arises from the prevalence of
winds from that direction during a few months of the year, the isobaric charts of the
separate months give a ready explanation of both maxima in the annual means.
But at places where both maxima appear in the same months, it is evident that
the isobaric charts can only furnish data towards the explanation of the greater
maximum direction ; and it may be assumed as equally evident that the smaller
maximum, of which the east wind of the British Islands is an illustration, can
alone be legitimately discussed by daily synoptic charts of the weather. Towards
the discussion of this and other questions of meteorology, the value of the
Daily Synoptic Charts prepared and issued under the superintendence of M.
LEVERRIER cannot be overrated.*
There are 115 stations in Table II. situated in the north temperate zone. I
have tabulated the two maximum directions at these stations where they occur
according to sixteen points of the compass—viz., N., N.N.E., N.E., E.N.E., E., &c.
of which the following Table shows the maximum directions most frequently
observed :—
Greater Max. Smaller Max.
Maximum directions of wind are— S.W. N.E. at 16. stations.
99 bh) 9? N, 8 39 8 by)
B. 4 B N.E. S.W, my Loan -,
+h] ” 9 N.W. Ss E 39 6 +B
> ?> 99 8. N. 9° as) 9°
) 99 ? W. N.E 3° 5 99
9° th) 39 N.W. S. 3° 4 39
bP} 9° 99 W. E. 9? 3 99
9 bb) 29 E. W. te) 3 99
3) 93 33 W.S.W. EK. be) 3 ”
a 7 Fe W.S.W. S.E. eee
* Atlas des Mouvements Généraux de l’Atmosphére pour 1864-5.
586 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
Thus the number of stations, at which the greater maximum direction of the
wind is S.W., and the smaller, N.E., is 15. Further, if the whole 115 stations be
examined, and those picked out at which the greater maximum direction is from
any point between S.S.W. and W., and the smaller maximum from any point
between N.N.E. and E., the number is found to amount only to 34, or less than
30 per cent. of the whole. Now, since these are the directions in which truly
equatorial and truly polar atmospheric currents should blow, it is evident that
these two currents, as often represented, are not the two prevailing winds
generally observed over the north temperate zone. For if the two great
currents of the atmosphere were, one flowing from subtropical regions towards
the poles, and the other flowing from the poles towards the tropics, it is plain
that a much larger percentage of the stations than 30 would follow the course of
these currents in the north temperate zone. If to these 34 stations, at which the
maximum directions are in the course of the equatorial and polar currents
respectively, we add 17 stations, at which the greater maximum direction is from
N.N.E. to E., and the smaller from 8.S.W. to W., the number of stations at
which the two prevailing winds follow the course of these two currents is only
51, or about 44 per cent. of the whole—a proportion, it need scarcely be said, .
which could not obtain, if it be the case that there is a general flow of the atmo-
sphere at the surface of the earth in the northern hemisphere from the tropics
towards the north pole, and from the north pole towards the tropics.
Further, if the two maximum directions be separately examined, it is seen
that the greater maximum direction being from any point of the compass from
S.S.W. to W. occurs at 47 stations.
WNW to Ne eas
NN to 24 deme
ESE. toS. nat DGiet,
and the Jesser maximum direction being from any point from
S.S.W. to W. occurs at 20 stations.
W.N.W. to W. 99 22 bb]
N.N.E. to 1D, ” 38 ”?
E.S.E. to S. # eas
Thus the chief prevailing winds in the north temperate zone blow from some
point from S.S.W. to W. at 41 per cent. of the stations, leaving 59 per cent of
the stations at which the prevailing winds are from other points of the compass;
and the secondary prevailing winds come from some point from N.N.E. to E. at
34 per cent. of the stations, or only a third of the whole. Hence, as in the for-
mer case, while the largest percentages of prevailing winds are in the directions
in which truly equatorial and polar currents should blow, the percentages from
other directions are so large as to preclude the supposition of a general flow of
AND THE PREVAILING WINDS OVER THE GLOBE. 587
the surface winds of north temperate regions towards and from the polar
regions.
An examination of the isobaric and wind charts for the months shows, as has
been already pointed out, that where there is a mean low pressure, such as
occurs in the north of the Atlantic in the winter months, and in the centre of
Asia in the summer months, thitherward the winds tend in all directions in an
inmoving spiral course; and where there occurs a mean high pressure, as in the
centre of Asia in winter, and in the Atlantic between Africa and the United
States in summer, out of this space the winds flow in all directions, or they
appear to be thrown out from the space of high pressure in a manner exactly
the reverse from that by which they are drawn inward upon a space of low
pressure. These spaces of low and high pressures may therefore be regarded as
the true poles of the winds, which blow at the surface of the earth, towards which,
and from which, the great movements of the atmosphere proceed. From the
unequal distribution of land and water, it results that the poles of the pressure
and movements of the atmosphere are, as in the case of the poles of temperature,
very far from being coincident with the north pole.
The causes which bring about an unequal distribution of the mass of the earth’s
atmosphere may be considered to be chiefly two, viz., the temperature primarily ;
and, secondarily, the moisture of the atmosphere, in their relations to the
geographical distribution of land and water. From the relations of land and
water to temperature, the summer temperature of continents greatly exceeds
that of the ocean in the same latitudes. Hence the abnormally high temperatures
which prevail in Asia, Africa, and North America during summer, in conse-
quence of which the air becomes specifically lighter, and ascends, as from a
furnace, in vast columns thousands of miles in diameter. In this way the
summer pressure of continents is diminished, the amount of the decrease being
greatest in Asia, the largest continent, and least in Australia, the smallest. At
Barnaul, in Asia, the pressure in July is 0-418 inch below the annual average ;*
whereas at Deniliquin, in Australia, the pressure in January is only 0:154 inch
below the annual average: at Great Salt Lake, in North America, it is inter-
mediate, being 0°333 inch.
In the remarks which follow on the vapour of the atmosphere, the principles
laid down in the two following extracts are assumed :—1. “ Air charged with
vapour, or vaporised air, is specifically lighter than when without the vapour;
or, in other words, the more vapour any given quantity of atmospheric air has in
it, the less is its specific gravity.”}+ 2. “It appears, therefore, that the explanation
suggested by Dr Jouz is correct; and that the condensation of vapour in ascend-
* Some part of this diminished pressure in Asia is doubtless due to the condensation of the
vapour of the south-west monsoon.
ft Daxton’s Meteorological Observations and Essays, 2d ed. Memncliester 1834, p. 100.
VOL. XXV. PART II. 7N
588 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
ing air is the chief cause of the cooling effect being so much less than that which
would be experienced by the dry air.”*
The influence of vapour in lowering the pressure is well illustrated by the
low pressure in the tropics towards which the trades blow, this belt being
characterised by a highly saturated atmosphere and heavy rains.
Again, much more vapour is observed in the air at places near the shores of
the north of the Atlantic in winter than at places in the same latitudes in the
interior of continents. In Great Britain, as compared with the interior of Asia,
the excess is great; and in the former case the skies are generally cloudy, and
in the latter clear. Also, over the same region, the atmosphere of which abounds
in vapour, the mean winter temperature is much higher than it is on the continent;
and from the conclusion arrived at by Sir Witt1am Tuomson regarding the
temperature of an ascending column of saturated air, the relatively higher
temperature over such regions must continue to prevail up to very great heights.
Hence, owing to the presence of a larger amount of vapour, and to a higher
temperature, the air resting on the north of the Atlantic and regions adjoining is
specifically lighter than in the continents which surround it; consequently the
charts show an enormous diminution of pressure over this region, as compared
with the continents. Similar depressions from like causes occur in the north of
the Pacific and in the Antarctic regions.
Since dry and cold air is, on the other hand, specifically heavy, we should
expect that in the interior of continents, where temperatures are low and the air
is dry in winter, that pressures would be high; and observations show (see the
Charts) that the highest mean pressures occur in Asia and North America at this
season. For the same reason, pressures are also highest in Australia, South
Africa, and the south of South America in the winter months.
There is another source from which atmospheric pressure is increased. It has
been shown from the Charts that the tendency of the prevailing winds on the surface
of the earth is to blow round and in upon the space where pressures are low, and
out of the space where pressures are high. Now, since in this way vast volumes of
air are poured into the space where pressure is low without increasing that pressure,
and vast volumes flow out of the space of high pressure without diminishing
that pressure, it follows that the air poured in is not allowed to accumulate
over this space, but must escape into other regions; and that the air which
flows out from the place of high pressure must have its place supplied by fresh
accessions from above. The exchange indicated here is probably brought about
in this way :—Since in winter, over the north of the Atlantic, the atmosphere is
specifically lighter than in surrounding regions, there are here the conditions of
an ascending current ; and it may be inferred that the ascent will continue until
* Sir Wittram Tuomson in Mem. Lit. and Phil. Soc. Manchester, vol. ii. 3d series, p. 131.
AND THE PREVAILING WINDS OVER THE GLOBE. 589
a height is attained at which pressures at that level are equal; thence the air
will flow over, as an upper current, towards those regions which offer the least
resistance to its course,—in other words, where the tension at that height is least:
Over what part of the earth’s surface is the pressure of the air least at great
heights? Evidently, that region over which the air is coldest and driest near
the surface of the earth; because, being thereby densest, the great mass of the
air is condensed or gathered together in the lower beds of the atmosphere, thus
leaving less air, or a diminished pressure, in the upper regions. Thus the extra-
ordinarily high pressure in Asia in winter will be due both to the low temperature
and great dryness of the atmosphere, and to proximity to the regions of low
pressure in the north of the Atlantic, the north of the Pacific, and in the,
equatorial regions to the south; from which it may be inferred that upper cur-
rents flow towards the centre of Asia, and that these upper currents compensate
for the drain arising from the surface currents, which flow out of this space in
all directions. In corroboration of this view, it is seen that while in winter the
winds in India at low levels blow from some northerly point, at Dodabetta, on
the Neilgherry Hills, 8640 feet high, the mean direction of the wind during winter
is from about E.S.E.; and, on the other hand, while in summer winds blow from
some southerly point at low levels, at Dodabetta they are almost wholly N.W.
But by far the most striking illustration of this principle, is the high
pressure in summer which prevails in the Atlantic, between Africa and North
America. If the principle here suggested, as regulating the movements of the
atmosphere, be correct, the following will be the explanation of this singularly
high pressure :—Since, at this season, the temperature of the air resting on this
part of the ocean is much lower than that of the land, it follows that the ascend-
ing currents which rise from the heated plains of Africa, South America, North
America, and Europe, and from the tropical belt of calms to the south, will, on
reaching the upper regions of the atmosphere, flow over upon this part of the
Atlantic, because the temperature being comparatively low in the lower beds, the
air is condensed there, thus leaving less pressure in the upper regions. It may
also be added, that since the surface winds of this region are constantly drawing
away the air poured down upon it by the upper currents, extreme saturation of
the atmosphere cannot take place; and hence the atmosphere is relatively cool
and dry. The high pressure maintained in the South Atlantic, between Africa
and South America in the summer of the southern hemisphere, corroborates this
view.
From these considerations, it may be concluded that the winds on the sur-
face of the earth are approximately known from the isobaric lines,—the direc-
tion being from regions of high towards those of low pressure, subject to the
changes in the direction of the currents produced by the earth’s rotation; and
that the upper currents of the atmosphere may be inferred from the isobaric lines
590 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE |
taken reversely, together with the isothermal lines taken directly. In other words,
the regionsof lowest pressure, by giving the ascending currents, point out the sources
or fountains whence the upper currents flow; and the isothermals, by showing
where, on account of the low temperature, the greater portion of the air is con-
densed in the lower beds, and so diminishing the pressure in the upper beds, point
out the regions towards and over which the upper currents diffuse themselves.
1. To travellers in the interior of continents and regions at a great distance
from places where Meteorological Observations are made, the Charts will be of use
in showing the approximate sea-level pressures for each month of the year. They
show at a glance the ze70 points from which the heights of places may be calcu-
lated, at which observations of the pressure of the atmosphere have been made.*
2. To sailors, the Charts will be useful as showing the prevailing winds at
many places in each of the twelve months, and still further as suggesting, from
the connection which is here pointed out between mean atmospheric pressure and
prevailing winds, the winds which are most likely to be met with in regions
where little is known of the general course of the winds from actual observations.
The charts of least prevailing winds in January and July (Plate XXVIL.), will also
be useful in this respect.
The following illustration will show the method of using the Charts in apply-
ing Buys Batuot’s Law or THE Winps. This law has been stated at the foot of
page 581, but it may be more popularly expressed thus,—Stand with your back
to the wind, and the low barometer will be to your left in the northern hemi-
sphere; or, reversing it, stand with the high barometer to your right, and the Jow
barometer to your left, and the wind will blow on your back. Suppose, during
the summer months, a person at Lisbon to stand so, with reference to the high
pressure in the Atlantic, and the low pressure in Africa, he should have a N.N_E.
wind; and as he proceeded southward along the coast of Africa, the wind would
wear more to eastward. On the north coast of South America, being between the
high pressure of the Atlantic and the low pressure of South America, the winds
should be about easterly; and on the north coast of Central America, the low
pressure in the Pacific being now to his left, the winds should be about N.N.E.
On passing through the West Indies towards Florida and the south-eastern States,
as the influence of the low pressure in North America in its relations to the high ~
pressure in the Atlantic comes into play, the prevailing winds should gradually
become E., E.S.E., 8., S.S.W., and S.W., and from this region to England to about
W.S.W. These are, it need scarcely be said, the prevailing winds of these regions.
* Note of the Determination of Heights, chiefly in the interior of Continents, from Observations —
of Atmospheric Pressure.—‘ Proceedings of the Society,’’ vol. vi. p. 465.
t In the southern hemisphere the low barometer will be to the right.
AND THE PREVAILING WINDS OVER THE GLOBE. 599
Further, the Table of Winds shows a total absence of westerly winds on the north
coast of South America, the winds there being almost always from N.E. to E. or
occasionally S.E.; whereas, at Bermuda, the winds, while mostly S.W., are more
distributed over the other points of the compass. The daily pressures charted
in LEvERRIER’s ‘‘Atlas des Mouvements Généraux de l Atmosphére,” give a ready
explanation of the winds of these two regions—pressures in the one case being
comparatively steady, whilst in the other they are fluctuating.
3. Since winds bring with them the temperature and vapour of the regions they
have traversed, it follows that the data mapped on the Charts may be considered
as furnishing the key to the climates of the different parts of the globe, since the
approximate temperature and rainfall of the different seasons may thereby be
known. Between the monthly isobars and the rainy seasons of portions of Asia,
Africa, America, and Australia, there is an obvious connection. The distribution of
the pressure also explains the greater rainfall which occurs in Russia and other
places in the interior of Europe in summer, as compared with the other seasons.
For, if the winds of July in Table II. be compared with those in January at British,
French. German, Russian, and other European stations, they will be found
uniformly to show a shifting of the prevailing winds farther to the west and
north,—a change, doubtless, arising from the low pressures in Asia in summer.
The effect of this is, to draw over these parts of Europe, during the summer
months, air-currents more directly from the ocean than in the other seasons, from
which result a larger rainfall and greater fertility to these regions.
The political importance even of such information will be seen when it is con-
sidered, that if there had been two or more years’ Meteorological Observations,
especially of atmospheric pressure and winds, at Aden, Massuah, and Suez, at the
beginning of the Abyssinian war, the time of the commencement of the rainy
season in Abyssinia could have been stated.
The Charts of monthly isobars, the monthly isothermals, and the information
tabulated in Table II., furnish materials from which more exact information
regarding the climate of a particular place may be obtained. Thus, suppose it
were required to know something of the climate of Shanghai, China. The mean
temperature in January is about 40°, being nearly that of the west coast of
Scotland; the isobaric lines show an increase of pressure from Shanghai in the
direction of the interior of the continent; the winds for January are these :—
Days each wind has prevailed
Re Ee, Si SSW. WW. NW. Calm
(January) at Shanghai, }
2 3 2 2 3 610 0
Thus the mean direction of the wind is nearly N.N.W.; and, since this wind
comes from the continent, it may be concluded that it is dry, and, consequently,
that very low temperatures are of certain occurrence. Again, since in nine days
winds blow from N.E., E., §.E., and 8., or from the ocean, and these winds, especially
VOL. XXV. PART II. ° 7 0
592 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE.
from the §.E. and S., may be expected to be warm and moist, it may further be
inferred, that the winter climate, so far as regards the two important elements of
heat and moisture, is subject to great fluctuation. On the other hand, since the
July mean temperature is about 80°, and in the same month the wind blows ten
days from S.E. and fourteen from S., it may be concluded that the summer
climate will be hot, stifling, and relaxing. These are shown, by observation, to be
the peculiar characteristics of the climate of Shanghai in winter and in summer.
4. An inquiry of still greater interest is suggested by the isobaric lines of the
Charts. Their position appears to be altogether determined by the geographical
distribution of land and water on the surface of the earth; and since the isobaric
lines determine the prevailing winds, and these in their turn the peculiar distri-
bution of temperature and rainfall,—in other words, the climates of the globe,—
it is evident that we have here a principle applicable not merely to the present
state of the earth, but also to different distributions of land and water in past
time. In other words, there is here a principle which the geologist will require
to apply in attempting to account for glacial and warm epochs, through which
the climates of great Britain and other countries have passed. In this way it
is possible to arrive at an approximate numerical statement, as regards tempera-
ture and rainfall, of Sir Cartes LYELL’s idea of the changes of climate brought
about through the displacements of continents.
The following instances will serve to illustrate the effect of the partial dis-
placements of continents in changing climate. On examining the chart for July
(Plate XXVLI.), it is seen that the fine summer climates of Western Europe, and of
the Eastern States of America, are caused by south-westerly prevailing winds,
which, having their origin in the region of high pressure in the Atlantic, possess,
in admirable proportions, the genial qualities of warmth and moisture. Since these
winds depend on the high pressure in the Atlantic between Africa and the United
States, whatever would alter this arrangement of the pressure may be expected to
change the character of the climates. Suppose, then, a displacement of the con-
tinents, either of Africa or South America, so that land would occupy the place of
the part of the ocean lying between Africa and the United States. With this new
disposition of the land, it is plain that the high pressure in the Atlantic would
disappear, and the spaces of low pressure in Asia, Africa, and North America
would unite into one region of low pressure, stretching from the west of North
America to the east of Asia. Simultaneously with this change in the pressure,
the winds of the United States and Western Europe, including Great Britain,
would become northerly, and, as a consequence, the summer climates of large
portions of these regions would be so seriously deteriorated that the cultivation
of cereals could not be attempted.
Observations show that the lowest pressures which accompany the storms
which traverse Europe, or the centres of these storms, pass eastward for the most
ee SY. 2 ee
AND THE PREVAILING WINDS OVER THE GLOBE 593
part, in a course lying somewhere between Iceland and Faro; as a consequence
of this, and of the mean low pressure in the north of the Atlantic in the winter
months, the prevailing winds in Great Britain at this season are south-westerly,
and even in stormy weather the wind seldom veers further towards the north
than N.W., and continues only for a short time in this quarter. To these con-
siderations we owe the mildness and equableness of the winter climate of Great
Britain. At Stykkisholm, in the north-west of Iceland, which lies on the north
side of the storms’ path, the great preponderance of winds in the six stormy
months, from October to March, are N.E. and E., as will appear from the follow-
ing Table, which gives the number of days on an average of the three years,
1866-69, winds from the different points have blown during these six months :—
Number of days the wind has blown N. N.E. E. S.E. Ne S.W. We N.W. Calm.
eee Be Be BT
years, viz., 1866-69,
Suppose a change in the distribution of land and water took place in this
part of the globe; on the one hand, land taking the place of sea to the west of
a line drawn through Spitzbergen, the north of Norway, Faro, and the east of
Newfoundland ; and, on the other hand, sea taking the place of land over part of
the north of Africa, and over the comparatively low plains of Europe and
Siberia, the following changes would take place in the distribution of atmo-
spheric pressure in winter:—The high pressure over Asia would be reduced
and contracted; the high pressure in North America would be increased and
extended, so as to include Greenland ; and the low pressure round Iceland would
be transferred to the south-east, so that the central space of least mean pressure
would probably stretch from the north of France to the Gulf of Finland. Under
these new conditions, mean pressure would increase greatly from the south of
Great Britain towards the north-west, and thus northerly and easterly winds would
become the prevailing winds in winter; and as the mean central track of storms
would lie in a line from the north of France to St Petersburg, the winds accom-
panying storms, particularly those in the rear of the storms, would be dry and
intensely cold. Further, suppose the Gulf Stream, or any oceanic current from
equatorial regions, to flow past Great Britain on its way to the Arctic Ocean,
through the Baltic and White Seas, from the lower mean temperature which
would be brought about by the now prevailing northerly winds, the vapour
brought by the Gulf Stream would be precipitated no longer in the form of rain »
but of snow, and frost would be of frequent occurrence. Since the heat of summer
would be insufficient to melt this snow, it would accumulate from year to year;
and thus the Gulf Stream, instead of ameliorating the climate, as at present,
would only the sooner and more effectually, by accumulations of snow and ice,
bring back to the British Islands the climate of the glacial epoch.
594 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE 1.—SHowine THE MEAN MONTHLY AND ANNUAL HEIGHT OF THE BAROMETER
Note.—Under column of “ Hours of Observation” “red.” signifies that a correction has been applied for Daily Range,
the p.m. after it. A Minus Sign before Latitudes signifies Latitude South, and before Longitudes, it
Autho-
ER Number Hours of Height
Places. Country. ae ™ Specified, Observa- | Latitude. |Longitude.| in Ts
635. ears. tion. Feet.
Stykkisholm, ‘ : Iceland 1 23 | 1846-68} noon | 65 4 |—22 43 37
Do., : ; do. 1 11 | 1857-67} noon | 65 4 |—22 43 37
Reykjavik, . ; 5 do. 2 13 | 1823-35| 8 or 9: | 64 40 |-22 0 36
Dor Soi) “athe do. 3 3 |1866-69| 9: 64 40|-22 0} 10
Eyafiord, . , : do. 4 2 | 1811-13 ? 66 0j—18 20 2
Thorshavn, . ‘ : Far6é 3 3 | 1866-69 9:9 G24 2 ie < 12
Armagh, . ; ; Treland 5 11 | 1857-67| 10:10] 54 21] -6 49] 210
Belfast, . do. 6 11 do, 9: 54 36] -—5 56 66
Dublin, : ; do. 7 22 |1831-52| noon | 53 22] —6 21} 162
Do., : : ; do. 8 11 1857-67| 92:31 | 53 22] —6 21 159
Monkstown, . : : do. 9 8 | 1859-66} 83:83 | 53 18] -6 8] 110
Cork, . : ; : do. 10 11 | 1857-67| 9:3 | 51 53} —8 38 25
Sandwick, . : : Scotland 3 11 do. 929 (59)? 25| Bais 94
Stornoway, . ' do. a 11 do. do. | 58 12] -6 21 a
Tongwe,.- , j A do. 3 11 do. do. 58 30 - ee
Culloden, . : s do. 3 11 do. do. 57 30] —4 104,
Elgin, . : , , do. 3 11 do. do. 57 38 | —3 19 40
Aberdeen, . : , do. 5 11 do. do. 57 9| -2 7} 110
Braemar, . : : do. 3 11 do. do. 57, 0} —3 24) uaa
Kettins, : ) : do. 3 11 do. do. 56 32] -3 16] 228
Barry, . : i do. 3 11 do. do. 56 31 | —2 44 38
Callion Mor, . do. 3 11 do. do. | 56 8| -5 30] 65
Glasgow, -. ~. : do. 3 11 do. do. 55 53| -4 18] 180
Nookton, . ; : do. 3 11 do. do. 56 11} -3 3 80
Smeaton, . : do. 3 11 do. do. 56 Oj] —2 40] 100
Thirlestane Castle, : do. 3 11 do. do. 55 43 | -2 45] 558
Milne-Graden, . ; do. 3 11 do. do. 55 Oj] —2 12] 103
Durham, . ; : England 11 11 do. 10:10) 54 46] —1 35] 352
Silloth, ‘ ; ; do. 12 11 do. 9:9 | 54 52| —3 23 28
Stonyhurst, ; do. 13 2 | 1848-68) ‘red. | 53° 51 | —2°28") gem
Do., : : : do. 14 11 | 1857-67| 7:1,9 | 53 51] —2 28| 381
orks <<) 35 acca oak do. 15 11 do. red. |.53 58 | —1 i 50
Manchester, é , do. 15 11 do. 8:11] 53 39] -2 14] 123
Liverpool, . é do. 16 11 do. 71 | 53 25 | —2 &9 3a
Derby, j ; : wkdge {7 11 do. 9:3 | 52 56] —1 28| 174
Holkham, . : ‘ do. 18 11 do. 9n3.. | 52.5 ay 0 48 39
Norwich, . : : do. 19 7 do. 10:3 -| 32- 3S 1 18 50
Cardington, gti do. 20 11 do. 9:3°°| 52 7 | +0 (2) eae
Oxford, ; ; ; do. Si 515) 1d do. biho. | 51 46{ -—1 16] 210
Greenwich, . 3 fc do. 2 ia, elt do. red. 51 28 0 O| 159
London, ; ; : do. 23 89 Ries do. various | various |various
Clifton, : : : Sac: 15 11 | 1857-67 do. ol 28 | —2 36 228
Worthing, . : : do. 15 11 do. do. 50 49 | —0O 22 34
Helston, ; : : do. 24 20 |1849-68|} 9:3,9 | 50 7) —5 16 106 |
Do. ‘ ‘ : do. 24 11 1857-67| 9: 3,9 | 50 7) —5 16 106
Guernsey, . : : Channel Isles | 25,15] 11 do. 9:3 49 98'|} —2 32) |\seoge
Hammerfest, ; : Norway 26 13 | 1848-60} 8: 2,8 | 70 40| 23 46 21 |
AND THE PREVAILING WINDS OVER THE GLOBE. 595
REDUCED TO 32° Faur., IN ENGLISH INCHES, AT DIFFERENT PLACES OVER THE GLOBE.
in all other cases no such correction has been applied; the Hours of the A.m. Observations are placed before the Colon [:],
signifies Longitude West. The Observations are reduced to sea-level at all places which are printed in Italics.
January.| Feb. | March.|. April. | May. | June. | July. | August.) Sept. |October.} Noy. Dec. Year.
Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. } Inches.
29-303 | 29-457 | 29-634 | 29-747 | 29-806 | 29-730 | 29-700 | 29-688 | 29-615 | 29-554 | 29-600 | 29-388 | 29.602
29-308 | 29-400 | 29-648 | 29-723 | 29-845 | 29-747 | 29-701 | 29-669 | 29-549 | 29-550 | 29-628 | 29-360 | 29.593
29-467 | 29-307 | 29-449 | 29-663 | 29-724 | 29-717 | 29-687 | 29-660 | 29-514 | 29-457 | 29-482 | 29-274 | 29.534
29-431 | 29-228 | 29-719 | 29-608 | 29-877 | 29-836 | 29-792 | 29-723 | 29-718 | 29-395 | 29-772 | 29-328 | 29.619
29-433 | 29-246 | 29-602 | 29.904 | 29-948 | 29-717 | 29-753 | 29-699 | 29-566 | 29-468 | 29-619 | 29-797 | 29-646
29-571 | 29-394 | 29-746 | 29-691 | 29-913 | 29.896 | 29-872 | 29-782 | 29.757 | 29-485 | 29-827 | 29-485 | 29-702
29-541 | 29-623 | 29-539 | 29-673 | 29-691 | 29-692 | 29-690 | 29-639 | 29-623 | 29-581 | 29-650 | 29-650 | 29-633
29-807 | 29-901 | 29-787 | 29-927 | 29-949 | 29.932 | 29-922 | 29-887 | 29-865 | 29-834 | 29-870 | 29-9Q0 | 29-882
29-684 | 29-693 | 29-752 | 29-747 | 29-796 | 29-732 | 29-772 | 29-751 | 29-754 | 29-688 | 29-600 | 29-747 | 29.726
29-678 | 29-759 | 29-640 | 29-777 | 29-789 | 29-796 | 29-795 | 29-740 | 29-734 | 29-681 | 29-757 | 29-775 | 29-743
29-761 | 29-873 | 29-730 | 29-955 | 29-915 | 29-899 | 29-944 | 29-857 | 29-847 | 29-798 | 29-814 | 29-882 | 29-856
29-813 | 29-934 | 29-823 | 29.894 | 29.932 | 29-998 | 29-959 | 29-929 | 29-909 | 29-833 | 29-881 | 29-933 | 29-903
29-535 | 29-661 | 29-574 | 29-774 | 29-820 | 29-786 | 29-753 | 29°697 | 29-658 | 29-642 | 29-716 | 29-620 | 29.686
29-523 | 29-660 | 29-580 | 29-743 | 29-788 | 29-776 | 29-748 | 29-688 | 29-634 | 29-628 | 29-700 | 29-628 | 29-676
29-586 | 29-690 | 29-639 | 29-809 | 29-840 | 29-820 | 29-808 | 29-739 | 29-698 | 29-697 | 29-798 | 29-704 | 29-736
29-534 | 29-665 | 29-564 | 29-758 | 29-788 | 29-764 | 29-732 | 29-673 | 29.631 | 29-617 | 29-705 | 29-636 | 29-672
29-627 | 29-752 | 29-652 | 29-836 | 29-867 | 29-840 | 29-803 | 29-750 | 29-732 | 29-697 | 29-779 | 29-718 | 29-754
29-598 | 29.730 | 29-614 | 29-793 | 29-830 | 29-802 | 29-759 | 29-715 | 29-692 | 29.663 | 29-747 | 29-704 | 29-721
28-494 | 28-607 | 28-495 | 28-678 | 28-709 | 28-703 | 28-684 | 28-628 | 28-611 | 28-589 | 28-647 | 28-592 | 28-620
29-495 | 29-610 | 29-494 | 29.668 | 29-688 | 29-665 | 29-632 | 29-584 | 29-571 | 29-548 | 29-635 | 29-600 | 29-599
29-700 | 29-828 | 29-708 | 29-883 | 29-905 | 29-885 | 29-839 | 29-795 | 29-776 | 29-763 | 29-847 | 29-832 | 29-813
29-617 | 29-730 | 29-624 | 29-786 | 29-803 | 29-777 | 29-778 | 29-722 | 29-704 | 29-676 | 29-771 | 29-721 | 29-726
29-534 | 29-641 | 29-515 | 29-694 29.712 | 29-694 | 29-677 | 29-622 | 29-606 | 29-581 | 29-668 | 29-615 | 29-630
29-682 | 29-803 | 29-674 | 29-853 | 29-876 | 29-853 | 29-825 | 29-780 | 29-770 | 29-749 | 29-820 | 29-788 | 29-789
29-651 | 29-769 | 29-646 | 29-835 29-850 | 29-826 | 29-803 | 29-750 | 29-744 | 29.717 | 29-786 | 29-765 | 29.762
29-171 | 29-288 | 29-157 | 29-328 | 29-365 | 29-34] | 29-314 | 29-261 | 29.249 | 29.228 | 29-293 | 29-269 | 29.274
29-675 | 29-793 | 29-650 | 29-823 | 29-846 | 29-811 | 29-793 | 29-747 | 29.736 | 29-712 | 29-778 | 29-768 | 29-761
29-415 | 29-530 | 29-379 | 29-560 | 29-555 | 29-559 | 29-510 | 29-500 | 29-500 | 29-460 | 29.523 | 29-524 | 29-501
29-739 | 29-860 | 29-714 | 29-880 | 29-895 | 29-896 | 29-868 | 29-818 | 29-823 | 29.772 | 29-850 | 29-858 | 29-831
29-457 | 29-499 '| 29-438 | 29-486 | 29-513 | 29-520 | 29-510 | 29.478 | 29.523 | 29-408 | 29-481 | 29-453 | 29-481
29-411 | 29.497 | 29-341 | 29-491 | 29-516 | 29-514 | 29-503 | 29-466 | 29.459 | 29-403 | 29-487 | 29.496 | 29-465
29-770 | 29-865 | 29-701 | 29-866 | 29-868 | 29-867 | 29-842 | 29-806 | 29-830 | 29-773 | 29-847 | 29-886 | 29-827
29-736 | 29-832 | 29-671 | 29-822 | 29-836 | 29-830 | 29-813 | 29.781 | 29-781 | 29-733 | 29-805 | 29-839 | 29-790
29-834 | 29-922 | 29-776 | 29-927 | 29-939 | 29-938 | 29-931 | 29-881 | 29-889 | 29-827 | 29-867 | 29-932 | 29-889
29-688 | 29-769 | 29-589 | 29-750 | 29-758 | 29-770 | 29-756 | 29-716 | 29-723 | 29-662 | 29-734 | 29-788 | 29.725
29-870 | 29-950 | 29-763 | 29-908 | 29-922 | 29.914 | 29-905 | 29-870 | 29-882 | 29-840 | 29.914 | 29-984 | 29.894
29-906 | 29-975 | 29-807 | 29-979 | 29-973 | 29.971 | 29-958 | 29-904 | 29-950 | 29-894 | 29-955 | 30-008 | 29-940
29-806 | 29-880 | 29.705 | 29-852 | 29-860 | 29.863 | 29-858 | 29-824 | 29-844 | 29-777 | 29-858 | 29-905 | 29.836
29-699 | 29-779 | 29-598 | 29-745 | 29-749 | 29.761 | 29-753 | 29-721 | 29-733 | 29-666 | 29-737 } 29-800 | 29-728
29-760 | 29.829 | 29-650 | 29-792 | 29-793 | 29-810 | 29-814 | 29.778 | 29-794 | 29-721 | 29-790 | 29-853 | 29-782
29-947 | 29-962 | 29-959 | 29-941 | 29-965 | 30-001 | 29-967 | 29-982 | 29-975 | 29-909 | 29-904 | 29-943 | 29.955
29-668 | 29-744 | 29-572 | 29-709 | 29-716 | 29-730 | 29-731 | 29-696 | 29-704 | 29-628 | 29-7035 | 29-764 | 29-697
29-926 | 29-967 | 29-797 | 29-933 | 29-934 | 29.947 | 29.965 | 29-925 | 29.931 | 29-869 | 29-937 | 29-988 | 29-926
29-810 | 29-986 | 29-857 | 29-863 | 29-866 | 29-929 | 29-924 | 29-900 | 29-903 | 29-796 | 29-856 | 29-893 | 29-882
29-849 | 29-919 | 29-772 | 29.886 | 29-888 | 29-930 | 29-932 | 29-899 | 29-893 | 29-796 | 29-867 | 29-947 | 29-882
29-777 | 29-789 | 29-651 | 29-766 | 29-759 | 29-811 | 29-819 | 29-788 | 29-780 | 29-695 | 29-737 | 29-836 | 29-767
29-515 | 29-366 | 29-614 | 29-726 | 29-798 | 29-728 | 29-726 | 29-682 | 29-651 | 29-568 | 29-594 | 29-478 | 29-620
VOL. XXV. PART II. 7P
596 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHOWING THE MEAN MonTHLY AND ANNUAL HEIGHT
Autho- Number
a Hours of Heigh
Places. Country. ae, Years | Observa- Latitude. |Longitude. in Hag
pisces Years. | 5P eeified. tion. _ Feet.
Alten (at 32°?) . - Norway 27 12) SHS37=48') 9.309% 69) 58) |eecoeee 2
Christiansund, . ‘ do. 28 8 |1861-68| 8: 2,8 | 63 7 7 45 65
Alesund, . ; : do. 28 8 do. do. 62 29 6°59 32
Bergen, ; : : do. 28 8 do. do. 60 24 5 20 50
Skudesnes, : ; do. 28 8 do. do. 59 9 5 16 37
Mandal, . ; : do. 28 8 do. do. 58 2 7 27 54
Sandésund, . ; : do. 28 8 do. do. DU AEeO 10 27 41
Christiania, . . . do. 29 31 | 1837-67 |7,9:2,4,10} 59 55 10 44 74
«
Do.sthye : ; do. 29 11 | 1857-67] do. do. do. 74
Do., 3 : . do. 28 8 |1861-68| do. do. do. 74
Haparanda, . : : Sweden 30 7% | 1859-66 Bi: 65 50] 24 11 0
Umea, ‘ ‘ ; do. 30 8 do. do. 63 50] 20 17 0
Hernésund, . ‘ : do. 30 8 do. do. 62° 438% 27ase 0
Goteborg, . ; a do. 30 7% do. do. 57. 42) 1168 0
Wishy helknt pLade do. 30 74| do. do. | 57 39| 1819] 39
Jénk6éping, : do. 30 8 do. do. 57 47 | 14 11 | 292
Kalmar, : ; ; do. 30 8 do do 56 40 16 21 0
Carlshamm, . ; : do. 30 8 do do 56 10] 14 52 0
Orebro, -do. 30 8 do do 59 _ 16 15 13 97
Upsala, : ; do. 31,30| 11 |1857-67| 7 or 8: | 55 52) 17 38 77
Do. 5 d : do. 31, 30 8 | 1859-66 8 55 52 17 32 77
Copenhagen, d : Denmark 32 11 | 1857-67] noo 55 41) 12 35 12
Biyjehes,. & loF8 +426, do. 33 11 do. 6: |54 19] 10 20 7
Groningen, . ; ; Netherlands 33 11 do. S: 2 NVR" “as 6 34 49
Leeuwarden, . : do. 33 25 | 1843-67) 8: 2,8 | 53 12 5 47 24
Do., e : 5 do. 33 11 1857-67 8:2 53. 12 5 47 24
Utrecht, . Z do. 33 20 | 1849-68 Bie 52 5 anes 44
Do., : < : do. 33 11 1857-67 8:2 52 5 Dein 44
Flushing, . . : do. 33 11 do. do. 51 26 3 35 0
Luxemburg, : ; do. 33 11 - do. do, 49 37 6 8 | 1020
| Maestricht, : ! do. 33 11 do. do. 50 52 5 37 | 174
Brussels, . : 5 Belgium 34 35 |1833-67| noon | 50 51 4 22] 186
Do., : : ; do. 34 11 | 1857-67 do. 50 51 4 22 186
Liege, Sat Pras gies do. 34 | 20 |1847-66| do. | 50 41| 5 23] 199
Namur, : : : do. 34 13 | 1849-63 do. 50 28 4 51 491
Metz, . : ‘ : France 35 22 | 1825-46] do. AD cod 6 10] 595
Paris, : F : do. 35 30 | 1816-45 do. 48 50 2 20 216
Dor. ¢ 5 é do. 36,37), 11 1857-67 do. 48 50 2 20 216
Strasburg, . : : do. 4 15 2 at 48 36 7 42| 460
Dijon, : ‘ . do. 38 23 | 1845-67) noon | 47 19 5 2] 806
Do., : ; : do. 38 11 | 1857-67 do. do. do. 806
Ahun, : : : do. 39 38 | 1828-65 2. 46. 210 2 0 | 147
Lyon, : 3 : do. 39 6 | 1861-66 oe 45 46 4 49 636
Toulouse, . : : do. 40 22 | 1839-60 |9.12:3,6,9| 43 37 1 28 | 650
St Rambert, : . ~ do. 41 G 11838-43075 lf toed, 5 26 | 1017
Alais, ; i : do. 35 35 |1802-36| noon | 44 7 4 4 2
Orange, 4 ¢ 5 do. 35 36 | 1813-48] 9:3 44 8 4 48 149
Montpellier, : . do. 42 7 |1857-63| noon | 43 36 3 54 | 193
Bordeaux, . . . do 93 | 10 |1847-56| :2 |44 50|-035| 75]
Oviedo, ; ; . [Spain & Portugal] “40 11 | 1852-62 |9, 12: 3,9| 43 24 |-10 29) 718 |
AND THE PREVAILING WINDS OVER THE GLOBE.
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches.
29-712
29-544
29-630
29-634
29-717
29-733
29-741
29-753
29-732
29-693
29-663
29-659
29-675
29-787
29-801
29-497
29-863
29-900
29-716
29-713
29-680
29-875
29-888
29-882
29-887
29-894
29-896
29-918
29-977
28-926
29-819
29-766
| 29-773
oe Lid
29-567
29-400
29-808
29-800
29-587
29-179
29-201
28-430
29-413
29-402
28-983
29-673
29-867
29-878
29-937
29-229
Feb.
Inches.
29-653
29-595
29-686
29-693
29-788
29-788
29-772
29-729
29-790
29-682
29-811
29-775
29-758
29-836
29-818
29-508
29-835
29-882
29-741
29-766
29-716
29-936
29-954
29-926
29-909
29-963
29-971
29-969
30-032
28-953
29-863
29-778
29-835
29-764
29-650
29-370
29-762
29-840
29-615
29-194
29-221
28-436
29-362
29-359
28-881
29-623
29-825
29-878
30-007
29-217
Mar.
Inches.
29-754
29-619
29-694
29-674
29-745
29-725
29-745
29-770
29-676
29-697
29-774
29-702
29-678
29-733
29-740
29-410
29-738
29-732
29-670
29-676
29-652
29-776
29-761
29-747
29-886
29-780
29-886
29-780
29-843
28-768
29-666
29-746
29-641
29-690
29-575
29-367
29-762
29-650
29-567
29-115
29-025
28-416
29-158
29-341
28-968
29-619
29-823
29-756
29-956
29-215
April.
Inches.
29-856
29-764
29-843
29-823
29-894
29-855
29-856
29-813
29-796
29-788
29-850
29-828
29-836
29-938
29-925
29-589
29-912
29-948
29-834
29-792
29-833,
29-909
29-922
29-910
29-909
29-934
29-916
29-930
29-985
28-894
29-812
29-743
29-770
29-685
29-520
29-286
29-708
29-753
29-526
29-100
29-135
28-388
29-362
29-278
28-882
29.553
29-762
29-741
29-870
29-185
May.
Inches.
29-892
29-843
29-902
29-859
29-934
29-898
29-897
29-831
29-835
29-812
29-838
29-850
29-850
29-892
29-872
29-613
29-922
29-966
29-848
29-855
29-842
29-947
29-959
29-914
29-933
29-941
29-915
29-934
29-993
28-886
29-796
29-758
29-763
29-697
29-532
29-310
29-723
29.735
29-533
29-108
29-113
28-435
29-316
29-290
28-904
29-548
29-788
29-735
29-901
29-175
June.
Inches.
29-802
29-788
29-855
29-832
29-890
29-843
29-827
29-734
29-777
29-756
29-832
29-822
29-513
29-848
29-863
29-560
29-869
29-903
29-791
29-816
29-790
29-914
29-927
29-914
29-940
29-941
29-951
29-945
30-020
28-938
29-819
29-786
29-791
29-733
29-540
29-366
29-780
29-786
29-612
29-172
29-173
28-522
29-355
29-366
28-976
29-601
29-840
29-787
29-980
29-261
VOL.
XXV. PART II.
July.
Inches.
29-781
29-710
29-780
29-752
29-792
29-764
29-730
29-691
29-696
29-670
29-694
29-693
29-697
29-781
29-772
29-511
29-810
29-872
29-704
29.692
29-695
29-857
29-848
29-894
29-932
29-922
29-954
29-934
30-009
28-953
29-815
29-795
29-794
29-745
29-575
29-376
29-771
29-796
29-590
29-192
August.
Inches.
29-808
29-686
29-749
29-721
29-772
29-756
29-745
29-726
29-718
29-686
29-740
29-700
29-680
29-756
29-750
29-470
29-780
29-844
29-681
29-734
29-684
29-873
29-906
29-878
29-913
29-898
29-925
29-914
29-981
28-928
29-800
29-779
29-767
29-725
29-567
29-359
29-767
29-768
29-606
29-179
29-164
28-5395
29-366
29-381
29-022
29-602
29-870
29-792
29-993
29-287
Sept.
Inches.
29-771
29-701
29-768
29-749
29-800
29-795
29-800
29-797
29-765
29-753
29-778
29-748
29-749
29-842
29-870
29-564
29-865
29-874
29-767
29-792
29-772
29-937
29.949
29-918
29-979
29-938
29-970
29-949
30-005
28-965
29-843
29-794
29-802
29-761
29-603
29-352
29-754
29-800
29-631
29-201
29221
28-509
29-395
29.355
28-965
29-621
29-829
29-812
29-973
29.281 |
October.
Inches.
29-698
29-666
29-737
29-737
29-796
29-812
29-831
29-736
29.772
29-776
29-792
29-778
29-795
29-894
29-906
29-599
29-921
29-961
29-818
29-805
29-817
29-921
29.919
29-871
29-867
29-894
29-886
29-894
29-941
28-902
29-776
29-728
29-739
29-686
29-524
29-383
29-757
29-728
29-573
29-157
29-158
28-464
29-316
29-329
28-949
29-544
29-862
29-807
29-919
29-208
Nov.
Inches.
29-668
29-630
29-713
29-705
29-776
29-764
29-772
29-756
29-806
29-717
29-771
29-776
29-745
29-841
29-865
29-548
29-870
29-907
29-793
29-795
29-786
29-918
29-937
29-910
29-911
29-930
29-928
29-938
29-989
28-910
29-815
29-741
29-781
29-705
29-560
29-315
29-721
29-775
29-563
29-156
29-146
28-414
29-339
29-321
28-875
29-611
29-827
79-772
29-978
29-153
Dec.
Inches.
29-662
29-583
29-678
29-701
29-788
29-800
29-799
29-789
29-803
29-745
29-725
29-740
29-725
29-886
29-886
29-594
29-917
29-943
29-797
29-787
29-785
29-947
29-907
29-973
29-969
29-985
29-981
29.989
30-052
28-989
29-897
29-835
29-860
29-776
29-611
29-409
29-804
29-869
29-548
29-227
29-218
28-494
29-366
29-421
29-085
29-597
29-884
29-886
30-024
29-239
597
Year.
Inches.
29-755
29-677
29-753
29-740
29-808
29-794
29-793
29-760
29-764
29-731
29:772
29-756
29-750
29-836
29-839
29-539
29-858
29-894
29-763
29-769
29-754
29-901
29-906
29-894
29-919
29-918
29-928
29-925
29-985
28-918
29-810
29-771
29-776
29-724
29-567
29-357
29-759
29-775
29-580
29-165
29-164
28-467
29-342
29-353
28-958
29-600
29-836
29-805
29-970
29-231
7Q
598 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHOWING THE Mean MontTHLY AND ANNUAL HEIGHT
Autho- é
-,. _ \Number Hours of Height
Places. Country. 2 a ee Observa- | Latitude. |Longitude.]in Eng.
z nee Years. eect tion. Rese
arte
Barcelona, Spain &Portugal] 33 4 | 1864-67; 7or8: | 41 22 2 9 ?
Oporto, do. 43 5, | R863-67))- 9:3 41 9 | —8 27 278
Madrid, do. 40 9 | 1853-62 ic 40 24) —3 52 | 2149
Lisbon, do. 43 11- | 1857-67 |9, 12:3,9| 38 43] -—9 8 336
Alicante, do. 33 4 | 1864-67] 7 or8 38 21 | —O 25 ?
San Fernando, do. 33 9 | 1859-67 do. 36 27) -—6 13 ?
Gibraltar, do. 44 6 | 1853-59) 93:32 | 36 6) —5 21 46
Gibraltar, do. 45 3 |1864-66| 9:3 36 6| —5 21 50
Zurich, Switzerland 46 10 | 1837—46 |9,12:3,9| 47 22 § 32 | 1432
Geneva, do. 40 25 |1836-60| biho. | 46 12 6 9 | 1335
Do., F : do. 47 11 |1857-67| noon | 46 12 6 9 | 1335
Great St Bernard, do. 47 11 do. do. 45 51 7 11 | 8174
Trient, : Italy 48 11 | 1856-66| various | 46 4/{ 11 4] 622
Udine, do. 40 40 | 1803-42 92: AO. ei 13 14 393
6, 12:
Milan, ‘ do. 48 16 | 1848-53 \° | 45 28 9. 9| 482
6, 12:3
Verona, do. 40 7 |1854-60| 8: 2,8 | 45 27/].1059) 186
sr: 2:9
Venice, do. 48 10} | 1853-63 or 45° 26% T1217 66
6: 2, 10
Turin, do. 40 74 | 1787-1860 ? 45 4 741 /] 915
Brescia, do. 40 27 | 1818-44} sr: 12:ss| 45 32 | 10 13 |) ag2
Bologna, do. 40 45 | 1814-58 e 44 30/ 11 21] 244
Genoa, do. 4 10 “4 ? 44 25 8 55 | 157
Do., do. 40 2 |1860-61/9,12:3,9| do. do. 157
Rome, do. 40 10 | 1852-61 73 41 54 12 28 163
Rome, . do. 40 15 | 1852-66 74 do. do. 163
Naples, do. 40 28 | 1833-60 93: 40 52 14 15 482
Palermo, do. 55 78 | 1791-1868 | various | 38 7 13 21 237
Do. do. 55 11 | 1857-67 do. do. do. 237
1853-55,|),, g
Malta, do. 44 6 { 1858-59 lox 34 | 35 54 14 31 232
Malta, do. 45 2 |1865-66| 9: 3 35 «54 14 30 111
Bodenbach, . Austria 48 19 | 1848-66] 6:2,10/ 50 46] 1410] 466
Prague, do. 48 19 do. do. 50) 5 | 14-23 4668
Do., do. 48 11 | 1857-67 do do. do. 660
Krakau, do. 48 19 | 1848-66) do 50 49) 19.55 | e7G8
Do., do. 48 11 | 1857-67 do. do. do. 708
Troppau, do. 48 7% | 1858-65| do 49 56| 17 52| 847
_pe |f 60r7:2,
Lemberg, do. 48 17 | 1850-66 19 or 10 49 50] 24- 0 | ' 928
Do., do. 48 | 11 | 1857-67 peat ay do. | do. | 998
Brunn, do. 48 19 | 1848-66) 6: 2,10} 49 I1 16 35 697
Vienna, do. 48 19 do. do. 48 12 16 20 638
Do., : do. 48 11 | 1857-67 do. do. do. 638
Kremsminster, do. 48 19 |1848-66| do. 48 3 14 6 | 1258
Debreczin, . do. as | 11 |1857-67 se ee 47 32] 2139] 417
\ .
| Ofen (Buda), do. 48 10. | 1856-66] 6:2,10 | 47-31] 19 1] 420mm
Klagenfurt, do. 48 19 | 1848-66) 7:2;9 | 46 37] 14 16 | 1438]
Szegedin, do. 48 12 |1853-66| 6:2,10| 46 15] 20 6] 276)
AND THE PREVAILING WINDS OVER THE GLOBE.
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches.
30-024
29-748
27-835
29-828
30-138
30-170
30-082
30-138
28-504
28-630
28-660
22-062
29-434
29-629
29-523
29-756
29-975
29-077
29-487
29-776
29-863
29-857
29-849
30-040
29-545
29-720
29-735
30-096
29-883
29-515
29-327
29-325
29-282
29-295
29-166
29-014
29-011
29-298
29-378
29-384
28-702
29-602
29-647
28-491
29-757
Feb.
Inches.
30-056
29-825
27-836
29-773
30-134
30-111
30-018
30-002
28-434
28-584
28-670
22-112
29-407
29-655
29-504
29-760)
29-970
29-068
29-441
29-764
29-813
29-787
29-798
29-989
29-503
29-718
29-734
29-915
29-825
29-472
29-288
29-355
29-208
29-297
29-120
28-952
29-027
29-235
29-320
29-388
28-664
29-592
29.604
28-427
29-709
May.
Inches.
29-985
29-634
27-739
29-665
30-020
30-000
30-017
29-965
28-430
28-538
28-565
22-227
29-289
29-569
29-392
29-634
29-872
29-112
29-406
29-666
29-774
29-796
29-760
29-961
29-519
29-693
29-680
29-973
29-854
29-428
29-221
29-240
29-189
29-120
29-053
28-917
28-939
29-170
29-241
29-265
28-602
29-430
29-476
28-371
29-593
June.
Inches.
30-016
29-747
27-816
29-735
30-091
30-091
30-075
30-015
28-520
28-626
28-630
22-337
29-311
29-590
29-438
29-749
29-890
29-166
29-424
29-705
29-804
29-800
29-817
29-993
29-582
29-729
29-705
30-016
29-846
29-449
29-253
29-265
29-211
29-219
29-053
28-943
28-932
29-202
29-281
29-290
28-661
29-415
29-491
28-424
29-644
July.
Inches.
30-004
29-754
27-830
29-747
30-064
30-044
30-050
29-998
28-536
28-650
28-658
22-394
29.322
29:576
29-445
29-741
29-915
29-176
29-415
29-701
29-779
29-751
29-813
29-989
29-572
29-714
29-718
30-031
29-808
29-471
29:267
29.258
29-220
29-219
29-061
28-936
28-937
29-211
29-297
29-297
28-683
29-427
29-508
28-440
29-625
Sept.
October.
Nov.
599
Year.
Inches.
30-071
29-762
27-741
29-745
30-123
30-056
30-080
30-042
28-516
28-634
28-676
22-377
29-387
29-630
29-496
29-815
29-972
29-176
29-450
29-760
29:786
29-823
29-850
30-032
29-589
29-743
29-753
30-060
29-903
29-526
29-332
29-337
29-300
29-322
29-094
29-043
29-047
29-287
29-360
29.376
28-715
29-558
29-570
28-496
29:745
Inches.
29-941
29-622
27-825
29-672
30-012
30-013
30-076
29-928
28-504
28-605
28-613
22-254
29-356
29-631
29-481
29-733
29-944
29-117
29-450
29-756
29-798
29-933
29-845
30-016
29-567
29-728
29-715
30-045
29-839
29-479
29-290
29-305
29-282
29-307
29-133
29-040
29-054
29-251
29-330
29-349
28-667
29.544
29-609
28-456
29-780
Inches.
30-024
29-741
27-752
29-678
30-127
30-079
29-995
30-047
28-434
28-570
28-618
22-146
29-362
29-624
29-446
29-686
29-928
29-068
29-441
29-756
29-753
29-774
29-766
29-949
29-520
29-713
29-695
29-996
29-896
29-489
29-286
29-323
29-246
29-298
29-111
29-023
29-036
29-240
29-320
29-364
28-652
29-568
29-606
28-431
29-735
Inches.
30-015
29-723
27-834
29-731
30-077
30-068
30-056
30-010
28-489
28-601
28-629
22-218
29-350
29-604
29-458
29-729
29-928
29-109
29-435
29-729
29-800
29-806
29-808
29.989
29-539
29-709
29-703
30-019
29-856
29-474
29-278
29-285
29-235
29-246
29-083
28-972
28-979
29-231
29-311
29-325
28-663
29-502
29-555
28-431
29-686
600 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHOWING THE MEAN MONTHLY AND ANNUAL HEIGHT ~
Autho-
oe Number Hours of Height
Places, . Country. se pate et ete FL pitas Latitude. |Longitude. a an:
° / cme
Agram, : : ; Austria 48 8 \ saris i fie 45 49 | 15 53] 448
Hermanstadt, . : do. 48 16 |1851-66| 6:2,10 | 45 47 | 24 7 | 1354
Do., ’ : do. 48 11 | 1857-67| do. do. do. 1354
Trieste, A ° - do. 48 -19 | 1848-66] 7:2,9 | 45 39 13 44 79
Do., ; ; s do. 48 11 | 1857-67) do. do. do. 79
6 or7
Pancsova, . : ; do. 48 7 | 1860-66 f or | 44 50] 20 35| 224
8 or 9
6 or 7:
| Lesina, : : do. 48 9 | 1858-67 (2 9 at 430c11)| , 06325 63
10
Munich, . ; 4 Bavaria 49 10 |1857-66| hourly | 48 9] 11 34 | 1676
Memel, : ; Prussia, &c. 50 7 | 1861-67 | 622,10 (959344) Obes ?
Kénigsberg, : ; do. 50 10 |1858-67| do. 54 43] 20 29 72
Dopey ee : : do. 50, 33 7 |1861-67| do. do. do. 72
Danizig, . ; . do. 4 32 ? do. a4 21 18 41 30
Do., : . : do. 50 7 |1861-67| do. do. do. 30
Putbus, : : : do. 50233) Ll }) 1857-67 do. 54 22 1335 173
Coslin, a : . do. 50 7 | 1861-67 do. 54 12 16 15 128
Stettin, . ’ , do. 50 if do. do. 53 25 | 12.30 49
Bromberg, . 4 do. 50 7 do. do. 53. 8| 18 0 | “246
Berlin, ; ‘ : do. 502331 lel 1857-67 do. 52 30 13. 3 153
Do., : : do. 50 7 |1861-67| do. do. do. 153
Posen, ‘ ; : do. 50 7 do. do. 52 25 | 17 5 | 28%
Halle, : : ; do. 50 Z do. do. 51 30] 11 57 | 372
Weipsig; cay aut | a; : do. 51 33 | 1835-67| do. 51, 20 | 12 21 |) sa86
Miilhausen, ; : do. 50, 33 105 1857-67| do. 51. -13-| 10 27 | S68Gam
Breslau, , . do. 50,33| 103 |1857-67| do. 51. 7 |. 1-2
Erfurt, é : ‘ do. 50 7 | 1861-67 do. 50 59 1] 4 682
Bucharest, . ' . |Turkey &Greece| 52 6 |1863-68| do. 44 26| 26 8] 700
Janina, : : : do. 3 5 |1864-69| various | 39 47 | 20 55 | 1570
Corfu, Be Ove do. 44 6 |1853-59] 93:32 |39 39| 1955| 74}
Constantinople, . : do. 52 11 |1858-68| 9: 41 0} 28.59 jee
Athens, ‘ ‘ : do. 52 11 do. 8: 37 58 | 23 439Rzae
Archangel, . : : Russia 4 18 ? ? 64 33 | 40 33 ?
Helsinfors, . ‘ ~ do. 26 10 | 1852-62) hourly | 60 14 | 24 57 50
St Petersburg, . i do. 26 19 | 1846-64] do. 59 56] 30 18 10 |
Do., 5 ; - do. 26,33) 11 | 1857-67 Se do. do. 10 |
Baltischport, . . do. 26 | 10 |1855-64/8,12:3,10} 59 21| 24 3 0 |
Dorpat, ; : : do. 33,53| 11 |1857-67| a.m. 58 17 | 26 47 | doGe
Kostroma, . : ; do. 26 7 |1850-56!7:2,2x9| 57 46! 40 56] 640°
Mittaa, C202 OSp-08, do. 26 | 12 |1852-63|6:2,10|56 35| 2343] 13)
1847-48,
Riga, . Swab, be : do. 26 10 seca do. | 56 57| 24 6| 20%
1863-64 |)
Moscow, ; , E do, 33 10 | 1858-67 A.M. 55 442 37, 39 400 |
Zlalouste, . : : do. 26 28 | 1837-64] various | 55 10] 59 40 | 1444 |
Gorki, 9 ; ; do. 26 4 | 1851-54) 6:2,10 | 54 15 30 35 690 |
‘Walnas.) TVS OOS-05, do. 26 | 9 { ty 2 | ba 41 | 25 17
Kaluga, . : ; do. 26 13 | 1851-6317, 2:29] 54 30] 36.15 | 57
AND THE PREVAILING WINDS OVER THE GLOBE.
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches.
29-556
28-597
28-602
29-939
29-956
29-898
29-968
28-220
29-844
29-913
29-875
29-980
29-894
29-706
29-829
29-862
29-789
29-818
29-774
29-758
29-668
29-610
29-283
29-550
29-303
29-308
28-323
30-036
30-081
29-730
29-743
29-820
29-915
29-850
29-857
29-690
29-336
29-910
29-901
29-483
28-634
29-305
29-473
29-470
VOL. XXV. PART II.
Feb,
Inches.
29-495
28-518
28-592
29-902
29-970
29-835
29-901
28-201
29-904
29-912
29.922
29-949
29-943
29-723
29-880
29-883
29-830
29-867
29-846
29-774
29-707
29-577
29-305
29-544
29-325
29-239
28-371
29-981
30-058
29-734
29-765
29-829
29-801
29-943
29-891
29-776
29-157
29-905
29-968
29-495
28-556
29-023
29-493
March.
Inches.
29-295
28-437
28-410
29-825
29-774
29-589
29-772
28-040
29-768
29-749
29-783
29-917
29-792
29-576
29-714
29-703
29-650
29-679
29-641
29-586
29-492
29-600
29-198
29-359
29-114
29:092
28-135
29-981
29-898
29-605
29-703
29-775
29-841
29-819
29-754
29-658
29-230
29-854
29-807
29-482
28-547
29-188
29-450
29-397
29-378
April.
Inches.
29-423
28-470
28-480
29-804
29-871
29-766
29-884
28-151
29-890
29-857
29-907
29-912
\
29-893
29-696
29-873
29-885
29-801
29-786
29-800
29-769
29-705
29-535
29-257
29-478
29-318
29-174
28-326
29-955
29.924
29-669
29-782
29-786
29-877
29-834
29-843
29-713
29-273
29-882
29-846
29-474
28-525
29-143
29-492
29-354
May.
Inches.
29-299
28-477
28-493
29-840
29-860
29-733
29-864
28-148
29-904
29-900
29-922
29-952
29-943
29-744
29-910
29-873
29-819
29-813
29-820
29-763
29-676
29-568
29-253
29-464
29.290
29-269
28-361
29-954
29-878
29-651
29-798
29-860
29-898
29-896
29-882
29-729
29-293
29-901
29-859
29-473
28-475
29-142
29-584
29-375
June,
Inches.
29.414
28-500
28-493
29-870
29-870
29-702
29-859
28-203
29-871
29-882
29-882
29.927
29-908
29-744
29-848
29-837
29-799
29-812
29-795
29-739
29-674
29-602
29-286
29-467
29-308
29-174
28-330
29-972
29-877
29-607
29-734
29-820
29-827
29-847
29-881
29-741
29-208
29-880
29-864
29-457
28-344
29-078
29-534
29-314
July.
Inches.
29-428
28-503
28-500
29-861
29-868
29-724
29-856 |
28-228
29-790
29-817
29-830
29-892
29-846
29-686
29-822
29-798
29-756
29-786
29-770
29-664
29-656
29-624
29-277
29-436
29-306
29-146
28-283
29-940
29-839
29-571
29-698
29-764
29-798
29-780
29-801
29-619
29-148
29-845
29-794
29-447
28-341
29-093
29-519
29.284
August.
Inches.
29-400
28-533
28-535
29-863
29-859
29-739
29-866
28-211
29-811
29-847
29-845
29-908
29-877
29-683
29-837
29-830
29-789
29-814
29-795
29-741
29-675
29-613
29-270
29.457
29-309
29-172
28-311
29-953
29-877
29-611
29-685
29:777
29-836
29-806
29-808
29-642
29.235
29-870
29-842
29-455
28-411
29-187
29-599
29-346
Sept.
Inches.
29-540
28-620
28-620
29-922
29-944
29-809
29-937
28-249
29-924
29-848
29-953
29-967
29-981
29-768
29-905
29-894
29-859
29-875
29-870
29-824
29-736
29-623
29-316
29-553
29-358
29-314
28-414
30-040
29-979
29-673
29-798
29-814
29-891
29-897
29-880
29-729
29.284
29-914
29-893
29-483
28-527
29-198
29-673
29-410
October.
Inches.
29-453
28-621
28-617
29-898
29-917
29-819
29-930
28-190
29-958
29-954
29-978
29-961
29-992
29-714
29-900
29-915
29-863
29-843
29-835
29-806
29-695
29-597
29-270
29-550
29-309
29-334
28-365
30-080
30-055
29-750
29-725
29-844
29-904
29-926
29-888
29-772
29-328
29-949
29-908
29-504
28-559
29-224
29-649
29-499
Noy.
Inches.
29-476
28-565
28-602
29-850
29-902
29-811
29-870
28-171
29-775
29-916
29-890
29-912
29-910
29-747
29-848
29-879
29-790
29-816
29-800
29-763
29-682
29-560
29-291
29-521
29-298
29-296
28-333
30-002
30-038
29-728
29-696
29-852
29-916
29-888
29-942
29-745
29-351
30-104
29-980
29-499
28-615
29.205
29-522
29-447
Dec.
Inches.
29-653
28-621
28-621
29-945
29-944
29-887
29-907
28-267
29-928
29-937
29-914
29-919
29-977
29-766
29-930
29.974
29-889
29-866
29-898
29-825
29-806
29-626
29-328
29-592
29-410
29-396
28-364
30-040
30-055
29-728
29-694
29-728
29-833
29-885
29-800
29-725
29-126
29-909
29-761
29-498
28-550
29-092
29-522
29-401
ce
601
Year.
Inches.
29-452
28-538
28-547
29-876
29-895
29-776
29-885
28-189
29-864
29-878
29-892
29-933
29-913
29-710
29-858
29-861
29-803
29-815
29-804
29-751
29-681
29-596
29-278
29-598
29-304
29-242
28-326
29-995
29-963
29-671
29-735
29-806
29-861
29-864
29-852
29-712
29-247
29-910
29-869
29-479
28-507
29-158
29-542
29-390
602 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHOWING THE MEAN MontTHLY AND ANNUAL HEIGHT
Autho- 2
Places Country. Bune, nee — he oo Latitude. aed in Bop
1 ee Ye, | tion. Feet.
° / ° /
ifs
Tamboyv, . ‘ : Russia 26 13 { peer \s:sor10 52 41 | 41 30] 580
Warsaw, : 5 : do. 33 10 | 1858-67 6: 52 14 21 7 | 460
., |) 10:2,10
Orenburg, . ; : do. 26 21 | 1844-64 h aniciiy 51 49] 35 6] 280
Asiracan (at 32°?), do. 4 1 ? ? 46 15] 48 4 40
Kursk, 5 : : do. 26 27 =| 1835-59 |9, 12: 3,9) 51 44 36 14 700
Morshansk,. . . do. 2 | 4 \ peed | 8:8 |52 27| 41 53| 520
Woltchansk, : do. 26 13 | 1852-64|6: 2,10} 50 17 36 56 370
Lugan, : : do. 26 23 | 1842-64] various | 48 35 39 20 330
Nicholaieff, . f do. 26 6 | 1859-64] 10: 10 | 46 58 31 58 85
Otlessa, ee qc a anne do. 2 | 9 | tees O| 9:9 | 46 28| 30 43 | aay
Kiew, . : , 3 do. 52 10} | 1858-68 Gr 50 27 30 34 578
Alagir, : : . do. 26 16 | 1848-63] 7:2,9 | 43 2] 43 53 | 2060
Derbent, . : : do. 26 4 |1852-55| do. 42 12) 48°15 | ie
Jakutsk, . ; . | Asiatic Russia d 12 ? ? 62 2] 129 14] 285
Bogoslovsk, t 3 do. 26 26 | 1839-64] various | 59 45] 60 2)| 593
6: 2, 10
Tobolsk, 0 0 : do. 26 11 1852-62 and 58 912 68 16 355
Piece) (|
Nijni-Tagilsk, . . do. 54 | 21 |1845-65| 8:3,8 |57 59| 6019| 7302
Catherinenburg, . : do. 26 19 | 1846-64} hourly | 56 49] 60 35] 997
Tomsk, His Dae ¢ do. 26 2 1852-53 8:8 56 30 85 10 300
gins aaa cone! peas ayee do. 26 2 |1847-49| 7:2,9 | 56 27] 138 96| ?
| Krasnoyarsk, - , do. 26 10. | 1838-47 |'9: or. 10:/ 56, “. 1.) 92.54 ?
Udskoi, : , ; do. 4 1 ? ? 54 30 | 134 28 ?
Bamaul 5. ; : do. 26 19 | 1846-64] hourly | 53 20] 83 57] 400
Peterpaulshavn, . ; do. 4 1 ? ? 53 °10.| 158 32°\ame
Irkutsh, : ; : do. 26 £50 || 1830 —44as fe 2e 0 oon ln 122 11 | 1253
Nertchinsk,. . . do. 26 | 18 |1847-64| hourly | 51 19] 119 36 | 2130
Fort No. 1, 2 ; do. 26 1 1865 6: 2,10) 45 465 64 27 170
Novo Petrovsk, . : do. 26 6 |1852-57| do. 44 27 | 50 8} 100
Kutais, - * 3 do. 26 3 1850-52) 7:2,9 | 42 31 42 27 470
Redut Kale, ; : do. 26 8 |1847-54| do. 42 16 | (41°36 20,
SRLS Bae ae (deers, do. 26 14 |1850-63} hourly | 41 42] 44 50 | 1500
Alexandropol, . 5 do. 26 I2 |1854-65| 7: 2,9 | 40 48] 43 49 | 5010
Baku, . c : S do. 26 17 ‘| 1848-64 do. 40 22 49 50] —53
; 7: 12 or
Aralikh, ; = - do. 26 , 3 | 1851-53 heetan 39 53 44 33 | 2600
Lencoran, . ¢ : do. 26 5 |1852-56| 7:2,9 | 388 44 | 48 52 | —65]
Wernoie (132 obs.), do. 26 1 1859 noon | 43 16| 77 0 | 2430 |
Chusan (at 32°?), ~. China 4 1 2 ? 30-30 | 122 6 jim
; Bs a9: Pe
= &ce., to | =e
Pekin, : 4 : do. 26 14 | 1842-55|) og og 39 54 | 116 26 ? te
hourly} “ti
Tien Tsin, . : : do. 105 1 | 1860-61] (9:3 39. 9) Tiww6 29 |
Shanghai, . : : do. 56 2 |1867-68| various | 30 4] 85 33 0}
Canton, : : : do. 4 10 3 ? 23 12 | 113 17 <
AND THE PREVAILING WINDS OVER THE GLOBE.
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches.
29-587
29-587
29-870
30-206
29-303
29-462
29-672
29-835
30-010
29-876
29-432
27-888
30-187
29-895
29-280
30-002
29-386
29-127
30-092
29-786
30-078
30-003
29-807
29-409
28-777
27-963
29-986
30-080
29-624
30-094
28-547
24-938
30-215
27-458
30-292
27-597
30-412
30-244
30-313
30-254
30-175
Feb.
Inches.
29-419
29-548
29-820
30-402
29-263
29-435
29-672
29-736
29-990
29-714
29-430
27-873
30-076
29-957
29-245
29-926
29-347
28-990
30-215
29-874
30-043
29-866
29-739
29-547
28-719
27-922
29-938
30-017
29-510
29-977
28-502
24-895
30-179
27-294
30-171
27-409
30-426
30-170
30-336
30-186
30-099
March.
Inches.
29-426
29-426
29-827
30-099
29-198
29-404
29-611
29-686
29-840
29-806
29-343
27-877
30-059
29-748
29-255
29-917
29-372
29-002
29-934
29-910
29-952
29-766
29-689
29-700
28-624
27-876
29-986
29.982
29-490
29-994.
28-460
24-905
30-132
27-200
30-152
27-579
30-009
30-132
30-108
30-018
April.
Inches.
29-397
29-497
29.742
30-000
29-236
29-418
29-538
29-622
29-825
29-732
29-337
27-827
30-020
29-620
29-216
29-802
29-303
28-999
29-822
29-806
29-813
29-766
29-521
29.921
28-590
27-662
29-804
29-901
29.439
29-911
28-397
24-874
30-023
27-164
30-099
27-419
29-826
29-950
29-944
29-849
May.
Inches.
29-397
29-520
29-618
29-899
29-230
29-456
29-549
29-626
29-788
29-720
29-378
27-844
30-001
29-472
29-185
29-681
29-241
28-922
29-600
29-751
29-662
29-590
29-375
29-805
28:353
27-604
29-736
29-866
29-458
29-936
28-398
24-925
29-988
27-202
30-065
27-294
29-668
Inches.
29-299
29-489
29-481
29-600
29-163
29-389
29-468
29-523
29-732
29-677
29-314
27-801
29-886
29-366
29-016
29-504
29-107
28-777
29-483
29-688
29-550
29-550
29-186
29-732
28-261
27-566
29-635
29-772
29-388
29-866
28-322
24-908
29.884
27-080
29-958
27-222
29-517
29-642
29-707
29-731
Inches.
29-265
29-445
29-439
29-600
29-148
29-322
29-437
29-480
29-740
29-667
29-291
27-781
29-834
29-383
29-055
29-462
29-103
28-778
29-350
29-633
29-536
29-463
29-104
29-685
28-192
27-566
29-512
29-724
29-328
29-819
28-291
24-871
29°815
27:022
29-904
27-182
29-470
29-571
29-719
29-656
August.
Inches.
29-381
29-504
29-534
29-899
29-224
29-379
29-499
29-595
29-822
29-691
29-348
27-831
29-936
29-435
29-104
29-498
29-165
28-843
29-561
29-754
29-672
29-412
29.228
29-714
28-264
27-649
29-624
29-794
29-365
29-829
28-362
24.912
29.907
27-061
29-962
27-270
29-586
Sept.
Inches.
29-413
29-611
29-688
29-899
29-309
29-465
29-620
29-690
29-884
29-768
29-425
27-912
30-016
29-711
29-188
29-571
29-282
28-963
29-601
29-766
29-818
29.568
29.409
29-709
28-443
27-752
29-756
29-923
29-484
29-945
28-473
24-982
30-025
27-214
30-095
27-425
30-027
29-813
29-927
29-903
29-685
October.
Inches.
29-432
29-603
29-761
30-201
29-343
29-441
29.729
29-800
29-963
29-838
29-498
28-018
30-162
29-670
29-205
29-719
29-300
29-000
29-819
29-855
29-907
29-655
29-556
29-626
28-588
27-834
29-945
30-120
29-595
30-037
28-589
25-060
30-183
27-339
30-246
27-578
30-176
30-008
30-076
30-062
29-912
Nov.
Inches.
29-483
29-556
29-908
30-300
29-352
29-442
29-754
29-864
30-047
29-937
29-479
28-013
30-134
29-829
29-261
29-816
29-384
29-058
29-852
29-743
30-041
29-788
29-667
29-600
28-657
27-856
30-120
30-137
29-572
30-055
28-608
25-049
30-219
27-376
30-262
27-665
30-193
30-154
Dec.
Inches.
29-455
29-670
29-844
30-300
29-277
29-515
29-608
29-785
29-907
29-709
29-461
27-941
30-153
30-060
29-253
29-803
29-317
28-957
29-835
29-752
30-112
29-860
29-703
29-720
28-677
27-848
29-986
30-034
29-598
30-076
28-561
24-976
30-166
27-364
30-243
27-700
30-344
30-217
30-245
30-205
30-123
603
Year.
Inches.
29-413
29-538
29-711
30-034
29-254
29-427
29-596
29-685
29-879
29-761
29-395
27-884
30-039
29-679
29-191
29-725
29-276
28-951
29-763
29-776
29-850
29-691
29-499
29-679
28-512
27-758
29-836
29-946
29-484
29-962
28-459
24-941
30-061
27-232
30-121
27-445
29-890
29-985
29-990
29-895
604 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHowincG THE MEAN MonTHLY AND ANNUAL HEIGHT
Autho- :
Number Hours of Height
Places, Country. es, aes Observa- | Latitude. |Longitude.|in Eng.
ee Years. sat tion. Feet.
a wstnell | cate
Macao, ‘ " : China 4 1 ? ? 22.15 | 113 36 ?
Hong Kong, 3 5 do. 44 6 |1853-59| 93:34 | 22 16 | 114 10 35
Nafa, . : : . | Pelew Islands 4 1 ? 4 26 14 | 127 46 ?
Chacodate, . ‘ : Japan 26 4,5;| 1859-63 | 7,9:2,9]| 41 48 | 140 47 | 150
Decima (Nangasaki) do 33 7, {| 1845-48, 6,9: 32,1] 35 44 | 109 42) 96
‘= pd : * (| 1852-55 10
Erzroum, . . . |Turkeyin Asia| 3 1 | 1836-38 daily } 39 57 | 41 13a
Scutari, ‘i : do. 45 2 | 1865-66; 9:3 Ail: 0s) 29in 8 60
Larnaka, Cyprus, : Syria 3° 3 |1866-69| 9:9 34 55] 33 39 25
Beyrout, . : . do. 4 1 ? ? 33.54) 25, 29 ?
Dore : : : do. 3 1 1868-69} 9:10 33 54 39 29 160
Jerusalem, . ; : do. 3 8 | 1861-68 9: 31 47 | 35°13 | 2500
jeHds,) eee ‘Creer, do. 57 1 \ aa 9:3 |21 28| 3913| 25
LSA Se ar do. 57 |. 3, |..1831..| 82:31 | 28..13'| 33 Some
Aden, . ‘ : ‘ do. 4 2 4 ? 12 46} 45 5} 199
Mooltan, . : ; Hindostan 58 6 | 1862-67; 10:4. |.31. 11,| -71 333
Roorkee, . : : do. 59 4 |1865-68| do. 29.52 | 77 57 | 8388
Nynee Tal, . ; , do. 59 4 do. do. 29 23) 79 31 | 6433
Agyra,-. : A é do. ~ 59 4 do. do. 27 +10 73,5 551
Nazirabad, . ‘ 4 do. 4 4 ? ? 26 18 | 74 45 | 1585
Benares, . 5 : do. 59 3 | 1865-68, 10:4-|25 2) 83 5 | 9269
Calcutta, . ; ; do. 60 12 |1856-67| hourly | 22 33] 88 21 19
Kurrachee, . : F do. 45 1 1864 9:3 24 ol) BT ae ?
Bombay. to. : do. 61 14 |1847-60| hourly | 18 54] 72 48 35
9, 10
Poonah, : : . do. 98 1 1830 is, | 1S ol 74 6 | 1823
10-11
Secunderabad, . : do. 62 1 1864 |4,10:4,10) 17 25 | 78 40 | 1700
Dodabetta, . : : do. 63 5 | 1851-55 9:3 11 32 76 50 | 8640
Madras, ‘ : : do. 64 5 |1846-50| hourly | 13 4] 80 19 27
Do, *. : : : do. 64 22 | 1822-43] red. do. do. 25
Merkera, . : d do. 27 3 | 1838-40 Oro 12 46 75 44 | 4500
Trivandrum, : A do. 4 83 ? ? 8 31) ‘77 “0))aaae
Colombo, . ; : do. 44 6 | 1853-59} 93:33 6 56 79 50 18
Gangaroowa, : ; do. 60 13 | 1863-64| do. 7 #17-| 80 37 | Tone
Ava, . ‘ j : do. 4 1 is ? 2t 50| 96 5 ?
Saigon, . . . | Cochin China | 51 14 | 1867-68 6,10: 4,10, 10 33 | 106 33| ?
East India
Honolulu, . : 5 Islands and 4 1 ? ? 21 16 |-157 59] ?
Pacific
Manilla, . , : do. 4 1 ? ? 14 36 | 129 0) 95am
Stncapore, . do. 66 1 1866 9: 1 17 103 51) age
Shales (Sin- it, do 66 2 |1866-67) noon | 1 9| 103 44) 65 |
Padang, . 3 : do. 33 34 | 1850-53 6,9:3,10,\-0 56| 100 2| ?
Batavia, . : : do. 4 1 2 ? —6 9 106 53/58
Buitenzorg: 5 sae: do. 33 | 12 | 1841-54 { Hee ah —6 37) 106 49| 889 |
Samarang, . } 3 do. 4 1 ? ? -6 50}| 110 33) ?
AND THE PREVAILING WINDS OVER THE GLOBE.
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches.
30-232
30-179
30-087
29-743
30-173
23-974
29-975
30-084
29-897
29-890
27-432
eee
29-823
29-653
29-153
23-873
29-496
28-475
29-882
30-022
30-092
29,935
28-087
28-267
22-176
29-986
30-019
26-130
29-739
29-909
28-359
29-801
29-985
30-027
29-992
30-017
| 29.951
29-686
29-747
28-983
29-953
VOL. XXV. PART II.
Feb.
Inches.
30:197
30-126
30-080
29-769
30-123
23-898
29-852
30-068
29-836
29-932
27-432
29-844
29-566
29-069
23-825
29-409
28-387
29-782
29.944
30-058
29-908
28-002
28-226
22-183
29-971
30-008
26-154
29-721
29-906
28-334
29-688
29-992
30-018
29-936
29-980
29-943
29-696
29-746
28-985
29-978
March.
April.
May.
Inches.
30-161
30-014
30-063
29-870
30-099
23°953
29-793
29-885
29-737
29-721
27-374
29-776
29-492
29-018
23-882
29-345
28-317
29-697
29-859
30-004
29-856
27-952
28-193
22-187
29-909
29-923
26-105
29-688
29-885
28-335
29-624
29-989
30-095
29-896
30-017
29-940
29-696
29-739
28-975
29-973
Inches.
29-997
29-951
29-991
29-799
29-983
23-869
30-032
29-932
29-772
29-830
27-341
29-701
29-342
28-876
23-823
29-210
28-224
29-557
29.754
29-914
29-794
27-908
28-113
22-171
29-816
29-848
26-080
29-653
29-841
28-280
29-546
29-961
30-122
29-854
29-970
29-875
29-662
29-707
28-969
29-983
Inches.
29-987
29-864
29-996
29-721
29-886
23-954
29-942
29-879
29-689
29-749
27-376
29-891
29-610
29-179
28-762
23-745
29-061
28-109
29-415
29-645
29-827
29-745
27-846
28-097
22-146
29-730
29-740
26-065
29-631
29-839
28-287
29-468
29-953
30-130
29-797
29-934
29-916
29-646
29-730
28-964
30-004
June.
Inches.
29-815
29-764
29-802
29-610
29-783
24-004
29-868
29-890
29-604
29-704
27-330
29-528
29-013
28-625
23-697
28-940
27-997
29-289
29-542
29-634
29-648
27-768
27-986
22-088
29-693
29-698
26-086
29-650
29-835
28-275
29-417
29-910
30-078
29-764
29-972
29-945
29-662
29-769
28-973
30-014
July.
Inches.
29-840
29-713
29-780
29-603
29-790
24-037
29-791
29-535
29-639
27-263
29-714
29-482
29-017
28-638
23-703
28-954
27-973
29-299
29-538
29-550
29-644
27-767
27-993
22-064
29-714
29-721
26:019
29-680
29-846
28-278
29-396
29-938
30-105
29-763
29-972
29-923
29-670
29-757
28-971
30-042
August.
Inches.
29-840
29-702
29-677
29-628
29-748
24-049
29-800
29-563
29-638
27-278
29-733
29-512
29-106
28-696
23-726
28-983
28-025
29-365
29-592
29-672
69-718
27-840
28-053
22-092
29-746
29-748
25-998
29-678
29-854
28-287
29-447
29-922
30-077
29-750
30-000
29-930
29-689
29-765
28-980
30-045
Sept.
Inches.
30-009
29-790
29-783
29-732
29-871
24-126
29-966
29-697
29-714
27-361
eee
29-632
29-273
28-779
23-784
29-099
28-137
29.446
29-676
29-826
29.772
27-925
28-105
22-128
29-763
29-772
26-030
29-694
29-880
28-304
29-472
29.922
30-084
29-759
30-000
29-922
29-698
29-769
28-983
30-041
605
October.
Inches.
30-055
29-981
29-918
29-840
30-033
24-052
29-972
30-004
29-723
27-443
29-778
29-437
28-969
23-884
29-301
28-305
29-670
29-827
29-993
29-829
27-924
28-192
22-149
29-827
29-846
26-045
29-707
29-881
28-308
29-583
29-922
30-105
29-820
29.974
29.922
29.704
29.782
28-993
30-041
Noy.
Inches.
30-165
30-104
30-065
29-838
30-143
24-027
30-002
30-040
29-792
27-446
29-876
29-604
29-109
23-904
29-429
28-431
29-808
29-968
30-094
29-897
28-018
28-230
22-155
29-918
29-932
26-098
29-708
29-886
28-328
29-684
30-040
30-058
29-888
29-967
29-934
29-666
29-757
28-964
30-010
Dec.
Inches.
30-263
30-143
30-115
29-715
30-170
23-978
30-124
30-002
29-818
29-922
27-431
28-247
22-171
29-957
29-995
26-120
29-730
29-909
28-350
29-774
30-064
30-105
30-005
30-000
29-904
29-691
29-730
28-973
29-911
va)
606
Places.
Tahiti (said to be red. to
sea-level),
Port de ge N. Cale- “|
donia,
Suez, .
Ismailia,
Port Said,
Alexandria,
Cairo, .
Gondar,
Massuah,
Tripolis,
La Calle,
Dellys,
Algiers,
Do., 7 ; :
Djidjilly, . . +
Medeah, ; é
Aumale,
Orleansville,
Oran,
Wor.
Laghouat,
Casa Blanca, :
St George d’Elmina,
Christiansburg,
Gondokoro, .
Lagos,
Cape Town,
Do.,
Worcester,
Simon’s Town,
Mossel Bay,
Somerset West,
Graham’s Town,
Graff Reinet,
Pieter Maritzburg,
Zambesi Delta,
Tamatave,
St Louis,
St Denis,
Socotra,
Somerset, Cape York,
Brisbane,
Brisbane,
TABLE I.—SHowi1ne THE MEAN MontTHLY AND ANNUAL HEIGHT
Country.
East India
Islands and
Pacific
do.
Abyssinia
do.
Tripoli
Algeria
Moroceo
Ashantee
do.
Benin
Slave Coast
Cape Colony
do.
do.
Mozambique
Madagascar
Mauritius
Bourbon
Queensland
0.
65
Autho-
ar Number
see page
635.
|
Years.
on
ee Oe bo
Years | Ghoorre:
Specified. tion,
1855-60 ‘< ay }
obs.
6,10: 1,
1863-64 | nes }
1866-68 |! ®9 aa
| 3, 6,9
do. do.
do. do.
1858-60 ene
? &
1832-33] 9:3
1831-32| 9:32
2 ?
1865-68 ?
do. ?
1857-67 ?
1865-68 ?
do ?
do. if
do. i
do. ?
1841-53 10: 4
1866-68 2
do. ?
1867-68} various
1860-62] 6:2,9
1829-40])__.
1833-34 | |vatious
? ?
1863 ?
hourly;
1842-55 |2 5,9:
1, 5,9
1862-65 |5,9: 1,5,9
do. 9:1,5
do. do
1862-63 do
1861-64 do.
1864-69| 93: 33
1863-65 | 9: 1, 5
1858-65 9:3
1858 mean
1863 9:4
34, 94:
1853-65 \ 32, a
? im
? 2
1865-67 9:3
1859-61 9:3
1867-69) 9:3
Height |.
Latitude. |Longitude.|in Eng.
Feet.
° 3 ° /
17 32 |—149 34) ?
—22 16 166 26 22
29 57 32: 32 20
30 38 32 13 25
31-18 32 18 10
31 11 29 50 50
30 6 31 26 ?
15 50 37 32 | 7422
15 36 39 21 5
32 54 13 19 is
36 52 8 23 30 |:
36 49 3 50 75
36 43 2 03 66
do. do. 66
36 17 5 42 49
36 13 2 43 | 3150
oGmag, 3 40 | 2933
36),..6 1 19 459
35 40 | -—0O 38 164
do. do. 164
33 47 2 54 | 2461
30 0} —-7 30 te
5 5| —1 20 75
5 24 0 10 60
4 30 31 40 | 1800
6 12 3°25 0
= oD OOF) “LS 7 37
do. do. Sif
—33 38 19 23 776
—34 12 18 24 50
—34 12 22 5 429
—34 2 18 46 124
—33 13 26 32 | 1750
—32 18 24 51 | 2517
—29 30 30 2 | 2096
—18 24 35 30 OF
-18 3 49 11 0
-— 20 10 57 30 (30
—20 51 55 30 142 |
—12 30 54 10 ie
—10 44 | 142 36 70 |
= 27 “b | lose 0 70 |
—27 28 | 153 6 140
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
AND THE PREVAILING WINDS OVER THE GLOBE.
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches.
29-868
29-913
30-095
30-062
30-080
29-998
30-000
23-338
30-097
30-138
29-977
29-953
30-073
29-985
29-982
26-977
26-956
29-686
29-984
29-941
27-512
30-268
29-877
29-862
28-356
29-940
29-937
29-162
29-947
29-576
29-845
29-919
27-395
27-786
Feb.
Inches.
29-846
29-946
30-127
30-079
30-103
29.929
30-036
23-302
30-010
29-993
30-024
30-004
30-061
30-083
30-028
27-000
27-067
29-784
29-956
30-024
27-665
30-335
29-857
29-838
28-300
29-966
29-911
29-146
29-911
29-557
29-821
29-955
27-416
27-802
29-854
29-687
29-399
29-785
29-837
29-875
March.
Inches.
29-856
30-008
29-938
29-906
29-934
29-993
29-900
23-268
29-955
29.928
29-831
29-867
29-934
29-863
29-775
26-812
26-890
29-520
29-924
29-819
27-391
30-001
29-844
29-829
28-317
29-968
29-954
29-184
29-961
29-576
29-878
29-966
27-414
27-844
29-925
29-679
29-380
29-847
29-916
30-015
April.
Inches.
29-864
30-008
29-939
29-920
29-950
29-919
29-821
23-267
29-926
29-956
29-985
29-902
29-944
29-934
29-886
26-890
26-981
29-611
29-858
29-886
27-441
30-154
29-849
29-837
28-349
29-984
30-002
29-232
30-000
29.598
29-915
30-050
27-480
27-914
May,
Inches.
29-910
30-107
29-902
29.896
29-906
29-827
29-842
29-946
29-953
29-902
29-930
29-914
29-867
26-886
26-986
29:585
29-836
29-874
27-500
30-048
29-882
29-874
28-425
30-087
30-065
29-298
30-066
29-680
29-982
Inches.
29-921
30-119
29-865
29-821
29-853
29-792
29-834
30-044
29-944
29-878
29-961
29-906
29-875
26-936
27-016
29-603
29-870
29-914
27-469
30-060
29-942
29-939
28-474
29-974
30-085
30-110
29-330
30-087
29-642
29-984
30-078
27-616
27-994
30-126
29-901
29-086
29-914
29-987
30-093
July.
Inches.
29-943
30-131
29-786
29-731
29-772
29-738
29-730
30-019
29-958
29-858
29-993
29-948
29-878
26-981
27-060
29-699
29-861
29-827
27-452
30-134
29-985
29.971
28-469
30-011
August,
Inches.
29-966
30-079
29-812
29-750
29-798
29-732
29-756
30-035
29-931
29-839
29-958
29-914
29-846
26-966
27-028
29-620
29-845
29-804
27-465
30-095
29-981
29-958
28-439
30-047
30-112
30-129
29-376
30-118
29-713
30-055
30-085
27-572
27-981
30-077
30-171
29-935
29-933
30-109
30-117
Sept.
Inches.
29-968
30-119
29-894
29.847
29-896
29-840
29-923
29-859
30-034
29-971
29-879
29-996
29-973
29-904
26-945
27-099
29-579
29-861
29-855
27-472
30-123
29-953
29-920
28-433
30-001
30-072
30-090
29-309
30-098
29-681
30-000
30-075
27-524
27-905
30-016
30-158
29-894
29-907
30-033
30-020
October.
Inches.
29-946
30-032
29-999
29-963
29-985
29-966
29-938
23-312
29-956
30-013
29-930
29-840
29-960
29.934
29-871
26-908
27-004
29-548
29.857
29-823
27-461
30-119
29-901
29-882
28-413
29-950
30-080
30-006
29-227
30-011
29-615
29-928
30-037
27-422
27-864
30-024
30-111
29-859
29-898
30-001
29-991
Nov.
Inches.
29-913
30-008
30:079
30-042
30-052
29-978
29-998
23-312
30-028
30-000
30-025
29-875
29-981
30-073
29-963
26-956
27-083
29-693
29-935
29-934
27-469
30-103
29-870
29-862
28-392
29-925
29-975
30-019
29-234
30-023
29-583
29.915
29-984
27-409
27-822
29-977
30-031
29-811
29-868
29-918
29-966
Dec.
Inches.
29-887
29-934
30-071
30-024
30-046
29-977
30-080
23-315
30-055
30-068
30-036
29-985
30-097
30-073
29.991
26-974
27-063
29-750
30-002
29-952
27-477
30-099
29.887
29-849
28-394
29-955
29-974
29-932
29-152
29-942
29-531
29-835
29-938
27-353
27-795
29-963
29-740
29-780
29-850
29-888
607
Year.
Inches.
29-907
30-034
29-959
29-920
29-947
29-891
29-904
30-014
29-960
29-900
29-986
29-967
29-906
26:936
27-020
29-640
29-895
29-888
27-481
30-128
29-901
29-885
608 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE J.—SHOWING THE MEAN MoNTHLY AND ANNUAL HEIGHT
Autho-
Number Hours of Height
rities, Years §
Places. . Country. see page - s Specified. cpr ae Latitude. |Longitude. a wires
a e J ° a
Casino & Richmond River,| Queensland 76 5 1858-62), 9:3) |—28.50) | h15s0 00 139
Armidale, . . |N. South Wales} 76 31 | 1860-63 9: -30 33 | 151 46 | 3195
Newcastle, 5 i : do. 76 9 |1858-66| do. |-32 57 | 151 47 18
Windsor, . : 5 do. 77 4 | 1863-66 9:3 —33 36 | 150 50 53
Paramatta, . ‘ é do. 76 33 |1858-61|} do. |-33 49] 151 1 60
Bathurst, . ‘ : do. 76 5 | 1859-63 9; —33 24 | 149 37 | 2333
Goulburn, . : : do. 76 8 | 1858-65 |9: 3,9,&9:|-34 45 | 149 45 | 2129
Sydney, 4 , : do. 76 11 | 1858-68 do. —33 52 | 151 11 155
Do., any pre, do. 76 9 |1858-66|9:3,&9:| do. do. 155
Deniliquin, . : : do. 76 9 doi” 79: 3,9,&9: +35 32 | 145 2 [> 416
Albury, ; ‘ : do. 76 8h do. do. |-36 6| 147 0 572
Cooma, ‘ : A, do. 76 7 | 1858-64| 9:3, & 9:|—36 13 | 149 9 | 2637
Sandhurst, . s : Victoria 78 5 | 1863-67] 9:3,9 |—36 43 | 144 21 778
Ararat, : ' ; do. 78 5 do. 9:3 —37 18 | 142 58 | 1072
Ballartts nye tae On: do. 78 5 do 93:33, 93-37 34 | 143 53 | 1438
Melbourne, . ; ‘ do. 78 10 | 1858-67 | 6, 9: 3,9|-—37 50 | 144 59] 121
Do., ; , : do. 78 5 | 1863-67] do. do do. 12]
Portland, . ‘ : do. 78 5 do. do. |—38 21 | 141 32 37
Cape Otway, ; ‘ do. 73 5 do. do. |—38 54] 143 37 | 300
Kupunda, . ; . |South Australia} 79 4 |1861-64| 9:6 |-—34 20] 139 0} 730
Adelaidenah s. + san yes do. yo hell { oa do. |-34 53] 138 39] 140
Strathalbyn, ; : do. 79 4 |1861-64} do. |-35 8 | 138 57} 220
Guichen Bay, : ‘ do. 79 4 do. do. —37 3] 139 42 19
Mount Gambier, . : do. 79 4 do. do. |-—37 51] 140 53 | 133
Freemantle, : . | West Australia| 44 3 | 1853-85] 93:32 |-—33 2] 115 45 16
Kent’s Group, . : Tasmania 80 5 | 1861-66] 6,12: 6 |—39 29 | 147 35 | 280
Swan Island, 5 : do. 80 23 | 1864-66 do. —40 45 | 148 10 14
Swansea, ; : do. 80 3 do. do. |—42 8] 148 5 18
Hobart Town, . : do. 80 28 | 1841-68 do. |—42 52] 147 21 37
Do. : ‘ : Poasley 80 5 1861-66 do. do do. 37
Port Arthur, ; : do. 80 5 |1861-66| do. |-43 9 | 147 54 55
Auckland, . . . | New Zealand Meo ak 11 { eee on: 33 |-36 50| 174 51| 140
Taranaki, . : : do. 81 5 |1864-68} 10:4 |—39 4] 174 5 70
Wellington, , : do. 81 5 do. do. |—41 16} 174 47 90
Nelson, : : . do. 81 3 do. 9:3 —41 16] 173 19 18
Hokitika, . . c do. 81 3 | 1866-68} 10:4 |—42 42 | 170 59 8
Christchurch, ; : do. 81 5 | 1864-68 )92: 34, 93/-—42 33 | 172 39 21
Do., : ; : do. 81 3 | 1866-68 do. do do. 21
Dunedin, . .. do. 81 52 |1862-68| 93:42 |-45 52] 170 31] 550
Southland, . : A do. 81 10 | 1859-68; 9:3,9 |—46 17 | 168 20 79
Upernivik, . i ; Greenland 2 5 | 1833-38] noon 72 48 |—55 53 15
Jacobshavn, ; ; Je | G0; 2 93 | 1842-51 do. 69 12 |-d1 0 10 |
Godthaab, . : : do. 2 5 1841-46 do. 64 10 |—51 53 15 |
Baffin Bay, ; : Arctic 82 1 | 1857-58/ various | °°" 722°) various “On
Van Rensselaer, . : do. 82 2 |1853-4-5) do. 78 37: |-73 O 07
Port Foulke, i , do. 82 1 | 1860-61 do. 78 18 |-73 0 Rep |
Port Kennedy . : do. 82 1 | 1858-59} do. 72 1|-94 0 0;
Boothia Felix, . ‘ do. 4 2 tee tee 70 3/-95 0 0]
AND THE PREVAILING WINDS OVER THE GLOBE.
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches.
29-776
26-631
29-912
29-847
29-846
27-655
27-766
29-773
29-774
29-506
29-238
27-241
29-109
28-783
28-464
29-811
29-827
29-931
29-701
29-062
29-805
29-676
29-878
29-792
29-936
29-620
29-933
29-677
29-744
29-807
29-791
29-968
29-906
29.838
29.874
29-903
29-783
29-812
29-859
29-789
29-580
29-634
29-582
29-532
29-778
29-834
29-979
29-823
Feb.
Inches.
29-780
26-617
29-936
29-869
29-888
27-668
27-796
29-792
29-795
29-554.
29-318
27-290
29-143
28-826
28-484
29-839
29-843
29-942
29-708
29-090
29-825
29-705
29.914
29-816
29-930
29-650
30-023
29-748
29-837
29-849
29-829
29-999
29-946
29-876
29-923
29.861
29-840
29-808
29-855
29-843
29-458
29-681
29-713
29-649
29-848
29-747
29-933
29-975
March.
Inches.
29-849
26-733
30-037
30-012
29-972
27-766
27-911
29-906
29-903
29-660
29-449
27-379
29-257
28-902
28-589
29-940
29-966
30-050
29-819
29-187
29-915
29-787
30-010
29-922
29-987
29-766
30-090
29-854
29-867
29:973
29-865
30-067
30-040
29-963
29.974
30-007
29-947
29.957
30-011
29-867
29-699
29-786
29-824
29-893
29-750
29-816
30-173
29-962
April.
Inches.
29-911
26-752
30-100
30-061
30-022
27-832
27-934
29-948
w
29-950
29-728
29-478
27-393
29-308
28-957
28-620
29-987
30-000
30-075
29-840
29-240
29-975
29-843
30-063
29.960
30-072
29-764
30-060
29-855
29-903
29-996
29-835
30-098
30-058
30-007
30-058
30-026
29-953
29-926
29-968
29-897
29-774
29-830
29-833
29-940
29-903
30-085
30-179
29-993
May.
Inches.
29-961
26-741
30-103
30-057
29-999
27-822
27-896
29-959
29-939
29-741
29-482
27-342
29-310
28-952
28-593
29-958
29-994
30-049
29-757
29-146
30-008
29.825
30-018
29-903
30-122
29-686
30-010
29-781
29-871
29.927
29-747
29-990
29-974
29-895
29-959
30-082
29-910
30-040
30-023
29-889
29-803
29-867
29-963
30-014
29-942
29-985
30-010
30-141
June.
Inches.
29-909
26-717
30-117
30-086
30-029
27-816
27-889
29-949
29-949
29-767
29-540
27-340
29-357
28-977
28-630
30-000
30-045
30-121
29-848
29-210
29-980
29-817
30-032
29-921
30-121
29-776
30-060
29-827
29-892
30-002
29-823
29-954
29-930
29-902
29-984
29-971
29-892
29-952
30-023
29-866
29-703
29-815
29-897
29-817
29-719
29-678
29-913
30-023
July.
Inches.
29-962
26-671
30-087
29-980
30-084
27-825
27-884
29-916
29-907
29-716
29-468
27-292
29-223
28-880
28-509
29-950
29-911
29-971
29-719
29.203
29-942
29-751
29-951
29-814
30-010
29-588
29-955
29-734
29-856
29-855
29-654
29-968
29-898
29-886
30-000
29-975
29-880
29-870
29-912
29-826
29.694
29-766
29-869
29-753
29-741
29.691
29-704
29-891
August.
Inches.
30-032
26-716
30-112
30-045
30-047
27-868
27-885
29-950
29-951
29-735
29-518
27-323
29-304
28-936
28-576
29-985
29-988
30-033
29-795
29-262
30-013
29-859
30-056
29-926
30-066
29-652
30-030
29-704
29-822
29-912
29-700
29-941
29-839
29-822
29-903
29-885
29-835
29-838
29-882
29-770
29-671
29.744
29-763
29-736
29-694
29-662
29.741
29-857
Sept.
Inches.
29-958
26-690
30-025
29-916
29-956
27-807
27-796
29-858
29-866
29-670
29-473
27-275
29-168
28-812
28-458
29-852
29-837
29-893
29-657
29-188
29-866
29-761
29-975
29-854
30-080
29-600
29-875
29-665
29-758
29-789
29-647
29-930
29-814
29-866
29-898
29-910
29-848
29-902
29-871
29-788
29.620
29-777
29.824
29-735
29-658
29-684
29-899
29-826
October.
Inches.
29-905
26-681
29-994
29-854
29-972
27-747
27-818
29-828
29-852
29-577
29-365
27-280
29-074
28-760
28-394
29-833
29-768
29-851
29-594
29-130
29-844
29-741
29-928
29-812
30-023
29-610
30-020
29-681
29-772
29-824
29-727
29-950
29-832
29-781
29-670
29-778
29-716
29-682
29-773
29-665
29.576
29.722
29-818
29-756
29-755
29-618
29-798
29-957
609
Year.
Inches.
29-886
26-682
30-024
29-949
29-966
27-767
27-842
29-874.
29-871
29-646
29-412
27-303
29-207
28-867
28:517
29-899
29-900
29-977
29-722
29-159
29-902
29-761
29-970
29-860
30-027
29-656
29-987
29-734
29-816
29-873
29-752
29-980
29-915
29-871
29-906
29-922
29-841
29-851
29.898
29-803
29-640
29-749 |
29-786
29-755
29-775
29-824
29-938
29-943
VOL. XXV. PART II.
610 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHowine THE MEAN MonTHLY AND ANNUAL HEIGHT
ac Number Hours of Height
rities, Years &
Places. Country an pase fe Specified. pee Latitude. |Longitude. i Eng.
. AY i Le TL ickatd Bo oats
Melville Island, Arctic 4 1 | 1819-20 ? 75 40 |-112 3 0
Port Bowen, do. 4 1 | 1824-25 ? 73 13 |-88 54 )
1807-12, 66 to about
E. of Greenland, . do. 83 7 \ 1822 } noon 30 34 | —7 of 0
. : ; , | hourly :
Sitka, . Russian America| 26 17 | 1848-64) 04g &o } 56 50 |—135 0] 20
2=9 *
New Westminster, British Columbia) 84 2 |1860-61| 93: 33 | 49 13 |—122 53) 54
Esquimault Harbour, Vancouver 85 1 do. ¢ 48 25 |—123 27 0
: ; 1859-60
Astoria, Oregon 86 2) 1866 ? 46 8 |-123 48} ?
Sacramento, California 86 9 | 1858-66] 7:2,9 | 38 35 |-121 28) 81
San Francisco, do. 86 9 do. do. 37 48 |—122 23) 86
Great Salt Lake City, : Utah 87 2 | 1858-59|6,9:3,9] 40 45 |—111 26] 4260
St John’s, . Newfoundland 44 6 | 1853-59] 94: 32 47 35 | —52 42) 130
Halifax, . Nova Scotia 44 4 \ econ do. 44 39 | —63 37 8
Do., do. 45 2 | 1864-65) 9: 3 44 39 | —63 36] 137
Albion Mines, do. 27 10 | 1843-52] noon 45 34 | —62 42) 128
1853-55,
Quebec, Canada Hast | 44, 45 | 1858, |/93: 34 | 46 48 | —71 12] 230
1866
St Martin’s, do. 87 6 | 1854-59] 6:2, 10 45 32 | —73 36) 118
Kingston, : ; Canada West 44 4} do. 93: 33 | 44 14] —76 31} 294
Toronto, : : : do. 88,71| 28 | 1840-67] 6: 2,10 43 39 | —79 2| 342
Do., do. 88 11 | 1857-67] do. do. do. 342
Do., do. 88 6 | 1854-59 do. do. do. 342
Hamilton, do. Si oo mel 1849-59} 9:9 43.15 | —79 57)2290
Gardiner, Maine, U.S. 87 5 | 1855-59] 7:2,9 | 44 11 | —69 46} 90
Steuben, do. 87 6 1854-59 do. 44 28 | —67 50 50
Amherst, Massachusetts | 87 6 ao. do. 42 22 | —72 34| 267
New Bedford, do. 87 6 do. do. 41 39 | —70 56) 90°
Nantucket, do. 87 6 do. do. 41 16 | —70 6) 30
1854-56,
Burlington, . Vermont 87 5 \ 1858-59 } do. 44 29 | -73 11} 346
Providence, Rhode Is. 89 29 | 1832-60 |sr: 2,10) 41 50] --71 23) 170
Do., do. 89 6 |1854-59| do. do. do. 170
Rochester, New York 87 4 | 1856-59| 7:2,9 43 8 | -—77 51) 516
Bedford, Pennsylvania | 87 4 \ tie do. 40 1 | —78 30) 900
Harrisburg, do. 87 6 | 1854-59} do. 40 16 | —76 50) 280
Pittsburg, do. 87 6 do. various | 40 30 | —80 00) 960
Lambertville, New Jersey 87 6 do. 7: 2,9 40 23 | —74 56) ?
Washington { Pere OF kaa? do do 38 56 | —76 58| 40
S000; Columbia f ; :
0, 3, 6,
Do., do. 90 5 | 1862-66 |< 9, ah 38 56 | —76 58) 103°
3, 6, 9 i
Portsmouth, Virginia 87 3 |1857-59| 7:29 | 3650] -76 19] 34]
Chapel Hill, N. Carolina 87 6 | 1854-59 do. 35 54 | —79 17| 500 |
All Saints, 8. Carolina 87 5 | 1855-59| do. 33 40 | —79 17) 20 |
Athens, =). Georgia 87 2 | 1857-59] do. 33 58 | —83 30 730 |
Savannah, (at sea ‘level 2) do. 87 6 | 1854-59} do. 32 5| -—81 7) ae
AND THE PREVAILING WINDS OVER THE GLOBE. 611
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.
Inches. | Inches.
30:077
29-717
29-551
30-074
30-110
29-985
30-106
30-070
25:880
29-924
29-985
29-744
29-696
30-104
29-842
30-062
29-647
29-650
29-670
29.693
29-874
29-988
29-813
29-972
30-043
29-668
29-807
29-857
29-508
29-145
29-820
29-043
30-058
30-145
30-031
30-140
29-602
30-090
29-410
30-135
pe A ny pn
Sn et
Feb.
29-769
29-886
29-644
30-042
30-030
30-138
30-074
30-043
25-780
29-781
29-797
29-681
29-687
30-055
29-753
30-014
29-624
29-654
29-643
29-648
29-782
29-895
29-730
29-915
29-970
29-572
29-779
29-773
29-420
29-045
29.765
28-952
29-982
30-047
30-030
30-083
29-525
30-006
29-275
30-087
March.
Inches.
29-803
30-107
29-648
30-022
30-090
29-957
30-060
30-040
25-670
29-690
29-685
29-748
29-672
29-901
29-639
29-941
29-596
29-577
29-538
29-608
29-702
29-773
29-788
29-788
29-873
29-488
29-743
29-674
29-358
29-005
29-678
28-923
29-933
29-963
29-921
29-967
29-468
29-962
29-270
30-038
April.
Inches.
29-979
30-068
29-852
29-711
30-000
30-030
30-094
30-011
30-004
25-685
29-942
29-931
29-842
29-702
30-010
29-693
29-970
29-597
29-583
29-572
29-606
29-750
29-848
29-648
29-827
29-900
29-558
29-740
29-718
29-348
29-110
29-675
28-914
29-920
29-952
29-956
29-887
29-448
29-942
29-210
30-015
May.
Inches.
30-109
30-051
29-870
29-836
29-984
30-030
29-996
29-938
29-938
25-640
29-943
29-959
29-780
29-746
29-864
29-770
29-965
29-574
29.564
29-593
29-663
29-824
29-918
29-687
29-878
29-963
29-612
29-722
29-773
29-385
29-048
29-695
28-912
29-953
29-967
29-844
29-963
29-453
29-920
29-233
29-985
June.
Inches.
29-823
29-888
29-852
29-814
29-962
30-060
30-067
29-888
29-897
25-655
29-934
29-976
29-823
29-674
29-934
29-719
29-917
29-572
29-577
29-542
29-650
29-746
29-862
29-717
29-853
29-928
29-555
29-725
29.722
29-338
29-060
29-670
28-910
29-945
29-938
29-912
29-927
29-463
29-960
29-293
30-010
July.
Inches.
29-668
29-817
29-870
29-877
30-032
30-100
30-067
29-869
29-891
25-645
29-993
29-974
29-778
29-710
29-955
29-796
29-999
29-599
29-593
29-613
29-707
29-792
29-923
29-673
29-925
29-973
29-618
29-722
29-797
29-405
29-112
29-733
28-968
30-025
29-990
29-914
29-977
29-478
29-968
29.273
30-037
August.
Inches.
29-726
29-683
29-850
30-012
30-040
30-023
29-867
29-890
25-675
29-964
29-950
29-810
29-770
29-947
29-773
29-977
29-622
29-606
29-608
29-700:
29-786
29-928
29-723
29-925
29-985
29-625
29-788
29-789
29-350
29-105
29-728
28-953
30-010
29-988
29-932
29-980
29-483
29-946
29-285
30-018
Sept.
Inches.
29-748
29-689
29-766
30-029
30-080
30-032
29-880
29-894
25-727
29-971
30-024
29-848
29-767
30-022
29-820
30-054
29-662
29-671
29-675
29-745
29-860
29-985
29-720
29-985
30-053
29-682
29-823
29-856
29-418
29-160
29-815
29-035
30-100
30-055
30-000
30-043
29-552
30-006
29-315
30-053
October.
Inches.
29-811
29-962
29-623
30-008
30-010
30-021
29-946
29-943
25-760
29-986
29-962
29-674
29-766
30-045
29-846
30-078
29-645
29-645
29-655
29-684
29-810
29-928
29-788
29-928
29-988
29-612
29-808
29-808
29-432
29-180
29-785
28-995
30-023
30-047
29-967
30-010
29-540
29-998
29-348
30-058
Nov. Dec. Year.
Inches. | Inches. | Inches.
29-945 | 29-865/| 29-860
29-899 | 29-869| 29-886
29-615] 29-630} 29-714
29-937 | 29-928] 30-002
30-100} 29-960} 30-053
29-992) 29-958 30-028
30-049] 30-080} 29-981
30-024 | 30-041] 29-973
25-705 (25-800)| 25-717
29-908| 29-842| 29-906
29-954 | 29-869] 29.922
29-836 | 29-737) 29-776
29-687 | 29-688] 29-714
29-936) 29-982) 29.980
29-800 | 29.852] 29.775
29-946 | 30-044] 29.973
29-612) 29-656| 29-617
29-595 | 29-676] 29-617
29-600) 29-672| 29.615
29-634 | 29-670) 29-666
29-850) 29-854} 29.802
29-920) 29-932| 29.908
29-737 | 29-788 | 29-730
29-900 | 29-925} 29.902
29-960} 30-008} 29-970
29-602 | 29-652) 29-604
29-783 | 29-784| 29-779
29-765 | 29-805 | 29-778
29-365 | 29-435] 29-397
29-102} 29-100} 29-097
29-770 29-803 | 29-745
28-980 | 28-983} 28-964
30-017 | 30-028; 30-000
30-028 | 30-080} 30-017
30-004 | 30-035 | 29-962
30-047 | 30-073) 30-005
29-550 | 29-570) 29-511
30-042 | 30-074} 29-993
29-410 | 29-340)| 29.297
30-085 | 30-118] 30-053
612 MR ALEX.
Places.
Jacksonsville,
Warrington,
Auburn,
Colum bus,
Washington,
Sisterdale,
Goliad,
Memphis,
Glenwood,
Springdale, .
Cincinnati, .
Marquette,
Ottawa Point,
New Harmony,
Wheaton,
St Louis,
Beloit, .
Dubuque,
Beaver Bay,
Lawrence,
Leavenworth City,
Cordova, . .
Vera Cruz,
Guatimala, .
Port of Saphea4
Belize,
Ber muda, :
Nassau, Bahama,
Havanna, Cuba, . ,
Up Park: Camp, Jamaica,
Barbadoes, ;
Do.,
Port of Spain, Trinidad,
Caledonia Bay,
Cartagena,
Bogota,
Caraccas,
George Town,
Cayenne,
Ghitietin Sophia,
Ceara,
Pernambuco,
Rio de Janeiro,
Asuncion (and vicinity),
Buenos Ayres (& vicinity),
Monte Video,
Santiago de Chile,
BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHOWING THE MEAN MONTHLY AND ANNUAL HEIGHT
Florida
do.
Alabama
Mississippi
Texas
Tennessee
do.
Kentucky
Ohio
Michigan
do.
Indiania
Illinois
Missouri
Wisconsin
Iowa
Minnesota
Kansas
do.
Mexico
do.
Central America
do.
Brit. Honduras
West Indies
do.
do.
do.
do.
do.
do.
New Granada
do.
Venezuela
British Guiana
French do.
Dutch do.
Brazil
do.
do.
Paraguay
La Plata
Uruguay
Chili
Autho-
rities Number Years
of :
See page] y pars, | Specified
Se Set poe crs
87 6 1854-59
1854-57
ea 4g | 1859
87 3 1855-57
87 4 1856-59
87 2 1858-59
87 1 1859
87 1 1858
87 24 | 1857-59
87 6 1854-59
87 6 do.
87 4 1856-59
87 23 | 1857-59
87 14 | 1858-59
if 6 1854-59
$7 2 1858-59
87 6 1854-59
87 6 do.
87 6 do.
87 14 | 1858-59
87 2 1857-59
87 13 | 1858-59
87 2 do.
87 24 | 1857-59
40 2 1860-6!
100 3 1857
71 4 | 1862-63
44 34 | 1855-59
a4 6 1853-59
40 3 1859-61
44 6 | 1853-59
44 6 do.
45 2 1865-66
87 aos | 1856-57
67 1854
67 2 do.
35 1848-50
92 1 1860
91 11 1846-56
35 6 1845-52
87 1858-59
37 1 1860
4 6 1851-56
101 434° | 1854-55
101 24 | 1853-56
102 10 1843-52
4 3 1850-52
Hours of
Observa-
tion.
Height
Latitude. |Longitude.| in Eng.
Feet.
AND THE PREVAILING WINDS OVER THE GLOBE. 613
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.| Feb. | March.}| April. | May. | June. | July. | August.} Sept. | October.) Nov. Dee. Year.
Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches.
30-220} 30-143} 30-100) 30-080) 30-023) 30-058 | 30-087| 30-060 | 30-083 | 30-088] 30-127} 30-178) 30-104
30-136} 30-092} 30-088 | 30-037| 29-912) 29-972) 30-004] 29-992) 29-996) 30-034 | 30-054} 30-102] 30-027
29-443] 29-377 | 29-353 | 29-343 | 29-260/ 29-300| 29-320| 29-357| 29-380) 29-383) 29-397 | 29-420) 29-361
29-990| 29-865 | 29-812] 29-768| 29-752) 29-780) 29-800] 29-768] 29-855 | 29-868] 29-880] 29-920} 29-838
29-750} 29-685 | 29-540] 29-575| 29-620] 29-625] 29-660) 29-595) 29-630] 29-675 | 29-705} 29-750) 29-650
28-850| 28-650} 28-560] 28-610] 28-570) 28-670} 28-680| 28-580| 28-660) 28-730| 28-720} 28-760} 28-670
30-060} 30-040) 29-940] 29-870} 29-900) 29-940} 29-970) 29-950} 30-020] 29-920) 30-080] 30-065) 29-980
29-890| 29-775 | 29-685} 29-650} 29-680 | 29-745 | 29-755] 29-720) 29-800} 29-817| 29-790} 29-830) 29-761
29-683| 29-587 | 29-545| 29-507| 29-477 | 29-513| 29-552) 29-543 | 29-593| 29-598| 29-558} 29-630| 29-566
29-500} 29-415) 29-387] 29-365 | 29-320] 29-377 | 29-398) 29-390) 29-448| 29-453 | 29-418] 29-470] 29-412
29-600| 29-513 | 29-488] 29-435] 29-375| 29-455 | 29-430) 29-453 | 29.522) 29-533) 29-500) 29-570) 29-490
29-325 | 29-330 | 29-160| 29-220} 29-330| 29-290/ 29-370] 29-330| 29-330| 29-370] 29-277| 29-320/ 29.304
29-440 | 29-340) 29-150) 29-260) 29-380] 29-400} 29-410] 29.370 | 29-445 | 29-405) 29-385) 29-395] 29-365
29-787| 29-702| 29-665) 29-612) 29-585 | 29-598 | 29-643 | 29-635] 29-688| 29-702] 29-667] 29-723 | 29-667
29-270) 29-215} 29-090} 29-070} 29-165| 29-210) 29-240} 29.215 | 29-235| 29-240] 29-200] 29-240] 29-199
29-632) 29-540] 29-498} 29-437 | 29-428| 29-448) 29-502) 29-512) 29.547 | 29-543 | 29-517) 29-578) 29-515
29-250} 29-188] 29-085] 29-085} 29-117 | 29-105} 29-188| 29-193| 29-215 | 29-220) 29-128] 29-205) 29-167
29-397| 29-338 | 29-293 | 29-238] 29.242 | 29-243 | 29-310] 29-327 | 29-340] 29-345 | 29-300] 29-352) 29-310
29-220) 29-220} 29-020} 29-160} 29-190| 29-160) 29-220) 29-160} 29-190) 29-220] 29-205] 29-200] 29-180
29-120} 29-080} 28-950} 28-945} 29-000} 29-050 | 29-077) 29-095 | 29-130} 29-095 | 29-010} 29-115] 29-055
28-745} 28-750 | 28-660} 28-560} 29-580} 28-550} 28-570) 28-640) 28-640} 28-540] 28-735] 28-720] 28-641
27-200) 27-125) 27-090] 27-070} 27-065) 27-095 | 27-165| 27-135 | 27-120| 27-140} 27-185] 27-180} 27-131
30-100) 29-995] 29-930) 29-920} 29-860) 29-863 | 29-957] 29-980 | 30-020] 30-020) 30-105/ 30-085] 29-986
25-269| 25-264| 25-252] 25-233| 25.922) 25.225 | 25-247) 25-235 | 25.208| 25-208| 25-254] 25-276| 25.241
siete 29-887 | 29-860| 29-893 ado pe Ane son ee
30-100} «+ ooo te tee tee oo 29-970) 29-950] 29-980} 30-080) 30-060) .-.-
30-114] 30-069 | 30-009} 30-049| 30-065) 30-120) 30-156] 30-093} 30-075 | 30-015 | 30-061} 30-155} 30-082
30-146| 30-125] 30-104] 30-079} 30-018) 30-066) 30-080) 30-057 | 30-024} 29-999) 30-033} 30-096} 30-069
30-063) 30-026] 29-998] 29-952] 29-896] 29-943] 29-981] 29-937) 29-915 | 29-885 | 29-982) 30-027) 29.964
30-060} 30-031 | 30-017} 29-998} 29-958 | 29-987 | 30-006} 29-984) 29-960) 29-950} 29-963) 30-015} 29-990
29-955| 29-950) 29-952} 29-935] 29-937) 29-949 | 29-950} 29-934) 29.927 | 29-904] 29-892) 29-914) 29.933
30-009} 30-010} 30-004} 29-985} 29-970) 30-018} 30-005} 29-950) 29-954 | 29-925 | 29.924] 29-942) 29.975
29-940] 29-890] -.. 29-870} 29-850} 29-890
ane 29-922] 29-8585] .. bcc ase g00 de ies
Ae dic aa 29-848] 29-856] 29-843] ... aoc ae ae oon ale occ
22-048| 22-060} 22-061} 22-079] 22-060 | 22-060} 22-058) 22-062} 22-076 | 22-068] 22-049 | 22-034) 22-060
26-960) 26-971} 26-954) 26-964] 26-984 | 26-975] 26-980} 26-964) 26-956 | 26-946] 26-938} 26-959} 26-963
29-943} 29-965| 29-957] 29-944] 29-933) 29-962 | 29-966] 29-954] 29-938} 29-913] 29-877) 29-910| 29-939
29-903 | 29-932} 29-924 | 29-925) 29-916 | 29-946] 29-957] 29-961 | 29-944] 29-917| 29-880) 29-889 | 29.924
29-890} 29-900| 29-880] 29-880) 29-870) 29-895 | 29-915} 29-890} 29-890/ 29-855] 29-870) 29-870} 29-884
29-823 | 29-863 | 29-855 | 29-831] 29-851 | 29-875 | 29-898; 29-875) 29-918) 29-871 | 29-823 | 29-819) 29-859
a9 30-181} 30-154} 30-081] 30-042) 30-042
29-745| 29-765| 29-796| 29-822) 29-912] 29-970 | 29-979| 29-917] 29-904 | 29-815 | 29-754| 29-744) 29-844
29-910] --- ooo ooo 30-070} 30-130} 30-172] 30-094| 30-050) 30-037 | 29-860) 29-884
29-824| 29-865 | 29-962] 29-990} 30-068 | 29-954] 29-950| 29-988] 30-015 | 29-925 | 29-849 | 29-860) 29-938
29-841| 29-876| 29-924 | 29-965) 29-959 | 29-990] 29-974] 30-049 | 30-012} 29-940} 29-900} 29-860 | 29-938
28-025 | 28-021 | 28-043 | 28-076| 28-074| 28-114) 28-095] 28-151) 28-117| 28-109 | 28-046) 28.044 | 28-077
Woke OX VePART IT: “0
614 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I.—SHOWING THE MEAN MONTHLY AND ANNUAL HEIGHT
Autho-
ais Number Hours of Height
rities, Years ae ; :
Places. Country. see page| y cam Specified. wes Latitude. |Longitude. ee
635. Rin | iia
Valparaiso, . : . Chili 67 $| 1853 | 93: 323 |—33 25 |—71 40 0
Port Famine, : 3 Patagonia 4 2 ? —53 38 |—70 52 %
Port Louis, . : . | E. Falkland Isl.| 104 qve| 1842 ? -51 40 |-59 0 0
St Michael (at 32°?), . Azores 27 10 | 1840-49 ? 37 35 |—25 30 ?
Ponta Delgada, . . do. 94 1 | 1868-69] hourly | 37 40 |—25 32 2
Funchal, . . . Madeira An ee \ ee ad en ; 3238 |-16 56| 95
Orotava, . : E Canaries 67 1 | 1856-57 | about 9:| 28 27 |—16 38 70
North Atlantic | 96 40to35 0
do. 96 35 to 30 0
do. 96 30to025 0
do. 96 25 to 20 0
do. 96 20to15 2 0
do. 96 15to10 i 0
do. 96 10to 5 “Bp 0
do. 96 —5to 0 a 0
South Atlantic | 96 -—Oto 5 Sj 0
22]
do. 96 —5to10 - 0
do. 96 —10to15) == 0
do. 96 | \—15t020} 3 0
do. 96 | |-20to25) 3 0
do. 96 — 25to30 2 0
do. 96 -—30t035| 5 0
do. 96 -35t040] 0
do. 96 —40t045 0
do. 96 — 45t050 0
do. 96 — 50t055 0
do. 96 — 55t060 0
Ascension, . : F do. 67 2 | 1854-55] 93: 33 | -8 8 |-14 28 0
St Helena, . , : do. 44 5 1854-59 do. -15 55 | -—5 42 40
Do., : c : do. 97 3y7,| 1844-47] biho. |—15 55 | —5 43 | 1763
ADDENDUM.
The Atmospheric Pressure of the Atlantic Ocean —The following Pressures are
the means of observations made in July and August by Captain ToynBeEz, during five
voyages to India, at different points on the Outward Route :—
Inches. Inches. Inches.
35° N. Lat. 30-252 10° N. Lat. 30-017 10° S. Lat. 30-082
S02 Gag, 30-166 oF re 30-025 lee FF 30-142
25° 53 30-092 Equator 30-042 20° . 30-245
20° a 30-022 5° S. Lat. 30-050 25° nS 30-236
15° .. 29-996
The results were published in the “ Proceedings of the Royal Society,” June 15,
1865, but not corrected for temperature.* The figures given above Captain ToyNBEE
has kindly corrected for temperature and height.
* The uncorrected means were used in constructing the charts exhibited in reading Part I. of this
paper.
AND THE PREVAILING WINDS OVER THE GLOBE. 615
OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued.
January.| Feb. | March.| April. | May. | June. | July. | August.| Sept. | October.| Nov. Dec. | Year.
Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches.
ose tee tee 30-090 30-079] 30-056] 30-098} = oon
29-405 | 29-646] 29-573 | 29-304) 29-279 | 29.571 | 29-286) --- oo.
ase os 580 29-428) 29-304) 29-396} 29-665 | 29-654] 29-576| --- ate 29-349] .--
30-214] 30-166) 30-255) 30-247 | 30-237 30-253) 30-311] 30-238| 30-210) 30-142] 30-115| 30-201] 30-216
30-020} 30-268) 30-343 | 30-056] 29-961, 30-180) 30-192] 30-243 | 30-052 | 30.241 | 29.989] 30-071] 30-135
30-012] 30-092) 30-016| 29-929] 29-978 30-068] 29-992) 29-997 | 30-025 | 29.941 | 29-898] 30-048 | 29-998
30-290] 30-116} 30-177 | 30-110} 30-100 30-140} 30-094] 30-095 | 30-125) 30-121] 30-119) 30-180) 30-144
30-210} 30-110} 30-150} 30-060} 30-070, 30-200) 30-190] 30-160} 30-110, 30-090) 30-020) 30-060) 30-119
29-293 | 29-539
30-260} 30-180) 30-200) 30-160 30-120. 30-200 | 30-240} 30-190} 30-150, 30-180} 30-030) 30-180} 30-174
30-250] 30-160| 30-130} 30-170 30-220, 30-230) 30-190} 30-160; 30-100 30-140) 30-060) 30-180] 30-166
30-100] 30-110} 30-100} 30-100, 30-140, 30-160) 30-090} 30-070 | 30-030) 30-070) 30-010] 30-000] 30-082
30-010} 30-060} 30-040} 30-000} 30:060) 30-030] 30-000] 30-000} 29-990) 29-990| 29-980} 30-010} 30-014
29-950} 29-970) 29-990] 29-970! 29-990) 29-960) 29-970] 29-930} 29-930) 29-950] 29-960} 29-960} 29-961
29-900] 29-940] 29-910| 29-920} 29-940) 20-940} 29-980} 29-970) 29-950| 29-930] 29-940] 29-910] 29-936
29-880] 29-910] 29-890] 29-900) 29-920) 29-930] 29-980] 29-970 | 29-980 | 29-950) 29-920| 29-910] 29-928
29-890} 29-910} 29-900] 29-920; 29-940} 29-940] 29-990] 30-000) 30-010} 29-960] 29-940| 29-930] 29.944
29-950) 29-940] 29-940) 29-940! 29-990) 30-010] 30-020} 30-030 | 30-030) 30-020] 29-990] 29-960] 29-985
29-970) 29-980) 29-960} 29-990} 30-040 30-050) 30-050; 30-060 | 30-090 30-070) 30-040} 30-000] 30-025
30-020) 30-010) 30-010) 30-030} 30-090, 30-090] 30-090} 30-130 | 30-110) 30-100} 30-050) 30-050} 30-065
30-060} 30-050} 30-070) 30-050} 30-060) 30-140} 30-110| 30-160| 30-170) 30-180} 30-080} 30-080] 30-101
30-070} 30-050} 30-060) 30-030; 30-140, 30-090} 30-130} 30-180 | 30-130 | 30-160] 30-080| 30-080] 30-100
30-050) 30-050) 30-040) 30-030] 30-100] 30-040} 30-120) 30-100] 30-080| 30-080] 30-090] 30-000) 30-065
29-980) 30-040} 30-020} 29-980] 29-900} 29-900} 30-040) 29-940] 29-950} 30-050) 30-050) 29-970] 29-985
29-920} 29-950) 29-990| 29-950) 29-880) 29-890} 29-950) 29-930) 29-960} 30-020] 29-940] 29-950) 29-944
29-710) 29-780| 29-770} 29-760) 29-720) 29-650) 29-820} 29-830] 29-870| 29-770] 29-700) 29-670] 29-754
29-410) 29-440| 29.490) 29-440) 29-410 | 29-480] 29-530) 29-560) 29-570)| 29-480} 29-310} 29-430} 29-462
29-250 | 29-230, 29-250| 29-200) 29-260] 29-280) 29-250} 29-280) 29-290) 29-100] 29-100) 29-210] 29-225
30-018 | 30-049! 30-037 | 30-036) 30-011 | 30-085 | 30-092) 30-086) 30-080) 30-058} 30-091 | 29-977] 30-052
30-048 | 30-043) 30-030) 30-039) 30-079 | 30-126] 30-163) 30-152) 30-137 | 30-107] 30-079} 30-085) 30-091
28-241 | 28-238) 28.228) 28.249 | 28-279) 28-328) 28-351) 28-349 | 28-305 | 28-286} 28.262] 28-247 | 28.280
The Pressures reduced to 32° and sea-level, on the Homeward Passage from
the Cape, being the means of five voyages in 1861-62—63-64-65, in the latter part
of February, in March, and beginning of April, are as follow :—
Inches. Inches. Inches.
35° N. Lat. 30-034 10° N. Lat. 29-986 15° S. Lat. 30-018
30° 0 30-098 aie ee 29-944 20° x 30-040
25 5. 30-202 Equator 29-950 Dig G0
DOgaes 30-122 5° S. Lat. 29-954 30% Us 30-076
T5s sf 30-062 OP 29-978
It may be noted, that if Captain Toynprn’s Chart (Proc. Roy. Soc. vol. xiv.
Plate VII.), and the Isobaric Charts for March and July be compared with reference
to Buys Battot’s Law oF THE WIND, it will be seen that the Prevailing Wind will
blow aft over nearly the whole Outward Tract and the Homeward Tract to India
_ or the Cape.
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
616
TABLE II.—SHowING THE AVERAGE NUMBER OF Days EACH MONTH THE WIND HAS PREVAILED FROM
Nortu, Nortu-East, East, &c., AT DIFFERENT PLACES OVER THE GLOBE.
, x oo j Tee i
— ee ———
aneeeeceen |
5 E - a | 3 so a s sninihaiaitecch
S ‘ oO pu P
Al ce SO OM oe Sees oan |S ‘2 ZB OTN HOY WHO won| 2 B ENN
ie) al
Cc . ~ . s .
a E ANY maw ON aa | Z EMM NBA AAN awa |g a FE OM M ONH HHN HAs |S
> 3 ce oe)
ra ® =i 5 ae
g.| F onw oOo nnw noalgZ Ha | Emon now nan pod bs Py Oe See aor ee eee Sto mares
pre | oe | = oe =
Soe D : ; = mer |e
AE) da Me NAM Aa ao |X aZ| a AVN own owe wae |S 32) 4 HON AMA MAN oven on | &
FAS |e a Seer anc arco AS : ase] A
z Moanin Horo ats one |Z am 2 AN 20 HHO mM aNM wen oo | S "Sp > el ANN FWHAN aca | a
3s S r
3 HAMANN OMA BAAN aa- | § a qm AN ANN AAA =-o(/8 o Gg tNM OMN BAN aaa] 3 ,
ee ————— aT [=| =
ie =) ce) 3 => oF 7s a er)
a4 TNMH HNN Be mt HOA a sae N MMM MAT WAS 3 3 7 OHH ON~D HMM HOMWAN
5 Z a eB z N A Zz SE
Se Se eee ee SS xs =
S) 2 3 =
BAe ANS A -a-|= a ZaAAN MAM HO aaa | 2 & Zommat Hw mot owe | 5
. : l
aS WUBRINNAN wees NAN oso | b UR Oe ase OO Aes on-=|S ai UWUtOM aR ae NAR Ae aoa |S
BS ;
|
i k |
i Fue wow wn aso | 5 1D Fatt mmm Ham owen |S o3 FM min me wn dH aon. |P
eo) ai wl ei eo Zi
4 ; * : q F
\ og F mmm OND AAD oon |% B OOM MHO HOD woo |Z a Emoto wtnr OWD now |e
a FX is 5
SS] FE aoe ons noe nro |Z Hoe | EF owo noo 00M ane|5 na Fowdt mno non van |S
oD nm lee ee) ei = oO mn
ao ™ for) Son :
Hl Aa MNN ANN ANM aaa | gel au HHN HON NWO vow |S TE8] Gg MON AAA MAN aan |S
xe & oO 35 3 he 3H 5 on
aA] aM Nn NMA ANN aan |S S| F nan owe aan aan |S a Bo pcre MAG crores or dt | oy
8 S) i
3) é a n : = op ; n
pi} ANMH ONnMM ANN woo |S RI H NNO HHO HAN aaa|e 3 ANIM DMHN AND MIDS | w&
n 3 =
: 3 : Es :
5 on Gn) Eth ont ana | 2 5 A Aen MH MAAN ana | x a atuee' oom ANH vow | 5
2 A a ce
3 x aS
i] ZaAANMAAN AN aan |x 2 ZANMD NBA AHA awa |e 'S) BANNAN ADA ADN aon |S
a UWL HOA att wen aaa |x = UtANNA ANN AMA aaa |e 5 UuRDANA ANN AMM aaa | 5
I 7 I
ine} = ioe
NX Foaan AAW ota =--|§ 5 F oven 6 mot own vo | Sy Fon oa ot mae Hoo ooo |S
TI & 4
~ . im : > o) S
a gS ee i ee N SLO) aan [2 8 Ewmno HHO OWO avo |S a Fone nan NOM oon |e
S + — o
o > 10
ar EF moo mmm mam won |S Ao EF ows Hot How wi |S iar FE nom mNno Or NON MW |
o': 2 al See n
rq = ao ca 10
re Rc ANM MMA aan |S ae Ag to mae ANG avo |S 2 A MOA Me MOOD ooo oo | 22
¥S + 2 BS
4° : =e) > RSS) 3 1D
ee Boeo oa NH Hid od 09 oD 09 aaa |i SH | 2 ooo nor 1H ron | 2 Biel) |. (op 09) 9) 960 HONE GANGS GI 8 99/09 | ce
S = 3 D eS
n gAwmwmno WOM MOP ono|S wm q Nam MOMNM BAAN aaa | 3 @ Gant WOT MAAN aan | 2
= BY: a
5 : Ss} = ro 5 ie)
iy pee ee eR rene woe | F — Se a ae aan | 5 5 i Revenoms ep ees aaa |i
= no) =
Ep | 4 = ; 19
a yZVwtw OWNM OOO 0 oie | '5 & ZANM MMA ANS ana |S 3 Zann ann ana am | 8
re] ES a ra ei et ms : d Ha
a a ro) : : 4 ey SI oO . 6 Pay rs 9 fA D Par Be elesta lines
Zz goes Bee Swe Sb o | a e Hoe a eS kes Bs |e das Bee 2Ha 8631/5
a aS Poe es Ses |? 6 ao Sess) Seo SS 25 2 S Sos 255 523 O40 |>
a baa aa5 Sdn O40 |H = Beeson Ore mel ae aie se ee
617
Wee
TABLE I1.—continued.
AND THE PREVAILING WINDS OVER THE GLOBE.
a j os
° Us N MHO OAM =aa|S 36 “UFO 00 MOM HHO reo |e s UHI HNN BANA AAM *
Cc a TT —_—_—_——.
sl E l
® BAAN MW Was aac | 3 = ar Aaa ANN aaa |2 GR Emo aA N moana! S
~ a eo ice)
| ° el rH
3 Pe Nore NE SUC 62) 260 et oo cv on | 3 o E MINN OHH SCH wonle & Boome a
© mw. i pa
Ho | eB NAN AAW NAA ANIM /|A sa | & WAN ten oo” wo | 3 mH EF Ho o9 a
no]. Re) 2% oes
ea an ODD OWN Hm non |e = n sss see ANON aaa| acd gag ~1oo A
BH 2H O65
> to na SS Ean] na = e n x
4D : S :
2 HAMM MDH HHA nan |e a AH WOW Hawt ato wae |B f Bg ANN S
< a : a :
g SH atlcal ANA ANAS aa-|s 3 E ho wt AH noo|S a ete a
5 5 S a"
s ZAND MMM ANN aaa|s = yaaa Ono Con aa | 4 tO 00 S
=a WR aa OAH MoS =-=/8 8 WRONANH MAN ANNA ana |S S THTBD of cv) <H =
co ee oe a — —— ——————
I - oo TA = > =
- OHI HOO OnhKrR NHM © a SH 1 : sH
8 = Ke EA ie HO WH nRinm aon | 3 BZ NAN x
Lan . il a ~ na .
op | E OO Bee ON aaa |x q SE NHN MMM HHH aon | 5 a ze Ne cu
u Ow o .
Sol F aMNA OFM BANOO See pO | ee pw | = a5
o ; -| F WMA MHM MNnH OAT ~| F aan
Pies a ests) oe Mee! for) co N a st oo ue oD
cor : : Ber) 3
oe) 2 Aa NAH AAS aaa ls Ben wh OnD NOM HOO ono|S Bo awit 9
ym . BS eae] 5
e5/ 2 mmm mmo Noo wa |S HS) 2 wmnm ANA ANM wno |Z Bol] A AM =4
Fg ee -— Ae a PAS. na
So ~ :
ZA HASCmM AMA Mas =aa|e a aHwmW ANN AAN aay | 5 x] a wos eS
:S A a j
3 BOF Ne VHA ON om | 5 & NN Aaa aan aca | a ‘S BOO SS
3 “4
> g = 5
zrNam HHH Hoe a--|& za Zz AMM OND O0OMN vor | 2 3) % 12 Hw 8
= [ue : Dit ae rs) MIRO A eD HHO 1919 woo | 19 QB | WIND om ON =
ates Sls eS wae a |e
2 B wwe wie nny went | 18 6 BZ TINN MOM WHO aan |o 2 BZ NAS
re n Lem!
« nN i - (oe) ce 0 eo
Z F ONO HHMI WOW nao |s 3 Eto ONnN oNnW 2 oo 0 | 2 g = AN a
ee Hod ® oS Ss
Re | FE C00 ONK 2HO wveo|e D2 | F wow dit coco wow | 3 Piet) ae Ounce =)
mo n LN n aN wm Lama!
“Sly manana ann aman | BOE) Me Mealesten Vag entriay Gad es cel eee OB) Gy mma 5
ees r) oF E an n D a ea ua a
mH oH es z
a5) ° Os |e S Fe) 3 es
Eine) Om AAs sete AOA | a Z DOD TNR -~“MO HH W]1o i 7 AAS nN
std |_a aw a Aa a
A :
is] gVwo ROW MOH now|2 5 A HTAM ANA BAM naw |s Z qa —m7aAN <
a 7 > qa 5 3
3 BN ey aes |X Sg 2 a Hmm won sa |5 BS 2 eS fe
nm n
ot rol
© a P q ;
eo Zmot Ht mons ooo on | 2 3 Zadae ANH WAN =au/3 a Zw Man Mra oot
| aq | re | | I
& Con = ) $ see | pees a : on r () . u ay =| () : H
Fa pb > ap oc ee) : H i Paspr a
3 ES S55 SPE SSS |S 6 | gS8 BES SPR EES) s E d63 B28 SPE SSS s
a bee dan 540 OFA | = Rea «aan h4n O40 |H a Bea 4465 14n O4A/H
VOL. XXV. PART II.
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
618
TABLE I1.—continued.
:
ri
oO
ee}
es
g
nee
all
Palle)
ge
a5
=
(=)
iy
EB
&
n -
oa
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g
nm
8 Years, 1859-66.
Hour 8:
Wisby, Sweden.
8 Years, 1855-62.
Hours 7: 2, 9.
Upsala, Sweden.
Monta.
ranwg se il a lai Pi] t g [MM m0 =
e i Sale ee) Me E ran
lie SRO ML Waa ace |S He) AMT OMM OW ana |2 © se ANG Bi CNS OD) OH GNC EIGN EA Ney
2 g al Nineees
. oO . ;
AMA onNN OOM aan | 2 EAMH MAH WM aoe | 8 a Eno HHnK DOW wie |S
SS eed s n
nm mM
EF anoo noo ma nen |S aa F 0 0 OnA OO roa | e FE ose Hino HNO onn |S
wm aie Oe
reed E HK
ANMM ANN MOH anon | x Fat Pap Mec CPCON AN aX NSS Ls) win o | SE} A DAH HIM aAMw ooo |f
es ian]
oo . .
Aondw ann mtn onn |3 AZM} A wmm ANN Ars owe |Z 3 A MAN AN aA ooo en | &
nm i nm
| f= SS
HANA MMA WAN anal x S| a tH MON ANN tian | 8 RS HANNAN AMA HAN aan | x
=
al : “ ;
: ©
2 Ore Hom BAAN wae |S ES aT iy WON OO Oo wen | a Bot et 1d HOD 6D OD SH aad |S
om 3
ev .
ZANN MMA MAN aca |S 4 ZatN MOHAN ANN ana |Q a ZHtodt ota mma aver cy | 2
WRANN BHNM BAN ~on|2 S “mB |: “weg ae
= a rho | oo as E Ole
BZ VON MMA Win vo | 8 2 BZ NH MoD AOS aac |S So | FW MM WINN vive | 3
Los]
bo ons
= ONM MOH OM owe |g a FRM tot ONO van |s Firs = Sem4e COO HHO mano
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= A el or E (=j | ->
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ow Las! rset at n
Tae . .
n MOH ANA Mm HW wet |S oo A weno COM ONT =a | 0 36 nan wtoo rROrY- OKnRD ono | 3
. _—
me bm :
: 3 if
Bonnin How AM win | 5 88/8 ono nnn mond non |Z ea | A Onn ANH AHN aan |
n fafan| n oH nn
ree> % os
H e .
BH mmr MAM ANN vt oo |B a Rm MHA ANN w von |S Ay | BH COnm COnm OOH =o |s
Bann mnt man ana |’ a Bunn Hon ANN AMA 2 ae Anne new mno non|S
%, ine) E 7, Ine) D 7 bt
. . . N
BAMA MON wad aad | 3 & Z mon OSO HOO cool|n Pepa esas ao Shpall Sa ieee ereelis9
“mye : £8 | : Ce ic 0) ee | : oi fueo cae : | :
E ae laa raisacih kcha |t-e =
ZB Yam ATA moo ote | 38 a) BZ Tam Sin OK vo oo | 3 wel gE AMM HH Woon aan] 3
cy) wo
rr 3 ‘
E HOON ANN OOO sien | x oo se SUNG MoCo Ss eos woe | gn bE wnNo miro ONnW wie |S
Ho er
=) os —
Food wo Hod vow |S par F 00 WIN WMO von [5 a Pace Se, Sonia eH otelare,
N oy
j nh) — E
A HHO MOH Hod om | 2 S| A MMM MNM HHO wit | 3 i: nM ANN AMS on |
> ad 4 - : = go ;
4 SAAN ANN ANA aaa |S a6 AH oWto WHM ote roo |Z cafe 4 ANN AANA AAN oon | 8
———— m|@ &o 8
‘=| on “
HANAN AMM HMM aaa | & 4 HANH AMM BAHN aan |S a Ba ANKTH HHH AANN woo [5
Eas!
. nn = no :
Aawtnm OKO Hod woe |'5 g se at AN ae vines | 8 $8 Boca en on MHA ANH aaa | 3
Za 2)
e 2 7
% ron HNOr- KYO noo | x a ZANN ANN sae mon | 2 Pay Zara N MMA ADA enn | 5
=
| ej | S| as
Oe =| (0) . : uw eS =| ® 245 : H a oO o . .
dace RpE PRR SES ls z cS a BPS Pa 58/5 5 dca ESS cee 5 Ss
ao Sees o o rob)
Bee dAS6 64n OZ2ZA|H = bee 4565 640 COZ = bees 4ae6 64n O4Aly
619
AND THE PREVAILING WINDS OVER THE GLOBE.
TABLE I1.—continued.
* e wd
EM ieee Eee See Se oa de || OOM Cha free ee ES S anh Gene oe ee nee ale
os E CR era Wage Se BE a ey Mattei eA) Mert se he ©
% z X2OR NA ATS roo|S 69 BAND AHH Waco awa | 3 63 a see ANS ---|3
oak Coca cs ae
ga| EE ano non now woo | 2 a E NAM NIH Wao aoe | BE) fo wee eee eee aaa |S
5 | gf oH
Pos | FAN aN A nese | 8 se Fonts CON NON ©oo|fh me EFmaso ooo =oN AoA
N .. Oo n n = Lon!
NN Hy CO 45
, S ‘ ,
T) an ANN BAN FAM aan |x a5] A NOH HHN NM ten |S gdp] a mann sae ane mae | 5
oom jan ao
cS) 3 oD . : 5 us 5
ae A ea 2 te e= |S e BAAN DAT MAN aan |g mo) BR AMS HOO Onn =ova | =
HS N 2 ———
& . =) 4 PH 2
an gy COO sexe OFS mea |s cee BE TDONnN HPN HMO AOE pel eas HB Nes On Oo s= OO onalo
a : == se] - =— Oy ;
5 Home Ne HOM aHoe/S 7 AH HOD HHO On OWHA|2 rs A yOnR OhwD nHno RoOo|®
= z — - & ~~
a 3 4 hand 5 Zi
fo) . . .
= AmaaAN ANN HHH aaa |R = ZmMoo MAM MOH avo |S 3 py ee Sey Srey Ses
—
< ‘mED ¢ 2: | : : wyBO : ate | z a “mTeO ' Rete | :
N = Phamns) 2 . . ° :
~ Yen) —
oD E SY i
oo BZ wt ONS nod oan |g a Foo RRO RWO van |g 92 Zhao ACH 00 one | 8
Yen) io) ~= —
7 3 co) 5 a 5
z EF WMnR CHA OMO ova |S a PE We ANH NOR ~a0 |& fF bE wd MMM WHwH am |S
S Se gD LS
i FHHH mit HH Howl] S goo | & Mae HANA CO = oe ie ee °
ol ee is Cae x mae | a SCS |e DO OMHD NMHM OMM!S
rin = 7 S
. co .
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é g
om : 2 . dn .
g AR aand aan onan aoe |S a3 ZB mON NDS COO aso [x ‘a5 BHAA SH Hoo oon eo | 5
i) 'S °
im : ad 7 n ‘
& HOOD OWN HHO non |S nD H CAN sea oO ood mon[é ee HrRODO MNO BOD ane |Z
« oS se
5 5 is) = > = x
3S sH a= 5
2 5 ill. — St aaa |x 3 S ipaaae en Se fe No Score & NOM nHOn ae acc | &
Lot i
3 BMA HHO ae ama |S © ZNOn ornwn onwn oa on oo | t S Za-ad oOo Onn =a |
m ‘mtg fs : eel ie q eet i9) : D |: WOH OD ONT ANN aac | &
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Pio n = ce anes n = ao aA os
m LS)
SE) Aa ttn man aan mt | 2 oi i MOI Wh 1910 oot | =o a ANN HNO NOK aan | 2
qi Ee f.e .
‘. 5 c : aor =
3 et ee oe el acres |S ae a ooo naa oon coo |a BY woos =—=S3S One on |o
q § Sip
E HMMA HDAN aA H aco | 8 $05 sta N MAN BAAN ona |S a AMON MnnNN aA awe | 8
e :
= : on = o :
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| 3S
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6 g8s Fh Fees s 3) 3 E Gos A855 sae ess) 8 6 SoS BSS BR 508) 8
oO A
= Sha 425 640 O70 |x a BRe <a6 ban O4A|H = Bee 446 640 O2A|m
MR ALEX.
620
BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE I1.—continued.
37’.
East of Nova Zembla, Lat. N. 70°
4} Years, 1832-35 (irreg.) Hour 8:
rt
“UBD on oD 12
oman
Eo igy cea eae
ZA
EF mine AH
Fana add
mM
mn mtn Aa
Hmna ane
nm
g =O NNO
A Wwnm om
Zz
Zrmn awe
Corfu, Italy. 5 Years, 1854-59.
Hour 9, 30:
UBD Oe
SS eS
: 3 : i |: of : : i |:
oO ——
Ee H T FE OaN re) ee
7 ID AN Ho IAM | 2 cS ortia hee Fee et ie ame
oO ao
foo} . .
x FE eRNN ANN MAN aaa | x ze EMM MAM HWM coo wt | 2
- iy
Bo es|
go. | =F mow Onn aHw oon |S on | FARA Aa ae aan |2
hae n Ln cn en ee Ay n
earl ad wat mon On aso | 3 S| hd WM HNN MOH wae |B
ole a go \ a ©
ne | RANNANM MAN aan | BE] FR COW MHH ANH oon |S
am n mn mn
& 3H
g a Oe) g 4
SDS ID TOD OH Hid 19 0 | oS 5 err Se See BS i>
o
A =
ZhMM HMMA AA ano |Z i Zwvwtnm Ono tad vis tt | 23
‘mya > 3 : : : | : cl [Mkhoeey GoS See anola
: wD
3 E aa + E ~
Gk FFE ale ition yew ode Ba re RAW HHO Hawt add | s
S ioe)
® : ; a am - NOOO COM HHM Ano |R
aa gS
Be] FE naw Hi Rim aan | ¥ i F ONH AMA ATH waa |S
oS | ot :
pre 10%
aol ua wHtHo DOK ROW ois | 2 ola Heo HHMm mon can |Z
are ——| | de},
mS 2] By
No)
SM] yg mtdt HMM AAS awe |S = BG Naa OMM ANS ana] 5
> 8
oO . u :
g a OHH AND MMO aoa|g 2 cc BACON HAN NAH aaa|s
[ext q
oOo
ZOCOowm nim HON rao] =| ZARA MMH AAN aan | x
coli Pic Skea : | : Pere [oc loa aa : : | :
ro) = io)
|
x F OOO MAH WOH 2s | °3 Ko) Re} che Sel Cole eh ighey ones S
oO i°.2)
; 00 ot :
a Ss 2S fee Sa SE ra | FOO Ant ANA one oy
n — ie
uw eo)
s
® Fann mat Anm ano |g by os F aan HAH 009 moo | is
la. wn on n
10 : oO i) : oO
st B n =aas NMN KH NN AH = (2 on SION St Se HAN an
a a oe 5 a
siz) A COHN AAN OMAN a=—|5 Zl A HAM AWN MONA WHAM |B
x Gq mAaAd ROO KNO van |Z SH] yg man Hearn ann onma|&
Lal
a : : :
2» Bo oad AD ANN aanls s Eas monk nMo aam | 15
Lan
le} bj
® ZmaAN ADNAN MAN aa | 3 = ZAHN AABN ONM aaa]
3 z F
I OS) SS) P : H iS 28 Gro : H
2 doa brs SPs 353) 8 : G38 RES SPS 85S| 8
° ® S ®
3 Bee da65 65407 O4A|H = BRe 44a6 64n O40 |H
5 Years, 1854-58.
Hours 6: 2, 10.
Debreczin, Austria.
Mont.
E Hon Hato
a
S KH NM ANH
esa aa =
n
nea Nee
Botti ON
Gy roa om
eB OKN HHO
Zowmini WOR
TmPO In en oD OOO N
F. aN ONO
= nn
Funan AHO
mn
nNnoro mwnm
A Sse SK NN
wn
Bq Nant OMN
R ae ON Se ion ioe
a
- BON OmMO
a — —= Sn Ah oe ee
ah
SoS O85
bee 4aa5
621
AND THE PREVAILING WINDS OVER THE GLOBE.
TABLE I1.—continued.
ik “uypey = iyi teyecs oo I~ a Siete Sonat Ss nl be wre Solos ~OWD DAD Sree an
| —
a is MHD ODO DOH ONNIS Ss ic AHN ANN MOAN Bas |S x) ie NAA DMHM HHAM MAK ou
boil re
ee) 5 ee : = 3
a FmHToO HTO MmHo Hno]/ ee EMH NOHO HIM Wrw |e g EMO MHD MOH HoH |
i) H Ores
a E No) By E S He| Ee H
S. | Won tHo mon now | © cae , MOOD MMM ATA AN~ |S as - TWN wot ann oon |S
HO n xs n o:s vn
te! = Ln} =
Hy] a OH MAN BHA te | S m5 Bh aAM ANA AnH ANNA ge | 2 AAD Emm ANN mma/|S
S : i ; ‘ng F
SA | FE Hom Hon tam Ham | 2 A By RUG ee CA eather 0 tia S35) aR N NAN ANN ARWHA!S
ae n BA wm td =
n Ss | n
Pe GID AOH Age Wi = et GZ mtn NOM Ain WOM |S ad Gg CAA NNN AHA ~ao |e
es = ap 5 > : -
a = HAN THAN mam maw |S ise fe HAM MMA ATA Amo |B 3 : MAM MAD MAN aan |R
) : 3 ‘S)
0
ie BAAN MAN MAN Nam 1A SI Zar N NAN ANNAN HH A/a a ZaNN AMM HON aan |Q
. a _
3 WONO OHH HoH Han |S Z URDR ea eee Aes ae | = COTE) cere) GNU GUS GUNG ST ES ES S
ev} I i - ——
wD
® Fann Ane MANA man |B 3 Fano aN MOAN aan | 3 ie Foam ANH ANA aan | 2
rt lee)
- 1
n ° . a 5
3 FE OnM NOM DMD oN | je ey Ew om WOO RRR DOW | 5 a Fm N OHM mmm Ma |S
3
val - P Sal eS) = ee) 3 =
S - WWD MON QDHH OMO ] is rales HOD ses ANN HHH | Q = - ©oCS Baws wes woo |]
VJ
Sa| hd mann mma mmm WH! S “3] d Hom ata maw maw | 2 “HE ANAND MMM NnMM NMoN | B
SEAN) :
am | s ‘a gid | ? é |g
n n p>) mn
- t=] a
ey ss
B Bi MAN ARN ANN ANN] A a BH POA AHS HHO HH) Da Gq CtdW AMH MMA HHO|F™R
2 a = oS »
aI = = ; ad 7
3 Pe AN OHH ONM ANA|S B Bana mam MMN Nam |X g Ee —een ee er | SS
ca Z a 5 Z of =| z 4
S|
4 2 2
3 ZAON MAM MAN ANA] SF 8 ZAnW mno KNOW owes | i a ZOon O©Onm OAH WHOA!
TOONS HHH MAN Hama | 5 BP [(UROANA ATA HAN ANH || ni UR AH MOO MHN Hi | F
‘ i
SS _ 2
a 2 VWOA NOW wm9M aac | 5 re F AMD Mmm MOH HAE | = E ANH ANM MAN AANA|R
Soy oI = s ss
o . . .
AS) FE MNT MAN AHN ao oo | 8 a EWM m CON ROO KRONA of FE mOAN HHO AdWw woo | &
“Sa Ee 3 = TS
s/ 2 nwo nnn nad oon |i HO | EF HN NM OH want | F Ho} EF aN NOM MMM AAA |A
5 n oN n oN n
n ¥ a 2 Ao
2 A Wino mitt oom. ros | 3 ~)| kh On OM MOH won |% “S| yg mon Hit mom amo |S
. ~ Q :
ao : a8 7 = af 5 a
da | F CON HAN AWA eae | 5 ae A wr o DHN ANN awe |% BE! PANN MIN AMA AND | F
aN16 =| 2) 5 td n
I : 5 : =
am Gq moto tam Wor soe |S a GB MON MAN ANN ava | & ms By SERS OO PORES Ta See
< 3S ae op
O16 7 5 o 5 -
Lat 5 SI
48 S sas ANH HHH aaa | 5 S Hon HMH NAS ~ao|s q . OOH NA ANA ANNA
a) A e's 3
7) ao
Zmonmnanatt Hon =a-=]8 a ZANN AND OWS ama | 2 Si ZMAN HAN ANN nan | a
td ra — Bt is a — i = — elon
q = SD Pepe é H a BS) acre eae) Sunt es Saar an lai a » 22 Bp eo pass : H
z ges BFS SHE SSS) 8 B BS 8 ASS SES 855/85 5 Se BSS SER ESS |S
S Re ae R4n O4A/H 3 BRE da45 64n O40] S BRea de6H 4n O4A/H
Tae 6
VOL. XXY. PART II.
10 Years, 1855-64.
Hour 9:
UBD OO ee
Barnaul, Siberia.
2 Years, Aug. 1847—
Sept. 1849. Hours 7: 2,9.
TABLE I1.—continued.
Ajansk, Siberia.
10 Years,
1855-64. Hourly.
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
Catherinenburg, Siberia.
622
Monta.
s
Nn oo fe
Nn % ron) a)
~ NAM DHH OMH WH | S
& Palos) [a i bila ics 4 Ro)
co aor . 1
= | F ANN MAH won ana | & <2) ANS wae HOM aaa | ©
pA go] - —) an ° eo) g a)
Z _ a a — a Mi
a yee: et 35 che Co SHH an NN OD soo oo |
ay} : ro
S ia all Maa | op AwWO RAO HON now |S
<a 5 2 = —
x 7:| 2 aoao nod Hao|e ira 20
nN ne ee se = OSS coy ia ANH HOO OMN SCNT NE Ie
: |
& eg gp oro Fo Hin = La] Hest FAN AMN ATO cs
ce a é
cA 2 oO <H sH awd |S a FAN BAAN AMA AAAS
~ 6 : Nn ie
a Z wR HHO Hm oo oo SH | OS HAM ANTM MOM awe |S
. |x" = =
i S “Lesjifo) Sec Oo Sor beh See | ae ac URONAK ANA ANA AA | 10
| ey (ve)
= 3 E on t Ne}
= fea) = Hoo ooo Made | i HOH HrHO OOW Wom | is
Lal == co
S = ao
pe zm EAN Hao vist | 8 te MAN ATM AHH waco |S
= oO H
(oo) As I= ~ $ om
eS af F OR N WHA maa | ba OAH MID HO nea |
a6 ke =
ine) re . | ice rere ~
Be dn | 2 COR Nee a ra WMO nAA HHH mon | &
£8 ke
o : 3
ve! 2a ROOH ANN ai eite), || 2 ‘ a=OoOMO RYH OWS 10 09 | &
rep) wm o ee
= Q
= “4 Bg COM NNN ooo SS n HN AMM Ae aa |
[=| -
A : Ad
= a Bean A op H =o = 4 aa THAN MAN ona [ht
= n
so 3 FN MANN Aaa | A iS aes eH HH Nee | os
rox 7, Aa ox} St N
iN : ‘WBRO MN Sc OD > + “UR - 1 ;
9) > : eet we val Gn Sls ‘i ONS MEESD USAGE OO Be SOR a
10 a E > ANIM WON a iS
a B | Boom ame See. |S ~Rbee Aaa Sag See hn
io.@) re 4 —
re . ~ .
B oe = SO CSS coo | a PoHOn wee HOH a= |e
=P as isd
sO o
o ta see ooo coo] a Foeosco ooo ono coo |
wt : =p |
oD Low m
aig ‘no
PA ere se sa} 3
2 ag. | pet Stee Saisie ooo 2 ANNO ONO OND how
() Go]
2h |— S
eo Da yg mmo OSS onrNn | xR A g Wow NAW AIS acl wt |
ay : eS
ADA ANH 2 £ Boos ooo cocl|o : 2 Hem ao He on |
ron) fH » DDS MNO aan | a Fe :
Ss SB NO ON Se = me x ay pe Pee a ae or) a Zi aANAN NM TAN AN
—
: q 5 =| ‘
— fae] Oo z jee] om o 5 J
=p OD pp wey u a Cs o H a ey te my ar
Be 8 ooo é z S35 kas SS Grae z dos EPa PRR EES
44545 ain S hee das CO4A |H S 5bRe da25 540 O47
55|
1
1
623
22
U1
9 |10 | 0
Ww
8
9
7
10
11 |12
0
0
1
1
1
3 Years, 1840-42.
1
Hours 6, 9: 3, 10.
4 Years, 1865-68.
Ss. |S.W
1
22| 26 | 84] 85
1
S.E.
Hours 10: 4.
. |N.E.| E.
Roorkee, India.
Chacodate, Japan.
4 Years, 1847-50.
Hourly.
(or) ley)
tre piatess Se tralitce)i¢) EO) Mea) = 60
= e =
BOD 11D 1D GIA co aS
EAN OMAN HAN x
= >)
~ Mas NN ANRN KH BN a
nm
n Onn ANA Bee =
BmMAN HOR WHts
wm ee ma rd
BANOS HAN ANH SS
2 om AaAN AnH XS)
Sa) Ses) eo S)
=~:
N.
5 Years, 1853-59.
UCSHO SBNa TAS
Madras, India.
39 | 68 | 14| 22| 85) 76)| 47 | 14}--
ONT HOMO OM
Now ONw COT
ANH Pha TH
se om
1} Year, 1866-67.
. |S.W] W. IN. W
iS)
0
o)
3
ony Ota
Sliema
Hours 10: 4.
Omyt MHNM OANA
Hours, 9.30: 3.80.
Mooltan, India.
TABLE I1.—continued.
Hong-Kong, China.
6 Years, 1861-65.
Hour 8:
Calcutta, India.
75 | 38| 14 | 28 | 65 | 64 | 22/35/19]| 4
AND THE PREVAILING WINDS OVER THE GLOBE.
2 Years, 1867-69.
Hour A.M. and P.M.
51 Years, 1863-69.
Hour 9:
54 | 48 | 58/50/18/30/50} 2 || 18/81/97 )63| 9 | 35) 19) 20) 23 18] 1 | 32/75,
Shanghai, China.
Jerusalem, Syria.
59
1
4 Years, 1865-68.
Hours 10: 4.
Agra, India.
DBNUNN ATO wee
4 HHN OMN COR
pH HMO NHN COR
: wna Ata sae
zm aa N ODMH ANC
MontH.
MonrtTH.
30 | 28 | 39 | 22 | 22 | 26| 94 | 28 | 76 || 56 | 19| 33 | 32 | 87 | 36 | 27 | 21
Mont.
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
624
TABLE Il.—continued.
~~ — ee a ee ee a
f WLINCO AMN ARO =on | 3 UROSOSO FOO HOO ~oo|a ie {ws : : :
le © is: a ao [re =
pal 2 WO HOW ANA AMA! 2 Sj ERR Fae So Bik st co 60 CY | 45 eas’ [ces US Se ae OL mes
Ye ues o : Pe)
eo . . 1D oe . > ti
“A]| FE OND OMA AMA =o |S 3 ENAN wee aA maa |h a| - LS ee aes
ee met :
HS . Sinn ‘4
$0} F CON NON HHO wou|3 4 FOODS MAH Ane aw | 2 SOLE noo Hot HOt won |S
mS |_2 (is | eet —_ as na
ayes
e48 uw OOn CON mor -oo0 |& ie A Anh HAN AMO won| es FIN pica aia Gar aps oad Sane =
ooh : ; en : A i
a yp Boma N Cnw HAM wao|R S AR OM HMA OHH con |z ag | Baa NTA ANOS aaa |=
‘ee S| Ke Bo “A
ee q Sal 5
Bae] eH COD DON HON wot |B 3 Aq ANN MOM WHE was | re | te SP ROBES: GO UN CME ORS “ce %
Pc} a i 5 Fea] (=) 20 = A
“4
a ; -
wwe oO aM HOM aan | x zANH DHOR ONO wan |g KM ZANM HHA am mma] sy
is “wyeO : : . . oJ URQOom= = ae O Saas ae Oo |o of ete) cei : :
nif Es Hie 3 E x re eeera tear 8 EN MAA RRA aaa | 8
. . Sl .
ip Ne — YG? cha aan |Z ef cr SH ee = 10 2 oF
a . = a x on z aa
a BE SOSS O-n ONMM acoo|f Bl Boe Se ae psec <A aac |x S| SSN ASH AWD OS |i
o a . —
3 : BO
i Pei Soros. sione aco |é Ee FANN Hat AMN are | = 4 Fmnnn HH4a Hod Senay =
. n n Lely 2]
12 mee 2 for)
Bla 2Nn ONO COn =o | = Z A rOW HAN AMN woo |g AS RTO NUCN, UN S600) Et Ses
a2 = aie = = i ios ai
oe FR Oor~ré~ HHO One woo | 5 ee a MOAR HAM ao |S 215 seer DoW ANN MAN] 6
& no Re) A
2 wh @ ra : S
3 BG COM MAA One tse |e zn GB OMO Haaw aam Horn |B Bags IDNs WAO ARN MN) S
; 2 3 a a
| RB 00D CNH CONM COO|S > Bonn mann anw onw/S | HE ipmo Hom wmOomM Horan |A
s REE = c a Zi re 3 Zz =
o
A Zwmonn Nnma Awnr can | oR Boma BAAN NAN =a] 3 ‘aa ZOOS Onn FHF HOO]
os [MOR OO OHH One aaa | 3 _. |(TMOnNtm COS COS eons ® Oma :
Va) — omer Loma
=e =H
oo Pee eee eS ace | 5 = it mo aos oan occa. |S D Fagan ana wan wan | x
3 Z Renye A= Sy a 4
cps fale u
- c) = 5 n . ie)
o FOmRN HHO AOD oao |x o2|/ EF mMa4 HOS CoS =oa|o a ESE Nic Nac) OT =P On =f 00) sae | &
a be Burs i)
3 : oe) (aXe) 5 oo
HS e SH 19 hRO OMHO =a-|s Rss) tal aN SF On BO een |S PA E MOD MMs NDOT TOS ! io
=) n =O —) a nm for) Le a
Oo aed 5
eS n Omn Maen HOw ano |S BS BR Onn BBN ANN =o-|% Bae nan HHH ANN ATA coo | 8
:5 I 2 fy
=I) : ea) = 7 4 fefjes) al
iS) = | ~ aN A S- eee NAM
am a Sat Bas O'S aa | 5 Sela ia gus eee eT SS) Saba g SCS Epon! or)
oO rm
oS _— ma is Ll =-— ee _— ~_ — Er
Q ; 5 5 5 o a ~
El a Se COO occ one |9 lal eae =) ome | a = COR SSC OS MERIC B Be baer
— — — + a}
fe) RA o 3 ~
ie) a I a SSaea oaSo Coe Sees ES) yt 09 0O0O OOM wt eo.o0 |
. fes| [ . ot = fe) é =
is Oo = o ee F, ss To 5 . | Oe Oe as ie H
: : ee = . : 5 | 3
5 | 22) Big ibe, os ES 8 E aas Beer eats, 8 eo 3 > a26 Bee pee ees )
3 Ses fae Sao se8\2 S Son fia FE o Seals S See 4qa26 640 OFA |
S Be q8365 64n OZAlH S bee 4q4a5 44m OZA|H S ac)
AND THE PREVAILING WINDS OVER THE GLOBE, 625
TABLE Il. —continued.
Moar Hobart Town, Tasmania. 5} Years, Port Arthur, Tasmania, 5 Years, Auckland, New Zealand. 8 Years,
i 1861-67. Hours 6, 12: 6. 1861-66. Hours 6,12: 6. 1853-59, 66-67. Hours 9.380: 3.30.
N. |N.E.| E. |S.E.| S. |S.W | W. |N.W E N. |N.E.| E. |S.E.| S. |S.W) W. |N.W c N. |N.E,| E. |S.E.| S. |S.W] W. | NW E
iS)
Jan. SAD | 21 4 | 3 Mi elllesleale Gal dealt Sell Qui Gils sealeenl cern i ve | Se Der WO) | Bei 2) ike
Feb. ae meee Dee Soe ile aieces ee Nea fb mmerl| Dee AL DE 7. iD) ole, al Bi || Se Onin aap On |t-aalire
March) 4] 1|2/7/)3/]2)|2/1!10 ipsa eddie spel i eal coe eam eS BW GW Be Be I aa ye sh 8
April So\eeni le | | 2) 4.1) 2 1 1d Dee OM Din) mises al 2'4)2)|41)] 38 }10 | 2) 3 | --
May AS eat te) Qe\-2)) 4.) 2) | 14.) = PIAA (0) a Ses heal) a7 EN Bt |e 1/3;1;)3)4 10/41] 5
damenie4s | Tit) i b | 3) a) 15 ON SP hey) a 2 SW Ga tf, Ly Be By ee a teh eta) 083
July Sele le 2a 3h) oy le! OM eet hl 2 i) eit GING: 4: PB) BB AEN ZB BY Wino
Aug. S233) 29) 4) 2) 13 AS EON De ON See lee 7ae| ween || de |) mel Ge (4a le: | Ob QA 4 ics
Sept. Seems lelecalee lear | 3) 1512) AS |e 3 | NON a) ||) ob Onl on |no Qa Ge 2a Se 2 We Sp 4s |efealis
Oct. Aen le Ga) 24) 42) 2) 110 Dede) IE Gy) 3 Gp eae 14 QA 1s els) TOF Gy |e:
Nov. Semone le ior) Na) a oe | 10 Oe} By WW By] ate 4 By Qn ee Ol eer ON Ge ee:
Dec. Smonleon i Ol 20) 2. |) 22-8 TE ES) LO || es) >) BN ly GO ee | Ze iB
Year | 45 | 22/16) 59| 23|39/30/131 21) 44/11) 59 | 26} 73 | 46 | 85 26 | 59 | 24) 31) 41)99) 41) 44
Monte Christchurch, New Zealand. 4 Years, Dunedin, New Zealand. 44 Years, Southland, New Zealand. 8 Years,
: 1864-67. Hours 10: 4. 1862-64,66-67. Hours 9.30:8.30: or 4.30. 1858-6, 1866-67. Hours 9: 3, 9.
N. |N.E.| BE. |S.E./ S. [S.w] W. |N.W g WN. |N.E.| E. |S.E.| S. |S.W] W. |N.W 5 N. |N.E.| E. |S.E.] S. |S.W] W. |N.W E
iS)
Jan. Ste Se Ve OF |) tel Ze) Le) 40 Pa NE 7h ML NDE N83 aN ath est PS OR ton) On| Om el 8] 9]:
Feb. A ete eee De eee fee Op 2. Gy By ey ee at OR 2h ese On ls On On ts7,
Mien naan eon le eT Oe le Dee De Vs Te Ne 2) Gal 7a!) LT | 6 i lO) 2) 6) oO} Wl 11! 10
April OR NKOM eon) 1) 1s) fel ee 2)| 3 1a eae ee esate Poe Seinen! 7 Lo @ SP aE at OTE) Tea
May ee eraeliecsin oe Mey Os | te ee tS Hs IE Oy a EO By Ze Poy) C0) 9/15]
Mamewie2e| 5 45) 26) Or12>| Qe) 1 | 2 1 Pom RON On nies iG ile ioe QeeOy eae. 2) OF al 8/12} +
July ae essen ee ene Me eee Te Om Oe Se Ons lel vor | Ga 2. Ori Qi tail ve) 451 Onl Oo 6/12
Aug. CO erie elas |e lee eae eel ee Om ee eles Dee ten om loa 2.1 1G i @ |] aE By ee
Sept. Na me erie | ten Van Sea) Deel | BN WW Ba et By a eG BO Ge eat ah aT 6] 8] ee
Oct. feos Ge) le. teu Se) le sd) ab 2a ee lee see On eae AT Oe ORT Om One 9; 9
Seem mOM Ge se | 2) | Le Fall ele| (Go) On Qe e7e\ 1) Qe) Qa" Ge | 4/2.) 45 i. te) On.) SP] S| Te] 8} 8]-
Dec. OR! tS) 1st Leow! as ea PAN YP ES ay EN Syn a es) TON oe OF) tei 9| 7|-
Year | 10) 94 | 62) 15 | 12|106) 17 | 27 | 22] 21 | 70} 13 | 16) 20| 59| 76/| 20|70 15] 1 |43/70/ 4 | 8 104/120
Mion Cape Town, Cape Colony. 4 Years, | Graham’s Town, Cape Colony. 43 Years,|| Graff Reinet, Cape Colony. 38 Years,
1 1862-65. Hours 5, 9: 1,5, 9. 1854-59. Hours 9.380: 38.30. 1863-65, Hours 9: 1, 5.
N. |N.E.| E. |S.E.| S. |S.W] W. |N.W a N. |N.E.| E, |S.E.| S. |S.W) W. IN. W 5 N. |N.E.| E, |S.E.] 8. |S.W]| W. |N.W Z
Memes) 1 0 | O| 2124) 1) 2) 4) 0) 3] 4) 9) 3/9) 2) fle plol i] pii9| 5] 3} 1
Feb. On SOs 2 ON AE a 2s) x PPP Shl nom |e faiect leo Oy it iO) 2) | yp
Warch) 1 |-0)| 1+) 2'\17| 1 | 316 SRI ECE Shue SL ede mom ssl Qe de We el T4e) or | 2) leet:
April DS On| LOM 3h 142529) 3916 1 28 S20 pa 25 ONS 7 4) ene Ten ets sali Ob) Onl Ol nase
May Sr On| LO) S25) 135 a Si 9) - 1) Ne De) ee De | Resin es | SHe Onl 25) 433) Pon es
June |5/0/]0)]1 9/3|)4/8]- 1 eles OR ee te (Geom ta 10) | 0) | 2 BYP I 22
July Bi |) ON Pee a ae ay GMail COP Ap ah 7 tay lat ele ele ss GI 2 wy ie
Aug. Sl On ROM Peel Wen soni as ON 2 2a 255 is \N9F) 5) LO @ | te) Oe Sih er ep Ss We
Sept. DS ROP | LOM eee 2 eZ on 7 1 ee suleoe | See Oe eae ede) eset ll 501 Ol OF] 3) E21) 3) -2) | oj he
Oct. Dai SOM On 14s |) 265/16 Wee [Pes ee rh es Ws} AD ON Ono |G) Qe hie | ponte
Nov. DOM On 2! Neg lea) Si sa OM 2a eae | Ph E4s 7ele ob ee TOs VOR 2 GH Gre | esi
Dec. LOM POs Pan 20))) 4) 35) 3 ee Ronse Por le oels ale? Sole Ob Pot eras |e Ze
Year |28/ 0 | 1 | 23 |178/ 19] 43] 73 9 | 25 | 26| 59/31 | 97) 37) 81 61) 7 | 5 | 27/134) 45 | 27 | 59
VOL. XXV. PART II. 7Z
6 Years, 1858-69. Hours
9.30: 3.30.
Mauritius.
3 Year.
Hour A.M.
Tamatave, Madagascar.
TABLE II.—continued.
2 Years,
Hours 9: 3.
1858-59.
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
Pieter Maritzburg, Natal.
626
Monta.
oon rw OC con |o WES ae ae AN HOS con|e ‘wre SOS © 0 ~ Sas wipes 2
”~ ms _—
Ee a 4 = 5
a ANB ANN AHH | { 3 2 OS Sin se ono|e 2 F mo° ooc HOe coo|a
H a
3 : 3S :
E =e aa N aaa |S oS Een O san NAO waelc a) Ea oS) Sa Ss sooo aso |
E jf | a sel Ee
r sHe COSC ONO] zs *, SESE OGIO), rN woo | 3 ce eee OOH OHM HOM MH H fr
aS 2 &5 Seal Lal
: ws = .
a OND NHN <aa|s Bo) dh ROW HOR FAAS =xo0 |e oa | a COS CSS Soo aco|-
OH : H
j oN Ney = 512 j
fa Oi Ne a sx oy te a MAN ANAN NAN ABH |S tay 5 MOM ACO sae cco |m
tg oH 4 2
: for) aaa |e tr 00 ; ee
i a benhcr ee tel ao A CAN DON MMH conn |z 2S8|/ fh CSCO COO HHO coo|a
. —&, 0
io) Sa B ; ra a
2 HAR CAN asic | x Ry EAM HWoOaA AN SH awn | % ees pee a EES
. . Ay
BAe Aas Ae aaa | epee Spee! SiC) Bog) aoe won | 5 %yonmm OCG OnAN coo[nx
“wyR9 fo TEE Se : | : : WyeD ; : | : URAHAN NM HHtmM mann ie
ae A
. . . . 12 mn
ce ee eon |: alt FnRwOo ROA AAA ooo |e 3 Enea eae N NOM Aaa lS
5 . . . ao . oe .
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m im!
= Lewd
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DO -
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4 nN
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m
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5 e so} n ° =
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425 647 O4A|H S BRe qa5 64m O40 |H = bee 4qe65 542 OZA]H
627
AND THE PREVAILING WINDS OVER THE GLOBE.
TABLE I1.—continued.
ne Ee eee SS —— ee St nn. a a ae eal. le OP ee,
Fe Be lie ° . . . , _ a see . . . e . . . . z .
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Sis N n
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fox) for)
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Paco = wt i ie}
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ae 2] 5 rag
- er n 210 z for)
ea qm aaw HANH MDS aaa|s i BH NOS HOt FISH ano|a Aw grrr ofnn MOO aro |Z
© tS) a : a
Sr BR ame ono ome onm |Z = A NSOn MHA WHM awo|s ce Fo St at O_o eo eet eet ge sow |S
NSCS nem ANM OHO |A BROW mot KYM HOH! Peace ie — Pa I oP Ta amy [hc
Za NX — eS 00
. - re
iss is] ars) — r . = fy ° .
o . h a Sites
> Z =e peer ee =e, we S 3
S) ) a OW 5 o 2
I a Smee dae5 4m O4A|H Ss
St John’s, Newfoundland. 6 Years,
rFRMOo HRN OOM HNO
66 | 68
6 Years, 1843-48. Hours 9: 8, 9.
20 117} ---
1809-59. A.m., Noon, p.m.
N.E.| E. |S.E.| S. |S.W] W. [N.W
mw
61| 36 | 36) 12| 60| 18 | 21 | 27 | 94
Brunswick, Maine, U.S. 50 Years,
N.
AAS
N. |N.E.| E. |S.E.| 8.
1
1
1
TABLE II.—continued.
N.W
“HUB oO OD 6D
~ws
N.W
4 Years, 1854-59. ||York Factory, Hudson B., Brit. America.
Hour 9.30:
7 Years, 1841-47. Hour?
Norway House, British Ame rica,
. N.E.| EB. /g.B.| 8. |S.w] Ww.
HL SH
N. |N.E.| E. |S.E.] S. |S.W] W.
3
2
2
2 10 CO
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
628
3
og
i on
|g CSA OHA OM nor]
= a
x ANNAN ANMANM BANA! GY
Bl Rant wat Adm oan |B
| QD
oO % a
a gr On Bane ANA AA =
re
ic sH
OF Aton HANK HAN]
BAMA HAR ANN MOMMY
wrRpCOoOO FeO ORM NBO]
3 F Amo OM =
Bo a on co ad
Br | FE AWE Ho x
rio
251 =F awnco wwe te
eS
n NX
Ae) Ep AMN NM IE;
0s
{=| 5
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8a m
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S56] yf ONM Ma on
ro |
By a To)
1 MNAN ANA |
n Zi N
yA BMH Fe
a |:
So
2 Fo aan man is
— Za
Zo) Food mmo Fe
Sod
oO
Pigs |) Beas oes He
a nm =
ag ; Nn
8 Ato M00 |
aba (2 v
BS ; =
ie Rmmt HAHN Ba
Loiets 7) mM
68 o
=e | H OOH HAN |
So ica} oO
= 1 Ramm NAA |
a z ag
ei a |
=. Orr : H
o sR Rs 3s
5 Ao S asa o
SI See 485 al
4} Years, 1854-59. || Kingstown, Canada.
Hours 7: 2, 9.
Montreal, Canada.
“WITRD oF 20 19
N.W
13 | 32 | 67 | 62| 70| 24 || 37| 50 | 24/22] 48 | 92 | 47 | 45
4 Years, 1855-59. Hours 7: 2, 9.
N. |N.E.| E. |S.E.] S. |S.W)] W. |N.W
Red River Settlement, British America.
36) 56] 5
Mont.
Monta.
N. |N.E.| E. |S.E.| S. |S.W] W.
0
0
1
74/11/15) 13 105) 32 | 33 | 36 | 46 | 59| 47 | 13 | 22| 75 | 26 | 16 | 59| 48 || 16 | 47/13 | 27) 11)114
629
AND THE PREVAILING WINDS OVER THE GLOBE.
TABLE I1.—continued.
os OTE are : |: — (MOOS Soo See aso|a Es WOAMOnN BOO ae ono |n
i = a 8
s ot nN oC i= 3
3 Br OmmN hom mn ra=|3 oe OHH NMID OMAN wow |S ae F 00 © Hoo oN 2oa|2
nl 3 ‘— Sp
i 10 x Z Hi *
a EF won~N Won OOO oon |i ‘ON E NAR On AHS aaa | > Sie} FANN BO aH eH ==-=|2
oan Er sae ad © ah |e + ae
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eo Ps = 4 — <) 1S) S| n a id
ae : 10 SS) a2) E
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ae| wa 9 ape |e eo | a
Sh a OL SS aye oot HL ea | a Ant HHH RHwD mond | NR ve Amat hnw noe aad |e
n ! ! ;
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a Bato ANN HANH HHH | Bg | HF ANA AMG AAM AHA iS ae BH ANN HAH ANN aa |
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oO Ss) Ai a = re = ~
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Gq Zsa s BNO CH ANS = RONNN HAs Hem aac |g x MON AwewT Saws aac |X
We, ~~ 5 . . wel
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Cra a= cs = |e =
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Te) |e aS ; Ps
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ay me nM a9 Q — — as
= n
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dor = Do SO = iS
= Paann won Bal a | & N eo | a
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ZmanNnmM NOR AHN an ]2 Zmntt ttm Hoo nddH | 2 Zorn Hts AaAm oan|s
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3 = Kes Zz 3 es a =
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ae
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= oi Ps n coal = se
dg | AANA AMD mam ana |S ao | 2H DOO COO HOW|D Ho] A ANA MAN AAR AHAN/S
eo) oS = BS) a
i = mn : ey 5
Fig BR NAM ma teo on on aca | 3 As mB NON no HH MNO marcy | 3 so | BAAN MHR OHM aaa |g
oO a a m
on . ian 5 To
& H MONM HAN NAM maa | A = HAN MAN ANN ana | § FS | oH Onn HHO ANH =ao]o
(>) ; 5 aS
Ae S
aa) <3) a ; on
: STN HOD CN CN en oo cacu ce | 33 EO) DR omdt wan ane aac |B “4 PookrR RAND WON enn |e
B aa a, 3 a = oo
: 3 5
a BANNAN FAA Ha ace | 2 =x ZANM AMM HH sence |B %ONN FAA OAN aaw | x
a | a g | j |
a alpen Merwe SO ogres sr dl a a 72 = © i ; “f A p= aD 2 , -
| 883 BSS See SoS | 8 é gee Bea ohe 2s 3} 3 z Go B ERE Soe wks] Z
o
S BHA 4qa6 542 O4Q|y S See 4a5 640 64Q/H- S| BoA 4ae46 647 OZA|H
SA
VOL. XXV. PART II.
1 Year, 1858.
Hours 7: 2, 9.
Goliad, Texas, U.S.
3 Years, 1857-59.
TABLE II.—continued.
Hours 7: 2, 9.
Austin, Texas, U.S.
Ee se OO HOO HOS son |
a
an rina aan
on
—
o
i
fe eoeo sec =o Oo coo|-
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
1854-56, 1857. Hours 9, 12: 3.
New Orleans, Lous., U.S. 23 Years,
630
Monts.
amr RMO NOOO
wo N Se NM Ne —
[or Ee oe Be Le wo |
2 NS ANN Od onn |g
AHO HHH BION eue\é
A Se — Sse =
WUteaee Ono OCS onn|e
Ee a 2)
o HMA AMR AR oO 10 on]
: ro)
Ee Ana Bee SS oven oo |
Foto Hho 19 0 one |S
B OMnR OhH AAD oon |
= _—
| sH
A AYO HHH 200 wan |
: a)
Ban O Res BANM ana |<
cathy AWA most aan |
Zmrmryo NNM ANW ane |x
= pine —
MUnROoOone Onn AMM ono |S
ar MAH ANS naw] &
SFANM ANN AND naa|&
EF mae ate NAH ana |S
AATH ODO NON mio |S
Raw moo nen ave |S
HWHH ORO NANO coco wt | fs
Fionn HANH AMO ron |B
An
BHM MmM MAM HH ane |s
ai
ye ist (0) 5 : y
Gah Bea Pwe ses] sa
SO SSeS Siig Oo, S io
bee aAeH Amn O4ZA|H
TU SoS SS Sse) sie
1829-50.
29 |136) 2
52
5
3
3
2
1
2
1
2
2
2
2
4
a
‘
3
3
3
2
3
1
3
1
1
MWr~o CHO OwWW
iol fom)
Om 390 0 SH
19 | 29 | 64 | 78
=A Ones
1855-59. Hours 7: 2, 9.
Mean of day observations.
N.E.| E. |S.E.} S. |S.W] W. |N.W
Hazelwood, Minn., U.S. 5 Years,
Marietta, Ohio, U.S. 22 Years,
20) 15/13 39) 84 | 2
N.
N.
S.W| W. |N.W
54 | 42 | 23 | 42} 66 || 78 | 12
8.B.| 8.
50
1854-59. Hours 7: 2. 9.
N.E.] E. |S8.E.) 8S. |S.W) W. IN. W
Glenwood, Tenn., U.S. 6 Years,
Greenbay, Wisc., U.S. 9 Years,
1822-30. Hours, sunrise, 9: 3, 9.
. |N.E.| E.
31] 38) 19
N.
S.W| W. |N.W
55 | 89] 71) 37) 33
1858-59. Hours 7: 2, 9.
KR. |8.E.! S.
52 | 34) 32 | 33 |119| 52] 26| --- 29 | 89 10 | 12 | 48 |125) 30 | 22} ---
Fort Towson, Indian Territory, U.S.
?Years,1833-42. Hours, sunrise, 9: 3, 9.
Detroit, Mich., U.S. 5 Years, 1854-56,
31 | 27 | 22
N. |N.E.
Monti.
Oct.
Nov.
Dec.
Year | 17
Monta.
631
TABLE II.—continued.
AND THE PREVAILING WINDS OVER THE GLOBE.
SP ap ReOs be aes Hen OF tr ees: |e ae |. ore Se sh a he Be a Oe chase. |! pe
Z A Sa SOs Oats pec Se One A + GNOME ars ens ek, BREN oS UOC 4 2
® Ee Ly = a ee
= prot aan ANH nwo |B SS > Hea HOC COSCO Ooo] xs oD F )
mic, ee ire: les —-
| F MIM MHM ONnH Waa |S ice oO SoS onole ae 5 S
ois (Te H 3 =
Bg - AN TANNA HH a4 18 ae Fane ==—O OOO coo|h HS ie 7)
- >
5H 5 OOM ANH Ye) 2 o
Ore) || Soe Sea Sh Sus “Hi bd O2MR MOO COS HW |e ke ; =
ze = — nel 4 a vw | ea be)
a | a) 3 : :
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oo 2 | eg |e a) ee (2 ©
no ;
AANH HM AA nN S ~5 MOMm~ MMO CHE wo SD S :
aie i I MOOSE es 2a La St sise eed uS oa A Ne
5 a 5 qi j
Z BATA ARS Gon san |S 5 Bo ANM HOw ono] x & fe =I
S) =] 3S =
ic %FMWNSD SHH DHMH AN 3 S ot 7 :
S NAA |S Ss Ze Erm on eS sere te A Zz &@
S [eagey : é
S Ww : | Py UMMAH AHI WAM ait |S “mye
& ES See ue
st OO SS a) od > OMIM HON mad mm | aS S =
a, 2) eee M9 6 Z io)
aos . a 1
fen] for} .
£ os E NaH 10 a OS, oom | os | FE OAT MMM HHH vaio | 3 3 E
4 oD
oh wa : ON BHO Dd 7 Vodt mdm ott tam |S vee 2 10
S 3 n ~~ nS val (ee)
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be BS Se 2 Boe Cae | BANN ANA AMA aan | x pa ae S
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q.° | & oo SHO AN AA sfi§ | AB NBRN MAM ATH MAN! S 7 j Xx
ox |— eae) ae ee eee =
a ; -
a pe onS on aan | £3) BF mmt KRHH modo soo | 2 S eI @
= Ao |_% ST Q Zi SH
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=
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Se - DMNS OINM NMH Non Ny “OM ROM aA MOO |] LS eo) : BH
mo, |e = o> at Zt a | © 19 %
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Bo | FANN ANH Hae ann] oa @ > i :
5 ¢ 5 lox] Ch Oe EFmoyrFy ROD Hot HHH 10 on = Sy
ae 7 Hina 320010 sH a Ee : Sa) e
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ea nas = ba 2 NS :
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ES = ®
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3°) Ams ANM ANMN cuca | er Bae ae Fee MOH ana | 8 = HANH ARH Sy
per) [=] > F oe =
OD] mmm wom om wera | 8 iS Anam Man HNM wan |X 5 HAAR ANN ©
eS ees oa Zi 5 3 Zi a
2 = 5 =
S Ziman MAN ANN asia | 3 ZCOn HHA ANOS non|Z io) Z OMI MAM SS
= = Sli oe | sw
is] re | :
a oS lo ; = a
a Pape H a) Sr 0) . A oOo mo
| dS BFS PES 25 8] 8 | G55 BPE PRR eES/S| | 2 | gee ERE SPR
o 6 oO 5 DB o
= Bee den 640 OZAlS SI bee 4d465 640 O40 |H a Bes <da65 54M
632
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
TABLE Il.—continued.
Montn,| Havanna, Cuba. 3 Years, 1859-61. Up Park Camp, Jamaica. 5 Years, Barbadoes. 6 Years, 1853-59.
i Hours, 8, 12: 4, 8. 1853-59. Hour 9.30: Hour 9.30:
N. |N.E.| E. |S.E.| S. |S.W] W. |N.W 5 N. |N.E.| E. |S.E.| S. | S.W] W. |N.W E N. |N.E.| E. |S.E.} S. |S.W] W. IN. W 2
Jan 4/ 6/8} tf] 2] 0] O} Oe) Z 1138) Bt] BO | @ he |i |+= |) @ le |W Po eo palo
Feb. 5 | 6 @9)) SB 1 2 OO Os) 8016 Ae | AE | 0) Oar iO} RS 21:0 1°38 | 16) £ | Gri Ges POR 0
March} 3| 9; 8|5;2/0)0/1j-+) 4] 5] 1/14) 1/1/11] 4 0|7/|20|}4};0|0/0;0)|0
Aprik |e} 8S (7-4 lt | Lio) oO 2a eA eed ley, On ae et ie O |S 117 29 | 0 OR RGs atein0
Mayt.|. 2) 6: G8) 3) | a2 | teeta Ql e8 | Qe D7. OO.) OF 2 @ | 2 | 19/10 |G) |); POs), 0
June | 2/8] 8/3/0/0/0/1 Dia | ex) || ore | 15) abe hs HO) ES 0|4/20;6;0;0;}0);0/0
Jaly® | 2) #)12) 410] ©) @ |e. ALON Qe LIP Oey aes eda a2 O | & | 201 | O: | :O, | R@s| Or) 20
FTE CVO 133} 3 ty OO 516) 27/15)! | | 1g] eo) PEO) AS |S) | Or SR GR ON gO
Sept eet INL ee Dee | aes |e |e Oenl c= 2 9) 9 LS) OR a Pelee aL 0 | 3.) 18) 8 | FO) Ge s0F) E08
Oct, 2 | G2 oe | OL | OOM) 4110) 2)12)/0)0)|0) 3 1: | 4/18] 8 | @ | O} 0} 0 |-0
Moe fol Ge SO )-O | © |) @ |) Gh V14e |) Qa) 6) ae On 20s | 52 O |) 8 1.16 |) So) Le eC) eae Ox sO
Dec. | Sie |} Ghnl Pleo 2 ee Ol On iat Oe (le (294. | CO: Oy FO a We 12) 1¢ | 2 | OO Gs) Onis0
Year | 32 76 |123/43/12}6]1]| 4 |---||52 109) 22/141) 3 | 8 | 5 | 25 2: |'79)|213) 67, | 2s) SIs OR AsO
Wore Georgetown, British Guiana. \Catherina Sophia, Dutch Guiana. 4 Years,| Cayenne, French Guiana. 7 Years,
‘| 65 Years, 1850-51, 1854-56. Hour? 1856-59. Hour 7: 2, 9. 1846-52. Hours, generally mean of day.
N. |N.E.| EH. |S.B.| S. |S.W|] W. IN. W g N. |N.E.| E. |S.E.) S. |S.W] W. IN. W a N. |N.E.| E. |S.E.] 8. |S.W] W. IN.W 5
Jan. O) | 11 | 19) 0) JO | Ol OOF) Wye WS ee | St @ |-O | BO fee 28) 5) Oh Oxon ea Ones
Feb. OF SS ORIOL IFO! OF (FOR OS KS eG) FS) 10) 8G) FO) eo 1. |. 23) 2-0 1.0) | OOS Om e2
March) 0/17/14) 0]0/0)|0/]0)0)] 2/21} 3|]4)]0) 1/0) 0 2/24; 3} 0/0/0)/0)9)2
Aprile | FOP E18) 1 PONG! FO) | FOR OR EZ G45 ip iO RON eo Lr }19) S| 2 |. 0 |: @lvenrones
May 0)'0: |) 9181) 4 OT! @ |G |FO| OL) Ie 12) Hh |) HS ek yea L id pls LY 1 O- ORG eOsiea
dune® |) 0) | 6/2212) O08) 0) | 0) | OF OR) FLO 9) 12 1b ROPE Wis OL) SUS 2 0) ON Gn On) me
Julyo| Oo} 8119), 4) 08) @ |) )208) 0%) 2) OPS rs hs LL ye pt 0 | 4/21) 3 | 0 | 0 10) Osis
Ang DPOF | Ti 21 FON OR NO) | Ly SOS S25 Fs LONE) ES) 2a ON tee 70) 2)24/-4 | 0) 0) OF Ont
sept.6| 0) |) 9120) Es POT O) | OF ROR On) EM harsh a phere eZ 0 | 4725) | 0) O PG POs s0
Oct. OF PD TOPE POUT OR NO) | FOR TORT Re US Gr ier ar PO. Oy rr Lb} 720) b | OF) Oar Ola
Nove | 0! |) 9) 20) 18 iO) FO} POF ON FOR Fas FS ap ine eet te | PON iO by | 10) 174-1 | O 8 Ol On) Oaies
Dec. OPV IT LON TO) FO} OF POR ONT le ae Sh 2s OL On eG 0/20) 9) 0 |} O | OPO Oale2
Year | 0 |/124/222 15) 0.) 0 | 1 | O | 3 || 16/161) 69) 80) 23) 8} 1) 7)0) 8 155/162 15; 0]0/] 0] 0 |24
M Cochahamba, Bolivia. 8 Months, 1852. ||Asuncion, Paraguay. 11 Months, 1854-|| Buenos Ayres, La Plata, 1} Year,
eae Hours, 9: 3. Hours various. 1853-4-5-6, Hours, 0, 3, 6, &e.
N. |N.E.] E. |S.E.) S. |S.W] W. /N.W, E N. |N.E.] E. |S.E.] S. |S.W) W. |N. W| E N. |N.E.| E. |S.E.] S. | S.W) W. IN. W é
is)
Jan. Ol) WP} OP RS |) O} | OO f Dal 4a Df en Fee Te Sy Wy WO) | Waa Se SB) 2) ica at ea)
Feb. (oan hs fey Lem pc an Vm 0 Da er AO Yon foe 8 el ee? | ool ei oes se|| cool) enn} Sead oradboocubocoMlmtSm el mex lmosele | a |) 2) |) i yw
Marchi! 0! |) 6i) 0) )8) | Of) 4) 1 1) Q100 Sey i ss 4s we Bi 2s) ONL GE |) Gd | St ees eo
Aprilt) 0!) 6! |-O)) S) OH) O26 S/S) 3) 6) 6) 240 | 2s) Ol 2a ) Se 4 ee
May | --s| soe] ees [eee] eee] eee | oon | oe] eel 151917) 311)0)/0]0/10)/9)/1)213)6)0),o)0
June” | 25) St -O) OR 45 Os) O 1) Fa Qe) 45 I 4y Ss | Se BO) Te OR 4a Oe zea SiS ie aed
July O°} Qe) Ob Pe OL} Bi] O) 23+) Qe Qi) 4e 2) Sp Se We |) 2 WOR On GPs 1G) | 2a O) erat Sie eae
Aug.) 1°] 1] OF] OFF Wl Wy 4) Qe) 3) Si) | ae] BS Ol) Qi) Ga a A Si) 2S Se
Sept Gh) 40) TE) Fa QE | OF) 2a sb 2. GOs 25) Go IP 2F i OL OR QE Qe eS iso) 2) ee eae ee
Oct. oo . 4/8) 7) 4) 3) 4] 0.) OF] I] 4) SP | 4) 2) 45) Oe
Nov. | cee] ces] cee |ece] cee 71 6) 5 1 4) 40h Ol We 2) OI Bs 4 Sei) Z| G4) 0) Se Se eee
Dec. co jee fers} one ll 41 8131/5) 4) 1] 2) 2) 31) 8/9) 4/4) 0) 4) 0) ee
Ryder eet h Belldca ties alsa Lay seal alleeed ales 69 | 65 64/49 |22|/53/19]21| 3
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VOL, XXV, PART If.
634
MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
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AND THE PREVAILING WINDS OVER THE GLOBE, 639
LIST OF AUTHORITIES,
Showing the sources from which the data in Tables I., II., and III. have been obtained.
A, For Barometers (TABLE I.)
_
. Letter from A. O. Thorlacius, Stykkisholm.
2. Collectanea Meteorologica sub auspiciis Societatis
Scientiarum Danice edita. Fasc. II. Reykjavik;
NI. Christiansborg ; 1V. Godthaab, Jacobs-
havn, and Upernivik.
3. Journal of the Scottish Meteorological Society.
4, Monatsberichte K. Akad. der Wissen. zu Berlin,
1842, p. 306; 1849, p. 177; 1849, p. 157;
1860, p. 646. (Papers by Dove.)
5. Letter from Dr T. R. Robinson, The Observatory,
Armagh.
6. Letter from Alexander Dickey, Bursar, Queen’s
College, Belfast.
7. Meteorol. Obs. taken from 1829 to 1852, at Ord.
Sur. Office, Phenix Park, Dublin, edited by
Captain Cameron, R.E., Dublin, 1856.
8. Abstracts of Meteorol. Obs. made at Ord. Sur.
Office, Phenix Park, Dublin, by Capt. Wilkin-
son, R.E.
9. Meteorol. Obs. taken at Monkstown, Co. Dublin,
by Arthur Pim.
10. Letter from Dr Caulfield, Royal Institution,
Cork.
11. Letter from John Plummer, Assistant to Professor
Chevallier, Durham Observatory.
12. Letter from the Rev. Francis Redford, The
Rectory, Silloth.
13. Abstracts of Meteorol. Obs. taken at Stoneyhurst,
1868.
14. Letter from the Rev. J. S. Perry, Stoneyhurst.
15. Quarterly Tables of Meteorological Society of
England. °
16. Letter from John Hartnup, The Observatory,
Bidston, Liverpool.
17. Letter from John Davis, Optician, Derby.
18. Letter from John Davidson, Holkham.
19. Letter from C. M. Gibson, Norwich.
20. Letter from John M‘Laren, Cardington.
21. Astron. and Meteorol. Obs., Radcliffe Observatory,
Oxford, 1857-66.
22. Greenwich Magnet. and Meteorol. Observations,
1857-66.
23. Letter from Henry Storks Eaton.
Note.—For the details of this long series of observa-
tions, see Proceedings Meteorol. Society of England,
vol. i. p. 273, which Mr Eaton has kindly extended to
31st December 1868, by adding the Greenwich Observa-
tions, 1863-68.
24. Letter and Annual Abstracts from Matthew P.
Moyle, M.R.C.S., Helston.
25. Monthly Meteorol. Obs. by Dr Hoskins, Guernsey.
26.
34.
48,
Annales de l’Observatoire Physique Central de
Russie, 1837-64. ;
. Reports of British Association.
- Meteorologiske lagttagelser i Norge; and Letter
from Professor Mohn, Christiania.
. Meteorologische Beobachtungen K. Universitiats-
Sternwarte zu Christiania, 1837-67.
. Meteorologiska Iakttagelser i Sverige, K. Svensha
Vetenskaps-Akademien, af Prof. Er. Edlund,
1859-66.
. Obs. Météorol. 4 Upsal 1855-62; and Letter from
Prof. Rubensen.
. Oversigt, K. danske Videnskabernes Selskabs, &c.,
Kjobenhavn, 1852-68.
. Nederlandsch Meteorologisch Jaarboek 1855-68.
Sur la Marche Annuelle du Thermométre et du
Barométre, en Neérlande et en divers Lieux
de l Europe, par C. H. D. Buys Ballot.
Météorologie de la Belgique comparée 4 celle
du Globe, par Ad. Quetelet, 1867. Annales
Météorol. de Observatoire Royal de Bruxelles,
1863-68.
- Annuaire de la Société Météorologique de France,
1849-53.
. Annales de l’Observatoire Impérial de Paris,
1857-64.
. Bulletin International, Paris, 1862-69.
. Letter from Prof. Alexis Perrey, Dijon.
. Ann. Com, Hydromet. de Lyon, 1861-66.
. Bulletino Meteorologico dell’Osservatorio del
Col. Romano dal P. Angelo Secchi, D.C.D.G.,
Dirrettore, 1862-66.
. Ann. Soc. Roy. d’ Agricul. de Lyon, 1852.
. Mem. Acad. des Sciences et Lettres de Montpellier.
. Letter from Prof. Cavallo, Lisbon.
. Abstracts Meteorol. Obs. at Stations of Royal
Engineers, 1853-59, edited by Col. Sir Henry
James, R.E. London, 1862.
. Reports of the Director-General, London, 1864—
66.
. Mittheilungen der Naturforschanden Gesellschaft
in Zurich, 1837-46,
. Résumé Météorol. pour Genéve et Grand St Ber-
nard, par Prof. E. Plantamour, 1857-67.
Uber den Jahrlichen gang der temperatur und
des Luftdruckes in Osterreich, von DrK. Jelinek,
Wien, 1866. Jahrbiicher der K. K. Central-
Anstalt fiir Meteorol. und Erdmagnet. von C.
Jelinek und C. Fritsch, 1864-66. Daily ob-
servations from Sixteen Stations in Austria
during 1867.
636 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE
49,
50.
51.
67.
78.
79.
. Reise in Abyssinien.
. Annual Reports on Meteorol. Obs. in the Punjab,
Resultate der an der K. Sternwarte bei Miinchen
von 1857-66. Angestellten Meteorologischen
Beobachtungen.
Preussische Statistik. Die Witterungserschein-
ungen des nérdlichen Deutschlands, von H
W. Dove, 1861-67. Berlin, 1864—7-8.*
Bul. Hebd. del’ Association Scientifique de France;
Atlas Météorol. de l’Obs. Impérial, 1868, D. 4.
. Letters from Dr Buys Ballot, Utrecht.
. Météorol. Beob. angestellt in Dorpat, 1867.
. Obs. Météorol. faites 4 Nijni-Taguilsk, 1845-65.
. Bull. Meteorol. del R. Osserv. di Palermo, vol. v.
p. 72.
. Observations sent by Harbour-Master at Shanghai,
and in China Mail.
Dr Edward Riippel, 1840.
by A. Kiel, M.R.C.S., 1866-67.
. Reports on Meteorol. Obs. in the North-Western
Provinces of India, by Professor Murray Thom-
son, M.D., 1865-68.
. Journal of the Asiatic Society of Bengal.
. Meteorol. Obs. at the Observatory, Bombay,
1847-60.
. Meteorol. Obs. at Secunderabad for 1864, by W.
Arnot Smith, M.D. Madras, 1865.
. Meteorol. Obs. at Dodabetta in 1851-55, by W. S.
Jacob and Major W. K. Worster. Madras,1875.
. Meteorol. Obs. at H.E.1.C. Observatory, Madras.
Madras, 1844 and 1854.
. Zeitschrift der osterreichischen Gesellschaft fiir
Metorologie, 1866-69.
. Letter from Capt. M‘M. Moyle, Sincapore.
Meteorological Papers of the Board of Trade, by
Admiral Fitzroy.
. Du Climat de l’Kgypt, par M. le Dr B. Schnepp.
Paris, 1862.
. Gazette Médicale de l Algérie, 1865-69, and Letter
from Dr Emile Bertherand.
. Bulletin de la Société de Géographie, Paris.
. Journal of the Meteorological Society of England.
. Results of Meteorol. Obs. at Royal Observatory,
Cape of Good Hope, 1842-56.
. Results of Meteorol. Obs. at certain Stations in
Cape Colony, 1861-65, compiled by a Com-
mittee appointed by Government.
. Letter from Dr Mann, Pieter Maritzburg.
. Proceedings of the Meteorological Society of
Mauritius, 1866, page 23.
. Meteorol. Tables of New South Wales; and
Meteorol. Obs. at the Government Observatory.
Sydney, 1858-69.
. Meteorol. Obs. by John Tebbutt, at Windsor.
Sydney, 1868.
Statistics of Victoria. Letter from R. L. J.
Hillery, President of Royal Society, Melbourne.
Climate of Victoria, by R. L: J. Ellery.
Meteorol. Obs. in South Australia, under the direc-
tion of Charles Todd, 1861-68.
80.
81.
90.
91
92.
93.
94.
95.
96.
97.
98.
99.
Results Meteorol. Obs. for Hobart Town, 1841-65,
by Francis Abbott, F.R.A.S.; Meteorol. Ab-
stracts and Monthly Notices and Papers of
Roy. Soc. Tasmania, 1856-68, do.
Statistics of New Zealand, 1866-68. Letters and
Annual Meteorol. Reports of Christchurch
and Hokitika for 1864-67, from R. L. Holmes,
Colonial Museum, Wellington. Meteorol.
Report, 1868, by James Hector M.D., F.R.S.,
Wellington, 1869. Letter from Charles Rous
Marten, Martendale, Southland.
. Physical Observations in the Arctic Seas, by Isaac
Hayes, M.D., Smithsonian Institution, p. 218.
. Scoresby’s Voyages to the Arctic Regions, and
Transactions Wernerian Society, Edinburgh -
1811-14.
. Abs. Meteorol. Obs. at New Westminster, British
Columbia, by Col. Sir Henry James, R.E.
London, 1861.
. Vancouver Island and British Columbia, by Alex-
ander Rattray, M.D. london, 1862.
. R. S. Williamson on the Use of the Barometer
on Surveys and Reconnaissances.
1868, pp. 79-81.
New York,
. Results of Meteorol. Obs. 1854 to 1859, vol. i.,
Smithsonian Institution. Washington, 1861,
. Canadian Journal of Science.
. Meteorol. Obs. made at Providence, R.I., United
States, by Prof. Alexis Caswell.
Institution.
Discussion of Meteorol. Phenomena, U.S. Naval
Observatory, App. I. to Washington Astron.
and Meteorol. Obs, for 1866.
Meteorological Elements, from Obs. at the Ob-
servatory, Georgetown, Demerara, British
Guiana, 1846-56, by Patrick Sandeman.
Greenock, 1857.
Smithsonian Report for 1867, p. 473.
Letter from Professor M. V. Raulin, Bordeaux.
Nouvelles Météorologiques de la Société Meé-
téorologique de France.
Le Climat de Madére, par F. A. Barral, M.D.
Pilot Charts for the Atlantic Ocean, issued by
Hydrographic Department of the Admiralty.
London, 1868.
Magnet. and Meteorol. Obs. at St Helena, vol. ii.,
edited by General Sabine, P.R.S. London,
1860.
Atmospheric Tides and Meteorology of Dukhun,
by Lieut.-Col. Sykes, F.R.S., Phil, Trans. Roy.
Soc. 1835, part i.
Meteorol. Abst. for Hamilton, C.W., 1849-53,
sent by the Rev. Charles Clouston, LL.D.,
Sandwick, Orkney.
Smithsonian
100. The States of Central America, by E. G. Squier,
p. 763. London, 1858. 3
101. La Plata, the Argentine Confederation and
Paraguay, by T. J. Page, U.S.N. New York,
1859.
* The Heights of the Prussian Stations are taken from a Paper by Dove in “ Geographisches Jahrbuch,” edited
by Behm. Gotha, 1868.
AND THE PREVAILING WINDS OVER THE GLOBE.
102. Descrip. Géograph. et Statist. de la Confédéra-
tion Argentine, par V. Martin de Moussy.
103. Annual Reports from the Registrar-General,
Queensland, Australia, 1866-68. Summa-
ries of Meteorol. Obs. taken at Brisbane,
Queensland. Sent by Edmund MacDonnell,
637
Government Meteorological Observer, Bris-
bane.
104. Voyage to the Southern and Antarctic Regions
during 1839-43, by Captain Sir James Clark
Ross, R.N. London, 1847.
105. Gordon on China. London, 1863.
B, For Winps (Tastss IJ. anp III.)
The authorities for Winds are the same as for the Barometers, if not otherwise stated below.
Curron.—Dr W. C. Burder’s Meteorology of Clifton.
London, 1864.
GrEEnwicu.—Proceedings Meteorol. Soc. Eng., vol. i.
p. 21.
Varpo, 70° 22’ lat., N., 31° 7’ long. E.; Tacanroa,
47° 12’ lat. N., 38° 57’ long. E.; East or Nova
ZemBia, 70° 37’ lat. N.—Annales Obs. Phys.
Cent. de Russie.
Smipstrup, 55° 46’ lat. N., 9° 33’ long. E.; Tarum,
55° 26’ lat. N., 8° 39’ long. E.—Aarsber. K.
Landhunsh. Meteorol. Comittee, 1861-67.
Bremen, 53° 5’ lat. N., 8° 43’ long. E.—Abhand-
lungen vom natur. Vereine zu Bremen, 1867.
Lisson.—Meteorol. Journal kept by Walter Ivens,
Lisbon.
Me tvitze Is., Ienoormx, Winter Is., Narn, 56° 25’
lat. N., 62° 15’ long. W.; Norway Ho., 53° 43’
lat. N., 98° 30’ long. W.; Fort Towson, 34° 0/
lat. N., 95° 33’ long. W.; Fort Jounson, 33° 54/
lat. N., 78° 3’ long. W.; Wazo11.—Professor
J. H. Coffin’s Winds of Northern Hemisphere.
Smithsonian Institution, Washington, 1853.
Fort Conrrpence.—Maen. and Meteorol. Obs. at Fort
Confidence, Gt. Bear Lake. By Sir John Richard-
son, C.B., M.D. London, 1855. P. 389.
San Drrco, 32° 42’ lat. N., 117° 14’ long. W. ; Srerna-
coom, 47° 10’ lat. N., 122° 25’ long. W.; Fort
Leavenworth, 39° 21’ lat. N., 94° 44’ long. W.;
Cantonment Lorine, 43° 4’ lat. N., 112° 27’ long.
W. (4800 feet); Fort Yuma, 32° 43/ lat, N.,
114° 36’ long. W.; Sanra Fr, 35° 41’ lat. N.,
106° 2’ long. W.; Maramoras, 25° 56’ lat. N.,
97° 36’ long. W.—Army Meteorol. Register from
VOL. XXV. PART II.
Obs. made at Military Posts of the United States,
1843-54. Washington, 1855.
York Factory, 57° 5’ lat. N., 98° 15’ long. W.
—Manuscript Register of Daily Obs., 1843-48,
sent by the Rey. Charles Clouston, LL.D.,
Orkney.
Rep River Serrrement, 50° 0’ lat. N.,90° 0’ long. W.;
New Orurans, 29° 57’ lat. N., 90° 0’ long. W. ;
Key West, 24° 33’ lat. N., 81° 48’ long. W.;
Derrorr, 42° 24’ lat. N., 83 °O’ long. W.; Green-
Bay, 45° 0’ lat. N., 87° 30’ long. W. ; Hazrnwoop,
45° 0’ lat. N., 95° 0’ long. W.; Oswxao, 43° 25’ lat.
N., 76° 35’ long. W.; New Yorn, 40° 43’ lat.
N., 74° 5’ long. W.—Results of Meteorol. Obs.
made from 1854 to 1859. Smithsonian Institu-
tion. Washington, 1861.
Brunswick, 43° 52’ lat. N., 70° 1’ long. W.—Results
of Meteorol Obs. made at Brunswick, Maine, by
Parker Cleveland, LL.D., Smithsonian Institu-
tion. Washington, 1867.
Marierra, 39° 25’ lat. N., 81° 29’ long. W.—Results
of Meteorol. Obs. made at Marietta, Ohio, by S.
P. Hildreth, M.D., Smithsonian Institution.
Washington, 1868.
CocHanamsBa, 17° 20’ lat. S., 65° 45’ long. W.—Ex-
ploration of the Valley of the Amazon, by Lieut.
Lardner Gibbon. Washington, 1854.
Asuncion, 25° 16’ lat. S., 57° 45’ long. W.—Do., and
same as for Barometer.
Bansermassine, Banyorwaneiz, PatEemBanc.—
Nederlandsch Meteorolo. Jaarboek.
Awnpenes, VitLA, Berern, Lister, Linprsnes.—Letter
from Professor Mohn, Christiania.
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Dickson, M.D. delt WHOM Farlane, Lith? Edin
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Plate XXIX.
s. Roy. Soc. Edin? Vol. XXV.
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( 639 )
XVIII.—On the Development of the Flower of Pinguicula vulgaris, Z.; with
Remarks on the Embryos of P. vulgaris, P. grandiflora, P. lusitanica, P. caudata,
and Utricularia minor. By ALExanper Dickson, M.D. Edin. & Dublin. ;
Regius Professor of Botany in the University of Glasgow. (Plates XXVHI—
XXX.)
(Read 19th April 1869.)
The order Lentibulariaceze is usually described in systematic works as
exhibiting affinities, on the one hand with Scrophulariaceze, which it resembles
in the bilabiate corolla, partial suppression of the androecium, bilabiate stigma,
and two-valved capsule; and, on the other, with Primulaceze and its allies, with
which it agrees in having a truly free central placenta.
Linbey places the order in his alliance of Bignoniales, along with Scrophu-
lariaceze, apparently following Mr Benrnam, whom he quotes in support of the
supposed affinity between the families.* Others, again, more impressed with the
importance of the placental character, place the family near Primulaceze, as has
been done by PayEr.+
In the hope that the study of the development of the flower in Lentibulari-
acese might throw some light on the question of the affinities of the order, I
have, from time to time during several years past, taken up the investigation of
the organogeny of the flower of Pinguicula vulgaris, according as opportunities
occurred for collecting suitable material; and I now venture to lay my results,
imperfect as they still are, before this Society.
If a plant of Pinguicula vulgaris be examined during the flowering season, it
is found to exhibit a short axis, on which are crowded a variable number of
leaves, spreading out in a rosette-like manner upon the surface of the soil or turf
on which the plant is found. This short axis is terminated by a contracted
indefinite inflorescence, consisting of a variable number of ebracteate flowers with
long pedicels—an unstalked umbel, in fact, analogous to that in the ordinary
form of Primula vulgaris. _ Immediately below the inflorescence, a leaf-bud is
found in the axil of the last leaf. As the fruit ripens, the leaves of the main
axis gradually wither off, and the main axis itself decays; the original rosette
becoming replaced in the autumn by a similar one, resulting from the develop-
ment of the axillary bud of its last leaf. On the approach of winter, the
* Vegetable Kingdom, p. 686. + Lecons sur les Fam. Nat. des Plantes, p. 14.
VOL. XXV. PART II. 8D
640 DR DICKSON ON DEVELOPMENT OF
expanded outer leaves of the autumn rosette disappear; the central portion
remaining as a firm, bulb-like, winter-resting bud, the outer leaves of which are
developed as somewhat fleshy scales. This bulb-like bud remains during the
winter sunk in the soil, or among the surrounding moss; and, on the return of
warm weather the next season, expands into the summer-rosette, terminated by
the inflorescence as above described.
Rudiment of the Inflorescence in Winter-Bud.
On removing the leaves from the winter-resting bud, the following struc-
tures appear :—1s¢, A cushion-like mass in the axil of the last leaf, the rudiment
of the bud which developes the autumn-rosette of the next season, and becomes
the flowering plant of the summer thereafter. This cushion usually (always?)
appears somewhat depressed, in a direction corresponding to the middle line of
the supporting leaf, as I have indicated in Plate XXVIII. fig. 1; but as to the
significance of this median furrow, I am unable to offer any suggestion. 2d, The
termination of the main axis, which appears as an unequally three-sided cushion,
nearly flat on the top, and with rounded angles, the largest and thickest of which
represents the rudiment of the first flower, the angle next in size representing
that of the second flower, and the remaining angle (often very obscure) that of
the third flower.
These floral rudiments continue, as to position, the spiral succession of the
leaves upon the main axis. If a number of plants be examined, the spiral will
be found running sometimes to the right, and sometimes to the left, in about
equal proportions (see figs. 1, 2, 3,4, 5, and 9). The fraction expressing the leaf-
arrangement appears to be ;®; approximately; and the spiral succession of leaves
developed upon the axillary shoot of the last leaf is homodromous with that
of the main axis.
Early Obliquity of the Floral Axis.
Almost as soon as the young flower has begun distinctly to project from the
axis of inflorescence, and before there is any appearance of sepals or other floral
parts, it is seen to be more developed on the anterior aspect (that furthest from
the axis of inflorescence) than on the posterior. At this stage the young flower
appears as a short cylindrical body, the free extremity of which is flattened ina
direction from above anteriorly, downwards posteriorly (see Plate XXVIII. fig. 2).
This very early indication of irregularity is noteworthy, from the circumstance
that, as a rule, irregularity commences to show itself only with, or shortly after,
the appearance of the appendicular organs.
Calyx. ;
The sepals make their appearance a little below the obliquely flattened
FLOWER OF PINGUICULA VULGARIS, ETC. 641
extremity of the floral axis. The two anterior are developed first (Plate XXVIII.
fig. 3). Of the lateral sepals and the posterior one, I have not been able satis-
factorily to determine the relative time of appearance; but there can be little
doubt that the lateral precede the posterior. The sepals soon become connate
with each other; but unequally so, the two anterior with each other, and the
posterior with the lateral, respectively forming an anterior lip with two lobes,
and a posterior with three. These lips are almost free from each other, the
antero-lateral connation being very slight. When the sepals are sufficiently
developed to cover in the young flower-bud, they are found, in the great majority
of cases, so arranged, that the posterior sepal is overlapped by the lateral ones,
which are in turn overlapped by the anterior (Plate XXIX. fig. 15). The anterior
sepals, as a rule, have not their surfaces in contact.*
Corolla.
The examination of the earliest appearance of the corolla has been the most
unsatisfactory part of my research. Its parts very soon become connate, if,
indeed, they are not ‘‘congenitally’ so. Jam inclined to think that, as in the
calyx, its anterior portion is developed first ; the anterior petal appearing to me
to be a more salient projection than the others in the early condition. In Plate
XXVIII. fig. 4, I have represented a young flower, where the corolla is seen as a
rim-like, faintly angular edging to the receptacle, just within or above the calyx,
its angles alternating with the sepals. Here the stamens have not yet made their
appearance, unless the very slight furrow in the middle line anteriorly be held
as indicating, indirectly, the presence of the anterior stamens, one on either side
of it. At this stage the centre of the receptacle is seen to exhibit a slight con-
cavity, chiefly in the antero-posterior direction, a concavity which becomes still
more marked in the subsequent stages represented in Plate XXVIII. figs. 5 and 6,
and which I shall have further occasion to refer to in connection with the de-
velopment of the pistil. The growth of the corolla appears to continue uninter-
ruptedly until its full development, not exhibiting the pause which occurs so
frequently in its course in other plants. As the calyx does not at all keep pace
with the corolla, the latter soon forces its way from between the sepals, which
at an early period are folded over it; and, in consequence of this, it is only
in comparatively young flower-buds that the eestivation of the sepals can be
observed. A little before the sepals are thus pushed aside, the spur of the corolla
begins’to appear, as a small dilatation from within of the tube of the corolla at
its base, in the middle line anteriorly, indicated externally by a rounded knob-
* Exceptions are sometimes met with. I have seen the posterior sepal overlapping only one of
the lateral ; or one, or both of the lateral sepals wholly external. A hasty observation of such an
exception as the last, probably led Payer (Legons, p. 14) to describe the estivation of the calyx as
quincuncial, which I can hardly believe it ever is.
642 DR DICKSON ON DEVELOPMENT OF
like projection. The process of dilatation or expansion commenced in this portion
of the corolla-tube progresses gradually until the period of flowering, by which
time the characteristic spur is fully developed. As in the calyx, the connation
of the parts of the corolla is unequal in extent, the anterior and lateral petals
forming an anterior lip, and the two posterior a posterior one. The estivation of
the corolla is similar to that of the calyx—that is to say, the odd part (here, of
course, anterior) is overlapped by the lateral, which are overlapped by the other
two parts.
Andrecium.
In the adult condition, the androecium of Pinguwiculu consists of two stamens
placed anteriorly. The examination of the flower in its earlier stages, however,
reveals the interesting fact of the presence of two lateral rudiments or staminodes.
The two fertile stamens appear first—at least they may be seen as distinctly
present when the staminodes are as yet very indistinct, if not quite inappreciable.
Their appearance seems to follow that of the corolla in quick succession, from
the great difficulty I have experienced in finding flowers having the corolla dis-
tinctly visible, with at the same time no trace of the stamens. Indeed, even in
the stage represented in Plate XXVIII. fig. 4, although the stamens can scarcely be
said to be visible, yet, as I have already said, the slight indentation in the middle
line anteriorly may possibly be held as indicating, indirectly, the presence of a
staminal elevation on either side of it. :
The stamens originate as rather large protuberances, which very soon exhibit
an oblong figure, being wider from side to side than deep from without inwards.
They alternate with the petals, being superposed to the two anterior sepals. In
their further development there is nothing very special to be noted. As usual,
the anther is formed first, becoming raised upon the subsequently developed fila-
ment. The connective forms the great bulk of the young anther, and broadens
upwards in such a way that the four anther-cells lie upon its upper surface, what
correspond to lateral furrows forming a single transverse one across the top of the
anther. Ultimately the anther becomes one-celled, by the occurrence of absorp-
tion in the substance of the connective and consequent fusion of the anther-cells.
Dehiscence takes place at the transverse furrow just mentioned.
The staminodes originate as mammillze of small size, compared with the
staminal rudiments, and are superposed to the lateral sepals. They are repre-
sented in different stages in Plate XXVIII. figs. 5-9. As a rule, they do not
proceed beyond the stage represented in fig. 7, and usually become wholly
obliterated by the disproportionate development of the neighbouring parts.
Sometimes, however, they are developed as shorter or longer styloid processes ;
and I have met with a good many instances where one or both presented a
terminal knob, or were even distinctly antheriferous; in the best developed cases
FLOWER OF PINGUICULA VULGARIS, ETC. 643
being scarcely distinguishable from the normal stamens. In Plate XXX. fig. 31,
I have represented the essential organs of a flower where a moderate degree of
this condition is to be seen, accompanied by an interesting reversion to regularity
in the stigma, to which I shall afterwards refer.
Pistil.
The pistil appears very quickly after the development of the androecium ; it
being a matter of some difficulty to find a flower with the staminodes visible
that does not, at the same time, exhibit some vestige of the pistil. It makes its
first appearance as a semilunar elevation placed anteriorly just within, or (from
the downward slope of the receptacle) below the two fertile stamens, with which
it alternates. The extremities of this semilunar elevation gradually extend
themselves around the organic centre of the receptacle, till they meet in the
middle line posteriorly. The ovarian wall, thus completed, grows up as a short
tube, which very soon exhibits a tendency to bilabiation, the result of pre-
ponderating growth, anteriorly and posteriorly (Plate XXVIII. fig. 9). The orifice
of the short tube constituting the young ovarian wall, at first nearly circular,
very soon becomes narrowed in the antero-posterior direction. This narrowing,
apparently, is mainly caused by the inclination of the anterior and posterior
walls towards each other, in consequence of the antero-posterior concavity of
the receptacle, to which I have above alluded.* The antero-posterior inclination
towards each other of the ovarian walls, is well seen in the sections represented
in Plate XXIX. figs. 12 and 13. The anterior and posterior walls thus inclined
towards each other, at last come in contact, whereby the cavity of the ovary is
closed in above. From this point of contact the lips of the ovarian margin, in
their further development, curve away from each other; the one posteriorly as
a narrow strap-like body; the other anteriorly as a broadly expanded lamina,
which rests upon and ultimately wholly conceals the anthers of the two fertile
stamens (Plate XXIX. fig. 11). These lips become covered on their upper
surface by papillee, and together constitute an unequally bilabiate stigma. The
part where the ovarian walls are in contact becomes somewhat elongated (ap-
parently to a variable extent), and constitutes the short style. The basal portion
of the pistil becomes dilated, forming the ovary proper. It is to be noted that
the ovary is to a certain extent inferior posteriorly—that is to say, its cavity
posteriorly extends distinctly below the level of the insertion of the calyx and
corolla.
Placenta and Ovules.
In the earlier stages of the development of the flower, and up to the time when
* The slight bilabiation of the ovarian orifice seen in Plate XXVIII. fig. 9, though real, is
doubtless in appearance considerably exaggerated by this antero-posterior narrowing.
VOL, XXV. PART II. SE
644 DR DICKSON ON DEVELOPMENT OF
the ovarian wall is completed posteriorly, by the coalescence of the extremities
of the original semilunar elevation, the organic centre of the receptacle is some-
what depressed. Almost as soon, however, as the ovarian wall is complete, the
receptacular centre enclosed by it begins to be developed as a more or less hemi-
spherical protuberance—the young placenta. At no period of its development has
it any connection with the ovarian wall: it is as truly ‘‘ free-central” as that in
Primulaceze. The ovules make their appearance first on the top of this hemi-
spherical placenta, and continue to appear in succession from above downwards,
until the surface is covered by them (Plate XXIX. fig. 16). This placenta does not
exhibit the slightest trace of the barren apex, which is so characteristically present
in that of Primulaceze—not even a bare spot,—but is uniformly and densely
crowded with ovules over its whole surface. The ovules originate as small
mammille, which become invested with a single integument, and undergo the
anatropal curvature, as represented in the series given in Plate XXIX. figs. 17-22.
They are placed so that the raphe is superior where the ovules project horizon-
tally, internal where they have an upward direction, and external where they
have a downward one.
Abnormalities.
In the course of the examination of numerous flowers, for the purposes of the
foregoing investigation, I have met with a considerable number of cases of abnor-
mality or monstrosity, some of which I think worthy of being recorded.
In Plate XXX. figs. 23 and 24, are represented two cases of remarkable modi-
fication inthe symmetry. In fig. 23, the flower is dimerous and regular, with two
sepals, two petals, and two stamens, in decussate succession. The ovary here is
as yet only faintly indicated.* In fig. 24, there are six sepals, of which one is
anterior, one is posterior, and four are lateral, these last being conveniently
distinguishable as antero-lateral and postero-lateral. Alternating with the sepals
are six petals. There are five parts of the andrcecium, viz., two fertile stamens
superposed to the antero-lateral sepals, and three staminodes, of which two are
superposed to the postero-lateral sepals, and the third is placed between the two
fertile stamens, and thus superposed to the anterior sepal.
The other abnormalities I have figured are some very interesting ones affect-
ing the pistil. In fig. 25, the posterior wall of the ovary is deficient, the
placenta and ovules being exposed; the result, doubtless, of imperfect coal-
escence of the extremities of the primitive semilunar elevation, a defect of
development analogous to spina bifida, cleft-palate, hypospadias, &c., in the
animal subject. In fig. 26, the posterior (small) lip of the stigma is seen
to be bipartite. In this, as in the last abnormality, we have impressed upon us
* This flower was unfortunately detached before I had ascertained whether the sepals weie
antero-posterior or lateral.
FLOWER OF PINGUICULA VULGARIS, ETC. 645
the fact that the posterior middle line of the ovarian wall is a line of suture,
and in consequence that the small posterior lip of the stigma is potentially
a double organ.* In fig. 27, the posterior lip is normal, but the anterior
(large) lip is tripartite. Fig. 28 represents a left} antero-lateral view of the
same pistil, showing a slightly marked lobule (/i/) at the base of the antero-
median lobe; the right antero-lateral fissure, however, was found to be uncom-
plicated by any such lobule. Fig. 29 exhibits a nearly anterior view of an ab-
normality very similar to the last; but where a lobule occurs on either side of
the base of the middle anterior lobe, that on the left side (to the right hand in
the figure) being developed to about the same exent as the corresponding lobule
in the last abnormality, while the lobule on the right side is considerably more
distinct.{ I have represented in fig. 30 a pistil with the posterior lip somewhat
broader than usual, though undivided, and the anterior lip cleft down the left
side, thus exhibiting one antero-lateral fissure.§ A very small notch is seen on
the right side, which possibly may be held as representing a right antero-lateral
fissure. In fig. 31 is seen an abnormality of quite another character. Here the
stigma is altogether undivided and almost quite regular, resembling a funnel the
walls of which are to a great extent turned inside out from reflection of the
margin. As I previously mentioned, when treating of the andrcecium, the two
staminodes here are well developed, with distinct filaments and anther-like
terminal knobs.
Morphological Constitution of the Ovary.
In connection with the monstrous pistils just described, and of course always
keeping in view the normal course of development, I would here make a few
observations as to the probable morphological constitution of the ovary. The
ordinary view has hitherto been, that the ovary in Lentibulariaceze is bicarpellary,
a view supported by the bilabiate stigma, bivalved capsule, and last, not least, by
the fact that of the somewhat numerous vascular bundles entering its walls, the
two strongest are in the mesial plane, one anteriorly the other posteriorly. This
view, however, must be set aside in the face of developmental facts, which show
the posterior middle line to bea line of suture. Ifit be objected that the presence
of a strong vascular bundle in the posterior middle line constitutes a difficulty, I
need only point to the interpetiolar stipules in Cimchona, where we have a well-
marked vascular bundle occupying the middle line of the stipule, although that
middle line is the line of a suture, and not of a true midrib. There are, it seems
* T have met with three instances of this bipartite condition of the posterior lip.
+ To the left of an observer supposed to stand in the axis of inflorescence.
t I have in my possession a third example of an ovary with tripartite anterior lip, but as I
have been unwilling to remove the stamens from the specimen, I cannot say what appearance is pre-
sented on an anterior view; its posterior aspect, however, is almost identical with that given in
Plate XXX. fig. 27.
§ This antero-lateral fissure is uncomplicated by any lobule.
646 DR DICKSON ON DEVELOPMENT OF
to me, only two suppositions possessing any elements of probability and com-
patible with the history of development: either the ovary consists of one carpel,
embracing the extremities of the receptacle; or it consists of five connate carpels,
as in Primulaceee.
With regard to the first supposition it will, I think, be admitted that it is,
a priori, improbable that a corollifloral plant, like Pingwicula, should have only
one carpel; all the orders with which it might possibly be compared having com-
pound ovaries. On this ground alone I should be inclined to dismiss the idea.
On the other hand, the 5-carpellary hypothesis has the support of the mon-
strosities just referred to. In some we have the posterior lip of the stigma bipar-
tite, in others the anterior lip tripartite.* Now, if we combine these monstrosities,
we obtain five parts, and these placed in the proper position—superposed to the
petals. Were we to take the ovary of Primula, which originates as an entire
annulus, and so modify its development that its anterior part should appear first
(just as the anterior part of the calyx in Pinguicula appears first), we should
have a structure originating in semilunar form exactly as in the young ovary of
Pinguicula. That five connate carpels should go to form a bilabiate stigma, is
just what might be expected in a family where the tendency to bilabiation is so
strongly marked. To take an extreme case, I may refer to Utricularia minor,
where the corolla, with two vascular bundles going to its upper and three to its
lower part, is bilabiate with two perfectly entire lips.
General Conclusions.
A few words may be said with regard to the probable affinities of the order
Lentibulariaceze. In the first place, I shall allude to the opinion of Mr BentHam,
as quoted by LinpLEY (Veget. Kingd. p. 686), to the effect that they are very
closely related to Scrophulariaceze, in ‘‘ having the same calyx, corolla, stamens,
and bivalve capsule, but distinguished solely by their realby unilocular fruit, with
a free central placenta, and the minuteness of their embryo. In respect of the
former character, they come very near to Limosella, Lindernia, and other Gratiolee,
with parallel dissepiments and entire valves; for in these plants the dissepiment
is very thin, and usually detaches itself from the valves before maturity, so that
being concealed by the seeds, which fill nearly the whole capsule, it often escapes
observation, and many of these genera have frequently been described as having
a unilocular fruit.”
Having, as I think, satisfactorily set aside the idea that the ovary of Lenti-
bulariaceze is bicarpellary, it is, perhaps, unnecessary on my part to refer to Mr
BENTHAM’s view, that the premature detachment from the valves of the thin
* The variable and inconstant lobules at the base of the middle anterior lobe in this form of
monstrosity I am, I think, justified in considering of secondary importance.
FLOWER OF PINGUICULA VULGARIS, ETC. 547
dissepiments in the Gratioleze is an indication of an approach to the structure of
an ovary with free central placenta; I would only suggest that this is an idea
of the same character, and quite as fallacious, as the popular one that the pecu-
liar splitting of the fruit in Platystemon indicates an approach in that plant to
the apocarpous Ranunculaceze. If, then, any affinity with Scrophulariaceze is to
be found it must be in the floral envelopes and stamens. In Lentibulariaceze we
have, no doubt, irregular bilabiate floral envelopes and partial suppression of the
andreecium with a tendency to the didynamous structure; but the value of this
combination of bilabiation with didynamy as determining the true affinities of a
given plant is seriously open to question. It must, I think, be evident to any
one reflecting on the subject, that such a combination of characters occurs in
several very different types, by what may be called a parallelism of development
or modification. Thus,
lst, In Scrophulariacee, with 2-celled ovary and axile placentation; a
modification of the Solanaceous type.
2d, In Gesneraceze and Orobanchaceze, with l-celled ovary and parietal
placentation ; a modification of the Hydrophyllaceous (?) type.
3d, In Labiate, with gynobasic style and spuriously multiplied loculi; a
modification (in spite of the difference in the position of the raphe)
of the Boraginaceous type.
4th, In Morina (belonging to the order Dipsacacee), where we have a
bilabiate corolla of five petals, and four stamens, two large and two
small.
On the whole, it seems to me that we have as little right to associate Lenti-
bulariaceze with Scrophulariaceze on account of bilabiate floral envelopes and
more or less didynamous stamens, as a zoologist would have to associate the
Echidna with Hedgehogs or with Porcupines, on account of the remarkable
correspondence in their prickly defence.
With regard to the supposed affinity with Primulaceze, we have a correspond-
ence in what may perhaps be viewed as the most remarkable structure in the
Lentibulariaceous flower, viz., the free central placenta; and I have shown at
least some plausible grounds for believing the Lentibulariaceous ovary to be com-
posed of five carpels, like that of Primulaceee. The important differences between
the orders may thus be reduced to the position of the stamens and the albuminous
or exalbuminous character of the seeds.
PAYER, in his Lecons sur les Fam. Nat. des Plantes, places the order Salvador-
acez (consisting of the single genus Salvadora) in juxta-position with Lenti-
bulariaceze. Both agree in the superposition of the stamens to the sepals, in
having a unilocular ovary with free central or basilar placentation, and in the
exalbuminous character of the seed. The question very naturally suggests itself,
VOL. XXV. PART II. 8F
648 DR DICKSON ON DEVELOPMENT OF
have we not in Salvadora, with oppositi-sepalous stamens and solitary exalbu-
minous seed,* a plant bearing the same relation to Lentibulariaceze, with numerous
exalbuminous seeds, as Plumbaginacez, with oppositi-petalous stamens and
solitary albuminous seed, bears to Primulaceze, with numerous albuminous seeds ?
I believe that in Salvadoraceze with Lentibulariacese, on the one hand, and
Plumbaginaceze with Primulaceze, on the other, we have two parallel nearly
allied series. I shall not, however, pursue this subject further, as my personal
knowledge of Salvadora is very limited.
Diagram of the flower of Pinguiewla vulgaris, L., showing the estivation of calyx and corolla, the stamens and
staminodes superposed to the anterior and lateral sepals, and the one-celled ovary with free central placenta.
The wall of the ovary is represented as divided into five parts by two plain and three dotted lines, the two
plain lines representing the division of the stigma into two lips or of the capsule into two valves, the three
dotted lines representing the abnormal fissures in the above mentioned monstrosities.
* Wicut (Icones pl. Ind. Orient. t. 1621), Enpiicuzr (Genera, p. 349), Linpiey (Veget.
Kingd. p. 652), and Payer (Legons, p. 14) agree in describing Salvadora as having a unilocular
ovary with solitary erect ovule. Professor Oxrver has kindly examined for me flowers of S. persica,
L., and S. Wightiana, Pl., from the Kew Herbarium, of which he reports in a letter as follows :—
“In each of these I find a 1-celled ovary with a solitary basal ovule.” My own somewhat limited
examination of the flowers of S. persica has led me to the same conclusion. On the other hand,
Prancuon (Sur les Salvadoracées, Ann. des Sc. Nat. 8° serie x. p. 190), and more recently MM.
Maovur and Decaisne (Traité de Botanique, p. 453) describe the ovary here (PLANCHON in the
genus Salvadora, Maout and Decaisyz in the order Salvadoracez) as bilocular, with two collateral
ascending ovules in each cell. The only explanation I can suggest for the statement in the “ Traité
de Botanique,” is that the authors have probably followed Prancuon, for M. Decaisnz had formerly
described S. oleoides as having ‘‘ovarium . . . uniloculare, loculo uniovulato”’ (Jacquemont
Voyage, p. 140, t. 144); while M. Prancuon’s description is so opposed to the results of other
botanists, and so unlike anything I myself have been able to see, that I am constrained to believe
that it was some other plant, and not Salvadora, that he examined. I should mention, however, that
Decatsne (Jacquemont Voy, t. 144) gives a figure of a fruit of S. Madurensis containing three seeds.
FLOWER OF PINGUICULA VULGARIS, ETC. 649
Remarks on the Embryos of Pinguicula vulgaris, P. grandiflora, P. lusitanica,
P. caudata,* and Utricularia minor.
The remarkable diversity in the structure of the embryo in the Lentibu-
lariaceze is, perhaps, one of the most extraordinary circumstances connected
with the order. A. DE St Hizarre pointed to the occurrence of a dicotyledonous
embryo in P. lusttanica, a monocotyledonous one in P. vulgaris, and an acotyled-
onous one in Utricularia vulgaris, as an instance of how the most important
characters may vary, even within the limits of a single order.t
TREVIRANUS, in 1838,{ was the first to show that the embryo of P. vulgaris
has only one cotyledon. In 1848, he published his researches on its germination,
which were called forth by a statement of Kiorzscn’s, that this embryo germin-
ates with two cotyledons, of which one is much smaller than the other. Here,
he showed that KLorzscu’s smaller cotyledon does not appear until germination
is considerably advanced, thus proving that it does not legitimately fall under
the definition of a cotyledon at all.§
P. vulgaris, L. (Plate XXX. figs. 33-40).
The embryo of Pinguicula vulgaris, taken as a whole, is of a cylindrical form,
with rounded extremities, and measures about 34,d of an inch inlength. The
single cotyledon constitutes about one-half of the entire length of the embryo,
and is folded upon itself in a conduplicate manner, its margins being approximate
and parallel to each other, except towards the base, where they diverge rather
suddenly, leaving a considerable interval, where the termination of the embryonic
axis (rudimentary plumule) is to be seen (fig. 33). The apex of the cotyledon is
almost constantly entire, or, at least, not sufficiently emarginate to appear dis-
tinctly so in a back view, such as is represented in fig. 34. In two, or at most
three instances, however, out of the large number of embryos that I have
examined, the tip of the cotyledon was somewhat bifid, as is seen in the back view
in fig. 35. When sections made in the mesial plane (fig. 38) and at right angles
to it (fig. 37) are compared, the rudimentary plumule is seen to be compressed
laterally, having a strong convex curvature from side to side, while there
is only the slightest possible convexity from before backwards. That there
* The observations on the embryo of this species were made after the paper had been sub-
mitted to the Society.
t Morphologie, pp, 755-6.
t In a communication to a meeting of naturalists, at Freyburg in Br., of which I have
seen no report, but which is referred to by Treviranus in his subsequent paper in the Bot.
Zeitung, 1848.
§ Botanische Zeitung, 1848, p. 444.
650 DR DICKSON ON DEVELOPMENT OF
is no trace of a second cotyledon is quite evident from examination of the
mesial sections.*
P. grandiflora, Lam. (Plate XXX. figs. 41-42).
After examining the embryo of P. vulgaris, I was curious to ascertain whether
there was any difference between it and that of this species, which is so nearly
allied to P. vulgaris that some botanists are disposed to combine them together ;
and I was gratified to find embryonic characters by which they may readily be
distinguished from each other. In front view (fig. 41), the embryo of P. grandiflora
(which is about the same size as the last) exhibits a single cotyledon having about
the same relative length to the whole as that of P. vulgaris. The base of the
cotyledon, however, is found almost completely to surround the extremity of the
embryonic axis, so that hardly a vestige of the plumule is to be seen from the
outside; and on back view (fig. 42), the tip of the cotyledon is seen to be
constantly and deeply bifid.+ The first peculiarity is, so far as I have seen,
absolutely distinctive between this embryo and that of P. vulgaris; while as to
the second one, it is, as I have just mentioned, only in very rare cases that the
cotyledon of P. vulgaris is bifid at its extremity. These embryonic characters,
combined with some other remarkable differences (such as the number of adven-
titious buds produced at the bases of the outer leaves of the autumn-rosette—
in P. vulgaris, usually only one in the middle line of each leaf; in P. grandiflora,
a considerable number in a single transverse row), go far, in my opinion, to
establish the validity of the claim of P. grandijiora to be ranked as a species.
P. lusitanica.
With regard to the very minute embryo of this species (about 3th of an inch
in length), I need not say much, beyond confirming the statements of St Hia1rE
as to there being two cotyledons. These are relatively considerably shorter than
the single one of P. vulgaris or P. grandifiora. I have to note the presence of a
trace of albumen in the seed here.
* Treviranus figure of the embryo from the seed is somewhat faulty, from the cotyledon
being represented as considerably too short in proportion to the radicle, and from the absence of any
indication of the rudimentary plumule. There is also no indication of the plumule in his figures of
the earlier stages of germination, the result, doubtless, of imperfect observation (Joc. cit. t. iv.).
He also makes a curious blunder in describing the apex of the embryo as pointed towards the hilum
of the seed (loc. cit. p. 442), the fact being that in this, as in all anatropal seeds, the apex of the
embryo points away from the hilum, the radicle being directed towards it. This mistake is probably
due to the circumstance that there is often a projecting portion of the testa at the chalazal extremity,
which is apt to be mistaken for the somewhat similar projection at the hilum,
+ I think it not improbable that back views of this embryo may have had something to do with
the statement found in most of the books, that there are two “ cotyledones brevissime” in Pingwicula.
{ I should mention that a very brief statement, by me, of the differences between the embryos
of P. vulgaris and P. grandiflora, has already appeared in the report of a meeting of the Dublin
Microscopical Club (‘‘ Quarterly Journal of Microscopical Science,” viii. pp. 121-2). I now take this
opportunity of describing them in greater detail, and with figures.
CO ———— a a
FLOWER OF PINGUICULA VULGARIS, ETC. 651
‘
P. caudata (Plate XXX. figs. 43-44).
Since bringing this paper before the Society, I have succeeded in extracting
an embryo, almost entire, from one of a very few seeds of this Mexican species
obtained from the University Herbarium in Dublin; and I find that there are
two cotyledons, whose length is about one-half of that of the embryo, which
measures about 1,th of an inch. The embryo here, like the seed containing it, is
very narrow and considerably elongated. I have given two views of this speci-
men, so as to show the division between the cotyledons on either side; from
which the fact that there are two cotyledons is abundantly manifest. In the
specimen figured, one cotyledon is a little shorter than the other; this, however,
is accidental, as the cotyledons were of equal length in another embryo which I
extracted in a somewhat mutilated condition.
Utricularia minor, L. (Plate XXX. fig. 45.)
The embryo here is somewhat globular, about ;,th of an inch in diameter,
and at first sight appears to have a smooth undivided surface; on careful inspec-
tion, however, a remarkable conformation is to be observed of that end of the
embryo which is remote from the hilum of the seed, viz., a minute, slightly
convex punctum vegetationis surrounded by four slight elevations placed so as to-
form the somewhat incurved sides of a square. Iam not exactly prepared to
call these elevations cotyledons; but the whole structure is interesting, as show-
ing this embryo to be a little in advance of a mere “ embryonal globule,” as are
most of the embryos described as ‘“‘ undivided” or “‘ acotyledonous.”’
Explanation of Plates XX VIIT., XXIX., XXX.
Prate XXVIII.
Pinguicula vulgaris.
Fig. 1. Extremity of winter-resting bud, showing rudiment of the inflorescence, and of the axillary
bud of the last leaf. 1’, 3d last leaf cut across; 7’, 2d last leaf; 7, last leaf; ad,
axillary bud of last leaf; #1, indication of 1st flower; #2, that of 2d flower. Leaf-
spiral from right to left of observer supposed to occupy the axis. x 77.
Fig. 2. Young inflorescence further advanced. The first flower (1) distinctly projects, and
exhibits irregularity, being flattened from above anteriorly, downwards posteriorly,
although not even the calyx has appeared. Leaf-spiral from right to left. x 77.
Fig. 3. Young inflorescence, in which the anterior sepals of the 1st flower are beginning to appear
(sa). Leaf-spiral from left to right. x 77.
Fig. 4. Young inflorescence. Here the calyx of the 1st flower is now complete, and the corolla is
visible. s/, lateral sepal ; sp, posterior sepal. Leaf-spiral from right to left. x 77.
Fig. 5. Young inflorescence. Fertile stamens (st) distinctly present, and staminodes (st’) faintly
so in the lst flower. pp, posterior, and pi, lateral petals. Leaf-spiral from left to
right. x77.
VOL. XXV. PART II. 8G
Fig.
Fig.
Fig.
Fig.
Fig
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
DR DICKSON ON DEVELOPMENT OF
6. Young flower. Ovary beginning to appear to the anterior side of receptacular centre as a
semilunar elevation alternate with the anterior (fertile) stamens. x 77.
7. Young flower. The extremities of the semilunar ovarian wall are now extending them-
selves round the receptacular centre. x 77.
8. Young flower. The ovarian wall is now completed by union of the extremities of the
semilunar elevation in the middle line posteriorly. The receptacular centre, hitherto
depressed, is becoming slightly elevated; forming the rudiment of the free central
placenta, x77.
9. Young inflorescence. In the first flower the ovarian wall is completed, and begins to show a
tendency to bilabiation. The fertile anthers now show themselves to be 4-celled.
Leaf-spiral from right to left. x 77.
Puate X XIX,
Pinguicula vulgaris.
10. Young pistil, showing larger or anterior (a) and smaller or posterior (p) lip of the
stigma, The disproportion between the lips is not yet very great. x 85.
11.* Young pistil, considerably further advanced, exhibiting nearly its adult form. Anterior
lip of stigma broadly expanded, the posterior narrow and strap-shaped. x 15.
12. Longitudinal section of young flower at about the stage represented in fig. 9, pst, pistil. The
placental elevation (pc) is now commencing to appear. x 30,
13. Longitudinal section of young flower at a further advanced stage. The ovarian cavity is
becoming somewhat “inferior’’ posteriorly. As yet no ovules. x 30.
14, Longitudinal section of half-mature flower-bud. The corolla now extends beyond the
sepals, and its spur (c) is of considerable length. The ovarian cavity is now nearly
half-inferior posteriorly. x 30.
15. Young flower-bud, showing the zstivation of the sepals, x 15.
16. Young placenta, showing the basipetal succession of the ovules (07), which have as yet
appeared only on its upper part. x 100.
17-22. Outline-sections (partly optical) of ovules at different stages of development. Nucleus
(n); integument (int), In fig. 22 the embryo-sac (es) appears to have wholly
replaced the nucleus.
Puate XXX.
Pinguicula vulgaris.
. 28. Abnormality. Young flower with dimerous symmetry and regular, ; 2 sepals (s), 2 petals
(p), 2 stamens (st). The ovary is faintly indicated. x77.
. 24, Abnormality. Young flower with hexamerous symmetry. Sepals—1 anterior (sa), 2
antero-lateral (sal), 2 postero-lateral (sp/), and 1 posterior (sp). Petals—2 anterior (pa),
2 lateral (pl), and 2 posterior (pp). Two stamens (sf), here antero-lateral ; and three
staminodes (st’), 1 anterior and 2 postero-lateral. x77.
. 26, Abnormal young pistil. Ovarian. wall deficient posteriorly, exposing the placenta and
ovules, «, lappet of doubtful significance. x 15,
26. Abnormal young pistil, with bipartite posterior lip of the stigma. a, anterior lip of stigma ;
p p’, the halves of the posterior lip. x 85.
27, Abnormal young pistil. Anterior lip of stigma tripartite, being divided into an antero-
median lobe (am), and two antero-lateral lobes, one right (ral), the other left (/al.) . x 85.
28. Left antero-lateral view of the same pistil, showing a slightly-marked “lobule” (02) at the
left side of the base of the antero-median lobe. x 8d.
* In this figure, as also in fig. 31, the capitate hairs scattered over the surface of the ovary are
not represented.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fic.
t—)
Fig.
> Hig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
29.
30.
él.
32.
33.
43.
45.
FLOWER OF PINGUICULA VULGARIS, ETC. 653
Nearly anterior view of a monstrous pistil resembling the last; but where there is a
“lobule” (dbl) on each side of the base of the antero-median lobe, that on the right side
(to left hand in the fig.) being considerably the larger. x 85.
Abnormal pistil. Posterior lip of the stigma (») somewhat broader than usual, but undi-
vided, Anterior lip with a fissure on the left side, separating off a left antero-lateral
lobe (Jal). x 85.
Abnormal pistil. Stigma funnel-shaped, and nearly regular, The staminodes (sé’) here
are greatly developed, showing distinct filaments terminated by anther-like knobs. x 15.
Monstrous pitcher-like leaf. The dotted line indicates where the cavity of the leaf termi-
nates below. Natural size.
Embryo. Front view. Solitary cotyledon (c); radicle (7); rudimentary plumule or
punctum vegetationis (pv). x41,
. Embryo. Back view. x 41.
. Embryo. Back view, exhibiting an unusual bifid condition of the extremity of the coty-
ledon, x4.
. Embryo. Side view. x 41.
. Embryo. Longitudinal section at right angles to the mesial plane. x 41.
. Embryo. Longitudinal section in the mesial plane. x 41.
. Embryo. Remarkably curved. x 41.
. Mesial section of embryo similar to the last. x 41.
Pinguicula grandiflora.
. Embryo. Front view. x 41.
. Embryo. Back view. x41.
Pinguicula caudata.
and 44. Views from both sides of one embryo, showing the presence of two cotyledons.
x 43. ”
Utricularia minor.
Embryo, showing punctum vegetationis (pv) surrounded by four very slight elevations (c)
forming the somewhat incurved sides of a square. x 43.
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( 655 )
XIX.—On the Boulder-Clay of Europe. By Davip Minne Home, Esq.
(Plate XXXI.)
(Read 19th April 1869.)
“‘ Boulder-clay” or “till,” abundant in Scotland, and occurring also in Eng-
land, Ireland, and in some other parts of North-Western Europe, has long been,
and still is, a puzzle to geologists.
Sir James Hatt, about fifty years ago, in this Society, was the first to draw
attention to the deposit, by describing its composition, and endeavouring to ex-
plain its origin. He saw that it could not be included in either of the two great
classes into which rocks were then divided. It was a deposit swz generis, bearing
no resemblance to anything known, except a heap of rubbish, there being in the
arrangement of its ingredients no regard to specific gravity or size.
Sir James Hatu ascribed the deposit to diluvial agency, and attempted to
show how the transport of the boulders and pebbles in it, their rounded forms,
and the abrasion of rocks covered by it, might all be accounted for, by supposing
that great waves of the ocean had swept over the country from west to east,
scattering debris in all quarters.*
This diluvial theory was generally accepted, and relied on as satisfactory, until
about the year 1840, when the “ glacier” theory was started, suggested probably
by the discovery that many of the shells found, if not in the boulder-clay itself,
at all events in other pleistocene beds, alternating with it, bespoke an Arctic
climate. |
A strong impulse was given to this new theory by the publication of a
magnificent work, on the Swiss Glaciers, by AGassiz, and by an account of
a visit which was shortly afterwards made by that naturalist to Scotland, in
company with the late Dr BuckLanp. -Both of these eminent men affirmed
that they had seen unmistakable signs of glaciers in almost every valley they
visited. Shortly afterwards, the late Principal Fornes, who had, by frequent
visits to the Swiss glaciers, made himself well acquainted with their action, went
to Skye, and discovered marks of ice on many of its rocks. He read a paper in
this Society, describing these marks; and as the learned Principal was distin-
* Sir James Hatu’s theory is explained by him in the following paragraph :—“I imagine
that a diluvial wave flowed at some remote period from a westerly or north-west direction, and
broke over our island; that its magnitude was such, that a great body of its water crossing the
ridge of country which separates the two coasts, overwhelmed the district, discharging itself into the
German Ocean.”—(Ed. R. 8. Tr. vol. vii. p. 202.
VOL. XXV. PART II. 8H
656 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
guished for accurate observation and cautious deduction, his discovery in Skye
added largely to the popularity of the glacier theory. The next quarter from
which light came was Wales, where Professor Ramsay recognised signs of ice
action. He was followed by Dr CuAmpBers, the late Mr Mactaren, and Mr
JAMESON of Ellon, who severally pointed out localities in many of the Scotch
counties.
But whilst generally adopting and helping to illustrate this theory, almost all
of these geologists admitted that there were some phenomena of the boulder-clay
which could not be explained by any imaginable local glacier; and they threw
out the idea that icebergs or icefloes, which it was discovered carried in the
Arctic and Antarctic regions enormous masses of rock and rubbish, might possibly
have in former times done similar work in North-Western Europe.
By this time Acassiz himself appears to have become satisfied that many of
the ascertained facts could not be explained on the theory of glaciers flowing
down from isolated mountain ranges. Having gone to reside in America, he
obtained there an opportunity of studying the phenomena on a much larger scale
than either Switzerland or the whole- of Northern Europe supplied, and was
greatly struck by seeing that boulders were scattered over an area of the earth’s
surface, extending to nearly 1000 miles in every direction, and that these boulders
generally had all been transported from one quarter, viz., the north. Having
learnt, from the writings of Murcutson and others, that the great mass of boulders
in Russia and Poland had also come from the north, and that in some cases the
parent rocks were more than 100 miles distant, he formally renounced the
theory of local glaciers, and propounded the notion that gigantic glaciers, more
than a mile in thickness, and derived from snow two or three miles deep, had
been generated in the Arctic regions, and were by some cause made to move over
the earth’s surface towards the south, encasing great continents, filling sea-beds,
rising up slopes of land, overtopping mountains, and pushing before them, with
a colossal ice-foot, immense heaps of detritus. From his recent work on the
Brazils, it appears that this enthusiastic naturalist contends that the huge glacier
which passed over North America, reached even to the tropics.*
I do not know or believe that this theory of Acassiz, in its full extent, has
been adopted by any geologist in either America or Europe; but Iam not sure
that it is not, to a modified extent, adopted by some of our Scotch geologists.
Mr GEIKIE, in a very valuable paper on the “ Glacial Drift of Scotland,” says,
“that the ice existed, not as mere local glaciers descending the chief valleys,
but as one wide sheet covering the whole, or nearly the whole, country” (p. 78).
* “Visit to the Brazils,” p. 403.—Agassiz in this work contends for the existence of “a sheet
of snow 10,000 or 15,000 feet in thickness, extending all over the northern and southern portions
of the globe,—which in the end formed a northern and southern cap of ice moving towards the
equator !”
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 657
“Down the whole of the west coast, from Cape Wrath to the Mull of Cantyre,
one long expanse of ice filled up the fiords, and stretched out into the Atlantic.
From the uplands of Wigtown and Galloway, the icy stream swept down into the
valley of the Solway, and onward for Ireland. From the hills that border the
lonely valley of Liddesdale, far away into the blue Cheviots, the same universal
mantle of ice threw its folds athwart the hills and dales of the north of England.”
(‘‘ Glacial Drift.” P. 84.)
The following passages in a later publication by Mr Gerxie (“Scenery and
Geology of Scotland,” 1865) may also be referred to :—
‘‘The massive ice of the great Highland area came down into Strathmore,
and kept steadily southward in such force as to mount over the chain of the
Sidlaws, and even it would seem over the Ochils, until it went out to sea by the
basin of the Forth.” (P. 300).
Referring to Scotch boulder-clay or till, Mr Grrxie says, that “land ice has
now given us the clue to the history of this remarkable superficial deposit, as
will be afterwards pointed out; its internal structure, and its striated stones,
show it to be the result of the abrasion carried on by the ice-sheet, as it moved
over the land.” (P. 183).
“ The high grounds of the interior receive a constant accession of snow; and
the accumulated mass, pressing down the valleys, goes out to sea in long wide
walls of ice.” ‘The moraine-rubbish of this great ice-sheet gathers into the
thick deposit known as boulder-clay.” (P. 345).
The Rev. R. B. Watson, in a paper on the “ Drift-beds of Arran,” read in
this Society in January 1864, says, that the phenomena indicated the existence
not of glaciers merely, but of a massive zce-cake, “‘more universal than even in
Southern Greenland now. Beneath this ice-cake the soil, and all of life it sup-
ported, would be gradually harried away to the sea; any traces of it left being
nests of debris niched into corners, ground over and disturbed in every conceiv-
able way by the ice above.” (P. 537 ‘“‘ Roy. Soc. Trans.” vol. xxiii.) ‘This being
so, we are entitled to say that the boulder-clay is the result of land glaciation.”
(P. 538). .
Dr Bryce of Glasgow, shortly after the publication of Mr Watson’s paper,
went to Arran to examine the sections described in it; and he concurs in holding
that the circumstances proved “ for the boulder-clay an origin on Jand.”’ (“* Lond.
Geol. Journal” for 1864, p. 211.)
The most recently published paper on boulder-clay, with which I am
acquainted, is by the Rev. Dr Tuomas Brown, who read in this Society an
account of the “Arctic Shell-clay of Elie and Errol.” In this instructive paper he
has a chapter on boulder-clay, which he says, both at Elie and Errol, lies beneath
the Arctic shell-clay, and rests immediately on the rock. He states his opinion
of its origin thus:—“ It would seem that this lowest deposit, so long an enigma,
658 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
has at last yielded up its secret. It is a Jand deposit, formed at the period when
Scotland, like Spitzbergen, lay beneath an immense covering of ice, which wrapped
the whole face of the country, hill and dale. Underneath such a covering, possibly
thousands of feet in thickness, the rocks would be ground down, and the boulder-
clay formed. Thus the absence of fossils is accounted for; inasmuch as none
of our usual forms of life could exist beneath such an ice-sheet ; and thus we see
also how the clay is so peculiarly hard and untractable.” (P. 630).
I have briefly sketched the various theories relating to boulder-clay, to show
the difficulty of the subject, and have referred more particularly to the views of
the latest writers. whose geological experience and knowledge are held in just
repute.
It is, therefore, with considerable hesitation that I venture to call in question
the soundness of these views, and I would not have done so, had it not been that
some observations, bearing on the subject, do not appear to me to have received
sufficient consideration. Most of the observations to which I allude are to be
found scattered through different publications, and have never yet been brought
together, so as to throw a combined light on the question ;—I am able also to
adduce some observations of my own, not yet published.
I shall advert, first, to the difficulties which beset the theory that our Scotch
boulder-clay ‘‘is a dand deposit,” the product of glaciers; and will afterwards
state the reasons which lead me to believe that it has been formed at the bottom
of the sea—by the action of floating ice.
I disavow any originality in presenting the iceberg theory. Moreover, it has
this presumption against it, that, having been formerly adopted by Mr Geixig, he
has lately intimated that he has had to abandon it, because, as he says, ‘‘ though
the iceberg hypothesis is generally the accepted explanation of the phenomena of
striated rocks and boulder-clay, its untenableness seems to me completely estab-
lished.”’ (‘‘ Glacial Drift,” p. 10.)
Notwithstanding this very decided condemnation, I think there are good
erounds for upholding the correctness of the iceberg hypothesis.
That there are some points not altogether explained by it, I will not deny;
but that there are insuperable difficulties with which the glacier hypothesis has
to contend, I shall now proceed to show—
1. If the boulder-clay was formed, as is alleged, by the action of glaciers; if it
consists of debris derived from the rocks which the ice grinds down in its passage
over them, and which are pushed forward by its ice-foot, we would see boulder-
clay now forming in those countries where glaciers are in action. But it has never
been alleged that in Switzerland, Norway, or Upper India, whose glaciers have
been described by competent observers, anything like boulder-clay is seen to be
produced. I have been twice in Switzerland; and, being anxious to watch the
effects of glaciers on the rocks, made them a subject of study, and penetrated
Se
ee eee
—————
ee ee
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 659
under three glaciers near their lower extremities, without discovering anything
like boulder-clay. Great abrasion of rocks there was undoubtedly. Blocks and
pebbles under the ice I saw in abundance, all grinding, and many of them scoring
the rocks. Much sediment there was, flowing out from under the ice. But what
became of this sediment? It was carried off into rivers and lakes, there to form
beds of mud or sand—none having any resemblance to boulder-clay. The terminal
moraines of glaciers, no doubt, resembled it in one feature—want of stratification ;
but the absence from these moraines, of clay, hard, tough, and compact, showed
that the deposits were essentially different.
It is no small confirmation of my own testimony on this point, that Acassiz,
when he visited Scotland to search for the signs of ancient glaciers, avowed that
he had never seen boulder-clay before he saw it in Scotland.*
2. The next difficulty with which the glacier theory has to contend is, the
prevalence of boulder-clay in districts where it is scarcely possible to suppose
that glaciers could have existed, or, if they did exist, a have had to do with
the production of the deposit.
Thus, in the flat districts of Norfolk, and in the still flatter districts of
Denmark and North Holland, boulder-clay is found. But there are no moun-
tains in or near these districts, where any glaciers could have been formed. The
same remark has been made by Mr Cummine of the boulder-clay in the Isle
of Man. +
Even in those parts where there are both boulder-clay and mountains, as in
the Highlands of Scotland, it appears that the boulder-clay is derived from a
quarter the very opposite from that where a glacier may have existed. Along
the coasts of Western Ross-shire and Caithness, this deposit abounds, and has been
studied by Mr Jameson of Ellon and Dr Roserrt CoAmBers—both of whom at
first advocated the theory, that its formation could be accounted for by glacier-
action. Mr JAmEson says—* The distribution of this dark grey mud harmonises
with the supposition that the transport of it has been from the N.W.; and a
movement of ice, from the N.W. to the S.E. across Caithness, is totally at variance
with the notion of the scratches having been caused by glacier-action proceeding
from the interior of the country towards the present coast.”{ And he adds ina
footnote, that the phenomena “ indicate a movement of ice from the N.W.,
where there is now nothing but open sea for an immense distance,” and ‘all
suggestive of marine conditions.”
3. The next difficulty to the glacier theory is suggested by the immense
extent of earth’s surface over which the transporting agent has moved in one
and the same direction.
* See Edin. Phil. Journal for 1842, p. 227; and Geological Researches, by James SuitH
of Jordanhall, p. 12.
t “Isle of Man,” by Cummine, p. 248.
t Proceedings of the Geological Society of London for 1866, p. 269.
VOL. XXV. PART II. SI
660 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
If the boulder-clay was produced by glaciers, its transport would be coinci-
dent with the direction in which the glaciers moved—that is, in directions parallel
with the valleys from which they emerged. We should expect, therefore, to find
that the boulder-clay, and the blocks embedded in it, indicated a movement and
transport from every conceivable point. The boulder-clay and boulders found on
the west coast of Scotland should indicate a movement from the eastward; on
the north coast, from the southward; and on the east coast, from the west-
ward.
But is this the true state of the case, as shown by most recent observation ?
The phenomena of the boulder-clay show in all parts, not of Scotland only, but
of Ireland, England, and even of the adjoining districts of North-Western Europe,
a general movement from the north-westward. That exceptions to the rule exist
I admit, and an explanation of these I shall afterwards offer; but I affirm that
there is a general and prevailing direction over the wide area just mentioned,
and that direction is from W.N.W. or N.N.W.
Before, however, giving proofs of this position, let us see what are the signs
of transport on which geologists are agreed.
(1.) Mr Gerxiz has pointed out a relation between the colour of the boulder-
clay and the rocks of the districts adjoining the deposit—as indicating transport.
Thus he says—‘“‘ The main mass of the boulder-clay, in the basin of the Forth
for instance, consists of the comminuted debris of the carboniferous and other
rocks which form the framework of that district. We can also gather that this
loose fragmentary material has moved (there?) from west to east. In the upper
part of the basin of the Firth of Forth, the coal-fields are covered with ved boulder-
clay, abounding in fragments of the rocks that lie towards the N.W., and deriving
its prevalent tint from the waste of the Old Red Sandstone which stretches up to
the foot of the Highland mountains.” *
The late HucH Mier had previously pointed out how the pale oolitic rocks of
Brora and Golspie are covered by a yellow boulder-clay, and the flagstones of
Caithness are covered by a boulder-clay of a grey leaden colour. So also Mr
Cummine showed how, in the Black Isle, the boulder-clay has the colour of the
red rocks there; whilst to the westward, the colour changes to a colour in corres-
pondence with that of the slaty rocks. The same author points out how, in the
Isle of Man, the colour of the boulder-clay is blwe near the limestone rocks, and
red near the Old Red Sandstone rocks; and how in each case these rocks are in
the same direction from the boulder-clay, as if a current had swept over the rocks
to provide materials for the clay.
Mr Nico has pointed out the same relationship in Cantyre.t
* Glacial Drift, p. 43.
+ Lond, Geolog. Journal for 1850, vol. vii—Isle of Man, pp. 115, 247.
t Lond, Geolog. Journal for 1852, vol. viii. p. 417.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 661
Arguing from this test, the late Dr FLemince showed very clearly that in the
neighbourhood of Edinburgh, the boulder-clay “had been in motion from west
to east.”*
These views are important, as proving also that geologists agree in holding
that whatever may be the case with regard to the erratic blocks in the boulder-
clay, the boulder-clay itself has been derived chiefly from the rocks over or near
which it lies, and (to use Mr Gerrkin’s expression) ‘‘ consists of the comminuted
debris of ” these rocks. ;
(2.) Another well-established indication of the direction in which the boulder-
clay has moved, is afforded by the striations and groovings of the rocks covered
by the deposit. Mr Jameson, after stating various facts bearing on this point,
says, ‘“‘all this shows that the boulder earth, with its embedded fragments, was
pushed along by the same agent that scored the rocky bed on which it lies.” +
So also Mr Gertz, after mentioning other examples, says—“ Here it will be seen
that the direction of transport of the boulder-clay exactly coincides with the
trend of the groovings and striations on the rocks below,” +
(3.) Farther evidence bearing on the same point is afforded by the nature of
the boulders or erratics embedded in the boulder-clay ; for when an examination
of the rocks composing them has led to a discovery of the locality from which
they have apparently been transported, the direction in most cases coincides
with that of the striations on the rocks, and with the direction of the movement
of the boulder-clay as indicated by its colour. Accordingly, AGAssiz does not
hesitate to admit, that the striz on the rocks are due to the same cause which
transported the blocks.§
This remark applies not merely to blocks in the boulder-clay, but to erratic or
transported blocks in other positions, whether on rocky knolls or on beds of gravel.
Whenever the quarter from which they have come has been clearly ascertained, it
is found that the direction of their transport agrees with that of strize on rocks
in the neighbourhood. ;
There is another circumstance, not undeserving of consideration, long familiar
to geologists, viz., that when erratics are of such a shape that their length greatly
exceeds their width, their longer axis generally lies in the direction of their
transport.
I believe, therefore, in common with other geologists, that the movement of
the boulder-clay, whenever that has been ascertained, the transport of boulders,
and the striations, groovings, and smoothings of the rocks, are due to one and the
same agent; and hence the phenomena to which reference has just been made,
* Lithology of Edinburgh.
t Lond. Geolog. Journal for 1866, p. 167.
Glacial Drift, p. 45.
fe
+
§ Edin, Phil. Journ, for 1842, vol. xxxiii. p. 223.
662 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
can be competently relied on to ascertain the quarter from which that agent has
come.
What, then, is the evidence on this point afforded by these phenomena? Let
me enumerate the localities where the direction has been clearly ascertained.
Caithness—Mr JAmMEsON, in his instructive paper on this subject, enumerates
about twenty localities in this county, where “ the glacial markings on the rocks
showed a pretty uniform direction over the whole district from the N.W.”
Mr Jameson also examined the directions in which “the dark grey mud”—
by which he designates the boulder-clay—derived, as he considered, “from the
Caithness flags, had moved,” and he found that it also had moved from the N.W.
He found that the Caithness flags—situated in the N.W. of the county—were
themselves covered by ‘‘ drift of a reddish-brown colour,” derived probably from
the north-westward.*
Ross-shire and Argyleshire—Dr CHAMBERS mentions that “‘ near Rhiconish we
find striz coming from the coast—.e., from the N.W., and passing across a
high moor, with no regard whatever to the inequalities of the ground. A little
further north, at Loch Laxford, a fine surface is marked with striation from the
N.W., being across the valley in which it occurs. At an opening in the bold
gneissic coast, which looks out upon the Pentland Firth, there are strong markings
in a direction from N.N.W.”+
In the small Isle of Kerrara, opposite to Oban, and also in the Island of Mull,
Dr CuAmbers found striation, pointing in the one case N. 68° W., and in the other
N. 60° W.+
Perthshire—tThe lofty mountain of Schehallion has been examined by both
Dr Cuampers and Mr Jameson. Dr CHampers§ found striz on it at a height of
above 3000 feet, pointing W. 30° N.; and Mr Jameson satisfied himself that the
strice he saw on the same mountain must have been made “not by ice flowing
down the sides of the hill, but by ice pressing over it from the north.”|| He
adds—“ On the Perthshire hills, between Blair-Atholl and Dunkeld, I found ice-
worn surfaces of rock at elevations of 2200 feet, as if caused by ice passing over
them from the N.W., and transplanted boulders at even greater heights.”
Forfarshire—Sir CHar_es LyeL1, in the year 1842, pointed out how the till
and its embedded boulders had been transported from the N.W.
Dr Howopen, of Montrose, has lately published a paper in the “Transactions
of the Edinburgh Geological Society,” in which he observes ‘that the general lie
of the range of hills is W.S.W: to E.N.E., while the -direction of the glacial grooy-
* Lond. Geolog. Journ. for 1866, p. 268.
t Edin. New Phil. Journ, for 1852, vol. liv.
+ Ibid.
§ Proceed. Geolog. Soc. of London for January 1865.
| Ibid.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE: 663
ings is from W. by N. to E. by S., so that the polishing agency must have crossed
the hills at an angle of 30°.”
Dumbarton and Renfrew shires—Dr CHAMBERS mentions that on the sand-
stone plateau between Campsie and Stirling, the striations on the rocks were
W. 20° N.
Having myself visited the moors, about three miles N.W. of Milngavie, in the
parish of Baldernock, I found the white sandstone rocks ground down and
flattened in large patches, with striz and rents on them, indicating a movement
from W.N.W. and N.W. (magnetic.)
The late Mr Situ of Jordanhall, in his Geological Researches, after enumerat-
ing several localities where boulders of various kinds of rock had been examined
by him in Clydesdale, observes—‘“‘ In these cases, the bearing of the supposed
parent rocks is N.W.; but in all of them the intervening space is intersected by
deep arms of the sea and steep mountain ranges (p. 13). One of the boulders
was found in the boulder-clay near Airdrie, the nearest granite rock being at
Cruachan, about 60 miles N.W. of Airdrie.” Mr SmirH adds—‘‘I never yet
saw or heard of an erratic block in the valley of the Clyde, whose course could
be traced, that did not come in an opposite direction to the flow of the river.
We can trace their course, not from the mountains to the sea, but from the sea
to the mountains” (p. 131).
Edinburghshire.—The general direction of the movement in this district has
been very accurately ascertained by Sir JAmMes Hatz, Mr Macuaren, Dr FLEMING,
Rosert CuamsBers, Mr Nicon, Hues Minter, Mr Gernts, and myself. All concur
in representing that the movement has been from points varying between W. by
S. and N.W., the most prevalent being from W. by N. (magnetic). The evidence
of this is well stated by Mr Grrxiz in the following passage in his Memoir of the
Geological Survey, No. 32:—“ The parallelism of the striations throughout the
district show that the floating ice must have moved in a pretty uniform direction ;
and that it was from the west, is clear by the striation of the western face of the
hills, the great depth of the drift on their eastern sides, and by the fact that the
transported boulders, when traceable to their parent rock, have been carried from
west to east.” Mr Gerxiz then specifies several of these boulders on the Pentland
Hills, and one in particular of mica slate, first noticed by Mr MacnarEn, weigh-
ing eight or ten tons, and at a height of 1060 feet above the sea, which he says
-had “undoubtedly been transported from Cantyre or the Grampians.” These
boulders Mr Geixiz at that time considered to be “ice-borne blocks dropped on
the submarine slopes of the Pentlands.”’ Whether he now thinks that they were
brought by the agency of a glacier, I do not know.
Stirlingshire and Lanarkshire.—On the west side of Damyat (one of the
Ochils) I found, at a height of from 500 to 600 feet, many patches of hard con-
glomerate rock, ground down and striated by an agent which had come from the
VOL, XXV. PART II. 8K
664 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
N.W. and N.N.W. At these places the general slope of the county is down
towards the N.W. Therefore the agent which ground down these hard conglo-
merate rocks must have moved up hill.
On the trap hill of Croy, near Aisyth, I lately found a conglomerate boulder,
which probably came from the hills of that rock, situated between Dumbarton
and Callander; and on the felspar hill at Stonebyres, I found pebbles of coal
sandstone and clay ironstone, which apparently had come from the west.
Sir James Haut describes a sandstone rock in Torwood, near Stirling, smoothed
and striated—the direction of the striations being N. 50° W. (Ed. R. S. Tr. vol.
vii. p. 200.)
Berwickshire.—In the parish of Eyemouth there is a brickwork of boulder-
clay, in which lumps of water-worn coal and ironstone are occasionally found.
In sinking a well lately on the farm of Blackhill (Coldingham parish) through
boulder-clay, lumps of water-worn coal were found. The nearest place from
which these erratics could have been transported is East Lothian, situated to the
N.W.—the Lammermuir range of hills intervening.
In the last-mentioned parish, lumps of hematite have been picked up on the
surface of the ground, resembling extremely the hematite worked on the Garlton
Hills, in East Lothian, situated about 30 miles to the W.N.W.
In the parish of Dunse,* there is a rounded boulder of mica slate, about one ton
in weight, which must have come from the Highlands of Scotland.
In the parish of Hutton, there is a brickwork situated on a mass of boulder-
clay, containing occasionally rounded pebbles and boulders. One of the boulders
is amass of blue greenstone, weighing about eleven tons, and angular in shape.
The nearest parent rock is on Borthwick Hill, near Dunse, situated about ten
miles N.W. from the boulder; and its longer axis points in that direction. In
the same brickwork there are smaller boulders of greywacke, old conglomerate,
and chert, all of which have most probably come from the Lammermuir Hills,
situated to the north and west. An angular block of coal sandstone has also
been excavated which adjoined the large greenstone boulder. No such sandstone
is known in Berwickshire. I know of no place nearer than Mid-Lothian where
this peculiar sandstone occurs in strata. It is of a yellow colour, and rather soft
in texture. As the block is of an angular shape, its transportation could have
been effected only by drift ice.
In Liddesdale, 1 found boulders of granite, which probably came from the
granite hills of Dumfries and Ayrshire ;+ and within these few weeks I have found
in Northumberland, north of Hexham, several granite boulders, probably from
the same quarter.
* This boulder was pointed out to me by Mr Stevenson of Dunse,
t Geology of Roxburghshire, Roy. Soc. Trans. vol. xv. p. 402.
=
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 665
Arran.—Dr Bryce* has pointed out that the rocks on the N.W. sides of many
of the hills have been denuded and smoothed, whilst on all other sides they are
rough.
Kirkeudbright—Mr Hay CunnineHam states that “large rounded frag-
ments of granites and syenites are abundantly scattered over the county, and so
arranged as to indicate that they have been dispersed by a force proceeding from
the N.W.”’+
In Northumberland, the following table compiled from the reports of Mr
Tait of Alnwick, Secretary to the Berwickshire Naturalists’ Club, [ shows the
quarter from which the transporting agent moved, judging by the striations and
groovings :—
Locality. Nature of Surface. True Bearings.
Ratcheugh, Limestone Rock below Boulder-clay. | N.
Do. Blocks in Boulder-clay. N.W.
Belsay. Limestone Rock. N.N.W.
pogsiores ao} Limestone Rock below Boulder-clay. | W.N.W.
stanborough.
Swinhoe. Bre ae do. N. 50° E.
Belford. Bee Be do. N.W. by W.
Sea-shore, Birling. | Sandstone Rock under do. N.E.
St Abb’s Head, Porphyry under do. N.W. and W.N.W.
Farne Islands. Basalt under do. N.N.W.
Alnwick. Limestone under do. N.N.W.
The plains of Yorkshire are strewed over with blocks transported from Cum-
berland, one of which is the well-known boulder of shap-granite, now standing
in one of the streets of the town of Darlington.
Near Liverpool, the direction of the striations on the rocks is between
N. 15° W. and N. 42° W.
In Cheshire, the direction is N. 30° W.§
In Wales and Somersetshire, chalk flints occur in the drift, which must have
come from the county of Antrim, Ireland—z.e., from N.W.
In Norfolk there are two boulder-clays, separated by a bed of sand containing
sea-shells. The upper boulder-clay, as the late Mr Trimmer showed,|| contains
fragments of oolite rocks, which must have come from the westward, passing
over a ridge of chalk rocks, which, however, do not indicate any abrasion. Mr
Trimmer, taking into view the levels of the country, held it impossible to ascribe
* Geology of Clydesdale, p. 271.
} Highland Society’s Transactions for 1843,
+ Transactions of Berwickshire Naturalists’ Club, vol. v. pp. 238, 372.
§ Lond. Geol. Journ. for 1862, vol. xviii. p. 377.
|| Lond. Geol. Journ. for 1858, vol. xiv.
666 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
the transport of the oolitic blocks to glaciers. Floating ice alone, in his opinion,
afforded a solution.
In the Jsle of Man, Mr Cummine found chalk flints in the boulder-clay, which
he thought must have come from the county of Antrim, in Ireland, situated to
the N.W.; and in the drift gravels of the island there were pebbles, which he could
only refer to rocks also situated to the N.W.*
In Ireland, the general direction of the transported boulders is the same as in
Scotland and England. Sir Ricnuarp Grirrira} says—“ If we look to the distri-
bution of erratic blocks, as indicative of the direction of the currents by which
they were distributed, we find in Ireland generally that they were carried from
N.W. to S.E., though the current was often modified by the opposition of moun-
tain ridges.”
“ The prevailing direction of our mountain ridges is N.E. and S.W., viz., at
right angles to the supposed direction of the current; and, as might be expected,
we find the gravel banks and detritus distributed on the N.W. declivities of the
hills, and intruding into the interior valleys.”
A later observer, Du Noyer, has identified the boulders lying on the moun-
tains near Cork with the granite rocks of Galway, situated on the N.W. coast of
Ireland, and has shown that the striz on the smoothed rocks have the same
direction. {
In the Shetland Islands, an examination was instituted by Mr Pracu, at the
request of Sir Roperick Murcuison, into the drift phenomena. Mr Peacu found
on the hard primitive rock of the islands, clear evidence of grinding and polishing.
The general inference which he drew was, that the agent, whatever it was, must
have passed over the islands from the northward. The only exact bearings
stated in his report were taken in the island of Unst, the most northern of the
group, containing about 36 square miles, and having one hill on it about 500 feet
high. The ruts in the rocks there all pointed W.N.W.; and the side of the hill
facing that quarter was (he says) polished to a depth from its top of about 150
feet.§
In the Faroe Islands, on the N.W. coast, the late Mr ALLAN,]|| when he visited
them with Sir Gzorce Mackenzig in the year 1812, was struck with a rocky hill,
the surface of which appeared ‘‘to have been worn down by the friction of heavy
bodies” over it. “The rock was scooped and scratched in a very wonderful
degree, not only on the horizontal surface, but also on a vertical one of 30 to 40
feet, which had been opposed to the current, and presented the same scooped and
polished appearance with the rest of the rock.” Mr ALLAN says, “it would be
* Lond. Geolog. Soc. August 1846, pp. 336 and 342.
+ British Assoc. Rep. for 1863, vol. xii. p, 51,
+ Geologist for 1862, p. 246.
§ British Assoc, Rep. for 1864.
|| Edin, Roy. Soc. Trans. for 1815, vol. vii. pp. 244-265.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 667
curious to investigate, whether this smoothness could be traced to any external
cause such as that observed by Sir James Haut, on Corstorphine Hill.” At an
early period geologists were unacquainted with the abrading effects of ice.
From Mr Auuan’s description of the markings on the hill at Eide, and from its
situation on the N.W. coast of Faroe, it is not difficult to see the agency of
icebergs.
In Iceland the striz, as Dr CHAMBERS states in his instructive little book,*
run N. 30° W. (true). Having endeavoured, through my friend, Mr R. M. Smrru
of Leith, who has correspondents in the island, to obtain farther information
regarding the markings on the rocks, I have had sent to me by Mr Smiru the
following extract from a letter by Dr Hysatre in, of Reykavik, Knight of the
Dannebrog, and principal physician in the island :—‘“‘ The diluvial scratches are
to be seen everywhere in the south part of our country.. They run in lines
parallel to one another, and can scarcely be occasioned by the action of rain or
water. Their direction is very much against this view. You see them on the
slope of the hills, not following the declivity of the rocks, but everywhere run-
ning in the well-known direction from N.W. to S.E., in spite of the declivity.
Many of these scratches are very unequal, and seem evidently to have been pro-
duced by a hard material gliding over the rocks in the aforesaid direction. It
must furthermore be remarked, that these furrows, which are unequal both in
depth and diameter, could hardly have such a regular parallel direction, if
occasioned by water or rain.
‘* These scratches are all round here in our mountains. In the lower flat lava-
fields, some deep and broad irregular scratches may also be seen; but they have
no constant direction, and seem to have been produced by pieces ‘ of hard material
gliding over the lava when still in a soft condition.’ ” + |
In Sweden, the markings on the rocks show a movement generally from the
N.N.W., which is also the direction of the osars or elongated gravel ridges, so
abundant in that country.
In Finland, on the Gulf of Bothnia, and on the Lake of Ladoga, in Russia, the
direction is N.W.
In Denmark (as ForscHAMMER shows), the markings on the rocks show a move-
ment from W. 25° N. (true). The following case mentioned by him at Gothenburg
(situated near the southern extremity of Sweden) leaves little doubt regarding
the nature of the agent which made the markings. There was a large furrow or
rut on a rock, the prolongation of which rut had been arrested or prevented by a
boulder lying on the rock and firmly jammed. The boulder was about 3 feet
thick vertically; and on its upper surface there was a rut, which being exactly
in a line with the rut on the rock, seemed to have been made by the same agent,
* Voyage to Iceland and the Faroe Isles.
{ Letter from Dr Hsatrexiy, Knight of the Dannebrog, and Chief Physician in Iceland.
VOL., XXV. PART II. 8 L
668 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
which agent must, therefore, have risen up from the rock about 3 feet, in order
to score the boulder.*
If the foregoing enumeration of localities correctly represents the general
direction of the markings on the rocks, it is impossible to avoid the conclusion
that they have been made by one and the same agent, and over a very large area
of the earth’s surface. How can it be conceived that glaciers should over that
large area have all moved in the same direction? Objections to the glacier theory
are suggested even by cases of isolated boulders.+ But the objections become
infinitely stronger, when it appears that over an area of North-Western Europe,
comprising Iceland, Faroe, Shetland, Scotland, Ireland, a great part of England,
and on some of the adjoining continental countries, the agent which affected the
boulder-clay, transporting blocks and striating rocks, moved almost everywhere
in nearly the same direction, and came chiefly from that quarter where there is
only the ocean.
The late Principal Forses, much as he was inclined to uphold the agency of
glaciers, felt the force of these objections, and makes the following confession in
his work on the Glaciers of Norway (p. 241):—“ I hesitate to ascribe everything
to glaciers. In fact, there appears to me to be situations along the coast of
Norway, where the action of abrasion having been parallel with the coast, the
movement of a glacier would be inconceivable. The general parallelism of the
strize, observed by Botuuink and others, over a large area of country, not
coincident with the general fall of the ground, would seem, if confirmed,
to be equally inexplicable on the pure glacier hypothesis. The continuation
of the striz across table-lands, and over cols, is of the like ambiguous character.
I have never hesitated to express, on similar grounds, doubts as to the
universal application of the usual glacier theory to the phenomena of our
own islands, which, on a small scale, are the counterpart of those of Norway.
For, though perfectly satisfied that our hills were in former times the seat of
glaciers which even approached the sea-level, I find the utmost difficulty in
explaining, by such an hypothesis alone, the facts which occur even in the
immediate vicinity of Edinburgh.”
In another part of the same work, Principal Forpes threw out a surmise
of the kind of agent which seemed to him probable. Referring to the range of
hills on the west coast of Norway (p. 190), he says that these bore “the
whole brunt of forces which appear to have come from the north, and not only
* Lond. Geolog. Journal for 1845, vol. i. p. 376.
t Thus Mr Macraren says—“ I have pointed out a boulder of mica slate in the Pentland Hills,
weighing 8 or 10 tons, which must have come 50 miles at least. It lies on a steep acclivity
1000 feet above the sea; and it must have passed over extensive tracts of country from 500 to 800
feet lower than the spot on which it rests. Even were all Scotland converted into a mer de glace,
like Greenland, no glacier could carry the boulder (and there are many such) from its parent rock, in
Perthshire or Argyleshire, to the Pentlands.’—Select Writings, vol. ii. p. 115.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 669
defended the entire north of Europe from the shock, but probably furnished by
their abrasion the materials, of which the low grounds of the Continent of Europe
are mainly composed. In this general disposition of the mountains of Norway,
we see a strong analogy to the west coasts of our own islands. It appears
almost certain, that a common cause has devastated the western shores of nearly
every continent.”
It is very evident what this “ common cause” alluded to by Principal Forsss,
as having left its mark on the western shores of North-Western Europe, must
have been nothing less than the ocean itself. Sir Jamms Hatt was, on the
limited body of facts known in his day, led to the opinion that a resistless rush of
waters over the country from the westward would explain the phenomena; and,
down to avery recent period, attempts have been made to show how boulders
could be carried by what are called waves of translation. These views have now
been generally abandoned; and in place of them, it has been suggested that
oceanic currents, with floating ice, and flowing over the submerged land, would
afford a better explanation—an explanation strongly supported by the great
extent of area over which the transporting agent has moved.
But in stating that the agent has moved over this large extent of area in the
same direction, let me repeat that there are cases where the direction of the
strie and the transport of boulders point to a different quarter than the north-
west. The percentage of these cases is so small, as not to affect the argument
based on the generality of that direction, and on the extent of area over which it
prevails.
Moreover, whilst some of these exceptional markings are undoubtedly
indicative of local glaciers,—the probable epoch of which will be afterwards
referred to,—others are not inconsistent with, but, on the contrary, are corro-
borative of the theory of oceanic currents. Thus, in the great glen of Scotland, the
lines of strize and the course of the transported boulders show a movement from
S.W.* So also in the estuary of the Forth, as well as in the trough which crosses
Scotland along the south slopes of the Kilsyth and Campsie hills, the striz and
many of the boulders indicate a movement from W. by 8. and W. by N. Now, in
each of these cases, the deviation from the general or normal N.W. direction
coincides with the range of the valley where it occurs; and it is not unreasonable
to suppose that the obstruction, caused by adjoining hills of considerable height
and extent, would modify the direction of the current so that it should flow with
some approach to parallelism with them.
Sir James Hatt, in his paper, brings out this point very clearly, when he
says “that the direction in the neighbourhood of Edinburgh may have been
occasioned by the local influence of the estuary, since the direction of the stream
* Lond. Geolog. Society’s Proceedings for April 1849, p. 13.
670 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE:
before entering it, and after quitting it, is nearly from N.W. toS.E.” Whilst he
shows from numerous examples, that the direction in the Lothians was from
W.35S., he shows that near Stirling it was from N. 50° W., and near St Abb’s
Head from N. 35° W.* (true bearings).
4. The next point bearing on this question which I wish to put, is the char-
acter of the fauna found in the boulder-clay ; which, being marine, afford strong
evidence not only adverse to the theory that it is a land deposit, but favourable
to the theory that it is a sea deposit.
The following enumeration of localities where boulder-clay has been found
containing sea-shells is not complete; but it is sufficiently extensive to establish
the fact :—
Near Airdrie (Lanarkshire), ‘‘in the till itself,” the late Mr Smirx “ found
broken and water-worn fragments of shells irregularly dispersed in it, and
amongst them the Cyprina islandica and a large species of Balanus.”’ +
In Wigtownshire, “in the genuine till or brown sandy unstratified clay,
with blocks of transported rocks interspersed through it,” Mr Moore found “one
perfect valve of Astarte compressa.” }
In Aberdeenshire, various species of sea-shells have been found in the boulder-
clay by both Dr Cuambers and Mr JAmzEson.§
In Caithness, at several places sea-shells and other marine ¢estacea have been
found in this deposit by Mr Jameson and Mr Peacz. ||
This point was seen to be of so much importance that a special examination
of the Caithness boulder-clay was undertaken by Mr Pracu and two other gentle-
men. They not only discovered in it many species of sea-shells, but by washing
it, and examining with the microscope, they discovered no less than ten or twelve
genera of Foraminifera, Entomostraca, and other minute marine organisms. In
a paper read by Mr Peacu before the British Association in 1864, and published
in their Transactions, it is stated that he and Mr ANDERSON had “ washed boulder-
clays from many localities extending from near John O’Groat’s to beyond Wick,
and all the samples tried yielded more or fewer of these animals, from whatever
part of the deposit the clay was taken.” He adds, that “he had not previously
found two valves of a shell united in the clay. He had, however, since got an
Anomia with both valves in place. It occurred in boulder-clay containing the
usual rubbed stones and broken shells. Mr. ANpERsoN has also a piece of shell
on which is a cluster of young Balan.’ Mr Pracu gives a list of no less than
“eighty-three species of shells, &c., from the boulder-clay of Caithness.” 4
In the same volume of the British Association Reports there is a list of thirteen
* Ed. B.S. Tr. vol. vii. p. 200. + Researches, p. 141.
t Smirn’s Researches, p. 143.
§ Proceedings of the Lond, Geolog. Society far 1866, pp. 274-5.
|| Ibid. p. 267, { Brit. Assoc. Reports for 1864, p. 62.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 671
species of marine shells from boulder-clay at Scarborough and Whitby, on the
Yorkshire coast. These shells were discovered by Mr Lackensy and Mr JEFFREYs,
both recognised authorities.*
The Rev. Mr CrosskEy, Vice-President of the Glasgow Geological Society, well
known for his knowledge of drift deposits, states that he found boulder-clay near
Sunderland, “ containing fragments of broken shells and many Lntomostraca and
Foraminifera.’ + That gentleman adds that he had found shells in boulder-clay
on the banks of the Mersey and on the coasts of Jreland.
In boulder-clay, near Zynemouth (Northumberland), fragments of Cyprina
islandica have been found by two accurate observers, Mr Howse and Mr Binnie
of Manchester. f
Dr THomas Brown, in the paper recently published in the Transactions of this
Society,§ has given a list of above twenty species of sea-shells found at Errol
(Perthshire), and at Elie (Fifeshire). Dr Brown mentions (p. 630), that at both
places the shells were in a bed resting on the boulder-clay. I had an opportunity
lately, in company with Dr Brown, of examining the deposit at Elie containing
these shells, and found that it consisted of a hard or tough clay of a dark grey
colour, presenting no stratification, and containing abundance of hard pebbles
and boulders, all rounded and some of them scratched. It had the usual appear-
ance of boulder-clay, and I expressed this opinion to Dr Brown.
The Elie deposit I have not seen; but from the account given of it in Dr
Brown’s paper, and also by Mr Jameson, I cannot doubt that it also is a true
boulder-clay. In the section which Dr Brown gives in his paper, he represents
boulders in the deposit ; and he expressly says that the shells “are found cluster-
ing around and beneath the enclosed boulders, a fact which seems to show that
at the time these shells lived, this part of the sea-bottom must have been swept
by a strong current.” Dr Brown adds, that he had obtained from the Errol
deposit ‘“ portions of the skeleton of a seal.” Mr Jameson says, that in the deposit
at Errol containing Arctic shells—-being the same bed mentioned in Dr Brown’s
paper—he found many of the included boulders “glacially scratched—occasionally
one may be found with barnacles on it;” and he adds, that “‘ Entomostraca of
the genus Cythere also occur.”’ ||
In Canada, where till or boulder-clay abounds, marine shells have been found
in the deposit. (Amer. Journ. of Science for 1866, vol. 1xxxvil. p. 235.)
The fact of sea-shells, of various species, having thus been found in great
numbers, and at places far distant from each other, in the boulder-clay, seems
so conclusive as to the marine origin of the deposit, as to render further evi-
* Brit. Assoc. Reports for 1864, p. 58; R.S. E. Tr. vol. xxiv. p. 617.
t Trans. Glasg. Geol. Soe. vol. ii. p. 150,
t Berwickshire Nat. Club, vol. v. p. 238.
§ Vol. xxiv.
|| Proceed. of Lond. Geolog. Society for January 1865, pp. 175 and 196.
VOL. XXY. PART II. SM
672 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROFE,
dence superfluous. It therefore may simply be mentioned, that confirmatory
evidence is afforded by numerous cases of boulder-clay alternating with strata,
the marine character of which is indisputable. Localities are mentioned by Mr
GEIKIE* as occurring in Roxburghshire, Lanarkshire, and Ayrshire, where beds
of unstratified boulder-clay, 30 to 40 feet thick, alternate with beds about the
same thickness of stratified clay and stratified sand, the former sometimes con-
taining marine shells. In such cases, the boulder-clay virtually forms part of
the series.
5. Several observers, who have found marine shells in the boulder-clay, have
been struck with their broken or fragmentary condition. This feature is not
observable in the stratified or laminated clay beds where the same shells occur.
In the brick clays of Lanark, Renfrew, and Ayr shires they are found perfect in
form, and apparently in their natural position. But in boulder-clay, the same
shells have been mutilated and smashed, so that it is difficult to identify the
species.}| Is it not a fair inference from this fact, that the beds in which, at the
bottom of the sea, these shells had lived, must have been disturbed and deranged
by some intrusive body of great weight and power, which both crushed the shells
and obliterated all traces of stratification or lamination in the structure of the
beds? It seems to me that such effects would result from the intrusion of ice-
* Glacial Drift, pp. 54 to 65.
+ Thus Dr Watson, in describing the boulder-clay of Arran, says that the shells in it “ are
very much broken. The shells may often be found crushed, yet with each fragment in its own place.
Some of the large specimens of Cyprina, though unbroken, are indented, as by a sudden violent
blow. The whole condition of the shells suggests that heavy stones have been dashed down upon
them.” Dr Bryce also notices that the Arctic shells found by him in Arran were “in single valves
or in a fragmentary state, yet not so small but that the species can be determined.”—Geology of
Arran, p. 168.
The shells in the boulder-clay of Caithness have been examined by a great number of com-
petent geologists, who all give the same testimony, Mr Pracu describes the shells so “ broken”
and “rubbed” he could find only one entire shell. Messrs Crosskey and Rogertson of Glasgow,
having gone to Caithness on purpose to examine the boulder-clay there, describe it as ‘‘ a hard and
compact mass, with striated and polished boulders, being in appearance similar to that in the west
of Scotland, The shells are thinly interspersed from top to bottom, and are of a water-worn and
fragmentary character. They appear equally distributed, as if the whole mass had been mixed up
and kneaded together.”—Geolog. Society of Glasgow Trans. vol. iii. p. 126. Mr Jameson of Ellon
says that the drift-beds of Caithness contain “ remains of sea-shells all through them, and these are
broken, rubbed, and scratched, and evidently by the same agency that marked the rocks and
boulders.” His theory to account for the facts, is, that “much floating ice seems to have passed
over the district from the N.W., which crushed and destroyed these marine beds, broke the shells,
and mixed them up with other superficial debris into that mass of rough pebbly mud which now
overspreads the surface.”—Proceed. of Lond. Geol. Society for 1865, pp. 176-7.
Mr Jameson has also the following statement regarding a deposit of boulder-clay near Paisley
which he examined. He says—“I sometimes found, on heaving up a boulder, a number of young
crushed mussel-shells beneath it, as if they had been squashed by the fall of the stone. The clay
around also occasionally exhibited black stains, as if from the decay of sea-weed that had been attached
to the stone.”
At the various places where the Rev. Mr Crossxey found sea-shells in boulder-clay, along the
coasts of Scotland, England, and Ireland, the shells were “ very fragmentary, and even single valves
are seldom found whole.”—Glasg. Geol. Soc. Trans. vol. ui. p. 151,
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE, 673
bergs, the lower portion of which penetrated the sea-bottom, pushing before
them boulders and pebbles, and pressing the sediment into-greater compactness.
Besides the generally mutilated condition of the sea-shells in the boulder-
clay, there is another circumstance, first pointed out by the late E>pwarp ForbEs,
which tends in the same direction. On examining the shells found in the drift-
beds of Wales, he observed that they belonged to different zones of life. These
drift-beds presented “a confused mixture of fragments of species from all depths,
both littoral and such as invariably live at a depth of many fathoms; inhabitants
some of muddy grounds, some of sandy, some of rocky. Deep and shallow
water species could not have lived together, or have been thrown up on one
shore.” His conclusion, therefore, was, that this confused and unnatural
mixture ‘indicated the action of some disturbing influence, through the agency
of icebergs, or a wave of translation, or of both combined.”
The beds to which this observation applied was, it is true, not boulder-clay
or till, but mud, gravel, and sand, “in the lowest beds of which were small and
large boulders of transported rocks polished and scored.” * The position of these
drift-beds was 1360 feet above the sea.
If icebergs acted on these drift-beds, as Epwarp Forses inferred for the
reasons mentioned by him, icebergs could have acted in like manner on the
materials of boulder-clay.
Those who look upon the boulder-clay as a land deposit, meet the fact of
marine shells being found in it thus :—They say that the glaciers which formed
the deposit reached the coast, as now in Norway and Greenland, and pushed
detrital matter out into the sea, where it became occupied by testacea. This
answer is not satisfactory, because the testacea are almost invariably found in a
mutilated state. These animals must have been bred and grown in asea-bottom,
which, whilst they lived, was undisturbed ; and if the disturbance of their dwell-
ings was due to the protrusion of glaciers, this would be admitting the marine
origin of the deposit. Moreover, if the climate was so severe as to bring glaciers
to the coast, icebergs would also abound in the adjoining seas; so that the
question would then be, whether the effects were more likely due to the pro-
trusion of glaciers, at the mouths of valleys, or to icebergs drifting in the sea
and grating along the bottom. On the former supposition, boulder-clay would be
formed only at particular spots, viz., at the mouths of valleys which reached the sea.
On the latter supposition, boulder-clay would be formed much more extensively.
The great abundance and continuity of the deposit in Northern Britain is there-
fore better accounted for by the iceberg than by the glacier hypothesis.
The advocates of the glacier theory of boulder-clay have also referred to the
fact that terrestrial remains occur in the deposit, from which an inference
* Notes of a Ramble through Wales, by W. S. Symonps, 1864, p. 12.
674 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
is drawn, that the deposit must have been formed, not in the sea, but in the
land, it being supposed that these remains were drifted into the boulder-clay
by rivers.* But rivers flow into the sea, as well as into lakes. It is true that
the boulder-clay near Glasgow and near Falkirk, at both of which places
elephants’ tusks were found, presented no marine shells. But it is equally true
that elephants’ tusks have been found in what are allowed to be sea-beds. At
Kilmaurs (Ayrshire), two tusks of an elephant were found in a bed of stratified
mud 9 inches thick, which was overlaid by a bed of sand containing sea-shells,
these shells being covered by boulder-clay. (Journ. Lond. Geolog. Soc. vol. xx.
p. 217). In Dumbartonshire, the bones of a rein-deer were taken out of a bed of
laminated clay, associated with sea-shells.+ (Edin. Phil. Journ. new series,
vol. vi. p. 105.)
Mr GEIKIE, in support of his view, endeavours to explain the association of
sea-shells and the bones of terrestrial animals in boulder-clay, by suggesting that
the mass of earth and stones may have been pushed forward by a glacier ‘“ close
to the sea-shore, and sea-shells might either be thrown up by high tides over
the bones previous to their entombment, or be deposited above them during the
slow sinking of the land.” He adds—“I mention this as a possibility, in order
that no difficulty need be felt in harmonising such a fact with the hypothesis
that the boulder-clay is a deposit from land ice, and not from icebergs.” (‘On the
Glacial Drift of Scotland,” p. 94.)
The possibility of the occurrence here suggested I admit. Its probability is
not so clear. But it is quite clear that the occurrence of elephants’ bones at two
places in boulder-clay, where no sea-shells were found, is no conclusive proof
that the deposit must have been formed on the land, when, at two other places,
similar bones were found in pleistocene beds, which must have been at the
bottom of the sea when the bones were drifted into them.
6. I now pass to other facts which indicate that the boulder-clay not only
has been disturbed and intruded on by some foreign agent, but has, n some
cases, been moved en masse by some agent of tremendous power.
Thus Mr Cumminc, in his “ Memoir on the Isle of Man” (Proc. Lond. Geol.
Soc.” 4th Jan. 1854, p. 213), says—‘ There are appearances, as if the boulder-clay
had been forced violently amongst the different beds of limestone. Fragments of
the latter are torn up and carried forward, and these remain angular, though
much scratched, at no great distance in the mass of clay which now covers the
limestone beds.” .
The late Dr Fiemine (“Lithology of Edinburgh,” p. 60) pointed out ‘“ near
Gilmerton, a sandstone quarry, where the outcrop of the rocks is seen, covered
* GEIKIE on Giacial Drift, p. 93.
+ Bones of elephants, rhinoceros, &c., are found in Siberia very generally associated with Arctic
sea-shells. (Lyexz, “ Principles,” i, 183; Quart. Journ. Lond. Geolog. Society, 1st Feb. 1848.)
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 675
by a sandy boulder-clay, which, having been in motion, has squeezed or bent the
ends of the sandstone and shale towards the 8.E.” Two other localities are
mentioned by this observer, where the outcropping strata of shale had been in
like manner broken off and carried towards the 8.H., by some agent pressing
down upon them.
Dr Howpen, in describing the superficial deposits of Forfarshire (‘‘Edin. Geol.
Soc.” vol. i. p. 139), says that “‘in the Brechin Quarry, and in other localities,
where the strata are nearly horizontal, especially if they consist of thin lamine,
the rock has been broken up into shivers, large detached masses being embedded
in the (boulder) clay.” Dr Howpen suggests no explanation, but it is evident
that here also some agent must have ploughed up the strata, and disturbed the
covering of clay.
I might refer also to the curious foldings observed in beds of clay, and even
of sand, which both Sir CHartes LyeLtt and Mr GEIKkiz admit cannot be ex-
plained in any other way, than by supposing that icebergs or heavy masses of
floating ice had pushed them out of their original position.*
But the most remarkable case, where boulder-clay is shown to have been
pushed and pressed forward en masse, was described some years ago by two
most competent observers, Captain BrickENDEN and Mr Marrmins of Elgin, ob-
servers who wrote independent reports, the former in the ‘‘ Proceedings of the
Geological Society of London,” + the other in the “Edinburgh Philosophical
Journal’’| some years afterwards. Being much impressed with the importance
of the facts related by both observers, and wishing to obtain further information,
I wrote to the only one whose address I could discover, Mr Martins, and received
from him a letter, in which the following passages occur :—
“The Linksfield strata consist of a series of bands of limestone, shales, and
blue clay. These have obtained the name of Wealden, from the fossils in them.
Under these bands there lies a great deposit of limestone, called Cornstone. In
some places, the Wealden bands are separated from the Cornstone by intercalated
boulder-clay, having all the characteristics of boulder-clay met with throughout
the country. It has the same tenacity, and the same want of stratification, and
contains the usual travelled pebbles and blocks. The only difference observable
is, that the clay when intercalated has a purplish tinge, evidently acquired by
contact with the blue clay of the Wealden. It also contains fragments of the
limestone from the band lying immediately above it. In some instances, large
* Ly=tt, “Antiquity of Man,” p. 138. Mr Gers (‘Glacial Drift,” p. 119), after alluding to cases
where ‘‘ beds of clay were fairly bent back upon each other,” says, ‘such contortion must he due to
powerful pressure. It may have been produced by masses of ice standing here, and pushed onward,
partly by their own impetus, partly by the action of winds or currents. The compression to which
such a weight of ice would give rise, would probably be quite sufficient to corrugate beds of clay and
sand.”
+ Proceed. of Geol. Society for 1851, vol. vii. p. 289.
t E. Ph, J. for 1856, vol. iv. p. 222.
VOL. XXV. PART II. SN
676 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
flakes of the laminated blue clay were lying in it. This mass of intruded
(boulder) clay always presents great irregularities in a section. At one place it
is scarcely a foot thick, allowing the Wealden beds to rest nearly on the Corn-
stone. Ata short distance it rises abruptly to the height of ten feet, in the form
of a cone, from the apex of which several narrow bands stretch up through the
fissures of the overlying mass, looking like veins of red granite among crystalline
rocks. At one place the boulder-clay formed a rounded mass, and the super-
incumbent bands of limestone were folded neatly over it, so as to present the
appearance of a stone arch. By the movement, a number of fissures had been
caused in the overlying bands, into which the clay had been forced up. Some of
these rents were 6 feet in length.”
‘“‘Tt may be noticed that the surface of the Cornstone, when cleared of the
till, is found finely smoothed and polished; any hollows on the rock are also
smooth and polished. The Cornstone strata are not in the least disturbed.”
Mr Martins had the goodness to send with his letter two or three sections,
showing the relative positions of the boulder-clay to the rocks above and below
it. These sections, it is right to add, were made by Mr Martins from memory, as
the quarry had ceased to be used, and was filled with rubbish. The sections,
therefore, can be taken only as giving a pictorial representation of what is
described in Mr Martins’ letter.*
Both Captain BrickENDEN and Mr Martins express their conviction, produced
by a study of the sections when they were exposed, that the boulder-clay had
been forced im between the upper Wealden bands and the lower Cornstone rock.
Captain BRIcKENDEN notices particularly the polished and striated surface of the
Cornstone, caused by the passage and attrition of the overlying boulder-clay.
He states that the direction of the striations was N.W. and S.E., and he inferred
from the appearances, that the boulder-clay had been thrust in from the N.W.
When he visited the quarry, the exposed boulder-clay had “a bright red colour,”
which made the embedded fragments of the purple Wealden rocks all the more
striking. The explanation suggested by Captain BrickENDEN is precisely the
theory which it is the object of the present Memoir to support, viz., that the
materials of the boulder-clay “had been subjected. to the action of vast and
extensive masses of ice, which by continuing to press onwards the accumulations
of clay retained beneath it, had, by a force superior to that which the beds above
could offer in resistance, eventually produced the phenomenon.”
If it be said that a glacier could have propelled and pushed the boulder-clay
between the rocks, quite as well as masses of floating ice, the question would be,
whether, in the places referred to, where the boulder-clay has apparently been
pushed forward en masse, there was any probability of a glacier having existed.
* Two of these sections are given on Plate XXXI.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 677
The low-lying, flat country of Elgin is, to say the least, most unfavourable for the
glacier theory; and the Isle of Man is, from the absence of mountains, equally
unfavourable.
The facts and views set forth in the preceding paragraphs, show that the
materials of the boulder-clay have been disturbed, intruded on, pushed forward,
and heavily pressed on by some extraneous agent; and if it be allowed that these
materials, when so acted on, formed a sea-bottom, very little doubt can exist that
floating ice was the agent.
7. But it will be asked, whether similar effects are now observable in the
Arctic regions, where there are icebergs and floes drifted about by the winds and
currents? Can it be shown that they do work on the sea-bottom or shores at all
analogous to the appearances presented by our boulder-clay and drift-beds ?
In all the channels and estuaries of the Arctic regions, we know that the sea
is constantly covered with floating ice in every variety of form. As icebergs, they
often strand in places where the sea is 1200 feet deep. On one occasion, the
keeper of the lighthouse at Belle Isle, near the mouth of the St Lawrence, in
latitude 50°, counted no less than 496 icebergs, some of them 200 feet high and
half-a-mile long. About 100 of them were stranded, or were grating over the
submarine banks.* .
It is not difficult to conceive what must be the effect on a sea-bottom, what-
ever the materials, of icebergs having a size greater than the hill of Arthur Seat.
Soft materials would be so disturbed and ploughed through, that any appearance
of regular bedding would be obliterated, testacea would be crushed, whilst hard
fragments of rock would be pushed forward and rounded by the enormous friction.
This inference as to the disturbance and tearing up of the sea-bottom is con-
firmed by Dr SUTHERLAND, a surgeon in one of the Arctic expeditions. He says
that in Davis’ Straits, the icebergs, by their action on the sea-bottom, produce
‘whole rafts of submarine forests” of sea-weed, which float on the surface of the
sea; and when the sea-bottom in these straits is dredged, little else than ‘‘broken
shells” are brought up.+
The disturbance and dislocation of the submarine beds where icebergs abound,
is further evidenced by the large amount of muddy sediment raised, discolouring
the sea not only to the surface, but for many miles round.
Messrs DrEAseE and Simpson, in the account they give of their Arctic
discoveries in the year 1838, describe a long low spit, composed of gravel and
coarse sand, in some places more than a quarter of a mile wide, the formation of
which they did not hesitate to attribute to the action of floating ice—judging
by what they saw done by ice.
* See a short paper on this subject by Principal Dawson, of Montreal, in the ‘ Canadian
Naturalist.”
+ Lond. Geolog. Journal, vol. ix. p. 306. + De La Bicuz, Geolog. Observer, p. 266.
678 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
Dr Hayes, in his account of a visit to the West Coast of Greenland in 1867,*
says, “ where the current is swift, and the ice is pressed down upon the land with
great force and rapidity, the rocks are worn away until they are as smooth and
polished as the surface of a table.” The bearing of this remark on the innumer-
able smooth and polished rock surfaces in Scotland and the north of England
needs not be pointed out.
Dr Hayes mentions another effect of floating ice. He says that “‘a shelf of
ice glued to the shore forms a winter girdle of all the Arctic coasts. It is
usually broken away towards the close of every summer, when the masses of
rock which have been hurled down upon it (during the previous eight months)
from the cliffs above are carried away and dropped in the sea. The amount of
rock thus transported is immense; and yet it falls far short of what is carried by
icebergs” (p. 403).
Much to the same effect, on both of these points, Dr Wa.uicu mentions that,
when dredging off Labrador at a depth of from 10 to 15 fathoms, he found the
sea-bottom to consist “ wholly of uncovered rock or of boulders” —‘‘ owing (as he
adds) to the long continued action of drift ice and currents.” +
Another effect produced by floating ice has been observed—the formation of
ruts and strice on the smooth surfaces of rocks. Many competent observers
have given evidence on this point.
The foregoing statements refer to what is now seen going on, wherever there
are icebergs and icefloes, and they show that these agents, if they existed in
Scottish seas, at a former epoch of the world, must have had the power of pro-
ducing most of the phenomena connected with our pleistocene deposits.
It is not unimportant to remark, in further confirmation of this view, that in
the Arctic regions there exist boulder-clay and boulders pretty high above the sea,
just as in Scotland, and that all the Arctic travellers who have paid attention to
the subject do not doubt that the chief agents in producing them were icebergs
and shore ice.
Thus Dr SurHERLAND found in Barrow’s Straits, up to a height of about
1000 feet, great numbers of boulders, all (he says) clearly transported by coast-
ice previous to the elevation of the land,—just as he saw them being transported
in that way along the existing shore of Greenland.
Mr Lamont, in his Memoir on Spitzbergen, takes notice of several places
where icebergs had evidently left their footprints, when the land was submerged.
At one spot, about 20 feet above the present sea-level, he found a trench, about
100 yards long by 3 or 4 feet deep, formed among boulders, and caused, as he
believed, by an iceberg drifting through them. At another spot, he found what
* The Open Polar Sea. Tt North Atlantic Sea-Bed, p. 40.
t Sir Cuarztes Lyetr—(1) Travels in North America, vol, ii. p. 173; (2) Lond. Geolog. Journal
fer 1849, Trapolli in Scandinavia ; Lond, Geolog. Journal for 1868, xcviii.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 679
had the appearance of a gigantic causeway of boulders, caused apparently by
icebergs sliding over them, and levelling them.*
It also deserves notice that true boulder-clay or till exists in the Arctic
regions, and in districts where there is much less probability of glaciers than of
icebergs having been at work. Sir Jonn Ricuarpson evidently describes this
deposit when he mentions “ a denacious and somewhat slaty blue clay, containing
many boulder-stones,” on the western shores of Hudson’s Bay,—a country very
little elevated above the sea, and possessing no mountains where glaciers could
be formed.t
Nor is it irrelevant to notice the occurrence of boulder-clay in the Antarctic
regions, and the opinion formed by that eminent naturalist, Mr Darwin, as to its
origin. After describing “great masses of mud of a dark colour, full of boulders
of primitive rocks derived from mountains situated to the W. or S.W. about
60 miles distant,” he says, that “the deposit in all respects resembles the till of
Scotland ;” and adds, that “at present the oceanic currents off Cape Horn set
from the west; so that if the ancient currents had the same direction, the
phenomena would be explained by floating ice.”
It thus appears that both in Arctic and in the Antarctic regions, where float-
ing ice has abounded, boulder-clay, boulders, and polished rock surfaces exist:
These phenomena do not occur in warmer regions of the earth. Wherever they
do occur, there are indications of the sea having stood much higher than at
present, so that ice could have drifted at the necessary level; whilst, on the
other hand, in many districts there is a total want of the conditions necessary
for the formation and for the movement of glaciers in the required direction.
8. In the previous part of this Memoir, I have attempted to show—1st,
That glaciers were not the agents to which boulder-clay owes its origin. 2d,
That an examination of the deposits, containing, in numerous localities, sea-shells
generally mutilated, suggests a submarine origin. 3d, That the way in which
the deposit has been driven forwards, and pushed between older rocks, indicates
pressure by some agent of enormous weight and magnitude. 4th, That icebergs
and shore-ice would probably answer these conditions, and are seen now in the
Arctic regions producing similar effects.
Assuming that the facts adduced at all events establish the probability of
the theory, that icebergs and shore-ice would account for most of the drift
phenomena in Great Britain, I proceed to offer a few remarks as to the circum-
stances and condition of Great Britain at that time.
Most geologists are agreed that, at the period of the boulder-clay, the sea
must have stood greatly higher upon the land than at present. Beds of sea-
* Lond. Geolog. Journal for 1868, vol. xvi. p. 433.
+ Franxuin’s Journey in 1823, pp. 499, 501, 583.
t Phil, Journal for 1841, vol, xix. p, 530.
VOL. XXV. PART II, 80
680 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
shells occur in the pleistocene beds of Lanarkshire, at a height of 526 feet above
the sea; and as one of these shells is the Cyprina islandica, which requires for
healthful existence a depth of at least 30 fathoms, that Lanarkshire deposit
implies a submergence of more than 700 feet.
But in Wales, sea-shells of a similar character have been found in drift-beds
at a height of no less than 1600 feet above the sea. And there are in many parts
of England and Scotland beds of clay, sand, and gravel, at a height of nearly
2500 feet above the sea, which, judging from their stratification and materials,
must have been marine.
If, therefore, the whole of the British Islands were submerged to the depth of
2500 feet lower than they are at present, they must have presented little else
than an archipelago of islands,—few of which would, at their highest points, be
more than 1500 feet above the sea.
As many of the shells found in these pleistocene beds are of an exclusively
Arctic type, the sea, during the period of submergence now referred to, was
favourable for the presence of drifting ice,—assuming, in the meantime, the
existence of some current to bring the ice.
But it is not Great Britain only which was submerged. In Sweden, sea-shells
of the same Arctic type have been found in drift-beds to the height of 800 feet,
there being also beds, apparently marine, which occur at a still greater height.
These Swedish shell-beds have furnished one or two instructive facts bearing
on the process of submergence, which probably apply to Northern Europe gene-
rally. Some of the beds are occupied almost exclusively by shells which lived in
shallow water. These are in some places covered by beds containing shells of
deep-water habits,—indicative not only of a submergence of the country, but a
submergence to a considerable extent. Farther, it has been ascertained that
these deep-water shells belong to much more Arctic types than those of shallow
water which preceded them,—indicating that as the submergence went on, the
cold was increasing. Then, again, other shell-beds have been discovered at a
lower level, and evidently, from their geological relations, of a more recent date
than those above mentioned, in which the Arctic shells are fewer in number and
species,—a fact which suggests that, as the land emerged from beneath the
waters, the climate improved.*
It is, however, not in Sweden only that these Arctic shells are found on the
Continent. Sir RopEr1ck Murcuison, in his great work on the Geology of Russia,
has shown that the drift-lands of that country are full of them, implying a
general submergence of the whole of Northern Europe under the waters of an
Arctic sea, reaching as far south as about latitude 51°.
* These interesting and instructive facts will be found stated in a Memoir, by Mr Gywn
Jerrreys, in the British Association Reports for 1863; and also in a paper, by Professor Sars of
Christiania, in the Edinburgh Phil. Journal for 1863.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 681
Assuming, then, that icebergs and shore-ice prevailed in the sea which covered
the British Islands and other parts of Northern Europe, how would these operate
as agents in the production of boulder-clay? In some places, boulder-clay lies
over stratified beds; in other places, boulder-clay is covered by them. In the
former case, it may be supposed that an iceberg pierced through the sea-bottom
only to a certain depth, leaving the part next to the rocks untouched. In the
latter case, it may be supposed that more sediment was subsequently deposited
by currents over the disturbed beds, and remained undisturbed. There are
cases where, in one section, there have been found as many as three layers of
boulder-clay, each from 20 to 30 feet thick, alternating with laminated beds of
clay and sand. In such cases it is only necessary to suppose that icebergs came,
drifted by currents, at different periods, some being larger and deeper in the water
than others.
If the glacier theory be adopted, which assumes that the boulder-clay was
formed on the land at the end of a glacier, or under its mass, then to account
for these alternations of marine beds with boulder-clay, there must have been as
many oscillations of the land below and above the sea as there are layers of
boulder-clay—a supposition surely very improbable.
9. But a difficulty here suggests itself. Where did these icebergs come
from? They could not have been generated by Scotch or English glaciers, if,
when the land was submerged, there were no mountains higher than 1500
feet.
. Where, then, was the high land to give birth to glaciers from which these ice-
bergs came; and was there a current in the ocean so strong and extensive as to
bring these icebergs over North-Western Europe, and in the direction indicated
by the transported boulders and rock surface striations ?
That the physical geography of the Northern Hemisphere must have been
totally different from what it now is, is plain from the circumstance that the
climate was so different. Perhaps the colder climate was brought about by the
same conditions, which would suit the formation of icebergs, and the existence of
a great current from the north-west by which they were drifted. The problem
is to ascertain what circumstances would produce an Arctic temperature in North-
Western Europe, and so far south as Jatitude 51°.
Labrador is in the latitude of Great Britain. What are the circumstances
which give to that country a mean annual temperature of 25°, and a mid-winter
temperature of—50°? Two causes co-operate—an Arctic current, loaded with ice-
bergs, which flows past its shores; and proximity to the high land of Greenland,
whose snow and ice chill the atmosphere.
From this fact, is it not probable that North-Western Europe, when it pos-
sessed a Labrador climate, was indebted for it to similar conditions ?
One thing is certain—the Gulf Stream could not then have flowed along its
682 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
present course. But its absence would cause the winter temperature of Scotland
to fall only by 28°; and a winter temperature of 10° would not give to us a
Labrador climate. Other conditions must therefore be sought for.
At present the Arctic current, which flows into the North Atlantic, is strong
enough to carry icebergs even farther south than latitude 50°. They have been
sometimes seen in latitude 40°. Of course, that Arctic current cannot cross the
Atlantic and float icebergs on Great Britain, because the Gulf Stream would
intercept it. But suppose the Gulf Stream not to run, as it now does, in a N.E.
direction towards Norway. Suppose that, by the Isthmus of Panama being 300
feet lower than at present, the equatorial current, instead of being deflected by
the American coast northwards, were to flow into the Pacific, and find its way
through Behring’s Straits, where there is now a current running from the Pacific,
the Arctic current which now flows into the North Atlantic would not only have
no Gulf Stream to interrupt it in its progress towards Europe, but would
be immensely augmented in volume and speed. The stream passing through
Behring’s Straits would carry with it a tendency to move eastwards, having
acquired that tendency in equatorial regions by the earth’s diurnal rotation.
If high land nearer than Greenland is thought necessary, evidence is not
awanting to justify that supposition.
In the first place, it is well ascertained that Greenland at its southern extremity
has long been sinking, whilst its northern parts are rising.* Dr Kane and Dr
Hayes endeavoured to find where the axis of oscillation is situated. The one
gives 76° of latitude, the other 7 7° of latitude. Both observers were struck with
the fact, that whilst to the north of this supposed axis, lines of raised beaches
were visible, none were visible to the south of it. Dr KANE saw and counted no
less than forty-one beach lines, at a part of the coast in latitude 78° 30’, or
about 150 miles to the north of the axis; the highest being 480 feet above the sea.
Now it is not unreasonable to suppose, that on the south side of the axis of oscilla-
tion, the sinking would be at the same rate as the rising on the north; in which
case, what is now the southern extremity of the continent, which is in latitude
60°, and therefore about 1000 miles from the axis of oscillation, must, before the
sinking began, have been 3200 feet higher than it is at present, and a great
deal of what is now sea-bottom to the S. and 8.E. of Greenland must have been
dry land.
The probability of changes having occurred in the bed of the North
Atlantic is all the greater on account of the volcanic convulsions to which it has
frequently been subject, of which not only Iceland is a proof, but the igneous
* Dr Hoatrerin of Iceland, in his letter to Mr R. M. Smrru, quoted on page 667, mentions—
‘‘ T have seen the secular elevation of the northern shores of this island ; and it is not unlikely that
the north coast of Greenland is in a similar state.”” Therefore it is probable that the north extremity
of Iceland rose up simultaneously with North Greenland.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 683
rocks in the Western Hebrides and the north of Ireland, which are certainly more
recent than the chalk, and perhaps belong to the glacial period. On the shores
of the Baltic, it has been made out that during this period there were great
fractures in the earth’s crust.
Whilst there are geological reasons for assuming the existence of high land in
the North Atlantic Ocean, now submerged, there are physiological reasons in
favour both of high land and of a great Arctic current from the north-west. It
was the late Professor Epwarp Forses who first drew prominent attention to
the light thrown on the past history of the earth, by reference to the migrations
of the fauna and flora of a country. His remarks, as applicable to Great
Britain, are these—‘‘ There could not always have been such a separating abyss
between Northern Europe and Boreal America as now divides them. ‘The sea,
through a great part, must have been a shallow sea; and somewhere, probably
far to the north, there must have been ezther a connection, or such a proximity,
of and as would account for the transmission of a non-migratory terrestrial *
and a littoral marine fauna.” +
In another passage he says—“ It is strongly impressed on my mind that the
close of the glacial period was marked by the gradual swbmergence of some great
northern /and, along the coasts of which the littoral mollusks, aided by favouring
currents, migrated; whilst a common flora { became diffused over its hills and
plains. Although I have made icebergs and icefloes the chief agents in the trans-
portation of flora southwards, I cannot but think that so complete a transmission
of that flora as we find on the Scottish mountains, was aided perhaps mainly by
land to the north now submerged.” (‘‘ Memoirs of the Geological Survey of
Great Britain,” vol. i.)
10. In considering the claims of the two. theories which have been proposed for
explaining the boulder-clay deposit and other drift phenomena, it is proper to
keep in view, that whilst there are many of these phenomena which are sus-
ceptible of explanation on either theory, there are others again which, whilst
* Allusion is probably here made to the remains of the woolly-haired elephant, rhinoceros,
musk ox, rein-deer, black bear,.and polar bear having been found in pleistocene beds in various parts
of Great Britain. If, as is believed, these animals belong naturally to North America, how did they
reach the small island of Britain ?
7 In a list of sea-shells given by Mr Jameson of Ellon, as found in the boulder-clay and other
pleistocene beds of Scotland, amounting altogether to 137, he represents 134 as now living in the
Arctic circle, 60 in North-Eastern America, 26 in the North Pacific, and 82 in British seas. The
number now living in the Arctic circle, North-Eastern America, and North Pacific, but not in British
seas, is 52.
{ Professor E, Forses mentions, in illustration of this point, the EHriocaulon septangulare,
“known in Europe only in the Hebrides, and at Connemara, in the west of Ireland. Elsewhere,’’ he
says, “it is an inhabitant of Boreal America, which is its true native country, and from whence, by
means of transport, it has in all probability been introduced naturally into the British Isles.” Pro-
fessor Batrour has given to me the names of the following additional plants, natives of Labrador
and Canada, which are found in Skye and on the west coast of Ireland, but nowhere else in Europe,
viz., Neottia gemmipara and Sisyrinchium anceps.
VOL. XXV. PART Il. 8P
684 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
difficult of explanation on the glacier theory, are very intelligible on the other.
A few of these difficulties will now be referred to.
(1.) It has been mentioned, as a result of the examination of the sea-shells in
the ‘pleistocene beds of Sweden, that the period of greatest cold was when the
land was most deeply submerged. If this be the case, which of the two theories
is most reconcilable with it?
When the land was most deeply submerged, the mountains would be elevated
above the sea less than at any other period; and therefore circumstances would
not be favourable for the formation of glaciers.
On the other hand, circumstances would be especially favourable for the
drifting of icebergs among the archipelago of the British Islands.
(2.) The unequal distribution of boulder-clay over North-Western Europe
deserves a passing remark. The deposit is much more abundant in Scotland than
in any other country. Whilst it exists in both England and Ireland, it is chiefly
in the northern and midland counties. In the southern parts of both England
and Ireland it is hardly known.
Then in Denmark, the beds which are there called boulder-clay appear not
to have been so disturbed as in Scotland. There are beds of clay which contain
boulders and pebbles, evidently transported, and which also contain Arctic shells;
but these are not described to be in a fragmentary or mutilated condition. These
shells are described as belonging to species which are known to inhabit shallow
water; and it is added by ForscrtamMer,* that there are extensive beds of sand,
containing boulders and pebbles, which seem to belong to the same epoch as the
boulder-clay. These beds of sand he also looks on as indications of a shallow
sea.
Why should there be in the south of England and Ireland a less develop-
ment of boulder-clay? May it not be that the icebergs melted before reaching
so far south ?
Why should there be little or none of the true “ till” in Denmark? May it
not be that the icebergs, brought by a north-west Arctic current, were inter-
cepted by the Scotch archipelago? and if any drifted towards Denmark, would
not the shallowness of the sea prevent them floating over and disturbing the
banks of mud and sand forming the sea-bottom there ?
Shore ice alone probably floated over these Danish waters, carrying boulders
and pebbles, and spreading them on the submarine banks.
Whilst some such explanation of the unequal distribution of boulder-clay is
suggested by the theory of water-borne ice, it is not easy to draw any explana-
tion from the glacier theory.
(3.) Many persons have been perplexed at finding a ridge dividing two valleys,
forming what is sometimes called in the Highlands a col, consisting of rock smoothed
* Journ, of London Geological Society for 1845, vol. i. p. 373,
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 685
and striated by the action of ice. Thus, for example, the late Mr Maciaren points
out that the ridge which divides the Gareloch from Loch Long, about 450 feet
above the sea, as also two other ridges to the eastward, the one 700 feet, and the
other about 1700 feet above the sea, present rocks the surfaces of which are
‘smoothed and rounded off.” Mr MActaren remarks upon this fact— A glacier
lodged within the valley would grind off the asperities of the rocks at its bottom ;
but what smoothed the very tops of the ridges? Is it not probable that it was
icebergs ?”’ *
The Duke of ArGyLz was struck with the same appearances on the ridge of
hills dividing Loch Fine and Loch Awe, and at a height of about 1800 feet above
the sea. In a letter addressed to the late Principal Forzers,} His Grace observes,
“Tn this case glacier action is impossible. Even if this hill had been the seat of
a glacier, it could only have been snow, so near the summit. The only explana-
tion which seems to me possible is, that this peak, when subject to the grinding
force, was a rocky islet above the surface of a glacial sea, and that floating ice-
bergs drifting from the N.E. were constantly grinding upon its sides.”
In Arran, as Dr Booc Watson points out, there are several ridges between
adjoining valleys which are smoothed in a like remarkable manner. He has no
doubt that they were smoothed by ice; but he leans to the opinion that glaciers
may have produced the effect, by overflowing the sides of the valleys in which
they were formed.
(4.) Another remarkable phenomenon is the position of isolated boulders on
narrow ridges of hills, or ledges of rock, from which to all appearance the slightest
force could dislodge them. The wonder is how these boulders could have been
placed in such precarious positions.
The Duke of Arcyte takes notice of a number of these boulders as being on
the hills about Loch Fine and Loch Awe, adding, that it is much less difficult to
account for their transportation on the supposition of floating ice than of glaciers.
Professor Ramsay, in his “ Ancient Glaciers of Wales,” gives a representation
of several of these boulders perched on the very edges of cliffs; and I can, from
personal observation, as well as sketches made by myself in Wales, confirm Pro-
fessor Ramsay’s account of the singular appearance which some of these “blocs
percés” present. One of these boulders, of angular shape (being 27 feet long, 15
feet high, and 6 feet broad), and weighing about 180 tons, is stated by Professor
Ramsay as being} ‘on the very crest of the slaty ridge of” a mountain, about
2000 feet above the sea. ‘The parent rock is at least a mile distant.” What
says Professor Ramsay to the question, how this boulder was transported? “I
am aware it has not been customary to consider accumulations at so great an
* Edin, New Phil. Journ, for 1846, vol. xl. p. 141.
t Proceedings Roy. Soc. Edin. vol. ii, p. 461.
t Ancient Glaciers of Wales, p. 80.
686 = MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
elevation as belonging to glacial marine deposits. But when we consider their
continuity with the shell-bearing strata,* their regular smoothly sloping outline,
and add to this the travelled boulders and masses of rock on the summits of hills
and ridges 2300 feet high, it seems impossible to resist the conclusion that the
whole is of marine origin, and due to the operation of one set of causes extending
over a definite period.” +
The conclusion which Professor Ramsay drew from these phenomena was,
“that the blocks of stone that now strew our continents and islands were chiefly
dropped by the same agency —icebergs—that is now sowing the Western Atlantic
with earth and boulders derived from the mountains and coasts of Greenland,
where glaciers descend to the sea.” |
There is another fact connected with the position of boulders which has often
arrested my attention. They are more frequently found in clusters, at or near
the tops of hills of moderate height, than anywhere else. On the hill of Croy,
near Kilsyth, and on several hills to the west of Dunfermline, examples occur.
Almost all the very large boulders, which are known to me, are situated near
rising ground, and on the east side of it—as in the case of the Clochodrick stone
in Renfrewshire, the great conglomerate boulder near Doune, the Carlin stone
in Dunmore Park, and the Auld Wives’ Lift, near Milngavie.§
Floating ice would ground most frequently on islets or shallow places, and
discharge its cargo there on melting. Glaciers occupying chiefly the lowest parts
of avalley would discharge their cargoes at the bottom. Therefore if boulders,
either singly or in clusters, most frequently occupy crests or ridges of hills, they
afford evidence more of icebergs than of glaciers.
(5.) There is, however, one phenomenon of a perplexing kind, which I admit
cannot be easily explained by either of the two theories. I allude to the boulders
whose present position has been ascertained to be higher than that of the parent
rock. Such cases have been made out in the Isle of Man, Cumberland, and
Roxburghshire. If floating ice will not explain these cases, still less will land
ice, which, being moved by gravitation, must carry everything to a Jower level.
On the other hand, instances are on record of stones and gravel being raised to a
higher level by means of floating ice. Sir CHarutes LYELL states, that on the
coast of Norway sheets of ice with pebbles and moderately-sized boulders have,
during a storm, been known to be driven up fully 50 feet above the sea-level. It
* Professor Ramsay mentions (p. 96), that sea-shells were found by him at a height of 1300
feet above the sea, ‘‘ two miles west of Snowdon, on a sloping plain of drift charged with erratic
blocks, one of which, of great size, is known as Maen-bras, or the large stone.”
t Proceed. Lond. Geolog. Society, vol. vii. p. 373.
t Anc. Gl. of Wales, p.-92.
§ De Luc (as quoted by Sir James Hatt, Ed. R. S. Tr. vol. vii. p. 160) says, “ that the granitic
blocks lying in the district between Berlin and the Baltic, occur frequently, and almost constantly,
in very numerous assemblages, upon the summits of the sandy hills with which that country is
interspersed, whilst none are to be met with in the intervening valleys.”
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 687
is also related that Sir James Ross once saw an iceberg capsize, bringing up mud
and stones to a height of more than 100 feet from the sea-bottom. Perhaps,
therefore, the anomalous position of some boulders, in respect of being above the
level of the parent rock, may, on the iceberg theory, admit of some explanation.
On the glacier theory they admit of none.
(6.) The chief objection to the views which they have submitted in this
Memoir, may be found in the following paragraph :—
“ The iceberg hypothesis will not account for the phenomena. We cannot
conceive of a set of ice-rafts moving for ages 7z one persistent direction within a
given area of the sea. <A group of huge bergs in high latitudes often exhibits, on
the contrary, a scene of the wildest confusion. If we could examine some parts of
the sea-bottom off the Greenland coast, we should find them bruised and scored
in every direction by the grounding of the bewildered icefloes.’*
Whilst, in this passage, it is admitted that rocks can be smoothed and striated
by icebergs and icefloes, it is said that the “persistent direction” in which the
agents must have moved to produce the ‘‘ phenomena,” indicates some other
agency than icebergs, because these icebergs would not have moved “for ages in
one persistent direction.”
The opinion thus expressed is not supported by evidence, and, moreover, is:
inconsistent with all the probabilities of the case. It is true we cannot see the
markings made on the rocks which form the sea-bottom off Greenland, but, as
there is an Arctic current always flowing past that coast out of the Arctic circle,
loaded with icebergs and shore ice, the great probability is, that the scorings are
not “in every direction,” but generally in a direction coincident with that of the
current. he
At the epoch of the boulder-clay in Scotland, I have assumed that there was
a north-west Arctic current which flowed down on Great Britain, a current of
ereater strength and extent than any of the existing Arctic currents ; and I have
suggested some reasons for the probable existence of such a current. If icebergs
were drifted by it over the submerged land, is it not presumable that the scorings
on the rocks would be all approximately ‘‘in one persistent direction?”
At all events, is there not more likelihood of this one persistent direction
being produced—keeping in view the great extent of the area on the earth’s
surface over which it prevails—by an oceanic current loaded with ice, than by
any imaginable system of glaciers or ice-cakes ?
11. In a former part of this Memoir I stated, that whilst the evidence from
various sources showed that the agency concerned in abrading, striating, and
transporting, had moved generally in a south-east direction, there were exceptions,
which, however, did not militate against my views as to the origin of boulder-
clay.
* Glacial Drift, by A. Gerxrs, p. 75.
VOL. XXV. PART II. 8 Q
688 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
These exceptions appear to indicate two agencies—one of a general, the
other of a local character.
(1.) It has been already noticed, that in the Norfolk cliffs there is a boulder-
clay, the lowest of all the drift-beds, which lies directly on the chalk rocks. In
this boulder-clay there are boulders which have been identified by Sir CHaRLEs
Lyext, Dr Mitcuett,* and other geologists, with the rocks of Sweden and Norway.
Mr GerxktE mentions (“ Geology of Scotland,” p. 303) that Professor Ramsay and
he found Scandinavian rocks at the mouth of the Tees. No one doubts that these
boulders must have been transported on floating ice, and by a current from the
N.E. or N.N.E. Acass1z+ himself allows the correctness of this view, observing
that the “Swedish blocks on the coast of England may have been transported on
floating ice.” And again—* The Norwegian blocks found on the coast of England
have been correctly assigned by LyE.t to a similar origin, viz., to masses of ice
set afloat.”
It is not merely on the Norfolk coast that these traces of a north or north-
easterly current, with floating ice, exist. Mr Tate of Alnwick informs me ina
letter (1st January 1869) that, at Alnmouth, “he took the direction of the strize
on two blocks as they lay in the clay, each block being about 3 feet long. In
one, the striz were from N. to S., in the other, from N.N.E. to 8.8.W. (true
bearings).” - In his “ History of Alnwick,” published since the date of his letter,
Mr Tate states, that at Abberwick, four miles west of Alnwick, there is a block
of grey granite like that at Aberdeen, which he refers to in proof of his remark
that there are in the district boulders which have been transported great
distances. The same accurate observer, in a note on the Farne Islands, in the
sixth volume of the “ Transactions of the Berwickshire Naturalists’ Club,”
mentions, “ that the surface of the whole of these islands had been ground and
smoothed by the passage of a powerful agent. Besides the smoothed surface, and
rounded little rock knolls, there are ruts or narrow hollows of some length,
whose sides and bottom are smoothed and striated. From the slope of the
dressings, it appeared that the agent had moved from the northward, which is
not from the land, but from the sea, and nearly parallel with the coast. On these
islands a larger area of glaciated surface is exposed than in any other part of the
north of England.”
The late Dr FLeEmine, in his “Lithology of Edinburgh,” p. 77, notices the
occurrence of flints in the drift beds of Fifeshire and Aberdeenshire, which he
infers, and with much probability, came from the chalk rocks of Denmark.
It is also a fact of no small significance, that in the Shetland Isles { the stria-
* Proceed, Lond. Geolog. Society for Nov. 1838.
t Proceed. Lond. Geolog. Society for Nov. 1838, pp. 179, 331.
{ Hisserr, Edin, Journ, of Science for 1831, vol. iv.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 689
tions on the smoothed rocks run N. 47° F., and in the Faroe Islands* N.E. 88°,
in each case pointing to Scandinavia.}
It is, therefore, highly probable that Scandinavia was, at a very early period,
cased in ice, and that icebergs from its glaciers flowed off towards the west and
south, loaded with boulders and pebbles, and leaving portions of these materials
on the east coasts of Eneland and Scotland. Such, as it strikes me, is the most
probable explanation of the north and north-east agency which is manifested
on our coasts.
At all events, no one has proposed to explain the transport of the Norwegian
and Swedish blocks to England by glaciers. Floating ice, in some way or other,
is the only imaginable agent.
If this be a right conclusion, it adds no little weight to the supposition that
the north-west agency, which is so much more clearly manifested, is of a similar
description.
(2.) But I freely admit that there are in England and Scotland manifestations
also of glacier action. Having been twice in Wales, and once in Cumberland, to
study the subject of these rock markings, I saw evidences of glaciers in both
districts. I have also seen glacial markings in the valley now occupied by Loch
Doon and the River Doon, in Ayrshire. I think that at Loch Skeen, and in the
valley north of Moffat, there are similar markings, and I cannot doubt that they
exist in Skye, as they were recognised there by the late Principal Forzgs.
The glacier markings, in several of the valleys where I have studied them,
appear to me more recent than the markings which belong to the general north-
west agency. In the valley of the Doon, and also in the valleys of Capel Curig
and Llanberis in Wales, it is not difficult to distinguish between the two sets. In
these valleys, the polished and striated rocks of the glacier are invariably low
down, and only a little way up the sides ; whilst the roches moutonnées and the
transported boulders, due, as I believe, to iceberg agency, are at a higher level.
Striations of the rocks, at these higher levels, are seldom or ever visible, unless
protected by boulder-clay ¢ from the influence of the atmosphere.
This distinction between two sets of drift phenomena, belonging to different
epochs, also arrested the attention of Dr Ropert CuHampers. He pointed out
some small valleys in the bosoms of which local glaciers had left their marks.
‘“‘ But (he adds) on the summits and high slopes of the hills, and on the portions
of the gneissic platform not connected with valleys, there are traces of an inde-
pendent and, I believe, earlier glaciation.Ӥ He then specifies a spot where the
* CHAMBERS on “ Faroe and Iceland,’ p. 28. é
} In Finmark and Northern Russia blocks have been found which have also been referred to
Scandinavia as their source.
{ At St Abb’s Head, the rocks, about 200 feet above the sea, were found striated, when the
boulder-clay was removed from them, but at no other places.
§ Edin, New Phil. Journal for 1853, vol. liv. p. 250.
690 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE.
two sets of glacial striz are seen crossing each other. ‘‘The strong normal
streaks athwart the hill from the N.W., a direction in which no local or limited
mass of ice could move, are chequered with fainter streaks, produced by this
simple down hill movement, which happens to be from W.S.W.”
12. The changes in the relative levels of sea and land, and the other events
referred to in this paper, may be briefly summarised thus—
(1.) A period existed subsequent to the epoch of the lowest Norfolk boulder-
clay before referred to, when the area now forming the British Isles was con-
nected with Continental Europe on the one hand, and with North-Eastern Europe
on the other, so as to permit terrestrial animals and flora to migrate from both
continents. |
At this period the climate was colder than at present, yet not so severe as to
prevent the growth of Scotch fir, spruce, yew, oak, and beech, the remains of
these trees having in England been found under the upper boulder-clay.*
(2.) Afterwards a great part of North-Western Europe was submerged, so
that in Scotland, and a considerable part of England and Ireland, mountains less
than 2500 feet above the present sea-level disappeared.
Most of the land animals which had inhabited the country (including elephants,
rhinoceros, rein-deer, musk, ox, &c.) would perish by starvation and drowning.
The climate became colder, so as to be suited for mollusks and other marine
animals of an Arctic type.
Shore-ice was formed along the coasts, and icebergs would be drifted by a
current from the north-west over North-Western Europe in great numbers,
stranding and grating along the sea-bottom.
It was at this time, probably, that boulders were transported and lodged on
the slopes of hills at great distances from the parent rocks; that rock surfaces,
especially on the ridge and crests of hills, were smoothed, and that the beds of
mud, gravel, and sand covering the rocks below the sea, were ploughed into and
frequently changed into the tenacious, unstratified deposit called boulder-clay.
The Arctic current which brought these icebergs, if it flowed from Behring’s
Straits eastwards across Hudson’s Bay, might have aided in the transport of
North Pacific mollusks and Labrador plants to Great Britain.
(3.) The next change was the elevation of Britain and the adjoining con-
tinental districts to such a height, that what is now sea between Great Britain
and the Continent and Ireland, became dry land, allowing again a migration of
plants and animals.
The land probably rose high enough to admit the formation of glaciers in the
principal valleys, in which case much of the boulder-clay previously formed when
* Sir Cu. Lyetn gives proof that the forest and lignite beds of Cromer were preceded and
followed by a period of glacial cold. These forest and lignite beds ‘‘ underlie the great mass of
glacial drift, in part unstratified, and containing boulders and angular blocks transported from great
distances,” —Prine. vol. i, p. 197.
MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 691
the land was submerged, would be pushed out, and moraines would be formed at
the mouths of these valleys.
By this time the general climate was improved, owing possibly to a rise in
South America, whereby the Gulf Stream was made to take its present course.
Forests of pine, beach, and oak, again appeared in the British islands.
Remains of these, under the present level of the sea, have been found round all
our coasts. In the estuary of the Tay the submarine forest and peat-beds are
situated ona blueclay. In the Firth of Forth, Dr Brown has pointed out that at
Elie, the submarine forest lies above the Arctic shell-bed.*
(4.) The land again sunk, though probably not to the extent to which it was
previously submerged—perhaps not more than to about 1000 feet above the
present sea-level.
It was probably during this period that the submarine banks and spits of
eravel and sand, called Zazms in Scotland, were formed. Some of these are at a
height of 750 feet above the sea (Berwickshire, Mid-Lothian, &c.)
The forests previously existing below that level would, of course, be destroyed,
and be covered over with sediment. On the Tay, the submarine forest and peat-
beds are covered with beds of clay and sand containing various species of sea-
shells of the existing species.+ The submarine forest in the Firth of Forth,
according to Dr Brown’s account of it, underlies a bed of clay full of the
Scrobicularia.}
During this submergence, any moraines formed by glaciers, situated in the
submerged parts of the country, would probably be levelled by submarine cur-
rents. The only mounds I have seen in Scotland, which I thought were moraines,
are at Loch Skeen, at a height of about 1700 feet above the sea.
(5.) The land again emerged from the sea, with intervals of suspension, when
the old beach lines were formed, described by Dr Rospert CHAMBERS in
* Ancient Sea Margins.”
* Trans. Roy. Soc. Edin, vol. xxiv. p. 633.
+ Newer Pliocene Geology, by Smitu, p. 35.
t Roy. Soc. Tr. vol. xxiv. pp. 619 and 633.
VOL. XXV. PART II. 8R
( 693 )
XX.—On the Connection betiveen Chemical Constitution and Physiological Action.
Part Il—On the Physiological Action of the Ammonium Bases derived from
Atropia and Conia. By Dr A. Crum Brown and Dr Tuomas R. FRAsER.
(Read 18th January 1869.)
ATROPIA.
Atropia is a nitrile base, obtained from Atropa Belladonna. All we know of
its constitution is, that by the action of strong acids and bases it is decomposed,
in accordance with the equation—
CHE NOD torr O: == CHO. + 2C HNO *
Atropia. Water. Tropic Acid, Tropia.
So that atropia may be considered as tropia, in which one atom of hydrogen has.
been replaced by tropyl, the radical of tropic acid.
Atropia has a somewhat complicated physiological action, for it directly
influences the functions of the cerebro-spinal and sympathetic nervous systems.
The principal effects produced by it on the former system are paralysis of the
sensory and motor nerves, and excitation of the spinal cord. By its action on
the sympathetic nerves, it influences the contraction of the unstriped muscles ;
but as the mechanism of this action is by no means exactly defined, we shall merely
allude to it in our comparison of the actions of the methyl and ethyl derivatives,
with those of the alkaloid itself. In addition to these general actions, atropia
influences, in a special manner, the functions of the vagi nerves and of the
_ iris, suspending the cardiac inhibitory power of the former, and producing
contraction of the latter.
To cause death in the lower animals, it is necessary that atropia be adminis-
tered in comparatively large doses, even when it is exhibited by subcutaneous
injection. Thus, the minimum fatal dose of sulphate of atropia for a dog, weigh-
ing eight or nine pounds, is about fifteen grains; fora full-grown rabbit, more
than fifteen grains; and for a frog, a dose equivalent to the zooth or the y3pth
of its weight.
Lodide of methyl-atropium.—Iodide of methy] acts very readily on atropia; a
good deal of heat is produced; and after the reaction is over, the iodide of
* Kraut, “ Annalen du Ch. u. Ph.” band exxviii. 1868, p, 280; band exxxiii. 1865, p. 87;
band exlviii. 1868, p. 236. Losszn, cbid. band cxxxi, 1864, p. 43; band exxxviii. 1866, p. 230.
VOL. XXV. PART II. 8s
694. DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
methyl-atropium remains as a white mass. From this, the excess of iodide of
methyl is removed by a current of air, and the dry salt dissolved in water,
filtered, and evaporated at a temperature not exceeding 40° C. The concentrated
solution thus obtained, on cooling deposits the salt in prismatic crystals, appa-
rently belonging to the monoclinic system ; sometimes, part of the salt separates
as a heavy oil, which soon crystallises. These crystals have the composition
C,,H,,NO,CH,I. They are tolerably stable, bearing a temperature of 100° C.
without much alteration. When they are powdered, or when their solution is
warmed, a pleasant fruity smell is observed.*
Pursuing the plan adopted in our former communication, we eke in the
first place, describe the effects of this substance when it is exhibited by subcu-
taneous injection. As it is tolerably soluble in warm water, we were enabled to
administer sufficiently large doses in the form of solution. In the previous part
of this research, we found that the chemical addition of iodide, or sulphate of
methyl, orof ethyl, greatly diminishes the lethal} activity of strychnia, brucia,
thebaia, codeia, morphia, and nicotia. We have now to announce that a
similar operation performed on atropia, in place of diminishing, considerably
increases the lethal activity of this alkaloid. In our experiments with iodide of
methyl-atropium, we were somewhat surprised to find that a dog was rapidly
killed by the subcutaneous injection of ten grains, and that a rabbit survived for
but a short period after the administration of three. We shall first describe the
experiment referred to on a dog, as it illustrates not only the difference between
the lethal activity of iodide of methyl-atropium and that of atropia, but also
some of the more prominent differences between the symptoms produced by these
two substances.
EXPERIMENT I.—A solution of ten grains of iodide of methyl-atropium, in
about one hundred minims of warm distilled water, was injected under the skin
of a healthy English terrier, weighing eight pounds and six ounces. In a few
minutes, there was some difficulty in performing voluntary movements, and in
ten minutes this was more marked. Soon after, the anterior extremities became
gradually more and more weak, until they could no longer support the body,
and the dog subsided on the chest, with the muzzle resting on the floor. In
thirteen minutes, it fell over on the side in a state of flaccid helplessness; the
respirations became somewhat laboured and shallow, and their frequency dimin-
ished until, at twenty-three minutes, only an infrequent gasp occurred. There
were now some faint twitches in the panniculus carnosus muscle and in the
musles of the limbs; and irritation of the skin still excited feeble reflex move-
* We shall give details of the chemical relations of the methyl derivatives of atropia on some
other occasion.
t We have employed the phrase “lethal activity” as a substitute for the French “ |’activité
toxique,”’- or death-producing action.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 695
ments. With the exception of these rare gasps, and of a continuance of the
cardiac contractions, at the rate of 100 beats in the minute, the animal appeared
to be quite dead at twenty-seven minutes after the injection; for even the
sensibility of the skin, conjunctiva, and cornea was at this time suspended.
The respiratory gasps, however, continued at the rate of five or six in the
minute, until thirty-two minutes after the administration of the poison, when
death occurred.
In autopsy, it was found, five minutes after death, that the heart was beating
at the rate of 96 per minute. The conductivity of the motor nerves and the con-
_ tractility of the muscles were retained for several minutes afterwards.
The dog, which was the subject of this experiment, had received, some weeks
previously, ten grains of sulphate of atropia; and it will be seen from the follow-
ing account of the experiment, that this dose produced in it some of the more
prominent effects of atropia-poisoning.
EXPERIMENT XXII.—Ten grains of sulphate of atropia was dissolved in fifty
minims of distilled water, and injected under the skin of the dog that was
used, some weeks afterwards, in Experiment I. Omitting many details of the
earlier symptoms that were observed, it is sufficient for our present purpose to
mention, that in five minutes, there was evident impairment of vision; that in.
seven minutes, some efforts were made to vomit; that in twelve minutes, urine
was voided ; that in thirteen minutes, partial paralysis was decidedly present ;
and that in thirty-eight minutes, frequent spasmodic starts and marked’ exag-
geration of the reflex excitability coexisted with considerable lose of voluntary
motor power. After this time, certain effects were observed that contrast in a
remarkable manner with those observed in the previous experiment. Gradually
the paralysis became more marked until the dog was unable to support itself on
its limbs; and the spasmodic action acquired a greater prominence, so that, in a
short time, it produced violent tetanic convulsions of an opisthotonic character.
The first of these convulsions occurred at fifty-two minutes, and it was succeeded
by a series, following each other at intervals of eight or nine minutes, until four
hours and ten minutes after the administration, when the observations were
interrupted. At nine hours, the dog was still affected with considerable para-
lysis, but no tetanic convulsions now occurred, though spasmodic starts and
exaggeration of the reflex excitability had not yet disappeared. On the following
morning, the dog was running about, and it ultimately recovered perfectly.
These two experiments appear to show that the chemical addition of iodide
of methyl to atropia increases the lethal activity, and removes the convulsant
action of this alkaloid. These changes have been carefully examined in many
experiments on rabbits and frogs. In rabbits, we have ascertained that a dose
of two and a-half grains produces marked paralytic symptoms, which do not
terminate in death; while three grains is a sufficient dose to kill a large animal.
696 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
The special symptoms that were observed with these doses will be best described
by a short narration of each experiment.
ExpERIMENT VII.—Two grains and a-half of iodide of methyl-atropium was
dissolved in fifty-five minims of slightly warm distilled water, and one-half of
the solution was injected under the skin at each flank of a rabbit, weighing three
pounds and thirteen ounces and a half. Before the administration, the pupils
measured 23ths x 44ths of an inch, and at six minutes after it, the size of the
pupils had increased to 47ths x 43ths of aninch. This was the first symptom
observed. At sixteen minutes, there was evident difficulty in retaining a normal
posture, and soon after the fore-legs yielded, and the rabbit lay on the chest,
with the Jower jaw resting on the table. At twenty-four minutes, some uneasy
movements were executed, during which the body was pushed forward, in the
position last described, by the use of the posterior extremities alone. There was
now a succession of very slight fibrillary twitches of the muscles of the head,
body, and limbs. At fifty minutes, the rabbit lay altogether on the abdomen
and chest, with the lower jaw still resting on the table, and it was obvious that
the posterior extremities had become powerless like the anterior. The respira-
tions were now shallow and abdominal, at the rate of 68 per minute; the
pupils were dilated to 42ths x 44ths; the common sensibility appeared to be
suspended ; and paralysis had so far advanced that the rabbit lay flaccid on the
abdomen and chest, with the head resting on the side. This condition continued
for about fifteen minutes, when the head was again raised from the side, and, for
short periods, even supported normally by the neck muscles. The symptoms
then slowly disappeared until a normal condition was reassumed.
Experiment VIII.—In this experiment, the rabbit weighed three pounds and
ten ounces, and it received, by injection under the skin of the two flanks, three
grains of iodide of methyl-atropium dissolved in sixty minims of slightly warm
distilled water. Dilatation of the pupils appeared in five minutes, and this symptom
was soon succeeded by trembling and unsteady movements. In fifteen minutes,
the head sunk until it rested on the chin; and in twenty minutes, the paralysis
had become so severe that the limbs were unable to support the body. In twenty-
eight minutes, the respiratory movements had diminished in number to thirty-
four in the minute, while they had become laboured and abdominal in character.
The rabbit was now lying on the side in a completely flaccid state. In fifty-four
minutes, the respirations were so weak and shallow that it was somewhat difficult
to determine the rate of their occurrence. In fifty-six minutes, merely an occa-
sional gasp occurred, and this was frequently accompanied by weak, successive
tremors. In fifty-eight minutes, all movement ceased, and death took place.
In the autopsy, it was found that, at three minutes after death, the conduc-
tivity of the motor nerves and the contractility of the muscles were retained; and
that, at six minutes after death, the heart was motionless and distended.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 697
These experiments are sufficient to illustrate the physiological effects that are
produced in rabbits by the subcutaneous administration of iodide of methyl-
atropium. They likewise show—and the result is confirmed by other experi-
ments briefly described in the table at the end of this paper—that iodide of
methyl-atropium is a much more active poison for rabbits than any salt of
atropia. We have already mentioned that the minimum fatal dose, by sub-
cutaneous administration, of even so soluble a salt as the sulphate of atropia, is
greater than fifteen grains; whereas it is proved by Experiment VIII. that three
grains of iodide of methyl-atropium, administered subcutaneously, is a fatal dose
for a rabbit.
We have not succeeded in obtaining any data by which to compare the
relative activity of these substances when given to rabbits by the stomach. We
have given in this manner as large a dose of both as thirty grains, but have
observed no obvious symptom with either substance, except dilatation of the
pupils.
Though iodide of methyl-atropium is tolerably soluble in water, it is less so
than sulphate of atropia. In Part I. of this investigation we have mentioned as
a condition which it is advisable to fulfil, ‘‘ that the substance is equally suitable
for absorption into the system before and after the change.”* In conformity
with this condition, we have examined, with considerable care and detail, the
poisonous activity and physiological action of the sulphate of methyl-atropium,
a much more soluble salt than the iodide, and, therefore, a more suitable
substance for comparison with sulphate of atropia.
Sulphate of methyl-atropium ((C,,H,,NO,CH,),SO,).—This salt was prepared
from the iodide by the method formerly described for the preparation of the
sulphates of methyl-strychnium, methyl-brucium, &c. It is a white, crystalline
substance, very deliquescent, and very soluble in cold water.
Apparently on account of its greater solubility, it is a rather more active salt
than the iodide; and both in rabbits and frogs its lethal activity was, accordingly,
found to be much greater than that of sulphate of atropia.
We administered it to rabbits by injecting it under the skin, and also by
introducing it into the stomach. The symptoms produced by the former method
of administration are in character exactly the same as those produced by the
iodide, as will be seen from the following detailed account of several of our
experiments.
EXPERIMENT XXXII.—We dissolved two grains of sulphate of methyl-atro-
plum in twenty-five minims of distilled water, and injected the solution under
the skin at the right flank of a rabbit, weighing three pounds and seven ounces
and a-half. In seven minutes, the animal moved about in an uneasy manner,
* Transactions of the Roy. Soc. of Edinburgh, vol. xxv. part 1, 1867-68, p. 153.
VOL. XXV. PART Il. 8 T
?
698 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
and, soon, some weakness of the limbs was observed. This weakness increased
until the limbs were no longer able to support the body; and, in fourteen minutes,
the rabbit subsided on the abdomen and chest, with the lower jaw resting on the
table. There were now some slight twitches in several of the muscles of the
chest and thighs, and the respiratory movements were weak, though they
occurred at the rate of sixty-two in the minute. During other seven minutes,
voluntary movements could not be performed; but at the end of this period, some
unsteady trembling movements occurred. In twenty-four minutes, the rabbit
succeeded in raising the head, though only for a few seconds. It continued at
short intervals to raise the head, until increasing strength at length enabled it to
support the head normally by the neck muscles. In thirty minutes, the partial
paralysis had so far disappeared, that the rabbit succeeded in raising the body on
the limbs, and in assuming a natural sitting posture.
Before the administration of sulphate of methyl-atropium, the pupils measured
ths x Gths of an inch, and seven minutes thereafter they had become dilated
to t6ths x 1&ths.
In the next experiment we administered a fatal dose.
EXPERIMENT XX XIV.—Two grains and a-half of sulphate of methyl-atropium,
dissolved in twenty minims of distilled water, was injected under the skin at
both flanks of a rabbit, weighing three pounds and half an ounce. In two
minutes, there were some uneasy restless movements; in two minutes and a
half, slight twitches occurred in the limbs; in three minutes, the rabbit had
ereat difficulty in going about, and weakness of the limbs was manifested by
frequent stumbles; and in four minutes, paralysis had so far advanced that the
limbs were unable to support the body. In four minutes and a half, the animal
lay flaccid on the side, with shallow and infrequent respirations, and now and
then’ a feeble jerking contraction of the diaphragm accompanied inspiration.
Soon, the respirations were so feeble as to be hardly recognisable, and they alto-
gether ceased at six minutes after the injection.
In the autopsy, it was found that the sciatic nerves retained their con-
ductivity at ten minutes after death, and that the heart’s contractions were
rhythmical, and at the rate of thirty in the minute, at eleven minutes.
In this experiment, also, the pupils were greatly dilated a few minutes after
the administration of the poison.
The account we have given of these two experiments shows that the effects of
the sulphate of methyl-atropium are exactly the same as those of the iodide, the
former salt, however, being more active as a poison than the latter.
In order to obtain some data by which to compare the action on rabbits of
iodide and sulphate of methyl-atropium with that of sulphate of atropia, we
made many experiments in which large doses of sulphate of atropia were
administered by subcutaneous injection; but we found that this method of
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 699
exhibition usually failed to produce any serious symptom, even when so large a
dose as fifteen grains was given. In this experiment (Experiment XXIII.), the
symptoms were merely dilatation of the pupils with impaired vision, increase in
the rapidity of the cardiac and respiratory movements, diuresis and catharsis,
general excitement and slight spasms, and languor. In a few minutes, many
of these effects had disappeared, and the rabbit recovered perfectly.
These experiments render it apparent that the action of the methyl deriva-
tives of atropia differs in several striking respects from that of the natural base.
We have seen from Experiments XXII. and XXIII. that large doses of atropia
produce diuretic and cathartic effects in both dogs and rabbits, effects that are
universally recognised among the symptoms of atropia action. These are not
- produced by the metliyl derivatives.
We have also seen, and our observations agree with those of many previous
experimenters, that when a salt of atropia is administered in a large dose to a
dog, the predominant symptoms are those of paralysis coexisting with convul-
sions. The experiments we have now described show that convulsions are never
produced by the salts of methyl-atropium, but that the predominating symptoms
of their action are those of paralysis alone. It is, therefore, obvious that by the
chemical addition of iodide or sulphate of methyl, some important change has
been effected in the action of atropia, by which its power to produce convulsions |
has been removed. The determination of the exact nature of this change can be
conveniently effected only by experiments on frogs, for the causation of the con-
vulsive symptoms that appear in mammals has not yet been referred with
certainty to any special organ or structure.
One of us has shown, in a paper published in this volume of the Transactions,
that when a dose of a salt of atropia near the minimum fatal is given to a frog, a
distinctly defined stage of paralysis is in the first place produced, which lasts for
many hours, or for several days; and that this stage is succeeded by one in which
violent convulsive and tetanic symptoms are present. Further, it is demon-
strated in that paper that the convulsive and tetanic symptoms which charac-
terise the second stage, are due to an action of atropia on the spinal cord; in fact,
to an action that may with propriety be likened to that of strychnia. From our
knowledge of these facts, we are enabled to examine if this strychnia-like action
of atropia is possessed by the salts of its methyl derivative. For this purpose,
we have made numerous experiments on frogs, of which the following are
examples.
EXpErtmMEeNT XXXVI.—Two minims of a solution of two-tenths of a grain of
sulphate of methyl-atropium, in forty minims of distilled water, was diluted with
two minims of distilled water, and the four minims of solution thus obtained,
containing one-hundredth of a grain of sulphate of methyl-atropium, was injected
under the skin of a frog, weighing 230 grains. In six minutes, the frog had
700 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
difficulty in jumping, and the anterior extremities were somewhat feeble, for they
could not properly support the chest. In ten minutes, progression was accom-
plished by vigorous pushing movements of the posterior extremities, the loss of
power being so decided that jumping was impossible. In twenty minutes, the
frog lay on the abdomen and chest, but still the condition was not one of complete
flaccidity, for the posterior extremities were flexed, and retained their proper
tone, while the anterior partially supported the head and upper part of the chest.
At this time, the respiratory movements were confined to the muscles of the
throat, and reflex contractions of a vigorous character followed slight irritations of
the skin. In thirty-five minutes, the paralysis was still more decided, for irrita-
tion now produced merely a series of interrupted and weak movements in the
extremities; but, otherwise, the frog was in much the same state as that last
noted. It continued thus for other twenty minutes, when the paralysis became
less severe. A normal posture was assumed, and, by-and-by, vigorous voluntary
movements were performed. In about two hours after the administration, the
frog was in a normal condition.
It is of interest to observe that these marked symptoms were produced by a
dose equivalent to only the sy45,th of the weight of the frog, while such a
dose of sulphate of atropia produces no obvious effect in frogs.
EXPERIMENT XXX VII.—We injected under the skin at the right flank of a
frog, weighing 407 grains, one-twentieth of a grain of sulphate of methyl-atro-
pium, dissolved in four minims of distilled water. Very soon after, the move-
ments were performed with some difficulty; and in five minutes, the anterior
extremities were sprawling, and the frog was unable to jump. In eleven minutes,
the frog was in a flaccid state on the abdomen, chest, and lower jaw; and but
feeble reflex contractions could be excited. In fifteen minutes, the reflex function
was suspended, and all respiratory movements had disappeared. In twenty-five
minutes, a sciatic nerve was exposed and subjected to galvanic stimulation, but
no muscular contractions were thereby produced, although direct galvanic stimu-
lation of the muscles caused vigorous contractions. The cardiac impulse was at
this time ascertained to be pretty strong, and the beats at the rate of thirty-two
per minute. During the two following days, the frog remained in this condition.
On the fourth day, however, it was found that the motor nerves had recovered
their conductivity, but still the reflex function of the spinal cord was suspended.
On the fifth day, the latter function was again present, and, indeed, the action of
the poison had now so far disappeared that the frog had resumed a normal
posture, and jumped freely when stimulated. There was no symptom whatever
on the following day.
The dose given in this experiment was equivalent to the ,;,oth of the weight
of the frog used. To produce complete paralysis of the motor nerves for more
than two days with sulphate of atropia, it is necessary to exhibit a dose of
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 701
about seven times the relative weight. The symptoms following the paralysis
produced by sulphate of atropia would, however, be very different from those just
described ; for in place of a gradual recovery to normality, violent convulsive and
tetanic symptoms would appear, and probably continue for several days, before
perfect recovery took place. This experiment, therefore, shows in the most satis-
factory manner that sulphate of methyl-atropium, administered in a dose rather
less than the minimum fatal, does not cause any convulsant action in frogs.
In the next experiment, a dose about the minimum fatal was given.
EXPERIMENT XL.—One-tenth of a grain of sulphate of methyl-atropium was
dissolved in four minims of distilled water, and injected under the skin at the
right flank of a frog, which weighed 460 grains. Symptoms followed with great
rapidity; for in two minutes, the frog could not jump, and the anterior extremities
were extended almost powerlessly at right angles to the body, while the respira-
tions were extremely feeble and infrequent. In five minutes, the latter had
entirely ceased, and, now, only feeble twitches of the toes could be excited by
rather severe irritation of the skin, the limbs being perfectly flaccid and motion-
less. In nine minutes, irritation caused no reflex movement whatever, and the
cardiac contractions were at the rate of thirty beats in the minute. In twenty-
nine minutes, it was ascertained that the motor conductivity of the sciatic nerves .
was suspended, while idio-muscular contractility was still retained. During the
two following days, the state of the frog was the same as that last described. On
the fourth day, however, it was impossible to discover any cardiac impulse. The
muscles still contracted vigorously when they were directly galvanised, and they
continued to do so until the seventh day, when 72gor mortis set in.
We learn from this experiment, that a dose of sulphate of methyl-atropium
equivalent to the z,4,th of the weight of a frog, is sufficient to produce a fatal
result. As we have already mentioned, the minimum fatal dose of sulphate of
atropia for frogs is about the 53th or the ;g,5th of the weight of the animal,
but after such doses death is usually preceded by a stage of tetanus. ‘This stage
was entirely absent in the experiment with sulphate of methyl-atropium.
As, however, it might be supposed that sulphate of methyl-atropium will
cause convulsive and tetanic symptoms if it be given in the same relative propor-
tion as is required to produce these symptoms with sulphate of atropia—viz., in a
dose equivalent to about the ;,5,th of the frog’s weight—an experiment was
performed to meet this supposition.*
EXPERIMENT XLIV.—A solution, containing four-tenths of a grain of sulphate
of methyl-atropium, dissolved in five minims of distilled water, was injected
* The frogs used in Experiments XXXVI., XXXVIL, and XL. had been. kept in the labora-
tory for more than two months before the performance of each experiment. The convulsive and
tetanic effects of atropia appear to be more readily produced in frogs that have been thus kept, than
in those recently obtained from their natural habitat.
VOL. XXV. PART II. 8U
702 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
under the skin at the right flank of a frog, weighing 461 grains. The usual
paralytic symptoms very quickly supervened; and in seven minutes and thirty
seconds, it was ascertained by galvanic stimulation that the motor conductivity
of the sciatic nerves was suspended, while muscular contractility was retained.
On the following day, this condition of the motor nerves and of the muscles con-
tinued, and the heart’s contractions were found to be occurring at the rate of
thirty in the minute. On the third day, the body was slightly rigid, galvanism
of the nerves and muscles caused no contraction, and the heart was motionless.
Similar experiments were made with iodide of methyl-atropium, and no con-
vulsive symptoms were produced by this salt. It was found that its poisonous
activity for frogs is less than that of the corresponding sulphate, though consider-
ably greater than that of sulphate of atropia, being equivalent to the 5,4 th of
the frog’s weight. Short details of these experimeuts will be found in the
Tabular Summary.
Having thus determined, by our experiments on dogs, rabbits, and frogs, that
the salts of methyl-atropium do not possess the convulsant action of atropia, it
is important that we should next ascertain by what action the paralytic symptoms
of the salts of methyl-atropium are produced. Before doing this, however, it
may be of advantage to show in what manner atropia itself produces paralysis.
The mechanism of the paralytic action of atropia is a complicated one, for
there is good reason to suppose that it consists of actions on the sensory and
motor nerves, and probably, also, on the spinal cord.* The following experiment
illustrates the order in which several of these actions are produced.
EXPERIMENT XXV.—The sciatic artery and vein were ligatured at the upper
part of the right thigh of a frog, weighing 215 grains; and, a few minutes after-
wards, one-fourth of a grain of sulphate of atropia, dissolved in four minims of
distilled water, was injected under the skin at the left flank. In eight minutes,
a slight degree of paralysis was present, but the frog was able to perform some-
what imperfect jumping movements until thirty-five minutes. In forty minutes,
however, it lay flaccid on the abdomen, with the head resting on the table, and,
now, irritation of the skin of any region caused no other effect than a number of
pretty vigorous movements in both posterior extremities, of rather greater energy
in the non-poisoned (right) than in the poisoned. These reflex contractions could
likewise be excited by gently touching the skin, in the poisoned as well as in the
non-poisoned regions. The heart was now contracting at the rate of twenty-six
beats in the minute. With the exception of a gradual diminution in the rate of
the heart’s contractions, no notable change occurred in the state of the animal
until one hour and twenty minutes after the injection. At this time, gentle
* Authorities differ somewhat in their interpretation of the relations of these actions, some con-
sidering that the motor nerves are paralysed more rapidly than the sensory (Botkin, &c.), and
others that the sensory are paralysed more rapidly than the motor (LematTre, Meunior, &c.).
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 703
stimulation of the skin of the poisoned region caused no movement whatever, but
feeble movements could still be excited in both poisoned and non-poisoned regions
by strong stimulation ; and the sensibility of the non-poisoned region was in much
the same condition. In one hour and forty-five minutes, it was impossible to
excite any reflex movement whatever. Galvanic stimulation of the right (non-
poisoned) sciatic nerve was followed by vigorous movements restricted to the
right leg ; and, when this stimulation was applied to the left (poisoned) sciatic
nerve, similar movements were produced in the left leg, and nowhere else. The
heart was now contracting at the rate of twenty beats per minute. This state of
suspension of the reflex function, with retention of conductivity in the motor
nerves and of contractility in the muscles, continued until at least three hours
after the administration of the poison, when the observations were interrupted.
On the following morning, it was found that the conductivity of the poisoned
sciatic nerve was suspended, while the poisoned muscles contracted when directly
stimulated by an interrupted current. ‘The conductivity of the non-poisoned
sciatic nerve was still retained.
We learn from this experiment, that although a large dose of atropia quickly
produces in frogs a condition of marked paralysis, the conductivity of the
sensory and motor nerves and the reflex function of the spinal cord are not -
completely suspended until considerable intervals after the administration. Of
these special paralytic actions, that on the motor nerves appears to be the last to
be effected; indeed, in this experiment an interval of least an hour and fifteen
minutes elapsed between the complete suspension of the reflex function and that
of conductivity of these nerves.
We shall now endeavour to discover if the salts of the methyl derivative of
atropia produce their paralytic symptoms by the same actions as atropia does.
Experiment XLII —Having ligatured the artery and veins at the upper
third of the right thigh {of a frog that weighed 235 grains, we injected under
the skin of the left flank one-tenth of a grain of sulphate of methyl-atropium, in
four minims of distilled water. Paralytic symptoms followed with great rapidity :
so that in five minutes and thirty seconds, the frog was motionless, excepting that
vigorous spontaneous movements frequently occurred in the right (non-poisoned)
posterior extremity; and stimulation of the skin of any part, even though severe,
did not produce the faintest muscular contraction in the poisoned region, although
it produced strong contractions in the non-poisoned (right) posterior extremity.
In six minutes, it was ascertained that the heart was contracting at the rate of
forty beats in the minute. Frequent observations were made, and it was found
that no change whatever occurred during the subsequent three hours—the con-
ductivity of the poisoned sensory (afferent) nerves, and the reflex function of
the spinal cord being retained, while the conductivity of the poisoned motor
nerves was completely suspended. On the two following days, this condition
704 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
was still present, except that on the third day, the rate of the heart’s contractions
had diminished to thirty-six in the minute. Death, with commencing rigidity,
occurred on the fourth day.
The dose given in this experiment was greatly above the minimum fatal. We
shall now describe the effects of a dose that was considerably below the minimum
fatal.
EXPERIMENT XXXVIII.—The blood-vessels at the upper third of the right
thigh were ligatured in a frog, weighing 379 grains, and immediately afterwards
a solution of one-twentieth of a grain of sulphate of methyl-atropium, in four
minims of distilled water, was injected under the skin at the left flank. In three
minutes, the respiration had ceased, and the frog was lying on the abdomen,
perfectly flaccid and motionless in the poisoned region; but retaining the normal
tone in the non-poisoned posterior extremity, where spontaneous vigorous move-
ments frequently occurred. Irritation of the skin of any region did not cause any
movement in the poisoned region, but it caused energetic contractions in the
non-poisoned. In ten minutes, the left (poisoned) sciatic nerve was subjected to
galvanic stimulation, with the result that no movement was thereby caused in the
left posterior extremity or in any part to which the poison had access, while ener-
getic reflex contractions were caused in the right (non-poisoned) posterior extremity.
The poisoned muscles freely contracted when directly stimulated. It was found
that the cardiac impulse was, at this time, powerful, while contractions occurred
forty-four times in the minute. Repeated observation showed that the conditions
of the poisoned heart, spinal cord, nerves, and muscles, and of the non-poisoned
nerves and muscles, described as being present at ten minutes after the injection,
continued unchanged during the succeeding three hours. On the following day,
the frog had resumed a normal posture. It moved and jumped about actively,
and there was now no symptom present.
We have made experiments similar to these with iodide of methyl-atropium,
and the same general results were obtained.
It has thus been shown, in the most satisfactory manner, that the salts of
methyl-atropium produce their paralytic effects in a very different manner from
atropia. The former substances do not appear to influence the sensory nerves or
the spinal cord, but they act solely on the motor nerves. We have seen that this
last action is possessed by atropia also, though in a comparatively feeble degree ;
and the experiment we have described confirms the opinion of previous observers,
that it is primarily restricted to the peripheral terminations of these nerves. The
evidence contained in the experiments we have narrated with sulphate of methyl-
atropium is in favour of the paralysis produced by this substance being likewise
due to an action on the peripheral terminations of the motor nerves, and the
following experiment clearly proves that such is the case.
EXPERIMENT XLII—The right gastrocnemius muscle of a frog, weighing
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 705
312 grains, was exposed, the blood-vessels that entered it were carefully ligatured,
and all the connections of the muscle divided, except its origin and insertion.
Immediately afterwards, a solution of one-tenth of a grain of sulphate of methyl-
atropium, in five minims of distilled water, was injected under the skin of
the back. Paralytic effects were quickly produced. In fifteen minutes, the
left sciatic nerve was exposed and stimulated by galvanism, with the result
that while no contraction was produced in the left limb, energetic movements
occurred in the right. The right sciatic nerve was then exposed and subjected
to galvanic stimulation; energetic movements occurred in the right leg, which
were ascertained to be entirely caused by contractions of the gastrocnemius
muscle (non-poisoned); and no movement occurred elsewhere. On directly
galvanising the poisoned muscles it was found that their contractility was still
retained.
We learn from Experiments XLII. and XXXVIII. that sulphate of methyl-
atropium does not paralyse the motor nerve trunks.. We further learn from
Experiment XLII. that certain terminations of a motor nerve protected from
the direct action of this poison are not paralysed, while other terminations
exposed to its action are very quickly paralysed. It is, therefore, apparent that
the paralysis of the motor nerves, which this substance so energetically produces,
is due to an action that is restricted to their peripheral terminations.
The valuable and interesting researches of Borxin,* Von Brzoitp and
BiorsauMm,+ Mevuriot,{ and others, have shown that atropia exerts a para-
lysing influence on the inhibitory cardiac branches of the vagi nerves. When
administered, even in very small doses, this substance so completely paralyses
these nerves, that powerful galvanic stimulation of the main trunk of one of
the vagi does not produce stoppage of the heart’s action, or even appreciably
diminish the rate of its contractions. It seemed important that we should
determine if the methyl and ethyl derivatives of atropia possess this remarkable
action.
EXPERIMENT XXIX.—The two vagi nerves were exposed in the neck of a
rabbit, weighing three pounds and eight ounces. On subjecting each vagus
separately to galvanic stimulation of a certain strength, obtained by the use of
Du Bors Rrymonp’s induction apparatus, it was found that total stoppage of the
heart’s contractions resulted on each occasion, during the ten seconds the gal-
vanic stimulation was applied. A solution containing half-a-grain of sulphate of
methyl-atropium, in fifteen minims of distilled water, was injected under the skin
of the abdomen.
* Vircuow’s Archiv. Bd. xxiv. 1862, p. 89.
+ Untersuchungen aus dem Physiologischen Laboratorium in Wiirzburg, ltes heft, 1867, p. 43.
{ De la Méthod Physiologique en Thérapeutique et de ses Applications 4 l'étude de la Bella-
donne, 1868, p. 76.
VOL. XXV. PART Ir. 8x
706 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
5 minutes after the injection, the heart was contracting 28 times in 10 seconds.
eh ’ ” ” ” 28 P) 29
7 ‘ and 10 seconds _,, the right vagus was galvanised* for ten seconds, and the heart con-
tinued to contract, during the galvanism, 28 times in 10 seconds,
LO sae. 5 the heart was contracting 29 times in 10 seconds.
19 ” 9 ” ” 30 ” ?
20" =}; is the left vagus was galvanised for ten seconds, and the heart con-
tinued to contract, during the galvanism, 30 times in 10 seconds.
20 ,, and20seconds ,, the heart was contracting 30 times in 10 seconds.
26 ” ” 39 29 30 ” »
26 ,, and20seconds _,, the right vagus was galvanised for ten seconds, and the heart con-
tinued to contract, during the galvanism, 30 times in 10 seconds.
No general symptoms of the action of sulphate of methyl-atropium were de-
veloped during this period, the dose that was administered being but small.
The paralytic action on the inhibitory cardiac branches of the vagi, which this
experiment clearly exhibits, would appear to be a very powerful one; for it was
not counteracted, within twenty minutes, by half a grain of extract of physo-
stigma subcutaneously administered, nor, within thirty minutes, by a second dose
of three-fourths of a grain of extract of physostigma, administered twenty minutes
after the first.
In other similar experiments on rabbits, we succeeded in completely para-
lysing the vagi nerves with one-tenth and with one-twentieth of a grain of
iodide of methyl-atropium, and with one-tenth of a grain of iodide of ethyl-
atropium.
We have seen, from Experiments VII., VIIL, XXXII, and XXXIV., that
iodide and sulphate of methyl-atropium, when acting through the blood, produce
marked dilatation of the pupils. A number of experiments were made to deter-
mine whether the topical application of these salts to the conjunctiva similarly
affects the pupil, and, thus, further exhibits a similarity in action to atropia and
its salts.
The largest dose we applied was the ;),th of a grain.
EXPERIMENT CXI.—This dose, dissolved in one minim of distilled water, was
applied to the left eyeball of a rabbit, and it caused extreme dilatation of the
left pupil (28ths x 48ths of an inch) in less than five minutes, which lasted
for more than three days. The left pupil was of normal size on the sixth
day.
In order to test the delicacy of this reaction, we made the following experi-
ments :—
EXPERIMENT CXII—One minim of a solution of one grain of sulphate of
methyl-atropium, in 1000 minims of distilled water (= zo th of a grain of
sulphate of methyl-atropium), was placed on the 77ght eyeball of a rabbit.
* Throughout the experiment the strength of the galvanic current was the same as that
which produced stoppage of the heart’s contractions before the administration of sulphate of methyl-
atropium. :
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION.
Before the application, the right pupil megpured.s
8 minutes after the application,
EXPERIMENT CXIII.—One minim of a solution
methyl-atropium, in 5000 minims of distilled water (
”
1 5ths x soths,
17 17ths x +Sths,
18ths x 18ths,
18ths x 13th,
18ths x 1 8ths,
19ths x Fths,
L7ths x +Sths,
1zths x 4 sas
16ths x t Sths,
eel
Te, DIVLOO
i8ths x 14ths
ths x +4ths
ths x + aths
ths x 1 14ths
ths x 1.4ths
a ft et cet Cet cal cet cf! |
sla ola SfP olan ola ola ola ol o
+
(=r
nm
oe
a
ol
t+
S-
nan
sulphate of methyl-atropium), was paced on the /eft eyeball of a rabbit.
Before the application, the deft pupil measured 33ths x 4
13 minutes after the application,
15 r
Lg, 99
20 x
2 hours
22
EXPERIMENT CXIV.—One minim
methyl-atropium, in 20,000 minims of distilled water (=
sulphate of methyl-atropium), was placed on the 77ght eyeball of a rabbit.
Before the application, the right pupil measured 4
35 minutes after the application,
45 ”
1 hour 10 minutes
25 hours
be)
39
HO
ae
(a5
Sa
n
14ths,
Liths x 2th,
8ths x 28ths,
soths x 18ths,
50
8
50
ol
oths x soths,
ths x 47ths,
ae ps 4 | cr]
2ths, and the right
13ths x 1
9560
a) cl
es)
ioe
f=7q
n
x
| Oy
\to S|
+
S
n
ths
ths
ola olto Slty olts lt o|
ehasct ct
SS
Ran
le
oto
t+
—
_
n
ys Oe et es =!
707
5ths x }4ths, and the left, soths x 14ths of an inch.
of one grain of sulphate of
th of a grain of
12ths of an inch.
of a solution of one grain of sulphate of
te x i4ths,
18ths x o cote
iz
Zths x 1Sths,
5ths x béths, and the left, 15ths <<
Sths xt Sths,
99
iSths x t aths
Sths x Hehe
5ths a 4ths
Sths x ¢ 4ths
=
olan
ol als
zosooth of a grain of
4ths of an inch.
EXPERIMENT CX V.—One minim of a solution of one grain of sulphate of methyl-
-atropium, in 50,000 minims of distilled water (
methyl-atropium), was placed on the r7zght eyeball of a young rabbit.
Before the application, the right pupil measured 1
42 minutes after the application,
1 hour 5 minutes
Tees sin iO pi 53
2, hours
D2
29
9
Sths x 15ths,
hs x zpths,
i8ths x 1iths,
L8ths x 12ths,
15ths x ths,
15ths x a ths
1 $ths x £8ths
as 5ths x4 bo aths
1ths x #aths
25ths x 1aths
=spdooth of a grain of sulphate of
5ths x eaths, and the left, + é Le x +3ths of an inch.
99
EXPERIMENT CXVI.—One minim of a solution of one grain of sulphate of
methyl-atropium in 100,000 minims of distilled water (=z 5,/g9oth of a grain of
sulphate of methyl-atropium) was placed on the right eyeball of a rabbit.
Before the application, the right pupil measured boths x eéths, and the left, 13ths x 44ths of an inch.
39 minutes after the application,
1 hour
1 ,, 380 minutes
2hours 10 __s,
22,
»
be)
”
39
1§ths x 18ths,
on x Laths,
18ths x biths,
38ths x 37ths,
15ths x 14ths,
pans x +4ths
18$ths x 4 4ths
ie + }4ths
15ths x 14ths
iSths x 14ths
9?
708 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
It seemed to us unnecessary to proceed further in our examination of the
delicacy of this action on the iris. The researches of De Ruyrer have placed at
our disposal a number of experiments with sulphate of atropia, similarly applied
in extremely dilute solutions. From these researches we learn that a drop of a
solution containing the 75,5 oth of a grain of sulphate of atropia is capable of
producing dilatation of the pupil in a dog, which lasts for eighteen hours.* Com-
paring this result with that obtained in our experiment with the ;pgogoth of a
grain of sulphate of methyl-atropium, we are justified in considering that the
addition of sulphate of methyl to atropia does not diminish the mydriatic action
of this alkaloid to any marked extent.
Lodide of ethyl-atropium (C,,H,,NO,CH,1).—Our investigation also includes
an examination of the physiological action of this ethyl derivative ofatropia. The
results of this examination prove that this substance acts in precisely the same
manner as the previously described methyl] derivatives.
Iodide of ethyl acts readily on atropia, but not so energetically as iodide of
methyl. In preparing the iodide of ethyl-atropium, atropia was treated with a
considerable excess of iodide of ethyl, in a sealed tube, at 100° C., for an hour.
The remainder of the process is the same as in the case of the methyl] derivative,
which in general appearance and character it closely resembles.
We found that two grains of this substance, administered by subcutaneous
injection, is a poisonous dose for a full-grown rabbit.
EXPERIMENT XLVIII.—In a rabbit, weighing three pounds and seven ounces,
it was found that the right pupil, under exposure to a full light, had a diameter
of 43ths x 12ths of an inch, and that the respirations were irregular and at the
rate of twenty-four in ten seconds.
A solution containing two grains of iodide of ethyl-atropium, in one hundred
and twenty minims of slightly warmed distilled water, was then injected under
the skin at the back of the rabbit. In two minutes, the pupils measured
i5ths x 14ths. In three minutes, the respirations occurred regularly at the rate
of twenty per ten seconds; but there was no other symptom present. In six
minutes, some faint quivers occurred, and a slight degree of paralysis was pre-
sent. The latter gradually increased in severity until, in sixteen minutes, the
rabbit was unable to move about, and lay on the abdomen with the head resting
on the table in an utterly flaccid state. The respirations were now shallow and
somewhat jerking in character, and they occurred at the rate of fourteen per ten
seconds. In twenty-two minutes, the respirations were extremely feeble, and at
the rate of only nine per ten seconds, After this, they quickly diminished in
number, until they altogether ceased in twenty-four minutes after the injection.
At the time of the occurrence of death, the pupils measured 43ths x 4éths of an
inch.
* Quoted by Meurior, op. cit. p. 118, from Nederlandsch Lancet, 1853.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 709
In the autopsy, it was found that the sciatic nerves retained their afferent
(motor) and efferent (sensor) conductivity for at least fifteen minutes after death,
and that the heart had ceased to contract previous to twenty minutes after this
event.
These general effects very closely resemble those that have been described in
the experiments with the iodide of methyl-atropium. We shall see from the
following experiment that the effects on frogs of this ethyl derivative are like-
wise the same in character with those of the methyl derivatives.
EXPERIMENT LII.—We injected under the skin of the left flank of a frog,
weighing 290 grains, three-twentieths of a grain of iodide of ethyl-atropium,
dissolved in eight minims of distilled water. In six minutes, the frog was per-
fectly motionless and flaccid ; and so complete was the paralysis, that even severe
irritation of the skin did not cause any reflex movement. The heart was now
contracting in regular rhythm, at the rate of thirty-nine beats in the minute. In
seven minutes, the right sciatic nerve was exposed, and it was found, by galvanic
stimulation, that its motor conductivity was completely suspended. The muscles,
at this time, contracted vigorously when the electrodes were applied to their
surface. This condition of the motor nerves and of the muscles was retained for
other two days; but on the second day the cardiac impulse was weak, and the
beats occurred at the diminished rate of twenty in the minute, while, on the
third day, no cardiac impulse could be observed. On the fourth day, the muscles
had become rigid.
These symptoms are in all essential characters the same as those we have
described, with fatal doses of iodide of methyl-atropium. We have besides, given
a dose considerably below the minimum fatal, and have observed a temporary
stage of complete paralysis of the motor nerves, which was recovered from with-
out the occurrence of the slightest spasmodic or convulsive symptoms. This ethyl
derivative of atropia, therefore, resembles the methyl derivatives, in that it does
not possess the well-marked convulsant action of atropia.
We have seen from the last experiment that the paralysis is accompanied by
total suspension of the conductivity of the motor nerves. It is important that we
should now discover whether the sensory nerves and spinal cord are also impli-
cated in the production of this paralysis. This may readily be determined by
experiments in which certain limited regions are protected from the direct action
of the poison—as has been done in experiments with the methyl derivatives of
atropia.
EXPERIMENT LI.—Having ligatured the blood-vessels in the lower third of the
right thigh of a frog, weighing 301 grains, we injected three-twentieths of a grain
of iodide of ethyl-atropium, dissolved in ten minims of distilled water, under the
skin of the left flank. Paralysis very quickly supervened; and in two minutes,
stimulation of the skin anywhere was followed by vigorous movements of the
VOL. XXV. PART II. SY,
710 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
right (non-poisoned) leg, but no movement occurred in any part of the poisoned
region. It was likewise observed that frequent spontaneous movements of an
energetic character occurred in the right (non-poisoned) leg. In twelve minutes,
the symptoms were as last described, and the heart’s contractions occurred
thirty-eight times in the minute. . In thirteen minutes, the left sciatic nerve was
exposed, and on being stimulated by galvanism, 7¢ was found that the conductivity
of its motor fibres was suspended, while that of its sensory fibres continued ; no
movement occurring in the left (poisoned) posterior extremity, although the
muscles of that limb yet retained their contractility unimpaired, while vigorous
reflex movements occurred in the right (non-poisoned) posterior extremity.
The occurrence of these reflex movements shows that the reflex function of the
spinal cord is not destroyed by the direct action of this poison. It is obvious,
from the details we have just given, that the sensory nerve fibres and the striped
muscles are likewise unaffected; while the motor nerve fibres are powerfully
affected. The paralytic effects of iodide of ethyl-atropium, like those of iodide
and sulphate of methyl-atropium, are, therefore, caused entirely by an action on
the motor nerves. The last experiment further shows that the trunks of the
motor nerves are unaffected, while their peripheral portions are paralysed. It
will be seen from the next experiment that the ultimate terminations of these
nerves in the muscles are the portions of the periphery that are affected.
ExperrMENT L.—In a frog, weighing 450 grains, the left gastrocnemius
muscle was carefully dissected from all its connections, excepting its origin and
insertion and the nerve fibres that entered it; and its blood-vessels were ligatured
and divided. Two-tenths ofa grain of iodide of ethyl-atropium, dissolved in ten
minims of distilled water, was then injected under the skin at the right flank.
In ten minutes, the frog was completely flaccid and motionless; and, when the
skin anywhere was irritated, no movement occurred in the poisoned region,
while well marked movements occurred in the left leg and foot. In twelve
minutes, the right sciatic nerve was subjected to galvanic stimulation, with the
result that while no movement occurred in the right leg, vigorous contractions
occurred in the left. The left sciatic nerve was then similarly stimulated, and
vigorous movements followed in the left leg, but nowhere else. Jt was seen that
these movements were due solely to contractions of the left gastrocnemius muscle,
which was protected from the direct action of the poison.
The results we have obtained from these experiments are of an extremely
interesting character. They clearly prove that the ammonium bases derived
from atropia possess an action which is very different from that of atropia itself.
The latter substance produces paralysis chiefly by affecting the motor centres and
the sensory nerves; it produces convulsions by stimulating the spinal cord; and
it produces diuresis and catharsis by influencing the urinary apparatus and the
intestinal functions. The salts of the ammonium basis possess none of these
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. (ala
actions. They, however, retain the dilating action of atropia on the pupil, and
the paralysing action on the cardiac inhibitory branches of the vagi, and on the
spinal motor nerves.
This last action, though resembling that of atropia in character, differs greatly
from it in degree. While in atropia, this action has only a secondary prominence,
and, in the presence of other and more potent paralysing actions, only a sub-
sidiary influence in causing paralysis and death ; in the methyl and ethyl] deriva-
tives, it assumes the prominence of the sole paralysis-producing action, and the
primary cause of the poisonous activity of these substances.
As it is shown by our experiments that the poisonous activity of the methyl
and ethyl derivatives is much greater than that of the salts of atropia, it is
apparent that the paralysing action of the former on the motor nerve terminations
must be very much greater than that of the latter.
In the following Table, we summarise the chief details of a few of our experi-
ments, so as clearly to exhibit the difference of poisonous activity.
Relation
No. of Substance Animal and its Dose, by subeuta- of Dose to Effect
Experi- Employed. Weight. neous administra- Weight of| ?
ment. tion. Animal.
ig Todide of methyl- | Dog, 8 lbs. 6 oz. | 1Ugrs. containing} syd. | Decided paralysis in10 minutes,
atropium. 6°6 gers. of atro- accompanied with very faint
pia). twitchings ; and death in 32
minutes,
XXIT, | Sulphate of atro| Dog (same dog |10grs.(containing| ;335d. | Diuresis in12 minutes; partial
pla. as in Expt. L.) § 48 ers, of atro- paralysis in 13 minutes;
pia). spasms in 88 minutes; de-
cided paralysis in 48 minutes;
tetanic convulsions in 42
minutes, and until 3 hours
and 18 minutes; and followed
by recovery.
VIII. | Iodide of methyl-| Rabbit, 3 lbs. | 3 grs. (containing| ,,,,th. | Decided paralysis in15 minutes;
: atropium. 10 oz. 2 grs. of atropia). and death in 58 minutes.
XXIII. | Sulphate of atro- | Do., 2 Ibs. 5 oz. |15grs.(containing| ,2,,th. | Diuresis, catharsis, and langour;
pia. 13:12 grs. of followed by recovery in more
atropia). than 3 hours and less than 9.
XXXIV. | Sulphate of me-| Do., 3 lbs. 03 oz. | 2°5 grs. (contain- | ,,1,,th | Slight paralysis and feeble
thyl-atropium. ing 2°05 grs, of twitches in 3 minutes; decided
atropia). paralysis in 4 minutes; and
death in 6 minutes,
alias | Da: Frog, 460 grs. | 0-1 gr.(containing | ,7,,th. | Decided paralysis in 2 minutes;
0:08 gr. of atro- complete paralysis in 9 min-
pia), utes ; and death on the7th day.
XXIV. | Sulphate of atro- | Do., 490 grs, 0°5 gr. (containing | ,3,th. | Incomplete paralysis 1st and 2d
pia. 0-42 gr. of atro- days; complete paralysis 3d
pia). day ; tetanus 3d to 5th days ;
an recovery 7th day,
XLVIII. | Iodide of ethyl- | Rabbit, 3lbs. 7 0z.| 2 grs. (containing | ,,3,,th.| Slight paralysis and tremors in
atropium. 1:27 gr. of atro- 6 minutes; decided paralysis
pia). in 16 minutes; and death in
24 minutes.
712 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
ConlIa.
This substance is obtained from Coniwm maculatwm (hemlock), and has been
shown by Von Pianta and Krxuii* to be a variable mixture of two bases, to
which they give the names of “ Conia” and “ Methyl-conia.” ‘These bases re-
semble one another very closely in physical properties. Their composition is
represented by the formule C,H,,N and C,H,,N. The chemists above named
investigated very completely the action of iodide of ethyl on conia, and proved
that “ conia”’ (or, as it is called in the present paper, normal conia) is an imide
base, and that ‘‘ methyl-conia” is a nitrile base.
The substances examined in the present paper are :-—
1st, Conta—samples of which were obtained from Messrs Duncan & FLockHart,
MaAcFARLAN & Co., and Morson. We are also indebted to Dr Curistison for the
opportunity of examining the action of a specimen of conia, which he prepared
in 1835.
2d, Methyl-conia—prepared from hydriodate of methyl-conia, produced by the
union of iodide of methyl and normal conta. Our experiments were made with
the hydrochlorate of this substance.
3d, Iodide of dimethyl-conium—obtained by the union of iodide of methyl and
methyl-conia contained in conia, as obtained from the plant.
Conia.—The careful and elaborate investigations of Curistison,} ScHRoFr, {
Von Praac,§ Ko.uiKker,|| and GurrmMann,§ have rendered important service to
our knowledge of the effects and mode of action of conia. From the results obtained
by these authors, it is now certainly established that this alkaloid is a poison of
great activity, and that it produces marked paralytic and less obvious spasmodic
symptoms. The former symptoms have been shown to depend principally on an
action on the peripheral terminations of the motor nerves; but the causation of
the latter is as yet unknown. It has also been ascertained, chiefly by the investi-
gations of KoLLIkeR and GUTTMANN, that conia does not directly iufluence the
functions of the sensory nerves, striped muscles, or heart.
In a general manner, our experiments confirm the above results; but they
also prove that considerable differences occur both in the nature of the action and
in the lethal activity of various samples of conia. In these respects, we observed
the most marked differences between the conia prepared by Dr Curtstison and
* Annalen der Chemie und Pharmacie, bd. Ixxxix. 1854, p. 129.
{ Transactions Roy. Soc. of Edinburgh, vol. xiii. 1837, pp. 398-415,
{ Wochenblatt der Gesellschaft der Aerzte zu Wien, 1856 ; and Lehrbuch der Pharmacologie,
1869, p. 531.
§ Journ. f. Pharm, i. 44.
|| Vircnow’'s Archiv. bd. x. 1856, p. 238.
{ Berliner Klinische Wochenschrift, 1866, pp. 45, 55, 71, 81.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 713
that obtained from Mr Morson; and as these, therefore, represent the extremes
among our samples, we shall describe in detail their action only.
Our experiments were made with the hydrochlorate, which we obtained as a
nearly colourless, imperfectly crystalline, and deliquescent substance. The differ-
ence of activity between the hydrochlorate of Dr Curistison’s conia and that of
Mr Morson was so great, that while two-tenths of a grain of the former speedily
caused death in a full-grown rabbit, this dose of the latter did not produce any
distinct effect, one grain being the smallest fatal dose for arabbit. The symptoms
that are produced in mammals by the different samples are very similar in
character. The more prominent ofthese are stiffness of the limbs, causing
difficulty in moving about; spasmodic starts; distinct increase of reflex excita-
bility; gradually increasing paralysis, with diminution, and, afterwards, dis-
appearance of the increased reflex excitability; and, finally, death by asphyxia.
The exact causation of the paralytic symptoms differs, however, in a remarkable
manner in different samples of conia; and the nature of this difference will be
shown in the detailed descriptions that follow.
We shall consider, in the first place, the action of hydrochlorate of Dr Cunisti-
son's conia. The following experiment illustrates the symptoms in mammals.
EXPERIMENT LIV.—Two-tenths of a grain of hydrochlorate of Dr CHRISTISON’S
conia, dissolved in four minims of distilled water, was administered by sub-
cutaneous injection to a rabbit, weighing three pounds and six ounces and-a-half.
In two minutes and thirty seconds, the limbs became somewhat stiff and
abnormally extended, so that the body was raised and an awkward posture
assumed. In three minutes, a slight touch of any part of the skin caused a
sudden spasmodic start; and soon after a series of starts in rapid succession
occurred spontaneously, during which the limbs were still stiffly extended.
In eight minutes, these starts ceased, and the limbs assumed a nearly normal
position; but the rabbit had now considerable difficulty in moving about, the
limbs being slightly paralysed. In sixteen minutes, the rabbit lay down and
rested in a crouching attitude, on the abdomen and chest. Soon after the neck
muscles were unable properly to support the head, which frequently subsided
on the table; but there was now no distinct evidence of exaggeration of reflex
activity. In twenty-five minutes, the paralysis was so decided, that even a
sitting posture could not be maintained, and the rabbit lay on the side. The
respirations were infrequent and laboured, while common sensibility seemed to
be unimpaired, and the heart was ascertained to be contracting with nearly
normal force and rapidity. In twenty-eight minutes, some convulsive movements
occurred in the body and limbs, and now the respirations were so weak as to be
scarcely observable. The convulsive movements continued for other two minutes,
but at the end of this period they consisted of extremely feeble spasmodic starts.
In thirty-one minutes, the sensibility of the conjunctiva and cornea had dis-
VOL, XXV. PART II. 8 Z
714. DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
appeared, the respirations had become mere infrequent gasps, but the heart was
contracting at the rate of 120 beats in the minute. Death occurred thirty-two
minutes after the administration. The pupils were frequently observed; they
retained the same diameter during the experiment as they had immediately
before it, but on the occurrence of death they contracted considerably.
After death, galvanic stimulation of the left sciatic nerve caused active move-
ments in the left leg, and also well-marked reflex movements in the right. The
exposed heart was contracting, six minutes after death, in proper rhythm, and
at the rate of 100 beats in the minute.
In our experiments with frogs, we found that a dose equivalent to the ~),,th
of the weight of the animal was sufficient to cause death. In the two experi-
ments with Dr Curistison’s conia, which we shall now describe, somewhat
larger doses than that above mentioned were administered, the complete physio-
logical action being but slowly developed with small doses.
ExpertMent LXI.—One-tenth of a grain of hydrochlorate of Dr Curistison’s
conia was dissolved in four minims of distilled water, and injected under the skin
at the right flank of a frog, weighing 300 grains. The frog jumped about actively
until five minutes after the administration, when it appeared to experience some
difficulty in moving about, and it was observed that this difficulty was chiefly
due to tonic spasm of the anterior extremities. This spasm, though by no means
powerful, was sufficient to retain the extremities in a constrained perpendicular
position, and in extreme extension, during the five minutes that succeeded its
first appearance. In ten minutes, the frog was unable to jump, and it lay on the
abdomen and chest; while the respirations had now ceased. In twenty-five
minutes, it was perfectly flaccid, and the head rested on the table, but the heart’s
impulse was still well marked, and the rate of its contractions was forty per
minute. At frequent intervals, the two posterior extremities were somewhat
suddenly pushed out to extreme extension, and after remaining in this posi-
tion, for one or two seconds, again partially flexed. In fifty minutes, these
extension movements of the posterior extremities ceased, and irritation of the
skin now caused merely faint twitches of the toes. In one hour and thirty
minutes, it was impossible to excite any reflex movement whatever; and on
applying galvanic stimulation to the trunk of a sciatic nerve, it was found that
the motor conductivity was completely suspended. The heart was at this time
contracting thirty-seven times in the minute, and the contractility of the striped
muscles was unimpaired. On the following day, the frog was still in a flaccid and
motionless state. The heart was contracting twenty-two times in the minute,
and the nerves and muscles were in the condition last described. On the morning
of the third day, rigor mortis was established.
In the next experiment, one limb was protected from the direct influence of
the poison.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. ols
EXPERIMENT LX V.—Having ligatured the sciatic artery and the two principal
veins at the middle of the right thigh in a frog weighing 195 grains, we injected
six-tenths of a grain of hydrochlorate of Dr Curisttson’s conia, dissolved in four
minims of distilled water, under the skin of the left flank. In two minutes, stiff-
ness occurred in the anterior extremities. They gradually became curved in-
wards until the fore-paws were pressed against each other, and they were re-
tained in this position by tonic spasm, the frog having apparently no voluntary
control over them. Jumping movements could not now be accomplished, but
the frog pushed itself about by vigorous contractions of the posterior extremities.
In five minutes, there was marked weakness on the left posterior extremity, the
right remaining unaffected. In eight minutes, the stiff incurvation of the
anterior extremities had disappeared ; and, now, the animal was flaccid every-
where, except in the right posterior extremity. In nine minutes, irritation of
the poisoned skin was followed by barely perceptible twitches in the toes of the
left posterior extremity, and extremely vigorous movements of the whole right
posterior extremity. Occasionally, the right posterior extremity was extended
stiffly, and retained thus for one or two seconds, the movements presenting a
somewhat spasmodic appearance. In thirty minutes, the reflex contractions that
followed irritation of the skin were confined to the right posterior extremity; and
the heart was now contracting at the rate of twenty-four beats in the minute.
In thirty-four minutes, the left sciatic nerve was exposed, the necessary dissection
causing vigorous movements in the right leg, and on stimulating the nerve by an
interrupted galvanic current, it was found that its motor conductivity was com-
pletely suspended, while its sensory (efferent) conductivity was retained; no
movements occurring in the left posterior extremity, while energetic contractions
occurred in the right (non-poisoned) posterior extremity. The contractility of
the poisoned muscles was still unimpaired. Irritation of the skin in the poisoned
region excited reflex movements of the right (non-poisoned) posterior extremity
until two hours and fifteen minutes after complete paralysis had occurred in the
poisoned motor nerves; but ten minutes after this, reflex movements could not
be excited. The frog did not recover from the poisoning.
A considerable interval occurred, therefore, between the complete suspension
of conductivity in the motor nerves and the loss of the reflex function of the
spinal cord; and, accordingly, it is evident that the condition of paralysis and
flaccidity caused by Dr Curisttson’s conia is mainly dependent on its action on
the motor nerves. The experiment further shows that this paralysing action is
restricted, in the first place, at least, to the peripheral terminations of the motor
nerves.
In the last two experiments, we have shown that certain slight spasmodic
symptoms are produced in frogs by conia. It is probable that these represent the
more violent convulsions that occur in mammals, and to which we have drawn
716 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
attention in the description of an experiment on a rabbit (Experiment LIV.).
Both in frogs and in mammals those spasmodic symptoms appear at an early
stage in the poisoning.
Although our main object, in describing the action of hydrochlorate of Mr
Morson’s conia, is to point out certain peculiarities in the mode in which it pro-
duces paralysis, it may be advisable that we should also give some evidence in
support of the assertion that its lethal activity is much less than that of the
hydrochlorate of Dr Curisrison’s conia. We shall thus be able to show clearly
that both the nature of the action and the lethal activity of various specimens of
conia may differ considerably, while the symptoms produced by them are very
similar in character.
In the following experiment, a dose below the minimum fatal was given.
EXPERIMENT LX VII.—We dissolved seven-tenths of a grain of hydrochlorate of
Mr Morson’s conia in fifteen minims of distilled water, and injected the solution
under the skin at the back of a rabbit, weighing three pounds and three ounces
and-a-quarter. The animal remained quiet until six minutes, when it moved
about in an excited manner, and during these movements it was observed that
the four limbs were abnormally and stiffly extended. This stiff extension of the
limbs. gradually became more marked, until it seriously impeded the movements
of the rabbit. In fourteen minutes, a slight touch of the skin excited a sudden
spasmodic start of the whole body. In twenty-five minutes, the stiffness of the
limbs had greatly diminished, and now it was obvious that a slight degree of
paralysis was present. From this time, these symptoms gradually but slowly
disappeared; and the rabbit was jumping about actively one hour after the
injection.
In the next experiment, the dose was a fatal one.
ExpERIMENT LXVIIJ.—One grain of hydrochlorate of Mr Morson’s conia,
dissolved in twenty minims of distilled water, was injected under the skin at the
right side of a rabbit, weighing four pounds and one ounce. The symptoms were
very similar to those observed with two-tenths of a grain of hydrochlorate of Dr
CHRISTISON’S conia. Stiffness of the limbs and tremors occurred in six minutes;
evidence of exaggeration of the reflex activity was obtained in eight minutes;
decided paralysis was present in thirteen minutes; and, after the occurrence of a
number of attacks of convulsive tremors, a condition of flaccid motionlessness,
interrupted by infrequent respiratory gasps, supervened, which terminated in
death, thirty-three minutes after the administration.
The general character of the symptoms produced by Mr Morson’s conia in
frogs was likewise found to be the same as that produced by Dr Curistison’s
conia; and, in proof of this, we shall briefly describe an experiment with a fatal
dose of the former.
EXPERIMENT LX XVI.—We injected three-tenths of a grain of hydrochlorate of
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 717
Mr Morson’s conia, dissolved in four minims of distilled water, under the skin at
the right flank of a frog, weighing 140 grains. The effects were very speedily
produced; for in less than two minutes, the frog was quite unable to jump, and
a decided degree of general paralysis was present. In four minutes, some stiff-
ness was present in the anterior extremities and the fingers, causing the latter to
be continuously and stiffly elevated until eight minutes after the poisoning. At
nine minutes, the frog was in a flaccid state, but, still, somewhat vigorous
movements were spontaneously made in the posterior extremities. These
consisted at first of extension and flexion movements of a normal character ;
soon, however, they became spasmodic, the extension being prolonged; and, at
fourteen minutes, they assumed an almost tetanic character, extreme extension
being maintained on each occasion for nearly two seconds. In twenty-five
minutes, the spontaneous movements of the posterior extremities were extremely
feeble, and in thirty minutes, they altogether ceased. In thirty-five minutes, the
frog was perfectly flaccid and motionless, and irritation, even of a severe char-
acter, failed to excite any reflex movement whatever. The heart was now con-
tracting in normal rhythm, at the rate of twenty-four beats in the minute.
On the following morning, the frog was dead and inrigor. In this experi- ©
ment, the dose (equivalent to the z3,th of the frog’s weight) was considerably
above the minimum fatal. Our experiments have shown that in frogs, as in
mammals, this sample of conia is much less active than that of Dr Curisrison,
for the smallest dose which we have found to produce death is equivalent to the
siopth of the weight of the frog used.
The last experiment shows that after a fatal dose of Mr Morson’s conia the
predominant symptoms are those of paralysis. We shall now describe some
experiments performed for the purpose of determining by what action or actions
this paralysis is produced.
EXpreRIMeNT LXXIJ.—We ligatured the blood-vessels in the right thigh of a
frog, weighing 112 grains, and, immediately afterwards, injected one-tenth of a
grain of hydrochlorate of Mr Morson’s conia, dissolved in five minims of distilled
water, under the skin of the left flank. Complete general paralysis was quickly
produced in the poisoned regions. In twenty-seven minutes after the injection,
irritation of the skin caused active and apparently tetanic reflex movements of
the right posterior extremity, but it failed to cause any movement in the parts to
which the poison had access. In one hour, the left sciatic nerve was exposed,
and subjected to galvanic stimulation; with the result, that no movement what-
ever was thereby excited in the left posterior extremity, or in any poisoned part,
while pretty active reflex movements were excited in the right posterior ex-
tremity. This condition continued until one hour and twenty minutes after the
injection, but at this time the reflex movements that were excited in the right
posterior extremity were extremely feeble. In one hour and thirty-five minutes,
VOL. XXV. PART II. 9A
718 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
it was impossible to excite any reflex movement, although strong irritations were
applied to the skin of both the poisoned and non-poisoned regions, and to the left —
sciatic nerve. At this time, the contractility of the muscles was unimpaired, the
conductivity of the right (non-poisoned) sciatic nerve. was retained, and the
contractions of the heart were at the rate of twenty in the minute.
It is obvious that, in this experiment, the motor nerves were completely
paralysed before the reflex function of the spinal cord was suspended.
ExpErIMEeNT LXXVIII.—After ligaturing the blood-vessels in the right thigh
of a frog, weighing 110 grains, we injected a solution containing three-tenths of a
grain of hydrochlorate of Mr Morson’s conia, under the skin at the left flank.
In forty-nine minutes, no reflex movements could be produced by irritation of
the skin, whether of the poisoned or non-poisoned regions. The left sciatic nerve
was now exposed; and, on galvanising its trunk, it was found that feeble
twitches occurred in the toes of the left (poisoned) posterior extremity, while no
reflex movements occurred in the right (non-poisoned) posterior extremity, or in
any part. It was ascertained, at the same time, that the muscles everywhere
contracted freely when directly stimulated, that the right sciatic nerve retained
its functional activity, and that the heart’s beats were occurring at the rate of
eighteen in the minute. The condition of retained, though impaired, conductivity
of the poisoned motor nerves, of retained conductivity of the non-poisoned (right)
sciatic nerve, of apparently unimpaired contractility of the muscles, coexisting
with complete suspension of the reflex function of the spinal cord, continued
until one hour and ten minutes after the administration of the poison. At one
hour and fourteen minutes, however, the left (poisoned) sciatic nerve was found
to be completely paralysed.
We learn from this experiment that Mr Morson’s conia may so energetically
affect the spinal cord, as to suspend its reflex function, before the motor nerves
are completely paralysed. The motor nerves, certainly, were affected at an early
stage, and, even before the suspension of the reflex function of the spinal cord,
their conductivity was so far impaired, that merely very feeble twitches could be
excited by galvanising them. The general paralysis that was present in the
poisoned region was, no doubt, to a considerable extent due to their impaired
activity. Still, the action of this substance on the reflex function of the spinal
cord was, at least, as important a cause of paralysis as the action on the motor
nerves. In Experiment LXXL., likewise, both actions co-operated in the produc-
tion of the paralysis, but the motor nerves were paralysed in it before the reflex
function of the spinal cord was completely suspended.
These two experiments represent two varieties of action, which we have
observed in our experiments with Mr Morson’s conia. In both, the motor nerves
and the spinal cord were markedly affected; but in the one, complete loss of
function occurred in the motor nerves before it occurred in the spinal cord, and
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 719
in the other, complete loss of function occurred in the spinal cord before it
occurred in the motor nerves.
The following Table contains a short account of these experiments :—
No. of | Weight |/Relation
Experi- of pe eres Dose. Effect.
ment. Frog. | > (7°82
to Dose.
LXXI. |112 grs.| y#,5th. | 0-1 gr. | Complete paralysis of motor nerves in 1 hour.
3 FA reflex function of spinal cord in 1 ho. 35 min.
LXXII. | 200 gers.} scoath. | 0:2 gr. | Complete paralysis of motor nerves in 40 minutes.
A BZ reflex function of spinal cord in 1 ho. 10 min.
LXXIII. | 256 grs.| yi5d. | 03 gr. | Complete paralysis of motor nerves in 1 hour 25 minutes.
a = reflex function of spinal cord in 1 ho. 25 min.
LXXIV. | 290 grs.| 535th. | 0°36 gr. | Complete paralysis of motor nerves in 18 minutes.
reflex function of spinal cord in from 2 to 18
hours.
LXXV. |110 ers.| z3oth. | 0:2 gr. | Complete paralysis of reflew function of spinal cord in 47 minutes.
motor nerves in from 1 ho. 20 min. to 22 ho.
” 2)
” »”?
LXXVI. | 140 grs.| zsth. | 03 gr. | Complete paralysis of reflew function of spinal cord in 35 minutes.
motor nerves in from 1 ho. 20 min. to 21 ho.
LXXVII. | 110 grs.| sisth. | 03 gr. | Complete paralysis of motor nerves in 30 minutes.
+5 8 reflex function of spinal cord in 1 ho. 30 min.
LXXVIII.| 110 grs.| s3sth. | 03 gr. | Complete paralysis of reflew function of spinal cord in 49 minutes.
re an motor nerves in | hour 14 minutes.
LXXIX. | 115 grs.| 237th. | 0-4 gr. | Complete paralysis of reflew function of spinal cord in 28 minutes. |
3 motor nerves in 35 minutes.
”
In the experiments in this Table, in which doses between the oth and
the =4;th of the frog’s weight were given, the complete paralysis of the motor
nerves occurred before the complete paralysis of the reflex function of the spinal
cord; and in the experiments in which doses between the ;4,th and the ,3,th
were given (excepting Experiment LX XVII.), the complete paralysis of the métor
nerves occurred after that of the reflex function of the spinal cord. As we have
already said, these two actions are, however, of nearly equal energy; for, at the
time when the one has been completed, the other is usually nearly so. Experi-
ment LX XVII., in which a dose equivalent to the ,4,th was administered, con-
spicuously illustrates this nearly simultaneous progress, by its occurrence as an
exception to the order in which the two actions are usually completed after such
a dose.
We have accordingly shown that Mr Morson’s conia differs from that of
Dr Curistison, both in lethal activity and in mode of action. We shall en-
deavour to explain these differences in a subsequent portion of this paper; the
explanation of the varieties in the mechanism of the paralysing action of Mr
Morson’s conia being dependent on results obtained by our experiments with
methyl-conia.
Hydrochlorate of methyl-conia (C,H, ,(CH,)NHCl).—Iodide of methyl acts
readily upon conia, producing a syrupy or crystalline substance, which is a mixture
720 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
of hydriodate of methyl-conia and iodide of dimethy]-conium—the former pro-
duced from the normal conia, and the latter from the methyl-conia. If the conia
be free from water, this action is very rapid, and as heat is developed it is
necessary that the vessel should be kept cool; if the conia contain water, the
chemical change is very slowly effected. Caustic potash is added to the mixture,
and it decomposes the hydriodate of methyl-conia, setting the base free as an oil,
while it leaves the iodide of dimethyl-conium unacted upon. The methyl-conia
was converted, after separation, into a hydrochlorate, which is extremely deli-
quescent, and has a brownish, semicrystalline appearance.
We found that this substance possesses a poisonous (lethal) activity, consider-
ably greater than that of Mr Morson’s conia, but nearly equal to that of Dr
CuRISTISON’s conia; for two-tenths of a grain, exhibited by subcutaneous injection,
speedily caused death in a rabbit, and a dose, equivalent to the zA;,5th of the
weight of the animal, is about the minimum fatal dose for a frog. The general
character of the symptoms is likewise similar to that of Dr Curisrison’s conia,
and, therefore, to that also of Mr Morson’s; but the causation of these symptoms
rather resembles that of the latter than-of the former conia. Paralysis is the
main symptom; and a careful examination, by experiments on frogs, of the
mechanism by which this symptom is produced, showed that it is a result of
actions on the motor nerves and spinal cord, and that with large doses the former
action is completed before the latter, while with small doses the latter action is
completed before the former.
We shall, in the first place, describe the symptoms that appeared in a rabbit,
after the administration of a fatal dose.
EXPERIMENT LXXXI.—Two-tenths of a grain of hydrochlorate of methyl-
conia was dissolved in twenty-five minims of distilled water, and injected under
the skin at the right flank of a healthy rabbit, weighing two pounds and ten ounces
and-a-half. The rabbit moved about in a normal manner until four minutes after
the injection, when the movements became constrained, and it was observed that
this was owing to stiff extension of the four limbs. A slight touch of the animal
caused a series of rapid tremors, during which, as well as at other times, the body
was elevated on the stiffly extended limbs. This somewhat remarkable condition
continued without change until ten minutes, when the stiffness of the posterior
extremities disappeared; but, in place of assuming a normally flexed position,
these extremities became flaccidly abducted ; and, when the animal moved about,
they trailed behind it in asomewhat powerless manner. In eighteen minutes, the
symptoms of exaggerated reflex activity, and the spasmodic extension of the anterior
extremities had disappeared; and, now, there was so great a degree of general
paralysis present, that the rabbit was unable to move about, and it lay quietly on
the abdomen and chest. In nineteen minutes, the neck muscles could no longer
continuously support the head, which, soon after, rested on the table. In twenty
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 121
minutes, the respiratory movements were laboured, and they occurred only
twenty-four times in the minute. The rabbit now lay on the side, quite flaccid
and powerless; and, at times, a series of slight tremors occurred. The respira-
tions gradually became weaker and less frequent, the common sensibility dis-
appeared, and death occurred, twenty-two minutes after the administration.
Three minutes after death, the exposed heart was contracting in normal
rhythm, at the rate of seventy-four beats in the minute; and it was ascertained
that the conductivity of the afferent and efferent nerve fibres of the sciatic nerves,
the reflex function of the spinal cord, and the contractility of the striped muscles
were still retained.
This description is sufficient to show that in rabbits hydrochlorate of methyl-
conia produces very similar effects to hydrochlorate of conia. That this similarity
also occurs in frogs will be seen from the following experiment.
ExPERIMENT LXXXVI.—A solution containing six-hundredths of a grain of
hydrochlorate of methyl-conia, in five minims of distilled water, was injected
under the skin at the right flank of a frog, weighing 185 grains. In ten minutes,
a slight degree of stiffness, with rigid elevation of the fingers, was present in the
anterior extremities, but the frog still jumped about actively. Gradually the
movements became less energetic; some sprawling occurred ; and, soon, the frog
lay on the abdomen and chest, quite unable to jump or move about. In twenty
minutes, the power of voluntary movement was completely lost, and irritation of
the skin caused but feeble reflex twitches in both posterior extremities. The frog
remained in this state until forty-seven minutes after the administration ; but in
fifty minutes, the most severe stimulation of the skin was unable to excite any
reflex movement whatever. The right sciatic nerve was now exposed and
galvanised; twitches were thereby excited in the right toes, but these were
unaccompanied by any movement in the left posterior extremity or elsewhere.
At this time the cardiac impulse was of fair strength, and the contractions of the
heart were occurring at the rate of forty in the minute.
On the morning of the following day, the frog was dead and in rigor.
These symptoms agree closely in their general character with those described
after corresponding doses of hydrochlorate of Dr Curistison’s conia (Experiment
LXI.), and of Mr Morson’s conia (Experiment LXXVI.); but the slight spasmodic
symptoms that appeared in the anterior extremities were not invariably observed
in our other experiments with this substance. Paralysis is shown to be the pre-
dominant symptom, and the causation of this paralysis, after the small fatal dose
exhibited in this experiment, appears to be due to an abolition of the reflex
function of the spinal cord, rather than to a suspension of the conductivity of
motor nerves. The action of hydrochlorate of methyl-conia, therefore, apparently
resembles that of hydrochlorate of Morson’s conia; and we shall see from the
following experiments that the special variations pointed out as occurring with
VOL. XXYV. PART II. 9B
722 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
different doses of conia obtained from that chemist, occur also with different doses
of hydrochlorate of methyl-conia. ;
EXPERIMENT LXXXVIII.—Immediately after ligaturing the blood-vessels at
the upper part of the right thigh in a frog, weighing 140 grains, we injected a
solution, containing one-tenth of a grain of hydrochlorate of methyl-conia, under
the skin at the left flank. In thirteen minutes, the frog was flaccid, and no
voluntary movements occurred in the poisoned region ; but vigorous movements,
consisting of extreme and somewhat spasmodic extensions, occurred at frequent
intervals in the right (non-poisoned) posterior extremity. Irritation of the skin
in the poisoned region now caused merely feeble twitches in the left (poisoned)
posterior extremity, and energetic movements in the right posterior. In fifty
minutes, however, no reflex movement could be excited anywhere by irritation
of the skin. The left sciatic nerve was exposed and subjected to galvanic
stimulation, with the result that, while well-marked movements occurred in the
left posterior extremity, no movement occurred in the right (non-poisoned). It
was at the same time ascertained that the motor conductivity of the right sciatic
nerve was not appreciably impaired, even in that part of the trunk exposed to
the direct action of the poison; that the poisoned muscles retained their con-
tractility ; and that the heart was contracting, in normal rhythm, at the rate of
twenty beats per minute. Several observations were made during the succeeding
fifty minutes, but no change had occurred during this time, with the exception
of a slight diminution in the rate of the heart’s contractions.
On the following morning, the frog was dead.
ExPERIMENT XCI.—The blood-vessels were tied at the lowest third of the
right thigh of a frog, weighing 200 grains, and two-tenths of a grain of hydro-
chlorate of methyl-conia, dissolved in four minims of distilled water, was then
injected under the skin at the left flank. The first symptom that was observed
occurred in three minutes, and consisted of a stiff extension of the anterior
extremities, causing unnatural elevation of the thorax. After a few seconds,
this symptom was modified to the extent that the anterior extremities became
rigidly incurved, with the fore-paws in contact with each other. Vigorous jump-
ing movements were still attempted, but as the anterior extremities took no part
in these, they were very imperfect, and frequently resulted in the frog falling on
one side. In ten minutes, this spasmodic condition of the anterior extremities
disappeared, and now the frog lay flaccid on the lower jaw, chest, and abdomen.
The power of voluntary movement seemed to be suspended in the poisoned
region, but it was retained in the non-poisoned (right posterior extremity), where
vigorous and somewhat spasmodic movements of extreme extension frequently
occurred. In thirty-three minutes, irritation of the skin caused energetic reflex
movements in the right posterior extremity, but no movement in any part of the
poisoned region. In thirty-four minutes, the left sciatic nerve was exposed, and
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 123
it was found that its motor conductivity was completely suspended—galvanism
of its trunk causing no contractions in the left posterior extremity; while its
sensory conductivity was retained—galvanism causing energetic reflex movements
in the right (non-poisoned) posterior extremity. The heart was now contracting
twenty-four times in the minute; and the contractility of the striped muscles was
apparently unimpaired. It was possible to excite reflex movements in the right
posterior extremity by stimulating the skin of the poisoned region, until one hour
and forty minutes after the administration. Very soon after this time, the
activity of the reflex function was completely suspended. Irritation of the skin
in the poisoned and non-poisoned regions, as well as galvanic stimulation of
the poisoned (left) sciatic nerve, caused no movement, notwithstanding that the
non-poisoned (right) sciatic nerve and muscles, and even the trunk of the right
sciatic nerve above the position of the ligatures, retained their functional activity.
These two experiments are selected from nine which were made on frogs with
different relative doses, and in which distinct evidence was obtained of the
primary cause of the paralysis. The conductivity of the motor nerves was
suspended before the reflex function was abolished in experiments in which doses
were administered, equivalent to the ,1,th, the ,4,th, the 5ioth, the goth,
and the ;;5 th of the weight of the frog employed; while the activity of the
reflex function was abolished before the motor nerves were paralysed in experi-
ments in which doses were administered, equivalent to the ;4,5th, the ;,,;th,
the +,15th, and the =,4:4d of the weight of the frog.
The details we have narrated of Experiments LXXXVIII. and XCI. demon-
strate that paralysis of the motor nerves is due to an action on their peripheral
terminations; as well when this paralysis precedes the abolition of the reflex
function, as when it occurs subsequently thereto. It would appear that the
abolition of the reflex function depends, at least in part, on an action on the spinal
cord ; for these experiments show that, after its occurrence, irritation of the skin
of a region protected from the direct action of the poison, or galvanic stimulation
of the trunk of a mixed nerve likewise protected from the direct action of the
poison, does not cause any reflex movement, notwithstanding that the motor
nerves and muscles everywhere retain their functional activity.
We have accordingly shown that conia and methyl-conia produce very similar
symptoms; the more prominent of which are spasms and paralysis.
Our analysis of the mode in which the paralysis is produced, has resulted in
proving its dependence on an action on the motor nerves and on the spinal cord.
The rate at which each of these actions is produced by the substances examined
(estimating this by the time of completion) varies in a remarkable, and, at first
sight, perplexing manner. In the case of the conia prepared by Dr CuristIson,
the former of these actions is the more powerful; while in that prepared by Mr
Morson, and in methyl-conia, the two are nearly equally prominent. In a series
724 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
of experiments on frogs with varying doses, it was found that Dr Curistison’s
conia invariably produced complete paralysis of the motor nerves before that of
the reflex function of the spinal cord; that Mr Morson’s conia usually produced
complete paralysis of the motor nerves before that of the reflex function of the
spinal cord in those experiments of the series where the dose was small, and
complete paralysis of the reflex function of the spinal cord before that of the
motor nerves where the dose was large; and that methyl-conia produced com-
plete paralysis of the reflex function of the spinal cord before that of the motor
nerves in those experiments where the dose was small, and complete paralysis
of the motor nerves before that of the reflex function of the spinal cord where
the dose was large.
As already mentioned, our chemical examination of the two specimens of conia
proved that that of Dr Curistison contains a much smaller proportion of methyl-
conia than that of Mr Morson. Our physiological examination has confirmed
this result; for the action of the latter specimen of conia more closely resembles
that of methyl-conia than the former. In other words, the conia containing the
smallest proportion of methyl-conia acts most purely as a paralyser of motor
nerves. It seems a legitimate deduction from this, that conia altogether free
from methyl-conia (7.¢., normal conia) will be free also from all spinal action, and
will, accordingly, produce paralysis solely by influencing the motor nerves.*
Our experiments have shown that the lethal activity of Dr Curistison’s conia
is considerably greater than that of Mr Morson’s. The comparatively feeble
potency of the latter cannot be explained by its containing a large proportion of
methyl-conia, for the activity of this substance is about the same as that of Dr
CHRISTISON’S conia; it may be due to the presence of ammonia.
Iodide of dimethyl-conium.—When a moderately dilute solution of caustic
potash is added to the mixture of iodide of dimethyl-conium and hydriodate of
methyl-conia, the latter salt, as stated above, is decomposed, while the former
remains in solution, and may be purified by crystallisation from strong aqueous,
caustic potash. It is tolerably soluble in hot solutions of caustic potash, but on
cooling the solution, it separates in the form of colourless silky needles. It is
readily soluble in water, and its composition may be represented by the formula,
C,H,,(CH,)NCH,I.
In various experiments, we have administered to rabbits, by subcutaneous
injection, doses of half-a-grain, two grains, two grains and-a-half, three, four,
and five grains. No obvious effects were produced by half-a-grain, or by two
erains; slight temporary paralysis was produced by two grains and-a-half, and
death by three, four, and five grains respectively. It is, therefore, obvious that the
* We have not as yet succeeded in obtaining a pure specimen of normal conia ; and the
quantities of ordinary conia at our disposal have not been sufficient to enable us to attempt a
separation of normal conia from methyl-conia.
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 725
lethal activity of iodide of dimethyl-conium is greatly less than that of either
conia or methyl-conia. That the character of the symptoms it produces is also
different, will be seen from the following experiment.
EXPERIMENT XCVIII.—Having dissolved three grains of iodide of dimethyl-
conium in forty minims of distilled water, we injected the solution under the skin
of a rabbit, weighing four pounds. The animal remained sitting quietly for more
_ than half an hour, during which time no symptom was observed. In thirty-two
minutes, however, it became restless, and faint tremors occurred. Soon, it had
difficulty in moving about; and after some endeavours to maintain a sitting
posture, it lay down on the abdomen and chest. In forty-one minutes, the head
rested on the table; and at this time the respirations were shallow, and at the
increased rate of 144 in the minute. The rabbit remained quietly in this position
until one hour and four minutes, when it succeeded, after some efforts, in rising
on its limbs, but, being unable to support itself thus, it again lay down on the
abdomen and chest, with the head resting on the table. The respirations were
now eighty-four in the minute. In one hour and eleven minutes, slight tremors
again occurred, and then the rabbit became perfectly fiaccid, and the respirations
infrequent and laboured. In one hour and twelve minutes, the respirations were
mere gasps, occurring at the rate of about twelve in the minute; and soon after
they became so shallow as to be hardly visible. In one hour and fifteen minutes, a
few twitches occurred in the muscles of. the face, and in a few seconds the rabbit
was dead.
In the autopsy, the motor nerves and muscles were found active, twelve
minutes after death ; but at this time the exposed heart was found to be contract-
ing irregularly and feebly. |
In this experiment, we frequently tested the reflex excitability, but never
observed the slightest evidence of its being increased.
We shall now briefly describe the experiment in which we administered five
grains.
ExPrErIMEeNnT C.—A solution, containing five grains of iodide of dimethy]-
conium, in fifty minims of distilled water, was injected under the skin of a rabbit,
which weighed three pounds and six ounces and-a-half. As in the previous
experiment, the first effects observed were a number of restless, uneasy move-
ments, which occurred in eleven minutes. Soon afterwards, paralytic symptoms
appeared ; and in twenty minutes, these had so far advanced that the rabbit lay
flaccid on the abdomen, chest, and lower jaw, while irritation of the skin was
followed by extremely feeble movements of the head, or one or other of the
extremities. In twenty-four minutes, the head fell over on the side, and rested
thus on the table; and the respirations were infrequent, shallow, and laboured.
After this, the respirations became greatly more infrequent and laboured, until
they altogether ceased, thirty-one minutes after the injection of the poison.
VOL. XXV. PART IL, I¢
726 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
In this experiment, likewise, we failed in discovering the slightest evidence of
exaggeration in the reflex excitability, or any spasmodic symptom.
These descriptions are sufficient to show that iodide of dimethyl-conium acts
simply as a paralysing agent, and that it does not produce any spasmodic effects
in rabbits.
The general symptoms that appear in frogs after the adininsvinltion of a fatal
dose are illustrated in the following experiment.
EXPERIMENT CVIJ.—Having dissolved one-tenth of a grain of iodide of dimethyl-
conium in four minims of distilled water, we injected the solution under the skin
at the right flank of a frog, weighing 150 grains. In two minutes and thirty
seconds, a slight degree of paralysis was observed in the anterior extremities,
which were scarcely able to support the chest; and the jumping movements
were now less active than before. Quickly, the paralysis became more decided ;
until at six minutes, the frog was lying on the abdomen and the lower jaw. The
respiratory movements of the chest had now ceased, while those of the throat
continued for several minutes longer. In nine minutes, irritation of the skin
produced merely feeble movements in the posterior extremities; and in thirty
minutes, it was impossible to excite any reflex movement whatever, even by
severe irritation of the skin. The right sciatic nerve was now exposed in the
thigh, and stimulated by an interrupted galvanic current, but no muscular con-
tractions were thereby produced, although the muscles contracted actively when
the electrodes were directly applied to their surfaces. At this time, the heart’s
impulse was of fair strength, and the beats occurred twenty-two times in the
minute.
On the following day, the frog was found to be in the condition last noted ;
but on tbe third day, the contractility of the muscles had disappeared, and the
heart’s contractions had ceased.
In many other experiments on frogs, the same general phenomena were
observed. The spasmodic symptoms to which we have drawn attention in our
description of the effects of conia and of methyl-conia were entirely absent in
our experiments with iodide of dimethyl-conium ; and, accordingly, the symptoms
we observed were those of paralysis only. We made several experiments to
determine what structures are influenced in the production of this paralysis.
Experiment CVIII.—Immediately after ligaturing the blood-vessels at the
upper part of the right thigh of a frog, weighing 192 grains, we injected three-
twentieths of a grain of iodide of dimethyl-conium, dissolved in four minims of
distilled water, under the skin of the left flank. In one minute thereafter, the
movements of the frog had become somewhat feeble, the poisoned extremities
being obviously weakened. In two minutes and thirty seconds, the frog lay on
the abdomen and lower jaw, apparently unable to execute any voluntary move-
ments with any part of the body except the right (non-poisoned) posterior
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 727
extremity, and there were no respiratory movements whatever. In nine minutes,
stimulation of the skin in any region was followed by energetic reflex movements
in the right posterior extremity, but no movements occurred in the poisoned
region. In fourteen minutes, the left sciatic nerve was stimulated by an inter-
rupted galvanic current, and, although active reflex movements of the right
(non-poisoned) posterior extremity were thereby excited, no movement occurred
in the left (poisoned) posterior extremity, or in any other part of the poisoned
region. The heart’s impulse was, at this time, found to be of fair strength, and
occurring forty-two times in the minute; and the muscles contracted vigorously
on direct stimulation. In three hours, the condition of the frog was the same as
last noted, excepting that the rate of the heart’s contractions had diminished to
thirty-eight in the minute. The observations were now interrupted until the
following morning, when the frog was found dead and in rigor.
In many other similar experiments with different doses of this substance,
the symptoms and mode of action were exactly the same as in the last experi-
ment. They show that the paralysis produced by dimethyl-conium is dependent
on an action on the motor nerves, primarily restricted to the peripheral termina-
tions. Even after the administration of a fatal dose, we have never observed
any action on the spinal cord, beyond its necessary implication in the progress
towards death. On the other hand, in experiments where doses below the mini-
mum fatal, and therefore considerably smaller than in Experiments CVII. and
CVIII., were given, the condition of complete paralysis of the peripheral termina-
tions of the motor nerves existed along with retained functional activity of the
spinal cord and sensory nerves, for periods protracted over many hours. Thus,
in an experiment where the dose was equivalent to the =4,th of the frog’s weight
(Experiment CIII.), the poisoned motor nerves remained completely paralysed for
more than twenty-six hours, while, during this time, the poisoned sensory nerves
and the spinal cord retained their functional activity.
We conclude from our experiments, that in physiological action iodide of
dimethyl-conium differs from conia and methyl-conia in being entirely free from
spasmodic and spinal-paralysing actions.
It is shown in the following Table of minimum fatal doses, that iodide of
dimethyl-conium is much less active than either conia or methyl-conia :—
728 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN
Relation
a 0, of Substance Animal and its aaa of Dose to Effect
es Employed. Weight. injection Weight of a
men J ‘ Animal.
LITT. | Hydrochlorate of | Rabbit, 3 Ibs. 01 gr. z7ss7zth. | Slight degree of stiffness in the
Dr Curistison’s| 142 oz. ; limbs, followed by recovery.
conia. ,
LIV. Do. Do., 3 lbs. 63 oz. 0:2 gr. xrsrssth. | Death, in 32 minutes.
LXVI. | Hydrochlorate of | Do., 2 Ibs. 12 oz. 0:2 gr. persath. | None.
Mr Morson’s
conia.
LXVIII. Do. Do., 4 Ibs, 1 oz. 1 gr. azt7zth. | Death, in 33 minutes,
LXXX. | Hydrochlorate of | Do., 3 Ibs. 144 oz. 0-1 gr. u7zs7ath. | None.
methyl-conia.
LXXXI. Do. Do., 2 lbs. 103 oz. 0:2 gr. szbezth. | Death, in 22 minutes.
XCOVII. | Iodideofdimethyl-| Do., 3 Ibs. 63 oz. 2°5 grs. sesxth. | Slight paralysis, followed by re-
conium, covery.
XCVIII. Do. Do., 4 lbs. 3 grs. past. | Death, in 1 hour and 15 minutes.
[This investigation into the physiological action of atropia and its methyl and
ethyl derivatives, and of conia and its methyl derivatives, was commenced in
July 1867; but, after performing a number of experiments, we considered it
advisable to postpone the further examination of these substances until we had
finished that portion of our researches which is published in Vol. XXY. Part 1 of
the “ Transactions.’’ Although an abstract was read before the Society on the 18th
of January 1869, this paper was not delivered to the Secretary for publication
until the month of October. |
The subjoined Tabular Summary contains the leading facts of all the Experi-
ments included in the present part of this investigation.
729
CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION
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PROCEEDINGS
OF THE
STATUTORY GENERAL MEETINGS,
AND
LIST OF MEMBERS ELECTED AT THE ORDINARY MEETINGS,
SINCE JANUARY 6, 1868,
WITH
LIST OF DONATIONS TO THE LIBRARY,
From Nov. 25, 1867, To Nov. 22, 1869.
VOL. XXV. PART II. 9G
PROCEEDINGS, &e.
Monday, 25th November 1867.
At a Statutory General Meeting, Professor Lyon Piayrair, Vice-President, in the
Chair, the Minutes of the Statutory Meeting of 26th November 1866 were read and con-
firmed.
The following Office-Bearers were elected for 1867-68 :—
Principal Sir Davip Brewster, K.H., LL.D., D.C.L., President.
His Grace the Duxe of Arcyti, Honorary Vice-President, having
filled the Office of President.
Principal Forszs,
Professor Innes,
Professor Lyon Puayrair, C.B.,
Davip Miitye Homg, Esq,
Dr Curistison,
Vice-Presidents.
Professor KELLAND,
Dr Joun Hurron Batrour, General Secretary.
Dr Grorce James ALLMAN ‘ ; :
> \Secretaries to the Ordinary Meetings.
Professor Tarr,
Davin Smitu, Esq., Treasurer.
Dr Macracan, Curator of Library and Museum.
COUNCILLORS.
Dr A. Crum Brown. James Sanverson, Esq. .
Dr Burt. Hon. Lord Neaves.
Dr Matruews Duncan. R. W. Tomson, C.E.
Wiiiam Turner, M.B. Gerorce Rosertson, C.E.
Dr Joun Muir. Professor Prazzt SMYTH.
Rev. THomas Brown. Patrick Dupceon, Esq. of Cargen.
The following List of Honorary Fellows was submitted before being printed in the
billet of the first ordinary meeting :—
I. FOREIGN.
Professor Bensamin Prince, Director of the United States Survey.
M. Cousin pe Remusat, Paris. Frreprich Wouter, Gottingen.
II. BRITISH.
James Prescott Jove, LL.D., Manchester. Cuartes Wueatstone, D.C.L., London.
PROCEEDINGS OF STATUTORY GENERAL MEETINGS. 743
Professor PLayrarr conveyed to the Society thanks from M. Curvreovt for his election
as an Honorary Fellow.
The Treasurer gave in his annual printed Report, certified by the Auditor.
On the motion of Dr Burt, Gzorce AvuLpso Jaminson, Esq., was.elected Auditor for the
year 1867-68.
It was announced from the chair that the Council had awarded the Keith Prize for the
biennial period ending April 1867 to Professor C. Prazzt Smyvu, for his paper on “ Recent
Measurements made at the Great Pyramid,” published in the Transactions.
On the recommendation of the Council, it was agreed that a ballot should take place
at next meeting for Dr Rosrerr Daun, who had resigned his seat in 1845, and who now
desired to be re-elected. ;
The Meeting then adjourned.
(Signed) D. Mitye Home, V.-P.
Monday, 23d November 1868.
At a Statutory General Meeting, Davin Minne Home, Hsq., Vice-President, in the
Chair, the Minutes of the Statutory Meeting of 25th November 1867 were read and con-
firmed. ‘
The following Office-Bearers were elected for 1868-69 :—
Professor Curistison, M.D., President.
His Grace the Duke of ARGYLL, | Honorary ice Premionts
JAMES Davip Forzss, LL.D.,
_ Professor C. Ixnzs,
Professor Lyon Piayrair, C.B.
D, Mitne Home, Esq.,
Professor KELLAND,
The Hon. Lord Nzaves,
Professor Sir Witt1am THoMSoN,
Dr Joun Hurron Baxrour, General Secretary.
Dr Grorce James ALLMAN,
Professor Tarr,
Davin Smitu, Esq., Treasurer.
Dr Mactaean, Curator of Library and Museum.
Vice-Presidents.
| Secretaries to Ordinary Meetings.
744 PROCEEDINGS OF STATUTORY GENERAL MEETINGS.
COUNCILLORS.
Dr Joun Muir. Patrick Dupcxon, Esq. of Cargen.
Rev. THomas Brown. Dr Hucu Ciecuorn.
JamzEs Sanverson, Esq. W. Ditrmar, Esq.
R. W. THomson, C.E. Dr James M‘Barn, Surgeon, R.N.
Grorcs Rozertson, C.E. Dr Wititam Rosertson.
Professor Prazzi SMYTH. Tuomas STEVENSON, C.E.
The following List of Honorary Fellows was submitted before being printed in the
billet of the first ordinary meeting :—
Gustav Rosert Kircuuorr, Professor of Physics in the University of Heidelberg.
Rupotpy Vircuow, Professor of Pathological Anatomy in the University of Berlin.
The Szcrerary announced that the Council had awarded the Makdougall Brisbane
Prize for the biennial period 1866-68 to Dr Atrxanprr Crum Brown and Dr THomas
Ricard Fraser for their conjunct paper on the Connection between Chemical Constitution
and Physiological Action, which had been printed in the Transactions.
The Secretary announced that the Council had awarded the Neill Prize for the
triennial period 1865-68 to Dr Witi1Am CarmicuarEt M‘Inrosu for his paper on the British
Nemerteans and on some New British Annelids, which was submitted to the Society last
session, and is to be printed in the Transactions.
The Meeting then adjourned.
(Signed) Pum Keanp, V-P.
LIST OF MEMBERS ELECTED. 745
LIST OF MEMBERS ELECTED.
December 2, 1867.
Joun F. M‘Lewnan, Esq., Advocate. Dr Rosert Daun (Re-admitted).
January 6, 1868.
Rey. Dr Davip AITKEN. Dr Rosert M. Fereuson,
February 3, 1868.
J. W. Larpray, Esq. of Seacliff. W. Wituiams, Esq.
March 2, 1868.
J. Samson GamaGee, Esq. Rey. D. T. K. Drummonp.
Rev. JosepH TayLor Goopsir. Major J. H. M. Saaw Srewart, R.E, Madras.
March 16, 1868.
Joun J. Stevenson, Esq. Rev. James F, Montcomery.
April 6, 1868.
Joun Dick Peppiz, Esq., Architect. Col. Szaton GuTHRIE.
SamvueE. Ratzicu, Hsq. Dr Tuomas SmitH Maccatt.
April 20, 1868.
Rev. Dr Tuomas GuTarie. Tuomas Key, Esq.
Avam Gituigs Suita, Esq., C.A. Joan Macmitian, Esq., M.A.
December 21, 1868.
Ouiver G. Mituzr, Esq. Wiuiam Dickson, Esq.
ALEXANDER Bucuan, Esq. Professor H. C, Fizemine JEnKin.
Joun Leveson Doveras Stewart, Esq. Joun Penper, Esq.
of Nateby Hall.
January 4, 1869.
Isaac Anperson-Hewry, Esq. of Woodend. Georce Exper, Esq.
Sir Cuartes A. Harttey, C.H. Davin MacGizsoy, Esq., Architect.
Rey. THomas Metvitte Raven, M.A. ALEXANDER Howe, Esq., W.S.
Viscount WALDEN. Professor ALEXANDER Dickson.
January 18, 1869.
Dr W. C. M‘Intosu. Dr Henry MarsuHatt.
Dr WitiiaAmM RUTHERFORD.
February 1, 1869.
Dr R, Craic Mactacan.
VON SOXGV. PART cle 9H
746 LIST OF MEMBERS ELECTED.
February 15, 1869.
James Dewar, Esq.
March 1, 1869.
Rev. H. CaLpERwoop, LL.D.
March 15, 1869.
Principal Sir ALEXANDER Grant, Bart, LL.D. Captain T. P. Wuire, Royal Engineers.
April 5, 1869.
Dr Joun Witson JouNsTon.
May 17, 1869.
Rosert Henry Bow, Esq., C.E.
May 31, 1869.
Maurice Lorutan, Esq. of St Catherine’s. Joun M‘Laren, Esq., Advocate.
1846
1868
1866
1867
1848
1856
1849
1845
1823
1867
1862
1849
1820
1843
1835
1867
1862
1830
1858
1843
1861
1866
1850
1863
1857
1862
1854
1869
1864
1859
1861
1835
1861
1867
1856
1833
1869
1857
1847
1869
1865
- 1866
1840
1860
1823
1863
1856
1844
ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY.
Corrected up to 1st November 1869.
N.B.— Those marked * are Annual Contributors.
*Alex. J. Adie, Esq., Rockville, Linlithgow
*Rey. Dr David Aitken, 4 Charlotte Square
*Col. Sir James H. Alexander of Westerton
*Rev. Dr W. Lindsay Alexander, Pinkie Burn, Mussel-
burgh
Dr James Allan, Inspector of Hospitals, Portsmouth
*Dr G. J. Allman, Professor of Natural History, 21
Manor Place
*David Anderson, Esq., Moredun, Hdinburgh
Dr Thomas Anderson, Prof. Chemistry, Univ., Glasgow
Warren Hastings Anderson, Hsq., Isle of Wight
*Thomas Annandale, Esq., 34 Charlotte Square 10
*T, C. Archer, Esq., Director of the Museum of Science
and Art, 9 Argyle Square
*His Grace the Duke of Argyll, K.T., (Hon. VicE-
PRESIDENT), Inverary Castle
Charles Babbage, K.H., London
David Balfour, Esq., Trenaby
Dr J. H. Balfour (GENERAL SECRETARY), Professor of
Medicine and Botany, 27 Inverleith Row
*George I. Barbour, Hsq., 11 George Square
*Hon. Lord Barcaple, 3 Ainslie Place
Dr Thomas Barnes, Carlisle
Edmund Chisholm Batten, M.A., Lincoln’s Inn, London
Dr Bennett, Professor of Institutes of Medicine, 1 Glen-
finlas Street 20
*George Berry, Esq., 2 Windsor V'errace, Portobello
*Adam Black, Esq., 38 Drummond Place
*Hugh Blackburn, Esq., Prof. Mathematics, University,
Glasgow
*Professor Blackie, 24-Hill Street
*John Blackwood, Esq., 3 Randolph Crescent
*Rev. Dr W. G. Blaikie, 9 Palmerston Road
Ernest Bonar, Esq.
*Robert Henry Bow, Esq., C.E., 7 South Gray Street
*Dr Alex. Crum Brown, Prof. of Chemistry, 4 Rillbank
Terrace
*Dr John Brown, 23 Rutland Street 30
*Rev. Thomas Brown, 16 Carlton Street
William Brown, Esq., 25 Dublin Street
*W. A. F. Browne, Bsq., Post-Office Buildings
*A.H. Bryce, D.C.L., LL.D., 42 Moray Place
*David Bryce, Esq., Architect, 131 George Street
His Grace the Duke of Buccleuch, K.G., Dalkeith Palace
*Alexander Buchan, Hsq., 18 Fettes Row f
*Dr W. M. Buchanan, 3 Carlton Terrace
*J. H. Burton, LL.D., Advocate, Craig House
*Rey, Henry Calderwood, LL.D. Professor of Moral
Philosophy, Craigrowan, Merchiston 40
*Alfred R. Catton, B.A.
*David Chalmers, Esq., Kate’s Mill, Slateford
Robert Chambers, LL.D., St Andrews
*William Chambers, Esq. of Glenormiston, 13 Chester Street
Dr Christison, D.C.L., Professor of Materia Medica
(PRESIDENT), 40 Moray Place
Dr H. ¥. C, Cleghorn, Stravithy, St Andrews
*Thomas Cleghorn, Esq., Advocate, 26 Queen Street
Dr Thomas R. Colledge, Lauriston House, Cheltenham
1829
1829
1850
1866
1843
1843
1863
1854
1830
1829
1853
1852
1823
1851
1841
1862
1868
1867
1848
1867
1869
1869
1869
1867
1863
1867
1866
1839
1868
1867
1860
1863
1851
1859
1866
1869
1856
1855
1866
1863
1866
1859
1868
1858
1852
1859
1828
1864
1858
1867
1867
1867
1867
1868
The Right Honourable Lord Colonsay, London
A. Colyar, Esq. *50
*Dr James Scarth Combe, 36 York Place
*Thomas Constable, Esq., 11 Thistle Street
Dr John Rose Cormack, 7 Rue d’Aguesseau, Paris
Andrew Coventry, Hsq., Advocate, 29 Moray Place
*Charles Cowan, Hsq., Mount Grange
*Sir James Coxe, M.J)., Kinellan
J, T. Gibson-Craig, Esq., W.S., 24 York Place
Sir William Gibson-Craig, Bart., Riccarton
Rev. John Cumming, D.D., London
*James Cunningham, Esq., W.S., 50 Queen Street 60
Liscombe J. Curtis, Esq., Ingsdown House, Devonshire
*H. W. Dallas, Esq., 125 Princes Street
James Dalmahoy, Esq., 9 Forres Street
*Nicholas Alexander Dalzell, Esq., Conservator of Forests,
Bombay
*Dr Robert Daun, 6 Picardy Place
*David Davidson, Esq., Bank of Scotland
*Henry Davidson, Esq., Muirhouse
*Wrancis Deas, Esq., LL.B., Advocate, 32 Heriot Row
*James Dewar, Esq., 15 Dublin Street
* Alexander Dickson, Professor of Botany, University of
Glasgow 70
*William Dickson, Esq., 38 York Place
Henry Dircks, Hsq., C.E., London
*W. Dittmar, Esq., Bonn
*James Donaldson, Esq., LL.D., 20 Great King Street
*David Douglas, Hsq., 41 Castle Street
Francis Brown Douglas, Esq., Advocate, 21 Moray Pl.
*Rey. D. T. K. Drummond, B.A., 6 Montpelier
*G. Stirling Home Drummond, Esq., Blair-Drummond
*Patrick Dudgeon, Esq. of Cargen
*Dr J. Matthews Duncan, 30 Charlotte Square 80
*Sir David Dundas, Bart. of Dunira
*Rev. Dr John Duns, 4 Mansion-House Road, Grange
*Dr James Dunsmure, 53 Queen Street
*George Elder, Esq., Knock Castle, Wemyss Bay
*W. Mitchell Ellis, Hsq., Wellington Lodge, Portobello
Robert Etheridge, Hsq., Clifton, Bristol
*William Euing, Esq., Glasgow
*J. D. Everett, LL.D., Prof. Nat. Phil., Queen’s College,
Belfast
*James Falshaw, Esq., C.E., 26 Castle Street
*Dr Fayrer, Professor of Surgery, Calcutta 90
*Robert M. Ferguson, Ph.D., 12 Moray Place
Frederick Field, Esq., Chili
Dr Andrew Fleming, H.M.I.S., Bengal
Major James George Forlong, Bombay
John Forster, Esq., Liverpool
*Dr John Foulerton, Manila
*Professor Fraser, M.A., 20 Chester Street
*Dr Thomas R. Fraser, College
*Frederick Fuller, Esq., Professor of Mathematics, Uni-
versity, Aberdeen
Dr Charles Gayner, Oxford 100
*Dr Arthur Gamgee, 27 Alva Street
J. Samson Gamgee, Esq., Birmingham
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(
*Archibald Geikie, Esq., Geological Survey Office, India
Buildings, George IV. Bridge
*Rey. Joseph Taylor Goodsir, 11 Danube Street
*L. D. B. Gordon, Esq., C.E., London
*Lieut.-Col. W. D. Gosset, R.E., Portsmouth
*Dr Andrew Graham, R.N.
*Principal Sir Alexander Grant, Bart., 21 Lansdowne
Crescent
*Rev. Dr James Grant, D.C.., 18 Great King Street
Dr Robert EH. Grant, Prof. Comp. Anat., Univ. Coll.,
London 110
*Dr Frederick Guthrie, M.A., Prof. of Physics, School
of Mines, London
*Col. Seton Guthrie, Thurso
*Reyv. Dr Thomas Guthrie, 1 Salisbury Road
*Dr D. R. Haldane, 22 Charlotte Square
*Prederick Hallard, Esq., Advocate, 7 Whitehouse Ter-
race
*James H. B. Hallen, Esq., Canada
Alexander Hamilton, LL.B., W.S., The Elms, Whitehouse
Loan
Dr P. D. Handyside, 11 Hope Street
*Rev. Dr Hannah, Glenalmond
Professor Robert Harkness, Queen’s College, Cork 120
Sir Charles A. Hartley, C.E., Sulina, Mouth of the Danube
*Sir George Harvey, 21 Regent Terrace
*G. W. Hay, Esq. of Whiterigg
*James Hay, Hsq., 3 Links Place, Leith
*Dr James Hector, New Zealand
*Isaac Anderson-Henry, Esq. of Woodend, Hay Lodge,
Prinity
Lieut. John Hills, Bombay Engineers
David Milne Home, Esq. of Wedderburn (VicE-PReEsI-
DENT), 10 York Place
* Alexander Howe, Esq., W.S., 17 Moray Place
Dr Adam Hunter, 18 Abercromby Place
*Robert Hutchison, Esq., Carlowrie Castle
*The Right Hon. John Inglis, D.C.L., LL.D., Lord Justice-
General, 30 Abercromby Place
*Professor Innes, M.A., Inverleith House
Edward J. Jackson, Fisq., 6 Coates Crescent
William Jameson, Esq., Surgeon-Major, Saharunpore
*George A. Jamieson, Esq., 58 Melville Street
Sir William Jardine, Bart., LL.D., of Applegarth, Jardine
Hall, Lockerby
*Professor H. C. Fleeming Jenkin, 5 Fettes Row
*Charles Jenner, Esq., Haster Duddingston Lodge
*Hon. Charles Baillie, LL.D., Lord Jerviswoode, 10
Strathearn Road 140
* Alex. K. Johnston, LU.D., March-Hall Park, Prestonfield
Dr John Wilson Johnston, India
*T. B. Johnston, Esq., 9 Claremont Crescent
*William Keddie, Esq., 5 India Street, Glasgow
*Dr Alexander Keiller, 21 Queen Street
Rey. Prof. Kelland, M.A. (VICE-PRESIDENT), 20 Claren-
don Crescent
*Thomas Key, Esq., 42 George Square
*J. W. Laidlay, Esq., Seacliff
*Charles Lawson, Hsq., 35 George Square
*Charles Lawson, jun., Esq., 34 George Square 150
*Dr Laycock, Professor of the Practice of Medicine, 13
Walker Street
130
748
*Hon. G. Waldegrave Leslie, 4 Heriot Row
*James Leslie, Esq., C.E., 2 Charlotte Square
*Dr W. Lauder Lindsay, Gilgal, Perth
* William Lindsay, Esq., Hermitage-Hill House, Leith
Thomas Login, Esq., C.E.
*Professor Lorimer, Advocate, 21 Hill Street
*Maurice Lothian, Esq. of St Catherine’s
*Dr W. H. Lowe, Balgreen, Slateford
*Dr Stevenson Macadam, 25 Brighton Place, Portobello 160
*Dr James M‘Bain, R.N., Logie Villa, York Road,
Trinity
*Dr Thomas Smith Maccall, Polmont
*John M. M‘Candlish, Esq., 4 Doune Terrace
*John M‘Culloch, Esq., Banker, 11 Duke Street
Dr Wm. Macdonald, Prof. Civ. and Nat. Hist., St
Andrews :
*W. Macdonald Macdonald, Esq., St Martins
*David MacGibbon, Esq., Architect, 89 George Street
John Mackenzie, Esq., 11 Abercromby Place
Dr Maclagan (CuRaTOR), Prof. of Medical Juris-
prudence, 28 Heriot Row A
Lieut.-Col. R. Maclagan, Royal Engineers, Bengal
*Dr R. Craig Maclagan, 5 Coates Crescent
*Dr William C, M‘Intosh, Murthly
*Peter M‘Lagan, Esq. of Pumpherston, M.P.
*Join M‘Laren, Esq., Advocate, 5 Rutland Square
*Jobn F. M‘lennan, Esq., Advocate, 81 Princes Street
*Jokn Macmillan, Esq., M.A., 16 Buccleuch Place
*John Macnair, Esq., 33 Moray Place
Sir John M‘Neill, G.C.B., Granton House
*Dr R. B. Malcolm, 126 George Street
Dr Henry Marshall, Clifton, Bristol
*J. D. Marwick, Esq., 10 Bellevue Crescent
*Professor David Masson, M.A., 3 Rosebery Crescent
*James Clerk Maxwell, Esq., late Prof. Nat. Phil., King’s
College, London, Glenlair, Kirkpatrick-Durham
*Sir William Stirling-Maxwell, Bart., Keir
*Edward Meldrum, Esq., Bathgate
*Graeme Reid Mercer, Esq., Ceylon Civil Service
John Miller, Esq., C.E., M.P., 2 Melville Crescent
*Oliver G. Miller, Esq., Panmure House, Forfarshire
Dr Patrick Miller, The Grove, Mount Radford, Exeter
*Thomas Miller, Esq., A.M., LL.D., Rector, Perth
Academy 190
Rear-Admiral Sir Alexander Milne, R.N., Inveresk
*Dr Arthur Mitchell, 6 Laverock Bank Villas
Joseph Mitchell, Esq., C.E., Viewhill, Inverness
*Dr John Moir, 52 Castle Street
*Rev. James F. Montgomery, 7 Walker Street
*Dr Charles Morehead, 6 Chester Street
*John Muir, D.C.L., LL.D., 6 Greenhill Park
Dr John Ivor Murray, Colonial Surgeon, Hong Kong
Dr Sheridan Muspratt, Liverpool
Robert Nasmyth, Esq., 5 Charlotte Square 200
*Hon. Lord Neaves, LL.D. (VicE-PRESIDENT), 7 Char-
lotte Square
*Thomas Nelson, Esq., Abden House, Prestonfield
*James Nicol, Esq., Prof. Nat. Hist., Aberdeen
*Hon. Lord Ormidale, 14 Moray Place
*David Page, LL.D., 44 Gilmore Place
Dr Richard Parnell, Melrose
*Dr Alexander Peddie, 15 Rutland Street
170
180
1868
1869
1849
1859
1834
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1865
1849
1863
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1859
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1839
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1866
1855
1846
1866
1850
1843
1847
1844
1868
( 749
*John Dick Peddie, Esq., Architect, 33 Buckingham
Terrace
John Pender, Esq., Manchester ‘
*W. Pirrie, Esq., Professor of Surgery, Marischal College,
' Aberdeen. 210
*Lyon Playfair, C.B., LL.D., M.P. (VICE-PRESIDENT),
4 Queensberry Place, South Kensington, London
Mungo Ponton, Hsq., W.S., Clifton, Bristol
Hyre B. Powell, Esq., Director of Public Instruction,
Madras
*James Powrie, Esq., Reswallie, Forfar
*Hon. B. F, Primrose, 22 Moray Place
*Samuel Raleigh, Esq., 30 George Square
Very Rev. I. B. Ramsay, Lh.D., 23 Ainslie Place
*W.J. M. Rankine, Esq., C.H., Prof. Civil Engineering,
University, Glasgow
Rev. Thos. Melville Raven, M.A., Crakehall, Bedale
*Rev. Francis Redford, M.A., Silloth 220
David Rhind, Esq., Architect, 54 Great King Street
William Richardson, Esq., Cheltenham
Martyn J. Roberts, Hsq., Crickhowell, South Wales
*George Robertson, Esq., C.H., 47 Albany Street
Dr Montgomery Robertson, Mortlake, Surrey
*Dr William Robertson, 28 Albany Street
*Dr E. Ronalds, Bonningtor Road
*Alex. James Russell, Esq., C.S., 9 Shandwick Place
J. Scott Russell, Esq., 5 Westminster Chambers, Lon-
don
*Robert Russell, Esq., Pilmuir, Leven, Fife 230
*Dr William Rutherford, Professor of Physiology, King’s
College, London
*James Sanderson, Esq., Surgeon-Major, 17 Claremont
Crescent
*Rey. D. F. Sandford, 19 Rutland Street
*Edward Sang, Esq., 2 George Street
*Dr Schmitz, International Institution, London
*Hugh Scott, Esq. of Gala, Galashiels
Sir William Scott, Bart., Ancrum
*Professor Sellar, LL.D., 15 Buckingham Terrace
Dr Sharpey, Prof. Anatomy, Univ. Coll., London
Sir James Y. Simpson, Bart., M.D., Prof. of Midwifery,
52 Queen Street 240
Ven. Archdeacon Sinclair, Kensington
*William F. Skene, LL.D., W.S. (VicE-PRESIDENT), 20
Inverleith Row
*Adam Gillies Smith, Esq., C.A., 5 Lennox Street
Arch. Smith, Esq., Lincoln’s Inn, London
David Smith, Esq., W.S. (TREASURER), 10 Eton Terrace
*Dr John Alexander Smith, 7 West Maitland Street
*Dr John Smith, 20 Charlotte Square
*R. M. Smith, Esq., 4 Bellevue Crescent
*Professor Piazzi Smyth, 1 Hillside Crescent
*Professor Spence, 21 Ainslie Place 250
*Dr James Stark, 21 Rutland Street
Henry Stephens, Esq., Red Braes Cottage, Bonnington
*Moses Steven, Esq. of Bellahouston, 12 Manor Place
David Stevenson, Esq., C.E., 25 Royal Terrace
*John J. Stevenson, Esq., Glasgow
)
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. 1853
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1866
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1868
1858
1834
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1864
1855
1864
1861
1863
*Thomas Stevenson, Hsq., C.E., 17 Heriot Row
*Rey. Dr Stevenson, Prof. Eccl. Hist., 37 Royal Terrace
Major J. H. M. Shaw Stewart, Royal Engineers, Madras
*John L. Douglas Stewart, Esq. of Nateby Hall, 13 Coates
Crescent
*Dr T. Grainger Stewart, 32 Queen Street 260
*Patrick James Stirling, Esq., LL.D., Kippendavie House
Captain T. D. Stuart, H.M.I.S.
*William Swan, Esq., Professor of Natural Philosophy,
St Andrews
Archibald Campbell Swinton, Esq., Kimmerghame
James Syme, D.C.L., Millbank House, Canaan
Dr John Addington Symonds, Clifton, Bristol :
*Professor P. Guthrie Tait, M.A. (SECRETARY), 17 Drum-
mond Place
Dr Taylor, Pau, France
Right Rev. Bishop Terrot, 9 Carlton Street
Dr Allen Thomson, Prof. Anatomy, Univ., Glasgow 270
*Dr Fraser Thomson, Perth
James Thomson, Esq., C.E., Norfolk Square, Hyde Park
London
*Dr Murray Thomson, Roorkee, Kast Indies
*R. W. Thomson, Esq., C.E., 3 Moray Place
*Sir William Thomson, Prof. Nat. Phil. (VicE-PRE-
SIDENT), Glasgow
*William Thomas Thomson, Esq., Bonaly
*Dr Wyville Thomson, Prof. Nat. Hist. and Geology
Belfast
Sir W. C. Trevelyan, Bart., Wallington, Morpeth
*William Turnbull, Hsq., 14 Lansdowne Crescent
*Professor Turner, M.B. (SECRETARY), 6 Kton Terrace 280
*Most Noble the Marquis of Tweeddale, K.T., Yester
House, Haddington
*Peter Waddell, Hsq., Claremont Park, Leith
*Viscount Walden, Yester House, Haddington
*Arthur Abney Walker, Esq., 32 Melville Street
James Walker, Esq., W.S., Tunbridge Wells
*William Wallace, Ph. D., Glasgow
Dr James Watson, Bath
*John K. Watson, Hsq., 14 Blackford Road
*Dr Patrick Heron Watson, 16 Charlotte Square
*Rev. Robt. Boog Watson, Madeira, 4 Bruntsfield Place
Edinburgh 290
Allan A. Maconochie Welwood, Esq. of Meadowbank
and Pitliver
*Captain T. P. White, Royal Engineers, 1 Drummond Place
*W. Williams, Esq., Veterinary College, Clyde Street
*Dr Thomas Williamson, 28 Charlotte Street, Leith
Dr Isaac Wilson
Professor John Wilson, College
*Dr J. G. Wilson, 9 Woodside Crescent, Glasgow
*Dr Alexander Wood, 10 St Colme Street
*Dr Andrew Wood, 9 Darnaway Street
Dr Wright, Cheltenham 300
*Robert S. Wyld, Esq., W.S., 19 Inverleith Row
*James Young, Esq., Limefield, Mid-Calder
*Dr John Young, Professor of Natural History, Glas-
gow 303
Fellows elected between the commencement of the Session and the 1st January of the following year are entered under the latter
date, by which their Subscriptions are regulated :—Thus, Fellows elected in December 1867 have the date of 1868 prejixed
to their names.
VOL. XXV. PART II.
91
( 0}
LIST OF THE PRESENT ORDINARY MEMBERS,
Corrected up to November 1, 1869.
IN THE ORDER OF THEIR ELECTION.
PRESIDENT.
Dr CHRISTISON.
HONORARY VICE-PRESIDENT, HAVING FILLED THE OFFICE OF PRESIDENT
His Grace tHE DUKE OF ARGYLL, K.T.
Date of
Election.
1818 Patrick Miller, M.D., The Grove, Mount Radford, Exeter.
1820 Charles Babbage, Esq., F.R.S., Lond.
Sir John F. W. Herschel, Bart., F.R.S., Lond.
William Macdonald, M.D., F.R.C.P.E., Professor of Natural History, St Andrews.
1822 Sir W. C. Trevelyan, Bart., Wallington, Northumberland.
1823 Captain Thomas David Stuart, of the Hon. East India Company's Service.
Warren Hastings Anderson, Esq.
Liscombe John Curtis, Esq., Ingsdon-House, Devonshire.
Robert Christison, M.D., Professor of Materia Medica.
1824 Robert E. Grant, M.D., Professor of Comparative Anatomy, University College, London.
1827 Very Rev. Edward Bannerman Ramsay, M.A. Camb., LL.D.
1828 John Forster, Esq., Architect, Liverpool.
David Milne Home, Esq., Advocate, of Milne-Graden and Wedderburn.
1829 A. Colyar, Esq.
Right Hon. Sir William Gibson-Craig, Bart. ef Riccarton,
Right Hon. Lord Colonsay.
Venerable Archdeacon Sinclair, Kensington.
James Walker, Esq., W.S.
1830 J. T. Gibson-Craig, Esq., W.S.
James Syme, D.C.L. Oxon., M.D. Dub., M.D. Bonn.
Thomas Barnes, M.D., Cavlisle.
1832 Montgomery Robertson, M.D.
1833 Rear-Admiral Sir Alexander Milne, R.N.
His Grace the Duke of Buccleuch, K.G., Dalkeith Palace.
Alexander Hamilton, LL.B., WS.
Date of
Election.
1834
1835
1836
1837
1839
1840
1841
1842
1843
1844
1845
1846
LIST OF ORDINARY MEMBERS. 751
Mungo Ponton, Esq., W.S., Clifton, Bristol.
Isaac Wilson, M.D., F.R.S., Lond.
William Sharpey, M.D., LL.D., F.R.S., Professor of Anatomy, University College, London.
John Hutton Balfour, A.M., M.D., F.R.S., Professor of Medicine and Botany.
William Brown, Esq., F.R.C.S.E.
David Rhind, Esq., Architect.
John Scott Russell, A.M., London.
Archibald Smith, M.A., Camb., F.R.S., Lincoln’s Inn, London.
Richard Parnell, M.D.
Peter D. Handyside, M.D., F.R.C.S.E.
David Smith, Esq., W.S.
Adam Hunter, M.D., F.R.C.S.E.
Rev. Philip Kelland, A.M., F.B.S., Professor of Mathematics.
Francis Brown Douglas, Esq., Advocate.
Alan A. Maconochie Welwood, Esq., of Meadowbank and Pitliver.
Martyn J. Roberts, Esq., Crickhowell, South Wales.
Robert Chambers, LL.D.
Sir John M‘Neill, G.C.B., LL.D.
Sir William Scott, Bart., of Ancrum.
Right Rev. Bishop Terrot.
Edward J. Jackson, Esq.
James Mackenzie, Esq.
John Miller, Esq., of Leithen.
James Dalmahoy, Esq.
James Thomson, Esq., Civil Engineer, London.
Robert Nasmyth, Esq., F.R.C.S.E.
A. D. Maclagan, M.D., Professor of Medical J: urisprudence.
John Rose Cormack, M.D., F.R.C.P.E., 7 Rue d’ Aguesseau, Paris.
Allen Thomson, M.D., F.R.S., Professor of Anatomy, Glasgow.
Joseph Mitchell, Esq., Civil Engineer, Viewhill, Inverness.
Andrew Coventry, Esq., Advocate.
John Hughes Bennett, M.D., Professor of Physiology.
D. Balfour, Esq., of Trenaby.
Henry Stephens, Esq.
Archibald Campbell Swinton, Esq., of Kimmerghame.
Sir James Y. Simpson, Bart., M.D., Professor of Midwifery.
David Stevenson, Esq., Civil Engineer.
Thomas R. Colledge, M.D., F.R.C.P.E.
Thomas Anderson, M.D., Professor of Chemistry, Glasgow.
A. Taylor, M.D., Pau.
Alexander J, Adie, Esq., Civil Engineer.
L. D. B. Gordon, Esq., C.E., London.
L. Schmitz, LL.D., Ph.D., International Institution, London.
Charles Piazzi Smyth, Esq., F.R.S., Professor of Practical Astronomy.
(oe LIST OF ORDINARY MEMBERS.
Date of
Election.
1847 Sir William Thomson, M.A. Camb., LL.D., F.R.S., Professor of Natural Philosophy, Glasgow.
John Hill Burton, LL.D., Advocate.
James Nicol, Esq., Professor of Natural History, Aberdeen.
William Macdonald Macdonald, Esq., of St Martins.
John Wilson, Esq., Professor of Agriculture.
Moses Stephen, Esq., of Bellahouston.
1848 Thomas Stevenson, Esq., C.E.
James Allan, M.D., Inspector of Hospitals, Portsmouth.
Henry Davidson, Esq.
William Swan, Esq., Professor of Natural Philosophy, St Andrews.
Patrick James Stirling, Esq.
1849 Sir William Stirling-Maxwell, Bart., of Keir and Pollok.
William Thomas Thomson, Esq.
W. H. Lowe, M.D., F.R.C.P.E., Balgreen.
Honourable Bouverie F. Primrose.
David Anderson, Esq., of Moredun.
W. BR. Pirrie, M.D., Professor of Surgery, Aberdeen.
His Grace the Duke of Argyll, K.T., Inverary Castle.
The Most Noble the Marquis of Tweeddale, K.T., Yester House.
Edward Sang, Esq.
1850 William John Macquorn Rankine, LL.D., F.R.S., Professor of Civil Engineering,
University, Glasgow.
Alexander Keith Johnston, LL.D.
Sheridan Muspratt, M.D., Liverpool.
James Stark, M D., F.R.C.P.E. (Re-admitted.)
Lieutenant-Colonel W. Driscoll Gossett, R.E.
Hugh Blackburn, Esq., Professor of Mathematics, Glasgow.
James Scarth Combe, M.D., F.R.C.S.E.
1851 Sir David Dundas, Bart., of Dunira.
E. W. Dallas, Esq.
Rev. James Grant, D.D., D.C.L., one of the Ministers of Edinburgh.
1852 Eyre B, Powell, Esq., Madras. :
Thomas Miller, A.M., LL.D., Rector, Perth Academy.
James Cunningham, Esq., W.S.
Alexander James Russell, Esq., C.S.
Andrew Fleming, M.D., Bengal.
1853 James Watson, M.D., Bath.
Lieutenant-Colonel Robert Maclagan, Bengal Enginecrs.
Rev. John Cumming, D.D., London.
Hugh Scott, Esq., of Gala.
Greme Reid Mercer, Esq.
1854 John Addington Symonds, M.D., Clifton, Bristol.
Robert Harkness, Esq., Professor of Mineralogy and Geology, Queen’s College, Cork.
Sir James Coxe, M.D., F.R.C.P.E.
LIST OF ORDINARY MEMBERS. 753
Date of
Election.
1854 Ernest Bonar, Esq.
1855 Stevenson Macadain, Ph.D.
Robert Etheridge, Esq., Clifton, Bristol.
Right Honourable John Inglis, D.C.L., LL.D., Lord Justice-General.
Wyville T. C. Thomson, LL.D., Professor of Geology, Belfast.
Thomas Wright, M.D., Cheltenham.
James Hay, Esq.
R. M. Smith, Esq.
1856 David Bryce, Esq.
William Mitchell Ellis, Esq.
George J. Allman, M.D., F.R.S., Professor of Natural History.
Honourable Lord Neaves, LL D.
Thomas Laycock, M.D., Professor of the Practice of Medicine.
Thomas Cleghorn, Esq., Advocate, Sheriff of Argyleshire.
James Clerk Maxwell, Esq., F.R.S., Jate Professor of Natural Philosophy, King’s College, London.
1857 John Ivor Murray, M D., F.R.C.S.E., Colonial Surgeon, Hong Kong.
John Blackwood, Esq.
W. M. Buchanan, M.D.
Thomas Login, Esq., C.E. :
Edmund C, Batten, M.A., Lincoln’s Inn, London.
1858 Thomas Williamson, M.D., F.R.C.S.E., Leith.
Robert B. Malcolm, M.D., F.R.C.P.%.
Frederick Field, Esq., Chili.
James Leslie, Esq., C.E.
Cosmo Innes, Esq., Professor of History.
Alexander Campbell Fraser, M.A., Professor of Logic.
Rey. William Stevenson, D.D., Professor of Ecclesiastical History.
1859 William F. Skene, LL.D.
G. W. Hay, Esq., of Whiterigg.
Robert Russell, Esq.
Joseph Fayrer, M.D., F.R.C.S.E., Professor of Surgery, Calcutta.
George Robertson, Esq., C.E.
Lyon Playfair, C.B., Ph.D., F.R.S., M.P., 4 Queensberry Place, South Kensington, London, W.
John Brown, M.D., F.R.C.P.E.
Rev. John Duns, D.D.
Lieut. John Hills, Bombay Engineers.
Major James George Forlong.
1860 William Robertson, M.D., F.R.C.P.E.
Frederick Guthrie, M.D., Professor of Physics, School of Mines, London.
George A. Jamieson, Esq.
Patrick Dudgeon, Esq., of Cargen.
William Chambers, Esq., of Glenormiston.
1861 W. A. F. Browne, Esq., F.R.C.S.E., one of H.M. Commissioners in Lunacy for Scotland.
Rev. Thomas Brown,
VOL. XXV. PART II. 9K
754 LIST OF ORDINARY MEMBERS.
Date of
Election.
1861 James M‘Bain, M.D., R.N.
Peter Guthrie Tait, A.M., Professor of Natural Philosophy.
John Muir, D.C.L., LL.D.
William Turner, M.B., Professor of Anatomy.
William Lauder Lindsay, M.D.
James Lorimer, A.M., Professor of Public Law.
Archibald Geikie, Esq., F.R 8., Director of the Geological Survey, Scotland.
George Berry, Esq.
James Young, Esq.
1862 Rey. William G. Blaikie, D.D.
Edmund Ronalds, Ph.D.
Thomas C. Archer, Esq , Director of Museum of Science and Art.
James Hector, M.D.
Nicholas Alexander Dalzell, A.M.
Hon. Lord Barcaple, LL.D.
Rev. Robert Boog Watson, Madeira.
1863 H. F. C. Cleghorn, M.D., Stravithy, St Andrews.
John Stuart Blackie, Esq., Professor of Greek.
Edward Meldrum, Esq.
Charles Lawson, Esq., of Borthwick Hall.
Alexander Peddie, M.D., F.R.C.P.E.
William Jameson, Esq., Surgeon-Major, Saharunpore.
Murray Thomson, M.D., Roorkee, India.
John Young, M.D., Professor of Natural History, University of Glasgow.
David Page, LL D.
J. G. Wilson, M.D., F.R.C.S.E.
J. Matthews Duncan, M.D., F.R.C.P.E.
W. Dittmar, Esq.
Honourable Lord Ormidale.
Joseph D. Everett, D.C L., Professor of Natural Philosophy, Queen’s College, Belfast. —
Honourable G. Waldegrave Leslie.
Honourable Charles Baillie, Lord Jerviswoode.
James Sanderson, Esq., Surgeon-Major.
Charles Cowan, Esq.
John Alexander Smith, M.D., F.R.C.P.E.
1864 Alex. Crum Brown, M.D., D.Se., Professor of Chemistry.
Alex. Wood, M.D., F.R.C.P.E.
Andrew Wood, M.D., F.R.C.S.E. .
Robert William Thomson, Esq., C.E.
James David Marwick, Esq. ;
Rev.. Daniel F. Sandford.
Robert 8. Wyld, Esq., W.S.
Peter M‘Lagan, Esq , of Pumpherston, M.P.
William Lindsay, Esq.
Date of
Election.
1864
1865
1866
1867
LIST OF ORDINARY MEMBERS.
W. Y. Sellar, M.A., Professor of Humanity.
Robert Hutchison, Esq., Carlowrie Castle.
Rev. John Hannah, D.D., Glenalmond.
William Wallace, Ph.D.
Arthur Abney Walker, Esq.
John Foulerton, M.D., F.R.C.S.E., Manila.
Alfred R. Catton, M.A., Camb.
Rey. Francis Redford, M.A., Rector of Silloth.
John Moir, M.D., F.R.C.P.E.
James Powrie, Esq., of Reswallie, Forfar.
Charles Jenner, Esq. ;
Charles Lawson, jun., Esq.
Alexander Keiller, M.D., F.R.C.P.E.
William Euing, Esq.
Fraser Thomson, M.D., Perth.
John M‘Culloch, Esq.
T. Grainger Stewart, M.D., F.R.C.P.E.
Colonel Sir James E. Alexander, of Westerton.
Charles Morehead, M.D.
David Masson, M.A., Professor of Rhetoric and English Literature.
David Douglas, Esq.
John Macnair, Esq.
James Spence, Esq., F.R.C.S.E., Professor of Surgery.
Thomas Nelson, Esq.
Adam Black, Esq.
Thomas Constable, Esq.
James Dunsmure, M.D., F.R.C.S.E.
Arthur Mitchell, M.D.
Patrick Heron Watson, M.D., F.R.C.S.E.
John Smith, M.D., F.R.C.P.E.
James Falshaw, Esq., C.E.
John K. Watson, Esq.
David Chalmers, Esq.
T. B. Johnston, Esq.
George F. Barbour, Esq., of Bonskeid.
David Davidson, Esq.
Peter Waddell, Esq.
Sir George Harvey.
George Stirling Home Drummond, Esq., of Blair-Drummond.
Frederick Fuller, Professor of Mathematics, Aberdeen.
Andrew Graham, M.D., B.N.
William Turnbull, Esq.
Archibald Hamilton Bryce, D.C.L., LL.D.
Francis Deas, LL.B., Advocate.
756 LIST OF ORDINARY MEMBERS.
Date of
Election.
1867 Arthur Gamgee, M.D.
Sheriff Hallard.
Thomas R. Fraser, M.D.
Thomas Annandale, Esq., F.R.C.S.E.
D. R. Haldane, M.D., F.R.C.P.E.
John M. M‘Candlish, Esq.
James Donaldson, LL.D., Rector of the High School
James Richardson, Hsq.
James H. B. Hallen, Esq., India.
Henry Dircks, Esq., C.E., London.
Charles Gayner, M.D., Oxford.
William Keddie, Esq., Glasgow.
P Rev. W. Lindsay Alexander, D.D.
1868 John F. M‘Lennan, Esq., Advocate.
‘Robert Daun, M.D. (Re-admitted.)
Rev. David Aitken, D.D. ;
Robert M. Ferguson, Ph.D. =
J. W. Laidlay, Esq., of Seacliff. ;
W. Williams, Esq., Veterinary College.
J. Samson Gamgee, Esq., Birmingham.
Rev. D. T. K. Drummond, B.A. Oxon.
Rev. Joseph Taylor Goodsir,
Major J. H. M. Shaw Stewart, Royal Engineers, Madras.
John J. Stevenson, Esq.
Rey. James F. Montgomery.
John Dick Peddie, Esq., Architect.
Colonel Seaton Guthrie.
Samuel Raleigh, Esq.
Thomas Smith Maccall, M.D., Polmont.
Rev. Thomas Guthrie, D.D.
Thomas Key, Esq.
Adam Gillies Smith, Esq., C.A.
John Macmillan, M.A.
1869 Oliver G. Miller, Esq.
John Leveson Douglas Stewart, Esq., of Nateby Hall.
Alexander Buchan, Esq.
H. C. Fleeming Jenkin, Esq., Professor of Engineering.
William Dickson, Esq. ;
John Pender, Esq., Manchester.
Isaac Anderson-Henry, Esq., of Woodend.
George Elder, Esq., Knock Castle, Wemyss Bay.
Sir Charles A. Hartley, C.E., Sulina, Mouth of the Danube.
David MacGibbon, Esq., Architect.
Rev. Thomas Melville Raven, M.A., Crakehall, Bedale.
“I
LIST OF ORDINARY MEMBERS.
Date of
Election.
1869 Alexander Howe, Esq., W.S.
Viscount Walden, Yester House.
Alexander Dickson, M.D., Professor of Botany, University of Glasgow.
William C. M‘Intosh, M.D., Murthly.
Henry Marshall, M.D., Clifton, Bristol.
William Rutherford, M.D., Professor of Physiology, King’s College, London,
R. Craig Maclagan, M.D.
James Dewar, Esq.
Rev. Henry Calderwood, LL.D., Professor of Moral Philosophy.
Sir Alexander Grant, Bart., LL.D., Principal of the University of Edinburgh.
Captain T. P. White, Royal Engineers.
John Wilson Johnston, M.D., India.
Robert Henry Bow, Esq., C.H.
Maurice Lothian, Esq., of St Catherine’s.
John M‘Laren, Esq., Advocate.
VOL. XXY. PART II. Oats
10
15
20
)
NON-RESIDENT MEMBER,
ELECTED UNDER THE OLD LAWS.
Sir Richard Griffiths, Bart., Dublin.
LIST OF HONORARY FELLOWS.
His Royal Highness the Prince of Wales.
FOREIGNERS (LIMITED TO THIRTY-SIX.)
Louis Agassiz,
J.B. A. L. Léonce Elie de Beaumont,
Robert Wilhelm Bunsen,
Michel Eugene Chevreul,
James D. Dana, LL.D.,
Jean Baptiste Dumas,
Charles Dupin,
Christian Gottfried Ehrenberg,
Elias Fries,
Frangois Pierre Guillaume Guizot,
Wilhelm Karl Haidinger,
Christopher Hansteen,
Hermann Helmholtz,
Gustav Robert Kirchhoff,
Albert Kolliker,
Johann von Lamont,
Richard Lepsius,
Rudolph Leuckart,
Urbain Jean Joseph Leverrier,
Baron Justus von Liebig,
Henry Milne-Edwards,
Theodore Mommsen,
Prof, Benjamin Peirce,
Cambridge, Massachusetts.
Paris.
Heidelberg.
Paris.
Newhaven, Connecticut.
Paris.
Do.
Berlin.
Upsala.
Paris.
Vienna.
Christiania.
Heidelberg.
Do.
Wurzburg.
Munich.
Berlin.
Leipzig.
Paris.
Munich.
Paris.
Berlin.
United States Survey.
25
30
34
10
15
19
LIST OF HONORARY
Adolphe Pictet,
Lambert Adolphe Jacques Quetelet,
M. Le Comte De Remusat,
Henri Victor Regnault,
Auguste De la Rive,
Gustav Rose,
Angelo Secchi,
Karl Theodor von Siebold,
Bernard Studer,
Rudolph Virchow,
Friedrich Wohler,
FELLOWS. 759
Geneva.
Brussels.
Paris.
Do.
Geneva.
Berlin.
Rome.
Munich.
Berne.
Berlin.
Gottingen.
BRITISH SUBJECTS (LIMITED TO TWENTY BY LAW X.)
John Couch Adams, Esq.,
George Biddell Airy, Esq.,
Thomas Carlyle, Esq.,
Arthur Cayley, Esq.,
Charles Darwin, Esq.,
Cambridge.
Greenwich.
London.
Cambridge.
Down, Bromley, Kent.
Sir John Frederick William Herschel, Bart., Collingwood.
James Prescott Joule, LL D.,
William Lassell, Esq.,
Rev. Dr Humphrey Lloyd,
Sir William E. Logan,
Sir Charles Lyell, Bart.,
John Stuart Mill, Esq.,
Sir Roderick Impey Murchison,
Richard Owen, Esq.,
Lieut.-General Edward Sabine, R.A.,
George Gabriel Stokes, Esq.,
William Henry Fox Talbot, Esq.,
Alfred Tennyson, Esq.,
Sir Charles Wheatstone, D.C.L.,
Clifpoint, Higher Broughton, Manchester.
Liverpool.
Dublin.
London.
Do.
Cambridge.
Lacock Abbey, Wiltshire,
Freshwater, Isle of Wight.
London.
( 760 )
LIST OF FELLOWS DECEASED AND RESIGNED,
FROM NOVEMBER 1867 TO NOVEMBER 1869.
HONORARY FELLOWS DECEASED (FOREIGN).
Marie Jean Pierre Flourens, Paris.
Jean Bernard Leon Foucault, Paris.
Carl Friedrich Philip von Martius, Munich.
Christian Friedrich Schénbein, Basle.
HONORARY FELLOWS DECEASED (BRITISH).
Thomas Graham, Esq.
Earl of Rosse.
ORDINARY FELLOWS DECEASED.
James Anstruther, Esq., W.S.
Professor G. A. Walker-Arnott.
James Begbie, M.D. .
William Brand, Esq., W.S. =
Sir David Brewster.
John Burt, M.D.
Henry Cheyne, Esq., W.S.
Right Honourable Sir George Clerk, Bart.
Allan Dalzell, M.D.
John Davy, M.D.
Right Honourable Lord Dunfermline.
Robert Dyce, M.D., Professor of Midwifery, Aberdeen.
Principal James David Forbes, St Andrews.
Robert Hamilton, M.D.
William Bird Herapath, M.D.
‘Rev. Professor Robert Lee, D.D.
Professor Patrick C. Macdougall.
Patrick B. Mure Maeredie, Esq., Advocate.
Thomas Mansfield, Esq., Accountant.
Dr Manson, Nottingham.
Robert Mayne, Esq., Indian Civil Service.
Rev. William Muir, D.D.
LIST OF FELLOWS DECEASED AND RESIGNED.
VOL. XXV. PART II.
Dr Frederick Penny.
James Richardson, Esq.
William Seller, M.D.
Sir James South.
Alexander Thomson, Esq. of Banchory.
James Wardrop, Esq.
ORDINARY FELLOWS RESIGNED.
Robert Campbell, Esq., Advocate.
Alexander A. Eugene Mackay, M.D.
Right Rev. Bishop Morrell.
Rev. Leonard Shafto Orde.
761
( 762 )
The following Public Institutions and Individuals are entitled to receive Copies of
the Transactions and Proceedings of the Royal Society of Edinburgh :— .
ENGLAND.
The British Museum.
The Bodleian Library, Oxford.
The University Library, Cambridge.
The Royal Society.
The Linnean Society.
The Society for the Encouragement of Arts.
The Geological Society.
The Royal Astronomical Society.
The Royal Asiatic Society.
The Zoological Society.
The Royal Society of Literature.
The Royal Horticultural Society.
The Royal Institution.
The Royal Geographical Society.
The Statistical Society.
The Institution of Civil Engineers.
The Institute of British Architects.
The Hydrographical Office, Admiralty.
The Medico-Chirurgical Society.
The Atheneum Club.
The Cambridge Philosophical Society.
The Manchester Literary and Philosophical
Society.
The Yorkshire Philosophical Society.
The Chemical Society of London.
‘The Museum of Economic Geology.
The United Service Institution.
The Royal Observatory, Greenwich.
The Leeds Philosophical and Literary Society.
The Historic Society of Lancashire and Cheshire.
The Royal College of Surgeons of England.
SCOTLAND.
Edinburgh, University Library.
Advocates’ Library.
College of Physicians.
Edinburgh, Highland and Agricultural Society.
Royal Medical Society.
Royal Physical Society.
Royal Scottish Society of Arts.
Glasgow, University Library.
St Andrews, University Library.
Aberdeen, University Library.
IRELAND.
The Library of Trinity College, Dublin.
The Royal Irish Academy. =
; COLONIES, &e,
The Asiatic Society of Calcutta.
Library of Geological Survey, Calcutta.
The Literary and Historical Society of Toronto.
University of Sydney.
CONTINENT OF EUROPE.
Amsterdam, Royal Institute of Holland.
Berlin, Royal Academy of Sciences.
Physical Society,
Berne, Society of Swiss Naturalists.
Bologna, Academy of Sciences.
Bonn, Cesarean Academy of Naturalists.
Bourdeaux, Society of Physical and Natural
Sciences.
Brussels, Royal Academy of Sciences.
Buda, Literary Society of Hungary.
Copenhagen, Royal Academy of Sciences.
Frankfort, the Senkenbergian Museum.
Geneva, Natural History Society.
Giessen, University Library.
Gottingen, University Library.
Haarlem, Natural History Society.
Jena, D. Gegerbaum, Editor of Zeitschrift Medi-
cinisch-Physikalisch Gesellschaft.
Leipzig, Royal Saxon Academy.
Lille, Royal Society of Sciences.
Lisbon, Royal Academy of Sciences.
Lyons, Agricultural Society.
Milan, Royal Institute.
Moscow, Imperial Academy of Naturalists.
Munich, Royal Academy of Sciences of Bavaria
(2 copies).
Neufchatel, Museum of Natural History.
Paris, Royal Academy of Sciences.
Geographical Society.
Royal Society of Agriculture.
Society for Encouragement of Industry.
Geological Society of France.
Ecole des Mines.
Marine Depot.
... Museum of Jardin des Plantes.
Rotterdam, Batavian Society of Experimental
Philosophy.
St Petersburg, Imperial Academy of Sciences.
Archeological Society.
Pulkowa Observatory.
Stockholm, Royal Academy of Sciences.
Turin, Royal Academy of Sciences.
763+)
Turin, M.-Michelotti.
Upsala, Society of Sciences.
Venice, Royal Institute.
Vienna, Imperial Academy of Sciences.
Geological Society.
Geologico-Botanical Society.
UNITED STATES OF AMERICA.
Boston, the Bowditch Library.
Academy of Arts and Sciences.
Society of Natural History.
New York, State Library.
Philadelphia, American Philosophical Society.
Academy of Natural Sciences.
Washington, the Smithsonian Institution.
Observatory.
Yale College, United States.
(All the Honorary and Ordinary Fellows of the
Society are entitled to the Transactions and
Proceedings.)
The following Institutions and Individuals receive the Proceedings only :—
ENGLAND.
The Scarborough Philosophical Society.
The Whitby Philosophical Society.
The Newcastle Philosophical Society.
The Geological Society of Cornwall.
The Ashmolean Society of Oxford.
The Literary and Philosophical Society of Liver-
pool.
Meteorological Office, 116 Victoria Street,
London,
SCOTLAND.
The Philosophical Society of Glasgow.
The Botanical Society of Edinburgh.
The Geological Society of Edinburgh.
The Meteorological Society of Edinburgh.
IRELAND,
The Natural History Society of Dublin.
COLONIES,
* The Literary and Philosophical Society of Quebec.
The Library of the Geological Survey, Canada.
The Literary Society of Madras.
China Branch of Asiatic Society, Hongkong,
North China Branch of the Royal Asiatic Society,
Shanghae.
The Royal Society of Victoria.
CONTINENT OF EUROPE.
Utrecht, the Literary and Philosophical Society.
Paris, Editor of L’Institut.
Cherbourg, Society of Natural Sciences.
Sicily, Catania, Academia Govenia de Scienze
Naturali.
UNITED STATES.
H. T. Parker, Esq., Harvard College, Cambridge.
Peabody Academy of Science, Salem, Massachu-
setts,
LIST OF DONATIONS.
(Continued from Vol. XXTY. p. 830.)
DONATIONS. DONORS.
TRANSACTIONS AND PROCEEDINGS OF SociETIES, ACADEMIES, UNIVERSITIES, &c.—
Amsterdam.—Catalogus van de Boekerij der Koninklijke Akademie van The Academy.
Wettenschappen gevestigd. Deel ii. Stuk 2. 8vo.
Jaarboek van der Koninklijke Akademie van Wettenschappen gevestigd. Ditto.
1866, 1867. 8vo,
Processen-verbaal van de gewone vergaderingen der Koninklijke Ditto.
Akademie van Wettenschappen, van Mei 1867 tot en met April
1868. 8vo.
Verhandelingen der Koninklijke Akademie van Wettenschappen. Ditto.
Deel xi. 4to.
Verslagen en Mededeelingen der Koninklijke Akademie van Wetten- Ditto.
schappen. Natuurkunde, Deel i1.; Letterkunde, Deel x. xi. 8vo.
Rapport fait 4 l’Académie Royale des Sciences des Pays-Bas, Section Ditto.
Physique. 8vo.
Baltimore.— Peabody Institute of the city of Baltimore. History of The Institute.
Baltimore. 1868. 8vo.
Basle.—Festschrift herausgegeben von der Naturforschenden Gesellschaft The Society.
in Basel zur der fiinfzigjahrigen Bestchens, 1867. 8vo.
Verhandlungen der Naturforschenden Gesellschaft in Basel. Theil Ditto.
iniy., v. Heft 1. 8vo. ;
Berlin,—Abhandlungen der Kéniglichen Akademie der Wissenschaften. ‘The Academy.
1866, 1867. 4to.
Monatsbericht der K6nigliche Preussischen Akademie der Wissen- Ditto.
schaften. March—December, 1868; January, February, 1869.
8vo.
Die Fortschritte der Physik in Jahre 1865, dargestellt von der The Society.
Physikalischen Gesellschaft zu Berlin. Jahrgang xxi. Abth. 1, 2.
8vo.
Berne.—Beitraege zur Geologischen Karte der Schweiz herausgegeben von The Natural His-
der Geologischen Commission der Schweizerischen Naturforschen- tory Society of
den-Gesellschaft auf rosten der Hidgenossenschaft. Lieferung, Berne.
3-5. 4to,
Mittheilungen der Naturforschenden Gesellschaft in Bern, No. Ditto.
603-653. 8vo.
Matériaux pour la Carte Géologique de la Suisse. Liv. 6e. 4to. Ditto.
Bombay.—Journal of the Bombay Branch of the Royal Asiatic Society. The Society.
No, 24. 8vo.
Meteorological and Magnetical Observations made at the Government The Observatory.
Observatory, Bombay, in the year 1864. 4to.
Boston.—Bulletin of the Public Library. Nos, 8 and 9. 8vo. The Library.
Sixteenth Annual Report of the Trustees of the Public Library, Ditto.
1868. 8vo.
Annual of the Boston Society of Natural History, 1868-69. 8vo. The Society.
VOL. XXV, PART II. IN
766 LIST OF DONATIONS.
DONATIONS.
TRANSACTIONS AND PRocEEDINGS OF SocIETIEs, &c.—continued.
Conditions and Doings of the Boston Society of Natural History for
1866-67, 1867-68. 8vo.
Memoirs read before the Boston Society of Natural History, Vol.
i, Parts 1-3, 4to.
Proceedings of the Boston Society of Natural History. Vols. x., xi.
8vo.
Bourdeaux.—Mémoires de la Société des Sciences Physiques et Naturelles
de Bourdeaux. Tomes iv., v., vi. 1,2. 8vo.
Bremen.—Abhandlungen herausgegeben von Naturwissenschaftlichen
Vereine zu Bremen, Bandi. Heft 1-3. 8vo.
Brussels—Mémoires couronnés et autres Mémoires.
8vo.
Mémoires couronnés et Mémoires des Savants étrangers publiées par
lAcadémie Royale Belgique. Tome xxxilil. 4to,
Mémoires de l’Académie Royale des Sciences, des Lettres, et des
. Beaux-Arts de Belgique. Tomes xxxvi.,xxxvil. 4to.
Bulletin de Académie Royale des Sciences, des Lettres, et des
Beaux-Arts de Belgique. Tomes xxiii, xxiv., Xxv., Xxvi., XXVii.
Nos. 1, 2, 3,4. Svo.
Biographie Nationale publiée par l’Académie Royale des Sciences,
des Lettres, et des Beaux-Arts de Belgique. Tome i. Partie 2;
Tome ii, Parties 1, 2. 8vo.
Tables Générales et Analytiques du receuil des Bulletins de l’Académie
Royale des Sciences, des Lettres, et des Beaux-Arts de Belgique.
Tomes i.—xx. 8vo.
Annuaire de Académie Royale des Scierces, des Lettres, et des
Beaux-Arts de Belgique. 1867, 1868-69. 12mo.
Annales de l’Observatoire Royale de Bruxelles publiées aux frais de
lV Etat, par le directeur A. Quetelet. Tomes xvii, xviii. 4to.
Annuaire de lObservatoire Royale de Bruxelles, par A. Quetelet.
1869. 12mo.
Cadiz.—Almanaque Nautico para 1869, 1870, calculado de orden de S.
M. en el Observatorio de Marina de la Ciudad de San Fer-
Tomes xix., xx.
nando. 8vo.
Caleutta.—Proceedings of the Asiatic Socicty of Bengal. 1867, 1868,
No. 1, 1869. 8vo.
Journal of the Asiatic Society of Bengal. Part i., Part ii., 1867-69.
Extra No. 8vo.
Do. Index. Vols. xxxv., xxxvi. 8vo.
Memoirs of the Geological Survey of India. Paleontologia, v. Pts.
1-4, 4to.
Memoirs of the Geological Survey of India. Vol. vi. Pts. 1 and
2. 8vo.
Annual Report of the Geological Survey of India, and of the Museum
of Geology, for 1866-67. 8vo.
Catalogue of the Meteorites in the Museum of the Geological Survey
of India. 8vo.
Cambridge.—Transactions of the Philosophical Society. Vol. x. Part 1;
Vol. x. Part 2, 4to.
Cambridge (U.S.)—Memoirs of the American Academy of Arts and
Sciences, Vol. ix. Part 1. 4to.,
Proceedings of the American Academy of Arts and Sciences.
vil. 8vo,
Proceedings of the American Association for the Advancement of
Science. 15th Meeting. 8vo.
Catania,—Atti dell’ Accademia Gioenia di Scienze Naturali.
1867. 4to.
Vol.
Tomo 1.
DONORS.
The Society.
Ditto.
Ditto.
The Society.
The Society.
Royal Academy.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto,
Ditto.
The Observatory.
Ditto.
The Observatory.
The Society.
Ditto.
Ditto.
The Survey.
Ditto.
Ditto.
Ditto.
The Society.
The Academy.
Ditto.
The Association.
The Academy.
LIST OF DONATIONS.
DONATIONS.
TRANSACTIONS AND PROCEEDINGS OF SocIETIES, &c,—continued.
Christiania —Meteorologiske Iagttagelser paa fem Telegrafstationer ved
Norges Kyst. 1866. 4to.
Meteorologiske Iagttagelser paa Christiania Observatorium, 1865-66.
4to.
Meteorologiske Iagttagelser det Sydlige Norge. 1863-66. 4to.
Meteorologische Beobachtungen an der Kéniglichen Universitits-
Sternwarte zu Christiania. 1837-63, 4to.
Norske Universitets-og Skole-Annaler udgivne af Universitetes
Seeretair. Jan., Aug., Oct. 1866; March 1867; Feb., March
1868. 8vo.
Det Kongelige Norste Frederiks Universitets Aarsberetning, for
1864-67. 8vo.
Nyt Magazin fur Naturvidenskaberne. Bind xiv. Hefte 2-4; Bind
xv. Heft 1, 2,3. 8vo.
Forhandlinger i Videnskabs-Selskabet 1 Christiania, Aaret 1864, 1865,
1866, 1867. 8vo.
Forslag til en Forandret Ordning af det Hoiere Skolevxsen. Deel 1.,
il., Wi. 8vo.
Columbus (U.S.)—Twenty-first Annual Report of the Ohio State Board of
Agriculture. 8vo,
Connecticut—Transactions of the Connecticut Academy of Arts and Sciences.
Vol. i. Parti. 8vo.
Copenhagen.—Det Kongelige danske Videnskabernes Selskabs Skrifter
femte rekke. Naturvidenskabeilg og Mathematiske Afdeling.
Bind vii, 4to.
Oversigt over det Kongelige danske Videnskabernes Selskabs, for-
handlinger og dets Medlemmers Arbeider. Aaret 1865-67.
8vo.
Cornwall—Journal of the Royal Institution of Cornwall, with the 49th
Annual Report. No.7. 8vo.
Dresden.—Novorum Actorum Academie Cesaree Leopoldino-Caroline
Germanice Nature Curiosorum. Tomes xxxii., xxxiv. 4to.
Dublin—Journal of the Royal Geological Society of Ireland. Vol. i.
Part 3. 8vo.
Journal of the Royal Dublin Society. Nos. 36, 87. 8vo.
Edinburgh.—Transactions of the Botanical Society, Edinburgh.
8vo
Transactions of the Highland and Agricultural Society of Scotland.
Vol ii. Parts 1, 2 (Fourth Series). 8vo.
Proceedings of the Royal Physical Society for Sessions 1862-63,
1863-64, 1864-65, 1865-66. 8vo,
Transactions of the Royal Scottish Society of Arts.
4,5. 8vo.
Transactions of the Edinburgh Geological Society. Vol.i. Parts 1, 2.
8vo.
Journal of the Scottish Meteorological Society. New Series.
15-20. 8vo.
Conference on Technical Education, held at Edinburgh, 20th March
1868. 8vo.
Forty-first Annual Report of the Royal Scottish Academy. 1868. 8vo.
Florence.—Memorie della Societa Italiana delle Scienze fondata da Anton-
mario Lorgna. Tomei. Parte 1. 4to.
Frankfort. —Abhandlungen herausgegeben von der Senckenbergischen
Naturforschenden Gesellschaft. Band vi. Heft 3,4. 8vo.
Tageblatt der 41 Versammlung Deutscher Naturforscher und Aerzte.
1867. 4to.
Volk ix:
Vol. vii. Parts 3,
Nos.
767
DONORS.
The Royal Obser.
of Christiania.
Ditto.
The University of
Christiania.
Ditto.
Ditto.
Ditto.
The R. Univ. of
Norway.
The Society.
The Royal Com-
mission.
The Board.
‘The Academy.
The Royal Aca-
demy of Sciences.
The Society.
The Institution.
The Academy.
The Society.
Ditto.
The Society.
The Society.
The Society.
The Society.
The Society.
The Society.
The Conference,
The Academy.
The Society,
The Society.
Ditto,
768
LIST OF DONATIONS.
DONATIONS.
TRANSACTIONS AND PROCEEDINGS OF SOCIETIES, &c.—continued.
Geneva.—Mémoires de la Société de Physique et d’Histoire Naturelle de
Genéve. Tome xix. Parties 1,2. 4to.
Glasgow.—Proceedings of the Philosophical Society. Vol. iii. Nos. 5 and
6; Vols. iv., v., and Vol. vi., Nos. 1-4. 8vo.
Transactions of the Geological Society. Vol. ii. Part 3; Vol. iii
Part i. 8vo.
Report of the Professor of Astronomy in the University for 1868.
8vo,
Gottingen —Abhandlungen der Kéniglichen Gesellschaft der Wissenschaften.
Band xiii. 4to.
Nachrichten von der K. Gesellschaft der Wissenschaften und der
Georg-August Universitat aus.dem Jahre 1867, 1868. 12mo.
Grcenwich.—Astronomical and Magnetical and Meteorological Observa-
tions made at the Royal Observatory in the year 1865. London,
1867. 4to.
Haarlem.—Archives Néerlandaises des Sciences Exactes, et Naturelles,
publiées par la Société Hollandaise des Sciences’ Haarlem. Tome
i. Liv. 5; Tome ii. Liv. 1,2. 8vo,
Naturkundige Verhandelingen van de Hollandsche Maatschappij der
Wettenschappen te Haarlem. Deel xxiv., xxv. 4to.
Archives du Musee Teyler. Voli. Fase. 3,4. 8vo.
Halifax, Nova Scotia.—Proceedings and Transactions of the Nova Scotian
Institute of Natural Science. Vol ii, Part 1. 8vo.
Harvard University.—Catalogue of the Officers and Students of Harvard
University, for 1866-67. 8vo.
Catalogus Universitatis Harvardiane, 1866. 8vo.
Reports of the President and Treasurer of Harvard College, 1865-66.
Cambridge, Mass., 1866. 8vo.
Report of the Trustees of the Museum of Comparative Zoology at
Harvard College in Cambridge, Mass., for 1866. 8vo.
‘iel.— Schriften der Universitat. Band xiii., xiv. 4to,
Kénigsberg.—Astronomische Beobachtungen auf der Kéniglichen Universi-
tits-Sternwart zu Konigsberg. 1865. Fol.
Schriften der K6niglichen Physicalish-Oekonomischen Gesellschaft zu
Konigsberg. 1865, Abth. 1, 2; 1866, Abth. 1,2. 4to.
La Haye—Archives Néerlandaises des Sciences Exactes et Naturelles.
Tome ii., Liv. 3-5; Tome iii., Liv. 1, 2. 8vo.
Lausanne.—Bulletin de la Société Vaudoise des Sciences Naturelles.
ix., Nos. 55-57. 8vo.
Leeds.— Annual Report of the Philosophical and Literary Society. 1866-67,
1867-68. 8vo.
Report of the Proceedings of the Geological and Polytechnic Society
of the West Riding of Yorkshire for 1867, 1868. 8vo.
Leipzig.—Abhandlungen der Philologisch-historischen Classe der Konig].
Sachsischen Gesellschaft der Wissenschaften. Band v. No. 3.
8vo.
Berichte tiber die Verhandlungen der Kéniglich Sichsischen Gescll-
schaft der Wissenschaften, Math. Phys. Classe. Nos. 1, 2, 4, 5.
Phil. Hist. Classe. 1866, No. 4; 1867, Nos. 1, 2. 8vo,
Tafeln der Egeria mit Zugrundelegung der in den Abhandlungen der
Konigl. Sachs. Gesellschaft der Wissenschaften in Leipzig ver-
ffentlichten Stérungen dieses Planeten berechnet und mit einlei-
tenden Aufsatzen versehen von P. A. Hansen. 8vo.
Von der Methode der Kleinsten Quadrate im Allgemeinen und in ihrer
Anwendung auf die Geodasie, von P. A. Hansen. 8vo.
Publications of the Astronomical Society. Nos, 1 to 8. 4to.
Vol.
DONORS.
The Society.
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The University.
The Observatory.
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Ditto.
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The College.
Ditto.
The University.
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The Society.
The Society.
The Society.
The Society.
The Society.
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Ditto.
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Academy.
Ditto.
The Society.
Leyden.—Annalen der Sternwarte in Leiden.
London.—Proceedings of the Society of Antiquaries.
LIST OF DONATIONS.
DONATIONS,
TRANSACTIONS AND PROCEEDINGS OF SOCIETIES—continued.
Vierteljahrsschrift der Astronomischen Gesellschaft.
iii.; iv. Heft 1. 8vo.
Preisschriften gekrént und herausgegeben von der Fiirstlich Jablo-
nowskischen Gesellschaft zu Leipzig. 8vo.
Tertullian’s Verhaltniss zu Minucius Felix nebst einem Anhang
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Uber Aarstellungen des Handwerks und Handelsverkehrs auf antiken
Wandgeniilden, von Otto Jahn. 8vo.
Jahrgang i.,, ii.,
Erster Band. 4to.
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pool. Nos. 20,21. 8vo.
Transactions of the Historic Society of Lancashire and Cheshire.
Vol. vi. 8vo.
Vol. ii. Nos. 3-7;
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Transactions of the Society of Antiquaries. Vol. xli, Parts 1, 2.
4to,
Journal of the Society of Arts for 1867-68, 1868-69. 8vo.
Memoirs of the Astronomical Society. Vols. xxxv., xxxvi.
Monthly Notices of the Royal Astronomical Society for 1867-68 and
1868-69. 8vo.
Journal of the Chemical Society (New Series) for 1867-69.
Catalogue of the Library of the Chemical Society. 8vo.
Transactions of the Clinical Society. Vol. i. 8vo.
Annual Report of the Geologists’ Association, with List of Members
for 1867-68. 8vo.
Quarterly Journal of the Geological Society.
ment. 8vo.
Quarterly Journal of the Geological Society. Vols, xxiii.—xxv.
List of the Geological Society of London, November 1867. 8vo.
Journal of the Royal Asiatic Society of. Great Britain and Ireland.
Vol. iii. Parts 1,2. 8vo.
Journal of the Royal Geographical Society, Vols. xxxvi., xxxvii.
8vo,
Proceedings of the Royal Geographical Society. Vols. xi—xiii.
Report of the Committee of the Harveian Medical Society, for the
Prevention of Venereal Diseases. London, 1867. 8vo.
Journal of the Royal Horticultural Society. Vol. ii. Parts 5, 6.
8vo.
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8vo.
Proceedings of the Royal Institution of Great Britain.
1-4. 8vo.
Transactions of the Royal Society of London.
elvii. Parts 1-2; Vol. clviii. Parts 1,2. to.
ato
Proceedings of the Royal Society of London. Vol. xv. No. 93; Vol.
8vo.
Nos. 92-94. Supple-
Vol. v. Parts
Vol. clvi. Part 2;
xvi. Nos. 94-101; Vol. xvii., Nos. 106-111. 8vo.
List of the Royal Society of London. Nov. 1866 and 1868. 4to.
Royal Society Catalogue of Scientific Papers. Vols. i., ii. 4to.
Transactions of the Royal Society of Literature. Vol. ix. Parts 1, 2.
8vo.
Proceedings of the Royal Medical and Chirurgical Society of London.
Vol v. No. 8; vi. Nos. 1-3. 8vo.
Transactions of the Royal Medical and Chirurgical Society. Vol. 50.
8vo.
VOL. XXV. PART II.
769
DONORS,
The Society.
The Royal Saxon
Academy.
Ditto.
Ditto.
The Observatory
of Leyden.
The Society.
The Society.
The Society.
Ditto.
The Society.
The Society.
Ditto,
The Society.
Ditto,
The Society.
The Association.
The Society.
Ditto.
Ditto,
The Society.
The Society.
Ditto.
The Society.
The Society.
Ditto,
The Institution.
The Society.
Ditto.
Ditto.
Ditto.
The Society.
The Society.
Ditto.
90
LIST OF DONATIONS.
DONATIONS.
TRANSACTIONS AND PROCEEDINGS OF SOCIETIES—continued.
Journal of the Statistical Society. Vol. xxx. Parts 2-4; Vol. xxxi.
Parts 1-4; Vol. xxxii. Part 1. 8vo.
Journal of the Linnean Society. (Botany) Vol. x. Nos. 41-49; Vol.
xi. (Zoology) Vol. x Nos. 38-45. 8vo.
Transactions of the Linnean Society. Vols. xxv., xxvi. Part 2.
4to.
Proceedings of the Linnean Society. Session 1868-69. 8vo.
List of the Linnean Society. 1867 and 1868. 8vo,
General Index to the first 25 vols. of the Transactions of the Linnean
Society. 1867. 4to.
Proceedings of the Mathematical Society. Nos. 12-15. 8vo.
Report of the Meteorological Committee of the Royal Society for
1857. 8vo.
Meteorology. Report on an Inquiry into the Connexion between
Strong Winds and Barometrical Differences, London, 1868. 8vo.
Proceedings of the Meteorological Society.
iv. Nos, 34-41. 8vo.
Transactions of the Pathological Society. Vol. xix.
Calendar of the University of London for 1868. 8vo.
Transactions of the Zoological Society of London. Vol. vi. Parts 1-7.
Ato.
Proceedings of the Zoological Society of London for 1866, 1867.
~ 8vo.
Jund.—ULunds Universitets Ars-Skrift-Mathematik och Naturvetenskap,
1866-67; Philosophi Sprakvetenskap och Historia, 1866,
1867 ; Theologi, 1866; Medicinska vetenskaper, 1866. Lund.
4to.
Lyons.—Mémoires de |’Académie Impériale des Sciences, Belles-Lettres,
et Arts de Lyons. > Classe des Lettres. Tomes xii., xiii, Classe
des Sciences. Tomes xiv., xv., xvi. 8vo.
Annales de la Société d’Agriculture, d’Histoire Naturelle, et des Arts
utiles de Lyon, Tomes ix.,x. 8vo.
Madrid.—Libros del Saber de Astronomia del Rey D. Alfonzo X. de Cas-
tilla, copilados, anotados y comentados por Don Manuel Rico y
Vol. iii. Nos. 31, 382;
8vo.
Sinobas. Tom.v. Pt.1. Fol.
Massachusetts——Proceedings of the Essex Institute at Salem. Vols. iv., v.,
Nos. 1 and 2. 8vo.
Melbourne.—Transactions and Proceedings of the Royal Society of Vic-
toria. Vols, vili., ix., Part. 1. 8vo.
Statistics of the Colony of Victoria for the year 1867. Part 3 (Inter-
change); Part 4 (Law, Crime, &c.) Fol.
Milan.—Memorie del Reale Istituto Lombardo di Scienze e Lettere—Classe
di Lettere, e Scienze Morali e Poktiche. Vol. ii. Fasc. 8-10;
Vol. iii. Fase. 1-10; Vol. x. Fase. 5, 6. Classe di Scienze Mate-
matiche e Naturali. Vol. ii. Fase. 9, 10; Vol. ii. Fasc. 1-9; Vol.
x. Fase. 8-5. 4to.
Rendiconti Reale Istituto Lombardo—Classe di Lettere e Scienze
Morali e Politiche. Vol. iii. Fase. 1-10. Classe di Scienze
Matematiche e Naturali, Vol, iv, Fasc. 1-10, 1866, 1867.
Svo.
Rendiconti Reale Istituto Lombardo de Scienze e Lettere,
Vol. i. Fase. 1-20; Vol. 11. Fase. 1-10, 1868-69. 8vo.
Solenni Adunanze del R. Istituto Lombardo de Scienze e Lettere.
Vol. i. Fase. 4. 8vo.
Annuario del Reale Istituto Lombardo di Scienze e Lettere. 1864.
12mo. ;
Serie ii.
DONORS
The Society.
The Society.
Ditto.
Ditto.
Ditto.
Ditto.
The Society.
The Society.
The Committee of
the Meteorolo-
gical Society.
The Society.
The Society.
The University.
The Society.
Ditto.
The University. -
The Academy.
The Society.
The Academy of
Sciences, Madrii.
The Institute.
The Society.
The Australian
Government.
The Institute.
Ditto.
Ditto.
Ditto.
Ditto.
LIST OF DONATIONS. ar
DONATIONS. DONORS.
TRANSACTIONS AND PROCEEDINGS OF SocIETIES—continued,
Montpellier —Mémoires Académie des Sciences et Lettres de Montpellier. The Academy.
Section des Sciences, Tomes i.—v., Tome vi., Fase. 1; de la Section
de Médecine, Tomes iii., iv., Fasc. 1,2; de la Section des Lettres,
Tomes ii., iv., Fasc. 1. 4to.
Moscow.—Bulletin de la Société Impériale des Naturalistes. Nos. 3,4, The Society.
1866; Nos. 1, 2, 1867; Nos. 1, 2, 1868. 8vo.
Munich.—Sitzungsberichte de Kénigl. Bayer. Akademie der Wissenschaften The Academy.
zu Miinchen. Band i. Heft 1-4; Band ii. Heft 1-4. 1868.
8vo.
Abhandlungen der Koniglich Bayerischen Akademie der Wissen- Ditto.
schaften. Band xi. Abth. 2. Historischen Classe. Band ix. :
Abth. 3.; Band x. Abth. 3. Mathematisch-Physikalischen Classe.
Band x. Abth. 1. 4to.
Munchen Gehalten in der Offentlichen der K. Akademie der Wissen- Ditto.
schaften am 28 Marz 1868, von August Vogel. 8vo.
Almanach der Koniglich bayerischen Akademie der Wissenschaften Ditto.
for 1867. 12mo.
Resultate der Miinchener Meteorologischen Beobachtungen, 1857— The Royal
1866. 8vo. Observatory.
Beobachtungen des Meteorologischen Observatoriums auf dem Hohen- Ditto.
peissenberg von 1851-1864. 8vo.
Annalen der Koniglichen Sternwarte. Band xv., xvi. 8vo. Ditto.
Naples.—Atti della Reale Accademia delle Scienze e Belle-Lettere di The Academy.
Napoli della Fondazione sino all’anno 1787. 4to.
Atti dell’Accademia delle Scienze Fisiche e Matematiche. Vol. ii. Ditto.
4to.
Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche. Ditto.
Anno iii. Fase. 7-12; Anno iv, Fasc. 1-12; Anno v. Fase. 1-12;
Anno vi. Fase. 1-5, 4to.
Rendiconto delle Tornate e dei Savori Geller adeanid di Scienze Morali Ditto.
e Politiche. Jan., Aug., Dec. 1868. 8vo.
Neuchatel.—Actes de la Société Hélvétique des Sciences Naturelles. The Society.
Comte-Rendu, 1866. 8vo.
Bulletin de la Société des Sciences Naturelles de Neuchatel. Tome Ditto.
vil., T. vili. No. 1. 8vo.
New York.—Report (Annual) of the Regents of the University of the The University.
State of New York, on the Condition of the State Cabinet of
Natural History. 1863-64—-65-66. 8vo.
Report (Annual) of the Trustees of the New York State Library for The Trustees.
1863-64-65—-66-67. © 8vo.
Ohio.—Report (Twentieth Annual) of the Ohio State Board of Agriculture The Board.
for 1865. Columbus, 1866. 8vo.
Oxford —Astronomical and Meteorological Observations made at the Rad- The Observatory.
cliffe Observatory, Oxford, in the years 1864-66, Vols. xxiv.,
XY, KEVIN BVO!
Palermo.—Giornale di Scienze Naturali ed Economiche publicato per cura The Institute.
del Consiglio di perfezionamento annesso al R. Instituto Tecnico
di Palermo. Vol. ii. Fasc. 2, 3,4; Vol. iv. Fase. 1, 2, 3. 4to.
Paris,—Annales des Mines. Tomes x., xi., xii., xiii, xiv., xv., Liv. 1. 8vo. The Ecole de .
Mines.
Annales Hydrographiques. No. 4, 1867; Nos. 1-3, 1868. 8vo. The Dépét de la
Marine.
Publications of the Dépét de la Marine, with Charts, Nos. 408, 422, Ditto.
428, 433, 485, 437, 436, 439, 440, 442, 443, 444, 447.
8vo.
Bulletin de la Société de Géographie. Nov. Dec. 1867, Jan. Sept. The Society.
1868. 8vo.
hie LIST OF DONATIONS.
DONATIONS.
TRANSACTIONS AND ProceEDINGs oF SocieTIEsS—continued.
Comptes-Rendus Hebdomadaires des Séances de l’Académie des
Sciences. 1867-68, 1868-69. 4to.
Mémoires de |’ Académie des Sciences de I’ Institut Impérial de France.
Tome xxxvii. Premiére Partie. 4to.
Nouvelles Archives du Muséum d'Histoire Naturelle.
1-4; Tome ii. Fase. 1-4; Tomes iii., iv. 4to.
Philadelphia.—Journal of the Academy of Natural Sciences of Phila-
delphia. New Series. Vol. vi. Parts 1,2. 4to.
Proceedings of the Academy of Natural Sciences of Philadelphia.
Vol. 1. 1841-43 ; Vol. iii. 1846-47; Vol. iv. 1848-49 ; Vol. vii
1854-55 ; 1862, Nos. 1-6; 1866, Nos. 1-5. 8vo.
Proceedings of the American Philosophical Society. Vol. x. Nos.
76-80. 8vo.
Rotterdam.—Nieueve Verhandelingen van het Bataafsch Genootschap der
Proefondervindelijke Wijsbegeerte. Deel i. Stuk 1-3. 4to.
Salem (U.S.)—Proceedings of the Essex Institute. Vol. v., Nos. 5,6. 8vo.
Shanghai.—Journal of the North China Branch of the Royal Asiatic
Society. No, 4. 8vo.
St Petersburg.—Annales de ]’Observatoire Physique Central de Russie,
1863, (with Supplement), 1864, St Petersburg, 1865-66. 4to.
Bulletin de l’Académie Impériale des Sciences de St Petersbourg.
Tome x. Nos. 1-4; Tome xi. Nos. 1-4; Tome xii. Nos. 1-8;
Tome xiii. Nos, 1-3. 4to,
Compte-Rendu Annuel adressé 4 8. Exc. M. de Reutern, par le Direc-
Tome i. Fase.
teur de l’Observatoire Physique Central A. T. Kupffer, 1864.
St Petersburg, 1865. 4to.
Compte-Rendu de la Commission Impériale Archéologique pour
l’Années 1865 et 1866, 4to (atlas fol.)
Mémoires de |’ Académie des Sciences de St Petersbourg. Vii® série.
Tome x. Nos. 3-16; Tome xi. Nos. 1-18; xii., Nos. 1-3. 4to.
Switzerland.—Verhandlungen der Schweizerischen Naturforschen Gesell-
schaft in Rheinfelden. Am. 9, 10, 11 Sept. 1867. 8vo.
Toronto.—Canadian Journal of Industry, Science, and Art. New Series. -
Nos. 63-67. 8vo.
The Canadian Journal of Science, Literature, and History. Vol. xii.
No. 2. 8vo.
Truro.—Journal of the Royal Institution of Cornwall, with the 49th
Annual Report. No. vii. 8vo.
Turin.— Atti della Reale Accademia delle Scienze.
Vol. ii. Disp. 1-3; Vol. iii. Disp. 1-8. 8vo.
Memoire della Reale Accademia delle Scienze. Serie seconda.
XXlll., xxiv. 4to.
Bollettino Meteorologico dell’Osservatorio Astronomico dell’Uni-
versita 1867, 1868. 4to.
Upsala——Nova Acta Regie Societatis Scientiarum Upsaliensis.
Fase. 2. 4to.
Utrecht.—Aanteekeningen van het verhandelde in de Sectie-Vergade-
ringen van het Provinciaal Utrechtsch Genootschap van Kunsten
en Wetenschappen ter gelegenheid van de Algemeene Vergadering,
1866, 1867. 8vo.
Meteorologische Waarnemingen in Aederland en Zijne Bezittingen en
Afwijkingen van Temperatuur en Barometerstand of vele Plaatsen
in Europa utigegeven door het Koninklijk Nederlandsch Meteoro-
logisch Instituut, 1864. Utrecht, 1865. 4to.
Nederlandsch Meteorologisch Jaarboek, 1864, 1865, 1866, 1867.
Utrecht, 1866. 4to.
Vol. i. Disp. 3-7 ;
Tomo
Vol. vi.
DONORS.
The Academy.
Ditto.
- Natural History
Museum, Paris.
The Academy.
Ditto.
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The Society.
The Institute.
The Society.
The Russian Go-
vernment,
The Academy.
The Russian Go-
vernment.
The Commission.
The Academy.
The Society.
The Canadian In-.
stitute.
Ditto.
From the Institu-
tion.
The Academy.
Ditto.
The University.
The Society.
The Society.
The Institute.
The Meteorologi-
cal Institute of
Utrecht.
Washington.—Astronomy.
LIST OF DONATIONS.
DONATIONS,
TRANSACTIONS AND PROCEEDINGS OF SoclETIES—continined.
Verslag van het Verhandelde in Algemeene Vergadering van het Pro-
vinciaal Utrechtsch Genootschap van Kunsten en Wetenschappen
gehonden den 16 October 1866, 1867. 8vo.
Naturkundige Verhandelingen uitgegeven door het Provinciaal
Utrechtsch Genootschap van Kunsten en Wetenschappen, Deel i.
Stuk 1. 4to.
Venice—Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti.
Tomo xii. Dispensa 4-9, 8vo.
Victoria.—Statistical Register of Victoria, with Astronomical Calendar for
1855. 8vo.
Statistical Summary of the Progress of the Colony of Victoria to the
Year 1865. Melbourne, 1865. 8vo.
Statistics of the Colony for 1867. Parts 1-8. Melbourne. Fol.
Statistical Fables of the Colony of Victoria. Fol. Melbourne,
1865.
Statistical Notes on the Progress of Victoria in relation to Agricul-
ture and Live Stock, from 1835 to 1867. Melbourne. 4to.
Vienna.—Jahrbuch der Kaiserlich-K6niglichen Geologischen Reichsanstalt.
Band xvii, No. 4; Band xviii. Nos. 1-4. 8vo,
Verhandlungen der Kaiserlich-Koniglichen Geologischen Reichsan-
stalt. 1867, Nos. 10-18; 1868, Nos. 1-18.
Jahrbiicher der Kaiserlich-Koéniglichen Central-Anstalt fiir Meteoro-
logie und Erdmagnetismus, von Carl Jelinek und Carl Fritsch.
Band i, 1864. 4to.
Verhandlungen der Kaiserlich-Kéniglichen Zoologisch-Botanischen
Gesellschaft in Wien. Band xvii. 8vo.
Die Fossilen Mollusken des Tertiar-beckens von Wien, von Dr Moritz
Hornes, 4to.
Denkschriften der Kaiserlichen Akademie der Wissenschaften. Phil.
Hist. Classe. Band xviiimMath-Nat. Classe, Band xxvi , xxvill.—
Philosophisch. Hist. Classe, Band xv, 4to.
Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften.
Math.-Nat. Classe (Mineralogie, Botanik). Band liv.—lvi. Heft
1-3.—Math.-Nat, Classe. B. lv., Ivi, Heft 1-3.—Phil.-Hist.
Classe. B. liii., Heft 1-3; B. lvi., lvii., Heft 1-3; lviii., Heft
1-3. 8vo.
Almanach der Kaiserlichen Akademie der Wissenschaften.
1868. 8vo.
1867,
Astronomical and Meteorological Observations
made at the United States Naval Observatory, during 1851-52
and 1865. 4to. Washington, 1867.
Discussion of Meteorological Phenomena observed at the U.S. Naval
Observatory, from June 1842 to January 1867. 4to.
Report of the Board of Regents of the Smithsonian Institution for
1865 and 1866. 8vo,_ .- é;
Smithsonian Contributions to Knowledge.
Vol. xv. 4to.
Miscellaneous Collections of the Smithsonian Institution. Vols. vi.,
vii. 8vo,
Memoirs of the National Academy of Sciences, Vol. i. 4to.
Annual Reports of the Commissioner of Patents for 1865 and 1866,
8vo.
Twenty-Second Annual Report of the Board of Trustees of the Public
Schools of the City of Washington. 1867. 8vo.
Monthly Reports of the Department of Agriculture for 1866-67.
8vo.
Report of the Secretary of War, with accompanying paper.
ington, 1866. 8vo.
Wash-
VOLE. xOSV, PART il:
773
DONORS.
The Society.
Ditto.
The Institute.
The Registrar-
General.
Ditto.
Ditto.
Ditto.
Ditto.
The Society.
Ditto,
The Society.
The Society,
The Geol. Society
of Vienna.
The Academy.
Ditto.
Ditto.
The United States
Government.
The Observatory.
The Smithsonian
Institution.
Ditto.
Ditto.
The Academy.
The United States
Patent Office.
The Trustees.
The Commis-
sioner.
The American Go-
vernment,
9P
774 LIST OF DONATIONS.
DONATIONS.
TRANSACTIONS AND PROCEEDINGS OF SOCIETIES— continued.
Report on Epidemic Cholera, Washington, 1867. 4to.
Whitby.—F orty-Fifth and Forty-Sixth Report of the Literary and Philo-
sophical Society. 8vo.
Zurich_—Neue Denkschriften der Allgemeinen Schweizerischen Gesell-
schaft fiir die gesammten Naturwissenschaften, [Nouveaux Mé-
moires de la Société Helvétique des Sciences Naturelles.] Band
xxli,, mit xx Tafeln, 4to.
Abbe (Cleveland), Dorpat and Poulkova. Washington, 1867. 8vo,
Arneth (Joseph). Die Antiken Cameen des K. K. Miinz und Antiken Cabinettes
in Wien. Fol.
—— Die Antiken Gold und Silber Monumente des K. K. Miinz und Antiken
Cabinettes in Wien. Fol.
-—— Die Cinque Cento Cameen und Arbeiten des Benvenuto Cellini und seiner
Zeitgenossen im K. K, Miinz und Antiken Cabinettes in Wien. Fol.
Baars (Herman). Berelning om den Internationale Fiskerindstilling i Boulogne-
sur-Mer, 1866. 12mo.
Les Péches de la Norwége. Boulogne-sur-Mer, 1866. 8vo.
Balfour (John Hutton). Obituary Notice of Professor John Goodsir. Edin-
burgh, 1867. 8vo.
Begbie (James), M.D. On the Causes of Death in the Scottish Widows’ Fund
Life Assurance Society, from 1st January 1860 to 3lst December 1866.
Edinburgh, 1868. 8vo.
Bert (Dr Paul). Note sur un cas de Greffe Animale. 8vo.
Recherches Expérimentales pour servir a |’Histoire de la Vitalité propre
des Tissus Animaux. Paris, 1866. 4to.
—— Recherches sur les Mouvements de la Sensitive (Mimosa pudica, L.).
Paris, 1867. 8vo.
-—— Notes d’Anatomie et de Physiologie Comparées. Paris, 1867. 8vo.
—— Sur un Monstre double Autositaire de la Famille des Monosomiens. Paris,
1863. 8vo.
Bigsby (John J.), M.D., F.G.S. Flora and Fauna of the Silurian Period, with
Addenda. London, 1868. 4to.
Boeck (Thorvald), Oversight over Literattur, Love, Forordninger Rescripter
M.M. Vedrorende de Norske Fiskeriar. Christiania, 1866. 8vo.
Boué (Ami). Recueil d’Itinéraires dans la Turquie d’Europe. Tomes i., ii.
Vienna, 1854. 8vo.
Broch (Dr O. J.). Traité Elémentaire des Fouchons Elliptiques. Fase. 1, i1.,
Christiania, 1866-1867. 8vo.
Brown (Robert). Das Innere der Vancouver-Inseln. 4to. Being a German
translation of his paper.
Brunn (Dr H.). Ueber die sogenannte Leukothea in der Glyptothek St Majestat
Konig Ludwigs I. Munich, 1867. 4to.
Brusina (Spiridione). Contribuzione pella Fauna dei Molluschi Dalmati.
Vienna, 1866. 8vo.
Burckhardt (Dr Fritz). Ueber die Physikalischen Arbeiten der Societas Physica
Helvetica, 1751-1787. Basel, 1867. 8vo.
Caruana (A. A.). Enumeratio Ordinata Molluscorum Gaulo-Melitensium (of
the late Mr Giuseppe Mamo). Malta, 1867. 8vo.
Caspari (Dr C. P.). Ungedruckte unbeachtete und wenig beachtete Quellen zur
Geschichte des Taufsymbols und der Glaubensregel. Christiania, 1866.
8vo.
DONORS.
The War Office,
US.
The Society.
The Society.
The Author.
Ditto,
Ditto.
Ditto.
Ditto.
Ditto,
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
LIST OF DONATIONS.
DONATIONS,
Castello de Paiva (Barone de). Monographia Molluscorum Terrestrium,
Fluvialium, Lacustrium, Insularium Maderensium. Olisipone, 1867.
4to.
Catalogue of the New York State Library for 1865. Law Library. First Sup-
plement. 8vo.
of the Printed Books and Manuscripts in the Library of the New College,
Edinburgh. 1868. 4to.
—— Index to the Catalogue of Books in the Bates Hall of the Public Library
of the City of Boston, First Supplement. Boston, 1866. 8vo.
—-— of the Surgical Section of the United States Army Medical Museum,
Washington, 1866. 4to.
—— of the Printed Books in the Library of the Faculty of Advocates, Part iii.
Edinburgh, 1867. 4to.
——— of Contributions transmitted from British Guiana to the Paris Universal
Exhibition. London, 1867, 8vo.
Catlow (Joseph Peel), M.R.C.S. Principles of Aisthetic Medicine. London,
1867. 8vo.
Chevreul (M. E.). De la Baguette Divinitoire du pendule dit Explorateur et
des Tables Tournantes au point de vue de |’Histoire, de la Critique et de
la Méthode Expérimentale. Paris, 1854. 8vo.
Notes Historiques sur la nature immédiate de Amer de Welter et de
VYAmer au Minimum. Paris, 1864. 4to.
—~— Considérations sur |’Histoire de la Partie de la Médecine qui concerne la
Prescription des Remédes. Paris, 1865, 4to.
——— Rapport sur ses cours du Muséum en Général. Paris, 1866. 8vo,
—— Histoire des Connaissances Chimiques. Paris, 1866. 8vo.
Des Arts qui parlent aux Yeux. Paris, 1867. 4to.
Examen Critique au point de vue de |’Histoire de la Chemie d’un écrit
Alchimique intitulé Artefué Clavis Majoris Sapientiz. Paris, 1867. 4to.
Childs (Geo. W.). Account of the Proceedings connected with the Opening of
' the Public Ledger Building, Philadelphia. * 1868. 8vo.
Cohen (Henri). Description des Médailles Grecques, Romaines, &c. Paris,
1869. 8vo.
Coleman (Rev. Lyman), D.D, The Great Crevasse of the Jordan and of the
Red Sea. 8vo.
Cooke (Rev. T. F.), M.A. Authorship of the Practical Electric Telegraph of
Great Britain, London, 1868. 8vo.
Crisp (Edwards), M.D. On some Points connected with the Anatomy of the
Hippopotamus. 8vo.
Cunningham (Alexander W.). Notes on the History, Methods, and Technolo-
gical Importance of Descriptive Geometry. Edinburgh, 1868. 8vo,
Danube,—Mémoire sur les Travaux d’Amelioration exécutés aux Embouchures
du Danube, par la Commission Européene (4to), accompagné d’un Atlas
de 40 Planches. 1867. Fol.
Day (St John Vincent), C.E. Malleable Iron Manufacture and the Richardson
Process. Glasgow, 1868. 8vo.
Present State of some Branches of Iron Metallurgy. Glasgow, 1868.
8vo,
Delesse (M.), et Lapparent (M. de). Revue de Géologie pour les Années 1864
et 1865. Paris, 1866. 8vo.
Diemer (Joseph). Genesis und Exodus nach der Milstater Handschrift, Band
i, ii. Vienna, 1862. 8vo.
Dircks (Henry), C.E., F.C.S. Inventors and Inventions. London, 1867. 8vo.
The Polytechnic College. A proposed Institution for aiding depressed
Talent to complete Works in progress connected with Science, Litera-
ture, or Arts, London, 1867. 8vo.
DONORS.
The Author.
The Trustees,
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The Library.
The American
Government,
The Faculty.
The Committee of
Correspondence of
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The Author.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto,
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
The Commission.
The Author.
Ditto.
The Authors.
The Author.
Ditto.
Ditto.
776 LIST OF DONATIONS.
DONATIONS,
Dorna (Alessandro, Prof.), Catalogo delle Leoneidi o Stelle Meteoriche del
periodo di Novembre Osservate nel 1867 al regio Osservatorio di Torino.
_ 4to.
Drifts (Auriferous), in Australasia, by ‘“ Research.” Melbourne, 1868.
8vo.
Ekker (A. H. A.), Exeunte Octobri.
1868. 8vo.
Erdmann (A.). Sveriges Geologiska Undersékning pa offentlig bekostnad
Utford under ledning af A, Erdmann. Nos, 26-30, with Charts.
8vo.
Exposé des Formations Quaternaires de la Suede.
Texte 8vo; Atlas 4to.
Carmen, ad filiolum. Amsterdam,
Stockholm, 1868.
Fayrer (Joseph), M.D. Address delivered at the Annual Meeting of the
Asiatic Society of Bengal. Calcutta, 1868. 8vo.
Flora Batava, afbeelding en beschrigving van Nederlandsche Gewassen door
Wiglen Jan Kops, vervolgd door Jhr. F. A. Hartsen, afgebeeld onder
opzigt van J. C. Sepp en Zoon. Nos. 200-207, Amsterdam.
4to.
Fouqué (M. F.). Premier Rapport sur une Mission Scientifique 4 l’Ile de San-
torin. Paris, 1867. 8vo.
—— Rapport sur les Phénoménes Chimiques de l’Eruption de ]’Etna en 1865.
4to,
——— Rapport sur les Tremblements de Terre de Cephalonie et de Mételin en
1867. Paris. 8vo.
Gamgee (Arthur), and Wanklyn (J. Alfred), On the Action of Permanganate
of Potash on Urea, Ammonia, and Acetamide, in strongly Alkaline Solu-
tions, 8vo.
Geikie (Archibald), F.R.S. Memoir of the late James David Forbes, D.C.L.,
LL.D., F.R.S. Edinburgh, 1869. 8vo. -
—— Address to the Geological Section of the British Association, 1867.
8vo.
Gianelli (Giuseppe Luigi).
Ato,
Gunther (Gustav Julius). Armour Plating, with a Description of a new
system of Iron or Steel Armour. London, 1868. 8vo.
Guthrie (Frederick), Ph.D. Elements of Heat and of Non-Metallic Chemistry.
La Vaccinazione e le sue Leggi in Italia. 1864.
London, 1868, 8vo.
Hammer Purgstall. Geschichte Wassaf’s. Bandi, Wien, 1856. 4to.
Handyside (Dr). Observations on Arrested Twin-Development. 8vo.
Hertzberg (N.), Indberetning om nogle Lererseminarier 1 premmede Lande fra
en Reise 1866 og 1867. Christiania, 1868. 8vo.
Hinrichs (Gustave). Atomechanik oder die Chemie eine Mechanik der Pana-
tome. lowa-City, Etats Unis, 1867. 4to.
Hirsch (A.), et Plantamour (H.). Nivellement de précision de la Suisse, exécuté
par la Commission Géodésique Fédérale sous la direction des auteurs.
Liv.i. Genéve, 1868. to.
Holmboe (C. A.). Ezechiels Syner og Chaldeernes Astrolab. Christiania, 1866.
4to.
James (Col. Sir Henry). Determination of the Positions of Feaghmain and
Haverfordwest Longitude Stations on the Great European Arc of Parallel.
London, 1867. 4to,
Jenkin (Fleeming), On the Education of Civil and Mechanical Engineers.
Edinburgh, 1868. 8vo.
DONORS.
The Author,
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Ditto.
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Ditto.
Ditto.
Ditto.
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Ditto.
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LIST OF DONATIONS.
DONATIONS.
Journal (American) of Science and Arts, conducted by Benjamin Silliman.
Nos. 129-140. New Haven. 8vo.
Karajan (Th. G. von). Das Verbriiderungs buch des Stiftes S. Peter zu Salz-
burg aus dem achten bis dreizehnten Jahrhundert mit Erlanterungen.
Wien, 1852. Fol.
Kronecker (L.). Uber Systeme von Functionen mehrer Variabeln. Berlin,
1869. 8vo.
Lawson’s Pinetum Britannicum. Parts xxix._xxxii. Imp. fol.
Lea (Isaac), LL.D. Check List of the Shells of North America (Unionide),
8vo.
——— Tables of the Rectification of Mr T. A. Conrad’s “Synopsis of the Family
of Naides of North America.” Philadelphia, 1866.
—— Observations on the Genius Unio, together with descriptions of new species
in the family Unionide, and descriptions of new species of the Melanide,
Limneide, Paludinz, and Helicide, with 24 Plates. Vol. xi. 4to.
Lesley (J. P.). Notes on a Map intended to illustrate five types of Earth-sur-
face in the United States, between Cincinnati and the Atlantic Seaboard.
Philadelphia, 1866. 4to,
Leuckart (Rudolf). Die Menschlichen Parasiten und die von ihnen herriih-
renden Krankheiten. Ein Hand und Lehrbuch fiir Naturforscher und
Aerzte. Leipzig, 1868. 8vo.
Maclaren (Charles). Select Writings, Hdited by Robert Cox, FS.A., and
James Nicol, F.R.S.E. Vols. i. and i. 8vo.
Maestri (Pierre). Rapport soumis a la Junte Organisatrice sur le programme
de la VI™ Session du Congrés International de Statistique. Florence,
1867. 8vo.
Mailly (Ed.). L’Espagne Scientifique. Brussels, 1868. 12mo,
Manuscripts. Facsimiles of National Manuscripts of Scotland, selected under
the direction of the Right Hon. Sir William Gibson-Craig, Bart., Lord
Clerk-Register of Scotland, and Photo-zincographed, by command of Her
Majesty Queen Victoria, by Colonel Sir Henry James, R.E., Director of
the Ordnance Survey. Parti. 1867. Folio.
Facsimiles of National Manuscripts of England, selected under the direc-
tion of Colonel Sir Henry James. Parts iii., iv. Fol.
Martius (Dr Carl Friedrich Phil. von). Beitrage zur Ethnographie und
Sprachenkunde Amerika’s zumal Brasiliens. 2 vols. Leipzig, 1867.
8vo.
Meiller (Andreas von). Regesten zur Geschichte der Markgrafen und Her-
zoge Osterrichs aus dem Hause Babenberg. Wien, 1850, 4to.
Miklosich (F.). Monumenta Lingue Paleoslovenice e Codice Suprasliensi.
Vindobone, 1851. 8vo.
Mitra (M. L.)}. The Ultimate Structure of Voluntary Muscular Tissue, and
the Mode of Termination of Motor Nerves. Edinburgh, 1867. 8vo,
Modderman (W.). De Wettelijke Bewijsleer in Strafzaken Utrecht, 1867. 8vo.
Molison (A. R.). Against the Theory of the Retarding Influence of Tidal Action
on the Axial Motion of the Earth, and showing the true Source of Tidal
Energy. 8vo.
Mueller (Ferdinandus), Ph.D., M.D. Fragmenta Phytographie Australiz,
Vols. iii. and v. Melbourne, 1862-66. 8vo.
Murchison (Sir Roderick Impey), Bart., K.C.B. Siluria; a History of the
Oldest Rocks in the British Isles and other countries. Fourth Edition.
London, 1867. 8vo.
Neilreich (Dr August). Nachtrage zur Flora von Neider-Oesterreich.
1866. 8vo,
VW OS SOO. ART TE.
Wien,
OtT
DONORS.
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Esq.
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9Q
178 LIST OF DONATIONS.
DONATIONS.
Neilreich (Dr August). Diagnosen der in Ungarn und Slavonien bisher beo-
bachteten Gefasspflanzen welche in Koch’s Synopsis nicht enthalten
sind. Wien, 1867. 8vo.,
Nomenclature of Diseases, drawn up by a Joint-Committee appointed by the
Royal College of Physicians of London. London, 1869. 8vo.
Oettingen (Dr Arthur von). Meteorologische Beobachtungen angestellt in
Dorpat un Jahre 1867. Dorpat, 1868. 8vo.
Paine (Martyn), A.M., M.D. The Institutes of Medicine, 8th edition. New
York, 1867. 8vo.
Peters (Dr). Report on the Longitude of Elmira. Albany, 1864. 8vo.
Report on the Longitude and Latitude of Ogdensburgh. Albany,1865. 8vo.
Pictet (M. Adolphe). Sur une Nouvelle Déesse Gauloise de ]a Guerre. Paris,
1868. 8vo.
Plantamour (E.). Des Anomalies de la Température Observées a Genéve pen-
dant les quarante Années 1826-65, 4to.
—— Résumé Météorologique de l’Année 1866 et 1867, pour Genéve et le
Grand Saint-Bernard. 8vo.
Pollender (Dr A.). Ueber das Entstehen und die Bildung der kreisrunden Oeff-
nungen in der ausseren Haut des Blutenstaubes, Bonn, 1867. 4to.
—— Neue Untersuchungen iiber das Entstehen, die Entwickelung, den Bau,
und das chemische Verhalten des Blutenstaubes, Bonn, 1868. 4to.
—~— Wem gehiihrt die Prioritaét in der Anatomie der Pflanzen dem Grew oder
dem Malpighi. Bonn, 1868. 4to.
Priestley (William O.), M.D. Lectures on the Development of the Gravid
Uterus. London, 1860. 8vo.
~~
Quatrefages (M. de). Observations relatives 4 un ouvrage de M. Claparéde,
intitulé Les Annélides Chétopodes du Golfe de Naples, et Réponse 4 ses
Critiques. Paris. 4to.
Quetelet (Ad.). Observations des Phénoménes Périodiques pendant les Années
1865 et 1866. Brussels. 4to.
—— Physique Sociale, ou Essai sur le développement des Facultés de ’Homme.
Brussels. 8vo.
-—— Mémoire sur ]a Température de l’Air 4 Bruxelles. 1867. 4to.
—— Des Lois Mathématiques concernant les Etoiles Filantes, 8vo.
Sur les Phénoménes Périodiques en Général. 8vo.
Communications extracted from the Annales de l’Observatoire Royale de
Bruxelles. 8vo.
Rankine (W. J. Macquorn), Mechanics (applied), Edinburgh, 1857. 4to.
Rein (Dr J. J.). Der Gegenwirtige Stand des Seidenbaues. Frankfort-on-
Maine, 1868. 8vo.
REPORTS :—
Report of the Superintendent of the Coast Survey, showing the Progress
of the Survey during years 1863-64 and 1865. 4to.
Report on Epidemic Cholera and Yellow Fever in the United States
Army during 1867. 4to.
Tenth, Eleventh, and Twelfth detailed Annual Reports of the Registrar-
General of Births, Deaths, and Marriages in Scotland. Edinburgh,
1867-1869. 8vo.
Thirteenth Annual Report of the Registrar-General on the Births, Deaths,
and Marriages registered in Scotland during the year 1867. 8vo.
Quarterly and Monthly Returns of the Births, Deaths, and Marriages
registered in the Divisions, Counties, and Districts of Scotland for
1867-68, 1868-69. 8vo.
DONORS
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The United States
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LIST OF DONATIONS.
DONATIONS.
Reports—continued.
Report of the Commissioner of American Patents for 1863 and 1864.
Washington. 8vo.
On the Amputations at the Hip-Joint in Military Surgery. Washing-
ton, 1867. 4to.
Robertson (George), F.R.S.E. Recent Marine, Hydraulic, and Sanitary En-
gineering in Scotland. Edinburgh, 1867. 8vo.
. Tide Signals as well as Storm Signals. Edinburgh, 1868. 8vo.
Rive (Professeur A. de la). Notice sur Michael Farady sa vie et Travaux.
Genéve, 1867. 8vo.
Rutherford (William), M.D. Electronus: A Physiological Demonstration given
in the Physiological Laboratory of the University of Edinburgh,
8vo.
Rizzoli (Francesco). Nuovo processo operatorio per la cura di una vasta aper-
tura Uretro-Cisto-Vaginale. Bologna, 1867. 8vo.
-—— Masseterotomia intrabuccale per la cura di una Anchilosi del Mascellare
inferiore Memoria. Bologna, 1869. 4to.
Ryan (Matthew). The Celebrated Theory of Parallels. Second Edition, with
Supplement Appendix. Washington, 1866. 8vo.
Sars (Michael). Mémoires pour servir 4 la Connaissance des Crinoides Vivants.
Christiania, 1867. 4to.
Schumann (J.). Die Diatomeen der Hohen Tatra, Wien, 1867. 8vo.
Schmidl (Dr Adolf). Die Grotten und Hohlen von Adelsberg, Lueg, Planina
und Laas. Wien, 1854. Fol. Plates.
— Die Grotten und Héhlen von Adelsberg, Lueg, Planina und Laas, Wien,
1854. 8vo.
Seguin (M.). Réflexions sur l’Hypothése de Laplace relative a ]’Origine et a
la Formation du Systéme Planétaire. Paris, 1867. 4to.
Settimanni (Capt. Cesar). D’une Nouvelle Methode pour déterminer la
Parallaxe du Soleil. Florence, 1869. 8vo.
Sexe (S. A.) Merker Efter en tistid i Omegnen af Hardangerfjorden. Chris-
tiania, 1866. 4to.
Smart (Andrew), M.D., F.R.C.P.E. Reports to the Lord Provost and Magis-
trates of the City of Edinburgh, on the Pathological Appearances,
Symptoms, Treatment, and Means of Preventing Cattle Plague. Edin-
burgh, 1866. 4to.
Smyth (Prof, C. Piazzi), F.R.SS.L. and E., F.R.A.S. On Intensified Gravity
in Centrifugal Governors of Driving Clocks and Steam-Engines, 12mo.
—— Life and Work at the Great Pyramid. Vols. 1-3. Edinburgh, 1867.
8vo.
On the Antiquity of Intellectual Man, Edinburgh, 1868. 8vo.
Sproat (Gilbert Malcolm). Scenes and Studies of Savage Life. London, 1868,
8vo.
Stevenson (Thomas), C.E. On ascertaining the Intensity of Storms by the
Calculation of Barometric Gradients. 8vo.
Storer (David H.), M.D. History of the Fishes of Massachusetts. Cambridge,
1867. 4to.
Struve (Otto). Jahresbericht am 24 Mai 1867-68, dem Comité der Nicolai-
Hauptsternwarte. St Petersburg. 8vo.
Tabule Auxiliares ad Transitus per Planum primum verticale reducendos
inservientes. St Petersburg. 1868. 8vo.
Sundt (Gilert), Om Szdeligheds-Tilftanden 1 Worge 3 die, Beretning. Chris-
tiania, 1866. 8vo.
—— Om Husflideni Norge. Christiania, 1867. 8vo.
Teale (James). A Dynamical Theory of the Universe. Manchester, 1868,
8vo.
179
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780 LIST OF DONATIONS.
DONATIONS.
Tebbutt (John, jun.). Meteorological Observations made at the Private
Observatory of John Tebbutt, jun. Sydney, 1868. 8vo.
Thomson (J. T.), F.R.G.S. Sequel to some Glimpses into Life in the Far East.
London, 1865. 8vo.
Thomson (Murray), M.D. Report on Meteorological Observations in the N.-W.
Provinces of India. Roorkee, 1868. Fol.
Thomson (William Thomas), Address delivered to the Students of the Edin-
burgh School of Design. Edinburgh, 1869. 8vo.
Tillman (S. D.), A.M. A new Chemical Nomenclature. Albany, 1866. 8vo.
Tschudi (J. J. von). Die Kechua-Sprache. Abtheilung i, ii., iii. Vienna,
18538. 8vo.
Uger (C. R.) Morkinskinna, Pergamentsbog fra forste Halvdel af det Trettende
Aarhundrede. Christiania, 1867. 8vo.
Vogel (August). Denkrede auf Heinrich August von Vogel. Munich, 1868.
Voit (Carl). Ueber die Theorien der Ernahrung der thierischen Organismen,
Munich, 1868. 4to.
Waage (P.) et C.M. Guldburg. Etudes sur les Affinités Chimiques, Christiania,
1867. 4to.
Watson (J. Forbes), A.M., M.D. Index to the Native and Scientific Names
of Indian Plants and Products. London, 1868. 4to.
Wetherill (Charles M.). Experiments on Itacolumite. 8vo.
Woodward (Henry). Man and the Mammoth. London, 1869. 8vo.
Will (H.). Jahresbericht iiber die Fortschritte der Chemie, etc., Register zu
den Berichten fiir 1857 bis 1866. 8vo.
Jahresbericht iiber die Fortschritte der Chemie, ete., fiir 1866, Heft
1-8; fiir 1867, Heft 1. Giessen. 8vo,
Winnertz (Joh,), Beitrag zu einer Monographie der Sciarinen, Wien, 1867.
8vo.
Ximenez (EI.R.P.F.F.). Las Historias del Origen de los Indios de esta Pro-
vincia de Guatemala. Vienna, 1857. 8vo.
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( 781 )
INDEX TO VOL. XXV.
Anperson (Professor Tuomas). On the Products of Destructive Distillation of Animal Substances.
Part V., 205.
Animal Substances, Products of the Destructive Distillation of. By Professor AnpERson, 205.
Annelids, New British. By W. Carmicuaret M‘Intosu, M.D., 305.
Archimedes’ Burning Mirrors. By Joun Scott, 123.
Atropia, its Action on Cold-Blooded Animals. By Dr Tuomas R. Fraser, 449.
Atropia and Conia, Physiological Action of the Ammonium Bases derived from. By Dr A. Crum
Brown and Dr Tuomas R. Fraser, 693.
B
Bebeeru or Greenheart Tree, Alkaloids in the Wood of. By Professor Mactacan and Dr Arruur
GamMGEE, 567.
Boulder-Clay of Europe. By Davip Mitne Hos, 655.
Brewster (Sir Davip). On the Motion, Equilibrium, and Forms of Liquid Films (Plates L.,
LCL ed Ub
Brown bos A. Crum), and Fraser (Dr T. R.). On the Connection between Chemical Constitu-
tion and Physiological Action. Part I. On the Physiological Action of the Salts of the
Ammonium Bases derived from Strychnia, Brucia, Thebaia, Codeia, Morphia, and Nicotia, 151.
On the Connection between Chemical Constitution and Physiological Action.
Part II, On the Physiological Action of the Ammonium Bases derived from Atropia and
Conia, 693.
Bucuan (ALexaNpER). ‘The Mean Pressure of the Atmosphere and the Prevailing Winds over the
Globe for the Months and for the Year. Part II. (Plates XXV.—XXVII.), 575.
Burning Mirrors of Archimedes. By Joun Scort, 128.
C
Caytey (Professor). On Polyzomal Curves, otherwise the Curves of ,/ 0+ eh V + &e.—0, jg
Chemical Constitution and Physiological Action. By Dr A. Crum Brown and Dr Tuomas R.
Fraser, 151, 693.
D
Davy (Joun). On the Temperature of the Common Fowl (Gallus domesticus), 119.
Destructive Distillation of Animal Substances, Products of the. By Professor AnpERson, 205.
VOL. XXV. PART II. IR
782 INDEX.
Dicxson (Professor ALEXANDER). On the Development of the Flower of Pinguicula vulgaris, L. :
with Remarks on the Embryos of P. vulgaris, P. grandiflora, P. lusitanica, P. caudata, and
Utricularia minor (Plates XXVITI.-XXX.), 639.
E
Embryos of Pinguiculas and Utricularia minor, By Professor Dickson, 639.
.
F
Fraser (Dr Tuomas R.). On the Connection between Chemical Constitution and Physiological
Action. (See Dr A. Crum Brown), 161.
— An Investigation into some préviously undescribed Tetanic Symptoms produced by
Atropia in Cold-Blooded Animals, with a Comparison of the Action of Atropia on Cold-Blooded
Animals and on Mammals, 449.
— and Prof. A. Crum Brown. On the Connection between Chemical Constitution and
Physiological Action. Part IT., 693.
G
Gallus domesticus (Common Fowl), Temperature of. By the late Dr Joun Davy, 119.
GamcEE (Dr ArtHur), and Professor Maccacan. On the Alkaloids contained in the Wood of the
Bebeeru, or Greenheart Tree, 567.
H
Hegel and the Metaphysics of the Fluxional Calculus. By W. Ropertson Smitu, M.A., 491.
J
Jenkin (Professor Freemine). On the Practical Application of Reciprocal Figures to the Calculation
of Strains on Framework (Plates XVII.—XXILI.), 441.
L
Lichenicolous Micro-Fungi. By Dr W. Lauper Linnsay, 513.
Linpsay (Dr W. Lauper). Observations on New Lichenicolous Micro-Fungi (Plates XXIII, ©
XXIV.), 513.
Liquid Films, Motion, Equilibrium, and Forms of. By the late Sir Davip Brewster, 111.
M
M‘Inrosu (Dr W. Carmicnar.). On the Structure of the British Nemerteans, and some New
British Annelids (Plates I1V.—XVI.), 305.
Mactacan (Dr T. J.). Observations on the Temperature of Newly-Born Children, 435,
MacraGan (Professor), and Dr Arrnur Gamcer. On the Alkaloids contained in the Wood of
the Bebeeru, or Greenheart Tree (Nectandra Rodiewi, Schomb.), 567.
Mean Pressure of the Atmosphere for the Months and for the Year. By ALEXANDER Bucnan, 575.
Mite Home (Davin). On the Boulder-Clay of Europe (Plate XXXI.), 655.
Molecular Vortices, Thermal Energy of. By Professor W. J. Macquorn Rankine, 557.
N
Nectandra Rodiwi, Alkaloids in the Wood of. By Professor Maczacan and Dr Artuur
GAMGEE, 567.
Nemerteans, British, their Structure. By Dr W, Carmicuact M‘Intosn, 305.
ay
(o.8)
[S)
INDEX.
-
Physiological Action and Chemical Constitution. By Dr A. Crum Brown and Dr Tuomas R.
Fraser, 151, 693.
Pinguicula vulgaris, Development of the Flower of. By Professor Dickson, 639.
Polyzomal Curves. By Professor Caytezy, 1.
Prevailing Winds over the Globe. By ALEXANDER Bucuan, 5795.
R
Rankine (Professor W. J. Macauorn). On the Thermal Energy of Molecular Vortices, 557.
Reciprocal Figures, their Practical Application to the Calculation of Strains on Framework. By
Professor FLEEMING JENKIN, 441.
Rotation of a Rigid Body about a Fixed Point. By Professor Tarr, 261.
S
Scorr (Jonny). On the Burning Mirrors of Archimedes, with some Propositions relating to the
Concentration of Light Produced by Reflectors of Different Forms (Plate III.), 123.
Smity (W. Ropertson). Hegel and the Metaphysics of the Fluxional Calculus, 491.
Strains on Framework. By Professor Fienmine JENKIN, 441.
T
Tarr (Professor). On the Rotation of a Rigid Body about a Fixed Point, 261.
Temperature of the Common Fowl (Gallus domesticus). By the late Dr Joun Davy, 119.
Temperature of Newly-Born Children. By Dr T. J. Mactacan, 435. -
Tetanie Symptoms produced by Atropia. By Dr Tuomas R. Fraszr, 449.
Thermal Energy of Molecular Vortices. By Professor W. J. Macavorn Rankine, 557.
Tuomson (Sir Witi1am). On Vortex Motion (Plate III.*), 217.
Vv
Vortex Motion. By Professor Sir Wrttiam THomsoy, 217
END OF VOLUME TWENTY-FIFTH.
PRINTED BY NEILL AND COMPANY, EDINBURGH.
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