PROCEEDINGS

OP THE

MANCHESTER

LITERARY AND PHILOSOPHICAL SOCIETY.

VOL. XIX.

Session 1879-80.

MANCHESTER :

PRINTED BY THOS. SOWLER AND CO., 24, CANNON STREET.
LONDON : BALLIERE, 219, REGENT STREET.

1880.

■••>>.- . ■

• V. , , .-'i.- -W ■'^ ■ V ’ " ;. ;• ' ' -''»‘r -

*- '•■!■• ■r.'S: . ••

I ,

/ ' :■'■■»■ »". 'VfV ,i ■ .i-i

' ..t.

n^:\

K<;’

' \ ■' te*

■i^

v -

f’ ' i

" . ■ ' , ' 'K'' 4tM

, ■ ■ . .

-Jv . ■

' '■.,

, ■ ■ /' .,

-..V, ■ : .

- i " ^ » '-■ •• V' '

'■■ ':. ■ v.', ■

’■■ -'V r

‘ ..'■ I il- ,-.ff/‘'--L ■. i,

^ ■ ■ ■ ' 1 .'V<ld,

1.-; M'J

<■ ■ '

■■■■ ■>■'■ Vr t v

.■"’■fAVV- .W"

;'^-

i

■.^^r'lLwW

~4

i

NOTE.

The object which the Society have in view in publishing their
Proceedings is to give an immediate and succint account of the
scientific and other business transacted at their meetings to the
members and the general public. The various communications
are supplied by the authors themselves, who are alone responsible
for the facts and reasonings contained therein.

INDEX.

Abney Captain, R.E., F.E.S.“On Photographs of the Ultra-red portions
of the Solar Spectrum, p. 49,

Axon William E. A,, M,R.S.L., F.S.S. — On the History of the word
Telegraph, p. 182.

Bailey Chaeles, F.L.S.—Oii specimens of Ophioglossnm Vulgatum,
L., var. /3. ambiguum, Coss. et Oerm., p, 34.

Baxendell Joseph, F.E.A.S. — Eesults of observations of the double-
period Variable Star E SagittaB, p. 120. Note on Three New
Stars, p. 171. Eesults of observations of the Variable Star T
Aquilee, p. 200.

Binney E. W., F.E.S., F.G.S.- — Notes of some Fossils from the Iron
Mines of Furness, p. 5. On the Meteor of November 11th, 1879,
p. 31. A Curious Eainbow, p. 74. Notes on a Bore through
Triassic and Permian Strata, lately made at Openshaw, p. 98,
On a Eucalyptus Globulus at Douglas, Isle of Man, p. 157.

Black W. J. — On a New Form of Marine Eain Gauge, p. 51.

Bottomley James, B.A., D.Sc,~On Colorimetry, Part III., p. 11. On
some Notices in Classical Authors of the Action of Sunlight on
Purple Dye, p. 33. Colorimetry, Part IV., p. 164. Colorimetry,
Part V., p. 190.

Cockle Sir James, F.E.S.— On the ^Differential Calculus’ of Du
Bourguet, p. 9. On a Proposition of Du Bourguet, p. 181.

Dawkins Professor Wm. Boyd, F.E.S. — On the Geography of the
British Isles in the Meiocene Age, p, 40.

Geimshaw Haeey, F.C.S. — On a Peculiar Feature in the Water of the
Well in Carisbrooke Castle, Isle of Wight, p. 44.

VI,

Gwtthee R. F., M.A. — On a form of Representing the Velocity at any
point of an Incompressible Fluid under Conservative Forces,
p. 114. On an adaption of the Lagrangian form of the equations
of fluid motion, Part I., p. 203.

Hartog M. M., M.A., B.Sc., F.L.S. — On the Means by which Hydra
Swallows its Prey, p. 29. Additional Note on Hydra, p. 40. On
some Undescribed Hairs in Copepoda, p. 41. On an Undescribed
Acinetan, p. 41. On the Anal Respiration of the Copepoda, p. 61.

Johnson William H., B.Sc.— On the Electrical Resistance and its
Relation to the Tensile Strain and other Mechanical Properties of
Iron and Steel Wire, p. 147.

Joule J. P., D.C.L , LL.D., F.R.S., President. — On a Simple Means for
Checking the Oscillations of a Telescope, p. 4.

Mackeeeth Rev. Thomas, F.R.A.S., F.M.S.—On the Rainfall adjacent
to the Sweetloves Reservoir, Sharpies, for 1879, p. 72,

Melvill J. Cosmo, M.A., F.L.S. — On the Occurence of Silene Oallica
(L.) and its Sub-species in Jersey, p. 68.

Murphy Joseph John, F.G.S. — On an Extension of the Ordinary
Logic, connecting it with the Logic of Relatives, p. 1.

Plant John, F.G.S, — Bog Butter {Butyrellite), from Co. Galway, Ireland,
p. 70. On Flexible Sandstone, p. 103. Uses of Infusorial Earth,

p. 106.

Ransome Arthur, M,A., M.D.— -On Epidemic Cycles, p. 75.

Rawson Robert, Assoc. I.N.A. — Screw Propulsion, Part II., p. 21. On
Screw Propulsion, Part III., p. 55. Notes on the Biquadratic
Equation

+ nx^ + ax^ ± + c = 0, p. 127.

Rogers Thomas. — On the Land and Fresh-water Shells of Tasmania

p. 101.

Schoelemmer Professor Carl, F.R.S. — On the Origin of the word
* Chemistry’, p. 35.

ScHUNCK Edward, Ph.D., F.R.S. — Note on modified Chlorophyll from
the leaves of Eucalyptus globulus, p, 157,

VII.

Schuster Arthur, Ph. D., P.R.S., and H, E. Roscoe, LL.D., P.R.S. —
Note on the Identity of the Spectra obtained from the different
Allot ropic Forms of Carbon, p. 46.

SiDEBOTHAM JOSEPH, F.R.A.S. — On some specimens of Helices and
Bulimi from Mentone, South France, p. 155.

Smith R. Angus, Ph.D., F.R.S.—-On the History of the word ‘Chemistry*
or ‘Chemia,’ p. 141.

Smith Watson, F.C.S., F.I.C. — The Castel Nuovo Lignite Deposit,
near San Giovanni, Tuscany, p. 135. Analyses of the Ash of
Wood of two varieties of the ‘ Eucalyptus’ tree, p. 139.

Stewart Professor Balfour, LL.D., F.E.S. — On the Long" Period
Inequality in Rainfall, p. 107.

Stirrup Mark, F.G.S. — Notes on the Mollusca of Blackpool, ji. 156.

Tatham J. F. W., M.D.—On a new form of Stephenson’s Binocular,
p. 155.

Thomson William, F.R.S.E.— On the Chemical Composition of the
Ink on Letters and Documents as Evidence in Legal Cases, p. 160.

Williamson Professor W. C., F.R.S.— On some specimens of Calamo-
stachys Binneana, p. 97.

Winstanley David, F.R.A.S.— Recording Sunshine, p. 31. The
Radiograph, p. 63.

Meetings op the Physical and Mathematical Section, — Annual,
p. 190. Ordinary, pp. 11, 72, 120, 164,

Meetings of the Microscopical and Natural History Section. —
Annual, p. 185. Ordinary, pp. 29, 40, 68, 101, 155.

Report op the Council. — April, 1880, p. 173.

PKOCEBDINGS

OF THE

LITERA.EY AND PHILOSOPHICAL SOCIETY.

Ordinary Meeting, October 7th, 1879.

J. P, Joule, D.C.L., LL.D., F.RS., &c.. President, in the

Chair.

“ On an extension of the Ordinary Logic, connecting it
with the Logic of Relatives,” by Joseph John Mukphy,
F.G.S. Communicated by the Rev. Robekt Haeley, M.A.,
F.RS.

All logic deals with relation, and in this paper the common
logic is treated as being that branch of the logic of relatives
which deals with the relations of inclusion and exclusion.

The proposition of the common logic “All A is B ” is here
expressed by “ A is included in B,” or “ A is an enclosure of
B.” The converse of this, as commonly stated, is “ Some B
is A ; ” but this is insufficient, because when reconverted it
only gives back “ Some A is B,” and reconversion ought to
give back the original proposition. The converse form here
proposed is “ B includes A,” or “ B is an includent of A.”

When all M is A and all M is B, the conclusion is ex-
pressed in the common logic by “Some A is B.” This
syllogism is here expressed thus : — “ A is an includent of M ;
B is an includent of M ; therefore A and B are co-includents
of M ; ” or if we drop the M, “ A and B are co-includents.”

When all A is M and all B is M, there is no conclusion
recognised by the old logic ; yet there is a valid conclusion,
which here appears in the following syllogism : — “ A is an
Peoceedings — Lit. & Phil. Soc. — Yol. XIX. — Xo. 1. — Session 1879-80.

2

enclosure of M ; B is an enclosure of M ; therefore A and B
are co-enclosures of M ; ” or, by dropping the M, “ A and B
are co-enclosures.” As an instance of this in expressing
actual relations : — “The Duke of Wellington was an Irish-
man; Lord Palmerston was an Irishman; therefore the
Duke of Wellington and Lord Palmerston were fellow-
irishmen ; ” or, by dropping the name of the particular
nation, “The Duke of Wellington and Lord Palmerston
were fellow-countrymen.”

The relation of inclusion is here expressed by L, and
its converse by L~^. Co-inclusion, or the relation of one

enclosure to another is expressed by ^ or X® ; co-includence,

jj—i

or the relation of one includent to another by or

In this system, so long as the contrary is not stated,
enclosure always means enclosure in the same includent,
and includence means includence of the same enclosure.
Consequently from the premises “A and M are co-includents;
M and B are co-includents ; ” we have the conclusion that
“ A and B are co-includents.” In the common logic, on the
contrary, the premises “ Some A is M ; some M is B,” yield
no conclusion.

The fundamental canon of this system is that the enclo-
sure of an enclosure is an enclosure ; and conversely, that
the includent of an includent is an includent. These are
expressed by the equations L^—L and The

former of these is the canon of the old “Syllogism in
Barbara ; ” the latter is the same read backwards. These
equations express that the relation of inclusion and inclu-
dence is transitive.

The relations of co-enclosure and co-includence are also
transitive, and they are, moreover, invertible, — that is to
say, if A=X®B or A=(X~^)®B, then B=X®A or B==(X“^)°A.
These are expressed by the equations and

To express this in words: — every term

3

with zero index is equal to its own second power, and also
to its own reciprocal. This is also true in arithmetic; but
it is moreover generally true in arithmetic that every such
term has the value of unity, which is not true in logic.

The four terms L, and (L~^y when combined

give sixteen equations, whereof each is the canon of a
syllogism. Two of these have been stated above as the
direct and the inverse expression of the canon of Barbara.”
Of the sixteen syllogisms, fourteen a.re conclusive ; that is
to say, in fourteen cases, whereof the two just mentioned
are examples, the two relations combine into one, which is
expressed by one of our four terms. Another example is
that given above where the middle term is Irishman”; —
this in the present notation is expressed by A = AM,
Mr=A“^B, therefore A=A®B ; or, simply as a canonical equa-
tion and without using any but relative terms, by L.L~^=L^.
The forms of the two inconclusive syllogisms are L^.(L~'^y
and

The truth of the equations of this system does not depend
on the interpretation of L as inclusion, but solely on the
transitiveness of the relation symbolized by L ; and they
consequently remain true if L means, for instance, superior,
or cause ; postulating in the latter case that the cause of a
cause is a cause.

For the purpose of the present essay, relation is regarded
as analogous, though not closely so, to ratio, and relative
terms to numerical coefficients. In logic, as in arithmetic,
if one of the following four equations is true, the rest are
necessarily so.

A

A = ZB B = A-A

A

where ^ is taken to mean, in logic, any relation whatever
of A to B.

4

The relation of exclusion is expressed by iV : — A is not
B ” is expressed by A=JSfB. Co-exclusion is expressed by
Exclusion is not a transitive relation, and it is in-
vertible ; in other words, iV is not equal to its own second
power, and is equal to its own reciprocal. The only
numerical coefhcient which unites these two properties is
negative unity. In logic the following equations are true :

A^.Az=JSr

N.N^=zN

That is to say

The exclndent of an excludent
is a co-excludent.

N\^^=N

The co-exchident of an exclu-
dent is an exclndent.

The excludent of a co-exclndent The co-excludent of a co-excln-

is an excludent. dent is a co-excludent.

And the interpretations are similar if N means not in
relation with’’ or ^^not related to, as either cause or effect.”
These four equations are also true in arithmetic, if N is
taken to mean negative unity and unity.

The President described a simple means for checking
the oscillations of a telescope. It consisted of a leaden ring
placed centrally about the axis of the tube of the telescope
and attached thereto by three or more elastic caoutchouc
bands. He had employed two of these rings for his tele-
scope, one placed near the object glass, the other near the
eyepiece. Their united weights were only one quarter of
that of the telescope tube, but nevertheless they diminished
the time required for the cessation of vibration to one sixth
of what is was before their application.

Dr. E. ScHUNCK, F.KS., exhibited some specimens of the
colouring matters, &c., referred to in his paper “ On the
Purple of the Ancients,” lately published.

5

Ordinary Meeting, October 21st, 1879.

J. P. Joule, D.C.L., LL.D., F.RS., &c,. President, in the

Chair.

Notes on some Fossils from the Iron Mines of Furness,”
by E. W. Binney, V.P., F.B.S, F.G.S.

In vols. YIII. and XII. of the Memoirs, and vol. VII. of
the Proceedings of the Society are printed papers by me on
iron ores and their origin. In the last I gave an opinion
that the hsematite ores of Furness were of the age of our
Lower Lancashire Coal Measures, owing to specimens of
carboniferous plants, especially the Sigillaria vascularis^
having been found in them. In the Transactions of the
North of England Institute of Mining and Mechanical
Engineers, vol. XXYIII., part Y., p. 2.34, Mr. T. D. Kendall,
C.E., F.G.S., in replying to some remarks in a paper of his
on the Hsematite Deposits of West Cumberland, said, “With
regard to the so-called vegetable remains mentioned by Mr.
Binney, he had, since his paper was published, shown them
to Professor Williamson, of Owens College, who pronounced
them not to be plants at all.” The chief evidence on which
I based my opinion was a most beautiful specimen of Sigil-
laria vascularis shown to me many years ago by the late
Mr. Bolton, of Swarthmoor, near Ulverston, exhibiting in
a marked manner all the characters of that plant. Where
this specimen now is I cannot tell, but I am pretty sure that
neither Mr. Kendall nor the Professor is likely to have seen
it. Other specimens presented to me by my friend the late
Miss Hodgson, of Ulverston, from Water Blain Mine, near
Broughton, were exhibited to the meeting at the time I
read my paper, and the above-named gentlemen could not
have seen them, for the simple reason that they have been

Pkoceedings — Lit, &PniL. Soc.~Yol. XIX. — Xo. 2. — Session 1879-80,

6

locked up in my cabinet and shown to no one ; so it puzzles
me how Mr. Kendall can have exhibited the “so-called
vegetable remains mentioned by Mr. Binney ” to Professor
Williamson.

On the table I have brought some of my specimens from
Water Blain, and others from Cark, Lindal Moor, and dif-
ferent places in Furness, kindly lent me by Mr. Swainson,
of the Poplars, Ulverston, so that the members may judge
for themselves whether they are the remains of plants or
accidental forms, notwithstanding that they are now con-
verted into good hsematite iron.

The stems of fossil plants found in our coal measures are
all in an altered condition; some have been calcified, others
silicified, and frequently ferrified, or converted into haematite
iron, bisulphide, or a carbonate of the protoxide of that
metal, and we have to determine them more from their ex-
ternal characters than from internal structure. On the
table are exhibited specimens of fossil wood converted into
peroxide of iron and silicate of alumina from the Smedley
sandstone at Cheetham, near this city, a rock in the upper
portion of the middle coal field. The vegetable origin of
these have never been doubted, although little evidence is
left of their external characters or internal structure. These
red coloured specimens were first, probably, in a partly
calcified state. The lime was afterwards dissolved out and
the iron converted into a peroxide, the silica and the alu-
mina remaining, and the fossils were thus altered into their
present ochrey condition. The white specimens are com-
posed of silicate of alumina and are mere pseudomorphs
with probably slight traces of iron.

From notes made by me in 18§6, the time I found the
fossils, the ochrey and white ones were met with at the
bottom of the sandstone in a stratum of soft argillaceous
matter of a dark red colour, mixed with streaks of white.
On clearing this away I observed a soft fibrous substance

7

resembling decayed wood, about two feet in length, four
inches in breadth, and varying from half to one inch in
thickness. On the slightest force being applied, it shelled
off the stone underneath in a similar way that bark comes
off the boles of decayed trees. This singular covering did
not extend around the whole of the stem which was em-
bedded in the rock, but appeared only on the upper surface
and reaching a short distance round the sides. It was
lying parallel to the stratification, but whether it was a
compressed stem or the bark of aii underlying stem, it is
difficult to say, but at the time I was inclined to the former
opinion.

Bischof, in his Chemical and Physical Geology, vol. I., p.
42, says that specular iron is a very remarkable petrifying
material, and gives instances of fossil shells which consist
entirely of crystalline laminae of specular iron, and that
fibrous red iron ore was met with by G. Sandberger as a
petrifying substance at a mine in the neighbourhood of
Oberscheld, in Nassau. The same author also adds that
these petrifactions are of no little importance in a geological
point of view, for they furnish altogether decisive evidence
that specular and fibrous red iron ores are formed in the wet
way, whether the oxide of iron occurs in veins or as a
pseudomorph.

The same author also states that as the brown iron ore
in displacement-pseudomorphs, and the material for its for-
mation can only be furnished by the soluble -bicarbonate of
iron, it is remarkable that such waters, though frequently
so occurring, have not oftener caused the petrifaction of
animal remains. However, according to Zippe (Jahrb. f.
Mineral. 1843, p. 616), spathose iron ore occurs as a petrify-
ing material of wood ajb the Postelberg in Bohemia. Wiser
recently met with black oxide of manganese as the petrify-
inof material of an ammonite from the mines at Gonzen
near Sargaus, in Switzerland.

8

Most of the specimens exhibited are of peroxide of iron,
but Mr. Swain son’s black coloured plants from Cark have
been converted into protoxide of iron.

It is of course impossible for me to know what specimens
Mr. Kendall may have submitted to Professor Williamson
when that gentleman is said to have pronounced my speci-
mens not to be plants at all, but I now bring before the
society Mr. Swainson’s and my own to speak for themselves.
The former show the rhomboidal scars on the outside as
well as the pith, and the internal and external radiating
C3dinders of Bigillaria vascularis from Lindal Moor. There
are also several specimens of Stigmccria ficoides, the well-
known roots of Sigillaria, exhibiting the rootlets of the
plant coming from the main root in regular quincuncial
arrangement from Cark, which Mr. Swainson has kindly
intrusted me with. My own specimens from Water Blain
I own are not in such good preservation as those of Mr.
Swainson, but most collectors of fossil coal plants would
recognise them as Lepidodendron, Stigmaria, and Catamites,
and their occurrence in any strata would be taken to prove
the beds to be of carboniferous age, notwithstanding that
Mr. Kendall does not believe them to be plants of any kind>
but simply what is known as “ ring ore.”

As to the origin of haematite iron, nothing that has come
under my observation has altered the opinion I expressed
in my paper printed in vol. XII. (2nd series) of the Society’s
Memoirs, that the iron was primarily derived from volcanic
sources, similar to that observed on the sides of Vesuvius
in 1817, as a chloride ; but how it was conveyed into the
places where it is now found it is difficult to say in the
present state of our knowledge. However, it is most
l)robable that the ores of Furness came into the places
where they are most found about the time the lower coal
measures of Lancashire were deposited.

9

the ‘Differential Calculus’ of Du Bourguet/’ by Sir
James Cockle, F.B.S., Corresponding Member of the So-
ciety.

In “Notes and Queries” for September 6, 1879 (5th S.,
vol. xii., pp. 182-3) I have given a bibliography of Du
Bourguet’s work* on the calculus (Paris, 8vo; vol. i., 1810;
vol. ii., 1811). From that work (viz,, from vol. ii., pp. 75-0)
I translate the following article, premising that Du Bour-
guet’s equation (at p. 75) is the well-known criterion of
integrability : —

“361. 2°. Every equation between three variables which

does not satisfy this (330), is not integrable, and consequently
appears at first sight destitute of significance. Nevertheless M.
Monge has demonstrated, in the Memoirs of the Academy of
Sciences of Paris (year 1874), that such an unintegrable differen-
tial equation, between three variables, represents an infinite
number of curves of double curvature possessing a common
property. Besides, we shall observe that, in these non-integrable
equations, this (330) gives a relation between the three variables,
which, as it stands, or augmented, or diminished by a constant
quantity, often satisfies the proposed ; such is, for example, the
equation

(y - z)dz + {z - y)dx + (^i? + a)dy = 0 . . . . (a),
for which the equation of condition (330) is not satisfied, since it
is in this case

z =■■ X y -{■ a

yet if we substitute this value of z in the proposed (a), we have
the identical equation 0 = 0.

“ Again, let there subsist

{1 ^ {z - y - x)[\ a^ {z - y - x) - {z-y - x)]]dx

+ [1 + x^ i^-y- so)\dy -dz = 0 (6),

for which the equation (330) becomes

/3a\i2

z = x + W-

* I first saw a copy of this work in July last, when my brother. Dr. John
Cockle, presented me with the two uncut volumes, bound in a printer’s
covering or binding of blue paper, and each with a white ticket on the back
whereon the words “ Du Bourguet. Calc. Dilf. et Integral ” are printed,
with the respective additions “Tome I.” and “Tome II.”

10

Thus the proposed (b) is not integrable, neither is it satisfied
on therein substituting the value of ^ given by the equation (c) ;
but if we cut off from this value the constant term, the remaining
equation z — x^y satisfies the proposed.”

We may apply to solutions obtained as suggested in the
above article the term “ discriminoidal.” But there exist
unintegrable equations having single solutions not to be so
obtained. Solutions of the latter class may be called ultra-
dis criminoidal. ”

The equation (7) given by Mr. Eobert Eawson at page
117 of his interesting communication ^^On Tertiary DifFer-
ential Equations '' {ante, vol. xvi., pp. 1 1 4-8) is very remark-
able as Avell as very general. It belongs to a distinct species
of discriminoidal solution. The reciprocal of the first factor
of the dexter of Mr. EaAvson’s (8) is an integrating factor of
his (7), provided that w is the product of a function of x
into a function of y. An analogous property is possessed
by every equation of the species to which Mr. Eawson’s
equation (7) belongs.

2, Sandringham Gardens, Ealing,

October 10, 1879.

11

PHYSICAL AND MATHEMATICAL SECTION,

October 14th, 1879.

E. W. Binney, F.R.S., F.G.S,, President of the Section,

in the Chair.

“ On Colorimetry, part III.,” by J ames Bottomley, D.Sc.

In this paper I give the results of some furthur experi-
ments to test the accuracy oi the assumption that when
light is transmitted through transparent coloured solutions,

the length of the column multiplied by the quantity of

»

colouring matter is constant if the colour is constant. In a
communication which I made to the Society in April of this
year, I gave the results of some experiments with ammonio-
sulphate of copper, which appeared to indicate a failure of
the law; but the failure was traceable to the decomposition
of the salt by water, and better results were obtained when
a suitable menstruum was employed. I was -wishful to
obtain some colouring matter which might be diluted with
water without decomposition ; it occurred to me that caramel
would be a suitable body. I prepared some caramel by
heating loaf sugar. The resulting dark brown vitreous mass
dissolved entirely in water. In these experiments I also
wished to see if the law would hold when one quantity was
a considerable multiple of the other; also the quantities
used are no longer mere traces. In order to avoid an
ambiguous result from any difference in sensbility to colour
of the two eyes, in making the determinations I used one
eye only. The cylinders used in these and previous experi-
ments were not specially made for colorimetric purposes.

12

At the bottom they were curved a little inwards. Measure-
ments were taken from the summit of the curve. When
in such cylinders we have short columns of fluid, the depth
not being uniform, the colour is not uniform over the whole
area as we look through the cylinder at an external white
surface. Manifestly the colour at the sides is more intense
than at the middle, but for purposes of comparison we must
restrict our attention to the middle. It is not easy to
confine attention to a limited portion of a coloured area so
as to receive no impression from, the remainder of the area
without some provision. Hence it is necessary to limit the
field of view at the bottom of the cylinder — this was done
either by placing small porcelain discs on a black ground
and holding the cylinder so that its axis passed through the
centre of the disc — or still better by covering the bottom of
the cylinder with a black external plate having a small hole
(about quarter of an inch diameter) in its centre. With
such a provision columns seemed in some cases to satisfy
the experiment, which otherwise would have given the
impression of too dark a colour. In these experiments I
used a method for determining colours indicated in my last
paper, regarding the proper colour as the mean of two sets
of determinations, one set giving too great and the other
too small values. Thus the determination of colour has
some analogy with the method used by old geometers for
determining areas bounded by curved lines; considering
them as the limits of internal and external polygons. In
these experiments A denotes the number of cubic c. of
caramel solution mixed with water ; B the length of the
column; and C the number of cubic centimetres thence

lo

derived by calculation. In one experiment the mean of
four trials for the greater limit gave 2 83 cm. ; and the mean
of four trials for the smaller limit gave 2*65. Hence the
result will be as follows : — Standard solution contains 10
cub. c. of caramel in 500 cub. c. of water, length of column
21 ’2 cm.

ABC
80 2-74 77-4

The above result was obtained by using the right eye
alone. I made another series of determinations, using the
left eye alone. For the greater limit the mean of four trials
was 2 '85, and for the smaller limit the mean of four trials
gave 2-58. Hence the result will be as follows — Standard

solution same as last.

ABC
80 2-71 78-2

I next made some experiments with stronger solutions.
For the greater limit the mean of four trials gave 278, and
the mean of four trials for the smaller limit 2*68. Hence the
results were as follows : — Standard solution 40 cub. c. of
caramel solution in 500 cub. c. of water ; length of column

21*2 — observations made with right eye only

ABC
320 2-73 310-6

I also compared a solution containing 820 cub. c. with
another solution containing 10 cub. c, the theoretical length
was 0-65 cm., a column between 0’6 and 0“7 would satisfy,
but the meniscus rendered the exact determination difficult.
I also made a further experiment with the solution con-
taining 40 cub. c. ; one determination for the greater limit
gave 57, and one determination for the smaller gave 5.
Hence the results are as follows : — Standard solution 10 cub.

14

c. in 500 cubic c. of water, length of column 21*2 cm. — obser-
vations made with right eye.

ABC
40 5*35 39-6

Thus the result is very near.

The solutions of caramel ought not to be kept many days.
After the lapse of twelve days some of the solutions were
turbid and unfit for comparison, owing to the development
of vegetable organisms. It seems very probable that even

with large differences between the lengths of the columns

0

and with larger quantities of colouring matter the relation
g^zrconstant, is valid when the colour is constant. But
suppose the colour to vary, what wiU be the connection
between the quantity of colouring matter, the length of the
column, and the intensity of colour ? If q denote the quan-
tity of colouring matter per unit of length, and t the total
length, we have the relation qt=c if the colour be constant;
but if the colour vary, c will be a function of the trans-
mitted light. Hence

if T denote the transmitted light, therefore qt=f(T) or as
we may write it Tz= (j)(qt), the probable form of this func-
tion may be obtained as follows: suppose we have two
perfectly transparent cylinders of unit area and a fluid of
such a nature, that if in any portion of it we dissolve some
colouring matter, on further addition of the fluid no decom-
position takes place. Suppose we have a standard solution
containing one unit of colouring matter per unit of volume.
If the colouring matter remain constant in quantity, then
the intensity of the light will be a function of the length
of the column of fluid only, say and if the length of

the column of fluid remains constant, the intensity of light
will be a function of the quantity of colouring matter only,
say, (p(q). Suppose, now, in the cylinders which we may
distinguish as A and B we pour a unit length of the standard
fluid, then the light transmitted will be the same in both ;
hence we shall have Dissolve in A another

unit of the colouring matter and make the column of the
standard solution two units long in B, the colour will
remain the same; hence we have ^(2) = ^(2). If we
dissolved three units in A and made B three units long,
we should again And ;//(3)=^(3), and generally
If then we know \p(n) we shall obtain ^(n). For the
intensity of light transmitted through a column n units
long, Sir John Herschel has given an expression (to which
I have referred in a previous paper) of the form

h being the intensity of light passing through a unit thick-
ness, a the intensity of the incident light, and the summa-
tion having reference to the composite nature of light.
This formula is given by Herschel in the “Encyclopsedia
Metropolitana,” also in an article on the absorption of light
by coloured media in the “ Transactions of the Royal Society
of Edinburgh.” In neither of these works do I And the ex-
perimental confirmation of the formula. It appears to have
been obtained a ^priori. If we assume its accuracy we
shall obtain for the expression ak'^, if we suppose we
are dealing with homogeneous light ; if we substitute q for
n we shall obtain ak"^ for the intensity of light which has
passed through a unit length containing q units of colour-
ing matter. We may now suppose the length to vary — for
two units of length the expression will be for three

16

and for t units a{l<f)\ Finally, if we suppose that
there are various kinds of light, we have

T =

As a probable expression for the intensity of light passing
through a column t units long and containing q units of
colouring matter per unit of length. I think that in many
cases where the relation qt^ constant fails, it may be
traced to some decomposition having taken place, or to some
change effected by light ; for example, I commenced some
experiments with ferricyanide of potassium, but as it did
not prove a suitable salt for making experiments without
some special precautions with regard to the action of light,
I discontinued them. As I am not aware that any one has
particularly noticed this darkening, a few remarks may be
interesting. A standard solution was prepared containing
0*8 grins, in 500 cub. c. In the afternoon having occasion
to use this standard for comparison with another, the result
was not satisfactory owing to its transparency not being so
perfect as when freshly made. On the following morning
I made a fresh standard solution of the same composition ; it
differed from the old in being more transparent, and I
thought that it had more of a greenish tint. This new
solution being left on the table before the window, after a
time became of diminished transparency ; also on looking
down into the cylinder a very faint red cloudiness was
perceptible. I also compared a solution containing 3*2 grms.
in 500 cub. c. which had been freshly prepared with a
solution containing 6*4 grms in 500 cub. c. this solution had
been prepared on the previous day and had been exposed to
light during that interval. I found the length of the
column indicated by theory decidedly too great; it occurred

17

to me that the discrepancy was due to some action of light
on the ferricyanide. About six o’clock in the afternoon I
again compared these solutions; the theoretical length gave
a colour which was still too dark, but the disparity of
colour was not so marked as at first. The comparison was
also disturbed a little by the slightly diminished trans-
parency of the weaker solution.

I now prepared a fresh solution, containing 6 ’4 grams in
500 cub. c., thinking that when we work with solutions
which vary gradually in colour we are apt to forget the
initial condition. This new solution seemed quite different
from the old one of the same strength. The latter was
much darker and browner. So great was the difference
that 9T cm. of the old seemed as dark as 22'5 of the new.
To find whether the darkening was due to the action of
light or to some intrinsic cause, I divided the newly made
solution into two equal columns. One I left on the table
before the window ; the other I kept in a cylinder which
was closely invested with black cloth. After the lapse of
six hours I compared them. The one exposed was so much
darker that 5 cm. of the exposed solution gave a tint as
deep as 10'9 cm. of the unexposed. This observation was .
made on the Saturday. On midday of the following Mon-
day, when I again compared them, the darkening had
evidently increased, for 3 cm. of the exposed solution gave
a tint about as dark as that furnished by 10 9 cm. of the
unexposed.

Wishing to ascertain whether keeping in the dark would
reverse the action of light, on Saturday, May 24th, I took
a solution containing 6’4 grams in 500 cub. c. The solution

18

Having been prepared three days previously and darkened
by exposure during that interval to light. The containing
cylinder was closely invested with black cloth and kept in
a dark closet. On the morning of the following Monday I
thought that it appeared not quite so dark as at first, and on
the evening of the same day I thought it a little lighter than
in the morning. After keeping it in the dark for a week I
found that it had become much lighter, and on June 4th,
when I examined it again, it seemed nearly as light as a
freshly prepared solution; there was, however, a minute
quantity of precipitate.

From these results it is evident that in some cases special
provision must be made to avoid needless exposure to light
in quantitative determinations by colorimetry, or in studying
the laws of the absorption of light passing through coloured
solutions.

I also made some experiments with chromate of potash.
This I thought a stable salt suitable for experiments.
Nevertheless some of the results were not satisfactory when
one cylinder contained a solution which was several times
stronger than the other. For instance : a standard solution
was made containing 0’8 grams in 500 cub. c. of water.
Another solution compared with this gave the following
results : —

A B C

6*4 3-7 4-5865

A repetition of the experiment gave nearly the same result,
namely, 3-6 for the length of the column.

It occurred to me that possibly, when potassic chromate
is diluted, there may be liberated a minute quantity of chromic
acid, which would increase its absorbent power ; this might

19

be inferred from the greatly increased absorbent power im-
parted to the bichromate by the additional molecule of
CrOg. I therefore took the cylinder containing the standard
solution used in the last experiment and divided its contents
into two equal columns : to one I added a few drops of am-
monia ; this column became slightly but perceptibly lighter
than the other, so that I have little doubt some change had
been effected in the constitution of the dissolved salt ; the
hypothesis of the liberation of a little chromic acid is, I
think, strengthened by the fact that a solution of the salt is
of a deeper yellow than the undissolved salt. I think that
probably a trace of carbonic acid in the water had liberated
a little chromic acid.

To try what the effect of the addition of a little weak
acid would be, I took a solution containing 1*6 grams in
500 cub. c. and divided it into two equal parts. To one I
added a little extremely dilute sulphuric acid. The colour
of this portion became decidedly deeper than that of the
other. I also tried what would be the effect of the addition
of a little ammonia to a strong solution, so I divided the
solution containing 6*4 grms. in 500 cub. c. into two equal
portions — one I treated with ammonia; this I thought a
little lighter than the other, but the difference was very
slight ; this however we might expect, for any small change
in intensity would be less noticeable in a strong solution
than in a dilute one.

I now made some fresh experiments with chromate of
potash, a little ammonia being added to both columns. The
mean of four trials gave for the greater limit 3-35, and the
mean of four trials gave for the smaller limit 2T8. Hence

20

the results will be as follows. Standard solution 0'8 grams

in 500 cub. c. of water; length of column 22*5 :

ABC
6-400 2-77 6-498

In this experiment I used the right eye. The theoretical
length is 2-81, and the above result is therefore a near
approximation.

With the same solutions, on the following day (June 26th)
the results were not so favourable ; the mean of eight trials
gave 2’57 cm. as the length of the equivalent column, the
left eye being used in the determinations. On the next
day (June 27th) I repeated the experiments with these
solutions, using the right eye ; the mean of four trials gave
2-8. To each solution I added 5 cub. c. of ammonia, and
repeated the experiment; the mean of four trials gave 2*13
as the result. These differences of results are probably due
to some internal changes in the coloured fluids.

I may also take this opportunity to correct two numerical
errors in the sixth volume of the Society’s Memoirs. Page
262, line 3, for 3-2 read 2-2 ; and on page 264, line 2, for 15
read 50.

21

Ordinary Meeting, November 4th, 1879.

J. P. Joule, D.C.L., LL.D., F.KS., &c., President, in the

Chair.

Screw Propulsion,” Part II., by Egbert Eawson, Assoc.
I.N.A., Hon. Member of the Manchester Literary and Philo-
sophical Society, Member of the Mathematical Society.

7. The articles in Part I. have been principally devoted
to the consideration of the normal velocity of the propeller
blade, an element which chiefly, if not entirely, regulates
the thrust of the screw in the direction of its axis; but
recent experience in screw propulsion seems to point to
another resistance arising from the friction between the
water and the surface of the propeller blades usually called
shin resistance. This skin resistance, therefore, appears to
depend, in some way or other, upon the velocity of the
rubbing surfaces. (See a paper by Eankine on the Mechani-
cal Principles, of the Action of Propellers.— Transactions of
the Institution of Naval Architects, 1865, page 21.)

Hence, the necessity of determining the velocity of the
element (a) in a plane perpendicular to its normal line.

8. This may be done as follows :

Let HP, in the annexed

figure, be perpendicular to
the plane AGP. Now the
velocity (rw) acts in the
direction of HP, resolve this
velocity perpendicular to the
normal PI, it will become
ru’sinv in the direction HI
and in the plane HPI, which
is evidently perpendicular to
the plane AGP. Again, re-
solve the velocity (v), which acts in the direction PK,

PROCEEDiNas — Lit, & Phil, Soc, — Vol.XIX. — No. 3. — Session 1879-80.

22

perpendicular to the normal PI, it becomes mna in the
direction KI and in the plane PIK. It is not difficult to
show that the cosine of the angle between these component
velocities will be correctly represented by the following
formula

Cos.KIH =

COSaCOS)/

sinasinv

(6)

Therefore, the velocity of the element (a) in a tangent plane,
that is, in a plane perpendicular to its normal line at P, is the
resultant velocity of rminv,vsina acting in directions making
the angle KIH, and, by the ordinary formula for calculating
the resultant it becomes equivalent to the formula

V rWsin^j/ + + 2mycosacosj/ (7)

9. The above result may be obtained in another way, viz.
find the resultant of rw and v in the plane HPK, then re-
solve this resultant parallel and perpendicular to the
normal line.

The formula (7) admits of the following form, easily ob-
tained, viz. :

V tV + - (rwQOBy - vcoBaY (^)

10. The point P moves with a velocity + v% and
describes the common helix whose radius is v and pitch
(2ttv) upon (w).

11. Taking 6080 feet to represent a knot or nautical mile,

V = feet per second = K x 1 *688
where K is the knots per hour.

If, n = number of revolutions of screw per minute.

u = angular velocity = ^

On the Slip of the Element (a) of the Propeller Blade.

12. Let it be supposed that the element (a) rotates in
water perfectly at rest, and also that its motion is the same
as the- motion of the nut of a screw. This condition is
evidently fulfilled when the normal velocity of the element

23

(a) is equal to zero. Let v’ be the angular velocity, the
velocity in the direction of the axis AB, respectively, which
will produce the above described effect, then

tw'qq^v - v'cosa = 0.
From which.

V

7

Vj

rcosj^

cosa

(9)

It now remains to find the distance H' traversed along
the axis of the element {a) viz. AB during one revolution,
then

space _ 27t
u'

27rrcosi/

Time of one revolution =

velocity

,-r# • 1 • 27T27

H' = time X velocity =

u

cosa

(10)

Again, to find the distance H traversed along the axis
AB during one revolution of the element (a), when it moves
with an angular velocity (u) and a velocity {y) in the direc-
tion of its axis, then

m- ^ w space 2ttv

Time 01 one revolution = — ~ — r— = —

velocity

u

H = Time x velocity =

2ttv

u

,(11)

13. The quantity H' is usually described as the measure
of the speed of the element (a) of the propeller blade, and
H as the measure of the speed of the vessel propelled.

When H' is equal to H, then the element (a) of tlie pro-
peller is said to move as fast as the vessel.

When H' is less than H, then the element (a) is moving
faster than the vessel.

When H' is greater than H, then the element (cC) is not
moving so fast as the vessel.

The quantity (H' — H) has been usually designated by
naval architects the sli]) of the element (ct).

The value of this sliy> is readily found from equation (10)
and (11) as follows;

= - j (12)

I cosa U ) ' '

24

14. Experience in'screw propulsion has recorded several
cases of the quantities (H' — H) having been negative, giving
rise to what is known to practical naval architects as
negative slip. Hannibal, a screw steamer of 8136 tons,
speed 7'999 knots per hour, 64'87 revolutions per minute,
propeller 17ft. diameter, pitch 12ft. 6in., length 2ft. lin.,
indicated horse power 1071, had a negative slip of ’601
knots per hour. Plumper, 8129 tons, speed 6*627 knots
per hour. 111 revolutions per minute, propeller 8ft. 8 Jin.
diameter, 6ft. Of in. pitch, ll|in. length, indicated horse
power 135, had a negative slip of *591 knots per hour.

Many other instances of this peculiar kind of slip have
been recorded in the history of screw propulsion ; but, its
occurrence has generally provoked, amongst those interested
in the progress of naval architecture, considerable discussion
as to its real cause, some affirming its impossibility by an
exclamation somewhat as follows how can the cart go
faster than the horse, &c.? while others have endeavoured
to see a cause for it, either in the flexibility of the propeller
blade when it is subject to pressure, or, in the state of the
water in which the propeller revolves. The history of this
discussion is curious, and many of the leading events in it
are recorded in the pages of the transactions of the society
of Naval Architects. With respect to the importance
attached to the subject of slip, it may be said that its
introduction into the investigations of screw propulsion has
been regarded by many in the light of an untoward event ;
inasmuch as its diminution does not necessarily imply an
increase in the speed of the ship produced by the same
effective horse power of engines. And, moreover, the advo-
cates of “ slip resistance ” would be sorely perplexed to
assign properly the element called slip in a propeller with a
variable pitch.

15. With a view, therefore, of freeing the question of slip
as much as possible from the elements which appear to me

25

to render difficult, to some minds, the right apprehension of
its action in regard to 'dhe motion of the vessel, it will he
necessary to consider here two ships being propelled by
a screw propeller, placed in two hypothetical positions
as follows.

Ship A. This ship is propelled by a screw revolving in a
position astern, that is, out of the wake of the ship in still
water.

Ship B. This ship is propelled by a screw revolving in a
position astern, that is, in the wake of the ship in water
which flows in the direction of the ship with a velocity Y.

With respect to the ship A, the slip of the element {a) is
computed on the above principal in Arts. 12 and 13, and is
correctly represented by the formula

H'-H = 27t| l (13)

( COSa u j

with a screw revolving as above described there would be,
indeed, just ground for surprise if (H' — H) was experi-
mentally observed to be either a negative quantity, or zero

16. With respect to the ship B. Put u', v'for the angular
velocity, the velocity of the element (a) in the direction of
the axis, repectively, in order to produce the normal velocity
equal to zero.

The slip will he here computed by the element {a) moving
in such a manner that its normal velocity is zero.

Now, having regard to Y, there results from formula (4)
Art. 6, the equation

Tu'cOBv - {v' - Y)cosa = 0.

(14)

. V Y TCO^V

r rom which, — , = — ; -l ,

' u u COSa

Next to find the distance H' traversed along the axis AB
during one revolution of the element (a) of the propeller
blade —

Time of one revolution =

space

velocity

.STT

u'

.*. H' = time x velocity = = 27t -f — , + 1 (15)

u I u COSa )

26

Again, find the distance H traversed along the axis AB
during one revolution of the element (a) when it moves
with an angular velocity (u), and, a translatory velocity {v)
along the axis.

Time of one revolution =

space

velocity

27T

u

H = Time x velocity =

2ttv

u

Therefore, by subtraction, there results

H'-H = 27t 1-, + ^''-- I (16)

17. In formula (16), although the form and dimensions
of the propeller, together with the -resistance to motion,
might be such as to make the quantity

rcosv V
COSa

equal to zero or even negative. Still, it would be surprising
to find by experiment that (H'-H) in equation (16), was
either negative or even zero.

In all probability the quantity

V rcosj/

— -[-

u COSa

would be considerably in excess of the ratio v upon u, pro-
viding the quantities Y and v! were correctly measured by
experiment.

Hitherto, when negative slip has manifested itself in
actual experiment, as in the case of the Plumper and Hanni-
bal, it has done so only on the assumption, which is by no
means a correct one, of V = 0.

The foregoing investigation appears to explain clearly
the perplexing mystery of negative slip, and it may be
added that the arguments and conclusions with respect to
negative slip advanced in these pages are not, in the slight-
est degree invalidated by the circumstance of having used
the element {a) of the propeller blade instead of the propeller
itself. The reason of this is, that the slip of the element {a)
is exactly the same as the slip of the ordinary screw pro-

27

peller blade as used in the navy, that is, the quantity rcosv
upon cosa is a constant quantity for every point on the
screw blade, viz., the pitch of the screw.

It is no part of my design here to investigate the law
which connects the distance {x) of the screw from the stern
of the vessel with the velocity V of the water in which the
screw revolves, the admission of a quantity Y is sufficient
for my present purpose.

It may, however, be observed that the velocity V varies
from the velocity (v) of the ship at the stern, to the velocity
zero at a point which is the limit of the wake of the ship.
Those who are interested in and investigating this subject
would do well to consult two papers printed in the Transac-
tions of the Society of Naval Architects, by Professor
Osborne Eeynolds. The first paper is entitled “On the
Effect of Immersion of Screw Propellers,” (see Transactions
of Ins. N. Architects, 1874*, page 188). The second paper is
entitled “ On the Unequal Onward Motion in the Upper and
Lower Currents in the Wake of a Ship, &c,, (see Tran, of I.
N. Architects, 1876).

18. The most recent experience in screw propulsion is
given in a paper by James Wright, Esq., Vice-President of
the Institution of Naval Architects, &c. The title of this
paper is “ The Steam Trials of Her Majesty’s Ship Iris it
was read and discussed at the Institution of Naval Architects,
April, 1879.

Here, in a four-bladed common screw, a negative slip is
recorded, which increases from 1’57 to 5 ’3 3 per cent, while
the speed diminishes from 16 to 8 knots per hour, and the
I.H.P. diminishes from 7,503 to 755, and the revolutions
per minute diminishes from 91 to 43. This circumstance
is passed over in silence by Mr. Wright, who very justly
directs the attention to the fact that a two-bladed screw is
a more effective propeller than a four-bladed one of the
same dimensions.

28

A most excellent paper “ On the Efficiency of Single and
Twin-screw Propellers ” was read and discussed at the In-
stitution of Naval Architects, April 11th, 1878, by W. H,
White, Esq., Assistant Constructor to the Navy, Member of
Council, in which is recorded two cases of negative slip.
The Invincible, with twin-screw, displacement 5,563 tons,
70*8 revolutions per minute, 4,882 I. H.P., with four screw
blades whose dimensions are 16ft. 2in. diameter, 20ft. 9|in.
pitch, speed 14*093 knots per hour, gave a negative slip of
1*89 per cent. The Alexandra, twin-screws, 9,432 tons dis-
placement, 64*2 revolutions per minute, 8,615 I.H.P., with
four screw-blades, 21ft. diameter, 22ft. 2 fin. pitch, speed 15
knots per hour, gave a negative slip of 6*5 per cent.

29

MICEOSCOPICAL AND NATUEAL HISTOEY SECTION.

October 13th, 1879.

Chaeles Bailey, F.L.S., President of the Section, in the

Chair.

On the Means by which Hydra swallows its Prey,” by
M. M. Haetog, M.A., B.Sc., F.L.S.

The current idea is that Hydra swallows by taking its prey
in its tentacles and turning tentacles and all into its stomach.
However, the part played by the tentacles ceases as soon as
the mouth comes in contact with the food. The hydra then
slowly stretches itself over the food in a way that recalls to
some extent the manner in which a serpent “gets outside” its
prey, or in which an automatic stocking might stretch itself
onto the foot and leg. No care seems to be taken, however,
to present the easiest point for deglutition, and an Ento
mostracan may be swallowed sideways, for instance. So
far are the tentacles from co-operating in the act, that they
are usually reflexed away from the food; occasionally, how-
ever, they are swung forward for a moment around the
mass as if to ascertain how much remains to be swallowed.

If the prey be at all bulky, immediately after the whole
act is completed the body cavity is everywhere filled and
on the stretch ; but after a short lapse of time the body
contracts forcibly along the long axis, so that the part con-
taining the food is globular, supported on a slender foot and
with a slender apical process bearing the tentacles around
the hypostome.

Mr. R. Ellis Cunliffe called attention to a paper by
Mr. H. J. Carter on the classification of the Spongiada, and
exhibited a series of slides prepared by Messrs. Cole from
the original specimens.

30

Mr. K D. Daebyshire, F.G.S., exhibited specimens of the
rare bivalve mollusc Panopsea Aldrovandi, from Faro Island,
Algarve, S. Portugal, a species almost confined to this iso-
lated locality. He also exhibited, for sake of comparison,
specimens of the British Panopsea Norvegica and various
Saxicavse, and sketched the distribution of the six species
comprised in the genus Panopsea, the range being a remark-
ably wide one.

Dr. Alcock read a paper on Lagena striata and its allies,
and exhibited many beautiful drawings illustrative of this
genus of foraminifera.

Mr. Linton distributed specimens of Helix lapicida (L.)
from Matlock, Derbyshire.

31

Ordinary Meeting, November 18 th, 1879.

J. P. Joule, D.C.L., LL.D., F.RS., &c., President,

in the Chair.

The President noticed the lamented death, since the last
meeting, of Professor J ames Clark Maxwell, an event which,
having occurred in the prime of his life and in the midst of
his usefulness and his splendid researches, was felt most
severely by the Society and the whole scientific world.

E. W. Binney, V.P., F.B.S., said: On Tuesday, the 11th
instant, at 5.80 p.m., my son informed me that he was
walking in Trees Street, Cheetham Hill, and on looking
towards the East he observed a very brilliant meteor in the
S.E. It appeared to be considerably larger in size than the
planet Jupiter, and gave out as much light as the half moon
and travelled slowly to the N.N.E., where it disappeared.
The colour of the meteor was white with a tinge of blue,
and it left a track of the same tint. At its greatest eleva-
tion it reached the altitude of the planet Mars, and it
appeared less in size as it travelled northwards and
disappeared in the N.N.E. The time he observed it from
first to last was about eleven seconds. The sky at the time
was partially clouded, and the meteor was only observed at
intervals and not along its entire course.

“Kecording Sunshine,” by David Winstanley, F.R.A.S.

So far as I have seen there is in use at present but one
form of apparatus which effects an automatic registration
of the duration and the times of sunshine, and that is the
instrument of Campbell, in which a sphere of glass is so
disposed as to burn a piece of wood or paper by the concen-
Proceedings — Lit. & Phil. Soc. — Vol. XIX. — No. 4. — Session 1879-80.

82

tration of his rays •when the sun may chance to shine.
During the past few years I have devoted some attention
to this matter and devised a number of appliances having
the same object for their end but differing materially both
in their construction and in the manner of their use from
the apparatus I have named.

One of these, with your permission, I will now describe.

It is an arrangement which places a lead pencil on a sheet
of paper and writes down therewith when and for how long
the sunshine lasts.

It consists essentially of a differential thermometer with
a long horizontal stem, in which latter is contained through-
out the greater portion of its length some fluid intended to
operate by its weight. This thermometer is attached to a
scale beam or some equivalent device which also carries the
pencil by means of which the record shall be made.

The whole is so arrauged that in its normal state it rests
gently — upon that side to which the pencil is not attached — ■
on an embankment provided for that end.

Close beneath the pencil point a disc of metal rotated at
the proper speed carries a paper dial whereon marks and
figures are engraved corresponding with the hours at which
the sun may shine.

When using this instrument I have it enclosed within a
box which permits one bulb only of the thermometer —
that most distant from the clock — to be affected by the
radiance of the sun, which when it shines expands the air
contained therein, forces the fluid along the tube and by
altering the equilibrium of the beam brings some portion
of its weight to bear upon the pencil point, and so the record
is commenced.

When the sun becom.es obscured, the air expanded by his
rays contracts, the fluid in the tube returns, the normal
equilibrium is restored, and the pencil ceases to produce its
mark.

38

In the instance of the instrument I use the stem of the
thermometer is 18 inches long and the eighth of an inch or
thereabouts in bore.

Mercury in consideration of its weight is the fluid I em-
ploy, and in conjunction with it some sulphuric acid is
enclosed, because of the mobility which is thereby gained.
I am aware that in these circumstances mercuric sulphate
is very slowly formed, but after two years’ lapse of time no
inconvenience has been caused thereby and the mobility of
the mercury remains.

The bulbs of the thermometer are two inches in diameter
or thereabouts, and that they may be more rapidly affected
the glass thereof is thin. Both are blacked, and the one
intended to receive the radiance of the sun projects above
the box in which the apparatus is contained into a dome of
glass.

“ On some Notices in Classical Authors of the Action of
Sunlight on Purple Bye,” by James Bottomley, B.Sc., F.C.S.

At a meeting of the Society on October 21st, Br. Schunck
exhibited to us some of his specimens of purple extracted
from shell-fish, and called attention to the remarkable action
of light in developing the colour. At the time I remem-
bered having seen some passage relative to a supposed action
of light upon the colour, showing that the ancients had
some obscure notions of the matter. This seems to me
additional evidence of the identity of the colour obtained
by Br. Schunck with the famous purple of the ancients.
The passage which I had in my mind is a note by Paley on
the following verses of the Helena of Euripides :

Kvavoeidlg afi^ vSwp

^ > V A /

erv)(ov EAiKa r ava ^Aoav
(j)OLVLKag aXtfj) ireirXovg
avyoLcnv iv ^pvaiaig
aju^i^aXrrova £v re SovaKog epvecnv.

34

Paley’s comment is aXiio. So Herm. for oXujj or aXtov.
See above on v. 170. Musgrave sliows from Pollux, i. 49
that the chemical effect of the sunlight on garments dyed
with the sea-purple is to refresh and heighten the hues,
Hippol. 125 : o^l fxoi tiq (j)i\a irorafiiq.

Spoarctj rlyyoucra, S’ Ittl vd)Ta Trerpeag evaXiou KarejSaXXs,

From this property of the sea-purple ^Fschylus calls it KtjKlg
Tray KaivicFTog, Agam. 933, “ capable of being entirely renewed
when faded.” The passage of Musgrave (and of Pollux)
referred to by Paley is as follows :

^oiviKag — TreTrXovg. Purpureas vestes. Has enim soli
exponere mos erat ad renovandum tincturse splendorem.
Pollux, lib. i. sect. 49, vXi(p bfiiXovcra Trig TTOp(j)vpag

71 (3a(j)7i Kal r) aKrlg avTTiv avaTrvpaevei, koX nXelw TTOiet Kal
(paidporipav ri)v avy^v.” The meaning of this passage I take
to be — “ The purple dye delights in association with the sun,
and the solar beam reddens it and makes more intense and
more dazzling its splendour.”

Mr. Charles Bailey, F.L.S., exhibited specimens of
Ophioglossum vulgatum, L., var. j3. ambiguum, Coss. et
Germ., which he had collected in July last on damp sandy
ground at the foot of the sandhills, on the land side, one
mile west of Dyffryn railway station, between Harlech and
Barmouth, in Merionethshire. This plant has been figured
on plate 46 of “British Ferns,” by the late Sir William
Hooker, and the Welsh specimens agree well with this
figure, though generally smaller in size. The variety amhi-
guum was originally detected more than twenty years ago
in the neighbourhood of Paris, and was found, shortly after-
wards, in one of the numerous “ laiches” at Arcachon. It
was first noticed as a British plant by Dr. J. T. Boswell,
who detected it in the Orkney Islands, and Mr.Curnow has
recently distributed specimens, through the Botanical Ex-
change Club, from the Scilly Islands.

35

The Dyflfryn locality is therefore a connecting link be-
tween the extreme stations of western Europe, from the
Orkneys in the north to Arcachon in the south. This
variety, in general appearance, is much more like Ophio-
glossum Luisitanicum, L., but the var. amhiguum produces
its fertile frond at the end of J uly, while 0. Luisitanicum
fruits, in Guernsey, five or six months earlier. M. Durieu
de Maisonneuve finds a separating character in the spores,
which are finely tuberculated in 0. vulgatum, and smooth
in 0. Luisitanicum.

On the Origin of the word Chemistry,” by Carl
SCHORLEMMER, F.KS.

Chemistiy as a science is first mentioned^' by Julius
Maternus Firmicus, a native of Sicily, and procurator under
Constantine the Great. He wrote at about 336 a work on
Astrology, which has been preserved only in a defective
state, and is commonly known by the name of Mathesis.

In this work he states that by observing the position of
the moon, in respect to certain heavenly bodies or constella-
tions, at the hour when a child is born, its future inclina-
tions can be predicted. He continues : Et si fuerit haec
domus Mercurii, Astronomiam. Si Veneris, cantilenas
et laetitiam. Si Martis, opus armorum et instrumentorum.
Si Jovis, divinum cultum et scientiam in lege. Si Saturni,
scientiam alchimiae. Si Solis, providentiam in quadri-
pedihus. Si in Gancero, domus sua, scientiam dahit
omnium quae exeunt de aqua.'^

Other editions of this work have also scientia alckimiae,X

but Vossius informs us that in the manuscripts it is
chimice.^ He says : Alchimice scientiam nominal Firmi-
cus, lib. HI., cap. XV. Ita quidem editum ah Aldo, sed
in chirograpMs est chimice.

Kopp, Beitrag’e zur GescMclite der Chemie, 43.
t Julius Firmicus de nativitatibus ; Ed. Simon Bivilaqua. Venice, 1497,
j Ed. Aldus ManutiuSj Venice, 1499 j Ed. Nicolaus Bruclmerus; Bale, 1533.
§ Etymologicon linguae latinaej Amsterdam, 1695.

86

Athanasius Kirch er also states that the manuscript in the
library of the Vatican has chymice and not Alchymice.^
Firmicus does not give any explanation of this term.
However another writer, who probably lived at the same
time, if not earlier, explains it. Zosimus, the Panopolite,
according to Georgios Synkellos, a writer of the ninth
century, states that ^Y]yda (or ')(yfxda, as some manuscripts
have) meant the art .of making gold or silver. "f*

The curious passage in which this word occurs is the
following : — -

“ The sacred Scriptures inform us that there exists a tribe
of genii, who make use of women. Hermes mentions this
circumstance in his Physics; and almost every writing
(Xoyoc)j whether sacred (^avepoc) or apocryphal, states the
same thing. The ancient and divine Scriptures inform us
that the angels, captivated by women, taught them all the
operations of nature. Offence being taken at this, they
remained out of heaven, because they had taught mankind
all manner of evil, and things which could not be advanta-
geous to their souls. The Scriptures inform us that the
giants sprang from their embraces. Chema is the first of
their traditions respecting these arts. The book itself they
called Chema ; hence the art is called Chemia”

It is not difficult to trace the origin of this myth. We
find it first in Genesis, chap. vi. : “ And it came to pass,
when men began to multiply on the face of the earth, and
daughters were born unto them, that the sons of God saw
the daughters of men that they were fair, and they took
them wives of all which they chose.”

“ There were giants in the earth in those days ; and also
after that, when the sons of God came in unto the daughters
of men, and they bare children to them, the same became
mighty men, which were of old, men of renown.”

* Kopp, loc. cit. 9.

t Thomson’s History of Chemistry, 5,

87

Alluding to this later writers state that the fallen angels
taught women all the secrets of nature.* That one of these
is the art of making gold and silver is however first
mentioned by Zosimus. Other Greek writers use the word
Chemia or Chymia in the same sense ; in print we find it
first in the Lexicon of Suidas, who lived in the eleventh
century and defines \r]ixua as the preparation of gold and
silver.”

All the earlier Greek writers who mention this word were
in close connection with the university of Alexandria; from
this it has been inferred that the artificial preparation of the
noble metals was first attempted in Egypt.

That country was conquered by the Arabians in 640.
Here they made undoubtedly their first acquaintance with
chemical science; they prefixed their article to the Greek
name and thus introduced the terms : Alchemy, Alchimy or
Alchymy.

The origin and meaning of these terms have often been
discussed. Plutarch states that the old name of Egypt was
X»jjuta ; that it was so called on account of its black soil,
and that the same word designated the black of the eye.
From this the conclusion has been drawn, that chemistry
originally meant the science of Egypt, or the black of the
eye being the symbol of darkness and mystery, chemistry
was the secret or black art. But alchemy has never been
called the black art, a name which was exclusively reserved
for magic or necromancy.

It has also been stated that the name was derived from
the Arabic hema, to hide, while others have maintained that
the founder of our science was Cham or Ham, the son of
Noah, or an Egyptian king with the name of Chemmis. It
has further been suggested that the name of the science was
derived from to melt ; or from x^i^oc, juice or liquid.

* Kopp, loc. cit. 4.

38

To this it has been objected that the original spelling was
Xnjuida and not which, although Hermann Kopp, the

great historian of chemistry, inclines to this view, has not
yet been proved satisfactorily. Humboldt believes that the
latter word got into some manuscripts by a mistake of the
transcriber, and continues : “ Alchirny commenced with the
metals and their oxides, and not with the juices of plants.”
This objection, however, cannot be maintained at all, because
vegetable juices or, at least, substances designated by their
names, are mentioned by the older alchemists as the most
potent substance by which transmutations could be effected.^

Some time ago my friend Professor Theodores called my at-
tention to an interesting paper on this subject, published by
Professor Gildemeister,"!* in which he maintains the deriva-
tion of the word chemistry from According to him

Mmiyd in Arabic does not originallyhave an abstract meaning,
and is the name, not of a science, but of a body by which, or
rather by a substance obtained from which, the transmuta-
tion of metals is effected ; it is synonymous with iksir.
Alchemy, as a science, was called : The preparation of
Mmiyd or iksir, also the science of the preparation of
Mmiyd or, more shortly, science of Mmiyd. In the Arabic
Lexicon (Qamus) al-iksir is explained by al-kimiyd, and the
latter again by the former, or by any medium which, applied
to a metal, transports it into the sphere of the sun or the
moon, i.e., converts it into gold or silver.

Even to this day the word is used in the concrete sense ;
KotschyJ relates that the pasha of Nicosia talked much of
flowers, chiefly kimia, a plant having the property of con-
verting metals into gold.

The later writers, however, called the science shortly
cd-kimiyd and retained the term al-iksir (elixir) for the
transmuting medium or the philosopher s stone. This latter

* Kopp, loc. cit. 76.

t Zeitsch. deutscli. morgenland. Ges. XXX., 684.

J Petermann. Geog. Mittli. VIII., 294.

89

word is identical with ^r}piov, as the writers of the
Alexandrine school called the philosopher’s stone, ^ while the
same name was employed by the physicians for a healing
powder, used for sprinkling over wounds, i.e., Si desiccative
powder (from ^rjpog, dry).*[-

Now the correlate to dry is moist or liquid,
from this is derived yu/itia, a moist substance corresponding
to Xi^eia, a material formed of or Kcpajusta, the

occupation with Kipajiog.

Ibn Khaldun, who lived in the 14th century, says that
from the philosopher’s stone a liquid or a powder might be
prepared called ihsir, which, when thrown on molten copper
converted it into silver, and molten silver into gold. In
opposition to its etymology the word is here used for a
liquid, because at that time Idmiyd no longer meant the
transmuting substance, but the science of transmutation,
and explains why to-day we may understand by elixir a
liquid.

We also find that the philosopher’s stone is often called
the red tincture, from tinguo, to moisten.

It appears, therefore, very probable that the name of our
science is derived from xvfxog, and the proper spelling would
therefore be Chymistry, as the “ Times ” newspaper for
a long time insisted upon. As however this derivation has
not yet been proved quite satisfactorily, the time-honoured
term Chemistry will remain in use, and I think be retained
even if it should be shown that was the original

spelling.

* Kopp, loc. cit. 209.

t Zosimus calls tlie substance by which copper is tinged yellow or
converted into brass : ro ^ovSlas ^^ptov, a powder prepared by means

of tutia ; now tutia (zinc oxide) is still to-day used in medicine as a
desiccative.

40

MICEOSCOPICAL AND NATUEAL HISTOEY SECTION.

November lOtb, 1879.

Chaeles Bailey, F.L.S., President of the Section

in the Chair.

Professor Boyd Dawkins, F.B.S., brought before the
notice of the Section a map on which was represented the
geography of the British Isles in the Meiocene Age. The
land extended northwards by way of the Faeroes and Ice-
land to Greenland on the one hand, and to Spitzbergen on
the other, and is now represented by the area included by
the 400 fathom line. This land barrier offered a means of
free communication both to Europe and North America, by
which both plants and animals were able to migrate from
the one to the other. It explains the many species common
to Meiocene Europe and America, such as the Sequoia, the
Bedwood, Magnolia, Tulip tree, and Swamp Cypress, and
others. The climate of the Arctic region was then tem-
perate, but not so warm as in the preceding Eocene age.

“ Additional Note on Hydra,” by Maecus M. Haetog,
M.A., B.Sc., F.L.S.

Since my last paper I think I have found the clue to the
false idea referred to. A Hydra that had swallowed a mor-
sel larger than itself disgorged, as frequently observed, on
my attempting to take it up for examination. On finding
it half an hour after, three of its tentacles were turned into
its digestive cavity, whence they were successively and
slowly withdrawn. As the mouth closes but slowly after
disgorging, I imagine the swallowing them to have been
accidental ; and a similar phenomenon carelessly observed
may well have given rise to a false interpretation.

41

“ On some un described Hairs in Copepoda,” by the same.

These hairs are very simple in form and so minute that
they can only be glimpsed with the objective. They are
planted in depressions of the integument and are circular in
section, the basal part thicker and tapered towards the
middle (what is termed biscuit-shaped by the German his-
tologists), the terminal part longer and ciliiform. Their im-
portance is shown by their constancy in position, and by the
bilateral symmetry of their distribution. They are found
on both the dorsal and ventral surfaces of the abdomen, but
I have only succeeded in seeing them on the dorsal surface
of the cephalo-thorax, where they are most numerous in the
frontal region. The pair on the tergum of the last abdomi-
nal segment are easiest to find ; and it was after seeing these
that I looked for them elsewhere. I have found them in
both Cyclops and Canthocamptus, belonging to distinct fami-
lies, whence I conjecture that their presence may be general
in the order. Similar hairs implanted in pits have long
since been demonstrated in Insecta, and possibly add to the
delicacy of touch required by flying and swimming animals
to enable them to thread their way through obstacles.

“ On an Undescribed Acinetan,” by the same.

The animal in question was found on the ventral surface
of Cyclops gigas (especially females), on and about the bases
of the oral appendages. In size it comes near Podophrya
Cyclopis and is similarly attached by a short rigid pedicel ;
but its form is usually much less distinctly spherical, un-
dergoing slow irregular changes. The body is invested in a
cuticle and the endosarc is usually full of reddish brown
granules. The nucleus is spherical, like the solitary con-
tractile vesicle which in one specimen was found to contract
at intervals of from SV to 44". The tentacles, which are
the distinguishing feature, are much thicker than in an
ordinary Podophrya, rounded, obtuse, and quite undilated
at the summit, a little below which a circular constriction
is seen. No other trace of organization is to be made out
in them when the animal is quiescent. After slightly press-

42

ing the cover glass the tentacles may be seen to wave slowly
about as if in search of prey; and this is accompanied by
changes in length. On crushing the Cyclops and thus
bringing to bear the stimulus of a large supply of food, the
tentacles at once become very active. The part beyond the
constriction expands into an open funnel : the rest shows
numerous equidistant circular wrinkles, and actively length-
ens and shortens. At the same time a canal is seen up
the middle of the tentacle opening into the funnel ; and food
particles may be seen to pass along this into the body. The
cuticle seems to form a fine investment to outside the ten-
tacles. The number of these is from 6 to 14, scattered
over the distal surface of the animal or sometimes
apparently gathered in two groups.

These characters would almost seem to warrant the
creation of a new genus, which, however, is best left to
those who have a more critical knowledge of the Protozoa.
For the present it may bear the name of Podophrya ?
infundibulifera; the character of the tentacles giving the
specific distinction thus : —

Podophrya infundihulifera n. sp. — P. tentaculis quies-
centibus crassis ad apicem rotundatis, sub apice leviter
constrictis, vel vivaciter elongatis et retractis rugis circulis
dense striatis apice infundibulatis et pabulum aspirantibus.

Mr. C. Bailey, F.L.S., exhibited specimens of Ophioglos-
sum Ambiguum from Barmouth, collected there by himself in
July, 1879. This variety of the common 0. vulgatum has
been hitherto found only in the extreme North and South-
West of the British Islands, viz. : in the Orkneys and Scilly
Isles. Hence the discovery of an intermediate locality is of
much interest. The exact locality was damp sandy ground,
close to the sea, near Dyfiryn Bailway Station, between
Harlech and Barmouth.

Mr. Bailey also exhibited a very complete and beautifully
mounted collection of Scandinavian Hieracia, or Hawk
weeds.

4^

General Meeting, December 2nd, 1879.

R x\ngus Smith, Ph.D., F.RS., &c., in the Chair,

Professor Alfred Milnes Marshall, M.A., Fellow of St*
John’s College, Cambridge, Professor of Zoology, Owens
College, was elected an Ordinary Member of the Society.

The following Minute from the Owens College was read :

“At a meeting of the Council held at the College on
Friday the 21st November, 1879,

“ It was Resolved ;

“That the Treasurer be requested to inform Dr. Joule
that the Council is deeply impressed with the
importance of proceeding with the erection of the
buildings necessary for the due accommodation of
the Natural History Collections, so soon as an
appeal can be made to the public for the necessary
funds with a reasonable prospect of success.”

On the motion of Professor Reynolds, seconded by Dr.
Balfour Stuart, it was resolved. That the Minute from the
Owens College be published in the Proceedings,

Ordinary Meeting, December 2nd, 1679.

R. Angus Smith, Ph.D., F,R.S., &c., in the Chair.

Professor Schoelemmer, F.R.S., translated a passage from
a drama by Christian Gryphius, entitled : ‘‘ Der deutschen
Sprache unterschiedne Alter und nacli und nach zuneh-
Eroceedings — Lit. & Phil. Soc. — Yol. XIX. — No. 5. — Session 1879-80.

44

mendes Wachsthum. Breslau, 1708/’ In this it is pointed
out that the German language would be held in much
higher estimation and more studied by foreigners if men of
science would write in their own language, as it was now
done in England. Every one wished to learn English since
a Boyle, Hook, Spraat, Backon, Brown, Simson, Plot,
Blunt, Gildrey, Sibhald, and many more ingenious men
investigated and elucidated the innermost secrets of Nature
in their own language.

‘^On a Peculiar Feature in the Water of the Well in,
Carisbrooke Castle, Isle of Weight,” by Harry Grimshaw,

F.C.S.

The sample of the above water was taken by me on April
19th, 1878, but was never opened or interfered with in any
way until the following September. The water when taken
was very bright and clear and free from sediment of any
description. It was totally devoid of odour and was of a
fresh and sparkling taste. The local features of the well
from which the water derives its origin are as follows : —
Carisbrooke Castle stands on a small isolated chalk hill, 239
feet above the level of the sea. The well is under cover in
the “well house,” and according to Jenkinson is 240 feet in
depth. It is perfectly free, even at the surface of the water,
from carbonic acid gas, or in fact of more than traces of any
other gas than atmospheric air, as a candle floating on th e
water burns freely.

The bottle containing the water was opened on the 1 2th
of September, and on doing so a very strong odour of
sulphuretted hydrogen was perceived, and on testing with
lead paper an equally strong reaction for that gas was
obtained. There was also apparent a slight sediment of a
white colour not originally seen in the water. The reaction
to litmus was perfectly neutral. The analytical data

45

obtained, which were all that was possible from the quantity
of water at command, were as follows :

Total Solid Matter. .42-00 grains per gallon (consisting of)

Mineral Matter 22*40 „ and

Volatile Matter 19-60 „

Total Hardness 12*30 ,,

Magnesia Hardness.. 1*70 „

Chlorine 4*50 ,,

The residue on heating blackened very much, and emitted
a very strong unpleasant odour like burning animal matter.

The peculiarity of this water is of course the production
of sulphuretted hydrogen, on standing for some time (in this
case for five months) out of contact with the atmosphere.
On leaving a small portion of the water in the bottle again
corked up for some time the presence of sulphuretted hydro-
gen was not exhibited. This production of sulphuretted
hydrogen proceeds undoubtedly from the reduction of the
sulphates contained in the water by the excess of organic
matter, and it is not unique in this instance, although it is
not a fact of very common occurrence. I regret very much
not having been able to bring back a sample large enough
to admit of a determination of the albumenoid ammonia,
and the nitrates and nitrites, as the quantity of these sub-
stances in a water of such a description would have been a
very interesting item in the case, as touching on a point of
great importance in pronouncing an opinion on the quality
of a water. It is very possible and even probable that some
chemists, given to judging for and against a water chiefly by
indications of a single description, to the comparative neglect
of many other analytical results, say by the amount of
albumenoid ammonia, might actually fail to condemn a water
such as the above ; for many chemists appear to consider
the ignition of the solid residue a comparatively unnecessary
detail ; and supposing even that the nitrates had been deter-
mined in this water, there are eminent chemists who have

46

considered the presence of nitrates in deep well waters, in
the chalk especially, as comparatively innoxious. The
Carisbrooke well, as I have said, is in the chalky strata, and
is 240 feet deep, and whether it contains nitrates or not, is,
in my opinion, on the results above detailed, a most unfit
water for potable purposes, and my reason [for bringing the
analysis of this water before the Society was to draw atten-
tion to the tendency often exhibited to draw the chief
inferences of the quality of drinking waters from what may
be called isolated reactions, without obtaining, or at all
events without giving weight to, other indications, chemical
and physical, which they exhibit.

“ Note on the Identity of the Spectra obtained from the
different Allotropic Forms of Carbon,” by Arthur Schus-
ter, Ph.D., F.KS., and H. E. Roscoe, LL.D,, F.KS.

Spectrum analysis serves as our most delicate test of the
chemical constituents of a substance. Hence it appeared
not uninteresting carefully to examine the nature of the
spectra obtained by the combustion of natural graphite and
of diamond in a vacuum of pure oxygen, and to compare
the spectra thus obtained with the well known spectrum
of carbonic oxide obtained from charcoal The preparation
of such an oxygen-vacuum which shall yield an oxygen
spectrum exhibiting no other lines than those of oxygen is
a matter of considerable difficulty. The slightest trace of any
impurity containing carbon produces the spectrum of car-
bonic oxide. For this reason the use of caoutchouc tubing*
and of greased stopcocks must altogether be avoided, and
thus the experimental difficulties are considerably enhanced.

In order to obtain a spectrum of pure oxygen entirely
free from the lines of carbonic oxide, a necessary preliminary
condition of our experiment, the following arrangement was

47

made. Fig. 1 exhibits the form of the tube i
employed, The part from A to B consists
of an ordinary Plucker’s tube. At the |
lower end of this a piece of hard glass
tubing (a) was sealed. Before the experi-
ment, the requisite quantity of permanga-
nate of potash or oxide of mercury was
brought into this to serve as the source of 1
the oxygen, and then the tube was sealed
at the lower end.

The other end of the Plucker’s tube
was closed by a ground glass stopper (S),
through the sides of which two stout
platinum wires were fused, and these
were joined together within the tube by a
spiral of fine platinum wire (e), into which
the graphite or the diamond was placed.

To prevent leakage between the ground
sides of the stopper and those of the tube
a drop of mercury, rendered less fluid by
the immersion in it of a bit of tin foil,
was introduced into the joint. The
tube was placed in connection with the
air-pump by means of a side tube sealed
on at (C). For this purpose a Sprengel
pump was used, to which the side-tube
was hermetically sealed. In this way and
in this way only was it found possible to
obtain a pure spectrum of oxygen. After
the connection with the pump had been made, the whole
tube was exhausted, and then the substance contained in the
hard glass tube was heated. The oxygen which is given off
was then removed by the pump, the tube filled a second
time with oxygen, this again removed, and this process
repeated over and over again, until at last no other lines
but those of oxygen are seen, when the spark from an
induction coil passes betweenThe electrodes {g and h).

48

When this stage had been reached, and when especially
no trace of the carbonic oxide bands could be seen in the
tube, the platinum spiral (e) containing either the diamond
or the graphite was rendered incandescent by means of an
electric current.

The spiral contained sometimes a piece of natural graph-
ite, sometimes a Cape diamond, but the result was the same
in the two cases. As soon as the platinum spiral had been
sufficiently heated, a channelled space spectrum appeared in
the capillary part of the tube. This channelled space spec-
trum was carefully compared with the spectrum of carbonic
oxide obtained from charcoal and found to be identical with
it. No band or line could be seen in the tubes thus pre-
pared which was not also seen in a tube containing carbonic
oxide. The spectrum which appears when a Leyden jar is
introduced into the circuit is different, but here also we
found that every line was due either to oxygen or to carbon.
Two lines were seen in the green and greenish yellow which
are not contained in any map of the spectrum of carbon or
of oxygen, lines which had not been seen in a great many
oxygen tubes prepared and examined by one of us. But it
was found on further investigation that these are really
oxygen lines, which only appeared at very high tempera-
tures. The capillary portion of the tubes we used were
much shorter than that in the ordinary Pliicker’s tubes, and
this accounts for the temperature of the incandescent as being
hi^ffier than usual. As one of the lines is near the unknown

O

aurora line, its wave length was determined and found to
be 5591, showing it to be decidedly less refrangible than the
aurora line.

The experiment was repeated in four different tubes and
many times in each tube ; but whether graphite or diamond

49

was employed, no line was seen which was not also obtained
in a tube of the same dimensions containing carbonic
oxide.

Captain Abney, E-.E., F.E.S., exhibited his photographs
of the ultra-red portions of the Solar Spectrum, and first of
all showed that the light transmitted by ordinary bromide
of silver was of an orange tint, showing absorption in the
lowest end of the spectrum. He then went on to explain
how he had tried to load the molecules comprising this
bromide of silver by means of gum resins, and that
he had thus been enabled to photograph slightly beyond
the lowest limit of the visible spectrum. Further re-
searches proved that bromide of silver could be prepared
in two molecular states, one that already shown, and the
other in which absorption takes place in the red as well as
in the blue. This was found sensitive to every radiation.
He pointed out that the blue form of the silver bromide
could be converted into the red form by simple friction, and
that after friction it was insensitive to the ultra red radiation.

Prof. Eoscoe here exhibited the different preparations
of gold in minute division made by Faraday himself,
some of which transmitted blue light and others red,
showing that at all events two cases of molecular condition
exist in the case of metallic gold.

Captain Abney then threw upon the screen photographs
of the prismatic spectrum, in one of which the lowest limit
of the prismatic spectrum was reached. He demonstrated
this on the black board, by setting up as ordinates the
wave lengths of the various portions of the photographs as
obtained from the photographs of the diffraction spectrum.

He then exhibited various photographs of the ultra-red
portion of the diffraction spectrum, extending from 7,600

to about 11,000. He stated that the photographs from
which he was making his final map were taken on double
the scale, with twice the amount of dispersion.

He then showed various prismatic spectra, exhibiting
difierent states of atmospheric absorption, in one of which
Piazzi Smyth’s rain band was markedly visible.

After a short discussion. Captain Abney exhibited some
photographs of the spectrum in natural colours.

51

Ordinary Meeting, December 16tb, 1879.

J. P. Joule, LL.D., D.C.L., F.RS., &c.. President, in the

Chair.

“ On a New Form of Marine Rain Gauge,” by W. J.
Black, Esq. Communicated by J. B. Dancer, F.R.A.S.

This marine rain-gauge for the collection and estimation
of rainfall at sea on board ship, is a cylindrical vessel, open
at the top and with a conical bottom, as in a wine bottle,
projecting upwards.

It is poised on an upright pivot, projecting into this from
the floor of the square box, that encloses it, which is made
large enough to allow of the swinging to and fro of the
gauge all round.

The gauge is thus preserved in a horizontal position in
all the rolling movements of a ship at sea, and it is further
secured from spinning round on its axis hy pins on opposite
sides, moving in slots fixed on the corresponding sides of the
box.

The gauge is formed of two parts, that fit into each other
half way down, the collector on the top, and the receiver for
the rain below, and each can be disconnected from the other
at pleasure.

At the bottom of the collector is a diaphragm perforated
with holes for the passage of the water into the receiver
below, which will also check evaporation of collected rain,
and prevent the upward splashing of the fluid by lurching
of the ship.

Proceedings— Lit, & Phid. Soc.— Vol, XIX.— No. 6. — Session 1879-SO.

52

From the bottom of the receiver is projected a right cone,
hollow from below, which constitutes its floor, so that the
rain collected in it will lie in the space between the cone
and the enclosing cylinder.

The gauge can be easily taken off the pivot out of the
box for the purpose of emptying its contents for measure-
ment and replaced by the pins sliding down the slots on
each side.

The box is square, and is broad enough and high enough
to allow of the swinging of the gauge, and is provided with
a lid on the open top, which secures the instrument from
injury, and will close any further use of the gauge.

The floor of the box is perforated with holes to permit of
the drainage of the rain falling down into it, and has handles
at the sides for carriage, and a canvas cover. The con-
tents of the receiver may be emptied, after disconnecting
the collector on the top, and measured by the usual glass
measure graduated to parts of inches of rainfall.

The box can be set down anywhere on the deck, as far as
possible out of reach of any sea-spray, or secured on the
bridge of steamers or the tops of sailing vessels, and left
there for the collection of rain.

In the event of the admission of sea-spray with the rain,
which is found uncommon in practice, it would be necessary
to take the specific gravity of the mixture in the glass
measure by the hydrometer, and thus find out the amount
of each.

This gauge has now been experimented upon in several
ships of the Royal Navy and Mercantile Marine, and found
to answer perfectly, and the results as far as ascertained
will be communicated.

The collection of rain at sea is found to be better carried
on on board steamers than sailing vessels, &c., as there is in
them less impediment by the sails, less rolling in motion,
and more independence of the wind. There is very little

apprehension of the sea water getting into it, as it can be
placed on the bridge, or on the top of the deck house, quite
free from spray, as is found in practice.

Abstract questions respecting the difficulties of correctly
ascertaining the rainfall at sea by reason of winds, course of
vessels, motion of ship, &c., may only be met by the answer
that all rain-gauges at sea must be placed under like con-
dition everywhere and at any time on board ship.

Some general idea of rain on the ocean could only be
gathered after at least 10 years’ continuous observations, as
the items of interest are few and far between, sometimes
many degrees of latitude and longitude apart.

It is found there is much less rain falling on the ocean
than is generally supposed, and that the quantity of fine
weather much exceeds that of stormy weather or wet
weather in long voyages.

The greatest quantity of rain falls along the equatorial
regions, the next in the tropical regions, while the intra
and extra tropical regions are unexpectedly much drier than
supposed. It will also be found there is much less rain
falling at sea than on land, which is naturally as it should
be, the warm ocean thus becoming the generator of the
vapours that finally get condensed on the cold mountains of
the land and descend to moisten the thirsty plains below.

Previous observations of rainfall at sea have been only
taken by counting wet days, hours, and minutes, as may be
seen in the meteorological returns of the Novara round the
world in 1857-59.

The following tables are statistical summaries of the
results of the observations taken by rain gauges on board
ship at sea for a period of about 5 years over the Atlantic,
Indian, Chinese, and Australian seas, but not on the
Pacific : —

54

Monthly Summaey. — Eainfall at Sea.

Jan.jFeb.|Mar.

Apr.

Mayi.

June

July|Aug.j

Sep.

Oct.j:

!7oT.|Dec.

Dot’ls

Dotal

Days

Foochoo

Rain

3-31

7-47

10-78

<D

Wet

Days

2

10

12

26

^ i

Rate
per diem

•734

•532'

•1361

•421

•659

1-20

1

•460 1

•410

•789

•397

•772

•134

-565

-135

M

Wet

Days

9

9

5 !

18

18

7

28

13

33

13

4

5

162

658

Equa-

Rain

Inches

6-61

4-80

•68

'7-59

11-87

8-42

12'88

5-34

26-05

5-16

3-09

•67

91-15 1

tor

Rain

Inches

1-50

3-06

4-23

15-36

13-69

5-51

2-18

9-20

6-86

•40

2-88

1-47

66-33

<i5

S-I

Wet

Days

8

11

14

25

25

25

13

35

14

1

6

2

182

787

South

Hemisphe;

Rate
per diem

•187

•278

•302

-614

-547

•220

•167

•262

•490

•400

•480

•735

•364

•092

Figi Is.
Rain

6-187

12-05

2*12

2-325

•40

•07

4-962

27-642

Wet

Days

17

16

10

6

1

2

13

65

134

Total

Rain

14-30

19-97

7-03

25-27

28-87

21 -4(

15-06

14-54

32-9

5-56

5-97

6-80

195-90

Total

Days

34

36

29

49

45

43

41

48

47

14

10

20

419

1605

Summary. — Kegional.

Total General 195 ‘902

Regions.

Totals .

.a

o.

xfl

g

©

w

.d

O

l^i

Temperate— W et
Dry

Tropical— Wet . .

Dry ..
Equatorial

a

in

a

©

.a

o

c/2

Tropical— Dry ..

Wet..
Temperate— Dry

Totals

Total N. & S. Hems. . .

Total Foochow & Figi.

.95-902

418

•692

•175

Rain

Rainy

Rate

Rate

Rate p.

Inches

Days

X Diem.

P Deg.

Tot. Day

91-15

162

•565

1-787

•137

16-55

37

0-45

1-38

06 .

7-635

26

0-29

0-36

CD 0

>, in

18-38

22

0-83

2-62

c3 ^
0 a
^ ft

6-88

12

0-57

1-71

>s

41-72

65

0-64

6-00

0 Cl

18-708

47

0-41

1-55

.

00 ID

!>• 0
0

23-94

44

0-54

2-98

o3 ^

16-97

59

0-28

0-84

C

^ p

eg

6-71

33

0-21

0-75

® p
en

66-33

182

•364

1-381

•084

157-480

344

•464

1-590

•110

38-422

74

•671

•240

Rate p.
100 Miles.

•m

I

o o

afrHp .
© • P.

3 iT’i’ '5;'

« -e S 03

rp c<i 9°
S T' o
lO (N .

lii 2 02 S

^ P.+3

3 © .?* ©

|i5 -tJ E> +3

a

K 3

44-25

Tnn^' I^atitude

50-56

•077 30-76

•095

39-77

87-64

40°— 51“
19“— 39°
12°— 18°
8°— 11°
1“— 7°

0“— 12°
13°— 20°

210—39“

40“— 48°

Days,

160

55

“ On Screw Propulsion/’ Part III., by Robert Rawson,
Assoc. I.N. A., Hon. Member of the Manchester Literary and
Philosophical Society, Member of the Mathematiccal Society.

On the Eesistence of the Element (a) to Angular and
Translatory Motion.

19. In the preliminary problem already discussed the
angular velocity (u) and the velocity (v) of translation along
the axis AB were assumed, without reference to the cause
by which these motions were produced and uniformly
maintained.

In this problem the only object of investigation was the
correct estimation of the velocity of the element {a) in its
normal direction when it was subject to a motion of rotation
and translation measured by (u) and {y) respectively.

For the solution of this problem it was not absolutely
necessary to enquire minutely into the cause by which the
motions of rotation and translation were produced, or, even
into the manner by which these motions are related to each
other during the time the cause of motion ds in full opera-
tion.

The application of the ordinary kinetic principles of the
resolution and decomposition of velocities was quite sufficient
for the purpose required in the problem, viz. to determine
the normal velocity of the element (a).

It is otherwise, however, when the cause of the motion of
rotation and translation is the subject of consideration. In
this case the application is required of other laws and
principles than those which were found adequate and
necessary in the solution of the preliminary problem.

56

20. The cause producing rota-
tion in the screw propeller is the
force of the engine which is
measured by a moment of force
(M), acting at H, a unit of distance
from the axis AB of the propeller.
Or, in other words, the force (M),
measured either in tons or in lbs.
avoirdupois, acting at the point
H in a direction perpendicular to the radius CP, must
balance exactly the force of the engines which are applied
to turn the screw round, and thereby to give motion to the
vessel.

To a given constant moment of force (M), applied through
the engines to give motion to the propeller in order to propel
a given vessel, there belongs necessarily a definite uniform
angular velocity (u) of the propeller, and, also, a definite
uniform velocity (y) of the vessel.

The determination of these velocities, in terms of the
moment (M), and the data supplied by the geometrical
form of the propeller, is the chief object of the following
investigation.

The case, then, to be considered here is, that in which the
acceleration, produced by the constant application of the
moment of force (M), has been entirely absorbed by the
resistance of the water in which the vessel is moving.

21. In accordance with the usual and well known theory
of plane areas striking fiuids with given velocities, it follows
that the normal pressure on the element {a) will vary in
proportion to the square of its normal velocity.

The normal pressure, therefore, on the element (a) is,
either

fxf^ruGOHv — vcosctj^a (17)

or, — (v - V)cosa}^a (18)

according as the propeller strikes the water when it is at
rest, or when it is in motion with a velocity V in the
direction of the vessel’s motion.

57

The constant fx can be determined by experiment only ;
it is the normal pressure when, and wcosv— 1,

upon the element (a).

22. The formulse (17) and (18) give therefore the normal
pressure on the element {a) in the two cases under con-
sideration.

This resultant pressure, however, remains to be decom-
posed, in the usual way, into three directions, viz. in the
direction of the axis AB, in the direction of the radius CP,
in the direction of a line at right angles to the plane AGP
respectively.

By the application of the principles of the decomposition
of forces the following equations readily obtain.

Pressure parallel to AB = Thrust.

= li[rueo^.v - {v- V)cos.a}^acos.a ...(19)
Pressure parallel to CP = ^{ri^cos.j/ - (v - V)cos.apacos./3 ...(20)
Pressure perp. to planeACB = fx^riceo^.v- (v - V)cos.apacos.j/ ...(21)

23. It may be observed with respect to the above three
pressures that each of them acts at the point P.

1st. The amount of pressure indicated by formula (19)
corresponding to each element of the screw popeller, must
be added together to balance the resistance to the vessel and
propeller.

If, therefore, this resistance, in accordance with the usual
theory, measured by v^, then it follows that

juV = /xS|mcos.v - (v- V)cos.a}^<xcos.a (22)

where jj} is the resistance of vessel and screw when moving
with a velocity unity; and, S signifies the sum of the quan-
tities

{rz^cos.v ~{v- V)cos.a}acos.a
for each point in the propeller blades.

2nd. The pressure indicated by formula (20) tends to
twist the axis of the propeller ; and must be counteracted
by an equal pressure from another blade placed in an oppo-
site direction to CP.

3rd. The pressure indicated by formula (21), correspond-
ing to each element of the propeller blades, must be added
together. Besides this force there is the skin resistance of

O

58

element (a); and, if this is considered to vary in proportion
to the square of the velocity of the rubbing surface it will
be measured by

jj," + y^sin^a + 2ruvco^pcoBa^a

(see Art. 8) where jj," is a constant to be determined by
experiment. It follows then that
M = jj.'Z^rttcos.v - {v - V)oos.a} Vcos.v

+ + 2rtwco^ycoBa + v^sin^aja

where S has a similar meaning to that which is given in
the first part of this article.

24. If, N—nv equations (22) and (23) admit of the fol-
lowing forms readily obtained.

(24)

Where, A2(r^cos^»/cosa)ct = (1 - ^^)E(rcosvcos^a)a

1

B2(?'^C0S^j/C0Sa)a = (1 - ?^)^.S(cos^a)a - -

And, M = i." I c(^y - 2d(~) + eI

J

(25)

Where, C = 2 { + juVsinV}a

D = 2{/i(l - :^)rcos^)/cosa - ju'Vcosj/cosa}a
E = S{ju(l - ^^)^cosvcos^a + ^''sinV } a

The quantities A, B, C, &c., are partly physical and partly
geometrical, whose values can be readily calculated by
integration over the surface of the propeller when jw, fj,",
and n are given quantities.

By solving (24) as a quadratic

w = v{k± - B) (26)

Substitute this value in (25) and it becomes

M = «/nC(A± v^A='-B)'‘-2D(A± Va^"B) + E} (27)

25. If (n) is regarded as a constant quantity for the same
ship and screw propeller, it follows from (26) that the ratio
of the sjpeed of the ship to the angular velocity of the
propeller is constant.

The data furnished by the trials of the “Iris” (see
Transactions of the Institution of Naval Architects for
1879) seem to confirm the truth of this inference.

The first series gives the following : —

59

Number of revolutions
Speed of ship

91-04

16-577

82-148

15-123

65-105

12-064

43-358

8-187

5-49

5-43

5-40

5-30

The remaining three series of experiments in the “ Iris ”
afford the same confirmation of this inference as that given
by the first series.

It follo’ws also from (27) that the resistance of ship
and propeller is proportional to the force of the engines to
turn the screw propeller.

The truth of this inference is strongly confirmed by the
following table given by Mr. Froude to show the manner
in which the indicated horse power is applied ‘4n the case
of the Merkara; but the table, mutatis mutandis, will
represent pretty nearly their relative values in other ships”
(see Transactions of the Institution of Naval Architects
1876, page 175, fig. 7 plate XI) : —

Speed of ship in
knots per hour.

H.P. friction of
unloaded engine.

H.P. friction of
loaded engine.

H.P. air and
feed pumps.

H.P. friction of
screw.

H.P. augment of
resistance.

H.P. net re-
sistance.

H.P. indicated
(Total).

H.P. friction of
engine, or sum
of A, B, C.

H.P. available to
turn screw.

Values of
/ G^K \

V speed 2/ |

A

B

c

Gr

K

a-K

D

3

84

6

10

6

20

34

160

100

60

6-6

4

100

10

15

10

30

65

230

125

105

6-6

5

117

18

20

15

45

95

310

155

155

6-2

6

160

. 30

30

22

60

133

435

220

215

6-0

7

180

45

45

30

90

190

580

270

310

6-3

8

225

85

60

40

110

255

775

370

405

6-3

9

265

140

90

50

150

340

1025

495

530

6-6

10

290

185

110

65

195

485

1330

585

745

7-4

11

310

260

160

76

264

680

1750

730

1020

8-4

12

335

325

180

90

400

990

2320

840

1480

10-3

60

The column D should be constant in accordance with
the above inference. It is nearly so, and the slight deviation
in the higher speeds may possibly arise from a slight increase
in the friction of the engine, or, a slight error in the approxi-
mate estimation of the above causes of resistances.

Another inference of importance readily follows from
formula (27) viz. that the best ^ro'peller for one ship is not
generally the best propeller for another ship. The force of
this inference is apparent from the circumstance that the
form and dimensions of the best propeller depend upon the
values of fx, y', p", n, which are generally different for different
ships.

26. Professor Osborne Keynolds, in his interesting com-
munication to the I. of N. Architects, 1876, has suggested
the existence, in the wake area of a ship, of a variable velocity
which increases considerably, when accounted for, the diffi"
culty of integrating the values of the forces in (19), (20),
(21) ; and, he applies this variability in the wake velocity
to the explanation of the propeller’s tendency to cause
vibrations in the ship. It is not, however, easy to see how
this effect is produced by the cause assigned, inasmuch as
the force which tends to twist the axis is a factor of cos.j3,
a quantity which vanishes in conoidal surfaces, particular
forms of which are used as propellers in Her Majesty’s navy.

A problem, however, of some interest and difficulty pre-
sents itself in formula (27), viz., required the form of pro-
peller so as to make the coefficient of a minimum for a
given value of engine power ?

A somewhat similar problem to the above occupied the
attention of the early writers on the calculus of variations.
Newton and others sought the form of the lines of a vessel
of minimum resistance; but the limited success, even of
Newton’s solution, to practical shipbuilding does not afford
much encouragement in a similar attempt, by means of the
same calculus, to solve the problem of the screw propeller.

G1

On the Anal Respiration of the Copepoda/’ by Makcus
M. Hartog, MA., B.Sc., F.L.S.

In a note on Cyclops read at the British Association I
pointed out that its respiration was exclusively anal. I
have now made out the same in Canthocamptus (fam. Har-
pacticidce), and Diaptomus (fam. Calanidce). In all three
the mechanism is the same; at regular intervals, after
the backward sway of the intestine, the anal valves
open for an instant and then close, giving just time for
a slight indraught of water after the opening, a slight
expulsion at the close. The necessary pressure to con-
fine the animal seems to interfere somewhat with these
movements, sometimes stopping them if excessive ; hence I
refrain from noting with illusory exactness the intervals
between each respiratory movement.

It is to be noticed that the rectum contains as a rule
liquid only, the bolus of faeces remaining in it but a short
time. By endosmose the liquid in the rectum will tend to
be at the same condition of gaseous saturation as the body
fluid around it, kept constantly agitated by the backwards
and forwards sway of the stomach. During the short inter-
val that the anus is open an approach to gaseous equilibrium
with the external water takes place, even despite the very
slight movement of the water (shown by the little change
of place undergone by suspended indigo or carmine particles).
In the absence of any other suitable respiratory apparatus,
no one can hesitate as to the function of the action I have
described.

In the Nauplius larvae of Cyclops and Diaptomus the
working is slightly different. The rectum is a subspherical
muscular sac, which at regular intervals contracts so as to
leave a linear cavity (along the long axis of the animal),
and immediately dilates, sucking up the water from
without

(32

An anal respiration, such as that of Cyclops, is found
widely among Crustacea— QY&n. those which have well
developed gills like Astacus, which is one of the highest
forms. It has been demonstrated in Phyllopoda and Glado-
cera, and is here probably the exclusive mode in Leptodora,
as shown by Weismann. That it is therefore primitive,
and should be expected to occur in the primitive or at least
very generalised group of the Copepoda, is an obvious
deduction. Hence I anticipate that the homoeomorphic
zooea larvae of the Decapoda will prove to have this same
mode of respiration.

If there be any connection between Kotifers and Nauplius,
it is easy to make out the origin of the arrangement in the
latter. The ciliated funnels and lateral canals of the former
can only be of service when there is a thin unchitinised
anterior surface through which water can transude into the
coelom : by the extension of chitinisation over the whole
surface these organs lose their function and abort, while the
cloacal contractile vesicle ” takes on an inspiratory as well
as an expiratory function, and becomes more or less con-
founded with the rectum, from which probably, even in
Rotifers, it takes origin.

Here must be noticed the wide diffusion of anal respiration
in aquatic Insect larvse, (alternate inspiration and expiration
by the pumping movements of the rectum). This would
point to a common origin with Crustacea.

A list of the groups in which anal respiration is made out
may be added.

Vermes :

Roiifera.

Gepliyrea.

Oligochoeto Limicola.

Ecldnodermata.

Ilolothuroidia.

Arthropoda.

Crustacea (general).

Insecta (most aquatic larvse)*

63

General Meeting, December 30th, 1879.

J. P. Joule, D.C.L., LL.D., F.RS., &c., President, in the

Chair.

Mr. Thomas Ward, Brookfield House, Northwich, and
Mr. J ohn Bell Millar, B.E., Assistant Lecturer in Engineer-
ing, Owens College, were elected Ordinary Members of the
Society.

Ordinary Meeting, January 13th, 1880.

J. P. Joule, D.C.L., LL.D., F.B.S., &c.. President, in the

Chair.

The Badiograph,’’ by D. WiNSTANLEY, F.B.A.S.

I have described already one of the several arrangements
which I have devised for the automatic registration of the
solar radiance.* The instrument in question places a lead
pencil on a sheet of paper and writes down therewith when,
and for how long, the sun may chance to shine, but it makes
no record of th.e intensity of his rays. I will now ask your
attention to the description of another and much more per-
fect apparatus, one which continuously records the inten-
sity of thermal radiation to which it is exposed. This
instrument I have called the ‘"radiograph.” It consists
essentially as follows : — A difierential thermometer of which
the stem is circularly curved is mounted concentrically
upon a wheel of brass in a groove cut with that object for
* Proceedings of Manchester Lit. and Phil. Soc., Nov. 18th, 1879.

Peoceedings — Lit, & Phil. Soc.. — Vol. XIX. — No. 7. — Session 1879-80.

64

its end. This wheel is supported with its plane in a per-
pendicular position by a knife edge of hardened steel which
passes through its geometric centre and rests on agate
planes. The tube of the thermometer is partly filled with
mercury — preferably through half its curve — and for the
reason given in my description of the simple sunshine
recorder, to which I have alluded, a little sulphuric acid is
introduced as well. If we now arrange it that the centre
of gravity of the solid portion of the system here described
shall be below the surface of the planes on which it turns
(and the apparatus is provided with adjustments by means
of which the point in question can be moved) it is clear
that the arrangement may be made to swing in pendulous
oscillations, notwithstanding the presence of the liquids it
contains, for these remain substantially at rest whilst the
tube which holds them does, in fact, slide over them (and
with very little friction too) in swinging to and fro through
arcs of the circles of which its parts are curves. Both bulbs
of the thermometer are closed. It is obvious therefore that
the tension of the air or gas which they contain will be
uninfluenced by the barometric variations of the outer air,
the temperature of which latter being experienced equally
in each bulb will also leave the equilibrium of the apparatus
undisturbed. When however one bulb is more heated than
the other, the air contained therein will press more strongly
on the heavy liquid piston in the tube and wheel the swing-
ing portion of the system round until a fresh position of
equilibrium is gained, and this will be (providing that the
centre of gravity of the system has previously been made
coincident with the point on which it turns) when the ten-
sion of the gases is equal in both bulbs. In fact, in so far
as now described, tlie instrument is a differential thermo-
meter, and is that alone, differing in this from Leslie’s, that
it is a solid and accessible portion of the thing which moves,
and not the liquid it contains. When however one of the

65

bulbs is blacked and the other one is silvered or left clear,
the apparatus becomes a radiometer” in the proper mean-
ing of the term,^ that is to say, a measurer of the thermal
radiance to which it is exposed and the intensity of which
it indicates by variations in the angular positions of a needle
prolonged from one or other of the radii of the wheel.

It is only needful now to so arrange it that this needle
shall make a tracing of its curves on a cylinder driven by
clockwork at an even speed, and the “ radiograph” is com-
plete.

Concerning the actual instrument I use, its wheel is 7'3
inches in diameter, and the weight thereof a trifle more than
two pounds. The other portions of the apparatus are of
the same dimensional proportions as are indicated in the
sketch. Of course some delicate method of recording has
to be employed, and I have thus far used the smoked paper
process so much adopted in the observatories of France. In
this way the radiograms” which illustrate this paper were
obtained.

When using the instrument to record the radiance of the
sun I have hitherto exposed it in a box of copper sur-
mounted by a dome of glass into which the bulbs of the
thermometer project. The line which joins them is in the
plane of the meridian of the place and the black bulb to the
north. The box itself is supported at an elevation of four
feet or thereabouts upon a stand of wood, the legs of which
are firmly embedded in the ground. The stand itself is
located at the extremity of a garden which overlooks a
valley and the sea. A small window in the box permits
the movements of the train to be seen and the promptness
with which the apparatus acts to be observed. If a cloud
‘‘ no bigger than a man’s hand,” and “ light as a feather” in

* The radiometer” of Crookes should in its simple form have been
called a “radioscope,” as it merely makes visible the elfects of radiance,
but does not measure their amount.

66

its texture, floats before the sun, and occupies but three or
four seconds in its transit, its presence, the duration ot
its passage, and the degree of thermal obscuration it eflects
are at once set down.

The cylinder of the radiograph passes over a space of
•875 of an inch per hour, a somewhat open range, but, as
will be seen on reference to the tracings, the needle often
moves for some considerable distance in both directions
along the same thin line, thereby showing a practical
instantaniety of action under very ordinary thermal changes
in the radiance from the sky. The influence of the sun’s rays
at daybreak is almost always shown, for some minutes at any
rate,'before the sun himself is seen, and occasionally it would
seem even for hours before his time to rise.

It is not, however, now my purpose to dwell upon the
interesting changes which take place in the intensity of the
thermal radiance from the sky, my present object being
to describe an instrument by means of which they may be
recorded or observed. Doubtless in several of its details
the ‘D’adiograph” may be improved, notably in the condition
of its bulbs, and it would unquestionably be better if it
computed for itself the areas included by its curves. This,
I dare say, I shall presently enable it to do. Meanwhile, as
a recorder of the duration and intensity of radiant heat the
instrument, so far as I have seen, is the only one whose
readings are uninfluenced by the temperature or the pres-
sure of the air.

67

MICEOSCOPICAL AND NATUEAL HISTOEY SECTION.

December 8th, 1879.

A. Beothees, F.B.A.S., in the Chair.

Mr. Herbert William Brockbank, of Manchester; Mr.
John Aitken, of Urmston; Mr. Peter G. Cunliffe, of Hand-
forth ; and Mr. William Ward, of Burlington Street, Man-
chester, were elected Associates of the Section.

Mr. Chaeles Bailey exhibited a simple form of live
box, which had been devised by Mr. Charles Botterill, of
Liverpool, and which was likely to prove very useful to
investigators who required to keep the objects examined
under prolonged observation. It was suggested that a
couple of small clips to keep the upper glass fixed would
add to its convenience.

Mr. H. A. Huest exhibited fruiting specimens of the rare
Ambrosinia Barsii (Linn.), from Algiers, and read some notes
thereon. Lindley classed it with the Lemnacese, but it is
an undoubted Aroid.

Mr. Hurst also read a paper “ On the Protective Mimicry
of Serpents exhibited by several of the Aroideae.”

January 19th, 1880.

Chaeles Bailey, F.L.S., President of the Section, in the

Chair.

Mr. Edward Paul Quinn, of 137, By dal Mount, Manches-
ter, was elected an Associate of the Section.

Mr. James Cosmo Melvill, M.A., F.L.S., read an account
of the occurrence of Silene Gallica (L.) and its sub-species
in Jersey. He mentioned that it was the first recorded

69

instance of the typical S. gallica (L) occurring within the
limits usually assigned to the British Islands, if we except
the recorded discovery of Dr. Bromfield in the Isle of Wight,
many years ago, and never verified. He exhibited speci-
mens of the five sub-species collected by himself at Gallows
Hill, St. Helier’s, Jersey, in June, 1879, and showed how
that they were all certainly forms of one Protean plant, to
which the term S. Gallica (L.) ought to be applied.

The forms were as follow : —

(I.) S. Gallica (L.) Stem erect ; branches not spreading, but
ascending ; racemes somewhat dense ; Lamina of petals
obovate ; roundish ; large j entirely white ; hairs of
calyx appressed ; fruit erect or patent.

(II.) S. Gallica-rosea, as the above, but petals rose-coloured.
(S. Silvestris, Schott.)

(HI.) S. Quinque-vulnera (L.) Petals white, with blood-red
disk. The common form in Jersey.

(IV.) S. Anglica Quinque-vulnera. Petals coloured as in No.
III., but of the form and size of No. V. ; plant erect,
ascending as in Nos. I. — III.

(V.) S. Anglica (L.) Stem somewhat flexuous ; branches
spreading ; racemes not so dense as in S. Gallica ;
Lamina of the petals elliptical, somewhat jagged ; very
small ; calyx with long hairs ; fruit reflexed.

Mr. J. C. Melvill also exhibited specimens of Briza maxima
(L.), a South European and Mediterranean grass, commonly
called Large Quaking Grass, which was very rapidly spread-
ing all over J ersey. He pointed out that it was both in
Europe, the Canary Isles, and America, associated with two
other grasses that have long been known as natives of Jer-
sey, Bromus maximus, and Cynosurus echinatus (L.). The
late Dr. M. M. Bull, of St. Helier’s, informed him that he had
first noticed it about the year 1872 in S. Saviour’s parish,
but that soon he expected it would overrun the island. It
had not yet been noticed in the other Channel Islands.

70

Bog Butter {Butyrellite), from Co. Galway, Ireland."

Mr. John Plant, F.G.S., exhibited a piece of a mineral
resin familiarly known in the west of Ireland as Bog Butter.
The lump weighed exactly I4oz. It came from a good depth
in a bog in County Galway. A few years ago, when in that
part of Ireland, he had been unsuccessful in meeting with a
sample of this curious substance, although he was informed
that it was not unfrequently met with by the turfcutters
during each summer. He heard of its origin and of some of
the uses to which it was said to be put by the poor people
if they got any of it, from a farmer at Killkee, but he could
hardly credit the statement that in hard times it was
melted down and actually used as a dripping to the pota-
toes; he rather concluded that the greasing was limited to
the axles of the potatoe cart. The Irish have a widespread
belief that bog butter was hidden by the fairies [in the bogs
long ages ago ; and it is affirmed that the butter is some-
times found in small wooden kegs in bogs along the coast
These kegs they say have been hastily buried by smugglers
running a cargo of contraband, though when bog butter was
declared an illegal article of trade in Ireland they are unable
to say. Unfortunately, Mr. Plant was not shown a keg, or
even the staver of a keg, but he was informed that speci-
mens of veritable kegs of bog butter are to be seen in the
Museum of the Royal Irish Academy and in the museums
at Edinburgh. The fairy origin of the bog butter he thought
mio[ht be ascribed to the active imagination of the Celtic
brain, many of the inexplicable things in nature being
readily put down to the good or evil doings of the indigenous
fairies of Erin.

By the aid of scientific analysis the substance called bog
butter can be shown to be a perfectly natural production
arising from the decomposition of the vegetable matters
forming the peat or bog, and to belong to the numerous
family of mineral resins, or hydrocarbon compounds, of
which Dana describes the composition of seventy species.*

* Dana, System of Mineralogy 5th edit., 1875, pp. 720 — 760.

71

Many of these are very well known under the names of
marsh gas, petroleum, ozocerite, asphaltum, naphtha, par-
affin, bitumen, amber, torbanite, coal, and its vaiieties.

Some of these singular minerals a.re obtained only from
bogs and peat beds.

Some time ago Mr. Plant showed to the Section a quan-
tity of one of these resinous minerals, which occurred under
the bark of pine logs found in a moss at Handforth by Mr.
P. G. Cunliffe. It proved to be known in Germany as
Fichtelite, but had not before been known to occur in Great
Britain. Afterwards it was found in pine logs in the peat
on Lindow Common. A waxy, greasy, or butter-like
character is distinctive of these bog products. The one now
exhibited was described first by Brazier in 1 825, and was
analysed by Williamson in 1815, its composition being

given as

Carbon 73'78

Hydrogen 12-50

Oxygen 13-72

When fresh from the bog it is soft and like butter, but
hardens in drying. The mass is dirty and bogstained on
the outside, but inside pure white and free from impurities.
It melts at 50° C., and becomes a yellow greasy resin,
dissolves in alcohol or in ether, and then crystallizes in
beautiful needles. When heated it gives off a peculiar
odour like acroline. By saponification with potash it yields
an acid which Brazier proves to have a composition similar
to palmitic acid.

There is a mineral waxy resin called Guyaquillite, which
is found in extensive deposits in the marshy plains near
Guyaquil, in South America, which has a similar composi-
tion to bog butter.

Johnson gives it as —

Carbon 76-67

Hydrogen 8-17

Oxygen 15-16

It has been proved that the slow decomposition or change
in the vegetable peat or moss will pi-oduce elements of
which these hydrocarbons are made.

72

PHYSICAL AND MATHEMATICAL SECTION.

January 20tli, 1880.

E. W. Binney, F.R.S., F.G.S., President of the Section,

in the Chair.

On the Rainfall adjacent to the Sweetloves Reservoir,
Sharpies, for 1879,” by Rev. Thos. Mackebeth, F.R.A.S.,

F.M.S.

The following rainfall observations for the past year
have been made at a station which is 481 feet above the
sea level, and on the southern slope of one of the several
spurs of the Pennine chain that take a south-westerly
direction. There are no less than seven rain gauges kept
within a radius of three miles of my station. Two of them
may be said to be in the town of Bolton itself, and of the
other five two are on the slope on which my gauge is
stationed, but from one to two miles west of me. The other
three gauges are situated on a spur still further west, at the
head of which stands Rivington Pike. But Belmont stands
at the head of the spur on which I am situated. I have
named the positions of these various gauges because I find
no rule to ascertain any ratio of the relative amount of rain
that may fall respectively into them. Sometimes a larger
amount of rain falls in a gauge at a lower station than at
a higher one, and at another time the reverse takes place.
And this irregularity occurs too in guages respectively east
or west of each other. Up to the end of 1877 a gauge was
kept at Belmont at a height above the sea of 800 feet. It
may be there yet for anything I know, but I can find no
records of it after 1877. I have the records of that gauge
for thirteen years, and in every insta.nce they far exceed,

73

with an almost constant ratio, the amount of rainfall regis-
tered in any of the other gauges to which I have referred.
There is some reason for this regularity, as well as for the
irregularity observed in the other gauges. It is an interest-
ing enquiry to which I intend to devote myself, in the hope
sooner or later to find a solution of the problem. I have
good reason for thinking that the irregularity is due to the
irregular surface of the country. When the late Mr. Vernon
made his observations at Old Trafford, and mine were
proceeding at Eccles, I could almost predict the amount of
rain that would fall in a given month at his station, as he
could at mine. The ground between the two stations was
practically level, and though the gauges were between three
and four miles apart, the rainfall at the two stations was
practically the same.

The following table shows the results obtained from a
rain guage with a 5in. receiver placed 22in. above the
ground at this station : — •

Days of
Rainfall
for each
Quarter.

1879.

Fall

in

Inches.

Ditto in
Quarterly
Periods.

(

January

£•342

50 ]

February

4-407

[ 9-435

t

Marcb

2-686

)

r

April

2-367

57 ]

May

2-628

[ 13-507

June

8-512

3

(

8-450

>

65 ]

August

10-630

V 23-034

1

September

3‘954

3

C

October

4-954

39 ]

November

1-604

V 10 797

1

December

4-239

3

211

56-773

56-773

There can be no doubt that similar rainfall facts to those
presented in the quarterly columns of the foregoing table
have occurred throughout the country. That being so, it is
clear that our crops, instead of being ripened by heat, Avere

74

more than deluged in rain. August, which is usually the
warmest month, experienced scarcely anything hut a con-
stant downpour of the heaviest rain. October is usually
the wettest month of the year, but this year August has
frightfully eclipsed it.

“A Curious Rainbow,” by E. W. Binney, F.KS., F.G.S.

On the 23rd of November last, at 12.45 p.m., I was on
Douglas Head, in the Isle of Man. The sky was pretty free
from cloud, except a slight cirrus overhead, the cirri
running from north to south, and the sun shining. Looking
southwards I noticed an inverted rainbow in the cloud at
at an angle of 75° with the horizon, making an arc of about
80°. No other rainbow was visible at the time. I observed
it for thirty minutes, when it gradually disappeared. The
sea in the direction of the inverted rainbow would be about
twelve miles distant. I did not observe that the colours
were inverted as well as the bow, but a party who saw it
stated that he distinctly noticed that they were. The
accompanying rough sketch will show the form of the bow.

75

Ordinary Meeting, January 27th, 1880.

E. W. Binney, F.R.S., F.G.S., Vice-President, in the Chair.

‘'On Epidemic Cycles,” by Arthur Ransome, M.A.,
M.D.

It is somewhat remarkable that amongst the many obser-
vations made by the older writers upon the subject of
epidemic diseases, no note appears to have been taken of
their recurrence in regular cycles of years.

From the time of Hippocrates, and probably even before
his epoch, much importance was ascribed to the rising and
setting of certain stars, to the occurrence of comets, and
even to eclipses of the sun and moon, and innumerable
allusions are to be found to the influence of the seasons,
and to variations in the atmospheric elements ; but most
of these circumstances are noticed rather with the view of
accounting for their irregular appearance than with the
object of showing that they observe regular periods.

The Karadraaig Xoi/xo)Sr)g of certain years is indeed pointed
out, and the rise and fall of certain epidemics at the several
seasons is marked with marvellous accuracy, but it does not
appear that any one observed their tendency to recur after
the lapse of a certain, often very deflnite, term of years.

At first glance it appears strange that such an important
phenomenon as this should have escaped the notice of such
keen observers as many of the early physicians certainly
were.

We can hardly doubt that such diseases as small-pox,
measles, scarlet fever, and wliooping-cough did actually
appear in other countries with at least as much regularity
as we shall presently find they did in Sweden. The plague
also, if we may judge from the records given by Dr. Guy
PiiocEEDiNGS — Lit. & Phil. Soc. — Vol. XIX. — No. 8, — Session 1879-80.

76

(Public Health, p. 87) appears to have observed approxi-
mately a ten or fifteen years’ period. But a little closer
examination will probably account for the neglect to notice
the recurrence of these events. The life of any one physician
would be too short to admit of the observation of more than
four or five such visitations, and he might well be excused
if he hesitated to draw any conclusion from so small a basis.

Intercommunication between medical men was also more
difficult than it has become now-a-days.

No numerical records of the causes of death were then
kept for subsequent scrutiny, and it is probable that many
of the less fatal forms of these diseases would pass through
a nation without much notice.

Even when there is a registration of sickness as well as
of deaths it does not always prove possible to mark the
occurrence of an epidemic period. Quite recently, in 1868,
Dr. Ballard, in an analysis of records of sickness kept in
Islington for 12 years, was unable to find any indication of
the cyclical recurrence of whooping cough, though he
assigns a period of two years to measles, and four to scarlet
fever.

It was, however, this disease, whooping cough, that first
impressed upon my mind the fact that epidemic cycles do
exist.

From the returns of sickness published every week by
the Manchester and Salford Sanitary Association from the
year 1860, it was evident that whooping cough tended to
reappear biennially. Every second year the curve of this
disease rose in the colder months of the year — in most
cases epidemically. The rise and fall of the wave is almost
perfectly regular. I have constructed a diagram that
displays its course graphically, and it will be seen from
this that whilst there are comparatively few cases in the
winters of 1860, ’62, ’64, ’66, ’68, ’70, ’72, ’74, ’76, and ’78,
in the cold seasons of the intervening years tliere was

77

always an increase in the number of persons affected. It
is evident therefore that the complaint has a true two years’
cycle.

I have noted the same regularity in returns of the
disease made in St. Marylehone, London, by Dr. Whitmore.

In the same returns of disease there are indications of
the observance of regular periods by other epidemic
diseases, but the records as yet extend over too brief a
time to show the fact with certainty.

The Registrar General’s returns of deaths also present
some evidence of a rhythmical succession of epidemics of
such diseases as small-pox, scarlet fever, measles, and
whooping cough ; but the causes of death have only been
given to the public since 1848.

Dr. Farr kindly sent me further returns for the five years
1838 to 1842, but, even with this addition, the area of
observation is too short to permit of a satisfactory
generalisation. I have, however, traced out diagrams
giving the information to be gathered from these sources.

But in Mr. Simon’s admirable papers relating to the
History and Practice of Yaccination, presented to the
General Board of Health in 1857, there is a diagram
(which I have copied and placed before you) showing the
small-pox death rates in the kingdom of Sweden for 100
years — from 1749 to 1849, inclusive.^'

This diagram, though it is only used by Mr. Simon as an
evidence of the protective influence of vaccination, shows
distinctly the regularity of the small-pox cycle up to the
year 1800, when vaccination was fully carried out.

A period of 100 years gives a fair basis for an indication.
It therefore occurred to me to enquire from Dr. Farr from

^Although it is beside my present purpose, may I say incidentally
that the chart in question proves to demonstration the wonderful pro-
tective power of thorough vaccination, and that I cannot understand
how any one with this evidence before him can for a moment doubt its
beneficent operation.

what source the Swedish records of small-pox’ were drawn,
and whether similar tables could not be obtained for other
diseases.

Dr. Farr, with his usual kindness, put me into communi-
cation with Dr. Berg of Stockholm, who then had charge of
the Government department of the registration of deaths,
and he at once sent me a list of the annual death-rates
throughout Sweden since the year 1774, pa^rticularizing the
mortality from scarlet fever, measles and whooping cough.

Dr. Berg accompanied the returns with a letter, which is
appended to this paper, in which he pointed out the
possibility of error in diagnosis having been made by the
earlier Swedish ecclesiastical registrars in the country.
In this caution, however, I tliink he does less than justice
to those observers. The tables contain internal evidence of
accuracy in the characteristic peculiarities of the course of
each disease, and they bear ample witness to the fact of the
regular succession of epidemics in distinct cyclical periods.

I have thrown these tables into the form of diagrams,
and have supplemented them by similar charts drawn from
the Begistrar General’s returns, and calculated so as to
afford a means of comparing the two series of statistics.

The details of these charts will be more closely studied
presently, but in the meantime it may be sufficient to
point out that whooping cough has a cycle of about four
years, that before the introduction of vaccination,

constantly i-e-appeared as an epidemic about every five or
six }mars, that measles prevailed on an average about every
seven years, and that scarlet fever had an extended period
of fifteen to twenty years between the great visitations of
this disease, with lesser undulations of three or four years.

I venture to bring these charts before the notice of
this Society (1) because I believe they are unique in
their kind, and (2) because they afford ground for a dis-
cussion of the probable causes of the remarkable regularity
of epidemic cycles.

79

It is indeed unnecessary, with these charts before us, to
enter into evidence to prove the existence of periodic times
in epidemics, and we may perhaps be allowed at once to
pass on to the modes in which such phenomena may be
supposed to be brought about.

1. It is natural in the first instance to attempt to connect
the epidemic cycle with some other coincident recurrent
events. As Prof. ''Jevons says, in speaking of the principle
of forced vibrations (Principles of Science, vol. ii., page 66),
“ Whenever we find two phenomena which do proceed,
time after time, through changes of exactly the same
period, there is much probability that they are connected.”

I have already pointed out in several papers that there
is undoubtedly some favouring influence exerted by seasons
upon the different epidemics. Even in non-epidemic years
there is an evident tendency for these complaints to rise
at that season in which other affections of the organs most

attacked by the special epidemic disease are most common.

Whooping cough and measles in the winter and spring,
scarlet fever in the autumn, when sore throat is most com-
mon, continued fever also towards autumn, when derangfe-
ment of the liver and bowels are frequent.

But it is impossible to discover any ordinary recurrent
meteorological element that will account for the cycles of
any one of these disorders. Atmospheric changes recur an-
nually, but epidemics come every two, four, six, or more
years.

There is indeed one interval that might possibly ha,ve
some influence either directly or indirectly upon measles,
small-pox, or scarlet fever that have an approximate five or
six year period, and this is the well-known sun-spot period
of astronomers.

I have obtained from different sources records of these
occurrences since the year 177*3, and have drawn out
charts of the periods in a fashion similar to that adopted

80

for showing the prevalence of disease, and upon the same
scale. An alteration in the extent of this scale is neces-
sary in the year 1826, as the early observations are much
less minute than those after this date, and include a smaller
number of spots. Both series will suffice for the purpose
of comparison with the mortality periods.

I must say at once, however, that I have been unable to
discover any definite relation between them.

In the case of scarlet fever, there are truly some very
curious coincidences between the rise and fall of the
disease, along with the number of new spots appearing on
the sun, notably in 1848, 1856, 1859, 1867, and 1870 (see
diagram), but a little further scrutiny will show that at other
times, as in 1843, 1850, 1854, and 1860, the extreme height
of the disease corresponds with a low sun-spot period,
and vice versa.

2. In speaking of possible cosmical causes, it is right
also to mention the theory of pandemic waves, originated
by Dr. Lawson, Deputy Inspector General of Army Hos-
pitals.

He believes that there exist world- wide influences afiecting
epidemics — influences that coincide in some way with the
isoclinal magnetic lines ; and from observations upon
diseases in the army, he endeavours to show that there is
a law by which “ a series of morbific causes originate, or at
all events become apparent, in the southern hemisphere,
and are propagated from that to the northern with great
regularity.” “These waves occupy about two years in
passing over a given station, the mortality from fevers and
other epidemics increasing during their passage, and sub-
siding again as they move onwards.” (Trans. Epidem. Soc.,
vol. ii., p. 95.) I do not now offer any opinion upon the
value of this hypothesis, but I may point out that it can
have very little bearing upon the question now before us.
It regards rather the rate of progress and the geographical

81

distribution of disease than its periodical return, and the
only disease, whooping cough, that from our data has a
two years’ cycle is not included in Dr. Lawson’s observa-
tions.

3. It has been suggested as an explanation of the
recurrence of epidemics after a certain period that only
certain years of life are prone to the disease, and that
when these have been cleared away the disease could not
prevail extensively until there were again persons of fit
age to receive the poison.

This simple “ age ” theory will, however, be found to
involve two important assumptions, in order to account for
cycles of several years’ interval. 1. It will be necessary
that the epidemic should in the first instance be capable of
only attacking persons at the superior limit of age suscep-
tibility. In the case of whooping cough at the age of two
years, and in the case of the other complaints at four, six,
or seven years of age ; and 2, that it should then travel
down to the lower ages, and so clear out of the way all
persons capable of taking the disease that the complaint
could not again appear until the most sensitive superior
limit was again attained.

I need hardly say that neither of these assumptions is
borne out by actual experience during an outbreak of
epidemic disease. Children of all ages take the complaint
both at the commencement and end of the epidemic.

If therefore age alone were the determining element, an
infectious complaint would be continuous, and not inter-
mittent in its ravages.

Owing to the constant occurrence of fresh births in a
population, there must always be present in it children of
fit age to receive the virus ; there is always food upon which
it is able to flourish. The disease would only be periodic
if the birth-rate were also periodic in its character.

4. A fourth possible explanation of epidemic cycles might

82

perhaps be found in Dr. Farr’s observations on the form of
the epidemic wave and its probable cause.

In the year 1865 Dr. Farr showed that the curve traced by
the course of the cattle plague was remarkably regular, and
that other epidemics showed traces of a similar formation. It
proceeded by continually decreasing increments from the first
week to the last, and by noting the rate of diminution of
the growing power of the disease in its first stages, Dr. Farr
believed that it was quite possible to foretell its probable
course and ultimate decline. He was actually able to do
this for the rinderpest, and his forecast of the mode in v>^hich
the disease would work itself out was proved to be singularly
correct by the result, tie accounted for this curve by the
hypothesis that the poison of the disease was itself so
diluted by successive transmissions through the bodies of
its victims that it became gradually less and less able to
propagate the complaint.

This hypothesis was supported by the history of most
epidemics, by the shape of the curve it describes, by the
fact of its greater fatality at the commencement of the out-
break, and by the observation that the longer the disease
was absent from the community, the greater was its viru-
lence when it did recur.

This theory would certainly account for most of these
phenomena, though they are also susceptible of a simpler
explanation, which I ventured to give in a paper “ on epi-
demics studied by means of statistics of disease,” which
was read before the Oxford Meeting of the British Medical
Association in 1868.

It is to be remarked also that no explanation is given by
this hypothesis of the resurrection of the disease after a
certain lapse of years. It would require the further
assumption that after a period of latency the poisons gather
strength enough again to attain an epidemic violence.

It has indeed been shown by Dr. Thiersch and by Dr.

83

Burdon Sanderson that the discharges of typhoid fever and
cholera patients gain in virulence for a few days after their
emission from the body, and Prof Pettenkofer’s Aground’
theory of the latter disease seems to demand the possession by
disease germs of some such property as this ; bnt no one has
hitherto ventured to suggest that a seclusion of several years
enhances the powers possessed by the materies morbi of
these disorders,

5. Equally problematical is the suggestion that each
epidemic is like a gigantic but disjointed organism, with a
life history of the whole as well as of its individual parts.

This notion would be on a par with Mr, Butler’s
humorous idea that the “ ovum when impregnate should be
considered not as descended from its ancestors, but as being
a continuation of the personality of every ovum in the
chain of its ancestry.” ^ 00^0^ 0^20 Qf being

“ actually the primordial cell which never died nor dies, but
which has differentiated itself into the life of the world, all
living beings whatever being one with it, and members one
of another.”

6. It would be more nearly in accordance with our know-
ledge of the ways of the lowest orders of beings if we were
to suppose that after a certain lapse of time in which the
disease germ was propagated by fission and by budding,
it at length reached a period at which an act of conjuga-
tion was necessary for its continued existence, and that
after this process the disease regained its former powers of
offence and virulence.

7. I am inclined to think, however, that a much simpler
explanation of the facts can be given than those hitherto
brought forward, and this is, that a certain density of the
population at susceptible ages is necessary before a disease
can spread with the vigour of an epidemic.

Probably all the facts would be accounted for if we
suppose that these disorders can only become epidemic

84

when the promixity between susceptible persons becomes
sufficiently close for the infection to pass freely from one
to the other.

Exanthematous diseases rarely attack the same indivi-
dual twice in his lifetime.

When, therefore, an epidemic has, by either a fatal or non-
fatal attack, cleared away nearly all the susceptible persons
in a population, mostly infants and children up to a certain
age, then it must necessarily wait a certain number of
years before the requisite nearness of susceptible individuals
has been again secured.

There must in the interval be a gradual re-stocking of
the nation with material fit for the epidemic to feed upon,
and it can only spread when the requisite proximity is
attained, when the meshes of the network of communication
are sufficiently close for it to include all susceptible persons
in one grand haul.

It will be found I think that this hypothesis is supported
by the peculiarities of the different epidemic curves, and
especially by the contrast between the courses followed by
these diseases in England and Sweden respectively.

1. We may note the extreme height of the epidemic
waves in the sparsely peopled country of Sweden, as com-
pared with the comparatively small excess of mortality in
epidemic years in the dense populations of England and
Wales.

Thus the death-rates from measles and scarlet fever during
an outbreak in Sweden are usually at least ten-fold those in
ordinary years, and in the case of measles they sometimes
rise to twenty-fold the number.

In England and Wales, on the other hand, scarlet fever
never sinks below 7,000 deaths, nor rises above 24,000 — a
ratio of less than one fourth — and measles is still more
certainly and equally present amongst us, the epidemic
never marking double the number of deaths of ordinary

85

years, and in some instances, as in 1863, only rising one-
sixth more than usual.

In small-pox the difference is not so manifest, except that
(in Sweden) in the 30 years 1772 to 1802, the waves of this
disease are about ten times the height of the non-epidemic
periods, a flood of disease that is only reached in England
in the great outbreak of 1872.

2, We may also note the fact that the intervals between
the epidemics are much shorter in England and Wales in
the case of both scarlet fever and measles ; and in Sweden,
with an increased density of the population from 1860 to
1875, there is also apparent some shortening of the period
of comparative immunity from scarlet fever.

It is indeed remarkable how very prevalent this disease
has become of late years in Sweden. After 1861, it never
sinks below a point that would have constituted an
epidemic in former years, and in 1865 and in 1869 and
1870 it reaches nearly five times the height it had ever
attained before 1830.

1 have not seen any explanation of this extreme prevalence
of the complaint in Sweden in recent times, though I have
no doubt that it is in some way connected with the greater
density of the population. The number of persons per
square mile has just doubled in the course of 100 years.
1 would point out that an increase to so great an extent is
not observable in the case of measles, which seems indeed
to ])ursue the even tenour of its way in the last decade as
in the first, only a slight increase being noticeable since the
year 1820.

Is this because nearly every person takes measles, and
only a portion of the population need contract scarlet fever ?

3. We may remark that even in Sweden whooping cough
and measles reappear as an epidemic after a longer in-
terval when the previous outbreak had been a severe one.
Thus, after the years 1793 and 1821, when measles reaches

86

its highest point, the cycle is extended to nine and eight
years, and after prolonged and severe epidemics of whooping
cough in 1790 and 1805 the interval is longer than usual.

4. When a small epidemic, or an attempt at an epidemic,
occurs in the middle of a period, the interval is usually
rather longer. This happens with measles in 1789 and in
1796, and in one case the gap between the highest points of
the curve is eight and in the other nine years, instead of
six or seven, as in other instances. In 1793 and 1817 there
are also small waves of whooping cough postponing the
usual outbreak of this disease from four or five to seven
and nine years respectively.

It is interesting further to notice in this regard the
inverse ratio that holds between the height of the epi-
demic and the lowness of the disease in the periods pre-
ceding and following it.

This is especially noticeable in the chart of whooping cough,
in which the amount of disease constantly present graduaUy
diminishes, and the epidemic waves rise higher and higher
until the }mar 1806, and after this date the reverse process
1ms been pursued. The disease, in fact, imitates the ocean
in its spring and neap tides — though from a different
cause — its ebb and flow following the same rule of a high
tide with a low subsequent ebb.

U])on tlie hypothesis now before us all these facts would
be readily explained by the varieties in the densities of the
susceptible populations.

The degi ee of proximity of susceptible persons would be
much more readily obtained in England in her crowded
towns, and with her large number of births in proportion
to acreage. In many parts of the country, in fact, it would
probably be difficult for an epidemic to clear the ground
so completely that in another year it would not again be
filled up with a number of persons in sufficiently close
Mioximity to one another to allow the disease to spread. In

87

Sweden also the less completely the ground was cleared of
susceptible persons at any one time the sooner might the
disease be expected to return, and after a time of compara-
tive quiescence, so much the more virulent would it become
on its return.

5. It seems probable that this theory will also account for
several pecularities in the cycles of different diseases, and
especially for the length of the interval between their chief
epidemics.

Thus, cceteris paribus, the larger the range of the suscep-
tible ages, and the longer is the epidemic period. When the
disease has once thoroughly cleared off the susceptible
persons at all ages, the requisite density for a great outbreak
will be attained early or late according to the ages most
prone to the complaint.

I'hus whooping cough has a short cycle, and it is most
fatal before the termination of the second year of life. It
kills every ten years 37,000 males, and 43,000 females in
the first two years of life, and only from 1,300 to 1,400 in
the next two years of life.

Measles, on the other hand, takes its chief toll at and
under six years of age. The numbers dying in the decade
before the fifth year of life is completed are over 40,000 of
each sex, but the disease still kills several thousands at ages
from 5 to 10, whilst in the next 5 years period its number
of victims sinks from thousands to hundreds. The actual
numbers are : — from 5 to 10 years of age, 2,900 males, 3,200
females; from 10 to 15 years of age, 297 males, 358 females.

It is scarcely possible to draw any conclusions respecting
small-pox, owing to the interference of vaccination with its
natural course, but so far as the English returns of mortality
go, they show that the age susceptibility is very similar to
that of measles, and we know now that its cycle is not very
different from that of this complaint.

Scarlet fever has the longest range of susceptible ages.

88

Although, like the other zymotic diseases, it kills the
greatest number under five years of age, it retains its
virulence to a much longer period than the other com-
plaints. 28,000 males and 27,000 females are carried off
by it from ages 5 to 10; from 10 to 15, 5,300 males and
6,000 females ; but up to the age of 20 its number of fatal
attacks in five years of life still reaches 1,500 and 1,600,
and amongst females it continues to kill over 1,000 persons
in the decade of life 25 to 35.

In relation to the lesser undulations of scarlet fever, we may
also note the fact that this disease kills its largest number of
victims between the ages 2 and 3.

I might at this point take my leave of the subject of
epidemic cycles, but I should like also to bring before you
one or two considerations suggested by the tables before
us bearing upon the question of the possibility of abolishing
altogether or mitigating the virulence of these complaints.

Sir Thomas Watson believes that he is not too sanguine
in trusting that the abolition of zymotic disease may be
looked for in the next generation, or at least by his grand-
children.^

And if it were possible to stamp out of the world
every vestige of the contagion of any one disease, we
might perhaps hope never to see it again amongst us. It
would certainly need something like a universal deluge to
accomplish this, but we may grant that after such a
thorough annihilation it would take many cons of ages
before the same disease could be evolved from the harmless
bacterium or the common septic ferment.

I fear, however, that something far short of this would
be the result of our interference, and the questions
naturally arise, whether by keeping a disease at bay for a
number of years, we may not be laying up a store of sus-
ceptible material for it to feed upon in time to come, and

* Abolition of Zymotic Disease, Kegan, Paul & Co., p. 55,

89

whether the epidemic when it does escape from its bonds
may not prove more fearful than ever in its ravages.

Not only do these tables show the fact, but the whole
history of epidemics proves that when a disease has been
long absent from a country, on its return it is always both
more virulent and more widely spread than when it is to
some extent endemic amongst the people. This fact comes
out very strikingly in the history of the small-pox, as
given by Mr. Simon, and in outbreaks of measles in remote
islands. Might we not then do serious harm by attempting
to postpone the evil day of visitation ?

This is a serious question for those who are now trying
to arrest the progress of epidemic disease, and I fear that
it would have to be answered in the affirmative if our
energies were mainly devoted to isolation and disinfection
whilst the other conditions are left intact, which are known
to favour the propagation and vitality of these disorders.
George Eliot is right in thinking that “you cannot fright
the coming pest with border fortresses, ” and whilst filth,
overcrowding, impure water supplies, and bad drainage are
permitted to remain amongst us, it is highly probable that
any temporary limitation of an epidemic will only serve
to husband its strength, and give it more material to feed
upon in the future.

But fortunately we are not necessarily impaled upon the
horns of the dilemma of either being destroyed now or at
some future period of our career.

In the case of the most serious of these maladies, scarlet
fever, it is certainly not essential that every one should
take it, and its power is probably greatly influenced by
sanitary conditions.

I can hardly doubt that the great increase of this com-
plaint of late years in Sweden is due to the circumstance
that sanitary regulations have not kept pace with the
growth of the population, and we must never forget that,

90

in the words of Dr. Addison, “ one blade of the destroying
shears is forged at home, without it the other cannot do its
work.”

By improvements in the construction of dwellings, by
thorough cleanliness, and other hygienic precautions, we
may hope to place our crowded populations in at least as
favourable a condition as the Swedes were 50 years ago,
and epidemics may be once more made to observe their
regular times and seasons.

We shall then moreover be armed with all the power
that proverbially comes to those who are forewarned, and
if we cannot arrest the progress of an epidemic we shall be
able to take our measures to mitigate its ravages. We can
then prepare our disinfecting armaments and our reception
houses and hospitals for isolation, with some hope of a
favourable result, and possibly at some future time it may
be practicable to ensure a milder type of disease, or even,
as in the case of small-pox, to substitute some allied and
less fatal disease, which shall by anticipation rob the virus
of the food upon which alone it can subsist.

Letter of Dr. Berg.

Dear Sir,

I am sorry that I cannot give you the wished for informa-
tion such as you needed.

The forms for the registration of the causes of death have since
1749 often been changed, sometimes totally obstructed.

The ecclesiastical registrars in the country are not always able
to make a correct diagnosis. Only for such diseases whose natures
are generally known by the country people the information from
older times can be supposed of some value.

There are to be distinguished three periods in the accom-
panying list of deaths.

The first from 1861 to 1874, where the numbers have real
value.

91

The second from 1831 to 1860, when the registration of the
causes of death which you ask was suspended. For a part of this
time 1851-1860 I find in the reports of our Board of Health
indicated epidemical exaggerations of Scarlatina in the years 1852
and 1857.

Measles 1855, ’56, and ’57.

Hooping Cough ’52, ’53, ’56, ’57, ’60.

The third before 1830, for which I have made extracts from
the manuscript table in our archives, going back to 1774.

In these extracts the numbers for scarlatina seem to have no
value, perhaps because this disease in former times may not have
been generally and specifically known. In the numbers for hoop-
ing cough may probably be entered cases of capillary bronchitis.
The measles is a disease generally known since a long time, and
as I found the numbers of deaths indicating the periodical exacer-
bations, I have supposed them to be of value for you.

I have added the total of deaths from all causes, and the mean
population for the years corresponding.

Most regretfully yours,

FRTH. BERG.

Stockholm, 17/11/75.

92

SWEDISH MOETALITY TABLES.

Registered Deaths from

Population in

Rates per Million of Population.

Whooping

Total

the middle of

Whooping

Tear.

Scarlatina

Measles

Cough

Deaths

the year

Scarlatina.

Measles.

Cough.

1871

2418

650

1309

87,760

4,319,766

555-0

150

365

1873

1244

293

1754

73,525

4,274,192

287-0

68

400

1872

1340

53

617

68,802

4,227,295

320-0

13

146

1871

2488

89

147

72,046

4,186,351

572-0

22

35

1870

4817

336

371

82,449

4,163,641

1150-0

85

89

1869

4396

5332

1262

92,775

4,165,910

1030-0

1300

313

1868

2199

1129

2414

87.807

4,184,381

525-0

270

575

1867

1903

126

768

82,072

4,178,179

456-0

31

83

1866

4063

165

468

82,666

4,137,409

968-0

39

114

1865

4448

182

602

79,216

4,092,101

1080-0

44

146

1864

2149

243

1148

81,937

4,046,313

590-0

61

275

1863

1354

2527

749

77,227

3,994,232

340-0

630

188

1862

1684

7407

1549

84,350

3,941,619

420-0

1830

395

1861

1453

507

1856

71,829

3,888,534

373-0

146

480

1830

129

524

2145

69,251

2,875,607

45-3

137

745

1829

221

5995

2084

82,719

2,854,960

77-3

2280

735

1828

739

3735

2117

75,860

2,837,254

260-0

1395

965

1827

389

446

2721

64,920

2,816,323

1390

160

965

1826

356

396

3061

63,027

2,788,089

127 -0

145

1070

1825

228

323

2271

56,465

2,749,065

84-0

119

800

1824

350

365

1513

56,256

2,707,954

130-0

135

510

1823

191

309

354

56,067

2,667,673

67-5

119

495

1822

243

650

2450

59,390

2,628,592

92-5

250

935

1821

176

6924

2990

66,416

2,597,780

67-5

2650

1195

1820

3129

1532

62,930

2,573,235

1190

600

1819

1556

1801

69,881

2,554,096

600

705

1818

470

1345

61,745

2,533,927

187

536

1817

477

2070

60,863

2,509,463

190

832

1816

426

1631

56,225

2,481,275

170

665

1815

1768

1174

57,829

2,454,804

715

485

1814

4203

1012

60,959

2,425,545

1750

410

1813

633

2127

66,266

2,412,114

265

878

1812

249

3458

73,095

2,402,130

102

1440

1811

63

301

2142

69,246

2,387,216

26-3

125

863

1810

90

320

958

75,607

2,379,963

38-0

135

403

1809

392

1574

628

95,532

2,400,458

158-0

655

263

1808

186

2436

563

82,311

2,426,781

77-5

1020

239

1807

65

500

2629

62,318

1,431,725

26-7

209

1043

1806

40

431

5046

65,728

2,428,069

16-5

180

2090

1805

38

400

1498

56,663

2,417,758

15-8

167

628

1804

72

367

440

59,584

2,399,973

30-0

152

184

1803

95

657

430

56,577

2,383,098

40-0

275

182

1802

198

2847

1057

56,035

2,365,193

80-5

1200

435

1801

73

633

3601

61,317

2,351,665

33-0

270

1550

1800

162

347

2320

73,928

2,352,148

70-0

150

1050

1799

137

453

1149

59,192

2,350,611

57-5

212

612

1798

246

511

1295

53,862

2,333,521

105-2

220

562

1797

360

588

3564

55,036

2,311,804

156-0

232

1550

1796

299

903

2744

56,474

2,290,965

130-0

390

1185

1795

264

562

878

63,619

2,274,064

120-0

250

392

1794

136

634

756

53,377

2,253,055

60-0

280

340

1793

168

3988

1160

54,376

2,225,381

71-0

1770

340

1792

167

2610

874

52,958

2,195,181

10-5

1190

528

1791

50

448

1139

55,946

2,168,476

23-0

219

478

1790

31

271

2924

63,598

2,169,999

143

128

1357

1789

59

618

2010

69,583

2,167,816

27-5

285

930

1788

29

248

2775

57,320

2,167,839

13-4

110

270

1787

53

283

1394

51,998

2,159,961

24-5

135

650

1786

61

2098

1447

55,951

2,152,941

28-4

980

653

1785

89

2411

1229

60,770

2,147,493

42-0

1120

573

1784

174

369

1239

63,792

2,144,392

82-0

175

576

1783

69

342

1752

60,213

2,142,278

32-3

160

845

1782

83

583

2524

58,247

2,136,949

39-2

273

1220

1781

138

438

1711

54,313

2,125,597

65-3

205

845

1780

174

296

1275

45,731

2,103,953

83-0

143

648

1779

255

514

1773

59,325

2,081,460

122-0

240

870

1778

330

2517

2416

55,028

2,065,222

162-0

1220

1209

1777

233

1551

1755

51,096

2,049,218

116-5

780

880

1776

217

231

2090

45,692

2,031,068

108 0

115

1050

1775

73

321

1852

49,949

2,009,328

36-5

160

930

1774

58

333

887

44,463

1,985,108

29-0

166

442

-3.1

I

93

3000

2500

2000

1500

1000

500

0

■■iMilHiMliginiMMMiiHM!iMP«MMMv^igira»»i!gMviigiilflwBB8MSagSMaagMKS8S8HBBBBii!iiili

aapaaas8aaaaggBaaagga8gaa8a8aaaKagg8aBBBBBBBBBBBBiiiniBiiBiBMaggaa8Bg

3000

40 JO

3500

3000

2500

2000

1500

1000

500

4000

3500

3000

2500

2000

1500

1000

♦

• ‘V.

/

■#

I

o

<Ji

94

2000

1800

1600

1400

1200

1000

800

600

400

200

0

2000
1800
1600
1400
1200
1000
800 j
600
400
200
0

o

00

lO

00

kA

00

21000

21000

18000

16000

12000

9000

6000

3000

0

24000

21000

18000

15000

12000

9000

6000

3000

0

95

00

210(0

I80CO

15000

12000

9000

6000

3000

21000

18000

15000

12000

9000

6000

3000

96

SUN-SPOT PEEIODS.

BBiffiBiiai

iSlIBHBBHMIl
IBHaHHHHHIl

■■■■■■■■■■■■■a

l■■BBBBBB■BBBBBB■BltIl)l■B■BBB■Bf BB B BBBiBBflBBBB BBI
l■BBBBBBBBBBBBB■BBBBBBBBBB■BiBBfl■BB■BB■■BBflaB■
BBBBBBBBBBBBflBBflBMBBBBflBBBBBBBifiBBBBBBBBBflBI
|■■■■BBB■■■B■B■■■BBfl■BB■BB■BBBBEiiB■BBBBBBBBBI
IBBBBBBBBBBBBBBBIBnilUlBBBBBBBBBBB BBB BBBBBBBBgB BBI

IBBBBBBBBB
IBBBBBBBBI
IBBBBBBBBI
■■■BBBBBII

■■■■■■■bbbbii

■■BBBBBBBBBB!!

■■BBBBBBBBBBln

BBBBBBBBBBB-BI

BIBBIBBBBBBBifll

IBBBBBBBB BBBBBBBBBBBK

■■■■■■■■■■■■■■■iBRItilBBBBBBBBBBBBBBBBBBBBBBBBMBI
BBBBBBBBBBBBBBBBBIBBBBBB BBBB BBBBBBBBBBBI bbbb bi
■■■■bbbbbbbbbbbbhPbbbbbbbbbbbbbbbbbbbb-bbBbbi

BBBBBBBBBBBBBBMBBfcBB BBBBB BBB BBBBBBBBBBB IBBBBB I
BBBBBBaaaBaMBBBBeiafflBBIBBBBB BBB BBBBBBBBBBB BBBBBB I
BBBiBflBBaBBBBBBBBBBBBBBBBBBBBBBBBBaflBBBBBBHBBI
-BBflBBBBBBBBBBBBBKVlIBBBBBBBBBBaBBBBB BBBBBBBBBBB^

JSBBSB:s;sB::s;ssir?o!:S:BHs;sBSS^^^

SBSBBBBSBBBBBBBBggSBSBSBBBBBBBBBBBBBBSB^^

BSBBBBBSBBBSBSBSBSifiSSBBBBBBBBSBBBBBSBBSBBBSBBBi

BBBBBBBBBBBBBB
BBBBB BBBBBB BbB

IBBBBBBBBI

BBBBBBrflBBBBBB
BBBBBBfl BBB BBBB

■■■■■■■■■■"■■■■■■■■■■■■■■■■■■■BI

BmuSSSuBBBBnBBBUBKBUU

IBBBBBBBBBBBBBBBB^BBBBBBBBBBBBBBBBBBB-BBBBBBBI

■■■■■■■■SHBBBBBBBBiSBUBBBBBBBBBBBBBBBBBBBBBBBI

iiilMllMBBBBBiBBHMBBBBBBBBBBBBBBBBBBBBBBBBBBBI

■■gHBSBBBBBBBiiBBgBBBBBBBBBBBBBBBBBBMBBBBBBBI

IBBrflBI

BBBBfll

■BBBBI

■BBBBBB BBB BBBB
■BBBBBBBBB BBBB

^BBBBBBBBBBBB

ibbBBBBBBBB BBBB
IBBBBBBBB BB BBBB
IBBBBBBBBSB BBBB
MBBBBBBBBBBBBB
■BBBBBBBBBBBBBB

a:sBSBssiSBa

soo

380

360

310

320

300

280

260

240

220

200

180

160

140

120

ioo

80

60

40

20

0

(Schwabe.)

(Kew.)

97

Ordinary Meeting, February 10th, 1880.

E. W. Binney, F.R.S., F.G.S., Vice-President, in the Chair.

Professor Roscoe, F.R.S., exhibited some specimens of
phosphorescent surfaces prepared according to processes dis-
covered by his late friend Mr. W. H. Balmain, of St. Helens.
These preparations are now being largely introduced under
the name of luminous paint. Mr. Balmain worked for
many years in conjunction with M. Becquerel upon the
phosphorescent compounds of the alkaline earths, and he has
succeeded in producing a material which when exposed to
diffused daylight, or direct sunlight, not only becomes
strongly phosphorescent in the dark, but remains so for
several hours after insolation. The proposal is now made
to utilise this property for special illuminating purposes, and
Dr. Roscoe showed various preparations made with Bal-
main’s paint, kindly furnished him by Messrs. Ihlee and
Horne, of Aldermanbury, London.

Professor W. C. Williamson, F.R.S., exhibited some
specimens of Calamostachys Binneana, especially one recently
discovered by John Aitken, Esq., in which the fruit displays
both microspores and macrospores, the former occupying
the upper and the latter the lower part of the same strobi-
lus. This discovery equally separates the Calamostachys
from the Equisetaceae with which so many authors have
associated it, and from the Gymnospermans Exogens of
which Brongniart was inclined to regard it as a pollenifer-
ous spike. Professor Williamson has long advocated its
association with Asterophyllites and Sphenophyllum, and
ranked the whole with the Lycopodiaceae. This interpret
tation seems to be now placed beyond doubt.

Peoceedings — Lit, & Phil. Soc.. — Vol. XIX. — No. 9. — Session 1879-80.

98

“ Notes on a Bore through Triassic and Permian Strata,
lately made at Openshaw/’ by E. W. Binney, Y.P.,

&c.

For many years attention has been given by local
geologists to the district lying between the Manchester
coalfield and that of Ashton-under-Lyne and Oldham.
The first authors that have treated on it were probably
Messrs. Conybeare and Phillips, in their Outlines published
in 1822. Mr. James Heywood, F.RS., in a paper published
in Yol. YI. (2nd series) of the Society’s Memoirs, also
noticed it. In a communication of my own, published in
the 1st Yol. of the Transactions of the Manchester
Geological Society, a horizontal section is given of the
country between Manchester and Waterhouses, showing
one great fault as then known. Afterwards, in Yol. XII.
(2nd series) of our Memoirs, evidence is given of another
fault at Medlock Yale, and lately in Part YI., Yol. XY, of
the Transactions of the Manchester Geological Society,
Messrs. Bradbury and Atherton have shown a third fault
at Openshaw. As the district is thickly covered by drift
deposits, and few natural sections are exposed, we have to
wait till evidence is afforded by borings and sinkings. In
several papers by me printed in the Memoirs, information
has been given as it was met with, and as Mr. John
Bradbury’s boring is one of the most valuable, I wish to
add it to my other communications on the subject, in order
to make them more complete.

Mr. Bradbury’s labours have shown the Permian sand-
stone, the one so well exposed at Yauxhall, in our city, to
be of greater thickness than hitherto proved in the district,
and as this deposit is a most formidable difficulty in sinking
to the underlying coal seams, it is desirable that all infor-
mation respecting it should be given to the public.

The bore was made near to the Ashton canal in Open
shaw, and adjoining the boundary of that township with

99

Clayton. According to Messrs. Bradbury and Atherton, it
was as follows : —

Drift Deposits

Trias (Pebble Beds)

Permian Marls, containing beds of limestone, one\
of which was 1ft. 4in. in thickness, and nodules
of gypsum. In the lower parts of the marls i-
and limestones were shells of Schizodus ohscurus,
Gervillia antiqica, &c

Feet.

36

46

200

Conglomerate 3

Permian Sandstone 752

Upper Coal Measures, containing 12 beds of]
Ardwick Limestone, one of which is 5ft. in > 263
thickness )

1300

The dip of the Permian strata was about 1 in 8, and that of
the Upper Coal Measures 1 in 3 to the S.S.W.

The strata found resemble those at Medlock Yale, except
that the Permian sandstone has increased from 420 to 752
feet in thickness. I have estimated that rock under Man-
Chester at 400 feet, but its entire thickness has never to
my knowledge been proved. In Chester Street, Chorlton-
upon-Medlock, at the sugar works of Messrs. Pryor & Co.,
on the south side of the fault which runs from N.W. to
S.E. between that place and the late Mr. Green’s dye works,
in Brook Street, the Permian marls and conglomerate bed
increased to 260 feet in thickness, were found resting on
upper coal measures containing the Spirorhis limestone
similar to that at Ardwick without any trace of the Permian
sandstone. Similar results have been found at the borings
and sinking of the Seedley print works and the Patricroft
colliery, and very lately Dr. Perrin informed me that the
same occurred in a sinking at Plank Lane Colliery, near
Leigh.

All the facts hitherto observed appear to show that the
Permian sandstone is found of great thickness under the

100

district iying between the Manchester coalfield and that of
Ashton-under-Lyne and Oldham, while to the south of
Manchester, under the Trias, it is replaced by the conglo-
merate of increased thickness. The former rock has pro-
bably never been deposited, nevertheless the fact of its
general absence is of great importance to all parties who
may sink for coal under the Trias.

At the present time the Permian strata of the N.W. of
England and the S.W. of Scotland, so far as my knowledge
extends, are represented in Lancashire in the following
descending order : —

1. Upper Permian sandstone of Moat, Shawk, St. Bees,
and Furness Abbey ; absent in South Lancashire, without
there is a representative of it in the Knowsley Quarry,
near Prescot.

2. Magnesian marls with limestones and gypsum, con-
taining Bchizodus ohscurus, Gervillia antiqua, and other
characteristic fossils,

3. Conglomerate.

4. Permian sandstone of Yauxhall, Manchester.

5. Lower Permian sandstone of Whitehaven and Astley,
by many English geologists taken to be uncomformable
coal measures, but in Germany termed Lower Rothliegende,

The old Magnesian Limestone formation, as described by
Professors Sedgwick and King, and my friend Mr. J. W.
Kirkby, in the East and N.E. of England under the four
first-named divisions, was pretty plain, although the line of
demarcation between the Brotherton limestone and the
Trias was not so easy to make out in all places. In the
N.W. of England, and adjoining Scotland, the St. Bees
sandstone, a rock of about 1,000 feet in thickness, cannot
be traced distinctly passing upwards into the Trias, although
doubtless it does somewhere betwixt Carlisle and the
Solway ; but in the valley of the Irk at Manchester the
beds Nos. 4, 3, and 2 are seen lying on each other appa-

101

rently passing into the overlying Trias, all the three rocks
dipping at the same angle and in the same direction.

Near Manchester the occurrence of Permian fossils has en-
abled us to* fix the position of the red sandstones and marls
of the Trias and Permian beds, but after leaving Barrow
Mouth, near Whitehaven, and traversing the country by
Maryport, Carlisle, and Longtown to Canobie, as yet no
fossil organic remains have been met with to help us, and
we have to trust chiefly to superposition to separate the
two formations. All who have investigated these forma-
tions know the difficulty of determining a Permian from a
Triassic sandstone by external characters.

In some places in Lancashire the coal measures are
covered by Triassic beds without the occurrence of the
intermediate Permian beds, but near Manchester the latter
are generally met with either as the upper deposits, the
marls, and the conglomerate (Nos. 2 and 8) most frequently
together, or with all the three beds of the series.

MICROSCOPICAL AND NATURAL HISTORY SECTION.

February 16th, 1880.

Alfred Brothers F.R.AS., in the Chair.

Professor Alfred Milnes Marshall, M.A., Owens College,
was unanimously elected a Member, and Mr. Lionel E.
Adams, of Victoria Park, Manchester, an Associate of the
Section.

Mr. Thomas Kogers read a paper on the Land and
Fresh-water Shells of Tasmania. He said that the total
number of land shells in Tasmania, so far as at pre-
sent determined, consisted of 115 species, comprised in five
genera, the genus Helix alone being represented by 79

102

species. These for the greater part were uniform in their
character, for the most part small in size, thin and horn-like
in the texture of the shell; the sculpture, when present,
being modifications of fine striae or well defined small riblets
placed more or less transversely on the whorls. The colour-
ing of the shells uniformly brown, relieved in some species
by mottlings of a reddish horn-colour like tortoise-shell-—
the general tendency in the forms of variation from the
typical Helix being in the direction of the smooth and
polished Zonites, and the few whorled and dilated mouthed
shells of Vitrina.

Helix Launcestonensis is however a marked exception to
the general type of Tasmanian shell, as it also is their largest
species, about lin. in diameter, strong and solid, with
wrinkled surface and granular edges on the top part of the
shell, and banded with yellow on a black ground under-
neath. It is not known to occur in any other part of the
world than in the immediate neighbourhood of Launceston,
Tasmania.

The rest of the land shells consist of 2 species of Bulimus,
3 of Vitrina, 2 or 3 of Succinea, and 3 or 4 of Truncatella.
Bulimus Hufresnii is the finest of the two species, being
about an inch long and well marked in its colourings
and style. The Vitrina is represented by two very fine
species, large in size, black in colour, and highly polished,
giving the shell a lacquered appearance. The animals are
of a bright red colour. The Succinea are very typical of the
genus generally.

The fresh-water shells number 36 species, comprised in 14
genera as follows : Lymnsea 3, Physa 9, Planorbis 3, Ancy-
lus 3, Gundlachia 1, Pomiatopsis 1, Bythinia 7, Amnicola 1,
Unio 1, Cyclas 1, and Pisidium 2. They are nearly all
small in size, the largest genera much resembling our British
species, except the Bythinise, which are more like our
own Hydrobise.

103

The most remarkable species of the fresh-water shells
is one recently discovered by Mr. Petterd, and belonging
to the rare genns Gundlachia. It has been named Gund-
lachia Petterdi. It is a very small species, not much unlike
a small specimen of Ancylus lacustris with a portion of the
mouth of the shell dilated widely like Ancylus fluviatilis.
The texture of the shells is very similar to Ancylus lacus-
tris, and it is found in similar habitats.

Mr. P. exhibited specimens of the Tasmanian shells, and
also spoke of several introduced European species which
have become, or are becoming, naturalised in that country.

Mr. Edwaed Collier, who was present as a visitor, men-
tioned that the fresh-water species of shells of Tasmania
were, with two exceptions, entirely different from those of
Australia, which suggests that the separation of the two
islands must have been remote.

Mr. Plant, F.G.S., exhibited a slab of flexible sandstone
12 inches long by wide and f thick. When supported
at each extremity the deflection in the centre amounted to

on one side, and when turned over to of an inch. It
also had a sensible deflection when tested edgeways.

Sandstones having this flexibility are obtained from
Georgia, South Carolina, the gold and diamond districts in
Brazil, and in the vicinity of Delhi, India. In Capt.
Burton’s “ Highlands of Brazil,” vol. 1, p. 878, he thus
states what he observed on the spot about the Brazilian
variety of this stone.

“The older writers apply the term ' Itacolumite ’ to a
white or yellow sandstone, flexible like a plate of gutta-
percha.” It greatly resembles that of the Lower Himalaya,
in which thin layers of the silicious granular matter are
associated with small plates of talc. The ‘Pedra Elastica’ was
described two and a half centuries ago by Padre Anchieta.
Dr. C. Wetherill (American Jour. Sci. Art.) declares that the

1

104

opinion that the elasticity of the stone is due to the presence
of mica is erroneous, for on close microscopic examination of
a slice of the rock it will be seen that the flexibility depends
upon the minute articulation where the sand grains inter-
lock.” “ In my specimens,” sa^^s Capt. Burton, “ the stone
abounds in light yellow mica, and when the friable material
crumbles the two main component parts at once separate.
Near Sao Thome das Letras there is a fine quarry of this
elastic sandstone. In the deeper parts the strata become
thin, and gradually pass into natural slabs of the flnest
quartzite, losing all elasticity. This flexible stone is not
the matrix of the diamond and topaz, though sometimes
associated with it.”

A description of the Delhi flexible sandstone will be
found in “ The Records Geological Survey of India, vol. vii.,
p. 81, by H. B. Medlicott, A.M., F.G.S,” of which the fol-
lowing is only an abstract : —

“The locality for the flexible sandstone is at Kaliana,
near Dadri, about 60 miles due west from Delhi. The hill
is 1,477 feet above sea level and 740 above the plain; it is
a double-crested ridge from the Punjab.

“ The projecting ribs on the double crest are formed of
quartzite and strong ironstone bands, black hsematite
chiefly. These ferruginous bands are regularly interstra-
tifled with mica and hornblendic schist and an earthy
cellular quartzite much quarried for millstones. All the
strata are nearly vertical.

“ The flexible sandstone is only found in patches in this
millstone quartzite, there being no regular seam of it. The
stone-cutters come upon it suddenly when cutting out
slabs of the ordinary stone ; often the rock in immediate
contact with a nest of the flexible stone is highly indurated
and quartzose. It is found both in the bedding and in the
joints. The quarrymen’s idea of the flexible stone is, that
it is a mere local peculiarity of the sandstone rock caused
by the percolation of rainwater and earth from the sur-
face and Mr. Medlicott thinks that the water expla^iation
is the correct one.

105

In his “ Manual of Geology,” Prof. Haughton gives his
opinion upon the cause of the flexibility of the stone.

“ A most remarkable circumstance sometimes occurs in
the formation of sandstones which are not composed of
pure particles of quartz, but a clay mixed with them^
namely, that the particles of quartz mixed in this clay or
paste are permitted a certain amount of motion.” If you
take an ordinary sandstone, with a lens you can see the
separate particles, and that each particle is touched on every
side by a number of other rounded particles that hold them
all in their places, so as to form of the whole a rigid rock.’’
But in the Delhi stone — “ you have a rock composed of par-
ticles of quartz which are not in contact with each other;
but lie embedded in a paste of felspathic clay, which clay
permits a certain amount of motion between the particles
of the mass.”

The specimen before the meeting came from the Kaliana
quarry. When superficially examined it ' will be seen that
it is not a schistoze rock, and hardly a particle of mica is to
be found in it. It looks very like some sandstones of the
Lancashire millstone grit. The grains of silica have a
flattened and matted structure, the whole being porous and
loosely held together — rather friable on the edges. It is
freely interspersed with particles of a yellowish clay; it
bends from its own weight, and when held up by one end
freely oscillates. The bending is easy up to a certain point ;
it then becomes suddenly quite hard and rigid. Any
further strain or a smart blow would then readily frac-
ture it.

Mr. Alfred Morgan, Proc. Liv. Geo. Soc., vol. 3, p. 151,
suggests that the true explanation of the flexibility of the
rock might be, “ That doubly metamorphosing conditions
were concerned in its production, a solidifying process to
give tenuity to the earthy paste, and a partial dissolution
to remove the rigidity of its first solidification.”

Mr. Plant also exhibited some fine fioccose infusorial
earth in thick deposit at the gold diggings, Talbot, Victoria-

106

The following are some of the uses to which it can be
applied : —

Uses to which Infusorial Earth is applied.

I. Article of food. Lapps mix it with bark of trees — in
famine time Indians of Amazon eat certain white earths
found on banks.

II. Manufacture of dynamite. The vehicle by which
nitro -glycerine is capable of being transported. “After
careful preparation, which consists in thorough removal of
all organic matter by heat, &c., the earth is rolled and
pressed and sifted, when it is ready for use. Fifty pounds
of the earth is put into a flat wooden tank and covered with
loOlbs. of nitro-glycerine, which is then thoroughly mixed
with it. After half an hour has elapsed it is ready for
removal to the cartridge moulds, in which parchment paper
is used.”

III. In agriculture.

IV. Floating bricks may be made of infusorial earth.

Forms a suitable covering for ice, beer cellars, fire-proof

safes, steam boilers, powder magazines, &c.

In pottery infusorial earth has received several important
applications, ex. : when fused with borate of lime an excel-
lent glaze is produced.

It has been of service in the manufacture of sealing wax,
soap, paper, ultramarine, &c.

Infusorial earth will take up three times its weight of
nitro-giycerine without becoming more than damp to the
touch.

Mr. Plant next showed a specimen of very fine clay
occurring under a deposit of dark chocolate-coloured basalt,
50 feet deep, and on a gold-bearing gravel or ancient river
course. The clay is filled with leaves or the impression of
leaves of a gum tree (eucalyptus) like the living species.
It is a meiocene deposit.

Mr. Marcus M. Hartog, B.Sc., F.L.S., exhibited, on
account of a visitor, Mr. Chadwick, a new organism, different
from a foraminifer, which he had found in Levant mud.

107

Ordinary Meeting, February 24th, 1880.

J. P. JoDLE, D.C.L., LL.D., F.R.S., &c., President, in the

Chair.

Mr. R. S. Dale and Mr. S. C. Trapp were appointed
Auditors of the Treasurer’s Accounts.

Dr. R. Angus Smith, F.R.S., exhibited a diamond he had
received from Mr. Hannay.

“ On the Long Period Inequality in Rainfall,” by Bal-
POUR Stewart, LL.D., F.R.S., Professor of Natural Philo-
sophy at the Owens College, Manchester.

1. If it be true that there is a variation in the power of
the sun depending on the state of his surface, this variation
might naturally be expected to make itself apparent
through a corresponding change in the rainfall of the earth,

so that when the sun is most powerful there ought to be’
the greatest rainfall.

2. While the connexion indicated above is that which
most readily occurs to the mind, yet the difficulty of
ascertaining the facts of the case in a manner bearing the

smallest approach to completeness is so great as to be at
present insuperable.

There is first of all an intense reference to locality in
rainfall, so that the rainfall at one place may differ greatly
from that at another place in its near neighbourhood
Again there are probably, in addition to possible secular
inequalities, very great oscillations in the yearly rainfall at
any one place, or accidental variations, as we may term
them in our ignorance of their cause.

Pbooeeditos-Iix.&Phii,. Soc.-Toe. XIX.-No. IO.-Session 1879-80.

108

Thirdly, it is in comparatively few places, and those
places chosen not with the smallest reference to this parti-
cular problem, that we have anything like a trustworthy
account of the rainfall throughout a considerable number of
years.

Fourthly, we have no information of any importance
with respect to the rainfall at sea.

3. Besides the formidable catalogue of difficulties now
mentioned, we ought to bear in mind the following con-
siderations. The convection currents of the earth are
regulated by two things, one of which is constant, while
the other may be variable. The constant element is the
velocity of rotation of the earth on its axis, while the
element of possible variability is the power of the sun.
Hence it follows that if the sun be variable it will cause a
variation in the direction as well as in the intensity of the
earth’s convection currents, on the principle which tells us
that the resultant of two forces, one constant and the other
variable, must vary both in magnitude and direction.

Now if it be true that we have a long period variation
not merely of the intensity, but also of the distribution of the
earth’s convection currents, and if we bear in mind the
intensely local reference in rainfall, it would be too much to
expect that the rainfall inequality should exhibit the same
years of maximum and minimum at all places. It is even
conceivable that some places might exhibit a maximum,
when others showed a minimum, while others again might
exhibit a double instead of a single period.

4. It appears to me that if we bear' in mind these con-
siderations it will not answer to add together the rainfall of
a few selected stations as they stand, with the view of
determining by this means whether there be a long period
inequality in the rainfall of the whole Earth. We are not
yet in a position to reply experimentally to this question.
It does not however follow that nothing can be done. Dr.

109

Meldrum and others appear to have achieved good prelimi-
nary work in the direction of indicating the existence of a
rainfall inequality depending upon the state of the sun.
Dr. Meldrum began by pointing out that in a good many
places there is a greater rainfall during years of maximum
than during years of minimum sun spots, and that this
phenomenon repeats itself from one solar cycle to another.
Again, Governor Rawson has pointed out the existence of
certain localities where the rainfall inequality appears to be
of a precisely opposite character, while Dr. Hunter has
showed the practical importance of the investigation with
reference to certain tropical stations. The subject has
likewise been discussed by Smyth, Stone and others.

5. The question has arisen whether it might be possible
to throw any light on this problem by the method of
detecting unknown inequalities, proposed by Mr. Dodgson
and myself (see Proceedings of the Royal Society, May 29,
1879). The essence of this method consists in a way by
which we may numerically estimate the indications of an
inequality. Let us suppose for instance that in ignorance of
the diurnal range of temperature we try to find whether
there be a temperature inequality of 24 hours or whether
there be not rather one of 26 hours. We should begin by
taking a large number of hourly readings of temperature
and we should group these into two series, the one
containing 24 numbers in each horizontal row, and the other
26. We should thus have 24 vertical columns from the one
series and 26 from the other, and we should take the mean
of each vertical column of each series as well as the mean of
the whole.

Now it would speedily be found that an inequality was
indicated by the 24 hourly series and none by that of 26
hours. For in the first series the mean of that vertical
column representing observations at 5 a.m. would be greatly
less than the mean of the whole, while the mean of that

110

column representing observations at 2 p.m. would be much
higher than the mean of the whole. On the other hand, in
the 26 hourly series, provided it be sufficiently extensive,
we should perceive no such differences. Thus in the 24
hourly series the differences of the means of the various
vertical columns from the mean of the whole would be
much greater than in the 26 hourly series, and the mean
amount of these differences might be taken to form a
numerical criterion of the presence or absence of an
inequality.

6. This method therefore, applied to the subject in hand,
might be expected to reveal the presence or absence of
inequalities in rainfall, provided we have observations
sufficient for the purpose. It is clear that the successful
application of this method does not require a previous
knowledge of the exact form of the inequality. Whether a
maximum rainfall occurs at epochs of maximum, or at
epochs of minimum sun spot frequency ; whether there be
only one rainfall maximum corresponding to the solar period,
or two, or even three, is a matter of no consequence, as far
as this method is concerned. All that is necessary is that
the rainfall should always be similarly affected by similar
states of the sun. Here however we must bear in mind
that this method of detecting inequalities by summing up
and averaging the departures from the mean caused by the
inequality, likewise sums up and averages the accidental
fluctuations. Now these accidental fluctuations are parti-
cularly large for rainfall, and it is therefore desirable to
lessen their disturbing effect as much as possible. This can
only be done by conflning ourselves to long series of obser-
vations in which the accidental fluctuations may be supposed
o counteract each other to a great extent, while the long

period fluctuations will remain behind.

7. Through the kindness of Mr. Whipple, Director of the
Kew Observatory, I have received copies of those catalogues

Ill

of rainfall wliich. lie has himself made use of in a paper
which was recently communicated to the Royal Society
(January 8, 1880). Of these Paris, Padua, England, and
Milan form the most extensive series, that of Paris em-
bracing 161 years, Padua 154, England (Symons’ table) 140,
Milan 115. Mr. Whipple has likewise furnished materials
by which the labour of applying the process in hand to
these series will be much abridged, and he has kindly
allowed me to make use of these. I will therefore apply
the process to these four stations.

8. Let us begin by grouping the Paris yearly values into
series of 8. We thus obtain the following final numbers
expressed in centimetres : — 51 ’4, 47’5, 4 5 -7, 48*7, 51*1, 49 ’8,
46*5, 47‘2, the mean being 48*5. From these we obtain the
following series of differences : —

+ 2-9 - 1 -0 - 2-8 + 0-2 + 2-6 + 1-3 - 2-0 - 1*3

In order to diminish the effect of accidental fluctuations,
let us equalise this series of differences by taking the mean
of each two. We thus obtain —

+ 0*8 + 1-0 - 1-9 - P3 + 1-4 + 1-9 - 0*4 - P7

If we now add these together, without respect of sign, and
divide by their number (8), we obtain P3 as the mean
departure from the mean of the whole, and bringing this
into a proportional shape by dividing it by the mean rain-

fall (48*5), we obtain

1-80

48-5

= 2'68 per cent.

9. These explanations will enable the reader at once to
perceive the principle of construction of the following
table : —

Proportional rainfall inequality, as exhibited by series of

English rainfall, \
Symons’ Catalogue. T

8 years.

9 years.

10 years.

11 years.

12 years.

13 years.

14 years,

2-63

2-14

1-55

1-79

3-15

1-69

2-57

Paris

2-68

3-07

L99

2*65

3-70

2-57

3*08

Padua

1-77

3’62

2 ’02

1-47

3-31

3-52

3*40

Milan

1-12

3*22

3*16

1-78

4*13

3 '78

2-49

We ought to give the English, the Paris, and the Padua
observations a somewhat higher weight than those of Milan,

112

as the former embrace a longer period. This will be done
sufficiently well by giving the first three sets -weights of 3
each and the Milan set a weight of 2. If we perform this
operation and then take the mean, we obtain as under :

Proportional rainfall inequality, as exhibited by series of
8 years. 9 years. 10 years. 11 years. 12 years. ISyears. 14 years

“wrightedtsabf™”’’} 2 3-00 2-09 1-94 3-52 2-81 2-92

A maximum corresponding to 9 years, and a still greater
one, corresponding to 12 years, is thus exhibited, each of
these being recorded at three stations out of four.

The proportional numbers indicated are not large, but it
must be remembered that it is the mean difference for all
the years that is given, and that the maximum and minimum
rainfall will represent differences above and below the mean
which will each be about double the numbers recorded
above.

10. Regarding the rainfall values as representing the
meteorological result of the sun’s action, let us now compare
these with declination-range values, which may be taken to
represent the sun’s magnetic effect. Professor Loomis has
compiled (American Journal of Science and Arts, Second
Series, Yol. L., page 153) what seems to be a very good
table, exhibiting a set of yearly values of magnetic declina-
tion-range extending, with slight breaks, from 1777 to 1868.

Let us take this table and treat it precisely as we have
treated the rainfall, except that it does not seem necessary
to make any attempt at equalisation such as that made in
article 8.

We thus obtain the following result : —

Proportional declination-rango inequality, as exhibited by series of
8 years. 9 years. 10 years. 11 years. 12 years. 13 years. 14 years.

^'""ToVrague^""''^} 3*37 3’39 10’07 4*66 9*33 4-09 4’98

Here we have decided maxima corresponding to 10 and
12 years. The result is thus not unlike that which has been
derived from rainfall observations where the maxima cor-
respond to 9 and 12 years — indeed we could hardly expect
a more perfect correspondence between the two, bearing in

113

mind the limited amount of observations which we have for
determining inequalities of long periods.

{Note added on March 6th.)

I take this opportunity of saying a few words on what I
imagine to be the proper line of policy that should be pur-
sued in this research.

( 1 ) There are manifestly two stages in the investigation.
In the first place we wish to ascertain whether there is any
connexion between the state of the sun’s surface (as revealed
by spots) and the meteorology of the earth, and in the
second place we wish to find the nature and laws of this
connexion should it be proved to exist.

(2) If the various meteorological elements at the various
stations of the earth are found to present the same periodic
inequalities as those which characterise sun spots, this
must be taken as decisive in favour of a connexion of some
sort between the two, quite irrespective of the exact form
of the inequalities. Nor will this evidence be invalidated
if an inequality at one station should be different in form
from that at another.

(8) Assuming the probability (from the evidence already
brought forward) of such a connexion, the most natural
hypothesis is that which supposes that the sun has inequali-
ties which affect his radiating power. Hence it is of great
importance (as proposed by Professor Stokes and others) to
ascertain by judicious actinometrical experiments whether
the heating effect of the sun’s rays be in reality variable.

(4) In absence of actinometrical results we have grounds
for believing that the magnetic activity of the sun is great-
est at epochs of maximum sun spots, and it seems most
natural that the meteorological activity of our luminary
should be greatest when his magnetical activity is greatest.

From the reasoning of the paper to which this note is
added we may conclude that there is no evidence which
can be deduced from rainfall against this hypothesis.

114

(5) But while there is considerable preliminary evidence
in favour of a variability in the heating power of the sun,
and while this is constantly accumulating we must not deem
it impossible that the sun affects ‘the earth in some other
way.

There is ground for supposing that the moon affects both
the magnetism and meteorology of the earth in a way
which we do not at present understand, and it is possible
that the sun may have a similar influence.

Since writing the above I have leaimed that Mr. Baxen-
dell made use of the method of mean departures described
in this communication in one of a remarkable series of
papers which he presented to this Society on March 8th,
1864. But I have no reason for supposing that he was
aware of the peculiar characteristics of the method devised
by Mr. Dodgson and myself in virtue of which we can with
comparatively little trouble ascertain the exact periods of
inequalities which are crowded very near together in the
time-scale.

On a form of representing the velocity at any point of
an incompressible fluid under conservative forces,’’ by
E. F. Gwyther, M.A.

1. The velocity at any point of a fluid may be repre-
sented in other forms than the usual velocity potential or
the vector potential of Helmholtz.

The form <r= v<^ corresponds to the case when SaSp is a
complete differential without a factor ; let us imagine it to
be made a complete difierential by a factor that is to be of
the form

0’ = Jc^\p

or to be a combination of the two, thus —

(T= V0 h

2. First let us consider the circumstances accompanying
the forms. If So-Sp is integrable by a factor the condition
is ScrVo" = 0 or Scrp = 0.

115

That is, the axes of vortex motion perpendicular to the
lines of flow. A case satisfying the conditions of parallel
cylindrical vortices, and circular vortex rings.

If (T-V0 integrahle by a factor, the condition is
S(<r - V0) V(o’ - V</>) = 0 or S(o- - V0)p = 0.

From this scalar equation cj) could be found, and we may
consider o- = v0 + a perfectly general form of expression

for the velocity at any point.

3. The kinematical condition that a must satisfy is the
“equation of continuity,” which if the fluid is incompres-
sible takes the form Svo- = 0 or

+ + ^ = 0 II.

and the angular velocity at any point in the fluid is given by

2p = Y „III.

The form taken by the equation of motion, when this
expression is substituted for cr, will now be found ; for

= y ^ may be written
U,(v^> + *V>/') = v(v+|-^

(\

Now D(V = V-I^t “ where A acts only on the cr in or
d^ - (So-v) ; therefore

Dj.v</> + = V. ^4 + ^V- + A { (So-v)<^ + Ic (So-v)v/^}

= V. V- J

and finally the equation of motion is

D,vD,.^ + D,fev>;' + /CV.D,1^' + = vfv + £j

Now this equation is equivalent to three scalar equations
and if we make in it the substitutions D/c = 0 D^xp = 0, we
reduce it to a single equation and solvable ; for then

vD,^=v(v + £-^)

^ p (T ,

or = V + - - 7T + V 0

^ m 2

116

where is independent of the position and may be

included in the (j).

Putting for (p - (S<7v)</> and substituting for a we get

or 2^ - (AfY + l\v<py = ^'y + ^ • • ■ IV.

In support of the substitutions D ^ = 0 and DfXp - 0 I
should state

1. That such surfaces can be found from the differential
equation.

2. That only three scalar equations have been used in
determining a so as to satisfy the equation of motion.

8. That as the intersections of such surfaces, if they
exist, are to move with the fluid, it is not unnatural to
make the trial of the possibility, and a fourth we shall see
later.

[It may not be out of place to notice that from the equa-
tion—

-(S,rvV = v(^V + £)
which may be written

; -2r<rp = Afv + ^'

‘ \ m 2 /

we may by operating with Sv get the equation

ip^ - 2Syp<r = V^P

where P stands for V + — + 77

m 2

an equation I have never seen stated.]

4. In order to interpret as far as possible the expressions
here introduced, we take first the last two conditions which
express that the surfaces h and ;// move with the fluid so as
always to contain the same fluid elements, and referring to
the expression for the angular velocity we see that they
intersect in the vortex lines.

It would be well to determine these surfaces more fully.
We have as yet treated them as distinct, however the sur-

117

faces k and \p coincide wliere vortex motion does not exist,
for the = 0 at all points, and the normals to the

surfaces at all points are parallel. Whence the surfaces
/:: = const, and ^ = const, coincide except at points where
vortex motion exists. In order therefore to apply this
method to the solution of rotational motion of a fluid, we
should consider k'^ip an additive term, and take for k and xp
values such as to make the surfaces k = const, and xp = const,
move with the rotational fluid, and always intersect in vor-
tex lines, while the term v0 would be taken to satisfy
the general irrotational motion.

5. To investigate the energy within a surface drawn
within a fluid we get by continually using a modification of
Green s Theorem and omitting Thomson’s correction

2T = y" adv = y' S (A(/> + k\;xp) (xdv = J Sa^(j)dv + J Sktryif^dv

= — J'S'^(T(f)dv + J SffipvciS

— / S\/ka'xpdv + f Sk\pirrdS

- - J Svo-(0 + k^p)dv - J Sxp\7ka-dv + J S{(j) + kxp)<ryd^

= -ff^^kadv + fs{cl) + k-p)(TpdS V.

where v stands for the unit normal to the surface, and where
the last term vanishes if there is no flow across the bound-
ing surface.

We may then use the equation of continuity to give
other forms to the volume integral. Thus
SxpykfT = il^Syk(y^ +

= pS(\7Jc\7(j) - k\7^(j) - k\^p)

forms which will allow us to use Green’s Theorem again.

From the rate of change of the circulation in a closed -
circuit moving with the fluid we get

D^y' crdr = 0 or J'Dtffdr + J ad.T)f = y'D^o’^r + J (rS(r = 0.

The second is zero over every closed circuit. In order that
the first may be so we must have Vv-Dto- = 0, or referring to

V{vD<^.V+ + =0 VI.

a further justification for our assumption.

118

The simplest way of finding Dp is as follows. We have
seen that

DjO- = O’ - (So'V)o’ = <7 - SYo-p -
operate upon this with YA, then

YvDto- = p - 2YvYo-p = p - (Sffv)p + (Spv)o-

= D,p -f (Spv)o-

But from the circulation YvD^o- = 0

.'.D,p= -(Spv> YIL

The value in terms of k and \p is not so simple as to deserve
notice.

The geometry of the motion is not easily explained
owing to the fact that </> is not the third surface satisfying
= Oj also k and \p will not generally be independent, as
the condition for irrotational motion is that they should
touch at the points of intersection.

‘‘Notes on some Quaternion Transformations,'’ by R. F.
Gwythee, M.A.

The following theorems are frequently required in physi-
cal problems, especially in the motion of fluids.

I.

If T denote the vector of any point and v Hamilton’s
operator, and if p and o- are any vector functions of r, then

V(p(y) = vpo- - pV<7 + 2(Spv)(T I.

More generally — If p and <t be any vectors depending on the
scalars a, 6, c, &c., and if a, j3, y, &c., be any vectors what-
ever; and if + yc^c + &c. = D, where denotes

differentiation with regard to a, &c.. Then
D(po’) = Dp.ff — pD(T + 2(SpD)(T.

For ad^ipcr) = ad^fp.ar + ap.daV

= adap.cr — pa.dg(T + 2(Spada)<T

since ap + pa = 2Spa

If we now form the similar quantities for &c., and add
the respective sides of the equation thus formed
.*. B(p<t) = Dp.a — pD(r + 2(SpD)(T

II.

119

But r may be written aa-\-h[5+cy, where a, j3, y are rect-
angular unit vectors. D in this case becomes identical with
V, and the preceding form may be deduced.

The more general form is occasionally useful.

From I. we may by taking scalar and vector parts get

Sv(po-) = Svpo" - Svpo- III.

Vv(po-) = Yypa - Ypycr + 2(Spv)o- YV.

whence we may deduce by putting

Vvo-^ = 2Yvo-(t + 2(So-v)o-

We may also deduce from (1) S values for

V(Spo-). To obtain forms more generally useful than the

more general forms put Syp^O in

yV(po-) = 5v(po- - ap) = S. vpo- - S.py/T + (Spy)o- - {So-y)p

+ (Syp)or - p(Syx>)

and we get

Sy Vp<r = S(vpo’ - pyar) V.

Vy Vpo- = (So-y)<r - (So-y)p VI.

These forms simplify still further when in fluid motion a is
the velocity at any point and Yy<7=2p gives the rotation at
any point.

Again, Helmholtz’s notation for the form of g gives
cr=y(<^ + w) where is a scalar and Sya»=0, and these for-
mulae are applicable in the reduction of the equations.

A slight adaptation of this method enables us to prove
that if p and q are quaternion functions of r, we should
have

y{pq) = ypq + Kpyq + 2(Spy)q

II.

These results are very useful in obtaining modified forms
of Green’s Theorem.

The general form of the theorem is

f Sy\pdv = JSxpv.ds.

where i// is a single valued vector function in simply con-
nected space, dv an element of volume, ds of its bounding
surface, and v the unit vector normal to ds drawn outwards.

120

Case I. Let \p=v(p(j).

Then by (V)

= Svpc - SpVo”

and we get

J’^'^padv — J'Sp'S/crdv = J'SYpff.vdS — JspffvdS VII.

Case II. Let \p=(p(T, where ^ is a scalar.

Then v+ =

and J'S'^(J)<T.dvJ'S'S/(T.(l)dv = J^(j)Sa’vdS. VIII.

Stokes’ Theorem can be made by similar treatment- to
give varied forms, both more and less simple.

PHYSICAL AND MATHEMATICAL SECTION.

March 2nd, 1880.

E. W. Binney, F.K.S., F.G.S., President of the Section, in

the Chair.

“Results of Observations of the double-period Variable
Star R Sagittce,” by J oseph Baxendell, F.R. A.S.

During the last two years I have observed six of the
principal minima of this interesting variable, and as I had
not made a redetermination of its elements since the end of
18C1, or only two years after the discovery of its
variability, I have reduced and projected all my observations
made since that time and have obtained the dates of 26
additional principal minima. The entire series from the

121

discovery of the star’s variability in 1859 to the end of

1879 is as

follows : — ’

No.

Date.

Mag.

Days

in

Interval.

Number

of

Periods.

1

1859, Oct. 27

9*8

2

1860, Jan. 7

9-6

72

1

3

„ May 31

9-7

145

2

4

Aug. 7

lOd

68

1

5

„ Oct. 19

10-3

73

1

6

„ Dec. 27

10-0

69

1

7

1861, May 1

10-0

141

2

8

„ July 25

9-7

69

1

9

„ Oct. 8

9*7

75

1

10

„ Dec. 17

10-0

70

1

11

1862, July 15

9-7

210

3

12

„ Sep. 19

9*2

66

1

13

1863, July 4

9*5

288

4

14

„ Sep. 11

9-7

69

1

15

„ Nov. 18

9-6

68

1

16

1864, June 19

10-1

214

3

17

„ Aug. 30

10-0

72

1

18

„ Nov. 6

9*4

68

1

19

1865, June 4

9-7

210

3

20

„ Aug. 15

9*7

72

1

21

„ Oct. 23

9-8

69

1

22

1866, May 25

9-7

214

3

23

„ Aug. 2

10-0

69

1

24

„ Oct. 12

9-8

71

1

25

,, Dec. 22

9-7

71

1

26

1867, Sep. 28

9 ‘8

279

4

27

„ Dec. 5

9-9

68

1

28

1868, July 5

9-3

213

3

29

„ Sep. 12

9-3

69

1

30

1878, Aug. 19

9-1

3628

52

31

,, Oct. 30

9*6

72

1

32

1879, Jan. 10

10-1

72

1

33

5? Aug. 5

9-9

207

3

34

,, Oct. 15

10-0

71

1

35

„ Dec. 24

9-8

70

1

122

Dividing this series into two, the first containing the
minima numbered 1 to 18, and the second those numbered
from 19 to 35, and determining the mean epoch for each series,
we obtain from the interval between the two epochs and
the corresponding number of periods, the value of the mean
period on the assumption that the period is uniform and
only subject to accidental changes. This value is 70T54
days, and the mean epoch for the entire series of minima is

1866, July 25-815.

Calculating the times of minima from these elements and
comparing the observed with the calculated times we obtain
the following difierences : —

No.

1. - 8-44 days.

No.

19. + 4-11 days.

5)

2. -6-59

yy

yy

20.+ 5-96

yy

JJ

3. -1-90

yy

yy

21. + 4-80

yy

JJ

4. -4-05

yy

yy

22.+ 8-34

yy

5)

5. -1-20

yy

yy

23.+ 7-19

yy

»

6. -2-35

yy

yy

24.+ 8-03

yy

?)

7. -1-66

yy

yy

25.+ 8-88

yy

)?

8. -2-81

yy

yy

26.+ 7-26

yy

9. + 2-04

yy

yy

27.+ 5-11

yy

J?

10. + 1-88

yy

yy

28.+ 7-65

yy

11. + 1-42

yy

yy

29.+ 6-49

yy

jy

12.-2-74

yy

yy

30.-13-51

yy

yy

13. + 4-65

yy

yy

31.-11-66

yy

yy

14. + 3-50

yy

yy

32.- 9-82

yy

yy

15. + 1-34

yy

yy

33.-13-28

yy

yy

16. + 4-88

yy

yy

34.-12-43

yy

yy

17. + 6-73

yy

yy

35. - 12-57

yy

„ 18. + 4-57
The distribution of

yy

the plus and

minus errors shows at

once that the period has not been uniform, but that it was
longer in the earlier than in the later years. I therefore
grouped the minima observed in the years 1859 to 1868 into
four groui>s, and on forming the usual equations, and treating

123

by the method of least squares, I obtained the following
results : —

1859, Oct. 27, to 1861, Oct. 8, nine minima gave the
mean period = 70*88 days.

1861, Oct. 8, to 1864, Aug. 30, nine minima =70*46.

1864. Aug. 30, to 1866, Dec. 22, nine minima = 70.44.

1866, Dec. 22, to 1868, Sep. 12, five minima =69.96.

The interval from 1868, Sep. 12, to 1878, Aug. 19, was
3628 days, and comprised 52 periods : the mean period was

= 69*77 days. 1878, Aug. 19, to 1879, Dec. 24, six minima
treated by the method of least squares gave the mean
period = 70*00 days.

These results show that the period had a minimum value
in the long interval from 1868, Sep. 12, to 1878, Aug. 19,
and that it has since slightly increased ; but as it might be
doubted whether an error of one period might not be made
in estimating the number of periods in so long an interval
it may be stated that if it be assumed that only 51 periods
elapsed during the interval the mean period would be 71*13
days, whilst 53 periods in the interval would give a mean
of 68*45 days ; but looking to the results for the nine years
1859-1868, and the two years 1878-9, it is evident that a
mean period of 71*13 days is too long, and one of 68*45 days
too short to be admissible.

The secondary minima I have observed from the discovery
of the star’s variability to the end of 1879 are as follows : — ■

No.

Date,

Mag.

Days

in

Interval.

Number

of

Periods.

1.

1859, Nov. 25....

.. 8*6

2.

1860, June 23

.. 8*7

211

3

3.

„ Sep. 10 —

.. 9*1

79

1

4.

1861, June 24

.. 8*8

287

4

5.

„ Aug. 30....

.. 9*1

67

1

6.

„ Nov, 11....

.. 9*2

73

1

7.

1862, Aug. 18

.. 9*1

280

4

8.

„ Oct. 28...,,

.. 9*3

71

1

124

No.

Date.

Mag.

Days

in

Interval.

Number

of

Periods.

9.

1863, May 30...

... 9*2

214

3

10.

„ July 29..

... 9-1

60

1

11.

,5 Oct. 15...

... 9*3

78

1

12.

„ Dec. 22...

... 9'2

67

1

13.

1864, May 25...

... 8-9

155

2

14.

„ Sep. 28...

... 8*8

126

2

15.

1865, July 9...

... 8'8

284

4

16.

„ Sep. 20...

... 8-9

73

1

17.

1866, July 5...

... 9-0

288

4

18.

„ Sep. 3 . . .

... 8'9

60

1

19.

„ Nov. 15...

... 9-2

73

1

20.

1867, Aug. 28...

... 9-1

286

4

21.

„ Nov. 6...

... 8'9

70

1

22.

1868, Oct. 17...

... 9'4

345

5

23.

1878, July 16...

... 9'4

3559

51

24.

„ Dec. 5...

... 9-4

142

2

25.

1879, Sep. 3...

... 9*4

272

4

26.

„ Nov. 14...

... 9-3

72

1

Treating

these data by

the method adopted with

principal minima the resulting mean period = 70 '173 days;
and the epoch 1866, June 20*929.

Comparing these elements with those derived from the
principal minima, it will be seen that the mean interval
between a principal minimum and the following secondary
minimum is 34'886 days, or almost exactly half the whole
period.

My observations have enabled me to determine the times
of 24 principal, and 19 secondary maxima, and comparing
them with the times of the preceding principal minima I
find that the mean intervals are respectively 14'8 and 45 '6
days. Dr. Schonfeld in his Zweiter Catalog von verander-
lichen Sternen, gives the mean intervals derived from his
own observations in 1865-70 as follows : —

125

Principal Minimum to

Schonfeld.

Baxendell.

d.

d.

First maximum...

...14*4

14-8

Second minimum

...34*6

34-9

Second maximum

...45'3

45*6

Considering the nature of the observations, and the
limited number of minima and maxima compared, the near
agreement between the two sets of results may be regarded
as satisfactory.

The mean magnitude of the variable in its
Principal minimum is 9 ‘75

First maximum 8'55

Second minimum 9 '08

Second maximum...... 8*68

An examination of the columns of magnitudes shows that
considerable irregularities in the light of the star take place
in both minima, the range of variation at the principal
minimum being 1*2 mag., and at the secondary minimum
0’8 mag. The range of variation at both maxima is 0*7, the
highest magnitude at the first maximum having been 8 ’3
and the lowest 9*0; while at the second maximum the
respective magnitudes were 8 '4 and 9T.

Grouping the magnitudes at each minimum into three
groups, and taking the means, we have the following
results : —

Principal Minimum. Secondary Minimum.

Number

Mean

Mag.

Number

Mean

Mag.

Differences

Group.

of

Mags.

Group.

of

Mags.

of

Means.

1

12

9-81

1

9

9-01

0*80

2

12

9-75

2

9

8-99

0-76

3

11

9-68

3

8

9-26

0-42

The numbers in the last column seem to indicate that the

126

mean difference between the magnitudes at the two minima is
slowly decreasing ; and it will therefore be interesting to
watch whether this decrease will go on until the difference
entirely disappears and the star becomes a single period
variable; or whether the difference is subject to periodical
changes, alternately increasing and decreasing within
certain limits.

127

Ordinary Meeting, March 9th, 1880.

J. P. Joule, D.C.L., LL.D., F.RSi, &c., President, in the

Chair.

Notes on the Biquadratic equation

+ c = 0 (1)/’

by Robert Rawson, Hon. Member of the Manchester
Literary and Phil. Society, Associ. of the Institution of Naval
Architects, Member of the London Mathematical Society.

1. This equation has received the earnest attention of the
greatest Mathematicians of Europe during the last three
centuries. There is one principle, however, common to all
their researches on this subject, viz., the formation of a
biquadratic, with indefinite coefficients, the roots of which
can be determined by means of cubic and quadratic equa-
tions. The form (1) can be readily reduced to the following
form :

ax^:^hx ■¥ c = 0 (2)

where a, 6, c are real numbers. Under this form the
biquadratic has been considered by nearly all writers on the
subject.

The various forms which have been successfully proposed
for the formation of the biquadratic, with indefinite coeffi-
cients, may be arranged in the following manner :

By Harriot.

{x — a){x — I3)(x — y){x — d) = 0 (A)

By Des Cartes, Bombelli, Oughtred, and Harriot.

(x^ + + l3)(x^ — ax + y) = 0 (B)

By Ferrari j Newton, Waring, Maclaurin, and Simpson.

(x^ + ^X + aY = fi.X + JyY (C)

By Euler.

x^ — (a + yY (D)

The quantities a, /3, y, S are indefinite constant, which may
be determined so as to satisfy four given conditions.
Procebdinus— Lit. & Phil. Soc.—Vol. XIX.— No. 11.— Session 1879-80

i28

2. The form (A), according to Wallis, was first introduced
by Harriot, a distinguished English mathematician at
Oxford in the middle of the 16th century. He was the
friend and tutor of Sir Walter Kaleigh.

In consequence of the* very general application of this
method of forming algebraical equations of all dimensions,
Wallis speaks of it in terms of high commendation. The
following opinions are gathered from his Algebra, pub-
lished in 1685 : —

“ Wherein lyes the main mystery of Algebra.” (Wallis*
Algebra, page 128.)

“ In this method of producing higher equations Harriot
is followed by Des Cartes.” (Wallis’ Algebra, page 140.)

“ Which is the great key that opens the most abstruce
mysteries in Algebra.” (Wallis’ Algebra, page 199.)

I can hardly expect any new improvement of pure
Algebra, other than what is built on the foundation laid by
Harriot, and assumed by Des Cartes.” (Wallis’ Algebra,
page 213.)

This is certainly high praise in favour of Harriot and his
discoveries in Algebra by the foremost thinker in specula-
tive mathematics before the Newtonian era.

It may be, however, fair to mention that both the French
and Italian Algebraists disagree with the above view of the
subject, and accuse Wallis of possessing an unfair partiality
for the inventions of his countryman Harriot.

The truth seems to me to be this. The revival of learning
in Europe in the 15th century no doubt had considerable
power in stimulating independent thinkers in the fields of
pure and mixed science. It is, therefore, only natural to
suppose that publication should disclose some remarkable
coincidences in the results of such independent investiga-
tions.

This conclusion is in strict accordance with the experience
of our own times* Here, then, is the solution of the con*

129

troversy respecting the first solution of biquadratic equations;
and it is not unreasonable to infer that the first solution of
a biquadratic known to English students, through the
excellent treatise on the theory of equations by Todhunter,
as Des Cartes, may justly be claimed by Bombelli, Oughtred,
and Harriot.

In Wallis’s Algebra, published in 1685, there is a copious
account of the works of Vieta’s specious arithmetic, Oughtred
and his Clavis, Harriot’s Algebra, published in 1631, Hr.
Pell’s Algebra, and several other works of European interest.

By multiplying out the form. (A) there results

— (a + /3 + V + + (a/3 + a?/ + + /3v + /3^ + vh)x^

— (a(3y + aj3B + + ayS)x

+ a/3r^ == 0 (3)

If this biquadratic is to coincide with (2) it can do so only
by determining the indefinite coefficients a, /3, r, S so as to
satisfy the following equations :

a+/3 + p + S = 0 (4)

a/3 + a?^ + a^ + (3^ + j3h + = a (5)

al3v + avh + + af3d = (6)

a[3vh — c (7)

These equations, though admirable in discovering the
various relations amongst the roots themselves, are but of
little use in finding each root in functions of a, b, c. For
instance square (4) and compare the result with (5), then

a^ + /32 + + -2a...

a^ + /3« + v® + a3= T35....
a^ + /3^ + v^ + a^ = 2a2-4c
a^ -t- /3® + V® + ± 5a6. .

..(8)

..(9)

ao)

(11)

The value of a’* + /3'‘ + + a” can be obtained by Newton’s

process in terms of a, 6, c.

3. The form (B) which is said to be due to Hes Cartes,
but according to Wallis is equally due to Bombelli, Ouo-htred,
and Harriot :

Multiply out, then,

iJ3 ■¥ V — a^)x^ + a(i^ — /3)o; + /3»/ = 0 (12)

This equation coincides with (2) when the following equa-
tions are satisfied :

l3 + V — a^ — a 'I

a(v-/3) = ±6 V (13)

(3v = c )

These conditions

give

2a

2a

(14)

(15)

And an auxiliary cubic

(a^)^ + 2a{aJ + {a? - ic){a?) ~b^ = 0 (16)

Now, if the three roots of (16) he represented by r, s, t

a- sjr )

r + s + f= -2a > (17)

rst = h^ j

Substitute these values in (14), (15),

^”4" 4

4 4

Then the form (B) becomes

*’+ + + =0...(18)

By solving these two quadratics.

2x= ^/r + ^~s:^s/l or, -

2x= ^ r+\/s'^Jt or, J

The upper sign applies when (h) is positive, and the lower
when (6) is negative. The auxiliary cubic is the same for
+ ax^ + hx + c = 0 as for + ax^ - hx + c — 0.

The omission of the double sign of (5) by Mr. Todhunter
and other writers on this subject render their solutions un-
necessarily restricted to the solution of x“^ + ax^ -^-hx + c = 0.

It readily follows from (19) that when the biquadratic
equation x^ + ax^zkhx + c = 0 has equal roots, the auxiliary cubic
(16) has equal roots. (See Todhunter’s Theory of Equa-
tions, page 115.) When the auxiliary cubic has equal roots
it would not be safe to infer that the biquadratic has equal

131

roots. In this case three roots only of the biquadratic are
generally equal.

“If the cubic equation has one positive root and two
negative roots, the biquadratic equation has two real roots
and two imaginary roots, or else four imaginary roots.”
(Todhunter's Equations, page 115.)

It would seem from (19) that the four roots of the
biquadratic are always imaginary in this case, except when
the two negative roots of the cubic are equal ; and then the
biquadratic has two imaginary roots and two real and equal
roots.

If the cubic has one positive root and two imaginary
roots, the biquadratic has two real and two imaginary roots.
(Tod hunter’s Equations, page 115.) This is readily proved
by expanding y/ p + ^

The sum of the squares of each root of (2) is equal to the
sum of three roots of the auxiliary cubic.

4. The form (C) is said to be due to Simpson, Waring,
and Ferrari, but it is certainly found in the Universal
Arithmetic by Sir I. Newton, in Maclaurin’s Algebra, as
well as in Simpson’s Tracts. It differs but little from the
form (B), to which it is readily reduced as follows : —

x^ + dx + a = rapt.x + \/ mv)

+ (^ — \/ mjS)^ + a — \/ rnv\ mj3)^ + a + \/ - 0. . . (20)

This reduces by multiplication to

x^ + 2^aj® 4- (^^ + 2a-‘ m(^)x^ + 2(^a — m \/ [iy)x + — 'mv = 0 ...(21)

An equation which coincides with (1) when the following
conditions are satisfied :

2d = '11^

+ 2a - m(3 = a

ah-m.ypv = ±^\ ....(22)

a^-mv = c J

These equations give

m/3 = 2a + - a

mv = - c

With an auxiliary cubic

(

3 ^2

2

nh\ cn^ ac ^

“^T>--8 + 2-8 = ‘^'

,(23)

Newton and Maclaurin pass over this auxiliary cubic in
silence, that is, their minds were evidently occupied with
illustrating the method of surd divisors to such an extent
that they did not obtain this cubic at all.

Simpson, following somewhat in the v/ake of Newton
and Maclaurin, does indeed slightly refer to it as being an
equation which “rises to the sixth dimension, and would
perhaps require more trouble to reduce it than even the
original propounded, little advantage would be reaped
therefrom.” (Simpson’s Tracts, page 108.)

This view is surprising from Simpson, by far the greatest
mathematician of his age. Had he used instead of

/3, V, in all probability he would have found the auxiliary
cubic referred to.

Emerson, writing twenty years after Simpson, in his
solution of biquadratic equations, makes no use of N ewton’s
method of surd divisors, a system which is never likely to
be resuscitated in the presence of Horner’s method of
solving numerical equations of all dimensions.

5. The form (D) is entirely due to Euler alone, and, like
many of the mathematical investigations of this wonderful
man, it is characterised by great clearness, simplicity, and
analytical beauty.

As there is no restriction on the constants a, /3, v, the
values v/a, \//3, will be used instead.

The following operations are readily performed from (C) ;

a + /3 + V + 2{ \/ a/3 + V

[a + ft + vY + 4(a + ft + v){\/ aft + \/ av + \/ ftv) + aft + av + \J ftvY

(a + ft-\-vY + 2(a + ft + v)\^0G^ — (a + /3 + j/)| + 4(a/3 + av + ftv) + 8 v/ aftv.X
- 2(a + /3 + v)x^ - S^/ aftv.X +{a+ft + v)^- 4(a/3 + av + ftv) = 0...(24)

The coefficient of x in (24) is the only term affected by
changing the signs of V Therefore, when any

138

two of these quantities are changed from positive to nega-
tive there will be no alteration in the biquadratic (24).
Hence,

are roots of (24) equally with (^/^, + + v' y)-

It remains, then, to determine a, /3, r, so as to coincide
with (2) ; for this purpose it is necessary that the following
conditions should be satisfied : —

a+(j + v=

^ ^ - 4c

ap + vv + pv=— Y0 —

By the theory of equations a, /3, v, are the three roots of
the auxiliary cubic —

(25)

q Ct a

+ —z^ +

2

- 4c ¥ ^

The coefficient of (x) in (24J is positive when any one of
the three terms or all of them negative.

Hence ( — \/ a — -v//3 — \/ v) ;—\/ a + a/ j3 + y/v) ; +

(\/a + - y/ v) are the roots oi x'^ + ax^ + hx + c = 0.

It appears, therefore, that the introduction “of the am-
biguities in sign” mentioned by Mr. Todhunter, page 120 of
his Equations, is not necessary to establish Euler’s results.

6. In Euler’s process there appears considerable latitude
for the exercise of the inventive faculty in the arrangement
and maojnitude of the roots.

O

The following occurred to me as being simple. Form the
biquadratic as follows —

I X-

v/ a

■ — Ih

\/ a_ y/P ^

\/A

VP

. Vy

\

m

m

m J\

m

m

m J

\ m

m

m

(

( \/ a

x + -

-XP

_\/y\ ^

0 ..

(26)

^ m

m

m J

■■■!

-

m )

_ (^/^ -

m

2

} {(^^

y/ a"'
m J

yVy

Or.

)

0

134

- illA±Ax^ + ~ ^(«/3 + gy /3v) ^ ^ .^7)

m* ’ ’ \ /

Now this equation will coincide with x^ + aa^ + hx + c = 0

when

a + P + c

m^a

n ri VtlHc^ - 4c)

aj3 + ay + Qv = — -

lo

a(^y

~U

Hence, a, /3, v are the three roots of the auxiliary cubic
o m^a „ mHa^ - 4c) ^

2“ + — 2^ -1 ^ “ = 0

2 16 64

(28)

As this auxiliary is the same when (h) is negative, it will
be necessary to change the signs of so as to

make the coefficient of x in (27) negative — this is easily
done when required. This mode of procedure renders
unnecessary the solution of two quadratics.

7. The following, which has occurred to me, seems to
combine all the advantages of the forms (B) and (C).
Assume —

{i(^ + a.x ^ (3 + V i'} ~ + \/ (3 - \/^y} =0...(29)

The biquadratic formed by multiplying out.

+ [2-^ (3 — n^a)x^ — 2nyJ ay.x + j3 — v = 0 (30)

The coincidence of (30) with (2) gi ves

2-)/ (3- n^a = a

— 2n \J av — ±5 y (31)

(3 — y = C J

From these conditions it follows that

b

V'v = =F;

VP =

With an auxiliary cubic

2n^/a
a + n^a

a^ +

2a

n

a^ +

- 4c 6^

= 0.

or

Let r, s, t, be the three roots of this auxiliary cubic.

.(32)

135

Then, by the theory of equations

r + S->rt-

2a

— — ^ a wr

:,x^-^ny/r.x= - \//3-\/v = 9-^±

2 2
_\2

2?i y' 'p

Tirr _

= ^ I I - -x/r - -v/6=F v/ « j

Similarly

»=§ {v'j'-Hv'sTv'q ^^Vr- V~s^V~t\

These are, therefore, the four roots of

x^ + an^Jtz^x + c = 0

8. There are other methods of solving biquadratics
depending upon general views applicable to equations of all
dimensions —

Tschirnhausen’s method is to reduce

x^ + 7io(^ + ao(^ + bx + c = 0 (33)

to j/^ + A2/^ + B = 0

by eleminating x between (83) and the following

oi^ + ax + p + y-O (34)

where a, (3, are indeterminate constants.

Lagrange has applied the theory of symmetrical functions
to the solution of equations of the third and fourth degrees.

The above methods effect the object in question, but, by
processes far more complex than those adopted in this paper.
Professor Young has given a very ingenious solution of a
biquadralic. (Young’s Equations, page 454.)

“ The Castel Nuovo Lignite Deposit, near San Giovanni
Tuscany,” by Watson Smith, F.C.S., F.I.C.

During the Easter of 1877, I had been requested by Jas.
Young, Esq., LL.D., F.KS., to execute a commission in South
Italy for him, and was on my return to him in Florence,
when on passing a small station, “San Giovanni,” still some

186

10 miles from Florence, I observed there at a siding a large
quantity of apparently good Lignite piled up, and ready for
delivery by rail. Further away I saw what appeared
very like an ironworks, and this being at a little
country place, with the beautiful hills of Yallombrosa in full
view, led me to believe the Lignite deposit could not be far
off, Reaching Florence I spoke of the circumstance to Dr.
Young, and found he had already taken note of it, and he at
once proposed I should go and investigate the matter, which
I did. Proceeding to San Giovanni, and finding a guide,
we drove out some four to six miles to a small village,
Castel Lfuovo’’ from which the deposit, or rather workings,
are about ten minutes walk distant. The country here is
hilly, very verdant, and abounding in trees, but in the
direction we came it is gently undulating, almost fiat, and
continues so to the Yallombrosa hills. The deposit appears
to commence in the fiat or gently undulating land, and
stretch out amongst the low hilly district around Castel
Nuovo.

The land surface covering the deposits, as far as yet
investigated, extends to a superficies of about 4,000 by 7,000
square metres. This is as far as yet discovered, but there
is more yet in all probability, the manager told me. The
deposit, so far traced out, is calculated to last for 400 years
yet. I was told the deposit was only discovered 11 years
ago, and work was commenced (i.e. output) a few months
after the discovery.

The entire deposit is owned by one company, and a tram
is laid from the deposit to the railway station and the iron-
works, owned by the same company, and close to the station
mentioned.

The workings have at first sight the appearance of a great
quarry, for the borings or tunnelling proceed longitudinally.
Through the whole depth of the seam run five or six
thin bands of greyish clay, 30 centimetres thick, they run

187

quite horizontal and parallel to each other, with these also
are to be seen one or two little bands of red ferruginous
clay.

I should mention that the ironworks belonging to this
company I was not able to visit, which I regret very much.
However, as I saw no blast furnaces, and outside a good
deal of “raw pig,” I conclude that they busied themslves
there merely with imddling” Most of the iron-ore, of
best quality, used in this part of Italy comes from Elba.

The Lignite itself is not so far advanced in mineral
character as the slaty variety known in Zurich, and occur-
ring on the banks of the Lake by Meilen as “ SchieferJwhl”
It is not so hard and slaty. It is more fibrous or woody
than this, and yet it is of a slaty texture. The bulk seems
mostly a little wet, though a great deal appears very dry.
It is all however exposed in the sun to dry. Some of the
best is cut evenly in blocks and dried on drying flats of
rough brick work, the fires underneath being maintained by
some of the worst, with dust, smalls, and refuse. The colour
of the Lignite is dark brown, much like the “ Schieferkohl”
of Meilen by Zurich.

In excavating the deposit, and detaching large blocks of
Lignite, very frequently a large escape of gas occurs; there is
a rush, and if torches are near, a flame, and then all is over
again, the flame soon going out. From this it would
appear that the fire-damp is pretty well diluted wflth Carbon
dioxide, in all probability. However, no gas is ever met
with, I was assured, which extinguishes candles. So it
would appear that the “ fire-damp ” or “ Marsh gas ” is
pretty uniformly in some excess, in the occluded gases.
There is a good deal of sieving done, to separate dust from
the coarser lumps. Now these sievings when thrown on
one side in heaps, are said to “ferment” and take fire
spontaneously. This is continually occuring and requires
watchfulness. This fact points to the very probable occur-

138

rence of iron pyrites in a finely divided state, amongst the
substance of the Lignite. I noticed in several places
portions of blocks of woody matter quite charred by the
combustion of gas, fired simply through intense heat, caused
by oxidation of a freshly exposed surface of lignite.

With regard to the output in 1878, this was 700 tons per
week, or 120 per day. 200 men were employed. Those
working the deposit are paid at the rate of IJ Liras per
diem, the lira being about 9;|d. of our money. So these are
certainly not overpaid colliers !

The price of the dried Lignite is 12 Liras per 1000 kilos,
which is not 10s. per ton, something near 9s. 6d. per ton.

On distillation, an aqueous acid liquid is obtained,
smelling of wood-tar creosote. The tar smells like wood-tar.
The pitch is bright, and very like wood-pitch. A kind of
lubricant is made for the wheels of the tram wagons by
mixing the crude tar with linseed oil. The gas obtained
by distilling the lignite is to some extent illuminating, but
not sufficiently so for house use. The manager said a
process had been devised by a Florentine gentleman for
conferring illuminating power on it, or of treating, or
distilling it, so as to obtain illuminating gas from it sufficing
for all purposes, and Florence was shortly to be lighted by
this gas.

Possibly this method depends upon the fact mentioned by
Percy in his work on “FueP’ (Metallurgy), p. 139, that “if the
volatile products from the carbonization of wood be subjected
to a considerably higher degree of heat than that usually
adopted in the charring process, instead of CO2, CO, and
CH4 being formed, a mixture of gases in which olefiant gas
is now present, is obtained, and this possesses considerable
illuminating power, and has been successfully applied for the
purpose of illumination.” I may just mention that in the
ordinary distillation of wood in closed iron-retorts or ovens,
just about the termination of the process, the gases evolved

139

/

become more and more strongly illuminating, and in fact an
arrangement had been used for the purpose of illuminating
part of the works, in one case I knew of, but it only
answered during the last few hours of the process.

“Analyses of the Ash of Wood of two varieties of the
* Eucalyptus’ tree,” by Watson Smith, F.C.S., F.I.C., De-
monstrator and Assistant Lecturer in the Owens College.

During Easter, 1877, Jas. Young, Esq, LL.D., F.RS.,
suggested to me that I should make analyses of the ash of
the two varieties of eucalyptus, viz. E. rostrata and E. globu-
lus, commonly known as red and blue gum trees. The pieces
of wood I was supplied with by Dr. Young. They appeared
to be stout branches, “ crop-wood,” and had the bark still
on. The wood of E. rostrata (“ red gum”) was evidently
closer and denser in texture than that of the “ blue gum” or
E. globulus. Its bark was also thinner and smoother. I
took the samples of the wood to a joiner in Zurich, and
requested him to plane them down to thin shavings, with
the exception of a transverse section of each variety, to be
reserved for specific gravity determinations. I requested
him also to notice any peculiarities he might notice in the
wood and report them, with his opinion of their quality.
On calling subsequently, I noticed on entering the shop the
odour of the gum or essential oil peculiar to the tree. The
whole shop was fragrant with it. On planing the wood to
shavings, this odour is quickly diffused around. The joiner
stated it as his opinion that the wood of the “ red gum” va-
riety, especially, was extremely hard. It had quite turned
the edge of his plane. The timber of such a tree, he said,
would be of great value. The wood of the “ blue gum” tree
was a little behind in point of hardness and solidity. De-
terminations were now made of the specific gravity of these
woods in what may be termed the air-dried condition.

140

The sections of both varieties had been placed in a dry
atmosphere for one month. The results were :

Eucalyptus rostrata. Eucalyptus globulus.

“ Red gum.” “ Blue gum.”

Spec, gravity 0‘8112 Spec, gravity 0’772

These sections were now planed (bark included) to thin
shavings, which were now weighed, burnt in a platinum
dish to white ash, and this was weighed. The results were :

E. rostrata. E. globulus.

Ash 2-25% Ash 2-01%

Analyses were now made of the ash obtained by burning
the shavings of the larger samples. This ash was white,
inclining to straw-colour.

Eucalyptus rostrata. Eucalyptus globulus.

“ Red gum.” “ Blue gum.”

KaO

NaaO

9-50

3-40

K^O 1

NaaO j

25-00

MgO

6*30

MgO

6-47

CaO

43-80

CaO

35-08

Ferric and aluminic

Ferric and aluminic

phosphates

0-78

phosphates

1-07

MnO

trace

MnO

trace

SiOa

0-29

AI2O3

trace

SOo

1-57

SiOa

0-34

Cl

0-60

SO3

1-55

Sand and carbon...

1-77

Cl

0-85

Sand and carbon ...

1-04

The leaves of the eucalyptus contain very considerable
quantities of tannin ; in fact, I think it is certain at some
time or other they may prove a valuable source of tannin if
the tree be largely cultivated. I have been told that in
some parts where the tree abounds, a kind of decoction is
made of the leaves, and drunk as tea is.

141

General Meeting, March 23rd, 1880.

J. P. Joule, D.C.L., LL.D., F.KS., &c.. President, in the

Chair.

Dr. Lloyd Roberts, of Kersal Towers, Higher Broughton,
was elected an Ordinary Member of the Society.

Ordinary Meeting, March 23rd, 1880.

J. P. Joule, D.C.L., LL.D., F.R.S., &c.. President, in the

Chair.

On the History of the Word ‘Chemistry’ or ‘Chemia,’ ”
by Dr. R. Angus Smith, F.R.S., &c.

The Author said that he had been led to a renewed con-
sideration of the meaning of the word chemistry because of
papers read lately on the subject by Professor Schorlemmer,
F.R.S., in Manchester, and Mr. McTear in Glasgow, a very
brief abstract of the latter being seen. He had always been
inclined to agree with Olaus Borrichius in his reference to
Egypt for the word chemia and the chemical arts as well as
the early attempts at a science, and he was especially in-
clined to do so on reading of the few Greek manuscripts
that have been published or described by sufficient extracts
being given. The eyes of the writers were evidently much
turned to the lajid of Chemi, whilst Isis and Osiris were
favourites. For many years he had occasionally tried to
interest young Greek scholars in the subject, and he had
hoped that when Dr. Kopp began his description in his
very learned work the “ Beitrage zur Geschichte der Chemie”
that the examinations would have been exhaustive, but
that author was not inclined to go further at the time.

Proceedings — Lit. & Phil. Soc. — Vol. XIX. — No. 12. — Session 1879-80.

142

If Formicus used the word chemia in the second, third, or
fourth century, and if chemistry were meant, we have a
good starting point ; hut Formicus was an astrologer, and
he gives no definition.

The tract by “ Democritus” speaks of several chemical
subjects, and he is said to have treated of metals and purple
dyeing, having learnt Egyptian and other Eastern wisdom.
Dr. Kopp considers that he may be referred to the fourth
century. No criticism of any point of Kopp’s enquiries was
proposed ; it was intended to begin where he had ended his
enquiries, and to go into earlier times.

The old belief that chemistry has something to do with
the soil of Egypt was not considered just. Brugsch says
that Egypt is called black in contradistinction to the Desert,
which is called red in hieroglyphic inscriptions. But the
soil is not really black, and even if it were so, chemistry can
have no direct relation to it. Still an art might receive
the name of the country it came from, as Japan gives us
japanning, &c. But so much came from Egypt to the West
that we have little reason to suppose that such an obscure
subject as chemistry would be the only one to take up the
name of such an illustrious country and carry it to the
West, whilst only those outside who foresaw tlie greatness
of the Science would give it a great name. The Egyptians
themselves would scarcely do so. Why should they choose
this as peculiarly characteristic of their country ?

Dr. Angus Smith came to the idea that the word UpH
Hema or Khema, meaning heat in Hebrew, was much
more likely to be the origin of the name chemia than
any hitherto fixed upon, and hoped by the later re-
searches in Egypt and Assyria to have some light thrown
upon it. Professor Theodores, of Owens College, being
asked, gave information which confirmed him in the
belief, and also showed that the word was not an Arabic
one. “ If Kimia be an Arabic word the attempt to graft it

143

on hot or black is futile,” and he quotes Bochart’s proposal
to derive it from Kama, to conceal, but wisely sets such
aside. To quote one of his letters again- — ‘‘ (cognate

in character to on') means to be hot ; from it are derived
the forms Hammah, ^‘heat,” also sun, “the receptacle of
heat.” Another noun is Hema, “ fiery anger.” This latter
form occurs in Deuteronomy 32, 24, in connection with the
names of snakes or some such animals.” This word is,
according to Professor Theodores, incorrectly translated
“ poison.” It would appear to be heat, as in hot with rage.
The author did not know how far Semitic scholars would
allow the next stage, which is to connect this with n^H,
which certainly softens the first letter, giving us the meaning
of noise and excitement ashy intoxicating drink.

On enquiry of Dr. Birch how such a word could be con-
nected with the Egyptian and Assyrian, he says, “ The word
for heat is Hhamamw or Khamamu.” Then he gives gam,
Egypt, or the black land, gam meaning in Egyptian black.

Having obtained the first idea, heat, it was impossible to
avoid going thus far, but there was a difficulty, namely, in
the connecting links between Egyptian and Semitic. Still
it is allowed that there is frequent connection, and this word
links itself with the Hebrew both towards Egypt and Assy-
ria. It was too early to stop here, because we have the
province of Egypt, Chem, which would seem to have been
the kernel of the Egyptian nationality, the nation keeping,
as it expanded, the original name. The metropolitan name of
Chem is Chemmis, although Thebes overshadowed it. In
Brugsch’s “ Egypt from the Monuments,”*' we learn that the
district was especially under the god Chem, who was the
divine representative of heat as emanating from the sun and
producing life in all nature — not the sun as the Glorious
Apollo, but the sun, we might say in modern phrase, as an

* A History of Egypt under the Pharaohs, derived entirely from the
Monuments, by Brugsch-Bey. Murray, 1879*

144

actinic agent. Chem was called Pan by Greeks and Romans
from some inferior cbaracteristics. Pan, like Chem, had his
high and his undignified position. Chem was “ the Lord of
Coptos,” to which place there was a road from the Red Sea,
through the very hot district of Hammamat (still from
heat), where stones for the temples were obtained, and
where attention was paid to the discovery of gold and silver,
and where Chem was held as “ the master of the tribes
which inhabit the valley,” and the Lord Protector of the
mountain.”* Many complaints were made of the heat of
this valley, where wells were dug in the time of Raineses
the Second, because others much older had been closed up.
It was a burnt land, and it still preserves its ancient charac-
ter. It is the earliest place where we know metals
to have been studied. On the west of the Nile and opposite
was Tini, famous for purple dye, another branch of chem-
istry. Tini, or Thinis, or This was the place where the
earliest king Menes sprang from. In Chem we are in the
land of Heat, where the God of Heat was worshipped, where
metals were worked, and where other chemical processes
were employed, and from which the first chemist, whose
writings are clearly on chemical subjects, and whose draw-
ings are clearly of chemical apparatus, sprang, viz., Zosimus
the Panopolite, or Zosimus of Chemmis, for this is the pro-
per name of his city. The translation of Chem into Pan has
been misleading, and still more of Chemmis into Panopolis.

We thus see that chemistry has received its name from
no trifling accident, but from that great natural agent which
has made the science, and the character of which we are
continually learning.

Pj'of Theodores had quoted for the author Bunsen’s “ Die
Stellung Acgypten’s in der Weltgeschichte,” v. 5, s. 2, where
he says, “ ‘Hem’ or ‘hem,’ Sieden gliihen (i.e. to boil, to glow
with heat) = Hebrew, ham,” and the next part of the quo-

* From Brugsch-Bey.

145

tation must be kept in view — “ h is related to S. The
Egyptian Som has the same value, and with this the Teu-
tonic Sommer. Sommer has some connection through Sun,
Sonne.” This helps us to bridge over some of the ground
to be seen.

Sayce’s Assyrian Vocabulary was then consulted in order
to see if an Assyrian or Accadian origin could be found for
the word. No Accadian word of the kind was found. We
are then guided to Semitic Assyrian, which has —

Samsu, the sun.

Samu, the heavens.

Samas, the sun-god.

Khamsa, fire.

Khamdu, light.

The word then had full force in the East beyond Egypt.

The examination of metals, dyeing, colour making, and
distilling seem decidedly to be referable to Egypt. Distil-
lation leads to alcohol readily, when juices of plants contain-
ing sugar are used, and still more so when sugar is added.

In Egypt there were drinks of great potency, but
the fullest idea seems to have grown in this direction in
Asia, where the Kh or Ch was much softened into h, and
converted into S. This is done by laws not to be examined
here, but received from those who have studied the tongues
of the regions under view (see the quotation from Bunsen).

The study of intoxicating liquors was carried out more
fully in Asia, where mysticism was most prevalent. It is
probable that the love of the spiritual, the unseen, and the
immortal, was among some tribes at an early period con-
nected with intoxicating substances. This itself is a great
field of historic enquiry full of interest.

We have seen how Kama is connected with Som, and if
we go far East we find the great Asiatic drink Soma used

146

%

by the inferior gods to strengthen them in their fight with
demons. Soma is the Sanskrit word for this drink, but
there are many Semitic words the same in Sanskrit, and this
evidently has the same root, which is seen in Egypt moving
towards metals and general chemistry : it had more force in
the far East in connection with the mystic drink, although
the idea may have arisen in Egypt. The vessel into which
the drink flowed, the receiver, was called kama (Indo-ger-
manische Chrestomathie, by Ebel, Leskien, Joh. Schmidt
and Aug. Schleicher). In old Bactrian the word appears as
haoma, whilst in Bussian we find it returned, in all proba-
bility, as koumiss, to more western lands. We have yet to
learn fully the medical effects of the asclepias acida, or
moon plant, from which the Soma was made. Ordinary
alcoholic liquids made by fermentation are notwithstanding
much condemned in the Institutes of Menu.

The connection of the earliest thoughts of civilization
and the later is remarkably seen in the history of this word.
The hope of happiness from intoxicating liquids is evidently
the direction which theory took in the minds of some
searchers for truth, and constant deception seems not to
have cured men entirely. We have removed the intense
faith in the delusion and retained the name of the sub-
stance, i.e., aqua vitae, eau de vie, uisge heatha, all meaning
water of life. The Germans simplified the word by calling
it burnt wine (Branntwein) or brandy, and we have cut
down the latter and Celtic form into whisky. This history
of the theory is believed to be correct, although quite apart
from the derivation of the word chemistry. The connection
of chemistry with moist or dry was considered as too
slight to form a basis for an opinion, and the superstition
concerning a plant that made gold was simply held to have
no solid place in the history. The belief that the word kem
in Arabic, alluded to the fifth element, or ether, as one of
the five existences spoken of in an important part of Indian

147

philosophy, was rejected — hut this abstract is already longer
than usually allowed.

“On the Electrical Resistance and its relation to the
Tensile Strain and other mechanical properties of Iron and
Steel Wire/’ by William H. Johnson, B.Sc.

It has long been known that there is a great variation in
the tensile strain of various qualities of iron and steel wire,
depending on the mode of manufacture and purity of the
material used, and it occurred to the writer that it would
be interesting to examine if this difference in quality was
accompanied by a corresponding alteration in the electrical
resistance.

If electricity is a mode of motion of the particles of
matter, then, it is only reasonable to suppose that anything
which constrains this motion will increase the electric resis-
tance and vice versa. Thus an annealed wire should conduct
electricity better than an 'i^^^iannealed and a hardened and
tempered steel wire, whose particles are in a state of tension
worse than a bright wire ; also from the analogy of copper
wire any increase of impurities in the iron would probably
augment the electrical resistance. The following experiments
will be found to confirm these views.

A series of preliminary experiments were made, beginning
with a pure iron, smelted and worked throughout with
charcoal and ending with a highly carbonized steel wire.

The apparatus used was a Wheatstone bridge, with
divided meter scale and reflecting galvanometer of low resis-
tance. All the wires except the piano steel were drawn in
the same way to No. 18J and then either hardened and tem-
pered, or annealed and finished by drawing one hole to
No. 20 = ‘038 inch. The length of wire tested electrically,
varied from 8 to 3 meters ; care was taken to select such a
length that the resistance was about I’Ohm., as then all four
arms of the balance were equal. A thermometer was placed

1

148

close to the wood drum on which the wire was coiled and
the temperature noted at the time of each experiment.

The circuit was first closed by pressing a button and then
connection with the galvanometer was made. By a suitable
arrangement of keys the current was allowed to circulate
through the wire such a short time that it could not sen-
sibly increase its temperature.

The wire was tested for breaking-strain in an apparatus
similar in principle to a steel-yard weighing macnine, the
weights could be added without any jar and the elongation
recorded at the moment of rupture. The length tested
measured always 10 inches between the jaws of the machine.

The diameter was measured by a decimal guage, manu-
factured by Elliott Bros., reading to i oVo inch.

The tortion tests were made by gripping a wire in two
vices 8 inches apart and turning one of them on to a
suitable apparatus till the wire broke.

The results are given in table A. Charcoal iron is here
seen to have the least electrical resistance, or about one half
that of piano steel. We also notice a regular increase of
resistance as the impurities augment. Charcoal iron is al-
most chemically pure, while dephosphorized iron, the next
on the list, has some impurities which increase in ordinary
iron v/ire. Again in the samples of steel, piano steel wire,
which has the highest electrical resistance, contains two or
three times as much carbon as mild steel, while steel wire
samples 3(X and 2a are intermediate in carbon as they are
intermediate in electrical resistance.

Table A shows that the breaking strain and electrical
resistance increase together.

A series of eight sets of experiments were made on
various specimens of charcoal iron wire to determine the
effect of annealing on the electrical resistance, but without
definite result, as the alteration caused by annealing appears

149

to be so small that it is difficult to distinguish it from
variations arising from change of temperature.

Annealing diminishes considerably the electrical resistance
of puddled iron wire, and has a marked effect on steel, the
exception in the case of sample 3a being probably due to
temperature.

The annealed samples were cut originally from the same
piece as the bright, and the same was the case with the
hardened and tempered, so they are identical in chemical
composition.

As the electrical resistance of steel wire seemed from
these experiments to increase very rapidly, the writer
determined to investigate it more closely. A set of seven
samples of cast steel wire were prepared, all of them manu-
factured in the same way, differing only in the amount of
carbon and other impurities. These samples were drawn to
No. 18 J and each coil divided, one half being hardened and
tempered, then drawn to No. 20 and tested, the other half
of each coil was annealed and drawn one hole to No. 20,
then tested in the bright state and afterwards part was
annealed and tested. The eighth sample was Bessemer
steel drawn and tempered in the same way as the others.
The tempering was done in melted lead at a constant tem-
perature.

The results are given in table B.

The electrical resistances in this table, as in A, are the
mean of two or more experiments differing very little
amongst themselves ; the method of experiment and appa-
ratus was the same as used before.

The figures denoting breaking strain, elongation and
torsion, as in table A are the mean of two experiments in

150

each case. These two experiments gave results sometimes
the same, at others differing 4 to 6 per cent in the annealed
samples, 3 per cent in the hardened and tempered and 4 per
cent in the bright wires, except in sample No. 6, where a
difference of 20 per cent was observed. This probably
accounts for the wide divergence of this sample.

These variations may seem large, but it must be remem-
bered that there is an essential difference between an obser-
vation on electrical resistance and one on tensile strain.
If we suppose the length L of wire under experiment
divided into a great number of extremely short pieces
etc., each one would have a slightly different breaking
strain, hi, h^, etc., and electrical resistance, Ti, r^, etc.,
depending on the physical structure of each length li, 4,
etc. Now the observed electrical resistance R of the wire L
is the sum of all resistances of the parts li, h, etc., or
Rr= S(r), while the observed breaking strain is not the mean,
but the minimum breaking strain of all the pieces li, U, Ig,
etc. It is an experimental fact, that the longer the piece of

wire under experiment, the lower will be the breaking
strain.

Some of the results of the experiments are given in table
B. Here we see again that the electrical resistance
and breaking strain increase together in a pretty regular
way, the variations observed probably being due partly to
differences in temperature, but chiefly to the fact just
explained, that in the electrical experiments we register a
mean, while in the experiments on tensile strain we register a
minimum observation. This law must be applied with due
care and only where the samples have been drawn in the
same way.

151

The mode of manufacture of the 8 samples of steel leads
one to believe that there is a regular increase of carbon and
other impurities from No. 8 to 1. The writer hopes shortly
to analyse these wires, as the resistance of some of the
samples is most remarkable, being no less than 3 times that
of pure iron.

No attempt has been made to reduce the electric observa-
tions by calculation to some fixed temperature, as it seemed
improbable that samples with such varied resistances would
increase in the same proportion as pure iron.

Table B shows us that annealing diminishes the electrical
resistance of bright steel wire some 1 per cent, while
hardening and tempering increases the resistance of an-
nealed steel about 5 per cent. Now we may observe that
the greatest increase of electrical resistance, viz,, 8T per
cent, and of breaking strain resulting from hardening and
tempering, is found in piano steel, thus clearly showing that
any process like wire drawing or tempering, which makes
the particles of steel more rigid and difficult to separate,
increases the electrical resistance.

The torsion tests vary a good deal among themselves, but
it is interesting to observe, from table B, that the mean
breaking strain of hardened and tempered steel is to that
of the same steel annealed in the inverse ratio of the
number of twists in 8 inches. The electrical resistance of
the samples of steel is seen from table B to be usually
inversely proportional to the number of twists in 8 inches.

It is generally allowed that the heat conductivity of
metals is nearly proportionate to their electric conductivity.
If this relation between the thermal and electric conduc-
tivity holds good for different qualities of iron and steel, then

152

the electric resistance is an important factor of all iron
and steel plates used in the construction of boilers, fire boxes,
etc. It is important that the plates exposed to the fiame
should conduct heat well, and one of the advantages claimed
for steel over iron, is that as a thinner plate can be used,
it allows more heat to pass than the thicker iron one.

Thus a J-inch steel plate can replace a |-inch iron plate,
but our experiments lead us to believe that as steel conducts
electricity worse than iron the thin steel plate may, after
all, let less heat through in a given time than a thick iron
one.

Suppose the iron plate has a resistance of *90 Ohms, per
meter gramme, and the steel plate a resistance of 111 Ohms.,
then a f -inch iron plate will allow as much heat to pass per
unit of area as a half-inch steel plate. If the steel plate be
more highly carbonized, say of Siemen’s Martin steel, then
the J-inch steel plate will allow no more heat to pass per
unit of area than an iron plate -j^e'-ii^ch thicker. There is
not space here to discuss this subject fully, but there is no
doubt of its importance, and it is probable the time will
soon come when our leading boiler makers will electrically
test their steel plates, perhaps by the induction balance, just
as they now test them for ductility and tensile strain.

153

Table A.

Electrical and Mechanical Tests of various qualities of Iron and Steel Wires.

Quality.

Sample No.

Length.

s

bJO

•rH

o

Eesistance 1 Meter
Gramme.

Temperature of Ex-
periment

Breaking Strain per
Square Inch.

1 Twists in Eight
Inches.

Elongation %

Diameter.

Annealed Charcoal
Iron

6a

M’ts.

8

Grms.

47-403

Ohms.

-7875

13°

Lbs.

50,280

138-5

27-75

Inch

-039

Bright ditto

7a

8

47-391

•7852

13°-5

105,840

57

2

-038

Dephosphorized Iron
Annealed

—

5

28-000

-8908

10°

63,504

189

23

•038

Annealed Iron

9a

6

35-040

1-0123

13°

66,740

134-5

25-5

•038

Bright ditto

8a

6

33-231

1-0696

ll°-5

112,896

49-5

0-75

•038

Mild Steel Annealed .

5a

6

32-890

1-1140

12°-5

70,268

207

19

•038

Ditto do. Bright.

4a

6

33-291

1-1270

15°-5

98,784

46

1-25

•038

Annealed Steel

3a

8

46-286

1-2520

15°

95,256

149

16-25

•038

Bright ditto

2a

3-50

20-081

1-2470

14°-5

132,600

69

1-5

•038

Hardened and Tem-
pered ditto

la

5-20

29-500

1-2832

13°-5

134,244

96

1-5

•038

Annealed Piano Steel

—

4

28-930

1-3422

10°-25

127,840

152

9-5

•043

Hardened and Tem-
pered Steel (Piano).

—

5

35-230

1-4497

ll°-25

287,540

75

2-62

•043

154

O)

a

o .

a 2

-p p*

d

.2^

&0 ®

d

o

O

d

• r-<

CO ,
d

H

x>

ft

xn

r-H

Srd

•rH o

• IH •'^

a 2‘

d “

• pH

w

•paiadoiaj}

pire

\c

!>.

WO

wo

XfO

1>

O

o

00

i>

00

<X)

ip

o

Cl

pauapj'BH

tH

rH

rH

rH

rH

iH

tH

01

rH

rH

O

o

o

cq

wo

wo

j>

o

05

(M

tio

VO

o

wo

CD

x>

00

o

•fl

rH

01

rH

tH

tH

tH

tH

tH

CO

rH

M

rH

o

i>

wo

wo

o

o

(M

o

05

rH

lO

00

(M

cq

wo

wo

rH

wo

'=fl

00

05

i>

(30

<35

<35

05

6

00

1=1

rH

r-l

rH

rH

tH

rH

rH

rH

rH

iH

•p9J9dtnaj,

wo

*P

wo

ip

©1

o

pa'B

CO

oo

CO

i>

00

<35

(M

rH

wo

o

(N

rH

CO

•5?

CO

CD

CO

CD

Tfl

rH

pauepiBH

CO

-P

wo

wo

rH

iH

CO

rJ=l

CO

CO

HH

<35

1>

WO

CO

<D

6

<35

’5h

tH

tH

WO

!>.

o

CO

wo

<b

fq

tH

rH

tH

1 '^'

*p

wo

wo

CO

t>.

05

WO

rH

CD

o

CD

4fi

i>

< cS

CD

CO

CD

00

<35

00

t>

00

00

^ Q>

rH

CD

rH

o

o

O

o

WO

wo

O

o

O

CD

CO

00

x>.

CD

pH

rH

rH

tH

<35

00

CD

•pajadraax

(M

rH

O

wo

rH

rH^

(M

(M

CD

pn-B

00

4'

05

o'

1>

CD

00

00

(M

WO

CD

pau9piBH

o

o

CD

t>

CD

CD

wo

wo

O

00

(M

<M

rH

rH

rH

iH

rH

rH

rH

rH

tH

lO

o

wo

wo

wo

o

<35

o

<35

<M

00

<J5

o

00

<35

<35

CO

<35

CD

r=3

i>

rH

CD

CO

1>

WO

WO

1>

WO

CD

J>

CO

wo

i>

(Of

1!^

r£

o'

wo'

t>

05

(30

CD

wo

CO

CO

00

(M

CO

CO

rH

CO

FQ

iH

rH

rH

rH

rH

rH

rH

iH

rH

rH

rH

1-4'

wo

o

wo

rH

CO

i>

00

CO

wo

(U

CO

rH

o

<35

CO

rH

o

'cS

CO

00

O

<35

rH

x>

(M

05

O

O)

oT

w:T

CD

p-T

<D

<35

00

<35

tH

CO

tH

o

o

05

05

<35

00

00

iO

05

<1

rH

tH

l>

. .

o

o

o

0

1

. '-<15’

rp(J«

0

0

o

HlN

O

1

&H CO

rH

o

cq

<M

o

rH

o

1

•p9.i9dra9|i,

pOB

rH

rH

rH

tH

rH

rH

rH

rH

1

ro- 'FO

o

tH

!>.

CD

wo

(M

00

CO

wo

p9U9pjBH

1 <?«

00

05

oq

rH

o

wo

Tfl

(M

05

CD

‘P

‘P

»p

ip

rH

tH

cp

WO

o

rH

rH

iH

rH

rH

rH

rH

CO

tH

o

rH

rH

o

0

o

H|<S

0

o

O

o

o

EH CO

rH

rH

cq

(M

o

rH

rH

•p

tH

tH

rH

rH

rH

rH

rH

rH

tj}

CO

wo

CD

wo

Tp

i>

00

!>.

CO

M

a

,d ’T'

tH

(N

CD

Tfi

CO

<35

rH

1>

o

M

05

*p

*P

o

CD

ip

rH

O (M

tH

rH

rH

tH

rH

tH

tH

(?1

tH

o

. rH

rH

o

o

o

0

0

o

O

• 0

wl-C

n|'#

h|(M

co]^

'HlCi

H CO

rH

O

rH

rH

00

<35

<35

0)

rH

rH

rH

rH

rH

cd

<L>

m O

CO

o

05

o

o

O

<35

i-H

d

o

CO

tH

IfO

CO

rH

1>

00

CD

1

'?

*p

<p

*P

rH

O cq

rH

rH

rH

rH

rH

iH

rH

<?q

iH

rH

•OK

9idniBg

rH

(M

CO

•<^1

wo

CD

00

rH

O

-H

o>

<D

d

•P

-M

&D

<D

C«

m

•S

»\

A

rH

o

4^

rH

O’

m

-p

CP

d

c3

o

>

<D

Q

H

155

MICEOSCOPICAL AND NATURAL HISTORY SECTION.

March 15 th, 1880.

Charles Bailey, F.L.S., President of the Section, in the

Chair.

Mr. Joseph Sidebotham, F.L.S,, sent specimens of some
Helices and Bulimi, collected by himself at Mentone, South
France, for exhibition, and the Secretary (Mr. Melvill) also
read a communication from him on the subject. The
principal form of interest was a Helix, to which Mr. Side-
botham had appended the name of Mentonensis. In the
opinion of the author, this snail, which was only found by
him in an isolated spot at Cap. Martin, near Mentone, was
originally a hybrid between H. pisana (Mull) and H. virgata
(L.), snails abounding in the locality, but that by perpetual
interbreeding it had attained a developed specific form. It is
characterised by being somewhat smaller than typical H.
pisana, yellowish, and banded as in H. virgata or ericetorum,
without any of the other tessellated markings which so
characterise H. pisana, but mouth formed as in that species.

Mr. E. P. Quinn called the attention of the geologists in
the Section to the fact at the present moment an unusual
opportunity was occurring at Oldham Edge, for those inter-
ested in Sigillaria to visit the place, some gigantic specimens
having been recently disclosed intact.

Dr. Tatham, of Salford, described a new form of Stephen-
son’s Binocular, which has been recently introduced by
Messrs. Baker, of Holborn;

The microscope being mainly intended as a working
instrument, is of firm, rather than of elegant construction ;

156

the stage is remarkably large and substantial, and is so firmly
mounted that it affords efficient support for the hands
during the manipulation of an object under the Microscope.
The stand does not possess the usual axial joint; but inasmuch
as that portion of the tubing which carries the eye-pieces is
bent at almost a right angle with the perpendicular portion
of the body which carries the objective, the axial inclination
of the stand is unnecessary. The binocular prism is remark-
ably well ground and set, and under it, objects of considerable
thickness, such as injected specimens, stand out in relief,
much in the same way as they appear under the Wenham’s
binocular. The instrument is capable of being used bino-
cularly with high, equally well as with low powers; the
prism acts as an erector, and when used in combination with
a ‘^combined two and four inch objective,” recently invented
by Zeiss, it forms a most useful dissecting miscroscope.

Dr. Tatham bore testimony to the great comfort he has
experienced in the use of this form of binocular, and augured
for it an extensive sale, more especially as the price of the
binocular, stand complete, does not exceed seven or eight
pounds.

Mr. Mark Stirrup, F.G.S., read some notes on the
Mollusca of Blackpool — the more noteworthy species being

Scalaria Turtonse.

Scalaria communis.

Cyprina Islandica.

Pholas crispata.

Mr. J. Boyd read some notes on the Haustellum of the
Haustellata, with diagrams, and also exhibited some micro-
scopical slides illustrative of the subject.

157

Ordinary Meeting, April 6th, 1880.

J. P. Joule, D.C.L., LL.D., F.RS., &c., President, in the

Chair.

E. W. Binney, F.R.S., F.G.S., said that in vols. XVI. and
XVIII. of the Proceedings of the Society he had given
accounts of a Eucalyptus globulus which he had planted in
his garden near the sea at Douglas, Isle of Man. During
the winter of 1878 and 1879 it suffered in its foliage and
young branches to a considerable extent; but during the
past winter, although the temperature of the month of De-
cember, in the Isle of Man, was lower than that of the same
month in 1878, the tree has almost escaped damage, and is
at the present time growing vigorously and giving out a
strong odour throughout the surrounding air. It has not
grown much in height during the last two years, as it is
now considerably higher than the sea wall near to which it
grows, but it has much increased in the diameter of its
stem. Up to this time it has shown no signs of flowering

“Note on modified Chlorophyll from the leaves of Euca-
lyptus globulus,'’ by Edward Schunck, Ph.D., F.RS.

Whoever has seen the Eucalyptus globulus growing must
have been struck with the peculiar glaucous appearance of
the foliage, such as few European plants show. I thought
it would be of interest to ascertain whether this peculiar
appearance might be in any degree due to the state in
which the chlorophyll exists in the leaves. A very simple
experiment however sufiiced to prove that the peculiar ap-
pearance referred to is owing to a covering of fatty matter,
such as is seen on fresh plums and other fruit, which,
though exceeding!}^ thin, is sufiicient to modify the green
Pboceedings— Lit. & Phil. Soc. — ^Vol. XIX. — No. 13. — Session 1879-80.

158

colour of the leaf. On washing the leaves with a little
ether the film of fatty matter disappears instantly, the leaves
then appearing green like ordinary leaves. The ether leaves
on evaporation a white semi-crystalline fatty residue which
melts at a temperature much lower than that of boiling
water, and is partly soluble in dilute alkaline lye boiling, so
that it probably consists in part of some fatty acid. The
leaves after washing with ether do not differ in appearance
from other leaves. The alcoholic and ethereal extracts of
these leaves show however a peculiarity, as regards the
chlorophyll contained in them, which I have not observed
in any other green leaf extract, though the same thing may
have been observed by others and recorded in one of the
numerous memoirs on chlorophyll, the whole of which I do
not profess to have read. If a few of the smallest and latest
formed Eucalyptus leaves from the tips of the branches are
extracted with ether a green solution is obtained which
shows the usual absorption bands of ordinary unchanged
chlorophyll. If however a little of the extract contained in
a tightly corked test tube be kept in a dark cupboard for
several days it gradually acquires a yellowish tint and now
shows absorption bands coinciding with those of so-called
‘ acid chlorophyll,’ that is, of the modification which is pro-
duced at once by adding a few drops of an acid, such as
acetic acid, to a solution of ordinary chlorophyll. The
change in the spectrum produced by the action of acids con-
sists in the disappearance of the chlorophyll band III, and
the intensification of bands II and IV, which now more
nearly approach band I in strength. An alcoholic extract
of more fully developed but still quite fresh and vigorous
leaves (I took for the purpose the pair next in order of de-
velopment to those at the summit of the branch) showed
the ordinary chlorophyll bands, though on attentive exami-
nation band lY was found to be a little more defined than
usual. After being kept in the dark however for 24 hours

159

the extract became yellowish, and now showed the bands
of ‘acid chlorophyir as distinctly as did the ethereal ex-
tract after several days. An alcoholic extract of fresh grass
after being kept in the dark for several days had not
changed in the least, and still showed the ordinary chloro-
phyll bands. On exposing the extract of grass for a few
hours to sunlight it gradually lost its green colour, became
of a pale yellow, and then showed hardly a trace of absorp-
tion bands, the band I being only just discernible. On ex-
posing the alcoholic Eucalyptus extract, after being kept in
the dark for 24 hours, to sunlight, it also became much
paler in colour, but the bands I,. II, and IN a, were quite
as distinct as before insolation, and in addition to these the
broad band IV b between the lines E and F of the spectrum,
which also belongs to the so-called ‘ acid chlorophyll,’ now
came out very neatly, it having been previously invisible on
account of the great obscurity in that part of the spectrum.
It appears then that an alcoholic or ethereal extract of Euca-
lyptus leaves undergoes even in the absence of light a change
whereby the normal chlorophyll contained in it is converted
into a substance which shows the same absorption bands as,
and is perhaps identical with, ‘ acid chlorophyll.’ I am in-
clined to attribute the change which takes place to the large
amount of essential oil contained in the leaves and conse-
quently in the extracts. Essential oils, it is well known, con-
vert inactive oxygen into ozone, and ozone, according to Ger-
land, produces a change in alcoholic solutions of chlorophyll
similar to the one I have described, whilst under the same
conditions ordinary oxygen is without effect, which Sachsse
seeks to explain by supposing that the ozone in Gerland’s
experiments led to the formation of some organic acid which
reacted on and modified the chlorophyll. Fresh Eucalyptus
leaves contain no acid soluble in water, for a watery decoction
of the leaves does not redden blue litmus paper and remains
neutral even on exposure to the air for some days ; but the

160

alcoholic extract shows after insolation a marked acid reac-
tion. It would be interesting to ascertain whether alcoholic
extracts of other leaves containing much essential oil behave
in the same manner as Eucalyptus extract. I made the ex-
periment with leaves from the orange tree, in which, as in
Eucalyptus leaves, numerous oil cells may be seen under a
lens, but the alcoholic extract, on being kept for several days
in the dark, remained unchanged. After insolation it dif-
fered slightly from an extract of grass made at the same
time and exposed along with it to sunlight, bands I and
IV(X remaining visible, while the corresponding bands of the
grass extract had disappeared.

“ On the Chemical Composition of the Ink on Letters and
Documents as Evidence in Legal Cases,” by William
Thomson, F.KS.E.

The ideas which I propose to bring before you are not
entirely new. They are based on the examination of the
ink on letters and documents as a valuable mode of inves-
tigation in civil and criminal law cases.

It frequently happens that circumstantial evidence of a
very simple character which is often overlooked, might
occasionally have the effect of conclusively proving the
innocence or guilt of an accused person, or of pointing in
some definite direction towards tracing the culprit. In civil
legal cases the same class of evidence may prove equally
useful.

If, for instance, a person be murdered on the highway and
any weapon or instrument found with which the deed had
been committed, it is needless to say that such implement
would be carefully examined for name, mark, or number, or
in fact any peculiarity by which it may be traced to its for-
mer owner. Again, recent foot-prints in the snow or in soft
clay often present sufficient individuality about them to
make them useful in the detection of crime, and these

161

means are usually employed. Seldom however is it sup-
posed that a common substance such as the ink used in
writing a letter or document, has any special individuality
about it. All ordinary inks are black or nearly so, yet it is
conceivable that the name and address of the writer of an
anonymous letter may, under a given combination of cir-
cumstances, be contained within the black fluid with which
the letter was written. If then a murderer has left his trace
behind him in the shape of paper and ink, it seems to me
not improbable that by a judicious use of the latter, some
important information may be obtained respecting him
which may ultimately lead to his capture. Some years ago
the information obtainable by the examination of the ink on
papers or documents would probably have been compara-
tively insignificant, owing to the fact that the number of
different kinds of ink in the market at that time would be
small, and the modes of preparation of the ink simple, and
the materials used not specially subject to variation. At
the present day however a large number of different articles,
many of which are subject to variation, are employed in the
manufacture of ink, and a large number of different inks
are in general use, and from these reasons the testimony
capable of being obtained by the chemical examination of
the ink on letters or documents at the present time may, in
some cases, prove to be of the greatest importance.

The reagents which I have found to act best in the test-
ing of the ink on papers are nine, viz.

1. Dilute sulphuric acid.

2. Strong hydrochloric acid.

3. Slightly diluted nitric acid.

4. Sulphurous acid solution.

5. Caustic soda solution.

6. Cold saturated solution of oxalic acid.

7. Solution of bleaching powder.

8. Solution of protochloride of t’’n.

9. Solution of perchloride of tin

o

162 i:

The method which I have adopted in applying these re-
agents is to moisten one or more strokes or letters of the
writing with each reagent, and then to absorb by blotting
paper the excess of fluid, a few seconds afterwards.

By thus treating the ink on different envelopes lately sent
to me I find they give very diverse results ; with sulphuric
acid, for instance, the black colours of the different inks are
changed, in some to bright crimson, in others to deep red,
whilst some become blue, green, violet, and grey of different
shades, and some remain practically unaltered ; and when,
as sometimes happens, the same or nearly the same colours
are produced in two different inks by one reagent, the
colours produced by another are very different, thus show-
ing clearly that the letters were not written by the same
inks.

The same kind of ink, sold by the same maker, but made
at different times, also varies more or less in its behaviour
with the reagents, as shown by the comparisons of three
samples of Lyon’s inks, sold in small penny bottles, which
were bought at different places.

Differences between inks which give nearly the same re-
actions may sometimes be observed by noticing the lengths
of time which the reagents require to bring about the ulti-
mate changes and by the shades of colour through which
the ink passes after applying each reagent. Changes also
continue to go on gradually for days and weeks after the
reagents have been applied. The colours and shades of the
same colour can be much more distinctly seen by the aid of
a good pocket lens.

It is evident that if two persons use ink made by the
same maker at the same time the reactions would be pre-
cisely similar, but it is easy to understand that after such
ink has been in use for some time, owing to the different
habits of the users, each may acquire a distinct individuality.

One, for instance, may have been more exposed to the air

163

or the direct sunlight than the other, and some of the colour-
ing matters present may thus have been more or less altered
or destroyed. One person may have a habit of leaving his
steel pen in the fluid, so that some of the iron may be dis-
solved, thus altering the character of the ink, whilst the
other may not do so, or may employ a quill in writing.
Again, some persons may allow their inks to dry up to a
certain extent and then add to them any fluid which may
be at hand, such as tea, coffee, wine, beer, water, &c., each
of which would alter the character of the writing fluid,
whilst others may use mixtures of two or more different
inks, in different and characteristic proportions. One can
therefore understand that many persons may have in their
ink-bottles fluids which are so peculiar in chemical compo-
sition that they may have as much individuality about them,
when treated with reagents, as the faces of their owners. I
have tested the same ink on different kinds of paper, and
the resulting shades of colour produced were identical in
each case.

To make use of this mode of investigation it would be
necessary to get the ink or inks used by a suspected person,
or preferably some writing made by him at or about the
same time as any letter or document in question and test
the two side by side with each other. The resulting shades
of colours may agree precisely and may thus tell strongly
against the suspected person, or they may differ very much
and so point towards exonerating him.

A case lately occurred in which the expert M. Chabot was
called and gave evidence to the effect that the handwriting
in a certain libellous letter was that of the person who was
indicted as the writer of it. As a witness for the defence
another person came forward and swore that he was the
writer of the letter in question, and on that evidence the
case was dismissed. One can, however, under some circum-
stances, understand that a suspicion of such a witness

164

having perjured himself may be justifiable, and such a sus-
picion may possibly be removed from an innocent person by
his producing for chemical examination a paper written
about the same time and with the same ink as that said to
have been used in writing the letter in question.

I have arranged on two sheets of paper the writings on
envelopes of fifty different persons, lately sent to me. One
sheet contains 24, written in Manchester and the suburbs,
and the other contains 26 from London and the provinces ;
and from a minute inspection of these it will be observed
that most of them are very different from each other, whilst
no two give exactly similar shades of colour with all the
different reagents.

PHYSICAL AND MATHEMATICAL SECTION.

April 13 th, 1880.

E. W. Binney, F.R.S., F.G.S., President of the Section, in

the Chair.

Colorimetry, Part lY.,” by James Bottomley, D.Sc.

On the Colour Relatioiis of Nickel and Cohalt
For some experiments which I was making in colori-
metry, I wished to obtain a solution which would absorb
all the kinds of light in the same ratio, so that whatever
sort of light we started with, after penetration through
such a solution, it would remain the same in character;
the only variation being a change in intensity. Hence
through such solutions white surfaces would appear grey of

165

various shades, verging towards blackness as the length of
the column increased. Such a fluid we might call a soluble
black. I am not aware of any single fluid that fulfils the
above conditions. It might be said, why not use ink ? but
such specimens of ink as I have examined are bluish or
violet on copious dilution. Moreover the colour alters with
the degree of oxidation; also it seems to be colouring
matter in suspension rather than in solution. I had some
hopes of succeeding by mixing solutions of nickel and
cobalt salts. On reference to the Phil. Magazine, vol. YI.,
page 15, I find that the colour relations of nickel and cobalt
had been studied by Mr. Thomas Bayley with a view to the
quantitative determination of these metals founded upon
the complementary character of their colours. He states,
“ The fact will have been observed by chemists that solutions
of nickel and cobalt salts are so far complementary in colour
that when they are mixed together the resulting liquid, if
moderately dilute, is hardly to be distinguished from pure
water.” After considering the nature of the absorption
spectra of nickel and cobalt salts, he states, “ If the spectra
were exactly complementary, on superimposing the nickel
spectrum upon the cobalt spectrum the dark part on the
one would cover exactly the light part on the other. This,

however, though nearly the case, is not exactly so this

is why the solution obtained by mixing strong solutions of
nickel and cobalt is not grey, but reddish brown in colour.”
Some experiments which I made seemed to confirm the
opinion of Mr. Bayley, the nickel solutions contained O'Oo
grms. of NiS04 per cub. c. and the cobalt solution contained
0*05 grms. C0SO4 per cub. c. A mixture consisting of 50
cub. c. of cobalt solution with 100 cub. c. of nickel solu-
tion contained in a white porcelain basin, seemed to
be a grey tinted with pink in the shallower parts, and
having a tendency to pass into a yellowish tint as the
depth increased. I now poured the fluid into a tall glass

166

cylinder covered externally with black cloth except a cir-
cular aperture of 8 mm. diameter at the bottom. When I
looked through the column of fluid at a white surface, the
colour was decided, resembling somewhat the pigment known
as yellow ochre. Also with a less proportion of cobalt to
nickel, namely 20 cub. c. of cobalt solution to 50 cub. c. of
nickel solution, I still obtained a tint in which yellow seemed
to predominate. Had I employed solutions so dilute that
no colour was perceptible in the mixture, this would not
strictly imply that the colours were complementary, but
that the resulting tint was too feeble to produce the
impression of colour, and if we filled a long tube with such
a dilute solution the colour might again become manifest.
Moreover, my aim was not to mix two coloured solutions so
as to obtain a fluid which exercised no perceptible absorption
of light, but to obtain a fluid which would exercise a
considerable absorption subject to a certain condition. The
following consideration seemed to me to render it hopeless
to obtain a soluble black by nickel and cobalt only. A
solution of cobalt when dilute is pink, but if we look through
a considerable thickness or through a concentrated solution,
the pink shows a tendency to pass into a scarlet. This
shows that as the quantity of the salt increases, the ratio
of the yellow to the red increases. The colour of the
undissolved salt is brownish red, and the colour of the
solution seems to approximate towards this as the concen-
tration increases. Hence the colour of a solution of cobalt
alters not only in intensity but also in kind as the amount
of the salt is increased. On the other hand, the green of a
solution of nickel varies in intensity, but does not seem to
vary in character, at least in any marked manner, as the
quantity of the salt increases. In order that it should be
generally complementary in character to cobalt, any
inconstancy in the ratio of the red to the yellow of the
latter would require a corresponding variation in the ratio

167

of the yellow to the blue in the former, and the tint ought
to pass from an emerald green to a bluish green. As this
does not seem to be the case, it would follow that even if
we mixed nickel and cobalt so as to obtain a perfect grey
for a column of definite length, a column longer or shorter
than this would still retain some colour. My experiments
seemed to indicate a deficiency of blue in the mixture, and
this I thought might be supplemented by another salt. So
I tried the addition of sulphate of copper. After some trials
I got a solution containing in 1,000 cub. c. 7*275 grms.
N1SO4, 4,868 grms. C0SO4, and 11,468 CUSO4, the solutions
also contained 30 cub. c. of strong sulphuric acid; this I
added to guard against any possible formation of sub-salts
on copious dilution. This solution seemed nearer to what
I wanted than a solution of nickel and cobalt only ; it did
not however appear wholly free from colour, and possibly
a variation of the quantities might have given a better
result; also the tint seemed to vary somewhat with the
nature and intensity of the incident light. When in the
failing light of approaching evening I held the containing
bottle against the grey sky I thought that there remained
a somewhat pinkish tint, whilst in the colorimeter when
looking at an external white surface through a column
sufficiently long to produce a perceptible absorption, I
thought the solution had a bluish tint. When viewed
against gas light it gave a greenish tint. Within the range
of coloured fiuids in Chemistry there may be some which if
combined would yield a mixture absorbing all colours in the
same ratio, so as to be truly a soluble black. The pre-
paration of such a fiuid would be an interesting problem in
physics. It seems to me that we might also have such
fluids which on spectral analysis would show not an
absorption of all colours in the same ratio, but would be
resolved into a violet and yellow, or an orange and blue,
or red and green, or some other combination of colours of a
complementary character.

Remarks on the Formulce for the Intensity of Light that
has passed through Absorbing Media, and on a Method
of Experimental Verification.

In my last paper on colorimetry I pointed out that the
function which expresses the connection of the intensity of
light with the quantity of colouring matter is of the same
form as the function expressing the relationship of the
intensity and the length of the absorbing column, and if we
accept Herschel’s formula ^a¥ for the latter relationship^
then an expression of the form must be taken to ex-
press the former relationship. The connection of these two
may be shown more directly than I indicated in my last
paper. If we grant one of the laws, the other may be
deduced from it as a corollary. Take for instance the law
as given by Herschel,

T = (i-Jc-i -f- "H &c.

Now it is manifest that if q be the quantity of colouring

matter per unit of length, we may write the above formula

i. L

T = adcP 4 + + &c.

1 1 L

For , kf, h , &c., substitute new constants ki, fca, Kg, &c.
Then we way write

T = Sa/c«'

Since q denotes the quantity of colouring matter per unit of
length and t the total length, we shall have (^—qt, when
Q denotes the whole quantity of colouring matter, so that
we finally deduce

T -

As the basis of a method of colorimetry, I took the rela-
tionship, that the length of the column was inversely as
the quantity of colouring matter present when the colour
was made constant. It may be readily shown to be a
consequence of the laws stated above. Suppose C to be the
constant colour, then

C =

The form of the equation shows that C is the sum of a
number of constants Ci, C2, Cg, &c., such that

Cl =

169

whence we obtain

log ^ = 2^1og^i

Oj\

log =

Ct2

log

a.

qt^ogk^

and by addition we obtain

Cl C

log— + log— + &C. = 2^(log^i + log^2 + ‘^0.)

Oi

«2

or

= constant.

log ( K)

In my last paper I stated that the law of absorption of
light given by Herschel appears to have been obtained
a priori ; 1 have not found in his memoirs any experimental
confirmation of it. The form of the expression has a some-
what formidable appearance, inasmuch as it involves the
measurements of infinite varieties of light. But suppose
that in the formula '2ak*, h is the same for every species of
light; then we may write T = ^*Da or T = ^*I, if I denote the
incident light. In such a case the emergent light will be of
the same nature as the incident light, and will diflfer only in
intensity. Suppose the incident light to be white, the
emergent light will be a white of less intensity, — that is,
will be a grey, approaching to blackness, as the length of
the column increases. A fluid medium, affecting white light
in this way, we might call a soluble black, and my aim, in
seeking to obtain such a fluid, was to apply it to the con-
firmation of the law. In a previous note I state that I had
tried to obtain such a body; what I got was not wholly
satisfactory, but I thought that with it I might obtain some
approximate results. The solution I used consisted of 500
cub. c. of the previously mentioned fluid with 500 cub. c. of
distilled water.

The mode in which I proposed to operate was as follows :
take two white lights of different intensities, say Wi and Wa,
and look at them through the liquid. Suppose the lengths
of the columns when equality of intensity is obtained to be
ti and U, then

170

Suppose we alter the lengths of the columns and in a second
experiment; we find,

by cross multiplication and elimination of the common
factor W1W2 we obtain

or as we may write it

T’hen taking the logarithms of both sides and dividing by
log k we get finally

= i^2 "f" h

In this way I proposed to test the law.

I took, as standard tints, a smooth surface of BaS04
and another of BaS04 and carbon, in the proportion of 10
grms. of BaS04 to 0006 grms. of carbon; these materials
were intimately mixed and the powder reduced by pressure
to a flat surface. The colorimeters used were glass cylinders
covered externally with black cloth, the circular apertures
at the bottom admitting light being 8 mm. in diameter.

One experiment gave the following results. Length of
column 2 2 ’2 c., standard tint Wi (BaS04). I now attempted
to get the same intensity when looking through the second
cylinder at tint W2 (BaS04+ carbon). The mean of two
trials gave 14’8 c. as the equivalent column. Hence we
have the following results :

I now made the length of the column over Wi 13 c. The
equivalent column over W2 was as the mean of two trials
7'5. Hence

From these experiments we get as the sum of h and U 29 ’7
and the sum of U and U, 27*8.

A second experiment gave

Here h + = 28 ’45 and + A = 28-76.

A third experiment gave

WiP®-S= W2F0-65

WiP'-» = W2F*‘'

Here Lx + = 25-3 and q' + ^2 = 24*93.

171

A fourth experiment gave the following results —

WiF'-® = W2F-2

Here h + = 28*4 and h + = 27*4.

A fifth experiment gave

WiF3-'^ = W2F'®^

Here we have tx + = 31 ’95 and tx + ^2 = 30 '35.

It seems to me that the above results are as favourable
as might be expected considering the difficulties of the
enquiry ; and even if all external circumstances necessary
for the successful completion of such experiments had
existed, there would yet remain the difficulty of deciding
about the equality of two grey tints. In such matters it
is difiicult to say where judgment ends and fancy begins.

That any discrepancies might be due to such a cause was
shown by the following experiments : — I took the two
cylinders and poured from one into the other with the
intention of obtaining the same tint in both. In one trial
I could not very clearly distinguish a column 16*4c. long
from one 14'6c. long, and in a second trial a column 16 '20.
long seemed to give the same tint as a column 14'6c. long.
In the above experiments I used one eye only, namely, the
right one,

I also made the following experiments : — I took as the
standard of intensity W seen through a column 12*5c. long.
On a former occasion I had made 6*2 as the equivalent
column to be used with W2. On the present occasion I
thought 6 '5c. gave a nearer result, so I took the column at
this length. Now if the law of absorption of light be true,
if we increase both columns by the same quantity, the
intensities should again correspond. So I added 4c. to each,
making one column 16’5 and the other 10*2. I thought
that the tints were the same. I now made one column
20' 5 and the other 14‘2. Again I thought the tints were
the same. Finally I made one column 24'5 and the other
18*2. The tints seemed again to correspond.

“Note on Three New Stars,” by Joseph Baxendell,
F.RA.S.

172

On the 25th November, 1879, I discovered a new star in
Can is minor ; it had a decided orange colour, and I estimated
its magnitude to be 8*8. In the beginning of December it
began to diminish in brightness, and on the 18th, 19th, and
20th of January its magnitude was estimated to be 9 '8.
It afterwards increased, and on February 2nd was of the
9*2 magnitude, but it has since again diminished slightly,
and on the night of the 11th instant was of the 9‘6 magni-
tude.

Its place from observations made at Lord Lindsay’s obser-
vatory, Dun Echt, is

1879-0 a = 7h. 34m. 45-67s. d= +8°39'39'6".

The second new star was discovered on the 28th of Janu-
ary, 1880, when it was of the 8*7 magnitude. It is in the
constellation Gemini, and precedes No, 1655 -f- 13° of the
Bonner Durchmusterung 37‘5s., and is about 7’3' north.
It is in a cluster of seven or eight very small stars, and is
in the same field with a small star which I had for some
time suspected of variability. It has a decided reddish
colour. In the middle of February it began to diminish in
brightness, and on the 24th it was noticed that its colour
had changed and become a deeper red. Its brightness has
since continued to diminish, and on the 11th inst. its
magnitude did not exceed 11*0. It will, in all probability,
prove to be a periodical variable, and will, in conformity
with Algelander’s system of nomenclature, be designated
V Geminorum.

The third star is in the constellation Bootes, and was
discovered on the 12th of March, 1880, when its magnitude
was 9 '4. In the latter part of the month it increased to
9' 2 magnitude, but on the 11th instant it had diminished
to 9'G. There is a small star near it of about 10*5 masmi-
tude, which I mapped down some years ago, and have often
seen since without noticing anything on the place of the
new star. It has a very slightly reddish colour, and its
brightness suffers more under contracted apertures of the
telescope than that of any of the neighbouring stars. It
precedes No. 2955 -f 18° of the B.D. about 47‘2 s., and is
about 0'‘4 south.

173

Annual General Meeting, April 20th, 1880.

J. P. Joule, D.C.L., LL.D., F.R.S., &c.. President, in the

Chair.

Report of the Council, April, 1880.

The Treasurer’s annual Account appended to this report
shows that the balance against the General Fund Account
has been reduced from £113 Os. lid. on the 1st of April,
1879, to £57 Os. 2d. on the 1st of April, 1880 ; that there is
now a balance of £56 10s. 5d. in favour of the Natural
History Fund Account; and deducting the difference between
these two sums from the Compounders’ Fund, £125, there is
a balance of £124 10s. 3d. in favour of the Society on the
1st April, 1880, against a balance of only £8 10s. on the
1st of April, 1879.

The number of ordinary members on the roll of the
Society on the 1st of April, 1879, was 160, and three new
members have been elected ; six members have resigned,
and the number on the roll on the 1st instant was therefore

157.

At the last annual meeting of the Society a resolution
was passed urging on the Governors of Owens College the
great importance of completing the buildings for a Museum
of Natural History with the least possible delay. In reply
to this resolution the following Minute from the Owens
College was forwarded to the President :

“At a meeting of the Council held at the College on
Friday, the 21st November, 1879,

“ It was resolved :

• “That the Treasurer be requested to inform Dr. Joule
that the Council is deeply impressed with the importance of
proceeding -with the erection of the buildings necessary for

Proceedings — Lit* & Phil. Soc. — Yol, XTX.— No. 14. — Session 1879-80.

174

the due accommodation of the Natural History Collections,
so soon as an appeal can he made to the public for the
necessary funds- with a reasonable prospect of success.”

The subject of the celebration of the Centenary of the
Society is at present engaging the attention of the Council :
they recommend the appointment of a Committee for the
purpose of drawing up a report on the 'Work of the Society
since its foundation. Further proposals of the Council will
be submitted to the Society in due course.

At the meeting of the Council held on the 18th of
November, 1879, a resolution was passed directing the
House Committee “to reconsider and report upon the terms
on which the Scientific Students’ Association is allowed the
use of the Society’s Meeting Room ; ” and at the following
meeting, on the 1 6th of December, the Committee reported
“ that as the number of members in the Scientific Students’
Association has increased more than twofold since the terms
of £1 per meeting were agreed upon, a fresh arrangement
should be made, and they suggested that £2 10s. per meeting
would be a proper charge, of which 10s. should go to Mr.
Roscoe, whose remuneration at present is quite insufficient.”
The Association, however, declined to accept these terms,
and ceased to hold their meetings in the Society’s Meeting
Room at the end of December.

The following papers and communications have been read
at the Ordinary and Sectional Meetings of the Society
during the Session : —

October 7tli, 1879. — “On an Extension of the Ordinary Logic,
connecting it with the Logic of Relatives,” by Joseph John
Murphy, F.O.S. Communicated by the Rev. Robert Harley,
M.A, F.R.S.

October 13th, 1879. — “ On the Means by which Hydra swallows
its Prey,” by M. M. Hartog, M.A., B.Sc., F.L.S.

October IJ^th, 1879. — “On Colorimetry, Part III.,” by James
Bottoml'ey, D.Sc.

175

October P.lst, 1879. — “Notes on some Fossils from the Iron
Mines of Furness,” by E. W. Binney, V.P., F.R.S., F.G.S*

“ On the ‘ Differential Calculus ’ of Du Bourgiiet,” by Sir
James Cockle, F.R.S., Corresponding Member of the Society.

November Jfth, 1879. — “Screw Propulsion, Part IL,” by Robert
Rawson, Assoc. I.N.A., Hon. Member of the Manchester Literary
and Philosophical Society, Member of the Mathematical Society.

November lOth^ 1879. — “Additional Note on Hydra,” by Marcus
M. Hartog, M.A., B.Sc., F.L.S.

“On an Undescribed Acinetan,” by Marcus M. Hartog, M.A.,
B.Sc., F.L.S.

November 18th, 1879. — “On the Meteor of November 11th,
1879,” by E. W. Binney, V.P., F.R.S.

“Recording Sunshine,” by David Winstanley, F.R.A.S.

“ On Some Notices in Classical Authors of the Action of Sun
light on Purple Dye,” by James Bottomley, D.Sc., F.C.S.

“ On Specimens of Ophioglussum Yulgatum var. Ambigium,” by
Charles Bailey, F.L.S.

“ On the Origin of the word Chemistry,” by Carl Schorlemmer,

F.R.S.

December "2nd, 1879. — “ On a Peculiar Feature in the Water of
the Well in Carisbrooke Castle, Isle of Wight,” by Harry Grim-
shaw, F.C.S.

“Note on the Identity of the Spectra obtained from the
different Allotropic Forms of Carbon,” by Arthur Schuster, Ph.D.,
F.R.S,, and H. E. Roscoe, LL.D., F.R.S.

“ On Photographs of the ultra red portions of the Solar
Spectrum,” by Captain Abney, R.E., F.R.S.

December 16th, 1879. — “ On a New Form of Marine Rain
Gauge,” by W. J. Black, Esq. Communicated by J. B. Dancer,
F.R.A.S.

“ On Screw Propulsion, Part III.”, by Robert Raw^son, Assoc.
I.N.A., Hon. Member of the Manchester Literary and Philosophical
Society, Member of the Mathematical Society.

“ On the Anal Respiration of the Copepoda,” by Marcus M
Hartog, M.A., B.Sc., F.L.S.

176

January 13th, 1880.— Kadiograph,” by David Win-
stanley, F.D.A.S.

January 19th, 1880. — “ On the Occurrence of Silene Gallica
(L.) and its sub-species in Jersey,” by J. Cosmo Melville, M.A.,

F.L.S.

“ Bog Butter (Butyrellite), from Co. Galway, Ireland,” by John
Plant, F.G.S.

January 20th, 1880 — On the Bainfall adjacent to the Sweet-
loves Eeservoir, Sharpies, for 1879,” by the Rev. Thomas
Mackereth, F.B.A.S., F.M.S.

‘‘A Curious Rainbow,” by E. W. Binney, F.R.S., F.G.S.

January 27th, 1880.-—^^ On Epidemic Cycles,” by Arthur
Ransome, M.A., M.D.

February 10th, 1880. — ‘‘Notes on a bore through Triassic and
Permian Strata lately made at Openshaw,” by E. W. Binney, V.P,,
F.R.S., &c.

February 16th, 1880. — “On the Land and Fresh Water Shells
of Tasmania,” by Mr. Thomas Rogers.

“ On Flexible Sandstone,” by John Plant, F.G.S.

February 2Jfth, 1880. — “ On the Long Period Inequality in
Rainfall,” by Balfour Stewart, LL.D., F.R.S., Professor of Natural
Philosophy at Owens College.

“On a Form of Representing the Velocity at any point of an
Incompressible Fluid under Conservative Forces,” by R. F.
Gwyther, M.A.

“ Notes on some Quaternion Transformations,” by R. F. Gwyther,

M.A.

March 2nd, 1880. — “ Results of Observations of the double-
period Variable Star R Sagitt£e,” by Joseph Baxendell, F.R.A.S.
March 9th, 1880. — “Notes on the Bi-quadratic Equation
+ nx^ + ax^±bx + c = 0,” by Robert Rawson, Hon. Member of the
Manchester Literary and Philosophical Society, Assoc. I.N.A.,
Member of the London Mathematical Society.

“The ‘ Castel Nuovo’ Lignite Deposit, near Giovanni, Tus-
cany,” by Watson Smith, F.C.S., F.I.C.

“ Analysis of the Ash of Wood of two varieties of the
Eucalyptus Tree,” by Watson Smith, F.C.S., F.I.C.

177

March loth, 1880. — “ On some Specimens of Helices from
Mentone, South France,” by Joseph Sidebotham, F.L.S.

‘‘ Description of a New Form of Stephenson’s Binocular,” by J.
F. W. Tatham, M.D.

“Notes on the Mollusca of Blackpool,” by Mark Stirrup, F.G.S.

March 23rcl, 1880. — “ On the Origin of the word Chemistry,”
Part II.,” by Dr. B. Angus Smith, F.R.S.

“ On the Electrical Resistance and its relation to the Tensile
Strain and other mechanical properties of Iron and Steel Wire,”
by William H. Johnson, B.Sc.

April 6th, 1880. — “ On a Eucalyptus globulus at Douglas,
Isle of Man,” by E. W. Binney, F.R.S., F.G.S.

“ On the Chemical Composition of the Ink on letters or docu-
ments as evidence in legal cases,” by William Thomson, F.R.S. E.

Several of the above papers have been printed, and others
passed by the Council for printing in the new volume of
Memoirs.

The Council consider it desirable to continue the system
of electing Sectional Associates, and a resolution on the
subject will be again submitted to the annual meeting for
the approval of the members.

ir.

MANCHESTER LITERARY AND

Charles Bailes, Treasurer, in account with the Society

Statement oe the Accounts

1879 — April 1. . ^

To Casl) in hand

1880. — March 31.

To Members’ Contributions

Arrears, 1876-7, 1 at £2 2s 2

„ 1877-8, 1 at £2 2s 2

„ 1878-9, 14 at £2 2s 29

New Members’ Admission Fees, 1878-9, 2 at £2 2s. ... 4

„ „ 1879-80, 3 at £2 2s ... 6

Half Subscriptions, 1878-9, 1 at £1 Is.... 1

1879-80, 2 at £1 Is. 2
\\ Subscriptions ,, ^

Old Members „ » 140 at £2 2s. 294

To one Associates’ Subscription for Library, 1879-80

To Sectional Contributions, 1879-80 : —

Physical and Mathematical Section ^

Microscopical and Natural History Section

To use of Society’s Rooms : — , i -lo/rn oa

Manchester Geological Society, to 31st March, 1^79 oO
Manchester Scientific Students’ Association, to 2oth
December, 1879

To Sale of Society’s Publications

To Natural History Fund : —

Dividends on £1225 Gt. Western Stock

To Bank Interest, less Bank Postage, to 31st December, 18/9

1879^0. 1878-9.

s. d. £ s. d. £ s. d.
8 10 0 1726 4 3

2

2

8

4

6

1

2

2

0

0

0

0

0

0

0

0

0

0

10 0
2 0

0 0
5 0

343 7 0 322 7 0

2 12 0 5 4 0

66 5
1 18

59

19

14

0

0

6

7

61

2

60

10

0

10

3

7

£483 6 1 £2186 19 il

1880.— April 1.— To Cash in Manchester and Salford Bank

.£124 10 3

April, 1880, Audited and found correct,

(Signed) R. S. DALE.

C. S. TRAPP,

PHILOSOPHICAL SOCIETY.

TROM 1st April, 1879, to^ the 31st March, 1880, with a comparative
for the Session 1878-1879-

(Ex\

1879-80.

1880— Mardi 31.

By Charges on Property no

Chief Rent ;

Insurance against Fire

Property Tax ^

Repairs, Whitewashing, &c

£ s. d. £ s. d. £

1878-9.
s. d. £

s. d.

0

17 6
10 10

18 2

12 13 6
12,17 6
3 10 10
3 14 0

By House Expenditure : —

Wages of Keeper of Rooms

By Publishing : —

Binding Boohs.

Geological Rec9rd for 1877 ..... • • •• • ■
Palseontographical Society tor iooU
Ray Society for 1880

. 12 16

1

. 19

4

3

. 6

7

6

. 5

5

8

,. 57

4

0

. 17

4

0

,. 11 :

19

0

,. 10

4

1

.. 30

1

6

17

0

.. 4

13

0

.. 50

0

0

.. 2

18

3

... 38

19

6

... 11

10

0

10

6

... 1

1

0

... 1

1

0

29 19 6

43 13 6

96 11 1

132 11 6

56 0 3

By Natural History Fund

luvGstiuGnt of Capital r und

Brokerage on ditto

Legal Charges

Works on Natm’al History
Grant to Section for Books

17

0 11

18 18 10

6

7

6

4 17

9

57

4

0

20

7

2

14 :

11

6

12 ;

12

6

50

9

6

57

11

0

14

11

0

50

0

0

78

10

6

50

4

6

12

4

0

10

6

1

1

0

3

i

3

0

9

1489

18

0

7

9

0

41

12

0

32 15 10

47 5 0

104 15 2

172 11 6

145 13 6

36

100

11

0

By Balance

124 10 3

1675
8

8 11
10 0

£483 6 1

£2186 19 11

i’nSur of this Account, April 1st, 1880
Natural History Fund :

Dividends as above •

Less Balance, April 1st, 1879

1879-80.

s. d. £ s. d.
125 0 C

59 19 6
3 9 1

Balance in favour of this Account, April 1st, 1880

56 10

£181 10

113 0 11

Balance against this Account, April 1st, 1879

Expenditure, 1879-80, as above

471 16 9
414 16 7

57 0

Receipts, 1879-80, as above

Balance against this Account, April 1st, 1880 ...
Balance in favour of the Society, April 1st, 1880

£124 10

180

On tlie motion of the Rev. Joseph Fkeeston, seconded
by Mr. James Smith, the Report was unanimously adopted
and ordered to be printed in the Society’s Proceedings.

On the motion of Mr. A. Brothers, seconded by Mr. R. S.
Dale, it was resolved unanimously : That the system of

electing Sectional Associates be continued during the ensu-
ing session.

On the motion of Professor 0. Reynolds, seconded by
Mr. A. Brothers, it was resolved unanimously : That the
following gentlemen be appointed a Committee to draw up
a report on the work of the Society since its foundation : —
Mr. Binney, Dr. Joule, Dr. Smith, Rev. W. Gaskell, Dr.
Schunck, Dr. Bottomley, and Mr. Nicholson, with power to
add to their num.ber.

The following gentlemen were elected officers of the
Society and members of the Council for the ensuing year :

EDWARD WILLIAM BINNEY, E.R.S., F.a.S.

JAMES PRESCOTT JOULE, D.C.L., LL.D., E.R.S., E.C.S.
EDWARD SCHUNCK, Ph.D., E.R.S., E.C.S.

ROBERT ANGUS SMITH, Ph.D., F.R.S., E.C.S.

HENRY ENEIELD ROSCOE, B.A., Ph.D., E.R,S„ E.C.S.

JOSEPH BAXENDELL, E.R.A.S.

OSBORNE REYNOLDS, M.A., E.R.S.

CHARLES BAILEY, E.L.S.

ERANCIS NICHOLSON, E.Z.S.

tfjie

REV. WILLIAM GASKELL, M.A.

ROBERT DUKINEIELD DARBISHIRE, B.A., F.G.S.
WILLIAM BOYD DAWKINS, M.A., E.R.S., E.G.S.
BALED UR STEWART, LL.D., E.R.S.

CARL SCHORLEMMER, E.R.S.

JAMES BOTTOMLEY, B.A., D.Sc., E.C.S.

181

“Oa a Proposition of Du Bourguet,” by Sir James
Cockle, F.E.S., Corresponding Member of the Society.

The remarkable passage which (Sup., pp. 9 — 10) I have
translated from Du Bourguet conflicts with reiterated
statements of Lagrange, who (Legons, 1806, pp. 340 — 1),
speaking of a certain equation, which is in substance the
same as Du Bourguet’s (380), and which expresses the crite-
rion of integrability, says

“ And this equation ought to hold in itself, that is to say,
“ to be identical, in order that the variable 0 may be capable
“ of being a function of x and y, and that, consequently, the
“ one proposed may have a primitive in x, y, and 0.”
Moreover, Lagrange says (ih. p. 841)

But when the equation of condition does not hold in
“itself, the proposed equation cannot subsist unless we
“ assume some relation between x, y, and 0, in such manner
“ that two of these variables become functions of the third.”
Again, speaking of a certain case in which the condition
is not satisfied, Lagrange (ih. p. 342) says

“ Thus it is impossible that 0 can be a function of x and y
“ considered as independent of each other.”

Still Du Bourguet’s conclusion from his example (a) may
be easily verified. Under these circumstances, when we
find Du Bourguet writing the following paragraph (vol. i.,
p. xxiij.),

“ At the end of each volume I have placed a Table recapi-
“ tulatory, article by article, of the subjects contained in the
“volume; and in order to save accomplished mathemati-
“ cians, who have scarcely the time to read the whole of an
“ elementary Treatise, the trouble of seeking for the articles
“ which may be of interest to them, I have marked in the
“ Tables recapitulatory of the two Parts, the articles the
“ most worthy of the attention of these mathematicians, by
“ one or two asterisks, according to the importance of the
“ subject.”

182

it seems strange*' to find no asterisk to Art. 861 at p. 590
(vol, ii.) of his copious Index, which might well be a model
to authors of similar works.

2, Sandringham Gardens, Ealing, near London, W.,

April 9, 1880.

“On the History of the word Telegraph,” by William
E. A. Axon, M.E.S.L., &c.

There has been considerable interest manifested this year
in the history of the word telegraph. Mr. Warren de la
Eue states in Nature that the earliest instance he can find
of its English use is in the edition of Johnson’s Dictionary
issued in 1818 ; and he quotes from Eees’s Encyclopsedia
an account of the machines for signalling which were em-
ployed by order of the French Directory in 1798. There
can be no doubt that we borrowed the word from the
French, and the Manchester Guardian has recalled an
instance of its early use in a literary form in this locality.
“Tim Bobbin the Second” was the pseudonym of Eobert
Walker, of Little Moss, who wrote in the Manchester
Gazette of about 1795 some dialogues in the Lancashire
dialect with great natural humour and a very great power
of faithful portraiture of the condition and speech of the
poorer classes in the county palatine. These sketches were
afterwards republished under the title of “Plebeian Politics,”
and one of the best known passages in it is that relating
the story of the Saddleworth Shouting Telegraph. Walker

^ Nor does it seem less strange wLen, in his footnote at p. 596 of vol. ii.^
we find Du Bourguet saying “ When, as in this chapter, nearly all the
articles ought to he preceded by asterisks, we shall content ourselves
with putting one or two asterisks, according to the importance of the
subject, before the title of the chapter.” He is here referring to chapter
IV. of Section III , but it is in chapter IV. of Section II. that Art. 361
is contained. In a footnote at page 20 of vol. i. he refers to the TMorie
of Lagrange, whom he alludes to (p. 212) or mentions (p. 483) subse-
quently in vol. i. and mentions in vol ii. (pp. 336, 471, 475, 481 and 502),
but not in connection with the Proposition. The quotations in this com-
munication are, of course, translations. — J. 0.

183

had doubtless read in the newspapers of the time references
to this wonderful invention of the French, but he was cer-
tainly one of the first to give the word a welcome to litera-
ture, assuming, of course, for the moment, that the debatable
ground of dialectal writing is literature.

The word “telegraph,” unlike the great bulk of words,
did not grow but was invented, and we have the testimony
of its godfather as to the time, place, and circumstances of
its baptism. Chappe was the inventor of an apparatus for
the transmission of news by aerial signals, and had the usual
difficulty of inventors. He haunted the office of the war
minister in order to induce him to adopt the new system.
One day whilst he was enlarging upon the advantages of
his apparatus, which he then called tachygraphe, Miot de
Melito observed that the word w^as badly chosen, and that
he ought to change it to telegraphe. Chappe acknowledged
the justness of this suggestion. Tachygraphy was a term
that had long been used as a synonym for shorthand, whilst
telegraph and telegraphy were quite new and fairly descrip-
tive of the novelty. M. Maxime du Camp has given a
very interesting account of the struggles of Chappe and of
the genesis of his invention in the R4vue des deux Mondes,
15 Mars, 1867; p. 464 Telegraphing by signals was known
in an elementary fashion to the Romans. In England
Robert Hooke invented a complicated arrangement for
alphabetical signalling. Guillaume Amontons, who died
in 1705, made experiments in the garden of the Luxem-
bourg, which were witnessed by the Dauphin. Linguet,
whilst a prisoner in the Bastille, invented a system of aerial
signalling. Dupuis was the author of a method for the
attainment of the same object, but he abandoned his plan
in favour of that of Chappe. The inventor of the French
telegraph, Claude Chappe, was born at Brulon (Sarthe), in
1763, and was destined for the priesthood. The seminary
to which he was sent being about three quarters of a league

184

distant from the school at which his brothers were receiving
their education, he set about devising a method by which
they might communicate with each other. Claude sug-
gested that by means of the flat black rulers they might,
upon the white exterior walls of the one school, describe
figures that would be visible by the help of a lorgnette at
the other. The figures, of course, had an arbitrary value
previously agreed upon, and answering to certain phrases
in their schoolboy vocabulary. This youthful freak had
probably vanished from his mind when, as a man, he began
to study the problem of distance-signalling, for his first
thoughts were turned in the direction of electricity ; after-
wards he tried combinations of colours, then experimented
with sounds, and finally recurring to his early experience,
invented the telegraph which became so efficient an aid to
the armies of France. When electricity was employed
nothing was more natural than to call the new apparatus
the electric telegraph, and as it superseded the invention of
Chappe the qualifying adjective became unnecessary, and
the old name became applied solely to the new thing.

Mr. R. E. CcTNLiFFE exhibited two slides of Fossil Diatoms
from the London clay, discovered by Mr. Schrubsole, and
mounted by Mr. Cole.

185

MICEOSCOPICAL AND NATUEAL HISTOEY SECTION.

Annual Meeting, April 12th, 1880.

Chaeles Bailey, F.L.S., President of the Section, in

the Chair.

The Annual Report of the Council was read by the secre-
tary (Mr. Melvill). It showed the Section to be in a very
flourishing condition numerically, consisting at present of
88 Members, and 17 Associates, of which 1 Member and 6
Associates were elected during the past Session.

18 papers or other communications had been read at the
meetings for the past Session, and the Council augured well
from the increasing interest Members and Associates alike
take in the proceedings, the average attendance being larger
than in the 3 previous years.

They called the attention of all interested in the study of
Natural History to the large additions that had been made
during the past years to the Library — including as it does,
the leading and standard works on most branches — and
they would particularly call attention to such expensive
works as Reichenbach’s Flora Germanise et Helvetise,
Reeve’s Conchologia Iconica, Hewitson’s Exotic Butterflies,
and others.

The Council also earnestly invite all Members and Asso-
ciates to favour them, at least once every Session, with
either some paper, the exhibition of some object of Natural
History, or microscopical slide. Whether new to science
or not, it is highly important for the vitality of the Section
that some subject should be found for discussion, and
unfortunately the number of contrihiding Membei's tmd
PEOCEEDiiSrGS — LiT. & Phil. Soc. — VoL. XIX. — No. 15. — Session 1879-80.

186

Associates is in small proportion to the total number. It
was therefore resolved, that in future the Secretary will,
every month, cal] upon three gentlemen in alphabetical
order in rotation to contribute something to the next
meeting.

Tlie Treasurer’s Report was then read and passed.

187

o

I— I

EH

o

m.

O

m

I— I

w

P

EH

fi

|25

P

Q

1— I
pH

o

o

m

O

P^

o

>H

EH

S

I— I

O

m

<1

o

I— I

pq

Ph

o

1/1

o

t— I

M

Ph

P

P^

<d .

P^
P W

EH pH

p ^

a

p

Eh
m P
P
W

Q P

tz;

<1

p

p

^ p

^ p
W ^

^ xA
o
W

EH

w

p

HH

P

o

o

M

P

o

p

Xfl

P

W

P

P
!>h g

O O
p p
m O

>-H -d

W

P M

<1

P

P

P

<1

P

5

o

M

P

o

o

m

9 -

P D3
o ^

P

® o

o o

^

o

>o

m

o

-+3

c3

M

rl

o

OQ

O

-+3 -p

P ^

p rr>

O

"0

c3

D

P

c:>

^ »>

p ''

1

p

o

-p

ffl

(D

O

P

P

go'

9

■Tj

o o o

o O ®

i-H rH

CM rH

P

d

o3

P

■T3

fH

'3

DQ

q:) dH

-p

o

P

§

ca CO

a

p ^

ffi

o
o
O)

p

“Is
o

• rH

be

1 1

a

• rH

m

xn

CD

d

0

1

-1-3

m

§

P P
Q W

c3

d

o

1-5

o

ft

o ^

o m

IS

0 ^

Si

o

P o

1 p
S g

O d

O P

>3

-+3>

O)

• rH

o

o

GQ

"§

©

c3

qT

©

P ^

-S o
d i

o ft

.& oT

f-( bo
© cS

CO _p
^ CO

m P

o

ft

03

(M

o

o

CO

cq

rH

cq

o

cq

o

tH

tH

iH

cq

o

03

<cq

c3

p

C>3

p

Tii

©

bO

"o

-^3>

m

©

©

-1-3

d

03

t>.

00

o

P

..

•>

t>.

o

CO

,

CO

iH

•

tH

tH

iH

tH

o

CO

o

CO

GO

P

9

Oct.

c3

«D

P

00

ft

rA

©

P

00

o

o

O

-p

o

©

o

o

TS

o

ft

tJ

Ti

©

.a

a

c3

p

o

CO

GO

Cd

^1

ft

<1

JOSH. BAXENDELL.
JAMES COSMO MELVILL.

The election of officers for the ensuing Session, 1880-81,
then took place.

l^rcsiUcnt :

ALFEED BEOTHEES, F.E.A.S.

F(cc=lPrcsitfents :
CHAELES BAILEY, F.L.S.

E. W. BINYEY, F.E.S.

E. D. DAEBISHIEE, F.G.S.

treasurer:

T. H. BIELEY (Somerville).
Secretary :

J. COSMO MELVILL, M.A., F.L.S.

CCoundl:

E. ELLIS OUNLIFFE.

J. BOYD.

JOSEPH BAXENDELL, F.EA.S.

W. C. WILLIAMSON, F.E.S.

JOSEPH SIDEBOTHAM, F.L.S., F.E.A.S.
HASTINGS C. DENT.

Dr. ALCOCK.

W. BOYD DAWKINS, F.E.S., F.G.S.

List of Members and Associates : —

JHcmticrg :

Alcock, Thomas, M.D.

Bailey, Charles, F.L.S.
Barratt, Walter Edward.
Barrow, John.

Baxendell, Joseph, F.E.A.S.
Becker, Wilfred, B.A.

Bickham, Spencer H., Jun.
Binney, E. W., F.E.S., F.G.S.
Birley Thomas Hornby.

Boyd, John.

Brockbank, W., F.G.S.

Brogden, Henry.

Brothers, Alfred, F.E.A.S.
CoTTAM, Samuel.

Coward, Edward.

Coward, Thomas.

Cunliffe, Eobert Ellis.

Dale, John, F.C.S.

Dancer, Jno. Benjamin, F.E.A.S.
Dent, Hastings Charles.
Darbishire, E. D., B.A., F.G.S.

Dawkins,W. Boyd, F.E.S., F.G.S.
Deane, W. K.

Higgin, James, F.C.S.

Hurst, Henry Alexander.
Latham, Arthur George.
Marshall, A. Milnes, F.L.S.,
Prof, of Zoology, Owens College
Melvill, j. Cosmo, M.A., F.L.S.
Moore Samuel.

Morgan, J. E., M.D.

Nevill, Thomas Henry.

Nix, E. W., M.A.

Eoberts, William, M.D.
Sidebotham, Joseph, F.E.A.S.,
F.L.S.

Smith, Eobert Angus, Ph.D.,
F.E.S., F.C.S.

Williamson, Wm. Crawford,
F.E.S., Prof. Nat. Hist., Owens
College.

Weight, William Cort.

189

^ssanatc3 :

Adams, Lionel.

Aitken, John.

Brockbank, Herbert W.
CuNLiFEE, Peter.

Hartog, Marcus jVL, B.Sc., F.L.S.
Labret, B. B.

Linton, James.

Peace, Thos. S.

Percival, James.

Plant, John, F.G.S.
Quinn, Edward Paul.
Eogers, Thomas.

Stirrup, Mark, F.G.S.
Tatham, John F. W., M.D.
Ward, Edward.

Young, Sydney.

Mr. R. D. Darbishire gave some notes upon, and ex-
hibited a case of eggs of the Black Back Gull (Larus
ridibundus), found at Pilling Moss, near Fleetwood, Lan-
cashire.

Mr. Darbishire also noted for record, that a pair of
Rooks had built their nest in a poplar tree standing in Oxford
Road, just beyond Ducie Street, about If miles from the
centre of Manchester, and in the midst of a very dense
district of small houses, Oxford Road itself being one of the
noisiest and busiest streets of the whole cit}^ The nest
was built and a brood hatched last year. This year the
birds were busy on 7th April,

Dr. Alcock read an introductory paper “ On the Forms
and so-called Species of Foraminifera.”

Mr. R. D. Darbishire proposed the following resolution —
“That this Meeting of the Microscopical Section of the
Literary and Philosophical Society of Manchester respect-
fully invites the serious attention of the proper authorities
of Owens College to the increasing disadvantage which
students and naturalists of this district suffer, while the so-
called Manchester Museum remains unexhibited and unde-
veloped in the private rooms of the College — while other
towns, and notably Liverpool, enjoy very largely the bene-
fits of free access to good and well arranged collections.

190

Manchester alone offers no opportunity of the kind. The
continued postponement of the promised development of
the Museum constitutes, in the opinion of the Section, a
grave departure from the spirit of the late Nat. Hist.
Society’s generous gift.”

PHYSICAL AND MATHEMATICAL SECTION.

Annual Meeting, April 27th, 1880.

E. W. Binney, F.R.S., F.G.S., President of the Section,

in the Chair.

The following gentlemen were elected Officers of the
Section for the ensuing year : —

E. W. BINNEY, .E.S., P.O.S.

JOSEPH BAXENDELL, P.E.A.S.

ALFEED BEOTHEES, E.E.A.S,

JAMES BOTTOMLEY, D.Sc., B.A.

:

EE'V. THOMAS MACKEEETH, F.E.A.S., E.M.S.

“Colorimetry, Part V.,” on the Absorption of Light by
Turbid Solutions, by James Bottomley, D.Sc.

Media containing colouring matter may be divided into
two classes, transparent and turbid. It might be considered
tliat in tlieir behaviour with regard to light they were
wholly dissimilar. But the question arises, is not the differ-
ence between tran.sparency and turbidity one of degree.

191

Experience in the laboratory brings under our notice cases
where matter is so finely divided as not to be separable
from fluids by filtration^ and showing but slight tendency
to settle as a precipitate, and in some cases we have liquids
which are apparently transparent, and yet are considered to
hold solid matter in suspension. May not such examples
be intermediate between solutions and cases where extremely
fine particles are uniformly diffused through some trans-
parent medium ? If then we consider the passage from
tranparency to turbidity as a continuous one, and if for a
transparent fluid we have established some law of absorption
of light, may not the same law be applicable to a turbid
solution ? The subject seemed to me interesting both as a
scientific enquiry and on account of its application to quan-
titative analysis.

Suppose we have diffused through a liquid some finely
divided solid matter; the action of such a turbid solution
on light will be twofold, it disperses light and it absorbs
light. By reason of the first action we are made aware of
the colour of the turbidity; by reason of the second, any
object seen through the liquid seems of diminished dis-
tinctness.

As a typical case, take carbon diffused through water. In
a paper which I read at the last meeting of the Physical
and Mathematical Section, I alluded to some attempts to
obtain a soluble black, in order to make some experiments
on the absorption of light. To assist my judgment as to
the appearance which such a liquid should present, I had a
cylinder containing a little carbon diffused through water.
Weak diffusions of carbon in the colorimeter gave the same
appearance when I looked at external white surfaces as I
should have expected a liquid containing a soluble black in
solution to give under the same conditions. A diffusion of
carbon both disperses light and absorbs light. The disper-
sion gives rise to a greyish tint, due to the light coming

192

from the innumerable particles of carbon. Owing to the
absorption a white surface seen through the column of liquid
seems of diminished whiteness. Hence, under ordinary
circumstances, tlie light which comes to the eye has a two-
fold origin, part being transmitted light and part dispersed
light. My first object was to dissociate these two pheno-
mena. I therefore used cylinders which were covered with
black cloth, admitting light by circular apertures at the
bottom, 8 mm. in diameter. In this way the dispersed light
was almost wholly cut off. In some cases a feebly nebulous
light could be seen around the apertures, but it was very
slight and did not interfere with experiments to determine
the absorptive properties. With any attempt to explain by
ph3^sical optics the analogy of the absorption of light by
solutions and diffusions I have nothing to do, but on the
supposition that there was continuity. I was led to expect
that a function of the same form would express the intensity
of the transmitted light in both cases. Also independently
of such considerations it seemed probable from a reflection
upon the mode of distribution of the particles throughout
the mass of fluid, that the function would be the same as
for transparent solutions. In thelatter case, both experiment
and reasoning from first principles concur in giving a
formula. 2a k for the intensity of light passing through a
column t units long. As I have pointed out in another
paper, this implies an expression of the form 2a/c,^
denoting the connection between the transmitted
light and the quantity of colouring matter. There-
fore we miglit expect a similar expression to hold
in the case of diffusions (the term seems to me more

convenient than to speak of turbid solutions). If such be
the case, one consequence will be that, if we have two
cylinders containing in equal bulks of water Q and Q' of
solid matter in suspension, if we adjust the columns so as
to obtain the same intensity of light when we regard exter-

193

nal white surface, then the lengths of the columns will fulfil
the condition Q^=Q/.

The carbon that I used was lamp-black recalcined in a
covered platinum crucible. After being so treated it
seemed blacker than it did before. Of this 0 4170 grams
were ground up in a mortar with 10 drops of a solu-
tion of gum. The contents of the mortar were then rinsed
out with water, and diffused by shaking through 500 cub. c.
of water. This was poured into a cylinder ; the length of
the column was 22*5 c.m. After the lapse of 24 hours I
drew off by a pipette the upper portion ; the column so
removed was 15 ’8 c.m. long. This carbon diffusion contained
so much solid matter that I found it inconveniently strong
for experiments, so as occasion required I made weaker
diffusions, containing in 250 cub. c. 5, 10, 20, or 40 of the
stronger diffusion. Of these weaker liquids portions were
taken and mixed with water so as to yield a bulk of 500
cub. c. I stated above that the carbon was ground up
with 10 drops of gum, so as to yield a smooth, thick con-
sistence. The amount of dry gum would be very small,
nevertheless it had a remarkable effect in increasing the
adhesion of the carbon to the water. When I had shaken
up carbon alone with water it had sensibly subsided after
the lapse of a few hours. After the addition of so small a
quantity of gum the tendency to deposit is much
diminished. The following are the details of some experi-
ments. The strength of the carbon diffusion is ghmn in
terms of the number of cub. c. of the strong carbon diffu-
sions in 500 cub. c. of water. The external white surface
was a sheet of white paper. In all cases I have used the
right eye only. The number under A denotes the mean of
two trials got by pouring into the cylinder, and therefore
likely to yield too low results. B denotes the mean of
two trials got by pouring out of the cylinder, and there-
fore likely to give too high results. C denotes the mean
of A and B. D denotes tlie length required by theory.

194

Standard diffusion, 1’2 cub. c. in 500 cub. c. of water,
length of column, 21*2.

Expt. I. — Comparison diffusion contains 1*8 cub. c. in
500 cub. c.

ABC
1435 16-35 15-25

A second trial gave

ABC

D

14-13

D

12-65 14-65 13-65 14-13

Expt. II. — Comparison diffusion contains 2-4 cub. c. in
500 cub. c.

A B C D

10-6 11-25 10-93 10-6

Expt. III. — Comparison diffusion contains 3-0 cub. c. in
500 cub. c.

A B C D

8-4 9-25 8-83 8-48

Expt. lY. — Comparison diffusion contains 3-6 cub. c. in
500 cub. c.

A B C D

6-85 7-6 7*22 7‘07

Expt. Y. — Comparison diffusion contains 4-2 cub. c. in
500 cub. c.

A B c D

5-6 6-1 5-85 6-06

Expt. YI. — Comparison diffusion contains 4-8 cub. c. in
500 cub. c.

A B C D

5-1 5-55 5-32 5-3

Expt. YII. — Comparison diffusion contains 5-4 cub. c. in
500 cub. c.

A B C D

4-1 4-5 4-3 4-71

On another occasion I got a nearer result, as follows :

A B C D

4-7 4-95 4-82 4-71

Expt. YIII. — Comparison diffusion contains 6 cub. c. in
500 cub. c.

195

A B C D

4i3 4-58 4-3G 4-24

Expt. IX. — Comparison diffusion contains 6*6 cub. c. in
500 cub. c.

A B C D

3-98 4-25 41] 385

Expt. X. — Comparison diffusion contains 7*2 cub. c. in
500 cub. c.

A B C D

3’48 375 3-61 3*53

Expt. XI. — Comparison diffusion contains 7*8 cub. c. in
500 cub. c.

A B C D

3-23 3*45 3*34 3*26

Expt. XII. — Comparison diffusion contains 8*4 cub. c. in
500 cub. c.

A B C D

3-03 3*45 3'24 3*03

Expt. XIII. — Comparison diffusion contains 9 cub. c. in
500 cub. c.

A B C D

2-9 3 2-95 2*82

Expt. XI Y. — Comparison diffusion contains 9*6 cub. c. in
500 cub. c.

A B C D

283 305 2-94 2*C5

Expt. XY. — Comparison diffusion contains 14*4 cub. c.
in 500 cub. c.

A B C D

1-98 2-08 2*03 1*77

Expt. XYl. — Comparison diffusion contains 19*2 cub. c.
in 500 cub. c.

A B C D

1-6 1*58 1-59 1’32

Many of the above numbers are close approximations. I
also tried columns of the lengths given by theory in all
experiments, except by the ninth, where by an oversight I

196

neglected to do so. The tints so obtained were in every
case satisfactory, until I reached Experiment XIV. In this
and in the succeeding experiments I thought that columns
of the theoretical lengths gave tints slightly lighter than
the standard diffusion. On some occasions I have wavered
in my opinion that the theoretical column gave too light a
tint in the fourteenth experiment. At another time I got
the following result : —

Expt. XVII. — Comparison diffusion contains 9 '6 cub. c.
in 500 cub. c.

A B C D

2-8 2-95 2-87 2*65

Here again the number under C is a little greater than that
under D. I afterwards repeated the experiment with this
variation — that the standard diffusion was contained in the
comparison cylinder, and the comparison diffusion in the
standard cylinder.

Expt. XYIII. — Standard diffusion contains 1*2 cub. c. in
500 cub. c. ; length of column, 22'6.

Comparison diffusion contains 9 *6 cub, c. in 500 cub. c.

A B c D

2-85

3-07

2-96

2-82

On another occasion I got —

A

B

c

D

2'85

815

8-0

2-82

Here again there still remains a tendency to make the
column a little longer than the theoretical.

I repeated the experiments in which the strength of the
comparison diffusion is several times a multiple of the
strength of the standard diffusion. The strength of the
standard diffusion was the same as in the previous experi-
ments, and the length of the column was 21*2.

Expt. XIX. — Comparison diffusion contains 9 '6 cub. c. in
500 cub. c.

A B C D

2-63 2-98 2-8 2-65

When I actually tried the theoretical column I thought
that tlie tint was perhaps slightly lighter.

197

Expt. XX. — Comparison diffusion contains 14’4 cub. c. in
500 cub. c.

A B C D

1-9 2-15 202 1-77

The tint given by the theoretical column I thought slightly
lighter.

Expt. XXI. — Comparison diffusion contains 19'2 cub. c.
in 500 cub. c.

ABO D

1*55 1‘63 1*59 1*32

The tint given by the theoretical column I thought slightly
lighter.

Expt. XXII. — Comparison diffusion contains 24*0 cub. c.
in 500 cub. c.

A B

1T5 1*3

0 D

1*22 1*06

The tint given by the theoretical column I thought slightly
lighter, but hardly distinguishable.

Expt. XXIII. — Comparison diffusions contains 28*8 cub. c.
in 500 cub. c.

A B c D

1*0 1*1 1*05 0*88

The tint given by the theoretical column I thought slightly
lighter.

Expt. XXIV. — Comparison liquid contains 33*6 cub. c. in
500 cub. c.

A B C D

0*88 0*9 0*89 0-76

The tint given by the theoretical column I thought slightly
lighter.

Expt. XXV. — Comparison liquid contains 38*4 cub. c. in
500 cub. c.

A B c D

0*73 0*83 0*78 0*66

The tint given by the theoretical column I thought slightly
lighter; they were, however, very nearly the same.

198

This second series of experiments confirms the result of the
first series that there is a slight departure from the rule, when
the strength of one diffusion is several times a multiple of
the other. Both series show a tendency to make the
column in the comparison cylinder slightly too long. We
must not hastily conclude that in these cases the theory is
not applicable. It seems to me that we should expect such
a result, for the medium is not perfectly transparent, and
in one cylinder we have a column of this medium (water)
several times a multiple of the length of the column in the
other. This would require some slight compensation. In
these experiments I have taken the lower level of the
meniscus as the proper reading. In some of the stronger
diffusions it was a little difficult to determine this exactly.
On the whole, I think that the above experiments are
favourable to the assumption that for a column of fluid
containing finely divided carbon in suspension the relation-
ship ^ constant holds, if the intensity of the transmitted
light remain constant. If we represent the above results
graphically, and take as the theoretical curve the rectan-
gular hyperbola cry =25 ‘44, it will be seen that the results
of the experiments do not depart far from the curve.

In a paper read at the last meeting of the section, I
suggested a method for testing the assumed laws of the
absorption of light. I also have applied the same reasoning
and method of experiment to carbon diffusions. In one
series of experiments I took a diffusion containing 1*934
cub. c. in 500 cub. c. The standard shades of grey used
were one consisting of 10 grms. BaS04 and 0*012 of lamp-
black— this I denote by Wa — the other consisted of 10 grms.
of BaS04 iJ^nd 0 0 48 of lamp-black — this I denote by Wb.
The materials were well incorporated by shaking and
grinding. To the powder I then added a little water so as
to obtain a mixture of suitable consistence to be used as
a paint. This was applied by a brush to pieces of cardboard

199

so as to obtain uniform surfaces. These surfaces were then
dried, the colorimeters employed were the same as in the
last experiments. I looked at Wb through a column 3 c.m.
long. I held the other cylinder over Wa and endeavoured
to get the same tint. The mean of two columns, one
probably a little too long and the other probably a little too
short, gave 8 ’2 as the proper length. So I made the column
of this length, I thought that the tints were the same. Now
if the law hold with regard to turbid solutions, if we increase
both columns by the same length, the tints will again
correspond. I took 4 c.m. as the common increment. The
lengths of the columns were made 7 and 12*2. I thought the
resulting tints equal. The lengths of the columns were
made 11 and 16*2. I thought they were about equal, possibly
Wa slightly lighter. My impression varied a little with
the illumination of the surfaces. The lengths of the
columns were now made 15 and 20*2, the tints seemed
about equal, possibly Wa slightly lighter. The difference
if any must be small, as is shown by the following experi-
ment. Taking Wb seen through a column 15 c.m. long, as
the standard tint, I endeavoured to get the same tint with
Wa seen through the other cylinder. For the lower limit I
got 19 '9 c.m., and for the upper limit 21-0 c.m., the mean of
these is 20*45, not far removed from 20*2. Afterwards I
thought a column of this length satisfied. I now made the
lengths of the columns 19 and 24*2. I thought that the
tints again corresponded.

Some experiments of a similar nature were made with a
stronger diffusion, it contained 3*747 cub. c. in 500 cub. c.
The tints of grey used were the same as in the last experi-
ments. The standard tint at the commencement was Wb
seen through a column 4 c.m. long. To get a similar tint
with Wa one determination for the upper limit gave 6*5,
and one determination for the lower limit gave 6*1. The
mean of these is 6*3. A column of this length seemed to

200

satisfy. The common increment is 8 c m. The columns
were made 7 and 9 3 c.m. long. The tints seemed to
correspond. The columns were made 10 and 12’3 c.m.
long. The tints again seemed to correspond. The columns
were made 13 and 15*3 c.m. long. The tints seemed
again to correspond. Finally, the columns were made
16 and 18 -3 c.m. long. The tints again corresponded.
In the two last experiments the greys obtained were
very deep. I also made the following experiment. I
took two grey tints : one consisted of 10 grms. BaS04
and 0'042 grins, of lamp-black. The other consisted
of 10 grms. BaS04 and 0*4003 grms. of lamp-black. These
greys were made into a paint by the addition of a little
water, and pieces of cardboard covered with them. They
were then dried. These we may denote by and W/3. I
looked at W/3 through a column 4*1 c.m. long, and
endeavoured to get a similar tint with W« under the other
cylinder. For the upper limit the column was 6*95 c.m.
long, and for the lower limit 6'2 c.m. long. The mean is
6*57 c.m. I next altered the length of the column over W/3
to 11-75. In the other cylinder for the upper limit the
column was 14-9 c.m., and for the lower limit 14-8. The
mean is 14-85. Hence we have

By cross multiplication and elimination of W/j

Theory requires the sums of the indices to be equal.

The sum on the right hand is 18*32, and on the left 18*95.
The difference is, I think, not greater than what might be
due to errors of observation.

“Results of Observations of the Variable Star T Aquilse,”
by Joseph Baxendell, F.B.A.S.

A notice of the discovery of the variability of this star

W1

was communicated to the Section on the 12th of November,
1863, and printed in the third volume of the Society’s
Proceedings. At that time I had observed only one mini-
mum and one maximum, and was therefore unable to deter-
mine, with any near approach to accuracy, the length of the
mean period and the mean range of variation of magnitude.
I have however since observed eight additional minima and
eight maxima thus making a total of nine minima and
nine maxima, which from the length of time over which the
observations extend afford the means of determining the
mean period and the mean epochs of minimum and maximum
with considerable accuracy.

OBSEEYED MINIMA OF T AQUILA5.

Mag,

Days in
Interval.

Number
of Periods.

1863. Aug. 24

11-3

1864. June 24

11-2

305

2

1865. Aug. 31

11-5

433

3

1866. June 10

10-8

283

2

Nov, 14

11-0

157

1

1867. Sept. 12

10-8

302

2

1868. June 23

10-7

285

2

1878. Nov. 18

10-8

3800

26

1879. Oct, 2

11-6

318

2

Forming the usual equations and treating by the method
of least squares we obtain

Mean Epoch = 1868, November, 16'38.

Mean Period = 146'671 days.

OBSERVED MAXIMA OF T AQFILiE.

Mag.

Day.s in
Interval.

Number
of Periods.

1863. Oct, 25

8-9

. . .

1861. Aug. 23

8-4

303

2

1865. June 30

10-1

311

2

Nov. 22

9-4

145

1

1866. Sept. 6

8-7

288

2

1867. Nov. 4

9-0

424

3

1868. Aug 15

9-0

285

2

1878. Sept. 15

9-0

3683

25

1879. Nov. 22

9-1

433

3

/6

202

The equations formed from these data, treated by the
method of least squares, give ;

Mean Epoch — 1869, January 23 •89.

Mean Period=14G*527 days.

The mean of the two values of the period is 146‘599 days,
and using this to calculate the times of minima and maxima,
we have the following differences between the calculated
and obsei'ved times of minimum : —

Days. Days.

5-6

... - 8-4

—

6-2

... - 0-2

+

0-6

... +11-4

4-

10*8

... -13*4

+

0.4

The average difference is 6*3 days, or about 2V of the
whole period.

The differences between the calculated and observed
times of maxima are

Days.

Days.

+ 12-1

+ 7-1

+ 2-3

+15-3

-15-5

- 2-7

-13-9

+ 4-1

- 8.7

The average difference is 9’1 days, or about of the
whole period. The irregularities in the times of maximum
are thei’efore greater than in those of minimum. The dis-
tribution of the plus and minus differences in the two
series of results does not seem to indicate that any sensible
change has taken place in the length of the period.

Like many other variables, T Aquilse increases in bright-
ness more rapidly than it diminishes, the mean interval from
minimum to maximum being 68’5 days, and from maximum
to minimum 78*1 days.

The mean magnitude at minimum is 11*08; the lowest
minimum yet observed is 11-6, and the highest 10-7, thus

203

showing a range of 0’9 magnitude. The mean magnitude at
maximum is 9 '07 ; the highest yet observed is 8-4, and the
lowest 101, the range of variation at maximum being there-
fore VI magnitude, or nearly double that at minimum.
The extreme range of variation in the star’s brightness is
3 ’2 magnitudes.

The following paper was read at the Annual General
Meeting, April 20th, 1880 : —

'' On an adaptation of the Lagrangian form of the equa-
tions of fluid motion. Part I.,” by R. F. Gwyther, M.A.

'fhe object of the Lagrangian form of equation is to follow
the motion of a particular element; and, although the
Eulerian forms suit the general purposes of fluid motion best,
there are certain cases, as that of vortex motion in a
perfect fluid (which may be termed steadily progressive)
where the course of an element might be investigated with
advantage.

For this purpose 1 propose investigating the course of a
fluid element, defined by means of surfaces moving with the
fluid, and expressing the results as far as possible in terms
of the parts of the element.

This method leads to a more general integral form than
that of Weber, and finally exhibits some of the known
properties of fluid motion in a novel manner.

If ^ be a scalar function of the position of a point in the
fluid, its total differential after time is andifD;(^ = 0,

the property of the point, of which (j) is the analytical
expression, is unchanged during the motion. Nowlet^=/x
be the equation to a surface all points on which enjoy the
same property, such a surface will, if D^^=0, move with
the fluid.

The number of independent surfaces of this kind which
can pass through any point, or the number of independent
integrals of the equation Vtcjy — O is three, or the dimensions

204

of the space considered. For the Jacobian of a higher num-
ber would vanish.

The position of a point in the fluid in motion may be
represented in terms of the three independent sets of
surfaces = = (l>s = i^s where /mi, fi^ and ^3 are parame-

ters.

I have avoided the use of theorems and terms such as
those of “ circulation,” as I think they are apt sometimes to
override and hide the more important facts which their
discoverers intended them to express, and I have en-
deavoured to bring the fundamental properties to the
surface.

Imagine an element of the fluid separated from the rest
of the fluid by the surfaces which we shall denote by

f^i, ^2? fts) /n + Sjiid ^3 + 3^3.

We will investigate expressions for the parts of this element.

First, V01, V02, V(f)3, represent vectors in the directions
of the normals to the three surfaces, such that if hi, h^, h^,
stand for their tensors, the thicknesses of the element will

be given by — and respectively.

The directions of the edges are given by Y V02 V</>3 = a say,
and the similar quantities (3 and y, so that

V/3y= -Sv<^iV(/)2V^s. say.

The length of an edge will be given by the thickness -j-
the cosine of the angle between the corresponding normal
and the edge. Thus length of the edge a is

Sjui hi^a ^jjiiYa

hi' S V 0ict H

and the vector edge is - (1)

Whence the area of the face 0, is ^^^^TY/3y = |T^/i2^/a3

and the vector of the faces V </n (2)

From either (1) or (2) we may get volume of element

hfXi^lXiClX^ T h^lhfX2^fX3 , .

— ■"

205

The condition of continuity is therefore that — 0

where p denotes the density, and this condition in an incom-
pressible fluid becomes DiH=0. Generally where

D(0=O.

Before proceeding to investigate any forms for o-, the
velocity, we will find some expressions from the action of
Dt on the expressions just found.

d

Remembering that ~ ^ V we see that

D^v = vB<+ a(So-v)

symbolically, where A is the same operator as v but acts
on the or only.

Thus D^V0= A(SffV0)

f^.d(T n,d(T rjdcf

— V + V V ^ + V V 0 4- V V 0 .... (4)

since V = V + V 0.^^ + V 03^^

[These other two forms of v will also be used
— H V = V 0lS V 02 V 03 V + V 02^ V 03 V 01 V + V 0sS V 01 V 02 V >
or =aSv0iV +/3Sv02V +ySv03V,
since v is in form a vector.]

Let us first apply these results to S v 0i V 02 V 03 or - H
- DtE = SDe V 01. V 02 V 03 + S V 0lDj V 02. V 03 + S V 01 V 02 V 03

'da da da

\d(f)i

= - Hsf

or iD,H
H ^

)

Sv«r= - HD

a)

,(5)

or is evidently rate of compression per unit of volume.

If again we act similarly on a or V V 02 V 03
Dftt = VD^ V 02. V 03 + V V 02Be V 03

- S V 02^ V V 01 V 03 + V 02^ V V 02 V 03

+ V 03^ V V 02 V 01 + V 03^ V V 02 V 03

= SV<r.a-S^Vi.i.a-S^V<p,.(}- V ?>s.y

= S Vff.a + Htt

d(pi

. 1 T^ T^ ^

• • H^‘“ ^ - df,

206

a da

,(6)

, • 1 , •

■whence we obtain v o- = v + V (t>2'jT- + V 0s^-~

Cv(j)i Cl^2 ^03

n

= y + V + V ^>aD(g

(7)

a /3 y S( V0i« + V«i2/3 + V^av)

Nowvi;.ijj+ Vc/>2g+ V^>8g = -^-^^

+

V(V0ia + V02/3+ V^sy)
H

of which the vector part is seen to vanish and the scalar
becomes - 3. Whence

T-xCt t^/3 -r. Ctx^ y

V0lD,g+ V<?)2Dt|J+ V03D^||= -DiV02||-D^V03g

and HVvo- = V(aD^v0i + /3DiV02 + yDiV03) (8)

Of these (7) gives the more convenient form, from which
we obtain

H V V <T = V V <^iDiV V 02 V ^3 + &c.

= V V 0lVD^ V 02- V 03 + V V 0lV V 02D« V 03 + &C.
and applying to each of these expressions the formula

VaV/3y — ySa/3 — /3Say,

we obtain

0gv{Sv0Av02 - Sv02r>tV0i} + &c.

+ DeV03{SV0lV02 - Sv0iV02} + &C.

= V0l{SV02Di03 - SV03DtV02} + &C. + &c.

Whence S v02DfV03 = Sv03D<V025 &c. , if the motion is irrotational
or expressing

H V'^o’ = lici + + l^y

we find by operating with Sv0i on each side —

- nil = Sv0iV02D«/3 + Sv0iV03b)iy
= S(yD,/3~/3D,y)

Whence — HWvo- = S (yD^/3 - /3D^y) a + <fec. + &c (9)

and Vv'T = S

{

H^'H

and D

,s(

~T) ~ — ~T) ~ i— S

ft d

D.

= sl ^ D'

( H f/02 H d(j)y

{h
.} =

H H ‘ H
s.(Vv0iv)P,<T
H

}

(10)

207

This form enables us to express in a general way the crite-
rion that the vortex motion may exist in the form which it
will be seen to take in a perfect fluid. Taking the two
other similar quantities, and equating each to zero, we get
YvDto- = b or D^rr of the form v?-

This notation also enables us to give a verbal expression
for V V 0-. Thus let PQB- lie on a line of intersection of two
surfaces 02 ^^nd 0g, and let them be distinguished by 0i,

01 + and 01 - Then the vector difference of the

2i ^

velocities at Q and R is -^^0i, and re-

solving parallel to the face 0i of the
element, having P for centre, these diffe-
rential velocities on the parallel faces 0i,

we get

^0iV^" U V 01 X area = -f~x area V

.d(T .
d(p\

K

— volume X V 0i

d(f)i ^

da

d(pi

V</»i

and similarly for the other faces.

volume X V V AT = resultant differential velocity and V v o- =
mean resultant differential velocity per unit of volume as
the result of three shears and rotations, and by a similar
method we may find the force due to viscosity, arising in
consequence of the motion noticed above, upon the faces 0i,
being due to the rate of change of the differential velocities
just found. It will plainly be proportional to volume

II.

The equation of motion is on the generally adopted
theory

Dto-v + vY ]o vSvo- + -^vV = 0 (1)

^9 9

where V Y represents what would be written in Cartesian,

- 1 {Xlx + Y<V + Zlz) + p. )

208

and therefore assumes each of these quantities perfect
differentials, and therefore p a function of p only.

We will first take fx = 0.

In any case ^ can evidently be written in terms of the
normals to the three surfaces (j>, determining the point at
which (T is the velocity. Thus

= KiV0i + KaV^2 + KgV03-

On the previous assumptions Ki, Kg, and Kg must be of a
definite form, which we proceed to find thus.

Dt(T = D^Ki. V (/)i + KiD^ V 01 + &c.

= (d,K. + + K.s|-

+ &c. + &c.

(d(T ^

DfKi + So-^ J V 01 + &c. + &c.

= D^Ki. V 01 + AK2. V 02 + D^Kg. V 03 + I V {erf (2)

whence the required form of the functions Ki, Ka, Kg is given

D,Ki = ^,D,Ka = ^-^, D,Kg =

d(j)i

c?0a

,(3)*

^03

,, dP ^ ^ rr f^P'“ ""

^

where P is a scalar and DjS = 0 2 a scalar function of

010203 only, and <r takes the form —

VP + 2l V01 + S2 V02 + 2gV03 r.(4)

Proceeding to find Yver, from this we get

V Vo- = Y( V2l. V01+ V22. V02+ V23-V0g)

(

o?2g (iSa'N p p

- - la + &C. + &C.

(5)

^c?0a d(pQ/

= Sia + 2a/3 + Sgy say

where D^2 = 0.

Whence if the motion is irrotational the S’s can be included
in the vP. under the above hypotheses.

Also V V o- may be written H2i.g + K^a.g + H2g.g., and since

“ &c. denote the edges of the element, the components of

* Conf. Mr. Hill’s paper on some properties of the equations of hydro-
dynamics, Q, J. of Maths., Feb,, 1880.

209

HS

Vv^are--^ times the corresponding edge, and if the

cp.1

fluid is incompressible this ratio remains unaltered in time,
and the manner of variation, if the fluid is compressible, is
indicated by the formula.

Also since = 0, if V v o- is ever = 0 it always was and
will be = 0, and the strength of the section of the vortex

S S — —

on the surface is S v</ji.2ia = and is constant in

all time.

If we compare the form of o- here obtained with that
assumed by Helmholtz, we find that his form is not suffi-
ciently general ; since he writes 2i v 0i + 2-2 v + 2g v 03 = V w
where w is a vector with the condition S v w = 0. That is, he
includes two undetermined quantities instead of three, and
does not obtain in a distinct form the essential condition,
nam ely = 0, affecting them.

The quantities 2 are in no way dependent on finite forces
which are acting (under the hypothesis), but entirely on the
initial conditions (boundary conditions not now being
entertained).

Unless the density be a function of the pressure only, the
relations just proved will certainly not hold, for then

DifT + V V + i = 0,

Ki = + 2i where 2i = /(0i. 02-03 and ().

d<pi

in which case the fluid pressure will of themselves cause
vortex motion.

This seems to be a quite possible condition in a gas
rapidly heated or expanded.

Now turning to the terms containing fx and imagining p
a function of p only, and remembering that p is independent
of p, then

P

210

will not necessarily be a function of p only, since is not
necessarily, nor even generally so. Hence the conclusions
we draw above will not generally hold good, for viscous

fluids even in the cases where v^o- = 0 or i vV = vQ, where

P

Q is a scalar. But if the fluid is incompressible in either of
these latter cases the theorems hold good.

Note. — Since writing tlie above 1 have seen a paper by
M. Bresse, Fonction des vitesses, extension des theoremes
de Lagrange au cas dflin fluide imparfait (Gomptes Rendus,
March 8, 1880), in which he seeks to show that if o-= aP
at any time it will remain so throughout the motion.
In the investigation, however, the author follows Navier in

taking — an absolute constant of the fluid. This, of course,

will not lead to correct results for a gas at any rate, and I
think his result must be wrong for any liquid even incom-
pressible, as it would follow that vortex motion could not
be generated owing to the fluid friction, if for instance it
starts from rest.

I should explain the defect in his reasoning thus. Wri-
ting M for and considering p constant, the equation

affecting a» is

+ (Sw V )o- + ^ V = 0 or V V T>t(T + — V = 0,

P P

from which M. Bresse concludes that if w is at any time
zero it remains so. Now this seems to require that for a
small value of w, should not take a value of an infinitely
greater order. It has been shown by Maxwell that if w be

a vector function of any point — represents the differ-
ence between the value of w at that point and its mean
value over a small sphere of radius r about the point, and
therefore I conceive that we can not conclude from the
above equation that vortex motion may not arise in lines
or surfaces, but merely that it could not appear in a solid
foi’in, a form of the existence of which we have no evidence.

The true criterion would be found by equating to zero the
expressions found above (10).

Although I conceive that the theorem is not proven for
the case which M. Bresse considers where fx “may have
any value other than zero/’ I think that if jx is sufficiently
small a proof may be given. For if fx were zero the pro-
position is true, and the terms owing to which it departs
from the truth will appear with ^ as a factor, and may
therefore be omitted from the term and under this

hypothesis if is ever zero it will continue so, and

the proposition is completed.

IIT.

Considering how the portion Si v 0i + S2 v 02 + 2g v 0s of the
velocity can be impulsively generated, we see that the initial
equation of motion will take the form

\hdt + / ~pdt.

) ^ 0 p

where T is the infinitely small time during which the im-
pulsive force -ip acts and p is the impulsive fluid pressure.
Now generally there will be no impulsive forces acting bodily
on the fluid, but the velocity will be generated by the
impulsive pressures only, and therefore if does not satisfy
Vvo- = 0, it must be on account of one of two reasons.
Either during the impulse p does not follow the law of
dependence on p, which is highly probable; or p is dis-
continuous, so that the form vp is an improper form.

IV.

The velocity can also be written in a form of simple appear-
ance. Thus —

01 ^2 . 03

(7- jja

since D<0i = 0i - (S(tV0i) = 0.

Cl ‘3

Whence D,o- = - D,0i.g - D^02,^ -

P - d ' d ' d

212

T) j. /ci \ ’ d ' d ' d

But + +

' ,d a —

^ • a T\' T\' y

and the condition for steady motion isDi0 = O, showing a
close resemblance in form between the velocity in this case
and the rotation in a perfect fluid.

We may at any time, by elimination of t, find two sur-
faces of the nature </> for which (^ = 0, and since in steady
motion = 0, the property will continue in the surface.
Taking the two such surfaces for </>2 and ^g, they will act as
fixed boundaries, their intersections will be the stream lines
and the form of (j will be

(T

a.

H" ;

In spite of the simplicity of this form, it does not appear to
yield a convenient form of condition affecting Difr, nor
for Vvo".

The following property can, however, be deduced. In a
perfect fluid under conservative forces, we must have (Sn-y)
of the form vP

But (So'V)o’ = + Vo-VV'T.

V.o-Y^cr = vQ_say,

^iSgV^2 + — vQ

or

dQ

whence ^ = 0, and and ^^become 0 when acted on by

d(j)i d(f)^

Dt, whence Q is a function of ^2 and ^3 only. The existence
of this surface Q, on which both stream lines and vortex
lines lie, is dependent on the existence of vortex motion,
but if the surface exists we may take if in place of the
surface ^3 to indicate the stream lines, and then we get Sg = 0

and 01^2 = 1, or 22 = ' ’ rotation would be given by

01

1

Vv<t = Si.Vv</>2vQ + --YvQv0i (3)

01 ^ ^

The cases of steady vortex motion will, I think, generally
occur in cases allied to the surfaces of discontinuity inves-’
tigated by Helmholtz, and the surface Q will then be such

a surface.

,y

Vri

^ '•

■j

i

■’!

)

1

'j

1

kW, • ■

;

? ',■■; »r^