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TRANSACTIONS

OF THE

Roy AL .SOQClLETY

OF

EDINBURGH.

VOL. XVI.

EDINBURGH :
PUBLISHED BY ROBERT GRANT & SON, 82 PRINCE’S STREET ; AND
WILLIAMS & NORGATE, 14 HENRIETTA STREET,
COVENT GARDEN, LONDON.

MDCCCXLIX.

* . PF ate CaM URS GS :. wee 7
a» : PRINTED BY NEILL AND COMPANY, EDINBURGH.

|

1

1

iV.

VI.

VET.

CONTENTS.

PAL

. On a Possible Explanation of the Adaptation of the Eye to Distinct

Vision at Different Distances. By JAMEs D. Forses, Esq., F.R.SS.
L. & E., Corresponding Member of the Institute of France, and
Professor of Natural Philosophy in the University of Edinburgh,

On the Modification of the Doubly Refracting and Physical Structure
of Topaz, by Elastic Forces emanating from Minute Cavities. By
Sir Davip Brewster, K.H., D.C.L., F.R.S., and V.P.R.S.,
Edinburgh,

On the Existence of Crystals with different Primitive Forms and Phy-
sical Properties in the Cavities of Minerals; with additional Observa-
tions on the New Fluids in which they occur. (With a Plate.) By
Sir Davip Brewster, K.H., LL.D., F.R.S., and V.P.R.S., Edin.,

Account of Experiments upon the Force of the Waves of the Atlantic
and German Oceans. By Tuomas STEVENSON, Ksq., Civil En-

gineer, Edinburgh. Communicated by Davip STEVENSON, Esq., —

. On the Geology of Cockburnlaw, and the adjoining District, in Berwick-

shire. (With a Map and Sections.) By WitLiAM STEVENSON,
Dunse. Communicated by DAvip MILNE, Esq.,

On the Extraction of pure Phosphoric Acid from Bones, and on a new
and anomalous Phosphate of Magnesia. By WILLIAM GREGORY,
M.D., F.R.S.E., Professor of Chemistry in the University of Edin-
burgh, 5 : : : : 4 ‘

Miscellaneous Observations on Blood and Milk. By Joun Davy, M.D.,
F.R.SS. London and ities: Inspector-General of Army Hos-
pitals, L.R., : ‘ ‘ 5

VOL. XVI. b

PAGE

1]

23

33

47

53

vi CONTENTS.

VILL. On the Advantages to be derwed from the Use of Metallic Reflectors for
Sextants and other Reflecting Instruments ; and on Methods of directly
determining the Errors in Mirrors and Sun-Shades used in Reflecting
Instruments. By Joun Aviz, Esgq.,

IX. On the Balance Magnetometer, and its Temperature Correction. By
J. A. Broun, Esq. Communicated by Sir T. M. BrisBaAng, Bart.,

X. On Wotzasron’s Argument from the Limitation of the Atmosphere, as
to the Finite Divisibility of Matter. By Grorcr Witson, M.D.,
Lecturer on Chemistry, : : :

PART II.

XI. On the Sums of the Digits of Numbers. By the Right Reverend
Bishop TERROT, ; : ;

XII. Results of the Makerstoun Observations, No. I. On the Relation of the
Variations of the Horizontal Intensity of the Earth’s Magnetism to
the Solar and Lunar Periods. (With Two Plates.) By J. A. Broun,
Esq. Communicated by Sir T. M. Brispang, Bart., °

XIII. On the Decomposition and Dispersion of Light within Solid and Fluid
Bodies. (With a Plate.) By Sir Davin Brewster, K.H., D.C.L.,
F.R.S., and V.P.R.S., Edin., ;

XIV. On the Constitution and Properties of Picoline, a new Organic Base
from Coal-Tar. By Tuomas ANDERSON, M.D.,

XV. Results of the Makerstoun Observations, No. II. On the Relation of the
Variations of the Vertical Component of the Karth’s Magnetic In-
tensity to the Solar and Lunar Periods. (With a Plate.) By J.
ALLAN Brown, Esq., Director of General Sir T. M. BRISBANE’s
Magnetical and Meteorological Observatory. Communicated by
Sir T. M. BrisBane, Bart.,

XVI. On the Solubility of Fluoride of Calcium in Water, and its relation to
the occurrence of Fluoride in Minerals, and in Recent and Fossil
Plants and Ammals. By GEorcE Witson, M.D.,

PAGE

61

67

2

99

lll

123

137

145

CONTENTS.

XVII. Observations on the Principle of Vital Affinity, as illustrated by recent
discoveries in Organic Chemistry. By Witi1AM PULTENEY ALI-
son, M.D., F.R.S.E., Professor of the Practice of Medicine in the
University of Edinburgh,

XVIII. Account of some Experiments on the Temperature of the Earth at dif-
ferent Depths, and in different Soils, near Edinburgh. (With Four
Plates.) By James D. Forses, Esq., F.R.S., Sec. R.S. Ed., &c.
Corresponding Member of the Institute of France, and Professor
of Natural Philosophy in the University of Edinburgh,

PART III.

XIX. On a Formula representing the Mean Height of the Barometer at the
Level of the Sea. By Professor HANSTEEN of Christiana, in a
Letter addressed to Professor ForBrs, Secretary of the Royal
Society of Edinburgh,

XX. On General Differentiation. Part III. By The Rev. P. Kenuanp,
M.A., F.R.SS. L. & E., F.C.P.S., late Fellow of Queen’s College,
Cambridge, Professor of Mathematics, &c., in the University of
Edinburgh,

XXI. Observations on the Principle of Vital Afinity, as dlustrated by re-
cent discoveries in Organic Chenustry. By WiLLiAM PULTENEY
Aison, M.D., F.R.S.E., Professor of the Practice of Medicine in
the University of Edinburgh. Part IT.

XXII. An Attempt to Hlucidate and Apply the Principles of Goniometry, as
published by Mr WARREN, im his Treatise on the Square Roots of
Negative Quantities. By The Right Rev. Bishop Terror,

XXIII. On the Reaction of Natural Waters with Soluble Lead Salts. By
ARTHUR CONNELL, Esq., F.R.S.E., Professor of Chemistry in the
University of St Andrews,

XXIV. On certain Products of Decomposition of the Fixed Oils in contact with
Sulphur. By Tuomas ANDERSON, Esq., M.D., F.R.S.E., Lecturer
on Chemistry, Edinburgh, : ,

Vil

PAGE

165

189

241

305

345

vill CONTENTS.

XXV. Experiments on the Ordinary Refraction of Iceland Spar. By Wit-
LIAM Swan, Esq. Communicated by Professor KELLAND, 375

XXVI. Observations on the Temperature of the Ground at Trevandrum, in
India, from May 1842 to December 1845. By Joun CatpEcort,
Esq., Astronomer to the Rajah of Travancore. Communicated in
a Letter to Professor J. D. Fores, : , ‘ ; ; 379

XXVITI. On the Parallel Roads of Lochaber, with Remarks on the Change of
Relative Levels of Sea and Land in Scotland, and on the Detrital
Deposits in that Country. (Witha Plate.) By Davip MILNE, Esq., 395

PART TV:

XXVIII. Memow of Dr THomas Cuarves Hore, late Professor of Chemistry
in the University of Edinburgh. By THomAs Stewart TRAILL,

M.D = : : ; : 419
XXIX. On the Colouring Matter of the Morinda citr sick By THOMAS
ANDERSON, M.D., 2 ; : . ; 435

XXX. Notice of the Orbit of the Binary Star a Centauri, as recently deter-
mined by Captain W.S. Jacos, Bombay Engineers. By Professor
C. Prazzi SMYTH, s : ; ; ‘ ‘ ‘ 3 445

XXXI. An Attempt to Improve the present Methods of Determining the
Strength and Direction of the Wind at Sea. (With a Plate.) By

Professor C. P1azzi SMYTH, . : : ; ; 5 455
XXXII. On the Products of the Destructive Distillation of Animal Substances.
Part I. By Tuomas AnpveErson, M.D., : : 463

XXXIII. On the Action of the Dry Gases on Organic Colouring Matter, and its
relation to the Theory of Bleaching. By Grorce Wiison, M.D., 475

CONTENTS.

PART V.

XXXIV. A Biographical Notice of the late Tuomas Cuatuers, D.D. & LL.D.
By the Very Reverend H. B. Ramsay, M.A., F.R.S.E.,

XXXV. On the Theory of Rolling Curves. By Mr James CLERK Max-
WELL. Communicated by the Rev. Professor KELLAND,

XXXVI. An account of Carvor’s Theory of the Motive Power of Heat ; with
Numerical Results deduced from Ruzenavtrs Haperiments on
Steam. By Witi1aAm THomson, Professor of Natural Philo-
sophy in the University of Glasgow,

XXXVI. Theoretical Considerations on the Effect of Pressure in Lowering
the Freezing Point of Water. By James TuHomson, Esgq., of
Glasgow. Communicated by Professor WILLIAM THOMSON,

XXXVITI. On the Gradual Production of Luminous Impressions on the Hye,

and other Phenomena of Vision. (Witha Plate.) By WiLL1AM
Swan, Esq., ; ‘ : ; :

Proceedings at Extraordinary Meetings, Sc. ; :

List of the present Ordinary Members, in the order of their Election,
List of Non-Resident and Foreign Members, elected under the Old Laws,
List of Honorary Fellows, :

Last of Fellows Deceased, Reged a and Cancelled ve 1844 to 1849,
Last of Donations, continued from Vol. X V., p. 722,

Index,

VOL. XVI. ¢

PAGE

497

. 5 ae 1
Ay is i
- f |
U > in

TRANSACTIONS.

*

I.—On a Possible Explanation of the Adaptation of the Eye to Distinct Vision at
Different Distances. By James D. Fores, Hsq., &.R.SSL. § E., Corre-
sponding Member of the Institute of France, and Professor of Natural Philo-
sophy in the University of Edinburgh.

[Read 16th December 1844, and 6th January 1845. ]

Iv is unnecessary to detail to this Society the various ingenious hypotheses
which have been proposed to account physiologically for the accommodation of the
eye to distinct vision at different distances. In later years, these different theories
have been so circumstantially and correctly recapitulated in systematic works
(as for instance in Youne’s Lectures and in MUtLER’s Physiology), that it would
be a waste of time to copy and recite them here. I will only do so, then, so far as
may be necessary to justify the attempt I have now to make, and to strengthen
my views by those of others, as far as they bear upon them.

The eye being the organ of sense best understood, and constructed upon the
most intelligible principles,—being one whose functions, up to a certain point, may
be accurately represented by an artificial apparatus, it is impossible to doubt that
the ultimate function of vision depends on the formation of a distinct picture of
an object upon the retina, and that the circumstances which affect the distinctness
of the picture in the instrument or artificial eye, must affect the clearness of
vision in the real eye. Such a circumstance is notoriously the distance at which
objects are placed from the eye. Now it is known by experience, (1.) That ob-
jects at very variable distances may, in the healthy organ, be distinctly seen ;
(2.) That such variations have limits, beyond which distinct vision cannot, by any
effort, be obtained; (3.) This limit varies in different eyes ; (4.) The limit may be
extended by optical aid, which would, in the model or artificial eye, produce the
same effect; (5.) The adjustment of the eye to different distances is felt to be
accompanied by a distinct muscular effort. On all these grounds, we conclude
that the focal adjustment of the eye is a real mechanical adjustment, tending to

VOU, XVi. PART I. A

2 PROFESSOR FORBES ON THE ADAPTATION OF THE EYE

form an optically distinct picture on the retina; and that the opinion of those
physiologists is to be disregarded, who have supposed that the distinctness of
vision at one distance or another arises merely from a mental effort of attention.

We assume it, then, to be granted that the adjustment of which we are in
quest is of a nature such, that when the eye is turned from a distant to a near
object, ether the retina is moved from the refracting apparatus of the eye, so that

the less convergency of the rays may be allowed for by the increased distance ;
or else, that the distance of the retina or pictured screen remaining the same, the
refraction of the eye is increased, so as to cause the rays to converge more rapidly
than they would have done in the previous state of the eye.

If the first alternative be true, the axis of the eye must undergo an elongation
of about one-seventh part (according to OLBERs* and Youne+), in passing from
the distinct vision of distant to that of very near objects. Dr Youne has described
two experiments, by which, he says, he satisfied himself that the elongation of
the eye could not be anything like the quantity required by the hypothesis. Dr
Youne’s experiments are obscurely described ; but perhaps a not less conclusive
and more simple proof of the error of this explanation is found in the fact insisted
on by TrevirANus and MULtEr, and which seems to me quite unanswerable,—
“that the tendency of the straight (vect?) muscles is merely to retract the eye,
and if resistance were afforded by the cushion of fat behind it, to flatten rather
than elongate it; their action would, therefore, have the effect of adapting the
eye to the vision of distant objects only, the image of which is formed nearer the
lens, than that of near objects; while it is in looking at very near objects, on the
contrary, that we are conscious of an effort within the orbit.” t

It seems difficult to admit with MULLER, however, that any conclusion as to
the mechanism of the eye can be drawn from the transient and anomalous changes
of.adjustment which it seems to undergo under the influence of narcotics, such as
belladonna.

The other class of explanations turn upon the production of an increased
refractive power in the eye, by the altered curvature of one of its numerous re-
fracting surfaces. Every one of these has been in turn fixed upon as the subject
of the change, as well as those parts of structure which, by their intimate con-
nexion with the principal parts, might be supposed to influence them. The
cornea, the lens, the iris, and the ciliary processes, have each been supposed to
be the part immediately affected. Most of the theories have been refuted with
consummate skill by Dr Youne, in his paper on this subject in the Philosophical
Transactions for 1800; and, as is well known, he himself attributed the change
of focal adjustment to a proper muscular power residing in the lens. This other-

* Quoted by Mixzer. t Nat. Phil. ii. 589.
+ Muxtzr’s Physiology, translated, p. 1148, 1144.

TO DISTINCT VISION AT DIFFERENT DISTANCES. 3

wise probable opinion is contradicted by the fact, that the muscularity of the
lens is unproved, and that this organ is wholly unprovided with bloodvessels
and nerves. The opinion now adopted by several eminent living authors is, that
the “first step in the process is the variation of the pupil, which seems, by a
mechanism at the base of the iris, to increase the distance of the lens from the
retina.”* This is very vague; it is shewn by conclusive experiments that the
simple contraction and expansion of the iris produces no effect on the focal ad-
justment ;+ and it isa mere conjecture that any of the organs connected with
the iris, the ciliary body for instance, has, or can have, any influence in pulling
the lens forward from the retina in any degree, much less through the consider-
able space requisite. We may, therefore, accept the reswmé of a late French writer
on Physics, as nearly expressing the opinion of the most candid authors upon
this vexed subject: “ Tout cela n’est pas trés-satisfaisant, et il faut avouer que
Yexplication de la netteté de la vision 4 des distances si differentes est encore a
trouver.”

Such being the present phase of the question, the suggestion of a “ possible
explanation” yet unthought of, of the manner of the adjustment of the eye, may
be received with indulgence, or at least proposed without presumption.

About three years ago, whilst lecturing on the subject of vision, I was struck
with the circumstance, that the crystalline lens possesses not only a remarkable
gradation of consistence or density from the centre towards the surface, and espe-
cially towards the edges, whereby, according to the common explanation, the
spherical aberration of the rays of light is completely corrected ; but likewise a
complex and singular figure, which it is plain might alone produce the same
effect by the modified curvature of the surfaces. Here, then, we appear to have
two peculiarities of structure to attain one end; and it seems so natural, that
the curves should be proper curves for destroying the aberration of sphericity,
instead of the spherical curves which are used in our instruments only from our
incapacity to form better ones,| that it occurred to me that the remarkable vari-
ations of density in the lens must be intended to answer another purpose.

This purpose I conceived might be the focal adjustment, and effected in the

* Brewster in Art. Optics, Encyc. Brit. 7th Edit. p. 513.

t+ See MiziEr and Brewster.

t The forms of curvature of the crystalline lens are said to have been actually ascertained by
M. Cuossar to be ellipsoidal. It is a curious proof of the vagueness with which this subject has been
treated, that, in the clear and able work of Professor Luoyp on Light and Vision, in one page, the form
of the surfaces is insisted on as the means of producing distinct vision ; and on another, the gradation
of density from the centre to the side of the lens; whereas, it is certain, that if the compensation for
spherical aberration due to the last cause be correct, the ellipsoidal form will be erroneous. Thus, as
in many other cases, the argument for design has been made to prove too much. See Luoyp on
Light and Vision, pp. 264-266, who refers to CHossat’s paper, Ann. de Chemie, vol. x.

4 PROFESSOR FORBES ON THE ADAPTATION OF THE EYE

following way: The crystalline lens, for example, that of the ox, is composed of a
nearly spherical nucleus of compact comparatively dense matter, of a hard pasty
consistence, which gradually, yet rapidly, passes into the gelatinous envelope of
a lenticular form, which has far less consistence, and less resistance to external
pressure than the central spherule. It therefore occurred to me, that any wniform
pressure applied to the lens, such as might be communicated by the external
muscles of the eye to the entire eyeball, and propagated by hydrostatic pressure
through the humours, would tend to make the exceedingly flattened ellipsoid of
the eye approach in figure to the dense spheroidal nucleus; the obvious effect of
which would be, without any change in the position of the lens, to increase its
curvature, so as to render the rays from a near object more convergent.

I proceeded, in April 1842, to endeavour to put my hypothesis to the proof,
by subjecting the recent crystalline lens of a bullock to considerable hydrostatic
pressure, in a suitable apparatus, and endeavouring to observe the change of focal
distance produced, making it act as the object-glass of a microscopic arrange-
ment; but, partly owing to the difficulty of suspending the lens in a secure yet
free manner, partly from the unfavourable form of the glass vessel used for com-
pression, partly from the small excess of refracting power of the lens above that
of the water in which it was suspended, and partly from the essential indistinct-
ness of the picture formed in the dead eye, and the consequent difficulty of deter-
mining its precise focal distance ;—from all these causes my experiments failed
in yielding a positive result :* and though I communicated my views soon after to
Dr Attson, I,postponed any farther consideration or publication of the subject,
until I should be able to support the theory by decisive experiments. My attention
has been wholly diverted since to other inquiries; and I see no prospect, at pre-
sent, of resuming the experimental part, which, no doubt, would be worth pur-
suit, and though difficult, is not I think, hopeless. In the mean time, the subject
of focal adjustment of the eye having been started at the late meeting of the
British Association at York by Sir D. Brewster, it occurred to me to state
verbally my notions; which having been thought worthy of attention, I have put
them into this more definite and permanent shape.

In the absence of a direct proof in favour of my hypothesis (and this, it will
be observed, no other theory possesses), I may be allowed to state one or two cir-
cumstantial evidences in its favour.

The first has been mentioned already, but is recapitulated for the sake of
connection.

1. The crystalline lens possesses, on the common view, a twofold structure

* It may be added, that the bullock’s eye is perhaps one of the least favourable on which the
experiment could be made. Owing to its very great convexity and thickness, it may be presumed
that the action of compression above described will be much less visible than in a comparatively flat
lens, such as that of man.

TO DISTINCT VISION AT DIFFERENT DISTANCES. 5

to produce a single end. I assume that each structural condition has a separate
end; the variable curvature to correct the aberration, the variable density to
alter the figure of it under pressure.

2. The attempt to view near objects distinctly is accompanied by a sensible
muscular effort within the orbit. Thisis expressly stated, incidentally, by MUtuEr,
in a passage already quoted ; and has been admitted by every one whom I have
questioned on the subject. From my own sensation, I have no doubt that it isa
simultaneous effort of the four recti muscles drawing the eye back within its
socket.* Such a retractive muscular action, fatal to the theory of elongation of
the eyeball, is just what we require to communicate to the fluid humours of the
eye, through the tough sclerotic coat in which they are bound, the hydrostatic
pressure which will act simultaneously upon all points of the crystalline lens.

3. This theory is free from the unanswerable objections urged by Dr Youne
and others, to all theories independent of that which ascribes the adjustment to
change of figure in the lens: and it is free from the objection to Dr Youne’s own
theory, which presumes a structure existing in the lens itself, unproved, and, to
say the least, improbable,—I mean its muscularity.

4. It is confirmed by the fact, that where the lens is reproduced after the
operation for cataract, the power of adjustment is almost or totally lost; for, in
that case, it cannot be supposed that the new lens is provided with the requisite
gradation of coats for modifying its elasticity.

5. The diminution of the adjusting power of the eye in old age is well ex-
plained by the collapse and induration of the lens, to the detriment of its elastic
properties. +

6. That the crystalline lens is actually possessed of variable elasticity in dif-
ferent directions is rendered highly probable by Sir Davin Brewster’s observa-
tions on its action on polarized light, in which tints are produced similar to those
in compressed jellies, and in minerals possessing different axes of elasticity.

POSTSCRIPT TO THE PRECEDING PAPER.

When this paper was written, I had not seen CHossat’s paper on the Forms
of the Refracting Surfaces of the Eye, which I have referred to. I have since read
it,t and find a remarkable confirmation of the views I entertain.

It is very plain, that, were the gradations of the refrangibility of the coats of

* Tam aware that this is opposed to the experiment of Mr Ramspen and Sir E. Home, which
seems to shew a protrusion of the eyeball. Supposing it correct, that protrusion must be equally the
result of muscular action producing pressure, due perhaps to the oblique muscles antagonising the
recti; for it is difficult to see where else it can be sought.

+ “In all animals the crystalline lens grows firmer with age.” Brewster Edin. Encyc., Art.
Optics, p. 475.

t In the Annales de Chimie, vol. x., published in 1819.

WiO Tim exeViley Pe AD oT, B

6 ADAPTATION OF THE EYE TO DISTINCT VISION AT DIFFERENT DISTANCES.

the crystalline intended to correct spherical aberration, this condition presumes
the sphericity of the surfaces. If the surfaces have the curve of no aberration,
for instance, an ellipsoid, with its longer axis parallel to the incident rays, any
variation of density of the medium is not only useless but hurtful, producing a
contrary error, and causing the central rays to converge too fast. On the con-
trary, if the variable density of the matter of the crystalline exist (which is an
undoubted fact), and has been so arranged for a distinct purpose, the form of the
surface of no aberration adapted to it will be a peculiar one, and, very probably,
will be more convex towards the lateral parts than even the sphere, much more
than the ellipsoid already mentioned, which is the curve of no aberration for a
lens of uniform density.

Having perceived this result, it was with no small satisfaction that I found,
on examining M. Cuossat’s paper, that whilst for the cornea (where the refrac-
tion is from air into the uniformly dense medium of the aqueous humour), the
surface is that of an ellipsoid, with the longer axis in the direction of the incident
rays, and which, therefore, destroys aberration by the appropriate curvature,—in
the lens, the figure is that generated by an ellipse revolving round its lesser axis,
and therefore possessing a contrary property to that ordinarily required for cor-
recting aberration; the curvature being greater for the lateral than the central
parts of the lens. This is surely an unanswerable proof, that the opinion main-
tained by, I believe, every modern writer on optics, without exception, namely,
that the variable density of the lens is intended to correct spherical aberration, is
a fallacy, since we find it combined with an appropriate figure for destroying its
aberration, in which the peculiarities of spherical refraction are exaggerated.

The measures and drawings of M. Cuossat appear so minute and correct, as
to leave no doubt of the fact of this antagonism to the common opinion.* Accord-
ingly, neither by himself, nor by the few authors who have quoted this singular
circumstance, has any explanation been given.

On our theory it is simple. The gradation of density has been provided for
the mechanical purpose of varying the elasticity of the lens in different directions ;
and the form of its surfaces has been then determined so as to render the lens
aplanatic.

* M. Cuossat’s experiments were made on the lens of an ox; but Dr ALLEN THomson tells me
that, without knowing his results, he had arrived at a similar conclusion, as to the opposite kind of

curvature in the cornea and in the lens of the human eye; the surface of the former lying without,
and the latter within the surface of the osculating sphere.

EDINBURGH, 20th December 1844.

Il.—On the Modification of the Doubly Refracting and Physical Structure of
Topaz, by Elastic Forces emanating from Minute Cavities. By Str Davin
Brewster, K. ., D.C. L., F.R.S., and V. P. R. S., Edin.

(Read 20th January 1845.)

WHILE examining, in polarised light, the form and structure of the numerous
crystals which I had discovered in the fluid cavities of Topaz, my attention was
particularly called to certain optical phenomena exhibited in other parts of the
specimen. These phenomena, when first presented to me, were very indefinite
in their character, and very imperfectly developed ; but after a diligent examina-
tion of nearly 900 specimens of topaz, I succeeded in obtaining the most satisfac-
tory exhibition of them under various forms, and in various degrees of intensity.

When an elastic force is propagated from a centre, in a soft and compressible
medium, an increase of density is communicated to the surrounding mass,—of a
temporary nature if the medium is a hard solid, like glass, but of a permanent
nature if the medium is soft, and becomes indurated during the continuance of
the compressing force. Both these effects may be exhibited experimentally, the
first by a pressure upon glass, and the second by the action of an expanded bubble
of air upon gum ina state advancing to induration.

The physical change thus produced in the transparent medium, whether it
be temporary or permanent, may be exhibited to the eye in two ways, either by
the property of the compressed parts in depolarising light, or in the unequal re-
fraction of common light produced by a varying density, and consequently a
varying refractive power. In the jirst of these cases, the depolarising action is
displayed in-the production of four quadrants of light, separated by the radii of a
black rectangular cross, similar to the central portion, or the tints of the first
order, in the uniaxal system of polarised rings; and, in the second case, the in-
equality of refractive density is shewn by the mirage of a luminous point, in the
form of concentric circles surrounding the centre of force, each circle marking
successive actions of the central force.

When the four luminous quadrants of depolarised light, shewn at A, B, C, D,
in Plate, Fig. 1, first presented themselves to me, I had some difficulty in perceiving
the seat of the force, by which I believed that they were produced. The centres, or
intersections of the black cross, were either too deep beneath the surface of the
topaz, or too much covered by fluid cavities, to be seen; but by removing the part
of the crystal which contained these cavities, I succeeded in finding that, in every
case there was a minute cavity in the centre of the luminous quadrants, or at the

8 SIR DAVID BREWSTER ON A MODIFICATION OF THE DOUBLY

intersections of the arms of the black cross, from which the compressing force
had emanated. One of these cavities is shewn at E., Fig. 2. It is of a quad-
rangular form, like the section of a rhomboidal prism, sometimes elongated, and
sometimes of a slightly irregular shape. When perfectly regular, these cavities
are between the 3000th and the 4000th of an inch in diameter. They are always
dark, as if the elastic substance which they contained had collapsed into an opaque
powder; and I have met with only one case in which there seemed to be a speck
of light in the centre. The degree of compression to which the topaz has been
subjected is measured by the polarised tint developed in the luminous quadrants.
It varies from the faintest pale blue to the white of the first order. In one case
I found the luminous quadrant of one cavity coinciding with a luminous quad-
rant of another cavity, and thus producing the sum of their separate tints. This
effect is shewn in Fig. 3.

In the phenomenon now described, the elastic force has spent itself in the com-
pression of the topaz. The cavity itself has remained entire, without any fissure
by which a gas or a fluid could escape. I have discovered, however, other cavi-
ties, and these generally of a larger size, in which the sides have been rent by the
elastic force; and fissures, from one to siz in number, propagated to a small dis-
tance around them. These fissures have modified the doubly refracting structure
produced by compression ; but, what is very interesting, no solid matter has been
left on the faces of fracture, such as that which is invariably deposited, when an
ordinary cavity, containing one or both of the two new fluids, is exploded by heat.
The form of some of the cavities which have suffered this disruption is shewn in
Figs. 4, 5, and 6.

The influence of the compressing forces in altering the density, and conse-
quently the refractive power of the topaz, is so distinctly seen in common light
as to indicate the phenomena that are seen under polarised light. When the cavity
is most distinctly perceived, it is surrounded with luminous and shaded circles,
as shewn in Fig. 7; and traces of these are distinctly seen, as shewn in Fig. 8,
when the specimen is examined in polarised light.

The cavities now described have obviously no resemblance whatever to those
which I have described in previous papers as containing two new fluids. When
any of the latter are either burst by heat, or exposed under high temperatures to
the compressing forces of the fluids which they contain, they exhibit none of the
phenomena peculiar to the former. The doubly refracting structure suffers no
change ; and when the cohesive forces of the crystal are overpowered, the faces of
most eminent cleavage separate, and are covered with translucent crystalline par-
ticles, which the evaporated or discharged fluids leave behind.

The peculiar character of the pressure cavities, as we may call them, is still
farther evinced by the nature of the specimens in which they occur. I have never
found them accompanying the ordinary cavities with two fluids. The specimens

REFRACTING AND PHYSICAL STRUCTURE OF TOPAZ. 9

which contain them have imbedded in them numerous crystals, differing little in
their refractive power from topaz, and exhibiting in polarised light the most beau-
tiful colours, varying with the thickness of the crystal, and diminishing in inten-
sity as their axes approach to the plane of primitive polarisation.

It is impossible to review the preceding facts without arriving at the conclu-
sion, that the topaz must have been in a soft and plastic state when it yielded to
the compressing force which emanated from the cavities, and that a mineral body
thus acted upon could not have been formed, according to the received theory, by
the aggregation of molecules having the primitive form of the crystal.

In a letter to Sir JosepH Banks, printed in the Philosophical Transactions for
1805, I deduced, from my experiments on+ depolarisation, the existence of a
new “species of crystallization, which is the effect of time alone, and which is
produced by the slow action of corpuscular forces ;” and I have remarked that
“ this kind of crystallization will probably be found to have had an extensive
influence in those vast arrangements which must have attended the formation of
our globe.” These views have been confirmed by various new facts, wholly inde-
pendent of each other ;—by the existence of crystals imbedded in topaz, and having
their axes in all possible directions, but especially by the nature and form of the
strata of fluid cavities in that mineral. These strata cut at all inclinations the
primary and secondary planes of the crystal. They are bent in the most capri-
cious manner, forming planes of double curvature; and, what is also true of indi-
vidual cavities stretching in every possible direction, they could never have
been formed but when the topaz was in a soft and plastic state.

An objection to these views may be drawn from the fissures which proceed
from the pressure cavities. The topaz must, doubtless, have been indurated when
these fissures took place; but it is equally obvious that the depolarisation pro-
duced by compression must have previously existed, and it is probable that the
fissures were produced after the crystal had been removed from its matrix, and
when, from cleavage or otherwise, its cohesive forces had been diminished.

St LEONARD’s COLLEGE, St ANDREWs,
January 16, 1845,

VOL. XVI. PART I. Cc

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{1l.—On the Existence of Crystals with different primitive forms and physical
properties in the Cavities of Minerals ; with additional Observations on the
New Fluids in which they occur, By Str Davip Brewster, K.H., LL.D.,
F.RS., and V.P.RS., Edin. he tp

(Read Feb. 17, 1845.)

In 1823 and 1826 I communicated to the Society two papers on the nature
and properties of two immiscible fluids, which I discovered, in contact with each
other, in the cavities of topaz and other minerals. Although the facts contained
in these papers were of so extraordinary a nature as to be received with scepti-
cism by some, and with ridicule by others, yet I am not aware that, during the
twenty years which have elapsed since their publication, any person has either
repeated my observations, or advanced a single step in the same path of inquiry.
In shewing to strangers some of the leading phenomena of the two new fluids,
my attention has been frequently recalled to the subject; but it was not till last
spring, when I discovered cavities in topaz filled with the most beautiful crystals
of various form, that I was induced to undertake a new investigation of their
nature and properties. In this investigation I have examined, with various mag-
nifying powers, and both in common and polarised light, more than 900 speci-
mens of topaz from Scotland, New Holland, and the Brazils; and I have had the
good fortune to observe many new phenomena connected with mineralogy, che-
mistry, and physics, which, in addition to the interest which they may possess as
scientific facts, promise to throw a strong light upon the existing theories of
crystallization, and to bring before us some of those recondite operations which
had been going on in the primitive rocks of our globe, before the commencement
of vegetable or animal life.

1. On the Form and Position of the Strata in which the Cavities lie.

The cavities which contain the two new fluids, and their accompanying crys-
tals, sometimes occur single, and in groups more or less numerous; but, in general,
they exist in millions, occupying extensive strata, which affect the transparency
of the mineral, and render it unfit for the use of the jeweller, or even for the
cabinet of the collector, who has not learned that it is in the deviations from her
ordinary laws that Nature often discloses her deepest mysteries.

Although the strata of cavities sometimes occur, as in artificial salts, in planes
paratlel to the primary or secondary forms of the crystal, yet they occupy every

}2 SIR DAVID BREWSTER ON THE EXISTENCE OF CRYSTALS

possible position in reference to these planes; and we, therefore, cannnot account
for them by supposing that certain spaces have been left in the crystal, without
the primitive molecules which ought to have been there deposited. The strata of
cavities, too, have every possible curvature. From a plane surface they pass into
a curved one, sometimes of variable curvature, and sometimes of contrary flexure,
cutting and intersecting each other in the most capricious manner.

In the shape of the strata the same irregularity presents itself; their outline
is sometimes rectilineal, sometimes curved, and sometimes singularly irregular,
In some specimens the whole crystal is intersected with the strata; and it is ex-
tremely probable, though it is impossible to determine the fact, that in every spe-
cimen some edge or angle of the stratum touches the surface.

The succession of the cavities in composing the stratum, and their form in
relation to the character of the stratum, present interesting phenomena. I have
found specimens in which the cavities lie in concentric arches, and have their
sides concentric, and, as it were, a portion of the same arches, as if they had been
formed under the influence of a rotatory force. In other cases they occupy
parallel lines, and are sometimes so equidistant that they might be advantageously
used as micrometers for microscopes. In.one remarkable specimen they radiate
from a centre, each radiation having a character of its own. One radiation will
sometimes throw off a diverging branch, while two or more radiations will con-
verge and then diverge again, subsequently uniting themselves into a single radi-
ation.

When different strata of cavities lie parallel to each other in the specimen,
which they sometimes do, to the number of four or jive, each stratum has generally
a distinct character; flat and exceedingly thin cavities occupying one stratum,
very deep cavities occupying another, minute cavities which the highest magni-
fying powers can scarcely resolve occupying a third, while a fourth consists of
the most irregular and indescribable forms.

When the forms of individual cavities are related to that of the stratum
which contains them, they, of course, cut at all angles the primary and secondary
planes of crystallization ; and the same is true of insulated cavities of great length,
which are sometimes turned, and twisted, and bent, in the most capricious
manner. It is impossible to read these details, and still more so to study the
phenomena themselves, without being driven to the conclusion, that the strata of
cavities must have been formed under the influence of forces propagated through
a soft and plastic mass, and carrying along with them gases and vapours which
came to a position of rest previous to the regular crystallization of the topaz.
This conclusion, which I have been led to draw, in another paper, from a series of
entirely different facts, will be still further confirmed by the phenomena of im-
bedded crystals, to which I shall have to refer in another section.

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IN THE CAVITIES OF MINERALS. 13

2. Additional Observations on the Nature and Properties of the two New Fluids.

In re-examining the phenomena exhibited by the two new fluids, I have
found no occasion to modify or to correct any of the results contained in my
former papers. In the cavities which appear to contain only one fluid, namely,
the dense fluid, I have sometimes found a very small quantity of the volatile
fluid, which, with a slight rise of temperature, passes into vapour, and prevents
the apparent vacuity from disappearing by the application of a strong heat. —
When there is no volatile fluid present in such cavities, the vacuity is a real one,
and disappears entirely by the application of such a heat. If the heat is not
instantly withdrawn on the disappearance of the vacuity, the crystal never fails
to burst with great violence.

In some specimens of Brazil topaz I have found cavities with two fluids, and
without any vacuity in the volatile fluid at the ordinary temperature of an apart-
ment. In such cases [ have generally produced a vacuity by the application of
ice. Had heat been applied, the crystals would have burst, as there were no
empty spaces into which the fluids could expand.

When the cavities are flat, and have their faces perpendicular to the axis of
the crystal, or parallel to the planes of easy cleavage, the application of heat does
not burst the crystal, but produces a very remarkable phenomenon. The cavity
opens at its weakest point, and the fluid passes by starts, through a succession of
resting places, to another part of the crystal where it finds the readiest exit. The
fluid penetrates, as it were, the solid gem, and the laminze which it has forced
asunder in its passage, again close into optical if not into mechanical contact. If the
heat is withdrawn when the first minute drop has passed, the laminze unite, and
we can discharge the rest of the fluid whenever we please till the cavity is ex-
_hausted. This phenomenon is represented in Plate, Fig. 9, where ABCD isa
shallow cavity in a plate of topaz MN, and EF another cavity, which has been
emptied of its fluid contents by reaching the surface at N, where it had been broken
through. Upon looking at the cavity A B C D when slightly heated, I observed dark
portions of fluid rushing from its sharp termination at D through the cavity at
a, and then reappearing at ) and ¢, and then passing into the empty cavity E F.
The small lakes, as we may call them, at a, 6, and c, disappeared entirely when the
discharged portions of fluid had passed, and reappeared with a change of form
and size when the operation was repeated.

In a specimen of topaz possessed by Major Playfair, and seen by many indi-
viduals, a white ball passed from one cavity to the edge of the specimen, as if
projected from a mortar; but by the application of too strong a heat it was
shattered in pieces.

In my first paper of 1823,* I have described and figured a phenomenon of an

* Edinburgh Transactions, vol. x. p. 11, Plate I. Fig. 5, 6.
VOL. XVI. PART I. D

14 SIR DAVID BREWSTER ON THE EXISTENCE OF CRYSTALS

analogous kind ; but as it appeared unexpectedly, and was instantly followed by
the explosion of the crystal, I could neither observe it accurately, nor confirm
what I did observe, by a repetition of the experiment. I have, therefore, some
satisfaction in describing a similar phenomenon, seen frequently, and under more
favourable circumstances, not only from its intrinsic interest, but because a dis-
tinguished philosopher had treated with an air of incredibility an observation
which I had made of a similar kind. There can be no higher testimony to the
novelty and importance of a scientific fact, than when a competent judge raises
it to the supernatural.

I come now to describe a property of the dense fluid, so new and remarkable
that it cannot fail to excite the attention of chemists. This fluid occupies the
whole of a large cavity ABCD E, Fig. 10, with the exception of a bubble at A,
which must be either a vacuum, as it is in all cavities containing only this fluid,
or a bubble of the expansible fluid, or the vapour of the dense fluid, or some gase-
ous body. It cannot be a vacuum; because it expands with heat, in place of being
filled up by the expansion of the fluid. It cannot be the expansible fluid; because
cold would contract it, and produce a vacuity. It cannot be the vapour of the
expansible fluid; because there is no expansible fluid to throw it off, and it has
not the optical properties of its vapour. It cannot be the vapour of the fluid
in the cavity ; for it does not disappear by the application of cold, and does not
become a vacuity, which fills up by the expansion of the fluid. It is, therefore,
an independent gas, which exhibits the following phenomena.

When heat is applied, the bubble A expands, not by the degradation of its
circular margin passing into vapour, as in the vapour cavities described in a former
paper, but by the rapid enlargement of its area. When it attains a certain size,
it throws off a secondary bubble B, which passes over a sort of ridge or weir mno,
in the bottom of the cavity, and settles at B. If the heat is continued, these two
bubbles increase in size ; but it was instantly withdrawn when B had begun to
swell. As the topaz began to cool, both the bubbles A and B quickly contracted.
The primary bubble A returned gradually to its original condition, and B, when
reduced to a single speck, would have disappeared, had the cooling not been stop-
ped. This speck swelled again by the application of heat, and so did the bubble A.
When the speck at B was allowed to vanish, which it did on the spot which the
bubble occupied, the fresh application of heat did not revive it at that spot, but
merely expanded the primary bubble A, which again threw off a secondary
bubble B, which exhibited by heat and cold the same phenomena as before. These
experiments I repeated many times with the same result. It will naturally be
asked, what was the condition of the fluid itself which has the property of expanding
by heat; and what became of it while a part of the space which it occupied was
appropriated by the bubble B, and the addition to the bubble A? An accidental
circumstance enables me to answer this question, which would have been

IN THE CAVITIES OF MINERALS. 15

otherwise a very perplexing one. Having applied too strong a heat to the speci-
men, the bubble A threw off beside B two or three smaller ones, which moved
along the upper edge AE. My attention having been thus directed to this part
of the specimen, I was surprised to observe a great number of capillary lines or
pipes P Q, rising from the edge A E of the cavity, and into which the fluid was
forcing itself, oscillating in these minute tubes like the mercury in a barometer,
and sometimes splitting the laminz between them. The force of cohesion, thus
overcome by the expansive efforts of the fluid, predominated over the capillary
attraction of the tubes and surfaces, and pressed back all the fluid into the cavity,
when the body of fluid had contracted in cooling.

If we now consider the body which occupies the vacuity A as a gas, and, con-
sequently, the other bubble B as the same, it follows, that the whole of the gas
in B was absorbed by the fluid while cooling, and again given out by an increase
of temperature. The gas, when in the act of being discharged, took its course to
the locality of the speck at B, and to the bubble A ; but to the bubble A alone when
the speck had disappeared.

Upon repeating these observations the cavity burst; and I have now before
me its two halves, forming its upper and its under surface. The portion of the
cavity at A has the same depth as the portion below m7 0, all the rest of the
cavity being much shallower. There was a fine doubly refracting crystal at MN,
which polarised the blue of the second order; and its outline is still left on the
cavity. There was a sort of crystalline powder disseminated round M N toa con-
siderable distance, and the roof of the bubble B, when the roof of the cavity was
entire, was always mottled with this powder.

In a former paper, I have distinguished vapour cavities from common cavities,
by the manner in which the vacuity in the expansible fluid disappears. In the
one case, the vacuity gradually enlarges by the degradation, as it were, of its mar-
gin, as the fluid passes into vapour ; in the other, the vacuity gradually diminishes
till it disappears. I have since found cavities of an intermediate character, in
which the vacuity, on the first application of heat, diminishes, and then, when it
has contracted to a certain size, it begins to expand; and its margin becoming
thinner and thinner, it finally passes into vapour.

3. On the Form and Position of Crystals in the Cavities of Topaz.

In a former paper I have described a moveable group of crystals of carbonate
of lime, which I discovered in a cavity in quartz from Quebec, containing a fluid
with the properties of water. The crystals to which I am about to call atten-
tion, are of a very different kind, and possess a very different kind of interest.

The crystals which occupy the fluid cavities of topaz are either fixed or

16 SIR DAVID BREWSTER ON THE EXISTENCE OE CRYSTALS

moveable. Some of the fixed crystals are often beautifully crystallized. They
have their axes of double refraction coincident with those of the crystal, and, as I
have ascertained by the examination of exploded cavities, they actually form part
of the solid topaz, though they exist in the fluid cavity. One or two of these are
shewn in Fig. 4, Plate XIX., of my paper of 1826,* and they may be distinguished
by their attachment to the sides of the cavity. In the same figure, as well as in
Figs. 10, 13, 20, and 21 of my Paper of 1823,+ I have drawn others which I then
believed to be fixed, but which I have no doubt are moveable, and produced from
one or other of the new fluids.

In re-examining my specimens of topaz, I have been surprised at the great
number of cavities which contain crystals. In some there are only one ; in very
many there are two, three, and four ; and in a great number of specimens the ca-
vity is so crammed with them, like a purse full of money, that the circular vacuity
has not room to take its natural shape, and often can scarcely be recognised, in its
broken-down condition, among the jostling crystals.

The crystals of which I am treating are sometimes found in the volatile, and
sometimes in the dense fluid, but chiefly in the latter. They are often found in
an amorphous state in the narrow necks and narrow extremities of cavities, posi-
tions in which they remain fixed while they continue solid ; and sometimes re-
gularly formed crystals remain fixed between the prismatic edges of cavities, in con-
sequence of having either fallen into that position, or of having been formed there.

The crystals in topaz cavities are, in general, beautifully crystallized, and have
a great variety of forms. I have observed the following :—

. The Tetrahedron.

The Cube.

. The Cube, truncated on its edges and angles.

. The Rhombohedron.

The Prism, with plain and pyramidal summits.

. The Flat Octohedron, truncated on its edges and angles.
. Rhomboidal Plates.

. Hexagonal Plates.

. Long rectangular Plates.

peal

SCOoONa a Sw dO

Besides these, there are amorphous crystals and crystallized masses of various
characters.

4. On the Physical Properties of the Crystals in Topaz Cavities.

Although it would be desirable to submit these crystals, as well as the fluids
which contain them, to chemical analysis, yet the task is too difficult to be ac-

* Edinburgh Transactions, vol. x. } Ibid., Plates I. and II.

IN THE CAVITIES OF MINERALS. Lal

complished in the present state of chemical science. I must, therefore, limit my
observations to such of the physical properties of these crystals as can be rendered
visible to the eye.

When I first applied heat to the crystals under consideration, I employed a
very fine specimen, with large and numerous crystallized cavities, of a prismatical
form, containing both the new fluids. In this specimen, there were seven cavities
unlike all the rest, and each of them containing a single crystal, and apparently
but one fluid, namely, the dense one. The cavities were exceedingly flat, and
irregular in their shape, and very unlike one another. Upon applying the heat of
only a lighted paper match beneath the plate of glass on which the specimen lay,
I was surprised to see the crystals gradually lose their angles, and then slowly
melt, till not a trace of them was visible. In this state, one of the cavities had
the appearance shewn in Fig. 11, where V was the vacuity, and v, v, other two
bubbles, one of which v7 soon joined the principal one V. In all the other six
cavities, the crystals were speedily reproduced, always at the point where they
disappeared, provided a small speck remained unmelted ; but otherwise in different
parts of the cavity. In the cavity A B, however, Fig. 11, the crystal was very long
in appearing. In the course of an hour, however, a fasciculus of minute crystals
appeared in the centre of the vacuity, as in Fig. 12, and to them the principal
crystal attached itself, as in Fig. 138, which exhibits a perfect rhomboidal plate,
truncated on its obtuse angles. The elliptical vacuity was pressed into the shape
of a heart; and, by the application of ice, I succeeded in precipitating the vapour
of the expansible fluid, which existed in a very minute quantity in all the seven
cavities. The expansible fluid is shewn between the two heart-shaped outlines
in the figure, and I repeatedly threw it into vapour, and reduced that vapour to
a fluid state. The phenomenon now described, of the melting of the crystals, and
their subsequent re-crystallization, I have shewn to various persons ; and it is very
remarkable that they generally reappear in this specimen of the same form, though
with considerable modifications.

Upon applying heat to other cavities, containing several crystals, I obtained
very different results. Some of them melted easily, others with greater difficulty ;
and some were not in the slightest degree affected by the most powerful heat I
could apply. When the crystals melted easily, they were as quickly reproduced ;
sometimes reappearing more perfectly formed than before, but frequently running
into amorphous and granular crystallizations.

In some specimens of topaz, all the crystals in the cavities refuse to melt
with heat, and seem not to suffer the slightest change in their form. Hence we
are entitled to conclude, that the crystals possessing such different properties
must be different substances ; and this conclusion is amply confirmed by an exa-
mination of their optical properties.

In making this examination, I used a polarising microscope, so constructed

VOL. XVI. PART I. E

18 SIR DAVID BREWSTER ON THE EXISTENCE OF CRYSTALS

that the plane, passing through the optical axis of the topaz, could be readily
placed either parallel or perpendicular to the plane of primitive polarisation. In
this case, the field of the microscope is wholly obscure, in so far as the depolaris-
ing action of the plate of topaz is concerned ; but if there is any crystal in the
topaz, either imbedded in its mass, or included in its cavities, that crystal will
exhibit its doubly refracting structure, if it has any, by its depolarising action.
It may, indeed, happen,—and it does happen,—that the plane passing through their
optical axes coincides, either accurately, or so nearly, with that of the topaz, that
its depolarising action is a minimum; but an experienced observer will have no
difficulty in distinguishing this want of depolarisation by position, from the want
of it by structure.

When the specimen of topaz is rich in cavities full of crystals, the display of
luminous and coloured crystalline forms in the dark field of the microscope, in-
dicating, too, the imprisonment of fluids, and the condensation of gases before
vegetable or animal life had visited our primeval globe, was as interesting to the
imagination and the judgment as it was beautiful to the eye. Having had the
privilege of being the first to see it, I felt the full influence of the sight; and I
have again and again contemplated it with renewed wonder and delight. When
the cavities are so numerous as to mock calculation, and so infinitely small as to
yield no visible outline to the highest powers, the bright twinkle of a crystalline
atom within them reveals to us their nature as well as their contents.

In the examination of the individual crystals, many interesting facts present
themselves to our notice. The crystals of the tessular class, which are modifica-
tions of the cube, are very numerous, and have no action upon polarised light.
Many of them melt easily, while others refuse to yield to the action of heat; and
hence, there must be two different substances in the cavities which assume the
same shape. In like manner, some of the doubly refracting crystals melt readily,
others with very great difficulty, and others not at all; so that there must be three
different substances, which belong to the classes of forms that give double refrac-
tion ; a conclusion which is confirmed by the different secondary forms which I
have already enumerated.

I have seldom found any crystals in these cavities which depolarise white
light, or the highest order of colours. I have found some that depolarise jour
orders of colours ; and when the crystal which does this is a flat hexagonal plate,
it is highly interesting to see it pass through all the tints which these orders in-
clude, while slowly melting, and again reproducing them during its re-crystal-
lization.

In a cavity which was so placed as to be entirely black from the total re-
flection of the light which fell upon it, I observed three white openings, a, b, c, of
a crystalline form, see Fig. 14. These appeared to be fixed crystals, or rather parts
of the topaz, surrounded by a cavity. .1 found, however, that the hexagonal one

IN THE CAVITIES OF MINERALS. 19

C depolarised white light, while the rest had no action upon polarised light.
Upon applying heat, the crystal ¢ melted, and took up a position at ¢ Fig. 15, in
a narrower part of the cavity, where it remains of an irregular form, having been
repeatedly melted and re-crystallized. Upon turning the cavity into a position where
it became transparent, I found that there was no fluid whatever in the cavity ; so
that we have here an example of a crystal melting and re-crystallizing without
having been dissolved in one of the fluids. From the irregular state of the la-
minze close to this cavity, there is every appearance of the fluids having escaped
from one of its extremities.

In the course of these observations, I observed a phenomenon, produced by
heat, of the most novel and surprising kind, and one which I feel myself utterly
unable to explain. It presented itself when I was studying the very interesting
collection of crystals in the cavity AB, Fig. 16. This cavity is filled with the
dense fluid, in which there is a vacuity V: the fluid swells to such a degree with
heat as to diminish very perceptibly the size of this vacuity; and as I can find
no trace of any portion of the volatile fluid, I have no doubt that this vacuity
would disappear by an increased degree of heat. The fear, however, of bursting
so rare and interesting a cavity, has prevented me from making this experiment.
The cavity contains a great number of crystals of different forms, not one of which
melts with heat, and almost all of which possess double refraction. When I first
submitted this cavity to the microscope, there were jive small crystals lying be-
tween D and the vacuity V; one a flat prism, another a hexagonal plate, a third
amorphous, and a fourth and fifth two irregular halves of a hexagon. Upon the
first application of heat, one or two of these crystals leapt from their resting place,
and darted to the opposite side of the cavity. In afew seconds, the others quitted
their places one after another, performing the most rapid and extraordinary rota-
tions. One crystal joined another, and, at last, four of them thus united revolved
with such rapidity as completely to efface their respective shapes. They then
separated on the withdrawal of the heat, and took the position which their gravity
assigned them. On another occasion, a long flat prism performed the same rota-
tion round its middle point ; and I have repeated the experiment so often, in shew-
ing it to others, that the small crystals have been driven between the inclined
edges of the cavity, from which I cannot extricate them. I have succeeded, how-
ever, in conducting a fine octohedral crystal, truncated on its edges and angles,
into the arena at D, where I have just seen it perform its rotation, as indicated
by the concentric circles on the right hand of D.

In seeking for the cause of so extraordinary a phenomenon, we are reminded
of the rotations of camphor and other volatile substances; but, in this case, no
gas or matter of any kind could be thrown off without becoming visible in the
fluid. The pyro-electricity of topaz next suggests itself as a moving power; but
though it might produce attractions and repulsions, we cannot see how it could

20 SIR DAVID BREWSTER ON THE EXISTENCE OF CRYSTALS

turn a crystal upon its axis. The experiments of Libri and Fresnel, on the re-
pulsions which heated bodies exert upon each other at sensible distances, afford
us as little aid. 'They may enable us to account for the mere displacement of the
crystals by the application of heat, or for their sudden start from their places of
rest, but they do not supply us with a force fitted to give and to sustain a rapid
rotatory movement. 7

I have already had occasion to state, that the cavities often burst when too
much heat is applied to the specimen. This generally takes place by a separa-
tion of the laminze, which fly off in splinters; but when the burst cavity is large
and insulated, a piece of the solid crystal is scooped out on its weakest side.
Sometimes a great number of cavities explode at the same time, and when they
are small, or exist in a part of the crystal where there are no large ones, the ex-
plosive force is not strong enough to separate the laminze. The fluid is merely
driven between the laminee to a small distance around the cavity, and shews
itself as a dark brown powdery matter, encircling the cavity as the burr of a
comet does its nucleus. When the cohesion of the lamine is great, it resists the
explosive force over a large cavity, and the contents of the cavity are thrown to
a considerable distance around it, and remains between the laminee, either as a
sort of powder, or as a congeries of minute crystals, which are sometimes large
enough to shew their depolarising action. When the lamin separate, we find this
crystalline matter either fluid or indurated; exhibiting, when fluid, the extraordi-
nary properties described in my former papers. If we breathe upon the indurated
matter it becomes fluid, re-crystallizes in new spicule and crystals; and, on
several occasions, I have found fine examples of circular crystallization.

After the explosion of cavities containing only the dense fluid, I have been
surprised to find, and that in large cavities, that no trace of matter was left upon
the sides of the cavity or around it. Whether this arose, as the fact seems to indi-
cate, from the dense fluid being a condensed gas, or from some other cause, it
will require new experiments to determine.

In avery remarkable specimen, in which the cleavage plane passed through a
great number of large flat cavities, the brown matter has been lodged near to the
edges of each cavity, and marks them them out even to the unassisted eye.
These cavities were filled almost solely with the volatile fluid; and since the faces
of the cavities are corroded as if by the action of a solvent, developing crystalline
forms, there is reason to think that the fluid has exercised this action, and that
the phenomenon is analogous to that external action, on the faces of hundreds of
Brazil topazes in my possession, which I have described in the Cambridge Trans-
actions,* and the singular optical figure formed by which, I have represented in
a late volume of the Transactions of this Society.t+

* Cambridge Transactions, vol. ii. Plate i. fig. 15.
t Edinburgh Transactions, vol. xiv. Plate x., fig. 1, 2.

IN THE CAVITIES OF MINERALS. 21

The only chemical experiment on the contents of these cavities, which I have
had occasion recently to make, is perhaps worth reporting. One angle of a cavity
was blown off by its explosion, and though the fiuids escaped, a pretty large pris-
matic crystal remained within the cavity. I introduced water and alcohol succes-
sively into the cavity, and raised them to a considerable heat; but they had no
effect in dissolving the crystal.

5. On Solid Crystals and Crystalline Masses imbedded in Topaz.

Among the new phenomena which this section embraces, there is at least
one intimately connected with the subject of the fluid cavities. How far the
other phenomena may have any such connexion, it remains to be seen.

The imbedded crystals to which I refer, presented themselves to me while the
specimens which contain them were exposed to polarised light. Mineralogists have
been long familiar with the beautiful crystals of Titanium, imbedded in quartz,
and I have found the same mineral imbedded under still more interesting circum-
stances in the Brazilian amethysts.

In topaz, however, the imbedded crystals have never been noticed, and I
have fortunately obtained specimens, in which they are displayed with singular
beauty. Their axes of double refraction are not coincident with those of the topaz ;
and hence they are seen in the obscure field of the microscope splendent with all
the colours of polarised light. These crystals are equally transparent with the
topaz, with a few slight exceptions They sometimes polarise five or six orders of
colours; and, in general, they have very beautiful crystalline forms, which can be
seen by the microscope incommon light. In some cases, they are mere crystalline
masses, often of a reniform shape, but still with regular axes of double refraction.

In some specimens of Brazil topaz, the crystals occur in branches or groups
of singular beauty, consisting of prisms and hexagonal plates, connected apparently
by filaments of some opaque matter.

I have, occasionally, met with another interesting variety of them, which
have no visible outline by common light, and which could never have been detected
but by the polarising microscope. In one of these cases, the crystalline mass,
which is nearly spherical, lies in a crowded group of small fluid cavities, none of
which enters its mass; a complete proof that the cavities were formed in the soft
mass of topaz, when‘it encircled the indurated crystal.

Along with these interesting phenomena, another occasionally occurs, which
may still require a farther examination. I have observed apparent doubly re-
fracting crystals, which differ in some essential points from those which have
been described. They depolarise a uniform, or nearly a uniform tint, notwith-
standing the different thicknesses through which the polarised light passes; and

VOL. XVI. PART I. F

Fe, ON CRYSTALS IN THE CAVITIES OF MINERALS.

that tint is less brilliant than in the real imbedded crystals. I conceive, there-
fore, that they are crystallized cavities, having their inner surfaces coated with a
doubly refracting crust. This is, in itself, a very natural supposition, seeing
that the fluid may have discharged its gaseous portion, and left behind it the
matters which it held in solution. The cavities, however, of this kind, which I
have described in a former paper, have no depolarising action; and I find that
those now under consideration have regular axes of double refraction. Hence,
the matter which covers them must be a regular crystalline shell, with optical
and crystallographic axes—a phenomenon which has no parallel in mineralogy.

St LEONARD’s COLLEGE, ST ANDREWS,
February 15. 1845.

( 23 )

IV.—Account of Experiments upon the Force of the Waves of the Atlantic and
German Oceans. By Tuomas Stevenson, Civil-Engineer, Edinburgh. Com-
municated by Davip STEVENSON, Esq.

In forming designs of marine works, the engineer has always a difficulty in
estimating the force of the waves with which he has tocontend. The information
on such a matter, which is derived from local informants, who, although intelli-
gent in the departments of trade which they follow, are, nevertheless, more or less
prejudiced from being constantly on the spot, is not satisfactory ; and it has, there-
fore, often occurred to me that it would be most desirable if the engineer could
be enabled, to some extent at least, to disregard the prejudiced statements of others,
and the vague impressions left by them on his own mind, and really to ascertain,
by direct experiment, what force, expressed in pounds per square foot, the sea
actually exerts upon the shores where his buildings are proposed to be erected.

Notwithstanding the want of all direct experiments* on this subject, and the
somewhat unpromising nature of such an enquiry, I was, nevertheless, induced to
attempt the construction of an instrument to effect the desired end; and after
several fruitless devices had been put to the test, I at length succeeded in forming
one whose indications I hope to be able to shew are trustworthy. Before con-
sidering the results obtained, however, I shall explain the construction of this
simple self-registering instrument.

The letters D EF D represent a cast-iron cylinder, which is firmly bolted at the
projecting flanges G to the rock
where the experiments are
wanted. This cylinder has a OQ
flange at DD. LL is a door, 5 peepee =
which is opened when the obser- =e
vation is to be read off. AA
is of iron, and forms a circular
plate or disc, on which the sea
impinges. Fastened to the disc
are four guide-rods BBBB. ee -
These rods pass through a circu- er or or on oe ee ee ee ae
lar plate C C (which is screwed
down to the flange D D), and also through holes in the bottom EF. Within the

‘ay

w
}
i
i

|

ILIA

re

www
}
MW

&

* Sir S. Brown has infleed stated, that at Brighton he found the impetus of the waves during
heavy gales was “ equal to 80 lb. to a foot upon a cylindrical column of 12 inches diameter.” The
hydrostatical pressure of a wave only 11 foot high is equal to 80 lb. upon a square foot.

24 MR THOMAS STEVENSON ON THE FORCE OF THE

cylinder there is attached to the plate CC a powerful steel spring, to the other
or free end of which is fastened the small circular plate KK, which again is
secured to the guide-rods BBBB. There are also rings of leather T T, that
slide on the guide-rods, and serve as indices for registering how far the rods
are pushed through the holes in the bottom ; or, in other words, how much the
spring has been drawn out or lengthened by the force of the sea acting upon the
plate or disc AA. The object of having four leathern rings, where one might
have answered the purpose, was merely that they might serve as a check upon
each other; and so perfectly did they answer the purpose intended, that in
every instance they were found equidistant from the bottom of the cylinder;
proving thereby, that, after the recoil of the spring, they had all kept their places.
The guide-rods are graduated, so as to enable the observer to note exactly the
quantity that the spring has yielded.*

This instrument, which may, perhaps, be not improperly termed a Marine
Dynamometer, is, therefore, a self-registering apparatus which indicates the maxi-
mum force of the waves. In the graduation of the instrument, the power of the
spring is ascertained by carefully loading the disc with weights, so that when the
quantity that the spring has yielded by the action of the sea is known, the pres-
sure due to the area of the disc exposed is known also. The discs employed were
from 3 to 9 inches diameter, but generally 6 inches, and the powers of the springs
varied from about 10 Ib. to about 50 lb. for every } inch of elongation. Their
respective effects were afterwards reduced to a value per square foot. The instru-
ment was generally placed so as to be immersed at about three-fourths tide, and
in such situations as would afford a considerable depth of water. It is not desirable
to have the instrument placed at a much lower level, as it has not unfrequently
happened during a gale, that for days together no one could approach it to read
off the result and readjust the indices to zero. It must, however, at the same
time be remarked, that it is in most situations almost impossible to receive the
force unimpaired, as the waves are more or less broken by hidden rocks or shoal
ground before they reach the instrument.

In connection with the apparatus above described, a graduated pole was
erected on an outlying sunken rock, for the purpose of ascertaining the height of
the waves; but the observations were not of so satisfactory a nature as could
have been desired, and the poles soon worked loose from their attachments, and
disappeared.

With the instrument which has been explained, I entered upon the following
train of observations :—

* It has been suggested to me, that the indications of the instrument might be made through
the medium of a flexible wire or chain at a considerable distance from the instrument, and thus the
impulse of every wave might be observed.

WAVES OF THE ATLANTIC AND GERMAN OCEANS. 25

In 1842 several observations were made on the waves of the Irish Sea at
the island of Little Ross, lying off the Bay of Kirkcudbright. Since April 1848 till
now, continued observations have been made on the Atlantic at the Skerryvore
and neighbouring rocks, lying off the island of Tyree, Argyllshire. And in 1844 a
series of similar observations was begun on the German Ocean at the Bell itock.
It will be seen, that in selecting these localities a varied exposure has been em-
braced, comprising the comparatively sheltered Irish Sea, the more exposed eastern
shore of Scotland, and the wild rocks of Skerryvore, which are open to the
full fury of the Atlantic, the far distant shores of North America being the nearest
land on the west.

Referring for more full information to the tables of experiments which are given
at the end of this paper, it will be sufficient in this place to state generally the
following, as the results obtained.

In the Atlantic Ocean, according to the observations made at the Skerryvore
rocks, the average of results for five of the swmmer months during the years 1843
and 1844, is 611 Ib. per square foot. The average results for six of the winter
months (1843 and 1844), is 2086 lb. per square foot, or thrice as great as in the
summer months.

The Greatest result yet obtained at Skerryvore was during the heavy westerly
gale of 29th March 1845, when a pressure of 6083 lb. per square foot was regis-
tered. The next highest is 5323 Ib.

In the German Ocean, according to the observations made at the Bell Rock,
the greatest result yet obtained is 3013 lb. per square foot.

It thus appears, that the greatest effect of the sea, which has been observed,
is that of the Atlantic at Skerryvore, which is nearly equal to three tons per
square foot.

These experiments, amounting to 267 in number,* and on the Atlantic alone
extending over 23 months continuously, are not intended to prove any thing far-
ther than the simple fact, that the sea has been known to exert a force equivalent
to a pressure of three tons per square foot, however much more. Now, when we
consider that the hydrostatic pressure due to a wave of 20 feet high, is no more
than about half a ton on a square foot, we see how much of their force the
waves owe to their velocity. There can be no doubt, however, that results
higher than this will be obtained. Were a train of observations made at various
points of the coast, the result would not only be highly useful in practice, as
they would by reference to existing marine works shew what sizes of stones and
proportions of piers were able to resist seas of a given force; but they would
form an interesting collection of information with regard to the relative forces
of the waves in our contracted bays and estuaries, as compared with those ob-

* It was not thought necessary to give all the observations in the table appended to this paper.
VOL. XVI. PART I, G

26 MR THOMAS STEVENSON ON THE FORCE OF THE

served in the ocean; and would thus supply the want which, as already stated,
all engineers labour under, to a greater or less degree, in designing marine works.

It is proper, however, to observe, that there may be some objection to refer-
ring the action of the sea to a statical value. Although the instrument might
perhaps be made capable of giving a dynamical result, it was considered unneces-
sary, in these preliminary experiments, to do any thing more than represent
the maximum pressure registered by the spring, because the effects of the waves
may, from supposing them to have continuity of action, be perhaps regarded as
similar to a statical pressure, rather than to the impact of a hard body.* The near
coincidence, or indeed almest perfect agreement of the results of the experiments
made with different instruments, goes far to shew that the waves act in very much
the same manner as a pressure, although both pressure and impact.must obviously
enter into their effect. In the experiments, begun February 1844, and given at
the end of the paper, the three instruments had not only different areas of discs,
but very different powers of springs, and yet the results were almost identical.
Now, the same force, supposing the waves to act like the impact of a hard body,
would, in the Marine Dynamometer, assume very different statical values, accord-
ing to the spaces in which that force was expended or developed; so that with
the same force of impact, the indication of a weak spring would be less than that
of a stronger.

In future experiments it may be interesting, however, to test the springs
dynamically, by means of the impact of a heavy body dropped from a given
height upon the plate or disc of the instrument. In some experiments lately made
in this way, by dropping a cannon-ball upon the disc, it appeared, that, within
the limits of the experiments, there was for each individual spring a ratio be-
tween the value registered by the leathern index and the calculated momentum
of the impinging body. These ratios were, of course, found to vary in springs of
different power, and to be constant only for springs of the same power. Did the
waves, therefore, act by a sudden finite impact, like the cannon-ball employed in
this instance, we could scarcely have found such harmony between the results of
instruments with different springs, as the experiments alluded to afford. At the
same time, the result cannot, perhaps, be in strictness considered correct ; but,
from the elongation of the spring being very small, the results may be regarded
as practically correct,—the more so when we find so remarkable a coincidence
of results as that alluded to.

* With reference to the continuous action of water, I may notice the effects produced by the failure of
Beith’s Dam, a reservoir situated upon the high grounds near Cartsdyke, immediately east of Greenock.
This dam had a head of 20 feet of water, and gave way on the night of the 21st November 1835,
when the water, after breaking down another reservoir below it, rushed through the streets of Carts-
dyke, causing the melancholy loss of no fewer than 41 lives. This continuous flow of water carried
away many houses ; and, among other instances of its power, it is recorded that a “ mass of rock about

16 tons weight was borne along by the torrent toa distance of 30 or40 yards.” This case, then, which
almost equals the records of the fury of the sea, shews the effects which continuous action may produce.

WAVES OF THE ATLANTIC AND GERMAN OCEANS. 27

I shall now contrast the indications of the Marine Dynamometer by stating a
few facts regarding the ascertained effect of the waves in the elevation of spray, and
in the transportation of heavy masses of rock. This is more especially important,
as to some, the results indicated by the instrument have appeared greater than
they could have expected; and it has even been supposed that, were they correct,
the stones which constitute our marine works would be scattered. Before passing,
from this point, it may be well to observe that the stones composing sea-works,
are not only wedged and compacted together, but they derive from the superin-
cumbent courses, (independently of the support afforded by the backing), a pressure
so great as to cause an amount of friction which is in most cases greatly more
than sufficient to preserve them in their places.

But to return to the facts of the ascertained effects of the waves, it may be
interesting, in the first instance, to give some idea of what may be looked for in
comparatively small expanses of water, such, for instance, as the lakes of North
America, which, however, exhibit during gales of wind, all the characteristics of
an open sea. Inthe north-eastern corner of Lake Erie, the harbour of Buffalo was
constructed at a cost of about L.40,000. It is mentioned in the “ Civil-Engineering
of North America,” that the author “ measured (at this harbour) several stones
which had been moved ; and one of the largest of them, weighing upwards of half-
a-ton, had been completely turned over, and lay with its bed or lower side upper-
most.”

In the Firth of Forth, at the Granton Pier works, on 19th December 1836,
after a gale from the north-east, one stone was moved measuring fifteen cubic
feet, or about one ton in weight, and thrown on the beach, after having been built
into the wall; and a stone containing 18 cubic feet was moved 30 feet from
its place; while the prerres perdues or mound-stones were washed down toa slope
of about 4 to 1.

The following instance, which occurred at the landing slip of the Calf Point,
Isle of Man, affords a proof of the great force of the waves even in the Irish Sea.
During a gale from the north-west, a block was lifted from its place in the wall
and thrown landwards, which measured 1234 cubic feet, equal to about 10 tons
weight.

In the German Ocean, we can refer to the Bell Rock Lighthouse,* which,
though 112 feet in height, is literally buried in foam and spray to the very top.
during ground swells, when there is no wind. It is, therefore, a very important
station for making such experiments, because the rise of the spray may be
regarded as a scale by which the results of the Marine Dynamometer can be
checked or compared.

* At such a situation as the Bell Rock, a column of water or of air could be conducted into the
interior of the house, and might, in the one case, shew the force of each wave as it struck the building

by the rise of the water column ; or, in the other, by a pressure-gauge, shew the same result in atmo-
spheres by compression.

28 MR THOMAS STEVENSON ON THE FORCE OF THE

In the published account of this work there occurs the following statement :—
On the 24th October 1819, the spray rose to the height of 105 feet above the rock.
“It may, perhaps, therefore,” says the author, “be concluded, that the maximum
force of the sea at the Bell Rock is to raise the sprays to the height of about 105
feet above the surface of the rock ;” and deducting 16 feet, which is the height that
the tide rises upon the tower, there is left 89 feet, as the height to which the water
is raised. This is equivalent to a hydrostatic pressure of about 24} tons on the
square foot. Since that time, however, there have been still greater proofs of the
force of elevation. On the 20th November 1827, the spray rose 117 feet above
the foundations or low water mark; and the tide on that day rose 11 feet upon the
tower, leaving 106 feet as the height of elevation (exclusive of the trough of the sea),
being equivalent to a pressure of very nearly 3 tons per square foot.

At the island called Barrahead, one of the Hebrides, a remarkable example
occurred during a storm in January 1836, in the movement of a block of stone,
which, from measurements taken on the spot, is 9 feet x 8 feet x 7 feet = 504
cubic feet, which, allowing 12 feet of this gneiss rock to the ton, will be about 42
tons weight. This great mass was gradually moved 5 feet from the place where
it lay, having been rocked to and fro by the waves till a piece broke off, which
rolling down, and jamming itself between the moving mass and the shelving rock
on which it rested, immediately stopped the oscillatory motion, and thus prevented
the farther advance of the stone.

Mr Retp, the principal keeper of Barrahead Lighthouse, the assistant keeper,
and all the inhabitants of the little island, were eye-witnesses of this curious exhi-
bition of the force of the waves ; and Mr Rerp also gives the following description
of the manner in which they acted upon the stone.

“‘ The sea,” he says, “ when I saw it striking the stone, would wholly im-
merse or bury it out of sight, and the run extended up to the grass line above
it, making a perpendicular rise of from 39 to 40 feet above the high water level.
On the incoming waves striking the stone, we could see this monstrous mass
of upwards of forty tons weight lean landwards, and the back run would uplift it
again with a jerk, leaving it with very little water about it, when the next incom-
ing wave made it recline again. We did not credit the former inhabitants of the
island, who remarked that the sea would reach the storehouse which we were
building; and when these stones were said to have been moved it was treated
with no credit, and was declared by all the workmen at the lighthouse works
to be impossible ; yet the natives affirmed it to be so, and said if we were long
here we might yet see it. They seemed to feel a kind of triumph when they called
me to see it on the day of this great storm.”

Having now detailed the various observations and facts of which I was pos-
sessed in relation to this subject, it may be necessary, in conclusion, to consider
the general bearing of such an inquiry.

WAVES OF THE ATLANTIC AND GERMAN OCEANS. 29

The advantages which may ultimately arise from a knowledge of the energies
of the ocean, can only be guessed at in the present state of our information. It
is not to be expected that, in the present train of experiments, much will be found
that is directly valuable in practice, as time is required before a true maximum re-
sult can be discovered. Buta very close and promising connection may easily be
traced between the present inquiry and the principles of Hydraulic Architecture, as
illustrated in the construction of breakwaters, sea-walls, lighthouses, and piers of
timber or of stone, and in the calculations for the strength of the booms which are
employed for excluding waves from the interior of harbours; also, in trying the
power of waterfalls, and in contrasting the action of waves at the surface with
that at the bottom, or at various depths along the sea slopes of breakwaters.

Theoretically, there is much also to invite to a prosecution of such observa-
tions. In connection with researches so successfully prosecuted by Mr Scorr
RUssELL in the Mechanism of Oceanic Waves, their height, their velocity, and their
distance apart, surely observations on the development of the gradually acquired
force of such undulations, when they become waves of translation, will form a
very important feature in Marine Mechanics. In the science of geology, the most
direct bearing of the results of the Marine Dynamometer is on the subject of
erratic boulders. It is no easy problem to account for the presence of enormous
boulders which are foreigners to the formation where they lie, and often, also, far
distant from the formation to which they belong. Accordingly we find that glacial
action has been suggested as the cause of transportation. Mr Mitnz has, in the
Transactions of this Society, suggested that a continuous rush of waters, due to
volcanic emersion, might, at any rate, account for the distribution of the largest
erratic boulders which are to be found in Roxburghshire. The results of the
Marine Dynamometer, and the facts above recorded of the action of different bodies
of water, will certainly be admitted to go far in proof of the competency of aqueous
action, to effect the distribution of the erratic blocks referred to by Mr Mine.

EXPERIMENTS.—With reference to the following experiments I have only
to observe, that those which were made at Little Ross, upon the Irish Sea, can-
not, from the unusual fineness of the weather at the time, be regarded as afford-
ing a true value of the effects of a hard gale in these seas. Of the others it is to
be noticed, that where two or three instruments were for some time employed
as a check upon each other, and only one or two readings are given, the want
has occurred either from the instruments being under repair, or being difficult
of access in stormy weather, or during neap tides. It often happened also, in
consequence of the springs proving too weak, when new ones had to be made,
or the area of the disc reduced. Registers of the state of the weather, apparent

VOL. XVI. PART I. H

30 MR THOMAS STEVENSON ON THE FORCE OF THE

height of spray, &c. were generally kept; but it was not considered necessary to
complicate the Tables by inserting these, excepting in one or two instances.

lbs. to a Ibs. to a lbs. to a Ibs. to a
Pees: Square Foot aie Square Foot. Mia Square Foot. et Square Foot.
Observations at Little Ross. 1844. 1844,
1842, 1842. Feb. 3 April 19
April 25 15 June 25 458.0 ES ore Sees
Sl lee 51 July 25 | 380.0 we 18 vee ee
June 1 36 Aug. 2 | 570.0 GD Oe ve 22
4 81.5 eh |, OBRM ay le sea lald
20 86.5 wee 6 380.0 BS" macs 296. gales
24 | 840.0 a) 79) S80 are ones
The Observations at the Skerryvore Rock, and oh es
the neighbouring Island of Tyree, distant 13 miles Sine
from the Skerryvore, are as follows :— er
1843. 1843.
April 24 455 Aug. 9 346 ae oS.
con | 707 See ee) 723 ve 026
May 7 243 Eee me Om 389 oY ae
Sco wei! 182 Sept. 5 866
12 243, nae wy ae 952
16 364 Octwao 1535
20 { 495 Bok: 6 1606
476 Nov. 18 1711
June 3 182 boule gfe) 1497
4 519 soe P06 1497
7 428 oan 4s) 2353
8 855 Dec. 5 2674
Sec 9 173 8 (Ath
July 2 476 ib At least
3 ie sa AE 2460
866 ear 26 1947
soa ele 433
In January, two instruments were placed beside

each other, but not set parallel. These instruments
had springs of different power, the one being about
double that of the other, and one had a dise of 3
inches diameter, the other 6 inches.

1844. 1844.
Jan. 6 962 Jan. 9 1925
Ste aoe 928 soc aoe 1000
ui 2353 5 fly 826
857 isis ok 1000

Both instruments set parallel.

1844. 1844.

Jan. 16 428 Jan. 16 427

Another instrument was placed beside them, but
the two marked thus * were found to be too weak, as
the leathers were found flattened, and one of the
instruments was broken, and was not repaired till
the 15th February.

1844. 1844,
Jan. 28 3422* Feb. 2 429
é aa 2285* Bee! Vice 457
aoe 3313

1 On this occasion, 14 stones were slightly moved, and 14 scattered, all of which had been built into the
round-head or end of Hynish Pier, which was still in an unfinished state, and a Dynamometer which was
attacked to the Pier, registered on this occasion 2557 lb. These stones weighed from 1 to 1} tons, and ex-
posed, when built into the wall, about 2 square feet of surface. The stone to which the instrument was fixed
was turned upside down, although it weighed about 13 ton = 2800 lb.

WAVES OF THE ATLANTIC AND GERMAN OCEANS. 31

lbs. to a 5 , Ibs. to a
Square Foot. : Square Foot.

Dates.

Nov. 8427
eee eee We 3199
ar 4112
ate H 1369

AS oes 9 2738

A more exposed point of the Skerryvore Rock was at this time chosen for
experiment; and with the view of ascertaining the effect of the waves at different
heights upon the rock, two instruments were fixed, the one (No I.) several feet
lewer, and about 40 feet seaward of the other (No. II.) It was observed, that
about half-flood the force of the waves was a good deal expended before they
reached the place where No. I. was placed, from there being so little water on
the rocks outside. Whereas when the tide was higher the waves were, from the
greater depth of water, not so much broken when they reached No. II. The re-
sults of the Marine Dynamometer shew generally about twice the force at No, II.
as at No. I.; a result which shews how important it would be to ascertain the
relative forces of the waves at different levels upon our breakwaters and other
seaworks.

Pressure in Ib.
Date. Remarks. No. of per
Instrument. | Square Foot.

—————————

1845.
Jan. 7 Heavy sea. : 1714
bane, «poe Bie ee : 4182
12 Very heavy swell. - 2856
se ee ace : 5032
16 Heavy ground swell. : 2856
oar aoe me c 4752
22 A good deal of sea. . 2856
tee ves 000 : 5323
28 Heavy ground swell. : 2627
Aone got Mie ae : 4562
Feb. 5 Fresh gales. , 856
21 sae ue : 1827
one eas Se . 3422
24 Fresh breezes. : 1256
“oc 008 a se : 3802
March 9 | Ground swell. . 1256
Waves supposed about
‘- 10 feet high, Sis
tf Short sea. : 1028
24 Heavy sea. . 2281
Waves supposed about
-_ { 20 feet high. ee
26 Swell. 6 1256
rib Waves about 6 feet high. : 3041
Strong gale, with heavy
sea, the highest waves : 2856
29 supposed 20 feet high,

and the spray rose c 6083.
about 70 feet.

32 MR THOMAS STEVENSON ON THE FORCE OF THE WAVES, &c.

Register of Observations on the force of the Sea, made at the Bell Rock, German Ocean.

lbs. to a Ibs. to a
Dates. Square Foot. Dates Square Foot.
1844, | _ 1845.
Sept. 15 853 Jan. 27
Some 2260 -- 30
Oct. 9 3013 BL
ee ae 2562 Feb. 6
aT) 1142 3. ot
ae OT 958 | Raecae TED
Nov. 12 1680 - = 27
mantis 1920 ae (28
Dec. 13 1560 March 4
cot oe 1459 OF FB. Ly
Jan. Fe 1559 nels 21
eS eekly 1439 we A:
reer 1439 Me OSB
nt tbe (= 1559 a. 38
LOM 959 . 30
“er 719

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SOYIMG JO SUOLPIM Wy fe 8207 INSET JO SHUNT

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dW Watters

( 33)

V.—On the Geology of Cockburnlaw, and the adjoining District, in Berwickshire ;
with a Map and Sections. By Witu1am Stevenson, Dunse.

The portion of Berwickshire, of which the object of this paper is to describe
the more remarkable geological features, comprises, within a very limited space,
an assemblage of phenomena of the highest interest, in relation to the wonderful
changes which this part of our island has undergone in the earlier periods of the
earth’s history. Its situation is immediately to the north of Dunse, and its area
is about 16 square miles, within which are comprehended the junctions of the
greywacke rocks of the Lammermuirs, with the strata of the old red sandstone
formation, and of the latter with the lower members of the coal measures. The
chief eminences within the district are Cockburnlaw, which attains a height of
912 feet above the level of the sea; Dunselaw, 630 feet; the Knock, Borthwick,
and Castlemains Hills; and the Staneshiel, a hill of the same formation as Cock-
burnlaw, from which it is separated by a ravine of 300 or 400 feet deep, in which
the Whiteadder flows. The general topographical features of the district will be
best understood by reference to the accompanying map.

In treating of our subject, we propose to describe, 1st, The stratified rocks of the
district ; and, 2d/y, The igneous rocks, and the changes of structure and position
which have been effected by their agency upon those of aqueous origin.

I. STRATIFIED Rocks.

1. The Greywacke of the Lammermuirs.

The strata of this important series of deposits (the most ancient of the district
under consideration) are finely exposed in many localities, consisting of arena-
ceous and argillaceous beds, of great, but as yet, unascertained thickness, the for-
mer constituting the greywacke proper, and the latter the greywacke slate. The
oxides of iron and manganese are widely diffused among these strata. Mag-
nesia enters pretty largely into their composition; but there seems to be an al-
most entire absence of calcareous matter, there being no beds of even impure
limestone interstratified with the greywacke, and but a small quantity diffused
through its masses. Sulphate of baryta is also very generally met with, in the
form of veins of various sizes up to a foot or more in width, and occupying fissures
in the greywacke. Near Elmford, the cleavage fissures of the greywacke strata
are filled with this mineral.

No decided traces of organic remains have hitherto been discovered in the grey-
wacke of this part of the Lammermuirs. On some slabs from a quarry near
Hoardweel, some curious relieved markings appear, which may prove to be of or-

VOL. XVI. PART I. I

34 MR STEVENSON ON THE GEOLOGY OF COCKBURNLAW,

ganic origin; but as no trace of organic matter is observable in these specimens,
it is uncertain whether they are not merely the effects of a chemical aggregation.

2. The Old Red Sandstone.

The formation which in this district immediately succeeds the greywacke, is
the wpper division of the old red sandstone, there being no strata on the flanks of
the Lammermuirs, referable to any of the intermediate formations, comprisingthe
Silurian system, and the lower and middle divisions of the old red sandstone. The
position of the red sandstones and conglomerates, with reference to the grey-
wacke, is unconformable. This is very distinctly seen at Cockburn Mill, where
the conglomerate, which constitutes the lowest member of the formation, is well
exposed, overlying the fractured ends of the greywacke strata in such a manner
that the planes of stratification of the two sets of rocks are nearly at right angles to
each other. The greywacke strata here are of the red variety, and dip at high
angles to NW., the vacancies between their uneven and broken ends being filled
up by the conglomerate. The latter is chiefly composed of fragments of the sub-
jacent red greywacke, together with pieces of the felspathic rocks of the Stane-
shiel ; the whole being firmly cemented by the finer arenaceous particles derived
from the adjoining rocks.

The variations in the thickness of the conglomerate at different localities of
this limited district are very great, and would appear to indicate the proximity
of the shore, at the period of its deposition ; a view which other circumstances, to
be hereafter detailed, tend strongly to corroborate. At Cockburn Mill, its thickness
may average about 20 feet ; whereas to westward of the Knock hill, it is at least
300 or 400 feet. At the latter place, it contains (besides fragments of greywacke,
which are its chief ingredients) several varieties of felspar porphyry, together
with rolled masses of quartz, hematite, and other minerals. In Kidshielhaugh,
and near the Knock hill, it consists almost entirely of fragments of the felspathic
rock, which occurs 77 situ at these places. These are cemented by calcareous spar,
which has probably been derived from the igneous rock, as the latter contains a
considerable quantity of carbonate of lime in its composition. Similar instances
of calcareous matter acting as a cement to the conglomerate, are not unfrequent
on the borders of the Lammermuirs.

At Cockburn Mill, the conglomerate passes, by a series of alternating conglome-
rates and sandstones, into the characteristic strata of the formation. These con-
sist of red and greenish-white sandstones, which alternate with red clays, the
thickness of the whole of which, as exposed in Prestonhaugh, is probably at least
300 feet; but, on account of the shattered nature of the strata, this cannot be ex-
actly ascertained. Much interest attaches to these strata on account of the orga-
nic remains, and the curious markings which appear to be of organic origin, m
which they abound. These we shall attempt to describe as concisely as possible.

AND THE ADJOINING DISTRICT, BERWICKSHIRE. 35

Organic remains were first discovered among these sandstones, in the summer
of 1840, in a fine section exposed by the Whiteadder about half a mile below Cock-
burn Mill. These chiefly consist of scales, occipital plates, ichthyodorulites, and
other bony parts of the Holoptychius Nobilissimus. Similar remains also occur in
the sandstones directly opposite to Cockburn Mill, and in those to the east of the
Knock hill. They are not distributed uniformly through the strata in which they
occur, but are found only in particular beds, in which they abound; while very
few or none are to be seen in the adjoining strata. At Cockburn Mill, the ichthy-
olitic beds are situated within a hundred feet of the conglomerate, from which
they are separated by a series of intervening beds of unfossiliferous red sand-
stones, and thin strata of conglomerate. One bed which is exposed here contains
the remains of the Holoptychius in such abundance, that a chip cannot be struck
off without disclosing a portion of a scale or plate. «It is of a coarse, sandy, gritty
texture, and is generally so brittle from being highly impregnated with animal
matter, as to be easily broken between the fingers. It is only a few inches thick.
Some of the thicker beds with which it is associated also contain these fossils in
considerable abundance, but they appear to be in greater quantity near the surfaces
of each stratum, few being found in the interior of a thick bed. These strata pre-
sent beautifully rippled surfaces, and (especially the gritty bed above mentioned)
shew other unequivocal marks of littoral deposition. A circumstance which tends
strongly to favour the view of their having been formed near the shore, is the fact
of their included remains being of such a fragmentary character, that although
pieces of scales and plates may be picked up in hundreds, it is very rare to find
one of either that is not more or less mutilated. Indeed, it would appear that after
those large fishes died, their osseous parts, being separated by decomposition and
the action of the waves, were tossed about on the sandy beach, and exposed to at-
trition among the coarse sand and pebbles, until they were reduced to the frag-
mentary state in which we now find them. The fact of the remains of the Holop-
tychius being chiefly found associated with appearances indicative of the proximity
of the shore, would almost lead one to suppose that these fishes were in the habit
of frequenting shallow water, perhaps because of their food being there more abun-
dant. At all events, their remains appear to be confined to these rippled strata; for
in the corresponding beds of the old red sandstone above Greenlaw, which are des-
titute of ripple marks, and bear evidence of having been deposited in deep water,
there are no traces of them to be found.

On the east side of the Knock hill, the ichthyolitic beds of this formation are
tilted up at high angles by the mass of grey porphyry of which that hill consists.
The remains found here are of the same fragmentary character as those of Preston-
haugh, and abound most in a few thin sandy beds within a few feet of the por-
phyry. They consist chiefly of the scales, plates, spines, and teeth of a fish allied to
the Holoptychius, but differing from it in several particulars, the scales being more

36 MR STEVENSON ON THE GEOLOGY OF COCKBURNLAW,

plainly marked, and the plates of a different shape and style of sculpture, being 7e-
ticulated instead of tuberculated. The teeth are beautifully fluted, and appear
to belong to the Dendrodus striatus of Professor OweEn, to which fish the asso-
ciated scales, plates, and spines probably also pertained.

In Prestonhaugh there are found, besides the remains of the Holoptychius,
other relics of a more obscure and puzzling, but highly interesting character, and
seem to be of organic origin, though all trace of their original organic matter has
which disappeared. These present many varieties of size and form, the most com-
mon being spindle-shaped bodies, which project in relief from the surfaces of the
strata in which they occur. These are generally about halfan inch long, detached, or
connected by threadlike ridges. Another sort resembles in form and size the cry-
salis of a butterfly, while others present a vermiform appearance. It seems pro-
bable that the majority of these curious markings are nothing else than the petri-
fied forms of soft-bodied animals that crawled in the mud of those ancient shores,
and which, being covered by a deposit of sand, left the outline of their forms im-
pressed thereon, the gases evolved in the process of decomposition escaping through
the sand, and being replaced by the infiltration of the finer particles of mud.
Others are perhaps coprolitic, and some, probably, mere concretions. ‘The appear-
ances presented by the bottom of a shallow pool which has been recently dried
up, afford an apt illustration of some of these markings, the smooth glazed surface
of the mud being marked here and there with worm-pits and castings, and furrowed
by the traces of worms and insects, while it is divided into irregular portions by
fissures of desiccation. In fact, some of these recent markings are almost perfect
fac-similes of those which occur among the rippled strata of Prestonhaugh. Nor
is evidence awanting among these strata of fissures having been produced by desic-
cation. ‘There is one bed, in particular, of whitish sandstone, overlying strata of a
softer and more clayey character, the under surface of which, wherever exposed,
is seen to be entirely covered with relieved mouldings, which ramify in all direc-
tions, forming a sort of irregular net-work, and in short, exactly resembling the
appearance which would be presented by the under surface of any plastic or mol-
ten substance poured into the cracks produced in mud by the heat of the sun.
The depressions between these reticulated mouldings are generally smooth and
shining, being coated with a fine red clay. Scales of the Holoptychius also occur
pretty frequently on the same surface.

These interesting strata are succeeded by others in which the clays rather
predominate, and which seem to be quite destitute of organic remains. They are,
however, profusely marked with greenish-white spherical spots, of various sizes,
from that of a pea, up to several inches in diameter. The colouring matter of the
sandstone (the peroxide of iron) appears to have been discharged by some power-
ful deoxidising process, probably the putrefaction of animal or vegetable matter.
Scales of the Holoptychius are sometimes met with, surrounded by a blanched

AND THE ADJOINING DISTRICT, BERWICKSHIRE. 37

space, the breadth of which seems to be /ess in proportion to the better preserva-
tion of the scale, and vice versa. Where organic remains are most abundant, the
strata are blanched in large irregular patches. In the centre of the spots a small
speck of protoxide of iron may be found, but this is generally so minute, as
not to be visible, unless the plane in which the spot is split passes through the
centre.

The only decided vegetable remains found in Prestonhaugh, occur in some
beds of soft red sandstone, overlying the spotted strata above described. The
matrix in which they are embedded has been unfavourable to their preservation,
so that they are obscurely marked, and when exposed to the weather for a short
time, become almost indistinguishable. They appear to bea sort of Algw. At
Cockburn mill, some slabs of rippled sandstone present markings in relief much
resembling fucoids, but shew no trace of carbonaceous matter, so that the vege-
table origin of these, though not unlikely, is at least doubtful. Great numbers of
the vermiform bodies before described are associated with these markings.

The strata in Prestonhaugh containing the vegetable remains, are succeeded
by other beds of red and variegated sandstones and clays, marked with blanched
spots and ripples, and containing, at least, one stratum in which the remains of
the holoptychius are very abundant. Among these also occur thin beds of coarse
sand, mixed with small rounded pebbles of white quartz, and presenting decided
indications of littoral deposition. A succession of red sandstones and clays,
which appear to have been deposited in deep water, follow, and may be traced
along the south bank of the Whiteadder to Preston bridge, where they are inter-
rupted by a large trap-dyke, accompanied by a very extensive fault or disloca-
tion. On the opposite side of this dyke the coal measures appear tilted up at
high angles, there being only the breadth of the dyke, which at this place does
not exceed 100 yards, between the two formations. In consequence of this dislo-
cation, and subsequent denudation, the upper beds of the old red sandstone, or
those which graduate into the coal measures, are awanting at this place, having
been entirely swept away on the west side of the dyke; while, on the east, they
are buried beneath a great thickness of the coal measures.

The transition rocks thus removed or thrown down at this place, are pretty
well developed in other parts of the county; as in the course of Langton burn,
about two miles SW. from Dunse, and in that of the Blackadder above Fogo.
They consist of thick beds, of a coarse, arenaceous, concretionary limestone, or
cornstone, with which are associated beds of shale and clay, also impregnated
with a considerable quantity of calcareous matter; and as regards colour and
general aspect, blending the characters of the argillaceous strata of the old red,
and the shales of the coal measures. They appear to be destitute of organic re-
mains, either animal or vegetable, and exhibit no appearances of ripple marks
or blanched spots.

VOL. XVI. PART I. K

38 MR STEVENSON ON THE GEOLOGY OF COCKBURNLAW,

3. The Coal Measures.

This important formation is represented in this district, by a small patch
east of the Cumledge trap-dyke. Its strata are well exposed in the bed of the
Whiteadder, near Preston bridge, about a quarter of a mile below which, are two
fine sections. There the sandstones, shales and clays, which characterize the for-
mation, are seen dipping away from the dyke at high angles, and presenting the
usual appearances by which this series of strata is elsewhere distinguished. The
shales and clays contain a large proportion of carbonate of lime in their composi-
tion; so much, indeed, that they might almost be termed limestones. The sand-
stones are of the usual white or yellowish colour, in many places highly micaceous.
and abounding in impressions of Stigmariz, Sigillarize, Lepidodendra, and other
plants of the carboniferous system. There is no appearance of animal remains.*
No coal seams appear, but there is a thin stratum of ironstone in nodules, which
abounds in remains of plants. The geological position of these strata, and the
other rocks of the same formation, which prevail in the Merse of Berwickshire is
considerably below the Encrinal limestone, which crops out near Berwick, and on
the sea-shore at Lamberton. Indeed, they properly belong to the mountain lime-
stone series, being situated far below the true coal measures. From their very
low position in the series, there is no reason to suspect the existence among the
Berwickshire strata of any coal-seams sufficiently thick to be worth working.

II. Igneous Rocks oF THE DISTRICT, AND THEIR EFFECTS UPON THE SEDIMENTARY
Rocks.

Throughout the district under consideration, trap-rocks are very abundantly
distributed, and present a field of speculation, no less attractive than those of
aqueous origin. The traps of the Lammermuirs and adjoining districts belong to
two great classes, differing from each other, as well in mineral character and
general aspect, as in regard to the epochs of their eruption. These are the Por-
phyries and Greenstones, or Felspathic and Augitic traps, both of which classes are
very abundant, but (with one or two exceptions, to which we shall afterwards
have occasion more particularly to refer) do not occur associated with each other;
for it is a remarkable fact, that while the traps which occur among the greywacke
of the hills are uniformly of the Felspathic class, those which appear in connection

* Within the last few weeks the remains of fossil fishes have been discovered in the course of
Langton Burn, about a mile SW. from Dunse, in strata belonging to the lower part of the coal mea-
sures. These remains consist of scales, spines, teeth, and other bones, similar to those found at Burdie-
house. They occur ina soft friable sandstone, which abounds also in Lepidodendra, and other plants
of the coal formation. Some remains of the Holoptychius have likewise been recently found in the old
red sandstone strata on the estate of Billie, about four miles NE. from Dunse.—21st April 1845.

AND THE ADJOINING DISTRICT, BERWICKSHIRE. 39

with the secondary strata along the flanks of the Lammermuirs, belong as exclu-
sively to the Augitic fumily. In considering these, we shall follow the natural
order, by describing, Ist, the Felspathic traps, and their effects upon the grey-
wacke strata; and, 2dly, the Augitic, or more modern traps, and the effects
which they have produced upon the more ancient rocks, both stratified and un-
stratified.

1. Felspathic Traps.

Rocks of this class are very abundant among the Lammermuirs, generally
occurring in the form of dykes or veins of various sizes, intersecting the grey-
wacke; or in large masses constituting entire hills. They consist of two or three
varieties of granite and syenite, with an almost endless variety of felspars, clay-
stones, and felspar porphyries. The following are some of the principal rocks of
this kind which occur in the district.

Granite of Cockburniaw and Staneshiel_—This rock shews a great variety of
aspects at different parts of these hills. Near the outskirts of the mass, where it is
in contact with the greywacke, its constituent crystals are very small, and its
cleavage structures rectangular, and according with the strikes and cleavages of
the adjoining strata. On proceeding into the interior of the mass, however, the
rectangular cleavages due to its refrigeration, in accordance with certain lines, are
superseded by the structures resulting from the crystalline tendencies of the
granite, which have of necessity had more time for their proper development, in
proportion as the distances from the cooling surfaces increased. The rock, in
consequence, becomes harder, and its crystals larger and better defined, while it
is divided by its structural planes into large, irregular, pyramidal blocks. Its
most common character is that of a regular granite, composed of distinct crystals
of white quartz, red felspar, and black mica; being identical, both in regard to
geological age and lithological aspect, with a granite which is associated with
greywacke near Fassney Bridge; and which, from being intruded among the
strata of the latter, in conformable beds, caused much discussion between the
Huttonians and Wernerians. In some places, as, for example, on the south side
of the Staneshiel, about half way up the hill, sulphate of baryta is added to the
usual ingredients of the granite; and near the top of that hill small quartz veins
- occur, containing galena and copper pyrites, though in very minute quantity On
the left bank of the Whiteadder, about 60 yards below Cockburn mill-dam, a
mass of syenitic rocks of extreme hardness appears in contact with the grey-
wacke, and projecting into the bed of the river. ‘This is evidently a process from
the Staneshiel hill, the granite of which, as well as that of Cockburnlaw (which
is indeed a part of the same mass), in many places passes into syenite. In fact.
after an attentive consideration of the phenomena presented by the transition of
one rock into another, and especially the changes effected upon both aqueous and
igneous rocks, at and near their junctions, of which many highly instructive

40 MR STEVENSON ON THE GEOLOGY OF COCKBURNLAW,

examples are seen in this district, it seems not improbable that the syenite of
Cockburnlaw and the Staneshiel is nothing more than greywacke, fused by the
agency of the molten granite, and the mineral characters of the two rocks thereby
blended together. The granite invariably assumes the aspect of syenite, as it ap-
proaches the greywacke. At Cockburn Mill dam, the greywacke is considerably
hardened, and dips to NNW. at high, but varying angles. Below the dam the
hardness increases, the planes of stratification become less distinct, while those
of cleavage grow more decided at every step. All these symptoms of meta-
morphism increase as we approach the igneous rock, the texture of the greywacke
being changed to crystalline, and the size of the crystals increasing with the hard-
ness, until we arrive at a point, where it is impossible to decide from the appear-
ances presented, whether the rock should be considered greywacke or syenite. Be-
yond this, it graduates into true syenite, which is divided by cleavage planes into
large rectangular blocks, arranged in the form of thick beds, having he same dip
and strike as the adjoining greywacke. The cleavage planes which run parallel
to those of the stratification of the greywacke (if, indeed, these are not merely
the original planes of stratification of the rock before it was converted into syenite),
are distinguished from those running at right angles thereto, by being occupied by
veins of heavy-spar, associated with crystals of quartz. These veins run con-
tinuously in a WSW. to ENE. direction. As we proceed further into the mass,
the syenite becomes more crystalline, and passes by a regular and gradual transi-
tion, into the well characterized granite of the Staneshiel. Two varieties of gra-
nite are here seen intruding in the form of veins, which have evidently been
poured, in a molten state, into fissures opened in the syenite, during the process
of crystallization. One of these is a beautiful and regularly crystallized granite,
larger in the grain than is commonly met with in the adjoining hills. The other
is small grained, and rather soft, and seems to be connected with a dyke which
occurs in the bed of the river a little above the dam, being identical in mineral
character. This dyke can be traced, when the water is low, for about 200 yards.
It is about five feet thick, and runs nearly NNW., but is frequently interrupted
in its course by the greywacke which it crosses. It contains, in some places,
fragments of the latter rock, which it has detached and brought up with it, in its
passage through the strata. The adjoining strata have been partially fused, and
present in some places a syenitic appearance. The alteration extends to a con-
siderable distance from the dyke, the strata being extremely hard, and frequently
exhibiting contorted laminee. In the immediate vicinity of the dyke the planes of
stratification are very obscure, being, in many places, merely marked by veins of
spar. Both the dyke and the adjoining metamorphic rocks are traversed by
numerous veins of heavy-spar, together with a few of quartz.

The summit of Cockburnlaw consists of beds of metamorphic greywacke,
which dip to NW. at an angle of about 65°. The metamorphism of the strata
increases as we approach the great body of granite, which lies immediately below

AND THE ADJOINING DISTRICT, BERWICKSHIRE. 4]

the summit to SE. They here present a highly crystalline and syenitic appear-
ance; and, in hardness, exceed even the granite itself, on the shoulder of which
they have been elevated to their present position.

Associated with this granite are several varieties of porphyry, belonging to
the same geological epoch. These appear at short intervals in the bed of the
river, from the eastern boundary of the granite, as far as Abbey St Bathans, a
distance of about four miles. The granite of which the steep hill opposite Cock-
burn-eastfield consists, is seen at the brink of the river to pass into a kind of
porphyry, consisting chiefly of whitish felspar, with crystals of dark coloured
mica. Another variety of porphyry, which also occurs at a short distance from
the eastern margin of the granite, is of a deep red colour, derived probably from
the peroxide of iron. But the most common variety is a porphyry, having a basis
of cream-coloured felspar, with disseminated small crystals. Of this Blackerstone
hill is composed; and it may be seen at intervals between the east side of the
granite and Hoardweel, underlying the greywacke. At some places, where the
latter rests immediately upon the porphyry, it appears to have been actually
fused, having lost every semblance of its original stratified structure, and being
divided, like the subjacent porphyry, into extremely sharp pyramids and wedges.
In some places, especially where it comes in contact with the whitish porphyry
before mentioned, the greywacke has, in the process of fusion, become blended
with the igneous rock, forming a curious mongrel sort of compound.

At the bend of the river, below Hoardweel, the porphyry is seen penetrating
the greywacke in the form of conformable dykes. From this place to the copper
mines, the channel of the river is narrowed by vertical rocks of metamorphic
greywacke. At the “Strait Loup” it rushes through a gorge so narrow that it
may in general be easily stepped over. The geological phenomena displayed here
_are very interesting. Within a space of about fifty yards by thirty, the porphyry
has forced its way through the strata in eleven or twelve different places. The
greywacke is much hardened and contorted; and, near the contact with the
ioneous rock, becomes cupriferous, and abounds in quartz veins. The copper ore,
which is of the green and grey varieties, occurs in the schists which alternate
with the greywacke. The porphyry is generally of the same kind as that further
down the river ; but in some places passes into a greyish-white compact felspar ;
and, in others, becomes a kind of granite (the felspar, however, predominating),
which contains disseminated specks of iron pyrites. In some instances it forms
dykes, which are, to a certain extent, conformable with the greywacke ; but it
commonly occurs in irregular masses of small extent, lying among the disturbed
strata, and connected with each other by veins or dykes.

The metamorphism of the greywacke is observed invariably to take place in
the vicinity of the granite and associated porphyries; and the process can be
traced in a most satisfactory manner, through all its stages, in many places

VOL. XVI. PART I. is

42 MR STEVENSON ON THE GEOLOGY OF COCKBURNLAW,

among these hills. At several localities, series of specimens may be obtained,
shewing the gradual transition from the unaltered greywacke, to where it becomes
converted into syenite, which again passes into granite; and the latter, in its
turn, graduates into porphyry,—the progress of transformation being so gradual,
as to render it very difficult to decide where the characters of the aqueous rock
become merged in those of the zgncous. In many cases, the only way of distin-
guishing the original planes of stratification from those of cleavage, which have
been superadded in the metamorphic process (unless, indeed, we can trace the
strata uninterruptedly from where they are unaffected), is by the schists which
alternate with the greywacke. These are sometimes much contorted, and present
the appearance of hornblende slates.

While the greywacke is thus altered, wherever it approaches the granite or
porphyries, the old red sandstone strata, being of a date subsequent to that of the
eruption of these older traps, are unchanged even at the place of contact. This
is seen on the SW. side of the Staneshiel, where the red sandstones are tilted up
against the granite at high angles, without any appearance of alteration,—the
granite and overlying sandstones having, in this instance, been elevated (as we
shall hereafter shew) by the agency of the augitic traps.

Porphyry of the Knock Hill——tThis rock is of a grey colour, having a felspathic
basis, and containing a considerable quantity of carbonate of lime. The hill to
westward of Burnhouses consists of the same rock, and is connected with the
Knock hill by a ridge running in a SSE. direction. To westward of the felspathic
mass of the Knock hill, the greywacke appears in nearly vertical strata, with a
NNW. strike, and is considerably altered by the proximity of the igneous rock,
being hard and full of quartz veins. On the east side of the hill, and within a
few feet of the porphyry, the red sandstones are seen tilted up at high angles, and
even partially retroflexed ; but being of more modern date (as in the case of the
junction of the granite and sandstones on the west side of the Staneshiel), they
shew no traces of metamorphism, but remain quite fresh and soft; and the re-
mains of scales, &c., of the Dendrodus which they contain still preserve their
original colour. Similar appearances are also observed in the vicinity of the por-
phyry in Kidshielhaugh.

2. Augitic Traps.

Rocks of this class also abound in the form of dykes, beds, and irregular
masses, and consist of several varieties of greenstone, basalt, amygdaloid, and trap
tuff. These have all been erupted subsequent to the deposition of the old red
sandstone and lower coal measures, as is evident from the disturbance and meta-
morphism apparent in these strata, whenever they approach to traps of this class.
With one or two exceptions (to be hereafter noticed) they do not appear in con-
tact with the older rocks, being confined to the secondary strata, which are much

AND THE ADJOINING DISTRICT, BERWICKSHIRE. 43

disturbed by their agency. Besides the veins and masses which are exposed,
there are, undoubtedly, many veins and extravasated portions concealed among
the strata. The principal masses of these traps which occur in the district are
the following :—

The Cumledge trap-dyke is a large body of trap of irregular thickness, which
is seen in the bed of Oxendean Burn, near Cumledge House, and about 200 yards
from the Whiteadder. It is here a sort of amygdaloidal greenstone, abounding
in veins of zeolite, steatite, and other minerals, and is probably not more than ten
yards in thickness. On-the west side it appears in contact with beds of a sort of
cornstone, which are excessively hard and crystalline at the junction, while the
trap becomes soft and earthy. On the east side a similar description of rock
occurs. From this spot to the Whiteadder the strata are hid by debris, but ap-
pear to belong to the coal measures, of which a fine section is presented a short
way below the place where the burn joins the Whiteadder, in a cliff of more than
eighty feet high. The shales, sandstones, and clays, are here seen dipping away
from the dyke at angles, which increase in proportion to the proximity of the line
of disturbance, until they become vertical, and even partially reversed. From
this place to Preston Bridge, the strike of the strata is very regular, and parallel
to the course of the dyke, which runs in a SSE. direction. At Preston Bridge its
thickness is upwards of 100 yards. The strata of the coal-formation come close
up to it on the east side; while on the west it cuts off the old red standstone.
On the north bank of the river, about 300 yards above the bridge, it is seen in
contact with strata of whitish sandstone and grey calcareous shales, which seem
to be equivalents of those strata which elsewhere constitute the transition beds
between the old red sandstone and coal measures. From this place it may be
traced in the bed of the river, presenting, in general, the aspect of an amygdaloid,
until we reach a place called “ Anglemyheart,”’ where it passes into a beautiful
columnar basalt. The columns are irregular hexaedral prisms, not arranged ver-
tically, but dipping at high angles to west. The basalt is more crystalline, and
the columns more regular towards the interior of the mass. Towards the out-
skirts it passes into an olive-coloured greenstone; and the latter graduates into a
trap-tuff, composed of fragments of greenstone and metamorphic greywacke,
agglomerated into a mass.

This trap-dyke appears to run under the granite of the Staneshiel and Cock-
burnlaw,—not, however, directly under the centre of the granitic mass of these hills,
but more to the west side. In the glen or ravine between these two hills, and ex-
actly in the line of continuation of the Cumledge dyke, a mass of basalt occurs,
which has burst through the older rocks. There is every reason to believe that
an eruption has taken place from a crater at this locality, and that the basalt now
occupies what was formerly a volcanic vent. A considerable quantity of trap-
tuff is seen in the bed of the river, in the vicinity of the basalt, and at intervals

44 MR STEVENSON ON THE GEOLOGY OF COCKBURNLAW,

for about 300 yards farther down, wherever it has been protected from denuda-
tion. It consists of a coarse sand (apparently triturated granite), containing
rounded nodules of various sizes, from that of a pigeon’s egg upwards, formed of
concentric coatings of the granitic sand round a nucleus, which appears to con-
sist of an imperfect sort of basalt.

The basalt is of a dark colour, approaching to black, and is very hard. It is
occasionally amygdaloidal, and has a tendency to assume the form of concretionary
masses of a spheroidal figure, consisting of concentric coatings. The granite is
seen in contact with it on the north side,—the line of junction running in an
ENE. direction. On the south side the two rocks are separated by a deep pool
in the river, which has probably been formed by the washing out of the inco-
herent tuff which here enwraps the basalt. On the west side of the basalt is a
very hard rock resembling syenite, and which is probably greywacke, fused by
the igneous rock. Its cleavages, as well as those of the granite and basalt, are
ENE. by NNW.

In the interesting section exposed by the Whiteadder at Cockburn Mill, a bed
of trap about 4 feet thick is seen overlying the old red sandstone strata fora con-
siderable extent. It is of a brown colour, and abounds in vesicles generally about
the size of small peas, some of which are empty, but the majority are filled up with
various minerals. Its texture is earthy, and it is much debased by being mixed
with the debris of the adjacent sandstones and clays, portions of which it had taken
up in its course when in a molten state. The embedded fragments are hard,
crystalline, and cherty, and the adjoining strata are discoloured, and their laminze
contorted, shewing very clearly the effects of igneous action. As this bed of trap
appears to be destitute of augite, it should, mineralogically, be classed with the
porphyries and other felspathic traps of the Lammermuirs. It is, however, more
recent than these, having been erupted subsequent to the deposition of at least
the greater part of the old red sandstones. At the same time, it seems to be more
ancient than the augitic traps by which the second upheaval of the Lammermuirs
was effected, as it shews some appearances of having participated in that move-
ment along with the adjoining sandstones.

The trap of Castlemams hill is amass of greenstone, which has forced its way
through the old red sandstone strata. The sandstones are much hardened at and
near their junction with the trap, while the same beds are seen within 300 yards
to NW., in contact with, and tilted up by, the grey felspathic rock of the Knock hill,
without the least appearance of alteration. The latter circumstance which seems
rather anomalous, is accounted for by a dyke of augitic trap, which runs from
under the Knock hill in a SSE. direction to Borthwick, and has upheaved at the
same time, both the felspathic rock and the more ancient sandstones.

Borthwick hill is a vast mass of basaltic greenstone, which has been erupted
through the old red sandstone strata at the place of intersection of several fissures

AND THE ADJOINING DISTRICT, BERWICKSHIRE. 45

which are likewise filled with trap. One of these already referred to, runs in a
NNW. direction under the Knock hill, not however directly under tts centre, but to-
wards the west side, and has thereby thrown the mass of felspathic rock, of which
that hill consists, over to east, producing a partial retroflexion of the sandstone
strata on that side. In this respect, it exactly resembles the Cumledge trap-dyke,
which, as formerly mentioned, has thrown the granitic mass of the Staneshiel hill
also over to eastward. Another striking point of resemblance between these two
dykes, is the occurrence of an insulated mass of onion basalt, exactly in the line
of continuation of each. The basalt in the line of the Borthwick trap-dyke oc-
curs (in the channel of the burn which falls into the Whiteadder at Elm Cottage)
about 3 miles NNW. from the Knock hill. It consists of concretionary masses of
various sizes, up to a foot or more in diameter, composed of nuclei of bluish grey
basalt, coarse in the grain, and very hard and heavy, surrounded by concentric
coats of a tufaceous substance. There is a slip in connection with the line of fis-
sure, from which the felspathic rocks of the Knock hill, and afterwards the augi-
tic traps now under consideration, were erupted. This has caused a downcast of
the old red sandstone strata on the west side to an extent of 300 or 400 feet.

At Oxendean Commonhaugh, a mass of basalt is wrought in three quarries. It
has been erupted through the old red sandstone, some of the strata of which are
seen resting on its surface, much broken and altered by the heat. The original
red of these beds has been changed to a dull purple, and the fragments into which
they have been shivered are much indurated. The trap immediately subjacent is
much debased by having absorbed, when in a molten state, a quantity of the de-
tritus of the sandstone. The result is a curious compound, which is neither trap
nor sandstone, but a mixture of both, and which graduates insensibly into the
aqueous rock on the one hand, and the igneous on the other. In some places,
also, the pulverized sandstone has got into fissures in the trap, where it has
afterwards consolidated, presenting the singular phenomenon of veims of sandstone
im basalt. The sandstone of these veins exhibits vertical lamination.

The Basalt of Dunselaw is similar to the above, with which it is connected. It
has also been erupted through the old red sandstones, which rise towards it
all along the south side, as shewn by excavations in the town of Dunse and neigh-
bourhood. A large block of metamorphic red sandstone, which is known by the
name of the ‘* Covenanters’ Stone,” may be seen near the top of the hill. It seems
to be a portion of a stratum which has been detached and borne up on the sur-
face of the trap. It is hard and granular, and dips to ENE. at a high angle.

The trap of the Castleknowes runs from Dunselaw in an ENE. direction, and
probably joins the Cumledge trap-dyke at right angles. At the New Tile Works,
about a mile east from Dunse, it is a beautiful amygdaloid, containing nodules
of various minerals, coated with green earth. On the face of the bank south of

VOL. XVI. PART I. M

46 MR STEVENSON ON THE GEOLOGY OF COCKBURNLAW.

the Castleknowes, the old red sandstone strata are seen dipping away from the
dyke, and divided by cleavages corresponding to those of the trap which are
NNW. by ENE. Nearer the dyke they are much shattered, and are very hard and
crystalline.

The trap of Grindean, is a basaltic ridge which runs in a SSE. direction, and
appears to be connected with a line of fault similar to that of the Cumledge dyke,
which runs parallel to it, the old red sandstone strata appearing on the east side,
and those of the coal measures on the west ; while the distance between the two
formations is much too small to admit of the strata, occupying an intermediate
space in the series, being brought on. The usual effects have been produced by
the trap upon the adjoining sandstones. In some specimens the transition from a
rubbly sandstone to a beautiful compact jasper is finely shewn.

A very interesting circumstance observable with regard to all the augitic
traps in this district, is, that their course is either in a NNW. direction, or in one
at right angles thereto, viz. from WSW. to ENE,—and these are invariably the
directions of their cleavages. They likewise appear to be all connected together,
forming one great system, indicative of one epoch of eruption. Thus the trap of
Borthwick hill is connected with that of Oxendean Commonhaugh, while the lat-
ter joins that of Dunselaw, by means of a ridge running by St Mary’s Cottage.
The Castleknowes trap, again, joins the Cumledge trap-dyke to Dunselaw. An-
other large trap-dyke (a small portion of the course of which is laid down on the
accompanying map), can be traced from Raecleughead hill by Langton, Gruel-
dykes, &c., for several miles in an ENE. direction, and seems to join the pro-
longation of the Cumledge dyke in the neighbourhood of Edrom, about four miles
from Dunse. <A line drawn from the Castlemains hill in an ENE. direction,
passes through the basaltic rocks of Anglemyheart, and meets the trap of Grin-
dean. This line appears to be that of an extensive fault, the effects of which are
manifest in the extraordinary disturbance of the old red sandstone strata, at the
end of the Prestonhaugh section, near Anglemyheart. Between the latter place
and Grindean, this dislccation (which is probably associated with a trap-dyke)
appears to separate the old red sandstone and coal measures, the latter being
thrown down on the south side ; but, unfortunately, no section is exposed in the
course of this line.

The consideration of the agencies which have influenced the directions of the
trap-dykes and lines of fault within the district, and changed the positions and
characters of the sedimentary rocks, is of great geological interest, but the princi-
ples involved are of too general a character to admit of being discussed in a me-
moir, descriptive merely of a small district. We therefore abstain from theorizing
upon the facts adduced, the more important inferences which these suggest being
for the most part sufficiently obvious. The views of the author on this branch of
the subject, are also in part indicated on the Map and Sections, lithographed on
Plate IT.

VI.—On the Extraction of pure Phosphoric Acid from Bones, and on a new and
anomalous Phosphate of Magnesia. By Witu1aM Grecory, Lsg., M.D.,
F.R.S.E., Professor of Chemistry in the University of Edinburgh.

[Read 3d March 1845. ]

I.—On the Preparation of Pure Phosphoric Acid.

Tue usual methods of obtaining pure phosphoric acid by the oxidation, with
nitric acid, or by combustion, of pure phosphorus, are well known ; but, although
they yield a pure product, yet, as the phosphorus must be prepared from phos-
phoric acid, it is obvious that we shall derive a great advantage from any method
of purifying easily and cheaply the phosphoric acid from bones, instead of first
reducing it to phosphorus, and then re-oxidizing it. In practice, phosphorus is
made from the superphosphate of lime, and it is from the same salt that phos-
phoric acid may be most economically prepared.

Two processes, already given for this purpose, are worthy of notice. It is to
be borne in mind, that the superphosphate of lime is the soluble compound ob-
tained by acting on burnt bones with sulphuric acid and water, and filtering to
separate the sulphate of lime.

In the first process, the solution of superphosphate is neutralized with am-
monia or carbonate of ammonia, which precipitates all the lime in the solution, with
about one-fourth of the phosphoric acid, as bone phosphate; while three-fourths of
the acid are converted into phosphate of ammonia. The filtered liquid being eva-
porated, deposits crystals of that salt, which, when purified, are decomposed by
heat in a platinum crucible; the ammonia and a great part of the water being
expelled, while the phosphoric acid, with one equivalent of water, or metaphospho-
ric acid, isleft. The objections to this process are the following :—The salt, when
heated, melts, spirts much in boiling, becomes viscid, and froths up to a most
inconvenient degree, requiring vessels of platinum of a large size for small quan-
tities of material. Secondly, a very high and long continued heat is required to
expel all the ammonia; and at that temperature, a portion of phosphorus is re-
duced by the hydrogen of the ammonia, and corrodes the platinum, leaving a
blue stain of phosphuret of platinum. Besides this, the purest phosphate of am-
monia often contains a trace of organic matter, which causes the glass of phos-
phoric acid, thus prepared, to be disfigured by carbonaceous particles. At least
I have always seen black particles in the phosphoric acid made by this process.
It is obvious, that if carbon be present, we have an additional source of reduced
phosphorus; and if the black particles are phosphuret of platinum, then they

48 PROFESSOR GREGORY ON THE EXTRACTION OF i

shew that the platinum has been strongly corroded. In short, this method, save
on a very small scale, is so objectionable, that it is seldom employed except for
illustration.

The second process is one recently proposed, I believe, by Lrepic, founded on
the fact, that the whole lime may be removed from the superphosphate of lime,
by the addition of sulphuric acid to the concentrated solution. This causes it to
become quite thick from the large quantity of sulphate of lime produced. Cold
water being added, the whole is filtered, and the filtered liquid and washings
again concentrated and filtered from any sulphate of lime deposited during the eva-
poration. The concentrated liquid is again tested for lime by sulphuric acid, and
if no change ensues, the lime has been entirely removed, as I ascertained by the
proper tests. The solution now contains only the whole phosphoric acid of the
bones, the magnesia which they always contain, and more or less free sulphuric
acid. I have described this process thus far minutely, because, up to this point,
it is the same as that which I recommend; and it is in the mode of separating
the magnesia that the advantage of my process consists,

Liesie acts on the concentrated acid solution, brought to the consistence of
syrup, by alcohol, which dissolves the phosphoric acid, leaving undissolved the
greater part of the phosphate of magnesia, and depositing the last traces when
allowed to stand. I cannot ascertain whether this operation is to be performed be-
fore or after the sulphuric acid has been expelled by heat; but I find, that after
expelling the sulphuric acid, a transparent and colourless glass is obtained, which
dissolves perfectly in boiling water, and the solution concentrated to a syrup, and
treated with alcohol, yields a solution containing much magnesia, and which, on
standing for weeks, deposits nothing. It is very probable that the alcohol did
not succeed in separating the magnesia in my experiments, because the phos-
phoric acid was in some one of its modifications, different from that in which
Liebic employed the same method. But I have not yet been able to manage
that process so as to answer the purpose intended ; and, even if it did succeed
better, it is well known that alcohol, at its present price, cannot be used in this
country on the large scale. I therefore endeavoured to find means of dispensing
with its use, and I began by studying the properties of the soluble glass above
mentioned, which contains only phosphoric acid, water, and magnesia.

This glass dissolves slowly, but perfectly, in boiling water; but the solution,
when again concentrated, and so far deprived of water, that its temperature in
an open platinum capsule rises to nearly 600°, suddenly becomes turbid, from
the separation of a powder, while crystals begin to form in the viscid mass, re-
sembling those which form in honey. When cold, water dissolves these crystals
instantly, and leaves undissolved only a heavy white powder, which is a peculiar
phosphate of magnesia. I shall return to it presently. It is quite soluble in
water.

PURE PHOSPHORIC ACID FROM BONES. 49

As this salt was evidently formed at a certain temperature, I could see no
reason why the whole of the magnesia might not be converted into that insoluble
form, although, in this first experiment, the filtered liquid was found to contain
much magnesia. I therefore again evaporated the filtered solution; and, at the
same temperature as before, it again became turbid. I kept up the same heat
for fifteen minutes; and when the mass, after cooling, was acted on by water, a
large quantity of the insoluble phosphate separated, and the filtered liquid was
now found absolutely free from the smallest trace of magnesia. It now clearly
appeared that the first heating had been too short, and that it was only necessary
to heat long enough to bring every part of the mass to the same temperature.

The process which I recommend, therefore, is as follows:—The glass re-
maining, after heating to redness in a covered platinum crucible to expel sulphuric
acid (after the separation by that acid of all the lime), is to be boiled in water,
and the solution evaporated, and, finally, exposed in a platinum capsule for a quar-
ter of an hour, to a heat of from 595° to 600°, or to that temperature at which
the acid begins to volatilize with the water. ‘Tt must not be heated more strongly,
lest the glass should be reproduced. When cold, the mass is to be softened with
water, and the solution of pure phosphoric acid filtered from the insoluble phos-
phate of magnesia. The acid is pure from magnesia, if, when diluted and super-
saturated with ammonia, it forms no deposit, especially after standing for one
or more days. I have repeated the process six or seven different times, and on
no one occasion did the filtered acid contain magnesia, except when I had pur-
posely heated too strongly. This proves that the degree of heat is not difficult
to manage. Indeed, after the first experiment I found it unnecessary to use
the thermometer, the appearance of the mass furnishing a sufficient guide. It is
evident that the above process has the twofold advantage of simplicity and
economy.

The quantity of magnesia which separates in the form of the insoluble phos-
phate is very considerable. It will be very easy to determine exactly the amount
of magnesia in bone-earth, by converting it into this salt.

II. On a new and anomalous Phosphate of Magnesia.

This is the salt so often mentioned above, as being separated by a heat of
600° from its solution in phosphoric acid. As the salt is perfectly anhydrous, it
is obvious that its formation is owing to the separation of water at that high tem-
perature. The analysis of the salt was made by fusing with carbonate of soda,
dissolving in diluted hydrochloric acid, adding, for precaution’s sake, a little phos-
phate of soda, and then precipitating by ammonia, collecting the ammoniaco-
magnesian phosphate on a filter, washing moderately with cold water, drying
and igniting. The residue, pyrohposphate of magnesia, was reckoned to contain

VOL. XVI. PART I. N

30 PROFESSOR GREGORY ON AN ANOMALOUS

36.67 per cent. of magnesia. In three analyses, the per-centage of magnesia in
the new salt was found to be 16.78, 16.92, and 15.94. In the last of these I
pushed the washing further than in the first two, and I did the same in three
more analyses, which yielded 15.12, 15.34, and 15.12, per cent. of magnesia. The
mean of the six analyses, all made with portions of salt prepared at different
times, is 15.87 per cent. of magnesia. As the salt lost no weight by ignition, it
contained no water, and therefore was composed of magnesia and phosphoric
acid alone: the absence of lime being previously ascertained. Its composition is
therefore,

Magnesia, : : , : 15.87

Phosphoric acid, : ; ; : , 84.13

The only formula which at all approaches to this composition is 3 P, 0, + 2 Mg0,
according to which, it is an acid sesquiphosphate of magnesia. The composition,
calculated according to this formula, is,

Magnesia, : : : : 16.18
Phosphoric acid, : : ; 4 83.82

Considering the imperfection of the means for determining the amount of
magnesia in analyses with precision, there can, I think, be no doubt, that the
above formula expresses, empirically, the composition of the salt in question.

But what is the rational formula of this salt? As far as I know, there are
no known sesquiphosphates of protoxides. Indeed, the very characteristic of
the three known classes of phosphates, is their tendency to form salts with 1, 2,
and 3 equivalents of base for 1 of phosphoric acid.

Metaphosphoric, or monobasic phosphoric acid, forms salts of the general for-
mula. P, 0,, MQ; and if our salt is to be classed as a metaphosphate, it must be
one with the very singular formula 2 (P, 0,, Mg 0) +P 0,; in which 2 eq. of
metaphosphate of magnesia are combined with 1 eq. of anhydrous phosphoric acid,
which has either entered the radical of the acid, without increasing its neutralising
or assumed a neutral character.

Pyrophosphoric acid, or bibasic phosphoric acid, forms salts of the general

formula, P, 0.,2 M0, or P, 0 M Me If our salt be a pyrophosphate, and the tem-
Pd 2“5) HO pyrop

perature appears favourable to its being so, its formula must be (P, 0,,2Mg 0)+
2 P, 0,, in which 1 eq. pyrophosphate of magnesia is combined with 2 eq. of
anhydrous phosphoric acid, in one of the characters alluded to above.

Lastly, common or tribasic phosphoric acid forms salts of the general for-
‘ 2M0 M0
mula, P,0,,3M0; P, 0, | Ho oF Pe 9; ‘2 10° Lf our salt belong to this class,

its formula will be P, 0, ae +P, 0,. Here, 1 eq. of phosphoric acid, act-
a)

PHOSPHATE OF MAGNESIA. oO

ing as acid, is united to 2 eq. of magnesia, and 1 eq. of phosphoric acid, acting
as base, while a third eq. of phosphoric acid acts in another capacity, possibly as
a neutral body, like water of crystallization.

In all these supposed formule, we have anhydrous phosphoric acid acting in
an unusual capacity ; and it is evident that, whichever we adopt, the occurrence
of the salt is favourable to the doctrine, that the so-called anhydrous acids are
not really acids. It is true that, on the old view of phosphoric acid and phos-
phates, there is nothing startling in a sesqui-phosphate; but, if we adopt this
view, we must cast aside all the knowledge recently acquired concerning the
phosphates, and which, to a great extent, is established by experiment.

On the whole, the composition of this salt is so anomalous, that we must
conclude, either that the received views on the subject of the phosphates are
erroneous, or that there exists a fourth modification of phosphoric acid, distinct
from the three usually admitted. We might suppose this acid to be 3 P, 0, =
P, 0,,, and to be neutralised by 2 eq. base, yielding the formula P, 0,,, 2M 0.

It is worth while to remark, that, on the theory of compound acid radicals
and hydrogen acids, according to which the formula of a tribasic phosphate is
P, 0,, M,, that of a bibasic phosphate, P, 0,,M,, and that of a monobasic phos-
phate, P, 0,, M, this salt cannot be represented as a sesqui-metaphosphate, al-
though, as we have seen, it may be so on the old view of acids and salts. . The
latter makes it 3 P, 0, + 2Mg0; but the former would require 1 eq. of oxygen
more to yield the formula of a sesqui-metaphosphate 3 P, 0,, Mg,, the salt contain-

2
ing only p.', Mg... In this point of view, the existence of the new salt may
P83)

2

turn out to be a serious objection to the above named theory of salts and acids.

The new phosphate is remarkable, among all the salts of magnesia, for its
extreme insolubility in water and acids, which is such, that it may be ranked be-
side sulphate of baryta. This imsolubility has hitherto defeated all my efforts to
ascertain the precise nature of the acid it contains, and whether that acid be new
or not.

As this salt is not only very insoluble, but easily washed, and less hygrome-
tric than any powder I have ever weighed, it would be well adapted for the deter-
mination of magnesia, and also of phosphoric acid, if we could, at pleasure, con-
vert these substances into this particular form of combination when mixed with
other bodies. The experiments I have made on this subject have convinced me,
that there are very great difficulties in the way of this application ; but, I trust,
they will not be found insuperable. It will, at all events, be easy to determine
the amount of magnesia in bones, by converting the magnesia, as in the above
process, into this insoluble form.

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( 53)

VIL—WMiscellaneous Observations on Blood and Milk. By Joun Davy, M_D.,
F.R.S., Lond. and Edin., Inspector-General of Army Hospitals, L. R

(Read April 7. 1845.)
1. On the State of Combination of the Alkali in the Blood.

The condition of the alkali in the blood—of that portion on which its alkaline
reaction depends—has been the subject of much speculation, and of many experi-
ments. ENDERLING is one of the latest inquirers who has given it his attention.
After having made an analysis of the ashes of the blood, he has come to the con-
clusion, that the alkali in it is in combination with phosphoric acid, the former
predominating in the form of the tribasic phosphate of soda.*

Granting the accuracy of EnpERLING’s analytical results on the ashes, does it
follow that his inference must be correct relative to the condition of the alkali in
the liquid blood? It appeared to me doubtful @ priori ; and the doubt I enter-
tained was confirmed by experiment. The doubt arose from considering the ten-
dency of the alkaline carbonates, when strongly heated with charcoal, to be
reduced ; and when heated with phosphate of lime in excess, to exchange their
carbonic acid for a portion of the phosphoric—the acid gas of course escaping,
and compounds of lime and alkali remaining, each with excess of base. In accord-
ance with this, when I have added carbonated alkali to the coal obtained from
blood, and have reduced the coal to ashes, I have not been able to detect in the
lixivium obtained from them any trace of carbonic acid. Moreover, I find that
the carbonate of soda is liable to loss when heated strongly, exposed to the air;
and, consequently, when it exists in a small quantity in a bulky coal, the whole
of it may be dissipated—carried over much in the same manner as boracic acid is
in combination with water as a hydrate, when it is subjected to heat.

If ENDERLING’S view were correct, the blood, after having been acted on by
the air-pump, ought not in its fresh state to yield any carbonic acid on the addi-
tion of an acid. This is the experiment alluded to, which confirmed my doubt.
I find that blood or its serum, after having been so acted on until perfectly tran-
quil, has effervesced strongly, when mixed either with dilute sulphuric or muriatic
acid purged of air, or with a solution of cream of tartar. And, in accordance with
this, I have also found that serum, after having been subjected to the air-pump,
gives on coagulation, by immersion in boiling water, a different result, whether

* See Mr Pacet’s Report on the Progress of Human Anatomy and Physiology, in the British
and Foreign Medical Review for January 1845,

VOL. XVI. PART I. O

54 DR DAVY’S OBSERVATIONS ON BLOOD AND MILK.

immersed unmixed, or after admixture with a little acid. In the one instance no
air bubbles are disengaged ; in the other very many.

Some years ago, when engaged in experiments on the blood, especially in
relation to the present question—the condition of the alkali in it—I noticed the
effect of cream of tartar in expelling carbonic acid, and that both from venous and
arterial blood, and from serum; an effect which, with other considerations, in-
duced me then to conclude, that the soda in the blood exists in the form of the
sesqui-carbonate ; an inference which appears to me still to be most in harmony
with the facts.*

In opposition to this view, perhaps, it may be said, that farther proof of its
correctness ought to be afforded by the effect of a solution of muriate of lime on
the serum,—that, if the latter contain the alkali as stated, a precipitate of carbo-
nate of lime ought to be the result. This experiment I have tried, with the aid
of the air-pump, sometimes with a doubtful result, sometimes with a negative
one, especially in the instance of serum from venous blood. But in these instances
I have also found the result the same, even on the addition of a portion of sesqui-
carbonate of soda, as much as ‘2 of a grain to 316 grs. of serum—a quantity of the
alkali, which, when dissolved in the same bulk of water, is more than sufficient
to give a precipitate with muriate of lime. Would not this seem to indicate that
in the blood and its serum the carbonated alkali is in a peculiar state of combina-
tion with the animal matter; and the same remark is applicable to the posphates
or their elements.

The trials referred to have been made on the blood and serum of the ox and
sheep, at a favourable time of the year, during the winter season, when the tem-
perature of the air has been little above the freezing point.

2. On the Viserd Quality of the Blood Corpuscles.

That the corpuscles of the venous blood of the mammalia, when quite fresh,
and in the act of coagulating, collect together in piles, as it were by a kind of at-
traction, is well known. The viscid, adhesive quality, I am about to notice, is
distinct from this, and, indeed, is best seen when the aggregation in piles ceases
to be witnessed, as in cruor, procured by breaking up the crassamentum, and
separating the fibrin by straining through linen.

The cruor thus obtained is essentially a semifiuid, the particles loosely ad-
hering forming a mass in some respects not unlike honey or molasses. I shall
notice some appearances connected with and indicating the condition referred to.

When poured into a fluid, such as water or serum, it rapidly falls to the bot-

* Physiological and Anatomical Researches, ii. p. 152.

DR DAVY’S OBSERVATIONS ON BLOOD AND MILK. 55

tom; and, in the instance of serum, if not agitated, remains as a connected mass.
If now a glass rod be put into it, and withdrawn through the supernatant serum,
it will come out not sensibly coloured by the red particles; the surface of the
cruor round the rod will be seen to be raised a little in the act from adhering to
it, and then to return to its former level, shewing that the corpuscles adhered to
each other in the mass more strongly than to the glass: and, if the serum through
which the rod has been drawn is examined with the microscope, a small number
only of blood corpuscles will be detected in it.

If, instead of allowing the cruor to remain undisturbed, it be broken up by
agitation with the serum, it will be found to be divided into clusters of corpuscles
and detached particles. When one of these clusters is placed under the micro-
scope, between two plates of glass, the adhering corpuscles forming the group are
seen to be attached, not by their broad or concave surfaces, as in the instance of
ageregation by piles, but by their narrow rims. Now, if graduated pressure be
employed, so as to break up the cluster, just before separating, the adhering cor-
puscles will be seen to be elongated, as if drawn out almost toa fibre, and yet
when detached, the adhesion being overcome, recovering, and that suddenly, their
circular form : and, on relaxing the pressure, many of them will be seen to reunite,
sticking to each other even when in motion.

This adhesive quality of the blood corpuscles is exercised, not only on each
other, but also on other substances, though, perhaps, in a less degree. Proof of
this is afforded when cruor has been allowed to remain, even but a short time,
in a glass tube, or any other vessel. The portion in contact with the bottom of
the tube is found to adhere to it, and is not easily detached ; whilst any that may
adhere to the sides commonly appears in streaks, the blood corpuscles being at-
tached to each other, and so producing a linear arrangement.

This viscid property of the blood corpuscles must, I apprehend, be considered
as specially belonging to them, quite distinct from the fibrin, which appears to
be viscid only in its transition state, in the act of coagulating,—previously even
more liquid than serum attenuating the blood, and subsequently, as soon as co-
agulated, constituting the firmest and the cementing part of the crassamentum.
The blood corpuscles, as regards this quality of viscidity, are far more constant ;
it belongs to them when fresh, probably when circulating in the vessels,—it is
exhibited in them long after removal from the living body, and is not even lost
with incipient putrefaction, and, connected with that, the change of the particles
to a globular form.

56 DR DAVY’S OBSERVATIONS ON BLOOD AND MILK.

3. On the Tendency of Fibrin in Coagulating to a certain arrangement of its
Particles.

Amongst the many remarkable properties of coagulable lymph, I am not
aware that a tendency of its particles to arrange themselves in a certain manner
out of the body, representing, as it were, what takes place in the body in the
process of growth and of reparation, has hitherto come under observation, or, at
least, has been the subject of commentary.

A striking instance of the kind I have witnessed in the buffy coat. When
the buffy coat is well marked, as in cases of acute rheumatism, when it is thick
and cupped, the blood abstracted having been slow in coagulating, it is easily
detached from the soft crassamentum ; and this is best done under water. Thus
separated, it may be described as a fibrous mass loaded with serum, enveloped in
a pellicle or membrane, performing the part of a sac. This pellicle, or containing
membrane, is very thin, yet of considerable strength, and with care may be dis-
sected off, especially after maceration in water for two or three days, at a low
temperature. It is very like a serous membrane, both as seen with the naked
eye, and under the microscope. Under the latter, it bears a strong resemblance
to the arachnoid, appears as a tissue of extreme delicacy; hyoloid, without any
visible pores or fibres, with a few particles like blood corpuscles, or their remains
(according to the method used of separating it), scattered through it. Whena
force is applied to it, it breaks less readily in one direction than another; and
exhibits, when drawn in one direction, more elasticity than in the opposite. When
the blood, as is usual, has been received in a circular vessel, and the buffy coat,
of course, is of the same form, tearing the membrane with a forceps towards the
margin, shreds of it, several lines in length, are easily detached in a line from
the centre to the circumference, but not in a line at right angles to this; and in
the same direction small portions of the membrane exhibit considerable elasticity,
which they do not in the opposite direction.

I may mention another example, also well marked. If the blood, in the act
of coagulating, is stirred with a glass rod, or a wooden skewer, or the like, the
fibrin, as it is well known, will adhere, with which blood corpuscles will be mixed.
The adhering clot, consisting of the two, the fibrin in excess, when pulled off,
which it easily is, exhibits a canal with a smooth inner surface. If it be well
washed to deprive it of colouring matter, and slit open, it will be found to bear a
close resemblance to an artery, especially to its middle coat, being composed of
fibres arranged seemingly transversely, that is, at right angles to the axis of the
tube. This is to be inferred from the effect of a force applied. If applied in that
direction, transverse shreds pretty readily separate; but if in the opposite direc-
tion, using a forceps, only small bits. And, in the one, the transverse direction,

DR DAVY’S OBSERVATIONS ON BLOOD AND MILK. 57

the tube is far more elastic than the other, after the manner of the middle arterial
coat.

Other instances might be given, tending to shew the same disposition on the
part of coagulable lymph to a certain regular arrangement of its parts, as it were,
of a nisus formativus, in the act of coagulation. In examining the buffy ccat, or
the fibrinous masses which are so commonly met with after death in the right
cavities of the heart, it is not uncommon to find in them, when divided, cavities
containing serum resembling cysts. And in the ventricles of the heart, and the
aorta and the principal veins, especially the iliac and femoral, fibrinous concre-
tions, as it is well known, are often found after death from lingering diseases, in
which a puriloid matter is contained, as in a sac,—a matter which has been imi-
tated by Mr Gutiiver, by the coction of lymph, at about the temperature of the
human body, and which, previous to his experiments, had been considered as
pus, and, erroneously, as the product of inflammation.

I would ask in conclusion, is not this disposition of coagulable lymph called
into play in other occasions during life, and may it not serve to explain certain
appearances which are commonly accounted for in a different manner, such as
the cysts which so rapidly form in the instance of aneurisms, the consequence
of wounds, and the lining membrane of the sacs of false aneurisms, which is hardly
in appearance distinguishable from the inner coat of the artery with which it is
continuous ?

4. On the Eject of Serum in promoting the Coagulation of Milk.

There is a marked difference, as is well known, between the albuminous part of
the serum of the blood and that of milk,—ordinary cow’s milk,—viz., that, whilst
the former is coagulated by a temperature below the boiling point of water, the
latter, in its fresh state, is not so affected, even by ebullition, but, on the contrary,
has its natural tendency to coagulate, connected with the absorption of oxygen
and the formation of an acid, retarded. A priori, perhaps, it would harldly be
expected, as regards the property of coagulation, that the one fluid mixed with
the other would have any material effect. But that it is not so, I have found on
trial. Milk, I find, when mixed with serum in certain proportions, is coagulated
by heat. I shall notice some results obtained, using mixtures of the serum of the
blood of the sheep, which coagulated at about 170° Fah., and cow’s milk.

Equal parts of the two remained liquid at 170°, and coagulated about 175°.
The coagulum was of an opaque white, very little softer than the coagulum of
the serum alone. Mixed with water it did not render it milky; and the watery
infusion was not rendered turbid by acetic acid, and only in a very slight degree
by the nitric acid.

VOL. XVI. PART I. P

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VIII.—On the Advantages to be derived from the Use of Metallic Reflectors for Sew-
tants and other Reflecting Instruments ; and on Methods of directly determaning
the Errors in Mirrors and Sun-Shades used in Reflecting Instruments. By
Joun ADIE, Esq.

(Read February 17. 1845.)

It has frequently occurred to me that the difficulty experienced by instru-
ment-makers, in obtaining for sextants and other similar instruments, reflecting
mirrors perfectly parallel in their polished surfaces, and also the greater difficulty
of procuring glass perfectly homogeneous in its structure, might be overcome by
the use of metallic reflectors.

It is well known, that, from the want of perfect parallelism in glass mirrors,
there arises an error in the reading of such instruments, inasmuch as the emer-
gent ray does not pass out of the glass at the same angle as the incident falls
upon it, and that from the want of homogeneousness in the substance, and the
unequal refractions caused by the veined structure of the glass.

Whether this structure of the glass arises from the process of its manufac-
ture, or the want of proper admixture of the component parts, before being cast
into plates, I am not prepared to say; but in all the plate-glass I have tried, by
polishing it on the edges, this structure was observed ; so much so, that the plates,
on being seen through perpendicularly to the plane of their surface, shewed ob-
jects perfectly distinct ; while objects, when viewed through the glass at right
angles to this plane, were seen with difficulty, distorted and twisted in all direc-
tions. Of such glass, the mirrors of sextants, and other reflecting instruments,
are made; and it is easy to conceive how very erroneous the angles may be, par-
ticularly when the incident ray falls on the mirror at a low angle, as it does
when large angles are observed, as in lunar distances and the like; while the
indistinctness of the image observed under these circumstances, detracts much
from the utility of instruments fitted with such mirrors. As a practical illustra-
tion of the above, if we take a number of objects, and observe with a sextant the
angles between each, then observe the angle between the extremes, suppose this
120°, it will be found, in the great majority of cases, that the sum of the angles
observed does not agree with the observed angle of the extremes, which should
be the case.

These errors, and sources of error, are obviated when we make use of metallic

reflectors, having their surfaces polished perfectly fiat ; a matter of no very difficult
attainment in practice.
VOL. XVI. PART I. Q

62 MR ADIE ON THE USE OF METALLIC REFLECTORS FOR

But, besides the avoidance of error, there are direct advantages in the use of
such reflectors, which may be stated thus:—In the marine sextant, or reflecting
circle, the reflection of faint objects is more easily obtained ; in other words, ob-
jects are seen reflected by metallic mirrors which cannot be seen by the ordinary
silvered ones. Another advantage is, that larger angles can be observed. This
applies more particularly to the pocket or box-sextant, used in surveying, both at
sea and land. From the small size of the index mirror, we cannot, when glass is
used, reflect an angle much above 100°, the thickness of the glass cutting off the
incident and emergent rays, when these fall on the silvered surface at low angles ;
whereas, with the metallic reflector, the refiected angle can be obtained to its ut-
most limit, or to about 140°, being nearly one-half greater than that which can be
obtained by means of a silvered glass reflector.

I am not aware of any account having appeared of the use of metallic mir-
rors heretofore in the construction of such instruments, although I have little
doubt, from the obvious advantages attending them, that the idea must have sug-
gested itself to many others; and that the fact of their not having been brought
into use, must be accounted for from the difficulty of obtaining speculum metal
possessed of the requisite qualities.

The liability of a highly-polished reflecting surface to be destroyed by tarnish
and rust, from exposure to the atmosphere, and more particularly from exposure
to the influence of sea air, is an objection that occurs on first view to the use of
metal.

All who are acquainted with the reflecting telescope, know how subject the
mirrors of such an instrument are to deterioration from tarnish; and that, in
many cases, even when due care has been taken of them, they have been alto-
gether destroyed. Yet, it should be stated, that this is not the case with all such
instruments. There are many reflecting telescopes, now very old, in which the
mirrors are in a state of perfect preservation ; those I am best acquainted with, as
having stood the test of time (and they are in general very good), having been
made by the late James Short of London, who lived about eighty years ago. On
the other hand, it is well known, that many speculum metals will not retain their
lustre for many weeks under ordinary exposure.

From these facts, we may infer, that it is the composition of the metal which
causes the difference in the permanency of the polish.

My attention was therefore directed to procuring pure metals to form the
alloy or speculum metal. Tin is not difficult to be had in a state of great purity ;
but it is otherwise with copper; for, as we advance in commerce, we find, that,
day after day, this metal is brought to market more and more impure; so much so,
that bar and cake copper of commerce are now so bad that they are nearly unfit
for compounding as brass.

The recently discovered process of electrotype, however, affords us the means

SEXTANTS AND OTHER REFLECTING INSTRUMENTS. 63

of easily procuring copper in a state of purity; and it is with the metal so pro-
cured my experiments have been made.
By compounding copper and tin in their atomic proportions of 16 parts of
copper to 14.92 parts tin, a metal of high lustre is obtained ; and, so far as my
experiments have gone, this metal is not liable to tarnish, if ordinary care be taken
~ to guard against this effect. My course of procedure was as follows :—I first ex-
posed polished pieces of this metal to the free open air, and found, after some
months’ exposure, that, when the dust and rain stains were rubbed off, the surface
was in a very good state of preservation. I next tried exposing the mirrors to
the fumes of acids, and watering them with sea water for a considerable length of
time. Under the operation of these corrosive agents, they still retained their
lustre. But, notwithstanding the encouragement held out from these experiments,
feeling yet reluctant to put such instruments into the hands of navigators without
first submitting them to the test of actual service; and a favourable opportunity
having last spring presented itself, through the kindness of Mr O. Mossman, one
of the surveyors on board of H.M. Ketch, Sparrow, then about to engage in a sur-
vey of the Pentland Firth, I put into the hands of that gentleman a sextant
fitted with these metallic reflectors, of which he politely took charge, promising
to give it a fair trial during a season’s survey. Mr Mossman amply redeemed his
promise; and I shall now take the liberty of quoting the letters which he was good
enough to address to me, giving an account of the working of the instrument.

“H.M. Keron, SPARROW,
THURSO, 26th October 1844.

“Dear Srr,—After you have examined the reflectors you will be able to
judge of the durability of them, after being in constant use for most part of the
season, during which, they have been exposed to all sorts of weather. As regards
the power of their reflection (although dark), they are beyond all the silvered
glasses I have ever had in use; also, for measuring large or small angles, they
excel the others by far. When we are once properly settled at Portsmouth, I
shall be able to make a full descant of the good properties of your metallic re-
flectors, and shall strongly recommend them to be in all reflecting instruments.
I have subjected them to all exposure which I could call fair play, only, at the
same time, having been careful not to put the instrument away damp.—Yours
truly, (Signed) “ Wn. O. MossMAN.”’

In a second letter, dated Portsmouth, 13th December, Mr Mossman says :—
“Tam sorry my spare moments are rather scarce, or I should have said some-
thing more concerning the merits of your metallic mirrors. However, I should
very strongly recommend them to be used in all instruments that are likely to be
exposed to much wet; because, if the instrument fall overboard, for instance, and

64 MR ADIE ON THE USE OF METALLIC REFLECTORS FOR

does not lie so long in the water as to allow the rust to commence, if it be care-
fully wiped dry, when taken out, there is no danger of spoiling afterwards. Now,
this is a very important matter, and more particularly to surveyors, than any
other class of nautical men; for such accidents frequently occur in boat-sound-
ings.”

I come now briefly to notice the second subject announced in the title of
this paper, viz., direct methods of determining the errors in the mirrors and sun
shades used in reflecting instruments. I am not aware of any method adopted
by practical men for the discovery of such errors, except that of a careful process
of what is termed parallel grinding, and testing the glasses in the instrument when
fitted up. This is effected by observing known angles, and noting that a contact
of the sun’s limb, by reflection, does not vary on changing the sun shades inter-
posedbetween the direct and reflected images seen in the telescope. This varia-
tion is noticed by Mr M‘Kay, in his work on Determining Longitude, and he re-
commends that it should be observed and applied as an index error affecting the
several shades. Errors may, however, exist in the reflectors and shades, which,
from the particular position they have in their settings, are not discovered by such
trials. The methods I have adopted are as follows :—

First, For the mirrors I place a mirror at about an angle of 45° before the
object-glass of a telescope, mounted on a divided circle, capable of reading an
angle of 10’; I have, besides, a moveable micrometer wire at the stop holding the
cross wires of the telescope, by which an angle of one second may be observed ;
the mirror placed before the object-glass rests on three smooth studs, to which it
is pressed up by a light spring at the back. In this position we turn the tele-
scope and mirror in azimuth till we obtain the reflection of a well-defined distant
object, which is brought to the intersection of the cross wires of the telescope. If
we now turn round, or reverse the mirror on these studs, and find the same object
in the intersection of the cross wires, we know that in that line there is no want
of parallelism; and if we have the same result on repeating the trial at right angles
to the first direction, the mirror is said to be perfect in respect to the parallelism
of its surfaces. If, however, we find on turning the mirror that the reflected
object is not intersected by the cross wires, then, the glass is not parallel; and
half the amount of error read by the circle or micrometer head, is the error which
would arise if such a mirror were applied to a sextant.

Second, For the sun shades I have a telescope whose object-glass is divided,
and the one-half moved over the other by means of micrometer screws, having a
divided head. The value of the divisions of the micrometer head is obtained by
measuring the sun’s diameter. In that which I use, two divisions on the head are
equal to one second.

Before one-half of the object-glass is placed a fixed sun shade ; and before

SEXTANTS AND OTHER REFLECTING INSTRUMENTS. 65

the other, an arrangement is made for placing the shades to be tested in such a
way that they can be turned round. Having placed in this frame a shade for
trial, I bring the two images of the sun seen in the telescope into contact, by
means of the micrometer screws ; and if, on turning the shade before the object-
glass, the contact remains perfect, then we know that its surfaces are parallel ; if,
on the other hand, the contact is broken, we can, by turning the shade, find the
point of nearest contact; and by turning the shade through 180°, we measure the
amount of opening of the images, by means of the divided micrometer head. This
gives double the error which would be caused by the shade when used in making
a direct observation. But as all angles observed by reflecting instruments are
double, or, in other words, the divisions on the limbs of reflecting instruments are
equal only to half those of an instrument used for direct observation, the double
error given by this method goes all to deteriorate the observation, as an unparallel
shade affects the angle when reflected by twice the amount’of direct observation.
Another important object is gained by this method of testing the shades. It being
a very difficult matter to obtain these altogether perfect, I reject all where the
error would amount to 10’, which is the usual reading of a sextant ; and when an
error of a smaller amount does exist, I find, by turning the shade, the line in
which the want of parallelism exists; and by placing this line at right angles to
the plane of observation in a reflecting instrument, the angles observed by such
an instrument are not affected even by the small error of the shade.

VOL. XVI. PART I. R

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VEBTe)

IX.—On the Balance Magnetometer, and its Temperature Corrections By J. A.
Broun, Esg. Communicated by Sir T. M. Brispaneg, Bart.

(Read 21st April 1845.)

1. Tue Balance Magnetometer was imagined by Dr H. Lioyp, of Dublin, for
the purpose of observing the variations of the vertical component of the earth’s
magnetic intensity. It consists simply of a balanced magnetic needle, with a
knife-edged axle, resting on agate planes, at right angles to the plane of the mag-
netic meridian. In the instrument from which the results in this paper are de-
duced, the position of the needle is observed by means of micrometer microscopes.*

2. If m be the moment of free magnetism of the needle, Y the vertical com-
ponent of the earth’s magnetic force, W the weight of the needle, g the distance
of the centre of gravity from the centre of motion, e the angle contained by the
line joining these two centres, and the magnetic axis of the needle when hori-
zontal; the equation of equilibrium will evidently be

1 Y GEOR ESE OS NOL AD)
By differentiation and division
oe Am
= ee stiged oer ee eee F500 (2e)

The differences a are obtained by means of the micrometers, and the differences

of Y in terms of Y will be obtained, if we can determine « and—™, ‘the latter

being the variation of the magnetic moment, due to temperature.
3. There are great practical difficulties in the way of rendering the needle
capable of giving ¢ accurately by inversion, but Dr Luoyp has shewn+ that

2 ie
tan €=cot Oa Sects unre Caenet o)

where @ is the magnetic dip, T’ and T the times of one vibration of the balance
needle in a horizontal and in a vertical plane. We have thus, instead of one, three
unknown quantities to determine ; and it becomes a matter of importance to shew
with what degree of accuracy this may be done.

The dip and time of vibration in a horizontal plane can be obtained with suf-
ficient truth for the purposes of this factor.

* See the Introduction to the Makerstoun Magnetical Observations for 1841-2,

f In his “ Account of the Magnetical Observatory of Dublin,” where the complete investigation
will be found.

68 MR BROUN ON THE BALANCE MAGNETOMETER,

Observations of the time of vibration in a horizontal plane ranging through

a period of three years, agree within 0.06, and this difference must be to a con-
siderable extent due to alterations in the condition of the needle between the dif-
ferent observations.

4. The time of vibration in a vertical plane is in widely different circum-
stances.

These differences I shall proceed to point out.

lst, The time of vibration in a vertical plane is found increased after the
needle has been, by any means, vibrated through a large arc.

The strongest evidences of this are contained in the following table; they
were obtained either by iron having been brought accidentally near to the mag-
net, or by the necessary removal of the box which covers it. In the latter case,
the magnet was vibrated through large arcs by currents of air.

One or two observations for the time of vibration are given for the periods
immediately before and after the disturbance of the magnet.

The last column contains the times of vibration corrected to 50° Fahr.; for
reasons that will be shewn, it is only these that are strictly comparable.

The observed time of vibration is generally the mean of two series, which
rarely differ one-tenth of a second.

Additional evidence of the above conclusionis furnished by Table II.

AND ITS TEMPERATURE CORRECTION. 69

TABLE I.

Observations for the Time of Vibration of the Balance Needle in a Vertical Plane,
before and after excessive Vibrations.

Observed Time of one
: rab. Temperature | Vibration
Date. CAUSE OF DISTURBANCE. Se one of Needle. | corrected to
50°.

| Ee

1842. Fs ‘ BD

March 19. 10.14 45.5 10.48
pee OD. Balance magnet vibrated excessively.
April 2. 11.02 42.5 11.59
se 9. 10.94 44.0 11.40
Oct. 31. ein of “ nee teas 10.05 55.9 9.60
air of compasses brought inadvertently near
Nov. 10. { the balance needle. *
555mg Ge 10.34 51.0 10.26
em LO. 10.02 50.8 9.96
1843.
Sept. 18. 10.60 65.0 9.46
me OP 10.62 63.7 9.58
The box of the magnetometer removed, and the
v1 26, { needle exposed to currents of air.
SIE 11.20 51.9 11.06
as BA 10.95 46.1 11.40
1844.
April 29 22 9.04 50.2 9.02
mm ) oO 7 9.50 60.5 8.70

Box lifted for the purpose of removing an insect,
wo. 30 7+ and replaced immediately afterwards; vibra-
tion not excessive.

a 00 8 10.03 60.5 9:25
Pe OO 22 8.97 Ov) le S83
July 22 0 8.23 62.3 7.30
con PRY 9.10 68.0 1:13
24 18 Box lifted, and insect removed from beside the
{ needle.
25 0 9.80 67.2 8.49
-. 25 23 9.67 64.5 8.57
a 26 8 The magnet vibrated by steel.
- 26 23 10.04 65.4 8.87
ee 20) 22 9.45 58.5 8.80
Oct. 30 22 6.97 47.9 7.13
Nov. 3 22 6.72 43.9 7.18
3.—78 poe in observatory, who had probably been
rea a near the magnet with a hammer.
7 23 7:30 42.5 7.87
Workmen brought a hammer near the magnet.
8 21 After the vibration thus produced, the needle
oa rested in a position differing 1’.6 from its pre-
vious position.*
ot 8.24 46.8 8.48
10 23 8.03 43.7 8.51

5. 2d, The time of vibration in a vertical plane depends, to a considerable
extent, on the magnitude of the arc of vibration.

3d, For the same arc, the time of vibration is greater, if it belong to a series

« This is the only case in which I determined, at the instant, the effect of excessive vibration on the posi-

tion of the needle; the effect, though small, is considerable, when compared with the hourly changes; for
several hours before this vibration, the magnet had not changed its position.

VOL. XVI. PART I. s

70 MR BROUN ON THE BALANCE MAGNETOMETER,

commencing with a large arc, than if it belong to a series commencing with a
small one.

These conclusions I had arrived at nearly two years ago, and accordingly
only small arcs were used in determining the time of vibration, seldom above 5’.0
commencing.

The following series of observations was made in January 1844, before re-
moving the needle for the purpose of determining its temperature correction.
Many other series made previously give the same result; but the following will
be sufficient to prove the facts stated above.

TABLE II.

Observations for the Time of Vibration of the Balance Needle in the Vertical
Plane, for different Arcs.

Semi-are of Vibration. Means.
Time at the Number
commencement off 7 > +) =i) pee een f. of
pack: Barley: Beginning. Ending. enone. Partial. Of the Series.
d bh WwW id ‘4
Jan. 26 22 15 1.8 0.4 14 9.58
22°25 1.4 0.4 14 9.58
22 40 25.0 18.6 6 VAS H
18.6 6.5 6 10.98 10.95 }
6.5 0.5 8 10.71
22 53 1.3 0.4 16 9.78
23 20 1.6 0.4 16 9.70
23 32 45.5 25.0 6 11.36
25.0 11.3 8 11.20
11.3 6.5 6 11.07 11.07
6.5 Bit 6 10.95
21 0.5 6 10.78
23 50 irg 0.4 14 10.17
Jan. 27 0 5 55.0 40.0 6 11.72
40.0 30.0 6 11.60
30.0 22.0 6 11.57
22.0 17.0 6 11.45
17.0 12.3 6 11.37 11.35
12.3 5.8 6 11.33
5.8 5D, 6 11:22
5.5 4.5 6 11.09
4.5 0.7 6 10.80
0 20 ky 0.4 18 10.60

The semi-arcs were observed by my assistant Mr Wetsu, at one microscope,
while the times of each vibration were observed by myself at the other.

It is not my intention, in the present communication, to enter into any
examination of the causes of these peculiarities; my object is simply to pomt
them out as sources of error. I shall therefore merely state my conclusions, with
their evidences.

6. 4th, The time of vibration in a vertical plane depends, to a considerable
extent, on the temperature of the needle.

AND ITS TEMPERATURE CORRECTION. 71

The following short series, taken at random from a great number of observa-
tions, at once prove the truth of this conclusion. From a comparison of a few of
the observations, it was found that an increase of 1° Fahr. was equivalent to an
increase of 0.076 in the time of vibration.

The last column for each series gives the times corrected by this quantity to
50° Fahr. That the correction obtained is only approximate, will, together with
errors of observation, account for much of the discrepancies in the corrected
quantities.

TABLE III.

Observations for the Time of Vibration of the Balance Needle in the Vertical
Plane at different Temperatures.

é Time of . Time of
Time of Observed time | Temperature BnolVabeation Time of posersed time Temperature BHOnURbration
Observation. | yitration. Magnet Bee eae ObReRERiton Vibration. Wiseatcts per a
Geb May 8 ) s s ° 8
Jan. 2 22 8.91 31.4 10.32 (eal 35.4 8.32
3 2 9.48 40.0 10.24 8.38 46.3 8.66
3°44 9.80 43.5 10.29 7.42 35.9 8.49
3) 9%) 9.96 45.2 10.32 6.72 27.0 8.47
3 22 9.74 41.4 10.39 6.42 21.5 8.59
7.64 38.7 8.50
April 30 22 8.97 6.93 32.6 8.25
May 1 8 SHCULEg 64.1 8.70 7.49 38.9 8.33
1 22 9.28 56.3 8.80
2 21 9.13 55.2 8.73 9 22 7.43 41.0 8.11
3.8 9.81 64.4 8.72 12 23 6.87 31.6 8.27
3 23 9.02 53.6 8.75 13 22 7.08 31.9 8.46
16 22 6.82 31.2 8.25
23 23 8.07 45.6 8.40
April 1 11 8.10 8.20

It should be remarked, that the series for January 1844 is not comparable
with the following series, as an adjustment of the instrument occurred in that
month; neither, indeed, are the other series comparable with each other, from the
circumstances given in Table I.

7. To take one of the most marked cases from this table, it will be seen that
the observed times of vibration on January 23d and 31st 1845, differ nearly two
seconds, while the corrected times do not differ one-tenth of a second.

8. While an inequality in the expansion of some parts of the needle would
alter its sensibility by elevating the centre of gravity, it seems very doubtful
if there is any thing in the form of the needle which is at all likely to render
this supposition sufficient. An alteration in the position of the centre of motion
would produce a like effect; and as the position of the needle depends, to some
extent, on its temperature, it is necessary to shew whether position or tempera-
ture only is the cause of the differences in the times of vibration. Had the read-
ings for the position of the needle been given with Table IIT., it would have been
evident from these alone that the differences were not due to differences of posi_

Vly 4 MR BROUN ON THE BALANCE MAGNETOMETER,

tion. The following series of observations made during a magnetic disturbance,
will, however, prove it more distinctly.
TaBLeE IV.

Observations for the Time of Vibration of the Balance Needle in a Vertical
Plane, the position of rest varying.

Gottingen Balance Magnetometer. Time of one Vibration.
eoiaaerncuns
i Reading. Thermometer. Observed. Sgt dati
4 ey al Mic. Div. s s
April 15 22 52 —148 47.7 8.84 9.01
17 150 +101 52.5 9.21 9.02
2 20 + 4 53.2 9.46 9.22
315 + 25 54.2 9.46 9.14
3 25 + 23 54.7 9.36 9.00
5 15 — 18 56.4 9.62 9.13
7 45 — 10 56.3 9.66 9.18
8 45 — 90 56.0 9.68 9.22
10 20 —190 55.2 9.42 9.02
10 30 —176 55.2 9.62 9.22
13 40 —310 54.3 9.23 8.90
13 50 — 293 54.3 9.35 9.02
22 15 —185 61.1 9.28 9.20
22 25 —185 Ole 9.38 9.30
18 22 30 —134 50.3 9.01 8.99

The positive and negative signs indicate that the north pole of the needle
was below or above the horizontal. It would have required a change of 50° Fahr.
to have produced alone a difference of 400 micrometer divisions. Such a change
of temperature, according to j 6, would have been equivalent to a change of

3.8 in the time of vibration. The observed times differ only a few tenths, and the
times corrected for temperature agree within the limit of the errors of observa-
tion.*

9. It results from these facts, that the time of vibration in a vertical plane
cannot be used at present in the reduction of the observations, as theory takes
no account of them. The theoretical corrections for differences of arc or the varia-
tion of the moment of inertia due to temperature would, in the examples given,
be inappreciable.

10. I shall now consider —, the temperature correction for the position of

the needle.
The method which has been adopted for its determination is as follows :—
The magnet, whose temperature correction is to be obtained, is placed at right
angles to a magnet freely suspended, which is thus deflected by an angle uw from
the magnetic meridian. If m be the magnetic moment of the deflecting magnet,

* The time of vibration throughout the year varies from other causes. The law which regulates
these variations I have not yet determined.

AND ITS TEMPERATURE CORRECTION. 73

and X the horizontal component of the earth’s magnetic force, the equation of
equilibrium is
[OnE D5 a ee Penn oe C1)
The variations of u are observed, while the deflecting magnet has its tempe-
rature altered 30° or 40° Fahr., by means of hot or cold water; by differentia-

ting equation (4) and dividing by it, these variations are connected with =" by the

equation.
Am

sy Cob uAu SMA ENS nt 8 otal Oe)
X and the magnetic declination being constant.

11. The chief objections to this method are the following :—

1st, The circumstances under which the magnet is placed are considerably
different from its usual condition. It is necessary to raise or lower the tempera-
ture 30° or 40° in water, within a few minutes, to obtain satisfactory results,
whereas the most rapid changes in the magnetometer-box will probably be under
2° in an hour. It seems doubtful to me whether it has been proved that the
changes of magnetic moment occur as rapidly as those of temperature in all cases.

2d, In the event of there being any other source of error due to temperature,
it is altogether omitted by this method.

3d, If the correction has not been determined before adjusting the instru-
ment, the series of observations is broken up by the necessity of removing the
needle.

12. As itis desirable that the observations of the balance magnetometer
should be made as valuable as possible, I shall proceed to consider how this may
be best done, as it is my opinion that they will be found ultimately capable of
giving diurnal and annual changes with considerable fidelity.

13. The observations of ae, the varying angle formed by the needle and the
horizontal, will at present obviously give comparative observations for the varia-
tions of vertical force, without reference to the value of the coefficient tan ¢, until
a good approximate value of the latter can be obtained, if the observations in
micrometer divisions can be corrected for temperature. In order to do this, it

would be necessary to convert the value of — obtained by deflection experiments
into micrometer divisions, if this value be g.

[2
Pata ea GC.)

qa tan 20
m

We cannot, however, use T, and therefore the method of deflections is, in this

way, insufficient; besides, if the alterations in the value of T from temperature

should be caused by changes in the position of the centre of gravity, this change
VOL. XVI. PART I. T

74 MR BROUN ON THE BALANCE MAGNETOMETER,

would probably not be altogether in the vertical, the portion resolvable to the ho-
rizontal would affect the position of the needle.

14. From these considerations I was induced, about two years ago, to endea-
vour to obtain the temperature correction from the usual daily observations of
the instrument. To most persons acquainted with the irregularities in the mag-
netical variations, from the changes of the magnetic intensity or its direction, this
might appear to some extent chimerical, and as at best only capable of giving a
rough approximation to, or verification of, the determinations by deflection. It
will, however, I think, be shewn, that a better coincidence of partial results, and
a better correction, may be obtained from this than from the usual method.

It will not be necessary to point out the methods which were at first tried;
I shall proceed at once to those which have been ultimately adopted.

15. Having selected a series of days during which the readings of the instru-
ment seem regular, and in which the changes of temperature from day to day
are considerable, rejecting any day of marked disturbance, the hourly or two-
hourly readings for the position of the needle and for its temperature are summed
for each day. Let us designate the sum of the micrometer readings for the first
day of the series y,. for the second day y,, and so on to Ys; the corresponding
sums of the thermometer readings being ¢,, ¢,, . . . . ¢,,;, the number of the days,
from the beginning to the end of the period, being 2 +1.

The most simple and probable hypothesis that can be formed, is, that the
mean vertical force increases or diminishes gradually throughout the period; let
the mean daily change be a.

If g be the temperature correction for 1° Fahr. in micrometer divisions, we
may form the following series of equations:

N=Hyt+atrh—-h)¢g Y=¥st+ A+(h-—&)G
Al = Yn+1 +nQ + (4 id +1) Yo = Yni2 af 2G (t, as nae (7.)

Yns2 = Yass + A + (nse — tags) g

There will be breaks in each series, as there are no sums for the Sundays. As
t, may be greater than ¢, and ¢,, the result of the comparison of y, with y; is not
equivalent to the comparison of y, with y, and y with y;.

From these equations the most probable values of a and g might be obtained
by the usual methods; but the labour which they demand is probably much be-
yond the greater accuracy to be attained. The following, it is conceived, will be
found sufficient. 7

First classing the equations in which t,> or ~¢,,,, and considering each
class separately.

AND ITS TEMPERATURE CORRECTION. 75

Placing the equations in the form

ER ee ra

age ike emer! git. so depen)
Naming the differences in which r=1, ay, and at, in which r= 2, ay, and
Aft, .... Ayn, At, Summing separately all the equations for a,, all those for
iS It will simplify the investigation, and be sufficiently accurate to

take for the divisor of ra, the mean of all the values of a ¢, naming this a h.
We obtain the following equations:

== a
EpATG to
ZA Yo _ a
Se: Ad (9.)
ZAYn _ n a
3 A.te oe A hy

If the difference of each equation be taken with every one following it, ano-
ther series of equations of the following form will be produced.
LAY, 2ZAYpsr ra
She TA yas Smaaeaiihd ost
Summing the equations thus formed, we obtain an equation which may be
put as follows:

ZAM TAY, ZA Yo ZA Yn-1 n+1.n.n—1 a
aril —_ 4 2), at A eA de big = ry, Be : Z
i a ae) 3(348 Tea 6 A ty ae
Summing equations (9.)
deme A ( n+1 a
es AE sO D8

16. The following example, from the Makerstoun observations, will shew the
method found most convenient in practice for the summations.

A period of 52 days, from June 1 till July 22. 1843, having been selected
as nearly free from disturbances, and containing considerable changes of tem-
perature, the 3d and 7th June being rejected on account of disturbances; the
sums for each day of the micrometer and thermometer readings were entered
into columns titled sy and s¢. Each sum was then compared with all the
sums up to the 27th day after, and the differences entered into columns titled

AY, At, AY Ah; . ~~ AY, Aty. Those differences, the fewest in number,
in which ¢,= t,,, were marked out, the others summed for each column, and
ss aA DAY:
the divisions —“ |. . AAS Hoy
Paee Se performed.

From these and equations (11), (12),

2A (y) te te ee Baty
2 a (t) = 8:88; . 7 = 0.0875; @ = 2.05; g = 7.882 Mie. div.

76 MR BROUN ON THE BALANCE MAGNETOMETER,

The differences, when ¢,>t,,, were too irregular and too few, on some days,
to give a good value of a.

17. It is very rare that periods of such magnitude can be found free from
considerable irregularities. In general, however, it is conceived that smaller pe-
riods will give equally good results, and by a shorter method.

If we consider the equations

_ Yo — Yprr ra

=e ae a EY
Se dy te ds 5p eee ae
Ynrr— 4 ra
q — Yor Yp de : fy tees
lpr 3 b lor = tp

it is obvious, that if the temperatures rise and fall considerably throughout the
period selected, and no attention be paid to the sign of ¢,—¢,,, in the summations
of the differences, the coefficients of a will nearly destroy each other.

18. In the following cases the sums for each day have been compared with the
sums of all the days after it in the period selected. By this means irregularities
in the force upon any day have their effect on the final result to a considerable
extent destroyed, as it is probable that the results will be as much too great in
some cases, as they are too small in others.

The whole differences have been summed without regard to days, and the
signs of ¢,—¢,,, have been disregarded.

The equation is, therefore, simply

ZA(y) _
LA)

TABLE V.

Determinations of the Temperature Correction for the Balance Magnetometer,
from comparisons of the Daily Observations at different periods.

Time of
PERIOD. ZA (t) ZA (y) q aa REMARKS.
: 50° Fahr.
1843. ° Mice. Div. Mic. Div. s
Jan. 16—21. 525.3 4315.3 8.21 9.20 In 1843, there were 9 daily observations
23—28. 817.7 5723.5 6.99 9.20 made at two-hourly intervals, from
Jan. 30—Feb. 4. 576.0 4151.5 7.21 9.02 5 aM. till 9 P.M.
Feb. 6—11. 609.9 4080.6 6.69 9.25 Sept. 2, the needle was remoyed, in or-
June 1—30. 14320.4 |114646.9 8.006 9.28 der to determine its temperature cor-
Sept. 6-—16. 1083.7 8730.4 8.04 9.92 rection by the method of deflections.
1844.
May 9—24. 8415.4 66621.7 7.93 8.38 In 1844, there were observations at
Aug. 3—Sept. 6. 21696.9 | 171460.5 7.902 8.06 every hour of the day.
For the series in The needle was removed between Sep-
1843. \ BOS LSI ee 7.898 tember and February for temperature
For all, 48045.3 | 379730.4 7.903 correction deflections.

From the above table it would appear that neither the removal of the needle
and readjustment, nor the alteration of the time of vibration, has affected the

temperature correction.

AND ITS TEMPERATURE CORRECTION. 77

The first values of g shew that periods of a week are insufficient for very
accurate determinations.

The mean for 1843 is almost identical with that for 1844.

19. The differences for three periods were also summed without regard to
days, but paying attention to the sign of ¢—Z,,,. The following table contains
the results.

TABLE VI.

Determination of the Temperature Correction for the Balance Magnetometer,
regard being paid to the signs of the differences of temperature.

Preceding temperatures greater than the Preceding temperatures less than the
succeeding. succeeding.
Value of

PERIOD.
sa@ | 2am | ¢ | 24@| 24a | ¢ 2

1843. 2 Mic. Div. Mic. Div. e Mie. Div. Mie. Div. Mic. Diy.
June 1—30. 3350.2 29096.6 8.68 10970.2 85550.3 7.80 8.24

1844.
May 9—24. 5404.3 37559.9 6.95 3011.1 29061.8 | 9.65 8.30
Aug. 3—Sept. 6. 4726.1 | 34249.3 6.68 | 16970.8 | 137211.2 | 8.09 7.39
For all the periods, | 13480.6 | 100905.8 7.49 30952.1 | 251823.3 | 8.14 7.813

The result No. 16, and the mean results in Tables V. and VI., for the whole
periods, agree very closely. As the value of one micrometer division, in parts of
the whole vertical force, is about 0.00013, the greatest difference of the three
final results, 7.83, 7.90, and 7.81, is 0.0000012.

The final results, from five days’ observations, by the method of deflections,
were .000085, .000077, .000079, .000062, .000073, differing 0.000023.

The results, from the comparison of daily observations, in parts of the whole
vertical force, will be about .000134, the time of vibration being about 9 seconds;
if 11 seconds were adopted, the result would be .000095 ; in either case consider-
ably more than the result obtained by deflections.

20. The satisfactory determination of q for the Balance magnetometer, led me
to determine the correction for the Bifilar magnetometer by the same method.

Besides the variation of the magnetic moment, temperature also affects
the length and interval of the suspending silver wires; it probably also affects
their elasticity.

The determination of the correction from the daily observations, at once sums
up all the effects of temperature. When the suspending threads are of silk, these
sources of error are avoided; but I conceive that much graver errors are intro-
duced, due chiefly to varying humidity affecting the torsion of the thread.

I shall give simply the results of the comparisons of the daily observations for
the Bifilar magnetometer.

VOL. XVI. PART I. U

78 MR BROUN ON THE BALANCE MAGNETOMETER.

TABLE VII.

Determination of the Temperature Correction for the Bifilar Magnetometer, from
comparisons of the Daily Observations.

Value of q
Preceding temperatures greater than Preceding temperatures less than Mean of the | ;
the succeeding. the succeeding. two values of ofthe aanae
q A(t
PERIOD. nee ( )

TA(t) | ZA (x) ZA SA(x) | q ine | “ee

1844. - Se. Div. - Se. Div. | Se. Div.
May 9—24. 5384.9 13066.8 , 2359.9 4033.0 | 1.71 | 0.000270 | 0.000289
May 29—June 28. | 11938.2 24597.2 : 26719.2 45966.3 | 1.72 | 0.000246 | 0.000238
July 17—30. 1843.1 3004.0 : 4637.8 8470.4 | 1.83 | 0.000225 | 0.000230
Sept. 2—25. 27322.6 58684.3 : 622.1 1260.8 | 2.03 | 0.000259 | 0.000255
Nov. 26—Dec. 13 | 17855.4 36791.6 J 2143.7 3104.5 | 1.45 | 0.000229 | 0.000259

| —_—

For all the periods, | 64294.2 |131143.9 | 2. 36482.7 62835.0 | 1.72 | 0.000244

When it is considered that the daily range of the Bifilar readings, in parts of
the whole horizontal force, is to the daily range of the Balance readings, in parts
of the whole vertical force, as 7 or 8 to 1, it will be seen that the results for the
Bifilar magnetometer are equal to those for the Balance. It should also be remem-
bered that the results for May and July are from short periods.

The results obtained by deflections on two days were 0.000291 and 0.000298,
the partial results agreeing very well.

Taking into account the expansion of the wires, the total temperature cor-
rection is 0.000304.

It will be observed, in this case, that the results by deflections are greater
than those from a comparison of the daily observations.

MAKERSTOUN, April 18. 1845.

X.—On Wollaston’s Argument from the Limitation of the Atmosphere, as to the
Finite Divisibility of Matter. By George Wuson, M.D., Lecturer on
Chemistry.

[Read 21st April 1845.]

In the year 1822, Dr Woxttaston published a remarkable paper “ on the finite
extent of the atmosphere.”* Its object is to establish, by observations on the
motions of certain of the heavenly bodies, that our atmosphere does not extend
into free space, and to deduce from this limitation in its extent, the conclusion,
that the air necessarily consists of particles “no longer divisible by repulsion of
their parts ;” 7. ¢. of true atoms. From this there is the further inference, that,
“ since the law of definite proportions discovered by chemists, is the same for all
kinds of matter, whether solid or fluid, or elastic, if it can be ascertained that any
one body consists of particles no longer divisible, we then can scarcely doubt that all
other bodies are similarly constituted.’ In other words, the existence of a limit to
the earth’s atmosphere is declared to supply a demonstration of the finite divisibility
of matter.

In pursuing this argument, WotuasTon first discusses the question, What is
the probable height to which the earth’s atmosphere extends? And after stating,
that, from the known laws of the elasticity of the atmosphere, we should infer that
it extends to the height of 40 miles, with properties yet unimpaired by extreme
rarefaction, he proceeds to say, “ Beyond this limit we are left to conjectures
founded on the supposed divisibility of matter ; and if this be infinite, so also must
be the extent of our atmosphere. But if air consist of any ultimate particles no
longer divisible, then must expansion of the medium composed of them cease at
that distance where the force of gravity downwards, upon a single particle, is.
equal to the resistance arising from the repulsive force of the medium.” Wo.ias-
TON, it will be observed, takes for granted two things. sty, He assumes that the
law which is known to connect the density of the air with the compressing force,
near the surface of the earth, prevails, without change, to the limit of the atmo-
sphere. 2dly, He identifies the divisibility of the mass with that of its component
parts or molecules. If the molecule be infinitely divisible, the mass will be so
also, and vice versa ; so that if the divisibility (finite or infinite) of either be as-
certained, that of the other will thereby be ascertained also. Now, the atmo-
sphere is not merely divisible, but, consisting like other gases of mutually repulsive
particles, contains within itself a power of division. We have only, therefore, to

* Philosophical Transactions, 1822, p. 89.

80 DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER.

permit this self-dividing force to come into play, and the result, according to
Wo ttaston, will shew whether the mass undergoing spontaneous division is infi-
nitely divisible or not. This experiment we cannot try; but it has long ago been
performed for us by the hand of Nature. Our atmosphere has divided itself to
the utmost limit which its susceptibility of division permitted, and has thereby
tested or ascertained that divisibility for us. Either that is infinite, in which
case, the atmosphere must have spread into space, and portions of it will be found
surrounding the different heavenly bodies, varying in amount according to their
respective dimensions, temperatures and the like. Or it is finite, and the air has
found a limit at no great distance from the earth; for the particles of which it
consists, although free, so far as their mutual repulsiveness is concerned, to re-
cede from each other, are not equally free to recede from the earth, to which the
force of gravitation binds them. They must come to rest accordingly at the point
where the attraction of gravitation is equal in amount, while it is opposite in di-
rection to the force of repulsion among them; so that they are balanced in equi-
librio between them. Now it appears on making the necessary observations,
that probably the Sun, and certainly that Jupiter, is devoid of an atmosphere of
the same nature as our own. Therefore, concludes WoLLASTON, our atmosphere is
of finite extent, and consists of particles only finitely divisible. And as the air
cannot be supposed to be peculiar in this respect, the conclusion is immediately
extended to every other substance, and all matter is inferred to consist of finitely
divisible particles, or bond jide atoms.

It cannot surprise us that so remarkable a paper as WoLLaAsTon’s should have
excited the greatest attention among men of science. If the argument pursued
in it were just, the vexed question of the finite or infinite divisibility of matter,
which, for some thousand years, physics and metaphysics had alike sought in vain
to decide either way, had all the while been answered for us. Every-attempt to-
wards the solution of that problem by experiment had failed, not perhaps, be-
cause ultimate atomic particles had not been arrived at, by the dividing forces
our command, (for this length the inquiry never reached); but because,
long before the divisibility of a body could be supposed to be exhausted, the
products of its division had become invisible to us, and we had no test by which
to tell when the atoms of a substance had been attained to. Both of these diffi-
culties, according to WoLLasTon, were taken out of the way, by the mode in which
Nature made the experiment. A dividing force co-ordinate with the divisibility
on which it took effect—finite, if it were finite, infinite, if it were infinite—was
brought into play. The result of this division, moreover, could be ascertained,
could, in truth, literally be seen; for it did not take place in a vacuum, but in a
space containing bodies, each of which would infallibly indicate the extension of a
self-dividing medium at least to itself; and as that, if it were infinitely divisible,
must reach to them all in its progress towards infinite division, should it certainly

DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER. 81

appear that it had not extended to any one, still more, if not to several, it would
suffice to prove that it was not infinitely divisible. In short, our atmosphere
being the self-dividing mass, and all the stars standing between it and infinity,
the absence of an atmosphere like the earth’s, from any one of them, shews that
that it can only be finitely divided ; and the decision in the negative of the ques-
tion of infinite divisibility should have dated from the discovery of the telescope,
and GaALILEo’s earliest observation of the eclipses of Jupiter’s moons.

My object in the following remarks, is to shew that WoLLASTON s identification
of the divisibility of the molecule, with the observed division of the mass of which
it is a part, is altogether unwarrantable ; that he takes for granted the very thing
to be proved; and that his whole discussion leaves the question of the finite or
infinite divisibility of matter exactly where it found it. Before doing so, however,
I am anxious to refer very briefly to the criticisms already offered on this part of
the paper under discussion.

The opinions hitherto expressed as to WoLLASTon’s argument may be arranged,
I believe, under four heads. 1sé, A few natural philosophers have entirely assented
to the truth of the conclusion contained in it. Among these was DauBENy,* who
has lately, however, withdrawn his assent ;+ and it is still advocated by Dumas,
who, whilst he objects to WoLLasTon’s arguments, on other grounds which will be
referred to immediately, appears to consider the conclusion of the latter unavoid-
able, if his premises are granted him.t

2d, A greater number, including Farapay,§ Granam,|| and TurNEeR,{ have
implied, by the terms of commendation in which they have referred to it, that at
least they detected no fallacy in the argument.

3d, It has been objected to by Dumas (following out the views of Porsson),
on the ground that the low temperature which is known to prevail in the upper

* Introduction to the Atomic Theory, 1831, pp. 103-5.

¢ Supplement to Introduction, &c., 1840, p. 11.

+ Dumas’ assent was entirely negative, but was strongly manifested, and is the more remarkable,
that he has directed special attention to the phenomena presented by those gases which combine without
undergoing diminution of their volume, as irreconcilable with the idea of the chemical equivalents of
these bodies being represented by single atoms, such as Datron assumed, (Lecons sur la Philosophie
Chimique, p. 263). Had this view been carried out and applied to the atmosphere, it would have
struck at the root of WoLLasron’s whole train of reasoning, and would have obviated the necessity of
appeal to the questionable views of Poisson, as to the cause of the limitation of the atmosphere. As
WHEWELL’s discussion of WoLuLaston’s speculations, which was specially intended to meet the argument
of Dumas, has appeared since the latter published his views, it may have led to some modification of
his opinion. But that distinguished chemist has not had occasion, so far as I am aware, to refer again
to the subject in public; so that, in the meanwhile, I include him among the acknowledged supporters
of the intrinsic validity of WoLLAsToN’s views.

§ On the existence of a limit to vaporisation, Phil. Trans., 1826, p. 492.

|| Elements of Chemistry, pp. 68 and 273.

{| Elements of Chemistry, 7th edition, p. 207.

VOL. XVI. PART I. x

_

82 DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER.

regions of the atmosphere, may be such at its boundary as to destroy the elasticity
of the air, and even to liquefy or solidify it.* DAvuBENny,+ Kane,{ and others,
have replied to this, that the temperature of planetary space, according to FourtEr,
ScHWANBERG, and others, is much higher than that to which air has been exposed
in experiments with solid carbonic acid and ether, without destroying its
elasticity. Dumas, in anticipation of such objections, has declared, that we are
not to consider the temperature which a thermometer would exhibit if placed in
the upper strata of the atmosphere, as necessarily identical with that of the air
around it.§ By which statement he means to enforce, if I understand him aright,
that non-elastic (liquid or solid ?) air may, like other diathermanous bodies, trans-
mit heat without being thereby raised in temperature itself, so that the outer
shell of air may be colder than the layers within it, or space beyond it. In allu-
sion to such a view, Professor JAmEes Forzes has pointed out the difficulty of un-
derstanding “ how it is possible that the higher strata of the atmosphere can
remain permanently colder than the strata beneath and the sky above them,
without admitting a paradox of the same kind with a mechanical perpetual
motion.’ ||

In reference to Dumas’ mode of disposing of WoLLAsTon’s argument, I would
only further observe, that natural philosophers are not at one as to the tempera-
ture, either of planetary space or of the upper strata of the atmosphere; so that
it is impossible at present to say what is the exact value of the objection I have
been discussing.

4th, Finally, several physicists have denied the justness of WoLLAsTon’s con-
clusion, on the ground of its intrinsic invalidity. Among these are Professor JAMES
Forses{ and Dr Kanr,** who have not, however, so far as I am aware, stated
in what way they dispose of the argument. Professor WHEWELL is likewise an
objector, and dissents from Wot.aston’s inference, on the plea that the latter was
not at liberty to assume that the law which connects the density of the air with
the compressing force at the upper boundary of the atmosphere, is identical with
that which is known to prevail near the earth. His own words are—“< We know
nothing of the law which connects the density with the compressing force in air
so extremely rare, as we must suppose it to be near the boundary of the atmo-
sphere. Now there are possible laws of dependence of the density upon the com-

* Lecons, &ce., p. 239.

} Supplement to the Introduction to the Atomic Theory, p. 11.
¢ Elements of Chemistry, p. 441.

§ Legons, &c., p. 241.

|| Report of British Association, 1841, p. 79.

Op. cit p- a 77%

** Elements of Chemistry, pp. 15 and 358.

DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER. 83

pressing force, such that the atmosphere would terminate in virtue of the law
without any assumption of atoms. This may be proved by mathematical reason-
ing. If we suppose the density of air to be as the square root of the compressing
force, it will follow that, at the very limits of the atmosphere, the strata of equal
thickness may observe in their densities such a law of proportion as is expressed
by the numbers 7, 5,3, 1. For the compressing force on each being as the whole
weight beyond it, will be for the four highest strata 16, 9, 4, and 1, of which the
square roots are as 4, 3, 2, 1, or as 8, 6, 4,2; and, though these numbers are not
exactly as the densities 7, 5, 3, 1, those who are a little acquainted with mathe-
matical reasoning will see that the difference arises from taking so small a number
of strata. If we were to make the strata indefinitely thin, as to avoid error we
ought to do, the coincidence would be exact; and thus, according to this law, the
series of strata terminates as we ascend, without any consideration of atoms.’’*

My object in the succeeding argument is to shew, that, although the law
which Wotiaston assumed to prevail in the higher regions of the atmosphere
were in operation, it would not justify the conclusion which he supposed it to
warrant. The discussion which follows differs from WHEWELL’s mode of disposing
of the subject, in conceding to WoLLASTON his own law; and from that of Poisson
and Dumas, in permitting him to take for granted as high a temperature as he
pleases, provided only the atmosphere have reached a limit.

On a little consideration of WoLLAstTon’s reasoning, it will appear, that all
that he succeeded at the utmost in establishing was, that the atmosphere consists
of a finite number of repelling molecules. He seems to have conceived that this
was sufficient, and that no one would dispute his subsequent assumption, that
these repelling molecules were ultimate particles or true atoms.

But such an assumption is, on a twofold ground, inadmissible. The more im-
portant chemical components of our atmosphere are, water-vapour, carbonic acid,
oxygen, and nitrogen. Let us set aside for the time, as we are at liberty to do,
the influence of the low temperature of the upper regions of the air in condensing
the water, and perhaps also the carbonic acid ; and suppose our atmosphere, with
a temperature at its boundary sufficient to retain all its constituents as elastic
fluids, to find a limit, in virtue of the prevalence of Wot.aston’s law. Each gas
would cease to expand for the same reason, and present a row of bounding mole-
cules, which were prevented from falling towards the earth by the repulsion of
the particles between it and them, and from receding from the earth by their own
weight. But the molecules of water-vapour, and carbonic acid, brought in this
way to a stand, would certainly not be ultimate particles or indivisible atoms.
The molecule of water, on the simplest view of its constitution, namely, that the
chemical equivalent corresponds to a single atom, would consist of at least two

_* Philosophy of the Inductive Sciences, vol. i., p. 420, and Atheneum, 1839, pp. 724-7.

84. DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER.

atoms, one of hydrogen and one of oxygen, with a centre of repulsion common to
both. The molecule of carbonic acid, for similar reasons, would consist of three
atoms, one of carbon and two of oxygen. And who shall assure us that oxygen
and nitrogen are not compounds with binary chemical molecules like those of
water, or ternary ones like those of carbonic acid? It is true that the chemist
names these gases simple substances. But the simplicity he attributes to them
is only, as he is careful to define, guoad analysis ; and the physicist is not at liberty
to convert this negative and relative simplicity into an absolute one, and make
deductions therefrom, as WoLLaston has done. If we argue from analogy, in re-
ference to this point, we should infer that oxygen and nitrogen are compounds;
for we know a much greater number of gases in which the molecule is a group of
chemically distinct atoms, than we do of elastic fluids, where, on the most favour-
able view, it can be supposed to be asingle one. But it is not necessary to pursue
any argument of this kind; nor is the objector called upon to shew that oxygen
and nitrogen are chemical compounds. It is sufficient for his purpose to decline
assent to Wortasron’s conclusion till he, or those who agree with him, supply
proof that the molecules of oxygen and of nitrogen are chemically simple. The
onus probandi clearly lies, not with the denier but with the asserter, of a positive
proposition like the one before us.

In so far, then, as WOLLASTON assumed the chemical simplicity of two of the
gases of the atmosphere, he employed an argumentum ad ignorantiam. He was
guilty also of a petitio precip. For even, if it could be shewn, that oxygen and
nitrogen are chemically homogeneous, and do not, on that account, admit of com-
parison as to the constitution of their gaseous molecule with water and carbonic
acid, it would not warrant the conclusion, that that molecule was an atom. Does
it follow as a necessary inference, that because a body is simple, its gaseous repel-
ling molecule must consist of but one atom? The answer is assuredly in the ne-
gative. The molecule might, on the other hand, be made up of a pair of atoms,
like a binary star, with a centre of repulsion common to the two; or of 10, or of 100,
or 1000 atoms (if such bodies there be), grouped together into a compound whole.
We have no means whatever, in truth, of estimating what the complexity of the
molecule may be. Without insisting at greater length on this, it is at least mani-
fest, that we are not even at liberty to identify the combining chemical mole-
cule with the repelling gaseous one, much less to identify either with the ulti-
mate atom. Yet, unless WoLLASTON was at liberty to do so, his argument was
useless towards settling the question of the divisibility of matter. ‘To prove that
the atmosphere consisted of finite molecules, was only to reach the threshold of
the difficulty : for each molecule supplied as good a text whereon to dispute the
question of infinite divisibility, as the whole atmosphere out of which it was taken,
The point which most of all demanded proof, namely, that the molecule was an
atom, was the very one which he took for granted.

DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER. 85

Wo.L.astTov, in truth, erred, in assuming that the self-dividing power pre-
sent in the atmosphere was able to divide, to the uttermost, the divisible mass
subjected to its action; in taking for granted that the divisibility was co-ordinate
with the actual division, so that the latter was the exact index and measure of
the amount of the former. ‘The fallacy of his argument will at once appear if the
latter be thrown into a syllogistic form. It will then run thus :—

1. An atmosphere consisting of an infinite number of mutually repulsive par-
ticles, must be infinitely extended.

2. But our atmosphere is not infinitely extended.

3. Therefore our atmosphere does not consist of an infinite number of particles.
Whereas it should have been.

Therefore our atmosphere does not consist of an infinite number of mutually
repulsive particles.

The premises fully warrant the conclusion that our atmosphere does not
consist of an infinite number of mutually repelling particles, but throw no light
on the question, whether or not it may contain an infinite number of mutually in-
different, or mutually attractive ones.

WOoOLLASTON’S argument, then, supplies no decision of the question of the divisi-
bility ofmatter. That problem still presents the same twofold aspect of difficulty
which it has ever exhibited. If we affirm that matter is infinitely divisible, we
assert the apparent contradiction, that a finite whole contains an infinite number
of parts. If, pressed by this difficulty, we seek to prove that the parts are as
finite as the whole they make up, we fail in our attempt. We can never exhibit
the finite factors of our finite whole; and the so-called atom always proves as
divisible as the mass out of which it was extracted. Finity and infinity must both
be believed in; but here, as in other departments of knowledge, we cannot re-
concile them.

It seems surprising that fallacies so palpable as those we have been discuss-
ing, should not have been detected long ago by the able philosophers who have
noticed WoLLASTON’s argument. It is especially singular, that Dumas, who holds
that, in the combination of gases, a division of the chemical equivalent frequently
occurs (so that he represents the latter as expressed physically by a group of
many molecules), should not have applied his views, as he could so easily have
done, to its full refutation.

As it is, I trust that the discussion I have laid before the Society will not
prove unacceptable to its members. WHEWELL’s reasoning cannot be appreciated
by those who are ignorant of mathematics; and the views of Porsson and Dumas,
even should they be fully established, leave unconsidered the question of the in-
trinsic validity of WoLLasTon’s conclusions. I am not without hopes, accordingly,
that a demonstration of a fallacy in the argument in question, on purely physical
grounds, which can be understood by every one, and which, so far as I am aware,

VOL. XVI. PART I. Y

86 DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER.

has not been offered already, will be of service in removing doubtful knowledge.
In particular, it may save beginners from seeking for a demonstration where none
is to be found, and from blaming themselves because they cannot acquiesce in a
conclusion, the truth of which great names have appeared to warrant. I would,
observe, however, that, although I have employed the words molecule and atom in
the preceding discussion, it has been for the sake of simplicity and convenience,
and to meet WoLLASTON on his own ground. Ido not wish to be understood as
offering any opinion as to the ultimate constitution of matter, except in so far
as I deny the success of the only attempt which has been made in modern times,
to establish, by direct observation, the existence of indivisible atoms.

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XI.—On the Sums of the Digits of Numbers. By the Right Reverend Bisnor TERROT.

[Read 2d December 1845. ]

Tue general properties of numbers, considered without reference to the nota-
tion in which they are expressed, have been very fully investigated by several of
the most distinguished mathematicians. Little attention, however, has been paid
to the particular properties resulting from the principle of the modern notation,
which is the expression of every number in a series, a + bn + cn’, &c. where a, b,c,
are the digits, and n the local value or root of the notation. Having been led to
examine some of these results, and to account for them, I am now desirous of
laying them before the Society. I do not flatter myself that they possess any
great practical importance; but as I have reason to believe that they are new, I
_ trust the Society will not think them entirely unworthy of their attention.

If, then, we look at the multiplication table, and examine, in the first place,
the multiples of seven, we find them—

7,14, 21, 28, 35, 42, 49, 56, 63, 70, 77, &e.
Sums 7, 5, d,s, 6,04, 2° 9) “7, 5, tee

If we also take, as above, the ultimate sums of the digits of these multiples, that
is to say, the sum of the digits of each if that sum be a single digit, or, if not, the
sum of the sum of those digits, till in each case we arrive at a single digit, it ap-
pears, that, for the first nine places, these sums range through all the digits of our
notation, without any recurrence, and then commence over again in the same
sequence as before.

On looking at the adjacent line of the multiples of stz, we find the case very
different. The multiples are,

6, 12, 18, 24, 30, 86, 42, 48, 54, 60, 66, 72, '&e.

and their sums 6, 3, 9, 6, 3, 9, 6, 3, 9, &e. &e.

Here only three digits occur in the series of sums, and these repeated over and
over in the same order. Farther, we may observe, that what is true of seven is
true of five, eight, and all numbers which are prime to nine; and that what is
observed of the multiples of six, occurs also in the multiples of three, the only
other digit which has a common divisor with nine.

I began with accounting for these facts; and, proceeding from simple mul-
tiples to the consideration of other integer series, such as the series of squares,
cubes, &c., the successive powers of a given root, the polygonal and figurate num-
bers, I found that wherever there is a fixed law of relation between the succes-

VOL. XVI. PART II. Z

88 BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS.

sive numbers, there is also a definite sequence and recurrence in the sums of the
digits which express them ; and the results of these inquiries, with the requisite
demonstrations, I will now, as briefly as possible, lay before the Society.

Prop. I.

If m and n are prime to one another, am cannot equal bn, unless a and b be
equimultiples of and m respectively. For, if am=bn, = = But by hyp. - is a

- fraction in its lowest terms, therefore b=pm, and a=pn.

Prop. II.
If N=P .»—1+r,,. being the local value of the notation, and P . n—1 being the
greatest multiple of x—1, which is less than N; then ,,, is the ultimate sum of the
digits of N.
Let N=a+bn+cn?+dn’, &e.

NT bake Ledeen 2 wee eee.) a eee
n—1 Fat

N=pn—l+atb+te, &e. = pn—1+r,

Again, let r,=¢.n—1+r,, where r, is the sum of the digits of r,, or the
second sum of the digits of N.

Then N=p+gn—1+7,. Let this operation be continued till 7,, becomes a
single digit, we have N=P . n—1+7,, where 7,, is the ultimate sum of the digits
of N.

Ex. In our notation »=10, and »—1=9.

Let N=567434=63068 x 9+2

here Ist sum =29
2d do. =11
3d do. = 2

Cor. If + =nx—1, then N is a multiple of n—1. And, conversely, if N be a
multiple of n—1, r,=n—1.

Prop. III.

If a be a number prime to x—T; and p, g be two numbers, whose difference is
neither x—1, nor a multiple of x—1, then pa and ga cannot have the same ulti-
mate sum.

If possible let pa=mn—1+r and ga=m,n—1+r, and let s=g—p, then
sa=g a—pa=m,—m+n—1; but by hyp. a is prime to x—I, and s is neither »—1,
nor a multiple of it; therefore, by Prop. I. sa cannot equal m,—mxn—1, and
therefore pa and ga cannot have same ultimate sum.

BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS. 89

Prop. IV.

If a have a common divisor with n—1 as v, then paand ga will have the same
n—1

ultimate sum if g—p= 3

Let pa=P.n—1+,r, therefore ga=pa+"—* a=P.n—1 ere tole. But v isa
divisor of a; therefore ga=P.n—1+7r+6n—1=P,n»—147, that is, pa and qa have
same ultimate sum.

Prop. V.

If a be a divisor of »—1, or nat =o, then paand qa will have the same ul-
timate sum if g—p=v.
Let pa=P.n—1+r, ga=pat+va=Pn—1l+r+n—1=(P4+1)nm—1+4r.

Prop. VI.
If P=Q+R. The ultimate sum of P = ultimate sum of (sum Q + sum R).

Let Q=mn—1+r, R=m,.n—1 +7,
P=Q+R=mim,n—l+r+r,

But 7 and 7, being single digits, their aggregate is either a single digit, or
n—1+ asingle digit. In the former case, the ultimate sum of P = sum of Q +
sum of R. In the latter, sum of P = sum (sum of Q + sum of R).

Cor. If R be a multiple of n—1, or r,=n—1, sum of P = sum of Q.

Prop. VII.

From these propositions it follows, that in any arithmetical series, whose
common difference is prime to n—1, the ultimate sum of any term (the pt) = the
ultimate sum of (p+g¢n—1)™: but that no two terms at any other interval can
have the same ultimate sum; and hence, that all the terms from the p® to the
(p+n—1)" range, as to their ultimate sums, through all the digits of the scale.
For if the p™ term =sn2—1+7, then the (p+g¢n—1)" term =s.n—1+rign—1.6
= st+ogn—1 +P

Again, let p™ term=a, g=a+g—p.; but by Prop. I., since 6 is now taken
prime to n—1, and g—p is neither n—1, nor a multiple of it, the g™ term must
have an ultimate sum different from the p*.

Ex. 1. The successive multiples of any number prime to 9, are an arithmetic
series whose common difference is that number. Thus, the multiples of 5 are,

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, Ke.
Sums 1G, 2, tnd, s, 4,9, 5, ¥, 6 de.

90 BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS.

Ex. 2. But let the number whose multiples are taken have a common divisor
with 9 (n—1) as 6.
The series is 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
Sums ~. .. (6,°3, 9; 6) a, Us me:
Where the sums recur at every third term, because 6 and 9 have a common

divisor 3, and = that is “— —* <3. (Prop. V.)

Ex. 3. The recurrence of the sums, according to Prop. V., may be more
strikingly illustrated, if we use a notation whose root is 13, and, consequently,
n—1=12. If we express the successive multiples of 6 in this notation, we must
adopt three additional characters for 10,11, 12. Let these be 1,,1,,1,. The
successive multiples in this notation are,

6,1,, 15, 11,, 24, 21,, 33, 39, 42, 48, &e.
Sums . . 6,1,, 6, 1, 6, 1,, &c, where we see the sums recur after

12
two terms, because »—1=12, and Goze

Prop. VIII.

If x be even, and »—1 consecutive terms of an arithmetic series be taken, the
ultimate sum of the digits of their aggregate is x—1. But if n be odd, the ulti-

: Loeset —I.n—2 : .
mate sum will be x—1, or sum ( on) according as b, the common differ-

ence, is even or odd.
n— =

For aggregate of n—1 terms of arithmetic series = (2a+n—2.6) .

2Gh =e tek ee. > If n be even sees is integer, whether } be even or odd.
Therefore the latter term is a multiple of »—1, and, consequently, the whole
a being a se of x—1, has n—1 for its ultimate sum (Prop. II., Cor.)

ED:

is integer only when 2 is even.

PRoPOEX.

If we assume as bases two numbers whose sum is s.x—1, and take a series
of the successive powers of each, then of the two series expressing the sums of
digits of successive powers, the even terms are identical, while the odd terms are
complemental, that is, their sum is x—1.

Let m+m,=s.n—1, m,=s.n—1—m
m' = (sm—1) — p(s.n—1pP_ : Wes emt as p is even or
Ait Here every term et the ee isa multiple of s.a—1

Therefore if p be even, sum of m,= sum of m’.

But if p be odd, sum of mn, = sum of (Q..—1)—sum of m =n—1— sum of m.

BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS. 91

To illustrate this and some of the succeeding propositions, I shall here
introduce a table of successive powers of digits prime to 9, with their ultimate
sums.

Powers 2, 4, 8, 16, 32, 64, 128, &c.

Base 2. Sums recur after 6 terms.
Sums” 2 4 Se erts Ly 2) s&e
Powers 4, 16, 64, 256, 1024, &e.

Base 4 Sums recur after 3 terms.
PS ho Ay oe wikis) SCs

Base 5 | POWeS 5 25. 125, 625, 8125, 15625, 78125, &e. | Sums recur after
Sms oO 7, 8, 40 °.2; 1, 5, &e. 6 terms.

Powers 7, 49, 343, 2401, 16807, &c.

Base 7
sums 7, 4, 1, 7% 4, &e.

Sums recur after 3 terms.

Powers 8, 64, 512, 4096, &c.

Base 8
Spams 8° 1, 8, “ih Ge.

| sums recur after 2 terms.

‘In this table, we may observe that in every case the sum of the digits recurs,
but at different intervals. Next, if we take two complementary bases, as 5 and 4,
_we find in the lines expressing the sums, that the first terms are respectively
4 and 5, the 2d terms 7 and 7, the 3d 1 and 8, and so on; as was proved gene-
rally in the last proposition. Lastly, we may observe that the digits 3, 6, 9, that
is n—1, and the digits having a common divisor with n—1, never occur among the
sums. It remains, then, for us to point out the reason of this last mentioned
fact, and to discover the principle which fixes the period of recurrence.

Prop. X.

Every power of a number prime to n—1, must have the sum of its digits also
prime to x—1.

Let m, which is prime to n—1, be reduced to its prime factors, or let
m=a.b.c, &¢. |

Then m” = (a’.t.c? &e.) Here m” has no possible divisors except a, 6, ¢, &c.,
and by hyp. none of these are divisors of n—1, therefore m” is prime to »—1.

Now let m” =gn—1+,r. Here gn=1 contains all the divisors of n—1. If,
therefore, 7 contains any of those divisors g#—1 +7, or m” contains such divi-

VOL. XVI. PART II. 2A

92 BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS.

sors; but m” has been proved prime to x—1; therefore r contains no divisor of
n—1, or is prime to it.

Prop. XI.

To determine the recurrence of ultimate sums in the series m, m?, m3, &c.,
m being any single digit. }

If we can determine what term will have 1 for its ultimate sum, the problem
is solved. For if m’ = pm—1+1, m’** = p’'n—1+™, or has same sum as first term,
m'** —»’n—1+m?, and so on, or sums recur after g terms.

Every number (m) is of the form 3p or 3p +1.

1. If m be of form 3p, every power of m after the first is a multiple of 9,
and consequently the sum of every power =9.

2. If m be of form 3p+1,

mi = 39M 4.9.3 pan clout ae +l * Sp +93pt1.

In this expansion, every term is divisible by 9, except the two last, or
m'=9s+3pq+l.

Consequently m? will have 1 for its ultimate sum, if 3q = a multiple of 9;
but since (m being one of the digits) p cannot =3, or a multiple of 3, g must. If,
then, g=3, 3p q=9p, and the sum 1 will recur at every third term.

3. If m=3p—1, m'=3p" — gp" . , . . =(8pq—1), the sign being —
if g be even, + if ¢ be odd. .

a. Let g be even. m’=9s—3pq+1; and this, as before, will give the ulti-
mate sum 1, if 3 pq be a multiple of 9, or pg =a multiple of 3. If p be prime
to 3, then g must be an even multiple of 3, as 6, 12, &c., or the ultimate sum 1
recurs at every 6 terms. But if p be 3, or a multiple of 3, the sum will recur at
every second term, for in that case g may be any even number.

B. If g be odd, m’=9s+3pq—1, but by hyp. m?=97r+1, .. r—s.9=3pq—2, or
3pq—2 is a multiple of 3, which is absurd. Therefore the sum 1 can never
recur at an odd power, when 2 is of the form 3 p—1.

If, now, we refer to the table given in Prop. IX., we see that of the bases

- there employed, 4 and 7 are of the form 3 p+1, and in them the sum 1 recurs at

every third term. 2, 5, and 8 are of the form 3p—1. In 2 and 5, p is prime to

three, and therefore the sum 1 occurs at 6th term. In 8, p=3, and therefore the
sum 1 recurs at every even term.

Cor. Hence, if m be not a multiple of 3, 7. e. if it be prime to 9, m* has 1 for

its ultimate sum, for 1 must occur at 2d, 3d, or 6th term, and 6 is a multiple of

2 and 3; therefore in any case the 6th power must have 1 for its ultimate sum.

BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS. 93

Hence m*=97r+1 or 97; the former when m is prime to 9, the latter when it has
a common divisor with it. This is a form not given by Bartow.

Prop. XII.

In the series of m* powers of successive integers, beginning from 1, the ulti-

mate sums recur after »—1 terms.

If m be odd, the ultimate sums of any two terms, whose roots together equal
n—I, are either together equal n—1, or are each n—1.

If m be even, the ultimate sums of such complemental terms are identical.

After what has been proved, the demonstration of these is so easy that it is
unnecessary to give it.

Ex. Series of 2d powers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121.

Ultimate sums ES lh Ol A Qu id.
Series of 5th powers 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 9°, 10°.
Ultimate sums eam on ei Dir pls 2. 9, 4, See OH tT

Here, in the ultimate sums of the squares, we have Ist and 8th, 2d and 7th, &c.
identical. In the ultimate sums of 5th powers, the Ist + 8th = 9, 2d + 7th = 9,
and so on.

It is worthy of notice, though rather out of place, that if, in the series of
5th powers, instead of taking the sums, we take the difference between the sums
of the odd and even digits, the difference will in every case be 1. This property
is proved generally by Bartow, in his Theory of Numbers, p. 172, in this form

m—1

that 2 7 , where misa prime number, is of the form am=+ 1.
Ex. To illustrate this, and the property of sixth powers mentioned in the
XIth Prop., we shall take the 5th and 6th powers of 5 and 8.

5'— 3125 therefore d,=(5+1)— (34 2)—1.

5°= 15625 therefore S,=19, S,=10, S,=1.

8= 32768 therefore d,=(8+7+3)—(6+2)=10, d,=1.
8°= 262144 therefore s,=19, S,=10, S,=1*

Cor. From the property above demonstrated of the sixth powers of numbers
prime to 9, it follows, that for every such base the seventh power has its ultimate
sum equal to the base ; that is, that e7=m.9+a. For a=p.9+1,.. a’ =pa9-+a.

Ex. 5'= 78125, S,=23, S,=5.

87 = 2097152, Ss, = 265) 1S, = 8.
* In these equations, d,, d,, &c., express the Ist, 2d, &c., differences between the sums of the
odd and even digits; S,, S,, &c., express the Ist, 2d, &c., sums of all the digits.

94 BISHOP TERROT ON THE SUMS'OF THE DIGITS OF NUMBERS.

Prop. XIII.—Of Polygonal Numbers.

In any series of polygonal numbers, » the root of notation being even, the
sum of the digits of the (s+—1)™ term = sum of s‘* term.

m— 2.8? —m—A4.s

9 , where m is

For every polygonal number is of the form P=

the number of the order, and s that of the term.
For s substitute s+n—1,

pata +A HG+n=D)

_

m—4.s m—2.(2sn—1+n—1\")—m—4.n—1
2

5 pee pecs Rae
But 7 being even, the fractional expression is integer, whether m be even or odd.
Therefore P and P’ have same ultimate sum. (Prop. VI. Cor.)

If n be odd, the fractional expression is integer only when m is even.

The same inference might at once be drawn from the consideration, that the
s* term of any order of polygonals is the sum of s terms of an arithmetical series.

Prop. XIV.
If, as in our notation, m be even, the s®, (s+yp.n—1)™ and (p.2—1—s+1)™ terms
of a triangular series have all the same ultimate sum.
In this case, m=8, and s™ term = sst1

2sp oo 1+P 5-7 a Here the co-efficient

Therefore, (s+p.n—1)® =
of n—1 is integer, whether p be odd or even: and therefore sum of (s+p.n—1)®

term = sum of s™.
pn—1—s+1).(pn—1—s)
2

Again, (pn—1—s+1)™ term =

ieee ee tate
and as the coefficient of n—1 is again integer, whether p be odd or even. Sum of
(pn—1—s+1)*= sum of s™. .
Ex. The triangular numbers are,— ’
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, &e.
Sums, Le’ oe OS aie Oy os A eos eeseeo.. iece:

BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS. 95

Here we observe that the Ist, 7th, and 10th, have the same sum; so also
have 2d, 6th, and 11th, and so on.

But the same series expressed in the tredecimal notation, and continued to
13 terms, is ;

1, 3, 6, 1,, 12, 18, 22, 21,, 36, 43, 51, 60, 70
Sums, 1, 35 6, Le 3, 9, 4, Le 9, ac 6, 6, 7

Here the 13th term has a sum, 7, different from the first.
But if we take p=2, n»—1=12, and s=11,
then pa—1—s+1=24—12=12; therefore 11th and 12th have same sum.
If s=10, 26—11=13, therefore 10th and 13th have same sum, and so on.
Note.—In the decimal series it may be observed, that not only the Ist, 7th,
and 10th terms have one for their ultimate sum, but, also the 4th, 13th, &c.

This happens, because in the decimal scale, fee

ae
but the “= * " term =— = ="? nate? Us and, consequently, its ultimate
sum is 1.
Prop. XV.
If the general term of any series be az"+ba"—14ee"—*? . . . . JC; then

evidently, if x+n2—1 be substituted for 2, the result will be the original term + a
multiple of »—1. Or, as in all the preceding forms, the same ultimate sum will
recur after »—1 terms.
If the general term be quadratic = az?+b2+c.
Let «,=y—z, then az*=ay?—2ary+ax?

oa by—bz
Os c
Therefore ax +ba,+c=ax2+b2+ c—2ayt+2batay+by

=ax?+bat+c+ayt+bxy—2e.

Now, let y be assumed such, that ay+=p.—1, then the 2 and a," terms
will have same ultimate sum.

Ex. Let 22 +382+1 be the general term. Substitute for x successively 0, 1, 2,
&c., we have the series,

1, 5, TU, 195 29, 41, 55,71, 89, 109, &e.
Ultimate Sums, bh DO ee be Se Bod ke:

Here a=1,5=3. If, therefore, y+8=9, or y=6, the two terms in which the

VOL. XVI. PART II. 2B

96 BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS.

numbers substituted for x are together equal to siz, will have the same ulti-
mate sum. Thus, in the above series, the Ist and 7th terms, in which O and 6
are respectively substituted for 2, have the same sum; so also the 2d and 6th, in
which 1 and 5 are substituted, and so on.

Prop. XVI.

In the series whose general term is mm+1 .. .. m+r—1,ifm+n—1 be
substituted for m, the ultimate sum of digits will remain as before.
If to each factor we add a, the term becomes

atmxatm+1xatmt2 . . . atmt+r—1
=ar+par—+g.av2 . . . . +mm+tilm+2 .. . . m+r—i1,
where a is a factor of every term except the last. Let a=n—1 then term
m+n—lm+n, &c. =mm+l1, &e. +sn—1, whose ultimate sum = that of
mm+1.m+2, &e.
Taking the same general term, if m+m,=n—r, m1=n—1—m+r-—1.

Therefore m,.m,+1.m,+2 . . . m+r—1l=n—1-m+r—1
xn—l—m+r—2
m GC:
xn—1l—m
In this product, n—1 will enter as a factor into every term except the last,
which is m.m+1 . . . m+r—1 with the sign + according asr is even or odd.

If be even, the m** and m‘ terms will have the same ultimate sum; but
if 7 be odd, the sums will be complemental.

All the terms from the n—r* to the n—1" must have x—1 for their sum; be-
cause x—1 must manifestly be a factor in each of them.

Ex. Let r=2. Series is 1.2, 2.3, &e.

=2, 6, 12, 20, 30, 42, 56, 72, 90, 110
Sums are, 2,.6,.3,. 2) 3, 6.2) 99) 2, ce
Let 7=3, or series 1.2.3, 2.3.4, &e.
=6, 24, 60, 120, 210, 336, 504, 720, 990

Sums, 6, 6,6; 18, 7 “8, 3 eas 19; de:

In the Ist example, 7 being even =2, m+m,=10—2=8;
therefore the Ist and 7th, 2d and 6th sums ought to be identical.

In the 2d, 7 being odd =3, m+m,=10—3=7 ;
therefore the Ist and 6th, 2d and 5th, &c. sums are complemental.

Prov. X VIII.—Series of Figurate Numbers.

mm +1 mm+1.m+2
J : iF th
1.2 i 33 &c., where each term is the m

* If the series be m,

a

BISHOP TERROT ON THE SUMS OF THE DIGITS OF NUMBERS. 97

term of the Ist, 2d, 8d, &c., order of figurates, the whole may be reduced to a
common denominator, and represented thus :—

of which the numerators follow the law of the series treated in the last pro-
position. If, therefore, in the series of figurates, the successive sums be taken,
and each multiplied by 1.2.3 .. . m—1, the products will form a series recur-
ring after »—1 terms.
bag + ee &c.

—4410+204+35 +56 +844 120 +165 + 220 +286 +3644 455
Soret 2 8 2, 3. 3 8 4 7%, 4 5,
Multiplying by 1 . 2. 3=6, the sums of products of sums become

6, Grromeso5 9, 0, 9,6, |,6, 6, 3.

By Aix

Prop. XIX.—Of the Ultimate Diference of Digits.

It is a well known property of digits, that the remainder, when any number
is divided by the root of the scale employed +1, is equal to the ultimate remain-
der of the even digits subtracted from the odd ; or, using a notation similar to that
we have before employed, that N=p.n+1+d,. As, however, d, must always be
+, if at any step the sum of the even digits be greater than that of the odd, »+1,
or such a multiple of »+1 as will make it the greater, must be added to the latter.

From this fundamental proposition, a series of propositions analogous to the
preceding may be deduced, relating, not to the sums, but to the differences of the
digits. The demonstrations are so similar to those already given, that I shall
merely illustrate the matter by examining the succession of differences in the
series treated in Prop. XV:

The general term was a2?+62+c.

Let w# become z+p.x+1, the term becomes

ax2?+2Q2aprn+l+ap%n+12+b2+bpnt1+c=ar?+bat+ct+gnt+l.

Hence the remainder, after dividing by +1, will be the same in both cases,
or the ultimate difference will recur after »+1 terms.

Next, let +2, =y, then

a4 +6%,+c=23 +boet+cet+ayt+by—2Qz-.

Assume ay+6=n+1, then the two terms will have the same ultimate differ-
ence.

Ex. Take as before for the general term z2+32+1,
here a=1, 6=3, n+1=11, therefore y +3=11, or y=8.

98 BISHOP TERROT ON THE SUM OF THE DIGITS OF NUMBERS.

If, therefore, the sum of the two numbers substituted for 2 in the expression
a°+32+1, be 8, the differences in the two cases will be identical.
Substituting successively 0, 1, 2, &c., we have the series
ey 3! 2 3 4 5 6 7 8 9 10 11 12
1, 5, 11, 19, 29, 41, 55, 71, 89, 109, 131, 155, 181, &e.
Differences/"1, 5, 40°98)" 7s; 0; bf Tey)? x0, \'o1, 5, &e.,
where we see, 1s¢, that the differences recur after 11 terms; 2d, that if 0 and 8,
1 and 7, 2 and 6, &c., be substituted for a, the differences are identical.

EDINBURGH, December 2. 1845.

( 99 )

XII.— Results of the Makerstoun Observations, No. I. On the relation of the Varia-
tions of the Horizontal Intensity of the Earth's Magnetism to the Solar and
Lunar Periods. With Two Plates. By J. A. Broun, Hsq. Communicated
by Sir T. M. BrisBane, Bart.

(Read January 5. 1846.)

1. Tue following communication is intended to be the first ofa series, in which
I propose to consider the results of observations made at Makerstoun, near Kelso,
Roxburghshire, in the Observatory of the President of this Society. These ob-
servations, and the tabular results, will be found ultimately in the volumes of
Makerstoun Observations, constituting volumes of the Society’s Transactions.

2. It has been found convenient to separate the observations of the varying in-
tensity of the earth’s magnetism into two parts, namely, its resolved components
in the horizontal and vertical planes. I shall treat at present of the variations
of the horizontal component. These variations are observed by means of the
bifilar magnetometer, an instrument devised by M. Gauss, and modified by Dr
Luoyp, described in the Introduction to the Makerstoun Observations for 1842.
It consists simply of a magnetic bar, suspended by two silver wires, the latter
being twisted out of a vertical plane, the magnet is forced from the magnetic me- |
ridian; the variations of its position afterwards are due to two causes, namely,
variations of the horizontal component of the earth’s magnetic force, or of the
moment of free magnetism of the bar; the former are due to changes of the total
force or of its dip, the ordinary variations of the latter are due to temperature;
and it is, accordingly, a point of much importance to determine the correction for
temperature with accuracy, in order that the simple effect of varying intensity
may be obtained. I have pointed out, in a paper read before this Society last
session, the imperfections of the method usually adopted for the determination of
this correction, and the method which has been adopted for the correction of the
Makerstoun Observations. I shall afterwards exhibit an example of the very dif-
ferent results to be deduced, after correcting observations by the two methods (11).

3. The horizontal force varies throughout the solar day, having, in that period,
two maxima andtwo minima. The hours of the principal maximum and minimum
were first pointed out by M. Hansrren, but I am not aware of the first determina-
tions of the secondary points. Inthe years 1844 and 1845, observations were made
at Makerstoun every hour excepting on Sundays. (See Curve, No. 1, Plate III.)
From the means of the whole observations for the year 1844, the principal mini-
mum occurs about 20” past 10 a.m. (Makerstoun mean solar time is used through-
_ out), or exactly when the sun is on the magnetic meridian of Makerstoun; the
force then increases rapidly till between 3 and 4 p.m., when there is a slight in-
flexion; again it increases with its previous rapidity till about 5} p.m., when the

VOL. XVI. PART II. 20

100 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

maximum is attained. It now commences to decrease slowly till 8 p.m., more
rapidly from 8 till 9, causing another inflexion in the curve, slowly again till
2» 20™ a.m., when there is @ minimum; the force then increases slightly till
5» 30™ or 40" when @ maximum occurs, after which it diminishes rapidly till
10° 20" a.m., the period of the minimum. These hours differ somewhat from
the periods obtained at other observatories ; and while some part of these differ-
ences may be due to errors of temperature correction, I do not think that such .
errors will altogether account for them, but that the accurate periods of maxima
and minima will be found to differ at different places. At Toronto in Canada,
for example, the maximum occurred a little after 4 p.m. in 1842; and as the
mean temperature of the magnet at the succeeding observation hour differs but
little from that at 4", the period cannot be affected by temperature. Some
observatories shew the maximum as late as 7 p.m. It does not, however, seem
improbable, that the periods of maxima and minima should differ at differ-
ent places, when it is known that these periods vary at the same place in the
course of the year; at Makerstoun, in 1844, the afternoon maximum occurred as
early as 3" 10™ in December and January, and as late as 6" 50" in June; the
minimum at 10° 20™ a.m. in the winter months, and at 9" 40™ a.m. in June; the a.m.
maximum occurs at 6" 40™ in December, and about 5" in the summer months,
while the earliest minimum occurs nearer midnight in winter than in summer.
In this way the periods of the principal maximum and minimum approach to
each other, and to noon in winter, and remove from each other, and from noon in
summer. (See Curve, No. 1.) The reverse to some extent takes place with regard
to the periods of the secondary maximum and minimum, which remove from each
other in winter, and approach each other in swmmer, till in June the maximum
and minimum seem to destroy each other.

The morning maximum is greater than the afternoon one in December ;—in
November, January, and February, they differ but little from each other ; and in
December, January, and February, the two minima are nearly equal.

4. The inflexions noted in the mean curve about 3 p.m. and 9 pP.M., become
minima in the winter months, so that there are then three or four maxima and
minima; the smaller ones nearly compensate each other in the mean of the winter
months, as they occur at different hours in each month.* I shall consider the cause
of these secondary afternoon maxima and minima on another occasion. With
regard to the 2 A.M. minimum and 6 s.M. maximum, these seem nearly to vanish
in the summer months. In the means for the months of June and July they can-
not be detected, excepting that the intensity decreases more rapidly after 6 a.m.
than before it; it should not be concluded on this account that this maximum and
minimum do not exist. Having projected the hourly observations made in each
day of June and July, I have not found one day in ten on which the secondary maxi-

* November, December, and January, have been taken as the three winter months.

Y,
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URINAIL [PERIOD

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102 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

the monthly means, as deduced from the observations of horizontal force made at
Toronto in 1842, at the following hours:—First, the hours corresponding to the
Makerstoun hours; this could not be done exactly, as the observations were
made at Toronto every two hours only, and for each of two of the Makerstoun
hours, the mean of two of the Toronto hours had to be taken; thus, one of the
observation hours at Makerstoun was 7 a.m.; the mean of the Toronto observations
at 6 and 8 a.m. was taken as equivalent (see the open curve, No. 3, Plate III.)
Second, from the whole two-hourly observations (see the open curve, No. 5, Plate
_ IV.) The monthly means from both these methods, gave the same, or nearly the
same, annual period as the Makerstoun observations.

10. [have since then verified this period by the monthly means of the observa-
tions made at Makerstoun in the years 1843, 1844, and 1845. I may first refer
to the Makerstoun and Toronto curves for 1842, which were exhibited to the
Physical Section of the British Association at Cambridge. (See Curves, No. 3,
Plate III.) From these I concluded that the horizontal force of the earth’s mag-
netism has an annual period, consisting of a maximum at each solstice, and a mi-
nimum at each equinox ; both curves present a curious inflexion in March, which
{ then considered due to some irregularity. The monthly means for the years
1842, 3, 4, and 5, have also been projected together ; (see Curves, No. 4, Plate III.)
the whole speak the same language, excepting that the inflexion in March 1842
does not occur in the other years, unless it may be said to do so in 1845. All the
curves shew a considerable secular change, the horizontal intensity increasing
throughout the whole period. Whether this be really an increase of the earth’s
horizontal intensity, or due to some instrumental cause, cannot be positively
stated; it is not at all likely to be due to an increase of the free magne-
tism of the bar, which is suspended at right angles to the magnetic meridian ; the
only apparent and possible cause is a stretch of the suspension wires; it must
be a matter for consideration, whether such a cause is likely to operate for such
a period, and to nearly an equal amount for two years. Whether a secular
change of horizontal intensity, or due to a stretch of the wires, it is evident that it
may be considered as a regular increase throughout the year. Upon this hypothesis
I have eliminated this increase from the monthly means of the last three years,
and projected the mean below the others. ‘This curve shews more strikingly the
annual period of solstitial maxima and equinoctial minima. The minima have
nearly the same value; the summer maximum is greater than the winter maxi-
mum, but so little, that an error of a thirtieth in the amount of the temperature
correction, would account for the difference. The annual range from the mean of
the three years is 0°000724, or about the mean diurnal range for the three
winter months.

11. M. HansTeEeEn concluded from his observations, that there was a maximum

of horizontal intensity in December, and a minimum in June. Colonel SaBinE con-

EARTH’S MAGNETISM TO THE SOLAR AND LUNAR PERIODS. 103

cludes from the Toronto observations for 1842 (corrected by the usual method), that
there is a maximum in June, and a minimum in December. I have projected
the monthly means of the Toronto observations as corrected by the usual method.
From these Colonel Saprne draws his conclusion. Under it I have projected the
temperature of the magnet in a broken line, and below both, the means from the
two-hourly observations, as corrected approximately by myself. (See Curves,
No. 5, Plate IV.) These will shew how much depends on the accuracy of the cor-
rection in arriving at sound conclusions. I conceive that the consistency of the
results at which I have arrived, independently of other considerations, will leave
little doubt as to which method of obtaining the corrections should be adopted.
12. It has been already mentioned (10), that the apparent secular change con-
sists of a considerable increase of horizontal intensity. Throughout the wholeperiod,
the rapidity of increase has been diminishing, and it is much less in 1845 than in
any of the previous years. Of all the puzzling problems in terrestrial magnetism,
that of connecting the secular change with some known or observed phenomenon
has been the most difficult; any fact, therefore, tending to this, will have interest.
One of the first questions which I proposed to myself, connected with it, was
whether all hours of the day were equally affected by the secular change? In order
to answer this more distinctly, the annual period was eliminated from the monthly
means, or, which is nearly the same thing, the mean of each month was reduced to
the straight line passing through January and December 1844.* I then found
that the mean horizontal force in the first six months of the year 1844, was almost
constant one hour after the period of the morning maximum, and also that it was
almost constant for the last six months, one hour before the period of the even-
ing maximum. When the diurnal curve for each month was projected, I found
the curves for the first six months to pass through a space of 3-4ths of a scale
division in the ordinate of 64 40" a.m., with the exception of the curve for Feb-
ruary, which is very irregular there. The curves for the last six months pass
through a space of 13 scale divisions, in the ordinate of 4° 40" p.m.; the increase
of horizontal force from January till December was 18 scale divisions. I next elimi-
nated all the larger disturbances from the monthly means of each hour, but this
neither affected the periods of the nodes, nor the values of the ordinates in which
they were contained. In this way, then, the horizontal force in its secular pro-
eress, seems to rest one foot during the first half of the year about an hour after

* The line should have been drawn through January 1844 and January 1845, but that there is an
irregularity in the progress of the horizontal force from December 1844 to January 1845, compared
with the previous years. I have, however, also reduced the means to the line passing through Janu-
ary 1844 and January 1845, and find the ordinate of the morning node slightly increased, but that
for the evening node diminished.

VOL. XVI. PART IL. 2D

104 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

the morning maximum, and extends the other forward at all other hours of the
day, making the greatest strides at the time of the afternoon maximum. During
the second half of the year, it rests the previously advancing foot about an hour
before the evening maximum, and brings the lagging foot forward at the other
hours, but with the greatest rapidity at the time of the principal minimum.

13. There is perhaps nothing more difficult in groping for the laws which regu-
late certain phenomena than the separation of the effects due to different causes ;
but it is quite obvious that, before we can arrive at any sound conclusion as to
simple laws, this must be done. In the determination of the diurnal period all
the observations at each hour for a calendar month or year are summed, and the
means taken; in these summations are included several irregularities named dis-
turbances ; if the disturbances occurred equally positive and negative at the same
hour, or were equally distributed over the twenty-four hours, a large enough series
of observations would serve to eliminate them ; neither of these suppositions seems
to hold, and accordingly, certain hours in some months are more affected by dis-
turbances than the same hour in other months, or than the other hours of the
same month; the diurnal curve, therefore, is complex. There are other causes,
as will be seen afterwards, which render it more so.

14. In the attempt to determine whether the horizontal intensity varies with the
moon’s declination, the days were numbered from the day of the moon’s greatest N.
declination, counting that day 0 till it returned to the greatest N. declination again ;
and, as 13 of the moon’s revolutions, with regard to node, are equivalent to 12
lunations, and nearly toa year, the 15 revolutions, with regard to declination, were
selected for summation; as, by this means, any effect due to varying phase, or to
annual period, would be eliminated. The mean intensity for each of the 13 days on
which the moon had its greatest N. declination were then summed together ; the
means for the 15 days numbered 1, in which the moon was moving south, and so
on. For the purpose of verifying the result thus obtained, similar summations
of the observations for 1845 were made; in this case, however, only 12 revolutions.
with respect to declination, were obtained, so that any effect of phase will not be
perfectly eliminated. No attempt has in either case been made to eliminate dis-
turbances. The results of these summations were projected, having previously
eliminated the effect of secular change. (See Curves, No. 6, Plate IV.) The
curve, from the observations of 1844, indicates a maximum about 2 days after
the moon has attained its greatest S. declination, and a maximum about a day
after it has attained its greatest N. declination—the maxima have nearly equal
values, so also have the minima. The branches ascending to and descending
from the period of greatest S. declination are greatest; so that the periods of mi-
nima are nearer, the greatest N. declination being about 5 days before and after it.
The curve deduced from the observations of 1845 shews the maxima nearly at

EARTH’S MAGNETISM TO THE SOLAR AND LUNAR PERIODS. 105

the same periods as in 1844; but the branch ascending to and descending from
the period of greatest N. declination is greatest, the periods of minima being
nearer the greatest S. declination, namely, about 5 days before it and after it.
The curve for 1845 is, however, more irregular after the 8. declination maximum
than in any part of the other curve. Besides the non-elimination of the effect
connected with varying phase and disturbance, there is another possible cause of
difference, namely, the varying distance of the moon; the period of perigee is
about two days before the greatest S. declination in 1844, and two days after it
in 1845. It should also be remembered that each point in these curves is a mean
of only 12 or 13 days; as for the minor irregularities in the positions of the
points, it is obvious that, as there are 27 days between the periods of the moon’s
greatest N. declination, if the full moon occurs on the day of greatest N. declina-
tion in one month, it will occur on the second day after the greatest N. declina-
tion on the next month, the fourth day on the next, and soon. It will be seen
afterwards that this will cause a slight irregularity. It is on this account that
I have projected the curves among the points, giving a preference to the mean
positions of each two points.

15. The similarity of the positions of maxima and minima in these curves, hav-
ing the moon’s declination for abscissee to the annual curve, or that having the
sun’s declination for abscissze, is at once evident; by taking the mean of the two
lunar curves, however, the cases will be identical, for then the moon’s perigee
will occur at the time of its greatest S. declination, and its apogee at the time of
the greatest N. declination; this is the case with us for the sun. The resulting
means have been projected below the other curves. By comparing the mean
curves of No. 4 and No. 6, it is at once obvious that the facts are the same for
both the sun and moon. I conceive, then, that I am justified in stating that the
same relation exists for the moon as for the sun between the variations of the
horizontal component of the earth’s magnetic intensity, and the variations of de-
clination and parallax.

16. We have, then, a law connected with two periods, namely, distance and
declination. To which does it belong, or does it belong to both? It will take a few
years’ observations to determine this for the moon: it may be determined for the
sun by observations for the annual period made in the Southern Hemisphere. Is
there a maximum at the greatest N. declination, and also at the greatest S. de-
clination ; or have changes of declination no effect? and are the maxima due to
the moon’s or sun’s distance solely? The supposition that at first sight seems
most probable is, that these variations are due to both; that a maximum occurs
at the time of perigee, a minimum at the apogee, a maximum at the greatest N.
declination, and a minimum at the greatest S. declination. It may easily be
shewn that two regular curves having these arguments, when superposed, would

196 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

produce two minima. Thus, if APA be the curve due to distance, NSN
that due to declination, the curve B PC, produced by the superposition of their
ordinates will have two minima, if the sum of the ordinates ab +a'b’ be less
than the sum DN+AB, and a” b”+a” b’” be less than EN+AC.

The fact, that in both the solar and lunar curves the maxima are nearly
equal, is against the supposition that both distance and declination are equally
concerned, as it seems rather improbable that the effect of increasing distance
should precisely counterbalance the effect of increasing N. declination. We have,
however, much more singular cases of compensation in the motions of the heavenly
bodies.

17. The range of the lunar declination curve for 1844 is 0:000455 ; for 1845,
0000390 ; and, for the mean of both years, 0:000380.

18. I have already mentioned (14), that, by taking 13 revolutions of the moon,
with respect to its declination, we eliminate any effect due to the varying phase of
the moon. Similarly, if we take 12 lunations, and sum the mean intensity for
the twelve days on which the moon was full, the twelve days on which it was one
day old, and so on, we eliminate the effect of varying declination, and also the
annual period very nearly. If, however, we may consider the intensity with
respect to N. declination similar to that with respect to S. declination, it is evi-
dent that 6 lunations will be sufficient to eliminate the effect of declination. (See
Curves, No. 7, Plate IV.) Ihave had the observations during the six summer
lunations for 1844 summed by themselves, and also those during the six winter
lunations; the mean intensities for both, for each day of the moon’s age, have been
projected, and also the mean for the year. All indicate a maximum of intensity
about two days after the new moon, and a minimum perhaps two days after the
full moon; the summer curve has an irregularity before full moon, and its range
is only half that for the winter months. The minor irregularities may be ac-
counted for in the same way as for the declination curve. The range for the

EARTH’S MAGNETISM TO THE SOLAR AND LUNAR PERIODS. 107

winter months is 0:001040. It appears to me, however, that it is exaggerated,
owing to the curious fact, that the chief negative disturbances in 1844 occurred
about the time of full moon.

19. It has not appeared to me necessary to verify this law by the result of ano-
ther year’s observations. Each of the winter months of 1844 shews the facts as
completely as the mean; in the summer months, the result is not so evident. It
would appear as if the effect of phase swallowed up the effect of declination in
the winter, while the reverse occurred in summer. I have projected the means
of the horizontal intensity for each day from January 4th till April 3d, 1844,
including three synodical periods. (See Curves, No. 8, Plate IV.) In each period
the curve shews the facts most completely; and the lunations in September, Oc-
tober, November, and December, shew them perhaps better. The periods of
greatest N. and S. declination, and of the syzygies, are indicated on the curves,
the open O being full moon. There are several curious facts, in connexion with
the observations projected, which I cannot enter fully into at present; I may
remark, however, the appearance of a weekly period. No observations being made

’ on Sundays, breaks occur in the curve, where the intensity for these days should

appear. A great disturbance spoils somewhat the form of the curve in March;
the point belonging to the 29th of March would occur about 14 inches below
the margin.

20. The law of the variation of the earth’s horizontal intensity with the moon’s
phase, is one productive of many speculations. There is an evident connexion of
the great diurnal variations of the horizontal intensity, with reference to the sun’s
hour angle; there is also a strongly marked connexion between the diurnal
range and the sun’s altitude ; and we have a certain connexion between the sun’s
declination and the annual period. Are these connected with the heating power
of the sun, its light, or its magnetism ? Sir Joun Herscuet has stated, that, as
the sun’s rays shine with their whole force on the moon’s surface for a fortnight,
unstopped by an atmosphere, the heat of the surface must be much more intense
than that of a tropical summer; while, after the next fortnight, the cold must be
more severe than that of a polar winter. M. Cournot, the French translator of
Sir Joun Herscue’s Treatise on Astronomy, opposes this opinion, and argues
that, as there is no atmosphere to prevent radiation, our knowledge of the laws
of radiant heat would lead to the conclusion, that the temperature of the
moon’s surface would differ little at the times of new and full moon.* Supposing
Sir Joon HEeRscHEL’s opinion accurate, if we could conceive the moon as a mag-
netic body acting by induction on the earth, then, according to our knowledge of
the effect of heat on magnetic bodies, its intensity would be greatest when it was
coldest, and least when warmest: the period of greatest cold we should expect

* Quoted by M. Francozur; Uranographie, p. 97.
VOL. XVI. PART II. 25

108 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

to be a day or two after the new moon, and of the greatest heat a day or two
after full moon, in the same way as our periods of greatest cold and heat are
after the winter and summer solstices. This seems to agree with the periods of
maximum and minimum horizontal intensity. If M. Cournor be right, or if Sir
Joun HerscHEL’s supposition be insufficient, then we must look to the solar ema-
nations reflected or radiated from the moon for the causes of the variations of the
earth’s magnetism, and to our atmosphere for a cause of the supposed retardation
of epoch.*

21. The connexion of lunar phase and horizontal intensity was first noticed
by me in July 1845. Iam not aware of any investigations on the relation of the
horizontal intensity to the lunar month, excepting a paper by M. Hanstesn, of
which I have lately merely seen the title, which refers to the connexion of the
horizontal intensity with the moon’s ascending node.

22. Having mentioned some time ago to Professor Forszs, that I was engaged
in examining the relation of the lunar periods to the variations of the earth’s
magnetism, I learned from him that M. Kreiiu of Prague had stated, in his
volume of observations for 1842, that the horizontal intensity was greater at the
moon’s passage of the inferior meridian, than at its passage of the superior meri-
dian. I know not whether M. Krerzy has verified his statement, or to what extent
his observations prove it.t I have now discussed the observations for 1844, with
reference to this period, and have verified my results by a similar discussion of
the observations for 1845. I shall, at present, merely state the leading facts, and
leave the details to another communication.

23. The observation at the hours on which the moon was on the meridian were
termed 0 hours, the observation the hour after one hour, and so up to 24; as the
moon takes about 25 hours to return to the meridian again. On some occasions
there were only 24 observations between the two passages; in these cases (few
in number) the hour of passage was reckoned as 24 hours, and also as 0 hours of
the next day. The summations for the hours were made for each month; I shall
only speak of the means for the whole year in this communication ; these means
have been projected. The large disturbances have been eliminated from the sum-
mations for 1844 and 1845. (See Curves, No. 9, Plate IV.) Any observation in
1844 which shewed a difference from the monthly mean, for the hour at which

* Tt is evident that the variations of horizontal intensity may be due either to changes of the
total intensity, or of its direction ; any reasoning, therefore, on these facts must be necessarily incom-
plete, until we are certain of the actual effect.

+ I have, since this was written, been favoured by Professor ForBEs with a copy of M. Krerz1’s
table for the horizontal force during the moon’s hour angle. It indicates a minimum of intensity
about two hours before the meridian passage, and maximum peaks at 12" and 15", giving the interpo-

lated period of maximum about 13 hours after the inferior meridian passage; the latter period agrees
completely with my own conclusion, the former differs about three hours from my result.

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EARTH’S MAGNETISM TO THE SOLAR AND LUNAR PERIODS. 109

it was made, of above twenty scale division (twelve times the resulting range of
horizontal force in the lunar hour angle curve), was rejected, and an interpolated
quantity substituted ; this elimination, however, was not found to affect the pe-
riods of maxima and minima; it reduced the range, and rendered the curve
somewhat more regular. In the observations for 1845, as a farther check on these
eliminations, a different test number was employed, namely, forty scale divisions,
or nearly twenty-five times the resulting range of the lunar hour angle curve.

24. In both years, he minimum occurs at 20%, or 5 before the meridian
passage; tie maximum at 14", or about 13" after the inferior passage: in both
years, @ minimum occurs at 8"; in 1844, @ maximum occurs before 4"; and in
1845, before 3". The maximum at 3°, for 1845, differs little from the maximum
at 14"; but the maximum at 4", in 1844, is considerably less than the maximum
at 14". The coincidences of these results may be considered extraordinary, when
it is known that the range in 1844 is only 0:000211, and in 1845 only 0-000213,
or less than the effect of one degree of Fahrenheit on the magnetism of the bifilar
bar.

25. Several questions spring from this result of the connexion of the intensity
with the moon’s hour angle. Does the range of the lunar hour angle curve vary with
the moon’s declination? If so, then we do not eliminate the lunar effect from
the solar day curve by a monthly or any other summation. Do the periods
of maxima and minima vary throughout the lunar month in the lunar hour angle
curve, as they do through the year in the solar day curve? These questions
I shall endeavour to examine at another opportunity.

MAxkERSTOUN, December 26, 1845,

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XIII.—On the Decomposition and Dispersion of Light within Solid and Fluid
Bodies. With a Plate. By Sir Davip Brewster, K.H., D.C.L., F.R.S., and
V.P.R.S. Edin. K AE

(Read 2d February 1846.) ;

Havy*, and other mineralogists, observed the two colours which are visible
in several varieties of fluor-spar. He regarded the two tints as complementary,
and explained them, as he did every other analogous phenomenon, by a reference
to the colours of thin plates. In describing a species of dichroism noticed by Dr
Proutt in thé purpurates of ammonia and potash, Sir Joun HeErscHEL ascribes
the green reflected light{ “to some peculiar conformation of the green surfaces
producing what may be best termed a superficial colour, or one analogous to the
colour of thin plates, and striated or dotted surfaces.” And he adds—‘“ A remark-
able example of such superficial colour, differing from the transmitted tints, is
met with in the green fluor of Alston Moor, which, on its surfaces, whether na-
tural or artificial, exhibits, in certain lights, a deep blue tint, not to be removed
by any polishing.”

Having, many years ago, found the same property in the Derbyshire fluor-
spars, I was led to study it with particular attention ; and, in 1838, I communicated
the results of my observations to the British Association at Newcastle.) In every
specimen in which the colour in question exists, I found it to arise from znternal,
and not from superficial reflexion. In an extensive series of experiments on the
absorption of light by the aqueous and alcoholic solutions of the colouring matter
of plants, I found this property of internal dispersion in thirty or forty of these
solutions. The most remarkable of these was the alcoholic solution of the colour-
ing matter of the leaves of the common laurel. At first its colour is a bright
green, afterwards changing into a fine olive colour; but in all its stages it dis-
perses light of a brilliant blood red colour, which forms a striking contrast with
the transmitted tint. After a long exposure to light, the transmitted tint almost
wholly disappears, while the dispersed light retains its red Golour.|| Another

* Traité de Mineralogie, tom. i., p. 512, 521.

t Philosophical Transactions, 1818, p. 424.

t Treatise on Light, art. 1076.

§ See Report of the Eighth Meeting, and Trans. of Sections, p. 10-12.

|| I shewed this experiment in 1836, at Lacock Abbey, to Mr Fox Tatzor, and several mem-
bers of the British Association. At the meeting of the British Association at Manchester, in 1842,
a friend handed to me, in the sectional meeting, a “solution of stramonium in ether,” which

VOL. XVI. PART II. 2F

112 SIR DAVID BREWSTER ON THE DECOMPOSITION AND DISPERSION OF LIGHT

very remarkable example of internal dispersion, pointed out to me by Mr Scuunckr,
is exhibited in an alkaline, or in an alcoholic solution of a resinous powder pro-
duced from orcine by contact with the oxygen of the air. Its colour by transmit-
ted light is reddish brown, and the light which it disperses is of an exceedingly
rich green colour.

Since these experiments were made, my attention has been called to two
interesting papers by Sir Joun HeRscHEL, in the last part of the Philosophical
Transactions; the one on a case of superficial colour presented by a homogeneous
liquid internally colourless, and the other on the epipolic (or superficial) dispersion of
light; and as these papers contain results incompatible with those which I had
previously published, I found it necessary to resume the investigation of the
subject.

The two papers now referred to are chiefly occupied with a description of the
phenomena of coloured dispersion, as exhibited in a diluted solution of sulphate of
quinine in weak sulphuric acid. Owing to the solution being nearly colourless by
transmitted light, the general phenomenon is very beautiful. The line of bright
blue light dispersed by the stratum of fluid immediately beneath the surface of
incidence, and about the 50th of an inch thick, appears to be confined to that stra-
tum, and it is in this respect only that the phenomenon differs from that which is
exhibited by fluor-spar and the vegetable solutions which I have mentioned.

1. On the Internal Dispersion of Fluor-Spar.

There are many varieties of fluor-spar in which no dispersion of the intro-
mitted light takes place. It does not exist in the yellow, red, and bright blue va-
rieties which I have examined. It occurs chiefly in the green fluor from Alston
Moor, and in several pink, and bluish-yellow varieties from Derbyshire. In order
to observe the phenomena of dispersion most distinctly, I transmit a condensed
beam of the sun’s light through the specimen, when partially covered with black
wax or black velvet. In some specimens, the intromitted beam is partially dis-
persed in a fine blue tint from every part of the solid which it traverses; but in
other specimens, which are composed of strata of different colours, parallel to the
faces of the cube, a very different and a very instructive phenomenon is displayed.
The intromitted beam A BC, Fig. 1, Plate V., is crossed with bands of dispersed
light of different colours, and of different intensities. In one case, a pink light was
dispersed from the stratum close to the surface of incidence; from the next stra-

dispersed a bright green light. I described the phenomenon to the meeting, and it is noticed in the
Transactions of the Sections, p. 14. Upon making the solution myself, I cannot obtain the same
tints, either from the stalk or the dried leaves of the plant. The solution of the leaves disperses a
brilliant red tint, like that mentioned in the text. The solution put into my hands must, therefore,
have been one of the seeds of stramonium, or of some other substance possessing internal dispersion
in a high degree.

WITHIN SOLID AND FLUID BODIES. 113

tum there was no dispersion at all; this was followed by a narrow stratum, which
dispersed a bright whitish light; then succeeded a stratum of non-dispersing fluor,
and alternately dispersing and non-dispersing strata, scattering the fine blue light
which has already been mentioned.

These results, which I have shewn to different persons, are incompatible
with those obtained by Sir Joun HerscueL with the very same variety of fluor-
spar. He regards the blue dispersed light as strictly an epipolic or superficial
tint,—so superficial, indeed, “that it might be referred to a peculiar texture
of the surface, the result of crystallization, were it not that it appears equally
on a surface artificially cut and polished.” * Were I to hazard a conjecture
respecting the cause of this difference in our results, | would ascribe it to the
different degrees of light in which the observations were made. While I used a
condensed beam of the sun’s light, Sir Joun HerscHEL seems to have employed
chiefly the ordinary light of day. In studying the phenomena in the solution of
quinine, he “ exposed it to strong day-light or sunshine;” and in another expe-
riment, which pre-eminently required a powerful illumination, he “ directed a
sunbeam downwards on the surface, by total reflection from the base of a prism,”
which was in reality inferior to the ordinary sun’s light. In the case of fluor-
spar, however, he states that the epipolic colour is seen in perfection when “ ex-
posed to daylight at a window.” In such a feeble light I could not have seen the
phenomena I have described, and it is owing chiefly to the intensity of the light
which I employed, that I have been enabled to place it beyond a doubt that the
blue light dispersed by fluor-spar is reflected from every part of the interior of
the crystal, and is not produced by any action either strictly or partially super-
ficial, or solely by any stratum near the surface.

Sir Joun HEeRscHEL mentions, that the green fluor-spar of Alston Moor is
the only solid in which he has observed an epipolic tint. It is the only mineral
in which I have found an internal dispersion, excepting, of course, the minerals
which exhibit the analogous phenomena of opalescence and chatoyance; but I have
found several glasses which possess it, one in particular of a yellow colour, which
disperses a brilliant green light, and another of a bright pink colour, which also dis-
perses a green light, and a third of an orange colour, which disperses rays of a
whitish green colour. In these cases, the glass has a decided colour of its own;
but I have found many specimens, both of colourless plate and colourless flint
glass, which disperse a beautiful green light.

2. On the Internal Dispersion of the Solution of Sulphate of Quinine.

Sir Joun Herscuent describes the epipolic dispersion of this solution as
“ occupying a very narrow parallelogram, having a breadth of about a 50th of

* Philosophical Transactions, 1845, p. 143.

114 SIR DAVID BREWSTER ON THE DECOMPOSITION AND DISPERSION OF LIGHT

an inch, of a vivid and nearly uniform blue colour over its whole breadth ;”* but
upon “ directing a sunbeam downwards on the surface, by total reflection from
the base of a prism, a feeble blue gleam was observed to extend downwards below
this vivid line to nearly half an inch from the surface, thus leaving it doubtful
whether some small amount of dispersion may not be effected in the interior of
the medium at appreciable depths.” By using condensed solar light, this doubt
is immediately removed, and the phenomenon ranks itself as one of internal dis-
persion, differing only in the law of its intensity from those which I have already
described. In the one the dispersible rays are thrown gradually, in the other
quickly, from the intromitted beam,—a phenomenon to a great extent identical
with what takes place in the analogous phenomena of absorption.

If the dispersing action of the solution were rigorously confined toa stratum
the fiftieth of an inch thick, it would have followed, of necessity, that “ an epi-
polized beam of light (meaning thereby, a beam which has been once transmitted
through a quiniferous solution, and undergone its dispersing action) is incapable of
further undergoing epipolic dispersion ;” hut as the dispersing action is not thus limited,
that conclusion must be incorrect. Sir JoHN HeErRscHeL, indeed, has deduced
this result from direct experiment with a plate of glass immersed vertically in a
quiniferous solution. In this case he could perceive no trace of colour either at
the ingress or egress of the epipolized beam which was incident upon the plate.
Sir Jonn does not mention the distance of the plate from the epipolising stratum.
If the distance was small, we are confident, from direct experiment, that the blue
tint would have been seen; but if the distance was considerable, then the beam,
incident upon the glass, must have been previously shorn of all its dispersible rays.

In examining the blue rays themselves, Sir Joun found that they consisted
of a “small per-centage of rays, extending over a great range of refrangibility.”
They formed, however, a continuous spectrum deprived of the less refrangible red,
nearly of the whole orange, and all the yellow; a rich and broad band of fine
ereen light, slightly fringed with red, passed into a copious indigo and violet
without the intermediate blue.

The comparatively feeble light of the dispersed blue rays renders it difficult
to ascertain their susceptibility of being a second time dispersed. Sir Joun HEr-
ScHEL could not obtain any indication of this susceptibility ; but we have no doubt
that with condensed light their second dispersion will be discovered: and we are
led to this opinion by the fact, that Sir Joun believed that the epipolic dispersion
takes place in all directions, and therefore expected to discover a second dispersion
under circumstances in which, according to my experiments, it could not be found.

* The best method of seeing this experiment, is to take the solution into the open air, where the
whole light of a blue sky can fall upon its surface. I have in this way seen the blue line perfectly
luminous at that stage of a December twilight when there was not light enough to read by. I con-
sider, therefore, the light of the sky as peculiarly susceptible of this species of dispersion.

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Trans RS Lidin! Late k p- Tia

‘ Fh: Schenck, Lith, Badin.

WITHIN SOLID AND FLUID BODIES. 115

Sir Joun has clearly shewn, that the light is dispersed outwards’as well as
laterally ; but as he was conversant only with the phenomena of a narrow blue
line, and had not seen the blue cone of rays dispersed from the cone of condensed
light, he could not be aware of the changes which take place in its colour while
the eye passes from the azimuth of 90° to that of 100°.

These changes are very decided, and will be understood from fig. 2 (Plate V.),
in which MN OP is a horizontal section of the vessel containing the solution ; R R’
a beam of solar light, incident upon an achromatic lens L L, and condensed into the
luminous cone AC B. Now, the blue colour produced by the first stratum, next to
the side A B, is exceedingly strong, and that which occupies the rest of the cone
ACB comparatively faint. When we view the bright blue stratum in the direction
NM, or in the azimuth of 90°, the tint is very brilliant, because the eye receives all
the blue rays dispersed by the whole length A B of thestratum ; whereas, when we
view it in the direction R’ C, in the azimuth of 0°, we only see the tint correspond-
ing to the thickness of the stratum. The tint, however, is, in reality, a maximum
in the azimuth of 0°, and gradually diminishes till it ceases in the azimuth of 180°,
or in the direction C R’.

If we now immerse in the fluid a plate of colourless glass, whose section is
DE, so as to receive the beam A BED, we shall find that there is no peculiar
dispersion, as Sir Joun HERscueEx observed, either at its surface of incidence or
emergence. Hence he concluded that the epipolised beam A BE D “ is incapable
of undergoing farther epipolic dispersion ;” and that having thus “ lost a property
which it originally possessed, it could not, therefore, be considered qualitatively as
the same light.”

Now, in using a condensed beam of light, as we have done, we find that the
whole cone A BC, even when two inches long, and with a December sun, disperses
the blue light, and the stratum behind the glass plate DE nearly as much as
the stratum before it. In fluor-spar, and in the other fluids I have mentioned,
this is still more strikingly the case,* and hence neither of the conclusions drawn
by Sir Joun HERscHEL are admissible.

The following appear to me to be the deductions which the experiments
actually authorize :—

1. A beam of light which has suffered dispersion by the action of a solid or
fluid body, (that is an epipolised beam) is capable of further undergoing epipolic

* In one of these experiments a piece of green fluor, from Alston Moor, when immersed in the
quiniferous solution, dispersed a fine violet blue light, at the distance of three-fourths of an inch from
its surface. In another experiment, a beam of light that had been dispersed in the solution of qui-
nine, again suffered dispersion at two inches distance from the surface of a piece of Derbyshire fluor.

A beam of light that has passed through the Esculine solution disperses blue light, but not co-
piously, when transmitted through the quinine solution; but the beam that has passed through qui-
nine is copiously dispersed when transmitted through Esculine.

VOL. XVI. PART II. 2G

116 SIR DAVID BREWSTER ON THE DECOMPOSITION AND DISPERSION OF LIGHT

dispersion, provided the thickness of the medium is not so great as to have dis-
persed all the dispersible rays.

2. When such a medium is thus rendered incapable of dispersing more light,
it is not because it has lost a property which it originally possessed, but because
it is deprived of all the dispersible rays which it contained.

It is no doubt an interesting fact, that a small number of differently coloured
rays, constituting blue light by their mixture, should possess this property of
being dispersed, while other rays of the same refrangibility are either less disper-
sible, or apparently indispersible, by the same medium ; but the fact will appear
less surprising and anomalous when we advert to certain phenomena of absorp-
tion in which the same property is displayed.

The difference between the absorption and the internal dispersion of light is
simply this. In the one case the portion of light withdrawn from the intromitted
beam is extinguished and invisible, and in the other dispersed and visible ; and we
may compare the two classes of phenomena by supposing that the light extin-
guished by absorption is rendered visible as if by dispersion. Now it is a remark-
able fact, that almost the whole of the blue light absorbed by the mineral called
native orpiment is extinguished during the passage of the light through the first
stratum, whose thickness is less than the fiftieth of an inch; and hence it is that
the thinnest slice of this substance has nearly as deep a yellow colour as the
thickest. Were the absorbed blue rays to become visible by dispersion, we should
actually see a more striking example of epipolism, or dispersion confined to the
first stratum, than in the quiniferous solution. Even the condensation of the
beam would not in this case give us a blue cone of light.

The analysis of the blue line indeed would indicate a difference between the
two phenomena. It would shew that the blue light was derived chiefly from the
violet, indigo, and blue spaces, and but partially from the green, yellow, orange, and
red, having appropriated the whole of the more refrangible rays, and but a very
small portion of the less refrangible ones; whereas the blue light from the quini-
ferous solution is derived almost in equal proportions from all the coloured spaces
excepting the least refrangible, red. The limitation of the rays capable of ab-
sorption, like the limitation of the dispersible rays in the quiniferous solution, is
shewn in the action of various bodies on the spectrum. Such bodies change the
colour of certain spaces in the spectrum, without continuing to absorb the resi-
dual rays; that is, when the absorbable rays are removed by a certain thickness
of the body, an additional thickness operates very feebly, as in the quiniferous so-
lution, in altering the colour of the residual beam.

I have pointed out these analogies between the phenomena of absorption
and dispersion to meet the case of the bright blue line in the quiniferous solu-
tions. The dispersion of fluor-spar, and of the glasses and vegetable solutions
already described, is of a different character. In fluor-spar the dispersion effected

WITHIN SOLID AND FLUID BODIES. 117

by the first stratum is by no means very abundant, and the intromitted beam,
even after passing through one or more undispersing strata, is dispersed nearly
as copiously as before. In the glasses and in the vegetable solutions there are no
peculiarities which require explanation, excepting those which arise from the
absorption of the dispersed beam in passing through the coloured medium.

When the phenomena of internal dispersion are exhibited in coloured fluids
and solids, the influence of absorption upon the dispersed light is very interesting.
Previous to its dispersion the light has the same colour as the transmitted light,
were it to emerge at that point of its path, and when viewed at an azimuth
above 90°, a portion of the dispersed light has that colour. The quantity of light
possessing this colour increases between the azimuth of 90° and 180°. In order
to see this effect disembarrassed from another influence, we must make the in-
tromitted beam parallel to the surface of the fiuid or solid, so as just to graze it.
In this way the dispersed light is not changed in its passage to the eye after dis-
persion. When the beam passes through the coloured medium without this
precaution, it again suffers absorption proportional to the thickness of the coloured
substance through which it has passed, and sometimes disappears altogether. This
effect is finely seen in the darker solutions, which disperse a brilliant red, or a
brilliant green light ; the colour of the former becoming yellowish green and whitish,
while that of the latter becomes whitish yellow.

3. On the Polarisation of Dispersed Light.

As the dispersed light is turned from its path by reflection, and is reflected
at angles proper for polarising it, its partial polarisation at least might have been
anticipated. Sir Joun Herscuen viewed it through a tourmaline, and states that
no signs of polarisation were perceived in it ; but his method of obtaining the
blue line from light diverging from a large area of the sky, and therefore reflected
at various angles far above and far below the polarising angle, rendered it im-
practicable to detect its state of polarisation. The method which I adopted, of
using a narrow cylindrical beam of strong light, affording a bright dispersed beam
more than an inch in length, enabled me to discover its polarisation, and to in-
vestigate its peculiarities.

Upon examining the blue beam in the quiniferous solution with an analysing
rhomb of calcareous spar, I found that a considerable part of it, consisting chiefly
of the less refrangible portion of its rays, was polarised in the plane of reflection,
while the more refrangible of its rays, constituting an intensely blue beam, had a
different state of polarisation.

This insulation of the bluer rays greatly increased the beauty of the pheno-
menon, and promised to throw some light upon its cause. I was therefore anxious
to ascertain their state of polarisation, which was not indicated by the analysing
rhomb. With this view! transmitted through the solution a strong beam of polarised

118 SIR DAVID BREWSTER ON THE DECOMPOSITION AND DISPERSION OF LIGHT

light, and was surprised to find that the blue beam which it yielded by disper-
sion, retained the same intensity in every position of the analysing prism, and
therefore possesses a quaquaversus polarisation, such as that which light receives
when transmitted through a congeries of minute doubly refracting crystals having
their axes in all possible directions.

In making the same experiment with other dispersing fluids and solids, I
found some in which the whole beam was completely polarised in the plane of
reflection, and others in which it exhibited solely a guaquaversus polarisation ; but
as these experiments indicate new processes in the decomposition and polarisa-
tion of light, which require a more extended analysis, I shall resume the subject
in a separate communication, contenting myself at present with a general account
of the more important facts, and the results to which they lead.

Having transmitted a condensed beam of light through an alcoholic solution
of the leaves of the Common Laurel, or of Tea, either green or black, I found that the
bright red beam which it dispersed, possessed, like the b/we one in the quiniferous so-
lution, a guaquaversus polarisation, a small portion of the light being polarised in the
plane of reflection. The gieen beam dispersed by the preparation of orcine, has the
same properties, the white portion of it disappearing and reappearing during the re-
volution of the analysing rhomb. In the aqueous solution of esculine,* the dispersed
pencil consists of two finely-contrasted pencils, the one whitish and polarised in
the plane of reflection, and the other a very deep blue, having quaquaversus pola-
risation. The white pencil is more intense than the blue one, which is the very
reverse of what takes place in the solution of quinine. The alcoholic solution of
the seeds of the Colchicum autumnale gives a bright and copious green beam of dis-
persed light, which consists of two pencils, one whitish and polarised in the plane
of reflection, and the other bright green, with a quaquaversus polarisation. The
same property is possessed by a solution of guzacum in alcohol, which disperses,
by the stratum chiefly near its surface, a beautiful violed light; and also by an
alcoholic solution of sulphate of strychnine, which disperses a green light, after it
has stood for some days. The same property is possessed by almost all the oils,
in some of which the dispersed light is exceedingly beautiful, varying from a pale
green to a blue tint.

The polarisation of the dispersed beam in one plane, namely, in the plane of
reflection, is exhibited in several fluids and solids. It is very marked in the bile
of the ox, which disperses an olive-green light; in a solution of gum-myrrh in
alcohol, diluted with water, which disperses a bright white beam; and in an
orange-coloured glass, which disperses a pale greenish beam.

In many fluid solutions, the beam with a quaquaversus polarisation is very
intense, when compared with the faint pencil which is polarised in the plane of

* In the alcoholic solution of Esculine, the faint-blue approaches to violet. The polarisation is

like that in quinine.

WITHIN SOLID AND FLUID BODIES. 119

reflection ; but in a specimen of yellow Bohemian glass, which gives a copious and
brilliant green beam by dispersion, the whole of the beam possesses a guaquaver-
sus polarisation.

When we view the dispersed beam in different azimuths, some very interest-
ing phenomena present themselves to our notice. In general, the colour of the
dispersed light suffers a considerable change, passing, between the azimuths of
90° and 180°, from the colour of the dispersed beam to the colour of the trans-
mitted beam. This effect is finely seen in the alcoholic solution of tea, where the
brilliant ed light passes into an olive tint; but it is still more remarkable in a
mixture of Prussian blue and water. The dispersed beam is polarised in the
plane of reflection. It is bluish in the azimuth of 90°: pinkish about the azimuth
of 100°; greenish in that of 120°; bluish in azimuth 150°; and again pinkish in
azimuth 170°. These three last tints may be all seen at the same time.

Such are the general phenomena of internal dispersion, a subject which pro-
mises to throw some light on the constitution of those solid and fluid bodies by
which it is produced. The apparently superficial dispersion in the quinine solu-
tion to which Sir Joun Herscuex has given the name of epipolism, is obviously a
single case of the general phenomenon in which the ordinates of the curve of dis-
persion diminish rapidly after the light has entered the stratum nearest the sur-
face; while the veal epipolism which he ascribes to fluor-spar, so far from being
an action of the surface, is much less so than that of the quiniferous solution, and
entirely similar in its character to that which is produced by the fluids and solids
which I have examined.

The phenomenon of internal dispersion, when considered merely as a case of
reflection and polarisation, possesses much novelty and interest. If the exciting
beam, as we may call it, is cylindrical, we have before us an experiment, in which
the phenomena of cylindrical reflection, and cylindrical polarisation, are at once
exhibited to us. The innumerable reflecting surfaces, receiving the intromitted
beam at all possible angles, reflect the incident light in all possible directions, so
that the eye, wherever it is placed, sees the beam as if it were self-luminous ; and
while the eye is made to revolve in a circle round the cylindrical beam, it receives
a pencil of polarised light—polarised in a plane passing through the eye and the
axis of the cylinder; or, what is the same thing, a thousand spectators viewing
this beam in the same azimuth, but in directions differently inclined to the hori-
zon, would all see exactly the same phenomena of reflection and polarisation !

4. On the Causes of the Internal Decomposition and Dispersion of Light.

In imperfectly crystallized minerals, such as particular specimens of adularia,
chrysoberyl, opal, and sapphire, the white and coloured opalescence, and the
asterial radiations, have been shewn to arise from minute vacuities, or from open
spaces with crystallized sides, or from narrow pipes, or linear spaces parallel to

VOL. XVI. PART II. 2H

120 SIR DAVID BREWSTER ON THE DECOMPOSITION AND DISPERSION OF LIGHT

the edges of the primitive or secondary forms of the mineral. In tabasheer,
where the vacuities contain air, which we can expel and send back at pleasure,
a fine blue light is dispersed, depending, no doubt, on the size of the vacuities.
In a very remarkable specimen of calcareous spar, crowded with hemitrope veins,
I have observed a copious internal dispersion produced by the reflection of light
at the different surfaces, which, though in optical contact, have different degrees
of extraordinary refraction.

All these phenomena, however, are essentially different from those which
form the subject of this paper, with the exception of the phenomena of fluor-spar,
in so far, at least, as they are the result of imperfect crystallization. The epipo-
lism which Sir Joun Herscuer ascribes to this mineral, or its internal dispersion,
according to my experiments, does not belong to the species, but only to particu-
lar varieties, and not even to the variety, but merely to particular parts of it.
It is therefore the result of inequal or imperfect crystallization. The nucleus is
perfect, a coating supervenes, having a different tint by transmitted light, and
dispersing a fine blue light, and so on through a succession of strata, dispersing dif-
ferently coloured lights, and separated by non-dispersing spaces. An extraneous
element, therefore, depending on the state of the solution, has been successively
introduced into the crystal, and if it had the same refractive and dispersive
power as the fiuor-spar, it could not reflect any portion of the intromitted beam :
But if there is any difference in the mean refraction, or in the dispersive power,
or if the difference consists merely in the unequal length of certain portions of the
two spectra, then, in all these cases, light will be dispersed by the extraneous
element. If, for example, we place a film of oil of cassia between two prisms of
flint glass, the light reflected from the film will be b/ue. The index of refraction
for certain of the red rays is the same in the glass and in the oil, and consequently
none of these rays enter into the reflected pencil, which must therefore be blue,
whatever be the inclination of the incident rays. If we now suppose this film of
oil to be solidified, and disseminated in infinitely small atoms throught flint glass,
or a fluid that has the same action as the glass upon light, we should have the
phenomenon of a blue dispersion.*

A beam of blue light thus produced should be polarised at the polarising
angle, and partially polarised at other angles; and if this is not its character, we
must look for some cause by which it has been counteracted. We have already
seen that, in the Bohemian yellow glass, none of the light is polarised by reflec-
tion, and that in the quiniferous solution only a part of it is so polarised, the
whole pencil in the one case, and the residual pencil in the other, having a qua-
quaversus polarisation. This effect cannot be the result of an opposite polarisation

* In the experiment with Prussian blue, which is a very splendid one, the particles are mechani-
cally suspended in the water; so that we have here an ocular demonstration that the particles are
the cause of the dispersion and the quaquaversus polarisation.

WITHIN SOLID AND FLUID BODIES. 121

by the refraction of the dispersed light at the surfaces of the reflecting particles,
because such an action would only reduce the amount of polarisation by refiec-
tion ; and I have found by direct experiment, namely, by making the blue light
pass through different thicknesses of the fluid, that such an effect is not produced.
Unless, therefore, we suppose that this guaquaversus polarisation is a new property
of light, produced by a peculiar action of certain solid and fluid bodies, we are
driven to the conclusion, no less remarkable, that it is produced by an infinite
number of doubly refracting crystals, having their axes of double refraction lying
in every possible direction, and therefore refiecting from their posterior surfaces
a pencil of light with quaquaversus polarisation.

Sr LEoNARD’S CoLLEGE, St ANDREWS,
January 30. 1846.

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XIV.—On the Constitution and Properties of Picoline, a new Organic Base from
Coal-Tar. By Tuomas ANDERSON, M.D.

(Read, 20th April 1846.)

THe careful study of the products of destructive distillation has enriched
organic chemistry with an extensive series of results of unexpected interest and
importance. These results have affected, in no inconsiderable degree, the recent
progress of the science ; and their influence has been of a twofold character, both
general and particular, exerted in the former case in the development of some of
the more remarkable general doctrines of organic chemistry ; in the latter, in the
important light thrown by their investigation on the constitution of the substances
from which they are derived, and the facilities they have afforded of following out
connections, which the examination of the original substance either does not at
all present to our view, or, at least, indicates only in an imperfect or dubious
manner. Added to this, we have the remarkable fact of the appearance among
these products of substances in some cases identical with those occurring in
organised beings; and in others, presenting analogies of the very closest charac-
ter with the actual products of vital affinity, which, taken together, afford abun-
dant reason for pursuing the investigation of substances which have already
afforded results of so remarkable a character.

Setting aside altogether those substances, the occurrence of which is so fre-
quent, that they may be called the general products of destructive distillation, such
as carbonic acid, light carburetted hydrogen, olefiant gas, acetic acid, &c., it may
be laid down as a general rule, that each individual compound produced during
such a process, is formed by the destruction of a limited number of substances
only, which bear to each other, and to the product, a more or less intimate con-
nection in constitution or chemical relations. In those instances in which we
have been enabled to submit to destructive distillation substances of a definite and
simple constitution, in a state of chemical purity, and where an uniform tempera-
ture has been preserved, the results have been, for the most part, of an exceedingly
simple and intelligible character; but in proportion as the atom becomes more
complex, so also do the products of its decomposition, and the explanation of the
results is found to be proportionately difficult and uncertain. These difficulties
and uncertainties are increased in a still higher degree, in the case of a substance
such as coal, where we have to deal not merely with one complex atom but with
a congeries of several such, and where the process is performed on the large scale,
and under a variety of perturbing influences. The distillation of coal is, in fact,

VOL. XVE-PART It, 21

124 DR ANDERSON ON THE CONSTITUTION AND PROPERTIES OF PICOLINE,

attended by the formation of about twenty different substances, the constitution
and properties of which have been examined with different degrees of accuracy,
and which present among them instances of almost every species of chemical com-
pound. The discovery of six of these substances is due to RunGE,* who pub-
lished, about fourteen years ago, a very interesting memoir, containing an account
of their general properties. Of these substances, three are possessed of acid pro-
perties, and three are bases, to the latter of which he gave the names of Kyanol,
Leukol, and Pyrrol, from the peculiar colours developed by the action of certain
reagents on their salts. The two former of these substances were afterwards sub-
mitted to a detailed examination and analysis by HorrmMan,+ who arrived at the
interesting result, that both are identical with substances which had been inde-
pendently obtained by the decomposition of certain well known bodies; Kyanol
possessing the constitution and properties of the Aniline of Frirscue, and the
Benzidam of Zin1n; while Leukol is identical with the substance described by
GERHARDT under the name of Chinoline, and which was obtained by him as a pro-
duct of the distillation of quinine, cinchonine, and strychnia, with caustic potass.
HorrMaN failed, however, entirely in obtaining any evidence of the presence of
pyrrol in the substance which he examined, and leaves in doubt the existence of
such a compound.

Having lately had occasion to examine a quantity of the mixed bases con-
tained in coal-tar, obtained by a method similar to that of RuncE, but which,
owing to a modification of the process, contained all the more volatile bases formed
during the distillation of coal, I was led to try whether or not pyrrol was to be
found in it, and I obtained immediate evidence of its existence, by the character-
istic red colour which it gives to fir-wood moistened with hydrochloric acid. The
attempt to separate this pyrrol proved that it was present in extremely minute
quantity only, but led to the discovery of a new base different from those of
Runce, for which I propose the name of Picoline, and the examination of whose
properties forms the subject of the present paper.

Preparation of Picoline.

For the crude substance employed in the preparation of picoline, | am in-
debted to the kindness of Mr AstiEy, of the Bonnington Chemical Works, and it
was obtained by the following modification of Runcx’s process. In the prepara-
tion of naphtha from coal-tar, the first product of distillation is agitated with
sulphuric acid for the purpose of separating any naphthaline which may be pre-
sent, as well as a variety of substances in extremely minute quantity, which
communicate to the crude naphtha the property of becoming dark-coloured

* Poggendorf’s Annalen, Band 31, u. 32.
+ Annalen der Chemie und Pharmacie, vol. xlvii..

A NEW ORGANIC BASE FROM COAL-TAR. 125

by exposure to the air; among these substances, of course, are all the basic

compounds contained in the oil. The sulphuric acid which had been used for
this purpose was neutralised by impure ammonia obtained by a single distillation
of the watery fluid of the gas-works. On the addition of the ammonia there was
no separation of any oil in quantity appreciable to the eye; but upon distillation,
the bases, which had been dissolved in the fluid, passed over with the first por-
tions of water, and collected in a separate layer in the receiver. This oil, when it
came into my hands, possessed a very dark brown colour, a somewhat viscid con-
sistence, and a peculiar pungent and disagreeable odour. It was heavier than
water, a layer of which, containing a small proportion of oil in solution, floated
on the surface. The examination of this oil proved it to consist, in addition to
picoline, of a mixture of pyrrol, aniline, an oily base possessing the general pro-
perties of leukol, and a thick heavy oil destitute of basic properties.

In order to separate picoline, the oil, along with the water which floated on
its surface, was introduced into a retort and carefully distilled. At first, water,
accompanied by a little oil, passed over, and then an oil by itself, which dissolved
completely in the watery fluid contained in the receiver. As the distillation pro-
ceeded, another oil made its appearance, which collected in a layer on the surface
of the fluid which had previously distilled. When about three-fourths of the oil
had passed over, the process was stopped, by which means the oil, destitute of
basic properties, which requires a very high temperature for its distillation, was
left behind in the retort. The fluid in the receiver was now supersaturated with
sulphuric acid diluted with water, care being taken to obtain a powerfully acid
reaction. The peculiar odour which the fluid possessed, was by this process en-
tirely changed, but not destroyed; and, on distillation, the water which passed
over, carried with it all the pyrrol contained in the solution, while the other bases
were retained by the sulphuric acid. Caustic potass was then added to the resi-
due in the retort until an alkaline reaction was manifest, and it was again distil-
led; the water which passed over carried with it the oily bases, partly dissolved,
partly floating on the surface of the solution, exactly as in the first distillation.
A few sticks of fused potass were introduced into-the product, and the whole was
left in repose ; as the potass dissolved, the oil, which is entirely insoluble in solu-
tions of the fixed alkalis, rose to the surface and there collected in the form of a
pale yellow layer, still containing a considerable quantity of water, which may
amount to 30 or 40 per cent. of the bulk of the oil. The oil was separated from
the watery fluid by means of a pipette and pieces of fused potass added so long
as they continued to become moist. The dry oil was then introduced into a retort
and distilled. A transparent and colourless oil passed over, which was tested
at intervals by allowing a drop of it to fall into a solution of chloride of lime. So
soon as the reaction of aniline made its appearance the receiver was changed.
The first portion was now picoline in a state approaching to purity; that which

126 DR ANDERSON ON THE CONSTITUTION AND PROPERTIES OF PICOLINE,

immediately followed, consisted of a mixture of picoline and aniline. The first
portion was again digested with fused potass and rectified ; that which distilled
at 272° was collected apart, and constituted pure picoline.

Constitution of Picoline.

The general analogy in properties which picoline bears to aniline and the
other oleaginous bases, permitted the assumption that it, like these substances,
was free from oxygen; I proceeded, therefore, in its analysis, upon this hypothesis,
and neglected the determination of the nitrogen. The following are the results
of the analyses :—

5°630 grains of picoline gave
Analysis I. { 15:954 ... carbonic acid,
3944 ... water.

15-100 ee carbonic acid,

5°347 grains of picoline gave
ii,
3670 «+ water.

Which give the following results per cent. :—

ile IRE
Carbon ; 7 MaaG : 77:18
Hydrogen. oe ee : 7°62
Nitrogen : rela 07 : 15:20
100:00 a 100:00

These results correspond closely with the formula C,,H,N; the calculated
result of which is—

Theory. Mean.

Criwy (re . 900:0 : 77°29 : ririt Wh
He oc aga 43” 7-69
N : Spats Lh : 15:28 : 15°14
1164°5 - 100-00 - 100-00

This formula is precisely the same as that of aniline, along with which pico-
line occurs in coal-tar. In order to ascertain whether the atomic weight of these
substances were also identical, I prepared the platinum salt of picoline, and de-
termined the amount of platinum contained in it. The salt was obtained by add-
ing bichloride of platinum to a solution of picoline in excess of hydrochloric acid :
no immediate precipitation took place unless the solutions were very concentrated,
but in the course of twenty-four hours the salt was deposited in fine orange-yel-
low needles. -When dried at 212°, it gave the following results :—

I { 9°670 grains of chleride of platinum and picoline gave
"(3147 ... platinum = 32°544 per cent.

rr, § 10°814 grains of chloride of platinum and picoline gave
“\ 3517... platinum = 32°522 per cent.

A NEW ORGANIC BASE FROM COAL-TAR. 127

From these analyses are deduced the following atomic weights :—

ue II.
1211°1 1213-7

These agree sufficiently well with the theoretical atomic weight, which is
11645. They correspond also precisely with the results of the analysis of the
aniline salts. The identity of these results.is shewn by the following table of
the analyses by FritscHe, Zinin, and HorrMan, of aniline from its different
sources, and of picoline, as well as of the plantinum salts of these substances :—

Aniline.* Benzidam.* Cyanol. Picoline. Theory.
Cree 10°08 77°32 76:67 CT 17-29
re 760 7°50 V72 7-69 7:43
N = 14:98 14°84 15°62 15:14 15°28

100°31 99°66 100°00 100-00 100-00

The following are the results for the platinum salts :—

Benzidam. Kyanol. Picoline. Theory.
Mean platinum, per cent. 32°501 32°886 32:°533 32:94
Atomic weight . 1216-1 1170°5 1212°4 1164:5

The results of all these analyses agree perfectly with one another; but the
properties possessed by picoline differ from those of aniline, which, whether ob-
tained from coal-tar, indigo, or nitrobenzid, presents a perfect identity in its
chemical characters.

Properties of Picoline.

Picoline is a perfectly colourless, transparent, limpid fluid, extremely mobile,
and destitute of viscidity. It possesses a powerful, penetrating, and somewhat aro-
matic smell, which, when very dilute, is replaced by a peculiar rancid odour, ad-
hering pertinaciously to the hands and clothes. Its taste is acrid and burning when
concentrated; but when very dilute, as, for instance, when its vapour is sucked
into the mouth, it is powerfully bitter, as are also the solutions of its salts. It is
not changed by exposure to a cold of 0°. Picoline is extremely volatile, and eva-
porates rapidly in the air. It boils at the temperature of 272°, and the thermo-
meter remains perfectly stationary during the whole period of the ebullition; it
is, therefore, much more volatile than aniline, which, according to Horrman,
boils at 359°. It may be preserved for a long time in a bottle containing only a
small quantity of it, and which is frequently opened, without becoming manifestly
coloured ; whereas aniline becomes rapidly brown, and, indeed, cannot easily be
obtained colourless, except by distillation in a current of hydrogen. The specific

* Not having’ the original papers of FrirscHe and Zrntw at hand, I extract these two results from
BrrzeELius’ Arsberattelse, 1844, p. 454, where they are calculated according to C= 75°12, the rest are
with C=75, but the difference is so small as not to affect the comparison.

VOL. XVI. PART II. 2K

128 DR ANDERSON ON THE COMPOSITION AND PROPERTIES OF PICOLINE,

gravity of picoline is less than that of water. I found it to be 0:955 at 50°, while,
according to Horrman, that of aniline is 1-020 at 68°.

Picoline mixes with water in all proportions, and forms a transparent and
colourless solution. It is insoluble, however, in solution of potass, as well as in
most alkaline salts, the addition of which causes its immediate separation from
the water. It dissolves also readily in alcohol, ether, pyroxylic spirit, and the
fixed and volatile oils. It is a powerful alkaline base: a rod dipped in hydro-
chloric acid, and held over it, is immediately surrounded by a copious white
cloud of hydrochlorate of picoline. It restores the blue colour of reddened litmus,
but does not affect the colouring matter of red cabbage. It does not coagulate
the white of eggs as aniline does.

The reactions which it produces with other substances are also quite distinct
from those presented by aniline. When brought in contact with the solution of
chloride of lime, it does not produce, in the least degree, the violet colour which
is so characteristic of aniline; on the contrary, the solution remains perfectly
colourless, unless, indeed, the picoline has not been well separated from pyrrol;
in which case a slight brown makes its appearance, but no violet. Picoline is also
incapable of producing the yellow colour in fir wood and the pith of the elder,
which is so readily obtained with aniline. When treated with chromic acid, even
when very concentrated, and after boiling, no change takes place in the colour of
the solution, and only a small quantity of a yellow powder is deposited; while
Aniline gives an abundant precipitate, which has, according to the degree of con-
centration of the fluid, a green, blue, or black colour.

Picoline precipitates from solutions of chloride of copper a portion of the oxide
of copper, while the remainder forms a pale blue solution, which, when evapo-
rated to a small bulk, deposits a congeries of prismatic crystals, which seem to
be a doubie salt. No blackening of the solution takes place, as is the case with
aniline. When an excess of hydrochloric acid is present there is obtained, on
evaporation, another double salt in large crystals, apparently derived from the
rhombohedral system. Picoline produces also double compounds with the chlo-
rides of mercury, platinum, gold, tin, and antimony. With chloride of gold it gives
an exceedingly characteristic compound, in the form of a fine lemon-yellow pre-
cipitate, which is soluble in a considerable quantity of boiling water, and is depo-
sited, on cooling, in delicate yellow needles. Aniline, under similar circumstances,
gives a reddish-brown precipitate resembling the ferrocyanide of copper. It gives,
with infusion of nut-galls, a copious curdy precipitate of a pale yellow colour,
which dissolves in hot water, and is deposited again on cooling. It does not pre-
cipitate the solutions of nitrate of silver, chlorides of barium and strontium, or
sulphate of magnesia.

The properties of picoline, as now detailed, are obviously different from those
of aniline. They recalled, however, strongly to my mind those of a base called

A NEW ORGANIC BASE FROM COAL-TAR. 129

Odorin, obtained by UNvERDORBEN* from Dippel’s animal oil. According to this
chemist, Dippel’s oil, which is obtained by several successive distillations of the
oleum cornu cervi, is a mixture of four different bases, to which he gives the
names of Odorin, Animin, Olanin, and Ammolin. Ofthese, the two first constitute
nineteen-twentieths of the whole oil, and the odorin, which resembles picoline in
its solubility in water, is obtained by simply distilling the oil and collecting the
product as long as it dissolves. These results, however, have been called in
question by subsequent observers; REICHENBACH, especially, asserts that he was
unable to separate any basic compounds, and considers the substances obtained
by UNVERDORBEN to be mixtures of empyreumatic oil with ammonia. As, how-
ever, the properties which UNVERDORBEN has attributed to odorin, approximate
in some respects to those of picoline, I thought it desirable to ascertain the ex-
istence of this substance, and whether or not it is identical with picoline. In
order to prepare odorin, I rectified the oleum cornu cervi, and then distilled the
product; but on allowing the first drops of oil to fall into water, they were not
dissolved as UNVERDORBEN has asserted, but floated unchanged upon the surface.
Finding this process unsuccessful, I agitated the crude oil with dilute sulphuric
acid; the acid fluid immediately acquired a very deep reddish-brown colour, and
when separated from the oil, and supersaturated with potass, a semisolid viscid
mass separated from the fluid. This, when distilled with water, yielded a mix-
ture of several oily bases, while a dark coloured resinous substance, probably
UNVERDORBEN’S Fuscin, was left in the retort. The mixed bases which I thus
obtained, formed an exceedingly small fraction of the oil employed. They were
purified by several successive rectifications, and generally in a method similar to
that employed for picoline, and the first portions of the product collected apart.
It then constituted a colourless oil which became brown in the air, dissolved
readily in water, and presented an odour similar to, though not quite the same
as, that of picoline. It gave with chloride of gold a dirty yellow precipitate,
which dissolved in hot water, and deposited, on cooling, in the pulverulent form,
and with bichloride of platinum, a compound in red wart-like crystals. By an ac-
cident in the laboratory, the small quantity of this substance which I had pre-
pared for analysis was destroyed, so that the evidence of their identity cannot be
considered as sufficient. The characters of odorin, as given by UNVERDORBEN,
are not perfectly identical, either with those of picoline, or the base which I ob-
tained. Odorin, according to UNVERDORBEN, boils at about 212°, and its salts are
oleaginous compounds which distil in the form of an oily fluid, whereas those of
picoline are mostly crystallizable. I am at present engaged with the examina-

tion of these substances.
It is obvious, from the observations contained in Horrman’st paper, that

* Poggendorf’s Annalen, vol. xi. + Liebig’s Annalen, vol. xlvii.

130 DR ANDERSON ON THE CONSTITUTION AND PROPERTIES OF PICOLINE,

picoline must have been present along with aniline and chinoline in the sub-
stance which he examined. He mentions, especially, that his aniline, as obtained
by distillation only, possessed a peculiar pungent and disagreeable odour, which
was got rid of only by several successive crystallizations of its oxalate from
alcohol, and that the impure aniline has a specific gravity less than that of
water. He observes, also, that the quantity of the substance present must have
been excessively minute, as it did not affect the results of the analysis, a pheno-
menon, the cause of which is sufficiently explained by the identity in constitution
of the two substances. Horrman did not obtain picoline in the separate state,
simply because the bases employed by him were obtained from the less volatile
portions of coal-tar, which necessarily contain it only in minute proportion.

Combinations of Picoline.

Picoline forms a series of compounds which are generally closely analogous
to those of aniline, but present in a less marked degree the regularity and facility
of crystallization which are so characteristic of the salts of the latter base. It
forms, however, with the greater number of acids, salts which can be obtained in
a crystalline form. These are all highly soluble in water, and some of them are
even deliquescent; they are also for the most part readily soluble in alchol even
in the cold. They are most readily obtained by evaporating their aqueous solu-
tions at 212°, and not by adding an acid to the etherial solution of the base; as in
the latter case the presence of even a minute proportion of water causes them to
precipitate in the form of a semifluid mass. Picoline forms a number of acid
salts, in which respect it differs from aniline. Its salts are less readily decom-
posed in the air than the corresponding aniline compounds, but they do event-
ually become brown, although without presenting any of the rose red colour
which the latter salts assume.

Sulphate of Picoline.—I obtained this salt by supersaturating sulphuric acid
with picoline. The solution obtained was perfectly colourless, and when evapo-
rated in the water-bath, it evolved picoline in abundance, and formed a thick
oily fluid, which, on cooling, concreted into a tough mass of transparent and
colourless crystals, apparently of a tabular form. Exposed to the air, it deli-
quesces rapidly into a transparent and colourless oil, which, after a time, acquires
a slight brownish colour. It is insoluble in ether, but readily in alcohol, both hot
and cold. . It is not deposited in crystals by allowing the hot alcoholic solution to
cool. I analysed this salt by evaporating to dryness in the water-bath, in a
weighed platinum crucible, and allowing it to cool under an exsiccator. It was
then rapidly weighed, dissolved in water, and precipitated by chloride of barium :—

4-364 grains of sulphate of picoline gave
5-230 ... sulphate of baryta = 41°20 per cent. of anhydrous sulphuric acid.

A NEW ORGANIC BASE FROM COAL-TAR. 131

This result corresponds with the formula C,,H,N+2H0, $0; as is shewn
by the following calculation :—

Theory. Experiment.
2 Eq. Sulphuric acid é 1000:0 ; 41°84 3 41:20
1 .--- Picoline ; 4 1164:5 4 48°74 , Aide
2 ... Water 5 - 225:0 : 9.42
2389-5 - 100-:00

The sulphate of aniline dried at 212° has a different constitution, it gives
28:67 per cent. of sulphuric acid, which corresponds to the formula C,, H, N, HO,
S 0.

Oxalate of Picoline.—This salt is obtained by mixing oxalic acid and picoline
in excess, and evaporating the solution over quick-lime. When the solution is
reduced to a very small bulk, it is deposited in the form of short prisms radiating
from a centre ; and on further evaporation, the whole concretes into a solid mass.
The crystals evolve the odour of picoline in the air; they are highly soluble in
water and alcohol, both absolute and hydrated. When heated to 212° it fuses and
evolves abundance of picoline vapours, and on cooling it forms a thick fluid
which slowly deposits crystals in the form of fine needles. These are probably
an acid salt. I did not obtain the oxalate in a state of sufficient purity for
analysis.

Nitrate of Picoline is obtained in a white crystalline mass, when a mixture.
of picoline and dilute nitric acid is evaporated to dryness at a moderate heat. At
a higher temperature it sublimes in white feathery crystals.

Hydrochlorate of Picoline may be prepared by mixing picoline and hydro-
chloric acid, and evaporating on the water-bath. On cooling, the thick fluid
which remains consolidates into a mass of prismatic crystals. When heated to a
high temperature, it sublimes easily, and deposits itself on the sides of the vessel
in transparent crystals, which deliquesce rapidly in the air.

Chloride of Platinum and Picoline.—This salt is easily obtained by adding
picoline to a solution of bichloride of platinum, containing an excess of hydro-
chloric acid; it deposits itself immediately, if the solution be concentrated, but
when moderately diluted, it makes its appearance only after the lapse of some
time. The crystals which are deposited are rather liable to retain an excess
of picoline, which renders it advisable to redissolve them in a dilute solution of
chloride of platinum with a little hydrochloric acid. From this solution it is de-
posited pure, on cooling, in the form of fine orange-yellow needles, which can
easily be obtained half an inch long even when operating on very small quantities.
It is much more soluble both in water and alcohol than the aniline salt, and
indeed than the platinum salts of the organic bases generally. It requires only
about four times its weight of boiling water for solution.

VOL. XVI. PART II. 21

132 DR ANDERSON ON THE CONSTITUTION AND PROPERTIES OF PICOLINE,

The crystals of this salt, after washing with alcohol and ether, and drying
at 212°, gave the following results of analysis :—

10°032 grains of chloride of platinum and picoline gave
8862 ... carbonic acid, and
2°760 --- water.

The determination of the platinum, as formerly mentioned, gave in two dif-
ferent trials 32°544 and 32°522 per cent., the mean of which is 32°533. The
analysis corresponds with the formula C,H, N, HCl, Pt Cl.

Theory. Experiment.
Cy = 900°0 : 24:07 : 24-09
H, = 100-0 : 2°67 . 3°05
Ni. = pred ae : 4:73 : ts
Cl =18804 . e899 . ol
Pt’ = 1238270 32°94 - 32°533
3739°4 100-00

Chloride of Picoline and Mercury.—When picoline is added to a concentrated
solution of bichloride of mercury, a white curdy precipitate immediately falls.
If, however, the solution be dilute, it is not precipitated for some time, and then
appears in the form of radiated silky needles. It is sparingly soluble in cold
water, more readily in hot. It dissolves pretty abundantly in boiling alcohol,
and the solution, on cooling, deposits it, sometimes in prismatic, sometimes in
feathery crystals. It dissolves readily in dilute hydrochloric acid, with the for-
mation of a peculiar compound which I have not particularly examined. Boiled
with water it is decomposed, picoline being evolved, and a white powder being
deposited.

In the analysis of this compound I interposed, between the combustion tube
and the chloride of calcium apparatus, a small tube in which the mercury and
water were condensed, and at the conclusion of the process, a current of dry air,
heated to 212°, was drawn through the tube, by means of which the water was
conveyed into the chloride of calcium apparatus. The salt was dried simply by
exposure to the air, as it loses picoline when heated ; when analysed it still smelt
of picoline, which accounts for the excess of carbon obtained.

The following are the results of the analysis :—

10.962 grains chloride of mercury and picoline gave
8:245 ... carbonic acid,
2°168 =... water.

This corresponds to the formula C,,H,N+Hg Cl, which gives the following
results :—

Theory. Experiment.
Cy = 900:0 : 19-63 , 20°51
Heyy). 8 ; 1-90 ; 2°19
NY 0 : 3°86 : ty
Cl, = 887:0 : 19°35 a
Hg = 2531°6 é 55:26 sus

4583°1 100-00

A NEW ORGANIC BASE FROM COAL-TAR. 183

This salt differs in constitution from the aniline salt, which is represented by
the formula 2 (C,, H, N)+3 Hg Cl; it tallies, however, perfectly with the compound
of chinoline and bichloride of mercury, which is C,, H; N + Hg Cl,.

I have not particularly examined the other compounds of picoline.

Products of the Decomposition of Picoline.

The small quantity of picoline at my disposal has hitherto prevented my ex-
amining particularly the products of its decomposition, a branch of the subject
which presents numerous points of interest. Such results, however, as I have
obtained, indicate a striking difference between the products afforded by it and
aniline.

When treated with nitric acid of specific gravity 1:5, picoline is immediately
dissolved, but without communicating to the fluid the fine indigo-blue colour
which aniline produces under similar circumstances. On the application of heat
there is produced an extremely slow evolution of nitrous fumes, which contrasts
strikingly with the tumultuous action which aniline produces. After very long-
continued treatment with nitric acid, the fluid was evaporated to a very small
bulk, when it deposited large crystals in the form of rhomboidal tables. These
crystals, on being treated with potass, evolved picoline unchanged. The potass
solution was red, but it contained no carbazotic acid, at least no carbazotate of
potass was deposited on evaporation.

An excess of bromine water added to picoline causes an immediate and abund-
ant precipitate of a reddish colour, which, on standing during the night, deposited
itself in the form of a transparent reddish oil. ‘This substance is destitute of
basic properties, and is readily soluble in alcohol and ether, but not in water.
Aniline, when treated in the same manner, gives, as is well known, the bromani-
loid of Frirscue, which is solid, and crystallises in silky needles, fusible at 232°.
It seems probable that the oily fluid obtained from picoline may possess a con-
stitution similar to that of bromaniloid, in which case it would have the formula
C,, (H, Br;) N, and would receive the name of bromopicoloid. I had not enough
of it for analysis.

The action of chlorine on picoline is remarkably analogous to that which it pro-
duces on aniline. When passed into anhydrous picoline it is rapidly absorbed,
and colourless crystals, apparently of hydrochlorate of picoline, are deposited.
In a short time, however, the fluid becomes dark brown, and is finally converted
into aresin. This resin was mixed with water, and a current of chlorine passed
through it for some hours. The fluid was then introduced into a retort, and dis-
tilled, a crystalline substance, passed over along with the water, and after all the
water had passed, another substance made its appearance, while a large quantity
of carbon was left in the retort. The quantity in which I obtained these sub-
stances was far too small to admit of their particular examination, but it appeared

134 DR ANDERSON ON THE CONSTITUTION AND PROPERTIES OF PICOLINE,

to me that the odour of the latter substance was different from that of chloro-
phenesic acid, which is produced by the action of chlorine on aniline.

The preceding investigation is sufficient to establish the identity, in constitu-
tion and difference, in properties of picoline and aniline. These substances are
then isomeric, in the strict sense of the term, possessing the same composition
per cent., and the same atomic weight.

Although isomerism has been recognised in a great variety of different classes
of compounds, I believe the present to be the first instance in which it has been
satisfactorily proved among organic bases. Two instances, indeed, have been
previously described, but in neither can the evidence be considered absolutely
conclusive. One of these cases is that of two bases discovered by PELLETIER and
CovERBE* in the husks of the Cocculus Indicus, to which they have given the
names of Menispermin and Paramenispermin. The characters which they have
assigned to these substances are sufficiently distinct, but their analyses of both
lead to the formula C,,; H, N O,. This result, however, is unsupported by any de-
termination of their atomic weights, without which the isomerism cannot be
admitted as proved. The other instance is that of bebeerine, which, according
to the analysis of Dr D. MacracGan,t is isomeric with morphia, both being repre-
sented by the formula C;; HN O,;; and as this result is supported by the analysis
of the platinum compound, the probability of their isomerism is much higher than
in the former case. Unfortunately, however, another source of fallacy enters
into the question in the amorphous condition of bebeerine, which renders it im-
possible to determine with certainty its freedom from impurity; even the consti-
tution of morphia, by far the most definite of the two substances, can scarcely be
considered as fixed, GERHARDT, for instance, representing it by the formula
C,,; Hy N O,, and not by that formerly given.

With aniline and picoline, however, these uncertainties disappear. Both
substances are possessed of definite boiling-points widely different from one
another, and of all the other physical characters of pure substances. The low-
ness of their atomic weight also precludes any possibility of doubt regarding the
true formula, and enables us to speak with certainty as to the identity of their
constitution. The isomerism of these substances is, moreover, of much higher
interest in a theoretical point of view. Menispermin and morphia are isolated
substances, entirely unconnected, in constitution or general relations, with any
other substance. Aniline, on the other hand, is a member of one of the most
extensive, widely distributed, and interesting groups of substances, with which
the recent discoveries of organic chemistry have made us acquainted, the Indigo
Salicyl and Benzoil series. The members of this larger group already present a
variety of instances both of isomeric and polymeric compounds, a few of which I

* Annales de Chimie et de Physique, vol. liv.
+ Proceedings of the Royal Society of Edinburgh, No. 26.

A NEW ORGANIC BASE FROM COAL-TAR. 135

have here brought together in the form of a table, which does not pretend to any
scientific arrangement, its sole object being to point out the remarkable relations
of aniline and picoline to the group.

Indigogene, . . ; . Cy.H, NO, Indine.

Indigo, . . 6 . Cig H, NO, cod

Isatine, : : : . C,H; NO,

Anthranilic acid, - 5 . C,H, NO, Boe

Salicylic acid, I : . Cy Hy Og (Re

Nitrosalicylic acid, . i . Cy H; (NO,) O, | -

Benzoic acid, : : . Cy HH, O, Salicylous acid.
Nitrobenzoic acid, . ¢ . Cy H; (NO,) O, Nitrosalicylous acid.
Chlorobenzoic acid, ; . CyH; ClO, Chlorosalicylous acid.
Hydruret of benzoil, , . Cy, O, Benzoine.
Benzonitril, . : ‘ . C,H N Azotide of Benzoil.
Stilbene, 5 ; ; . CyH, ae

Phenol, : : ; . Cy HH, Oo Rete

Aniline, : : : . CyH,N Picoline.
Tribromaniline, . : . C,H, Br, N Tribromopicoline ?
Benzin, : ; 3 «| Gy i, ?
Nitrobenzid, . , : . Cy H; (NO,)

The facility with which aniline can be obtained by the decomposition of dif-
ferent members of this group, renders it by no means impossible to anticipate the
artificial production of picoline also.

As we can start from benzoic acid, and convert it into benzin, benzin into
nitrobenzid, and that finally into aniline by the action of sulphuretted hydrogen,
it seems by no means improbable that salicylous acid, the isomeric of benzoic
acid, may be made to undergo a similar series of changes, the final result of
which would be the formation either of picoline, or of some other compound
isomeric with it and aniline. In order to subject this hypothesis to the test of
experiment, I mixed salicylous acid with equal weights of slaked lime and caustic
baryta, and distilled in the oil bath, with the view of obtaining a substance which
should be isomeric with benzin. The greater part of the salicylous acid, how-
ever, passed over unchanged ; but by agitating with solution of potass, there was
left undissolved an excessively minute quantity of a solid crystalline substance.
Finding this mode of operating unsuccessful, I passed salicylous acid over spongy
platinum heated to a very low red heat in a glass-tube. <A dark viscid oily fluid
passed over into the recipient, of which the greater quantity dissolved in caustic
potass, but left behind a larger quantity of the solid substance than was yielded
by the first experiment. By distillation with water this substance passed into
the receiver in the form of oily drops, which solidified on cooling, and formed a
crystalline mass in which minute needles could be detected. It had a peculiar
pleasant smell which resembled that of benzin; but the quantity which I ob-
tained was much too minute to admit of its analysis, or of any attempt to con-
vert it into picoline.

* Geruarpr has observed (Precis de Chimie Organique, tom. ii., p. 21), that benzoic acid, when
fused with hydrate of potass, evolves’ hydrogen, and gives the potass salt of a new acid. This may pos-
sibly be isomeric with salicylic acid.

VOL. XVI. PART II. 2™M

POSTSCRIPT.

Although the analogy existing between picoline and the other oleaginous
bases is perfectly sufficient to warrant the assumption of the absence of oxygen
in that substance, I have thought it advisable to append here an experimental
determination of the nitrogen. As the volatile bases cannot be readily analysed
by VARRENTRAP and WILL’s method, I made a combustion of the platinum salt,
and determined the proportion by volume of the carbonic acid and nitrogen in
four tubes, which gave the following results :—

I. 94 volumes gave 8: nitrogen.

II. 240 Be: 18:
Ill. 84 aad 6°5
IV. 421 oars 35°

839 67:5

These results give the gases in the proportion of 114 to 1; in other words,
they shew a slight excess over the theoretical result, according to which they
should be in the proportion of 12 to1. They confirm perfectly, however, the
absence of oxygen.

£ igeli7 jy)

| XV.— Results of the Makerstoun Observations, No. II. On the Relation of the Varia-
tions of the Vertical Component of the Harth’s Magnetic Intensity to the Solar and
Lunar Periods. With a Plate. By J. Attan Broun, Esq., Director of General
Sir T. M. Brispanr’s Magnetical and Meteorological Observatory. Communi-
cated by General Sir T. M. BrisBane, Bart.

(Read 20th April 1846.)

1. The following results are deduced from the observations of the balance or
| vertical force magnetometer, which consists of a magnetic needle, balanced hori-
zontally, and resting, by a knife-edged axle, on agate planes. Much doubt has been
| entertained as to this instrument’s capability of shewing changes of moderate
| nicety, and it has been considered altogether unavailable for changes of long
| period :* it has been shewn (Vol. XVI, p. 67), that there are several difficulties
| in the way of an accurate interpretation of the observations, independent of the
| instrumental capacity. If it be added, that disturbances seem to affect the daily
| means of the vertical component,} in a more serious way than they do those of the
horizontal component, it will be seen that there are a series of difficulties, which
tend to render good and consistent results from the balance magnetometer nearly
_unattainable. It will be judged afterwards how far these difficulties have been
| overcome in the present instance.
2. The changes of the vertical component are, in general, very gradual and
| regular; even during considerable disturbances the balance needle moves gradu-
| ally to an extreme position, remaining there, with moderate fluctuations, for a
_ considerable period, and afterwards returning slowly to its mean (or nearly mean)
| position; the bifilar magnet, on the contrary, moves with considerable rapidity
from one extreme position to another. This difference in the mode of distur-
bance, I do not conceive due to a want of sensibility in the balance needle, but
rather to a difference in the nature of the disturbances of the dip, and of the total
intensity. |

3. The changes of the vertical component, then, during disturbances, will
evidently have little or no effect on the regularity of the diurnal curves, although
the periods of maxima and minima may be affected; it will be different for the
daily means, for, as the disturbances will, in general, be almost wholly negative

* Revised instructions by a Committee of the Royal Society of London, p. 37.

+ I shall generally use the terms vertical or horizontal component, instead of vertical or horizontal
force ; the latter are not at all expressive where the changes may be altogether due to variations of dip.

VOL. XVI., PART II. 2M

138 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

or positive, there will be sudden and considerable daily decrements or increments
of the vertical component. If the effect of these disturbances be equally positive
and negative, it may be expected that, in the mean of a sufficient number of ob-
servations, they will destroy each other, or, if almost wholly negative, that they
will be distributed equally over any period for which the,law is desired. If,
however, we expect consistent and regular results, from short series of obser-
vations, especially when the range of the variations for the resulting law is small,
it is evidently desirable to eliminate disturbances as far as possible. To do so com-
pletely, requires a knowledge of the observations which should be classed as dis-
turbed, a matter of difficult attainment, as disturbances have various magnitudes,
and we have to distinguish between variations which are periodic, and those
which are not so; the latter constituting what are distinctively termed disturbances.
Without doubt, disturbances seem to obey an zrregular periodic law, that is to
say, they occur more frequently at certain hours than at others; but there are
whole months in which they are not at all apparent, and in which, each day’s
observations represent equally, in range and periods of maxima and minima, the
diurnal law; thus, in the months of June and July 1844, each day’s observations
of the horizontal component when projected, exhibit, with a few slight excep-
tions, a complete representation of the monthly curve, affected, however, to some
extent by the varying hour angle of the moon.

4. As it is only the larger disturbances which affect the periodic result to a
marked extent, the complete elimination of disturbances is fortunately not of much
moment; the methods which I have adopted for the elimination of these will be
be stated afterwards; it will be found, however, that I have depended as little as
possible on these eliminations.

5. The results as yet obtained for the variations of the vertical component
of the earth’s magnetic intensity are confined, as far as | am aware, to determi-
nations of the mean period of diurnal maxima and minima. These may be obtained
from a good instrument, with moderate exactness, in spite of considerable imac-
curacy in the temperature correction, as the mean diurnal variation of temperature,
in well closed rooms and boxes, will not exceed a few degrees of Fahrenheit. The
Toronto observations for 1841 and 1842, give consistent results, indicating

A principal maximum at 6" Toronto mean time.
A principal minimum at 14°
A secondary maximum at 20°
A secondary minimum at 22”

_ There are only three months of the twenty-four indicating a single maximum and
asingle minimum, namely, the months of November 1842 and September of each

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EARTH’S MAGNETISM TO THE SOLAR AND LUNAR PERIODS. 139

year ; the diurnal range is greatest in summer, and least in winter.* These re-
sults will be found to differ considerably from the following, excepting in the
periods for the whole year.

6. The mean of the vertical component for the year 1844, at Makerstoun,
was least at 14° (Makerstoun mean time); it increased gradually, from that time,
till nearly 21"; it then diminished slightly till nearly 23"; after which it increased
rather rapidly till 5° 30"; it then diminished with much rapidity till midnight, |
increasing slightly from 12" to 13", and diminishing slightly again to the minimum
at 14°; or the vertical component has

The principal minimum......... at 14" 10" Makerstoun mean time.
A secondary maximum ......... at 20" 50"
A secondary minimum ......... at 22" 50™
The principal maximum ...... at 5° 30"
Perhaps a third minimum...... at 12" 10
And a third maximum ......... at 13" 10"

The slight infiexion at 13" (See Mean Curve, No. 1., Plate VI.) would not have
been noted as a maximum, but simply as.a slight irregularity probably due to dis-
turbances, were it not for the evidence which, with one exception, every month in
the year gave to the same effect. If, however, it be considered simply as an
irregularity (it will be the only one in the whole period), 13" 10" must be taken as
the actual period of the principal minimum, the vertical component having nearly
equal values at 12° 10™ and 14° 10".

7. The form of the diurnal curve, and the periods and number of maxima and
_ minima vary throughout the year. Having found that the diurnal curves, for
_ each of the two months symmetrically placed with regard to the solstices, were
nearly identical in periods and range, only the mean curves for each couple have
_ been projected (Curves, No. 1, Plate VI.), namely, the means for the months of

January and December, April and September.
February and November. May and August,
March and October. June and July.

8. The transitions of the periods of maxima and minima throughout these
| months is curious; the principal maximum occurs about 6" at the solstices, near
| 4 at the equinoxes, and about 5" at the intermediate periods. The principal
| minimum occurs about 17" at the winter solstice, about midnight at the equi-
| noxes, and about noon at the summer solstice. In January and December there

* Toronto Observations for 1840, 1841, and 1842. Abstracts, &c., p.lx. The Toronto observations
| were made every two hours, and the Makerstoun observations every hour.

140 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

is no minimum visible near noon; in February and November an inflexion occurs *
there ; in March and October there is a marked tendency to a minimum at that
time; there is a well-marked minimum near noon in April and September; a
strongly marked one about the same time in May and August; and the principal
minimum occurs in June and July near mid-day. The same progression holds for
the maximum, which occurs near 20", excepting that it never becomes the prin-
cipal maximum, though in June it differs very little from it. The inferior
maximum and minimum are best marked near the equinoxes.

The following table will exhibit the transitions of the periods with more dis-
tinctness ; the negative sign (—) is placed before the hour of the principal mini-
mum, and the positive sign (+) before the hour of the principal maximum.

TaBLE of the Hours, Makerstoun mean solar time (astronomical reckoning), of the
Maxima and Minima of the vertical component of Magnetic Intensity for
1844.

Months. Minimum. | Maximum. Minimum. Maximum. Minimum. Maximum.

h.
January and December, | —17

February and November, | — ?16
March and October, —16
April and September, 15
May and August, —14
June and July, 13

It will be observed that the hours of the first minimum and maximum in
this table occupy a year in completing their transitions, that the hour of the second
minimum in the table is constant, and that the hours of the second maximum,
and of the last minimum and maximum in the table, complete their transitions
in six months.

9. Neglecting the inferior maximum and minimum, it will be remarked that
the period of duplication in the forms of the curves differs completely from that
for the horizontal component. For the latter, it is summer in which the diurnal
curve becomes single, and winter in which it becomes double. It is the secondary
or morning maximum of the horizontal component which becomes the principal.
maximum in water ; it is the secondary or noon minimum of the vertical com-

* The principal minimum in the mean for the months of February and November actually occurs at

12" 40™. This is due to an apparent irregularity in the month of November, that month being the only
one which does not shew the inferior maximum near midnight.

EARTH’S MAGNETISM TO THE SOLAR AND LUNAR PERIODS. 14]

ponent which becomes the principal minimum in swmmer. For the horizontal
component the 22" minimum is ¢#e minimum throughout the year ; for the vertical
component the 5" maximum is ‘hé maximum throughout the year.

10. Perhaps the most curious fact in connection with the vertical component
is that of the annual variation of the diurnal range. It has always been ima-
gined, I believe, that the diurnal range of all the magnetical elements increased
from winter to summer. This has been shewn to be the case for the horizontal
component (No. L, 6*), and will afterwards be shewn to be true for the magnetic
declination. It is not so, however, for the vertical component, as may be seen by a
glance at the six diurnal curves projected (Curves, No. 1, Plate VI.). The transition
in form and range is evidently worst exhibited by the mean for February and
November ; this, however, and other irregularities, may probably be due to dis-
turbance. The elimination of these (which I have not at present attempted), or the
observations of other years, must decide this. When the range for each month is
projected (Curve No. 2, Plate VI.), it is at once evident that the diurnal range is

least at the solstices, and greatest at the equinoxes. The mean of the ranges for
_ January and December, and also the mean for June and July (the solstitial months),
is about 000028, the whole vertical component being unity, while the mean for
each of the couples of equinoctial months, namely, of March and April, and of
September and October, is about 0:00068.

11. It might have been expected that this curious variation of the ranges
would shew itself more or less in the ranges for the horizontal component. If we
refer to No. I. of these results (6), page 101 of this volume, and to the projected
curves, No. 2 of that series (Plate III.), we shall find this actually the case, although
in that place it was supposed that the variations in the regular increase of the
ranges might be due to disturbances. These facts seem to point to a difference in
the modes and causes of increase of the diurnal range for the magnetic dip, and
for the total magnetic intensity ; the diurnal ranges of the latter seeming to obey a
law which is equally related to the two solstices, and also to the two equinoxes,
a circumstance in favour of the annual period previously announced (No. I., 10).

12. The mean values of the vertical component, at 21" and 0", are nearly
equal to the mean for the year, but no single hour, as for the horizontal component
(No. I, 8), indicates the mean for each month.

13. Proceeding in the order of No. I., I should now consider the annual period.
» The results for the different years are discordant. This, it is my opinion at present, is
due to an insufficiency in the temperature correction, which will be found alluded to
elsewhere.t The results of the years 1842 and 1843, the latter more strongly, indi-
enke a period similar to that found for the horizontal component, namely, maxima of

* Reference to Results of the Makerstoun Observations, No. I., p. 99 of this volume.
+ Introduction to the Makerstoun Observations for 1843.

VOL. XVI., PART II. 2N

142 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE

the vertical component about the solstices and minima about the equinoxes; 1844 ~
and 1845 also indicate a maximum at the winter solstice, but the maximum at
the summer solstice is imperfectly shewn, if shewn at all.

14. It is quite evident that a moderate error in the temperature correction
may be sufficient to destroy all appearance of an annual period, especially when
the range of the temperature may be 30° Fahrenheit, and the range of the com-
ponent for the annual period may be small. It is, | am inclined to think, due to the
existence of a lighted stove in the Observatory in the winters of 1842, and in the
beginning of 1843 (by means of which the annual range of temperature was much
diminished), that these years give a somewhat distinct indication of the annual
period. For many reasons, however, it is to the observations made in the years
1844 and 1845 that I look for a consistent exhibition of the annual period; and
to the result for these years I shall return when the insufficiency alluded to has
been remedied.

15. The vertical component has diminished considerably since 1841, the
yearly rate of diminution becoming less in each year. Something of this apparent
change may be due to a loss of magnetism in the balance needle ; but it is believed
that this is only partially, if at all, the case. There is a curious change in the
rate of diminution of the vertical component in the year 1845: in October, No-
vember, and December, it was constant or very nearly so; it was remarked of the
horizontal component for 1845, that it had increased much less than in the pre-
vious year. Does this point to an approaching turning-point for the diminution
of the magnetic dip ?

16. Similar summations, to those indicated for the horizontal component
(No. L., 25), were made for the vertical component, at the varying hour angles of
the moon; the larger disturbances were also eliminated similarly, the test num-
ber for disturbances being taken more than twice as great in 1845 as in 1844.
From a mean of 12 lunations in 1844 (see Curves No. 3, Plate VI.), the maximum of
vertical component occurred when the moon had passed the inferior meridian
about three hours, the value of the component then diminished considerably till
19» (counting the moon on the meridian 0, and so up to 24, when it wants one
hour, or, more exactly, #4 of an hour of being on the meridian again; each of the
so-called hours having only this value, 19* corresponds to about 5 45™ before the
moon’s meridian passage) ; it diminishes slightly from 19» till 22", when there is a
minimum ; it then increases slightly till 24" or 0" when there is a maximum ; after
this it diminishes moderately again till 7°, when the principal minimum occurs ;
it then increases rapidly to the maximum at 16". When the disturbances are
not eliminated the maximum occurs at 15", the component then diminishes rapidly,
with some irregularities, till 2", which is -the time of the principal minimum; a
secondary maximum then occurs at 4", and a minimum, differing very little from
the other in value, occurs at 6° or 7°. A more complete elimination of distur-
bances, it is conceived, would render the maximum about 0° still more evident.

EARTH’S MAGNETISM TO THE SOLAR AND LUNAR PERIODS. 143

17. In 1845 the maximum occurs between 14° and 15°, or about 2" after the
moon has passed the inferior meridian, the value of the vertical component then
diminishes till 21" when there is a secondary minimum, it then increases consi-
derably till 2; a secondary maximum occurring about 13", it again diminishes till
7*, when the principal minimum occurs, after which it increases rapidly to the
principal maximum. This year’s result is little affected by the elimination of dis-
turbances ; the curve is rendered somewhat more regular.

18. The results for the two years differ slightly from each other. The
principal maximum occurs about an hour later in 1844 than in 1845 ; the princi-
pal minimum occurs at the same time in both years; but the secondary maximum
and minimum are not nearly so well defined in 1844 as in 1845. The mean of
the two years gives the following periods :—

The principal minimum about 5 hours before the moon’s passage of the inferior meridian.
Pietprincipal maximum about d hours after ...............-.ceeeserseces caceceeccnerseceseerecs
A secondary minimum about 4 hours before ............:.ceceeseee cee eee eens superior .........
A’secondary maximum about 1 hour after — ...........sescensesess seen eceeeenereseeeeeeeenesens

19. These periods are surprisingly near those indicated (No. I., 23), for the
horizontal component, the principal maximum and secondary minimum of the
vertical component occurring about an hour after those of the horizontal com-
ponent, while the principal minimum and secondary maximum occur an hour or
more before those of the horizontal component; seeming to indicate that these
variations belong chiefly to the total intensity.

20. As evidence of the accuracy of the results obtained after eliminating
disturbances, nothing perhaps could be more conclusive than the fact, that in
those months in which no disturbances occur, the general law is found well
marked: it would not be difficult to bring this kind of evidence to bear, both
for the horizontal and vertical components. I shall satisfy myself at present by
giving the projection of one month’s results, namely, the results for the lunation
included by December 15. 1845, and January 10. 1846 (Curves No. 3, Plate VL).
From this single month the same, or very nearly the same, periods of maxima and
minima are obtained as in the mean for the two years. The maxima have nearly
equal values, and so also have the minima; the principal maximum and minimum,
however, occur at the times of the secondary maximum and minimum of the mean
curve. Such a difference in the values of the maxima might be expected; for,
though the moon has every declination in the course of one lunation, it is full
only at one of these declinations. It would not have been difficult to have ob-
tained a curve from one month’s observations representing the mean curve better.

21. In order to obtain the variations of the vertical component with respect to
the moon’s age, summations were made similar to those indicated (No. I., 18) for
the horizontal component. It should be mentioned (as it should have been before
for the horizontal component), that in all the results for monthly periods mean

144 ON THE VARIATION OF THE EARTH’S MAGNETISM, &c.

values for Sundays were used. These were obtained by interpolation ; the mean of
the three days preceding, and of the three days succeeding, were taken as the
means for the Sundays. The want of approximate means for these days would
tend to destroy the regularity and distinctness of the results, owing to the varia-
tions, due to different causes, which it is desired to eliminate, and that the blank
days enter irregularly into the days of the mean monthly periods.

22. The results of these summations (Curves No. 4, Plate VI.) are, that each year
indicates maxima of the vertical component near the quadratures, and minima near
the syzygies. In order to render the fact more distinct, and the curves somewhat
more regular, eleven days* of greatest disturbance were eliminated in each of the
‘years 1844 and 1845, namely, those days on which the mean value of the verti-
cal component was greater than the mean of the previous and succeeding days
by more than 26 micrometer divisions (about three times the resulting range).
The principal minimum in 1844 occurs at the period of full moon; in 1845 it
occurs about three days before the new moon. In the mean of both years the
principal minimum occurs at the time of full moon, the secondary minimum about
two days before new moon; the maxima occur between these periods, and they
are nearly equal. The lowest curve of No. 4 is the projection of the mean for
the two years without eliminating disturbances. It differs little in regularity from
the other in which the large disturbances are eliminated. The irregularities in
these curves may be partially due to the cause of error already stated (17),
namely, an insufficiency in the temperature correcticn.

23. Whether due to the cause just mentioned or not is uncertain, but the
results for the relation of the variations of the vertical component to the moon’s
declination are neither distinct nor consistent for the two years, and the elimina-
tion of the days of large disturbance does not improve them. The mean for the
two years seems to shew something like the law found for the horizontal com-
ponent, namely, maxima about the periods of greatest north and south declina-
tion; but I do not place any trust at present in this result.

Maxerstoun, April 13. 1846.

‘

* Each of these days was actually observed (observations were made) at the time as a day of dis-
turbance. ;
\

Camas

XVI.—On the Solubility of Fluoride of Calcium in Water, and its relation to the
occurrence of Fluorine in Minerals, and in Recent and Fossil Plants and Am-

mals. By GrorcEe Wison, M.D.
(Read April 6. 1846.)

1. Introductory Remarks.

TuE investigation I am about to bring before the Royal Society, was under-
taken in consequence of a discussion which took place in the Zoological Society
of London in 1843,* in reference to the chemical composition of the bones of the
gigantic bird the Dinornis, discovered some time previously in New Zealand. At
the meeting in question, the distinguished paleontologist Dr Fanconer drew
attention to the frequent, if not constant, occurrence of fluoride of calcium in fossil
bones, and, as he stated, also in those of mummies; and threw out the sugges-
tion, that the fluoride might shew itself in these animal remains, not as an origi-
nal ingredient of the bones, or as derived from the matrix in which they were
found, but as a product of the transmutation of their phosphate of lime. The
idea of such a conversion taking place, is as old at least as the days of KLaprotu,
who suggested the possibility of phosphoric acid becoming changed into fluoric.+
It is commented upon by Fourcroy and VAuQquELin,t{ as well as by Gay Lussac,§
as a thing possible but not probable, and which their ignorance of the nature of
fluoric acid prevented them from discussing satisfactorily.

The revival of this suggestion by Dr Fatconer, at a period when the possi-
bility of the chemical elements undergoing transmutation was occupying the
attention of English chemists, and avowedly with a view to shew at least the
possibility of such an idea proving true, excited much discussion, and led, I be-
lieve, to the researches of Mr MippLETon and Dr Dauseny, which I am presently
to mention, and of which my own may be considered the sequel. I have to re-
quest the forbearance of the reader, whilst, with as much brevity as possible, I
refer to the labours of my predecessors in relation to the presence of fluorine in
different bodies.

In 1802, Moricuint of Rome discovered fluoride of calcium in the molars of
a fossil elephant, and was led, in consequence, to search for it in the enamel of
recent human teeth, where he also found it.|| His results were confirmed by
Gay Lussac, who experimented along with him,§ and by Brerzetius, who found

* Literary Gazette, Dec. 2, 1843, p. 779. + Annales de Chimie, tome lvii. (1806), p. 43.

t Ibid., p. 44. § Ibid., tom. lv., p. 265.
|| Ibid., p. 258. | Ibid.

VOL. XVI. PART II. 20

146 DR WILSON ON THE SOLUBILITY OF

the fiuoride in the recent bones of man and of the ox; and ascertained the pro-
portion in which it was present in both.* On the authority of these chemists,
fluorine was ranked among the constituents of animal bodies. Many excellent
observers, however, soon after declared themselves unable to detect that element
in recent bones. Among these are Fourcroy, VAUQUELIN,+ WOLLASTON, BRANDE,
Dr T. THomson,{ GirarDIN, PreissErR, and REEs;§ the last of whom is not con-
tent with stating that he found no fluorine in unburied bones, but affirms that no
one else can have met with it in them. More recently, Mr MippLErTon|| and Dr
DaAvuBENY have experienced no difficulty in confirming the original results of
MoricuinI and BerzEeLIus. An American observer has been equally successful.**
Dr Grecory informs me that he has made many examinations for fluorine in
recent bones, and has always found it present in them. My own experience of
the subject is to the same effect. I shew the Society glass etched by recent hu-
man bones, male, female, and foetal, which were obtained, without special selec-
tion, from the dissecting-room; likewise glass corroded by hydrofluoric acid from
the tusk of the recent elephant, and the teeth of the recent hippopotamus, walrus,
leopard, and shark.

I shall return, in another section of this paper, to the consideration of the
question, how the discrepance in the statements of observers concerning the pre-
sence of fluorine in recent bones is to be accounted for. It was the occurrence of
that element in fossil bones which gave rise to the discussions concerning its origin,
to which I shall have occasion to refer. Fluorine is not a constant ingredient of
the animal remains in question, according to Fourcroy and VAUQUELIN, who
examined some which contained none. But in the greater number of cases it has
been found present, so that GrrARDIN and PREISSER have even proposed to con-
sider its existence in an unknown bone as a proof of the latter not having be-
longed to man or to any recent organism, but to some “ antediluvian animal.” +

It is acknowledged, moreover, that in buried bones, especially in those that
are petrified, fluorine is frequently present in larger proportion than in recent
ones. Thus LAsSsAIGNE found fifteen per cent. of fluoride of calcium in the bones
of the Anoplotherium;{{ MippLETOoN ten per cent. in those of various animals from
the Sewalik Hills ;§§ Grrarpin and PREISsER nine per cent. in those of the La-
mantin. || || Mr MrppLeTon, indeed, has endeavoured to shew that the proportion
of fluoride of calcium increases according to the period of the entombment of the
bone at the rate of 14 per cent. in a thousand years, and has proposed to estimate

* Annales de Chimie, tom. Ixi. (1807), p. 256. + Ibid., 1806, t. lvii., p. 41.
{ Chemistry of Animal Bodies, p. 236.
§ Guy’s Hospital Reports, quoted in Edin. Phil. Journal, vol. xxviii., p. 93.

|| Chemical Society’s Memoirs, vol. ii., p. 135. q Ibid., p. 101.
** Edin. Phil. Journal, vol. xxxix., p. 235. tt Ann. de Chim., t. ix. (1843), p. 381.
{{ Quarterly Journal of Geological Society, vol. i, p. 216. §§ Ibid.

I|l| Ann. de Ch, et Ph,, t. ix., p. 375, 1843.

FLUORIDE OF CALCIUM IN WATER. 147

the age of bones, and of the rocks containing them, by the per-centage of fluorine
in the former.* This idea, however, is certainly unwarranted. In the bones of
five fossil animals, including the Plesiosaurus and Ichthyosaurus, GrrARDIN and
Preisser found from one to two per cent. of fluoride of calcium ;} whilst in those
of the recent ox, BERzELIus found nine per cent.{ In the ancient bones there was
thus, instead of a much higher per-centage, seven per cent. less of fluorine than in
the recent bones. Many other objections might be made to Mr MIppLETON’s view.

Those who deny the existence of fluorine in recent bones, consider the whole
amount of that element found in ancient buried ones, as in some way or other a
product of fossilisation. According to those, on the other hand, who affirm the
presence of that element in recent organisms, only a portion, at most, of the fluo-
rine found in osseous remains has been added since they ceased to be parts of
living animals. It is impossible, however, to separate the two questions. We
have no data from which to determine whether or not the bones of an extinct
animal contained fluorine during its life, and, if it did, how much was present.
It will be sufficient, therefore, if I consider what progress has been made in an-
swering the one question, How does fluoride of calcium come to be present in
bones, either recent or fossil ?

Three replies have been proposed to this query. 1st, That of Dr FALconer,
already referred to, which, taking for granted that fossil bones contain more fluo-
rine than they possessed whilst parts of living animals, assumes, or rather sug-
gests as possible, that phosphate of lime has been transmuted into fluoride of
calcium.j 2d, That of Liesie, which, going on exactly an opposite assumption,
takes for granted (if I understand him aright) that bones of living antediluvian
animals contained the same proportion of fluorine which we find in their fossil
remains; and refers its greater abundance in these, either to its having been
present in larger quantity in the food of their living possessors, than it is in that
of existing animals, or to its having been appropriated to a larger amount from
it.|| The third is that of Mr MippLEeron, who supposes every bone to possess
normally two per cent. of fluoride of calcium, and considers all above that which
a fossil bone contains, as added to it whilst buried in the earth, by the infiltra-
tion of water containing that salt held in solution by some unknown solvent.

It is unnecessary to discuss the first and second propositions referred to. It
is impossible, in the present state of our knowledge, either to prove or to disprove
them. The idea of transmutation of a phosphate into a fluoride, was doubtless
suggested solely because there seemed no other way of accounting for the accu-
mulation of fluorine, and will be abandoned, if it shall appear that recognized

* Quarterly Journal of Geological Society, vol. i, p. 216.

7 Annales de Chimie, 1843, pp. 370-78. { Ibid., t. lxi., p. 257.
§ Literary Gazette, 1843, p. 779.

|| Chemistry of Agriculture, 3d edition, p. 123.

148 DR WILSON ON THE SOLUBILITY OF

chemical forces can explain the phenomenon. The great German chemist, also,
(whose view may be the true one,) will probably modify his opinion, when he
finds that fluoride of calcium is soluble in water.

Mr MrppLETon’s supposition that all bones contain two per cent. of fluor, is
certainly untenable, and so is his belief that bones invariably gain fiuorine whilst
undergoing fossilisation ; but he brought satisfactorily to the test of experiment
his view that fluoride of calcium may reach the bones both of living and dead
animals through the medium of water. His experiments were not made with
aqueous solutions, in which a mere trace of fluoride could at best be expected to
be present, but with sedimentary deposits, of natural and artificial origin. “I
was led,” says he, “to institute a series of experiments on aqueous deposits
of different ages, and I found, that, with one exception (a pure but incompact
stalactite of carbonate of lime), fluorine exists in all, from the most recent deposit
down to the old red sandstone, and that it is present in the older in larger pro-
portion than in the newer beds. I think it is, therefore, beyond a doubt, that it
is present in water, though, perhaps, in very minute quantity. What its solvent
may be I know not ; but that it is so held in solution my own experiments have
demonstrated ; and if they had not, the simple fact that the blood conveys it to
the bones, would, I apprehend, sufficiently refute any scepticism on the subject.’”’*

It may justly be questioned, whether the fact of a substance being soluble in
a highly complex fluid like blood, would entitle us to infer that it was equally
soluble in pure water. But it is singular that Mr Mipp.eron, holding such a view,
and after finding fluorine in so many aqueous deposits, should not have endea-
voured to dissolve the fluoride of calcium in water. He was, doubtless, prevented
from making any trials on the subject by the universal statement of chemists, that
the salt in question is quite insoluble in water.

2. Of the Solubility of Fluoride of Calcium in Water.

Many substances are spoken of by chemists as insoluble in water which are,
nevertheless, known to possess a certain slight solubility in that fluid. But
fluoride of calcium has been considered so well entitled to the character of total
insolubility, that our most accurate analysts, as BerzExius and Ross, have pur-
posely converted fluorine into this salt in their quantitative determinations of the
former, and have washed the latter freely with water, and, as they believed, with-
out its suffering any loss. Their example has been followed by all other analysts,
and the fact supplies a better proof than any quotation of individual authors could
do, that fluoride of calcium has been considered quite insoluble in water. Rely-
ing implicitly on the truth of this belief, I sought for a solvent of fluor-spar which
could retain it in union with water, and carry it into the tissues of plants and

* Quarterly Journal of Geology, vol. i, p. 215. . Mr MrppiEron’s other papers on fluorine are
in the Chemical Society’s Memoirs, vol. ii., p. 184; and in the London Phil. Mag., No, 164, p. 14.

FLUORIDE OF CALCIUM IN WATER. 149

animals. The frequent association of phosphate of lime and fluoride of calcium
in minerals, naturally suggested that whatever substance enabled water to become
charged with the one salt, would cause it to dissolve the other. Carbonic acid is
known to be one agent which confers upon water the power of taking up phos-
phate of lime ; it seemed worth while, therefore, to try whether it would cause it to
dissolve fluoride of calcium as it does so many other lime-salts. I was not aware
that Dana the American mineralogist,* and Professor Granam of London,+ had
anticipated me in this idea, or I should probably not have performed any experi-
ments on the subject. In ignorance of their views, the following trials were made.
A portion of pale green crystallised fluor-spar was reduced to fine powder and
digested for some hours in warm nitromuriatic acid, so as to remove any car-
bonate of lime, metallic oxides, or other foreign matters, which might be present.
It was then washed on a filter, dried, and suspended in pure distilled water,
through which a current of carbonic acid was passed for two hours. At the end
of this period the liquid was filtered through paper, and tested for lime by oxalate
of ammonia. A cloudiness was soon occasioned, and speedily a white precipitate.
On evaporating the liquid to dryness, a greyish-white residue was Jeft which gave
off sharp acid fumes when moistened with oil of vitriol. When this residue was
warmed with Nordhausen sulphuric acid in a platina crucible covered by glass,
the latter was deeply corroded in a few minutes. The process was repeated many
times, and always with the same result. I shew the Society squares of glass
which were etched in this way ; the engraved words having been traced through
wax, as in the ordinary method of testing for hydrofluoric acid. The experiments
referred to were made in January last, and were supposed to justify the idea
which led to their trial, namely, that carbonic acid was the agent which enabled
water to dissolve fluor-spar.

If carbonic acid, however, had been essential to the retention of fluor in solu-
tion, the expulsion of that gas, by warming the liquid, should have been followed
by the deposition of the fluoride. I was struck, however, by observing that the
solution could be raised to the boiling-point, without any troubling or opalescence
appearing, and that no precipitate shewed itself after protracted ebullition. It
was manifest that water was able of itself to retain in solution the fluoride if once
dissolved in it; and highly probable that it would prove equally sufficient to com-
mence the solution of the lime-salt. The experiment was accordingly tried of
suspending fluoride of calcium in cold distilled water, and shaking it occasionally
in a stoppered bottle for two hours. The liquid, after filtration, shewed lime with
oxalate of ammonia as readily as the carbonic acid solution had done, and left,
after evaporation, a residue which gave, with oil of vitriol, acid vapours etching

* Edin. Phil. Jour., vol. xxxix., p. 255.
t Note to Mr MipprzTon’s paper, Quart. Jour. Geol. Soc., vol. i., p. 216.

VOL. XVI., PART II. 2P

150 DR WILSON ON THE SOLUBILITY OF

glass. Distilled water was then boiled upon powdered fluor-spar and filtered
whilst hot. It precipitated oxalate of ammonia instantaneously ; and deposited,
after cooling, a small quantity of a white precipitate, which answered to the tests
of lime, and, when moistened with strong oil of vitriol, gave off an acid which
corroded glass. The supernatant liquid likewise precipitated oxalate of ammonia,
but more slowly, and yielded, on evaporation, a residue identical in characters
with the deposit from the hot aqueous solution. When the deposit or residue
was mixed with pounded glass and oil of vitriol, and heated in a flask, a gas was
given off which deposited gelatinous silica when passed through water, and had
all the characters of fluosilicic acid. It was manifest from these trials, that water
can dissolve fluoride of calcium ; and that it is more soluble in boiling than in
cold water.

The experiments I have mentioned are of so simple and decisive a kind, that
the conclusion they warrant cannot be evaded. That no error might arise from
impurity of material, many of them were made with water twice distilled, and
ascertained to be quite free from foreign matter. On the other hand, specimens
of fluor-spar were obtained from different cabinets; some massive; the greater
number well crystallised. The fluor was finely powdered, and thereafter, in the
greater number of cases, digested in warm aqua regia, washed and dried. The
only foreign body likely to be present, which could escape removal by this treat-
ment, is silica, a substance which would lessen rather than increase the solubility
of the fluor. Lest, moreover, the agents employed to purify the fluoride of cal-
cium should be supposed to have conferred on it a solubility which it did not ori-
ginally possess, other trials were made with native crystals, which, without preli-
minary treatment, were reduced to powder and boiled with distilled water. In
every case solutions were obtained, which, when cooled, yielded a deposit, or,
when evaporated, a residue, which gave off hydrofluoric acid when moistened
with oil of vitriol, and left sulphate of lime.

The pieces of etched glass which I shew the Society were corroded by hydro-
fluoric acid obtained from the fluoride of calcium previously in solution in water.
They will be observed to be as deeply dztien in as if undissolved fluor-spar had
been made use of. Four liquid ounces of the cold aqueous solution will be found
to leave sufficient residue to etch glass permanently. The residue from the same
amount of solution made at 212° Fahr. will act still more decisively.

The solution of fluoride of calcium in water at 60° is colourless, transparent,
tasteless, and precipitates oxalate of ammonia. Chloride of barium and nitrate of
baryta occasion a white precipitate. These reagents act more readily with the
solution at 212°.

The only one of these reactions I have yet found time to examine with any
attention is that of the salts of barium. The precipitate they occasion yields
hydrofluoric acid abundantly, when treated with oil of vitriol. I have not ascer-

FLUORIDE OF CALCIUM IN WATER. 151

tained whether it is simply a fluoride of barium, as it is likely to be, when nitrate
of baryta is employed ; or a double fluoride and chloride of barium, as it may be,
when the latter is the precipitant. Brrzerius has described such a salt. But I
have frequently availed myself of the fact that barium forms a sparingly soluble
compound with fluorine, in seeking for the latter in liquids. They are often most
conveniently tested for that substance by precipitating them by a salt of baryta,
and testing the precipitate for hydrofluoric acid. This reaction, moreover, has an
important relation to qualitative chemical analysis, inasmuch as it throws an
unsuspected difficulty in the way of distinguishing dissolved sulphates from
fluorides. The barytic precipitate, with solution of fluoride of calcium, is soluble
in excess of nitric and hydrochloric acids, but it requires a much larger addition
of these to redissolve it, than the carbonate, borate, or phosphate of baryta does.
A fluoride, therefore, may readily be mistaken for a sulphate, or a mixture of
both for only the latter. This mistake must have been frequently made in
analysing mineral waters, where fluorine is certainly more abundant than has
hitherto been suspected. When fresh analyses of these bodies shall be made, I
have little doubt that where fluorine is met with, as Mr Mrmp.erton has already
discovered it in the pipe-water of London, and I have detected it in one of the
wells of Edinburgh, it is the sulphates that will be found to have been over-
estimated, at the expense of whatever proportion of fluorine was also present.

The fact of the solubility of the fluoride of calcium in water introduces an
insurmountable objection to the present method of estimating fluorine quanti-
tatively. It accounts in part for the discrepance between the result obtained,
when fiuorine has been estimated by the loss which a substance containing it
sustained when heated with sulphuric acid, as contrasted with that which has
been procured when the hydrofluoric acid evolved was condensed in ammonia,
and precipitated by solution of chloride of calcium. Dr Davuseny, for example,
mentions that phosphorite from Estremadura, yielded, according to the first
method, fifteen per cent. of fluoride of calcium, according to the second, not nine
per cent.* Part of the difference was doubtless owing to the difficulty with
which fluor-spar is made to abandon all its fluorine when distilled with oil of
vitriol, in consequence of the pasty condition of the sulphate of lime which is
formed. But when we find Dr Dauseny mentioning, that he subjected the pre-
cipitated fluoride of calcium to “repeated washings with water,” in order to
remove any accompanying sulphate of lime, we may well suspect that fluoride of
calcium was also washed away.

T regret that I cannot yet announce the proportion of fluor-spar which water
dissolves. Owing to the corroding action which the solution occasionally exerts
on glass, I thought it unadvisable to employ vessels of that material, or of porce-

* Chemical Society’s Memoirs, vol. ii., p. 98.

152 DR WILSON ON THE SOLUBILITY OF

lain. I endeavoured to substitute for these, silver basins, but found it impossible
to prevent them gaining weight from the sulphuretted hydrogen constantly pre-
sent in an analytical laboratory. Through the liberality of Dr Grecory I have
recently obtained a platina basin of much larger dimensions than the resources of
my own laboratory afforded, and by means of it I shall be able to announce the
proportion of fluor-spar taken up by water. Meanwhile, we cannot doubt that
the proportion of fluorine has hitherto been estimated too low in most of the
substances ascertained to contain it. In some cases the error must have been
considerable.

Thad hoped that the barium salt of fluorine would prove suitable for the
quantitative estimation of the latter. It certainly would be much better than the
fluoride of calcium, but according to BERzELius it possesses a certain though
slight solubility in water. Fluoride of barium must accordingly be rejected also,
unless no better compound for estimating fluorine quantitatively can be discovered.
I may remark, in passing, that the fact that fluoride of barium is soluble in water
might have led to the discovery that the similar salt of calcium was so likewise.
The salts of barium, as a class, are much more insoluble than those of calcium,
If, therefore, the barium compound of a salt-radical be soluble in water, the
calcium salt of the same radical should, a fortiori, be still more so.

The observation of the previously unsuspected solubility of fluor-spar in
water, promised to throw light on some interesting problems connected with
geology, mineralogy, and physiology. I was induced, in consequence, to make a
series of researches in reference to these points, the results of which I shall now
briefly state.

Many of the investigations were very tedious, and I take this opportunity of
expressing my obligations to two of my pupils, Mr Henry C. Briaes and Mr
Henry WILLIAM STANSFELD, for the cordial and untiring assiduity with which
they aided me in my researches. To my assistant, Mr Davip Forpss, I have
likewise been greatly indebted for the most active co-operation throughout the
inquiry.

3. Of the presence of Fluorine m Well, River, and Sea Water.

It was impossible to doubt, after the facts I had observed in the laboratory,
that fluorine must be no infrequent constituent of well and river as well as of sea
water. BERZELIUS mentions that fluoride of calcium has been found in the waters
of Carlsbad.* Dr Curisrrson has pointed out to me that HuNEFELD detected a
trace of it in the waters of Gastein in the Tyrol,t and that PLantava found
or. 0:07 of the fluoride in 10,000 grains of the water of Lukatschowitz in

* Lehrbuch der Chemie, vol. ii., p. 607.
+ Bulletin des Sciences Médicales, vol. xvii., 425. From Jahrbuch der Chemie und Physik, xxii. 458,

FLUORIDE OF CALCIUM IN WATER. 1538

Moravia.* MippLEeTon has found it in the London pipe-water, and in three
other waters, the localities of which he does not mention; but as the experiments
were made in London, they were probably English. Traces of it have been found
in other waters also.

I was induced to search for it in the water used in certain of the breweries
in Edinburgh, in consequence of learning that these rapidly corrode the ther-
mometers employed to regulate the temperature of the boilers and vats. The
fact was first mentioned to me by a gentleman, who, before I made any trials on
the subject, inferred that the corrosion of the glass must be owing to the pre-
sence of a fluoride in the water. I discredited the statement when I first heard
it, supposing that an incrustation or deposition of sulphate and carbonate of lime
had been mistaken for a true corrosion. I thought it impossible, moreover, that
fluoride of calcium, even if it were present, could act upon glass. But in the
course of the experiments already detailed, I had once occasion to notice that a
new Berlin porcelain basin, in which a considerable quantity of the aqueous
solution of fluoride of calcium was boiled down, had its glaze completely re-
moved. On observing this fact, I applied to our intelligent instrument-maker, Mr
Stevenson, through whose hands the greater number of the thermometers used
by the Edinburgh brewers pass, in the course of receiving necessary repairs. He
informed me that he was quite familiar with the rapid dimming of the thermome-
ters, and that it was a true corrosion; in proof of which he gave me two pieces of
broken thermometers, which I shew the Society. They are certainly abraded,
and present a surface like that of ground glass. The roughening which is so
manifest was not the result of friction against the sides of the brewing vessel, or
any other kind of mechanical action; for the corroded part of the thermometer-
stem was enclosed in a brass-tube, and completely protected from external
violence. It is proper to mention that the workmen in some of our breweries are
in the practice of scraping the stems of their thermometers, to remove the de-
posit of lime-salts which rapidly gathers on them, and are ready to affirm that
the apparent corrosion is an abrasion occasioned by their own knives. To guard
against the possibility of any deception having occurred in this way, I visited the
brewery of Mr CampseELt, situated in the Cowgate, behind Minto House, and was
shewn by his manager a thermometer which had never been scraped with any
instrument, and had been in use only a few weeks, but was nevertheless so
dimmed, that it required to be dipped into water in order to confer upon it a
temporary transparency, before the included mercury could be distinctly seen.
Mr Stevenson informs me that he finds the protected parts of the thermometer-
stems, which are enclosed in brass-tubes, as much corroded as those which are
exposed.

* Bulletin des Sciences Medicales, vol. xvii. p. 425. From Zeitschrift fiir Physik und Mathematik.
VOL. XVI. PART II. 2 Q

154 DR WILSON ON THE SOLUBILITY OF

It seemed well worth while to seek for fluorine in one of these waters. I
obtained accordingly from Mr CampBeLv’s brewery, a portion of the abundant
deposit, consisting chiefly of sulphate and carbonate of lime, which collects with
great rapidity in the boilers. It was treated with nitric acid, the dissolved portion
poured off, neutralized with ammonia, and precipitated by nitrate of baryta. The
precipitate, after being washed and dried, was warmed with Nordhausen sulphu-
ric acid, in a lead basin; a square of waxed plate-glass, with characters traced
through the wax, being laid as a cover overit. In this, as in all other experiments
of the kind, a wall of wax was raised on the edges of the upper side of the glass,
so as to retain a portion of water sufficient to keep the plate cool, and condense
the hydrofluoric acid on it. This simple, but useful device, I borrowed from Dr
Daupeny.* Three squares of glass were very distinctly, though not deeply, etched
in this way.

Fluorine, then, was present in this water; and the fact has an interesting
relation to the circumstance pointed out to me by Mr Ross, that the well from
which it was obtained is sunk through a bed of sandstone, containing much mica,
a mineral in which Rost,t Turner, Grecory,t and other analysts, have found
between 1 and 2 per cent. of fluorine. In reference to the corrosion of the brewery
thermometers, however, I wish it to be distinctly understood, that I do not seek to
refer the whole abrasion of the glass to the action of a fluoride dissolved in the
water in which they are immersed. ‘The well-known experiments of LavoisrIER,
made in the end of last century, proved that even distilled water, if long boiled
upon glass, can corrode it. Every chemist is familiar with the rapid action of
solutions of the fixed alkalis, and of phosphate of soda on flint-glass. The in-
ferior kinds of bottle-glass, especially when containing too little silica and excess
of lime, have been shewn by Farapay|| and Warrineton to suffer corrosion by
the action of wine, and of diluted hydrochloric, sulphuric, and tartaric acids;
and it would be rash to suppose that these are the only re-agents that can act
upon. artificial silicates, especially upon those which contain excess of basic
oxides.

On the other hand, it is impossible not to connect the fact that the thermo-
meters are corroded, with the circumstance that the water which occasions this
corrosion contains fluoride of calcium. The other constituents of the brewery
water are chloride of calcium and sodium, sulphate of lime and of soda, carbo-
nate of lime and of magnesia, silica and organic matter; no one of which is known
to have any action on glass.

In connection with this fact I may mention, that Mr Srevenson finds the
thermometers used in the breweries in the valley of the Cowgate much more

* Chemical Society’s Memoirs, vol. ii., p. 101. + Poaernporr’s Annalen, vol. i., p. 80.
{ Brewsrer’s Journal of Science. || Chemical Society’s Memoirs, vol. ii., p. 247.

9

FLUORIDE OF CALCIUM IN WATER. 155

rapidly corroded than those employed in the similar establishments in the Canon-
gate. As the action of the water may be supposed to be the same at both places,
and the attending circumstances similar, it must be some constituent of the Cow-
gate wells that occasions the difference. It may be the fluoride of calcium.*

To conclude this part of the subject, I may state that Dr Curistison informs
me, that he has frequently had occasion to notice that considerable quantities of
natural waters evaporated to dryness in glass basins, permanently destroyed the
transparency of the latter. From all that has been mentioned, it will appear
that fluorine is likely to prove a frequent, though not an abundant, constituent of
ordinary water. If the proposal to construct the pipes of our water-works of
glass be put into practice, we may have an opportunity, on the large scale, of
testing the truth of this idea.

It follows as a corollary, from the truths already detailed, that fluorine must
be present in sea-water. ‘The inference that it must be there, had been drawn
by Mr Mippteton from the fact, that fluoride of calcium occurs in the shells of
marine mollusca.+ SILLIMAN junior has come to the same conclusion, apparently
without a knowledge of MipDLETON’s views, in consequence of invariably finding
the same fluoride in calcareous corals.t In the teeth of the walrus and of the
shark, the only marine animals I have examined, I found fluorine very distinctly,
especially in the latter.

I attacked the problem, however, directly, by examining the water of the
Frith of Forth. <A portion of the mother-liquor or dittern, from the pans at
Joppa, near Portobello (three miles from Edinburgh), in which sea-water is con-
centrated so as to yield culinary salt, was precipitated by nitrate of baryta. The
precipitate, after being washed and dried, was warmed with oil of vitrol in a lead
basin, covered by waxed glass, with designs on it. The latter were etched in two
hours, as deeply as they could have been by fluor-spar treated in the same way,
the lines being filled up with the white silica, separated from the glass. To the
acknowledged constituents of sea-water, fluorine, then, must now be added.

* As the fact of the frequent presence of fluorine in water must hereafter enter as an important
element into all speculations as to the cause of the corroding action of water on glass, I place here on
record the result of an accurate quantitative trial on the latter subject.

I am indebted to Mr Joun Aniz for the particulars of the following experiment, which was made
with a view to discover what peculiarity in the structure of glass unfits much of it for optical purposes. A
cube of glass, two and a half inches square, was inclosed in a fir box, and fixed immovably in it by pieces
of wood. Holes were pierced in the sides of the wooden case, so as to permit the free passage of the
water, and the whole was placed in an engine-boiler, supplied with the Edinburgh pipe-water, and left
there for six months. During that period the boiler was in action twelve hours each day ; the water
being under a pressure of 35 pounds on the square inch, and at a temperature of about 260° Fahr. The
cube weighed, when first immersed, 9157 grains, and, when taken out, had lost 457 grs., or about 34th
part of its weight. It is right to mention, that the condensed steam was returned to the boiler, so that
fresh saline matter was only furnished in the water added, from time to time, to supply the waste.

+ London Phil. Mag., No. 144, p. 14.

{ On the Chemical Composition of Calcareous Corals, by B. Sizniman junior.—American Journal
of Science, vol. i. Second Series.

156 DR WILSON ON THE SOLUBILITY OF

This fact, besides its interest in relation to natural history, will be welcome to
chemists, as adding another link to the lengthened chain of analogies between
chlorine, bromine, iodine, and fluorine. In teaching the beautiful law that bodies
closely allied in chemical characters occur together in nature, I have always felt the
force of the argument weakened, by the absence of fluorine from sea-water where
the other members of its class are so abundant. Its detection in bittern removes
the difficulty, and adds another to the many relations which are common to the
well-marked natural family of simple-salt radicals to which it belongs.

4. Of the presence of Fluorine in Minerals.

It remains to connect the initial fact of this paper with the occurrence of
fluorine in minerals, and in plants, and animals ; and, first, of minerals. I exclude,
in the meanwhile from notice, fossil bones, which will be best considered in rela-
tion to animal remains.

The solvent power of water over fluoride of calcium is likely to throw some
light both on the appearance and disappearance of that substance from particular
localities, in relation to geological changes. In connection with this branch of
our subject, Mr Rose has reminded me of a phenomenon familiar to mineralo-
gists, namely, the frequent occurrence of quartz with deep cubical impressions on
its surface, believed to be casts of crystals of fluor-spar, which had been dissolved
away after the deposition of the silica. It is possible that the markings may
have been occasioned by galena or iron pyrites, the latter of which we know, in
contact with air, can change into sulphate of iron and sulphuric acid, and is then
quite soluble in water, and might be readily carried away. Cubical iron pyrites,
however, in general is quite permanent, and suffers no change even with the freest
exposure to air; and galena is an exceedingly insoluble substance. Mineralogists,
accordingly, have universally agreed that the square impressions on quartz are
the imprints of fluor, and the very frequent association in nature of the latter
with silica, seems to justify their view. It has been a problem, however, what
agent has removed the fluor ; and it seems not impossible that water may have
been the body which dissolved it away. In confirmation of this idea, I may
refer to a paper by Mr Roperr Were Fox,* in which he describes certain
pseudomorphous octohedrons of quartz, “ more than an inch in diameter,” which
‘«‘ were broken from a copper vein in [z//as, at the depth of about 160 fathoms from
the surface.” The crystals were hollow, and many of them contained, hermetically
enclosed within them, water, or rather an aqueous saline solution, and numerous
pieces of fluor. “Of these,” Mr Fox says, ‘all the fragments are corroded, and
indicate, by their rounded edges and indented surfaces, the action of a solvent

* Transactions of the Royal Polytechnic Society of Cornwall, quoted in Edin. Phil. Journal, vol. xl.,
p. 115.

FLUORIDE OF CALCIUM IN WATER. s 157

which penetrated most readily between the planes of cleavage.” The contents of
the different crystals were not alike, and, unfortunately, Mr Fox, doubtless from
the belief that fluor-spar is insoluble in water, made no search for that substance
in the liquid procured by breaking the hollow octohedrons. In several cases,
however, it precipitated nitrate of baryta and oxalate of ammonia, an action re-
ferred to the presence of sulphate of lime, but which may, in part at least, have
been owing to fluoride of calcium being present in solution. Inthe matrix of these
crystals, alternate layers of quartz and fluor-spar were found in lines like fortifica-
tion-agate. When we connect these facts with the solubility both of fluoride of
calcium and of silica in water, and with the observed presence of fragments of the
former in the hollow crystals, it will be acknowledged that water, if not the true,
would at least be a sufficient cause of the phenomena described by Mr Fox, and
of the still more familiar one of square impressions on quartz, previously referred
to. I have tried the experiment of placing powdered fluor-spar on a filter, and
percolating distilled water through it, and have found that the latter precipitated
oxalate of ammonia. Whilst, however, I think it cannot be denied that water in
contact with fluor-spar must round off the edges of its crystals and dissolve it
away, we have no data from which to determine what effect salts held in solution
by water may have in increasing or diminishing its solvent power.

It is necessary to mention here that fluorine is already known to occur in
many minerals besides fluor-spar. It has been found in hornblende, as well as
in mica, in apatite, wavellite, wagnerite, urinite, phosphorite, &c., along with
phosphate of lime. Brrzexius and Rose* found it in sulphate of baryta; so did
Mipp.LetTon. I have found it there also; I have likewise obtained it in one case
from gypsum. It has been found in other sulphates, and MippLeTon has fre-
quently detected it in carbonate of lime. In general, it may be expected to occur
along with the insoluble salts of baryta, strontia, and lime, and probably also
with those of lead, especially when these are of aqueous origin. MmppLETON’s
detection of fluoride of calcium in the shells of marine mollusca, and SrLLIMAN’s
recent elaborate analysis of corals, which resulted in shewing that in nine different
species (the only ones in which it was sought for) fluoride of calcium occurred,
lead directly, as the latter gentleman has indicated, to the conclusion, that shell,
coral, and metamorphic limestones, may be expected to contain that salt. When
to these sources of fluorine we add animal remains, especially their bones and
excretions, but in truth their whole mass, it will be manifest that in all parts of
our globe, water may meet with fluorine, and carry it into the tissues of plants
and animals. This remark leads directly to its occurrence in the two latter ;
and, first, of plants.

* Griffin’s Rosé’s Quantitative Chemistry, p. 348.
VOL. XVI. PART II. 2k

158 DR WILSON ON THE SOLUBILITY OF

5. Of the presence of Fluorine in Plants.

Comparatively few examinations of plants have yet been made, in reference
to the occurrence of fluorine in them ; but these, on the whole, have been satis-
factory. SPRENGEL appears to have been the first to suggest the likelihood of its
presence in vegetables, but failed in detecting it in any of them, and referred his
failure “to its existing in such a state of combination as caused it to be dissipated
by the heat necessary for expelling the carbonaceous matter, so that it could not
be detected in the ordinary method.”*

Dr DavBeny “ascertained that no sensible action is exerted on glass by heat-
ing, with sulphuric acid, the earthy phosphates present, in twelve pounds of
barley.”+ Iwas equally unsuccessful with the ashes of Kanaster tobacco, and
of peas, and with those of charcoal and of coal. I ascribe the failure, however,
not to fiuorine existing in a peculiar state of combination in plants, but to the
presence of silica, which, when in any quantity, makes the detection of fluorine
very difficult. I took no measures to separate the silica in the few experiments
I made on the subject, and SpreNGEL and DAvuBENY appear to have omitted the
same essential preliminary. Dr Wrx1 of Giessen, who kept this point carefully
in view, states that “ careful experiments, conducted under his own superin-
tendence, by Messrs JAMES MULLER and BLAKE, severally, have shewn that the
ashes of French barley, grown in Switzerland, contain very distinct traces of it ;
both straw and grain were employed.” {

To Witt the credit of first finding fluorine in plants is entirely due. As
barley, however, contains a large amount of calcareous phosphates, which the
fluoride of calcium has been supposed to accompany in a peculiar state of combi-
nation, I thought it well to examine the ashes of a plant containing little phos-
phate of lime, and which might be considered as having derived any fluorine it
contained directly from the water its roots absorbed. I chose for this purpose the
crudest American potashes, which, as they are obtained in part by burning the
young and succulent branches of trees, should contain portions of all that is soluble
in the sap. A pound weight of ashes was supersaturated with hydrochloric acid,
the liquid poured off, neutralised with ammonia, and precipitated by nitrate of
baryta. The precipitate washed and dried, when treated with Nordhausen
sulphuric acid in a lead basin, in the way already described, etched glass dis-
tinctly.

Whether the fluorine found in plants is essential to them, and serves some
purpose in their organization, or merely circulates in their sap, as other soluble
matters do, without being appropriated by the living organism, cannot be deter-

* Chemical Society’s Memoirs, vol. ii., p. 103. + Ibid. ¢ Ibid, p. 182.

FLUORIDE OF CALCIUM IN WATER. 159

mined in the present state of our knowledge. But fluorine may be expected
to occur in the fluids of all the higher plants. On this subject Wit. observes,
“fluorine occurs in the teeth and bones of animals, having been derived by them
from vegetable food; it will doubtless, therefore, exist still more abundantly in
the ashes of plants.”* This expectation was probably founded on the supposed
insolubility of fluoride of calcium in water, and is not likely to be fulfilled.
Animals which may derive fluorine both from their solid food, whether animal or
vegetable, and likewise from the water they drink, are likely to excel plants in
the proportion of fluorine they contain.

6. Of the presence of Fluorine in Animals.

As there exists, then, a twofold source of fluorine for animals, we may antici-
pate its occurrence in various parts of their structures. Passing by for the
moment, as a disputed point, the occurrence of fluoride of calcium in recent
bones, and excluding the consideration of its presence in shells and corals, it may
be noticed that the urine of man is the only animal product in which fluorine has
been quite certainly ascertained to occur. Gay Lussac appears to have been the
first who suggested the probability of fluorine being found in the secretion of the
kidneys,+ but he did not make any experiments on the subject. With the pre-
cipitate obtained by adding lime water to human urine, Berzeius etched glass
distinctly ; and from the period of his experiments, fluorine has been ranked among
the normal, or at least the occasional, ingredients of the fluid in question. The
fact, however, has always been referred to with a kind of hesitation, and had it
rested on the authority of any less distinguished chemist than the great Swedish
one, it would have dropped, I fear, out of notice altogether. t

REEs repeated BERZELIUS’ experiment, but quite unsuccessfully, and, as in
the case of bones, affirms that fluorine cannot be found in urine. I made but
one trial on the subject, but it was so decisively confirmatory of BERZELIUS’
original result, that it seemed unnecessary to repeat it. About 50 ounces of
urine (wrina potus), were precipitated by nitrate of baryta, which, for reasons
already fully detailed, is preferable to lime, as forming a less soluble salt with
fluorine. The precipitate, consisting chiefly of sulphates and phosphates, was
collected on a filter, and dried without washing. Warmed with Nordhausen
acid, it corroded glass deeply, the lines being filled with white silica, exactly
as if fluor-spar had been used. In none of my experiments, except with the
dissolved fluor, and with sea-water, has the etching been so distinct as it was
in this case. I recommend those who wish to succeed in this experiment to
employ what the older physiologists distinguished as wna potus. In districts
where fluorine is not abundant in the soil or waters, it may not so frequently

* Chemical Society’s Memoirs, vol. ii. p. 182. + Ann. de Ch., t. lv.
{ Smon’s Animal Chemistry, vol. ii.

160 DR WILSON ON THE SOLUBILITY OF

occur in the bodies of animals, as it does in those of the inhabitants of other
localities. The experiment in question was made in Edinburgh.

It could not be doubted, after the facts I have detailed, that fluorine would
be found in the two great formative liquids of the animal body, blood and milk ;
T have found it in both. So far as I am aware, it has hitherto been overlooked
in all the analyses that have been made of these liquids; probably it has not
‘been sought for.

I employed the blood of the ox, and in two cases obtained markings on glass,
which only become visible when breathed upon, but are then quite manifest.
Tn the third the glass was distinctly, though faintly, corroded.

That others may know exactly how the experiment was made, I may men-
tion, that in the most successful case, about 128 ounces of blood were taken, which
had been freed, by stirring, from much of its fibrine, and was boiled till the liquid
solidified. The broken coagulum was burned in a large crucible, the ashes boiled
with dilute muriatic acid, and the liquid filtered and evaporated:to dryness. The
residue was then heated to redness to expel chloride of iron, and afterwards
washed with a small quantity of water, sufficient only to remove the accom-
panying chloride of sodium. The insoluble matter, which was in brilliant metallic
crystalline scales, was reduced to fine powder, and heated with Nordhausen
sulphuric acid, in a basin covered by waxed plate-glass. As the experiment per-
formed in this way gave the fluorine only or chiefly of the serum, we may expect
a still more decisive result to be obtained when the whole blood is taken. But
it is so difficult to burn the fibrine of blood, that I was content, in a first trial, to
experiment chiefly with the serum. As already mentioned, where the entire
blood was made use of, glass was marked, but not corroded. Both of the trials,
however, with the entire blood, were conducted so as to involve many washings,
which were avoided in the third and most successful experiment.

In examining milk, I thought to have saved myself the trouble of boiling down
large quantities of that liquid by using cheese, which was burned, and the ashes
digested in muriatic acid. The filtered solution was supersaturated with ammo-
nia, and the precipitate which fell (consisting chiefly of phosphates), washed, dried,
and tested with Nordhausen acid and glass. In three cases I totally failed to
detect fluorine whilst operating in this way. I was not more successful with
two quantities of milk treated similarly. I mention these failures to shew the
necessity of avoiding methods which imply much washing upon filters, when
fluoride of calcium is sought for. The large quantity of liquid made use of in the
course of the process referred to, may have held in solution and carried away all
the fluoride present ; especially as the addition of ammonia could only separate
fluoride of calcium previously dissolved by an acid. In the last and successful
attempt to detect fluorine in milk, the hydrochloric solution was neutralised with
ammonia and precipitated by nitrate of baryta. The precipitate, which was

FLUORIDE OF CALCIUM IN WATER. 161

slightly washed, etched quite distinctly. A still better process would be that
followed with the blood, where washing was reduced to aminimum. These expe-
riments throw no light on the condition in which fluorine exists in blood or milk;
nor would it be easy to ascertain in what state of combination it occurs. In the
meanwhile we may suppose it to be present as fluoride of calcium.

There is one other animal fluid, the last towards which suspicion as to its
containing fluorine was likely to have been entertained, in which hydrofluoric
acid has been declared to occur, namely, the gastric juice. BruGNATELLI states
that fragments of rock-crystal and agate inclosed in tubes, and introduced into
the stomachs of hens and turkeys, were found in ten days to have lost 10 or 12
grains in weight. TREVIRANUS, also, is said to have found that chyme from hens’
stomachs corroded porcelain capsules. These experiments are thought to prove
the presence of free hydrofluoric acid in the gastric juice. TIEDEMANN and
GMELIN placed the gastric juice of ducks in platina crucibles covered with plates
of glass, having lines traced on them through a coating of wax; but found no
action on the glass after 24 hours digestion with the aid of heat.* That hydro-
fluoric acid exists in the gastric juice of birds, in such quantity as to round off
pebbles with the rapidity implied by BRuGNATELLI’s observations, is not probable ;
but the force which is able to evolve hydrochloric acid at the stomach from the
chlorides which enter the system, is probably adequate, in similar circumstances,
to convert fluorides, along with the elements of water, into hydrofluoric acid. We
may now look for fluorine in all the animal fluids.

‘7 Of the presence of Fluorine in Fossil Bones, and its relation to Animal Life.

The facts detailed in the preceding sections remove much of the difficulty that
has attended previous speculations as to the source of the fluorine found in fossil
bones. It will now be conceded, that water must be constantly conveying that
element into the organs of animals, whilst other portions are also added in their
solid food. Whether this fluorine be supposed simply to travel through the
organism, dissolved in the circulating fluid as fluoride of calcium, or as some other
salt, and to quit the body as it entered it, without serving any purpose therein; or
be imagined to fulfil some important end in relation to the functions of life, it
must be expected to shew itself as a very frequent, if not constant, ingredient in
the bones. We may quite safely infer that a portion, at least, of the fluorine
found in fossil osseous remains must have been present in them when they were
parts of a living structure; and when we find only two per cent. of fluoride of
calcium in many ancient bones, while certain recent ones contain nine per cent.,
it may well be doubted whether a trace of the salt has been added during fossili-
zation. Nay, it is a question I think worthy of discussion, whether there may not

* These speculations will be found noticed in Berzextus’ Traité de Chimie, or in Simon’s Animal
Chemistry, vol. ii., art. Gastric Juice.

VOL. XVI., PART II. 258

162 DR WILSON ON THE SOLUBILITY OF

have been a decrease in the proportion of fluoride, water having washed it out,
and dissolved it away. We naturally turn for light on this problem to the con-
sideration of the question, What proportion of fluorine is found in the bones of
existing animals? Here, however, we are at once met, as has been already stated,
by the most contradictory declarations on the part of able chemists ; some affirm-
ing that fluorine is found in all bones; others, that none can be detected in any.

When it is considered how extremely simple the process of testing for fluorine
is, and how little room there is for difference in manipulative dexterity affecting
the result, I am constrained to admit, that, in the meanwhile at least, we must
refuse to fluorine the character of being a constant ingredient of bones. On the
other hand, it is certainly a very common one, more frequently present than ab-
sent; and we may encourage the expectation, that future researches will explain
satisfactorily the cause of failure where negative results have been obtained, and
prove fiuorine to be an ever-present constituent, not only of bones, but of other
animal tissues.*

The suggestion, accordingly, of Lirpic, that fossil bones contain only the
fluorine which was added to them whilst parts of living structures, may be found

* Certain of the recent observers have endeavoured to reconcile the conflicting statements of their
predecessors in reference to this subject, but with little success. Dr DaupEny conceives that the failures
may have arisen, in part, from the bones examined not having been deprived of their gelatine before
being tested for fluorine, so that the animal matter prevented the hydrofluoric acid from acting on the
glass.* But on the one hand, Fourcroy and Vavu@uELin, who were unsuccessful searchers for the
element in question, pointed out long ago the necessity of burning away the gelatine as a preliminary
step, and always did so before looking for fluorine.t+ On the other hand, Mr Mippieron, who found that
substance abundantly in bones, simply broke the latter into small fragments, and heated them with con-
centrated sulphuric acid. He states, moreover, that the time occupied by each experiment was only
between five and ten minutes.{| Dr Davseny refers likewise to the presence of salts of volatile acids
and salt radicals, such as chlorides and carbonates, from which hydrochloric and carbonic acids are evolved
when sulphuric acid is poured on the bones, and which sweep away the hydrofluoric acid before it has
time to corrode the glass. He has accordingly described a method of procedure which gets rid of the
volatile bodies in question, but only at the risk of losing, in the liberal washings prescribed, much of the
fluoride of calcium. It cannot be doubted that the acids which accompany the hydrofluoric, when sul-
phuric acid is poured upon burned bones, dilute and carry away the body sought for. But Fourcroy
and VAUQUELIN’s experiments, which were made by distilling bones with sulphuric acid in glass vessels,
could have been but little affected by this source of fallacy; and Brerzexius’ successful results were
obtained in the very same way.

After trying DauBENny’s process several times, I am constrained to acknowledge that I did not find
it give any better results than the simpler one previously in use. If it be deemed requisite to get rid of
the carbonic acid of bones before testing for fluorine, I believe it could be done most efficaciously by
digesting them, after being burned and reduced to powder, in a solution of tartaric acid, and, after the
whole carbonic acid had been expelled, drying up the mass.

Rzzs, taking the opposite view from Davzeny, has endeavoured to prove that, where fluorine
has been supposed to be present, it was in reality phosphoric acid that corroded the glass.§ He acknow-
ledges, however, that this explanation applies only to those cases where the bones were distilled with
sulphuric acid, and the product of distillation evaporated to dryness in glass vessels. He regards as un-
exceptionable, experiments made with platina crucibles covered with waxed glass; and as MIDDLETON’s,
Davseny’s, and my own trials were made in this way, and distinct corrosion or etching obtained, his
suggestion must be considered as leaving the subject where it found it.

* Chemical Society’s Memoirs, vol. ii., p. 100. t+ Annales de Chimie, tome lvii., p. 38.
t Memoirs of Chemical Society, vol. ii., p. 135. § Edin. Phil. Journal, vol. xxviii., p. 93.

FLUORIDE OF CALCIUM IN WATER. 163

quite sufficient in many cases, especially if we add to the food, the drink of ani-
mals as a source of the ingredient in question. But when we find fossilized bones
containing ten or fifteen per cent. of fluoride of calcium, whilst, at the same
time, they have lost to a great extent their original structure, and have acquired
a crystalline or mineralized one, it seems highly probable that Mr MippLEron’s
belief that water may have infiltrated that salt into them, will prove worthy of
adoption. I cannot, however, agree with him in thinking, that it is enough to
shew that water may bring fluoride of calcium to bones, to account for its accu-
mulation in them. Water, as my own experiments prove, may carry away fluo-
ride of calcium from osseous remains, as well as transport it tothem. We require
to account for its detention in bones, as well as for its conveyance to them. From
an experiment made in the laboratory, as well as from their association in nature,
I am inclined to think that there is a double phosphate of lime and fluoride of
calcium, much less soluble than the latter salt is; and that the production of this
compound fixes the fluoride, and prevents its abstraction by water. Further re-
searches will decide this point. Till quantitative analyses of a considerable num-
ber both of recent and fossil bones are made, as to the proportion of fluoride of
calcium in them, it will be impossible to decide how far individual fossils which
contain that salt are to be looked upon as coming under Lirpic’s or MIpDLETON’s
explanation, or as requiring, as many probably will do, a reference to both.
Some, as already stated, may appear to have lost, instead of gaining, fluoride of
calcium, during their entombment.

Allusion was made, in the commencement of the paper, to the possibility of a
conversion of fluoride of calcium into phosphate of lime having occurred. Few
would more gladly see the idea of elemental transmutation realized by natural
phenomenon or laboratory experiment than I should do. I can find nothing,
however, to support it in the phenomena I have been discussing.

In conclusion, I would observe, that physiologists will doubtless now be
tempted to speculate on the possibility of fluorine performing some essential
function in living animals. Its occasional absence from their bones would not
disprove that it may be necessary for the perfection of certain organs, though not
for all. Quantitative analyses appear already to have indicated that the enamel
of teeth contains more fluorine than any other part of the body. If that result
shall be confirmed, we may suppose that, if fluorine be furnished when the deve-
lopment of the teeth is proceeding, it may be wanting at other periods, without
injury to the animal; just as chloride of sodium must be considered as essential
to the healthy life of most creatures, though they may be deprived of it for long
intervals, without death ensuing.

The small quantity of fluorine found in living structures can be counted no
argument against its occasional or constant importance. Quantity, is at best,
but a rude measure of the value of an ingredient, in relation to the necessities

-

164 DR WILSON ON THE SOLUTION OF FLUORIDE OF CALCIUM IN WATER.

of an organism. The law of final causes, in truth, would indicate that only
a minute proportion of fluorine should occur in any organ ; for it would be peril-
ous to an animal to introduce into its system a large quantity of fluorides, which
can so readily be changed into the deadly hydrofluoric acid. Such speculations,
however, are premature. It will be time enough, when many qualitative, but
especially quantitative, researches have been prosecuted, as to the presence of
fluorine in animal structures, to consider of what service it is to them ; if it be

of any..

Enpinzurex, April 4. 1846.

( 165 )

XVIL.—Observations on the Principle of Vital Affinity, as illustrated by recent
discoveries in Organic Chemistry. By Witt1amM Putrenry Auison, M.D.,
F.R.S.E., Professor of the Practice of Medicine in the University of Edin-
burgh.

(Read, 2d February 1846.)

Part I.

THE most important steps in a science are those which lead most directly to
the establishment of principles or laws peculiar to that science itself, and which
constitute its claim to be regarded as a distinct branch of human knowledge. It
has been long acknowledged that such is the character of many of those pheno-
mena of living bodies which depend on mechanical movements, or changes of po-
sition in their particles, and therefore that the laws of vital contractions are to
be regarded as equally elementary and distinctive principles in physiology, as
the laws of motion or of gravitation in natural philosophy. But a difficulty has
been long felt, as to whether a similar claim to peculiarity of the principle on
which they depend, can be urged for the chemical phenomena of living bodies.

In laying down the first principles of Physiology and of Pathology, I have,
however, uniformly maintained the existence of a power peculiar to living bodies,
and to which the term Vital Affinity, as recommended by several authors, may
be properly applied ;—a power by which “the elements of nutritious matter are
thrown into the combinations necessary for forming the organic compounds, and
restrained from entering into other combinations, to which they are prone as soon
as life is extinct;—a power which supersedes and counteracts ordinary chemi-
cal affinities in living bodies, as completely as vital contractions counteract gra-
vitation or the inertia of matter.”—(Outlines of Human Physiology, p. 22.) And
in delivering lectures on physiology, I always expressed my belief that a time
would:come, when discoveries in the chemical department of the science,—connect-
ing the ingesta of living bodies with the nourishment of their different textures,
and with the nature of the different excretions,—would elucidate the chemical
changes which are continually going on in them, and are essential to their living
state, as completely as the discovery of the circulation of the blood illustrated
many of the conditions of the existence of living animals. It appears to me that
this anticipation has been more nearly realized by recent chemical observations,
than professed physiologists have yet admitted ;—that not only the existence of
the principle of vital affinity has been established, but its limits and mode of

VOL. XVI. PART II. 2T

166 DR ALISON’S OBSERVATIONS ON

action, the cases in which it acts, and those in which it is unconcerned, are to a
certain degree defined ;—and that a short and general illustration of these points
may be of some advantage, if not to the progress of the science, at least to the
due appreciation, and proper generalization and expression of the knowledge
which has been already acquired.

To shew the importance of this inquiry, I need do no more than quote a
single sentence from Cuvier, with a statement which is nearly a commentary
upon it by Professor WHEWELL. “It belongs to modern times to form a just
classification of the vital phenomena; and upon the zeal and activity given to
the task of analysing the forces which belong to each organic element, depends,
according to my judgment, the advancement of physiology.”* “ As the vital
functions became better understood, it was seen more and more clearly at what
precise points of the process it was necessary to assume a peculiar vital energy,
and what sort of properties this energy must be conceived to possess. It was
perceived when, and in what manner and degree, mechanical and chemical
agencies were modified, overruled, or counteracted by agencies which must be hy-
per-mechanical and hyper-chemical.” “Tn attempts to obtain clear and scientific
ideas of the vital forces, we have first to seek to understand the cause of change
and motion in each function, so as to see at what points of the process peculiar
causes come into play; and next, to endeavour to obtain some insight into the
peculiar character and attributes of these causes.” +

When we say that the chemical changes which take place in living bodies
are elucidated, we mean, of course, that they are referred to general laws, by
which the phenomena observed in this department of Nature are found, by expe-
rience, to be regulated. And when we say that these are laws of vitality or of
vital action, we mean merely, that they are laws deduced from the observation
of phenomena peculiar to the state of life,—taking for granted that it is always
possible to describe, and practically to distinguish, those substances which we call
living, from inorganic or dead matter; and that the only correct definition of
vital principles or vital powers, is, that they are the laws or the powers which
regulate the phenomena that are peculiar to the state of life. They are the gene-
ral expression of the results of the observation, and generalization of the facts,
which are observed in this department of nature, and which are ascertained to
belong to this department alone.

We are not, indeed, justified in asserting the existence of laws peculiar to
the state of life, merely by the negative observation, that the phenomena referred
to them are inexplicable by any known laws of inorganic or dead matter; we must
have the positive observation that they are inconsistent with—that they take place

* Hist. des Sciences Naturelles depuis 1789, p. 218.
T Philosophy of the Inductive Sciences, vol. ii., pp. 39 and 47.

THE PRINCIPLE OF VITAL AFFINITY. 167

in despite of—the laws which regulate the changes of dead matter. It is thus that
we are led to ascribe the visible movements of living bodies to vital powers; not
because we do not perceive how gravitation, elasticity, or any other known
causes of movement in dead matter should produce them, but because we do
perceive, that, in the circumstances in which we see these motions, all those
principles, deduced from the observation of dead matter, would determine either
rest, or motion in a different direction from that which really takes place.

I formerly laid before this Society the grounds of an opinion, then much
disputed, but now, I think, pretty generally admitted, that there are Attractions
and Repulsions, as well as contractions, peculiar to the living state: chiefly, but
not exclusively, observed at those parts where chemical changes are effected in
living bodies, and connected with these changes; and, without reference to this
general fact, I maintain that it is impossible to have a right understanding of
many phenomena of essential importance in physiology and pathology.*

But the general principle is obviously equally applicable to chemical changes
as to mechanical movements. It is not, indeed, so easy to ascertain, in regard to
chemical changes in living bodies, that they are truly inconsistent with the chemis-
try of dead matter; the science must be allowed to make some progress before
this can be confidently asserted in regard to any individual chemical change; but
no one can doubt that, as science advances, it must become possible to say with
certainty, whether the chemical changes in living bodies are consistent with those
laws which regulate chemical changes elsewhere, or not; 7. ¢., whether the same
chemical elements can be so brought together by the chemist, as to tend to the
same combinations as are found in living bodies; or whether, in his hands, they
will enter uniformly into other combinations, and form different compounds.

Farther, it appears to me that, even before any of the recent discoveries, it
might be legitimately inferred from facts already known, that this last descrip-
tion is truly applicable, in some cases, to the chemistry of living bodies. It was
known, for example, that when water, impregnated with carbonic acid and with a
small proportion of ammonia, is brought into contact with vegetable substances, in
a certain stage of their existence, the elements of these bodies rapidly combine so
as to form starch, albumen, and oil, which are added to the substance of the vege-
tables,—that under no other circumstances can water, carbonic acid, and ammo-
nia, or their elements, be made to form these compouds,—and farther, that after
a time, when brought into contact, at the same temperature, with the same vege-
table substance in an ulterior stage of its existence, they will form no such com-

* Professor WHEWELL, in his instructive abstract of the general principles ascertained in Physio-
logy, regards it as established, chiefly on the authority of MiiLiER, in regard to the vital force concerned
in assimilation and secretion, that “« it has mechanical efficacy, producing motions, &c. But it exerts
at the same point both an attraction and a repulsion, attracting matter on one side and repelling it on
the other ; and in this it differs entirely from mechanical forces."—Philosophy of Inductive Sciences,
vol. i1., p. 51. See also Carrenter’s Manual of Physiology, § 597, et seq.

168 DR ALISON’S OBSERVATIONS ON

pounds, but will aid and participate in the successive changes to which vegetable
matter is liable after the phenomena of its living state are over, and of which the
ultimate result is, the resolution of that matter into its original constituents.
And from these facts it seems quite reasonable to infer, that during the former, or
what we call the living state of the vegetable, certain affinities peculiar to the
living state—7. ¢. certain vital affinities—actuate the elements of which it is
composed.

In asserting the existence of vital affinities, we do not, in the first instance,
give any opinion whether it is by the addition of certain chemical attractions, or
by the suspension of others, during the living state, that the chemical changes
peculiar to that state are effected; we assert nothing more than what is, as I
think, correctly stated in the following sentence of Liepic :—“ The chemical
forces in living bodies are subject to the invisible cause by which the forms of
organs are produced.” ‘The chemical forces are subordinate to this cause of
life, just as they are to electricity, heat, mechanical motion, and friction. By
the influence of the latter forces, they suffer changes in their direction, an increase
or diminution of their intensity, or a complete cessation or reversal of their action.

“ Such an influence, and no other, is exercised by the vital principle over the
chemical forces.”

“« The equilibrium in the chemical attractions of the constituents of the food
is disturbed by the vital principle, as we know it may be by many other causes.
The union of its elements, so as to produce new combinations and forms,
indicates the presence of a peculiar mode of attraction, and the existence of a power
distinct from all other powers of nature, viz., the vital principle.”—(Organic
Chemistry, S§c., pp. 355, 357).

In these passages I think that Lizsic has expressed himself with per-
fect accuracy; but in other parts of his writings he uses language in regard
to the nature and results of chemical changes in living bodies, which seems to
me vague and speculative, and even inconsistent with what he had stated in the
passages just quoted, ¢. g., when he says that “the ultimate causes of the differ-
ent conditions of the vital force in nutrition, reproduction, muscular motion, &c.,
are chemical forces.” —( Organic Chemistry, p. 10).

The following sentence by MutprEr expresses the very same idea, although it
might be thought, from the manner in which this author expresses himself against
any introduction of the vital principle in this department of physiology, that he
considers all the chemical changes in living structures to be referable to the same
laws as in inorganic matter.

“ By asmall organ of a plant @ force is exercised, exciting forces which slum-
bered in the carbon, oxygen, and hydrogen, or rather modifying the forces which
existed in these, so that 12 equivalents of carbon unite with 10 of hydrogen and
10 of oxygen; and from 12 equivalents of carbonic acid (12 C O,) and 10 of water

THE PRINCIPLE OF VITAL AFFINITY. 169

(10 H O) starch is produced, 12 C 10 H10 O, 24 of oxygen passing off.” —(Chemistry
of Vegetable and Animal Physiology, p. 67).*

But it is important to fix our attention, for a short time,on the instances
adduced by Mutper, of the formation of starch, or some of its allied compounds,
out of carbonic acid and water, by the combination of the carbon of the acid with
the elements of water, and the expulsion of the oxygen of the acid ; because this
is the grand and fundamental power, which must have been called into operation
when organized structures were first created on earth, and on the continued
exercise of which the existence of all such structures, vegetable and animal, is
still essentially dependent ; and because the simplicity of the process makes it a fit
case for considering the question, whether the power here named is strictly en-
titled to the epithet vital; or whether, as some eminent physiologists in this
country maintain, the idea expressed by that term is incorrect and unscientific.

The opinion of those who oppose the doctrine of vital affinity, is thus dis-
tinctly stated in the Anatomy of Drs Quarn and SHARPEY:

“ Although the products of chemical changes in living bodies for the most
part differ from those appearing in the inorganic world, the difference is never-
theless to be ascribed, not to a peculiar or exclusively vital affinity different from
ordinary chemical affinity, but to common chemical affinity, operating in circum-
stances or conditions which present themselves in living bodies only; and un-
doubtedly the progress of chemistry is daily adding to the probability of this
view.”

I consider this to be a hasty and ill advised statement; and to shew this, I
request attention, jist, to the perfect simplicity of the apparatus by which this
change is effected. “In all plants,” says Muuper, “there exists a small organ,
of the most simple form, although employed by nature for the most varied pur-
poses. It is a small filmy sac, a thin membrane, which encloses a small space,

which it enables to communicate with the exterior space through invisible pores.
These little sacs or cells are'the chief organs of plants. A countless multitude
of them, grouped together, forms the whole bulk of the plant, so that if every thing
except the cells be destroyed, the shape and size of the plant are not in the least
changed or diminished.”

Into this simple apparatus in certain parts of plants, water, impregnated with
carbonic acid, is introduced, while the plants exhibit the phenomena of life; and

* In the foregoing and other translations from recent German writers, the word force is used in
a sense which I think would be much better expressed by the term power or property, merely on this
account, that the English word force, in physical discussions, has usually a precise and limited meaning
assigned to it, as a cause capable of producing visible motion, and of which we have a measure, either
in the velocity or in the quantity of motion which it can excite ; whereas the term power or property,
applied to any material substance, has a more general meaning, as simply the cause of change of any

kind, and is therefore applicable where the result of the property ascribed to any substance may be very
different from visible motion.

VOL. XVI. PART II. 2U

170 DR ALISON’S OBSERVATIONS ON

let us next observe the intensity of the action by which the carbonic acid is
there decomposed, the carbon attached to the elements of the water, and the
oxygen set free. “This is done by a power,” says Liste, “to which the strongest
chemical action cannot be compared. The best idea of it may be formed by con-
sidering, that it surpasses in power the strongest galvanic battery, by which we
are not able to separate the oxygen from carbonic acid. The affinity of chlorine
for hydrogen, and its power to decompose water, under the influence of light, and
set its oxygen at liberty, cannot be considered as nearly equalling the power and
energy with which a leaf, separated from a plant, decomposes the carbonic acid
which it absorbs.”—Organic Chemistry, p. 134.

Next let us observe the extent to which this energetic power is exercised by
living plants. Perhaps the most accurate idea of it may be formed from attend-
ing to the statement of THEopoRE DE Saussure, that on a mean of 54 observations
made ina country district, the proportion of carbonic acid in the atmosphere
during the night was to its proportion in the day-time as 432 to 398, 7.¢., the
carbonic acid existing in the atmosphere was found to be diminished very nearly
10 per cent. in a few hours of every day; and for this diminution we know no
cause, except that this power of the green parts of vegetables, of decomposing the
carbonic acid of the atmosphere, is exercised only under the influence of light.*

Now if a power of this extraordinary energy and extensive operation, and
acting in so very simple a manner, were really to be regarded as depending
only on ordinary chemical affinities, exerted under peculiar conditions, it might
surely be expected, that the chemist might so regulate the conditions under which
he might bring together carbonic acid, air, and water, as to exhibit some traces
of this power, and effect some decomposition of the carbonic acid and evolution
of oxygen. But we know, not only that this cannot be done, but that when air,
water, and carbonic acid, are introduced into the very same vegetable cells, with-
in half an hour after they have exhibited this phenomenon, at the same spot,
under the same light, and at the same temperature, they will not only fail to
exhibit the same change, but will uniformly exhibit the very reverse, 7. ¢., the
absorption of oxygen and the formation and evolution of carbonic acid.

Nay, we know that it is only in certain cells of the living vegetable, that this
peculiar chemical change, under the action of light, is effected; the same fluid,
introduced into cells composed of the same material in the parts of fructification,
undergoes no such change; but, on the contrary, gives occasion only to the reverse
process, the absorption of oxygen and evolution of carbonic acid.+ .

Then it is to be remembered, that this complete inversion of ordinary che-
mical affinities, in the case of the living plant, is only one of several cases to

* See Macarre’s Memoir of THEoporE DE SaussuRE, in Edinburgh Philosophical Journal, vol. xl.
p. 3l. (Jan. 1846,)
+ TxHeEopore bE Saussure, in Edinburgh Philosophical Journal, vol. xl. pp. 22, 23.

THE PRINCIPLE OF VITAL AFFINITY. 171

be afterwards noticed, where we see chemical compounds uniformly formed in
living bodies, quite distinct from any that can be formed by the chemist from the
same elements, and quite distinct from those to which the same elements uni-
formly revert, after the phenomena of life are over.

Lastly, we must remember, when we see this apparent inversion or altera-
tion of the ordinary chemical relations of matter, taking place in the interior of
_ living bodies, that in that scene, by the admission of all, matter comes under the
| dominion of mechanical laws, which operate in no other department of nature;
so that it is quite conformable to analogy to suppose that its chemical relations
will undergo a similar modification.

When all these considerations are duly weighed, I cannot perceive what fur-

ther evidence can be required in order to justify the expression which I have
quoted from LiepiG, viz., that the “new combinations,’ as well as the forms,
assumed by that matter which goes to the composition of organized beings, “ indi-
| cate the existence of a power distinct from all other powers of nature, viz., the
| vital principle ;” 2. ¢., that the vital principle regulates the changes of chemical
| composition, as well as the changes of position which the particles of that matter
' undergo; which is more simply expressed. by saying, that there are vital affinities
as well as vital contractions and attractions.
But even if we are to regard it as doubtful whether or not ordinary chemical
_ affinities can determine, under any conditions, this decomposition of carbonic acid
_ and evolution of oxygen by its contact with carbon and the elements of water, I
| maintain that it is sound philosophy, when we see this and other rapid and exten-
_ sive and important chemical changes, essentially different from those which the
| same elements present under other circumstances, uniformly attending the pheno-
mena of life in vegetables,—to investigate and generalize the laws by which these
| changes are regulated, as laws of living action, leaving it open to future inquirers,
| if they can, to resolve them into other laws of more general application. For
| although I acknowledge the force of the aphorism, “ Frustra fit per plura quod
| potest fieri per pauciora,” still I apprehend, that in every case to which this
aphorism is applied, the potest jiert must be established, not by conjecture, but
| by experiment; otherwise we fall into the error, so strongly condemned by Bacon
| and others, of prematurely generalizing, and supposing the laws of nature to be
| fewer and more comprehensive than they really are.

| Having thus, in reference to this first and simplest example, vindicated the
| soundness of the principle which I propose to illustrate, I think we may next
| shew, that the main object of inquiry in the chemical department of physiology
| is more simple and precise, and the extent of that inquiry, necessary to elucidate
| most questions in physiology, much less than might be supposed from the multi-
| plicity of details, of which what is called the science of organic chemistry is made

172 DR ALISON’S OBSERVATIONS ON

up. After what Lizsie calls the “ peculiar mode of attraction” which operates in
living bodies, has led to the formation of certain organic compounds, these com-
pounds lose their connection with living bodies, become liable to an infinite
number of changes and decompositions, and thus give origin to an infinite variety
of substances—generally of temporary duration only, because retained in their
form by attractions of no great intensity—applicable to many useful purposes,
but foreign to the inquiries of the physiologist. He is concerned only with the
chemical changes which take place in living bodies themselves, and during the state
of life; and the results of recent inquiries seem to me sufficient to shew, that the
fundamental and peculiar arrangements of chemical elements there observed are
less numerous, and the laws regulating them more simple, than they have usually
been thought.

In considering this subject, we are enabled, by the results of the inquiries of
geologists and physiologists, to revert to the period of the introduction of living
bodies into the world, and reflect on the conditions then assigned for their exist-
ence. We are justified, by reason, in allowing the imagination to fall back on
the time when this Earth rolled through space an inanimate mass; and if any
minds, besides that of the Great Ruler of the universe, were connected with it, they
did not hold their connection through the medium of any organized structure.
For I believe we are justified in laying down these propositions as established,
jirst, That the simply physical arrangements of this globe were completed be-
fore any organised beings were created ; secondly, That vegetables were created
and lived chiefly on the atmosphere, fixing large quantities of carbon from it on
the earth’s surface, before animals were called into existence; and, thirdly, That at
whatever time their existence began, either the first living being of every species,
vegetable and animal, or the first ovum from which that being was developed,
must have been formed in a manner wholly different from that in which any
living bodies, at least of the higher orders, are now reproduced ; 7. ¢., that they
must have been formed in a manner strictly miraculous, and, of course, beyond
the limits of physical science.

But although we cannot ascend higher, in prosecuting this subject, than to
inquire in what manner the first plants, or the germs of the first plants, were
enabled so to act on the inorganic matter around them as to extract from it the
materials, first of their own growth and sustentation, and afterwards of all other
organized beings,—yet in the inquiry, thus limited, important progress has been
made. From the time when these nascent organized bodies sprung into existence,
we must regard it as an ultimate fact, that they were endowed with the power,
which all the vegetables that have succeeded them have exercised, of so modify-
ing the attractions existing among the particles of matter, as to cause many of
these particles from the air and the water immediately surrounding them, to
enter into their substance, by their roots and leaves, or by the organs which soon

THE PRINCIPLE OF VITAL AFFINITY. 173

became their roots and leaves, and then to arrange themselves there, in those
peculiar forms by which the numberless species of the vegetable world are cha-
racterized. I apprehend we must also regard it as an ultimate fact, that they
were endowed with the power of so modifying the chemical relations of the ele-
ments composing those absorbed matters, as to select and retain certain of these
elements, and allow others to pass away from them, to decompose the carbonic
acid, fix the carbon, and invest it with those peculiar affinities for the water, the
hydrogen of the water, and a few other elements, contained in the surrounding
media, by which all the proximate principles, first of vegetables and then of ani-
mals, and therefore the whole substance of organized beings, are formed.

But it is important to have a precise exposition, although not an explanation,
of the power thus exercised by the first plants; and it is still more important
and satisfactory to be able to shew how, by the exercise of these and analogous
vital powers, the atmosphere must have been gradually changed, the propor-
tion of carbonic acid in it diminished, and the proportion of oxygen increased ;
how it became fitted, and is kept fitted, for the residence, first of cold-blooded and
then of warm-blooded animals ; how most of the other conditions of existence of
these animals have been, and still are, continually prepared for them by these
living actions of vegetables ; how-all the variety of the textures of all organized
bodies, from the origin of vegetables to the death and decomposition of animals,
-are continually formed and maintained ; and how, in both divisions of organized
beings, Nature has provided, not for the permanent existence, but for the deve-
lopment and decay of successive generations of individuals, and thus for the per-
petuation of the species. These are the subjects of investigation in the chemical
department of physiology ; and if it can be shewn, that, by a few simple laws,
regulating what we call vital attractions and affinities, 2. ¢., modifying, in organ-
ized bodies, the attractions and affinities to which matter is everywhere liable,
provision is made for all this succession and continual renewal of the phenomena
of life; then, although we cannot explain the introduction of living beings into
the world, any more than we can explain the dissemination of the stars through-
out space,—although we must always regard the appearance of organized bodies
on the earth’s surface as the clearest indication which human knowledge presents
of the subjection of the universe, not only to general laws, but to an arbitrary
Will, superior to these laws and changing them at pleasure,—yet I think it may be
said that we have nearly as clear an insight into the designs and arrangements
of Providence for the maintenance of living beings upon earth, and for the eternal
reproduction of them there, so long as these laws shail be in force, as we have
into those by which the movements of the heavenly bodies are directed and
controlled.

I. Our first business is to study the facts that have been ascertained in regard

to the simplest form of chemical change to which the term vital may be applied,
VOL. XVI. PART II, 2 x

174 DR ALISON’S OBSERVATIONS ON

which is merely the selection, by a portion of a living structure, of some one sub-
stance existing in a fluid, and the consequent attraction of this to a particular
part of the structure, while other materials, equally presented to that living part,
are excluded.

We need not here enter into the question, on which chemists and agricul-
turists are not yet agreed, whether the nourishment of plants, in the present con-
dition of the earth’s surface, does or does not require the pre-existence, in the soil,
of organic compounds, resulting from previous living beings, which are absorbed
from it. But we may justly give the name of vital attraction or affinity to
that power by which certain saline matters, dissolved in the compound fluid
which is absorbed, are retained in the substance of the plant, while others are
returned to the soil. ‘‘ The experiments of Macarre PRINcEP,” says LEIBIG,
“ have shewn that plants, made to vegetate with their roots, first in a solution of
acetate of lead, and then in rain-water, give back to the latter all the salt of lead
which they had previously absorbed. Again, when a plant, freely exposed to the
air, rain, and light, is sprinkled with a solution of nitrate of strontian, the salt is
absorbed, but is again separated by the roots, and removed farther from them by
every shower of rain, so that at last not a trace of it is to be found in the
plant. A fir-tree, the ashes of which were analysed by a most accurate chemist,
grew in Norway, on a soil to which common salt was conveyed in great quantity
by rain-water. How did it happen that its ashes contained no appreciable quan-
tity of salt, although we are certain that its roots must have absorbed it after
every shower? We can explain this only by the observations above referred to,
which have shewn that plants return to the soil all substances unnecessary to
their own existence ; and we are thus led to the conclusion that the alkaline bases,
existing in the ashes of plants, must be necessary to their growth, since, if this
were not the case, they would not be retained.” (Ib. p. 103, 4.) Another in-
ference is at least equally obvious, that plants have the power of fixing and
retaining within them, those matters which are suited or essential to their com-
position; and this power we regard as the simplest form of vital affinity. It
may be said, that the alkaline bases are thus fixed in plants, because they enter
into combination with organic acids, and that, therefore, it is the formation of
these acids, not the retention of the bases which combine with them, that is truly
the vital change. But this does not apply to other saline matters contained in
vegetables, which must have been taken up from the soil in the same state in
which they are found in the plants, e. g., the phosphate of magnesia, which is
‘“‘an invariable ingredient in the seeds of grasses ;” or the silica which is found
in certain parts of various plants.

Were it not for this sclecting and appropriating power, indicating a simple
attraction of some parts of the vegetable for certain earthy or saline matters only,
we should find some salts of alumina, as well as of lime or magnesia, in the ashes

THE PRINCIPLE OF VITAL AFFINITY. 175

of almost all vegetables,—that earth existing in large quantity in all fertile soils,
whereas it is “ very rarely found in the ashes of plants.”

In the animal kindom the same power of simple selection and extraction is
more fully exemplified, perhaps most strikingly in the development of many of
the lower classes, of which the organization is simple, and the matters deposited
from the nourishing fluid remarkably diversified, as in many of the radiata and
mollusca, which have horny and earthy integuments. And in all animals, so far
as any chemical change is effected in the vital actions of absorption, secretion,
and even nutrition, it would appear to be chiefly of this simple kind, consist-
ing in the selection and appropriation of compounds already existing in the
fluids on which these functions are performed, not in the formation of new
compounds. The chyme which is found in the intestines of an animal during
digestion contains all the compounds (albuminous, fatty, and extractive matters)
which are found in the chyle absorbed from it, although these are in a different
state of aggregation, and associated also with other matters which are not ab-
sorbed. Since it has been ascertained that the compounds which used to be
thought peculiar to the greatest secretions in the body, the bile and the urine,
pre-exist in the blood, and are only evolved at the liver and kidneys,—accumu-
lating, therefore, in the blood, when the secretive action of these organs is sus-
pended,—it has become obvious that the main office of these organs is not forma-

tive, but only attractive, to extract from the blood compounds already existing

there. And, although there is one material extensively employed in the forma-
tion of animal textures, viz., gelatin, which cannot be detected in the blood; yet,
as this is the only material so employed which cannot be found there, and as a
substance very closely resembling it is found there under certain circumstances,
Wwe may assert that in animals by far the greater part of the act of nutrition,
numerous and diversified as the compounds forming the solid materials of animal
bodies may be, is likewise of this simple kind.

We may consider, then, the selection and extraction, from a previously exist-
ing compound fluid, by the agency of a previously existing compound solid, of
certain portions of that fluid already elaborated, as a chemical action, essential
to all living beings, and so peculiar to them that it may be, at least with high
probability, termed an exercise of a vital affinity. And, in regard to this simplest
kind of such action, the following points may be considered as ascertained :—

1. It seems to be always performed, in the perfect vegetable or animal, by
an agency, not of vessels, as was formerly supposed, capable of a vital contraction,

_and of changing the nature of their contents by the degrees of that contraction,

but of cells, either pre-existing in the solid structure, or carried about in the
nourishing fluid, and having the name of the globules or corpuscules of that
fluid. Most of the textures seem to be formed by the gradual transforma-
tion, elongation, or flattening of cells, which have sprung from nuclei at-

176 DR ALISON’S OBSERVATIONS ON

tached to previously existing cells; and it seems to be only by the successive
formation, distension, rupture, and disappearance of cells, that secretions make
their way into the excreting ducts of glands, or on the surface of membranes.

The dependence of all living structures, and of all secretions, not simply on
vascular action, by which nourishing fluids are circulated through them, but on
cellular action, by which this nourishing fluid is changed, appropriated, and re-
tained, or restored to the circulation, is the great step which has been recently
gained in physiology by the use of the microscope; and seems to me to be one of
the clearest proofs of the dependence of all vital phenomena, on peculiar attrac-
tions and repulsions, actuating both solids and fluids, and causing motions in the
latter,—not on any vital powers residing exclusively in solids. When it is stated,
é. g. by Mr Pacer, that “the purpose to which the capillaries are habitually sub-
servient, is only the passive one of conveying blood close to those parts of the
body which either grow or secrete, and that it is proved that if a part be only
able to imbibe the fluid portion of the blood from an adjacent vessel, it nourishes
itself as completely, and after the same method, as one whose substance is
traversed by numerous capillaries,”*-—it becomes obvious that the movements of
the fluid portion of the blood, whereby they are applied to growth and secretion,
must be determined by causes quite distinct from the contractions of vessels.

2. Living and growing cells, therefore, whether acting on the nourishing
fluid just taken into the system (as in the case of the intestinal villi, or the tufts.
of the placenta), or on the blood brought to them by the capillaries (as in the
nutrition of the different textures), appear always to have two functions to per-
form,—to extract from the nourishing fluid the matter of which they are them-
selves composed, and to extract from it, likewise, the matter which is contained
within them,—.e¢., in the organs of secretion, the secreted fluids, and in the
different solid textures, that additional matter which is always found, whether
lignin, oil or fat, fibrinous, cartilaginous, or bony substance, in a granular or less
definite form, incrusting the walls of the cells. It does not appear possible to
explain what is distinctly seen in all these cases, without supposing that the pre-
existing cells exert a peculiar attraction or affinity, both for the matter by which
they are themselves to be nourished, and their successors to be reproduced,—and
likewise for another matter, different in the different parts of the structure, by
which they are to be filled or distended. And in the case of vegetables, there
seems to be this general distinction between the two,-—that the former is a
matter destitute of azote, and the latter one containing that element.

3. The cell; growing always by attracting to itself a compound matter,
existing in the fluid state, and giving it a simple increase of aggregation, the
nature of the change which takes place as this matter becomes solid, is simply

* Report in Forses’s Medical Review, July 1843.

THE PRINCIPLE OF VITAL AFFINITY. 177

consolidation, not precipitation, just as the fibrin of the blood, differing from the
albumen only in its stronger (vital) tendency to aggregation, is consolidated in
its compound form from the liquor sanguinis in the act of coagulation. And thus
it happens that these organic solids possess (as was particularly noticed by Dr
Prout) that peculiarity which, in the inorganic world, is observed only in fluids,
that even the minutest portion of them contains the very same ingredients
(whether earthy or saline, animal or vegetable matters) as is found in the whole
mass.

The absence of all crystalline arrangement, and the complex nature even of
the smallest particle of an organized body, are the characteristics of matter
which has assumed the solid from the fluid form,—not by a chemical precipita-
tion, or separation from matter formerly united to it, but by a vital attrac-
tion, subjecting it to “the invisible cause by which the forms of organs are
produced.”

4, In the next place, we may inquire what difference exists among the cells
in different parts of the same structure, to explain the great difference of the
compounds which are deposited in them from the same nourishing fluid; and I
apprehend, that, on this point, we must come to the same conclusion which
Cuvier drew from examining, throughout the animal kingdom, the structure of
the different glands, the vessels entering them, and the ducts passing out of them,
viz., that there is no difference of structure or of composition, corresponding, in
the slightest degree, to the great difference of the products which appear. All
cells, in the vegetable kingdom, appear to consist of the same matter, cellulose,
and in the animal kingdom of the same matter, protein ; and in the first instance
they are quite similar to one another. When we attend to the early stages of
the existence of a living body, when the difference of textures is only beginning
to appear, we find only that a fluid passing through similar capillary vessels, and
effused into similar cells, in different parts of the structure, acquires different
properties. And when we carry our inquiries farther back, and observe the first
development of cells themselves out of the granular matter inclosed within the
sac of the yolk, it appears obvious that the particles of this matter are attracted,
not into cells already existing, but to points where cells are about to be formed.
The facts known as to the evolution of the chick in ovo from the matter that
lies in contact with the germinal membrane, sufficiently indicate that the powers
which effect the separation of the different component parts of that matter, so as to
form the beginning of the different textures and organs, reside, not in pre-existing
cells of different composition or structure, but simply in different points of a
pre-existing membrane, which, in the first instance, is homogeneous. The expres-
sion of Lizzie, that “ the chemical forces in living bodies are subject to the in-
visible cause by which the forms of organs are produced,” when the action of that
cause is duly considered, implies, that they are subject to a cause which un-
doubtedly acts differently at different points of the same matter; but the differ-

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178 DR ALISON’S OBSERVATIONS ON

ence of the action of which, at these points, is determined by no other condition,
that we can see, than their position.

This mode of limitation of the vital affinities by which the selection and ap-
propriation of living matter is effected, is only a statement of fact, and the most
general fact that has been ascertained; and it seems highly probable, that it will be
found an ultimate fact, in this department of science. It may serve to familiarize
our minds with this principle to observe, jirst, that it is precisely analogous to
the principle which is now well established as a first truth in the physiology of
the nervous system, that portions of nervous matter, precisely similar in structure
and composition, have perfectly different endowments according to the anato-
mical position which they occupy; and, secondly, that the same principle seems
distinctly exemplified in various cases of diseased action. The phenomena of
inflammation, and especially the easy recurrence of inflammation once excited
at any one spot in a living animal, indicate that certain vital attractions and
affinities existing among the particles of the blood, and between them and the
surrounding textures, are peculiarly modified, not merely in a particular manner,
but exclusively at a particular spot. From the spot where it commences (e. g.,
on a serous membrane), this alteration of vital actions extends, as from a centre,
to parts that are contiguous to, although having no vascular connection with,
that where it commenced, as we see in tracing it from one fold of the peritoneum
to another. And when we examine the results of the inflammation in the dead
body, we see what clearly shews the operation of a force, producing chemical
changes of the kind we are now considering, but acting only at one part, and
in one direction. “ The capillaries which have taken on the appearance of inflam-
mation, are all on one side of the fine membrane, and the serum and lymph, effu-
sions from these vessels,” by which the diseased state is essentially characterized,
“ are all on the other.”—(Goopsir, Anatomical and Pathological Observations, p. 43.)

In saying that the fundamental property of chemical selection, essential to
the growth of all living bodies, is strictly a vital property, we do not overlook the
fact that various substances, composed of inanimate or inorganic matter, have
likewise different powers of attraction for different elements or compounds
- brought into contact with them. It appears to be only by reference to this pro-
perty, that we can explain the well-known phenomena of endosmose and ex-
osmose, in which different fluids, brought in contact with a solid body, are
attracted into its pores with very different degrees of force. It is not the nature
of the process by which the selection, in the case of the living body, is effected ;
but the peculiarities of the selections themselves, their great force, and yet uniformly
temporary existence, that entitle us to regard them as indicating a vital property.

II. But when we attend to the peculiar changes effected by living solids on
the fluid matters which are brought in contact with them, we find that these are
by no means confined to the selection and appropriation, at particular points, of

THE PRINCIPLE OF VITAL AFFINITY. 179

compounds pre-existing in that fluid; but that, under the influence of the living
solid, transformations or new arrangements of the chemical elements take place,
and new compounds are formed.

In regard to the precise nature, or seat, of some of these transformations,
there is considerable difficulty, but we are at present concerned only with the
principle; and may state in illustration of it, two cases of transformation, of
which there is no doubt, the change from carbonic acid and water to starch in the
cells of plants (oxygen escaping), and the change from starch to fat in the cells
of animals (carbonic acid and water escaping). And that Iam correct in asserting
that the organ which exercises this and other chemical powers in living plants is
not only of the simplest construction, but of uniform construction, while the pro-
ducts of its action are very various, will appear from the following statement by
MULDER.

“ Pure cellulose is easily obtained from the pith of the elder-tree, from very
young roots, and from other young parts of plants. From these parts it is pre-
pared by digesting them, after being minutely divided, with alcohol, ether, di-
luted potash, hydrochloric acid, and water. In this manner, the starch, gum,
fats, resins, vegetable alkalis, salts, sugar,—and at the same time the peculiar
woody matter are separated.”

«« After the action of these solvents, and especially of the alkali, the cellulose,
which was formerly solid and dense, appears in a spongy form. We may state
as a fact, that the proper tissue of all plants which have been previously exposed
to the influence of these solvents, leaves a substance which 1s identical in all of
them, a substance which contains carbon and the elements of water.”—(Ohemistry
of Vegetable and Animal Physiology, pp. 188-195.)

MuLper annexes to this statement a speculation in regard to the influence
of forms in organized bodies, as affecting their chemical powers or properties,
which, so far as I can understand it, I think fitted to convey an erroneous im-
pression.

* One of the first and chief laws visible in organic nature is, that the form
has as much influence on the character of the phenomena as the substance of
which that form consists. The effects of the primary forces existing in the
molecules, have become, by the combination of elements into hollow globules,
altogether peculiar.”

“« Tn organic nature, besides all the peculiarities existing in the carbon, hy-
drogen, and oxygen, we must suppose, as a chief consequence of this, a tendency
| to form membranaceous, concave, spherical little bodies, in which, because of this
| form, new peculiar properties manifest themselves, which cannot be brought out
by other forms. Thus, by matter and form, all that we observe in nature is, to
a great extent determined.”—(Zbid., p. 189.) If by this it is meant that the acqui-
sition of the form is the physical cause of the existence of the properties which
cells, or any other organized structures present in the living state, two questions

180 DR ALISON’S OBSERVATIONS ON

immediately present themselves, first, How are the cells themselves formed (e. g.
on the germinal membrane of the ovum) out of a matter which is originally with-
out form, otherwise than by those very properties which are here ascribed to their
existence? and, secondly, If the properties are dependent only on forms, why do
they not exist in the dead state, when the forms are, in many instances, still per-
fect? The enunciation of these questions seems to me sufficient to shew, that
the correct expression of the state of our knowledge on this point is that already
quoted from Lerpie, that the chemical forces in living bodies are subject, not
simply to an influence of forms, but to “ the invisible cause by which the forms of
organs are produced,” i. e., that we must include under the head of vital properties,
both the mechanical, or simply attractive power, by which cells or other organs
are formed out of amorphous matter, and likewise the chemical powers with
which these cells are endowed.

It is no objection to what has been stated, of the strictly vital nature of these
chemical powers, to admit that their action is very often analogous to the principle
to which the name catalysis is given by chemists, and which is exemplified likewise
in the chemistry of inorganic compounds, where the combination of two sub-
stances is determined by the presence of a third, which nevertheless takes no
part in the combination itself; or that it is analogous to that disturbance of the
equilibrum of chemical compounds, by which the fermentation of an organic com-
pound is transferred to another in contact with it, although the changes in the
two go on separately, and the compounds formed are different. It is quite true,
that these modes of chemical action resemble and illustrate the manner in which
living solids, themselves undergoing continual changes of composition, determine
new arrangements of the elements of the compound fluids which are brought
in contact with them. But this analogy is far from being an explanation or
resolution of the one phenomenon into the other. In the first place, the analogy
is essentially defective; because although it is true that in any living being,
already existing, different chemical compounds already exist in different parts of
the structure, which may act in these modes on the nourishing fluid, and deter-
mine distinct transformations of these at different parts; yet this does not apply,
as already observed, to the first formation of each of the textures, at its appro-
priate point, from a homogeneous semi-fluid matter. But farther, although we
were to admit the analogy of all the chemical processes going on in living beings,
to these forms of simply chemical action, we should not thereby be authorised to
conclude that the vital processes have not that peculiarity which makes it in-
cumbent on us to regard them as a separate class. We say that the decomposi-
tion of carbonic acid, the combination of the carbon with the elements of water
to form starch, and the evolution of the oxygen, is a vital action,—not because it
is a change different in kind from the decomposition of water and evolution of the
hydrogen by iron and acid,—but simply because it indicates an affinity peculiar
to the state of life ;—because in no other circumstances, when the elements of

THE PRINCIPLE OF VITAL AFFINITY. 181

water are brought into contact with carbonic acid, is any such decomposition
effected. So also, although it is true that the presence of spongy platinum enables
oxygen and hydrogen to unite and form water, or the presence of fermenting
yeast enables sugar to undergo transformation into carbonic acid and alcohol,
still these facts do not interfere with those essential peculiarities on which the
doctrine of vital affinity depends, viz., that the presence of living cells composed
of carbon and the elements of water, determines both the addition of new mat-
ter, from a compound fluid, to those cells, and likewise the formation of other
compounds within the cells, varying in different parts of the same structure,—
all these compounds being different from any which the chemist can form out of
the same elements, and different from those to which the same elements inevi-
tably return, after the phenomena of life are over. The physical principle of
catalysis may be said to dlustrate the transformations in living bodies, as that of
endosmose illustrates the selection and appropriation of chemical elements or
compounds in living structures; but these principles, as exemplified in dead mat-
ter, include none of the peculiarities of the vital chemical actions, and therefore
furnish no explanation of them. |

The materials of which animal bodies are composed, have been now so gene-
rally found to have been prepared for them by vegetables, that it has been rea-
sonably doubted, whether any such power of decomposing the fluids presented to
them, and forming new compounds, exists in animals. There are some cases,
however, in which it appears certain that an action of this kind goes on in living
animals, and that it is effected, as in vegetables, by an agency of cells. Thus, there
is good evidence that, in the natural state, much of the bile which is discharged
into the intestines from the liver is re-absorbed in its passage along the Prime
Vize; yet it never appears in the chyle, nor, in the natural state, in the blood ;
which seems to imply that it is decomposed, and its elements thrown into other
combinations, in the course of the cellular action which attends the absorption of
chyle.

In like manner, the formation of fatty compounds out of starch, or its kin-

dred principles, as illustrated by the recent precise observations on the formation
of wax by bees, and the formation of gelatine in the living animal, are undoubted
instances of chemical transformations thus effected. The precise scene of these
transformations is not yet ascertained, but we have strong reason from analogy
to suppose that they are effected in the course of the circulation. And as we are
certain that the greatest of all the chemical changes which are peculiar to living
_ beings are effected within the cells of vegetables, it seems in the highest degree

probable, that the corpuscles or cells (both red and white) which form so large a
part of the blood ef animals, are concerned in the chemical transformations which
take place in blood; and therefore, that we are to regard organized and liv-
ing cells as the agents or instruments employed by nature in effecting all those
chemical changes which are peculiar to the state of life. And if we consider this

VOL. XVI. PART II. 2 Z

182 DR ALISON’S OBSERVATIONS ON

principle as established, it goes far to explain several facts, long regarded as
obscure, in regard to the structure and position of the lymphatic and lacteal ves-
sels. We know that the mode of origin of these vessels gives time and opportu-
nity for cellular action, (2. e, the development, growth, and rupture of cells,)
and consequent chemical changes, at their extremities; we know that such
cellular action does in fact go on there, particularly in the lacteals; and we know
that the substances absorbed there, and probably elsewhere, by these vessels, are
in fact altered, and so far assimilated, in the act of absorption ; as in the case,
already mentioned, of bile absorbed from the intestines. Thus we are led to see
the importance of these vessels being placed at all points where substances are to
be absorbed, which are foreign to the animal economy, or require chemical change,
in order that they may be introduced with safety or good effect. Hence, also,
we see the use of the lymphatic glands, at which another opportunity for cellular
action, for chemical changes and assimilation, according to the observations of
Mr Goopsir, is provided.* And this also enables us to understand a general fact,
which, although disputed, I believe to be both true and important in pathology,—
that a substance destined for excretion, but retained in the blood by reason of
disease of its excreting gland (particularly the bile or urine), is more injurious
than the same matter when secreted by the gland, but re-absorbed from a mucous

surface, and consequently subjected to cellular action, and thereby to chemical
change.

Ii. Another general fact appears to be sufficiently illustrated by observa-
tions on the chemical changes in living bodies,—viz., That the vital properties by
which these are effected are transferred from the portions of matter already pos-
sessing them, to those other portions of matter which are either taken into their
substance, or deposited in their immediate neighbourhood. It is, indeed, obvious,
that if we are right in saying that living matter possesses these peculiar vital
properties, the act of assimilation which we know to be continually going on in
living bodies, is not merely the attraction and addition of new matter, but must
include this transference of vital properties to the matter which is continually
added to the existing solids.

“‘ The force with which life is kept up,” says Professor WHEWELL, “ not only
produces motion and chemical change, but also vitalizes the matter on which it
acts, giving it the power of producing the same changes in other matter, and so on
indefinitely. It not only circulates the particles of matter, but puts them in a
stream, of which the flow is development as well as movement.”—(Philosophy of
Inductive Sciences, vol. ii., p. 52.)

Several facts which are known in physiology and pathology, may be noticed
as more special exemplifications of this principle. Thus, we know that vessels in

* See Carpenter’s Manual of Physiology, § 493.

THE PRINCIPLE OF VITAL AFFINITY. 183

any part of the body communicate certain properties to the whole mass of blood
which lies in contact with them, so as to modify or suspend for a long time the
coagulation of such blood ;—that the blood which enters the vessels of any part
where inflammation has been excited, has peculiar properties impressed on it,
and even changes on its composition effected, merely by coming in contact with
the portions of vessels where that process is going on, and with the portions of
blood previously subjected to it ;—that the exudation from inflamed vessels ac-
quires peculiar properties from the contact with the living surface on which it
lies, first arranging itself as an organized structure, and then selecting and appro-
priating, from the neighbouring bloodvessels, those materials by which it is assi-
milated to the texture with which it is connected ;—again, that, in the sound
state, every portion of matter which is deposited from the bloodvessels, to form
part of a muscle or of a nerve, immediately acquires the peculiar vital properties
of the part which it nourishes; and, in the case of muscles, even that the change
produced in a portion of a fibre by the application of a stimulus, is instantly com-
municated to the whole length of that fibre, and to many adjoining fibres. It
appears to be nearly in the same manner that every portion of carbon and water
which enters into the composition of any living vegetable cell, acquires the power
of exerting the same vital affinities as actuated the matter which it replaces, or
to which it is added.

IV. Another principle, at least equally important and characteristic, may be
stated in regard to this communication of vital properties to the materials which
are added to living bodies, viz., That such powers are imparted only for a brief
period of time, and that long before the time of the death of the structure to
which they belong, all those materials lose the vital properties which have been
given to them; perhaps, as has been lately stated, as a consequence of the ex-
ercise of their peculiar vital powers, perhaps merely as a general law of vitality ;
but equally, whether the peculiar properties which they acquire in living bodies
are of the nature of nervous actions, vital contractions or attractions, or vital
affinities. But as this principle is best illustrated by reference to the phenomena
of excretions, we delay doing more than merely enunciating it at present.

Having so far considered the general nature of the chemical changes which
are peculiar to living bodies, and the kind of apparatus provided by nature for
carrying on these changes, we may next take a more special view of the different
chemical changes themselves, beginning with the greatest and most fundamental
of all, the formation of the amylaceous matters by vegetables, acting on the water
and carbonic acid with which they are supplied, both in the liquid form by their
roots, and in the gaseous form by their leaves,—and the consequent evolution of
oxygen. In regard te this grand function of living plants, the following facts
seem the most important that have been ascertained.

184 DR ALISON’S OBSERVATIONS ON

1. We see this change effected, in the present order of things, only by the
agency of one of the amylaceous principles themselves, although the quantity of
that pre-existent matter, in the case of the seeds of many vegetables, is exceed-
ingly minute. We need not enter on the question how far, besides the pre-exist-
ence of matter capable of forming cells, in the textures of the plant itself, previ-
ously existing organized matter, in the dead state, is essential as part of the nu-
triment of vegetables,—farther than to observe, that, as the seed of every plant
contains a store of organic compounds already formed, there is certainly a strong
presumption that a certain quantity of such compounds, formed by previous
living processes, is highly useful, if not necessary, to the nourishment of vege-
tables as well as animals. This, however, appears most important in the early
period of the existence of plants, when their power of decomposing the carbo-
nic acid has not yet attained its full intensity. The evidence of the greater
part of the nourishment of vegetables being from carbonic acid, water, and
ammonia, applied to their leaves, or absorbed by their roots, is quite conclusive ;
and when we consider that vegetables preceded the appearance of animals on
earth, that the first vegetables (as is well observed by Liesic) were of the kind
which depend least on their roots and most on their leaves for subsistence, and
that the kinds of animals which first inhabited the earth, were those which con-
sume the smallest quantity of oxygen, and can live, therefore, in air highly
charged with carbonic acid,—it appears in the highest degree probable, that a
gradual purification of the atmosphere by the agency of vegetables abstracting
carbon, was a necessary prelude to the introduction of animals, especially of
warm-blooded animals, into the world: and that the greater part of the carbon
now existing in the soil on the earth’s surface, originally existed in the form of
carbonic acid in the atmosphere, and has been gradually fixed, and enabled to
become the chief support of all living beings, by this vital affinity of vegetables,
and of those tribes of the lowest marine animals, which have been found to pos-
sess the same property, whereby carbon is separated from oxygen, and combined
with the elements of water, to form the amylaceous matters.

2. The dependence of the exercise of this property on the presence of light,
and its connection (according to the statements of Dr Draper), not with the heat-
ing portion of the rays, nor with those which effect other chemical changes, but
simply with the luminous portion of the rays, shews distinctly that all living
action on this globe is equally dependent on light as on heat, although it is, and
may long be doubtful, in what manner the influence of light is exerted in pro-
ducing this change; whether the theory long ago proposed by Sir H. Davy is
admissible, that light enters into the composition of oxygen gas when disengaged
from any solid or liquid compound containing it ; or whether the agency of light
may be better expressed by saying, that it is the necessary stimulus to that kind
of vital action which leads to this primary transformation of the elements of
which organized beings are composed.

THE PRINCIPLE OF VITAL AFFINITY. 185

3. It is unnecessary to enter here on the varieties of this amylaceous matter
which are formed in different vegetables or parts of the same, the cellulose of
which the cells are formed, the starch, the dextrin, the gum, the inuline, which are
deposited in different species and in different parts. AJ] these appear to have the
same simple fundamental composition, consisting almost entirely of carbon with the
elements of water, and all are formed out of the same compounds and by a
vital affinity essentially the same; it may be partly owing to some imperceptible
difference in the relative position of the ultimate atoms, partly to differences in
the minute quantities of inorganic matter, and of other organic compounds not
yet mentioned, which enter into their composition, that so many varieties are
found, not only in these compounds themselves, but in the qualities which they
present as found in different species of plants, and even in different individuals
of the same species. In the case of a graft inserted on the stem of an individual,
or even of a species, different from that which furnishes the shoot, we see that the
vital affinities of the particles composing the shoot are capable, not only of
extracting from the nourishing fluid of the stock all the compounds required for
its development, but of imparting to the living textures formed of those com-
pounds which they extract, all those peculiar properties of form, of colour, of
smell, of roughness, smoothness, &c., by which species, and even individuals of
the same species, are characterized. And when we consider these facts, I ap-
prehend we must admit that, under the influence of the vital affinities which
operate in the cells of living vegetables, much more minute differences of com-
pounds are produced, than can be detected and explained by any chemical ana-
lysis.

4. An important question here is, whether the carbonic acid of the air is
decomposed in the leaves where it is chiefly taken in, the amylaceous compounds
immediately formed with the help of water, and the oxygen set at liberty, cr
whether that acid is taken into the juices of the plant, as we now know that
oxygen is into the blood at the lungs, and gradually decomposed there, letting its
| oxygen escape gradually, and aiding in the formation of different compounds,
| besides the varieties of starch. That the latter is the more probable supposition
| may be inferred, partly from the analogy of the action at the lungs of animals,
| but chiefly from the fact, that a separation of oxygen is equally required for the
_ elaboration, which certainly takes places in vegetables, of other compounds, of
| the varieties of oil, and of protein, which are chiefly deposited in other parts of
| their structures.

5. The relations of compounds of this class to sugar demand more special

_ notice. It seems doubtful whether this is ever the first compound formed; it ap-

pears in the sap of various plants when the fluids from the soil are ascending and

| dissolving the starch which had been formed and stored up by the living actions

_ of the preceding year ; it appears in almost exactly the same circumstances dur-
VOL, XVI, PART II. SA

186 DR ALISON’S OBSERVATIONS ON

ing the germination of seeds, and in both these cases is useful as giving a
greater degree of solubility to the starch whence it is formed. In both cases it
disappears, and probably is converted into some of the varieties of starch, as the
vital actions of the plant become more vigorous. Its composition, in its different
varieties, as given by most analysts, C12 Hu Ou, or Cio Hio Oro, or even Cy His Ox,
denotes that if it be formed from the starch, C12 Hio O10, it must be either by the
addition of the elements of water, or by the abstraction of carbon ; and as its for-
mation, during the germination of seeds, is attended with evolution of carbonic
acid, it seems most probable that, in that case at least, it is formed in this last
way, under the influence of the oxygen of the air. It appears again in the nec-
taries of flowers, and in the ripening of fruits, as one of the latest results of the
vital action of plants, in those parts of them which are fully exposed to air and
light, but at a time when we may reasonably suppose that the vital affinities are
becoming comparatively ineffective, and when carbonic acid is again evolved. It
may be formed by the chemist from some of the varieties of starch by a kind of
fermentation, excited by diastase, as in malting; or by a catalytic action of
sulphuric acid; and it is formed from starch merely by the agency of cold, as
in frozen potatoes, and from inuline merely by continued boiling in water; so
that its formation from starch in vegetables seems to be most probably a simple
chemical change, not the effect of a vital affinity. Farther, it is a compound
which takes the crystalline form, essentially different from any form assumed
by those parts of organized structures which exhibit truly vital phenomena,
and retains its properties when exposed to air and water better than any of the
matters of which organized forms are composed. [rom all these facts it may,
be inferred, with great probability, that sugar, as it appears in the living vege-
table, is generally to be regarded as a first product of decomposition of starch, by
the agency of water and of the oxygen of the air, which appears to be the
great agent in the resolution of those compounds, which the vital affinities have
built up.

6. On the other hand, the relation of starch and cellulose to the lignin,
which forms the greater part of the solid matters of dicotyledonous plants seems
to be nearly the reverse of their relation to sugar. This matter is always found
incrusting, or incorporated with, the cells of vegetable textures; it gives them
their solidity and strength, which all decompositions by chemical agents impair ;
it cannot be formed from the compounds of starch by artificial means, but is
formed from them in greatest quantity when the vital actions of plants are
strongest ; and its composition is always stated as differing from the amylaceous
compounds by containing more carbon; and less oxygen, in proportion to the
hydrogen, than exists in the composition of water; its formula being stated as
Caso Hy3 Oys. This, therefore, would appear to be clearly the result of truly vital
affinities, continuing to actuate the elements of starch, after the formation of the

THE PRINCIPLE OF VITAL AFFINITY. 187

starch from carbonic acid and water has been completed, and effecting a decom-
position of part of the water, as well as of the carbonic acid, presented to the
living vegetable. .

In studying this first and most striking of all the changes which are to be
ascribed to vital affinities, it is especially necessary to understand the parts as-
signed to Carbon and Oxygen; and, in taking this general view, we must regard
vegetables and animals as inseparably linked together, and look to the whole
series of chemical changes which intervene between the origin of vegetables and
the death and decomposition of animals. We must regard the carbon, originally
existing in combination with oxygen in the atmosphere, in the proportion of one
equivalent to two, as the great agent employed by Nature in the formation of the
whole organized creation, insomuch that all organic chemistry may be said to be
the chemistry of compounds of carbon.—(Gregory’s Chemistry, p. 241.) That it
may fulfil this office it is invested with peculiar but temporary powers; it is se-
parated at particular points and under certain conditions from the oxygen, and
attaches itself to the elements of water, always present where vegetables grow,
and so forms various compounds, beginning with the varieties of starch; in ali
which it is the principal ingredient. The compounds thus formed next attack and
partially decompose the water and appropriate the hydrogen, thus causing a far-
_ ther evolution of oxygen, and forming oil; and afterwards nitrogen, in small quan-
| tity, is introduced, and fresh transformations take place, by which the protein
compounds are formed. All the solid structures of vegetables, and indeed of
_ organized beings generally, are made up of these compounds of carbon, in which
_ oxygen exists either in the proportion to hydrogen which forms water, or in a
_ less proportion than that ; and the formation of these may be confidently ascribed

to vital affinities. But it is easy to conceive that other compounds of carbon with
_ hydrogen and oxygen will exist in plants in which the oxygen will be in larger
proportion than this, without supposing oxygen from the air to be added; because
_ the vital affinities may not have been in sufficient force to separate the oxygen
_ completely from its original union with carbon, and these, therefore, may be re-
_ garded as compounds of carbon, water, and undecomposed carbonic acid. Such
| are the different organic acids (the citric 12C 8H 140=9 C+8 HO+3CO,, the
| malic 8C 6H 100=6C+6HO+2CO., the tartaric 8C 4H 100=5C+4 HO
+3 CO,, the oxalic 4 C 2H 8 O=C+2 HO+3 CO.) which are found in the juices
| of many vegetables, particularly in the immature state.

Again, it is always to be observed, not only that all organized bodies are
destined ultimately to revert to the water, carbonic acid, and ammonia, from
| which they were originally formed, but that, in the case of animals at least, there
| is a process always going on during the state of life, by which these same inor-
| ganic matters are continually evolved from the living frames. Therefore, we
| cannot be surprised to find that the fluids of all living animal bodies contain other

188 DR ALISON ON THE PRINCIPLE OF VITAL AFFINITY.

compounds, in which the characteristic predominance of carbon is not perceived ;
because they are those which are formed in circumstances where the vital affini-
ties are losing their power, and where a step has been made towards that final
dissolution of organic compounds, when the oxygen is to resume its power over
the carbon, and this is to revert, directly or indirectly, to the condition of car-
bonic acid. This general principle as to the respective offices of carbon and oxy-
gen in living bodies,—the one the main agent in nourishing and supporting living
structures, the other in maintaining the excretions by which these structures are
continually restored to the inorganic world,—we shall find to be applicable, not
only to the excretion of carbonic acid and water by the skin and lungs, as com-
pared with the amylaceous compounds taken into animal bodies, but likewise
to the excretions by the liver and kidneys, as compared with the two other
great constituents of the food of animals, viz., the oily and the albuminous sub-
stances.

Oxygen, in its elementary state, although indispensable to all living action,
—although a condition of vitality equally universal as heat,—yet hardly enters,
if it enters at all, into any of the combinations which are due to the vital affini-
ties. Although taken into the interior of every living being, it appears to com-
port itself there almost, if not entirely, as it does in acting on dead matter. The
expression of Lizpiac, that the action of the oxygen of the air in living bodies is des-
iructive, is perhaps fitted to convey an erroneous idea, but we are certain that its
chief, if not its sole, action in the animal economy, is on those portions of matter
which have novital properties; either because they are redundant,—not required for
the nourishment of the tissues,—or because they have been re-absorbed from them,
having lost their vital affinities; and with these it unites, only to carry them off
in the excretions, particularly in the great excretion by the lungs. We now know
that the speculation as to the connection of the oxygen of the air with vital
action, long and ably maintained by the late Mr Extis, viz., that its sole use is to
dissolve and carry off excreted carbon, and therefore that in the bodies of animals
it goes no farther than the lungs, was erroneous; but we may assert with much
confidence, that it goes no farther than the circulating blood; and that, although
its action there is essential to all the metamorphoses which are there accom-
plished, yet all the combinations into which it actually enters, are destined to
immediate separation from the living body,—being, in fact, the media by which
all living bodies, at all periods of their existence, are continually resolving them-
selves into the inanimate elements from which they sprung. This principle will
be better illustrated, however, by a review of the leading facts lately ascertained
as to the formation of the other compounds peculiar to organized bodies, and the
excretions of animals.

Epinsureu, April 1846.

To be placed before Professor Forbes’ Paper on the Temperature
of the Earth, &c.

ERRATA.

P. 195, line 17, for north read south
P. 205, first Table, line 3, for 0°38 read 1-38

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( 189 )

XVIII.— Account of some Experiments on the Temperature of the Earth at diferent
Depths, and in diferent Soils, near Edinburgh. By James D. Forses, Esq.,
F.R.S., Sec. R.S. Ed., &. Corresponding Member of the Institute of France,
and Professor of Natural Philosophy in the University of Edinburgh.

I. History of the Observations.

THE proper temperature of our globe is a question which, formerly aban-
doned to speculation and hypothesis, has only lately been made the subject of
direct experiment. Preliminary to it, and intimately connected with it, is an-
other inquiry of great interest, namely, What is the thermometric effect of the
whole solar heat which falls in a year on the surface of the globe? How much is
transmitted to the interior? How much dissipated at the surface? To what
depth does the influence of the seasons extend, and in what manner is that in-
fluence modified at different depths? It is impossible to say to how many curious
and important inquiries a solution of these preliminary questions may lead the
way; and it is to them that our attention is at present to be confined. We shall
not speak, except incidentally, of the absolute heat of the interior of the globe;
we shall only discuss the modifications of the solar heating influence near its
surface.

This inquiry was perhaps first agitated by the illustrious LAMBERT, a ma-
thematical philosopher of Germany, who yields, in originality, in comprehensive-
| hess of mind, and in the successful application of mathematics to a wide range of
' important physical subjects, to very few of his contemporaries or successors.
His experiments were made by M. Orr, a merchant at Zurich, who had a conve-
nient garden for introducing the thermometers.*

Having claimed for Lampert the first systematic inquiry on this subject (for
the previous essays of Marrorre and Hatszs could not lead to any exact conclu-
sions), [ shall not trace the subsequent history of the problem, which is fully stated
in M. QuETELET’S papers, in the Transactions of the Brussels Academy for 1836
and 1840, and in the Annales de l’Observatoire de Bruxelles, tome iv. (1845).
Such observations were made by HnrRENSCHNEIDER, at Strasbourg; MUNcKE, at
Heidelberg; by Lustre, at Raith, near Edinburgh; by Araco, at Paris; by QuE-
TELET, at Brussels; and by RupsBere, at Upsala. As it does not appear, that, in
making or discussing these observations, regard has been had to the influence of

* LamBERT, Pyrometrie, 4to, 1779, page 356.
VOL. XVI. PART II. OB

190 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

a peculiar character of the soil or rock whose temperature was observed, it oc-
curred to me, several years ago, to make several series of observations, under cir-
cumstances as exactly similar as possible, with the exception of the nature of the
soil or rock. The neighbourhood of Edinburgh, from its variety of geological cha-
racter, offered peculiar facilities for this purpose; and the British Association, at
my request, undertook the expense of providing and inserting thermometers in
three different positions, at depths corresponding to those already employed at
Brussels, namely, 3, 6, 12, and 24 French feet below the surface. The results have
already been partly published in the Proceedings of the British Association, and
of the Royal Society of Edinburgh. Deeming it advisable that the curves contain-
ing the details of the observations should be published at large, I requested per-
mission from the Committee of Recommendations of the British Association, in
1845, to communicate them, for this purpose, to one of the Royal Societies; and
the Council of the Royal Society of Edinburgh having agreed to be at the neces-
sary expense of the plates, I am enabled to present the results in their present
complete form, and founded upon five years’ observations.

II. Lesuie’s Observations at Abbotshall, in Fife.

I shall here reproduce the particulars of the observations of the temperature
of the ground at Abbotshall, in Fifeshire, on the property of Raith, close to the
town of Kirkcaldy. The distance from Edinburgh is sufficiently small (11 miles
in aright line) to render these observations comparable with ours; but I quote
them more particularly, because those who have hitherto made use of them, being
unaware of the original account published by Sir Jonn Lesi1z,* have made almost
every possible mistake as to the locality, circumstances, and depths of these ob-
servations. It will be seen that they were made by Mr Frreuson of Raith’s
gardener. The following extract contains all the important details.

“Tn order to throw distinct light on a subject so curious and important, Ro-
BERT FerGuson, Esq. of Raith, a gentleman whose elegant mind is imbued with
the love of science, caused, lately, a series of large mercurial thermometers, with
stems of unusual length, to be planted in his spacious garden at Abbotshall, about
50 feet above the level of the sea, and nearly a mile from the shore of Kirkcaldy,
in latitude 56° 10’... The main part of each stem having a very narrow bore, had
a piece of wider tube joined above it; and, to support the internal pressure of the
column of mercury, the bulbs were formed of thick cylinders. The instruments,
inclosed for protection in wooden cases, were then sunk beside each other to the
depths of one, two, four, and eight feet below the surface, in a soft gravelly soil,
which turns, at four feet, into quicksand, or a bed of sand and water. These
thermometers were carefully observed from time to time by Mr Cuar.es Norval,

* Supplement to the 6th edition of the Encyclopedia Britannica, article CuimaTe, incorporated in
the 7th edition.

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 191

the very intelligent gardener at Raith; and we have now before us a register of

their variations for nearly three years. It thence appears, that, in this climate,

and on naked soil, the frost seldom or never penetrates one foot into the ground.”
* + * * * *

«‘ These observations are quite satisfactory, and exhibit very clearly the slow
progress by which the impressions of heat or cold penetrate into the ground. It
will not be far from the truth to estimate the rate of this penetration at an inch
every day. The thermometers hence attained their maximum at different periods,
though in a tolerably regular succession. ‘The mean temperature of the ground,
however, seemed rather to increase with the depth; but this anomaly has evi-
dently proceeded from the coldness of the two last summers, and particularly that
of 1816, which occasioned such late harvests and scanty crops. Thus, the ther-
mometer of one foot indicated the medium heat of only 43°8 during the whole of
the year 1816. But it will be satisfactory to exhibit the leading facts in a tabu-
lar form. The following are the mean results for each month, only those for De-
cember 1817 are supplied from the corresponding month in 1815.

TABLE I. LESLIE’S OBSERVATIONS.

1816. 1817.

2 Feet. | 4 Feet. | 8 Feet. . | 2 Feet.

January
February

September
October

SHAIDAARE RK DSH

Mean of whole Year : : 46 -0

“Tf the thermometers had been sunk considerably deeper, they would, no
doubt, have indicated a mean temperature of 47°7. Such is the permanent tem-
| perature of a copious spring which flows at a short distance, and about the same
_ elevation, from the side of a basaltic or greenstone rock.”
| I had intended to have engraved the curves of the course of temperature from

192 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

1816 to 1821, which I find preserved in the Natural Philosophy Collection; but
my inquiries led me to discover that most of these curves had already appeared
in the 4th volume of ConsTaBLe’s Edinburgh Magazine for 1819, where they have
remained apparently quite unknown to scientific men, together with the details
of the observations on which they were founded, from May 1815 to March 1819,
and an explanatory article, which I understand was written by Mr Grorer Bu-
CHANAN, Civil-engineer. These observations, particularly at the commencement,
were not made with great regularity, sometimes only a single observation being
made in a month, at other times as many as eight. Indeed, they have not ap-
‘ peared to me to be worth reprinting at length; but I have condensed into the fol-
lowing Table the information which they contain, shewing the mean monthly tem-
perature, at different depths, for nearly four complete years.

TABLE II. MEAN RESULTS OF LESLIE’S OBSERVATIONS.

1815-19.

2 Feet. 4 Feet. 8 Feet.

38°-9 ; 43°°8
36° 42
38 ° 42
40: 42
45° 44
52 46
54 48
54 50
September : 53 ° 51
October . 49 - 50
45° 48
40° 46

OWMnNODORWNHW OC.
ORO DWOHEWAOD
WDROOSOHNW OAD

III. Construction of the Instruments.

In commencing the observations at Edinburgh, it was determined that the
thermometers should consist of three sets of four each, the lengths increasing in
geometrical progression, and the localities being fixed so as to embrace within a
small radius, as great a variety of soil as possible. As the deepest thermometers
were to be sunk to a depth of 24 French feet (25-6 English), and the portion of the
tube, including a column sufficiently long to register the variations of temperature
of the fluid which filled the ball (alcohol), must project a foot or two above the
surface, the construction, graduation, and depositing of such unwieldy instru-
ments, were attended with no small practical difficulty. The execution of the

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 193

whole was entrusted to Mr Apig, to whose experience and skill I am greatly
indebted for the completion of the whole without any material accident.

For the larger thermometers it is of great consequence that as little liquid
as possible should be contained in the stem of the instruments, otherwise the
apparent expansion of the column will depend greatly upon the variable tem-
perature of the different parts of the stem, as well as on that of the level. This
correction being difficult to apply with mathematical exactness, it was desirable
to make it as small as possible (although it would be unwise to overlook the
correction altogether, as most observers have done). I accordingly had twelve
tubes drawn, each of about 26 feet in length; of the external thickness nearly of
a common barometer tube (about half-an-inch), but whose internal diameter
was nearly capillary. These were carefully examined throughout, by means of a
column of mercury passed through them.

The proportional numbers, representing the calibre of the tubes, were en-
tered in a table now before me, corresponding to every foot of their length; and
the tubes were numbered, so that the degree of uniformity of any portion could
at any time be ascertained. From these tubes twelve lengths were cut from the
most uniform parts, amounting altogether to about 144 feet, for the construction
of the three sets of thermometers.

It is to be understood that the capillary tube now spoken of was made with
a view to reach the surface of the ground, above which the tube should expand
into one having degrees of a convenient length. So small, indeed, was the stem
compared to the bulb, that a degree of Fahrenheit in the capillary tube would
have occupied, in one case, a space not less than 51 inches long. The wide tube
to which the scale was attached, had a bore of about +5 inch, and was made long
enough to include the expected range of temperature at their respective depths.
These ranges were, however, in some cases rather under-rated.

The bulbs were cylindrical, and varied in size from about 6 to 8 inches long,
and 14 or 25 wide. They were blown at the glass-house separately from the
tubes. The deepest thermometers had the largest bulbs and longest degrees, be-
cause the required range was less.

From the length and fineness of the tubes much trouble would have been ~
experienced in filling the thermometers in the usual way. The lower end of the
cylindric bulb was, therefore, drawn out into a tube, by which the liquid (freshly
boiled alcohol, slightly coloured) was admitted, and it was drawn in by the action
of a syringe fixed at the extremity of the long stem. Both ends were then closed

_ in the usual way, an expansion being left at the top as in common alcohol ther-
| mometers, but most necessary in this case, in order to allow for the changes of
temperature to which the instruments were exposed before sinking them in the
ground.

The graduation was one of the most delicate parts of the construction. The

VOL. XVI. PART II. 3 C

194 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

instruments were suspended during winter in a staircase, with their bulbs in
water, and the temperature of the air surrounding the stems was carefully noted,
and a correction applied for any difference between it and that of the water. The
staircase was artificially heated through a few degrees, and after being left for a
night, a second point was fixed. The temperatures of the water were determined
by the mean of three standard thermometers, which agreed extremely closely
indeed, when the error of their freezing points was corrected. The first was a
standard by TroucHTon and Simms, belonging to and corrected by myself.* The
second was a standard constructed by Mr Apis for the Royal Society of Edin-
burgh; and the third a standard having very long degrees, constructed by Mr
Aptis for his own use. The first pair of observations were made by Mr ADIE
senor alone, and scratches marked on the tubes at temperatures corresponding
to 41°73 and 50°77 by the mean of the standard thermometers. To verify these
results I made two additional comparisons with the assistance of Mr ALEXANDER
ADIE junior, at temperatures 41°-97 and 46°42, which agreed by interpolation
remarkably closely with those of the first experiment, considering the difficulties
of the observation. In only one case (the 13 feet thermometer for the Experi-
mental Garden), was the difference at all considerable. A mean result was
adopted. The length of 1° in the 24 and 12 feet thermometers being from 1 to
2 inches, and divided into 20ths, 13s can be easily read by estimation. In the
others the approximation is less.+

IV. Localities—Sinking of Thermometers.

Whilst the preparation of the thermometers was going forward, I had holes
prepared for inserting them in the positions already fixed on with reference to
the geological peculiarities of the soil. These were— °

1. In the Observatory enclosure on the Calton Hill, at a height of 350 feet
above the sea. The rock is a porphyritic trap, with a somewhat earthy basis,
dull and tough fracture. The exact position is a few yards east of the little
transit-house. There are also other buildings in the neighbourhood. The ground
rises slightly to the east, and falls abruptly to the west at a distance of about
15 yards. The immediate surface is flat, partly covered with grass, partly with
oravel.

* Philosophical Transactions, 1836, p. 577.

+ More lately Mr Anpiz has constructed two sets of thermometers resembling these, one, extend-
ing to 24 French feet for Greenwich Observatory ; the other, including only the 12 feet thermometer,
for Mr Catpecort of Trevandrum in India. Both of these sets of instruments were fortunately trans-
ported to their destinations without any accident. The graduation of the Greenwich instruments was
performed by myself, and a much larger number of points fixed than above described. The result was
examined, and the scale determined, by a simple method of graphical projection and interpolation,
which led to the most satisfactory results; I should, therefore, recommend this method to others under-
taking the same tedious and difficult operation.

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 195

2. In the Experimental Garden, adjoining the Royal Botanic Garden at In-
verleith, almost exactly 1 mile NW. of the Observatory, and 280 feet lower, being
about 70 feet above the sea. The soil here is a remarkably pure sand, resembling
sea-sand, extending to a great depth, and including few pebbles of any size. The
precise locality was the flat summit of the rising ground, immediately to the
south of the large building or show-room in the Garden. The perforation of the
sand was exceedingly easy, owing to the uniformity and dryness of the strata.
The four thermometers were inserted in three boxes, near to one another, the two
shortest thermometers being placed together in the same hole. The surface is
garden mould, whereas, at the Observatory and Craigleith, it is covered with ve-
getation (in the former case interrupted by buildings and gravel walks). This
circumstance may not be without some effect. Sir Joun Lesiie has observed* that
cold penetrates deeper through bare soil, or compact pavement, than through turf.

3. At Craigleith quarry, 21 miles west from the Observatory, in a mass of
coal formation sandstone, which has for many years afforded an abundant and
durable building material for the city of Edinburgh. The spot chosen was situ-
ated in a field 50 yards north of the house called Craigleith Hill, immediately to
the east of the quarry, and about 75 yards distant from its north escarpment.
The field was under grass during the first two or three years of the observations,
afterwards under crop. The height above the sea is about 150 feet. The ther-
mometers were inserted here, as at the Observatory, in one hole, six or seven
inches in diameter at the top, and three at the bottom, which it required several
weeks to form with boring-irons in the usual manner. When the hole was
empty some water always flowed into it, and stood at a certain height, however
often removed.

The insertion of the thermometers into the holes required the greatest pre- —
caution ; the length and flexibility of the stems of the longest exposing them to
ereat risk of casualty. The operation was managed in the following manner. A
strong tripod, 12 or 15 feet high, was erected over the hole, and a ladder still
longer attached it, so that a man ascending it could command completely the
upper part of the instrument. The tube lay in the angle formed by two united
pieces of wood, similar to a roof gutter, where it was secured by loops of string.
Being raised, with this defence, into an erect position directly over the hole, the
loops were successively cut, and the thermometer allowed to slip from the wooden
shield, and to sink to the required depth. Dry sand was then poured in to half
the depth of the hole. The second thermometer was then similarly planted, and
so of the others ; the aperture being well closed round the tubes with clay puddle.t+

* Encye. Brit., Article Curate.
{ Subsequently (May 1838), a quantity of Roman cement was employed to secure completely the
opening of the holes.

196 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

Strong wooden boxes painted green, having doors open to the north side, were
then firmly fixed over the projecting stems, which boxes were afterwards pierced
with holes, in order to secure a free ventilation. Small thermometers graduated
to whole degrees were hung in air within the boxes; and afterwards (May 1838)
other thermometers were placed with their bulbs just covered by the soil within the
boxes. These last thermometers are referred to in the tables as ¢;. After the in-
struments were finally placed, slight metal scales were attached to the respective
tubes with fine copper wire. I should add that, for the defence of the bulbs and
the capillary tubes, at their inferior extremities, before mentioned, they were half
inserted into tin cylindrical boxes filled up with plaster of Paris.

I had hoped to have commenced the observations with 1st January 1837 ;
the unexpected difficulty experienced in boring the holes, and subsequently the
severe weather, prevented the insertion of the thermometers before the 18th Jan-
uary in the Experimental Garden, the 20th on the Calton Hill, and the 21st at
Craigleith Quarry ; the whole was happily accomplished without the slightest ac-
cident. In all my arrangements, I was aided by the civility of the Directors of
the Astronomical Institution and of the Experimental Garden, by the astronomer
Mr Henperson, and other official persons.

V. Observations and Observers.

Not the least of the difficulties of carrying on such observations as the pre-
sent has ever been found to be, that of getting perfectly trustworthy and zealous
observers. In this matter I esteem myself particularly fortunate. Professor
HENDERSON undertook, in the kindest manner, the personal superintendence of
the thermometer placed on the Calton Hill in the Observatory grounds. At the
Experimental Garden I received the services of Mr JAmEs M*Nap, the superin-
tendent ; and at Craigleith, those of Mr Macxintosu, whose official connection
with the quarry ensures his constant residence. The observations were made
weekly, and were registered in degrees and hundredths of Fahrenheit’s scale (by
approximation). The general superintendence which I have been able to give,
assured me that all the observations were made, not only with fidelity, but with-
out any sensible error arising from want of familiarity of two of the observers
with instruments so minutely divided. And, were other proofs wanting, fortu-
nately the ultimate projection and comparison of the three sets of observations
affords the most perfect check upon any considerable inaccuracy, either in the
observations or computations.

With a view to check any permanent change in the reading of the instru-
ments, such as might arise from a permanent displacement of the freezing point,
I had a spirit thermometer constructed with a bulb similar to those buried, with

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PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 197

a view to its occasional verification ; the freezing point being accurately ascer-
tained. Nine years after (January 1846), this instrument being re-examined,
shewed no appreciable change in the position of the zero point. It could not
have amounted to #s of a degree. A common thermometer would have altered
appreciably under similar circumstances. Is not this owing to the strength of the
glass bulb ?

The permanent influence of the pressure of sand in the holes was suggested
to me as a possible source of a change of figure of the instruments ; but the con-
clusive experiments lately made in America and France on the pressure of sand,
convinced me that this could have no appreciable influence.

The observations were made weekly ; generally on Mondays. Asit was com-
_ monly supposed that the diurnal variations of the temperature disappear at the
| depth of three feet, I did not take particular precautions to have all the obser-
| vations made at the same hour. I find, however, that, at the Observatory, the
| readings were taken immediately after noon, at the Experimental Garden, about
2 o'clock, at Craigleith Quarry, regularly between 11 and 12 o’clock. The later
| hour of the second series may account for some irregularities observable. The
| observations, at all the stations, were made regularly from February 1837 down
| to May 1842, about which time, the thermometers at Craigleith were maliciously
destroyed ; but these five years of complete observations have yielded all the results
which were looked for in commencing them. The boxes covering the thermome-
ters, in the Experimental Garden, were blown over in the winter 1844-5, crushing
| the thermometers. Those at the Observatory still remain in good order, and are
regularly observed. The numbers, from the original registers, are exactly given
in the table at end of this paper, together with the corrections applied to them, in
| the manner to be described in the next section. It is not to be supposed that the
| registers are without some errors, at least, in the case of the two less experienced
| observers (at Experimental Garden and Craigleith) ; but they are only oversights
| of the eye or hand, which can affect none of the conclusions, as the admirable coin-
| cidence of the three independent series, in Plate VII., sufficiently proves.
| The following table contains the data necessary to be known, respecting the

scales and dimensions of the thermometers, for correcting the temperature of the
stems and exposed columns in the manner which we shall next proceed to inves-
tigate.

VOL. XVI. PART II. “oD

198

Range of Wide

No. Tube.

41-6—51:0
41-0—51°0
36-0—54-0
30°5—55-0

39°5—52°9
38°5—53°2
35:0—55'9
26°5—60'0

40:5—51°5
40°7—50-7

TABLE III. THERMOMETRIC CONSTANTS.

Inches

of Wide} Degrees

Tube in| in Fine
Fine Tube.
Tube.

Length of Length of | Degrees of

Fine Tube 1° in inches} Fine Tube

sunk below
ground.

of Fine

in inches.
Tube.

OBSERVATORY.

13-7 | 316
4-5 | 162
48| 86
57 | 48

EXPERIMENTAL GARDEN.

30°0 | 24°5
9:2 8-4
4:2 6:2
1:8 3°8

CRAIGLEITH.

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

Degree
from which
the column
exposed to

external
temperature
is reckoned.

19°7
81 | 49

12°5
3:2

37:0—53°6 ; 10 6:4 65
31:5—55°4 : 10 1:4 2°1

* This supposes the Atmospheric Temperature to penetrate 9 inches. The tubes at the surface

would have the following readings :—
41-2 40°7 35:5 29:4 | 389 38:2 34:3 25°7 | 401 40:5 36:2 31:1

May 14. 1834, No. 4. Observatory was lowered 3°12, by withdrawing alcohol. May 15, No. 4.
Craigleith lowered by 1°.95. Corrected scales were immediately applied.
In the above Table, No. 1 is the longest, No. 4 the shortest, Thermometer.

VI. Corrections of the Observations.

It is very evident that the readings of the thermometers cannot indicate ex-
actly the temperature of the point corresponding to the centre of the bulb, be-
cause the stem between that point and the surface of the ground never has a uni-
form temperature throughout; and the portion of the column above ground is
affected by the temperature of the air at the moment. Of these two corrections
in our thermometers, the latter is by much the most important, which is fortunate,
because it is also determined with the greatest accuracy.

These corrections, however obvious, have, according to M. QUETELET, been

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 199

overlooked by all observers previous to himself and M. Araco. It seems that
M. Araco ascertains the expansion of the buried column of spirit by sinking,
alongside of each thermometer, a stem similar to its own, having a scale above
ground, but no bulb: the variations of bulk of the contained spirit being thus di-
rectly shewn are eliminable from the readings of the adjacent thermometer.
As far as regards the correction due to the portion of the stem buried in the earth,
this mode of correction is ingenious and satisfactory ; but, when the ‘tubes are
capillary, the reduction is so small that it may readily be obtained otherwise, with
sufficient accuracy. It does not, however, apply to the portion of the scale above
ground, since the quantity of alcohol, so exposed, varies with the degree shewn
| by the thermometer. And this correction, as has been said, is, in our observations,
the more important of the two. The method which I propose to employ is the
| following :—
| The distribution of the thermometers, in geometrical progression, enables us
to employ the temperatures indicated by the thermometers, Nos. 2, 3,
ae and 4, for the correction of the reading of No. 1 (that is, to reduce the
temperature of the column ab to the temperature of the bulb); the
“ temperature of Nos. 3 and 4 to correct No. 2; and of No. 4 to cor-
rect No. 3. It was matter of consideration (1.), how this might be
most correctly done; and (2.), to select a formula of sufficient (not
superfiuous) accuracy, and adapted to calculation.
The mode of doing this was partly arbitrary, and justified by ap-
plication to cases where the variation of temperature in the stems was
a maximum selected from the journals of observation. Thus, the
depth of the successive thermometers being—
0, a ; 2a 3 224 . 23a . ec.
The intervals of depth are—
a a 2a 22a Se.

And the product of the temperature and depth must lie between
two series, one of which supposes the temperature of any interval
equal to the temperature of the thermometer at its superior limit, the
other supposes the mean temperature equal to that at its inferior limit.
It is evident that the truth must lie between these suppositions, or
that denoting by T, the superficial temperature ; and ¢, ¢,, 4, the in-
dications of each thermometer successively in descending, we must
| have the product of the temperature and depth between the values of the two
| series,

Tat+t,a+2t,a+2°t,a

| and ; t,a+ t,@+2 t,a+ 2%t,a

| Farther, it will be nearer the latter result than the former, since the variation of
_ temperature diminishes as we descend.

200 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

Until after May 1838, no superficial thermometer (or one in the uppermost
stratum of soil) was used. There was simply a thermometer suspended beside
the scales in the box, to indicate the temperature of the part of the column ex-
posed to the air. Fortunately, however, the correction for the temperature of the
first interval a, or 3 feet, is very small indeed. The extreme excess of tem-
perature of the air in the box above the highest thermometer, or (T—¢, during
1837, was 20° Fahr. In the most capacious of the tubes employed, supposing that
the temperature of 20° had been applied through the whole depth of 3 feet, an
expansion would have been produced, which would have raised the alcohol on the
scale of that thermometer by 0°:07; but the expansion could not possibly amount
to half of this, seeing that the mean temperature of the 3 feet of soil would more
nearly approach to that of the inferior limit of it, than to that of the air in contact
with its surface. We can hardly err -01 (a quantity in this particular case much
less than the errors of reading), by assuming that { of the column of 3 feet had
the temperature of the air, and the remainder that of the thermometer bulb itself.*
In both the other three-feet thermometers, the error, owing to the smaller capa-
city of the three-feet capillary tube, would be but about half as great.

Now, by reasoning by the method of limits as above, and applying the above
correction to the upper 9 inches of all the tubes, I find the following formula to
be a more than sufficient approximation in every case. For the deepest thermo-
meter, No. 1, whose temperature is ¢,
= Temperatures x depths

depth
making 3-2 feet = unit of depth,

Mean temperature of stem =

Lt, +2, 447,487
ee ore eee

mean temperature

And as the reduction of the temperature of the stem to that of the bulb depends
on the excess of the former above the latter, we have

Mean excess of temperature = aid elle 1) ee) =) File A) (2.)
Farther, to adapt this to calculation, let the successive intervals of tempera-

ture of the series of thermometers be taken, and make

f,—f,=a

f,—t,=6

t,—t,=c
the above expression becomes

3{(a+6+c¢)+2(a+b)+4a}
=3{7a+36+c} for thermometer No.1, . . (8.)

* The application of this correction becomes exceedingly easy, by considering the correction for air
temperature to apply, not only to the exposed part of the tube, but also to the first 9 inches of the buried
stem,

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 201

For the other thermometers, we have only to make a and 0 successively = 0, and
substitute 4 and 2 for the depths, which give

4{3 6+c} for No. 2.
kc for No. 3.

And the correction for No. 4 will be exclusively that derived from the observation
of the thermometer in air T, and has for its argument
SUE tae chen ien Met rakes Riel att AR yis-poen ia) CPAs)

I should have observed, that, in order to ascertain that these formulee repre-
sented the state of the instruments with sufficient accuracy, I first calculated how
nearly the mean temperature of the whole column of each thermometer must be
known, in order to entail no greater error than that of the reading, say of -01 de-
gree. This, in the case of the deepest (26 feet) thermometer, with the widest bore,
amounts to 1° of temperature, and in the three-feet thermometer to 3°.

For the second or Air Temperature correction, the quantity of alcohol to be
expanded, depends on the height at which the liquid stands in the tube, and the
amount of expansion on the temperature to which it is subjected.

Let us suppose, that in any thermometer the degree of temperature is known
at which the surface of the column would just contract below the level of the
soil. The number of degrees above this, which the thermometer at any time
marks, points out the quantity to be corrected for expansion. If this correction
is also to be applied to a part of the tube 9 inches lower, we have only to start
from a degree of the scale corresponding to that point instead of to the surface.
The number of degrees for which it is to be corrected, is the excess of the tem-
perature of the air above that of the bulb, or T—Z,, ¢, denoting the temperature
shewn by the nv“. thermometer in an ascending order. Table III. in page 198, gives
the point on the scale of each thermometer, corresponding to a position 9 inches
below the level of the soil; let that point be /,, /,, 7,, 7,, for each thermometer in
| succession, then the number of degrees of temperature to be corrected for, will be

Z—7., T—1,, &c.

Thus, both the corrections required to reduce the observed readings amount
| to finding by a table, the increased (or diminished) length of a given column of al-
_ cohol (measured in degrees), for a given excess (or defect) of temperature, assigned
| in degrees. Such a table I have constructed, and I have thought it advisable to
_ employ the correct value of the expansion of alcohol at atmospheric tempera-
| tures, instead of its mean amount between the freezing and boiling points. This
latter quantity as given by Daron, and commonly employed, is ‘11 of the volume,
from 32° to 212°, or 000611 for 1° Fahr. Now, it appears from Muncxe’s elabo-
| rate experiments, that alcohol, of density -808, expands at common atmospheric
| temperatures (viz. between 0° and 20° cent.), almost precisely -001 of its volume
VOL. XVI. PART II. 3E

202 PROFESSOR FORBES ON THE TEMPERTAURE OP THE EARTH.

at freezing for 1°. cent.,* or ‘000555 for 1° Fahr., a quantity one-tenth greater than
its mean dilatation usually adopted. I accordingly had a Table constructed on
this basis, with a double entry, one for the number of degrees, or space in the
tube filled with the expanded liquid, and the other for the excess of temperature to
which it is exposed. The arguments used for the two corrections, with this Table,
were the following :—

1st Argument. 2d Argument.
Capacity in Degrees Degrees of Temperature
to be corrected. to be corrected for
5 7a+36
1s¢ Correction (for Temperature of Stem), Table, p. 198. fees 3 aS
2d Correction (for Temperature of Air), . T-/ Bie

The sign of the correction is always opposite to that of the second argument.

* Fecuner’s Repertorium, II, 430. The expansion of absolute alcohol is somewhat greater as
given by MuNcKE, in a paper in the Petersburg Transactions, read 5th September 1834.

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aio

204 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

VIL. Results of the Observations.

A. Mean Temperature at different depths,

It has been observed at Brussels and elsewhere,* that, even at depths less than
25 feet, the mean annual temperature indicated by the lower thermometers is
greater than that of those nearer the surface. This appears to be also clearly
established by the observations at the three stations near Edinburgh, as contained
in the following Table.

TABLE V. MEAN TEMPERATURE FOR FIvE YEARS.

3 French Feet, (No.4). 6 French Feet, (No. 3). 12 French Feet, (No. 2.) 24 French Feet, (No. 1),

Experi-
mental
Garden.

Experi-
mental
Garden.

Experi-
mental
Garden.

Experi-
mental
Garden.

Observa-
tory.

Observa-
tory.

Craig-
leith.

Observa-
tory.

Craig-

Craig-
: leith.

leith.

Observa-
tory.

Craig-
leith.

46°46
45:97
45°87
46°18
45°87

47°28
47°05
46°98
47°04
47-08

47°29
46°89
46°68
46°77
46°79

46°87

46°90 |
46°44
| 46°67
| 46-91

46°89

46°65
46°12
46°18
46°43
46-44

46°70
45°90
46°43
46°58
46-51

46°23
45°35
45°75
45°99
45°99

46°26
45°22
45°83
45-97
46:13

46°54
45-44
46°14
46:26
46-29

45-94
44°81
45°48
45°56
45°66

45°49 | 46-13

1837-1838
1838-1839
1839-1840
1840-1841
1841-1842

Means

45°88 | 45°86 | 46:42 46°36 | 46°76 47-09 | 46:07

Mean of Observatory,
Experimental Garden,
Craigleith, . ;

46°14 Elevation,
46°60 ss
45°95 ”

350 feet.
70 feet.
150 feet.

Adie’s Observations, 45:28

Mean Temperature of Air from Mr 240 feet.

Mean of 3 Feet Thermometers, 45°83
nO ' 46-07
sol As 46°36

24. 46:68

The cause of the increased mean temperature below, is by no means clear.
From its irregularity, it is most probably due to several causes, of which the cen-
tral heat of the earth is perhaps one; its effect at 25 feet need not be insignifi-
cant, since the average rate of increase at great depths is 1° Fahr. for from 40 to
50 English feet. In the present case, the increase is not uniform, and it is also
decidedly different in the different soils, and will appear by the sequel to be inti-
mately connected with the conducting power of the strata. The order of magni-
tude of the increase is this, 1. Observatory, 2. Experimental Garden, 3. Craigleith ;
—or, Trap, Sand, Sandstone, which is also the order of the conducting power. The
following table shews that, in every instance but one (from 6 feet to 12 feet at
Craigleith), the increase was apparent.

* QueETeELET, Annales de l'Observatoire Royale de Bruxelles, iv. 150.

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 205

TABLE VI. SHEWING THE RATE OF INCREASE OF TEMPERATURE WITH DEPTH.

Experimental

Observatory. anaes.

Craigleith.

From 3 to 6 feet, | +037 | +029 | + 0-04
... 8to0 12 + + 0:87 + 0:63 + 0:04

++ 38 to 24 +. + 0°38 + 0:96 + 0:19

To complete the comparison of Meteorological data, I subjoin Mr Apte’s ob-
servations on the mean temperature of the air and the quantity of rain fallen dur-
ing the same period, at Canaan Cottage, near Edinburgh, 240 feet above the sea,
excepting the months previous to May 1838, which were observed on the Regent
Terrace, Calton Hill, at about the same elevation above the sea.

TaBLE VII. M&AN TEMPERATURE AND QUANTITY OF RAIN FOR THE YEARS 1837-38-39-
40-41-42, OBSERVED AT EDINBURGH BY MR ADIn.

1837. 1838.

Thermome- Thermome- Thermome-

Rain. Gon. Her Rain.
January 36 33 | 1:23 || January 31:73 January 33°05 | 1°76
February 37°23 2:14 || February 30°06 : February 38°53 1°45
March 35°24 1:28 || March 38:12 5 March 36:98 147
April 39°65 | 1:61 || April -| 40-25 ° April 42°53 | 0°33
May 48°37 1:53 || May 44°87 : May 46 82 0°47
June 57°30 2°86 || June 53 98 June 53°42 3°91
July 60°42 | 4:54 || July 58:94 July 57°77 | 351
August 51°77 4-13 || August 56°88 . August 55°51 e7/7/
September | 53:18 | 1°73 || September | 5204 : September | 52:13 | 309
October 50°17 2.02 || October 46 27 : October 46°50 2:38
November 40°45 2.03 || November 38°38 - November 43:13 1°65
December 42°68 1:67 || December 3817 : December 37°46 1:66

Sums 552°79 \ 26°77 529-69 ; 543°83 | 23°45
Mean 46:07 44°14 45°32

1840. 1841. 1842,

Thermome- Thermome- Thermome-
ter. ter.

January 38°74 January 33°00 January 35°45
February 36°55 : February 38°39 : February 39°55
March 42°74 ‘43 || March 45°62 : March 42-04
April 48°16 ' April 44:26 : April 45°03
May 47-13 May 51°74 May 5-22
June 52°53 June 52°43 June 57:53
July 52°75 : July 53°58 : July
August 44°51 ; August 53°88 : August
September | 48°57 : September 54°36 : September
October 44°32 : October 43°48 ‘53 || October
November 48°66 ; November 39°10 ‘ November
December 87°31 December 39°65 December

Sums 541:97 ; 549°53 “ 270°82 8-13
Mean 45°16 45°79 45°14

VOL. XVI. PART II. 3F

206 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

B. General Observations on the Thermometric Curves.

Some of the most important results depend upon the annual ranges of tem-
perature at different depths. But the determination of the extremes is no easy
matter. I will first direct attention to the curves in Plate VII, which convey a
great deal of valuable information, which can here be only slightly touched upon.
They are reduced to one-sixth of the size of the original projections, in which one
degree occupied two-thirds of an inch vertically, and one day occupied one-tenth
of an inch horizontally. The corrected temperatures are those which have been
projected.

The curves extend over five years; and are placed in the order of depths
(vertically) to which they belong: the uppermost undulating curves shewing the
variations at the three stations 3 French feet below the surface, the lowest set
shewing the variations 24 French feet below the surface.

The most obvious results are the following :—

1. In the upper set of curves, though the irregularities are greatest, yet the
three curves follow one another with singular fidelity throughout these irregulari-
ties. The curves separate a little in summer, and regularly in the same direction
every summer, shewing the influence of exposure, the Experimental Garden being
most heated, then Craigleith, and lastly the Observatory, which is also the order
of the elevations of the stations above the sea. It may also be added, that the
diurnal change may possibly have some slight influence upon the Experimental
Garden, where the observations were made fully two hours later than at the other
stations. (See Section V.)

2. As the focal irregularities diminish at increasing depths, the range dimi-
nishes, and the times of maxima and minima are continually retarded.

3. At increasing depths, the curves, which followed one another so closely
and exactly amidst the irregularities of temperature near the surface, systemati-
cally separate from one another, both owing to a variation in the range or degree of
undulation of the curve, and owing to a greater or less degree of retardation in
the maxima or minima of the different curves.

4, The effect last described is least sensible in comparing the observations
at the Observatory and Experimental Garden, but most sensible if either of these
be compared with the Craigleith observations, for which last the range diminishes
more slowly, so that, at 24 French feet, it is about double that of either of the
others, and the retardation of the maxima and minima is much less.

5. In the trap and loose sand, the range is diminished to one-tenth part in
descending from 3 feet to 24 feet; but in the sandstone it is not quite diminished
to a fifth part. The epoch of maximum temperature is retarded in the two former
cases nearly five months, in the latter only three.

From these statements it is easy to see that the influence of the conDUCTING

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 207

POWER OF THE DIFFERENT SOILS OR ROCKS FOR HEAT is very palpable. But to
submit it to numerical calculation, a more elaborate analysis is necessary. Each
year has been first considered by itself, and then the whole united.

C. Thermometric Ranges.

To ascertain the range for each year, the maximum and minimum points of
the curves of each thermometer were ascertained graphically by the aid of an
elastic wire, bent so as to represent a curve which should pass through the zig-
zags of the temperature curve, and connect the observed points with tolerable
accuracy. The points of greatest and least temperature in each year were thus
represented with a certain degree of approximation, and the results are shewn in
the following table.

TABLE VILL. SHEWING THE MAXIMUM AND MINIMUM TEMPERATURE AND RANGE
FOR EACH OF FIVE YEARS.

Observatory, Trap. Experimental Garden, Sand. Craigleith, Sandstone.

: ate Range = rae Range, “ oon Range,
Maxi- Mini- | pahren- || Maxi- Aultievic SRL eaa Maxi- Mino ravens
mum. mum. wows mum. mum. Tact, mum. mum. heit.

1837-38 || 56-25 | 37-30 | 18°95 || 57-20 | 37°55 | 19-65 || 55-90 | 37°65 | 14-25
1838-39 || 53-40 | 35°70 | 17-70 || 55:45 | 35-12 | 20°33 | 53-90| 35:38 | 18:52
1839-40 |] 53-05 | 38:10| 15-55 || 56-50| 37-50 | 19-00 || 54:30 | 37-85 | 16-45
1840-41 || 53-87 | 38:95 | 14-92 || 56-35 | 38:10 | 18:25 || 55°10 | 38-95
1841-42 || 52°85 | 38:88 | 13-97 || 54:50 | 37-85 | 17-65 || 53:15 | 38-25

1837-38 || 52°30 | 40°40 | 11°90 || 54:65 | 39°70 | 14:95 || 53:80 | 39-90
1838-39 || 50°90 | 39°70 | 11:20 || 53°20) 38°63 | 14°57 || 52°35 | 38°10
1839-40 || 50°97 | 40°65 | 10°32 || 53°67 | 39°70 | 13°97 || 52°53 | 39-20
1840-41 || 51°35 | 41°10] 10°25 || 53°75 | 40°52 | 13 23 || 53°15 | 40.05
1841-42 || 51:07 | 40°78 52°95 | 39°55 | 13°40 || 51°90 | 38-95

1837-38 || 49°40 | 43°90 p 50°65 | 43:10] 7:55 || 51:10 | 41-70
1838-39 || 48°65 | 43°60 : 49°95 | 42°85 : 50°05 | 40°75
1839-40 || 48:57 | 43°73 ; 50°19 | 43-08 : 49°80 | 41°45
1840-41 || 48°80 | 44°30 : 50°30 | 43-60 : 50°45 | 42°12
1841-42 || 49°00 | 44.20 ; 50°40 | 43°50 5 50°30 | 41°60

1837-38 || 47°85 | 46:40 : 48:25 | 46°15 : 48°50 | 44°40
1838-39 || 47°45 | 46:20 ; 47°88 | 46-00 3 47°88 | 44:05
1839-40 || 47°35 | 45°97 ; 47°40 | 45°97 : 47°82 | 43°87
1840-41 || 47°38 | 46°15 : 48°00 | 46°10; 1: 48°12 | 44°40
1841-42 || 47°50 | 46:12 : 48°10 | 46°10 : 48°25 | 44°35

Theory shews, that the annual range ought to decrease in geometrical pro-
gression, as the depths increase uniformly. In other words, the ranges may be
represented by the ordinates of a logarithmic curve. And that such is the case
may be seen from the curves in Plates IX. and X., where the logarithmic curves
are drawn through points so as to represent, as well as is practicable, the law of
decreasing range at the different stations. These diagrams were constructed with-

out any reference to one another; and their general coincidence is highly satis-
factory.

208 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

To express the results geometrically,
Log. A= A+ Bp

Where a is the thermometric range at a depth p in French feet; A and B are con-
stants, the second of which is always negative. These constants are important,
and their determination may be considered as the primary object of this investi-
gation. A is manifestly equal to the logarithm of the thermometric range at the
surface, or when p=0; B is a constant which determines the rate of diminution
of the range in the interior of the earth, being smaller in proportion as the heat
penetrates more readily, or as the conductivity of the soil is greater. It was
shewn by Fourtrr to be directly proportional to the square root of the specific
heat of the soil, and inversely as the square root of the conductivity.*

These quantities A and B have reference to the thermometric scale employed,
and therefore it is convenient, in order to obtain comparable results, to use the
same unit as MM. Poisson and QuETELET have done in their comparison of theory
with observation, that is, the centigrade scale. For this purpose, the ranges are
expressed in the following table in centigrade degrees.

TABLE IX. RANGES IN CENTIGRADE DEGREES.

3 Feet. 6 Feet. 12 Feet. 24 Feet.

Experi-
mental
Garden.

Experi-
mental
Garden.

Experi-
mental
Garden.

Experi-
mental
Garden.

Craig- || Observa-

Craig- || Observa-
leith. tory.

Craig- || Observa-
leith. tory.

leith. tory.

Craig-
leith.

Observa-
tory.

1837 ||10°53 |11-22 | 9:58 | 661 | 8:30| 7-72 3:05 | 419 | 5-22 || 0-80 | 1°16 | 2:28
1838 || 9:83 |11-30 |10-29 | 622 | 810 | 7-91 | 2:80] 3-94 | 5-16 || 0-70 | 1-05 | 2:13
1839 || 9:64 |10-55 | 9-14 | 5°73 | 7-76 | 7-40 | 2-69 | 3-95 | 4-64 || 0-76 | 0-79 | 2:20
1840 || 8-29 |10-14 | 8:98 || 5-70] 7-35 | 7-28 || 2:50] 3:72 | 4-63 || 0-89 | 1-06 | 2-07
1841 | 7-79 | 9:80] 8:28 || 571 | 7-45] 7-20] 2:66 | 3°83 | 4:83 | 0-76! 1-11 | 2-16

Means,| 9°02 |10°60 | 9°25 || 5°99 | 7°79 | 7:50 || 2°74 | 3:93 | 4:89 || 0-78 | 1:03 | 2-17

Two results are sufficient for eliminating the constants A and B at each sta-
tion, and the most probable combination may be had by the method of least
squares. I have preferred, however, the graphical method already referred to for
finding, by means of a diagram and a pair of proportional compasses, the loga-
rithmic curve which best represents the observations. This being done as shewn
in Plates IX. and X., the values of A and B may be deduced thus. A, as al-
ready observed, is the logarithmic range at the surface. Taking a space equal to
10° Cent. (or 18° Fahr.) in the compasses, find the depth at which the curve has
this quantity for an ordinate, let p,, be this depth. Then, since Log. a=Log. 10=1,
the equation above becomes

1=A+ Boy
dL. Aik
Pio

and B=

* For farther particulars, see the Appendix at the end of this memoir, and also Sub-Section F.

PLATE IX Royal Soc. trans. Edi Vol. NV pp 208 &
1857 1858

‘ 1859 1840

10° =o a 202 xo °
Is 20 25° 30 oO 0 o 10 Is? 20° 25° 30° 0

10°
—CRAIGLEITH

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 209

Also p,, Por, Pou Aenoting the depths corresponding to a range of 1°, 0°1, 0°01
Cent., we have

1+A

2+A
Pui = — B

Po-01 — whle .

yn=-

bol

Numerical Example. By the projection for 1837, Plate IX., we find

Observatory. Experimental Garden. Craigleith.
The superficial range 14°-6 Cent. 15°-0 Cent. 11°-9 Cent.
Pi=depth where range=10° Cent. 3:0 F. ft. 4:0 F. ft. 2-4 ¥F. ft.
Whence A : : : : 1:164 1:176 1:076
B ; : : ‘ . —0°0547 — 0:0440 —0:0317

Bin i : : ‘ ‘ , ; 21:4 F. ft. 26-7 F. ft. 341 F. ft.
Por 39°7 49°5 65-7

Poot 58:1 12:2 97:3

The numbers in the last line may be taken (arbitrarily) as a limit of compa-
rison for the point at which the annual variation sensibly vanishes, and its dif-
ference in the three stations shews the marked influence of the conducting soil
or rock. The following tables contain a summary of these results for five years.

TABLE X. SHEWING THE VALUES OF A AND B.*

VALUES OF A.

VALUES OF B.

Experi- _ | Experi-
Ob eee | erent Craigleith. phos mental | Craigleith.
LOD. Garden. J: Garden.
1837 1:164 1:176 1:076 1837 |—-0545 | —-0440 | —-0316
1838 1173 1°217 1114 1838 |— :0641 |—-0517 | —-0345
1839 1:086 1:182 1:049 1839 |—-0516 | —-0498 | —-0305
1840 1:073 1155 1:044 1840 |—-0550 | —:0470 | —-0308
1841 1:031 1141 1:019 1841 |—-0474 | —-0460 | —-0281
Means, | 1°105 1174 1-060 Means, | —-°0545 | —-0477 | —:0311
TaBLE XI. SHEWING THE DEPTHS AT WHICH THE ANNUAL RANGE IS REDUCED T0

0°01 CENT.
Observatory. eee Craigleith.
1837 58'1 72°2 97°3
1838 49°3 61:8 91:0
1839 59-2 63°5 100-0
1840 050°9 67°1 98°8
1841 63:9 68:3 107:4
Means, 57°3 66:6 98-9

* The French foot and centigrade degree are here taken as units.
VOL. XVI. PART II.

oa

210 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

On these results it may be remarked, that A, which is the logarithm of the
superficial range, is necessarily variable according to the season, and that it ap-
pears, singularly enough, to have been constantly on the decrease throughout the
period of these experiments. This gives a great probability that the mean of
these will be very nearly an average result for this climate. The depth at which
the annual variation disappears is also evidently dependent, in part, on the qua-
lity of the season. B is the only proper constant, depending solely upon the spe-
cific heat and conductivity of the soil; and the mean results of Table X. are evi-
dently near approximations to the truth.

These computations have been made on the supposition that the logarithmic
law of the diminution of the range is correct, and that the deviations from it are
due to accidental errors. These deviations appear, however, to be too systematic
to admit exactly of this conclusion. The observations at Craigleith coincide most
nearly with theory ; those at the Observatory much less so, although there is every
reason to believe that the observations there were in every respect the most un-
exceptionable of the three. At the Observatory, the observations at great depths
indicate a less rapid contraction of the range than do those at the surface, as an
inspection of the curves in Plates IX. and X., and the points through which they
have been drawn, sufficiently proves.

To illustrate this difference, I had the constants A and B separately computed
from all the possible combinations by pairs of the observations of 1837-38, with
the following results.

D. Progress of Heat downwards.

The curves of Plate VII. plainly shew that the periods of maximum and
minimum temperature occur later and later as we descend. The epochs of maxi-
ma and minima were obtained graphically at the same time with the greatest and
least temperature, in the manner already described. The results are contained in
the following Table :—

a

ah S 1-075

TABLE XII.
Observatory. Experimental Garden. Craigleith.

2 12 Feet. 6 Feet. 3 Feet. 12 Feet. 6 Feet. 3 Feet. 12 Feet. 6 Feet.
& A= 1:08 26 A Ha 26 ASS" 182 Ar 1180) | A 204 Ar Oi rac 1-077 Ace ere Ale .
2 24 Feet. || p — —.0484| B = —-0510 | B = —0533 || B = —0465 | B = —-0475 | B = —0459 || B = —-0300 | B = —0294] B — —-0297})
ee en A= 1156 |A= 1-202 A= 1216 |A= 1-193 || A= 1-058 |A=— 1-069
8 oo lhe Sus { B = — 0560 | B = —-0598 Seat She B= — 0495 | B = —-0476 oS Baas B = — 0283 | B = —-0293})
a pes PP eee Sees es =
& |A= 1-225 A= 1-182
s GUE 6 Sg 6 0 BG od oe {|B = 0674 } ee { i 2 geen } rec eee eee suc. > { B= —0318
5 7

Mean Values, . { as gee Mean Values, . { a ab Mean Values, . { a me

j
@

—

PLATE X. Royal Soc trans iidin Vol AV pp 208 &e!
‘MEAN 183741

DIAGRAM SHEWING THE PROGRESS OF HEAT DOWNWARDS
BY THE MEAN OF FIVE YEARS.
ay February March April May June July August Septem? October Novem’ Decem? Jan?

3 ¢
eee Tis 26 4 218 261 8 i 220 6B wW2 SWUM wa 1 8 22.29 § : W199 62 2 9 Wb 2330 79 WM 0 28 4 Th 18 26 2 9 1 23.30 6 13
= x ica T T Se a | T = iz cae Ga GGL | 7 a aa | r

\ T | ] | | ee]

| |
| |
| |
ae
|

|
|
att

C
—GRAIGLEITH

aa

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH 21

TaBLE XIII. Epocus or Minimum awD MAximuM TEMPHRATURE (BY INTERPOLATION)
FROM 1837 To 1842.

MINIMUM.

3 Feet. 6 Feet. 12 Feet. 24 Feet.

Experi-
mental

Experi-

Experi-
mental

Experi- . .
epee Craig- || Observa- | j.cntal Craig- || Observa- Obserya- ae
eith.

Observa- | Inental

tory. Garden. leith. Une Garden. leith. tory. Garden. tory. Garden.

May 6] Apr. 30 July 26 | July 12 May
Feb. 26 | Mar. 3) Feb. Mar. 14 | Mar. 19 } Mar. Apl. 20} Apr. 22] M r. July 18] July 8/ May
Mar. 14/| Feb. 24] Feb. 24 || Mar. 27 | Mar. 25 | Mar. Apl. 30 | Apr. 22 A July 12 | June 24 | May
Mar. 1] Feb. 25 | Mar. Mar. 14 | Mar. 15 | Mar. Apl. 19 | Apr. 18 Fi July 5] June 26 | Apr.
Feb. 1/ Feb. 1] Jan. Feb. 17 | Feb. 15 | Feb. Mar. 24 | Mar. 20 July 5| June 15 Apr.
Jan. 25| Jan. 22 | Jan. Feb. 19] Feb. 15} Feb.

Feb. Feb, 14 ; Mar. 7| Mar. 7 | Feb. 21 || Apr. 20} Apr. 4 June 29 | May

MAXIMUM.

1837 || Aug. July 31 : Sept. Aug. Aug. 19 || Oct.
1838 || Aug. Aug. 6 ". Sept. Aug. Aug. 23 |) Oct.
1839 || Aug. July 30 30 |} Aug Aug. Aug. 14 | Oct.
1840 || Aug. Aug. 18 : Sept. 4] Sept. Aug. 23 || Oct.
1841 || Sept. Aug. 23 . Sept Sept. Sept. 15 | Oct.

Means || Aug.15}| Aug. 9 Sept. Sept. 1 | Aug. 25 | Oct.

It will readily be understood, by the inspection of the curves, that these de-
terminations are liable to considerable uncertainties,—in most cases amounting
to several days. The curves at small depths are liable to many anomalous fluc-
tuations, and even occasionally present an appearance of two minima; and at
great depths the curves, though even, are so flat, that a considerable error may
occur in detecting their highest and lowest points. It does not appear, however,
that more real accuracy would be obtained by the methods of calculation which

have usually been employed, instead of interpolating curves. We shall presently,
however, shew how the two may be advantageously combined.

We thus see that the greatest cold of winter attains the depth of 24 French

feet,—
At the Observatory (trap rock), on the 13th July;
At the Experimental Garden (loose sand), on the 29th June ;
At Craigleith (sandstone), on the 3d May ;

and that the greatest heat occurs on the 4th January, 25th December, 3d Novem-
| ber respectively ; shewing, in both cases, the very same order of facility in con-
: ducting heat which-we had before deduced from the diminution of ranges, namely,
| that the Observatory ground is the worst conductor, that of the Experimental
Garden but little better, and the rock at Craigleith by far the best.
: Unfortunately, the measure of the retardation of epochs has, as yet, been so

212 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

imperfectly reduced to theory, that we cannot satisfactorily compare it with ex-
periment ;* but one law of great simplicity has long been known from theory
to be approximately true, namely, that the retardation of epochs is uniformly
greater as the depth increases. This is also easily verified graphically. By tak-
ing the depths in a vertical direction, and setting off the day of greatest or least
temperature horizontally, a series of points is obtained through which a straight
line should pass. I have not engraved these projections for each year, but that
for the mean of the whole will be seen in the lower part of Plate X., where the
interpolating lines in general pass so nearly through the dots that they cannot be
distinguished. From these projections the mean rate of propagation downwards
is easily determined, and affords a palpable illustration of the conducting powers
of the soil.

TABLE XIV. SHEWING THE NUMBER OF DAYS REQUIRED BY THE IMPRESSION
oF HEAT TO PASS THROUGH ONE FooT oF SOIL.

MAXIMA. MINIMA,

Observa- |Experimen-

Observa- |Experimen-
tal Garden.

Craigleith. tory. tal Garden.

Craigleith.

Days. Days. Days.
1837 : 3 4:9 nate : 34:
1838 : : 3°6 6°5 ; 3°6
1839 : : 4:6 6:0 - 3-6
1840 35 | 61 3-05
1841 . ; 3°0 6-4 : 3°6

Means : 2 3°92 6:25 i 3:46

It must be added, that in the several years the law of wniform progression is
by no means accurate, although, in the mean of five, the accidents are nearly
compensated. And here, again, we find the good conductor, the sandstone, gives
by far the most regular and consistent results.

E.—On the Form of the Annual Curves.

With a view to approximate more nearly to the form of the annual curves of
temperature at different depths, I have had the mean temperature for each week
of the year taken by the mean of five years, which has the effect of disposing of
the more irregular fluctuations, as may be seen in Plate VIII., the curves in which
are taken from the following Table :

* See the Appendix.

aS
ry
: ' a
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Lf es ee cS gene SS Soe Al SS Nieg
S 22 i ~ = = = S Ny =~ I
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199.1 "1909.7 F

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VoL. x

214 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

The dates in the preceding Table are the mean of the corresponding days of
observation during the five years. More correctly they ought to be about half
a-day earlier; thus, the temperature of February 4 belongs to February 3°5, or
to midnight of the 3d, instead of the 4th at noon, and so of the others.

The practice of denoting periodic variations of temperature by a series of the
form

Yo= A+B sin (n+ 6) + C sin (Q2n+c) + &e.

(where y, is the temperature corresponding to the fraction of the year denoted
by x, and A, B, C, 6, c, are constant quantities), has prevailed in Germany at
least since the time of Lamprert.* I have thought it worth while to compute
the equations for each of the 12 curves, so as to facilitate comparison with the
results of QUETELET} and others. But my method of proceeding has been some- -
what different from his. I sketched very carefully interpolating curves through
the curves of Plate VIII., so as to diminish their remaining irregularities, and
having divided the horizontal space corresponding to a year into 12 equal parts
(each of which may be represented by the space of 30°, the whole period of varia-
tion being 360°), I measured and inserted in a table the ordinates of the inter-
polated curve corresponding to these points; and with the aid of these ordinates,
the equation to the curve was calculated by the aid of the tables given at the end
of the second volume of Dove’s Repertorium. The results were as follows :—The
first term is of course the mean temperature of the year, which has been taken
from Table V.

TABLE XVI. CONTAINING THE EQUATIONS TO THE ANNUAL CURVES.

3 FEET.

Observatory, y,=45°49 — 7°39 sin (n . 30°+ 43°) + 0°362 sin (n . 60° + 29°)
Ex. Garden, y,=46-13—9-00 sin (n . 30°+49°) + 0°737 sin (n . 60°+ 63°)
Craigleith, y,=45:88— 8°16 sin (n . 30°+47°) +0°284 sin (n . 60° + 34°)

6 FRET.

Observatory, y, =45°86 — 5:06 sin (n . 30°+ 28°) +0.433 sin (n. 60°+ 7°)
Ex. Garden, y, =46'42—6°66 sin (n. 30°+ 29°) +0°501 sin (n.60°+ 5°)
Craigleith, y,,=45-92—6-16 sin (nm . 30°+36°) +0.368 sin (n . 60° + 340°)

12 FEET,
Observatory, y, =46°36 — 2-44 sin (n . 80°+ 344°) +0:075 sin (nm . 60° + 330°)
Ex. Garden, y, =46-76— 3°38 sin (n . 80°+ 348°) + 0-280 sin (n . 60°+ 319°)
Craigleith, y,=45°92—4-22 sin (n. 30°+4 13°)

24 FEET.
Observatory, y,=46°87 — 0°655 sin (n . 30°4+ 85°)
Ex. Garden, y, = 47°09 —0°920 sin (n . 30° + 275°)
Craigleith, y,=46-07—1-940 sin (n . 30 + 327°)

The following table contains the experimental ordinates, and those obtained
from the preceding equations. The coincidence would have been somewhat
closer had the mean of the 12 equidistant ordinates been taken for the mean tem-
perature (A), instead of the mean of the entire observations.

* Pyrometrie, § 675. t+ Ann. de l’Observatoire de Bruxelles, iv. 169.

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 215

TABLE XVII.

3 FEET.

Observatory. Experimental Garden, Craigleith.

=

Cale. iff. : Cale,

|
|
|

—6:10 : — 5:85
—8-21 : —7:68
— 8°57 ? . —7'66
— 6:60 . : — 568
— 2-38 . . —2:07
+2:93 : ; 4+ 2°30
+ 7-42 : + 6:16
+9°45 ; : + 8:25
+ 8-48 . +7:90
+ 5:28 : b + 5°36
+1:15 : : +1:50
—2°85 | +° — 2°55

ao
HOODIA NRwWNWr OS
=a | i gieceae

6 FEET.

—o lo Sls)
— 5°25 5 P45)
— 62 — 6°25
—6'0 87)
—4:-0 —Sptsie3
— 0°65 — 0-52
+33 Sil
+ 6:2 +6:16
+6:8 + 7:07
+5°75 | +5°78
+3:°3 = 297
= 0:7 — 0°30

FOoUNmMIA KAP wWNWr oO
I++ |
ll t+) bee bed

ie
ae Le iat
+

12 FEET,

+ 0°35 4-0°55
ee, —0:97
—2°45 SPOTS
—3°35 —o3'15
=o 00 —3 28
O27 — 2°49
—1:0 — 0°85
35 110) te Teil
+2°7 +2°74
+3°25 | 43-45
+2°9 +3°14
+ 2-0 + 2:03

ieee

(aes

HOD DIHAMRWHHO
[ttt++etts 1 +

= pd

t+t++te+t+¢t++4+4+4

+1 +41

24 FEET.

igs

+
+ .

Bm whdo eH ©

POO COAT ON

aot

O16 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

The following method of determining the absolute maxima and minima of
the temperature curves and the epochs seems to be simpler in its application than
those hitherto in use.

Although the temperature-curves cannot be represented, either altogether or
in great part, by parabolas, the summits may always be represented sufficiently
accurately by osculating parabolas, which may, of course, be determined from three
points of the curve, and that with the less error as these three points approach
more nearly to the point of maximum or minimum sought. In the preceding
cases, the ordinates of the curve are already calculated for abscissee corresponding
to every 30°. It is easy to find, by simple inspection of the Tables, between which
two ordinates the summit of the curve lies. It will necessarily be between those
having the greatest values (+ or —); or, if there be two ordinates with the same
value, it must be precisely half way between (supposing the portion of the curve
to be parabolic).

Let 7, y”, be the two greatest ordinates (calcu-
lated by the formula), and let y” be an ordinate half
way between them (calculated from the Equations,
Table XVI.) Then the difference of abscisse MN,
N O, is in this case 15°. Let it be more generally m,
a number always positive. Let VP be the axis of |
the parabola whose position is sought; and let its Mi NP 0
distance from the ordinate y’, or NP be 2 (+ if to the right hand, — if to the
left). Then, supposing the parabola found, and the tangent to the vertex drawn,
by the property of the curve,

a. Mm=MV
a.Nn=NV
a.00=O0V-
where a is the parameter. Or,
a(V P—y') =(m+2) : : Z (1)
a(V Pay") =F : 4 : , (2)
a(V P—y”)=(m— 2)? ; : : (3)
Subtracting (2) from (1),
a(y’—y)=m?+2Qm2 ; ; (4)
Subtracting (2) from (38),
a(y”—y")=m*—-2mx : : ; (5)

Making y’—y'=A and y’—y'”=B, and adding together the last two equations,
a(A+B)=2 m?

2 m?

A+B

a=

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 217
Subtracting (5) from (4),
4mx=a(A—B)
and substituting the value of a just found

m A—B
DP joN sR

which determines the position of the greatest ordinate, whence that ordinate may

be deduced.
The results are contained in the following table.

z=

TABLE XVIII.
Ne mee ae ee ee ee ae a aU aT Rac Ge Mee mR a ee pene re tte pret ee

MAXIMA. MINIMA.
Eprocu. Epoca.
y q Fraction of | Month and g x Fraction of | Month and

3 FEET. Year. Day. Year. Day.
Observatory . . 53°20 | 224° 30! 624 Aug. 16:7|| 36:39 50° 29’ "140 Feb. 21:0
Experimental Garden 55°73 | 214° 48’ “597 Aug. 7:0|| 37:46 50° 12’ 139 Feb. 20:5
Craigleith . . .~ 54:29 | 220° 50’ 613 Aug. 12°7|| 37:96 44° 49/ 124 Feb. 15:3

6 FEET. :
Observatory . . 51:23 | 240° 19’ “668 Sept. 2:0]/ 41:02 om AW bala Mar. 19:0
Experimental Garden| 5350 | 235° 29° 654 Aug. 27:7|| 40:12 67° 30/ 188 Mar. 10°7
Craigleith .. . 52°45 | 234° 39’ "652 Aug. 27:0|| 40:18 538° 00’ 147 Feb. 23:7

12 FEET.
Observatory . . 48°85 | 282° 30’ 785 Oct. 14:7]/ 48:86 | 108° 58’ 303 April 21:7
Experimental Garden 50°23 275° 41’ ‘766 Oct. 77 43°39 109° 15’ -303 April 21°7
Craigleith .. . 50°14 | 257° 00’ ‘714 Sept. 18°7|| 41-70 77° 00’ *214 Mar. 20:0

24 FEET.
Observatory . . 47°53 5° 00’ 014 Jan. 6:0] 46-21 185° 00’ 514 July 7:7
Experimental Garden 48:01 855° 00’ *986 Dec. 27:0|| 46:17 “75> O0F “486 June 27:3
Craigleith . . . 48:01 | 303° 00’ "842 Nov. 4:3] 44:18 123° 00’ "342 May 6:0

These results, obtained in a different manner, may be compared with those
in Tables VIII. and XIII. The inspection of the deviations of the annual curve
in Plate VII., from the average results in Plate VIIL., illustrates well the remark-
able variations in the character of the seasons in these five years, and renders it
probable that the mean effects of ordinary atmospheric temperatures throughout
the year may be most conveniently and accurately studied, and the annual curve
ascertained, by observations at a moderate depth in the soil.

F. On the Influence of “« Specific Heat” on the Results.
The quantity which we have, in page 208, called B (after M. QUETELET*) is
equal to
ee log e
Where 7 = 3:1416, ¢ is the base of natural logarithms, and a the symbol used by

* Annales, &c., vol. iv. p. 112.
VOL XVI. PART II. ol

I18 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

Poisson to express the ratio “f) ‘ where k is the conductivity of the soil and c is
c

specific heat. Whence, if the whole quantity B be known, and c the specific heat
be deduced from direct experiment in the laboratory, £ may be found. [In the
present instance, it is to be recollected that the Pench foot is taken as the unit. |

M. Exre bE BEAumonrt, who has taken much interest in the experiments de-
scribed in this paper, very obligingly requested M. Recnavutr of Paris (whose
skill in this matter is well known) to determine the specific heat of specimens
taken from the grounds of the Observatory, Experimental Garden, and Craigleith
respectively ; and M. Reanautr had the goodness promptly to submit them to
experiment, and he communicated to me the following results :—

Specific Heat.

Porphyry of the Calton Hill, . j , : 0:20654
Another Experiment, : : : : 0°20587
Mean, , 0-20620

Sand of the Experimental Garden, : : : 0°19432
Sandstone of Craigleith Quarry, i f 3 0°19257
‘Another Experiment, : : ; ; 0°19152
0-19205

Some correction would, no doubt, require to be made for the moisture con-
tained in the soil, but this appears difficult to apply, and probably would be in-
considerable. The above results evidently represent specific heats referred to
unit of weight of the body, but that referred to in the theoretical investigation, is
taken with respect to unity of volume.* The above results require, therefore, to
be multiplied by the specific gravities (water being the standard in each case)
which I have found to be, when reduced to 60° F.

Trap. Sand. Sandstone.

Specific gravity, : : . : ; 2-562 1-547 2-408
Whence we have speeific heat referred to unit of volume, 0:5283 0°3006 0:4623

G. Final Results.

The value of Porsson’s constant a, expressive of the ratio a o being obtained
C;

from our constant B by means of the relation
T

= log e

a=

* Poisson, Théorie de la Chaleur ; Suppl., p. 4.

+ Mean of two experiments, 1°556 and 1538. It is evident, that since it is required to find the
specific heat of unit of volume of the mass to be heated or cooled, we must take the aggregate of sand
as we find it in the soil, and not the specific gravity of the individual grains. Accordingly, the specific
gravity was determined by comparing the weights of closely packed sand and of distilled water contained
in a stoppered phial.

PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. I19

| (which is equivalent to the expression in the Theorie de la Chaleur, p. 499, Eq. (26) ),
gives the following numerical result :-—

Trap. Sand. Sandstone.
14:124 16°137 24-750
but if referred to the French Metre instead of foot as unity (the centigrade de-
gree has been already employed), they become

a 4:588 5:242 8:040

which are comparable with Porsson’s result, 5-11655 for the Observatory of Paris.
Now, the specific heat c having been found in the last section, we may eliminate
it, and obtain the following numerical values of /, the conducting power of the
strata, which it may be presumed has rarely been so accurately determined for
any kind of matter.

Trap. Sand. Sandstone.

k 11°120 8:260 29-884

There is another constant 6 employed by Poisson, which involves the character
of the recipient surface of the ground as well as the interior conductivity, and
which is determinable from the retardation of epochs by equation (27) of page 499
of the Theorie de la Chaleur.

ie | cot [2 (0 + )-2ave | 360°—1 \
where 6 and 6, are the epochs of maximum and minimum temperature at any
given depth, reckoned from the 21st March in fractions of a year (= 1), the metre
being also the unit. Instead of taking observations at a single depth, we may
take the epoch for 24 French feet from the interpolating lines in Plate X., which
represent not merely the observations at that depth, but the result of their com-
bination with all the others.

Trap. Sand. Sandstone.
Maxima at 24 F. ft., aly 8 = Sit ui ialridiy=f498 May 6.=234
Minima, é ; : Jan. 4.=1-008 Dec. 26.=:984 Noy. 4.=°841
Mean reckoned from Ist Jan., : 461 740 591
Reckoned from 21st Mar.=3 (0+ 0,) +545 “594 “BIT

Substituting the values of z=7°7961 metres (24 F. ft.), and of a before found, we

obtain
Trap. Sand. Sandstone.

b 0:4972 _ 01007 0-0772

M. Potsson finds for 6 at the Paris Observatory, the value 1:057. If we examine
the circumstances which influence the value of }, we shall admit that its determi-
nation in this manner is liable to so great errors as to render it almost worthless.

220 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

I shall not follow farther the application of these results, of which a and k are
the most immediately important. In particular, 1 shall not attempt to find, with
Poisson, the whole climateric effect of the solar influence which he deduces from
the quantities a and 6 found above; both on account of the uncertainty of the
value of 6, and because I have attempted elsewhere to shew that the physical
assumptions, upon which the great French analyst has founded the determination
of this quantity, are exceedingly precarious.*

I have only farther to add, that the extensive reductions and computations
of which the results have been given in this paper, were performed under my im-
mediate superintendence by different persons at different times. My thanks are
due to Mr Broun, Mr Morrat, Mr Linpsay, and especially to Mr Greee, for their
attention and accuracy in conducting them.

EDINBURGH, June 1846.

APPENDIX,

Containing Remarks on the Connection of the Preceding Observations with the Theory of

Fourier and Poisson.+

“ So far as the effect of SOLAR HEAT is concerned, the @ priori solution of the problem of
the temperature of any part of the earth’s surface may be thus imagined :—(1.) The whole
quantity of sunshine which falls on any part of the earth’s surface in the course of a year is
to be found, and also the law of its variation of force at different seasons. (2.) The part of
this heat which becomes effective in heating the earth’s crust is to be found by multiplying
the amount by a constant depending upon the absorbent power of the surface. (3.) This
quantity of heat thus reduced is propagated towards the interior, according to the laws of
conduction, which again presuppose the knowledge of two constants proper to each soil,
namely, the Conductivity and the Specific Heat.

‘© (1.) The measure of the quantity of sunshine received by any place in a year, and its
distribution at different seasons, has been a favourite problem with mathematicians. In ul-
timate analysis, it depends of course on the astronomical elements which affect the progress
of the seasons, viz., the obliquity of the ecliptic (vy), the latitude of the place (u), the excen-
tricity of the earth’s orbit («), and the longitude of the sun’s perigee (a). But there are also
elements quite as important as any of these ; the imperfect transparency of the air and its
varying thickness, owing to differences of obliquity of the transmitted rays, and the condition
of opacity depending on the weather. Neither of these is insignificant, neither of them
compensatory ; both may be considered as functions of the hour-angle and fraction of the
year, and the second is besides subjected to the most capricious changes. Yet of these ele-

* See Second Report on Meteorology, Arts. 104, &., in the British Association Reports for 1840,
+ Taken from the Second Report on Meteorology, British Association Report, 1840, Art. 88, &c.

.PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 221

ments theory has hitherto taken no account, and consequently the expression for the quantity
of sunshine obtained, in terms of the astronomical constants, with so much labour, we must
hold to be nearly useless as a physical datum. Itis vain to say, with M. Poisson, “ Les lois
d’absorption de la chaleur solaire & travers l’atmosphere, les variations diurnes et annuelles
sont également inconnues, et l’on peut seulement supposer qu’ elles sont peu considérables.” We
know, on the contrary, that they are so considerable, that, estimating the loss of radiant heat
by a vertical passage through the atmosphere at only twenty-five per cent., at an angle of
elevation of 25° the force of the solar rays would be reduced to a half, and at 5° to one-twen-
tieth part. We know, indeed, that the difference of the direct effect of a vertical and a hori-
zontal sun is due to this cause alone, exaggerated, of course, immensely by the variable me-
teorological state of the atmosphere, which again is a function of the latitude.

«(2.) The receptive power of the surface is a datum which we find it very difficult directly
to determine, and which, since the quantity of sunshine cannot (as we have seen) possibly be
directly computed, must be inextricably mixed up with it. It might be a question, whether,
by covering a tolerably extensive surface of soil, in which thermometers are inserted, with a
composition of known superficial conductivity, this element might not become known.

“‘(3.) The specific heat (c) and conductivity (&) of the soil are also inextricably mixed up
together in the analysis ; but either becoming known, the other may be inferred from ther-
mometric observations carried below the surface. The specific heat seems that best adapted
for laboratory experiments ; M. ELIE DE BEAUMONT has assigned 0:5614 for the value of ¢
(that of an equal bu/k of water being=1), proper to the soil at the Observatory at Paris.

“ To obtain the conductivity of the soil @ posteriori, it is fortunately not necessary that the
preceding theoretical estimation of the distribution of sunshine should be correct; but there
are other estimates into which it essentially enters, and which must therefore be received
with corresponding caution. To facilitate reference to M. Poisson’s work, I will shew how
the simple and very satisfactory observation of maximum and minimum temperature of the
earth’s crust at given small depths (above the invariable stratum) may be made to yield a
knowledge of some of the constants above referred to.

“ Let the excess of the annual maximum above annual minimum temperature at a depth p
be expressed by A,; then

log AA=A+Bp
in which A of course denotes the log. range when p = 0 or at the surface, and B determines
the common ratio of the geometrical progression according to which the range diminishes.
From observations with two thermometers at different depths, A and B may be obtained a
posteriori.

“ Now when we consult M. Poisson’s work, we find that his equation (23.), page 497,
which is equivalent to the preceding one, is thus composed. The quantity A, on which the
superficial range depends, contains (1) astronomical constants of climate y, u, «, » already
mentioned ; (2) a temperature 4, depending on the mean force of the solar rays which have
traversed the atmosphere and entered into combination with the earth's surface by absorp-
tion at a given place ; (3) the constant of conductivity &, and of specific heat c.

* The coefficient B, on which the rad of diminution of the range depends, is fortunately a
very simple quantity, involving neither astronomical constants, nor those proper to the super-

ficies. Itis, in fact, an absolute number multiplied b ca and from a knowledge of it (by
P aay g M)

VOL. XVI. PART II. o kK

992 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH.

observations with two or more thermometers) this quantity may be very readily and accu-
rately determined ; and it affords the only unexceptionable manner of ascertaining the conduc-
tivity of the earth’s crust on a large scale.

* * *% *

“ The epochal retardations for the annual curves at the depth of a few feet, follow, gene-
rally speaking, a simple law, for they are propagated uniformly downwards with a velocity
which is easily connected with the constants proper to the soil, determined from the range at
“two given depths, as just explained. It must not be concluded, however, that the epochs of
earth-temperature at the surface coincide with those of air-temperature in the adjoining
stratum. The difference of epoch may be obtained in terms of the conductivity and superfi-
cial characters of the solid stratum. But the complete expression for the epoch at any depth
in terms of the dates of maximum and minimum at some other depth, and of the constants of
conductivity and surface, derived from two observed ranges, is so complex, that, so far as I
know, no attempt has been made to verify M. Porsson’s formule except in a single example
by himself, taken from M. ARAGO’s observations.”

TABLES.

meonctes the deepest, ot 24 feet Thermometer, ¢, at 12 feet, t, at 6 feet, ¢, at 3 feet (French Measure)

i; at the
surface of the ground ; 7’, the temperature of the air in the Thermometer box.
OBSERVATORY.
t Cor. | Cor. | | t, & Cor. | Cor. ts t; Cor. | Cor. ts t, Cor. | Cor. t, \
uncor- | for | for cor- || uncor-| for | for cor- || uncor- | for | for cor- || uncor-| for | for cor- ts, Ei

rected. | Col. | Air. | rected. || rected. Col. Air. | rected. || rected. | Col. | Air. | rected. || rected. | Col. | Air. | rected.

RTE BRTOWRDONMONUNOAKE KBRWTOWNTSCWRAWOWA

= OO

48-10 |+-03
47-98 |+-03
47-87 | 4-03
47-79 |4.03
47-73 |4-03
47-63 |+-03
47-52 |+-03
47-42 |+-03
47-34 |4-03
47.29 |4-03
47.22 |4:03
47-12 |4-03
47-05 |4-03
46-96 |4-02
46-92 |+-02
46-82 | 4-02
46-78 |+-01
46-70 |+-01
46-65 |+-01
46-58 | -00
46-55 | -00
46-53 |—-01
46-52 |—-01
46-49 |—-01
46-48 |—-01
46-49 |—-02
46-53 |—-02
46-59 |—-02
46-65 |—-09
46-70 |—-02
46-78 |—-02
46-86 |—-02
46-96 |—-02
47-06 |—-02
47-16 |—-02
47.24 |—-01
47.33 |—-01
47.38 |—-01
47-43 |—-01
47-50 |—-01
47.57 |—-01
47-63 | -00
47-69 | -00
47-74 |+-01
47-76 |+.01
47-82 |+-01
47-84 |+-01
47-82 |+-01
47-79 |+-01
47-76 |+-01
47-75 |+-02

+-0

eee ee

senate

48-15
48-04
47-92
47-84
47-75
47-66
47-58
47-46
47-41
47-33
47-25
47-16
47-06
46-98
46-90
46-83
46-74
46-68
46-60
46-51
46-50
46-45
46-43
46-42
46-41
46-44
46-45
46-51
46-58
46-65
46-73
46-81
46-90
47-00
47-10
47-19
47-27
47-36
47-43
47-51
47-59
47-66
47-72
47-78
47-81
47-82
47-84

47-84
47-85
47-83
47-81
47-78

45-93
45-59
45-37
45-22
45-09

| 44-94

44-75
44:59
44-42
44.26
44-08
43-87
43-83
43-82
43-90
44-00
44-16
44-35
44:60
44-88
45-18
45-55
45-98
46-44
46:82
47-32
47-78
48-10
48-38
48-60
48-87
49-05
49.21
49-27
49-35
49.34
49-37
49-34
49-30
49-25
49-09
48-86
48-62
48:35
48-05
47-82
47-45

47.24
47-02
46-86
46-70
46-41

Seas es nba Hae wean pi te
So

+++
Baas ei

|
=)
on

P+tt+t++s+
SDR ea
ms

eee a as

poset a

39-11
40-54
40-89
38-90
39-39
39-40
38.08
37-49
37-11
37-69
38-72
40-09
41-73
43-13
43-23
45-31
46-57
47-42
48-69
50-99
52-69
53-46

53:88
54-66

54-40
52-67
52-25
51-48
52-12
51-10
51-80
50-84
50-28
47-30
45:05
45-73
43-47
43-35
42-75
41-70
41-80
42-79

43-65
42-50
40-20
38:88
37-80

ee.

+

aS so ae

Dates.

i Mar.

| Apr.

| May

i June

| Nov.

Dec.

Feb.

Mar.

ee eee ee ar ae oy

Tee eterno te Mee Se eae ae

Beas a ae a es ai

Ht HO ae

Pe eet SNe ana

th
cor-
rected.

47-75
47-70
47-66
47-60
47-52

47-45 |;

47-38
47-29
47-20
47-08
47-01
46-92
46-82
46-75
46-66
46-57
46-46
46-40
46:35
46-29
46-20
46-23
46-19
46-19
46-19
46-20
46-22
46-27
46-30
46:35
46-41
46-48
46-55
46-63
46-71
46-79
46-86
46-94
47:00
47-07
47-16
47-21
47-28
47-30
47-33
47-37
47-38
47-38

47-37
47-37
47-34
47-32
47-27
47-24
47-20
47-14
47-09
47-02
46:95
46-88
46-80
46:74

+-01

Eclceuon:

Shes

ae te ee Ie ee tee

Jt,
1

ee a ae

ey ae caer se eng hog eke

OBSERVATORY.

t,
cor-
rected.

46-18
45-69
45-47
45-18
44.77
44.44
44-18
43-98
43-86
43-69
43-69

uncor-

41-79
40-99
40-65
40-17
39-60
39-60
40-06
40-21
40-46
40-75
41-15
41-37
41-59
41-95
42.80
43-37
43-85
44.44
45-11
45-78
46-57

|| 47-36

48-20
49-10
49-66
49-84

|| 50-14

50-55
50-70
50:84
50-76
50-70
50:31
50-42
50-30
50-10
49-59
48-96
48-70
48-16
47-35
46-61
45-57
45-00
44-91
44-68
44-22
43-80

43-50
42.99
42-61
42-12
41-68
41-34
41-55
41-30
41-09
41-03
40-65
40-69
40-80
40-72

|

aa

Veer

[eete tee!

ts
cor-
rected.

41-81
41-02
40-67
40-20
39-60
39.59
40-05
40-20
40-45
40-73
41-15
41-36
41-56
41-87
42-78
43-33
43-82
44.37
45-05
45-75
46-45
47-33
48-08
48.98

ca

ee ee

a

t, Cor. | Cor. t
uncor- ae 4 cor=
rected. | Cl. | Air | rected.

| F a
5 || 46-63 |+:03] -00/} 46-66
1911 46-57 |+-03 |—-02 | 46-58
9 || 46-51 |+-02|—-02| 46-51
6|| 46-41 |+:02| -00) 46.43
3||46-34 |+-01| -00| 46.35
10 || 46-30 |+-01 |—-03 | 46.28
17 || 46-26 |+-01|—-05 | 46.22
31/1 46-18 |+-01|—-02 | 46.17
0|\ 46-15 |+-01|—-04| 46.12
7|| 46-13 -00 | —-06 | 46-07
4 || 46-06 |—:01|—-05 | 46-00
1//46-06 |—-01 |—-06| 45-99
81| 46-06 |—-01|—-07 | 45.98
5 || 46-04 |—-01 |—-04 | 45.99
21|46-05 |—:01| --05 | 45-99
9|| 46-09 |—-02 |—-05 | 46-02
5 || 46-14 |—-02 |—-06 | 46-06
2||\ 46-16 |—-02|—-04)} 46-10
9|| 46-19 |—-02|—-01 | 46-16
§\| 46-27 |—-02|—-04 | 46.21
2|| 46-33 |—-02|—-04 | 46.27
9|| 46-40 |—-02 |—-04 | 46.34
6|| 46-49 |—-02|—-03 | 46.44
46-58 |—-02 |—-04 | 46.52
0|| 46-65 |—-02|—-03 | 46.60
46-72 |—-01|—-03 | 46-68
4|| 46-79 |—-01 |—-02 | 46.76
1/|46-88 |—-01/—-03 | 46.84
8 1146-94 |—-01 |—-01 | 46.92
4|/46-99 |—-01] -00) 47-00
1|| 47-06 -00|}—-01 | 47-05
8 1147-11 -00 -00 | 47-11
47-14 -00|+-03 | 47-17
9 1147-17 -00 |+-04 | 47-21
9|| 47-20 |+-01/+-04 | 47.25
6 || 47-24 |+-01|}+-02 | 47-27
3|| 47-28 |+-01/+-01 | 47-30
1 || 47-28 |+-01 |+-02 | 47-31
6 || 47-27 |+-01|+-04 | 47-32
3/| 47-29 |+-02| -00) 47-31
01/47-25 |+-02|4+-02 | 47-29
7 || 47-22 |+-02/+-04 | 47-28
3 || 47-20 |+-02/+-03 | 47-25
1|| 47-17 |+-02 -00 | 17-19
T!| 47-13 |+-02|+-02 | 47-17
| 47-08 |+-02|+-02 | 47-12
2 || 47-02 |+-03|4+ -02 | 47-07
9|| 47-01 |+-03 |—-03 | 47-01
6||46-91 }+-03)+-01 | 46-95
3|| 46-84 |+-02|+-04/ 46-90
0/} 46-79 |+-02| -00/ 46-81
6 || 46-72 |+--02|)+-01 | 46-75
B || 46-69 |+-02|—-04 | 46-67
0 || 46-62 |+-02|—-03 | 46-61
W7 || 46-58 |4+-01|~-05 | 46.54
5 || 46-47 |+-01|+4-01 | 46.49
46-40 }+-01/\+-01 | 46-42
46-35 |+-01|—-01 | 46-35
46-32 |+-01|—-02| 46-31
46-31 |+-01|—-05 | 46-27
46-29 -00 | —-07 | 46-22
46-25 -00 |—-04} 46-21
VOL. XVI. PART II.

ty

uncor-
rected.

°
43-74
43-65
43-63
43-65
43-76
43-93
44-10
44-24
44-45
44-71
44:99
45-36
45-72
46-05
46-42
46-76
47-01
47-35
47-62
47-89
48-07
48-24
48-36
48-50
48-56
48-60
48-59
48:55
48-49
48-39
48-31
48-18
48-02
47-87
47-68
47-45
47-18
46-86

46-65
46-44
46-18
45-91
45-72
45-48
45-30
45-10
44-95
44-81
44-59
44-42
44-34
44-26
44-26
44-24
44-30
44-40
44-55

44-80
44-97
45-10
45-24
45-40

ee ee eee eo

++

[oie ae ry aegis

ie

OBSERVATORY.

ty
cor-
rected.

43-74
43-64
43-61
43-65
43-76
43-91
44-06
44-22
44-42
44-66
44.94
45-29
45-64
45:99
46.35
46-69
46-92
47-29
47-60
47-83
48-00
48-19
48-32
48-45
48-52
48-56
48-57
48-52
48-49
48-40
48-30
48-18
48-05
47:92
47-74
47-49
47-19
46-89

46-70
46-45
46-21
45-95
45-75
45-49
45-32
45-12
44.97
44-80
44-60
44.45
44.34
44.26
44-23
44-21
44-26
44-40
44-55
44.79
44-95
45:05
45-17
45-36

ts
uncor-
rected.

40-68
41-26
41-89
42-67
43-33
43-60
44-09
44-80
45-57
46-42
47-65
48-32
48-76
49-49
49-87
50-19
50-62
50-99
51-02

Cor.
for
Col.

-00

ae

le I

Atte nek eet a Ome aR nace va,

| | 42-94

| 42-27

40-66
41-23
41-84
42-66
43-32
43-53
43-99
44-76
45-49
46-28
47-54
48-18
48-60
49-39
49.76
50-06
50-46
50-91
51-03
50-74
50-72
50-76
50-74
50:47
50-22
49.84
49.27
49-05
48-70
48-24
47-73
47-42
47-16
46-36
45-50
44-63
44.29
44-15

43-64
43-14
43-08

42-45
42-06
42-06
42-07
41-59
41-19
41-25
41-69
41-74
42-07

42-84 |
43-48
44.74
45-32
45-08
45-06
45-44
46-10
46:82

ty
uncor-
rected.

oO
39-98
41-00
42-68
44-50
44-32
44-18
45-57
47-21
48-64
49-54
51-72
51-04

|

fp

Hose

Estas

by
cor-
rected.

(°)

39-92
40-90
49.57
44.49
44-31

44-05
45-37
47-15
48-50
49.29
51-57
50-82
52-43
52-86
52-66
53-29
53-90
53-81

52.68

52-48
52-38
52-19
51-42
50-90
50-53
48-66
48:97
48-00
48-05
46-53
46-25
46-30
45-19
43-05
41-65
41-60
42-10
40-62

40-70
40-02

225

—e
=
Bb
i=)

226 OBSERVATORY,

t Cor. | Cor. t te Cor. || ‘Cor: te t Cor. | Cor. t; t, Cor. | Cor. t,
Dates. sears || ae for one saree || LOE for com uncor- | for for co finda || hue for cons
rected. | Col. | Air. | pected. || rected. | Cole | Air. | rected. || rected. | Col. | Air. | pected. || rected. Col. | Air. | pected.
1840. ° ° ° ° i} ° ° °
June 22 || 46-24 -00 |—-04 | 46-20 || 45-62 -00 | —-04 | 45-58 || 47-42 -00|—-08 | 47-34 || 49-70 -00 |—-13 | 49-57
29 || 46-26 |—-01|—-05| 46-20 || 45-89 | -00|—-05| 45-84 || 47-79 —-12 | 47-67 || 50-02 —-21/ 49-81
July 6)|) 46-22 |—-01|—-03| 46-18 || 46-09 -00 |—-03 | 46-06 || 48-25 —-06 | 48-19 || 50-60 — -07 | 50-53
13 || 46-26 |—-01 |—-05 | 46-20 || 46-36 |—-01|—-06 | 46-29 || 48-63 —-12/ 48-51 || 50-98 —-18}| 50-80
20 || 46-26 |—-01 |—-04| 46-21 || 46-59 |---01 |—-04 | 46-54 || 48-99 —-08 | 48-91 || 51-43 —-13 | 51-30
27 || 46-31 |—-O1 |—-07 | 46-23 || 46-84 |—-01|-—-08| 46-75 || 49-42 —-17| 49-25 || 51-87 —-26) 51-61
Aug. 3/|| 46-33 |—-01|—-06 | 46-26 || 47-06 |—-01|—-07| 46-98 || 49-75 —-13 | 49-62 || 52-43 —-21 | 52-22
10 || 46-36 |—-02 |—-04] 46-30 || 47-28 |—-01|—-06| 47-21 || 50-20 —-10| 50-10 || 53-95 —-13 | 53-82
18 || 46-41 |—-02 |—-05 | 46-34 || 47-59 |—-0O1 |—-07 | 47-51 || 51-01 —-12| 5089 || 53-67 —-17 | 53-50
24 || 46:45 |—-02|—-05 | 46-38 || 47-81 |—-01|—-06 | 47-74 || 51-08 —-10/ 50-98 || 53-94 —-13 | 53-81
31 || 46-51 |—-02|—-05 | 46-44 || 48-07 |—-01 |—-06 | 48-00 || 51-33 —-10 | 51-23 || 53-87 —-13| 53-74
Sept. 7 || 46-57 |—-02|—-04| 46-51 || 48-30 |—-01|—-06/| 48-23 || 51-40 —-09 | 51-31 || 52-90 —-1]2)| 52-78
14 || 46-60 |—-02|—-01 | 46-57 || 48-45 -00|—-01 | 48-44 || 51-10 +-01/ 51-11 || 51-92 +-03 | 51-95
21 || 46-68 |—-02 |—-02 | 46-64 || 48-63 -00 |—-02 | 48-61 || 50-69 — -02 | 50-67 || 50-39 — -06 | 50-33
28 || 46-76 |—-02|—-05 | 46-69 || 48-74 -00 |—-06 | 48-68 || 50-20 —-09/| 50-11 || 49-76 — +16) 49-60
Oct. 5 || 46-82 |—-01|—-02] 46-79 || 48-74 -00 |—-02 | 48-72 || 49-79 —-03 | 49-76 || 48-95 —-07 | 48-88
12/| 46-91 |—-01|—-03 | 46-87 || 48-72 -00 | —-04 | 48-68 || 49-31 —-06 | 49-25 || 48-40 —-10)| 48-30
19 || 46-96 |—-01 |—-02 | 46-93 || 48-64 -00 |—-02 | 48-62 || 48-93 —-03 | 48-90 || 48-45 —-05 | 48:40
26 ||47-01 |—-01 -00 | 47-00 || 48-54 -00|+-01 | 48-55 || 48-65 +-02 | 48-67 || 47-30 +-02 | 47-32
Nov. 2// 47-08 |—-01 -00 | 47-07 || 48-46 -00 00 | 48-46 || 48-03 -00 | 48-03 || 46-27 — -02 | 46-25
9 || 47-12 -00|+-01 | 47-13 || 48-33 -00|+-02 | 48-35 || 47-60 +-03 | 47:63 || 45-90 +-02 | 45-92
17 || 47-18 -00|+-03 | 47-21 || 48-15 -00 |+-04 | 48-19 || 46-99 +-05 | 47-04 || 44-41 +-06 | 44:47
23 || 47-25 -00 |—-02 | 47-23 || 48-06 -00 |—-02 | 48-04 || 46-40 —-04 | 46-36 || 43-07 — -09 | 42-98
30 || 47-29 -00 | —-02 | 47-27 || 47-86 -00 |—-02 | 47-84 || 45-86 — -04 | 45-82 || 43-01 —-10}| 42-91
Dec. 7 || 47-30 |+-01/+-01 | 47-32 || 47-61 -00 |+-01 | 47-62 || 45-50 -00 | 45-50 || 43-44 —-02 | 43-42
14 || 47-29 |+-01|}+-05 | 47-35 || 47-35 |+-01 |+-06 | 47-42 || 45-20 +-07 | 45-27 || 42-64 +-09 | 42-73
21 || 47-31 |+-01|+-05 | 47-37 || 47-15 |+-01|}+-05 | 47-21 || 44-58 +-05 | 44-63 || 41-25 +-06 | 41-31
28 || 47-30 |+-01 |+-05 | 47-36 || 46-93 |+-01|+-05 | 46-99 || 43-89 +-05 | 43-94 || 39-80 +-05 | 39-85
1841
Jan 5 || 47-29 |+-02|)+-05 | 47-36 || 46-63 |+-01|+-05 | 46-69 || 43-18 +-04 | 43-22 || 39-83 + -05 | 39-88
11 || 47-28 |+-02/+-05/47-35 || 46-38 |+-01/+-05 | 46-44 || 42-72 +-04 | 42-76 || 38-31 + -04 | 38-35
18 || 47-27 |+-02|+-04| 47-33 || 46-10 |+-01 |+-04| 46-15 || 41-96 +-03 | 41-99 || 37-43 +-01 | 37-44
25 || 47-25 |+-03 |+-04 | 47-32 || 45-79 |4+-01|+-03 | 45-83 || 41-39 +-02| 41-41 || 37-25 +-01 | 37-26
Feb. 1)| 47-21 |+-03}+-05 | 47-29 || 45-46 |+-01|+-03 | 45-42 || 41-09 +-03 | 41-12 || 38-43 + -04 | 38-47
8 |} 47-15 |+-03 |+-05 | 47-23 || 45-15 |+-01|}+-03 | 45-11 || 41-00 +-03 | 41-03 || 37-56 + -03 | 37-59
15 || 47-14 |4+-03/+-01]47-18 || 44-91 |4+-01 -00 | 44-92 || 40-63 —-01 | 40-62 || 37-75 —-05 | 37-70
22 ||47-10 |+-03|—-01 | 47-12 || 44-66 |+-01|—-01 | 44-66 || 40-87 —-03 | 40-84 || 39-46 —-08 | 39-38
Mar. 1/||/ 47-01 |+-03/+-01|47-05 || 44-45 |+-01 -00 | 44-46 || 41-29 —-01 | 41-28 || 39-92 — -02 | 39-90
8 || 46-97 |+-03 |—-02 | 46-98 || 44-34 |+-01 |—-02 | 44-33 || 41-40 —-04 | 41-36 || 39-89 —-11)| 39-78
15 || 46-91 |+-02/}—-04 | 46:89 || 44.27 :00 |—-03 | 44-24 || 41-78 —-06| 41-72 || 41-87 —-15| 41-72
22 | 46-82 |+-02 |—-02 | 46-82 || 44.21 :00 | —-02 | 44-19 || 42-45 —-04| 42-41 || 42-88 —-09 | 42-79
29 || 46-75 |+-02|—-03 | 46-74 || 44.24 -00 | —-02 | 44-22 || 42-92 — -05 | 42-87 || 43-37 —-11 | 43-26
Apr. 5||46-65 |+-02] -00]| 46-67 || 44.29 -00| -00| 44-29 || 43-20 —-01 | 43-19 || 42-90 —-03 | 42-87
12 || 46-59 |+-02| -00|46-61 || 44-37 -00|—-01 | 44-36 || 43-30 —-02 | 43-28 || 42-89 — -06 | 42-83
19 || 46-53 |+-02|—-01 | 46-54 || 44.44 -00 |—-01 | 44-43 || 43-38 — -04 | 43-34 || 43-10 —-09 | 43-01
26 || 46-48 |+ -02 |—-02| 46-48 || 44-49 -00 |—-01 | 44-48 || 43-50 —-04 | 43-46 || 43-26 —-10| 43-16
May 3// 46-41 /+-01 -00 | 46-42 || 44-53 :00| -00)| 44-53 || 43-80 —-02 | 43-78 || 44-96 —-03 | 44-93
10 || 46-39 |+-01 |—-03 | 46-37 || 44-61 -00 |—-03 | 44-58 || 44-30 —-07 | 44-23 || 45-23 —-+14 | 45-09
17 || 46-34 |+-01 |—-02 | 46-33 || 44-71 -00 |—-02 | 44-69 || 44-80 —-04| 44-76 || 46-55 —-09 | 46-46
24 || 46-34 |4+-01|—-07 | 46-28 || 44-89 -00 |—-05 | 44-84 || 45-49 —-14| 45-35 || 47-29 —-28/| 47-01
31 || 46-31 -00 |—-06 | 46-25 || 45-06 -00|—-05 | 45-01 || 46-15 —-14| 46-01 || 49-18 — -26 | 48-92
June 7 || 46-25 -00 | —-02 | 46-23 |) 45-24 -00 |—-01 | 45-23 || 46-99 — -04 | 46-95 || 49-70 —-05 | 49-65
14 || 46-24 |—-01 |—-02 | 46-21 || 45-50 -00|— 02) 45-48 || 47-50 —-05 | 47-45 || 50-39 — -06 | 50-33
21 || 46-24 |—-01 |—-05 | 46-18 || 45-80 |—-01|—-05| 45-74 || 48-10 —-11 | 47-99 || 50-62 —-18) 50-44
28 || 46-21 |—-01|—-03| 46-17 || 46-07 |—-01 |—-03 | 46-03 || 48-45 —-06 | 48-39 || 50-60 —-11)} 50-49
July 5 |1|46-22 |—-01 |—-03| 46-18 || 46-35 |—-01|—-03 | 46-31 || 48-80 —-06 | 48-76 || 51-90 —-09 | 51-81
12 || 46-25 |—-01 |—-05 | 46-19 || 46-63 |—-01 |—-06 | 46-56 || 49-30 —-11 |) 49-19 || 51-30 —-20/ 51-10
19|| 46-27 |—-01 |—-04| 46-22 || 46-87 |—-01 |—-04| 46-82 || 49-44 —-09 | 49-35 || 51-79 —-13 | 51-66
26 || 46-30 |—-O1 |—-05 | 46-24 || 47-11 |—-01]—-06 | 47-04 || 49-82 —-11)49-71 || 52-37 —-20 | 52-17
Aug. 2 || 46-34 |—-01 |—-05 | 46-28 || 47-33 |—-O1 |—-06 | 47-26 || 50-10 —-11 | 49-99 || 51-93 —-17| 51-76
9 || 46-39 |—-02|—-04| 46-33 || 47-55 |—-01 |—-05 | 47-49 || 50-27 —-10) 50-17 || 52-58 —-13 | 52-45
16 || 46-44 |—-02 |—-06| 46-36 || 47-79 |—-01|—-07 | 47-71 || 50-42 —-13 | 50-29 || 52-03 — -20| 51-83
23 || 46-48 |—-02|—-03 | 46-43 || 47-94 |—-01 |—-04 | 47-89 || 50-52 —-07 | 50-44 || 52-67 | — —-09 | 52-58

t Cor. | Cor. t, tp
Das. |) uncor-| for | for cor- || uncor-
rected. | Col. | Air. | pected. || rected.

\. ° [e} °
1830 || 46-54 |—-02)]—-03 | 46-49 || 48-10
6 || 46-59 |—-02|—-02 | 46-54 || 48-26
13 || 46-69 |—-02|—-03 | 46-64 || 48-47
20 || 46:75 |—-02|—-04| 46-69 || 48-56
27 || 46-80 |—-02 |—-02 | 46-76 || 48-67
4 || 46-87 |—-02|—-01 | 46-84 || 48-80
11 || 46:94 |—-02|)—-01/46-91 || 48-91
18 || 47-00 |—-01] -00| 46-99 || 48-92
47-06 |—-01| -00| 47-05 || 48-89
1|| 47-13 |—-01| -00/47-12 || 48-80
8 || 47-21 -00 |—-01 | 47-20 || 48-65
15 || 47-23 -00|+-03 | 47-26 || 48-39
22 || 47-28 -00|+-03/ 47-31 || 48-20
9 || 47-34 00} -00/ 47-34 || 47-98
6||47-39 |+-01| -00/ 47-40 || 47-68
13 || 47-41 |+-01 |+-01 | 47-44 || 47-37
20 || 47-38 |+-01/+-05 | 47-44 || 47-07
27 || 47-41 |+-01/+-02 | 47-44 || 46-86

i

8 || 47-40 |+-02|+ -04/ 47-46 || 46-62
10 || 47-35 |+-02)+-06 | 47-43 || 46-32
17 || 47-34 |+-02|+-03 | 47-39 || 46-10
4 || 47-31 |+-02)+-04 | 47-37 || 45-83
B1 || 47-28 |+-02|+-02 | 47-32 || 45-57
7 || 47-22 |+-02|)+-03 | 47-27 |) 45-29
4 || 47-19 |+-03)+-01 | 47-23 || 45-08
21 || 47-12 |+-02 |+ -02 | 47-16 || 44-87
28 || 47-06 |+-03)+-01 | 47-10 || 44-72
7 |\ 47-02 |+-03 | —-02/ 47-03 || 44-61
14 || 46-95 |+-03}—-O1 | 46-97 || 43-49
21 |) 46-85 |+-02}+-01 | 46-88 || 44-37
28 || 46-81 |+-02|—-02)| 46-81 || 44-33

G Cor. | Cor. t; ty
uncor- | for for cor- uncor-
rected. | Col. | Air. | rected. || rected.

rf ° Q °
4 |) 48-13 |+-05/+-03 | 48-21 || 45-41
12 || 47-96 |+-05|+-04| 48-05 || 45-04
20 || 47-88 |+-05/+-03 | 47-96 || 44-75
27 || 47-85 |+-05/+-03 | 47-93 || 44-61
) 6 || 47-70 |+-05}+-02| 47-77 || 44-45
13 || 47-63 |+-05/+-01 | 47-69 || 44-25
20 || 47-48 |+-06|+-03 | 47-57 || 44-07
27 || 47-32 |+-06|+-06| 47-44 || 43-87
1 3||47-20 |+-06|+-06 | 47-32 || 43-68
10 || 47-20 |+-06|+-01 | 47-27 || 43-48
{17 || 47-07 |+-06 |—-04| 47-09 || 43-35
24 |) 46.94 |+-05|-.02| 46.97 |) 43-20
| 1 || 46-86 |+--05 | —-06 | 46-85 || 43-08
8 || 46-74 |+-04|—-05 | 46-73 || 43-18
hs 46-70 |+-04|—-11| 46-63 || 43-35
22 || 46-58 |4+-04|—-05|46-57 || 43-51
29 || 46-50 |4+-03]—-08] 46-45 || 43-79
9 || 46-45 |+-03|—-10| 46-38 || 44.09

Boi cen cag: eta eis died

Cor.
for
Col.

FHt+t++t++ts+
eeeocesess

OBSERVATORY.

ty
cor-
rected.

48.04
48-22
48-43
48-50
48-63
48-78
48-90
48.93
48-90
48-80
48-64
48-44
| 48-25
47-99
47-69
47-39
347-14
46-89

Sige

46-66
46-38
46-14
45-87
45-59
45-33
45-10
44-89
44.74
44-61
44-50
44-38
44-32

ieee sh Seaman ee Me ae

es

ts
uncor-
rected.

50-70
50-90
50-71
50-96
51-09
50 92
50-43
49.90
49.03
48-13
47-50
47-18
46-24
45-20
44-75
44.77
44-40
43-62

43-24
43-03
42.45
41-96
41-63
41-50
41-41
41-57
41-73
41-56
41-64
41-94
42-04

Cor.
for
Col.

Cor.
for
Air.

ts
cor-
rected.

50-62
50-87
3 | 50-65
50-88
51-07
50-91
50-42
49-94
49-06
48-13
47.47
47-25
46-29
45-21
44-75
44.77
44-46
43-64

43-27
42-98
42.43
41-94
41-63
41-49
41-41
41-57
41-73
41-52
41-61
41-94

Wpue 8

42-00

EXPERIMENTAL GARDEN.

t,

cor-
rected.

se

ak ed

ts
uncor-
rected.

{e)
40-99
40-88
41-11
41-21
40-78
40-72
40-50
40-11
39-79
39-74
39:98
40-48
41-25
41-98
42-80
43-60
44-81
45-62

—-O1
—-01

Cor.
for
Air,

ts

cor-
rected.

.00 | 40-99
.00 | 40-88
00 | 41-11
.00 | 41-21
01 | 40-77
.02 | 40-70
.00 | 40-50
.02 | 40-13
.02| 39-81
.02 | 39-72
.05 | 39-93
104 | 40-44
.08 | 41-17
07 | 41-91
-14| 42.66
07 | 43-53
-10 | 44-70
.13 | 45-48

ts Cor. | Cor. ty
uncor- | for for cor- ts,
rected. | Col. | Air. | rected.

ie} (eo) °
53-05 -00 |—-12 | 52-93 ||57-00
52-05 —-04/ 52-01 ||/48-90
52°19 —-10/ 52-09 ||58-30
53-25 —-12 | 53-13 ||56-80
52-34 —-03 | 52-31 |/51-30
51-34 —-03] 51-31 |/47-80
50-07 —-03 | 50-04 |/48-60
48-68 +-05 | 48-73 |/42-00
46-48 +-01 | 46-49 |/41-10
45-41 —-02| 45-39 ||43-00
45-25 —-07 | 45-32 ||47-20
44-75 +-10) 44-85 |/33-50
41-74 +-03) 41-77 ||35-50
41-15 —-04] 41-11 ||39-00
42-61 —-03 | 42-58 ||42-80
42-42 —-02 | 42-406 ||/41-00
40-99 +-08)] 41-07 ||/31-40
39-85 —:04/ 39-81 ||34-30
41-06 :00 | 41-06 || 36-20
39-42 -00 | 39-42 ||31-20
38-42 —-03 | 38-39 ||/32-40
38-63 —-02 | 38-61 ||/32-00
38-26 — -02 | 38-24 ||37-00
39-07 —-03 | 39-04 ||31-60
39-42 —-05 | 39-37 || 36-50
40-13 —-02)| 40-11 ||37-80
39-51 —-04 | 39-47 ||/36-10
39-72 —-09 | 39-63 |/41-10
40-10 —-08 | 40-02 ||41-70
41-11 — -04] 41-07 || 35-90
40-65 —-08 | 40-57 || 44-20

t, Cor. | Cor. t
uncor- | for for cor- ts,
rected.| Col. | Air. | rected

fo} [o)
38-39 -00 |—-03 | 38-36
40-06 -00 | 40-06
40-53 —-01] 40-52
38-63 —-03 | 38-60
38-99 — -04 | 38-95
39-30 —-05 | 39-25
37-68 —-03 | 37-65
37-58 + -02 | 37-60
37-48 +-02| 37-50
38-03 —-06 | 37-97
39-10 —-13| 38-97
40-63 —-08 | 40-55
42-52 —-16| 42-36
43-90 —-15| 43-75
44-81 — -28 | 44-53
46-42 —-13 | 46-29
47:98 —-18| 47-80
48-80 —-23 | 48-57

228

t, Cor.
uncor- | for
rected. | Col.
46-41 |+-01
46-39 |—-01
46-35 |—-02
46-34 |—-02
46:35 |—-04
46-35 |—-05
46-39 |—-05
46-44 |—-05
46-53 |—-05
46-62 |—-05
46:69 |—-06
46-82 |—-06
46-93 |—-05
47:03 |—-05
47-21 |—-05
47-34 |—-05
47-46 |—-04
47-60 |—-04
47-68 |—-04
47-75 |—-04
47-81 |—-03
47-96 |—-0O1
47-98 |—-01
48:04 -00
48:09 00
48-15 |+-03
48-15 |+-03
48-23 |+-03
48-22 |+-03
48-18 |+-03
48-10 |-+-03
48-00 |+-04
48:03 |+-04
47-90 |+-05
47-89 |+-05
47-85 |+-05
47-70 |+-07
47-65 |+-07
47-65 |+-07
47-55 |+-08

-42 |+-07
47-30 |+-07
47-17 |+-07
47-05 |+.07
46:93 |+-06
46-80 |+-05
46-65 |+-05
46-66 |+-04
46-50 |+-04
46-41 |+-03

3-30 |+-03
46-30 |+-01
46-20 |+-01
46-15 -00
46-20 |—-01
46-12 |—-0l
46-15 03
46-16 |—-04
46-26 |—-04
46:30 |—-04
46-30 |—-05
46-42 |—-05

|

ae ae eee

|

Pepe ee

eo aay a

42-86
42-91

42-83
43-05

43-32
43-62

44-25
44.64

46-43
47-00
47-50
47-90
48-37

Cor. | Cor.
for for
Col. | Air
—-01/-—-09
—-02)—-11
—-02|—-12
—-02/-—-13
—-03 |—-17
—-03|}—-15
—-03)—-15
—-02|-—-08
—-02)—-21
—-02|—-16
—-02|-—-12
—:02)--11
—-01/—-08
—-01)|-—-04
—-01}—-11
—-01)—-04
-00 | —-09
-00 |—-05
-00 | —-04
, 00 |+-04
-00 |+-07
+-01|—-02
+-01/+-06
+-01|/+-06
+-01/+-06
+-01/+-02
+:02)+-07
+-02)—-02
+-01)-—-01
+-01)4+-03
+-01/+-08
+-:01)+-07
+ -02/+-05
+-02/+-05
+:-02)+-05
+-02\)+-01
+-02)+ 04
+-02|+-05
+-02|—-06
+ -02|—-03
+-02/—-01
+-02)—-01
+-01)—-01
+-01)—-01
+-01)}—-01
+:-01} -00
-00 -00
-00 | —-08
-00 |—-02
-00 |—-03
-00 | —-04
—-01/—-07
—-01|}—-05
—-01}—-03
—-01}—-10
—-02|—-03
—-02|—-07
—-02)}—-09
—-02)--11
—-02)—-12
—-02/—-10
—-02/--11

EXPERIMENTAL GARDEN.

ty
cor-
rected.

44-35
44-82
45-16
45-74
46-29
46-98
47-56
48.41
48-67
49-17
49-56
49-89
50-21
50-41
50-50
50-53

ts
uncor-
rected.

46-72
48-12
49-29
50°62
51-98

53°34
53°82
54:30
54°52
54:39
54:60
54-83
54-30
53-54
53-23
52-74
52-50
52-26
52-12
51-50
50-83
49-30
48-29
47-34
46-41
45-60
44.70
44-20
44-01

44-20
44:06
43-49
42-58
41-70
41-00
40-52
39-90
39-40
39-02
38-62
38-60
38-90
39-30
39:91
40-58
40-90
41-30
41-92
42-99
43-70
44-50
45-32
46-10
46-90
48-03
48-98
50-04.
51-08
51-63
52-10
52:50

52:91

Cor.
for
Col.

ies ls aoa, A,

eet eee.

Cor.
for
Air.

Saal edie cot ise

ts
cor-
rected.

46-53
47-89
49-06
50-37
51-65
53-08
53-58
54-20
54-20
54-15
54-44
54-69
54-21
53-51
53-08
52-71
52-39
52-20
52-07
51-58
50-93
49-27
49.35
47-40
46-46
45-60
44.77
44-16
43-97

44-21
44-13
435-56
42-62
41-75
41-04
40-52
39-92
39-43
38-96
38-59
38-58
38-88
39-28
39-88
40-56
40 89
41-29
41-77
42-97
43-64
44-43
45-19
46-01
46-85
47:84
48-93
49.92
50-91
51-44
51-92
52-35
52-77

ty
uncor-
rected.

50-41
53-00
54-80
55-80
57:82
57:91
58-09
56-72
56-38
56-89
57-83
56:34
54:40
53-62
52-68
53-10
52:00
52-93
51-61
50-79
47-98
44-81
45-95
43-05
43-08
42-38
41-00
41-20
41-48

43-34
42-03
39-62
38-42
37-60
37-10
36:50
36-00
35-50
35:38
35-06
37-20
37-40
39:49
40-08
41-05
40-63
41-52
43-51
45-70
45-23
46-42
47-80
49-10
50-20
51-71
52-81
54-51
55-50
595-00
54-83
55:90
55:82

Cor.
for
Air.

oe a a a

ee see

ty
cor-
rected.

bs,

50-11
52-67
54.47
55-45
57-35
57-58
57-78
56-61
55-91
56-57
57-65
56-15
54.27
53-59
52.46
53-05
51-84
52.85
51-53
50-89
48-08
44-72
46-01
43-07
43-11
42-34
41-04
41-10
41-40

43-35
42-12
39-69
38-43
37-63
37-11
36-46
36-00
35-52
35-24
34-96
37-13
37-35
39-44
40-01
41-01
40:60
41-49
43-23
45-68
45-12
46-28 |
47-58
48-98
50-16
51-43
52-79
54:38
55:30
54-75
54:58
55-73
55:65

t, Cor. | Cor, t,
Mncor-| for for cor-
rected.| Col. | Air. | rected
46-49 |—-05 |—-06 | 46-38
46:61 |—-05 |—-14 | 46-42
46:66 |—-05 |—-09 | 46-52
46-80 |—-05 |—-09 | 46-66
46-86 |—-05 | —-07 | 46-74.
47-01 |—-04|—-10 | 46-87
47-15 |—-04|—-11/ 47-00
47-25 |—-04|-—-10 | 47-11
47-30 |—-03 |—-08 | 47-19
47-42 |—-03 |—-07 | 47-32
47-48 |—-03|—-01 | 47-44
47-59 |—-01|+-04 | 47-62
47-61 |—-01 |+-02 | 47-62
47-67 00 | + -02 | 47-69
47-70 |+-01 |+-05 | 47-70
47-71 |+-01 |+-03 | 47-69
47-82 |+-01 00 | 47-83
47-81 |+-03 |/+-03 | 47-87
47-80 |+-03 |+-03 | 47-86
47-81 |-+-04/+-01 | 47-86
47-75 |+-04|+-05 | 47-84
47-72 |+-04 |+-04 | 47-80
47-70 |+-05 |+-06 | 47-81
47-70 |+-05 |+-07 | 47-82
47-53 |+-05|+-06 | 47-64
47-51 |+-04|+-01 | 47-56
47-42 |+-05 |+-04 | 47-51
47-38 |+-05|+-02 | 47-45
47-30 |+-06/+-03 | 47-39
47-32 |+-06|+-02 | 47-40
47-05 |+-06/}+-01 | 47-12
47-01 |+-06 -00 | 47-07
46-85 |+-06/+-03 | 46.94
46-81 |+-06 |—-04 | 46-83
46-75 |+-06 |—-04 | 46-77
46-60 |+-05 |—-03 | 46-62
46-51 |+-05 |—-04 | 46-52
46-30 |+-03 |—-02 | 46-31
46-39 |+-03|—-01 | 46-41
46-30 |+-02|—-05 | 46-27
46-40 |+-02|—-11| 46-31
46-10 |+-01|—-05 | 46-06
46-02 -00 | —-08 | 45-94
46-03 |—-01 |—-14 | 45-88
46-10 |—-02|—-09 | 45-99
46-20 |—-03 |—-13 | 46-04
46-20 |—-03|—-13 | 46-04
46-20 |—-04|—-10 | 46-06
46-30 |—-04 |—-09 | 46-17
46-40 |—-04|—-13 | 46-23
46-41 |—-06|—-09 | 46-26
46-49 |—-06 |—-02 | 46-41
46:55 |—-06|—-08 | 46-41
46-73 |—-06|—-07 | 46-60
46-85 |—-05)|—-10| 46-70
46-92 |—-05 |—-06 | 46-81
47-08 |—-05|—-10 | 46-93
47-17 |—-04|—-09 | 47-04
47-26 |—-04|—-06 | 47-16
47-30 |—-04|—-04 | 47-22
47-42 |—-03|—-07 | 47-32

VOL. XVI. PART II.

49-10
48.72

48-01
47-61
47-30
46-95

46-60
46-32
46-02
45-61
45-30
45-01
44-60
44.35
44-21
43-85
43-70
43-50
43-32
43-25
43-25
43-05
43-20
43-20
43-41
43-70
44-00
44-40
44-60
44.98
45-40
46-00
46-50
47-01
47-50

48-49
48-85
49-28
49-53

‘| 49-90

49-96
50:05
50-18
50-22
50-19

50-20
50-01

fete teeters

EXPERIMENTAL GARDEN.

etal

er ene Se pee ee a

ty

cor-
rected.

48-66
48-94
49-23

ts
uncor-
rected.

53-12
53:29
53-11
52-80
52:40
52-48
52-21
51-82
50-99
50-22
49-82
49-10
48-03
47-01
45:82
45-10
44-91
44-51
44-91
43-20

42-91
42-28
41-82
41-20
40-60
44.32?
40-60
40-30
40-01
40-04
39-71
39-99
40-05
40-12
40-20
40:97
41-01
42.90
43-70
44.30
44.90
45-96
47-26
48-20
49-51
50-50
51-20
52-10
52-60

53-52
53-73
53-80
53-52
53-30
53-30
53-02
52-70
52-28
51-68
50-84
50-61

zt

ee

ee:

ee og!

om

beersisloge sy

ts
cor-
rected.

Cor. t,

cor-
rected.

—.08 | 55-43
—.33 | 54-49
—.18| 54-45
—-19 | 52-31
2 1458.37
—.22| 52.49
—.25 | 52-35
~.23| 49.47
—.19 | 48.62
—.16 | 48-52

.00 | 48-89
+.07 | 45-85

.00 | 45-00
—.01| 43.03
+-03 | 42-06
—-11| 42-50
~.06 | 41-99

.00 | 41-70
~.02| 40-51
—.05 | 40-45

+-01 | 40-02

230 EXPERIMENTAL GARDEN.

L , t ‘or. | Cor. t, i : t rn «| Cor. t 4
uncor- uncor- for cor- o uncor- for cor-
rected. : . || rected. - | Air. | rected. . . . || rected. Air. | rected.

47-52 |—- .45 ||49-91 |. .04.| 49-87 95 || 49-02
47-50 |—- 50 ||49-60 | - .04| 49-64 || 49. ; ; .26 ||47-10
47-70 \—- 71 ||49-40 49-44 : .46 || 46-60
47.70 |—- 71 || 49-40 49-44 .22 || 46-70
4772 | . 76 || 49-06 49-12 4 75 || 45-03
AG75 |0 .82 || 48-74 48-83 : 70 || 42-70
47-73 48-50 48-61 60 || 41-01
47-80 48-30 48-37 || 44. 03 | 44-54 || 41-03
47.75 47-70 47.73 || 44. ; : -02 || 41-90
47-80 47-20 47-26 : -63 || 40-10

47-80
47-73
47-70
47-68
47-60
47-52
47-50
47-40
47-30
47-22
47-20
47-10
47-01
46-75
46-70
46-70
46-70
46-50
46.42

47-02
46-61
46-30
45-92
45-62
45-30
45-00
44-61
44-50
44-30

47-08 : . : 40-02
46-64 : . . 39-10
46-36 : : : 40-30
45:99 . . . . 39-80
45-68 . : . : 38-02
45-30 : . . ‘06 || 39-00
45-03 02 . . . 39-70
44-62 . : : 38-72
44-52 : . : 37-60
44-29 . : : : 37-60
44-10 44-10 . . . 39-50
43-80 . 43-81 : . . 40-10
43-75 . : 43-73 . : . : 41-05
43-65 . . 43-65 : . : 41-50
43-70 : . 43-64 : . : 42-70
43-65 : : 43-60 4 . ; 44-10
43-85 . . 43-76 : : : : 47-01
44-01 . . 43-94 : : . : 49-01
44-30 : . 44.27 . 2 . : 46-60
46-40 44-68 : : 44-64 : : . : 46-52
46-30 . 45-01 : . 44.94 - . : 47-70
46-30 . . : 45-23 : . 45-15 ° . : 49-60
46-34 . : 45-45 . : 45-29 : : . 50-95
46-30 . : 45-75 : . 45-66 : . : 51-80
46-30 . . 46-14 : . 46-05 3 : : 52-12
46.32 . : 46-45 : : 46-30 : : . : 52-43
46-30 0: . 46-82 : . 46-73 : . : 52-80
46.28 : : 47-20 : : 47-06 : . : 53-48
46-51 : . : 47-63 : . 47-49 : a . 53-92
46-50 . . : 47-98 : . 47-84 . . . : 54:50
46-51 : : J. 48-32 : . 48-16 . : c : 55:20
46-51 : : : 48-50 : . 48-39 . : : 56:80
46-60 : . : 48-90 ¢ : 48-73 , : 56-30
46-55 . : : 49-25 : : 49-13 : . . 56-30
46-80 . : . 49-60 : . 49-43
49-85 : : 49-73 : : :
50-50 : . 50-43 : : : 53-49
50-25 . : 50-17 : . 51-97
50-24 . : : 51-11

. 50-23
50-20 . : 50-13
50-04

: : 49-83
49-57 : , 49-54
49.55
49-38
48.93

FL+thtt Fett tts

|e Ad ah Sept he

t+t++tee+tset+ ++
5665555555555 SSE
SHR DNF NWNWNWNWN NW WY

fe ee ete Bea teed ok ee ea

seta pan tae

++
S6
on

+-05 | 38-65

OW NDE ANTE BTOWDONNONADHENUDHE ROE A.

OWS

t
uncor-
rected.

47-70
47-75
47-75
47-70
47-60
47-50
47-50
47-45
47-25
47-30
47-20
47-00
46-80
46-70
46-72
46-62
46-50
46-48
46-43
46-40
46-30
46-35
46-30
46-30
46-30
46-30
46-30
46-35
46-40
46-52
46-60
46-62
46-75
46-80
46-92
47.22
47-16
47-22
47-35
47.35
47-49
47-50
47-60
47-70
47-80
47-80
47-85
47-80
48-00
48-00
47-90
47.92

47-90
47-81
47-80
47-70
47-70
47-60
47-51
47-50
47-40
47-20

eesooeoegeesesso
ARKHAHBIBABAAAGHE

FEE EHH HHH HHH +++ $$

++eetttttt+ Fttttt |

Cor.
for
Air.

Bs eee eee

i lle WH
eos
IA ©

|
=)
Per

ic ee canna eee se ey Gs ee ae
oS
No}

i
cor-
rected.

47-81
47-89
47-87
47-83
47-74
47-64
47-59
47-49
47-33
47-31
47-22
47-01
46-77
46-64
46-70
46-61
46-50
46-48
46-38
46-35
46-15
46-21
46-23
46-22
46-16
46-20
46-20
46-23
46-28
46:34
46-43
46-49
46-59
46:67
46:78
47-06
46:99
47-10
47-22
47-26
47-38
47-46
47-58
47-69
47-77
47-82
47-91
47-76
48-03
48-03
48-02
47-99

48-01
47-95
47-89
47-81
47-76
47-71
47-59
47-56
47-45
47-27

t,
uncor-
rected.

| 46-80

46-40

45-60
45-20
44-75
44-45
44-10
43-80
43-72
43-60
43-60
43-65
43-75
43-90
44-00
44.20
44-35
44-46
44-61
44-90
45-20
45-45
45-91
46-35
46-85
47-30
47:60
48-01
48-35
48-62
48-91
49-20
49-35
49-60
49-95
50-03
50-09
50-30
50-32
50-40
50-31
50-25
50-10
49-80
49-50
49-15
48-80
48-42
47-98
47-40
47-10

46:50
46-25
45-90
45-70
45-20
44-80
44:55
44-30

44-10
43-90

EXPERIMENTAL GARDEN.

Cor. | Cor. tp ts Cor. | Cor.
for for core imeoran) 10m for
Col. | Air. | pected. || rected. | Col. | Air
+-02 |+-05 | 46-87 || 42-30 |+-01 |+-03
+-02/+-07 | 46-49 || 41-70 |+-01 |+-05
+-02/+-05 40-95 }+-01/+-02
+-02}+-05 | 45-67 || 40-30 |+-01 |+-02
+-02/+-04/ 45-26 || 39-90 -00 |+-02
+ -02|+-05 | 44-82 || 39-60 -00 |+ -02
+:02| -00| 44:47 || 39-30 -00 | — -02
+-02|—-02 | 44-10 || 39-60 -00 | — -04
+-01 -00 | 43-81 || 40-20 -00 |—-01
+-01 |—-04| 43-69 || 40-40 -00 | — -06
+-01/}—-03 | 43-58 || 41-01 -00 |—-05
-00 | —-04 | 43-56 || 41-70 -00 |—-06
-00 | — -05 | 43-60 || 42-40 -00 | —-09

00 |—-01 | 43-74 || 42-70 -00 |—-03

00/—-05 | 43-85 || 43-05 -00|—-09

00 | —-04 | 43-96 || 43-30 -00 |—-07

00|—-03 | 44-17 || 43-50 -00 |— -05

00 |—-02 | 44-33 || 44-00 -00 |— -04

00 | —-06 | 44-42 || 44-60 -00|—-10
—-01|—-05 | 44-55 || 45-50 -00|—-10
—-01|—-14| 44-75 || 46-30 -00 |—-25
—-01/—-13 | 45-06 || 47-30 |—-01 |—-24
—-01|—-05 | 45-39 || 48-51 |—-.01|/—-08
—-01|—-07 | 45.83 || 49-33 -00|—-12
—-02|—-11]| 46-22 || 50-30 -00 |—-20
—-02/—-09 | 46-74 || 50-70 -00|—-13
— -02 | —-07 | 47-21 || 51-08 -00 |—-10
—-01)—-08 | 47-51 || 51-50 -00 |—-14
—-01|}—-09 | 47-91 || 51-60 :00|—-13
—-02|—-15 | 48-18 || 52-10 :00 |—-24
—-01 |—-14| 48.47 || 52-41 -00 | — -23
—-01 |—-09 | 48-81 || 52-53 -00 |—-13
—-01|—-14] 49.05 || 52-78 -00 |—-21
—-01|—-09 | 49.25 || 52-80 -00 |—-13
—-01|-—-09 | 49-50 || 52-00 -00 | —-24
—-01|—-13 | 49-81 || 53-00 -00 |—-18
—-01 |—-16 | 49-96 || 52-09 -00 |—-23
—-01|—-08 | 50-00 || 53-00 -00 |—-10
—-01|—-09 | 50-20 || 53-00 -00|}—-11
—-01 |—-03 | 50-28 || 52-73 -00 | —-02
-00 | — -07 | 50-33 || 52-12 -00|—-08
00} -00)| 50-31 || 51-50 -00; -00
-00|+-03 | 50-28 || 50-30 |4+-01/+-04
+-01|/+-03 | 50-14 || 49-00 -00/+-03
+-01/|—-01 | 49-80 || 48-10 -00 | —-03
+-01/+-05 | 49-44 || 47-65 -00 |+-05
+-01|+-06 | 49-08 || 46-52 |+-01/+-06
+-02|—-05 | 48-77 || 45-20 |+-01 |—-09
+-02|+-01 | 48-45 || 44-30 -00|} -00
+-01/+-01 | 48-00 || 44-40 -00; -00
+-02)+ -07 | 47-49 || 43-92 |+-01 |+-07
+-02|+-03 | 47-15 || 43-00 -00 |+ -02
+-02)+-05 | 46-57 || 42-30 -00 | +-03
+-02)+-06 | 46-33 |} 42-10 |+-01/+-04
+ -02}+-03 | 45-95 || 41-50 |+-01 -00
+-02|}+-04| 45-76 || 41-00 |+-01 |+.02
+-02| -00/} 45-22 || 40-40 -00 ;—-03
+ -02|+-03 | 44:85 || 40-30 -00}+-01
+-02| -00/ 44-57 || 40-30 -00 |—-0O1
+-01)—-01 | 44-30 || 40-50 -00 |— -03
+-01|—-02 | 44-09 || 40-90 -00 |—-04
+-01 -00 | 43-91 || 40-60 -00 |—-01

i

o
cor-
rected,

42.34
41-76
40:98
40:33
39-92
39-62
39-28
39-56
40-19
40-34
40-96
41-64
42:31
42-67
42-96
43-23
43-45
43-96
44-50
45.40
46-05
47-05
48-42
49.21
50-10
50-57
60-98
01-36
51-47
51-86
52-18
52:40
52:57
52:67
51:76
52:82
51-86
52-90
52-89
52-71
52-04
51-50
50-35
49.03
48-07
47-70
46-59
45-12
44.30
44-40
44-00
43-02

42-33
42-15
41-51
41-03
40-37
40-31
40-29
40-47
40-86
40-59

by
uncor-
rected.

38-60
37-50
36-50
36-50
36-70
36-30
36-60
38-70
39-10
39-70
41-90
42.80
43-50
43-00
43-20
43-58
43-62
45-90
46-30
48-20
49-10
51-60
52-10
53-50
53-40
53-10
54.30
53-45
54-15
54-62
54-23
55-00
54-20
55-00
55-30
53-21
53.09
54-90
53-48
52-63
51-30
49-50
46-80
45-80
45-32
44-80
41-40
40-10
42-20
42:00
40-51
38-88

40-00
38-50
37-70
37-50
37-80
38-10
38-60
39-50
39-00
39-70

Cor.
for
Col.

-00

Uy
cor-
rected.

38-62
37-53
36-50
36-51
36-72
36:32
36-55
38-61
39-07
39-57
41-80
42.68
43-31
42-95
43-03
43-46
43-54
45-84
46-11
48-05
48-68
51-22
52-00
53-35
53-28
52-91
54.19
53-26
53-97
54-30
53-91
54-83
53-90
54-83
60-13
52-95
52-76
54-79
53-33
52-60
51-17
49.47
46.82
45-81
45.24
44-83
41-43
39-95
42.17
41-97
40-59
38-88

40-04
38-54
37-69
37-50
37-74
38-10
38-57
39-44
38:92
39-66

42.75
52-25

57-80
55-75
95-25
59-25

58-75
58-50
62-00

49-25
48-75
43-25
41-25

33-75

41-25
40-75
31-50
33.25

33°25
30:50
31-75
31-50
37-50
31-50
37°25
38-25
37-75
36:25

232

EXPERIMENTAL GARDEN.

t, Cor. | Cor. t tp Cor. | Cor. t, ts Cor. | Cor
Dates. mncoral ee toL for alee sien || ROE for eae uncom) Lor for
rected. | Col. | Air. | rected. || rected. | Col. | Air. | pected. || rectea.| Col. | Air
1842. 4 _ A fs E
Mar. 14 || 47-10 |+-05 | —-02 | 47-13 || 43-80 |+-01 |—-03 | 43-78 || 40-80 -00 | —-04
22 || 47-00 |+-05 |—-03 | 47-02 || 43-70 |+-01 |—-03 | 43-68 || 41-30 -00 | —-05
28 || 46-90 |+-05 | —-02 | 46-93 || 43-75 |4+-01)|—-02| 43-74 || 41-42 -00 | —-04
Apr. 4|/ 46-80 |+-05|—-06 | 46-79 || 43-63 |+-01 |—-05 | 43-59 || 41-60 -00 | —-08
11 || 46-71 |4-04|—-04)| 46-71 || 43-62 -00 |—-03 | 43-60 || 42-00 -00 | —-06
18 || 46-70 |+-04|—-07 | 46-67 || 43-70 -00 |—-05 | 43-65 || 42-62 -00 | —-09
25 || 46-55 |+-03 |—-06 | 46-52 || 43-80 -00 |—-04| 43-76 || 43-50 -00 |—-08
May 2/|| 46-50 |+-02|—-08 | 46-44 || 44-10 -00 |—-06 | 44-04 || 44-70 -00|—-11
9 || 46-41 |+-01 |—-07 | 46-35 || 44-20 |—-01|—-05 | 44-14 || 45-50 -00 |—-09
16 || 46-35 |}+-01|—-10| 46-26 || 44-60 |—-01 |—-07 | 44-52 || 46-14 -00 |—-14
23 || 46-25 -00/}—-08 | 46-18 || 45-00 |—-01 |—-06 | 44-93 || 47-00 -00 |—-11
30 || 46-24 -00 | —-09 | 46-15 || 45-34 | —-01 |—-07 | 45-26 || 47-50 -00 | —-12
June 6]|| 46-30 |—-01|—-13| 46-16 || 45-60 |—-01|—-10] 45-49 || 48-30 |—-01 |—-20
13 || 46-30 |—-02|—-17 | 46-11 || 46-10 | —-02|—-17]| 45-91 || 49-65 |—-01 |—-29
20 || 46-20 |—-03|—-08 | 46-09 || 46-40 | —-02]—-08 | 46-30 ||51-10 |—-01 |—-14
27 || 46-30 |—-04|}—-09 | 46-17 || 47-10 | —-02|—-10| 46-98 ||52-20 |—-01|—-15
July 4/| 46-30 |—-04|—-06 | 46-20 || 47-50 |—-02|—-06| 47-42 || 52-34 -00 |—-08
11 || 46-30 |—-06 | —-06 | 46-18 || 48-10 |—-02|—-07 | 48-01 || 52-50 -00 | —-08
18 || 46-40 |—-05 | —-09 | 46-26 || 48-45 | —-02|—-09 | 48-34 || 52-70 -00 |—-13
25
Aug. 1/|/ 46-70 |—-06|—-16 | 46-58 ||49-20 |—-02|—-20| 48-98 || 54-30 |—-01 |—-31
8 || 46:50 |—-07|—-08 | 46-35 || 49-50 | —-02}—-10/ 49-38 || 54-90 |—-01 |—-12
15 || 46-80 |—-.07|}—-10| 46-63 || 50-00 | —-02|—-14| 49 94 || 55-35 -00 |-—-19
22 ;
29 || 47-10 |—-07|—-14| 46-99 || 50-80 |—-02)—-16| 50-62 || 55-80 -00 | —-24
Sept. 5 || 41-10 |—-07|—-04| 46-99 || 50-90 —-02|—-03 | 50-85 || 55-70 00; -00
12 || 47-30 |—-07 | —-14| 47-09 || 51-26 |—-01|}—-17 | 51-08 || 55-70 -00 | — -23
19 || 47-40 |—-07 | —-02| 47-31 ||51-30 —-01]| -00) 51-29 || 55-30 00 |+-03
26 || 47-50 |—-06|—-04| 47-40 ||51-50 |—-01 | —-03 | 51-46 || 55-10 ‘00 |—-01
Oct. 3)|| 47-60 |—-06|—-03 | 47-51 |/51-55 |—-01|—-02] 51-52 || 54-30 -00|—-01
10 || 47-80 |—-05 |—-05 | 47-70 || 51-65 | -00|—-04) 51-61 || 53-51 -00 | —-04
17 || 47-87 |—-04|—-04| 47-79 || 51-55 -00 |—-02| 51-53 || 52-90 -00 | —-03
24 || 47-96 |—-04/+-01 | 47-93 ||51-40 | -00|}+-03) 51-37 || 52-10 -00 |+-06
31 || 48-10 |—-02/+-01 | 48-09 || 51-22 +-01|}+-05/51-16 || 50-80 |+-01|+-06
Nov. 7 || 48-12 |—-01|+-03 | 48-10 ||50-95 +-01]+-06 | 50-88 || 49-80 -00 |+-06
14 || 48-25 |—-01/+-01 | 48-25 ||50-65 +-01|+-04! 50-60 || 49-10 -00 |+-03
21 || 48-30 |—-01)+-04/ 48-33 ||50-28 +-01]+-07 | 50-20 || 48.20 |+-01|+-06
CRAIGLEITH.
t, Cor. | Cor ty t Cor. | Cor. t, t; Cor, | Cor
Dates. creavoayon || OE for cone ragaree | On for cor- itr || Mo for
rected. | Col. | Air. | rected. || rected.| Col. | Air. | rected. || rected. | Col | Air
1837. ° ° ° So; °
Feb. 4/| 46:54 |+-03|)+-02| 46-59 || 43-54 00} -00)| 43-54 || 41-02 -00| -00
12 || 46-30 |+-02|+-02| 46-34 || 42-90 -00 |+-01 | 42-91 || 41-42 -00
21 || 46-02 |+-02|+-01! 46-05 || 42-88 -00} -00| 42-88 || 41-52 -00
27 || 45-87 |+-03|)+-01| 45-91 || 42-76 -00| -00| 42-76 || 40-47 —-01
Mar. 6/|| 45-69 |+-02|+-01 | 45-72 || 42-70 -00| -00| 42-70 || 40-77 —-01
13 || 45-57 |+-02|) -00)| 45-59 || 42-63 00) -00)| 42-63 || 40-93 —-01
20 || 45-38 |+-03|+-01 | 45-42 || 42-15 -00| -00}| 42-15 || 39-70 -00
27 || 45-22 |+-03)+4-02| 45-27 || 41-98 00} -00| 41-98 || 39-71 -00
Apr. 4/| 45-02 |+-03)+-02) 45-07 || 41-84 00} -00)| 41-84 || 39-52 -00
10 || 44-92 |4+-03|—-01 | 44-94 || 41-74 -00 |—-01 | 41-73 || 39-77 —-02
17 || 44-71 |+-02|+-01 | 44-74 || 41-73 00} -00| 41-73 || 40-42 --01
24 || 44-60 |+-02|—-01 | 44-61 || 41-68 -00|—-0O1 | 41-67 || 41-38 —-03
May 1/|| 44-50 |+-01|—-03 | 44-48 || 42-10 -00 | —-02 | 42-08 || 42-52 —-05
44.37 |4+.- . 44-38 || 42-62 : : 42-62 || 43-60 .

i
cor-
rected.

40-76
41-25
41-38
41-52
41-94
42-53
43-42
44.59
45-41
46-00
46-89
47-38
48-09
49-35
50-95
52-04
52:26
52-42
52-57

53-98
54:77
55-16

55:56
55-70
55-47
55-27
59:09
54:29
53-47
52-87
52-16
50-87
49-86
49-13
48-27

ts
cor-
rected.

41-02
41-42
41-52
40-46
40-76
40-92
39-70
39-71
39-52
39-75
40-41
41-35
42-47
43-60

b
uncor-
rected.

39-70
40-60
40-39
41-50
42-50
43-50
45:70
47-50
48-00

uncor-
rected.

39-15
40-69
40-18
38-21
39-50
39-10
38-00
37-70
37-86
38-73
39-68
41-25
43-15

44-45

Cor.
for
Col.

-00

-00

Cor.
for
Air.

~00
== (il
— -02
—-02
—-03
—-02

-00

-00
—-04
—-01
—-04
—-09

ty
cor-
rected.

39-60
40-49

40-30 —
41-34 |

42-39
43-33
45-54
47-32
47-85
47-28

49-13 |

49-91
52-00
54-78
56:36
55-42

55-02 |
54.52 |

55-64

57-98
58-49

58-38

57-76
57-64
56-41
56-79
54-98

53-07 |

52:01
51-66
48-94
46-51
47-05
46-11

44.35 |

ty
cor-
rected.

—-01 | 39-14

40-69
40-17
38-19
39-48
39-07
37-98
37-70
37-86
38-69
39-67
41-21
43-06

-01 | 44-44

peted Col. | Air
5 (144-36 |+-01 |—-03
2||44-38 | -00|/—-03
0|| 44-44 |—-01|—-04
5 || 44-53 |—-01|—-04
2\| 44-67 |—-01)—-06
9|| 44.88 |—-02|—-07
”7 || 45-04 |—-02|—-06
3 || 45-22 |—-03 |—-07
0|| 45-50 |—-03|—-08
7 1145-77 |—-03|—-08
4|| 46-10 |—-03 |—-08
46-38 |—-03|—-05
46-72 |—-03|—-09
46.94 |—-03|—-09
A715. || -03)|—-07
7-35 |=-03|\—-04
47.58 |—-03|—-04
47.84 |—-02|—-07
48-02 |—-02|—-04
48-12 |—-02|—-04
48-25 |—-02|—-06
48-34 |—-01|—-05
48-39 |—-01|—-04
48.42 |—-01|--01
48-45 |--01| -00
48.47 | -00|+-02
48.40 | -00|+-05
48.40 |+-01/+-03
48-27 |+-01|+-04
48.37 |+-01/+-05
48-00 |+-02|+-05
47-17 |+-01|—-01
Page lee -03)|—-01
+-01|+-02
+01 |+-05
4+.-02 |+-07
+ -02|}+-04
+-03/+-04
+-03 |+-04
+-03|+-06
+-03 |-+-02
+-03 |+-05
+-04|+-02
+-03 |+-01
+.-03|—-01
+: .

+.

+:

+:

+:

h
cor-
rected.

44-34
44.35
44.39
44.48
44.60
44-79
44.96
45-12
45.39
45-66
45-99
46-30
46-60
46-82
47-05
47-28
47-51
47-75
47-96
48-06
48-17
48-28
48-34
48-40
48-44
48-49
48-45
48-44
48-32
48-43
48-07
47.17
47-63

47-36
47-20
47-01
46-83
46-72
46:52
46-29
45-95
45-76
45-51
45-24
44.94

Sept e

Page eee t

Sai SS

CRAIGLEITH.

t
cor-
rected.

ts
uncor-
rected.

52-83
52-30
52-37
51-72
51-85
51-18
50-66
49-30
47-50
47-27
45-70
45-10
44-43
43-60
43-18
43-57

44.17
43-60
42-34
41-15
40-00
39-62
39-00
38-50
37-75
37-45
38-08
39-20

Nee casemate

Reig el eee

52-72
52-25
52-30
51-63
51-78
51-12
50-66
49-31
47-53
47-34
45-73
45-13
44-46
43-64
43-15
43-54

44-18
43-64
42.39
41-16
40-01
39-63
39-02

38:50
37-76
37-45
38:07
39-18

ty
uncor-
rected.

44.39

46-58
47-68
49-05
49-68
52-40
04-00
53-98
04-60

Above
Scale.

ease tel

Rese ce en sione

ty
cor-
rected.

44-30

46-49
47-54
48-90
49-49
62-19
53:86
53-75
54:35

54:56
53-32
53-37
52-39
52:59
51-34
52-01
50-61
49-95
47-07
46-73
45-42
43-41
42-98
42-59
41-23
41-65
42-85

43-01
41-52
39-44
37-85
37-28
37-00
36-47
35-35
35-09
35-49
37-13
38-14

233

234 CRAIGLEITH.

t, Cor. | Cor. a to Cor. | Cor. G Up Cor. | Cor. ts t, Cor. | Cor. t,
Dates. || uncor-| for | for cor- || uncor-| for | for cor- || uncor-| for | for cor- || uncor-| for | for cor-
rected, | Col. | Air. | pected. || rected.| Col | Air. | rected. || rected. | Col | Air. | rected. || rected. | Col. | Air. | pected,
1838. if " } i 5 i
July 30]| 45-74 |—-03|—-05 | 45-66 || 48-54 |—-01|—.07 | 48-46 |! 51-32 -00|—.10]| 51-22 |, 53-02 -00 |; —-13 | 52-89
Aug. 6]| 46-00 |—-03]—-06 | 45-91 || 48-82 |—-01 |—-08 | 48.73 || 51-74 — .12)| 51-62 || 54-00 —-15 | 53-85
13 || 46-25 |—-03|—-06 | 46-16 || 49-17 |—-01 |—-07 | 49-09 || 52-15 —.10} 52-05 || 54-22 —-13 | 54-09
20 || 46-45 |—-03 |—-05 | 46-37 || 49-45 -00 |—-06 | 49-39 || 52-05 —.07|51-98 || 53-62 — -08 | 53-54
27 || 46-73 |—-03 | —-08 | 46-62 || 49-68 -00 | —-10| 49-58 || 52-07 —.15 | 51-92 || 53-52 — -20 | 53-32
Sept. 3 || 46-90 |—-03 |—-06 | 46-81 || 49-80 -00|—-08 | 49-72 || 52-08 —.11| 51-97 || 53-25 —-15 | 53-10
10 || 47-26 |—-02|—-04| 47-20 || 50-19 -00|—-04] 50-15 || 51-75 — .04/51-71 || 52-00 — -06 | 51-94
17 || 47-28 |—-02|—-04 | 47-22 || 49-85 -00 | —-04| 49-81 || 51-45 — .05 | 51-40 || 52-80 — -05 | 52-75
24 || 47-43 |—-02|—-05 | 47-36 || 49-89 -00|—-05 | 49.84 || 51-35 —.08| 51-27 || 51-88 —-10}] 51-78
Oct. 1)]| 47-55 |—-02|—-04] 47-49 || 49-84 -00|—-04| 49-80 || 51-10 — .06| 51-04 || 51-90 — -07 | 51-83
8 || 47-62 |—-01| -00!| 47-61 || 49-72 -00/+-01 | 49-73 || 50-20 +-01)| 50-21 || 49-68 +-01 | 49-69
15 || 47-72 |—-01 | —-02 | 47-69 || 49-45 -00 | —-03 | 49-42 || 49-25 — .04| 49-21 || 47-80 —-06 | 47-74
22 || 47-80 |—-01|—-04| 47-75 || 49-07 -00|—-04| 49-03 || 48-60 — -06 | 48-54 || 48-16 — -09 | 48-07
29 || 47-78 |—-01|+-01 | 47-78 || 48-76 -00 |+-01 | 48-77 || 48-64 +.02/ 48-66 || 47-90 + -02 | 47-92
Nov. 5 || 47-85 -00| -00) 47-85 || 48-48 00} -00) 48-48 || 47-20 -00 | 47-20 || 45-68 —-01 | 45-67
12 || 47-82 |+-01]+-05 | 47-88 || 47-92 ‘00 |+-05 | 47-97 || 46-32 +-06 | 46-38 || 44-70 +-08 | 44-78
19 || 47-74 |4+-01 |+-04 | 47-79 || 47-43 -00 |+-03 | 47-46 || 45-40 +-03 | 45-43 || 43-08 + -02 | 43-10
26 || 47-62 |+-01]+-01 | 47-64 || 46-50 |4+-01|+-01 | 46-52 || 43-72 -00 | 43-72 || 41-42 — -03 | 41-39
Dec. 3)| 47-57 |+-01]| -00| 47-58 || 46-12 -00|—-01 | 46-11 || 43-78 — -02| 43-76 || 43-02 — -04| 42-98
10|| 47-35 |+-01| -00) 47-36 || 45-85 :00|—-01 | 45-84 || 43-83 — -02| 43-81 || 42-40 — -04 | 42-36
17 || 47-14 |+-01|4+ -03 | 47-18 || 45-55 -00 |+-02 | 45-57 || 43-40 +-01|43-41 || 41-68 +-01 | 51-69
27 || 46-95 |+-02]+-03 | 47-00 || 44-85 -00/+-02 | 44-87 || 42-38 +-01 | 42-39 || 40-50 +-01 | 40-51 »
31 || 46-84 |+-02|+-03 | 46-89 || 44-64 -00|+-01 | 44-65 || 22-12 +-01 | 42-13 || 40-85 +-01 | 40-86
1839.
Jan. 7]|| 46-68 |+-02/+-02 | 46-72 || 44.21 -00|+-01 | 44.22 || 41-77 +-01] 41-78 || 40-00 -00 | 40-00
14]| 46-48 |+-02}+-02 | 46-52 || 43-70 -00|+-01 | 43-71 || 40-95 -00 | 40-95 || 39-90 -00 | 39-90
21 || 46-28 |+-03|+-02 | 46-33 || 43-40 |+-01|+-01 | 43-42 || 40-25 -00 | 40-25 || 38-25 -00 | 38-25
28 || 46-06 |+-03/}+-03 | 46-12 || 43-07 |+-01/+-01) 43-09 || 40-04 +-01}| 40-05 || 38-02 +-01 | 38-03
Feb. 4]| 45-85 |+-03]+-01 | 45-89 || 42-58 |+-01] -00| 42-59 || 39-28 00 | 39-28 || 37-24 — -02 | 37-22
11 || 45-67 |+-03) -00| 45-70 || 42-12 -00 |—.01 | 42-11 || 39-70 —-02| 39-68 || 39-12 — -04 | 39.08
18 || 45-43 |+-03 |+-03 | 45-49 || 42.07 -00|+-01 | 42-08 || 40-10 +-01}40-11 || 38-90 + -02| 38-92
25 || 45-23 |+-03/+-01 | 45-26 || 41-95 00} -00} 41-95 || 39-33 — -01 | 39-32 || 37-98 —-02| 37-96
Mar. 4]| 45-00 |+-03|+-01 | 45-04 || 41-84 00} -00/ 41-84 || 39-67 —-01| 39-66 || 38-78 — -02 | 38-76
11 || 44-80 |+-03 |+-01 | 44-84 || 41-75 -00| -00/ 41-75 || 39-30 —-01 | 39-29 || 37-42 — -02 | 37-40
19 || 44-70 |+-03|—-01 | 44-72 || 41-60 -00| -00} 41-60 || 39-45 — -02 | 39-43 || 38-57 — -04| 38-53
25 || 44-55 |4+-02/+-01 | 44-58 || 41-37 :00| -00) 41-37 || 39-75 -00 | 39-75 || 39-43 — -02 | 39-41
Apr. 1|| 44-37 |4+-02]+-01 | 44-40 || 41-45 -00| -00}| 41-45 || 40-08 -00| 40-08 || 39-22 —-01 |} 39.21
8 || 44-22 |4+ -02|)—-01 | 44-23 || 41-55 -00| -00| 41-55 || 39-68 —-02 | 39-66 || 38-65 — -05 | 38-60
15 || 44-10 |+-02]—-01 | 44-11 || 41-45 -00} -00/ 41-45 || 40-26 — -02| 40-24 || 40-98 — -05 | 40-93
22)| 44-00 |+-01 |—-02 | 43-99 || 41-68 -00|—-O1 | 41-67 || 41-21- —-04| 41-17 || 41-70 —-08 | 41-62
29 || 43-92 |4-01]—-05 | 43-90 || 41-98 ‘00 | —-02 | 41-96 || 42-32 — -06 | 42-26 || 43-41 —-11]| 43-30
May 61] 43-90 -00 | —-03 | 43-87 || 42-74 -00 | —-02 | 42-72 || 43-40 — -06 | 43-34 || 43-80 —-10 | 43-70
13 || 43-88 -00 | —-01 | 43-87 || 43-10 -00 |—-01 | 43-09 || 43-90 — -03 | 43-87 || 44-06 —-13 | 43-93
21 || 43-93 -00|—-03 | 43-90 || 43-34 -00 | —-03 | 43-31 || 44-15 — -07 | 44-08 || 45-50 — -12| 45-38
27 || 43-98 -00 | —-04 | 43-94 || 43-62 -00 | —-04] 43-58 || 44-80 —-09 | 44-71 || 46-10 —-16| 45.94
June 3//44:07 |—-01|—-02| 44-04 || 44-04 -00 | —-02 | 44-02 || 45-77 —-06 | 45-71 || 47-17 — -08 | 47-09
10 || 44-17 |—-01]—-03 | 44-13 || 44-52 -00 | —-03 | 44-49 || 46-58 —-07| 46-51 || 48-60 —-10| 48-50
17 || 44-31 |—-01 | —-06 | 44-24 || 45-05 -00 |—-07 | 44-98 || 47-38 —-15 | 47-23 || 49-82 — -23 | 49-59
24 || 44-53 |—-01|—-05 | 44-47 || 45-84 |—-01 |—-07 | 45-76 || 49-04 —-13} 48-91 || 51-35 —-18] 51-17
July 11) 44-68 |—-02|—-06| 44-60 || 46-40 |—-01/—-08]| 46-31 || 49-60 —-15 | 49-45 || 51-75 —-21/ 51-54
7 || 44-82 |—-02|—-06 | 44-74 ||46-85 |—-01|—-08 | 46-76 || 50-49 —-15 | 50-34 || 53-50 —-19| 53-31
15 || 45-20 |—-03 | —-04| 45-13 || 47-87 |—-01|—-05 | 47-81 || 51-42 —-08 | 51-34 || 53-72 — -08 | 53-64
2211 45-33 |—-03|}—-05 | 45-25 || 48-10 |—-01 |—-07 | 48-02 || 51-49 —-11} 51-38 || 53-84 —-12) 53-72
29 || 45-58 |—-03|—-06| 45-49 || 48-57 |—-01|—-09 | 48-47 || 52-10 —-14} 51-96 || 54-68 —-17}| 54-51
Aug. 5]|| 45-87 |—-03}—-08 | 45-76 || 49-04 |—-01|—-11]| 48-92 || 52-47 —-18| 52-29 || 54-70 — -23 | 54-47
14}| 46-17 |—-03|}—-05 | 46-09 || 49.44 -00 | —-06 | 49-38 || 52-50 —-08 | 52-42 || 54-15 | — -08 | 54-07
19 || 46-35 |—-03 | —--03 | 46-29 || 49-58 -00|}—-03 | 49-55 || 52-10 —-04] 52-06 || 53-27 — 04 | 53-23
26 || 46-62 |—-03)}—-06) 46-53 |) 49-68 -00|—-07 | 49-61 || 51-92 —-10; 51-82 || 53-43 — -13 | 53-30
Sept. 3]|| 46-85 |—-02|—-05 | 46-78 || 49-78 -00 |—-06 | 49-72 || 52-03 —-08} 51-95 || 53-27 —-11/53-16 |
10 || 47-07 |—-02}—-06 | 46-99 || 49-90 -00|—-07 | 49-83 || 51-95. —-09 | 51-86 || 53-17 —-12 | 53-05
16 || 47-28 |—-02}—-04 | 47-22 || 50-09 -00|—-04/ 50-05 || 51-67 — -04] 51-63 || 52-30 — -06 | 52-24
23 || 47-37 |—-02|—-06 | 47-29 || 49.94 -00 | —-07 | 49-87 || 51-30 —-10} 51-20 || 51-67 —-13 | 51-54
30 || 47-47 |—-02|—-04| 47-41 || 49.78 -00 | —-04 | 49-74 || 50-88 —-06| 50-82 || 51-17 — -09 | 51-08
Oct. 7{| 47-60 |—-01|—-04147-55 || 47-65 -00|—-03 | 49-62 || 50-05 —-06! 49-99 || 49-17 — -09 ! 49-08

. ~~

Noe pore

ST PWTORMONDON ELDER OE KDOWTOWRONNDHEROMBTIORAOSOHRTONRTOCWNISCWHR SWaONW

t Cor.
for

or-
uncor Col.

rected.

Cor.
for
Air.

47.66 |—-01|—-02
47-62 |—-01|—-03

47-80 |—-01
47-77 | -00
47-80 -00
47-77 -00
47-68 -00
47-60 |+-01
47-47 |+-01
47-43 |+-02
47-28 |+-02
47-03 |+-02
46-90 |+-02
46-69 |}+-02
46-53 |+-02
46-32 |+-02
46-14 |+-0%3
45-97 |+-03
45-73 |+-02
45-50 |+-02
45-34 |+-03
45-20 |+-03
45-02 |+-02
44-80 |+-02
44-68 |+-02
44.55 |+-01
44.45 |+-01
44.41 00
44-40 00
44-38 |--01
44-40 00
44-60 00
44-64 |—-01
44.72 |—-01
44-84 |--01
44.94 |—-01
45-18 |—-02
45-26 |—-02
45-50 |—-02
45-63 |—-02
45-88 |—-02
46-05 |—-03
46-26 |—-03
46-47 |—-03
46-78 |—-03
46-93 |—-03
47-15 |—-03
47-35 |—-03
47-50 |—-02
47-68 |—-02
47-83 |—-02
47-88 |—-01
47-95 |—-01
48-00 |—-01
47-98 00
48-02 -00
47-92 | .00
47-94 |+.-01
47-82 |4-01
47-70 |+-01
47-54 |+-01
47-34 |+.01

47-25 |4.0214.04

++it +1
Oo aa.
bo

05

th
cor-
rected.

47-63
47-58
47-79
47-77
47-80
47-77
47-71
47-67
74-53
47-48
47-30
47-11

46-97
46-70
46-57
46-38
46-19
46-00
45-76
45-54
45-38
45-20
45-01
44-82
44-70
44-55
44.44
44-37
44-35
44-35
44-40
44-58
44-60
44-66
44-78
44.87
45-10
45-18
45-43
45-56
45-79
45-95
46-15
46-37
46-68
46-83
47-05

3 | 47-26

47-43
47-63
47-74
47-85
47-93
47-97
47-98
48-00
47-93
47-95
47-85
47-69
47-56
47-40
47-31

t,
uncor-
rected.

49-34
49-15
48-88
48-59
48-27
47-97
47-68
47-20
46-66
45-94
45-50
45-25

44.63
44.27
43-96
43-73
43-41
43-03
42.94
42.92
42-65
42-29
42-04
42.14
42-16
42.34
42.55
42.82
43-22
43-76
44-32
44-60
44-70
45-05
45-57
45-98
46-49
46-94
47-55
47-84
48-30
48-68
49-10
49-45
50-09
50-11
50-34
50-46
50:44
50-34
50-14
49-88
49-55
49-23
48-95
48-55
48-18
47-74
47-14
46-84
46-34

46-00

1145-40

Cor.
for
Col.

Cor.
for
Air.

CRAIGLEITH.

t,
cor-
rected.

—.02 | 49-32

—-03

eter ae) or eee ee
So
is

49-12

ts
uncor-
rected.

49-62
49-12
48-77
47-94
47-47
47-20
46-55
45-16
44-20

Cor.
for
Col.

-00

Cor.
for
Air.

lb

sie ASE Bes
(>)

ty
uncor-
rected.

49-64
48-20
48-37
46-98
46-98
46-65
45-30
43-30
41-68
42-26
42-68
40-50

40-39
40-73
40-83
40-20
39-00

39-40 |

40-64
38-92
37-82
38-00
40-46
39-97
41-28
41-95
43-10
43-88
46-22
47-56
45-20
45-93
47-38
48-68
49-56
50-50
50-78
51:76
52-10
52-90
53-68
53-90
54:39
55:58
54:28
54-81
54-80
53-72
52-58
51-36
50-75
49-56
48-92
49-00
46-98
46-60
45-70
44-30
43-01

42-18
43-25

41-88
40-90

Cor.
for
Col.

-00

a, Ee i SO

t,
cor-
rected.

49-61
48-12
48-36
46:98
46-97
46-64
45-34
43-37
41-74
42.27
42-66

} | 40-56

40-43
40-67
40-84
40-23
38-99
39-37
40-62
38-91
37-81
37-91
40-36
39-93
41-25
41-90
43-02
43-76
46-03
47-50
45-21
45-86
47-30
48-53
49-39
50-32
50-61
51-57
52-00
52-78
53-45
53-75
04-18
09-43
54-14
54-65
54-66
53-61

52-51
51-31

50-59
49-53
48-91

48-97 |
46-97 |

46-55
45-71
44.27
43-00
42-11
43-23

141-93

40-93

235

236 CRAIGLEITH.
ty Cor. | Cor. t ts Cor. | Cor. Gb t; Cor. | Cor.
Dates. |] uncor- | for | for | cor- || uncor-| for | for | cor- || uncor-| for | for
rected, | Col. | Air. | pected. || rected. | Col. | Air. | rected. || rected, | Col. | Air.
1840. 3 5 ° 5 °
Dec. 28]| 47-02 |+-02|+-05 | 47-09 || 45-04 |+-01]+-03 | 45-08 || 41-70 00 |+-03
1841.
Jan. 4/||46-87 |+-03|+-05 | 46-95 || 44-30 -00|+-02 | 44-32 || 41-15 -00 | + -02
12/|46-58 |+-03|}+-05 | 46-66 || 43-84 |+-01|}+-02| 43-87 || 40-15 -00 |+-02
18 || 46-44 |+-03|}+-05 | 46-52 || 43-12 |+-01|)+-02)| 43-15 || 39-38 -00|+ -02
251141-15 |+-03 |+-04 | 46-22 || 42-75 |+-01/+-02| 42-78 || 38-98 -00/+-01
Feb. 11|/ 45-90 |+-03|+-04| 45-97 || 42-32 -00|+-01 | 42-33 || 39-28 -00|}+-01
8 || 45-60 |+-03|+-05 | 45-68 || 42-13 -00|}+-01 | 42-14 || 39-13 -00 | + -02
15 || 45-45 |+-03/+-01 | 45-49 || 41-68 00} -00/ 41-68 || 38-92 -00|—-01
22 || 45-22 |+-03 | —-01 | 45-24 || 41-64 -00|—-01/ 41-63 || 39-92 -00|—-02
Mar. 2]| 44-93 |+-02|+-01 | 44-96 || 41-93 00} -00) 41-93 || 40-48 -00|—-01
8 ||44-80 |+-02|—-03 | 44-79 || 42-02 -00 | —-01 | 42-01 || 40-48 -00 | — -04
15 || 44-66 |+-01 | —-02 | 44-65 || 42-14 -00|—-01 | 42-13 || 41-74 -00 | — -04
22|| 44-54 |+-01|—-02 | 44-53 || 42-54 -00|—-01 | 42-53 || 42-70 -00 | —-03
29 || 44-48 |+-01|—-03 | 44-46 ||} 42-94 -00 | —-02 | 42-92 ||} 43-31 -00 | —-06
Apr. 5||44-45 |+-01|—-01 | 44-45 || 43-25 -00 | —-01 | 43-24 || 43-38 -00 | —-02
12|| 44-45 |+-01 | —-01 | 44-45 || 43.44 -00 | —-01 | 43-43 || 43.48 -00 | — -02
19 || 44:50 |+-01 | —-02 | 44-49 || 43-62 -00 | —-02| 43-60 || 43-85 -00 | — -04
26 || 44-53 |+-01]—-01 | 44-53 || 43-83 -00 |} —-01 | 43-82 || 44-10 -00 | —-03
May 3)| 44-56 -00|—-01 | 44-55 || 44-08 -00 | —-01 | 44-07 || 45-26 -00 | —-03
10 || 44-64 -00 | —-04 | 44-60 || 44-54 ‘00 | —-04 | 44-50 || 45-84 -00|—-10
17 || 44-70 |—-01 | —-03 | 44-66 || 45-02 -00 | —-04 | 44-98 || 47-09 -00 | —-08
94 || 44-84 |—-01 | —-06 | 44-77 || 45-62 -00|—-08| 45-54 || 47-80 -00 |—-17
31 || 44-97 |—-01 | —-06 | 44-90 || 46-14 -00|—.07 | 46-07 || 48-29 |—-01]—-13
June 7||45-12 |—-02]—-03|45-07 || 46-73 -00 | —-04 | 46-69 || 49-50 -00 | —-07
14]| 45-30 |—-02|—-04| 45-24 || 47-17 |—-01)—-05| 47-11 || 50-05 -00 | —-09
21 || 45-52 |—-02|—-06| 45-44 || 47-62 -00 | —-06 | 47-56 || 50-19 -00 | —-12
28 || 45-72 |—-02|—-04| 45-66 || 47-90 -00 | —-06 | 47-84 || 50-28 -00 | —-09
July 6// 45-94 |—-02|—-05 | 45-87 || 48-19 -00) —-06 | 48-13 || 51-02 -00 | —-09
12)|46-10 |—-02)—-06| 46-02 || 48-50 -00 | —-07 | 48-43 || 50-97 -00|—-11
19 || 46-31 |—-02|—-05 | 46-24 || 48-72 -00|—-07 | 48-65 ||51-18 -00;—-10
27 || 46-50 |—-02|—-05 | 46-43 || 48-95 -00| —-05 | 48-90 || 51-40 -00|—-08
Aug. 2||46-66 |—-02|—-08 | 46-56 || 49-18 -00|—.10)] 49-08 || 51-39 -00|—-17
9 || 46-80 |—-02 | —-04 | 46-74 || 49.27 -00| —-05 | 49.22 || 51-46 -00|—-08
16 || 47-00 |—-02|—-06 | 46-92 || 49-45 -00 | —.07 | 49-38 || 51-30 -00|—-10
23 1147-20 |—-02|—-04] 47-14 || 49-71 -00 | —.05 | 49-66 || 51-76 -00 | —-07
30||47-27 |—-02|—-06| 47-19 || 49-68 -00 | —-08 | 49-60 || 51-86 -00 |—-12
Sept. 6||47-36 |—-01 | —-06| 47-29 || 49-83 -00 | —-02| 49-81 || 51-60 -00 | —-02
13 || 47-55 |—-02|—-08| 47-45 || 49-88 -00|—-.10| 49-78 || 51-40 -00|—-12
20/1 47-66 |—-02|—-06| 47-58 || 49-98 -00 | — .06 | 49-92 || 52-25 -00 | -- -09
27 || 47-80 |—-02 | —:02| 47-76 || 50-28 -00 | —.02 | 50-26 || 52-00 -00}—-02
Oct. 4/|/47-88 |—-02|—-02)} 47-84 || 50-25 -00 | —-01 | 50-24 || 51-55 00; -00
12|/ 48-08 |—-01|—-01/ 48-06 || 50-22 -00|—-01 | 50-21 || 50-58 -00 -00
18 |) 48-15 |—-01 |+-02| 48-16 || 49-95 -00}+ -04| 49-99 || 49.73 -00|+-05
26 || 48-15 -00 |+-02| 48-17 || 49-28 -00 | + -04 | 49-32 || 47.96 -00|+-04
Nov. 11|/48-15 -00 -00/ 48-15 || 48-75 -00 -00 | 48-75 || 46.96 -00 | —-02
: +-01|—-01 | 49-12 || 48-06 -00|—-01)| 48-05 || 46.22 -00 |—-03
+-01/+-05/|48-11 || 47-54 -00/+-05 | 47-59 || 45.88 -00 | +-05
+-01|+-04]47-95 || 47-04 | -.00/+-03) 47-07 ||43-95 | -00/+-03
+-02|+-02 | 47-86 || 46-03 -00|+-01 | 46-04 || 42-70 -00} -00
+-:02| -00/47-66 || 45-36 -00| —-01 | 45-35 || 43-08 -00 | —-03
+ -02/+-02/|47-42 || 45-10 -00| -00| 45-10 || 43-08 -00} -00
+-02|+-06|47-22 || 44-86 -00 | + -03 | 44-89 || 42.30 -00)+ -04
+-03 |+-03|47-01 || 44-34 -00/+-01 | 44-35 || 41-24 -00|}+-01
+-02/+-03 | 46-79 || 43-93 -00|+-01 | 43-94 || 41-61 -00}+-01
+-02|+-04 | 46-53 || 43-78 -00|+-02 | 43-80 || 40-85 -00)+-03
+-03/+-04 | 46-32 || 43-35 |+-01|/+-01 | 43-37 || 40-03 -00|+-01
+-03 }+-02/|46-12 || 42-60 00} -00)42-60 || 39-57 -00| -00
+-03/+-01 | 45-92 || 42-27 00} -00} 42-27 || 39-19 00; -00
+-03|+-04 | 45-65 || 42-19 -00 |+-01 | 42-20 || 39-72 -00 |+ -02
+-03|] -00|45-43 || 41-85 -00| -00/41-85 || 39-76 -00|—-01
+ -02)+-02|45-21 || 41-90 :00|} -00/41-90 || 40-22 -00| -00
+-02/+-01 | 44-93 || 42-02 00} -00) 42-02 || 39-95 00} -00
+-02|—-01|44:89 |/41-78 | -00! .00141-78 || 39-95 -00 | — -02

ts t, Cor. | Cor

cor- uncor- | for for
rected. || rected. | Col. | Air
41-73 || 38-98 ‘00 |+-03
41-17 || 39-40 +-02
40-17 || 37-17 +-01
39-40 || 36-78 + -02
38-99 || 36-50 +-01
39-29 || 38-28 +.02
39-15 || 37-03 +.03
38-91 || 38-40 —.03
39-90 || 39-45 — -06
40-47 || 39-60 —-01
40-44 || 40-28 — -09
41-70 || 42-58 —-09
42.67 || 43-20 — -06
43.25 || 43-97 —-10
43.36 || 43-48 — .04
43-46 || 43-54 — -03
43-81 || 44-20 —-08
44.07 || 44-40 —-06
45-23 || 46-78 —.02
45-74 || 47.20 —.17
47-01 || 48-95 rae
47-63 || 49-58 — -26
48-15 || 51-42 — -20
49-43 || 51-19 — -08
49-96 || 52-48 — =n
50-07 || 51-94 —=6
50-19 || 52-00 —-12
50-93 || 53-17 —-12
50-86 || 52-46 =e
51-08 || 53-12 01/3:
51-32 || 53-48 —-10
51-22 || 52-64 2p,
51-38 || 53-10 —-09
51-20 || 52.43 —:14
51-69 || 52.98 —-09
51-74 || 53-58 eollic
51-58 || 51-98 — -04
51-28 || 52.94 SIC |
52-16 || 53-82 — on
51-98 || 52-68 —-01
91-55 || 51-58 —-01
50-58 || 50-48 —-02
49-78 || 48-86 + -06
48-00 || 46-32 + -04
46-94 || 45-45 — -04
46-19 || 45-58 — -05
45-93 || 44-00 +-06
43-98 || 41-21 +-02
42-70 || 40-78 —-01
43-05 || 42.43 —-05
43-08 || 42-02 -00
42-34 || 39-90 +-05
41-25 || 39-26 +-01
41-62 || 40-88 +-02
40-88 || 38-46 +-02
40-04 || 37-68 +-02
39-57 || 37-72, -00
39-19 || 37-61 —-01
39-74 || 38-17 +-03
39-75 || 38-98 — -04
40-22 || 39-96 4--01
39-95 || 38-82 -00
39-93 || 39-62 —-05

( 237)

XIX—On a Formula representing the Mean Height of the Barometer at the Level of
the Sea. By Professor HanstEeEn of Christiania, in a Letter addressed to
Professor ForseEs, Secretary of the Royal Society of Edinburgh.

OBSERVATORY NEAR CHRISTIANIA, 26th September 1846.

Srr,—You have communicated to me, that the Royal Society of Sciences in
Edinburgh has done me the honour to elect me as a corresponding member. I
beg you to render my humble thanks to the Society, and to assure, that it shall
be my earnest wish to fulfil every task in my power which the Royal Society
should demand.

That this letter may not reach your hands without any scientific communi-
cation, I subjoin the following :—From November 1822 to April 1824 inclusive, I
observed the height of the barometer in Christiania, and found the mean reduced
to 0° R., and to the level of the sea =757™°763 = 335’”-913 lign. de Paris. As the
mean height of the barometer observed at Paris by Bouvard, and reduced to 0°, and
the level of the sea is = 337’”53, I was surprised at the great difference of 1-62
between Paris and Christiania. Ifp denotes the pressure of the atmosphere at
the level of the sea, m and / the density of the mercury and its height in the
tube, g the force of gravity, we have p = mgh, and, in another place, p’= mg/h’.

If f=pisgh=l'’,orl’= . h. Tf, in the first place, the latitude is = ¢, in the

—e g _ 1—0-0025911 e082 1 ang, taki yc
second, = ’, we have © = 799095911 cos? 1—0-0025911 (cos 2 p—cos2*”) ;

h—h' =h, 0:0025911 (cos 2 ?—cos 2 9’). Taking $=0°, ¢’ =90°, we have
h—h’ = 1-74; and when ¢ = 4850’ (Paris), ¢’ = 59°-55’ (Christiania), we have
h —h’ = 0/32. But the observations have given for Paris and Christiania
h—W’ = 162 ; consequently, the mean pressure of the atmosphere is not the
in different latitudes (“‘ Magazin for Naturvidensk.” 1824, page 282-291).

Professor ScHouw in Copenhagen has, in the Memoirs of the Royal Society
of Sciences at Copenhagen for 1832 (page 291-342), collected all the known obser-
vations of the mean height of the barometer, which, with exactness, could be re-
duced to the level of the sea, and to 0° R. In the following table I have added
the result of five years’ observations here at the Observatory, and of the year
1844.at Bosekop. I have found that the observations can tolerably be represented
bythe formula

) = 336-8097 + 13038 cos 2 ¢ — 07478 cos 4 bd — 09145 cos 6 p + 0’-5435 cos 8 @.

VOL. XVI. PART. III. 30

238 PROFESSOR HANSTEEN ON THE MEAN HEIGHT OF

Place. Observer. ime. Difference.

Christiansborg Trentepohl & Chenon| 22 mo.
Guayra. . Boussingault
St Thomas . Hornbeck

Rio Janeiro

Eschwege

Santa Cruz, Teneriffe | Escolar . Bix.
Madeira. . Heinecken . . Dy.
Cape of Good Hope Puhlman and Wahlst Oy
Palermo : Cacciatore 5 y.
Naples Brioschi TY:
Florence Inghirami 9y.
Avignon Guérin 0 y.
Bologna Caturegli and Moratti| 5 y-
Padua The Astronomers . 5 y-
Paris Bouyarde. sj. ly.
London . Royal Society . 1 ¥:
Altona Schumacher 6 y.
Danzig : Strehlke 2y-
Konigsberg Sommer . 8 y.
Apenrade Neuber . 5y.
Edinburgh . Forbes 3 y.
Christiania . Hansteen 5 y.
Reikiavik Thorslenson zy
Godthaab Mihlenpfort 5 y.
Godhaven Graah and Baan 23 y.
Bosekop. . | Thomas . by:
Melville Island ~») | Parry ly.
Spitzbergen . . | Scoresby 6-1

The formula gives a minimum for > = 0°, and ¢ = 68°28’8, and a maximum
for @ = 86°:12’6, and ? = 90°. The following table gives y for every fifth degree
of latitude.

? + Q Y

0 336-995 45 338-101

5 7-012 50 7-246
10 7-096 55 6:240
15 7-291 60 5345
20 7-623 65 4-801
25 8-057 70 4-715
30 8-478 75 5-037
35 8-714 80 5-561
40 8612 85 6-034
45 8-101 90 6-216

* So in the original, and also in Schouw’s Tables; but surely a mistake.-—J. D. F.

THE BAROMETER AT THE LEVEL OF THE SEA. 239°

The greatest observed difference is between Madeira and Godthaab, 339/”:2
—333/"3 = 5/”9; the formula gives only 4’”-0. According to this table I have
constructed a curve, which represents the variation of from equator to the pole ;
but it is too voluminous for a letter.

If the observations are correct, there is a discontinuity between the eastern
and western coasts of the Northern Atlantic Ocean ; for instance, Christiania,
Bosekop (Norway), compared with Reikiavik (Iceland), and Godthaab, Godhaven
(Greenland) ; as also St Thomas (West Indies), compared with Santa Cruz, Tene-
riffe, and Madeira. If the whole globe was only an ocean, there would certainly
be no such irregularities.

The Norwegian Government has, according to the demand of the Royal So-
ciety in London, resolved, that magnetical and meteorological observations, which
stopped at the end of June 1843, shall be continued herea year. They were again
commenced the 15th August this year, and will be continued to the same date in
1847. The unifilar is observed every tenth minute, mean time Gottingen; the bi-
filar and meteorological phenomena, every full hour. I am, Sir, sincerely yours,

CHRISTOPHER HANSTEEN.

iota: heiale be tin erintrat ee ars vu
vat | alitea enilt wag swifnowihes Oe; ef ine iy
5 alg Silt ed OMY po cop ees obitniterract? ales
an af | ae batt st

eh ae | ‘stadia pi mee WP wire ra Abn ai
ee hl aay at
aa atic) JnadsborSuueatSi talent} Aivedbiall veiw Larunigh eee A
ane it sie ee chines desta WY. ea rey

At i
j g a | ue 7 :
A | ‘uate Liam, artis roe bl) ND (- 4 Hestolgyalyidar» a Ay
i
U 7 a!

=

r Pm

aoe a # * . mu)

es =| 4 t | { i. ‘ c ru : "
@ Pe aupsl ab? fh bogus 1} oxi Gi Ya i Up ra ai) we ree tal iy me
i ialdbur mare idar ri suiles th igaldtoy bate Dini Land a Yiviamer obi
‘ (ae aa es 1#A'f ni pai bau tid gunk og Lk tly, eran fub.ad
7 | Aver: Hiadad sine od} of henna ‘liars, ooh Live iin rouge Ah
ar elie ns Ae te METS Te i NoQtT Tir i earn yah Levuaado et +f
my = ng . te ae
a, | "9 PRL, Vit SONU 11 Atte L tru |! lu : YIB¥3 Hien yrs a bt

i 7 " * ee
a ' nl We to] ae awe RO ite
4 . EEE Tare no Pala") alta sa
bi ia . af Men . -
t i ir
é ’ »
Ms ‘g )
a 7
f x,
j | '
ey

(P24) 4

XX.—On General Differentiation. Part III. By the Rev. P. Ketiann, IA,
FRSSL.GL., FCP.S., late Fellow of Queen’s College, Cambridge ; Professor
of Mathematics, §c., mm the University of Edinburgh.

(Read December 21, 1846.)

Nearly six years ago, I presented to the Society two Memoirs on the subject
of Differentiation, with fractional indices. The method which I adopted to extend
the signification of a differential coefficient consisted in assuming that the func-
tion / , which enters into the value of the coefficient deduced from a particular
hypothesis, is limited only by the definition jx+1=n/n. This generalization ap-
pears to be perfectly satisfactory, and promises to offer, if not the only, cer-
tainly the best extension of the Differential Calculus. Considering the length of
the interval which has elapsed since the publication of my former Memoirs, it is
remarkable that so little addition has been made to our knowledge of this branch
of analysis. With the exception of one or two papers in LIiouVILLE’s Journal,
and a few remarks by Professor Dr Moreay, in his Treatise on the Differential
Calculus (pp. 598-600), [ am not aware that.anything has been written on this
subject since that time. Seeing, therefore, that others are not willing to enter on
this very promising field, I consider it not improper that I should make known a
number of extensions of this science to which I have been subsequently led, many
of which have been in my possession a considerable time.

I must premise, that the object of this generalization of the differential cal-
culus is, not only to extend the bounds of research beyond the limits of that
science, but also to group and classify the results of the science itself. It is,
perhaps, as important in the latter aspect as in the former ; for its very first conse-
quence is the union of the elementary forms of the two separate branches of that
science—the differential and the integral calculus—into one, so that the integral

becomes simply the negative differential. Now it is evident that this can only
be done by extending to some form, which is general for the existing calculus, a
universal and unrestrained interpretation. Such a form, properly selected, be-
comes, in the new science, a defining property, precisely in the same way
that the common differential coefficient is the defining property of the differen-
tial calculus. There are several forms which might appear appropriate to this
purpose: that which I have adopted is the differential coefficient of «”. The
assumption, therefore, on which the science is based, is the following: that
VOL. XVI. PART III. 3 P

YAP PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

dt x eg :
— =(—1)" a a”, whatever ben and yw. This form can be proved to be
Lx i

the correct one in every interpretable case, and can be deduced from the gene-

; : d¥ e&”
ralization of :

3 when n is negative.* We shall at present assume it as the

defining property or definition of —

When, from this definition, we can deduce the differential coefficients of ¢*
and of log a, that is, of the ascending and descending index-function, we are in
possession of the three fundamental forms from which all others may be de-
rived. The following mode of arriving at those differential coefficients is differ-
ent from that which has hitherto been given, and appears to leave nothing to be
desired.

dé e*
1. To find 2
f d x
aa Cm eo Weer
e sltexty gt pa 3t &e. goes
ey fee cf gt
d xt [=o oi free

=(Sicyr iM { ( a) 4 CP ad eee” +&e.}

[0 1-p = d-»)@-}»
UL = il! —2
=f & {= " + aueaes 1 pee 2" + be, } 3 where z=cz;

* See Part I., and the excellent Memoir of M. Liovuvit.e, referred to in that Treatise.

Another formula has been proposed, viz.

dt eet ie
da /T+n—w
I have lately received from Mr W. Center, of Langside, some judicious remarks on these formule,
contrasting the results arrived at by them respectively. He shews that (without continual introduction

of an infinite arbitrary constant) the latter formula is inapplicable in many of the most simple cases :

for example, in d“ of expanded positively, it gives, when applied, infinity on one side and not on

1
l+a
L Sih} ID Ce d” a
the other, and when expanded negatively, infinity on both sides; and again, it gives for ‘asf or
d

0
qa”
edie the value
d x” me

a ™, which is a function of « when wu is a positive proper fraction.

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 943

_(_ ot +) tae (4 sacha
=(—c) io {1~ (= } 25 (7-1) rere. 1

Let Bela Vegeta hn th
€ =(5- ) agert mits en
dy iiss
dz dt}
etl
y=e (c+ a 2he—* ae )
wet
Now er 1=0, except when p is a negative whole number; in which case

y= Ceé ; except when yu is a negative whole number, in which case

—p-1 geal
sj) Ss.
u-2 p=2
Now, im all cases we omit the arbitrary functions in differentiation to any
= w—l
index ; they being readily supplied when required. But pra + &&., is evi-

dently included in the arbitrary function, in the case in question ; we may there-
fore omit it, and write generally,

== Ces OF
tes za new
Se er il ci Gite s oaltdahchin cdl (4)

This result has been deduced from the definition without any assumption
whatever relative to the function |, except that it satisfies the condition /n+1=n/n.
We may, consequently, obtain the value of the constant C, by admitting, that
when n is positive, /n coincides with LrecEnpRE’s function /. In this case,

[as “a e~“*q"—-ld a
Po 0 ‘

Therefore, differentiating, to the index p,

[n+ Me
T+ be

—Cfa“*"-1e-*"aa, by the definition and equation (1).
x

But if n+ be positive, /n + also coincides with Lecenpre’s function, there-
fore,

nN
[O+ PB _ fj-aeqr+u-lda, or O=1.
ela

D44 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

Now C is altogether independent of n: if, therefore, we take n positive and
greater than (—/), which can always be done, we shall have proved generally,
that

dt e&

ae Oyen (a)s

It will be observed that the properties on which the truth of equation (2) is
based, are these,— :

Mn n+
j, MAE pla, |
dl xt gee whatever be n.

2. -/n+1=nj/n j

3. : = = “e~*"a"~1q a, when n is positive.
d* log x
2. To find “Ge
1 : . . Pare a” log x
n my previous Memoir, Art. 19, I obtained an expression for ae by as-

suming that of fF log 2 ; an assumption which owes its correctness to the admit-

ted possibility of the introduction of an arbitrary constant of integration. Con-
sequently, the conclusions at which I arrived can only be correct generally, by the
aid of an arbitrary function of differentiation. Now, it is our object to avoid the
use of such functions, and to obtain expressions for the general differential coeffi-
cient of all functions which shall be complete in themselves, so far as relates to
the satisfaction of every law of combination to which they may be subjected. It

; : ‘d :
becomes necessary, therefore, to-reject the equation ie = = log x, and to substitute

in its place some other function of 7. The following process appears to be per-
fectly satisfactory.

The value of

eat 1+p log x+ &.—1—g log r—&e.
Pp P
=log «—T logz+Ap+t &e.

If, therefore, g be of a higher order than p, such as p’, it is manifest that
a? — a1
pP

will be a simple representation of log x, provided p=0 and i —O,
By adopting this mode of representation we obtain,

r= it | = 1
(-1y"42 pee end
P| —p (ie

d“log a __
hee at g wee

ad x”

This expression comprehends every case, and appears to be the most simple

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 945

form under which the pth differential coefficient of a logarithm can be repre-

sented.
We shall reduce it in the different cases :
1. When p is a negative whole number =—=m.
|u—p=|—(m+p); and [—p=(—p—1)/—p—1
=(—p—1) (—p—2)...(—p—m) |—(m +p)
nlL+m+p
(aj) ee
=P _ pr ilte
—? =(-1)
[-p /l-p+p
dag’ ge pple
lag [l—p+¢
Hence aenee =(—1 Peel Py Nemes hy peer g har tae!
d xt eee P ean + qian
jl+p Deu. 2
—————— 1—pA+& eS yocaaet
But anew: = mh pA+&c.) where A= Tat =
and pit
[l+q 1
al SS == 5S SS (ld) Oi
vi=1+¢ log x+&c.
d* log x _#@ * G-pA+t&e.) (1+p log x + &e.)
dx [i—u p
pee (l—~gA+&c.) (1+glog a2 +&c.)
jl—p P
1 i*
= — (log «— A— j log at + se.)
= Be
= = (log x—A), since p and - are both equal to 0.
a lore rea 1 Ne Y cir n
Hence is -aail log #— G +5 + &e. +— ) \ which is a well known

(m)
expression for da log x
2. If w be not a negative whole number, / is finite; and
(PaaP [E=p [7
f_* = —*_*=—/n(1+Bp+ &e.)
ERS ees:
by supposing this function (which is finite) expanded in terms of p ;

VOL. XVI. PART III. 5@

PAG PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

——s

similarly qa =—/u%(1+Bg+ &.);
and from the expression in Art 2.
Oee# (1H a4 Bp+ Be) (1 +p log # + &e.)
=e (L+By+ &e.) (1+glog # &e.) 4
=(— af

3. The expression given above for the differential coefficient of a logarithm is,
therefore, perfectly general, and is applicable to all cases. It is essentially ana-
lytical in its nature, and does not appear to be reducible to a more arithmetical
form so as to retain its general character. The expression which I previously
gave exhibits very simply the mth differential coefficient of a logarithm as well as
its nth integral, when n is a whole number, and may be, consequently, regarded as
the most comprehensive arithmetical form of this function which we can at pre-
sent obtain.

It may not be considered out of place here to introduce the deduction of the

d”" log x : se ' :
value of ae , when is a positive or a negative whole number, from this form

also.

The equation is
d” log x_|n(—1)"+1 1 a a
ae = x {toe ge (az In * n(w—1) *

1 it 1 i:
2 (w—1) (m—2)* 3D ars &) }
(Part I, Art. 21.)

(1.) If be a positive whole number, the only terms in this expression which
are not indefinitely small, are,

a = 1 1

; j=1a” +09 (gerne) * wa) (n—n) ares,
_/n(—1yr** i eee 1
Fie Cae, Ga ee)

jn(—1yr*? __ fn(— 1)" *7Jn=n

a a" (n—n) a" |n—n—1/n—n+1
_ fa(—1"*2(m—n—1)_|n(—1)"*? _ Cee 12) aaa)

a” a x

the well known form.

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. QAT

(2.) If n be a negative integer = —m ;

gmtl ml ymt2 ii ~m+s

Let y = a2 1) 2G@=)@-2 * 3@—2) GH ss
gmt i} gm+2 1 gint3 x
= m(m+ 1) * 2(m+1)(m+2) * 3(m+2)(m+8) 1”
1
Coals 2 + Be,
whence, by eee
2 ill Me a Sra one er
= ala RIED oO Ga ae pe
ik 1 ym gm 1
3: Wee Ht ia DIG re ioe =|
1
Stee =, log —2)— te zs (L-2).

Consequently, the value of y between the limits 0 and 1 is

1 Le 1
~ m(m — Ea dee nears ary)

LNG ten 1 1
fiat. aan eee aaT ~ m—1

: (F+5+ke. + al ee

~ m(m— m(m—1) \I m m—1
1 naa 1
Fee awa 15 = 3 t &e. + =;
—m a3 iF) m+1
and 3 WEP =! Sr Cen { log @—1—m(m—Ly }
Cpe | Sj

Mee ae Nii, (C2
ama). (2) 7 NI e+)
pole? rf 1} plies eabtyh
~ m(m—1)...2 og a (7+5 Bea a
es : (m)
which is the expression for d x” log x.

4. In my previous memoirs, I have obtained the general differential coefti-
cients of several functions, and have applied the results to the solution of analy-
tical and mechanical problems. It will be my object at present, to extend the
science itself by exhibiting the solution of differential equations, and by investi-
gating some of the properties of finite differences. In every instance I shall select
the most simple problems which will serve to illustrate the process employed.
Of the process itself, consisting entirely of the application of the calculus of opera-

YAS PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

tions, it is, perhaps, necessary to say a few words. The principle on which that
calculus is founded is this:

If the laws which regulate the combinations of symbols of operation be the same
as those which regulate the combinations of symbols of quantity, then all forms which
would be equivalent relative to the latter, must also be equivalent relative to the former.

The laws to which symbols of quantity are subject, may be briefly classed un-
der the seven following heads.

1. Their affections by numbers, or numerical quantities, are the same as if
they themselves were numbers, or numerical quantities.

2. The law of signs.

3. The order of simple operations is indifferent.

4. The order of combined operations is indifferent.

5. Combined operations may be distributed.

. and 7. The laws of indices.

Hence, if d, @, ~ are any symbols of operation, subject to these laws (a and

6 being numerical quantities) :

1. a+b) p=aptbhp=agPt Hd; &e.

2. (at) (b= VW=ab=aytig-OGy; &e.
3. ptdadto

4. v=o

5. d(p+y=dpidy

Grd ad =o"

on)

itt. (a*) =q*’

results which would be equivalent were d, », » numerical quantities, are equiva-
lent when they are operations. For example,

n n n—1 es n—-2 2
(d+) =d +nd — = gp + ke.

The symbols of differentiation = = and of difference A,, A, satisfy these con-
ditions.

It must be observed, in applying the principle which I have laid down, that
it is inapplicable, unless it hold with respect to every symbol which enters into the
operation. It will evidently apply to the ordinary symbols d and A as combined
with each other, and to the symbols z, y as combined with each other; but it will
not apply to the symbols d and x as combined with each other, because the fourth
law is violated by their combination: For example,

ee Ae tee

dAv?=Adzx?:;

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. YAO

But Ott, ae ae
ad” is not equal to dx 2?.

In proof of the sufficiency of the principle here laid down, it may be re-
marked, that both symbols of operation and symbols of quantity are defined or
characterized by the above laws. The symbols of combination are indeed origi-
nally framed from arithmetic, but are subsequently generalized, and the basis of
generalization is obedience to these laws. Thus the symbols + and — are gene-
ralized by collective symbols the reverse of each other, expressed by the equation
+a—a=+0=—0; where +0 is arithmetical, or signifies (as an operation strictly)
increased by 0: x and ~ are ‘ cumulative symbols the reverse of each other,’ ex-
pressed by the equation x@—+a=x1=-+1; where x1 signifies strictly multiplied
by 1. These definitions are in perfect conformity with the above laws. And a
similar remarks applies to the general definition of an index.

Now certain symbols of operation, although not, like symbols of quantity,
framed with direct reference to the above laws, do, notwithstanding, satisfy them.
Consequently, algebraic formule which are results of these laws and of nothing else,
must be correct forms also when the algebraic symbols are replaced by such symbols of
operation.

Section I. Linear DIFFERENTIAL EQUATIONS.
Preliminary Theorems.

CY ele

d Cx ° . ° . d
5. Since (=) "= ce”, it is evident that if e (=) be any function

whatever of = we hab have oF (=) eee aj (re. (AY.

z

Let uw be a function of z, and suppose it expanded in the form w=3 a,,e”"” ; then

e""u=3a,e"+")*. and hence

(=)° Cee Sa (m + ry“ Pees by (A)

=e 2a, +r)! ee

=e" 3a, (a +7)*e"* by (A)

VOL. XVI. PART III. 3R

250 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

f (=): é ux" f (s+ r).u (B)

Let x=e and suppose w expanded in the form vw=3a, «~": also write D for

d
aie then
aye 1 n+ —n
iy (oy ee 8 a (ate | Bb
a (=) a” ( ) In z
d\& —n
soe |
=(—1)" 3a, se
/—D+p —né
=(-1f 30, 6 by (A)
=(-1)" asked 0h Pe
=p :
[-D+e
(1) C
(“I tae: a0)
As a particular case of formula (B) we have
pe eDea EDs,
iy Epemiee ee:

These four theorems will be found of the utmost importance in reducing dif-
ferential equations. Formule somewhat analogous have been applied to the so-
lution of common differential equations by M. Caucuy, Evercices, vol. i., p. 163,
and Lxercices d Analyse, ii., 343; by Mr Grecory, Cambridge Mathematical Jow-
nal, 1., 22, &c.: and by Mr Boots, Philosophical Transactions, 1844, 225. Under
the different heads in which we shall arrange differential equations, we shall
solve only the most simple examples, our object being to illustrate the method of
proceeding rather than to exhibit its power.

Cuiass I. Equations which are capable of solution without transformation.

2
o- Exo id —ay=0.
dx?
ae d : :
By writing d for ae this equation becomes

a
(fey oe0 ory =e 8G

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 251

Suppose y=34,,e""; then by (A)
36, (m —a*) e”*=0; which can only be satisfied when =a.
y=Ae’” is the solution of the equation.

We might have proceeded in a somewhat different manner, as follows:
Put 0¢”” for 0, then

MX

Dae: aay. : i : by (A).
m —a
But a a is finite only when m=a; and then it is constant; .. y=Ac*”,
as before.
Ex. 2. — y=X,; X being any function of z.

We have y=(d!—a!)"!. X+(a*—-a})"* . 0.
if X=%b,e"

b “#5
gee > 2 e* (Ex. 1.)

r rv . . . .
Cor. 1. Ify =a, ~—je becomes infinite. In this case put «+a in place of r:
r —a

atltaxe+a&c.
a

2 at + &e.

b :
then. = 2 =Ge becomes 4, ¢
r—a

2 x
ea on 42 a awe , when a=0;
a

aX

of which the first term may be incorporated with A e
tion is

; and the complete solu-

b est
s
ae

y= Ae "+2 b, a? re eS

Cor. 2. If X= x2”, we have, by the well-known formula

a0
ay eee a”™-1 da,
fue |n 7)

PE ON hewialige 7° Sagi eae
(d*—a*) ae aera by (A.)

b 2
---f{* ee + ie.) “a da
|n SJ o a a”

a

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

=-=( e 4 (=D te a+ = Be. )
[nm \q* a” ag ** aes

pnt seal be n n (n+ 1)
i ie ar a gets &e. )

yp R(_1 th DOD, y,
ar m \aat? gat? ag ts ey

x“ n

dx

ees Bae ee eee 4782
=a’ e a6 da+/— 72 e
n

Pa

Weep ee eee et (
y ée be jaf x dx+V/—1 iB ay 2 |

7. The solution of the foregoing examples might have been obtained very
differently, thus :

by 3
if d} y-a' y=X; y= {= Gt8e

Now ae X is the solution of the ordinary differential equation ce —av=X; its

value is, consequently, e*” ( a8 e* Xdar+ c) . Hence

4
(=z,

===. et ( sof oe Xdax+ ) +a® e* (eo °* Xda + c)
dx
For instance, if X=0, the solution of the equation is

y=2a* Ce%* ;
which is the same as that given above.

Se Hix: 3. ae ad'y

This may be written (d+ad}+b).y=0; or (d}—a®) (d?—@*).y=0; where
a} + B!=—a, and (a 8)?=8, or a}, GB are the roots of the equation 2? +az+6=0.
: y=A(d}—at)-1.0+ Bd}—6?)-1.0
=Ae**+Be®? (Ex. 1.)
Cor. 1. If a=, we must write a+e instead of G, and proceed as in similar
cases.

The result is y=Ae** +Bae**

Cor. 2. In precisely the same way we may find the solution of the equation

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 2583

If a=, 63, y2 be the roots of the equation z+ 2?+62+¢=0, the solution is
y=A e** + Beh* + Cer

And a similar process applies to equations of all orders, with constant coefficients.

9. It will be seen that in solving these equations, we treat symbols of ope-
ration in exactly the same way as if they were symbols of quantity. Our jus-
tification for so doing is an appeal to the fact, that the laws which regulate
the combination of the former symbols are precisely the same as those which
regulate the combination of the latter. Were it otherwise,—were one of the sym-
bols, for instance, to be subject to a different law relative to its combination with
one class of symbols from that which regulates its combination with another, we
should not be at liberty to separate the operations of such symbols, nor even to
combine them otherwise than in the form in which they are actually presented
to us. An example will illustrate this remark. The combination (d”d”) x (dd”) . u
may be written (d” x d”)?. vu, in which form it is equivalent to a?” a?".u: but the
combination (d”x”) x (d”x").u, when written (as we shall write it) (d™x”)? . u, is not
equivalent to @"2".u. The commutative law, or the law according to which
operations may be taken in any order, is not true of the symbols a”, x”, in their
combination with one another.

We may remark, in addition, that when an operation on y has been changed
into the reciprocal operation on 0 or on X, giving the solution

if

1 : - il :
= = —h6?7>) for instance; the operation :
(D!_ a) (DIB) 0, p (Dia) MB) is resolved
: . 1 1 iE ik ;
into the two operations apt Di oak af g) DE er in the same manner as a

fraction is resolved into its equivalent partial fractions. On this subject the
reader may consult an excellent paper by Mr Boots, in the Cambridge Mathe-
matical Journal, vol. ii., p. 114, where this method is first employed.

dy, #y hs
10. Ex. 4. ae by =X.
This gives y= (dt—a*)—1(d+— B2)-) . (X +0)
N x eps ase nha?. Sit ar o's Saeenle Sae
ey @—a) (@—B}) at_Bi@—at ai—B! a—B?
1

yo=ANe** + Beet

ema { (@t—a)-1X-(@-6) 1X} (Ex. 3,

Cor. -1.. If X=abe;

y=Ae* +Beo*4

dt 1 1
ae (a
apt” \A-at 7p}
VOL. XVI. PART III. OAs

D5A PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

Di eae
r+ar? +b
Cor. 2. If X=6, a constant, ... ,=0 and

aA eo Bie aS

y= et" + Beer + x
Cor. 3. Ifr+a74+b=0, r must be equal either to a or to @. Suppose r=a:

=| __ becomes, by writing a’ +c in place of ,’,
r+ar?+6

then 6,e

,@ +2 are x + ke.) _¢ ots b we*2a?
Qatc+ac Qat+a
2areen® BEE

Qat+a “stast+b

and y=Ae*"+Be +b,

2 en d-ty
Ex. 5. Ea + by=X.
da-1 da? 4

This gives (d~14ad~*+6).y=X.
or (d~!—a-}) (d~*—@-4).y=X; where a~?, B-? are the roots of the equation
#+az+6=0;
(d~t—a-*)-1.X (@-#-B-*)-
C=O aa 2

4 (3:
=e Bee TE {@t-ah-t.ab S d: o> (a! ahi aX —
ae

y= ei ery:

which is reduced to Ex. 2.

ne
In precisely the same manner we may solve the more general equation 2
@

a Sy, 7 ma

+ +&e. +y=X, n being a multiple of a.
dx-* da” 2a

+a

Cuass Il. Hlementary Equations.

11. The form to which more complicated equations can generally be reduced
by
iS y—-mar De) =X; and it is with equations of this form that we are now to be

d x*
occupied. The simplest case, when »=0, we have already solved.

_dby
Bx, y—m/ a5 =O.

__/=D+4
By (C) this is reduced to y—m/— = oy=0,

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 255

or y= (1-myai 2) =i OE
Suppose J=2a.e8. G

3a, foe —m/=T th) =0 by (A);

which can be satisfied only by making 1—m/—1 [n = =0; giving, consequently,

only one value of n -

AS 3
y= —n 1S the complete solution.

Hence
2 2
Cor. If m= Bae Fa
oe ay Oe =|f= pase
|n YT 2 Al ?
n=1 and y= —
—dty ‘ad
Ex. 2. SSN Tee ae
The equation in @ is ff e~

0 (1-my aa Beh) liewest

ea +36. (1—-mv=1 244) ! (Ex. 1 and A)

Cor. If =n; this expression becomes infinite. We must, in this case, write
n+c in place of 7, expand in terms of c, and finally put c=0.

ae —"4(1c 6+ &e.
We have, thus, ~— ie are a S = == ‘ roe
A 7 ay lm 1-mV=1("2? 4 2 fF c+ a.)
|r In dn
—né —né
i. e ahs ce = an ae
Lie ee a RE
ne e-n4 i e-”46

256 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

ee 6, logw 1
7a m/—1 x d n+}

ea 3
Bx.3- ee is i ae =.
d xt
Suppose y=a,2~"; then
jr+1

[r+
1 [r+2
or a a ae i)
nN ay Orit)
Hence the lowest value of 7 is 0, and the values succeed at intervals of 5.
y=A+ o + = + &c., with the relation expressed by (1). By substitution
a tlie ee ae 1/3
oe Cie afg Av Ae=— ap &e
2 Se eee
sc gh tS chen A=7A
x | fa 2/1 [3/9 2
Pipe TE yey ure St) ea
a® /1 /3 |2 & CPA Sipe
Va |2/§ Jr 1 L. 22 <4 Etat pees
Bie sero ies a1 gh te ot.3 Sq a oe
&c., &c., so that
ve 2? 2°
gael lta tage * esa te
1 1 1
= ———
Jt lore 1 ant wate) |
2 2?
Let alt oat T Zqige t &e
1 1
then Gav 3) 9p F Gee &e.
iL i

d 1 1 1
_ ee

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

257
Again, let a + &e
ean Ta V@ 1. a3 x3
1
then Tan NPY 2)= 1.a3 5 — &e
oY 1
ee aa?
dYs 1 il “1
or tea i + 2p =) ¥2=0
CO
and y=A (y,— 7 y,)

By solving the equations for y, and y, we obtain finally
i iL
2 hee, ec enihy
mre (ale tS}
The equations from which y, and y, are determined differ only in the term
which does not contain y; and it will be seen hereafter that similar equations

serve to give the solution of the other differential equations of this class, when 7
is an integer. If a\/—1=m, these equations are

a eee Sly A
dx Tome) a2

ea ey calee | z
dae (5, ~ mm) ¥2= 0

The following method of solving this equation has the ad-

vantage of not appearing to take for granted the form in which y is expressed
in terms of 2.

12. OTHERWISE.

—av =1ae—“=0 gives y= ————__;
g ; d xt 5 d 1—-a/_—1ed!
_liaV=Ied ,

l+atad ad

Now

yg Is the solution of the equation
l+a?ad’ xd

v+a@ad?adiv=0, or of
v dv 1

2 =a
aE RE SO —()
qin ine 2 ,

f EY pe eo

oe dx \2Qa =e) poe

which is the equation for determining y, given above.
VOL. XVI. PART III.

I58 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.
1
wok He,

and y=(l+aV—I1ed)v

which will be seen to coincide with the solution already given.

This second method of solving the equation is by far the most simple and
satisfactory, when once the principles of the calculus of operations are thoroughly
mastered. For the purpose, however, of exhibiting the analogy amongst the dif-
ferential equations which determine the values of the different series which make

3
up a function satisfying the conditions y—m x? “40, I shall employ the first me-
x

thod in the three following examples.

pay
13. Ex. 4. y—ma? —7=0.
let y= A, +4 Bf + &e
t Fi 2
then a ( yi{h Ay 2 As ge
da /L a js a
[z 6
and Ag+ — + > &e =m(—1)'| 2 A, + a a2 +80}
|
OD wee mie gcc eee
eae mr — 1” a mae TA oa
De eA oF a Fie Ae
heap N er Ae ree a,
i Soe ee eee a a gs
25) (68.138 Lia al 688th ote 5.3.13). 1 1; m* mr
&e. = de.
2 1 oF * iz, 1 28 gl i
and y=A, {1+q ma/—an 3.1 ° 1" veo 5.3.1 °3.1 1 i /ln We. }
dy
Rx2 5: — 2—_=(.
It is easily seen that the form of the series into which y may be expanded is this
Be iCe iD
aad ee Soe &e.

C)
+a Bes jy Oy, &e.
eC ee

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 959

and that the result of substitution is

Bee Oe «D) i iS 4
Av+—+—+—+ & e js Ce D )
7 24 | = B + — — ——————— °
of | at m/ i x PARE +r oa &e
eee Oy &e ioe AEN Ye EE &e. )
2 2 IB [3 a |g @
so that
(lL m/-1’ |g m/—1 [l jg m
Soe aC: Sa
[A m/—1 1 ig 4 mV —
pai 2/5 1 4,
/1 |g |4 Pp m*
and also
eB ae a ae a Sala oo 8 oe 6
P= 5 m/v [2 |g m® 2 fg [5 mF —1
2 8 2 [6 a g.
2 |e B ppm
1 eat eA: xd
f= {@j 3m? x * 2 i ee ee

5 5 11
2

2 pao PALL, ay
+3 (ena ag 1 2. Sa 6m 253 2.3.5.6.8.9mé pot &e.) \

kus ie 2-4 a-$-'s )}
eS (2 ade ee ic,
mV —1\ai 3.4m? x? 3.4.6.7 mtx?

Each of these four series is the integral of a differential equation of the se-

cond order.
ay, 1 1 4!
Let da” 3.3m @*t.3.5.3mias &e
a 1
then Cae are a &e.
and PY ay, 5 3 Caan 1 1 &
ad x? nie . 2 2 m? a? 4 A 3 m* ve c
Ws 1 dy,
WS) hah decide
d? y, 1 1 dy, y, 15
or da Ce = dz Az 8

960 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

ar 5 ‘a2
Again, let ae JS 2 + aa
8 dx JH 2.3m? 4% 2.3 5.6m+*t x® a
then Y = 2 are yee 2
2 2 3 m2 xt 9 3 5 6 Fi ae &e.
a2 xy 5
and dx : mnt 2 Eds Re
ee ee ee
a2 ok ax
Py. = i dy, 5 ie
d x? a mnt) da 42
dy 2 2.5
Also let ie tie 2 ee
HN 2
then La re Sma 3.8.23 iagege
P/zy, 3 1 1 2
and de 3 Dye iti. ia Bal s+ &e.
we 1 dy,
4a meat dx
‘ d’ y, (;- il dy, Digi
d x* 2 om =| da 42° 4x
yee es Be * .g-
Lastly, let di, Ge Cidpee See eee
i 1 eS
then =->=+——— - Sere
Ys at 3.4m? at 3.4 Sree Me:
; day + ee
and ’ ae fat eo 4m! ae * ae
1 dy,
m? «i de
Pace en eg
7 da GS= oe

Having found 7, ¥., y;, y, from these equations, we obtain
Sy (89s. TE As dy,, Nw dy,
—— a a ana ae dx )

The remarkable similarity between the equations which determine 4, y,,
ys, Ys leads us to conclude that the form of this function is common to all similar
equations. It may be seen that the equations for y, and y, are identical: the
arbitrary constants must, however, be determined differently in the two: the one
function vanishes when #=o0, the other does not. By solving the equations in a
more general form, and by a more purely symbolical method, we shall be able to

,

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 261

see the reason of this analogy. We shall, in Example 7, exhibit a complete and
general solution of all equations of this form.

dé
Ex. 6. —m x? —2 =0
A B C A B
= 2 1 1 1 ae ae
Let y=Axv?+Ba+C+ eh eS gamers ae
pes ao Be + &e.
av Ue
then Aa? +Bo+C+ 1 4 &e, <mV=1 (Eo? A, +&e.)
Aw Aes |B A, |B
1. —— =, A, = t —,A,= 2__ '— &e.
Payette St my =! 6 .
B B [4 B. jee
pe EN eer eel Np es ed I
emf —Tj2° 2 mf fg? mV I fF ;
Cals C iall8 C, [|
2 Gia ee Gy, ee gn,
BPS 6 wears ° my 1 8
This gives us six separate series.
f AC ah 2 1.2 1.2.6.7
te Ad + wt gtte=AW—sz a) a wy) eee
G2 yak ee 1.2
Let ater Tne Bae eas,
AEE 12
ee 1 345.3 me eee. yt
ii ile piineiatesead wit Lj 2 Und
das 3.4 mat 4.3.$mtat
gl05 ee tA ay
= 32 m x= a 2"
d*y, 3 d*y, 3 dy, 3 105 era y
or Ce Pee ee da So, BF es aot
dy, 3 La, 3 dy 3 105
Br ee ae S270 ace ae
A A Ris 1 te eee 17 eesa9
ait +k, gives — a({-5 7S eet: :
e's, 7-1 sik Age igias ° 5.4.5.8.9.100P oF
Bey. eh Z.3
re al Vik Sema aS

VOL. XVI. PART III. 7 Lit

262

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.
th —2 293 ys vl eee, a 5-3 &e
eS eee 3.4.5 m%0t 3.4.5.8.9.10ma¥
Po ae ad £2
de mx 36 os mt oe
re ES:
2 a’ d x?
dy, Oe Lv \ 2g, 3 dy, . 3 ni
d x3 ve aa) du 42 dz Sg 72—
x 3 Dy, Spates
3°. Ba+ —2+-3 i eel hare es os WE Ceo

43 i Bape 3%
hen 923 pie Pay vee
de/xny, _ §. 8a af 2.3 Sectesiae
d x? 2.3 mat 3.8. Lm4 ge
ee kd 9,
et ie Le ae dx?
aE a aE he 2 LS I
d x3 22 m*x*} dx? 422 dz oe oe lama 16
Bir (dee de
434+ 4+6= = (4- ass y + &e.)
4 xe 2 > m/—1\7? 4.5.6 m? x:

Riis d?
Safi Bs Ti Suppose

| IS en a ee
then ¥,=—2D ee oe
a> zy, me ee 1 th ti f
ae mig © =— ay, the same equation as for y,.
C C, 3.4
5°. Cote: +S fee = ee stat + &e.)
at 4s
he ad x2
x 1
Joo iT ag say Bigg
Tag) Bel, Ae ee
d x? —2°O°O fa? mat ae
Veep L id5 9.

Pus + (5 eC tok ee 3 dy, 3 15
22 =m

d x3 2r6) dx? 422 dx at 84375 — Sa

————

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 263

C, , Gs SmG, oe. =) aBow,oF dd
e : a dk (Ao, Se =— — ae = See)
4 xt ES avai (ae 2.5.6.7 ma?
_vro #y,
m/f —1 dz?

ie ed
ae rea the same as y, ;

Sa ca vm dy, PY 4 vm wy,
and y=4 (75 Ne Ek a) +B (Se + im Jat —

Py, Num _ ay,
ie (ae on i ae)

It is scarcely necessary to point out the analogy which exists between the
differential equations which determine the value of the transcendentals in this

and in the preceding examples.
14. We proceed now to exhibit a general solution of equations of this kind.

pad) =0; » beng any integer.

Bx,.-/. ae psc
The symbolical form of this equation is
a ee Rb d>
2 {naedt (Tata dk x” db

(1)

d
=(1+ m2” d*)v=v+m2x"
dx}

where v is determined by the equation

1
(a ee es
$ dk wv
Le pao pir ame © (gn 5 —0 9
v—m x” d? x” d? 7 = 0 Or v ma © (ano) (2)
Tins dt» _ d®-*z
Let = ————_ + pee
th ee then da”—4
2 (72) ee 1 won ge—ly
dat dat da 2 a x1

(Part I. Art. 11.)

264 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

By substituting this in equation (2) we obtain

gee shi */( nt 2 ill pope &
dank Mm LV) &@ 7 Re td dan) + e.) =0
ne d” z rE ae ib Pimae 1.1 a@—1) dz
ax” 24 m?a2™)dam-1 2.4 242 gan-2
1.1.3%(n—1) (n—2) qr-3 z n-11.1.3...2@n—3
‘oy ding: eae ge cogs Ott SAL a ona 5, oem
' n(n—1)...1_9
qn

When z has been determined from this equation, we shall have the complete
value of y by means of Equation (1.), viz.
Ya a o a —t2

ae pss

y=
Cor. If Wes

0.

d «3 2a m2 ae6)/da?® Aatda 823

d3 z (= ll i Heo oO

which is the same equation as that which we obtained by a totally different pro-
cess for determining y, and y, in Ex. 6.

n d?y
Bx. 3. —ma ——~= XK
2 ° d a?
The solution is
1 Lima dt
=— ——,(X+0) = x
Y 1—m2” ag A +2) 1—m? x" d? a” dt Ce
=(1+m" d?) (v+w)
n au n aw
—v+me +wtm az
dat d xt

where 7 is the same as in the last Example, and w is determined from the
equation

4 nm qt
w—m x” 2 (5) —X
d xt dat

n—1

or by writing — for w, and proceeding as in the last Example,

=] a” n erat d?-ly
oh se ee en ee Se Or
da®—} d x” 2 ae

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION,

di oe: (F5- ax) qv-1 le n(n —1) q-2 4

Dw m2 v2 % dat-1 2.4 a Get Se
Sit yy St eS) =
AWA hee! m(n—1)....1
eu) ST Ske Ra a cae
Cor. 1. If n=1, the equation for determining w is
ies, ( 1 1 xX
dx erase 0S ne
ees -
: i “ e ma mn X
of which the solution is “= ———_— ee Ee
AED m= wt
Ms Ae mz
WE a
: il aE 1
Mm? 22 mx
and y= (1+mx <5) ee 2 oe ee ae

Cor. 2. Ifn=1, X= = it is evident that

u=

Jax ae aaa

6 : b mbV/—1
Ris

where y, is the solution of the equation without X (Ex. 3.)

265

It appears, therefore, that the complete solution of equations of this form is
reduced to the solution of ordinary linear equations, and the determination of the

half differential coefficient of the results.

Ex. 9. y—mnx

nm gr+ &
aethave X+0 limad

Pm at PE me a aE a att

where v+w is the solution of the equation

‘ (1m? 2" drt a q’+t

CeO)

(1)

Now qd’ t+% n dren nN gGrtly

Captian pe BOT Ree, DENG 7 n+
darth” dattt =e dz2ttl a (7+ 3) nx

(r+4) (7-4) ayaa 8
+ 1.9 n(m—1) x eal =

VOL. XVI. PART III.

&e.

oD,
jd" »
daz”

5 =x, where » and r are any whole numbers.
x .

2.66 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

ae ee ed) Siakomsts q27—n+1 Ps
s a pe re
d d®-l x
—s nu Je + 1 n—1 2
ax” G a)ne ie
aoe oe (r— ante Ae oie

qr-@ r+1) Zz

.. the equation for eer v is

(r+3)n ad sit , CES) n(m—1) d™-?

— 2 Wi nudatcr 1.2 ae dx" gt Ge.

aes (r—4)....(r—2 +8)
SOs Pane n

-n(#—1)...1L.2

1 d™-@rtl) » il
hee” CP Cres | ee BET NE Tp FON)

w is the particular value of v corresponding with X=0. Having thus obtained
and w, equation (1) gives the complete value of y. It must be observed, that the
transformation from v to z is only to be made when » is greater than 27+ 1.

Crass III. Equations which are capable of solution by transformation, without
chvision of operations.

15. Ex. 1. y—mx? ay ==)

By (C) this equation is transformed into

y—m(—1)? — Pty =() or
ae
y= (14 m/—1 + SEE 10,

: ; A : 5
Hence, as in Ex. 1, Class 2, the value of y is Y= where 7 is determined

jn+3
|n

by the equation 1+ m/ 1 “+2 —o,

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION
ix. 2. y—m x ce a
ad x?
ae He EN eel
This gives meas (Lim /-1 art) xX
yt /—D
a asi (lamV=1 i a a
gee |r
Cor. If =n, this expression must be reduced, as in Ex. 2, Class 2, to
A b- loge 1 eee +#) -1 1
a” mrt 2x i eee (1tmv=1 cage oi) x
. dn In
Cor. 2. As a ae case, the solution of
dz Ser a
a a Vag is
d as
Ag al 86 i
Pe GEN, EP F

These equations might have been included in the preceding Class, to which
to that Class
Ex. 3.

both in their form and in the mode of their solution, they are very analogous
They are, however, particular cases of Example 5, below, which does not belong

ytaVvx a

— +b al
The equation in 0 is (by C

ga
— /-D+3 —D+1
yravat 2s yo 770
—/—-D+3 ,/-D+1
or {1sav=1 =F — 28 \ _y=0
Suppose y=%a,e "’; then
za, f1+av—7 "tt

_,imtd
|m |n

\ —n Peat 0 by ( A)
Hence any value of » which will satisfy the equation

live «aun ed 2g
In |”
will give a term in the solution.
Lote PEs is Fy
Cor. le If 5 Tee ee aaa

268 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

4—7—n (4—2 1) —2 vii tt
. n

which is satisfied by »=3 and n=1.

Th 8:
Hence ee ere

Cor. 2. If be a whole number 7; /n=1.2...(r—1)

and /n+$=4.3...(7—) Jv

12 tea a1 oe ee eee

will determine the integral values of 7.

If n=r+k, |n =t3 Or va, jos 28 or

and BeBe OPO fir Va 1.2.2 pb OED ee 26

which determines the fractional values of x which have 2 as their denominator.
Now it is evident that these are the only forms which n can assume; there-
fore the determination of the values of 7 is reduced to the solution of these two

equations.
Ex. 4. yravel 4s bn St x.
Let X36 ce . then
y=da,e "+36, (1+4 Vestn — one
wae —nb is La ia ad a
(he Ves [r+1

the values of n being determined as in Example 3.
Cor. If r=p, n=p, we obtain, as in other instances,

ay, log x ae aa
=> —+ C +2 ————— :
g ar P g SS isae /s+1
Vea 2 5 |
/s /s .
h C : |
where = —
ae 7 | i
aV=ig Pts —6b
|p

Ex.

Or

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

The equation in 0 is

which may be written /(—D)y=X;

and y={f(—D)}-! . 0+ff(—D)}-! . X
eS 6b, 27
Tie se

the values of n being determined by the aia f (n)=

d™y “By
Ex. 6. (aarp * +a(axv+)” —_7 + &e. 2)

d a”

Let 2 =a2+, then “2% =a" "4% (Part 1, Art. 27.)
Oa Ol

&. = ae.

1 — ieee ie hy

ae 7 + &e. oe

Py
Ex. 7. i ie

By multiplying by 2 and reducing to differentials in 6, we get

eu —— taVx(— pi /=D+s Set y+) Ly=0

[- D
= D+1 +5)y ge a pedi, Fy 30

/-—D /-D+4
—D+1 4
or —D+4 ; _p! 2 y=
(“Day ta(—1 aoe
eS So
or y+a(—l) Dri y=
Fae
or yta(—l1)’ e aah 0
or ielbu ogy ies aaeetlas) 2
x =D *
ew
or Jig. 4 *#=0,
© du-*

VOL. XVI. PART III.

69

270 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

iLie 2 =0; this gives

-— d-ty
dxz-t
whence pa eee
and y=va=Are”®.

This equation may be integrated in the following manner. The equation

D+1 3 Ls
IDEN oy oy

may be made to depend on the equation

yal ee

6
e? v=0

OB
aA lire res?

: D+1 /—D+4
by the relation y=P, ae 2 5 v, Where

P, f(D)=s (D) f D-4) f D-1) &e. .......
y=? 4 ”
DO) =a.

== ov -

=F, ()= te
= Dv

ao e? v=0 is equivalent, by (D), to

|=
Now v+avVv—1 a yee Tea

‘0-4

we ON ROL ex fe v=0

d-*
or ae ae

whence p= Ane
y= Axe“* the same result as before.

This process, which is due to Mr Bootg, is of great importance in the solu-
tion of certain classes of ordinary linear equations, but I have not, as yet, found
it very extensively applicable to equations with fractional indices.

Ex. 8. More generally, to investigate the conditions of integrability of the equation

dy ak OO
Det aie ere

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

The symbolical form is

c- /=D+1 gauge ts ag

=D [=D
or +(-DadgtaV—t Sees .e"’ y=0, by (D).

This is reducible,
1. When c=n—2; and it becomes, by dividing, by —D+n-—3,

/—D+n
or ; a =A ed y= Es s7=0
or aVaTy-e $ DF BOA) 6
a mh fives ae 0
If yx——) =», this equation becomes
av gt a4 =0, or
aope-nte ee =0

which is integrable when n=, 0, —3, —1, &c. (Class. 2.)
2. When c=n, the equation becomes

[/—-_Dint+t 4,

2 7) =
ytanv ies e 0
or LZ eal aaa eg,
[-D+n+%
pee 4/—D+4 _ ane
or a —ly—e fae 1 ore 0
d® y
or CL aoe re ere
If = == this equation becomes
Brean
av+e@r cae =0; the same as before.

dy 3d? y 3 4.—
Ex. 9. adel a —2y=0.

71

279 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

The symbolical form is

ae yra(—l)*e a “y+ ty=0.
—D+3 3
or _ 3)y+a(—l1l o> 70)
(=D4fyte(—1) Sot y
2 a
or yea (1 D =e 7 y=0,
sg UIST EL wl
or Pears =p =a)
Y
or y—ae’ ea =
dxt
a,
dt
Ogos =O
or = aay

1
ee = i
y=AVae (5 JX

Rx. 10: =

The symbolical form of the equation is

d +
ytan # +2" (£4 +Cx

eee, asl,
vinta ff timing

dz

(Ex. 3, Class 2.)

d

} +0.
Hed

gl D+l pte = ee +4) ws
ee: ey ea
or (+@¢D)y—60/—1e" = (1+¢D- 5) -y=0 (1).

This equation may be reduced in several instances :

Anode — - the equation becomes

(1+aD)y—6b ns ]

- taD) y~ 56/27

or y 5 = /—Dyn—3
/—D+n

(—D— /—D+n—-%)

or yt ave

ieee 2 =1—n, equation (2) is reduced to

1) Pa
=p

(n

(n—4)6

y—0,

[D+ (6-49 py (D)

e ~ DP y =0. (2.)

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. O78

n— D+
which is equivalent to y yet Oe aero 26 /—

=== 0
a
4 26 rdiay 1 _
or Oe Cee =0, or, if v=zy,
2b ,@ »v Pee : , ;
v + =— x” — =0, which is the form integrated in Class 1
3a dau?
b= ee 5 =n, equation (2) becomes
Dh din ep {/=D+n (n—4)6
Zo) Gig BA Set —0
which is equivalent to y + —_,—— a alle ere ea z y=0
=
: 2b ,dby

which is of the same form as in the last case.
B. If ¢ is not equal to z, we have from equation (1) by (D.)

CMOS re ca ee DE D+n (1+e D—en)

_ o(— 48 0
/—D+n—-4 ; aes
—-l+eD-—cn /—Din i
6b — = (m-3)b yy —
yro¥—l ey a0). =) caer ie

3. If re =a this gives

—Een

yt+b/—1 (1l-en) ——— .y=9

db y
or yt+b(l—cn) a” —— Jab = the same form as before.

16. It would be improper to dismiss this equation without remarking the
fact that it would appear to have been solved by M. BesGE in LiovuvILue’s Jowr-
nal 1844, ix., 294. The solution is, however, given without any demonstration,
and is, if I mistake not, rather a differential equation jormed than a differential
equation solved. The whole which appears is as follows :

66 1 6) diy dy d? Y
Let m, n, p, q be functions of w, and 7 t™ ne ca te ae the
proposed equation.

“If we have a +mn—p=0, the given equation can be reduced to the follow-

5 bs : . : d ”
ing, ot +my=z, where z is obtained from the equation at nm 2=9-
a

aa
VOL. XVI. PART III. BoZ,

274 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.
Now, on examination, it appears that the proposed equation is nothing more
: : 6 :
than the differential coefficient of the quantity em y—z=0 added to n times
x

the quantity itself: Thus,

d (dty diy a
4 (Sons) sn(Zfomrer)

gives
dy doy. dm dz d>y
es MO Oe — Ge thy tmny—nz=0
or FD ON eae Cae (“2 +m n— =
dx: dx dat PI~ de dx p)u=a

; d d
provided 7. tne=g and 7 tmn—p=0.

Thus it appears that the equation is not solved but formed: and this is pro-
bably all M. Besce intends. How he can justify his additional remark, that
d* y
d x?
able to conjecture.

———+my=z can be solved if m is a constant, or a linear function of 2, I am un-

Ciass 4. Equations which are capable of solution by the division of operations.

17. We have already met with several equations in Class 1, where the total
operation was found to be equivalent to the product of two or more partial opera-
tions; and in Art. 9 we have pointed out the manner in which the partial opera-
tions are applied, viz., by decomposing the total operation in exactly the same way
as an ordinary fraction is decomposed into partial fractions.

ES

4
ze a a 0.

Bx ai. Dee * 74

This equation, when reduced to the symbolical form, is

a

+

—_
i ii os

Oty eae es
y+ae pete PIE Ditth ep tile [alts 09

|-D ie

a Th oe PS
eps EBED. dy te (SEE). domo

Now pH es egg | aE ee
/—D+1 /-D+% /—D+2 /—D+1

/—-D+2 ye /-D+14/-D+1 @
— —3 = .e?y by (D
(S55 Abe =Dae /2Da4 ey by (D)

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 275
and the equation is reduced to

+. /—D+1 /—-D+1 ¢/—D+1 ¢
4 = .e a GH: Dry fy yar ‘

: SDT a
Let us abbreviate the operation = = = €* by @, and the equation becomes

(1+6/7—1 b—2a¢°) .y=0.
If14+6/—1z2—-2a2=(1+az) (1+); this equation is equivalent to
(l+a$)+8)y=0

1
or

as > 5 = us : 1 0 — p Celene
Q+ap)Q+8p) “a-B I+ap ~ a—B1+8
Now Lea pala ap tea a
ite A/a

Hence the solution of the given equation is reduced to the solution of the
two equations

=e 24D ee
age Cl). ares 0

or Teer ees “Troi =0, y¥,-@W— 122 =

Now these equations have been solved in Class 2, Ex. 3, and they give
1

1
Ae Ss ve)
oa hee DSO ia Ta

L
Ber ad“ ze 3}
eS REG oi

a 1
y=

(l—a@) a8)

and

oY Se
= Gap kroy Nap 1 eG) :

- .
“aap eh eee

a

28 ae Pes fal Ja ae)

It will be readily seen that B is not an arbitrary constant, independent of A

276 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

(See Art. 18.) For when 6=0, the equation becomes an ordinary linear equation

u
e2ax

of the first degree, of which the solution is y=C

AB ;
In this case a=@ and A=—B:

we may therefore write B=—A generally, and we obtain as the complete solution

1
Lf is ps Ni ect yA re ue =
The above son may be reduced Li thus. The symbolical form
jee bee Spt 2de —— ==)
may be written
1 nt see i
by Sale |S Die 2 alias ie. Nagel
or aac pay DS ig hs ee y=0,
: bf 1 (/—D__*. | Le J pas
or hee =e eer a Ee ae a | eis,
or ee =D en? age a = iD. Ones
2 Nal os Diaae : 2a /—D+4 = pes BAS
hich is of the f lee ee PT
which is of the form (1——5—— ae yea )y=0;
of which the solutions are
i
I+ [Pl y=o and (1 + ao) y= 0, OF
1 2Spes iy = Se
y +— e= ———— == (()- and ¥+— eF ——— 4 y=0,
Yate € ap Ome y 8° an Cay,
i di they 1 Gt oy
id — ———— = 0, and — Se
is Val dat-# ‘ce/aidat =
which, on differentiation to the index 4, give the same results as before.
s dty ody
Ex. 2. ee Oe es +2ax Ten
The solution is, as in merce A
y= X +0 mics Bam X+0
; ap ae ye: a6 1+ 66 af)

a

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. aT

Now eae! is the solution of the equation y,-—aW/—1~2 a ib See ot 83 which
(Class II, Ex. 8, Cor. 1) is
1 1 1
ds (act Age of fo )
(I+av= alias oe) Ma tn wae

and a similar equation results for 6. Hence the solution of the given equation
is known.

18. It must be remarked of this solution, that it is not in all cases complete
without the introduction of the complementary (or arbitrary) function. This
arises from the circumstance that when y contains positive integral powers of «,

Ps + 4
ad) =(0, whereas 2 ey Asp uv is not equal to 0.
da x dx dx

Hence «? = + tay can be replaced by the latter function only by the con-

Y a
vention that = is not to be written 0 when n is a positive integer.

5 : : é : 1
On account of this convention, the solution of the equation Itap y=X must

contain, besides the expression given for it above, a series of positive integral
powers of 2; and hence y, the solution of Equation (2), is incomplete without the
addition of such a function. It is probable, however, that the determination of a
relation between the arbitrary constants may give a solution possessing all the
generality which the science is capable of. We have already given an example
of the mode of avoiding arbitrary functions by introducing such a relation in
Example 1. We shall offer another as a corollary.

Cor. If X= ie the solution is (Class 2, Ex. 8, Cor 2.)

a “eB (eee ge) aa (4-5

=y,+ = —(a + B) a3 + arbitrary function

) +arbitrary function

Sak oe + 8) qe Pete + he.

Now if we examine the equation which connects together p, g, &c., we shall
find that it is the same as that which determines y, in Class 2, Ex. 3, having only
2a in place of a2. Hence it is contained in the solution of the given equation
when 6 and X are omitted. It is, therefore, itself only a supplementary term
in the sclution of the given equation, and its place may be supplied, appa-

VOL. XVI. PART III. 4A

278 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

rently without any sacrifice of generality, by the introduction of a relation be-

tween A and B. The relation is, gee
Hence the complete solution of the equation
dt y

ion
ody
ytaxnytbhea ee: 4+2ax qe =

eiakes Pte) (at beled) Lhe

= ly
19. Ex. 3. Paton Tae

=—3
To (a4 bx) “Y 1954 356,
dx-

Multiply by «—%, and the result will be
a? i ly —2 —3
a2 y+anu-2 tears @ 234.6 2-2) @ Pate pt2be-% 549

of which the symbolical form is

—26 _,/—D-1 =) oe
Vein Be waa SG CR" 4h) a ry
1 /-

which is equivalent to

vs OF LP 1 ) -1 ( 1 2

ee et GS neat (D+1 (D+2)) 7 +1) D+2- Ds) 1D Ws9) 9=
24 Ale — 1 =

or He EERO ya! Pay aan

Hence, by multiplication,

a iL 1 9
-5(D+2) (D+3) e-* 4 y—| (D+2) (D+3) e-24 y=0
1
or —F (D+2)e~4 y— (D+2)e~* (D+.2)e~" y=0 by (B)

which is of the form ( ty > 2 79”) ys
which, being put under the form
(l+a@) (1+@¢)y=0 gives
y=A(l+ag)-!.0+B(14+6¢)-!
Now (1+a¢)~'.0 is the solution of the equation

aad
y,+a(D+2)y,e- ’=0 ONT =

=

: Be ge
of which the result is n=> e *,

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 279

a

Hence — e %+ = e ® is the complete solution of the given equation.

In my second Memoir on this subject, | exemplified the use of a theorem in
general differentiation, by solving the problem of determining the law of force by
which the particles of a sphere must act on a point, so that the whole attraction
may be the same as if the sphere were collected at its centre of gravity. The
solution of this problem led to a differential equation which was shewn, by an
indirect process, to be satisfied by the law of force varying as the distance, or in-
versely as its square. I propose, at present, to solve this differential equation.

Ex. 4. The equation is (vol. xiv., ae 608).

2+3aR+

be 7 [8 aR (a+R)

d-> 4 Aq
att =FR LS

where y= f (e+ a), 2=2R, a=a—R.
This becomes, by substitution,

2 \d Ay Bond, & gy da? y
MR a) pee ga

d~*y tray ay? 2
+24(a4 +5) aes g4Q 4 = 5a ue 2.

Dividing by z*, we get
4a? d-*y 2a d-Py Seda gititads y 2d- ry

z+ dz-2 if dz-2 28 ae Ze de 8 2 d2-8
Q4ad-*y 12d-*y 24d 2 a? f (a)
Te Ce eS ee 55 2
Writing < for z, and (—1)-« === :
| ead 2
lical form
— D=2 Deo D8
ON ad i el 1p Gen Eas ye 8 ate —26/
= y a =p y <a eeaa ay —=— y
J Sis pa a
+i 7 — +2! — OL rp ee
ae = y =D yt ae ED y
D—4 D 2 .
+12 Sy 424 a ya Fe f(a) mle

or, collecting the terms,

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

280
+ae* {2s Ot elo 2}
rate {go 4D} y = 2 af (a)e-*

which being reduced gives

2(D+1)(D+2) =a

=a O41) —
1
Or ~ +3) O+H WF5)7

1 i
2 g2e-24 he 26
+2a’e (D+2)(D ay? Tae ee

Now y=/(a+z), but since a is itself a function of 2, we cannot proceed fur-
ther with the reduction of this equation by division, but must proceed to obtain a
relation between « and R or a and z.

To do this we shall expand / (a +z) by Taytor’s Theorem.

The result is

y= tL = = which being substituted in the reduced equation, cives by (A)
In

ey a ee
(D+ 2) (D+ 3) (D+4)

d™ f(a) en? =A
a es d a =) erarese (n+ 9)

ah at e274 \-2 —26
*Gib@sa Gab. “Gamat sis eo

But a=a—R= a—5: hence

f(@)_@fa w*tya.
ia? is ioe

which being substituted for a the sum being taken for n and p, we get

pt eal aires le Se
mP QP da®*P [n+] fp+1 { (m+) (w+ 4) (wn +5)
emg sea 2a tP 2 \ ae fa
+ (1 +2) (n+8) +4) * 42) (n43)$ —3
every integer value of n and p being taken from 0 to 0.
When x=0, p=0, the left-hand side gives

—fa. adfa
60° Se

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 221

Ped Ue tl ee Gi ee
a ilgeaenen ete

et 2 a fa a2. d fa psdrarian
IP Song ie ait eae 12 a?
a aM sf d fa ata’ fa- a d* fa
n=2,2=0, 799 aa * 120 d@ +20 dat?

&e., de.

Hence we obtain, by collecting the terms and equating their sum to ae

Chie apa ae Afia a a? fa -
32 60. 60 da, 420 dae * + *tRAt Se.

Equating coefficients of like powers of z, we obtain
S@. G@4f a @ Gd fa
0 + 00 da ti da ~?

This equation will determine / (a), the only law of force by which a sphere
can attract an external particle exactly as much as if it were all collected at its
centre of gravity.

The symbolical form of the equation is

{D (D—1)+2D—2}fa=0

or (D? + D—2) fa=0, or (D—1) (D+ 2) fa=0.
Hence (D—1) fa=0, (D+ 2) fa=0,
or <f4_ Fa, and “14 =—2f¢

that is fa=Aa, and fa= 2 are particular integrals, and the complete integral is

y=Aato which is the law required.

SEecTION If. SIMULTANEOUS EQUATIONS.

20. To effect the solution of simultaneous equations, we must eliminate one
of the quantities differentiated. This is best effected by treating both the differ-
VOU. Vi. PART III. 4B

229 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

entiation and the multiplication by a constant in the same manner, regarding both
the one and the other as an operation. A similar process has been employed for
the solution of ordinary simultaneous equations by Mr Grecory in the Cambridge
Mathematical Journal, i. 1738.

1p. Syed
° : . 2
By taking the 4 differential of the first equation, we get - +a vt =0; which,
by virtue of the second, gives

of _abe= 0; ora=Ac** oy=—A [Pore

dt at
‘ KA ,
Ex. 2. Te +ay +b6x=0, at + dy + bax 0.

These equations may be written

sabi of ey Pee
(, +)e+ay= (+) y+la=0;

whence, by eliminating y, we obtain

{ (Fa+4) Gat) -av} 20
Let a?, G2, be the roots of the equation

(e+a’) (¢+6)—av’=0

then i= — a’) - 6") x=0; which gives

a=A e*'+ Bet

and fae ee er

dt x
Ex. 3. es

{ Gat?) Gat?)—o¥} == Gare) 10-9

= (4)
This coincides with Ex. 4, Class 1, and the solution is

1 1
Lay Ab ace Bt, pee, Be Oe No
ee ge -- a) $i ote 6) b (0)

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 283

+

Ex. 4. +ax+by+e2=0
aby ;
a9 +a x+Uy+e72=0
d} z

ae % pa’utd'yte’z=0

These equations can be written in the form
Agv+by+ez=0
adx+By+e2=0
a’ a+b" y+O0"z=0
_ By eliminating y and ¢ we obtain
fA B C’—8'¢ A—a’ cB—a' 60" +a b' c+" bclw=0

3

or { a? +(a+0' ) d ee cl b ua d? b Ui
18 +e qt @ ac’ + Se ae c

de d* dé
0 Ae a Oe 0 Ct 0 C= 0 Ol e.
d t? d t} dt}
+a'era’be } «2=0

4 a tacl4¥ e—be'—a'e Ha

dz
or { ;
d ¢

capital eiieeiar

dt?

which is of the same form as Cor. 2, Ex. 3, Class 1, and its integral is therefore
known.

oe az, we have by + cz=/(t) by the first of the three equations,

by
and ae oH 229 (¢) by differentiation, whence, by substituting the values of
bs
vt oo and © = = from the second and third equations, there results a second equation

between y, z, and ¢. From these two equations y and z are determined in terms
of t.

, dz
Ex. 5. Given Eee pg SID ic A

These equations may be written
(d+ad!+b)x=(pdtqdit+r)y
(d+ dt+6)a=(pd+qddt+r)y

284 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

(p'd+q di+9) (d+adi+b)x=(pd+qd?+r)(d+ad+v)z

/ ad x / / / d? x av if
or (p—P’) Fda da dae Mae Oar eo
t d t?
, dx U / d? x
—p b—ga-r) 7 +qbtra'—g b—ra) if

+rb'—r b6)x=0
which coincides with the general form Cor. 2, Ex. 3, Class 1.

Section III. Parriat DIFFERENTIAL EQUATIONS.

21. In order to effect the solution of partial differential equations in which
the operation with respect to x is totally independent of the operation with
respect to y, we must distinguish the operation of differentiation in the two cases
by different symbols. Let d stand for = 0 for i : then in solving the equation
with respect to d, we may treat 0 as a constant, and vice versd.

Bx. 1. Bs #2 Wo,
dx? dy*
Write this equation (d!—006!)z=0: In this form it coincides with Ex. 1,
Class 1, and its solution is z=Ae”*®*.
Now A is an arbitrary function of y; call it f(y): then z=e”** f(y), where

e” => represents an operation on / (y).

But since ty rkasys Ze ks
=(14+40+ he.) f(y)
ey)

it is evident that z=f(y+02).
‘ d>z dz
Ex. 2 wae a dy’

This equation may be written (d}—a 0) z=0.
aera
Now ve y dwe@-” -J/a (GREGORY'S Lxamples, p. 499.)

vy co
Vref ae ae ae ev *™ Fy)

9

=y Zdwe *ee2X" sy) Gt o=aVzd)

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

=f jawem “f(yt2wanz)
which is the solution of the equation in the form of a definite integral.

diz Das
a aS SS ar,
dx dy

The first form of the solution is evidently
ze D+ePa Fy)
which is reduced to exe” ® o@ f(y + 2acz)

Hx. 3.

—e 2 2
ie dwe * f(y+2acx+2wa,/z)
ae pe
as in Example 2.
dz d ad az
tls feed eS p Cn,
Ex. 4. ea ae dt da

This equation may be written (d—2ad>5+a? 6?—c*)z=0,
which is of the form of Ex. 3, Class 1, and the solution is
gaeiee@eP f2aced f(y) 4 p—2a0nd b (y)}
=e te ah § Fy 4+ 2acz)+h(y—2acz)}

= f aee* tf(yt2acat+2wa/x)+p(y—2acx+2waJa)}

dz ad? di dz
Ex. 5. de ae dy NS ae
This equation gives (d—2ad}! 6!+.a?0)z=0
or z=e™™ Fy) tee"? h(y) (Class 1, Ex. 3. Cor. 1.)
=f(yt+a@ x)+a (y+a?x)
5
Ex. 6. Teta g 7 ae

Fes +a ek . dy! 2+ dy
This equation may be written (d+a0! d}+6d0—c)z=0
which coincides with Ex. 3, Class 1; and the solution is
amer* f(y) +e (y)
where a?, @? are the roots of the equation in 7
v+a 0? vt+b0—c=0:

2 Teayintal) .
or A pth a OA (G—2) d+

VOL. XVI. PART III. 4c

285

9286 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.
a? 4 a Ny :
or c— 50) d+e-ad (G2) d+6

B= Se Mca a
pe Ee AE py 0 AE

S(y)t+e

s—_—

C4

o(y}

nh ae ety J (2 -)re r(v+¢ a eps} adn J (2-> pre ila +09) }

These expressions do not appear to be susceptible of further reduction, ex-
cept in particular cases.

2
Cor. Let b=F3 then

pee er gs Ca a) + en BME oh (yO i

To reduce this expression, it may ay be sufficiently Biles: to suppose
the symbol 6! to include both the positive and negative signs, in which case we

may write only one of the functions e- *° oy I ( y+ >).

co _- east: Jee
Now a = pe dae ( =) (See Grecory’s Hwamples, p. 499.)
c Of
Let ees then
a x5
ety Ls = ( 2022
eee as rae ( FRA
ey oe 2
and z=e°" | alae
+ eee?
ae 4 29
me — ts Cage
ne ase f(9+4 aay

SrectTIon IV. DIFFERENCES.

22. The definition of the difference of wu, as it is commonly written by

English authors is v.41 —2. We shall retain this definition, and generalize it by
d d
writing ¢* u, for vz+1, and consequently (c?*—1) «, for Ave.

The results which we shall produce from this definition, as applied to frac-

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 287

tional values of the index of difference will, in most cases, differ not at all from
the results obtained in the ordinary calculus of differences. We offer them only
for the purpose of exhibiting those formulze which possess all the generality which
can be desired, at a single glance.
Suppose, then, Aw,.=/(w,)=%,
d ad

Bo oa (et i) Gye (t= 1)?u,, &e.

and, according to the axiom of the calculus of operations that the repetitions of
d
equivalent operations are equivalent, we shall have generally A“ u. = (e¢*—1)"u, :

whatever » may be. This, then, may be said to be the definition of A” uz.
d d
Also, since ve+n=¢ ¢* uw by Taytor’s Theorem, and A w»=(e7*—1) ue; it fol-
lows that Ue tn= (1+ A)” Ugs .
We proceed now to apply it to the demonstration of the theorems which con-
nect together A” u,4;, and we+p, &C.

d

d d
ae Ce (n—1) — ae (n— 2)
Cl): Anu,=(e4*—1) u,= (e d2_ ne aay paar ee —&e.) Ux
n (n—1)

—Ugen—eUzen-1 Yo Uy +n XC.
Corn. I. if »=—t1; AW! ty = Uy 1 + Uy 9+ Uy + he.
Ge BM, =U, _1 + Uy_9+U,_3+&c. together with an arbitrary constant ;
or Uy =A Un 1 +A Ug gt AU, 3+ Ke.
Cor. 2. Ifm=—2; Yu,=uy_9+2t,_3+3Uz_4 +&e. together with A+B«.
d d

d
whe as Ne
Q). an u,=(—1)" (1—oF Yu, =(—" dnt" Ne a2_bou,

=(-1)"(u, —nu,..+"

-1),

n
Tg “+2—8)

Cor. 1. Ifm=—1, a7? u,=3u,= — (vp +Un41+%r42+&e.); to which we may
add an arbitrary constant.

Cor. 2. If n=—2, Pu,=u,+2u,41+3uU,42+&e. together with A+Bz.

nd = a n ad = os
(3). A u,=e** (‘ — ) tigeed® - ) Un
ole ed e_y

d d
—n

=e 42 (1+¢%—-1-1) Un

288 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

d d ad
—g de {1—n (et eDiets (e4 2 aay tsice, }

d

=f 7 {aga es Un, + ——— saw U »—ke, |
=Up ind ees A” tty pn —&e.
‘ = n (n+ 1)
or Meant gen Ti a Be tn 7 We:
a
n —n ett Sl
(4). gal) ce : ) Un
Atte |
d d d
ae

2d
—n — —1 a —2
=(—1) {l+nel (e* *—1) +2 Qe) fe (*—1) + de. } we

= n(n+1
=(-1) { te 3 tty a+ Mee eh te 2+ ke. |

n et —n
(5). A U,=\—; —1 Uy
=
apo tod " eee * EIS 7
={e el (ee 1) +ne A aes 1) +é&e Yue
1 n(n+1 2
=A"u, ,tna”* Meee ee Un m9 + Wie.

These formule are all quite independent of the value of n, and serve to con-
nect the nth difference of a function of # with differences of functions of x +n, &.,
z+1, &e.

We shall now obtain the converse series of connections, those of u,,,, with
Un, &C.

(6). Unyn=A1+A)"u,=1+nAa+

n(n—1) ,» -
“To & + &.) wu,

=n, +n Au, es 5) A? ng + &e.

(7). tig an =(A+1)"a, = rbecritene Te

+ Ge.) u,
n(n—1) )y

TD unt be.

=i
=A Up tMA’ thy +

If n were a positive integer, formula (1) would coincide with formula (2) ;
and formula (6) with formula (7); but in our present calculus they are by no
means the same thing.

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 989

1 —n A —n
A n(nm+1) A? )
=(1+n,2-+ io (eae ye

n(n+1
=U, +n AU, 1+ = ue Uy, 2+ &e.

Cor. If 2=1, wu, 41 =Uy +A Ug_1 +A? U,_9+ &e.

9.) u=(-1)” (53-1) ms

=(—1)-” (a-” (1+a)y"+na-@t) (14 a)"*! + &e.) u,

7: —n fn n+1 n (n+1) n+2
=(—1) {3", +72 Ue to ts ngat hee}

In strictness we ought to write a-” for 3", but the latter notation is more
familiar to the eye.

PELL TIAN OTA Aa eine i
(10.) Bama (—) Un, =A G-75) ta

=A, + n A” ty A GODT Ke U, 9+ Me.

Formula (10) is a particular form of formula (1), for by formula (1),
mau, +mM U,_1+&e., which is reduced to (10) by multiplying by a”. Inthe
same manner we may reproduce formula (2.)

The last class of relations which we shall produce are such as do not depend
on the general expansion of the binomial.

NEO

ae no ett]

ax a“

(11.) Usps = 2 = u,
et %@_]

d d d
(n—1)— (n—2)-— + (n—3)——
=(e*"—1) (e OS ae Cielo 7? 1 &e.) the

d
=" 1) (Me 4n—1 + Up 4n—-2Un+n—3 + &e.)

=A Ua nH 1tA Upen—at A Uptn—3+ Ke.
Cor. 1. Ifn=0; u,=Au,_1+44,_9t AU, 3+ &e.,
which coincides with Cor. 1., formula (1.)
Cor. 2. If n be a positive integer
Un n= Ug an LEA Upin—-gt Ge. +AU, 7 +AU, +A U,_1+ he.
=A Upp nt Ugyn—gthe. +AU, 1+ 4%, +%~; by Cor. 1.

VOL. XVI. PART III. 4D

29() PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

(12.) Ue og ee ee,

a al. (Moretti 42) 2.
= —(e%*—1) (e 7 * +e dO @
= —(A Ug i ntA Ugengt1 tA Uganso+ Xe.)
Cor. If 2=0, 3 a, = —(uypt+ Up 41 +494 &e.),

which coincides with Cor. 1, formula (2.)

d \d d
(n—1) — Ease (m —1)— 1
(13.) Wa, =e da oda Un =e = 5

“=e 5 + &e. ) Up

=Up4n—-1tA Ue 4m — Qt A? Ue -n—3 + Ge.
which coincides with the Cor. to formula (8).
Thus formule (1), (2), and (8), include formulze (11), (12), and (13).
It is evident that by the same process all the ordinary formule in finite dif-

ferences, which are usually obtained by the aid of generating functions, may be
easily obtained.

For example the following :

1)?-1 1yP—1?. ~+1?—2
(14.) tear = (0) faye GEESE at, + StU at u,_2+&e. }
2_ 42
—n {te +7 534? t-9+ ke.
a
We have ane ‘Tra =
Loo {1-a +a) } {1-;%. \
1+A
a

1 1l+a ¥

an 5 in?

oN aia Da pace

Now aaa when expanded in terms of a, gives as the coefficient of a”,

(n+1)?—1?

(n+) {1+ e353

2 + &e. }

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 291

Hence, if we equate the coefficients of a” in the two equivalent expressions

a

me ET) and si ta ap du eat rh

l—a(i+a)” ( Sees ee aad) e
@-a?-$2 aa 4#*

the result will be
(ESD; Ss on
eo (FIIs Tse wanes ha

(1+a)"u;=(n+1) {1+
a? i
of +i33 Z. 5 5 eat he pewee

—_

— 12
or tig n= (N+) pee =

Die A265. }

n?—l? |
—n A ae ty 9+ ave. }

24. Let us apply these formule to examples.
Ex. 1. Let w,=e°*, then

a
Au, w= (et “—1)" e%%= (e%—1)" e** (by A.)
Ex. 2. Let u,=«, n=4, then, formula (2),

aaa=V_1 abe So a (a +3) +60. }

ie ieee
=/-1e pele

+ &e.)

Ex.3. a"e=(-1)"(2-n@+1)+ Levees )
= (Te -2"=n(-1)" (1-4 G9) _ ae.)

=(—1)"2(1—1)"—n(—1)" A—1)"-3
which is zero when z is greater than 1, finite only when »=1, in which case it is
1; and infinite when n is less than 1.

It is evident that this introduction of « may indicate simply that the form
of the expansion is incorrect: for a © #=0(*#+1)—« «=2+ const. is the analytical

result of the equation a z=(2+1)—z=02. +const., by dividing both sides by the
symbol 0.

292 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

When 1 is less than 1, therefore, it is necessary to seek some other method
of obtaining the nth difference. The following method, analogous to that by
which we obtained the nth differential coefficient of a logarithm in Art. 2 appears
to be the most simple.

Let x be represented by “ Sa where q is of a higher order than p, and
both are 0.
Then aC r= (e? —1)” Co (e4—1)” el ®

ie

(p+ Pat E+ be)" o? (gt be.)e”
iL,

5 2
(p +77 5 + &e.)" (l+p2+ &e.)— (9+ 445+ &e.)" (1+9¢2+d&c.)

Pp

wd n prt? n(3n+1) n+2 es n_ ng t!_n(8n+1) wee ;

n+1 ngrt?

n+2
a gL ah ts a a Sr

Pp

per? gut?
5 + &e—= + &e.
es = a

+ &e.

If n>0<1, every part vanishes except the constant, which is infinite: if
n=1, Ax=1; if nl, every term is zero.

If n is negative, there will still exist the infinite constant which may be re-
garded as part of the arbitrary constant; there will also exist in some instances
infinite functions of «, which, as will easily be seen, may be considered in those
cases as part of the arbitrary functions.

Let »=—1; then

p+ &e.
A7 a = const. eS aaa

= const. + —_

Let n= —2) ‘and

2

pa
A” “#=const. + const. 7— tae

and so on.
Ex. 4, NA aaa Hetn (nin Dae (~w+n—2)"—&e.

by the first formula.

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 993

Ex. 5. pee. =(-— oy fs eel oad 2 +é&e. }

(a+a)” (a+a)” (at+a#+1)™

=(-—1)”" ay 3 if aw=at+e2

Ex. 6. To find att

piiey ete eh ay 1
By formula (2), 4° >= =i{- i | at onan he
9S ages
Let aes Free Cc
d 1 bet
then dg 79" g9- 5G 9” &e,)
=y"* (1-9)
oe 1
— and tiaviif y-*(l-y)' dy
= of Mae fT ee
ju+3

Ex. 7. To find a” z

ey ees 1 n n(n—1) 1
(Sat oo sea 8}

: a+ 1
Let en + &e.
Zz z+1
d n
then oa =y’-!(1-y)
nl n I nol n
and are a(-1 fl x) day" dy

Cay Fenny EE

Cor. 1. If n be a whole ERED [etn+1 =z (441)... (e+n) |x

oak a 1.2.
ae 1 z (e+)... (+m)
Con. 2. Ifm=4.a ee gaa

Ex. 8. To jind, a" —, m being any integer.

nel 1" a 1 a n (n—1) 1
a ee) gn ~ a4 y™ 1.2 (4+2)™
VOL. XVI. PART III. 45

—é&e. } by formula (2).

994 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

Let putin Sas
Bm "Cee 1)”

then (v 7) “omy (L—y)”

v= fief --..- (m times) ... y? d—y)?.
and a =(- i seas -y (l-y)".

Ex. 9. To find a” sin az.

+ &.

d
feet = 1 daz “ aazVv—1 -arV—1
A” sin Cer, Fry (e ° — 1)” ( e )
Ps 1 aWV—1 n a2V¥—1 —aV=1 n ~atV—1
aha —1)"e ( —1)"e \
1 SV=1 0 SVT WT tara
BY sae | {@ ih

SV=1 0 -SVIL EW Ti taeWN1
—(-1)"(e —e \"e

1 Ader ale sete a Sa BLS
SSS sins)" { (cos ax+ "4 VW —1 sinazx+ >)

—(cos 2X4 1n7—V/—1 sin2X+4+1n7) (cosa +S —~/—1 sin ars) }

i (Dn/ sin 4 cos (ax+ >) + /—1 sin (ax+ 5)

—cos (2XFInw+ax+ 2) +/—1 sin (20a wart) }

= 2” (/—1)"-1 sin” 5 sin (ax+ at 2A am) (sinDAF1 AZ be,
=2" (cos nrm—V/ —1 1 sin 2 r 7) sin "5 sin (ax+~ en):

r and A being any integers.
Ex. 10. To find a” e™® sin ax.

d
A” eme sin aa (e°*—1)" (emat ae A al —eme—aaN—1)
1 Vr1 Voi es Gaal
=- —— {(er* -1)"e emerax Ser a =? emt—ae }
2/1
em x

ae ev me

; {(e" cosa+e"/—1 sin a—1)" (cosax+ /—1 sin az)

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 995

—(e™ cos a—e” 4/ —1 sina—1)" (cos az—V/ —1 sin az)}

Let e™ cos a—1=P cos 0, e” sin a=P sin 0;
a
then P2—e?™ Je" cosa+1, and tan 0=—° 9?
ée” cos a—i

me x ee, ——— =
o. A®e™? sinaw=——-— P” {(cosm2AT+04+V—1sinn2A7 +0) (cosax+V/—1 sin a2)

27-1
—(cos2N 7+ 0—V/7 —1 sin 2 7 + 0) (cosaz—V/—1 sina 2)}

e”™

= {W/ =Te0s n (N—D) w+8in n (WD) Ttsin(ax+nO0+nX+N T)

=e"* P® (cosrnT—V—1 sinrnT) sin (av+n0+nAT)
rand A being any integers.
Similar expressions may be obtained for the wth differences of cos ax and
of e”* cos ax.
25. We shall now proceed to the demonstration of certain theorems analogous
to those in the ordinary calculus of differences.

it 1 nb ai n(n—1). 6

Pp. l. = — &e.
Pro Vn +n Vy Vx Vx+1 Vy Vx 41 Vz42
where ¥,=a+ 62 OF Ave=d.
5 1
By formula (6); putting — for «,
x
1 1 1 n—1 1
ce ba Cee ) 7 + &e.
Opies Oe Vy ee? 0;
N a 1 A Uz b Ae 1 IL Bs fs
ow = + ae ie eS
e Vy Vx41 Vy Up41 Vy Vy Vez4+1 Vx42 rae
1 1 b —1)2
ERE eh OP a.
Vpin Vx Vy Vy 41 Vy Vp41 O42

Prop. 2. A similar result may be obtained from formula (8).
1 b Pet Puh SIR 2 Noe

For A =— eA = &e.
Vz—1 Vg Vy J Vy, 2 Vy Vz—Y Vz 2
1 it nb n (n+1). 6?
oe ee pera
Uxz+n Vx Vz Vz_] Vy Vz_} Vz_—2
n a n n—1
PRop. 3. A” Uy, 0, =0, A” u,+W hv, A” u,, + &e.

For {(1+ 4) (1+ 4’)—1}, v, being an operation on “, % may be repeated accord-
ing to any law, consequently

A" uw, 0,={(1+ A) (1+4’)—1}” w, v,: and every step in the demonstration is the
same as when » is a whole number.

296 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

Cor. The same is true of the formula for the nth difference of w:,,: for
A Ug, y= (1+ Ag) (1+ Ay)—1} ag, y
AU, yo {l+a, hee Ay Se Ye, y
d d

— + —_
or (07 4249-1)"

and the same results are produced as when m is a whole number.
Prop. 4. F (A) &*f (2) =e" F (e&*" 144-1) f(z)
Let %=e'*; and %,=/(«) in Prop. 3.
AM er® f(x) = fF (@) Ave +n Asan” ott se.
= f (a) (e"—1)” &* +n Afa(e—1)"-1! ef? +7 + &e.
=e"* (e"—-1+6 A)" fe)
=e"* (el +A—1)"f (2)

which being true for all values of n, shews that the following theorem is also
true:

F (4) . e°* f (2) =e" F (e” 144-1) . f(z)

Prop. 5. AU,= ((1+5)?-1) w = {+a ie ate oe 1},

Let z=e’, and let u, be represented by ~ when e’ is written for 2, let also
ay be the symbol of difference w.1—ws. Then by (C), when ~ is an integer,

“=D (D- (D2 2)\< 7). Waare,
a”
d
eee Oe ee ay oe ees ee
Ree te Getr & +ra3 (3) +e.) a,
“Grr oa 1) (D=2) + &e.) 4
But A, u=(eP—1) wy o. ag =(1L+ Ay)
or D=log (1+ Ay).
1
D log (1+ —
Hence (1+ =) = (14.2) O04) (+5)

u
D log (14+ —
and = Aa, = (+2) —1) w= { +4) ®( "1h w
log (142) ,

Cor. Un n= (1 t+ Ag) ug

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 297
log (1+
Prop. 6. Uy n= (1 + dy) ( Day

d
d Mt aes
nT eal
For =e @* eine

Ux+-n=e Tk ae ne
v
= (ts = Lye 5 D (D—1) + &e.)u,

fe ((1+ =) ew ug
=a) Ct),

It must be observed that x is considered constant with respect to 4) in the

1\ log 1 +Ay)
3) :

formula (1+ Had we supposed it otherwise, we must have taken

account of the differential coefficients of * itself. This would have given the fol-
lowing theorem.

Prop. 7. Au,={(l—e~*)-P+D_1hu,

= {(1+ Ay)~#8O-¢ 91 e-4)—1_ 11,

d
For A u,=(e7*—1)u,= Gar (7) *+6&e.) u,

i
— (;D TT 9 Pe 1 D@D-1) +e. )w
= (D+He"+ +542) (D+l)e-# +&e.) Up (B)
={(l—e-")-O7D_1tu,
=f{(l—e~*); be A +4,)-1_ in,

mh ae etal a a

d 2
Prop. 8. “ets ug= (line 4 3 (z) +ée.) Un

a eke 5 (D+2) (D+1)e-*"+ &e.) ue

=(1l—ne-4))-@+Dy,

It is manifest that these formulze do not follow the distributive law. They
cannot, consequently, be applied with any great advantage to the solution of equa-
tions of differences. We shall exhibit their application only in one instance.

VOL. XVI. PART III. 4F

998 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

EQUATIONS OF DIFFERENCES.

26. As the method of solving equations of differences of the second and
higher orders, by treating the symbols of operation as symbols of quantity, and
reducing the resulting fraction by decomposing it into partial fractions, has been
little, if at all, employed, we shall commence with an example or two in ordinary
equations of differences.

Ext. Un 4 3tE Uy o4+b Up +6 U,=X.
This may be written
{+4)?+a(1+4)?+6(1+a)+clu,=X

If we write a, for 1+, and suppose a, 8, y the roots of the equation

A3+aA2+6A,+c=03 we get (A,—a) (A,—) (4,—Yy)u,=X, or
te 1
" (4,—4@) (4,—8) (4,—)

This equation is reduced, by the decomposition of the fraction of operation

into its equivalent partial fractions, to

. (X+0).

2S eS ee </e (X +0)
=) (a—y) (a —a) ‘ PAE ieee y) Oa =
1
(X +0).

W-a a) (y—B) (4, —¥) =

Now “a (X+0) is the solution of the equation v,,,; —av,=X+0;

hence it is equal to ax (a+ =) ; and similarly of the others.
Hence the complete solution of the given equation is
1 xX i xX’
th) = eo A+ ——— —S——_—_————— 9 ———
“=Gopa@an® Ata) * ray Gan Bt gee)

1 D4
aa ees C+
(=a) (y—8) * Se? 1)
Cor. If a=, we must, as in similar cases, put a+c for 6, and expand in
terms of c. The result is

1 x

1 ae a* x X (#+1)
at ae (fu xara} -<) (Bite Ssyrsat)

igri koga se
+(—ap (C+2 35)

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 209

A. a® Baa*-! vat—} a” xX a’ X (@ +1)
2 En a ED Pee
a-y a-Yy a—y (a-—‘)? ait a—y aoe

xX
“Ea a (° oe AEH. ,
In precisely the same manner we may integrate the general equation with
constant coefficients.
Let us apply the formula of Prop. 6 to the following example.
Ex. 2. Uy—3 (@+1) Uy 414+ 2(@t1) (+2) uw, 4 0=0.

Calling | (1 +5) 1 we get

4 1 6 4 |(a+2)
my —B (eo +1) (14s) % +2 +1) (C8 +2)A4+4,) * wy =0

Now since ef? (1+ Ag) zeW" (1 + ay)he” ug
we have

rae aa
w— 3(L+e7*)e7 "(1+ Ay) ef ay +2 (e? +1) (4 26-*ye-!4 fal atlas : ef 4, =0.
l 4 [a+2) ,
or Uy —3 (1+ Ay)’ e% uy, +2(e° +1) (14+4,)' 2’ ef uw, =0.

Pot 8 +a,) + +a,)) for + ages)
where a, in the former operates on the z in the latter.
uy — 8 (1+ Ay) eu +2(1 te “Jed (L+a,). (L+4,) ef wy =0
or ty —B (+ Ay) ety + 2 (1+4,) € . (1404) eu, =0
or ty —3(L+ Ay)! ey +2 (14 Ay)! ef P uy =0
which can be resolved into the two

l= Gn), e hay =0 and {1-—2(1+ Ay)! e! } uy =0

or U,—(*#+1) 4,41=9 and u,—2 (#@ +1) u,,,=0
U,=- a U,= B
where (ia ja + 1 or U, ~ 9x jeri
and therefore generally, ~, ae which is the complete solution of the equa-
e+
tion.

It is evident that the process employed in Example 1, applies equally in this
Example, when a function of 2 appears on the right-hand side of the equation. —
Hence

Ex. 3. Uy —3 (@41) Wey +2 (441) (742) Upp o=X gives

300 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. .

= X+0 9 X+0
= TOA) hes Eee
_A+B.2-" 2-

1 a+1
je+1 rce Si a je+1 oe
Cor. In the same manner may the more general equation
U,—a(X#+1) UW, 21+6(a4+1) (+2) u,,0+&ce.=X, be solved.

It is not necesary to solve such equations as u,,,+au,+&c=X, since it

is evident that, by putting z=4 7, this form of equation is reduced to
v, +av,,1+&c.=X, which has been already solved.

We proceed then to the solution of equations involving fractional differences.
Here we must, at present, confine ourselves to very simple examples.

Ex. 4. at U, —4U,,=90.
Since at eme=(em —1)} pme
It is evident that if m = log (a?+1) the solution of the equation is w,=A e™*

=A gee’) — Aer 1)

Ex.. 5. At u,—@ U,=C e**
Uy, =A POE ge malas ie cm
( ) (@aiioa
or, if e*=14+0,u,=A (@ +1)" +5— (841)

Cor. If 6=a, this solution fails. Put 6=a+@ as in similar cases in Differ-
ential Equations :

c

b—a

(82 +1)"= © (a? 414208)" =< (a? +1)"+ $2082 (a2+1)"7}

pB 6 8

Cy (a24+1)?+2acz(a?+1)"-+

then

A, being an arbitrary constant.
It may be interesting to verify this solution.
At (a? +1)*—a. (a? +1)"=0 evidently,
and At Qacz(a?+1)*-! =2acxa(a?+1)*-!+42ac (a +1) by Prop. 5.
=2 a? ex (a?+1)*-1+¢ (a? +1)”
A? .2Qaca(a?+1)*-1-a. 2acx (a? +1)*-1=c (a? +1)"=ce** as it ought.

Ex. 6. Generally, let a?u,—au,=X
then Up=A (a2 +1)*+(at—a)-1X

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 301

ae
—qQ

=A (a?+1)* + x

xX
=A (a? +1)? +(a* + a) (a? +1)" 3 pet
Cor. 1. Let X=6z; then the solution of the equation a*x,—au,=62 is
tip =A (a? +1)" — (ab +a). (3 ah =)

auta+l1

then the valueof (a—a@%)-!X is — 2

therefore the solution of the equation a? u, — a ees ont
a (z+1)
is u, = A(a? + 1)?— (at + a)*
a ee © Mitral 1 ee Ee (by Ex. 6, Art. 24.)
Ex. 7. paren

This equation may be written
(A+ aat+b)u, =0.
Let a, @ be the roots of the equation 2?+az+6=0, then
(a*—a) (a*—f) uw, =0
u,=A (A?—a)-1.0+B(a?—8)-!.0
=A (1+a’+B(1+ 2)" (Ex. 4.)
Cor. If a=, we obtain, by the usual process, u,=(A+B2) (1+a?)*.
Ex. 8. AU,+@ A? U,+buU,=¢ (1 +e)"
The solution is
maz plet— a0 + el Fe ays B10 + ole)
else) ete)
(a—8) (e—a) (a—f) (e—8)

me 2\a 200 ce (1+e?)”
=A (1+a’)”+B (1+) + aaah
Cor. If e=a, we must proceed as in Cor. 3, Ex. 4, Class 1, of Differential

Equations, and we shall obtain

=A (1+a?)"+B(1+?)"+

ex(1+a’)-*
2a+a
VOL. XVI. PART III. 4G

u,= A (1+)? + B(1+ 6)" 4

302 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION.

Ex. 9. AU,+ aA? U,+6U,=X
1 z =i 1 ? =a
Sha 0+X) — — =
tes gS Re OO ee B)~ 0+)
a 1 4 -—1l aff 4 “oat
= 2\x 2 ae: hs x, Velie a
=AGs Ope eR Agee @auak aap Ee
= AC + a%)"+ BQ + 6)°4—, (a? +a) (1 + a2)? 3
a—6 (1+a?)e+1
ae carad eae | 2 aa
ae TEE ae) * 4 Br
Ex. 10. Wy tax d® 1c—2. ©
: : : A i
This equation gives “= 7G
__l-art_y

~ 1l-a? wat ax at
=(1—awa*)?,, where v, is determined by the equation

0, -@ 2d? wo dtv,=X

ak
Now AP @ A? v,=@ AV, +4 Pr 41 (Prop. 3.)
2 92 a” x
0, —@ 22Av,——20 =
ax a 2 a+l
Aa - a 1+a?*2? | 2x
a+1 a? 44+22° a” @ (#+227)

which being solved by the ordinary method, v, and therefore u, (provided A? Uy can
be found) is known.

Equations of Differences with two independent variables are not capable of
solution to any great extent. An example or two will suffice to illustrate our
process.

Ex. Ll. Ay Uy, y—Ay Ue, y= 0.

The solution is ub, = aw

Treat 4, as a constant c, then the solution of (4.—¢) #2, y=6 is
a b
Uy, y= (c+1)7JA oar
ty, y= (Ay +1)? zy —4y—1 6

d
—— Nia
= (a) Uy—by

=VUyp~—5y

vy+« being an arbitrary function of y+z2.

PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 308

Z 7
Bx 12: A,” Un, y— 4? Uy, y=
Thi ae 1
1S equation QIVES Uz, y=
q 5 yl Bn? — Ay?
Ate + Ay b
~ A,—A

=(a?, +4#,) (Py 40—5Y) (Ex. Ln)

We have thus succeeded in solving equations with fractional indices of all
forms corresponding with the ordinary forms of Linear Differential Equations,
whether total or partial,_—whether solitary or simultaneous. We have also
placed the Calculus of Fractional Differences on the same footing with respect to
the ordinary Calculus of Fractional Differences as that which the Calculus of
General Differentiation occupies relatively to the ordinary Differential Calculus.

P. KELLAND.
EprinsureH, October 10, 1846.

verre oF! Te
Me ero Lo ee
- : Aa ' : Pr . P “
- Hy P 4x: ~ * lth
; : * r he. i - - ' =
i Sl lait 3, Ti aie ae aie
irs ve fas FT | : Lo

ait.

,
he

il q .

' 1. “iow A : , y as p ; 7 Ps ae
oo Oa . 7G, ) ae Y Ts ye ‘5 5 4 Ae Sp.
: \ Jat =. a r Lim oY Z
i - = ? ;
7 yi 1 .
ae , ..«t) A ‘ q ? = Ta
a 7 x) un a" as ‘ oe <4

sory Sai r
: tO Aahae MntO a, Qh ator Rei oy | jv) Sue ud Se
r AITO RIV, . Rainer #./° See entgliifes si) dow pithimeaale
a Lh. fat yy ML \ LAU wy raat ve Aivtsy wi a a ll

yi : . . : | > "
ve HL ic ee Uo vom t Pits TROT Pe ho arte haey
; fui ; a i le : a
vty ' goo Tee! Lengel to multAla
; sve silt pt choi tal et age meas a
1

( 305)

XXI.—Observations on the Principle of Vital Affinity, as illustrated by recent
discoveries in Organic Chemistry. By Witit1amM PuLrenry Atison, M.D.,
F.R.S.E., Professor of the Practice of Medicine mm the Unwersity of Edin-
burgh.

(Read 1st and 15th February 1847.)

Part II.

It may be remembered that, in the paper formerly laid before this Society on
this subject, I endeavoured to establish the principle still disputed by some phy-
siologists, that the laws which regulate the chemical relations, as well as those
which regulate the visible movements of the particles of matter, undergo a cer-
tain determinate modification or change in living bodies, which is essential to the
commencement and to the maintenance of the organization of those bodies; and
farther, that I undertook the task of attempting to deduce, from the numerous
but somewhat discordant experiments and observations lately made on the sub-
ject, certain inferences which appear to be well ascertained, although not gene-
rally admitted, as to the essential nature of this change, 7. ¢., as to laws which
regulate those chemical actions which are peculiar to the state of life, and essen-
tial to the maintenance of organization, both in vegetables and animals.

In confirmation of my statement of the general principle of Vital Affinity, as
distinguished from simply chemical affinities, I have much satisfaction in quot-
ing two sentences from the last edition of LrzBie’s “ Animal Chemistry.” Some of
the statements of general principles made by this author, seem to me open to ob-
jection, and some I do not profess to understand; but the following is simple
and precise ; and, considering the authority of LirBic as a chemist, may, I think,
be held nearly decisive as to the soundness of the principle. “A fundamental
error, committed by some physiologists is, that they suppose the chemical and
physical forces alone, or in combination with anatomy, sufficient to explain the
phenomena of vitality. It is, indeed, difficult to understand how the chemist,
who is intimately acquainted with chemical forces, should recognise in the living
body the existence of new laws, of new causes, while the physiologist, who is
little or not at all familiar with the action and nature of chemical and physical
forces, should think himself ready to explain the same processes with the aid of
the laws of inorganic nature alone.”—Animal Chemistry (third edition, p. 252.)

The first and most fundamental of these general principles (iikewise consi-

“dered in my former paper) is the power of vegetable life, under the influence of
light, to decompose the carbonic acid existing in the atmosphere,—set the oxygen
free, fix the carbon, and form with it and the elements of water, starch, sugar,
gum, and the analogous compounds. Our knowledge of this power, of the effects

VOL. XVI. PART III. 4H

806 DR ALISON’S OBSERVATIONS ON

which result from it, and of the period when it must have been first exerted on
the earth’s surface, enables us to assert with confidence, that by means of it,
the whole organised creation has been, as Dumas expresses it, the offspring of
the air; and that it was by enabling the rays of the sun to excite this action
in certain particles of matter, existing in the atmosphere, but destined to be
either the first specimens, or the first germs of vegetable life, that ‘“‘ a beneficent
God,” to use the striking expression of LAvoIsIER, “has strewed the surface
of the earth, first with organized structures, and then with sensation and
thought.”

In proceeding farther to inquire into the laws of Vital Affinity, we must
always keep in mind the general arrangement or classification, long ago made
by Dr Prout, of all the organic compounds, of which any organized structures,
vegetable or animal, are composed, into three groups or classes, the Saccharine or
amylaceous, the Oily, and the Albuminous ; and the important observation, I be-
lieve first made by him, that the food of most animals contains all these com-
pounds, and that no complex animal structure can be maintained without the
concurrence of at least two of these kinds of compounds in its food.

I do not think it is going too far to say that we have now a general know-
ledge of the laws or conditions under which all these compounds are formed in
living bodies, taking the starch formed from carbonic acid and water as the foun-
dation of all. But we perceive farther, that that these laws, varying in diferent
parts of the same structure, and at dierent times in the same paris, and being of
transient duration in all, are liable to an influence of time and of place, and in
animals to a farther influence of mental changes, which is quite analogous to the
vital actions, both of muscular and nervous organs, but is strongly contrasted
with the uniformity of the laws that determine the changes of inorganic matter.
And if this be so, we may assert that considerable progress has been made, both
in establishing and in illustrating the doctrine of vital affinity, as a first principle
in physiology.

I. The formation of Oil or Fat in living bodies is, perhaps, that part of the che-
mical processes there carried on, which is now the best understood, and the study
of which gives us the clearest insight into the nature of vital affinities. We need
not enter into any of the simply chemical questions as to the mode of combination
of the fatty acids and bases in the different kinds of fat; it is sufficient for our pur-
pose to observe that they are found very generally, though very variously disposed,
in almost all vegetables and animals, and even in the earliest stages of their ex-
istence; the store of nourishment contained in the seed and in the egg, contain-—
ing a proportion of fatty matter. And though there is considerable variety in
the different kinds of fat or oil, they all differ from the varieties of starch, by
having a much smaller proportion of oxygen, and, of course, a larger proportion

THE PRINCIPLE OF VITAL AFFINITY. 307

of carbon and hydrogen. The composition of most fats is stated by Liebig to be
Cw» Hy O,; and we have thus, therefore, another compound formed apparently by
vital affinity, indicating a peculiar attraction of the two first elements for one an-
other, and a feeble attraction for oxygen. Indeed, in the composition of wax
(one of this family of compounds), as stated by MuLDER, the proportion of oxygen
is only one equivalent to 24 of carbon; in cholesterine, the proportion of carbon
to oxygen is stated as high as 36 to 1; and in many volatile oils, no oxygen has
been detected.

Supposing such a peculiar affinity to act, there is obviously no difficulty (on look-
ing at the numbers indicating the proportions of the elements) in understanding the
formation of these compounds out of starch (Cy Hi, O,), just as there is none
in understanding the formation of starch or sugar (although by an affinity occur-
ring only in living bodies, and which we regard as vital) from carbonic acid and
water (CO, + HO), in living vegetables, where a continual evolution of oxygen
attends the growth; particularly if we suppose that the carbonic acid taken in
by the leaves and roots, is carried to, and decomposed in, all parts of the plant :
the formation of the fatty compounds, is, no doubt, one of the processes by which
the oxygen is set free. But in the case of animals, where (with the exception of
some of the infusory tribes) there is no evolution of oxygen, the formation of
fat from starch presents a difficulty. Yet the numerous observations and expe-
riments of Lirpic and of CHEVREUL and MILNE-EDWaRDs, leave no room for
doubt that various animals, fed chiefly on varieties of starch, or bees fed on sugar,
form a much larger quantity of fat, oil, or wax, than they have received mixed
with their food, and this when they are exhaling no pure oxygen, but, on the
contrary, compounds of hydrogen and carbon with oxygen, viz., water and carbonic
acid. Indeed, Dr Ropert THomson having ascertained by repeated experi-
ments, that the quantity of butter yielded by cows bears no fixed proportion to
the quantity of oleaginous matter contained in their food, varying indeed from
one quarter to nearly the whole of the oleaginous ingesta, thinks himself justified
in inferring that “the butter cannot be supplied from the oil of the food.” (On
the Food of Animals, p. 156.)

It is quite certain that in this action, in all animal bodies, the greater part of
the oxygen of the starch employed must unite with a portion of its carbon and
hydrogen, and pass off in the excretions just noticed, leaving the small remainder
of the oxygen in combination with the predominant quantities of carbon and hy-
drogen.

It appears possible, indeed, that a// the oxygen which must be separated
from starch before it can be converted into fat, may be evolved in combination
with part of the carbon and hydrogen of the starch, without any constituent of
the air taking any part in the process; but the quantity of fat formed would
then be small, and it is also possible that the oxygen of the air may be concerned

308 DR ALISON’S OBSERVATIONS ON

in the metamorphoses to which starch is liable in a living body ; and as we know
the importance of oxygen in maintaining (in one way or other) all vital action, the
latter supposition is more probable.

If, e. g., we suppose 4 atoms of starch to yield 2 of fat, we must subtract from

48 C 40 H 40 O
24 C 20 H 20

leaving 24 C 20 H 38 O=20 HO 9 CO?2+15 C;*

so that on this supposition 15 atoms of carbon are set free, and as these do not
appear, they must unite with the oxygen of the air, and take the form of carbonic
acid ; and then the fat which appears, together with the water and carbonic acid
thrown off, will account for all the elements concerned in the action. In this pro-
cess, therefore, supposing the quantities of starch taken in, and of fat formed to
be as above, 30 equivalents of oxygen must be absorbed ; so that we perceive the
use of oxygen in the change, and the necessity of its presence, although the fat
formed contains so much less oxygen than the starch.

That this should be the real nature of the change is just what we ought to ex-
pect, if, agreeably to the supposition formerly made, the starch taken into the
blood of a living animal, is acted on at certain parts of the body by two powers,
and divides itself between them, viz., a vital affinity, in which carbon is the chief
agent, which leads to the formation of fat, and the simply chemical affinities, ex-
erted chiefly by oxygen (continually taken into the blood), by which, if removed
from the living body, we know that it would gradually be resolved into carbonic
acid and water. And that this is the real state of the case we are fully assured
by a simple but very important observation, viz., attending to the effect of exercise
on the formation or deposition of fat in the living animal body. As we see by the
numbers given above, that a certain amount of oxygen must be absorbed, and a
certain quantity of carbonic acid and water, formed by its help, must be excreted,
to enable starch to yield oil or fat by the process there represented, we can un-
derstand that moderate exercise should favour the change; but when exercise
is carried beyond a very moderate extent, we know that the circulation and res-
piration being much accelerated, and the quantity of oxygen taken into the
living blood being much increased, the effect is, to increase the exhalation of car-
bonic acid and water, and proportionally to diminish the deposition of fat ; 2. e., to
give a preponderance to the simply chemical affinities exerted by the oxygen,
over the vital affinity, which would tend to the formation of fat.

From this simple fact we may infer, 1. That the vital affinity by which oil is

* It need hardly be said, that all these numbers are given, not as indicating the exact changes
which take place when the organic compounds are formed, but only as illustrating their general nature.

THE PRINCIPLE OF VITAL AFFINITY. 309

formed from starch, or by which its elements are held together, does not super-
sede its natural chemical relations, but only adds a new chemical power to
those which can operate on it, and allows of a division of the starch between
the result of a vital and a simply chemical affinity; and, 2. That the vital
action by which fat is formed or maintained, is of no great strength, as com-
pared with the simply chemical affinities to which the same matter is liable;
being superseded simply by an imcreased supply of oxygen. And we cannot
doubt that, in this as in other vital chemical processes, the oxygen, although
not taken into the organic compound formed, aids its formation materially, by pro-
moting, on the principle of divellent affinity, the other parts of the metamorphoses
whereby itis produced. We shall see afterwards the importance of having it esta-
blished by this simple example, that the oxygen of the air, when taken in full quan-
tity into the blood, is capable of combining, somewhere in the course of the circula-
tion with a part of that carbon and hydrogen, recently absorbed into the blood,
which, under a smaller supply of oxygen, would form a living texture ; and that
the combination of these portions of the ingesta with oxygen, are one source of
the excretions.

There are other facts which lead to the same conclusion, as to the affinity by
which fat is formed, being more nearly akin than most vital actions to simply
chemical affinities; particularly,—

1. The formation of Adipocere, not from starch, but’ from albumen, after
vitality is over, when undergoing decomposition under ground, where there is a
full supply of water and but little air, so that the supply of oxygen is less than
in ordinary putrefaction, which may be understood thus :—

C N H O
48 6 36 14= Albumen
Add 12 12 Water
1 Oxygen

48 6 48 27
Subtract 36 30 3 Fat

iY, 6 18 24= Carbonic Acid and Ammonia

which escape, and the attraction of which for each other, no doubt in part deter-
mines the result.

2. Again, in the living body, but in a feeble constitution, along with great
emaciation, and a deficient supply of oxygen, a morbid deposition of fat some-
times takes place, in circumstances where it could not have been anticipated, but
only in particular parts. Some distinct cases of this kind have lately attracted
attention, one in the kidneys, in one form of Briaut’s disease, another in the
liver, as in many phthisical cases, and a third in the atheromatous exudations

VOL. XVI. PART III. 41

310 DR ALISON’S OBSERVATIONS ON

so common on the arteries. It may be suspected that in these cases the forma-
tion of fat is by an affinity hardly more vital than the formation of adipocere,—in
both cases the decomposition of albumen to form the fat, being aided by the
simply chemical affinities, of carbon for oxygen, and of hydrogen for azote.

3. The same peculiarity of the attractions by which fat is formed in the animal
economy may be admitted in explanation of the more general fact, that in a
healthy constitution, when more, particularly of amylaceous, food is taken than
is required for the nutrition of the more important textures, and when little oxy-
gen is taken in, the excess always tends to the deposition of fat, which implies
that a large portion of the oxygen of that food has gone off as carbonic acid and
water.

The process of the formation of oil from starch in the animal body, admits of
an instructive comparison with the simply chemical one of the formation of alco-
hol from the same matter,—at least, from a compound fluid of which starch (first —
converted into sugar by the kind of fermentation formerly mentioned) is the
chief constituent, in fermentation ; ¢. g., the changes in the vinous fermentation
of grape-sugar, are represented thus,—

Cy H,, Oy =2-(C, H, 0,) +4 CO, 4+ 2 HO,

that is, the elements of grape-sugar resolve themselves into two equivalents of al-
cohol, four of carbonic acid, and two of water. In this case, as in the formation of
fat, the starch or sugar is divided into three parts, water, carbonic acid, and a pecu-
liar compound fluid. In both cases, the oxygen of the air is necessary to the com-
mencement, and probably to the continuance, of the process, although in both, the
new compound formed contains less oxygen than the starch or sugar from which it
is produced. In both cases, a third body is present, and its influence somehow pro-
motes the process, besides the oxygen and the starch, viz., in the one case, yeast,
or some kind of ferment, itself in a state of decomposition, which it imparts, without
giving up any part of its substance, to the starch or sugar; in the other case, a living
cell, composed of gelatin, which is itself undergoing a simultaneous change, by a
living process. In both cases, extension of the change takes place, as from a centre,
from this third body, through the fluid in which the change commences. In both
cases, the compound formed is not stable; and the portions of the starch which
go to form it are destined ultimately to follow the same course as those portions
which are resolved into carbonic acid and water. In the one case, the com-
pound formed, C, H, 02, contains a less proportion of carbon than any of those
which we regard as endowed with strictly vital properties; while, in the other,
the compound formed, C,, Hi O,, has the characteristic predominance of carbon.
3ut if we are asked, Why we regard the one as the result of a simply chemical
process, and the other of a vital affinity ? I apprehend the sufficient answer to be,

THE PRINCIPLE OF VITAL AFFINITY. 311

that the one is a change which uniformly results when the sugar is exposed to
the influence of air, water, and a certain temperature ; and is in contact with a sub-
stance undergoing some part of that decomposition and chemical change to which
living bodies are liable after the phenomena of life are over ; whereas the other is
not seen, in the presence of those substances, and under those conditions as to air,
water, and temperature, in which it here takes place, unless the starch is at the
same time in contact with living cells,—. ¢., cells forming a part of a body in
which the peculiar phenomena of life are then exhibited.*

II. The next question is as to the formation of the Albuminous, or what have
lately been called the Protein, compounds in animal bodies. The late acrimoni-
ous dispute as to the existence of Protein, should rather be termed a dispute as to
the exact composition of the compound to which MuLDER gave that name, and
which is thrown down from the solution of either albumen or fibrin, in potash.
by acetic acid. Of the precipitate being the same in both cases there is no doubt:
and we shall avoid the controversy entirely, by using the term Albuminous Com-
pounds, as Dr Prout did, instead of the term Protein.

Since it has been clearly ascertained, that the vegetable gluten is identical
in composition with the albuminous compounds,—~. ¢., fibrin, albumen, and ca-
sein of animals,—no doubt can exist that the formation of a great part of the al-
bumen found in animal bodies must take place in vegetables; and, I presume, it
is also generally agreed that the chief agents in this farther change, beyond the
formation of starch and of fat, are sulphur, and ammonia or its elements, taken
into the fiuids of the vegetable, although it is still doubtful from what sources
this ammonia or its elements may be originally derived, and particularly whether.
in any circumstances, the azote of the atmosphere is concerned in producing it.

Some experiments recorded by Dumas,t however, seem to leave no room for
doubt, that certain families of plants, in one way or another, fix azote from the
air, being found to add largely to that contained in their seeds, when ger-
minating and growing merely in silica and water; and it is by no means as-
certained, that this azote passes necessarily into the state of ammonia be-
fore it is applied to the nourishment of those vegetables. And the state-
ments of MULDER seem equally conclusive as to the fact, that ammonia may be

* It is no objection to this statement, that oily matters may, in different cases besides that of
adipocere already noticed, be formed from organic compounds in the dead state, 7. e., by simply chemi-
cal affinities. To establish that the affinity by which it is formed in a living structure is vital, it is
not necessary to shew that oil cannot be formed, under any circumstances, by simply chemical laws, but
only to assure ourselves, that it cannot be formed by those laws from the substances, and in the circum-
stances, in which it is continually formed in certain living cells.

+ Balance of Organic Nature, p. 77.

312 DR ALISON’S OBSERVATIONS ON

formed by the union of azote from the atmosphere with hydrogen from water,
whenever another substance, exerting an attraction for the oxygen of the water,
is present.—(Chemistry of Vegetable and Animal Physiology, p. 149, et seq.)
Now, as carbonic acid and water form starch, or its allied compounds, in the
living vegetable, by the attraction of carbon for the elements of water, to the ex-
clusion of oxygen; and as the starch then forms oil, by the attraction of the
carbon to hydrogen, to the exclusion of great part of the remaining oxygen;
so, on the introduction of ammonia, or its elements in a state fit for entering into
new combinations, into the scene of those metamorphoses, it is only in accordance
with what we know of the nature of these vital affinities, to suppose that the car-
bon may attach to itself the elements of this ammonia, to the exclusion of the
elements of water and of oxygen, matters which are known to be continually
thrown off by vegetables, during the continuance of these vital processes. Thus
we have the elements of starch, 48 C, 40 H, 40 O plus the elements of ammonia,
6.N, 18H, —48C, 6N, 58H, 400 =48C, 6N, 36H, 140 (the elements of albu-
men) plus 22 HO + 40, a considerable quantity of the water, and a small quan-
tity of the oxygen, which are continually exhaled by the plant.

Thus, during the whole process of the formation of organic compounds in the
vegetable, we see that the vital affinities shew themselves by the attractions of
Carbon, first for the elements of water in preference to oxygen, then, either for the
hydrogen of those elements, in preference to the oxygen, or for the elements of
water, with an excess of hydrogen, along with those of ammonia ; and thus, by
these peculiarities of attraction of Carbon, for the elements of water, for hydrogen,
and for azote,—to the more or less complete exclusion of oxygen,—we see that the
essential materials of all organized matters may be easily formed,* while water
and oxygen, the known excretions of vegetables, only escape.

The point at this moment most disputed, and the settlement of which is most
essential to the precise comprehension of the nature of vital affinities, is, Whether
there is any formation of albuminous matter in animal bodies? and it is obvious,
that there is a difficulty in regard to its formation from starch, just similar to
that which was stated as to the formation of oil in the animal body, because
we see no evolution of oxygen; but it is also certain that this may be got over,
precisely in like manner as in the former case, by supposing—what is quite
in accordance with known facts—that a considerable absorption of the oxygen of
the air attends the process, and that, with its help, a large portion of the carbon

* This may be shortly stated thus CO, + HO = Carbonic acid and water. From this is formed,
C+H+0 = Sugar, oxygen going off. From this,
Ci, ay On, = Starch, water going off. From this, either
Cy, OF = Fat, oxygen going off. Or, :
Cy N, “H 6O,, = Albumen, ammonia being added, and water and

a little oxygen going off.

THE PRINCIPLE OF VITAL AFFINITY. 313

and hydrogen are thrown off in carbonic acid and water. Thus, supposing a large
quantity of starch, 60 C, 50 H, 50 0, to unite with a small quantity of ammonia,
we have

c N H 0
60 6 68 50 and adding 20 of oxygen,
we have 60 6 68 70=48 OC, 6N, 36H, 14 0,

(the elements of albumen) + 32 HO + 12 CO,, the water and carbonic acid which
escape. Or, adding an equivalent of oil, we may have

Cc N H O
48 im, 40 40 Starch.
Add 12 ae 10 tT On
6 18 -» Ammonia.

60 6 68 41
Subtract 48 6 36 14 Albumen.

2 Pat ace 32 27 Adding 29 oxygen,

we get 12 CO, + 32 HO carbonic acid and water.

It is certain, therefore, that if the elements of ammonia can be set free in
the primee vise of an animal, starch absorbed from thence, with or without the
addition of oil, may be converted into albumen in its blood, without any other
matter being thrown off than the water and carbonic acid, which undoubtedly
escape from every animal. If this be so, we have here another division of the ele-
ments of the ingesta, between substances exerting a vital and a simply chemical
affinity for them, and another formation of part of the excretions, by the help of
the oxygen of the air, from matters recently absorbed, and which aid in the nou-
rishment of the animal. But whether this is a process that actually goes on in
the animal economy, or whether all the albuminous compounds of animal bodies
have passed into them, directly or indirectly (but ready formed), from vegetables,
is the point at this moment the most important to be ascertained.

As it is obvious that the albuminous compounds, and the gelatinous compounds
. (which are closely related to them, and are generally thought to be formed from
them), compose the greater part of the animal textures, and are equally the ground-
work of all animal structure, as starch is of vegetables, this inquiry involves the
essential point of distinction, so far as chemistry goes, between vegetables and
animals. It is well known that both Lirpic and Dumas have expressed a de-
cided opinion that no albumen is formed in animals; and the latter author has
contrasted, in a lively manner, vegetable and animal life in this respect, repre-
senting the former as always a reducing or deoxidating apparatus, and the latter
as an apparatus of oxidation or combustion, 7. ¢., of the destruction, never of the
formation, of any organic compound. But he does not appear to have adverted
particularly to the question which seems to me the most essential in a physiolo-
gical view, viz., what are the chemical changes during the state of life, whether

VOL. XVI. PART III. 4k

314 DR ALISON’S OBSERVATIONS ON

in vegetables or animals, which are distinctly at variance with the ordinary laws
of chemistry, and which we must therefore ascribe to vital affinities ?

It is evident that what, in physiological language, is commonly called Assimi-
lation, includes two distinct actions, both, in many cases, as I believe, strictly vital ;
Jirst, the mere selection and attraction of a part of a compound fluid, to be added
to a living body ; and, secondly, the transformation of the elements of two or more
compounds, so as to form a new compound, similar to one already existing in the
living body wherein this change occurs. If Dumas’s view of the subject were to
be adopted, we should say that animals can exert only the first of these powers,
the simple selection and attraction of one of the ingredients of a compound fluid
by each organ or texture, without any power of transformation, or formation of new
compounds; and accordingly, he says that “ it is in plants that the true labora-
tory of organic chemistry resides.”

But if we state the proposition thus generally, we may state various facts
to shew, that it is incorrect. It is quite certain, as already stated, that oil or fat
may be formed in animal bodies, by a new arrangement of the elements of starch,
attended by an evolution of much of its oxygen, and of part of its carbon and hy-
drogen. effected by the aid of the oxygen of the air; and the influence (already
noticed) of exercise, 2. ¢., of an increased application of oxygen, on this change,
shews distinctly that the recent ingesta are liable to two influences in a living
animal, one of which is an action of oxidation or combustion, throwing off water
and carbonic acid, but the other is strictly an action of reduction, by which a
quantity of oxygen is separated from its combinations in an organic compound,
while a fresh compound, constituting part of the animal frame, is formed. And
the fat of the animal body, which may be thus formed, is not to be considered as
a merely unorganized appendage to the textures. It appears from some of LiEBiI@’s
observations, that the muscular flesh of all animals, after being cleared of all visible
fat, still retains a considerable and variable quantity in its substance; and we
know that in two of the most important textures of the body, nervous matter
and bone, fat is an essential ingredient.

In like manner, the formation of the essential ingredient Gelatin in the ani-

mal body is the result of a new arrangement of elements, attended with evolu-
tion of carbon and hydrogen, by the aid of the oxygen of the air, but probably
not with absorption of oxygen.

In the case of Inflammation, we see distinctly that, im connection with an in-
creased action of nutrition or deposition of plastic lymph, there is a transforma-
tion of portions of the blood to form the compound, very similar to gelatin, termed,
by Mutper, the Tritoxide of Protein, which is found there in very unusual quan-
tity; and in other morbid actions, in certain chronic malignant diseases, we see
compounds, altogether foreign to the natural organization, formed and even ra-
pidly extended ; the formation of which is certainly neither a simply chemical act

— oa

THE PRINCIPLE OF VITAL AFFINITY. 315

of oxidation, nor a mere selection and appropriation of compounds previously
formed in vegetables.

On the other hand, it is known that there is an evolution of carbonic acid as
well as water from vegetables,—from the parts of fructification during their deve-
lopment even in the day time, and from all parts during the night ; and it appears
quite possible that, in both cases, this may be by a process of slow combustion,
similar to the process of oxidation which Dumas considers as characteristic of
animal life only. For, although it has been stated by Dumas that the carbonic
acid given up by vegetables during the night is only what has been absorbed by
their roots, and passed unchanged through their substance, yet I do not find any
distinct proof of this in his writings. It is certainly true, that the organic com-
pounds formed by vegetables, and taken into animal bodies, ultimately undergo
in them a chemical change nearly equivalent to slow combustion, and are thus
returned to the inorganic world; but this is in the processes of absorption, de-
composition, and excretion, of the animal textures, to be considered presently ; and
this fact affords of itself no proof, that in the previous growth and development
of animal textures, there may not be an actual formation of albuminous com-
pounds, as well as of gelatin and fat.

These facts appear sufficient to shew, that there is no such direct opposition
between vegetables and animals, as to the chemical results of their vital action,
as Dumas has represented; and even to make it probable, that, during the or-
ganic or vegetative life of animals, there will be a formation of albuminous
matter, equally as of gelatin and fat.

In fact, this question can be only finally decided by experiments to shew
whether or not the whole quantity of albumen deposited in the textures of a
growing animal may be greater than that contained in its food; or whether the
azote excreted, during a pretty long period, from an animal, by the bowels, kid-
neys, skin,* and lungst (for it appears to be well ascertained, that, from all these
parts, there is a frequent, if not an habitual, excretion of azote), is greater, under
any circumstances, than the quantity of that element contained in the albumi-
nous portion of its food, which is the only ascertained channel of the introduc-
tion of azote into the animal system ; and, although this is a difficult inquiry, we
cannot suppose that the difficulties are insurmountable. If such an excess of ex-
cretion of azote shall be ascertained, it will be nearly enough to entitle us to con-
clude that albuminous matters can be formed in the animal body, and yield it
during their decomposition there. It is not enough to say, that there is no occa-
sion for more azote in the animal economy than is contained in the albuminous
ingesta, because what is there contained is already in just the same proportion to

* See Goxpine Birp on Urinary Deposits, p. 104.
+ See Du Lone, quoted by Dumas (Organic Nature, p. 106).

316 DR ALISON’S OBSERVATIONS ON

carbon and hydrogen, as that which exists in the blood, or in the textures of ani-
mals. As there is, in the whole of the ingesta of animals, a great excess of car-
bon and hydrogen over their proportion to azote in albumen, and as oxygen is
always present in the blood, it is quite possible that a part of the azote of the
albumen taken in, may be thrown off in combination with portions of those other
elements, by the bowels and kidneys, without entering into the textures; and —
that the nourishment of the textures may be in part due to fresh albumen, formed
in the animal body by help of oxygen from the lungs, and of azote taken in by
another channel; just as we are nearly sure that part of the oil taken into an
animal is often decomposed and thrown off, and that fresh fat is often formed
from the starch or sugar of the ingesta.

There is one mode, pointed out by Liesic, in which we can have no doubt
that azote must be introduced into the blood of animals, independently of the al-
buminous ingesta, viz., by the air which is contained in the water, and still more
in the saliva, continually taken into the stomach. ‘ During the mastication of
the food, there is secreted into the mouth, from organs specially destined to this
function, a fluid, the saliva, which possesses the remarkable property of inclosing
air in the shape of froth, in a far higher degree than even soap-suds. This air, by
means of the saliva, reaches the stomach with the food, and there its oxygen en-
ters into combination, while its nitrogen is given out through the skin and lungs.”*

Now, what proof is there that the azote, thus believed to be set free in the
stomach, is excreted, unchanged, by the skin and lungs? Is it not much more
probable that it enters into fresh combinations in the prime vie and in the blood,
and is only separated from the blood, when, by the agency of the oxygen of the
air, acting, under the circumstances to be afterwards stated, with peculiar energy
on some of the constituents of the blood, itis disjoined from its union with carbon
and hydrogen.

In fact, the azote thus set at liberty in the stomach, must be in circumstances
almost exactly similar to those in which, according to the statements of MULDER
and others, ammonia is formed from air, even by the help of inorganic matter ; still
more when organic matter, although non-azotised, is present in a state of decom-
position, or an analogous condition.+ ‘By all porous substances ammonia is pro-
duced,—provided they are moist, are filled with atmospheric air, and are exposed
to a certain temperature.”

“¢ When reddened litmus paper is hung up in a bottle, filled with pure atmo-
spheric air, and when pure iron-filings, moistened with pure water, are laid at the
bottom, then the red litmus is quickly turned blue by the action of ammonia,
formed from the nitrogen on the air, and the hydrogen of the decomposed water,
the oxygen of which had combined with the iron.

* Liepie’s Animal Chemistry, pp. 113-4.
+ Mutpkr, p. 149, et seq.

THE PRINCIPLE OF VITAL AFFINITY. 317

“ Such a formation of ammonia continually takes place in the soil. There, at-
mospheric air is present, and consequently nitrogen ; hydrogen is continually libe-
rated, and thus the conditions necessary to the formation of ammonia are ful-
filled as often as cellulose, ligneous matter, starch, &c., are changed either into
humic acid, or into other constituents of the soil.”

That a partial decomposition of organized matter takes place in the stomach,
and is, indeed, the first part of the changes occurring during digestion, seems to
be sufficiently proved by some curious and important observations of Lresic
himself.* “ The fresh lining membrane of the stomach of a calf, digested with
weak muriatic acid, gives to this fluid no power of dissolving boiled flesh or coa-
gulated white of egg” (the supposed property of the Pepsin, or extract of the mu-
cous membrane there.) ‘“ But if previously allowed to dry, or if left for a time in
water, it then yields, to water acidulated with muriatic acid, a substance in mi-
nute quantity, the decomposition of which is already commenced, and is com-
pleted in the solution. If coagulated albumen be placed in this solution, the
state of decomposition is communicated to it, first at the edges, which become
translucent, pass into a mucilage, and finally dissolve. The same change gradu-
ally affects the whole mass, and, at last, it is entirely dissolved.”

I think we cannot doubt, therefore, that the air introduced into the stomach
of animals, and decomposed there, as Lrrzic supposes, must be in circumstances
peculiarly well adapted for the generation of ammonia, or the setting free of its
elements; which, as we have seen, is all that appears necessary to explain the
gradual formation in the matters absorbed from the stomach, of albumen out of
non-azotised ingesta; under the influence of vital affinities, similar to those by
which albumen is formed in vegetahles.

I am aware that Lizsie states with confidence that experiments prove that
the whole of the azote excreted in a given time by an animal, is not more than that
which is taken in by its albuminous ingesta; but in this he relies chiefly on the
experiments of BoussINGAULT, and these experiments are not considered by the
author himself as altogether satisfactory ; nor can they be satisfactory without
farther investigation of the quantity excreted by the skin and lungs, into which he
did not inquire. (See Dumas, p. 106.)

I admit it to be certain, however, from a simple comparison of the quantities
of albuminous ingesta and the azotised excretions, that the formation of albumen
in animals can be to no great extent; and I am clearly of opinion that the distinc-
tion drawn by Lizzie, of the azotised and non-azotised ingesta of animals, and the
evidence he has given of the chief destination and use of each, constitute the most
important improvement lately made, in this department of physiology. It ap-
pears now ascertained ; 1s¢, That the latter class of aliments are incapable, wm

* Animal Chemistry, pp. 110-1.
VOL. XVI. PART II. 4.

318 DR ALISON’S OBSERVATIONS ON

themselves, of adding to any of the animal textures except the fat ; but that they
are the chief material on which the oxygen of the air acts to keep up the animal
heat. 2d, That the main reliance of the animal body for the nourishment of all its
parts must be on the former class of aliments; their adequacy for that purpose
being beautifully exemplified in the life of the chick in ovo, where all the textures
are formed out of the albumen, partially converted into gelatin in the process, and
with the addition of a small quantity of oil from the yolk ; the oxygen of the air
being essential to the vital movement, but no farther concerned in the results,
- than as it carries off a certain portion of the carbon and hydrogen from the moy-
ing matter, and so occasions a loss of substance during the process of incubation.
3d, That the azotised ingesta, or the textures formed from them, are themselves
liable to this action of the oxygen when the non-azotised ingesta are deficient;
and, therefore, that an important use of the non-azotised food is, to protect the
albuminous constituents of the blood and the animal textures, from an influence
of the oxygen of the air, which, but for that protection, would be injurious, and
ultimately destructive. And I may perhaps be allowed to state what seem to me
the most important results, both as to Physiology and Pathology, which are in-
volved in these principles. j

1. Our ideas of the use of the digestive apparatus of animals are rendered
much more simple and precise. I have stated, indeed, that Dumas appears to
have erred in the way of extreme simplification, when he says that “an animal
only assimilates” (7. ¢. selects and attracts) “organic structures already formed ;
that he forms none ;” that “ digestion is therefore a simple process of absorption,
soluble substances passing directly into the blood (7.e. by the veins), for the
most part without alteration, and insoluble substances making their way into the
chyle after having been sufficiently comminuted, to be imbibed by the lacteals.”
But although we suppose that certain transformations, as well as simple absorp-
tion, must be commenced, at least, in the digestive organs, we are sure that no
complication of apparatus is necessary for accomplishing them ; the most import-
ant of all transformations necessary to life taking place in vegetables, and in or-
gans of extreme simplicity.

The following may be stated as the purposes which are served by the diges-
tive apparatus of every kind of animal, whether carnivorous or herbivorous, and
the greater complexity of the arrangements in the latter tribes must be considered
as intended merely to present a larger surface, and afford a longer time, for the
accomplishment of changes which are, in fact, identical in kind, and all of which
may be effected in the simplest form of apparatus.

(1.) This apparatus is obviously necessary, as stated by Cuvier, for the sup-
port of textures whose vital action is dependent on a continuous supply of nou-
rishment, to afford that continuous supply from aliments, the reception of which,
in the case of animals, is only occasional, and sometimes long delayed.

(2.) It is useful, as providing for the separation and immediate expulsion

THE PRINCIPLE OF VITAL AFFINITY. 319

from the body of those parts of the ingesta which are wholly inapplicable to nu-
trition, and for which no part of the living structure has any vital attraction.

(3.) It is especially useful, as giving the necessary fluidity to aliments which
must be moved to all parts of the animal frame, and applied to the nourishment
of the organs in a state of minute subdivision, but which are often introduced
into the system in a solid form, having been formed in one living structure, vege-
table or animal, and applied to the purpose of nutrition in another, and often
after a long interval of time. For this purpose, it appears certain, that various
contrivances are employed: in many cases, the mechanical process of attrition is
an essential preliminary ; in all cases, water is employed; in most cases, it would
appear, especially from the observations of Lirsic, that a certain degree of inci-
pient decomposition— speedily arrested by the action of vital affinities, but begin-
ning on the mucous membrane, and extending to the mass of aliments—precedes
and aids the action of the solvent; just in like manner as an incipient decompo-
sition of starch, and formation of soluble sugar, precedes the development of ve-
getable shoots and flowers; but especially the requisite fluidity is given by sol-
vents, applied at different spots, and which are prepared from the blood, under
the influence of appropriate stimuli, by a vital attraction, or selecting power, ex-
isting at those parts. Thus, an acid liquor is prepared at the stomach and at the
ceecum, and, with a similar intention, according to recent observations, it would
appear, that an alkaline liquor is prepared in the salivary glands, liver, and pan-
creas.

(4.) The most soluble part of the ingesta, and especially the amylaceous por-
tion, must necessarily be taken up by the veins, and carried directly to the liver
to form bile; and as this portion, unless combined with azotised matter, is inap-
plicable to the nutrition of any texture except the fat, we see here one ground for
the opinion to be afterwards stated, that the animal matter of the bile is chiefly
useful as a part of the provision for the agency of oxygen, and the maintenance
of animal heat.

(5.) Although we are uncertain how far transformations of the organic com-
pounds are effected in the animal economy, as preliminary to nutrition, yet we
_have seen that some such transformations must be admitted as a part of the
living power of animals, for the formation of fat, of gelatin, perhaps also of
albumen; and this process is pretty certainly commenced in the chyme, in the
primee vice, and particularly in the organized globules there formed, to be after-
wards carried on in the course of the circulation.

2. In the next place, the principles laid down by Lirsia as to the distinction
between the azotised and non-azotised classes of aliments, enable us distinctly to
understand the law of Prout, as to the necessity of a mixture of at least two of
the three kinds of aliment which he distinguished, the albuminous, oily, and sac-
charine, in order to maintain life. In fact, I have no doubt we may go farther (in

320 DR ALISON’S OBSERVATIONS ON

consequence of the discoveries made as to the existence of albuminous matter in
vegetables since Dr Prout wrote), and assert that more or less of albuminous mat-
ter is always necessary, because it alone, of all the solid or fluid ingesta, contains
the azote which is a necessary constituent of animal textures; and that it must be
combined either with starch or with oil, or both; partly because oil is an essential
constituent of parts of the body, and must either be furnished ready made, or
formed in the body from starch ; and partly because the animal heat, the first re-
quisite of vitality, can only be maintained by the oxygen of the air combining with
carbon and hydrogen in the blood; and if it does not find these elements in suffi-
cient quantity, and in a fit state for such union, in the other constituents of the
blood or of the textures, it will attack the albuminous portions of the blood and
textures, and so cause decomposition and wasting of the body.

We see likewise the importance of oily food, which, containing the largest
proportion of carbon and hydrogen, will yield to the oxygen the largest quantity of
carbonic acid and water, and therefore evolve the greatest quantity of caloric,—in
cold climates; and of saccharine and amylaceous food which, containing more
oxygen in itself, will furnish a smaller quantity of calorific compound with the
oxygen of the air,—in warm climates; particularly as the supply of heat from this
kind of ingesta is farther regulated and moderated by the action of the liver, in
a way to be afterwards considered.

3. We understand the principle, on which the wasting of the body is effected,

either in cases of denial of aliments, or of disease preventing their reception or
digestion ; 7. é., we understand that the oxygen of the air, introduced regularly
and uniformly in the blood by respiration, but meeting there with very different
compounds as the privation of ingesta continues, is the main agent in the process ;
acting first, as it must do in the healthy state, on the non-azotised compounds
existing in the blood, oil, cholesterine, er other constituents of the bile, and starch,
or matters recently formed from starch, and nearly destitute of azote, and which
readily give up their carbon and hydrogen; next acting on the non-azotised por-
tion of the solid textures, 7. e., the fat, and causing emaciation; afterwards acting
on the albuminous portions of the blood itself, rendering it more serous ; and then
acting directly or indirectly on the solid textures, determining ultimately such
absorption of the substance of the brain and nerves as causes delirium and in-
sensibility, and such absorption of the muscular textures, as causes death by
asthenia. It can only be by successively acting on these different matters, that
the oxygen can find the quantity of carbon and hydrogen with which it must
unite in the course of the circulation, to account for its own disappearance and
for the quantity of carbonic acid which is known to be still thrown off, for days
and weeks, while no carbonaceous matter is added to the blood ; and the order in
which the successive changes on the sensible qualities and functions of the body
occur, corresponds perfectly with the belief that the oxygen, acting on the dif-

THE PRINCIPLE OF VITAL AFFINITY. 821

ferent parts more or less rapidly, as they give up their carbon more or less easily,
is the immediate agent by which the extenuation of all is effected.

4. We understand, certainly not completely, but better now than formerly,
the nature of the changes which take place in animals long fed on one kind, even
of albuminous food, equally as when albumen is withheld; and which appear
in both cases to indicate a deficiency of the albuminous constituents of the blood ;
and likewise, certain phenomena in disease, connected with deficiency of those
albuminous constituents.

There are several facts connected with such diseases which we cannot under-
stand, until we have some farther information as to the relation to each other in
the living body, of the different constituents of the blood which are albuminous,—
the red globules which contain the largest portion of that matter,—the white glo-
bules which seem to be more immediately concerned in nutrition,—the albumen
of the serum,—and the fibrin, which is in the smallest quantity, and which differs
from the albumen only in the peculiar (vital) attraction or aggregation among its
particles ; and which appears to exist in the living state partly, and, according to
ANDRAL’s observations, entirely, in the white globules above noticed. Until the
relations of these different matters are better understood, we cannot explain how
some of the most striking symptoms of that disease which seems to be the most
directly produced by inadequate nourishment, viz., the Scurvy, are produced.
But in that disease we now know that there usually is a great deficiency in the
quantity of red globules, as well as either in the quantity or in the vital power
of the fibrin; and we can now distinctly understand how it should happen that
scurvy snould shew itself, both when there is a long-continued deficiency of suf-
ficient albuminous nourishment, and likewise when the nourishment taken is too
exclusively albuminous;—most frequently, in this last case, when it is at the same
time salted and hardened, and difficult of solution in the gastric juice, but, like-
Wise, as repeated experience has shewn, when it is fresh and nutritious, but
uniform.* In the first case (exemplified in several prisons of late years), there
is a simple deficiency of azotised nourishment ; in the other, there is a deficiency
of the non-azotised matter which should protect this nourishment; the oxygen
of the air thérefore acts upon it, and the chief result seems to be, that the formation
of the globules, apparently both of red and white globules, is prevented. Both cases
are illustrated by what happens in Bricut’s disease of the kidneys, where there
is such a change in the vital action of these organs, that they throw off prema-
turely much of the albumen of the blood ; the effect of which on the constitution
of the blood is to diminish greatly all its azotised constituents, even although a full
quantity of azotised food is taken; the specific gravity of the serum falling, and
the proportion of the red globules to the other constituents of the blood becoming

* See Bupp on Scurvy, in the Library of Medicine.
VOL. XVI. PART III. 4M

322 DR ALISON’S OBSERVATIONS ON

as small as in the worst diseases of the stomach ; while at the same time there is
a tendency to extravasation, not indeed of the red globules as in scurvy or pur-
pura, but of the serous part of the blood,—equally dependent as the extravasa-
tions in scurvy, on the condition of the blood itself.

But not only do we understand that there should be this great deficiency of
the albuminous contents of the blood in scurvy, resulting after a time from the use
of exclusively albuminous food, equally as from the denial of such food, or the
continued morbid discharge of albumen from the blood, or the deficiency of diges-
tive or assimilating power, as in chlorosis; but we understand, likewise, what ap-
pears at first sight paradoxical,—how the evils resulting from this state of the
blood should be remedied by the use of food which is not albuminous, by succu-
lent vegetables and vegetable acids. I do not say that we can understand exactly
the efficacy of the small quantities of the vegetable acids in particular, which ap-
pear to be effectual in relieving the symptoms of scurvy; but we can distinctly
perceive the principle, that, when a quantity of non-azotised matter is taken into
the blood, the oxygen of the air will have less power to act injuriously on the
albuminous constituents of the blood.

But although the distinction of the azotised and non-azotised ingesta, and
the view taken of the chief offices of the two, enable us to understand much that
was formerly obscure in regard to these points, yet it is not necessary, in ac-
quiescing in this doctrine, to deny the possibility of the formation of albumen in
the animal body. We may state other facts, occurring both in health and in dis-
ease, which are hardly consistent with the belief, either that no albuminous mat-
ter can be formed there, or that none of the albuminous matter taken into the
body is applied immediately to the formation of excretions.

1. When we attend to the invigorating effect of pure air and of exercise on all
vital action, and to the evidence we have of the increase of the red globules of
the blood (the chief part of its albuminous constituents), and of the muscular
texture throughout the body under their influence, it seems hardly possible to
doubt, that the effect of the increased introduction of oxygen into the system is
a real increase of the deposition of albuminous matter. Now, if there be no
formation of albumen in the animal body, the increased introduction of oxy-
gen is the increased application of a cause only of degradation or destruction
of such matter; whereas, if albumen can be formed out of the non-azotised in-
gesta, as we have seen that there must be a considerable discharge of carbon
and hydrogen, by help of the oxygen of the air, before the remaining elements
can fall into the arrangement necessary for that purpose, we at once perceive
that the effect of pure air and of muscular exertion must be, to increase the io
tion of that albuminous matter in the blood.

The effect of exercise in preventing or relieving the symptoms of Scurvy, ap-

THE PRINCIPLE OF VITAL AFFINITY. 298

pears to me peculiarly important in this inquiry. If we suppose that the imme-
diate cause of the diminution of the albuminous matter in the biood, which takes
place in that disease, is the action which the oxygen exerts on that matter,—in
consequence usually of the small proportion of non-azotised matter which it finds
in the blood,—and if the animal system has no power of forming albumen, we
do not see how the increased introduction of oxygen should have any but an in-
jurious effect ; but if by means of it a part, even a small part, of the blood, con-
sisting of amylaceous and oily matter, can be made to yield albumen, at the same
time that it gives out carbonic acid and water, we can distinctly understand how
the accession of scurvy should be retarded or prevented. And, in fact, we find
that this effect is very generally observed, as the result of habitual and invigora-

ting exercise.

It is stated by Sir E. Parry, that in Greenland the scurvy seldom makes its
appearance among the natives until they confine themselves in their close huts
for the winter, although the diet which they use when thus confined is the same
as when they are moving about.

In our own country we have had various examples, on a large scale, of scurvy
affecting prisoners long confined, although the diet on which they lived would not
appear to have been materially different from that on which many of the lower
ranks, particularly in Scotland, when at large, preserve their health, and are fit
for much muscular exertion. Thus the diet of the prisoners at the Millbank
Penitentiary in 1822, on which more than half of them became scorbutic (indeed
three-fourths of those above three years confined), consisted of 14 lb. of brown
bread daily, with one quart of soup, which soup had been made with from 2 to 3
oz. of the meat of ox-heads, with 3 oz. of garden stuffs, and was farther thickened
with peas or barley; and at Coldbathfield Prison, about the same time, scurvy ap-
peared pretty extensively within a few weeks after the diet had been reduced to
14 lb. of white bread, with 1 pint either of soup or gruel in the day, and 3 Ib. of
beef on Sunday.* Comparing this diet with that of many labouring men in Scot-
land, consuming about 14 lb. of oatmeal, and perhaps 1 pint of milk daily, we can
hardly doubt that the air and exercise of the latter exert an influence to improve
the condition of the blood; whereas, upon the supposition that the oxygen of the
air can give no help in forming albumen, that influence, in so far as the produc-
tion of scurvy is concerned, should be only injurious.

2. All the phenomena of Scrofulous disease appear clearly to indicate that
what we call the scrofulous diathesis, is necessarily connected with a deficiency
in the nutritious or albuminous constituents of the blood; and we can now put
that proposition in a definite and tangible form, in consequence of the important
observation of ANDRAL,—that in numerous trials made on the blood of persons

* See Hoxrorp's Second Vindication, &c. &c., pp. 4, 5, 10.

324 DR ALISON’S OBSERVATIONS ON

affected with tubercular disease, even in its earliest stage, he had always found the
proportion of the red globules, in which the largest part of the albuminous matter
is contained, less than the lowest proportion which he had ever found in healthy
persons (less than 100 in the 1000 parts, the average proportion being 127). Now
there is no proposition, in regard to the external causes of the scrofulous diathesis,
which has been more anxiously investigated of late years, or, on the whole, more
fully established than this, that it is, ceteris paribus, increased by atmospheric im-
purity and by sedentary habits, and diminished by pure air and exercise. Yet,
if the animal frame cannot form albuminous matter, the only effect on the albu-
minous portion of the blood, of the increased introduction of oxygen which is im-
plied in these circumstances, must be, to hasten the decomposition and expulsion
of the albuminous matter absorbed from the prime viz. I do not state this fact,
as affording more than a presumption against that opinion, because I am aware
it may be said that, under the influence of fresh air and exercise, a larger quantity
of albumen is taken into, or is absorbed from, the stomach and bowels, than in
sedentary persons breathing impure air; but in so far as we can judge from the
quantities taken into the body, I am pretty certain that the experience of medical
men goes to prove that, when the quantities and kind of ingesta are the same, the
beneficial effects of air and exercise in counteracting the scrofulous tendency,—
i. €., aS I believe, in increasing the proportion of albuminous matter in the blood,
may be distinctly perceived.

Indeed, independently of disease, | am strongly inclined to believe, that the
nourishment of the animal body, and especially of the muscular textures, by a
given quantity of ingesta, may be distinctly observed to be promoted by exercise,
which is hardly conceivable on the supposition, that the only truly chemical
changes which take place in the body are of the nature of oxidation, or slow
combustion, and consequent excretion, in which the oxygen of the air is the chief
agent.

3. The phenomena of Diabetes seem to me very adverse to the idea of the
amylaceous matter taken into the system, being wholly inapplicable to the forma-
tion of albumen. In that disease, the digestion and appropriation of albuminous
matter appear to go on even with unusual rapidity ; and the urea which is con-
tained in the urine, often in increased quantity in the early stage, and which is
always easily obtained from it in full quantity immediately before death, shews
that this matter is ultimately disposed of in the usual way in the animal econo-
my ; the amylaceous matter taken in must be the source of all the sugar which
is formed in so great quantity, and which characterizes the disease ; and it seems
to be liable only to that kind of decomposition to which such matter is liable, by
simply chemical affinities, at that temperature, and under the influence of water
and oxygen; it is converted into sugar, and runs off by the kidneys, 2. e., it
seems to be actuated by no vital affinity. Now, if all the starch taken into the

aa}

THE PRINCIPLE OF VITAL AFFINITY. 325

living body were useful, as this theory supposes, only by yielding to the simply
chemical action of oxygen, and so giving off caloric, we do not see how these
changes in diabetes should interfere with that office, or how they should involve
so great derangement of the system, and particularly so much gradual wasting of
all the textures. But if the starch taken into the system is liable to transforma-
tions resulting from vital affinities, and in which albumen is generated, then we
can understand, that a disease in which starch seems to lose all tendency to vital
action, and is rapidly thrown off, should be attended with this emaciation and
debility.

4. When we attend to the phenomena of Lithiasis, 7. ¢., the morbid forma-
tion of uric acid, and the effects of different kinds of diet upon it, we meet with
facts hardly to be reconciled to the idea of the albuminous ingesta being all des-
tined for nutrition, and the non-azotised for combination with oxygen and excre-
tion. It is well known, that Liesic pointed out that this diseased state depends
on imperfect oxidation of the albuminous matter in the blood, which is destined
to excretion (causing a formation of uric acid, when a fuller oxidation would pro-
duce urea and carbonic acid); and that he supposed all the albuminous matter
which unites with oxygen in the blood, to be the product of absorption from the
textures, the recently introduced albumen being, according to his theory, destined
for nutrition only. Hence he argued, that a vegetable diet, increasing the quan-
tity of non-azotised ingredients of the blood, with which the oxygen most readily
unites, would leave less oxygen for the azotised or albuminous constituents, and
ageravate the disease. But experience has shewn, particularly since the obser-
vations of MAGENDIE were published, that the disease is more generally mitigated
by a vegetable diet, under which, as it would appear, the whole quantity of azo-
tised matter in the blood and in the urine is diminished, and the oxygen taken in
is sufficient for its full oxidation. And the experiments of several authors have
shewn, that the quantity of azotised matter thrown off by the kidneys increases
greatly (may be nearly doubled) within a few hours after highly azotised food
is taken. From which facts it would appear, that the azotised matter thrown off
by the kidneys, is derived not merely from absorption of the textures, but like-
wise directly from the ingesta; and if so, the distinction of the azotised ingesta,
destined only for nutrition, and the non-azotised, destined only for excretion, is
not observed by nature; and it becomes extremely probable, that, as part of the
albuminous ingesta are excreted, so a portion of fresh albuminous matter is formed
in the blood, and applied, in the first instance, to the nutrition of textures.

IV. It is at all events certain, that Gelatin is formed in the living body, and
its composition, as stated by LirBic, Cy; Nis Hs, Ox

or by Muuprr, Cuz Nis Hoo Ors
compared with that of albumen, Cin Nis His Ow
VOL. XVI. PART III. 4N

326 DR ALISON’S OBSERVATIONS ON

seems evidently to denote that it is most probably formed from the elements of
albumen, by a farther separation of carbon and hydrogen; aided by the agency of
the oxygen of the air. Lresie seems to consider it as certain, that this separa-
tion must be from the elements of albumen, and, therefore, that gelatin can only
be formed from albumen ; but it is possible, also, that it may take place from
the elements of starch with ammonia, oil being formed at the same time.

If we take the numbers given by MuLpER as representing the composition of
gelatin, this appears very distinctly. Thus,

C N H O
To starch, oa UO “LUU
Add ammonia, A) 6 18 nhs

From this subtract,

Elements of gelatin, 39 6 30 15
co) ee 88 85

And again, 5 equivalents of fat, 60... 50 5

+ Sala 38 80

which is exactly 21 equivalents of carbonic acid with 38 of water, excreted by
the skin and lungs.

The “ tritoxide of protein,” lately so fully considered by Mu1.DER, approaches
so nearly in its properties to gelatin, that we may presume its formation will de-
pend on nearly the same conditions; and accordingly we find, that it may be
formed from albumen by the long-continued application of heat, air, and water ;
and that it is formed in large quantities in inflamed parts, where the stagnation
of arterial blood (carrying oxygen) and the increased temperature plainly indi-
cate that an increased application of oxygen is going on.

But as there is a remarkable discrepancy of statement as to the chemical rela-
tion of gelatin to the albuminous compounds, we must regard the precise na-
ture of the change effected in this department of the animal economy as some-
what doubtful.

In thus attempting to trace the nature of the processes, wherever they may
be carried on, by which carbon, nitrogen, hydrogen, and oxygen, uniting with
other elements in smaller proportion, fall into the combinations which constitute
the animal textures, and in attempting likewise to assign the province of the
vital affinities in these processes, we must admit very material deficiency of inm-
formation. We do not perceive, for example, how it should happen that the amy-
laceous matter, which forms the greater part of the ingesta of so many animals,

THE PRINCIPLE OF VITAL AFFINITY. 327

should hardly appear in their blood, even in that diseased state (diabetes) in
which it passes off so copiously, in the form of sugar, by the kidneys. Neither is
it easy to understand why the gelatin, formed probably in the course of the cir-
culation, and deposited in so large quantities from the bloodvessels, should not
appear in the blood. We are very imperfectly informed as to the origin, the use,
or even the composition, of that animal matter, or rather congeries of animal
matters, to which the name Extractive is applied. We are still in doubt as to
the purposes served by the globules of the blood, both red and white, and the
place and mode of their composition and decomposition.

But, admitting all these difficulties as to the details of the chemical changes,
still these leading facts are ascertained :—that, in the cells of living vegetables,
amylaceous, fatty, and albuminous compounds are formed,—and that, in the cir-
culation through different parts of animal bodies, these compounds are selected
and appropriated, and, in some instances, farther transformed, so that a farther
formation of oily matter, and a new formation of gelatin, and probably of al-
buminous matter, takes place, applicable to the immediate nourishment of tex-
tures; that all these materials are formed ultimately from carbonic acid, water,
and ammonia, existing in the atmosphere; that the carbon, originally fixed from
the carbonic acid, is the most essential of all the ingredients, and the proportion of
oxygen in all these organic matters, much less than in the inorganic compounds
from which they are derived : that the affinities whereby the carbon is enabled
to enter into these combinations with the other elements, existing in these organic
compounds, to the exclusion of much oxygen, are peculiar to the state of life,
and liable to variations by causes which do not affect dead matter; and that, in
so far as the oxygen of the air is concerned in the formation of any of these com-
pounds, it acts only by carrying off such portions of carbon and hydrogen, as en-
able the remainder of those elements to fall into certain new combinations with
the others which are there present.

We may state another difficulty here, as leading directly to the next important
question in vital chemistry, the rationale of the Excretions; viz., Why does the
oxygen, which certainly attaches itself to the red globules in the lungs, not give
evidence of its combining with the carbon in them, by giving them the dark colour,
until it has passed along the arteries, and through the capillaries of the system,
and entered the veins? This fact is noticed both by Prout and Linpic. “ The
oxygen absorbed at the lungs,” says Dr Prout, ‘remains in some peculiar state
of union with the blood (query, As oxygenated water, or some analogous com-
pound ”) till the blood reaches the ultimate terminations of the arteries. In these
minute tubes the oxygen changes its mode of action ; it combines with a portion of
carbon, and is converted into carbonic acid.’”—(Bridgewater Treatise, p. 536.)

Li=zsBiG goes a step farther in explanation of the change of mode of action of
the oxygen, when he says, ‘‘ The globules of the blood serve to transport the oxy-

398 DR ALISON’S OBSERVATIONS ON

gen, which they give up in their passage through the capillary vessels. Here the
current of oxygen meets with the compounds produced by the transformation of the
tissues, and combines with their carbon to form carbonic acid, and with their hy-
drogen to form water.”—(Animal Chemistry, p. 60.) But neither author has
stated as clearly as I think may be done, on what principle it is that the oxygen
changes its mode of action when it meets with these products of the transforma-
tion of the tissues ; or, in simpler language, with the matters that have been ab-
sorbed from the living tissues. I believe the true reason to be, that this is an ex-
emplification cf a general principle of essential importance, which has been par-
tially stated, but never, so far as I know, fully developed, viz., that all vital
affinities are of transient duration only ; and that those which actuate the matter
of animal bodies especially, soon fail of efficacy, and at the temperature, and
under the other conditions there present, give place to simply chemical affinities,
which determine the formation of a very different set of compounds ; therefore,
that as long as the oxygen is passing along the arteries, and is in contact with
albuminous matter, to which vital properties have been recently communicated,
and which are actuated by vital affinities, it has little power to affect them ; but
when it meets with the same compounds in the substance of the textures, or
already absorbed from them, 2. ¢., with albuminous or other animal matter, which,
according to the expression often, but vaguely, used, has become effete, or has lost
its vital properties, it can act on them in the living body in like manner as it
does, at the same temperature, in the dead body.

But, in order to establish this point, it is necessary to enter on the second
part of our inquiry into the chemical changes of animal bodies, 7. ¢., the pecu-
liarities of the Excretions ; jirst, of the greatest and most general of all the excre-
tions from living bodies, the carbonic acid thrown off from the respiratory organs,
both of animals and plants, of which Dr Prout says, that “ the precise use of its
constant evolution we know not,”—and then, of the other excretions from animal
bodies. Until we have precise knowledge of the purpose which is served, and of
the laws which are obeyed, by the matters which are continually expelled from
living bodies, it is obvious that our notions in regard to vital affinities must be
very unsatisfactory. In entering on this subject, I assume it as ascertained that
all the matters, peculiar to the excretions from the living body, pre-exist in the
blood, and are only eliminated from the blood at the organs where they appear;
so that any chemical changes necessary for their formation, take place either in
the cells of the textures, or in the circulating blood, or both, not in the glands
which separate them, at least not externally to the vessels of those glands.

The first idea that must occur to every one who considers that large quantities
of extraneous matter enter into every living body, different from those that can be
traced in any of its textures, is, that the excretions from living bodies are simply ~
those portions of the ingesta which are not applied to the maintenance of the or-

THE PRINCIPLE OF VITAL AFFINITY. 329

ganized structure. And that certain excretions are strictly of this character,
seems to be fully ascertained, ¢. g., the great excretion of oxygen from living vege-
tables, is merely separated from the carbon of the carbonic acid which enters them,
when that carbon unites with the elements of water to form starch; and a part,
at least, of the carbonic acid and of the water which are thrown off from a living
animal, when it lives on sugar or starch, and forms oil or fat, or when it lives on
albuminous compounds and forms gelatin, appears, from what was formerly stated,
to be formed, by help of the oxygen of the air, from such portions of the carbon
and hydrogen, of the starch or of the albumen, as are excluded when the new ar-
rangement takes place, by which fat and gelatin are formed.

It is important to keep in mind, that, in regard to ail the excretions, we have
sufficient evidence of their being partly furnished in this way; 7. ¢., consisting of
elements which have been taken into the body, but which are either redundant,
or inapplicable to the nutrition of its textures; and that these are thrown off
either alone, or combined only with a portion of the oxygen absorbed from the
air, and the influence of which on the excretions will be considered afterwards.
Thus it is certain, that part of the excretion from the bowels consists merely of
unassimilated ingesta. It has been lately stated, with much probability, that
certain matters in a putrescent state, absorbed into the circulation, find a natural
vent in the mucous glands of the lower intestines.* When we consider that the bile
is secreted chiefly from the venous blood of the vena portee, and that this must ne-
cessarily be usually loaded with matters recently absorbed by the gastric and me-
senteric veins, and not yet taken into the general circulation; and when we farther
remember the small proportion of azote in the animal matter of bile, and the large
quantity of this secretion in herbivorous animals, we can have no doubt that much
of the matter (particularly the non-azotised matter) taken up by the veins, is brought
to the liver only that it may be discharged thence in the form of choleic acid. We
know likewise, that certain volatile matters, as alcohol or turpentine, however taken
into the system, are excreted by the lungs, either unchanged or united (as in the
case of phosphorus), with a certain portion of oxygen. And, in like manner, we
have evidence, already stated, in regard to the secretion at the kidneys (although
that evidence was not duly considered by Liresia), that a considerable part of it is
frequently formed from matters recently absorbed into the blood from the prime
viee, and which had never been applied to the nutrition of textures. As we know
that the quantity of uric acid and urea, the most highly azotised of the animal
compounds excreted, is much greater under the use of animal (7. ¢., highly azo-
tised food) than of vegetable, while the health and even the muscular strength

* See CarreNnTER’s Physiology, 3d edition, p. 685. This principle is probably of great impor-
tance in the pathology, both of hectic and typhoid fever, aud of that form of dysentery which seems to
result, as a specific inflammation, from certain putrescent miasmata.

VOL, XVI. PART III. 40

330 DR ALISON’S OBSERVATIONS ON

may be equal; and that by the use of highly azotised animal food, the animal
matter of the urine may be increased, according to CHossat’s observations, from
9-9 grains in the ounce to 17; and the proportion of urea voided may be even in-
creased from 237 to 819; and, as we learn from the experiments of CHossat, that
a great part of this increase may take place within a few hours after animal food,
rich in azote, is taken, we can have little doubt that a considerable part of that azo-
tized food must have passed off by the kidneys without having been applied to
the nutrition of any of the textures. And this appears to be confirmed by obser-
vations on that disease which arises from a morbid formation of uric acid in the
system, because I think two facts may be regarded as nearly ascertained in re-
gard to that state, viz., 1. That it depends essentially on imperfect oxidation of
the azotised matters contained in the blood, and destined to excretion ;* and, 2.
That it is most generally and effectually diminished by a vegetable diet, lessening
the quantity of azotised matter taken into the body; whereas, if all the azotised
matter destined to excretion had been the production of absorption in the body it-
self, the introduction of much non-azotised matter, with which the oxygen of the
air certainly combines in the circulation, would have left less oxygen to unite
with that effete azotised matter, and would have determined, therefore, a greater
production of the imperfectly oxidised uric acid, as proportioned to the urea.

These facts seem sufficiently to illustrate and justify the common opinion,
that the excretions are furnished, in part, by such portions of the ingesta as are
either inapplicable to nutrition or redundant; and which are, therefore, either

* This is shewn thus—

C N H O

Uric acid 100 40 40 60
Add water sia ss 40 40
5 OXON, | on. oo SH 60

100 40 80 160
Subtract urea, 40 40 80 40

60 we ... 120 = 60 CO, Carbonic acid.

{ Leste, taking for granted that it is the non-azotised portion of the ingesta only, that is united
with oxygen from the air in the course of the circulation, thought the use of vegetable food improper in
this state of the body, as absorbing the oxygen, and causing, therefore, imperfect oxidation of the azo-
tised matter absorbed from the textures, and about to form urea and uric acid. But the observa-
tions of MacEnpre and others, shewing that both in health and disease the proportion of urie acid
formed is generally less under a vegetable diet than an animal, particularly when taken in connec-
tion with the facts stated above as to urea, must be regarded as proving, that the idea of non-azotised
food having that exclusive tendency to unite immediately with oxygen in the blood, must be erro-

neous.—See Carpenter’s Physiology, § 849, 850.

THE PRINCIPLE OF VITAL AFFINITY. 331

excluded from the new combinations which are formed in a living body, or re-
jected from the selections which are there made.

Now, if we consider it as ascertained, that a part of all the aliments taken
into a living animal body, combines immediately with the oxygen of the air, in
the blood, and is thrown off by the excretions in the form of water, carbonic acid,
and ammonia,—or in forms which tend towards, and quickly resolve themselves
into, these compounds,—we see a distinct confirmation of what was formerly
stated, as to the nature of vital affinity, viz., that it does not, properly speaking,
supersede ordinary chemical affinities, but is merely superadded to them ; so that
chemical compounds, taken into animal bodies, are subjected to these attractions
as well as others, and are divided between the substances thus acting upon them,
in proportions varying probably, as in other cases, according to the strength of the
affinities and the quantities of matter exerting them. This, indeed, appears suf-
ficiently demonstrated by the effect of exercise (already considered) on the excre-
tions by the skin and lungs, on the one hand, and on the deposition of fat or of
albuminous compounds, on the other; we know, that, as the quantity of carbonic
acid and water thrown off are increased by that cause, the quantity of fat de-
posited from the blood is diminished,—implying that, by the increased quantity
of oxygen presented to them by the blood, portions of the carbon and hydrogen
of the ingesta, which would otherwise have been subjected to the vital affinity
which forms fat, have yielded to the simply chemical affinity which disposes them
to unite with oxygen and pass off; and again, it is at least highly probable, that,
under this increased supply of oxygen, increasing, by a simply chemical attrac-
tion, the proportion of carbon and hydrogen which escape from the ingesta, the
effect of the vital affinity by which the remaining elements of the ingesta combine
to form albuminous matter, is likewise increased.

But we have next to consider the evidence for the existence, and the object
and importance of another and totally distinct source, long believed to contribute
to the formation of the excretions, viz., matter which has formed part of the tex-
tures of the living body, and been re-absorbed from them, with the intention of
being thrown out of the body; 2. ¢., the dependence of excretion on what Dr Prout
calls “ destructive assimilation.”

The mixture, of this matter with the blood appears to be necessary for all
the changes there, from which the different excreted fluids result; or, it may be

' supposed not merely to escape itself, but to act as a ferment, promoting these

changes, and thereby determining the entrance into these combinations, and the
expulsion from the body, of the portions of the ingesta which are not required
for nutrition.

The term efete matter has been very generally employed in discussions on
this subject ; but it does not appear to me, that any very definite idea has been
annexed to the term, nor that any principle has been pointed out to explain how

332 DR ALISON’S OBSERVATIONS ON

animal matter becomes effete,—why the absorption of matter once deposited in the
textures should be a necessary concomitant of animal life,—or why the elements
composing these textures should enter into new combinations, and then should
require to be expelled from the body. But I am persuaded it will appear, on ex-
amining the subject, that the principle formerly stated, of the transient ewistence
of vital affinities in every portion of matter which becomes endowed with them, is
both supported by sufficient evidence, and adequate to the explanation of these
phenomena.

The leading facts on which this conclusion may be rested are the following :—

1. We know that a continual process of absorption and change of materials
is always going on in every living animal texture, and is, in fact, the cause why
a continual act of nutrition (the most characteristic of all the functions of animals)
is essential, not only during growth, but even in the decline of the body, to the
maintenance of its structure and properties.

2. We know that, simultaneous with this absorption, there is a continual
process of excretion going on from every living animal, and that, by these excre-
tions, a quantity of all the elements constituting the animal textures is con-
tinually thrown off; and farther, it appears to be indicated, although I cannot
say fully established by Lresic, that the sum of the chemical elements thrown
off by the different excretions sufficiently accounts for (the presence of oxygen
and water being kept in mind), not merely the part of the blood which is not ap-
plied to the nourishment of the textures, but the whole of the blood.*

3. We know that the excretions, at least that some of them, not only con-
tinue but increase, particularly under any increased muscular exertion, and that
their nature remains the same, in an animal deprived of aliment, and in a
state of rapid emaciation, as in one that is fully supplied with aliment, and per-
fectly nourished. ‘‘ In a starving man, who is in any way compelled to undergo
severe and continued exertion,” says LieBic, “ more urea is excreted than in the
most highly fed individual, if at rest. In fevers, and during rapid emaciation,
according to Prout, the urine contains more urea than in health.” +

While these facts prove incontestably that a great part of the matter thrown
off from every living body must be the product of absorption from the body it-
self, let us next consider the information that we have, as to the change which
is wrought upon the absorbed materials before they are expelled from the body.

1. The most leading fact in this part of the subject is, that, in the natural
state, none of the organic compounds which exist in the textures, appear in any of the

* See Animal Chemistry, p, 186 and 152. This conclusion, however, is not to be regarded as
established, various fallacies being connected with it. In fact, it seems to me only certain that the
carbon and nitrogen are in the same proportions in the excretions as in the blood.

} Animal Chemistry, p. 139.

= —_—————_—_
———

THE PRINCIPLE OF VITAL AFFINITY. oo

excretions, although it can only be through the excretions that they disappear
from the body, and although the earthy or saline matters absorbed from the tex-
tures are there found. The animal compounds existing in the textures must
therefore have undergone a great chemical change, in the process by which they
are removed from their place in the living body, and finally expelled from it; and
this notwithstanding that they are placed in circumstances exactly similar to
those, in which their previous original separation and deposition from the blood
in the minute capillaries took place.

2. The substances into which these animal compounds (with or without ad-
ditions derived directly from the prime viz) have resolved themselves almost en-
tirely before they are thrown off in the excretions, must be, the water which is the
basis of all, the carbonic acid thrown off by the lungs and skin, the choleic acid
thrown off by the liver, and the urea and uric acid thrown off by the kidneys.
All these last we know to be formed in the course of the circulation, not in the or-
gans by which they are separated from the blood ; and all possess these essential
peculiarities, distinguishing them from the compounds forming the textures ;
Jirst, that they are crystallizable, z.¢., the elements composing them are so ar-
ranged as to be capable of assuming the definite forms peculiar to inorganic
matter; and secondly, that they are poisonous to the living body when they are
allowed to accumulate in the blood, and, therefore, that their continual expulsion
is essential to life.

3. When we farther examine these compounds, into which the animal tex-
tures have resolved themselves before they are expelled from the body, we
find that they are substantially the same as those, into which these textures are
ultimately converted after death, by help of union with oxygen, when in contact
with air and water, and at a certain temperature,—viz., water, carbonic acid, and
ammonia, the small quantities of sulphur and phosphorus contained in the ani-
mal textures, combining likewise with oxygen so as to form sulphuric and phos-
phoric acids before they are expelled.

C N H O
Thus Urea consists of 100 100 200 100
Add water, bets see 100 100

100 100 300 200 =Carbonic acid and ammonia.

Again, choleic acid consists of 76 2 60 2
Subtract urea 2 2 4 2
74 ae 56 20 Adding oxygen freely,
184
We have, 74 Abed 56 204 =74 CO, + 56 HO carbonic

acid and water.

VOL. XVI. PART III. 4p

334 DR ALISON’S OBSERVATIONS ON

Thus the general fact seems established, that the excretions from the living
body are only an intermediate stage between the organic compounds, forming the
animal textures, and the inorganic chemical compounds into which these are ulti-
mately resolved after death ; and that in the same living body, and in the same
parts of it, at the same temperature, and when in contact with the same sub-
stances, the same chemical elements, carbon, nitrogen, hydrogen, and oxygen,
are continually acting on one another so as to form two distinct sets of com-
pounds; the one set peculiar to living bodies, always attaching to them certain
saline and earthy matters, sulphur or phosphorus, and always taking the form of
cells or fibres, never of crystals,—and building up the organised frame; the other
set rejecting those adventitious matters, tending always to the crystalline forms,
and to the same mode of combination of the elements as takes place, under the
same temperature, where no living structures exist,—and which are always ex-
pelled from the organised frame. These are facts of such obvious importance,
so generally observed and characteristic, that the physiologist cannot decline to
take cognizance of them, and arrange them together, and have some general ex-
pression for them. It does not appear possible to express these facts otherwise
than by saying, that the particles of these elements taken into living bodies, are
under the influence of different chemical laws at different times; which is exactly
what we mean by saying, that they are first actuated by vital affinities (called
vital because they are seen only in living structures, and in connection with the
indications of life), by which the organised structure is gradually formed, and
afterwards by simply chemical affinities by which it is gradually worn down ; and
that both are in continual operation during Jife. And thus it appears that the
chemical change, which always attends the absorption, and discharge by the ex-
cretions, of all parts of a living body, is simply this.—that they lose their vital pro-
perties, and become liable to the same affinities among themselves, and the same
action with the oxygen brought to them by the blood, as prevail in the dead state.

This inference as to the loss of vital properties, has been stated by several
authors of late years, in regard to those portions of the living solids which per-
form distinctly vital actions in a visible or tangible form, as the portions of mus-
cular fibre or nervous matter, which are employed in vital motions and sensations ;
but as the facts from which we draw the inference are equally true of bones and
membranes, and other animal solids, unconcerned in any such vital actions, it
seems to me necessary to extend the inference to all those portions of matter which
exhibit in a living body the vital affinities, as well as to those which take on any
kind of vital movement, or are concerned in any nervous actions.

That oxygen must be the main agent in effecting the changes of these animal
compounds, which precede their expulsion in the excretions, is sufficiently proved
by observing, jirst, that it is uniformly and necessarily applied to them when
these changes are going on; secondly, that the compounds into which the animal

a ct GO OGL

THE PRINCIPLE OF VITAL AFFINITY. 335

matters are converted before they are excreted, contain a much larger proportion
of oxygen than those compounds themselves ; and, thirdly, that it is also neces-
sarily applied to all dead animal matter when the decomposition, leading to the
same ultimate results, takes place in it.

It is true that the Bile does not contain a larger proportion of oxygen than
albumen, but it contains a larger proportion than any kind of oil or fat, from
which it appears certain that it is partly formed ; and, farther, we have perfectly
good evidence, very well stated by Lresie, that by far the greater part of the
bile in all animals, and nearly the whole in the carnivora, is re-absorbed into the
blood, and exposed gradually to the action of oxygen on it above indicated, and
therefore that the secretion of the liver, so far as it is destined to excretion, re-
solves itself chiefly into the excretion of carbonic acid and water by the skin and
lungs, and partially also into that of urea and uric acid by the kidneys; which
arrangement, we have reason to believe, is designed with a view to the main-
tenance of animal heat, to be considered afterwards.

It may here be a question, whether the simply chemical attraction of the

oxygen, carried to the extremities of the vessels in the blood, is the cause, or part

of the cause, of the act of absorption, antagonizing the strictly vital attraction by
which the elements of nutrition are brought into the cells of the textures. But
the power exercised by the excretory glands themselves appears manifestly to be
merely that of selection and attraction of the material destined to pass out by
them, by an agency of cells quite analogous to that by which the cells of the
textures appropriate their own nourishment; and by this simple and beautiful
principle, of certain cells, or the cells in a certain part of the structure, exerting a
peculiar attraction for certain matters only, existing in the compound fluid pre-
sented to them, nature has provided both for the nutrition and growth of all the
textures, and for the expulsion of such matters as must be evolved from the
blood, and have not such a property of volatility as might enable them to pass off

by the skin and lungs.

It may be objected to the statement now made as to the respective provinces
of vital and simply chemical affinities, that vegetable and animal substances re-
moved from the living structures which formed them, are often of long and
nearly indefinite duration; but it would be an error to infer from this fact, that
the affinities which led to their formation act as long as they endure; we can
only infer that the conditions, under which other chemical affinities act on such
compounds, are not present ; and the general property of the inertia of matter
prevents their changing the condition into which they have been once brought,
just as the same substance reduced to the state of charcoal may remain long
unaltered, although in contact with oxygen, and liable to an affinity with that
gas, which, under a slight variation of circumstances, would convert it into car-

330 DR ALISON’S OBSERVATIONS ON

bonic acid. ‘There exists,” says Liesiec, “in every compound a statical momen-
tum (moment statique) of the attractive powers which combine the elements ;
the inertia of the elementary atoms, or their disposition to persist in the same
state, or in the same place, where they actually exist, acts there as a special
force. If the atoms of sugar were held together by as strong a force as the
elements of sulphate of potass, they would suffer as little disturbance as these,
from the presence of a ferment or a putrescent body. But this is not the case.
The elements of all organic compounds which are capable of undergoing transfor-
mations preserve their condition only in virtue of the inertia, which is one of
their properties.”*

Again, it has been reasonably objected to the doctrine of the nutrition and
growth of animals being due to an affinity between their textures and the in-
gesta taken into them, which ceases when these ingesta lose their vitality, that
these aliments are very generally in a dead state before they are submitted to
the organs of digestion.t But I apprehend the proper answer to this to be,
that,—so far as the chemical phenomena of life are concerned, the death of an
entire living structure is quite distinct from the death of any one of its com-
ponent parts. The whole of a living structure dies when its nutrition, the most
essential of its functions, is brought to a stand by the failure of circulation; but
the organic compounds, formed, as I believe, by vital affinities in that structure,
remain for very various periods of time unaltered, or are preserved, as LIEBIG
expresses it, by the inertia of matter, from forming those inorganic compounds
to which they are ultimately destined ; and as long as they remain fresh, or, al-
though undergoing decomposition, have not yet reverted to those inorganic com-
pounds, they seem to be still capable of being acted on by the vital affinities of
animals. But, when the simply chemical affinities have really resumed their
power, when a part of the body has undergone a certain degree of putrefaction,—
when the carbon of these compounds has passed into the state of carbonic acid,—or
even when this and the other elements have combined so as to form the excretions,
which are steps in the process by which they revert to carbonic acid, water, and
ammonia,—they are no longer capable of being applied to the nutrition of animal
bodies, until they have been again subjected to the influence of vegetable life.
The fact of their falling into the combinations which form the excretions, in the
act of absorption from the living textures, must be regarded as proof that they
have lost their own living properties, and can no longer form part of a living
texture, although still within a living structure. This death of the individual
molecules forming the living textures, I take to be the counterpart of the conti-
nued nutrition of those textures during life, as a general fact in the history of

* « Sur les Phenomenes de la Fermentation,’ &c. Annales de Chimie, t. 1xxi., p. 19, 193.
+ See the Review of Prout’s 4th edition, in British and Foreign Review.

THE PRINCIPLE OF VITAL AFFINITY: 337

living animals. It is by thus losing their vitality that these molecules become
liable to the interstitial absorption (of HuNnTER); and their places are taken by
fresh molecules by virtue of the vital attraction which constitutes nutrition.

It appears certain also, that the healthy exercise of the vital functions of any
texture (although within certain limits it strengthens all the vital properties, and
augments the living structure, apparently by attracting an increased flow of blood)
determines the more speedy death of the molecules composing it, and the more
rapid change of its particles by absorption. This may be expressed by saying,
that this mode of vital action, as well as all muscular and nervous action, is sub-
ject to the general law of alternate increase and diminution. Hence the in-
crease of absorption, and therefore of the excretions from exercise, even when
all ingesta have ceased. And hence, also, if the vital act of nutrition in any tex-
ture is morbidly excited, as happens in every case of inflammation tending to the
formation of plastic lymph, we have subsequently an increased loss of vitality
in the molecules of that part; and therefore, either the formation of purulent
matter destined to excretion, or the increased absorption of the newly formed
or effused lymph, or the ulcerative absorption of the solids previously existing,
or sloughing, or gangrene, —all well-known results of the inflammation, but which
have not been duly regarded as all implying more or less partial loss of vitality,
and therefore dependent on the same principle; and which experience shews to
be linked together and even to graduate into one another.

In like manner the progressive absorption of HuNTER is probably to be ascribed
to the influence of pressure, injuring and permanently destroying the vitality of
parts not intended nor fitted to undergo pressure, and thereby preparing them for
absorption and for the action of oxygen.

It is hardly necessary to add to this statement, after the researches of DuLone
and Desprerz, of Dumas and of Liesic, that the combination of oxygen with
the other constituents of the excretions, and particularly with the carbon and
hydrogen, is (as has always been maintained by most physiologists in this coun-
try) the true cause of Animal Heat; and it cannot be doubted that one of the
uses of the aliments, especially the non-azotised aliments, continually taken into
the body, is merely to enter into this combination, and fulfil this purpose. But
there is one principle on this subject, not so generally recognised, but which the
observations of Lirsic, and likewise of ScHERER, of PETTENHOFFER, and of
BovcHarpaT and Sanpras,* seem to make nearly certain, viz., that a principal
use of the secretion of the Liver (7. ¢. of the animal matter there secreted) is, to
serve as a reservoir for the most easily combustible matter which is taken into
the primee vie ; so that,—just as the chyme of the stomach and intestines fur-
nish a pretty constant supply of nourishment from occasional supplies of aliment,—

* See Pacer’s Report in Forses’s Journal, April 1846, pp. 561 and 562.
VOL. XVI. PART III. 4Q

338 DR ALISON’S OBSERVATIONS ON

so the Bile from the liver, likewise reabsorbed as it passes down the prime vie,
furnishes to the blood a pretty constant supply of matter fit for calorific combina-
tion with oxygen, out of the occasional ingesta.

The proofs of this proposition, and its importance, appear from the following
facts, ascertained by these authors. 1. That by far the greater part of the amy-
laceous matter taken into the stomach, is converted into soluble matter (dextrine
and sugar) in the primee vise, and these must necessarily be absorbed by the
veins, and of course carried to the vena portze and liver. From thence a part of
this matter, no doubt, will pass immediately by the venze cavee hepatice to the
right side of the heart and lungs, and come immediately into contact with the
oxygen ; but a part, meeting a portion of effete animal matter in the venous blood
will aid in the formation of bile in this way :

C N H 0)
4 equivalents of starch 48 ane, oS 40
Add 1 of ammonia vee 1 3

Subtract elements of choleic acid 38 1 33 inl

10 = Ad 29

requiring only one part of oxygen to pass into 10 CO, + 10 HO, carbonic acid
and water; which accounts for the great quantity of bile secreted by herbivorous
animals; and accounts likewise for the secretion of bile being chiefly from venous
blood, inasmuch as very little oxygen is required for its formation, and its chief
pabulum has been recently absorbed by the veins. In so far as bile is formed
from fat, it must be by help of more oxygen, and, therefore, probably from
arterial blood.

2. That of the bile formed and discharged into the intestines, the greater part,
even in the herbivora, and almost the whole in the carnivora, is reabsorbed into
the blood, and decomposed in the process, the pure bile appearing distinctly in
the feeces almost exclusively in the case either of diarrhoea, or of the operation of
cathartics. When to these facts we add these considerations, that biliary matter
retained in the blood, as in one form of jaundice, acts as a poison, and that it
cannot be of use in the nutrition of the textures, which is provided for by the
albuminous contents of the blood, we can hardly doubt that it is reabsorbed into
the blood, only that it (or its elements) may unite with oxygen, and be thrown
off as carbonic acid and water, with a little urea; and therefore, that the liver
is an appendage to the digestive organs, destined for the proper disposal of the
calorific, rather than the nutritious portions of the food, and for the necessary
separation of these two; and that the circulation of the matter destined to this

THE PRINCIPLE OF VITAL AFFINITY. — 339

ultimate object, through the liver, answers the important purpose of equalizing
the quantity of matter in the blood, which is always ready for this calorific union
with oxygen.

This doctrine, as to the chief use of the animal matter of the bile, appears to
correspond perfectly with several known and important facts. When the quan-
tity of bile thrown off by the liver, and discharged by the bowels, is decidedly
greater than usual, the animal heat is remarkably depressed, as in cholera, appa-
rently because the quantity reabsorbed and applied to the evolution of heat, is
diminished. In herbivorous animals, the quantity of bile discharged from the
bowels is much greater than in the carnivorous, because the quantity of amy-
laceous matter which they consume is so much greater, that a much larger quan-
tity is secreted, and if all reabsorbed into the blood, it would cause a morbid in-
crease of heat. Again, in warm climates and seasons, the formation of bile is
apparently stimulated, the liver is excited to increased action, and there is such
an increase of the discharge by the bowels, as serves to lessen the quantity of
combustible matter in the blood, and keep down the temperature of the body ;
but then this increased stimulation of the liver renders it more liable to various
forms of disease.

When we say that oxygen, acting on the redundant, on the non-azotised, and
on the effete matters with which it meets in the blood, is the main agent in form-
ing the excretions, and causing the waste of the body, we use language which is,
toa certain degree, ambiguous. It seems to me that the oxygen is probably capable
of acting on all the matters in the blood for which there is no strong vital
affinity in the body; and that the action of the oxygen on the matters which
are ready to be, or have been, absorbed from the textures, is rather the con-
sequence, than the cause, of their having lost their vital properties, and thereby
come under the dominion of ordinary chemical affinities. The oxygen is, no
doubt, the agent by which the gradual extenuation of the body, in death by
famine, or by many lingering diseases, is effected, but this agency of the oxygen
is in itself salutary, and even necessary to life; the real cause of death is, that
cause which prevents the loss of substance effected by the oxygen from being im-
mediately repaired, 7. ¢., it is the deficiency of nourishment, to take the place of
those portions of the textures which have lost their vital properties, and therefore
come under the dominion of the oxygen.

This seems to be confirmed by the fact which appears to have been fully as-
certained by CuossatT, that the rate of waste, 2. ¢., the rapidity of absorption of
the textures of the body, is greatest shortly before death, 7. ¢., when the supply
of the oxygen must be diminished, rather than increased, from the state of the
circulation and respiration,— but when the vital powers, and especially the vital
affinities, are losing their power, and the supply of nourishing matter has ceased.
This fact alone seems sufficient to shew that the absorption. which is constantly

340 ‘DR ALISON’S OBSERVATIONS ON

going on in the textures while life continues, is due to the partial loss of vital
power of these textures themselves, and is the cause, rather than the conse-
quence, of the agency of oxygen upon them.

When we consider, farther, how exactly this is in conformity with the gene-
ral fact, that all other kinds of vital action are essentially temporary,—that all
nervous actions, and all muscular contractions, necessarily alternate with periods
of repose,—I think we can have no difficulty in acquiescing in the general law of
all Vital Affinities, at least so far as animals are concerned, which explains at
once the necessity of constant nutrition of all animal bodies (even when their
weight is stationary or declining), the principle of interstitial absorption, the use
of respiration, the maintenance of animal heat, and the necessity and nature of
the excretions; viz., that as the perpetuation of each species is provided for only
by the successive life and death of numberless individuals, so the life of each in-
dividual is sustained only by the successive life and death of all the portions of
matter of which its body is composed; and that each portion, as it dies, falls
under the power of the oxygen absorbed from the atmosphere, as it would do
in the dead body, and enters into new combinations which are injurious to the
living system, but pass off by the excretions; gradually reverting to those inor-
ganic compounds, from which the power of vegetable life only can again raise
them to the condition of organized and living matter.

The general conclusions regarding Vital Affinity, which seem to me to be
warranted by this review of the subject, and to be sufficiently established to be
stated as principles in Physiology, are the following :—

1. That it is by a power peculiar to the state of life, and equally vital as the
irritability of muscles, but varying in the different parts of each organized struc-
ture, that the solids, and especially the cells of organized matter, attract, se-
lect, consolidate, and arrange in their substance, and within their cavities, cer-
tain substances, usually compound, which are brought into contact with them, and
reject or exclude others.

2. That in the cells of organized matter, during the living state, and ap-
parently by an influence of these cells analogous to that chemical influence to
which the term Catalysis has been applied, analogous also to fermentation, certain
definite transformations of chemical elements take place, which are equally pe-
culiar to the state of life; which transformations, at least in animals, appear to be
effected more in the cells or corpuscles which float in the fluids, than in those
which compose the solid part of the structure.

3. That although we have proof that the origin of all the organized beings now
seen on the earth’s surface has been of recent date, in comparison with the earth
itself, we see these powers, thus exercised, continually transmitted to successive
sets of cells in each individual, and to successive generations of individuals, with-

THE PRINCIPLE OF VITAL AFFINITY. 341

out being able to remount to the origin of this kind of action in this, as in others
of the sciences lately called paleetiological.

4. That the first essential condition necessary for the development of all or-
ganized life, is that vital affinity by which, under the influence of light, the cells
of vegetables appropriate and decompose the carbonic acid of the atmosphere, fix
the carbon, and attach to it the elements of water, so as to form amylaceous
matter.

5. That the ulterior changes, effected within organized structures, by which
oily, albuminous, gelatinous, and perhaps extractive compounds, are formed and
assimilated to the living textures, appear to belong to certain definite vital affini-
ties of the carbon, originally fixed from the air, and which is the basis of all or-
ganized substances, not only for the elements of water, but for hydrogen, for azote,
for sulphur, phosphorus, and various salts; that most or all these ulterior
changes are effected both in vegetables and animals; and that the oxygen taken
in by the organs of respiration, although it may be necessary to the play of all
the different affinities in living bodies, appears hardly to enter, if it enter at all,
into the constitution of any of the compounds thus formed and applied to the
nourishment of the textures.

6. That these compounds, in order that they may be applied to this purpose,
must be moved within living bodies, and applied, in the fluid form, to the textures
which they are to nourish, although in various instances, both in vegetable and ani-
mal life, they have themselves the solid form; and that the requisite fluidity is
given by various contrivances, chiefly seen in the prome vie of animals,—by me-
chanical attrition, by incipient decomposition of the materials employed, but espe-
cially by a simply chemical solution of these,—for which purpose certain parts of
living structures are endowed with a vital power of separating acids, and others of
separating alkalies out of the compound fluids pervading them, and thus prepar-
ing solvents for those solids.

7. That the vital affinities do not, strictly speaking, supersede ordinary che-
mical affinities in the living animal body, but are superadded to them, so that
the ingesta, as they come under their influence, are divided between the combi-
nations to which those different kinds of affinity dispose them, and _parti-
cularly are partly under the influence of the substances exerting vital affinities,
and partly of the oxygen of the air, brought to them by the arterial blood ; and that
as these ingesta often contain large quantities of matter, especially of non-
azotised matter, either inapplicable to the formation of the animal compounds,
or redundant, these portions, fall immediately under the influence of the oxygen,
and form one source of the excretions from the animal body.

8. That the vital affinities, like all living properties, are liable to an influ-
ence of place and of time, which is not seen in the inorganic world, but is an es-
sential attribute of the organized Creation, which has been superadded, in later
times, to the original arrangements of the universe. They are acquired by por-

VOL. XVI. PART III. 4k

349 DR ALISON’S OBSERVATIONS ON

tions of matter which are brought to particular points in previously existing or-
ganized structures ; they are vigorous for a time, and are then lost. In all the
compounds constituting the animal textures, these affinities become gradually
enfeebled, whereby the elements constituting these textures become liable to ab-
sorption into the blood, to changes in their arrangements, chiefly effected by the
oxygen of the air, to combinations with the redundant matters above noticed, and
to the formation of other compounds in the blood, which are either the same as,
or rapidly tend to, the combinations with oxygen to which animal matter is liable
in the dead state; which are, therefore, properly speaking, due to simply che-
mical affinities, and therefore crystallizable, like other inorganic compounds, and
are noxious to the animal economy. This is another source of the excretions,
for the separation of which appropriate organs are furnished, capable by their
vital power of absorbing and abstracting them from the blood.

9. That the simply chemical power thus exerted by the oxygen, taken in by
respiration, over the redundant (especially non-azotised) matter in the blood,
and the efete matter of the textures, is the source of Animal Heat.

10. That there is thus effected during the life of animals, but in consequence
of the failure of their vital affinities, and restoration of the simply chemical rela-
tions of their component elements, a change equivalent to the slow combustion
of the organized matter, which had been first prepared by the vital affinities of
vegetables; and that the carbon, hydrogen, and other elements employed in the
formation of that matter, are thus continually resuming that condition, from
which the power of vegetable life is continually abstracting them again, to com-
municate to them a set of properties at variance with those which they perma-
nently possess; and apply them to a succession of organized beings which can
only terminate, as at no very distant period of time it must have originated, by
an arbitrary act of Divine power.

The gradual change both in vegetable and animal structures which results
from age,—the increase of the proportion of earthy and saline matter, and dimi-
nution of the proportion of strictly organic matter,—must be regarded as indi-
cating a peculiarity of the vital affinities equally an ultimate fact as their limited
duration in every portion of a living body. And the modification to which these
affinities, as well as all other strictly vital powers, are liable in animals, from
certain actions of the nervous system, must likewise be regarded as an ultimate
fact, quite distinct from any principles that have been ascertained in regard to the
nature of the vital affinities themselves.

On reviewing the statements and reasonings which I have laid before the
Society on the subject of Vital Affinity, although | may have committed errors in
the details, I cannot accuse myself of having occupied their time, either with a
vague and useless speculation, or with a verbal dispute.

That there is something in the history of all living bodies which is peculiar to

THE PRINCIPLE OF VITAL AFFINITY. 343

them, at variance with the laws that regulate the changes of inorganic matter.
and requiring to be investigated by a separate induction of facts, must be ad-
mitted by all; and is indeed the only reason we can give for treating Physiology,
and the branches of knowledge dependent on it, as a separate science; and this
being so, it belongs to the very elements of the science to determine what are
the portions of the history of living bodies which come under this category.

I have always held in high respect the aphorism of HEBERDEN, which Dr
GREGORY used to recommend to the special attention of his pupils, that the great
desideratum in medical science is the detection of the Vital Principle, by which
all that goes on in the living body is regulated and governed; but I have always
thought likewise, that the object of this investigation is rightly limited by Dr
Prout, when he says that we should inquire, ‘‘ not what the vital principle or
vital power is, but what it does.” In fact, in all the sciences, we can acknow-
ledge only one principle and one Power, as the origin of all the phenomena that
we investigate; and when we use these terms in reference to living beings,—when
we say that we inquire how the vital principle acts,—we use the term only as a
convenient and simple expression for an investigation of the laws according to
which the Divine power acts, in regulating the changes which are continually
taking place in the last and noblest of the works of creation, and which differ
from the changes that we see around us in other departments of nature.

This precise and definite object of all physiological researches—the deter-
mination of the laws that are peculiar to the science—has always attracted the
attention of physiologists, but has not always been placed in the proper point of
view ; and the common error in this, as in other sciences, has been, to regard the
laws of nature as simpler than they really are, and to stretch a principle, ascer-
tained as to one set of phenomena, in the hope that it would be found sufficient
to embrace many more. Thus it was easily observed that the phenomena
of sensation and thought, and the visible motions in animals, were quite peculiar
to them; and when it was ascertained that the first of these, and that a large
portion of the latter (viz., all voluntary motions), depend on the living state of
the nervous system, it was hastily concluded that all the phenomena peculiar to
animal bodies, depend on their Nervous System. This is illustrated by the title
of one of the chapters in GrEGoRY’s “ Conspectus.” ‘“ De solido vivo, seu genere
nervoso,” as if there were no living property in any of the animal solids but what
is given to them by the nervous system; or, by the explicit declaration of CULLEN.
that he considered the vital principle as “lodged in the nervous system.”

The progress of the science has, I think, distinctly shewn that these ideas, as
to the parts of the animal economy in which the peculiar laws of vitality operate,
were limited and erroneous; although physiologists (trained in the schools of medi-
cine where the authority of these and other teachers, adopting similar doctrines.
has been held in just veneration) have been generally reluctant to admit the error.

I have endeavoured, in papers laid at different times before this Society, to

344 DR ALISON’S OBSERVATIONS ON THE PRINCIPLE OF VITAL AFFINITY.

limit and define our notions of the powers exercised by the Nervous System, in
producing the phenomena of the life of animals, maintaining on that subject the
different parts of one general and fundamental proposition ; viz., that there is no
good evidence, and that in the absence of such evidence it is unphilosophical to
assume, that any changes in the nervous system are essentially concerned in pro-
ducing any phenomena in the healthy state of the system, except those in which
some mental act is necessarily involved ; but that all the powers which are exer-
cised, in the natural and healthy state, by the nervous system, in a living body,
are those by which it fulfils its destined office as the seat, and the instrument, of
mental acts,—of Sensation, Thought, and Instinctive or Voluntary effort; and
that the nature of these powers, and the uses or intention of the different parts,
and of all the arrangements of the nervous system, if judged of simply in refer-
ence to these, the specific objects of its creation, are tolerably well ascertained ;
vindicating, at the same time, the doctrine of HALLER, in regard to the separate
vital property of Irritability or Contractility in muscles, and its different modes
of connection with the nervous system.

I likewise stated, on a former occasion, to this Society the evidence of another
fundamental principle in physiology—of the existence and the chief agencies of a
power exercised by living bodies, and peculiar to their living state—which is
capable of producing motion, or of influencing motion otherwise produced, but
which acts in the way of Attraction and Repulsion; and is, therefore, quite dis-
tinct from that living power of animal solids, acting in the way of contraction
and impulse, which is well understood; and to which, since the time of HAaLuEr,
the name of Irritability, or the more general term Contractility, has been applied.

Although both these principles have been strongly contested, I have had the
satisfaction of seeing them adopted, and their importance acknowledged, by most
of those who have prosecuted the science of Physiology in this country of late
years, with the greatest diligence and success. I have now laid before the So-
ciety the general grounds of a third opinion, which I hold to be of equal rank in
physiology ; viz., that there are laws, peculiar to living bodies, acting to a limited
extent only, and already in a considerable degree ascertained, which alter and
control the ordinary chemical Affinities of the matter composing those bodies, as
distinctly as the laws of muscular contraction, or of vital attractions and repul-
sions, modify the effects of the ordinary mechanical properties of matter within
them. And if this doctrine shall, as I confidently expect, be equally admitted to
be correct, then, although laying claim to no credit as a discoverer, I hope I may
be allowed the satisfaction of reflecting, that I have contributed somewhat to-
wards fixing the foundations of the noble science of Physiology ; and establish-—
ing those principles in that science, to which continual reference must necessarily
be made, in any speculations to which we can apply the epithet scientific, in re-
gard either to the nature of diseases or the operation of remedies.

( 345)

KxT— An Attempt to Elucidate and Apply the Principles of Goniometry, as pub-

_ symbolized, as to length and position, by a or

lished by Mr WarrEN in his Treatise on the Square Roots of Negative Quan-
tities. By the Right Reverend Bishop TErRot.

(Read 18th January 1847.)

1. The symbol /—1 is called an impossible or imaginary quantity, because,
in analogy with the received laws of algebraic symbolism, it must mean such a
quantity as, being multiplied into itself, gives for a product —1. Assuming, then,
that every quantity must be either plus or minus, it follows that the square of
every real quantity must be plus; and hence /—1, which gives its square minus,
is called an imaginary or impossible quantity.

If, however, we consider the most simple application of algebra to geometry,
we shall perceive that the assumption that every line must be considered and sym-
bolized as either + or —, is inconsistent with fact. In algebraic geometry, +a
or +1 xa symbolizes a line whose numerical length is a, drawn in some given
direction ; while —a or —1 x a, symbolizes a line of the same length, drawn from the
same extremity in the same straight line, but in a directly opposite direction. To
say, then, that all lines must be either + or —, is as much as to say that all
lines drawn from the common extremity must be drawn in this one assumed line;
and that it is impossible any line should be drawn making an angle with it.
But it is evident that an infinite number of such inclined lines may be drawn,
and none of them can have +1 or —1 as a factor, in accordance with the defini-
hition just given of those symbols.

The assumption, therefore, upon which Fig. 1.

/—1 is considered and spoken of as an im-
possible quantity, is unfounded. All lines
drawn from C (Fig. 1.) are as real and pos-
sible as CA, which we symbolize by +1 «a,
or CB, which we symbolize by —1xc. None
of them, however, except CA and CB, can be

¢ multiplied into either a positive or a nega-
tive quantity ; since that would be equivalent

to saying that they are coincident with CA
or CB.

VOL. XVI. PART III, : As

346 BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES.

Ordinary algebra, however, has not provided any system of symbols by which
these inclined lines may be expressed, both as to length and position, but affords
symbols only for the two extreme cases CA and CB. This deficiency Mr WarREN
has undertaken to supply in his Treatise on the Square Roots of Negative Quan-
tities, published in 1828; and has proposed a system of symbols, which, on the ©
same principle as justifies the use of —1 as the coefficient designating the position
of CB, designate as coefficients the position of all lines drawn from C, and making
angles with CA.

. On some points, however, Mr Warren has been too sparing of his words, and
has thus apparently used the common symbols of algebra in a sense very different
from their ordinary acceptation. In the following paper I have endeavoured to
supply this deficiency of explanation; and then to apply the system of symbols
so established to some important problems of goniometry to which, as far as I
know, it has not yet been applied. Dr Peacock, in his Treatises on Algebra, has
made a somewhat similar use of the coefficients of direction, though arriving at
his conclusions by a different route.

Il. If from C (Fig. 1.) we draw any number of straight lines in the same
plane, such that CA, CA,, CA:, &c., shall be continued proportionals, according to
Euciip’s definition; and make, at the same time, the angles ACA,, A,CA,, A,CA,,
&c., all equal; then if we call CA=1and CA, =a, CA, will equal a?, CA, =a’, and so
on. The several lines then are arithmetically represented as to their respective
lengths by the series 1, or a°, a1, a2, &c. But it is manifest that the several in-
dices which determine the length of the several lines, designate, at the same time,
the angles which they make respectively with CA. Thus if a makes with CA,
or unity, an angle 3, a? makes with CA an angle 23, a an angle 33, and so on.
And conversely the line which makes with CA an angle »3 is properly represented
by a. If, instead of calling CA unity, we re-
present it by R or Rx1, then CA,=R. a’,
CA,=R. a?, and so on.

III. If, next, we assume that the several
lines CA, CA, &c. are all equal, 2. e., that they
are the consecutive radii of a circle making
equal angles with one another (as in Fig. 2.),
the first property, proportion, is not there-
by destroyed; and we may still properly re-
present them (beginning with CA,) by the
series a', a2... a”.

Now let » be a divisor of 277; or, 3
being that angle which each line makes with

Fig. 2.

2 te X
the succeeding, let »3=2r 7, or ga Then from the last proposition we infer

é

,

a

BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES. 347

| that », which is the index of the last term, is also the coefficient of the angle which

it makes with that line whose coefficient we assume to be unity, that is, with CA.

But »3=2r7, or an integer number of complete circumferences. Hence the radius

symbolized by a” coincides in length and position with the original AC, or a”=1,
Iai i9

therefore a’ =1" =12"".

Now we know, on ordinary algebraic principles, that the several nth roots
of unity are properly represented by the several terms of the geometric series
a, a?,a?....a”, or 1. Since, then, the two series, first that of the successive radii
of a circle making equal angles with one another, and secondly, that of the several
nth roots of unity are in symbolism the same, it follows, that, dropping this com-
mon symbolism, we may take the several roots of unity to represent the succes-
Sive radii, and conversely.

If, as before, we take not unity but R for the numerical length of the radius,
$

then R . 1””” is the expression for that radius which is inclined to that symbol-

ized by Rx 1. atan angle 3. And as the direction of the radius, or its angularity
>

to the original position is noted by the numerator of the index, we call 17" * the
coeficient of direction. We have thus found a function of the angle of inclination
which, being affixed as a coefficient or multiplier to the arithmetical expression
for the length of the radius, represents the radius so inclined, both in length and
position; and which may be employed according to the ordinary rules of alge-
braic calculation, to find the length and position of other lines under conditions of
relation to it.

These coefficients of direction, however, it must be observed, have no quanti-

tative or arithmetical value. Thus a. cles) expresses a line whose length is

affecting not the length, but only the direction

simply a; the coefficient Lives

of the line.

IV. As illustrative of this reciprocal symbolism, let us suppose that the suc-
cessive radii are two in number, or, in other words, that a radius revolving round
C takes only one fixed position, and makes only two equal angles before it returns
to its original position (Fig. 2). Then the circumference is divided into two equal
parts, AB is the diameter, and if CA=1, CB=—1. In this case n=2, therefore
@?=1 or a?-1=0 .. a=+1. But the radii being a, a?, a must evidently be
—1, and a?=+1.,

Next let the circumference (Fig. 2.) be divided into four equal parts, then
CA, CD, CB, CE are the four roots of the equation at_1=0. But these roots are
+1 and +/ =i.

19 ee

348 BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES.

Here CA and CB are, by Art. 1, symbolized by +1 and —1 respectively;
therefore CD and CE must be symbolized by +/—1 and —./—1. It is, however,
quite optional which direction from C we consider positive, whether in the hori-
zontal or perpendicular line.

V. It appears from the foregoing propositions, that if a line is presented to
9

us under the symbol a . 17"7, we know both its length and the angle 3 which

it makes with a given line whose coefficient of direction we assume to be unity,
9

and which, therefore, we symbolize by a simply. The symbol a. jae therefore,
represents the actual transference of position in

space which a point would undergo by moving from Fig. 3.

the one extremity of the line to the other, as from A B

to C (Fig. 3.). Butit is clear, also, that ifa point be

supposed to be removed from A to B, and then from

B to C, the actual transference in space, though not

the distance travelled, would be the same asifthe A B,C
transference had been direct from A to C. There-

fore the symbol which properly represents the one transference, must be symbo-
lically equal to the sum of the two symbols which respectively represent the
other two transferences, or AC x its coefficient of direction = AB x its coefficient
of direction + BC into its coefficient of direction.*

This fundamental proposition is given by Mr Warren as a definition, That
the sum of any two lines making an angle with one another is the diagonal cf
their parallelogram completed. Even in this startling form, it is only the general
assertion of a proposition, particular cases of which are admitted, when we say
(Fig.3.) that AB, + B,;C=AC, or that AC + CB, = AB,.
By such assertions we really mean that if a point
moves from A to B,, and then from B, to C, the
whole transference in space will be represented by
the sum AB,+B,C; and that if the point moves
from A to C, and then from C to B,, the whole
transference is expressed by the sum AC+CB,,
which is the same thing as the arithmetical differ-
ence AC—B,C.

As examples to elucidate this proposition, let
us take (Fig. 4.) an isosceles right-angled triangle

Fig. 4,

* This appears to be the view taken by Sir W. Hamizron, in the first of his series of papers on
Symbolical Geometry, printed in the Cambridge and Dublin Mathematical Journal. He there says, —
“ This symbolic sum of lines represents the total (or final) effect of all those successive rectilineal mo- —

tions, or translations in space, which are represented by the several summands.”

bi

BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES. 349
ACB. If we call AB the radius or hypothenuse, a, then each of the sides AC CB
is in length ee and AB (being inclined at an angle of 45° to AD, which we as-

sume as the original position of the radius) is symbolized by a x 1°°* =a x 1? =
; = But AC=J75, CB being perpendicular to the original position equals

phen =i Len ol
ar: ./—1. (Prop.IV.) Therefore AC +CB=a. [vst 75 |= Fe ae
2. Let BAC represent a right-angled triangle ae angle at A=60°, then
AB in length and direction =a. 1° =a. 1'=a. meee g

/8

ay oes x? CB = in length

Bis Ea oe
Sy Pi Eea AB Ue

= and therefore in length and direction jointly a.

a J —3 ay ge)
AC+CB=5ta. 5) So ee aaa

3. Let the triangle (Fig. 5.) be equilateral, and AB be taken as the original

Aus

position. Let AB=a, AC=a.1*, CB=a.17*

ne cep =a[ 141" "=«. coe al ae

=.a al Gare x 2 = Boo 22S =e
i [ 2 if eee 2 agonal roti

VI. In the foregoing Propositions and Exam- Fig. 5.
ples, it has been assumed that we know not only Cc
the several nth roots of unity, but also their proper
order, that is, the order in which, as coefficients, ‘

they express the radii drawn so as to make angles
§, 29, 39, &c., with the original radius. But when
by any analytical process we find the roots of
—1=0, we procure the symbolical representa-
tives of these radii in no determinate order. To
discover this order, we must observe that two roots
are always of the form a/ —é ; comparing which
expression with figure 6, it is evident that a is the D
part symbolical of the cosine, and /—¢ the part symbolical of the sine, because
it is affected by the coefficient »/—1, and is therefore perpendicular to the original
radius. It is clear, then, that in the general expression a--/—d, the sign + be-
longs to those radii which lie in the upper half of the circle, and — to those which
lie in the lower half; and that the two radii whose symbols differ only in the
VOL. XVI. PART III. 4 T

300 BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES.

sign of ./—, are at equal angles to the original radius, in different directions,
that is, on different sides of it.

Again, of those roots which symbolize the wi
radii in the upper half of the circle, that which A?
has a, representing the cosine greatest, is the
nearest to the original radii. Thus the roots of
n6—1=0, in the order given by Dr PEacock,
—144/—B Ten

2 2

?

tala

Ales i, p,%128, “are “1,

; 1 Wes, ay a
q 2 ‘ 2 p
their proper order, if +1 be placed first, then ~ n-1
—1, as having no sinal part, and being therefore,
neither in the upper nor lower half, must stand in the middle of the remaining
ee aml aie

To arrange these in

roots. Next these are two roots, , each having the sinal

part +, which must be arranged in this order, because the sign of 1 in the former
indicates that the cosine is in CA, and in the latter in CA,. Finally, considering
those roots of which the sinal part is minus; we must place them in the order
plist 9) ene because they are thus equidistant from unity with =i

2
1+/—3 3
and jo Hence the roots in their proper sequence are

1 1t+V¥—-38 -1l4+V—-3 _, -1-V-3 1-V-3
“apelin: RETO EOS es mer
symbolizing severally the radii drawn to the extremities of the arcs
0 or 360°, 60°, 120°, 180°, 240°, 300°.
VI. It appears from Props. IV., V.. that the radius drawn to the extremity
3

of an arc 9, is properly expressed by 1°"*, and this again by a+/—é, where a is
what is called in trigonometry the cosine of 3, and »/é the sine.

Now let CA, (Fig. 6.) make with CA an angle 3, CA, an angle 23 .. . CA, an
angle ps.
Then CA,=CD+/7-1. DA, =cos3+V7—1. sind
CA, =cos p3+/—] . sinps.
But by Prop. Il. CA,=CA,|?=(cos3+/7—T. sin3)?
(cos3+/—1 Z sin3)?=cospS+V7 41 . sin p 8,
which is DemMorvre’s Theorem.

BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES. 351

Cor. Ifp3=27, cosp34+V7—1. sinp3=1.
Hence (cos 3 + /—1. sin3), (cos 29+/—1. sin29) &e. represent the several
pth roots of unity. If, instead of the order 3, 23, 39, &., we arrange the several
angles thus in pairs 3 and p—1.3, 23 and p—2.3, then the several expressions

for z minus the several pth roots of unity, or the several simple factors of the
equation 2?—1=0, taken in pairs corresponding to the above, will be

(a—cos3—V/ —1 . sin$) and (z—cosp—1 .3—»/—1 . sin p—1 .9),
the latter of which equals (x—cos . p3—93—W/—1. sinp3—9)
=r—cos27—3—V7 —1 . sin2 T—S=x—cos$+W/—1. sind.
In the same way the next pair must be
(a—cos29+4+/—1 sin23) and (x—cos29—s/—1. sin23), and so on.
If these several pairs be next multiplied together so as to produce the quadratic
factors of 2”—1=0, we obtain the products (#?—2%cos3+1), (22-22. cos23+1) ke.

And if it be remembered that in every case z—1=0 isa factor; and that if p be even,

z—1and +1 are simple factors, and consequently x?—1 a quadratic factor ; there-
fore if p be even,

a? —1=(a?—1) . (a? -—2xcos3+1).(#?-—22%. cos23+1) &e. tof terms.
But if p be odd,

x? —1=(4—1). (@ —2a@c0s$+1). &e. vee terms.

Where 3, it may be observed, equals “S.

VIII. From these fundamental propositions, Mr WarREN, in his Treatise on
Negative Roots, has deduced—

1. The value of each side of a triangle in terms of the other sides and angles.
(§ 141.)
2. That the three angles of a triangle are equal to two right angles. (§ 142.)

3. That the sides are respectively proportional to the sines of the opposite
angles. (( 143.)

4. That cosA="*°—". (9 144)

He then asserts, that from these and the preceding propositions, all the for-
mule of plane trigonometry may easily be deduced. In the following proposi-
tions, I have applied his principles to the solution of some of the most simple,
and to some of comparatively the more difficult problems usually given in ele-
mentary books of trigonometry.

352 BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES.
IX. sin (A+B)=A x cos B+ cos A x sin B
cos (A+ B)=cos A x cos B—sin A. sin B.
Let arc AB (Fig. 7.) =A, BD, and AD, each=B.

A Fig. 7.
Then by Prop. Ill., CB=r . 17”, Dgsysn igs
By A+B
CD,=r.1°7, CD,=r.17” «
ea gs
OD,=rx1°7x 1°”
But Prop. VIL, =
ee
1°*= csp A +V—1.sinA
B.
177= cosB+ /—1.sinB
A+B
1°” =cos A xcosB—sinA.sinB+/—1. (sin A . cos B+cos A. sin B
A+B
but 177 =cosA+B+V7—1.sinA+B

Equating, then, the possible and impossible, or, more properly, the sinal and
cosinal, parts of these equal forms

cos A x cos B—sin A . sin B=cos A+B
and sin A x cos B+cos A . sin B=sin A+B.

This demonstration is the same in principle, and nearly the same in detail,
as that given by Dr Peacock, in his Algebra, vol. i., p. 392. In his 2d volume,
Dr Peacock goes more fully into the consideration of the roots of unity as coeffi-
cients of direction. Yet there he proves these propositions, not upon that consi-
deration, but by the ordinary geometrical method.

Der. It should be observed that in the following propositions, a line ex-
pressed by letters simply as AB, must be understood as considered in respect
both of length and direction; while by the same letters in brackets, thus (AB),

is understood the same line in regard to its length only. Thus, if 3 be the angle
3
which AB makes with unity, (AB) . 127=AB.
X. In any right-angled triangle, the sum of the squares of the sides is equal
to the square of the hypothenuse.
9 9
. Let CA (Fig. 6)=r, then CA,=r . 127, and CA,_;=r.1 27
9
CPCUA, 17 ox 127 x

flows
ay

127

BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES. 353

Also CA,=(CD,)+V—1. (D,A,)
CA, _1=(CD,)—V/—1. (D,A,) for ©,4,)=(0,4An_1)
OA; x CA, 7 =(CD?)+ (yA, which = =(CAy

or its equivalent in area (CA,)?.

XI. Cotes’ Properties of the Circle.
Let the circumference of the circle be divided into n equal parts; and to the
extremities of these let lines be drawn from the
centre (Fig. 8), as OP,, OP,, &c., and from any
other point C in the diameter. Then
CP, = OP, — OC, CP, =OP, — OC, &c.
CP, xCP,x CP, .... OP,
=r OA) sua (OAS ah yy. yf eiOC*
Where 5, is the product of all the coefficients A
of direction for OP,, OP,, &c., 3,_1, the sum of these
coefficients taken »—1 together, and so on. But
these coefficients (Prop. III.) are also the values of

Fig. 8.

i
1”, or the roots of the equation x*—1=0. Now the
product of the roots of this equation with their signs changed is —1, and 3, is the
product with the signs unchanged.

Therefore if m be even, 3,=—1, and, if m be odd, 5, = +1; and in either case,
fn 2, we. each =0.

Hence CP,xCP, .... xCP,==+(OA)"+(0C)"; the upper signs being used
when 7 is even, the lower when 7 is odd.

But CP, CP,, &c., represent the lines considered in relation both to length
and direction ; therefore, to change the equation into one in which the length
only of these lines shall be expressed, we must divide the first side, or muitiply
the second by the product of all their coefficients of direction.

If n be even, the several pairs, as CP,, CP,,_;, are evidently of the form

3 9
(CP) . 127 and (CP,,_3). 1. 2* ... CP, x CP,. 7=(CP,) x (CP,=1)

and the same is true for every pair except CA=(CA). +1 and CB=(CB) . —1
(CP,) x (CP,) .... OP, =[—OA"+00"] x —1=0A"—0C".

If, again, 7 be odd, the several pairs remain as before, only, no P falling upon
B,—1 is not a coefficient of direction :
(CP, x (CP,) x &e., =OA"— OC” as before.
VOL. XVI. PART III. , 4uU

354 BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES.

Cor. 1. If C be on the opposite side of O from A, the other conditions re-
maining the same, OC is negative. Ifm be even, the expression deduced in the
proposition remains unchanged. But if » be odd, (CP,) x (CP,) x &., =OA”" + OC".
And here it may be remarked, that when lines, as OA are in the original direc-
tion, since the coefficient of direction in that case is unity, it is immaterial whether
we write OA or (OA).

Ex. Let »=3 and OC=4

then (AC) =3, (CP) =(CP,) =e
(CA) . (CP,) x(CP,)=ax ‘ Veep

Cor. 2. If C be in OA produced, the reasoning and the result will be the
same as in the proposition ; only, that now CA and CB being of the same affec-
tion, —1 is not a divisor of the second number of the equation, and

(OP,) x (CP,) x &e., =(O0)"—(OA)".
XII. If from A, the extremity of the diameter (Fig. 8), the- circumference

be divided into 2 equal parts, and lines be drawn to their several extremities from
A, then

(AP,)x(AP,) .... (AP,_y)=n. CA"-1
As in the preceding proposition AP,=CP,—CA, AP,=CP,—CA, and so on.
Therefore AP, x AP, x .... AP,_1=CP,—CA x CP,—CAx &e., to n—1 factors
=Rr-1, { S.-1-Sn—2 Be, 8,41}
, 1

where §,, S., are the sum, sum of products 2 and 2, &c., of all the values of 1” except
unity, there being no line drawn from A to the circumference in the direction

CA. S,, S,, &ce., are, therefore, the coefficients of the equation ae or of
ar—l4gr-2 .... +1=0, with the signs changed for the products of odd numbers
of roots, unchanged for even ones.
If, therefore; »—1 be even, §,,.;=+1, S,_2=-—1, and So on:
If n—1 be-odd, 8, ;=—1,8,_2= +1, and so on.
AP: x AP Mes. 3 0 et RO Ay eR 1 to terms} ==tn R"-1

according as n—1 is even or odd.

If x—1 be even, then AP,+AP, x &c. =(AP,) x(AP,) &., the several pairs of
coefficients of direction giving unity as their product.

BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES, 350

If n—1 be odd, then the several pairs give as before the product unity; but
there remains the factor — AB, which has for its coefficient —1.
@herefore, in either case, (AP,)x(AP,) .... (AP, 1)=2 R"-1.

XIII. The symbolism employed in the foregoing propositions appears to be
applicable to Plane Trigonometry in all its parts. To the elementary proposi-
tions of Geometry it is either inapplicable, or applicable by processes and con-
siderations unsuitable to the demonstration of elementary truths. Thus, if by
this method we undertake to prove that the angles at the base of an isosceles tri-
angle are equal to one another, we have (AC)=(BC). (Fig. 5.)

A

But AC=(AC) . 127=(AO). [a+/7—5]
B
CB=AD=(AC).1 27=(AC). [a +V/V—0)
But AC+CB=AB.

oe (AC). [at +/— 64+/—0]=AB a positive quantity ; consequently the im-
_ possible or sinal parts of the coefficient of direction must destroy one another, or
/—b=—/—b or b=-U- Therefore the angles A and B have their sines equal
in length, but of different affections. The angles themselves, therefore, being to-
gether less than 7, are geometrically equal to one another.

Cor. Much in the same way we might prove that in every triangle the greater
angle has the greater side opposite to it; and, conversely, that the greater side
has the greater angle opposite to it.

i ¥ ; ) 7 a, > ee
Hite”. Seren Aid et ke

ual yy iy ie ahhw Rtas euesiill Latin tcaliinc
sd eNOS ati Tob saa! Wy eaeag .
UN te HARE RE, MK Et i ‘hts
¢ Rea w/b ebin Eso., cette ee Oh :
di A enadiige esi tien | Me tt eae Jiao ia
uhdalegtig Puy Th 0) Hy.0( : \ APU, ER al yrughy brid 1a
ny bet Sie, Altai. to Aldaibanan psidig a % |
. "9 wen ditect ict i / fi ’ Lik Mane} at rr iia a)
“yd tala” sb oebP eel ecto” Satta Wray 0) vhosts.

i Te Tore | le wwdhlonn Cty OZ

" v r| - be mal if
Sy ouch de ify we SOD)

tse Oy

4) 7 (iiain i wou
. i a is ed Mh, Be LB
; 4 ;
' ‘ 4 } } Vhs
mT : . Thi anor T's
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p? oa)
dui f ia A ree
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Fi ’ u hgh ld al ‘ Tile
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(64857 Gh)

XXIII.—On the Reaction of Natural Waters with Soluble Lead Salis. By Artuur
ConnELL, Esq., F.R.S.E., Professor of Chemistry in the University of St Andrews.

(Read 19th January 1846.)

In a former communication to the Society, I noticed a reaction presented
by all spring, well, and river waters which I had examined, that, even after
being boiled, they yielded, with acetate of lead, a precipitate readily soluble, in
whole or in great part, in acetic acid. This easy solubility in acetic acid shewed
that the precipitate was neither a sulphate nor a phosphate, and the comparatively
slight action of nitrate of silver proved that it was not a chloride. There seemed,
therefore, to remain only the conclusion that it was either acarbonate, or was due to
organic matter. The former alternative, of course, depended on whether the solu-
tion in acetic acid was attended with effervescence or not; and as this seemed usually
not to be the case, and as, on decomposing some of the precipitate by sulphuret-
ted hydrogen, some organic matter in solution was obtained, the conclusion seemed
to be, that the appearance was caused by organic matter, probably of the nature
of the crenic and apocrenic acids of Berzetius. I have since, however, found that
by very careful observation, effervescence may be noticed during the solution of
the precipitate more frequently than I at first supposed. It is not so easy as
might be imagined to determine this point. If acetic acid is added before the
precipitate has subsided, no effervescence can be noticed, in almost any case, from
the water dissolving the carbonic acid evolved and diffused through the whole
liquid. And even when allowed to subside, and the greater part of the liquid is
decanted, the addition of acetic acid not unfrequently causes solution without
apparent effervescence. The cautious addition, however, of a heavier acid, such
as the nitric or even the muriatic, after allowing the lead precipitate to collect at
the bottom, and decanting the greater part of the liquid, seldom fails to shew the
effervescence where a carbonate is really present.

In so far, then, as the precipitate is dissolved by acids with effervescence, we
may conclude that it has been caused by some carbonate remaining dissolved
after boiling the water; and in so far as the solution may not exhibit efferves-
cence, we may conclude that it is due to organic matter, provided silver salts do
not indicate the presence of a sufficient quantity of chlorides, and provided acetic
acid instantly causes solution in whole or great part. In some instances I have
found that acetate of lead does not yield a precipitate, wnless the water has been
previously boiled, a circumstance obviously due to excess of carbonic acid retain-
ing the carbonate of lead in solution. In regard to chlorides, I have never met

VOL. XVI. PART III. 4x

342 PROFESSOR CONNELL ON THE REACTION OF NATURAL WATERS

with any spring, well, or river water, not coming under the denomination of a
mineral water, which contained so much of any chloride as to be indicated by a
lead salt. The chloride of lead is too soluble to become visible, unless where the
contamination is considerable. The portion of the precipitate not soluble in acetic
acid is usually due to the presence of some sulphate.

Taking the fact as I have now ascertained it to be, that natural waters which
have passed through the strata or soils of the earth, 7. e., well, spring, and river
waters, very commonly or invariably yield, even after boiling, and filtering, if ne-
cessary, a greater or less amount of precipitate with acetate of lead, readily dis-
solved, in whole or in part, by acetic acid with effervescence; in other words,
that such natural waters contain frequently or invariably, even after boiling, one
or more dissolved carbonates, the question arises, What is the nature of such car-
bonate? As these waters, when they have been much concentrated after being
boiled and filtered, and have then been made up to their former bulk by distilled
water, are found to have lost their power of shewing the same phenomena as be-
fore with lead salts, and to have deposited carbonate of lime during concentration,
the effect must have been due to this carbonate of lime whilst held in solution. The
farther question, therefore, arises, how this carbonate of lime came to be dissolved ?

I tried to ascertain whether water would dissolve carbonate of lime in its
nascent state as precipitated by boiling a solution in excess of carbonic acid. A
current of carbonic acid was passed through lime water prepared with distilled
water, until the precipitate at first formed was redissolved. The solution was
then boiled for a simiJar short time as in the original experiments, and filtered.
It was then found to be affected only very feebly either by oxalate of ammonia
or by acetate of lead; the action being not at all equal to that produced on boiled
natural waters by these reagents. The carbonate of lime in the act of precipita-
tion by boiling, had evidently not been dissolved except in very insignificant
quantity by the water. I then, before boiling the solution, exposed it for a day to
the air in an evaporating basin, after keeping it for some days in a close vessel ;
but did not find that the quantity of carbonate retained after ebullition, short
subsidence, and filtration, was increased.

As it was possible that some of those saline matters contained in natural
waters might promote the solubility of carbonate of lime, minute quantities of
solutions of muriate of lime, sulphate of lime, muriate of magnesia, and chloride
of potassium were added to lime water prepared with distilled water. A current
of carbonic acid was then conducted through the liquid so as to redissolve the
precipitate which it at first caused. The liquid, after ebullition, short subsidence,

and filtration, was found scarcely to be affected by acetate of lead; and any feeble

deposit formed was not soluble in acetic acid, being sulphate of lead due to the
sulphatesw hich had been added.
It thus seemed evident that by the aid of carbonic acid no sufficient quantity

WITH SOLUBLE LEAD SALTS. 309

of carbonate of lime can be dissolved, independently of the continued presence of
the free acid, to cause the appearances referred to.

I next tried the solvent action of water alone on finely divided carbonate of
lime. Distilled water, which had been boiled and cooled, was left in contact
with marble in impalpable powder for several days in a close vessel. It was
then found by the action both of acetate of lead and of oxalate of ammonia, that
rather more carbonate of lime had been taken up by the pure water than was left
in solution after boiling the carbonated water, but still that the amount was con-
siderably less than the reactions which have been referred to, indicate in ordi-
nary natural waters ; and it is remarkable that the effect of the lead salt is usually
more decided than that of the oxalate.

I incline, therefore, to think, that the carbonate of lime present, in such cir-
cumstances as have been described, has a different origin, viz., Double Decompo-
sition, between a lime-salt and a carbonated alkali; as it would seem that the
carbonate of lime formed is, in this kind of nascent state, dissolved more readily
than when precipitated by boiling from a carbonic solution. The following expe-
riments illustrate this origin of the reaction. To half an ounce of distilled water,
a few drops of a solution of sulphate of lime in water were added. A single drop
of solution of chloride of calcium, and a single drop of solution of carbonate of
potash were then added. The liquid remained quite transparent, and did not
affect turmeric or cabbage paper. When boiled it still remained transparent.
When a drop of solution of acetate of lead was added to a portion of this liquid,
either before or after boiling, a considerable white cloud was formed, which dis-
appeared on the addition of a drop of acetic acid. Thus was the reaction of the
spring waters exactly imitated. I at first inclined to think that in such cases no
actual double decomposition ensued until the liquid was concentrated by heat,
and that the action on the lead-salt was due to the carbonated alkali present.
But farther experiments lead me to believe that the carbonate of lime is actually
formed, at least to a considerable extent, and then dissolved by the water ; for,
if a couple of drops of solution of chloride of calcium and a drop of solution of
carbonate of potash be added to a few drops of distilled water, muddiness will be
produced; and this will disappear when half an ounce of distilled water is
shaken with the mixture, without any deposit being formed by rest. The solution,
however, of the carbonate of lime is dependent on the action of the water taking
place either on the nascent salt, or at least immediately after its formation ; for I
found that when carbonate of lime, precipitated by double decomposition, was col-
lected on a filter, washed, and allowed to stand some minutes, and then left in con-
tact all night with boiled and cooled distilled water, acetate of lead had only a
very feeble effect on the liquid.

It was, of course, necessary, in order to establish this view, to ascertain that
those natural waters which exhibit the reaction referred to, actually contain

360 PROFESSOR CONNELL ON THE REACTION OF NATURAL WATERS

alkaline matters. This was, accordingly, done in numerous instances by ordi-
nary methods. Although the potash or soda present may have been originally
dissolved as a carbonate ; yet we, of course, ultimately obtain it on evaporation,
as a chloride or sulphate, through double decomposition with the lime or magne-
sian salts present ; or through the stronger affinity of the acids of these salts, if
their earths have been previously removed by chemical means. In no instance of
a natural water which gave the reaction with lead salts, did I fail to detect either
potash or soda, or both; and it ought to be recollected that a very minute quan-
tity of either is sufficient. It will be found that one drop each of solutions of car-
bonate of potash, of sulphate of magnesia, and of chloride of calcium, added to
several ounces of distilled water, will produce the reactions referred to with lead
salts and acetic acid.

If these views are well-founded, it is evident that lead salts become a pro-
bable indication, at least where their effect is considerable, of the presence of
alkalies in natural waters. And, in general, we may conclude, that if after boil-
ing, and filtration if necessary, any water yields a considerable cloud with acetate
of lead, readily soluble by adding a drop or two of acetic acid, the cause will be
either carbonate of lime, probably due to double decomposition, or it will be
organic matter, if any such matter precipitable by lead salts is present in suffi-
cient quantity.* In so far as it is dissolved by an acid, after subsidence, with
effervescence, it will be due to the former cause; in so far as, without effer-
vescence, to the latter.

It seems, at all events, evident from the experiments which have been de-
tailed, that the carbonate of lime present has not owed its presence to the solvent
agency of carbonic acid, even when first taken up.

It is plain, that the carbonate of lime thus held dissolved by spring waters,
from whatever source it may be obtained, must be of considerable importance in
the economy of nature in furnishing a supply, through the intervention of these
waters, of that lime which is so essential a constituent, in its various states of
combination, of the inorganic portion of plants. This will hold whether such
waters are applied to the land in the way of irrigation, or by the more slow pro-
cesses of natural infiltration.

* Dr Curistison informs me that moss-water is not precipitated by acetate of lead. This, I have
no doubt is a correct observation ; but still other states of organic matter may occasion a precipitate.
The crenic and apocrenic acids are both known to precipitate lead salts.

Although fluorine is now known to be occasionally present in ordinary natural waters, and although
fluoride of lead is sparingly soluble in water, yet I am not aware that fluorine is ever present in such
quantity in such waters as to affect lead salts ; and, if it were, acetic acid might very likely not dissolve
the precipitate. Dr Witson mentions that fluoride of barium is less soluble in acids than carbonate or

phosphate of barytes.

nn nn nnn nnn nn nn eee Nemec ee

WITH SOLUBLE LEAD SALTS. 361

POSTSCRIPT.

Since this paper went to press, I have ascertained that the town water of
St Andrews, which is one of those which gives the reaction referred to with lead
salts, yields by evaporation, after having been boiled and filtered, 54,, of its
weight of carbonate of lime. . Other waters may of course contain more. I also
observe, that Fresenius found, that when distilled water was boiled a long time
(probably, from the context, several hours) with freshly precipated carbonate of
lime, so as to form a saturated hot solution, and this solution was then kept for
four weeks at common temperatures, in contact with undissolved carbonate of
lime, under frequent agitation, it yielded by evaporation ;,4,, of its weight of
carbonate of lime.—Lvzebig’s Annalen, July 1846. In so far as regards spring
waters, it is unnecessary to say, that Nature does not take such pains to charge
them with lime. The method suggested above seems a more simple one, and may
often be as effectual, possibly even more so; when the still more simple means
of free carbonic acid are not brought into play. From the experiments of FRE-
SENIUS, it appears, that carbonate of lead is much less soluble in water than car-
bonate of lime, viz., in 50,551 parts, which is quite conformable to the results
above stated.

VOL. XVI. PART ILI. 4 Y

XXIV.— On certain Products of Decomposition of the Fixed Oils in contact with Sul-
phur. By Tuomas ANDERSON, Esq. M.D., F.R.S.E., Lecturer on Chemistry,
Edinburgh.

(Read 19th April 1847.)

-

Numerous researches have established as a general rule that the products
of the decomposition of organic substances vary with the circumstances of the
experiment, and the nature of the agents under the influence of which it is per-
formed. If, for instance, we examine the action of heat alone, we find it caus-

‘ing a set of decompositions specially characterised by the evolution of carbonic

acid, formed by the union of part of the carbon of the substance with the whole
or part of its oxygen; and this action is rendered more definite, and the number
of the products circumscribed by all circumstances facilitating the formation of
carbonic acid, such as the presence of a base, which will even cause its evolution
when heat alone is incapable of producing decomposition. Acids, on the other
hand, have a precisely opposite effect, they, in some instances, altogether prevent
the formation of carbonic acid, and cause the oxygen to exert its action on the
hydrogen of the compound, and to eliminate one or more atoms of water which
do not generally exist ready formed in it.

In these particular instances decomposition takes place at the expense of the
constituent atoms of the compounds themselves, the extraneous substances serv-
ing merely as disponents to the oxidation, in the one case of part of their carbon,
in the other of their hydrogen; but there is another class of agents which, besides
eliminating one or more substances, are capable at the same time of entering into
union with the residual atoms, and forming a new derivative of the original com-
pound. The best investigated of this class of agents are chlorine, bromine, nitric
acid, and ammonia, the three former of which exert their action on the hydrogen,
the latter on the oxygen of the substance, and form compounds the complete in-
vestigation of which is important, not merely in a purely chemical point of view,
but also from the light which they seem likely to throw on the general question
of the atomistic constitution of matter. In fact, the great object of the researches
of organic chemistry at the present moment is that of developing the relations
which the individual atoms bear to the molecules of their compound, by a know-
ledge of which we hope eventually to arrive at some definite conclusions with re-
gard to the mode in which the elementary atoms are grouped together in a com-
plex molecule. Almost all the scanty information which we possess on this sub-
ject has been derived from investigating the products of the action of different
agents upon organic substances; and it is sufficiently obvious, that the more va-
ried the circumstances, and numerous the points of view under which these re-

VOL. XVI. PART III. 4Z

364 DR THOMAS ANDERSON ON CERTAIN PRODUCTS OF DECOMPOSITION

actions can be examined, so much the more likely are we to arrive at definite
results.

It was the consideration of these points which led me to undertake an inves-
tigation into the nature of the action of Sulphur in the free state upon organic
compounds, a subject hitherto totally uninvestigated, unless we except the curi-
ous researches of ZEISE* on the simultaneous action of ammonia and sulphur
upon acetone, which yields a variety of remarkable products, the properties of
which he has described, without however determining their constitution. The
results at which I have already arrived in these researches are contained in the
following pages. They are, however, to be considered only as the commencement
of the investigation ; and I am desirous of submitting them to the Society even in
their present very imperfect state, as it is impossible to fix a period within which
a series of researches, surrounded by so many difficulties, can be completed. No
one who has not been specially occupied with such experiments can have any
conception of the numerous sources of annoyance which they present, and of the
expenditure of time and labour which is necessary for their performance. Indeed,
I have more than once felt inclined altogether to abandon a subject occupying so
much time in proportion to the results obtained, and the completion of which is
further protracted by the nauseous odour of the compounds, which is so disgust-
ing that it is impossible to pursue the investigation for any length of time conti-
nuously.

At the commencement of these researches I endeavoured to examine the ac-
tion of sulphur upon some of the simpler organic compounds, in the hope of ar-
riving at results of corresponding simplicity. My expectations, however, were dis-
appointed, and I was obliged to have recourse to the fixed oils, on which sulphur
has been long known to exert an action; the product obtained by heating together
olive oil and sulphur until an uniform balsam-like substance was formed, having
been employed in medicine by the older physicians under the name of the Balsam
of Sulphur.

The phenomena which manifest themselves during the mutual action of Sul-
phur and a Fixed Oil are these :—At the first application of heat the sulphur melts
and forms a stratum at the bottom of the oil; but as the temperature rises it
slowly dissolves, with the formation of a thick viscid fluid of a dark red colour.
As the heat approaches that at which the oil undergoes decomposition when
heated alone, a violent action takes place attended by the evolution of sulphu-
retted hydrogen in such abundance that the viscid mass swells up and occupies a
space many times its original bulk. If at this point the mixture be allowed to
cool, it concretes into a tough sticky tenaceous mass, adhering strongly to the —
fingers. and having a disagreeable sulphureous odour ; if, however, the heat be

* Forhandlingar vid de Skandinaviska Naturforskarnes tredje mote, p. 303.

OF THE FIXED OILS IN CONTACT WITH SULPHUR. 365

sustained, the frothing and evolution of sulphuretted hydrogen continue, and at
the same time, an oil of a peculiar disgusting odour, resembling that of garlic.
but more disagreeable, passes into the receiver.

_ In the investigation of the products of this action, the first and most essen-
tial step was to determine the particular constituents of the oil from which they
are derived. In order to do this, it was necessary to examine separately the
action of sulphur upon each of its components. 1 commenced, therefore, by mak-
ing use of stearic acid, which can be readily obtained in a pure state: experi-
ment however, shewed, that none of the peculiar products were derived from it;
for when mixed with half its weight of sulphur and distilled, mere traces of sul-
phuretted hydrogen were evolved, and the products were identical with those
obtained from the unmixed acid. The nauseous smelling oils being then obviously
derived either from the oleic acid, or the glycerine of the oil, I prepared a quan-
tity of pure oleic acid, by the decomposition of the ethereal solution of the oleate
of lead. This, when mixed with half its weight of sulphur, and distilled in a
capacious retort, underwent decomposition precisely as the crude fixed oil did:
sulphuretted hydrogen was developed in great abundance, and the product of the
distillation could not be distinguished from that which I had previously obtained.
I was unable to obtain glycerine in sufficient quantity to make a separate inves-
tigation of the products of its decomposition, but these must also be peculiar, as |
could not distinguish the presence of acroleine during any period of the distilla-
tion of an oil with sulphur.

The product of the distillation of oleic acid was in the form of a reddish-
brown oil, having an extremely nauseous odour, in which that of sulphuretted
hydrogen was apparent. When rectified, this sulphuretted hydrogen was driven
off, and the first portions which distilled were perfectly transparent and colour-
less. As the process continued, however, the products became gradually darker
in colour, and the last portions which distilied became semisolid on standing,
from the deposition of a quantity of white crystalline plates. These were sepa-
rated by filtration through cloth, expressed strongly, and purified by successive
erystallizations from alcohol, until they were entirely free from smell and colour.
The product was then in the form of white pearly scales, which possessed acid
properties, and were totally insoluble in water; they were not therefore sebacic
acid, no trace of which could be discovered among the products ; but, on the con-
trary, possessed all the properties of margaric acid. These crystals were obtained
from quantities of oleic acid, prepared at different times, and with the greatest
possible care, and must have been formed during the decomposition. In order,

however, to set this point at rest, some of the same oleic acid was distilled alone,
_ when abundance of sebacic acid was obtained, and the latter portions of the rec-

tified product did not deposit any crystals on cooling, but remained perfectly
fluid. As this solid acid is produced only in comparatively small quantity, and °

366 DR THOMAS ANDERSON ON CERTAIN PRODUCTS OF DECOMPOSITION

I was unable to obtain enough of oleic acid, I made use, in preparing it on the
large scale, of pure almond oil, which, according to ScHUBLER and GassEROW, is
entirely free of margarine. The oil which I employed was expressed specially for
these experiments, at a temperature slightly above 32°; and in order to satisfy
myself of the absence of margaric acid in the products of its ordinary decomposi-
tion, a quantity was distilled alone, and the product rectified. The latter por-
tions being collected apart did not deposit margaric acid; and this I have also
found to be the case with the ordinary almond oil of commerce, in the expression
of which a moderate degree of heat is employed.

In distilling the oil and sulphur on the large scale, it became impossible to
perform the process by the simple admixture of the substances, the frothing being
so great as inevitably to expel the materials from the retort. After a trial of
various methods, I found it most convenient to employ the apparatus, of which
this is a sketch. The oil was introduced into a large glass balloon, to the mouth

of which two tubes were adapted, one descending to near the middle, and fur-
nished with a cork at the upper end, the other which constituted the neck of the
distilling apparatus passed into a tubulated receiver, kept cold by immersion in
water or ice. To the tubulature, a doubly bent tube was affixed, which descended
into a vessel of alcohol, for the purpose of retaining any of the more volatile por-
tions which might be carried over by the rapid current of sulphuretted hydrogen.
The heat must be applied by means of an open charcoal fire, and the furnace
should be so constructed, that the fire may be rapidly withdrawn in the event of
the action becoming too violent. It is very desirable too, that the balloon should
go down into the furnace, so that it may be entirely surrounded by hot air. The
oil is introduced into the balloon, of which it must not occupy more than a fifth,
or a fourth at most, along with a few small pieces of sulphur, and heat is gradu- —
ally applied. So soon as effervescence commences, the cork of the small tube is
withdrawn, and a small piece of sulphur is introduced; and this is continued
gradually, so as to keep up an uniform action. A dark reddish-brown oil passes

= : . - = — - — Le ee

OF THE FIXED OILS IN CONTACT WITH SULPHUR. 367

into the receiver, and at the same time sulphuretted hydrogen passes in torrents
through the alcohol; it there deposits a certain quantity of oil, and on escaping,
may be kept burning during the whole operation, with a flame eight or nine inches
high. The principal difficulty of this process consists in regulating the heat, so
as to keep up a steady action. Ifthe heat be allowed to fall, the contents of the
balloon become so viscid, as inevitably to boil over; and at the same time too
high a temperature causes the whole action to go on with excessive violence. I
have generally operated on quantities of three pounds, each of which requires a
complete day for its distillation, during which time the operator must never leave
it, but constantly attend to the regulation of the heat, and the gradual addition
of sulphur in small quantities. When a quantity equal to about half the oil em-
ployed has distilled over, the remaining mass becomes excessively viscid ; and just
at this point the balloon frequently cracks, the contents escape, and the whole
catches fire, and blazes off with a bright yellow flame, and smell of sulphurous acid.

The product of this distillation, which exactly resembled that of the pure
oleic acid, was rectified, and the crystals which deposited from the latter portions
were expressed and purified by successive crystallizations in alcohol. They then
presented all the characters of margaric acid, and gave the following results of
analysis :—

14:558 oe carbonic acid, and

5:275 grains of the acid gave
lip
POLS ts. .y water:

17-548 tn carbonic acid, and

6-358 grains of the acid gave
If
T2002 | water,

Which gives the following results per cent.—

Experiment. Calculation.
poe
il; 108
Carbon ily wT V7527 75°40 75°55 Czy 2500-0
Hydrogen, . . 1251 1266 1259 Hy 425.0
Oxygen; .|)-) ue 1222 11:94 11-86 O, 400-0
100:00 100:00 100-00 3325°0

These results agree completely with the formula for margaric acid, and were far-
ther confirmed by the analysis of its silver salt and ether.
4-643 grains of the silver salt gave 1-325 of silver = 28-53 per cent.

7-926 grains of the silver salt gave 2°284 of silver = 28°70 per cent.
The calculated result for margarate of silver gives 28:65 per cent.

VOL. XVI. PART III. G 5A

368 DR THOMAS ANDERSON ON CERTAIN PRODUCTS OF DECOMPOSITION

The ether was prepared in the usual manner, by dissolving the acid in abso-
lute alcohol, and passing dry hydrochloric acid gas through the solution. The
product, which possessed all the properties of margaric ether, gave the following
results of analysis :

5'596 grains of the ether gave
15-662 ... carbonic acid,
6:399 de water.
Experiment. Calculation.

—_————_——F———————__
Carpon, )'. 20 « = doo 76°51 Cag 2850.0
Hydrogen, yg EAT 12°74 Jal 475-0
Oxygenyn fsa. cee a Lom 10°79 O, 400-0
100-00 100-00 3725°0

These analyses establish, in a satisfactory manner, that the acid produced
was margaric acid. It is scarcely possible, however, in the present state of the
investigation, to give anything like a rational explanation of the mode in which
it is here formed. Its production from oleic acid has been already observed by
LavuRENT as the first product of oxidation by nitric acid; but the action of sul-
phur is certainly of a very different character, and cannot be considered as bear-
ing any analogy to that of an oxidising agent. The quantity of margaric acid
produced does not appear to be constant, but varies with the rapidity of the dis-
tillation, and is always most abundant when it is slowly performed.

The oil which distils previous to and along with the margaric acid, and con-
stitutes by far the most abundant product of the action of sulphur upon oleic acid
and oil of almonds, is a very complex substance, and contains some of its consti-
tuents in very small proportion. On this account I found it necessary to prepare
it in very large quantity; and in doing so I abandoned the use of almond oil and
employed linseed oil instead, which is a much cheaper substance, and yields the
same fluid products. When the product of the action of sulphur is carefully rec-
tified, the first portions which pass over, are perfectly transparent and colourless,
highly limpid and mobile, and boil at the temperature of 160° Fahr. Only a
small quantity, however, passes at this temperature, and the immersed thermo-
meter gradually rises without indicating any fixed boiling point for the fluid. My
first attempts to purify this oil, and separate it into its various constituents, did
not afford any satisfactory conclusions. Numerous analyses of the more volatile
portions were made without obtaining comparable results, although all indicated
the presence of carbon and hydrogen nearly in the proportion of equal atoms. The
following are the details of three of these analyses :—

OF THE FIXED OILS IN CONTACT WITH SULPHUR. 369

12:688 4¥z carbonic acid, and

4-657 grains of the most volatile oil gave
I
5127 =... ~~ water.

15:762 Nee carbonic acid, and

5°501 grains of an oil less volatile than the preceding gave
IT
6292 ... water.

12:185 ak carbonic acid, and

4-191 grains of another portion of oil gave
tl
4720 ... water.

Which correspond to the following results per cent. :

lip 105 THe
Carbon, .:... .s 45°08 78:79 79-95
Hydrogen, . . . 12:20 12°72 12-75

All these oils, when treated with fuming nitric acid, yielded an abundant
precipitate of the sulphate of barytes; but as the results of the combustion were
not constant, no quantitative determination was made.

The action of precipitants, however, upon this oil, afforded a more satisfac-
tory method of obtaining some of its constituents. It gives, with corrosive subli-
mate, a bulky white precipitate, and with bichloride of platinum, a yellow com-
pound, the characters of which vary slightly, according as it is prepared from the
more or less volatile portion of the oil. Nitrate of silver and acetate of lead,
mixed with the alcoholic solution of the oil, produce only a slight cloudiness, but
on boiling the solutions, the sulphurets of silver and lead are deposited.

The Mercury Compound. In order to obtain this substance in the pure state,
the oil was dissolved in alcohol, and an alcoholic solution of corrosive sublimate
added. The precipitate which fell was collected on a filter, and washed with
ether, until the oil was thoroughly extracted, for which purpose a considerable
quantity of ether is required. It is then boiled with a large quantity of alcohol,
which dissolves a part of it, and the solution being filtered hot, allows the com-
' pound to deposit, on cooling, in the pure state. It is then in the form of a white
crystalline powder, having a very fine pearly lustre, and exhibiting under the
microscope crystals of a very peculiar form. They are six-sided tables, two oppo-
site angles of which are rounded off, so as to give them a very close resemblance
to the section of a barrel. It possesses, even after long-continued washing with
ether, a peculiar slight sickening smell, which becomes more powerful on heating,
and its powder irritates the nose. It is insoluble in water, which moistens it
with difficulty. It requires several hundred times its weight of boiling alcéhol
for solution, and is almost entirely deposited, on cooling, in microscopic crystals.
In ether, it is almost insoluble. When heated, it is decomposed with the evolu-

370 DR THOMAS ANDERSON ON CERTAIN PRODUCTS OF DECOMPOSITION

tion of a peculiar nauseous smelling oil. The sparing solubility of this compound
in alcohol renders its preparation in sufficient quantity for analysis an extremely
tedious process, and I have sought in vain for a more abundant solvent. The
only substance which I have found capable of taking it up in larger quantity, is
coal-tar naphtha, but its employment is inadmissible, as the best which can be
procured is an extremely impure substance, and the crystals of the compound
deposited from it always acquire a rose or violet tint from some of its impurities.
Oil of turpentine likewise dissolves it, but not more abundantly than alcohol.

By many successive solutions in alcohol, I obtained enough of this substance
for an analysis, of which the following are the results :—

6°592 ++ of carbonic acid, and

12-302 grains, dried in vacuo, gave
3018 _--- of water.

8:061 grains, deflagrated with a mixture of nitre and carbonate of soda, gave
7:297 grains of sulphate of baryta = 1:0067 = 12°48 per cent. of sulphur.

The mercury and chlorine were determined together by mixing the substance
with quicklime, and introducing the mixture into a combustion tube. The end
was then drawn out into an elongated bulb, into which the mercury sublimed,
and which was afterwards cut off, dried in the water-bath, and weighed, both
with and without the mercury; the chlorine was determined in the usual way
from the residue in the tube.

9958 grains gave 5:976 mercury = 60°01 per cent., and 4:310 grains chloride
of silver = 10°67 per cent. of chlorine.

5797 grains gave 2:409 of chloride of silver = 10°25 per cent. of chlorine.

These results correspond closely with the formula C,, Hi, 5S; Hg, Cl, as is
shewn by the following comparisons :—

Experiment. Calculation.
I. II.
Carboni? 3)". = S68 Bis 14:46 Ci, 1200-0
Hydrogen) "2 92:72 Boh 2°42 Hig 200:0
Mereury . . . 60°01 Ba 60°32 Hey 5003°6
Chlorine . . . 10:67 10-25 10°67 Cl, 885°3
Sulphur . . . 12-48 aes 12:18 8; 1005°8
100:49 -- 100-00 8294-7

It is sufficiently obvious that the formula C,, H,, S; Hg, Cl, cannot be sup-
posed to represent the rational formula of this substance. On the contrary, the
remarkable analogy between its properties and those of the mercury compound
of stlphuret of allyl appear clearly to indicate a similarity in their chemical con-
stitution,—a similarity which, as we shall afterwards see, is borne out by the
properties of the platinum compound. I consider this substance to contain an or-

OF THE FIXED OILS IN CONTACT WITH SULPHUR. 371

ganic sulphuret, analogous to sulphuret of allyl, the constitution of which must
be represented by the formula C,; H;S,, to which I give the provisional name of
Sulphuret of Odmyl (from dz odor), and that the rational formula of the mer-
cury compound is—

(C, Hy S, + Hg, Cl) + (Cs Hs S, + Hey 8).

On contrasting this with the formula of the allyl compound, which is—
(Cg H; Cl + Hg» Cl.) + (Cg H;S + Hg, 82),

two important points of difference are apparent, namely, that in the-new com-
pound we have the sulphuret, and not the chloride, of the base in union with cor-
rosive sublimate, and the presence of subsulphuret in place of sulphuret of mer-
cury in the second member of the compound. It is even possible to approximate
more closely the formule of the allyl and odmyl compounds, by assuming the
sulphuret of odmyl to be represented by C, H,S; in which case, the mercury
compound becomes :—

{3 (C, H, S) + Hg, So} + (C,H, Cl + Hg, Cl).

This formula is, however, incompatible with its reactions, as it involves the
presence of calomel in the compound. ‘Treatment with caustic potash, however,
shews that this is not the case; as it immediately becomes yellow, from the sepa-
ration of oxide of mercury, while the black suboxide would have been formed had
calomel been present.

When a current of sulphuretted hydrogen is passed through the mercury
compound suspended in water, it becomes rapidly black, a peculiar smell is ob-
served, along with that of sulphuretted hydrogen, and, by distillation, an oil
passes over, which is obtained floating on the surface of the water. It is per-
fectly transparent and colourless. Its smell is peculiar, and resembles the nau-
seous odour developed by crushing some umbelliferous plants. When dissolved
in alcohol, it gives, with corrosive sublimate, a white precipitate, soluble in hot
alcohol, from which it is deposited in crystals precisely similar to those from
which it had been originally separated, and, with bichloride of platinum, a yellow
precipitate, slightly soluble in hot alcohol and ether. This oil is, in all probability,
the sulphuret of odmyl C; H, S., but the small quantity in which I have been
able to obtain it, has prevented my performing any analysis of it.

The Platinum Compound. When a solution of bichloride of platinum is added
to the alcoholic solution of the crude oil, a yellow precipitate makes its appearance,
which does not fall immediately, but goes on gradually increasing for some time,
precisely as is the case with the allyl compound. The properties of this precipi-
tate are not, however, perfectly constant, but vary according to the portion of the
oil employed to yield it. That obtained from the more volatile portion has a fine
sulphur-yellow colour, but the less volatile oil gives an orange precipitate. It is

VOL, XVI. PART III. 5B

372 DR THOMAS ANDERSON ON CERTAIN PRODUCTS OF DECOMPOSITION

insoluble in water, sparingly soluble in alcohol and ether. When heated it be-
comes black, an oil is evolved smelling exactly like that obtained from the mer-
cury compound and sulphuret of platinum is left: behind, which requires a high
temperature to drive off all its sulphur, and leaves metallic platinum as a silver-
white mass. When treated with hydrosulphuret of ammonia, it is converted
into a brown powder, exactly like that obtained under similar circumstances
from allyl.

The analysis of the yellow compound has not hitherto given results of a satis-
factory character. I have found the amount of platinum to oscillate between
43°06 and 49°66 per cent. The former of these was obtained from the most vola-
tile oil, the latter from that which boiled between 300° and 400° Fahr., and inter-
mediate results were obtained at intermediate temperatures. The results obtained
from the oil which boiled at a high temperature were remarkably constant; thus
I have found, in different experiments, 49°00, 49°51 and 49°66 per cent. of pla-
tinum, which appear to indicate the presence of some compound of rather’sparing
volatility. The precipitate obtained from the most volatile oil appears to be that
corresponding to the mercury compound which has just been described. Of it
I have been able only to perform a very incomplete analysis, which is insuffi-
cient to establish its constitution, especially as it is impossible to ascertain whether
it is a homogeneous substance. As the results, however, approximate to a for-
mula analogous to that of the mercury compound, I give the details, such as they
are.

9-155 grains of the platinum compound gave
7474 te carbonic acid, and
3294 ... Water.

5-701 grains gave 2°455 grains of platinum, =43-06 per cent.

These results approximate to a formula similar to that of the mercury com-
pound :—viz.
(C, H, 8, +Pt Cl,)+(C, H, S, +Pt 8).

Experiment. Calculation.

TE a

Carbony. «ee we wo 20°83 Cig 1200-0
Hydrogen, . . 3:99 3°47 Hy, 200-0
Platinum, . . 43:06 42°84 Pt. 2466°6
Chlorine.” Wo ee Wwe. 15:38 Cl, 885°3
Sulphur, gett AA 17-48 S, 1005:8
100:00 5757-7

The analogy which those substances bear to allyl is exceedingly interesting,
as shewing the possibility of forming, by artificial processes, substances similar im
constitution to so remarkable a compound, which is not a product of decomposi-
tion, but exists ready formed in a variety of different vegetables, where it must

——

OF THE FIXED OILS IN CONTACT WITH SULPHUR. 378

obviously be produced under circumstances very different from the artificial sub-
stance; for allyl cannot exist at all at a high temperature, and is entirely decom-
posed at, or even below, its point of ebullition. Unfortunately, however, the ex-
amination of this substance is much complicated by the necessity of examining its
compounds in place of itself. Had it been possible to separate it directly from
the crude oil, the determination of its constitution and that of its compounds
would have presented comparatively little difficulty, and been arrived at with
much less labour than that expended upon the imperfect details I have been able
to accumulate. Another point worthy of observation, is the total alteration of
the products of decomposition of oleic acid produced by the presence of sulphur ;
no sebacic acid, and, in fact, none of its ordinary products being evolved, although
all the substances produced contain carbon and hydrogen in the proportion of
equal atoms, just as they exist among the ordinary products,—a circumstance
which, taking into consideration the abundant evolution of sulphuretted hydro-
gen, we certainly should not have anticipated.

The oil which remains after the separation of the mercury compound, like-
wise contains sulphur as one of its constituents; but I have not yet had time to
commence the investigation of this part of the subject. The discussion of it, as
well as various other points connected with the compounds -already described, I
hope to make the subject of a future communication.

en 0. Soa Mae iran eerie
padre tairitia aig dd, snAididiatitiseetbealebaiclacala

“reqs aim: hie at ishenctoltehierion ay: i? soe
Ley shasta addy Lederle <ioati Wotigwie ec :
by gutta ice Vanaghhesgdiiins 0 gall Miles ea
‘inutt oliamnib aesanmaeeben at nt sob Di Dien isa Deaarotgally
vel ivinen perio «ssh peiher ili ruc suaieai eed gion “ak rt
(icy dasbarivis coed bith. leeieh alint verter tone
1" Las alia wn tanh heap Lancto eeninkens ee it
. to etetaot ofd.ab celia wey Bae r |
_ 6008 hepa Rooters rep val thos aborney jab nant
Aye Midis pbiedevr retstiaet istdogatiekeeeetomaae
tematiermepricnh whh vee auabys baa soda Ps evn te
- ND Ae ve She ahve igtinihetyecksin ineentihaidindsd
afb ey obsdjownuig!as benign dol susie, atl. (rai kama heir Sete:
Wyn? Vet Salado!) anbitegiated' seed furs 2e ils 2 “"
~ollik: Uti sogne.crreteris oi? to. giiobeo-r ge Ockd Til de enti oy dane
cn -weenaw served toy tee weed bs uit ~ carmen mel © ate
Huacyiey leapt treaties ls ate yebote ead Lex tay: ett ee ca cuit all
‘* below Chipeta: abetinegerests unio Tea dei Ton eevee ‘pist
ee mal ied Sonera Ta sAaitae oan i
wry y Powe fia hy su as abi "

Cara!)

XXV.—Experimenis on the Ordinary Refraction of Iceland Spar. By Wiu1am
Swan, Esq. Communicated by Professor KELLAND.

(Read 19th April 1847.)

According to the theory devised by Huycens, to explain the phenomenon of
double refraction in Iceland spar, a pencil of light transmitted through that sub-
stance is divided into two pencils; the index of refraction for the one being con-
stant, while for the other it varies with the inclination of the transmitted light
to the optical axis of the crystal.

Dr Wottaston, in 1802, verified the spheroidal form of the wave of light,
which Huyerns had assumed to account for the refraction of the extraordinary
pencil, by a careful experimental investigation, conducted by means of his elegant
instrument for ‘“‘ examining refractive and dispersive powers by prismatic reflec-
tion.”* In 1810, Matus, in his Théorie de la Double Réfraction, also demonstrated
experimentally the accuracy of the Huygenian law for the extraordinary pencil.
I have not had an opportunity of consulting the memoir of Matus, so as to
know the precise nature of his experiments, with reference to the refraction of
the ordinary ray; but the object of Dr Wotiasron’s researches was simply to
prove the law of extraordinary refraction, and the constancy of the index of re-
fraction for the ordinary ray, is therefore tacitly assumed by him.

More recently, Professor MaccutLacu of Dublin, in order to account for cer-
tain phenomena observed by Sir Davip BREewsTER, in the reflexion of light from
Iceland spar, was led to propose a law of double refraction, according to which
the ordinary ray in that substance has a variable index of refraction; and at his
request, Sir Davip BREWSTER made an experiment to ascertain whether the
ordinary refraction of Iceland spar is different at different inclinations to the
axis. Two prisms were cut out of the same piece of spar, so that in one the
transmitted ray was at right angles to the axis, and in the other, it was coinci-
dent with it; and both being cemented to a plate of glass, had their surfaces
ground and polished together, so as to ensure the equality of their refracting
angles. It was then found that the images of a narrow slit, illuminated by
homogeneous yellow light, seen through the prisms, were perfectly coincident,
which proved that the index of refraction for the ordinary ray was the same in
both prisms, ‘“‘ within the limits of the errors of observation.” +

* Philosophical Transactions, 1802, pp. 365 and 387.
+ See Experiment on the ordinary refraction of Iceland spar, by Sir Davin BrewstER.—Notices
and Abstracts of Communications of the British Association, 1848, p. 7.

VOL. XVI. PART III. 5¢

376 MR SWAN’S EXPERIMENTS ON THE

Some time ago, Mr Wixx1am Nicot of Edinburgh, whose skill in cutting and
polishing Iceland spar is well known, requested me to undertake the examination
of the ordinary refraction of several prisms of Iceland spar, with which he had
the kindness to entrust me, and which he had cut so that the transmitted light
is inclined at various angles to the axis. The refractive power of these prisms
was examined by means of an instrument devised by me for facilitating such in-
quiries, and described in the Transactions of the Royal Scottish Society of Arts
for 1844, p. 293.* It will be sufficient here to explain that the prism is mounted
in front of the telescope of a theodolite, with plates of sextant glass in accurate
contact with its faces. The deviation of the refracted rays is then measured as
in FRAUNHOFER’s method of determining refractive powers; and the refracting
angle of the prism is ascertained by measuring the deviation of rays that have
suffered two reflexions at the surfaces of the sextant glasses. The prism being
placed in its position of minimum deviation, the index of refraction is ascertained
sin } (0+a)

6

ate where 6 is the angle of the prism, and a the mi-

from the formula up =

nimum deviation of the refracted rays.

The theodolite I used in this investigation is made by Troucuton. The
horizontal limb, measuring 6°5 inches in diameter, is furnished with two verniers
reading 20", and the telescope magnifies twelve times. As I had not the means
of observing an object at a greater distance than 40 feet, and as the correction for
parallax due to the distance of the prism from the centre of the theodolite could
not be ascertained with sufficient accuracy, owing to the difficulty of finding
the exact position of the pencil of incident rays, I determined to adopt a method
for avoiding this correction.

This consisted partly in mounting the prism over the centre of the theodolite
by means of a simple and ingenious arrangement suggested by Mr Joun ApIE.
A rod of well-seasoned mahogany, fitted to the Ys of the theodolite, was furnished
at one end with temporary 1's, placed so as to shift the telescope out from the
centre of the instrument; while, at the other, it carried a counterpoise to the
weight of the telescope. To this I added stays of wire passing from the ends of
the rod to the extremities of the horizontal axis of the theodolite, which were
tightened by means of screws so as to prevent any lateral shake. The whole —
apparatus was mounted on a very firm portable tripod, and was sufficiently stable.

But although the prism, from its position at the centre of the instrument,
did not suffer any material displacement on turning round the telescope, it
was still desirable to get rid of any remaining uncertainty as to the direction of
the incident light. The method I devised for effecting this object, was to use a
collimator so as to obtain a beam of sensibly parallel rays, and thus to place

* Also in the Edinburgh New Philosophical Journal, January 1844.

EO

eee

Ln Aare

ORDINARY REFRACTION OF ICELAND SPAR. 374

the luminous object I observed, virtually at an infinite distance. Having fitted a
pair of cross fibres of silk* in the anterior focus of the object-glass of a telescope,
I carefully adjusted it to distinct vision on a star, so that, on moving the
eye up and down, its image remained fixed on the wires. The eye-piece being
then cautiously removed, the wires were illuminated by a lamp; and the beam
of rays issuing from the object-glass having been directed upon the prism, the
optical axis of the collimator was made parallel to the horizontal limb of the
theodolite by means of adjusting screws. A common oil-lamp was used in
ascertaining the angles of the prisms; but when the deviation of the refracted
rays was observed, the wires were illuminated with the homogeneous yellow
light of a spirit-lamp with a salted wick: and it must be regarded as a re-
markable proof of the perfect homogeneity of this light, that the refracted image
of a single fibre of silk was always distinctly visible with a good prism.

I shall now give the results of the examination of Mr Nicot’s prisms, to
which I shall refer according to the numbers he has attached to them. The an-
gle of the prism was generally determined by four, and the deviation of the re-
fracted rays by six observations.

The prism marked No.1 is cut out of the crystal, so that in the position
of minimum deviation the transmitted rays are parallel to the axis; and Mr Nico.
has worked with such accuracy, that the images produced by the ordinary and

‘extraordinary rays coincide almost exactly in this position. The angle of this

prism was found to be 60° 8’ 8”, the deviation of the refracted rays 52° 14’ 36’,
and consequently u = 1°658367.+

The plane of refraction in the prism No. 2 is perpendicular to the axis. Its
angle was found to be 44° 29’ 20’, and the deviation of the refracted rays
33° 17! 8”. From which p=1°658366.

Two other prisms, No. 3 and No. 4, were also examined, in which the trans-
mitted rays are perpendicular to the axis; but in either case the prism is cut so
that the plane of refraction differs from that of No. 2.

For No. 3, the angle of the prism was found to be 59° 36’ 32”, the deviation
of the refracted rays 51° 25’ 25”, and H=1-658384.

For No. 4, the angle of the prism was found to be 44° 55’ 24”, the deviation
33° 42’ 34”, and u=1°658361.

In No. 5, the transmitted rays are inclined 45° to the axis; the refracting
angle of the prism was found to be 45° 3’ 51”, the deviation of the refracted rays
33° 50’ 58”, and w=1°658385.

* Silk is not the most suitable material for the purpose, owing to its Mame but I could pro-
cure no better at the time.

+ I have also examined another prism, No. 1, and hate found 6=44° 23’ 2”, 6=33° 11’ 0”, and
“= 1°658362.

378 MR SWAN ON ICELAND SPAR.

In No. 6, one of the faces is a cleavage plane, and the principal section of the
prism is in the same plane with the axis. Therefore, since the cleavage plane is
inclined 45° 23’ 25” to the axis, it follows that the inclination of the transmitted
rays in the position of minimum deviation is nearly 66° 51’. The angle of this
prism was found to be 44° 28’ 29”, the deviation of the refracted rays 33° 16’ 22”,
and =1'658389.

These results are combined in the following Table :—

Inclination of the
plane of incidence,

or of the principal Inclination of the Index of refraction Difference of each

Pai aden oe en | ne Se
0 the optical axis
of the crystal.*
No. 1 0° 0° 1:658367 — 0:000008
2 90° 90° 1:658366 — 0:000009
3 0° 90° 1658384 +0:'000009
4: 45° 90° 1658361 — 0-000014
5 0° 45° 1658385 + 0:000010
6 0° 66° 51’ 1:658389 + 0:000014
Mean 1.658375 0-000011

From this summary it will be seen, that the greatest difference between the
observed index of refraction of any prism and the mean of the whole results is
only ‘000014; while the difference of the greatest and least results is less than
‘00003. So close an agreement in six essentially different cases, seems to render
it very probable that the index of refraction is really constant; and the result of
the investigation thus confirms the accuracy of the Huygenian law.

* As the term, principal section, is employed in more than one sense, it may be proper to observe,
in order to avoid ambiguity, that I use it to denote a plane perpendicular to both faces of the prism.—
See Sir John Herschel’s Treatise on Light, in the Encyclopedia Metropolitana, p. 370, art. 197.

Pi (508790)

XXVI.— Observations on the Temperature of the Ground at Trevandrum, in India, from May
1842 to December 1845. By Joun Catpecortt, Lsq., Astronomer to the Rajah of Travancore.
Communicated in a Letter to Professor J. D. ForBeEs.

(Read 15th March 1847.)
122 Patt Matt, Feb. 3, 1847.
My Dear Sir,—I have taken the opportunity of a short visit to England to bring with me

a complete copy, to the end of 1845, of the Observations of Terrestrial Temperature, made at

Trevandrum (of which I have already sent you a partial account), and which I have now the

pleasure to forward to you herewith, to be dealt with in any way you may think proper.

Should you think them worthy of presentation to the Royal Society of Edinburgh for publica-

tion in their Transactions, it will be gratifying tome. The observations made with the 12 feet

thermometer are now at an end, in consequence of the fracture of the instrument during a high
wind last year ; but, after rejecting those made immediately on the introduction of the instru-
ments, say all those of 1842, there will still remain three entire years of trustworthy read-
ings, which I hope may be found to be sufficient for any purpose for which such observations

in a tropical region may have been considered desirable.
JNO. CALDECOTT.
Professor Fores, Edinburgh.

EXPLANATION.

These three thermometers, made by Messrs ADIE and Son of Edinburgh, were put down on May 1,
1842. They are buried at the respective depths of 12 French feet, 6 French feet, and 3 French feet, on the
top of the Observatory hill, which is composed of the stone called “laterite.” The situation is about 200
feet above the sea.

In December 1841 and January 1842, they were suspended in the Observatory, and compared with a
standard thermometer by Traughton and Simms, as follows, viz. :—

No. 1, or the 12 feet thermometer, by a comparison made 12 times in 24 hours for 29 days, 7. e., by 348

_ comparisons, requires, in order to reduce it to the standard thermometer, the addition to the readings here
given of 2°133. The greatest deviation from this mean of any single comparison is 0°-54.

No. 2, or the 6 feet thermometer, by the same number of comparisons, requires the addition of 2°-172 ;
the greatest deviation from which is 0°69.

No. 3, or the 3 feet thermometer, by the same number of comparisons, requires the addition of 2°922 ;
the greatest deviation from which is 0°57.

Latitude of Trevandrum Observatory, . . . 8 30 82’N.
Longitude from Greenwich, BE atte oy To umen mb Os! iy

[It may here be stated, that the original registers furnished by Mr CALDECOTT include four observa-
tions, daily (except on Sundays), at 6 a.M., Noon, 6 P.M., and Midnight. The extent of the Tables is, con-
Sequently, very considerable ; and, in printing them, it was necessary to ascertain whether these six-hourly
observations possessed a value proportional to the great additional space which they would have occupied. ~
A careful examination shewed that the variation from one hour to another, in the different thermometers,
was due mainly to the influence of the heat of the air in expanding the exposed part of the column of spirit,
and did not at all indicate the course of the diwrnal curves at different depths ; nor were there data given
for eliminating this discrepancy. It was, therefore, decided to publish the 6 A.M. observations alone,* as
representing fairly the general result, and as being less liable to error from the irregular expansion of the
exposed column of spirit by the intense heat of the tropical sun.

It will be observed that all the temperatures in the Register, and the means, are UNCORRECTED for the
large index error of the instruments. A corrected summary will be given, together with a few deductions,
at the conclusion of the paper.—J. D. F.]

bey * The monthly means, four times a day, are, however, given in a separate Table.
,

MR CALDECOTT’S (UNCORRECTED) OBSERVATIONS OF

No. 2.

12 feet | 6 feet
Therm. | Therm.

380
When blanks occur, the liquid is above the Scale.
No. 1. | No. 2. | No. 3. | Mean No. 1.
12 feet | 6 feet | 3 feet | Temp. ;
Date. Therm. |Therm.|Therm.| of Rain. Date.
6a.M.|64.M.|6a.M.| Air. 6 A.M.
1842. fe) fo} fo} fe} in. °
May 1 The Thermometers were put down this day, 0-1852 Sunday 1 84-90
2 | 83-80| 84-02| 83-40; 82-58] 0-0168 2 | 85-00
3 | 83-91] 84-16} 83-54| 84-40] ------ 3
4 | 84-03 | 84:37] 83-78) 84-00/} ------ 4 | 84-90
5 | 84:11] 84-54} 83-89) 79-71] 0-1095 5 | 84-92
6 | 84:22] 84-74] 84-10| 79-79| 0-3915 6 | 84-90
7 | 84-24) 84-83] 84-17) 75:97| 3-8596 7 | 84-88
8 0:9639 Sunday 8 | 84-88
9 | 84-90| 84-82] 83-85] 77-33} 0-6902 9 | 84-88
10 | 84-44] 85-21] 83-55] 78-41] 0-4168
11 | 84-54] 85-32) 83-40} 81-05] -:-:-- :
12 | 84-57] 85-32} 83-20| 81-77| ------ 12 | 84.04
13 | 84-67! 85-35} 83-18] 81-22] ------ 13 | 84-83
14 | 84-70} 85-33} 83-15] 81-50/ --+--- 14 | 84-82
15 Sunday 15 | 84-80
16 | 84-90} 85-28} 83-11] 81-24] ------ :
17 | 84-76} 85-18} 83-19} 79:57] ------
18 | 84-84] 85-21} 83-38} 80-73} 0-084 :
19 | 84-78} 85-17| 83-50} 82-10] ------ 19 | 84:74
20 | 84-90} 85-23} 83-70| 82-69} 0-0379 20 | 84-80
21 | 84-88] 85-21) 83-80) 82-87] -----: 21 | 84-78
22 Sunday 22 | 84-67
23 | 84:98] 85-27} 84-22] 80-51] «------ :
24 | 84-99} 85-29} 84-43|] 81-13} 0-0505
25 | 84-88} 85-34] 84-52) 82-58; ------ .
26 | 85-02} 85-48 | 84-70| 77-44} 0-3620 26 | 84-60
27 | 85:00] 85-42] 84-59} 76-08| 2-0667 27 | 84-55
28 | 85-20} 85-54] 84-70! 75-00} 0-5393 28 | 84-55
29 1-6878 | Sunday 29 | 84-51
30 | 85-08] 85-61 | 83-66| 74-87] 2-7737 :
31 | 84-88] 85-60] 83-20) 78-89} 0-2736
Means 84-66 | 85-11] 83-77) 80-09 | 14-5134

6 A.M.

°

84-21
84-21

84-10
84:07
84-01
83-89
83-82
83-80

83-71
83-70
83-68
83-60
83-57
83-49

83-40
83-41
83-40
83-42
83-31
83-30

83-22
83-20
83-17
83-18

83-16

83-18

83-62

No. 3.
3 feet
Therm.
6 A.M.

°

81-62
81-62

81-29
81-21
81-18
81-00
81-20
81-20

81-05
80-94
80-88
80-70
80-79
80-65

80-88
80-70
80-74
80-79
80-70
80-72

80-80
80-86
80-90
80-88
81-00
81-02

Mean

Temp.
of

Air.

eeeeee

tee eee

wena

teeta

eeeeee

80-97

Means

79-32

Sunda

OBNAOunrK wn

_—
Ke)

83-72
83-72
83-74
83-71
83-73

83-75
83-72

83-74
83-75
83-71
83-73
83-72
83-73

83-69
83-72
83-75
83-70
83-68
83-65

83-64
83-65
83-64
83-63
83-65
83-61

\¢
.
]
|

83-65
83-64
83-63
83-63
83-64
83-65

83-68

83-30
83-26
83-25

83-10

83-10
83-18
83-21
83-37
83-27
83-32

83-12

82-85

83-00

82-91
82-81
82-81
82-80
82-79
82-75

82-69
82-75
82-70
82:72
82-75
82-72

82-87
82-93
83-02
83-07
83-10
83-19

83-36
83-40
83-42
83-41
83-48
83-54

83-50

80-44 | 77-76
80-30 | 79-34
80-51

80-45
80-60
80-76
80-75
81-02
81-10

81-45
81-64
81-72] 79-18
81-88
81-96
82-00

82-10
82-10
82-10
82-00
81-85
81-74

81-28
81-11
80-85
80-78
80-70

81-28

80-55

80-50
80-49
80-50 | 79-66
80-51
80-50
80-64

80-78
80-85
80-99
81-09
81-25
81-35

81:70
81-90
82-05
82-20
$2-09
82-31

82-39
82-30
82-30
82-23
82-14
82-06

§1-:70| 74-50

Means | 83-68] 83-04] 81-44| 79-10

OCOOnaunr WWE

TERRESTRIAL TEMPERATURE AT TREVANDRUM.

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Means

83-29
83-26
83-30
83-32
83-32
83-31

83-27
83-35
83-36
83-40
83-35
83-34

83-34

78-96

0:0631

teens

seen
eenwes
seeeee
cones
esceee

eee eee

Sunday

| Sunday

Sunday

Sunday

OMOWNHNP wh

Means

Feb.

Means

MR CALDECOTT’S (UNCORRECTED) OBSERVATIONS OF

No. 2. | No. 3.
6 feet | 3 feet
Therm. | Therm.
6 A.M. | 6 A.M.

aeeeee

aneeee

seeere

eee eee

eeeeae

eereee

oeeene

eeeeee

weeeee

eeeeee

eeeees

eveeee

ee eeee

eccees

scene

eovewe

wee eee

eeeeee

83-85 | 84-53 | 84-00] 80-09

—_

0-033

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

——--

Means

No. 1.
12 feet

Therm. | Therm.

6 A.M.

°

84-11
84-12
84-12
84-18

84-19
84-23
84-22
84-24
84-27
84-29

84-44
84-38
84-40
84-39
84:46
84-45

84-52
84-58
84-53
84-62
84-65
84-68

84-72
84-72
84-76
84-76
84-80

No. 2.
6 feet

6 A.M.

°

85-43
85-52
85-58
85-51

85-74
85-85
85-90
85-98
86-02
86-12

86-29
86-28
86-41
86-31
86-48
86:49

86-50
86:54
86-51
86-55
86-62
86-63

86-73
86-81
86-74
86-90
86-92

No. 3.
3 feet
Therm.
6 A.M.

°

85-42
85-49
85-67
85-50

86-09
86-24
86-29
86-42
86-48
86-61

86-73
86-61
86-50
86-10
86-22
86-17

86-22
86-33
86-37
86-58
86:74
86-82

87-08
87-01
87-11
87-14
87-18

84-43 | 86-27] 86-41

84-82 | 86-79 | 87-25

sesece

eeeeee

ee eene

ereeee

erases

eeeeee

eeeeee
se eeee
Beeeee

eeccee

eeeeee
scenes
eee eee
ee eeee
feeres

86-61
86-52
86-50

84-51
84:49
84-50

Mean
Temp.
of
Air.

82-72
82-44

84-92| 86-60| 86-17} 81-58

we eeee
eeeeee

feeeee

ee eeee

0-092
Sund

Sund

Sund

Sund

|

9-274 ona

TERRESTIAL TEMPERATURE AT TREVANDRUM. 883

i 82-51
. 2
Bi] cere 86-18| 84-63| 85-39] 0-057 3 | 84:34) 82.37] 79-32| 74.34] 0-573
4 | cere 86-20| 84-76] 84-82] «-.-.- 4 | 84-31] 82-31! 79-28] 76-16| 1-144
bb. 5 | cress 86-10| 84-80| 83-75| «+. 5 | 84-29] 82-25) 79.12] 76-50| 0-298
6 | cree 86-12| 84-86] 85-57| «----- 6 | 84-25| 82-17) 78-89| 77-54| 0-048
: 7 Sunday 7 | 84-22) 82-15] 79-05| 76-31| ----
ee 86-10| 85-17| 80-34] 0-204 8 | 84-15] 82-05| 78-90| 74-33] 1-411
Q | veers 86-12| 85-30| 84-33] --.-.. 9 1-301 | Sunday
10 | +++ 86-12| 85-38| 83-57| 0-014 10 | 84-11] 81-88| 78-79] 75-31] 0-965
11 | -+---- 86-15 | 85-37] 80-66] 0-172 11 | 84-09} 81-85| 78-77| 76-60| 0-338
* 12 | ---- 86-17| 85-38| 83-60| --.-.. 12 | 84:01] 81-71| 78-60| 77-65] 0-241
13 | +++ 86-25| 85-55] 81-80] -..--- 13 | 83-95 | 81-61] 78-50| 75-30] 0-598
14 Sunday 14 | 83-91] 81-55| 78-50| 76-42| 0-787
15 | see 86-32| 85-44| 81-37] 0-299 15 | 83-92] 81-55| 78-54| 75-92] 0-342
16 | -+---- | 86-26] 85-38] 78-46| 0-122 16 0-270 | Sunday
17 | ------ | 86-21| 8540] 78-24] 0-563 U7 83-81) 91-41 78-49). 78-58) --<-00
18 | +++ 86:35 | 85-30] 81-46] «.---. > 18 | 83-82| 81-46] 78-61 | 78:44| ..--.-
19 | veer 86:30 |s85-25'| (80-82) -...;. 19 | 83-80| 81-47| 78-67| 78-19| «.....
20 | «++ 86-28| 84-99] 80-97] «..-.- 20 | 83-71] 81-40| 78-65| 77-01| 0-166
21 2.407 | Sunday 21 | 83-74] 81-40! 78-25| 78-41| 0-282
22 | ree 86-27| 84-50] 76-99] 2-267 22 | 83-79| 81-40| 78-58] 78-62| 0-192
23 | «---- | 86-16} 83-98| 77-25| 1-647 23 0-080 | Sunday
BEEN Y..\0 86-12| 83-45| 78-81| 1-471 24 | 83-62| 81-38] 78-86] 78-95 | «--.-.
sal te'<2.- 85-92| 82-81| 79.97] .....- 25 | 83-60| 81-40] 78-95) 78-64] 0-041
26 | .-.-.- 85-78 | 82-52| 76-89| 0-261 26 | 83-59| 81-38] 78-85| 78-16| .«-.--.
27 | ---+-- | 85-62| 82-19| 77-90] 2.343 | 27 | 83-55| 81-39| 78-90| 78-08| 0-062
28 0-902 | Sunday 28 | 83-52| 81-35| 78-89] 79-33] «.....
1) eo 85-25| 81-17] 76-50] 1-188 29 | 83-51| 81-40| 78-95| 79-57| <3...
SM a2. 85-07| 81-41| 77-23] 1-320 30 0-465
El irset 84.94] 81-22] 78-97] 0-745 31 | 83-45] 81-35] 79-00} 79-30| 0-464
“Means | ...... 86-03| 84-26| 80-62] 15-989 Means | 83-90/ 81-70| 78-82] 77-29| 10-899
Same 1 | --.... 84-73 | 81-05/| 81-35| 0-432 Aug. 1 | 83-41| 81-35] 78-99| 79-05] «---.-
a 2) | SE 84-58| 80-90] 80-16| 0-065 2 | 83-39| 81-31] 78-99| 79-55 | «+++
4 2 See 84-45 | 81-01] 79-23] 0-196 3 | 83-39] 81-37| 79-05| 80-00] -----.
4 0-042 | Sunday 4 | 83-44| 81-38] 79-07] 79-91| -----.
By |Poce ss. 84-25 | 81-10] 79-22] 0-211 5 | 83-43] 81-35| 79-10| 78-70] «+...
4 6 | eee 84-17] 81-15| 78:74| 0-451 6 0-003
77\eeeeee 84-13] 81-30| 77-62| 0-128 7 | 83-24] 81-35] 79-11| 79-28| «..-.
| aaa 84.09 | 81-25] 79-18| 0-560 8 | 83-27] 81-42] 79-30| 79-49] «----
Me 9 | «eens 84-04 | 81-35| 79-60| .------ 9 | 83-28] 81-41] 79-29| 79-72| --+-+
‘ ae 83-99| 81-30| 77-55| 0-178 10 | 83-23] 81-44] 79-31| 78-62] ---.-.
11 Sunday 11 | 83-30] 81-40 | 79-29] 78-79 | -s-++
ae 83-89 | 81-21] 78-60| 0-162 12) }$83-18)/18 1-48) 79-38 079041 | /=2.3..
13 | 85-00| 83-88] 81-24] 78-60] 0-240 13
14 | 85-00| 83-81] 81-00] 79-60| 0-454 14 | 83-19} 81-50 | 79-53| 79-53] --+-.
15 | 84-96| 83-77] 81-16] 76-36| 2-322 1S SS007'| 80-61). 79:60)|\ 79-69 | _s2..--
16 | 84-90| 83-65| 80-85] 74-97] 1-941 16 | 83-13 81-51 | 79:70| 79-85| °:.....
17 | 84-89| 83-54| 80-65| 75-55| 1-263 17 | 83:13 | 81-59 |'79-79 | 79-37 | +-<.-..
18 1-768 | Sunday 18 | 83-10] 81-59 | 79-90| 77-11] 0-108
19 | 84-81] 83-26] 81-14] 79-39] 0-020 19 | 83-07| 81-60 | 80-04] 76-23] 0-505
20 | 84-85| 83-28] 81-17| 78-31| «+--+ 20 0-089 | Sunday
21 | 84-75| 83-08] 79-85| 78-05| 0-147 21 | 83-06] 81-60] 80-02] 77-31| 0-229
. 22 | 84.69] 83-02! 80-03| 78-89] 0-275 22 | 83-05| 81-70} 80-22] 78-05| 0-101
. 23 | 84-65] 82-98| 79-91| 77-26| 0-230 23 | 83-00] 81-73] 80-20] 78-19] 0-541
24 | 84.84] 82.93) 79-99] 75-56] 1-168 24 | 83-04] 81-81] 80-21] 79-85} 0-009
25 Sunday 25 | 83-04] 81-88] 80-24] 80-55 | ..++-
26 | 84.59] 82.87] 79-90] 79-17] 0-858 ) 26 | 83-00| 81-89| 79-90] 80-66] ---+-
84:56| 82-90| 80-05} 78-60] 0-038 27 Sunday
84-54 | 82-84) 80-02] 76-61] 1-767 > 98 | 83-01 | 81-88 |"S0-12)|°79-82 | .:.-..
84-48 | 82.62| 79-60| 76-72} 1-780 29 | 82-95] 81-85] 80-13] 79-09| 0-029
84.44| 82.54| 79-55| 76-50] 0-236 30 | 82-95| 81-85| 80-09| 77-67| 0-084
31 | 83-00] 81-90} 80-21] 78-87| 0-400
Means | 84.75] 83-59! 80-68! 78-21| 16-932 Means | 83-16! 81-58] 79-66| 79-05| 2-098

OL. XVI. PART: III.

=

MR CALDECOTT’S (UNCORRECTED) OBSERVATIONS OF

384
No. 1. | No. 2. | No. 3. | Mean Rain
12 feet | 6 feet | 3 feet | Temp.| 84 4.M
Date. Therm.|Therm.|Therm.| of to
6A.M.|6A.M.| 6 A.M. | Air. 84 A.M
1843. : : E iS in.
Sept. 1 | 82:99} 81-91| 80-31] 77-79} 0-800
2 | 82-98] 81-91] 80-31] 76-48| 1-872
3 0-565 | Sunday
4 | 82-95 | 81-95} 80-20} 79-80} 0-093
5 | 82-92| 81-99} 80-10} 79-10| «+--+.
6 | 82-98} 81-98| 80-09) 79-09) ---+--
7 | 82-95] 81-91] 79-81| 79-17] ---+-
8 | 82-91] 81-88| 79-80) 79-58) ------
9 | 82-91| 81-85| 79-65 | 79-64] .-----
10 Sunday
11 | 82-91} 81-81) 79-61] 79-60] ------
12 | 82-94} 81-80| 79-70) 80-22] .---.-
13 | 82-91] 81-79| 79-70| 79-83] --.++-
14 | 82-92) 81-75) 79-92| 80-18] -.----
15 | 82-87) 81-70! 79-85| 80-40] -----.
16 | 82-90) 81-75| 79-98| 80-12] .--.-.-
17 Sunday
18 | 82-90] 81-81} 80-30| 79-74] -..++-
19 | 82-91] 81-80} 80-27) 79-13} --.-.-
20 | 82-86] 81-85) 80-56| 79:81) --.-.-
21 | 82-85] 81-88} 80-61] 80-06] ------
22 | 82-85) 81-92) 80-88} 80:14] .....-
23 | 82:88) 82-03} 80-90! 80-79| --:-..
24 Sunday
25 | 82-80] 81-97) 81-02) 80-44] .--....
26 | 82-85} 82-19} 81-23) 80-37] ------
27 | 82-81} 82-22) 81-30] 79-94] ......
28 | 82-81} 82-28) 81-47| 79-45| ....-.
29 82-85) 82-40) 81-64} 79-95) ...---
30 | 82.84] 82-40} 81-67} 79-01] ....--
Means 82-90 | 81-95) 80-46! 79-54) 3-330
Octzus! 0-616. | Sunday
2 | 82-82] 82-87| 81-88] 78-23] --...
3 | 82-81| 82-62| 81-81] 78:39] 0-297
4 | 82:82] 82-68) 81-87] 78-05| 0-046
5 | 82:90] 82-82] 81-90| 77-51| 0-266
6 | 82:89] 82-81] 81-86] 77-32] 0-335
7 | 82-88| 82-84| 81-61| 78-22] ......
8 Sunday
9 | 82-85) 82-82} 81-27] 79-22] .-...-
10 | 82-91] 82-88} 81-50} 77-19} 1-239
11 | 82-94] 82-87 | 81-22} 76-36| 1-689
12 | 82-89} 82-80} 81-06| 78-00) .--.---
13 | 82-91] 82-82] 81-01] 78-48] ..-.-.. |
14 | 82-90} 82-71) 80-75) 79-13) ..--.-
15 0-092 | Sunday
16 | 82-91} 82-68} 80-50] 78-89] .------
17 | 82-98} 82-66} 80-61] 79:78} .--+-.
18 | 82-95) 82-61} 80-60} 80-30] 0-012
19 | 82-95 82-56} 80-64| 80-37] 0-019
20 | 82-85] 82-48) 80-55] 79-44] «--...
21 | 82-90} 82-48} 80-61) 79:42} 2-290 |
22 0-150 | Sunday
23 | 83-00} 82-49} 80-80} 76-92) 0-135
24 | 82-99} 82-49} 80-81/| 79-31] 0-046
25 | 83-00} 82-46} 80-89| 80-59] .-.----
26 | 82-98} 82-42} 80-85| 81-00] .-.--..
27 | 82-95| 82-45} 80-80} 79-10] 0-420
28 | 83-00 | 82-50} 80-95] 78-39] 0-598
29 0-051 | Sunday
30 | 83-10} 82:50] 80-91] 80-14] .-....
31 | 82-96} 82-49} 81-08} 80-54] 0-531
78:86 | 8-830

OO OND Oe woe

Means

No. 1.
12 feet

No. 2.
6 feet

No. 3.
3 feet

Therm. | Therm. | Therm.

6 A.M.

fo}

82-95
83-10
82-99
82-95

82-96
82-95
82-92
82-98
82:96
82-96

82-98
82-91
82-99
82-98
82-95
82-91

82-90
82:95
82-95
82-96
82-90
82-95

82-95
83-01
82:95
82-90

82-96

82-92
82-94

83-02
82-97
82-98
82-98
82-95
82-97

82-91
82-94
82-90
82-94
82-94
82-86

82-81
82-88
82-86
82-92
82-86
82-82

82-84
82-89
82:80
82-80
82-82

| 82-80

82-90

6 A.M.

fe)

82:48
82-90
82-56
82-51

82-52
82-50
82-52
82-60
82-57
82:60

82-50
82-60
82-68
82-68
82-68
82-67

82-65
82-74
82-69
82-70
82-65
82-68

82-67
82-75
82-63
82-60

82-63

82-61
82-60

82-86
82-70
82-71
82-62
82-58
82-68

82-32
82-28
82-10
82-16
82-10
82-02

81-95
82-00
81-98
82-05
82.02
82-08

81-92
82-02
81-92
81-95
82-00
82-00

6 A.M.

°

81-00
81-06
81-10
80-99

81-16

82.24| 80-17

Mean
Temp.
of
Air.

79-72

76-80
78-42

76-70
76-90
75-90
77:78
79-07
78-79

77-50
77-27
78-50
78-35
76-06
74-20

78-81
76-50
78-50
79:57
80-00
77:08

73-12
77-57.
79-70
79-32
78-70
78-30

77-69

‘ R .
8} a.m.
to
84 A.M.

Sund

Sund

seneee
fences
See eee

Sund

eee eee

weeeee

Sund

see eee

1-813

CONOorrwn

| 83-02

| 83-08

No. 1. | No. 2.

| 12 feet | 6 feet

Therm. | Therm.
6 A.M. | 6 A.M.

fo} oO

82-60 | 82-06
82:75 | 82-01
82-71} 82-00
82-75 | 82-08
82-75 | 82-10
82-82 82-06

82-75
82-80
82-75
82-75
82-78
82-73

82-24
82-00
82-31
82-34
82-38
82-40

82-75
82-77
82-78
82:78
82-79
82-75

82-54
82-60
82-65
82-60
82-70
82-69

82-80
82-88
82-80
82-84
82-81
82-85

82:80
82-82
82.92
82-92
82-90
83-02

82-90
82-88
82-86

83-16
83-12
83-14

82:78 | 82-54
82-98
82-90
82-95

83-21
83-31
83-40
82-92| 83-48
83-56
83-57
83-64
83-70
83-80

82-98
82:98
83-02
83-04

83-94
83-97
84-08
84-12
84-25
84-24

83-08
83-10
83-13
83-12
83-12

83-18
83-20
83-23
83-28
83-26
83-28

84-40
84-41
84-52
84-52
84-63
84-67

83-37
83-40
83-46
- 83-44

84-77
84-82
84-82
84-86

No. 3.
3 feet
Therm.
6 A.M.

°

80-10
80-32
80-45
80-45
80-53
80-57

81-71
80-42
80-90
81-04
81-15
81-12

81-22

aeeees

eeeeee

eneeee

eeseee

wee eee

eeeeee

see eee

eeeree

sens

saceee

seseee

eeneee

eoneee

teeene

wanes

wee eee

sen eee

seeeee

oy

83-14] 84-11] 83-62] 80-13

_—_———

0-038

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Means

Peete

ats eee

eecece

se eeee

84-65

TERRESTRIAL TEMPERATURE AT TREVANDRUM.

sence

eee eae

eereee

eeeeee

eeeces

aevene

eeeere

eee nee

sen wee

teeeee

eeenee

87-61
87-70
87-75
87-90
87-90
87-71

87-90
87-92
87-90
87-88
87-94
87-92

87-79
87-72
87-81
87-80
87:81
87:79

87-65
87-64
87-59
87-61
87-61
87-73

87-84
87:82

87-78 | 84-53

aeaeee

eecces

wees

seceee

ese eee

seeeee

eenene

ewes

woe eee

Sennen

385

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday |

Sunday

Sunday

386

Date.

1844.
May

seeeee

eeeeee

eeeeee

eesece

oy

seeeee

eneces

seneve

eeoree

eeeecee

eeeces

oceese

seceee

No. 2. | No. 3.
6 feet | 3 feet
Therm. | Therm.
6 A.M. | 6 A.M.
Above | 87-93
the | 87-94
Scale. | 87-88
psisiniale 87-70
isis aele 87-67
coetes 87-62
waleielate 87-53
Gialvisiers 87-50
Riciaieias 87-54
eovece 87-54
eleeisisle 87-42
Saialvlele 87-30
piatuyaiate 87-36
nate siels 87:25
claviee 87-22
Smee |eSiyailley
coucee 87-09
avocee 86:94
oovcce 86-73
arbodc 86-48
ccccce 86-23
seca 86-08
Sistah 85-61
ateletateta 85-40
Stetetatetty 85-27
ateiatafele! 85-09
ecccce 84-93
slecces 86:93
158% 84.60
Buettt 84-07
86-62 | 83-80
86-54 | 83-66
86-38 | 83-50
86-24 | 83-45
86-20} 83-38
85-98 | 83-22
85-88 | 83-10
85-81 | 83-07 | -
85-72 | 82-85
85-62 | 82-89
85-50 | 82-78
85-36 | 82-48
85-25 | 82-27
85-12} 82-06
85-10} 82-00
84-93 | 81-82
84-72 | 81-80
84-62 81-86
84-55 | 81-76
84-51 | 81-81
84-61 | 81-88
84-45 | 81-91
84-40 | 81-88
85-40 | 82-72

MR CALDECOTT’S (UNCORRECTED) OBSERVATIONS OF

Mean

80-06

eeveee

wecene

seeree

eccece

eeccce

eeeree

eeccee

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

No. 1. | No. 2.
12 feet | 6 feet

No. 3.
3 feet

Date. Therm. | Therm. | Therm.

6 A.M. | 6 A.M.

1844. 4 oe
July 1 | eeeees 84.48

6 A.M.

°

81-92
81-98
82-07
82-05
82-03
82-03

81-98
81-90
81-93
81-78
81-78
81-76

81-45
81-32
81-22
81-08
81-02
81-08

81-03
81-00
81-05
81-11
81-03
81-05

81-10
81-12
81-00

81-48

81:00
81:07
80-98

80-93
80-85
80-78
80-62
80-71
80-45

80-35
80-29
80-22
80-18
80-12
80-22

80-21
80-20
80:37
80-40
80-35
80-38

80-50
80-51
80-61
80-50
80-67
80-71

80-54

Mean
Temp.
of
Air.

°

80-19
79-98
81-21
80-88
80-45
78-26

75-29
77-77
77-65
77-08
76:50
77-67

79-45
79-87
80-38
78-80
77-86
78-71

78:33
79-43
79-53
76-02
76-85
79-54

79-34
78-41
79-09

78-69

77-75
75-64
76-70

78-25
79-26
79-65
77-73
75-85
77-75

78:77
78-41
78-63
80-07
79-82
79-30

78-37
78-14
78-06
79-20
79-67
79-64

79-85
79-85
78-98
79:77
79-62
79-36

78-65

Rain
8} a.m.
to

8} a.m.

eeeeee

seeeee

ory

wan eee
seeeee

weeees
seceee

teeeee
eeceee
secee

4.066

No. 3.
3 feet
Therm.
6 A.M.

CONOUKwWwnNre
oO
oo
oO
IS

83-29
83-41
83-50
83-50
83-50

82-59
82-69
82-70
82-62
82-58

83-34
83-69
83-66
83-52
83-49
83-40

82-50
82-10
81-74
81-35
81-00
80-81

83-20
83-10
83-07
83-01
82-98
82:88

80-61
80-60
80-65
80-69
80-70
80:68

83-58
83-58
83-56
83-55
83-52
83-54

82-92
82-91
82-90
82-87
82-92
82-91

80-90
80-90
81-01
81-02
81-11
81-12

83-55
83-50

82-95
82-95

81-18
81-30
83-51] 82-97| 81-39
83-51] 83-00) 81-40

83-55 | 83-18] 81-41

Ms VOL. XVI. PART III.

Mean
Temp.
of
Air.

eeeeoe

eeeeee

eecere
een eee
eeeeee
sees
er ery

ene eae
aeneee

eesece

eeseee

eeeees

eee eee

feeres

es neee

eoeeee

eee eee

eeeeee

eaeeee

weseee

eeeeee

Sunday

Sunday

Sunday

Sunday

78-94 | 14-399

Sunday }

OCOOnNoanP who

INo# di:
12 feet
Therm.
6 A.M.

is)

83-50
83-50

83-48
83-54
83-50
83-40
83:48
83-50

83-49
83-49
83-48
83-51
83-47
83-48

83-48
83-48
83-48
83-47
83-45

83-44
83-45
83-49
83-46

83-46
83-46
83-45
83-50

83-51
83-50
83-51
83-50
83-54

83-52
83-58
83-61
83-50
83-59
83-60

83-61
83-57
83-61
83-61
83-64
83-65

83-68
83-64

83-55

No. 2.
6 feet

6 A.M.

°

82-96
83-02

83:08
83-12
83-11
83-10
83-15
83-18

83-13
83-19
83-12
83-19
83-12
83-10

83-12
83-18
83-19
83-18
83-21
83-22

83-33
83-31
83-34
83-42
83-44
83-47

83-19

83-51
83-53
83-51
83-55
83-61

83-70
83-75
83-75
83-78
83-81
83-78

83-72
83-88
83-82
83:80
83-85
83-81

83-80
83-78
83-89
83-80
83-80
83-80

83-78
83-79

TERRESTRIAL TEMPERATURE AT TREVANDRUM.

No. 3.
3 feet

Therm.| Therm,

6 A.M.
°o

81-51
81-50

81-62
81-50
81-52
81-45
81-40
81-40

81-38
81-45

80-17
79-79

80-11

78-57 |

ey

sueeee

eonces

eoeeee

eeeeee

esccoe

eereee

seneee

eecces

eecsee

eceees

eoseee

eeccee

eereee

se eeee

eeeeee

387

Sunday

Sunday

Sunday

83-73

on

79-09

388 MR CALDECOTT’S (UNCORRECTED) OBSERVATIONS OF

No. 1. | No. 2. | No. 3. | Mean Rain No. 3. | Mean

12 feet | 6 feet | 3 feet | Temp. | 8} a.m. 3 feet | Temp.
Therm. | Therm. | Therm. of to Date. Therm. | Therm. | Therm. of
6a.M.| 6 A.M. | 6 4.M. | Air. 84 A.M. 6 a.m. | Air.

°

82-61

° ° ° ° in.

83-64 83-84} 82-14] 76-99) 0-005
83-65 | 83-70] 82-08} 80.23] ------
83-65 | 83-78| 82-11) 79-50| 0-406
83-68 | 83-77 | 82-08 | 79-46] 0-705

°

84-88

84-87 | 82-16] «--e0-
84-00 | 85-38 | 84-80} 82-36) ------
84-00 | 85-44) 84-99} 84-36} ------
84-06 | 85-48 | 84-90} 80-38) 0-534
84-06 | 85-54| 85-00| 79-38} 0-022

85-03 | 82-52] «s.0s-

Sunday

83-66 | 83-72} 82-07} 78-33] ------
83-65 | 83-68} 82-09| 78-55] ---+--
83-59 | 83-74| 82-04| 79-16] ------
83:66 | 83-70| 82-00| 79-36| ------
10 | 83-69 | 83-70} 82-04| 77-98| ------
11 | 83-68} 83-65} 81-95 | 79-17] «+++.

OOonNrnrnp wwe
o
[o>]
No)
oS

2

3

4

5)

6

u

8

9

10 | 84-11 | 85-52] 85-12) 81-43 | ----.-
11 | 84-13} 85-60} 85-08) 82-43] -----.
12 | 84-:17| 85-65] 85-10!) 79-23] 1-291
13 | 84-18} 85-65} 85-05} 79-13] 0-263
14
15
16
L7
18
19
20

13 | 83-65 | 83-67 | 82-11} 79-09] .--.---
14 | 83-65 | 83-64| 81-80 | 77-66] .------
15 | 83-68} 83-63 81-61| 77-51] ------
16 | 83-68} 83-60) 81-55 | 78-86| ---+--
17 | 83-65 | 83-59} 81-60] 78-15] -----
18 | 83-66} 83-52] 81-38) 78-31] ------

84-20 | 85-70 | 85-05 | 80-74] 0-322
84-24 | 85-70 | 85-01 | 78-89

84-27 | 85-71] 84-84} 80-12} 0-040
84-28 | 85-68 | 84-60} 78-58) 1-928
84-27 | 85-68] 84-68} 80-50} 0-286
84-32] 85-70 | 84-42 | 80-62; ------
21 | 84:35) 85-67 | 84-38} 83-00) -:--->-
84:06 | ---+e-

20 | 83-69] 83-56 | 81-50| 77-85} «--+-
21 | 83-60) 83-50 | 81.46| 79-63] ------
22 | 83-68) 83-47 | 81-35 | 79-42) ---.-
23 | 83-68) 83-50| 81-50| 79-69| .«---.-
24 | 83-68} 83-55 | 81-61 | 80-43| .-...-
25 | 83-68 | 83-48 | 81-58} 82-13] --.--.

24 | 84-44] 85-61) 84-21) 84-92] «-....
25 | 84-44] 85-58| 84-13} 84-91] ------
26 | 84-44] 85-53) 84-20] 85-64} 0-003
27 | 84-45 | 85-58| 84-25 | 84-89] -.-....
28 | 84-49) 85-61) 84-40} 84-92] ......
84-89 | ....--

27 | 83-66 | 83-52| 81-94| 78-97| 0-280
28 | 83-66] 83-52) 81-98} 79-33) ----.-
29 | 83-66} 83-57| 82-16} 81-07| ------
30 | 83-68] 83-60} 82-20} 80-98| .--.---
31 | 83-65] 83-59) 82-18} 80-54] ----.-

855i beaesee

82-22

83-66 | 83-62} 81-86} 79-20] 2-086

84-23
84-49 | 85-50 | 84:82/| 83-90| ------
84-52] 85-58] 84-92| 83-50| ------
84-60 | 85-62] 85-08| 83-84| ..-.---
84-55 | 85-65 | 85-20} 83-76) .«..--.

83-66 | 83-70) 82-40! 80-04) ------

Sunday

! 1
2 2
3 | 83-70| 83-77] 82-65| 80-09] -+---- 3
4 | 83-68| 83-78| 82-70] 80-49] «..-.. 4
5 | 83-65| 83-81| 82-70| 80-26| ------ 5
6 | 83-68| 83-90] 82-80] 80-30| «+++ 6
7 7
8 8
9 9

10

83-68 | 83-92 | 82-90} 80-65) «----.
83-65 | 83-90} 82-92} 81-13] .------

84.55 | 85-72 85-31 | 84:91) -.....
84-55 | 85-79] 85-40} 85-15 | -..---

Sunday 84-54| 85-76 | 85-48 | 83-95 |...
10 | 83-64| 84-05 | 83-05] 91-47]... 84-55 | 85-88| 85-54| 84.30) .-.
11 | 83-76| 84-12) 83-12] 81-08] ...... 11 | 84-64| 85-79| 95-61 | 84-58| ....-.-
12 | 83-70| 84-15 | 83-41| 81-04]... 12 | 84-60| 86-00] 85-78| $4.45] ---.--
13 | 83-70| 84-18] 83-50| 81-78] s+... 13
14 | 83-72| 84-21| 83-55| 81-30| -.---. 14 | 84.66| 86-12| 86-.01| 94-22| ---..
15 | 83-71| 84-32) 83-75| 81-00]... 15 | 84-60| 86-15| 86-15| 84-20| --.-+
16 Sunday 16 | 84-64| 86-13| 86-19| 84-74| -.-++
17 | 83-75 | 84-46] 84-10] 81-44| «.--. 17 | 84.66 | 86-20| 86.25 | 84-57| «+--+.
ig | 83-72] 84-50| 84-20| 82-01]... 18 | 84-70 | 86-37| 86-56 | 83-75| 0-280
19 | 83-72| 84-60| 84-32] 81-83| ....-- 19 | 84-68] 86-45| 86-50! 83-02| 0-078
20 | 83-82] 84-70] 84-50] 92.09| ....-- 20 0.275
21 | 83-82] 84-78| 84.61| 80-29]... 21 | 84.64! 86-50] 86-39] 82-60| -.-++
22 | 33-80| 84-70| 84-691 78-85| 0.006 22 | 84-78| 86-65| 86-92| 83:71| «+.
23 0-960 | Sunday 23 | 84-78| 86-69| 86-81| $4-42| ...--
24 | 83-78] $4-95| 84.90! 80-64]... 24 | 84.78] 86-70| 86-65 | 81-72| 0-162
25 | 83-86] 85-08] 84-99| 80-41) «..-. 25 | 84-75 | 86-69| 86-70| 84-35 | «+++
26 | 83-88| 85-10] $5-01| 81-89| ...-- 26 | 84:82 -e-e-- 86-50| 83:19 |.
27 | 83-87| 85-15 | 84-90] 81-26]... 27
28 | $3-88| 85-18] 84-95| 81-26| ...-.- 98 |sg4ig4)) wee 86-41| 84.97 | -e-+
29 84-98 | ---e- 86-35 | 83-11 eeieinioln
30 | 84-88 | «+++. | $6-50| 84-83] «seer
Means 84.38| 83-78! 80-941 0-966 Means | 84-66| 86-06| 85-72| 84-00

No. 1. | No. 2. | No. 3. | Mean
12 feet | 6 feet | 3 feet | Temp.
Therm. | Therm. | Therm. of
6 A.M.
1845. F
May 1 | 85-00 | ------ 86-50] 81-61] 0-351
st 2 | 84-92) ------ 86-60} 81:52} 1-351
3 | 84-98] ---..- 86-64] 81:91] 0-357
4 0-595
5 | 84-95 | --.--- 86-64 | 78-92) 0-490
6 | 84:90} --.--. 86-52] 80-81} 0-550
P 7 | 84-90] ---..- 86-41 | 82:67] 0-372
B | cesses | weenee 86-45 81-77 0-201
Q | ceeeee | ceeeee 85-99 79-49 1-211
10 | cesses | eoevee : 5 .
11
TD | coasce | wnoeee . Aya | mcsleisiere
13 | cress 86-70} 85-10) 82:90} 0-080
14 | «+--+: , . AGS [Lee eusieieiors
15 | ceeeee +60) 84-80) 82-43 | ceenee
16 | ------ | 86-50} 84-71! 82-90| ------
17
18
: 19 a . a 4
20 | «++ 86-25 | 84:48] 81-89} 0-230
D1 | «sccee Fs = 82-57 0-042
DD | euee- me Shico 38
% 23 | ------ | 86-10} 84:50] 83-78 | «----
24 | ...... | 86-10!) 84:50] 83:39 | «+++.
25
26 86-11] 84:53} 82-83) 0-156
DT | assess 85-98 | 84-55 | 82-79| «-.-..-
28 | ------ | 85-99} 84-47] 83-72] ------

eevee

ae reee

eee eee

eeenee

Teans_| 84-94] 85-17

seaeee

83-74] 80-38] 0-922
83-50 | 79-69| 0-022
83-49| 78-45} 1:649
83-00] 80-27] «-.---
83-33 | 79-94] 0-048
83-30 | 78-09)| a«s00.
0-655
82-98} 75:99) 1-552
82-80] 78-23] «+.
82-71| 79-53] 0-144
82-73 | 80-58] ---++.
82-31] 81-49} -:----
82-02) 80-07] ---:::
0-047
81-90 | 76-75| 1-276
81-86} 76:03} 0-981
81-90} 76-36| 0-744
81-77| 76-30| 0-355
81-69} 78-40} 0-112
81-61 | 76-43} 0-857
1-280
81-33] 76-31} 1-059

82-95| 78-80! 13-584

Sunday

TERRESTRIAL TEMPERATURE AT

TREVANDRUM.

COONOOK WHE

Sunday

Sunday

Sunday

Sunday

Means

83-89
83-95
83-85
83-86
83-85
83-80

83:90
83-76
83-81
83-79
83-80
83-81

83-76
83-88
83-79
83-75
83-75
83-76

83-11
83-22
83-33
83-36
83-35
83-34

83-40
83-37
83-36
83-30
83-32
83-40

83-89 |83-10

ececee

er eoee

se eeee

Sunday |

| Sunday

Sunday

Sunday

Sunday

Sunday

| Sunday

Sunday

| Sunday

Date.

OCMmANOrhWhN

OMND LP wwe

eceeee

eeeeee

see eee

sees

ea neee

eee eee

essen

eee eee

eeeeee

Seenee

eoeeee

seceee

eeeees

eensee

79-43| 17-458

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday

Sunday |

Sunday

Date.

OBNaOor wd =

Means

Nor 1.
12 feet

6 A.M.

°

84-10

84-10
84-10
84-08
84-05
84-10
84-05

84-00
84-00
84-00
84-05
84-00
84-02

84-00
83-95
84-00
84-00
84-00
84-00

84:03
83-92
83-98
83-96
83-89
83-92

83-96
83-74
83-70
83-84
83-92

83-90
83-90
83-88
83-90
83-86
83-86

84-00
83-84
83-84

83-82
83-80
83-78

83-79
83-82
83-90
83-75
83-76
83-80

83-75
83-76
83-70

83-80

Therm. | Therm.

No. 2.
6 feet

No. 3.
3 feet
Therm.

6 a.m. | 6 A.M.

° °

83-72 | 81-87

83-72
83-75
83-73
83-75
83-72
83-81

82-12
82-11
82.20
82-15
82-20
82-22

83-86
83-85
83-85
83-90
83-90
83-89

82-30
82-25
82-24
82-18
82-12
82-10

83-84
83-78
83-72
83-82
83-85
83-75

82-05
81-98
81-94
81-90
81-81
81-80

83-70
83-74
83-70
83-60
83-59
83-57

81-84
81-59
81-70
81-72
81-70
81-70

81-51
81-75
81-33
81-30
81-40
81-22

83-51
83-34
83-29
83-42
83-48

81-23
81-15
81-10
81-12
81-20
81-20

83-46
83-35
83-29
83-50
83-25
83-21

83-44
83-20
83-20
83-21
83-20
83-16

81-30
81-19
81-21
81-18
81-17
81-20

83-19
83-20
83-18
83-19
83-26
83-31

81-29
81-10
81-15
81-24
81-42
81-39

83-28
83-44
83-30

81-32
81-52
81-32

83-31} 81-28

Mean
Temp.
of

76-80
77-46
78-80
79-90
79-99

79:47
78-49
79-58
79-08
79-02
78-91

79-44
80-76
80-51
79-97
78-81
79-29

80-11
79-59
80-14
79-85
77-60
79-54

79-84
79-56
79-50

79-31

MR CALDECOTT’S (UNCORRECTED) OBSERVATIONS OF TERRESTRIAL TEMPERATURE.

|

Rain
83 A.M.

eereee

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aenees

seeeee

eoueee

aeeene

( 398°)

ABSTRACT

Monthly Means of Terrestrial Temperature, at the Trevandrum Observatory.
Lat. 8° 30’ 32” N. Long. 5° 7’ 59” E.

No. 1. INow2: No. 3.
12 feet Thermometer. 6 feet Thermometer. 3 feet Thermometer. Mean Average of
Temp. Rai Four Daily Observations,
of Re corrected
Air for Index E
_ Noon. oe Mid. oar Noon. aa Mid. seve Noon. | ? an Mid. i eae ale

84°74| 84:73} 84°57 || 85°11] 85-25) 85-20| 85:18 || 83°77| 83:92] 83-80] 83°79 || 80-09 |14-5134 || 86-808 |87-357 |86°742
seccee | cereee | sesees 84:58| 84:°66| 84:57| 84:48 || 82:00) 82°10} 82°11] 82°01 || 79°32| 8°7473 || ...--. |86°742|84:977
84°83] 84:87) 84°76 || 83°62| 83-61| 83°59} 83-62 || 80°97 | 81:07] 81:03} 80°99 || 78°73] 5-9516 |/86-938 |85-782 |83-901
84:29| 84-24| 84:23|| 82°74] 82-82| 82-77| 82-74 || 80°18} 80°29] 80:22} 80°21) 77:90| 4:4240 |86-380 |84:940 |83-148
83°86| 83°79| 83°74 || 82°85} 82:92] 82-88] 82-87 || 81:28] 81°38} 81°31} 81-29|| 78°28] 7°7238 |85-918 |85°052 |84:237
83°78| 83°71| 83°69 || 83:04) 83°16] 83-07) 82°99 || 81°44} 81°60} 81°51! 81°49]| 79°10) 5°4928 |/85°843 |85-237 |84°437
83-72| 83°65| 83°61 || 82°69} 82-80| 82-73) 82-69 || 80°37 | 80:45| 80°38} 80°34|| 77°82 | 88053 ||85-783 |84:899 |83-307
83:49 | 83°41] 83°37 || 82°89} 82-98) 82°85) 82-82] 81:52} 81°73} 81:58} 81:51 || 78°96} 0°1642 ||85°535 |85-057 |84°507

83°74| 83°67 | 83°58 || 83°94| 84:14] 84:06} 84:02]| 82°75| 82:92] 82°86} 82°82|| 79:05] 1154 ||85-783|86-212 |85-759
84:05] 83°99| 83°92 || 84°53! 84-78} 84-70| 84:54 || 84:00} 84:30] 84:16] 84:04|| 80°09] 0:033 ||86-085 |86-809 |87-047
84°60| 84:52) 84°46 || 86°27| 86-68] 86°37] 86-31 || 86°41} 86°70| 86°55 | 86°48 || 82°36] 1°721 ||86°643|88°579|89°457
85°01| 84:94] 84:96 || 86°60| 86°68} 86:59| 86-53 || 86°17 | 86°33) 86°16) 86°11 }| 81°58 | 9°274 ||87-090|88-772|89-114
Pesese | ceecee | seecee | sereee 86:03 | 86°12] 86:07| 85:99 || 84°26| 84:38] 84:27] 84°21 || 80°62 |15°989 || ....-. |88:224|87-202
84°78] 84°74] 84°71] 83°59] 83°59] 83°56} 83°53 || 80°68} 80°65) 80°60) 80°58 || 78.21 |16°932 ||/86°878|85-739 |83°549
83:96 | 83°90| 83°88 || 81-70] 81:77| 81-70) 81-66|| 78°82 | 78°91| 78°85] 78°84 || 77-29 |10°899 ||86-043 |83°879 |81°777
83°22| 83°17| 83°16 |) 81°58| 81-67} 81-60| 81-58 || 79°66| 79:79| 79:74| 79°72 || 79°05} 2°098 ||85-310|83-779 |82°649
82-99} 82-97] 82°94|| 81°95] 82-06} 82:00| 81:96 || 80°46] 80°55| 80°45] 80°44 || 79°54) 3°330 |/85:083 |84:164 |83°397
83:01| 82:96] 82°94]| 82°65| 82°74] 82-66] 82:65 || 81:09) 81:18} 81-11} 81-09|| 78-86} 8-830 |/85-098 |84:847 |84:039
83°05| 83:00) 82°95 ]| 82°63| 82°75| 82°68) 82°54 | 81:19) 81°33] 81:25] 81:20]| 79°72] 1:813 ||85°123 |84°822 |84-167
83°00| 82°92] 82°89 || 82:24| 82°35| 82-26] 82-22 | 80°17| 80°26| 80°20} 80°10) 77:69 13-400 |/85-060|84-439 |83-104

82°92| 82°84| 82°78|| 82°54) 82-73) 82-64| 82-58 || 81-19) 81:43] 81-30] 81-20] 78-54] 0-438 ||84:963/84:794 84-202
83°29| 83:21| 83°17 || 84°11} 84-34] 84-23) 84-15 || 83°62] 83°90| 83°74] 83°64 || 80°13] 0°038 ||85°335|86°379 |86-647
84:04| 83°94] 83°89|| 85°72 | 85-92) 85-80) 85-73 || 86°16 | 86°51] 86°33] 86°28 || 83°61] 0°610 ||86:063/87-964|89°242

84:77) 84°68] 84°65 || ----0. | wees | cee eee sauveer 87°78| 88:06] 87:86] 87-80] 84:53] 1°860 ||/86°820| ...--- 90°797
NS lS ccaceen'|limectweMllewoweseNMescace | eacene 86°93| 87:06} 86°94] 86°84 || 82:11) 6-601 || ..---- | ------ |89°864
BP i cccces |. evens 85°40 | 85:49} 85°38] 85:34|| 82°72 | 82°82] 82:70) 82°65 || 80-:06| 7:°389 wees 187°574185°644
84.84] 84°79| 84°74]| 83°9L| 84:01] 83°91] 83-86 || 81:48) 81°57] 81°49] 81:44] 78-69] 4:647 || .-...- 86°094 |84°417

84:27 | 84:21} 84:15|| 82°91] 83-01] 82-92) 82-89/| 80°54) 80°63] 80°55| 80°50) 78°65| 4°066 ||86°338|85-104 |83°477
83°80 | 83°74| 83°69 || 82°89] 83°03) 82°95] 82-90|| 81°23] 81-44] 81:35] 81:29) 79°70 | 2°527 |/85°868 |85:114 |84-249
83°66 | 83°59} 83°53 || 83°18) 83°28] 83:22] 83-17 || 81-41} 81-52] 81:42) 81°36 || 78°94 |14°399 ||/85-715 |85-384 |84:349
83°59 | 83°51| 83°47 || 83°19] 83°33] 83-24) 83-19 || 81-74| 81-92] 81°81] 81°76|| 80-02} 3°873 185-645 |85-409 |84-729
83°78 | 83°59| 83°54 || 83°73 | 83°91} 83°80| 83-73 || 82°35 | 82°53} 82°41| 82°36 || 79:09 | 3-700 85°964|85°334

@
a
~T
i
@o

83°80| 83°71| 83°65 || 83°62} 83°79| 83°68| 83-62] 81°86 | 82-30| 81:91} 81°85 || 79°20) 2:086 ||85°838}85°850 |84:902
83:91| 83°82| 83°74] 84-38} 84°79) 84-49| 84-40] 83°78) 84:06] 83:92] 83°84 || 80°94] 0°966 ||85°933 |86-687 |86:822
84°39 | 84:28] 84°22)| 85°57| 85°74| 85-61] 85°54|| 84-70 | 84°88] 84°73) 84°68 || 82°22] 5-303 |/86-415/87-787 |87-669
84:79| 84:72| 84°66|| 84:06} 86-20| 86:13] 86-06|| 85°72 | 86:20| 86°09| 86°03] 84:00) 0°870 ||86°840|/88°284 |88-932
tees 84°91 | 84°84 || 86°22| 86°24} 86:22) 86-17|| 85:23) 85°40| 85°23] 85:15 || 82°08] 9:902 |] ....-- | «+--+ |88°174
84:98| 84:96] 84°92) 85:17] 85°31] 85-15} 85-°03|| 82°95 | 83:04| 82°89) 82°81] 78°80 |13°584 || .---.- 87°337 |85°844
84:59 | 84:52| 84:46]| 83°18] 83:29] 83:18) 83:14] 80°59} 80°75| 80°63] 80°57 || 79°37 | 2°788 ||86.658|85°369 |83°557
83:99} 83°90} 83°85 || 83-10} 83:24] 83:17| 83°11]| 81°60) 81°77] 81°65} 81°58 ]| 79:27} 1:139 |/86.035|85°327 |84-572
83:90 | 83°82] 83°76 || 83°89| 84:05| 83°97| 83°89] 83°08] 83°28] 83°17| 83°10]! 80°68| 0-248 ||85-948/86°122|86:079
84:20 | 84:09) 84:03 || 84:48| 84-60| 84:49| 84:41 || 82-82) 82:96| 82°85] 82°80]! 79°43 |17°458 ||86-228/86.667 |85-779
| 84:14] 84:06] 84°00|| 83°36] 83:52) 83-42| 83°35 || 81:99| 82°15] 82:06| 82:00|| 79°51| 5-422 ||/86:185|85°584|84°972
84:01 | 83°88| 83°84|| 83°31] 83:45 | 83°30| 83:28 || 81:28] 81°44] 81°32) 81:26 || 79:31] 4997 ||86-015|85'507 |84:247

OL, XVI. PART III. 5G

Ll

( 392 )

Remarks on the Preceding Observations. By Professor J. D. ForBss.

Mr CaLDECOTT’s observations possess an extraordinary interest from being
the first of the kind prosecuted between the tropics, from the great care and ex- -
tent of the observations, and from the circumstances being altogether comparable
with those of observations lately made in Europe. [The depths of the thermo-
meters are the same as those at Brussels, Edinburgh, and Greenwich. ]

In conformity with Mr Ca.LpEcott’s suggestion, I have had the corrected
means. of 1843—4—5 united, so as to give the mean temperature of each month
(the observations of 1842 being omitted). The results are given in the following
Table. The readings of Nos. 1 and 2 are deficient in some of the months, owing
to the liquid having risen above the scale :—

MEAN OF THREE YEARS, 1843—5.

No. 1. No. 2. No. 3.
12 feet Thermo- 6 feet Thermo- 3 feet Thermo-
meter. meter. meter.

Air
Temperature.

January 85° 85618 84:954 78°930
February : 86°625 86°838 80°386
March i 88°110 88°789 82-730
April ; 88°527* 89°614 83°370
May 88°224F 88°413 81-603
June 86:878F 86°883 85°012 79°023

July 86°537 85°114 83°250 78°450
August 85°894 84°736 83°566 78:990
September 85°633 85°133 84°575 79973
October 85°680 85°632 84°722 79-076
November 85°651 85:271 84°622 79°750
December 85°607 85°303 84228 78:030

Means 86:043 86°264 85°715 80°025

* Mean of Two Years only. t Result of 1843 only.

The following conclusions are plainly deducible :—

I. The Temperature of the ground at Trevandrum is from 5° to 6° Fahr.
higher than that of the air. This result is confirmed by observations on the tem-
perature of springs and wells at Trevandrum, which have been obligingly com-
municated to me by Major-General Cutten of the Madras Artillery. These
observations are printed in the “ Proceedings” of this Society.

II. When the monthly means of the thermometers are projected, so as to
shew the curves of annual temperature, they are found to have one great inflection
and a smaller one. The principal maximum of the temperature of the air occurs
about the beginning of April, after which the rainy season sets in, and the annual

( 398 )

curve goes through its extreme range in three months; the principal minimum
occurring about the middle of July. The remaining fluctuations are compara-
tively insignificant, but indicate a slight maximum about the middle of October.

III. The epochs of temperature are retarded with the depth below the sur-
face in the usual manner, and, at the same time, casual fluctuations disappear,
and the ranges diminish. At 12 French feet, the principal maximum occurs five
weeks later than in the open air, and the range is still at least a degree and a half.

From these facts, it is easy to infer that the phenomena of the propagation
of heat into the ground near the equator resemble those of temperate latitudes,
though modified in extent and character. Mr CapEcorr’s experiments con-
clusively establish (as he himself has pointed out) the error of the doctrine of
BoussincautT (at least for the eastern hemisphere), that the annual tempera-
ture near the equator remains unchanged at the depth of a foot below the surface
inthe shade. This mistake it is the more important to correct, because M. Poisson
has attempted to confirm his mathematical theories of heat by applying them
to this alleged fact.*

Mr CaLpEcoTT’s experiments appear farther to prove a considerable excess
of the temperature of the earth above that of the air at Trevandrum. This result
is in opposition to the opinion of Kuprrer, which supposes the earth temperature
to be Jess than that of the air between the tropics, and that of Boussincautr,
which supposes them to be the same.

The results of Mr Caxprcort are confirmed in both particulars by Captain
Neweso.p of the Madras Army, in a paper lately published in the London Philo-
sophical Transactions.+

* Théorie de la Chaleur, p. 508. } For 1845, p. 125.

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VOL. XVI. PART III. a) ae AROSE

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MAP OF
ART OF LOCHABER
SHOWING THE SHELVES IN THE GLENS.
TO ILLV STRATE
ME MILNES PAPER
In the Transactions of

THE ROYAL SOCIETY OF EDINBURGH
Vol. AVE p. 306.

The Shelves ave marked by Ted Lines
The Number} denotes the llighest 2.5.1 the succeeding ones.

1M WL WV. are te Snommit Levels between die Glens
sees

SCILE OF E:
1

= & Mites

(IS054 4)

XXVII.—On the Parallel Roads of Lochaber, with Remarks on the Change of
Relative Levels of Sea and Land in Scotland, and on the Detrital Deposits in
that Country. By Davin Mixng, Esq.

(Read 1st March and 5th April 1847.)

There are few questions in geology which have given rise to so many theories,
and so much speculation, as the origin of the parallel roads in the valleys of
Lochaber.

In the year 1817, the late Dr MacCuLLocu gave an elaborate description
of them, in a paper read before the Geological Society of London. In the year
1818, Sir Toomas Dick Lauper read before the Royal Society of Edinburgh a
paper, full of equally interesting details. Both of these observers suggested, in
explanation of the shelves which mark the mountain sides of these valleys, that
they had been occupied by lakes, which, by earthquakes or other violent convul-
sions, had been drained. This theory was generally received, until, in the year
1839, Mr Darwin, so justly celebrated as a geologist, and an accurate observer,
published his views, and pronounced the shelves to have been formed by the sea;
an opinion which, besides being rested on proofs derived from the locality, he en-
forced also by his observation of similar appearances in South America.

Mr Darwin’s opinion has received the assent of Sir RopEricxk I. Murcutson,
Mr Lye, and Mr Horner, all successively Presidents of the Geological Society,
besides other geologists, both at home and abroad, who are justly regarded as
authorities in physical science. Relying on the soundness of their views, I confess
that when I went to Glen Roy, in the year 1845, it was with a strong conviction
that the lake theory was indefensible ; a view to which I was the more inclined,
from having studied certain marks along different parts of the Scottish coast, on
both sides of the island, which satisfied me that the sea had recently stood at a
much higher relative level than at present; and that, in its recession, it had
formed, all round our coasts, shelves or beach lines, very analogous to those in the
Lochaber valleys. I had not been two days in Glen Roy, before I satisfied myself
that these views were inapplicable to the shelves in it and its associated valleys.
But I was unable, during my visit of 1845, to remain long enough to obtain evi-
dence of the manner in which the lakes had been dammed up, and eventually
drained. I therefore resolved to defer the farther consideration of the subject,
until I could pay a second visit. This | accomplished in September 1846, when
I spent a week in the examination.

In the following paper, I shall attempt to explain my reasons for thinking

VOL. XVI. PART III. 5H

396 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

Mr Darwin’s theory inadmissible, and to point out the manner in which, as it
appears to me, that the lakes were drained,—not as supposed by Dr MacCutiocu
and Sir Tuomas Dick LaupEr, by convulsions of nature, but by the gradual ope-
ration of ordinary causes.

Though it. is the principal object of this paper to account for the formation of
the Lochaber shelves, there are no views regarding them which can be suggested,
which have not a more general bearing, and the soundness of which may be tested
by evidence supplied from other sources. Former writers, accordingly, and espe-
cially Mr Darwin, have felt it to be necessary, after giving their explanation of
the parallel roads, to shew, that the principles on which it rests, are, at least, not
inconsistent with any established truths in other branches of geology.

I shall not shrink from subjecting the Lake theory, which I have to submit,
to a similar ordeal; and the more so, as I feel satisfied that it receives great sup-
port from geological considerations now held to be well established.

As the whole details of the parallel roads have been fully described by for-
mer writers, I shall limit myself to points on which I have obtained new informa-
tion, or with regard to which doubts have been expressed.

1. One of the points of the class last referred to, is the absolute horizontality
of the shelves. Mr Darwin, referring to Sir THomas Dick LAupER’s observations
on this point (p. 76.), hints at the possibility of errors and omissions in the calcu-
lation. M. Bravais, in his paper on the lines of former sea-level in Finmark, sug-
gests, “that an accurate geodetic levelling should be applied in the case of the
doubtful lines in Scotland,” evidently referring to Glen Roy. Mr Horner, the
president of the Geological Society, in his last year’s address, observes; ‘‘ Mr
Darwin’s explanation of the parallel roads of Glen Roy, that they are ancient sea-
beaches, appears to be now generally accepted ; and it would be most interesting,
if it were ascertained by exact levellings, such as those of M. Bravars, whether
they really are parallel.” Similar doubts had been expressed by Sir R. I. Mur-
cHison, Mr Horner’s predecessor, in his anniversary address of 1843; in support
of which, he refers to the concurrent opinion of M. de BEaumont and Professor
PHILLIPS.

In accordance with the doubts expressed by these authorities, the Geological
Section of the British Association, at their last meeting, agreed on an address to
Her Majesty’s Government, requesting them to cause the parallel roads of Lochaber
to be examined by the officers of the Ordnance Survey, to ascertain their supposed
horizontality.

I have no doubt that the result of this official survey, if made, will be to
establish the absolute horizontality of the shelves. In August 1844, Mr D. STevEN-
son, at my request, was so obliging as to examine them, and the conclusion at
which he arrived, is explained in a letter to me, from which I make the following
extracts. “I have had a number of levels taken, the particulars of which I shall

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 397

give you afterwards. The result, I think, leaves no doubt as to the perfect horizon-
tality of the ‘roads.’ The glen is much more extensive, both as regards length
and breadth, than I[ anticipated, and the height of the roads above its bottom is
also very considerable, and any thing like a series of cross sections, referred to the
same datum, would be a work of very great magnitude; a month, I should say,
would not complete it. The whole we have been able to do, therefore, is to test
the uniformity of the levels of the different roads, by viewing them with a good
instrument from several points, as was done by Sir THomas Dick LavupEr; and, in
addition to this, a section was made along the middle road, where it is pretty well
defined from Glen Turret downwards, for a distance of nearly 35 miles, and
throughout that stretch, the road was found to be perfectly horizontal.” ... “Tf 1
had seen that any thing further could be done, I would have left my assistants
for a few days longer; they were there a week.”

These observations of Mr SrEVENSON, whose professional accuracy is undeni-
able, confirming, as they so completely do, the result of Sir Toomas Dick LaupER’s
survey (and he, too, was aided by an engineer), leave no doubt in my mind, as to
the horizontality of the roads. It is scarcely necessary to refer to any farther
and weaker testimony on the subject. But it may be proper to add, that during
the two occasions when I visited Glen Roy, I had a pocket-level with me, which
I constantly used ; and that on the last visit | was accompanied by Mr R. Cuam-
BERS of Edinburgh, who had a larger spirit-level, and we never could detect any
deviation from horizontality.

2. There is a point of some importance bearing on the theory of the shelves,
about which former observers have disputed. MacCuttocu found by his barometric
observations, that the Glen Gluoy uppermost shelf is 12 feet above the highest in
Glen Roy; but he attributed this difference to errors of observation, and his
theory in regard to the formation of the shelves proceeds expressly on the assump-
tion, that these shelves are precisely on the same level. Sir THomas Dick LAUDER
mentions, however. that Mr M‘LzeAn, the engineer who assisted him, made the
Glen Gluoy shelf 12 feet above that in Glen Roy, whilst Sir Toomas himself made
it 15 feet. According to the observations made by myself and Mr Cuampers last
September, the difference is much greater. By levelling, we made it 29 feet: by
joint barometric and sympiesometer observations, I made it 23 feet.

3. Whilst on the subject of Glen Gluoy, I may mention that I discovered in
it a second shelf, which the barometer shewed to be 200 feet, and the sympie-
someter 213 feet, below the level of the one before referred to. I detected it first
immediately above the mouth of Glen Fintec. It is traceable on both sides of the
glen, and for several miles upwards.

4, There is a circumstance of great importance, in the theory of these roads,
on which I was so fortunate as to obtain farther information. 1 allude to the
- fact. that most of the shelves are coincident with some summit level, so as to ad-

398 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

mit of the waters flowing over that level as over a lip. Thus the uppermost shelf
of Glen Gluoy No. 1, in Sir Tuomas Dick Lauper’s Memoir, is (as he explains)
exactly coincident with the water-shed ridge which divides Glen Gluoy from Glen
Roy, so that the waters (whatever they were) which stood at that height and
formed the beach No. 1, must have fiowed out at the head of Glen Gluoy into
Glen Roy. In like manner, the uppermost shelf in Glen Roy, No 2 in Sir Tuomas
Dick LaupER’s Memoir, is (as he also mentions) exactly coincident with the water-
shed ridge which divides Glen Roy from the valley of the Spey; so that the waters
which stood in Glen Roy at No. 2 beach, must have flowed over the head of the
Glen into Spey valley. In like manner, the only shelf which occurs in Glen Spean,
No. 4 in Sir THomas Dick LauDER’s Memoir, is exactly coincident with, or rather is
a few feet above, the pass of Mukkul at the head of Loch Laggan, through which
pass, the waters standing at the level of No. 4 must have flowed eastward into
Spey valley. These coincidences, as Mr Darwin admits, “ are so remarkable,
that they must (I use his own words) be intimately connected with the origin
of the shelves; although such relation is not absolutely necessary, inasmuch as
the nuddle shelf of Glen Roy, is not on a level with any water-shed.” (P. 43.)

The middle shelf here alluded to is No. 3 in Sir THomas Dick LaupEpr’s list.
The discovery which I made, was its exact coincidence with a water-shed at the
head of Glen Glaster, a glen which, though branching up from Glen Roy near the
bottom of it, oddly enough does not appear to have been visited, and certainly not
to have been described, by any former observer.

Shelves 3 and 4 are the only shelves which enter and run up this glen. Sir
Tuomas Dick LAuDER’s map inaccurately represents shelf 2 as marking it on both
of its sides. Shelf 2 stops. however, on both sides of Glen Roy a little to the east-
ward of, or above the mouth of Glen Glaster.

In following shelf 3 to the head of this glen, I found that it was there lost in
a low mossy flat. A little beyond this flat, and a few feet below the summit-level,
an old river-course can be distinctly traced down a slope towards Loch Laggan.
It has a rocky bed, over which a great body of water had evidently flowed at some
former period. The breadth of the rocky bed is from 30 to 40 feet ; the knolls of
rock are from 2 to 5 feet high, and amongst them are rounded blocks of stone,
such as occur in all great Highland rivers. I traced this rocky channel for about
a mile towards Loch Laggan; and I afterwards found the place where it had
discharged its waters into Loch Laggan, when that loch stood at shelf 4. It is
marked by a huge delta, forming a projecting buttress at the level of that shelf,
and bulging far beyond the general side of the Laggan valley.

On examining the rocky knolls attentively in this ancient river-course, I
found that the smooth faces were all towards Glen Glaster, and the rough faces
in the opposite direction, affording proof, if such were needed, that the stream
which flowed there had come from Glen Glaster.

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 399

A small rivulet trickles now among the rocks, infinitely too feeble to have
produced the appearances.

It is now, therefore, established, not only that the whole of the 4 shelves of
Lochaber are coincident with water-sheds respectively, but that a great body of
water had filled Glen Glaster, and of course Glenroy, the outlet of which was
down this ancient river-course to shelf 4 in Loch Laggan, which is at a lower
level by 212 feet.

Whilst on this subject, I may mention farther, that I examined narrowly the
interval of space between shelf 1 at the head of Glen Gluoy, and shelf 2 at the
head of Glen Turret, where the last shelf is nearest to Glen Gluoy. This space
also appeared to me to exhibit the features of an ancient river-course, though they
are not so striking as those just described. The distance from the one shelf to
the other, is about a mile. Where the Glen Gluoy shelf ends, rocky knolls rise
above the moss, water-worn below the level of the shelf, but rough above that
level. Their smooth faces are all towards Glen Gluoy. Near shelf 2, in Glen
Turret, the rocks have evidently been excavated and cut into by some considerable
stream ; at present a very small burn runs in this rocky channel, quite inca-
pable of producing the appearances.

The grandest exhibition of an ancient and deserted river-course is, however,
at the head of Loch Laggan. The Pass of Mukkul is a channel, the bed and sides
of which are entirely rock. It is, at its narrowest part, about 70 feet wide, the
wall faces being on each side from 40 to 50 feet high. The rocks at the sides are
evidently water-worn for about 30 feet up. To the eastward, this gorge expands
into a broad channel of several hundred yards in width, divided in the middle
by what has formerly been a rocky islet, against which the waters of this large
river had chafed in issuing from the pass. For nearly a mile towards the east,
the rocky banks continue on each side, but they gradually diverge, having between
them a mossy fiat sloping gently eastward. The smooth faces of the rocks with-
in the probable reach of the river-waters, are all towards the west, where Loch
Laggan is situated. The height of shelf 4 above the highest point of this deserted
channel, is, by barometric measurement, about 21 feet, which affords, therefore,
some probable estimate of the average depth of the river. I have only to add,
that no stream whatever now occupies this water-course, except where, for a short
part of it, the river Pattaig flows in a reverse direction into the head of Loch
Laggan. This stream was, when I visited it last September, only about 18 inches
deep and 30 feet wide, and must be quite inadequate to have formed the rocky
banks on each side of it.

The ancient river-course now described is of much greater size than that at
the head of Glen Glaster, just as the Glen Glaster river-course is of greater dimen-
sions than those respectively at the head of Glen Gluoy and Glen Roy. The rea-
son is obvious. The river at Mukkul had to discharge not merely the waters

VOL. XVI. PART III. 51

400 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

which belonged to Glen Spean, but also those which flowed out from Glen Glaster,
comprehending Glen Roy, Glen Collarig, and Glen Gluoy. The Glen Glaster river-
course discharged the waters of Glen Collarig, Glen Gluoy, and Glen Roy, whilst
the Glen Gluoy stream discharged only the waters of one lake. Mr Darwin did
not visit the Pass of Mukkul. If he had studied the appearances presented by it,
and by those almost as strikingly exhibited at Glen Glaster, he would have found
it impossible to deny that the waters which formed shelves 3 and 4 flowed down
river-courses, and therefore could not be arms of the sea.

His proposition is, “that the waters of the sea, in the form of narrow arms
or lochs, such as those now deeply penetrating the western coast, once entered
and gradually retired from these several valleys;’ and he adds, that after
considering the ‘‘ several and successive steps of the argument, the theory of the
marine origin of the parallel roads of Lochaber, appears to me demonstrated.”
(P. 56.) LTregret that Mr Darwin should have expressed himself in these very
decided and confident terms, especially as his survey was incomplete; for I ven-
ture to think, that it can be satisfactorily established, that the parallel roads of
Lochaber were formed by fresh water lakes.

1. The first circumstance which I shall notice as fatal to Mr Darwin’s theory,
is suggested by the fact last referred to, that the waters which formed the different
shelves, must have jlowed out of the glens, and descended by river-courses to lower
levels. 'The waters which formed No. 1 shelf in Glen Gluoy descended nearly 29
feet by flowing into Glen Roy. The waters which formed No. 2 shelf in Glen Roy
flowed in like manner into the valley of the Spey. The waters which formed
No. 3 shelf were discharged over the head of Glen Glaster, down a slope of about
212 feet in vertical height, into Glen Spean. Lastly, the waters which formed
shelf 4 in Glen Spean, issued out of Loch Laggan by the ancient river-course at
Mukkul.

Now, any one of these cases is irreconcilable with the notion, that the shelves
had been formed by arms of the sea. There is no such thing in nature as a river
flowing out of an arm of the sea, to a lower level.

Mr Darwin, as we have seen, admits that this coincidence of the shelves with
water-sheds, must be in some way connected with their origin ; and, accordingly, he
endeavours to give an explanation of it consistently with his theory. He says that
these water-sheds are land straits, with sea on each side of them, and that they
consist of littoral deposits or accumulations of matter formed by the opposition of
tides. This opinion, however, is altogether inconsistent with the actual circum-
stances of the case. In the first place, there is at these water-sheds, no accumu-
lation of littoral deposits or detrital matter. They consist, generally, of bared
rocks, forming sloping channels or water-courses. In the second place, there is no
trace of water at the same level, on each side of these water-sheds. In the third
place, when land straits are formed by the accumulation of matter from opposition
of tides, it is not in situations like the heads of glens which narrow to a point, and

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 401

at that point are separated by a small neck of land,—it is where there is space for
a considerable current on each side of the strait.

For these reasons I consider that Mr Darwin’s explanation of the coincidence
of the shelves with the water-sheds before described, is quite inadmissible.

2. The second serious objection to Mr Darwin’s theory arises from the fact,
that the shelves in the different glens are not coincident in level. If they had been
formed by arms of the sea, as the land rose out of it, the sea should have formed
lines in all the valleys which it entered, at precisely the same levels. But neither
of the Glen Gluoy shelves is to be seen, in any of the other valleys. So also the
No. 2, or highest shelf of Glen Roy, and the next lowest, or No. 3, do not occur
in the lower part of that glen, or in the adjoining valleys of Glen Glaster, Glen
Spean, and Glen Treig.

Mr Darwin attempts to explain one, but one only, of these circumstances,
viz., the difference of level between No. 1 and No. 2 shelves, by a theory of very
questionable soundness. He says, that the tide in Glen Gluoy may have risen 20
feet higher at the head of the estuary, than at the head of Glen Turret. It would
be necessary that it should rise 29 feet higher. But if this were the case, then
the shelves, at all events, in Glen Gluoy, would not be horizontal, or nearly so ;—
they would have sloped upwards towards the head of Glen Gluoy, by 29 feet in
the course of 6 or 7 miles,—the length of the glen. But this would be inconsistent
with the great and well-established fact so characteristic of these Lochaber shelves ;
and moreover, though the beach-lines at the heads of the two glens might not be
exactly coincident in level there, they ought, at all events, to be so at the mouths
of the glens where the supposed arms of the sea joined the main body of the ocean,—
which is not pretended.

This theory, however, would explain merely the non-appearance of shelf 1 in
Glen Roy. The non-appearance of all the others is accounted for by Mr Darwin,
simply by supposing that something or other had prevented them being marked
in the other glens.

In support of this view, Mr Darwin refers to two intermediate shelves which
are faintly traceable on Tombhran and elsewhere, in order to shew that the
water did produce marks at some places, and not at others. But, from the faint-
ness of those intermediate lines, it is manifest that the water had stood at their
level for a much shorter period than at the levels of the principal shelves ; and,
therefore, no fair inference can be drawn from the former applicable to the latter.

3. These considerations suggest, however, a separate and even a more serious
objection. Not only should the sea have made markings at the same levels in all
the Glens of Lochaber, but it should have produced similar appearances, and at
the same levels respectively, on all the mountains of Scotland, high enough for the
purpose. Mr Darwin says, “that it would be more proper to consider the pre-
servation of these ancient beaches as the anomaly, and their obliteration from me-
teoric agency the ordinary course of nature.” (P. 60.) Supposing him right in

402 MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 2

this, he ought to have shewn how circumstances caused that anomaly at Glen
Roy and its adjoining valleys. But he has not shewn, and cannot shew, that the
sides of the Glen Roy mountains, are in any respect different from those other
highland mountains. Indeed, he has himself pointed out a similar beach line at
Kilfinnin, in a glen towards Inverness. I take leave farther to doubt the sound-
ness of Mr Darwin’s proposition, that the preservation of ancient beach lines is
anomalous. The whole of Scotland, and I believe also of the British Islands, is
begirt with lines of ancient sea beach.

4. The ancient sea beaches, now alluded to as caste along our coasts, pre-
sent avery marked contrast with the Lochaber shelves. If these shelves had
been formed by the sea, it will, I presume, be admitted that, considering their
great altitude, they are of much older date than beach lines at a lower level. If
older, then they should be less perfect and entire. But the contrary is the case. They
are incomparably more perfect and entire than any of the lowest ancient sea
terraces which occur along our coasts.

5. If the Lochaber roads were formed by the sea, the well-known actions of
the tides, to which Mr Darwin refers, would have precluded the formation of
them along lines absolutely horizontal.

Mr Darwin refers to a case in South America, where, in 18 miles, the tidal
wave rises at one place 20 feet higher than another in the same estuary. Nearer
home, in the Bristol Channel, the sea rises at its head about 50 feet higher than
at its mouth.

The tide at Blackwall rises 12 feet higher than at Yarmouth. In the Firth
of Tay, the tide rises at Perth 18 inches above the level at Newburgh. The tide
at Alloa is said to rise 2 feet 9 inches above its level at Leith. At Glasgow, the
tide rises 10 or 11 inches above its level at Greenock. On the Dee, the level of
high water is, at Chester, 8 inches above what it is at Flint, near the mouth of
the river, a distance of 11 miles.

On this principle, the beaches of Lochaber, if formed by arms of the sea,
ought all gradually to rise to the head of the Glens—narrowing, as these glens
do, towards the head. But this is negatived by the fact.

6. On more narrowly considering the effect of tidal action, it will readily
occur, that the beaches formed by the sea must be materially different from those
of a lake, in which there is no movement of the water at the sides, except such as
is caused by winds common to both. In the case of the sea, there is not only a
vertical rise and fall of water (which, on the west coast of Scotland, is from 8 to
16 feet) twice in the 24 hours, but also a good deal of lateral current alternately in
opposite directions. Hence the sea, whilst it will eat into the land more rapidly
than a lake, will also spread out more completely the detritus washed down into
it. Ina lake, on the other hand, which has no movements of water either ver-
tical or lateral, the detritus deposited on the sides of a valley occupied by it, will

ay

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 403

be scarcely if at all removed, and will thus form projecting buttresses nearly flat
in their upper surfaces, and presenting steep escarpments towards the lake.

Now, applying these two principles of tidal action to the shelves of Lochaber,
we seek in vain for any actual cndentation into the sides of the hills. The shelves
consist entirely of buttresses which stand out from the sides of the mountains; and
these buttresses, so far from sloping at an angle little less steep than that of the
sides of the mountains (which would be the case with the sea), form flats or ter-
races which deviate in general very slightly from the horizontal.

7. If the shelves were formed by the action of the sea, they should be most dis-
tinct at places where the hill sides had been most exposed.

Thus, on the north and north-west sides of Craig Dhu, and on the west side
of Bohuntine, where there must, on Mr Darwin’s theory, have been an open ex-
panse of ocean, the shelves should have been most distinct. But at these places, the
three highest shelves are entirely absent ; the fourth alone is visible, though, being the
lowest, it must have been less exposed. It is quite anomalous, on the marine
theory, that the shelves should not have been formed where the force of waves
and of tidal currents must have been greatest, and that they should have been
most distinctly formed in the higher and more sheltered parts of Glen Roy.

The hills at the mouth of Glen Roy seem rather to indicate that the highest
shelves had not been formed on them,—the very reverse of what might have been
anticipated if Mr Darwin’s views are sound. If they had been formed, they would
not have been obliterated, as is manifest from the perfect preservation of shelf 4
on Craig Dhu and Bohuntine.

8. Having stated these objections to the theory of Mr Darwin, I proceed to
consider his objections to the theory, that the shelves were formed by lakes.

These objections resolve entirely into the difficulty of explaining the disap-
pearance of the barriers, which must have dammed back the water in the valleys.
But it would be no good reason for rejecting an explanation founded on the exist-
ence of barriers, even though we could not very clearly account for the disappear-
ance of them, provided that there is direct and conclusive evidence that such bar-
riers existed. Now, I conceive that there is such evidence furnished by the con-
siderations before referred to.

Let us examine, however, the alleged difficulty of explaining, how the waters
could have been dammed up in the valleys to the height of the several shelves.

Shelf 2 is distinctly marked on both sides of Glen Roy, down to a certain
point,—and also on both sides of Glen Collarig, down to a certain point. At this
period, the water flowed from the east end of Glen Roy into the valley of the
Spey. Something must have existed, therefore, in both glens at the points above
referred to, to prevent the extension of the shelf westward.

Shelf 3, in both glens, extends a little more to the west than shelf 2. We

VOL. XVI. PART III. 5K

404. MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

have seen that, whilst Glen Glaster is exempt from shelf 2, it is well marked on
both sides by shelf 3.

To explain these facts, I assume that there was a blockage of some sort, in
Glen Roy, which filled the lower part of the valley up to the level of shelf 2, and
which blockage extended a little farther east than the mouth of Glen Glaster. I
assume also a similar blockage in Glen Collarig, which filled the lower part of the
valley, and as far eastward as the place where shelf 2 stops in that glen. This
blockage may have been gravel, clay, or any other detrital matter.

Such is the supposed state of things, whilst the waters stood at shelf 2 in
Glen Roy; at which period, it will be remembered, they were discharged to the
eastward.

Former writers have assumed, that when the waters sunk from shelf 2, the
amount of sinking must have been 82 feet, the distance of shelf 3 below shelf 2:
and that this sinking had been one act, caused by an earthquake, or other violent
operation, which all at once lowered the barrier by that number of feet. But
this is a mistake. MacCuttocn takes notice of a shelf faintly marked on Tom-
bhran hill, between shelf 2 and shelf 3, though he expresses afterwards some
uncertainty about it. In fact, there are two intermediate shelves visible there :
and they are also discernible, at precisely the same level on Ben Erin, and also
more distinctly near Achavaddy, on the south side of Glen Roy; the one being
about 14 feet below shelf 2, and the other about 36 feet lower down.* These two
intermediate shelves clearly indicate, that the water which filled the valley, did
not all at once sink from shelf 2 to shelf 3. They prove that the water first sunk
down 14 feet, and was stationary at this level for some time; that it then sunk
down other 36 feet, and continued at this level for some time; and that it again
sunk other 32 feet, at which level it remained for a much longer period, till it
formed shelf 3.

It is evident, from these facts, that the lowering of the barrier (of whatever
material composed) which confined the water in Glen Roy, was a process of a
more gradual and ordinary description than what former writers, and especially
Mr Darwin, suppose. It is plain, also, that the barrier which kept in the waters
was less rapidly worn down, when they stood at shelves 2 and 3, than at either
of the intermediate levels. We see that at shelves 2 and 3 the waters flowed over
rocky ledges, in the one case into Spey valley, in the other case by Glen Glaster.
Is it not fair from this to infer, that at the intermediate shelves, the water flowed
over a blockage of such a nature as was capable of being more easily worn down
and obliterated, such as detrital matter? It is, at all events, obvious, that when

* There are hummocks or knolls of stratified gravel and sand in Glen Glaster, the tops of which
are all about 36 feet above shelf 3. It is probable that they were deposited when the lake stood at one

or other of the intermediate points last mentioned.

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 405

the water sunk 14 feet, the discharge must have ceased at the east end; and that
it henceforward would go on at the west end, probably near the mouth of Glen
Glaster. At every other place, the rocky mountain sides rise so high, as to pre-
clude the possibility of overflow or attrition.

Keeping these principles in view, let us suppose that the detrital matter
which blocked up the lower parts of Glen Roy extended a very little to the east
of the mouth of Glen Glaster. How easy it is to suppose that this detritus was
scooped away, so as to allow of the recession of the waters westward, and of their
flowing round the east jaw of Glen Glaster, and on towards the head of that glen,
from which they would descend to Glen Spean? For this purpose, it is not ne-
cessary to suppose, that there was any lowering of the supposed barrier in level.
even by asingle foot. All that is required is the scooping or wearing away of the
detritus, so as to allow of the extension of the lake a little to the westward ;—a
few yards would be sufficient. As the discharge at this first sinking, must have been
at the west end, it is fair to infer that the wearing away of detritus took place
there; and when once a flow of water was established through detrital matter.
the process of removal would go on rapidly, so as to allow of repeated sinkings of
the lake, till it reached the water shed at the head of Glen Glaster, the rocky
nature of which would for a time stop any farther sinking, and thus allow of the
formation of shelf 3.

According to the foregoing views, we see how the waters would, by suc-
cessive steps, sink from shelf 2 to shelf 3, and. after entering Glen Glaster, form
a marking on both of its sides. We see, also, that the same removal of detritus
which allowed the formation of shelf 3 in that glen, would allow also the exten-
sion of it on Bohantine Hill, beyond the point where shelf 2 terminates.

Whilst this process of attrition was going on in Glen Roy, there need have
been no contemporaneous change in the blockage of Glen Collarig. But there
also, at some time or other, a similar scooping out of detritus must have taken
place, to allow of the extension of shelf 3 beyond the point where shelf 2 termi-
nates.

Nor is it difficult to conceive, how this removal of detritus was effected. Thus,
in Glen Collarig, there are, on both sides of the glen, burns of considerable size
and power (from the steepness of their channels) which flowed into the lake.
There are three of them, which now descend in that part of the glen marked by
shelves 2 and 3. If the detritus which formed the blockage in the lower part of
the valley consisted of the same loose sand and gravel which now abounds there,
forming cliffs from 70 to 80 feet high, nothing is more easy or natural than the
scooping of it out, by such means.

The same observations apply to the blockage in Glen Roy, which, to prevent
the waters when at shelf 2 flowing into Glen Glaster, must have been near the
mouth of Glen Collarig, called Gap in the maps, out of which, from the number of
streams in it, a considerable current had flowed.

406 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

So far with regard to the first depression to shelf 3, at which period I sup-
pose the Collarig blockage to be still existing (scooped out a little towards the
west), and the blockage in Glen Roy to have been, by a similar process, removed
below the mouth of Glen Glaster. The next well marked shelf is No. 4, which is
seen on Craig Dhu and Bohuntine, and on both sides of Glen Collarig, and which
infers the necessity of removing the blockage entirely from both Glen Roy and
Collarig.

This may have been, as in the case of the previous depression, a gradual
operation. There is no improbability whatever in the ultimate removal by rivers
and burns, of a blockage of the nature supposed. There flows into Glen Roy, from
Bohuntine hill, and at or near the very place where the blockage must have existed,
the Tundrun Burn, the sides of which shew mica-slate rocks cut through by it to
the depth of about 70 feet, and detrital matter above these rocks cut through to
the depth of 130 feet. If, since the drainage of the lake, it has thus cut through
and removed blockage to the depth of 200 feet, of which one-third is solid rock,
this rivulet must have had nearly equal power to wash away the more superficial
blockage which existed at this place previously to that event.

The same observations apply to the detrital matter in Glen Collarig, which
could easily be carried away by the numerous mountain torrents flowing into that
glen.

The following is the manner in which Mr Darwin alleges that the two de-
pressions must have taken place, according to the lake theory. He says, that
there are two barriers, one in Glen Collarig, and the other in Glen Roy: “ Let
one of the two barriers, we will say the smaller one in Glen Collarig, give way from
the effects of an earthquake, or other cause, the lake will now stand at the level of
the middle shelf, the barriers having given way 82 feet vertically. Again let it burst,
and this time rather more than 212 feet vertical must be swept away. Let all this
have taken place, but still a barrier nearly a mile long and 800 feet in height is
left standing across the mouth of the Roy. Must we suppose that each treme the
barrier in Glen Collarig failed, the one in Glen Roy gave way the same number of feet,
through some strange coincidence?” It is plain, from this representation, that
Mr Darwin had not in his view, the more simple and gradual process of removal
which I have ventured to suggest. It is not in the least necessary to imagine,
that there was any sudden sweeping away of barriers of the magnitude supposed ;
and which would certainly imply the existence and operation of some stupendous
agent; but the effect of which would, as Mr Darwin truly says, have also probably
obliterated the shelves. The process which I have suggested, implies the continu-
ous working of ordinary and natural agents,—agents which are now seen at this
very place, producing results similar to those required.

Mr Darwin says, that the barrier across the Roy must have been 800 feet
high. This is on the assumption, that the valley of the Roy was then of its present
depth and form. But is there to be no allowance made, for the removal by the

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 407

river Roy of detritus from the valley? It is manifest, from many appearances
along its sides, that the river Roy has cut down at least 200 feet below what was
the original bottom (whether of lake or estuary), formed when the waters stood
at shelf 4 ; so that the height of the supposed barrier to retain the waters at shelf
2 would not exceed 600 feet above the bottom of the valley, and might be much
less, if the valley were more filled up. Mr Darwin considers it probable (p. 83),
that the buttresses existing on the sides of Glen Roy indicate, that the valley, up-
wards from Bridge of Roy, had been filled with detrital matter to the very level of
shelf 4; in which case the blockage or barrier requisite to form a lake at the level
of shelf 2, would have been only about 300 feet above the bottom of the valley.
My belief, however, is, that the whole not only of the lower part of Glen Roy,
but also of the district about Unachan, High Bridge, and Fort-William, was blocked
up with detrital matter, which, in the course of time was washed away by rivers ;
and that, when the blockage of Glen Roy was removed, the depressed waters stand-
ing at shelf 4 were dammed back by detrital accumulations near Unachan, so as to
force a discharge by the Pass of Mukkul. This 4th, or lowest shelf, seems to me
to stretch much farther to the north, on both sides of the Spean, than former ob-
servers have noticed. On the hills flanking the east side, this shelf can be traced
to within nearly a mile of Spean Bridge. On the opposite side of the valley, it can
be traced to within 6 or 7 miles of Fort-William. The width of the valley where
this shelf on both sides ceases to be visible is about 4 miles. Across the mouth
of this valley, a little beyond a line joining the extreme visible points of shelf 4,
lies the high and elongated hill of Tomnempearaichin, the top of which I found,
by the level, to be only 50 or 60 feet below shelf 4; and there is no great
difficulty in imagining that the whole of this district, as far as Fort-William,
where the enclosing hills are greatly higher, was filled by detritus. There are,
even now, detrital remnants of enormous size, of which the well-known Hill of
Tomnahurich at Inverness (about 180 feet high and half a mile long), and a hill
to the west of it (240 feet high), are specimens indicating the prodigious accumu-
lations once existing in the great glen.

To this point I shall revert. But, in the mean time, taking for granted that
such detritus did fill the lower parts of the valleys, it is easy to understand how
it should have dammed up the waters into lakes, and how, by a gradual and long-
continued process of wearing down, this detrital blockage should have been lowered
to the requisite extent.

I have endeavoured to explain the damming back and the depressing of the
lakes to their successive levels, without imagining that the level of the sea was
then different from what it is at present. Ifthe sea stood at a higher level, then
the difficulties of the explanation become less ; because the valleys must then have
been previously less excavated than they now are, by the operation of rivers.
There are good reasons for believing, that since the period of the deposit of the

VOL. XVI. PART III. 5

408 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

boulder-clay in Scotland, the sea has stood at least 1000 feet higher on the land
than at present. Of course, it must have been after the land rose out of the sea
to some extent, that the Lochaber shelves could have been formed by lakes ; but
the lowest of these might have existed when the sea stood 900 feet above its pre-
sent level, in which case the depth of detrital matter required to dam up the
valleys would be comparatively small.

I have attempted to explain how the valleys of Glen Roy, Glen Collarig, and
Glen Spean; were blocked up. There still remains Glen Gluoy, which, as before
mentioned, contains two shelves, one of which is about 29 feet above the highest
of Glen Roy. Glen Gluoy being unconnected with the other valleys, requires a
separate blockage. There would be no great difficulty in imagining the existence
of detrital blockage in this glen, at the place where its shelves terminate towards
the west, as it is generally, throughout its whole course, exceedingly narrow ; and
being unconnected with Glen Roy (though MacCuntoce# states the reverse), its
blockage may have been worn down at periods, and in a way, independently of
Glen Roy and Glen Collarig.

Before, however, forming a very decided opinion as to the position of the
blockage applicable to Glen Gluoy, I should like to examine more particularly
than I was able to do, some of the other Glens which open into the Caledonian
valley on both sides, with the view of ascertaining whether they contain traces of
‘horizontal shelves about the same height. Mr Darwin takes notice of one in
the valley of Kilfinnin,* about 10 miles to the eastward, and which he says is
(by his barometric observations) about 40 feet above the highest shelf in Glen
Roy ; in which case it would be only 10 or 11 feet above that in Glen Gluoy, a
difference quite within the limits of error.

I have observed several places along the Caledonial Canal, where there are
traces of one or more horizontal terraces, at a height of from 650 to 690 feet above
the sea. From these considerations, I infer the possibility of there having been a
blockage which applied not merely to Glen Gluoy, but to other glens opening into
the great Caledonian valley ; and it would, therefore, be most important, that
future observers should turn their attention to the adjoining districts.

My explanation of the Lochaber shelves depends entirely on the accuracy of
the supposition, that the valleys were, in the lower parts of them, filled up with
detrital matter, capable of being gradually worn down and washed away. ‘This
supposition is not only not improbable on general principles, but is verified to a
great extent by the remains of such detrital matter at and above the heights
required for it. Thus, in Glen Collarig, there are to be seen, near the east end,

* It is to be regretted that Mr Darwin, when he visited Lochaber, was not provided with a
spirit-level. His statement as to the horizontality of this shelf at Kilfinnin, depends entirely on

ocular inspection and barometric measurements.

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 409

and withinabout half a mile of the place where the blockage must have existed.
enormous heaps of boulder-clay, gravel, and sand. These detrital deposits must
have existed in Glen Collarig before the shelves were formed, because shelves 2
and 3 are seen distinctly indented upon these deposits; and I was particularly
struck with the fact, that these deposits reach to a height of more than 100 feet
above shelf 2. Here is proof, that in Glen Collarig, before the formation of the
lake which filled it, there was detrital matter of sufficient depth and consistency
to have retained water at the required height. At the place where shelf 2 termi-
nates in this glen, the valley, even at present, is only about 236 feet deep, and
300 yards wide, so that the depth of detrital matter does not exceed the limits of
probability—nay, is exemplified by the occurrence of much larger accumulations
of detritus in all parts of the Highlands.

It is here proper to explain, that there are in these valleys, as elsewhere in
Scotland, two distinct sorts of superficial deposits,—the one consisting of the well-
known boulder-clay, and the other of ordinary gravel and sand. This boulder-clay
exhibits the same general characters, which it commonly possesses elsewhere ; it
is unstratified, exceedingly obdurate, of a dark-bluish colour, and filled with water-
worn boulders. This boulder-clay I found at the following places ;—Spean Bridge,
where it is covered by sand; Bohuntine Hill, where it is covered with laminated
clay, sloping to the centre of the vailey, and about’250 feet below shelf 4; Bohina,
on the south side of Glen Roy; Inverlair Bridge, near Loch Laggan; Glen Glaster
(on the west side of the valley), from 50 to 80 feet above shelf3; Glen Collarig
(near the gap), where it rises above shelf 2; Glen Gluoy, as seen at the water-
shed between it and Glen Roy, and on a level with shelf 1. The deposit occurs
also at Clenichan, at the river Roy, where the mica-slate rocks, through which
the river now runs, are covered immediately by boulder-clay,—the boulder-clay
being here covered by deposits of irregularly stratified beds of gravel and sand.
from 150 to 200 feet thick. At this place, I observed among the boulders in the
hill, granites (with red and grey varieties), old conglomerate, and red porphyry.—
rocks, all of which must have come from a distance.

From the fact that this boulder-clay occupies alike the highest and lowest
parts of the glens; and, more especially, that in several places it is seen distinctly
covered over by laminated clay as well as by stratified gravel and sand, it may be
inferred that the boulder-clay, with its imbedded blocks, was deposited, certainly
not after the drainage of the lakes, but either before the valleys were occupied
with water, or during that period.

In regard to gravel and sand, I do not remember having, in Glen Roy or its con-
tiguous valleys, observed any considerable beds of it, so high up as the boulder-clay.
But at lower levels, there are everywhere enormous cliffs of it to be seen, several of
which I measured, and found to exceed 180 feet in height. These cliffs are formed
out of the ancient bottom of the lake or estuary which filled the valleys, and are

410 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

composed of materials washed down from higher levels. The adjoining moun-
tains of the district afford ample evidence, that gravel as well as boulder-clay had
been, by some cause or other, brought and deposited over all this country, filling
the valleys to heights exceeding the highest of the Glen Roy shelves. Thus, on
the turnpike road between Tyndrum and Inverournan, near the summit level be-
tween the two valleys, which I estimated to be about 1030 feet above the sea,
there is great abundance of sand and gravel. On the Black Mount, about 4 miles
north of Inverournan, and at a height of 1300 feet above the sea, there is an im-
mense accumulation of gravel and boulders, particularly on the south side of the
summit. In the high ground north of Dalwhinnie, which I estimated at 1200
feet above the sea, there are great heaps of gravel, forming mounds and ridges.
These facts, taken in connection with the undoubted fact, that detrital matter has_
been spread over the greater part of Scotland, to a height of at least 1500 feet
above the sea, pretty clearly indicate, that detrital matter not only may have
been, but actually was spread over the Lochaber district, and filled its several
valleys, to the height of at least the highest of the Glen Roy shelves, thus afford-
ing ample blockage for its lakes.

I may mention that there are, in this part of the Highlands, several lakes
of small size, at very high levels, the existence of which renders the lake
theory of the Glen Roy shelvés less improbable than to some it may appear.
Thus, at the well-known pass of Rest-and-be-Thankful, there is a small lake,
which is about 800 feet above the sea, and there are traces of its having
stood formerly from 40 to 50 feet higher. To the south and west of Loch Treig
about 3 miles, there are two considerable lakes, one called the Lake of Corry; and
the other called Benofflap, which appear, from the accounts received of them, to
be about 1200 to 1300 feet above the sea. There are several also on the Black
Mount, at about the same high level.

Before concluding what I have to say regarding the parallel roads of Locha-
ber, I may briefly notice the theory, that the lakes which filled them may have
been confined by glaciers, or by the moraines of glaciers.

This was one of the districts which, in the opinion of AGassiz and Buck-
LAND, afforded undeniable proofs of the existence of glaciers. The former pub-
lished a paper* on the subject, in which he says: “ When I visited the parallel
roads of Glen Roy with Dr Buckuanp, we were convinced that the glacial theory
alone satisfies all the exigencies of the phenomenon; and as this locality is the
best known, I may limit myself to this example for the explanation of all others.”

M. Acassiz, in the paper now alluded to, explains the grounds on which his
theory rests; and it is accompanied by a plan of the locality.

It appears to me, (1.) That the facts on which M. Acassiz rests his theory

* Ed. Phil. Journal, vol. xxxiii., p. 236.

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 411

are incorrect. (2.) That, assuming as true the facts stated by him, they still
afford no evidence that glaciers existed in the Lochaber valleys.

(1.) There are three main facts relied on by M. Acassiz. He states, First,
That in Glen Roy, and in that part of Glen Spean, between Bridge of Roy and Loch
Treig, there are 3 shelves visible ; Secondly, That these shelves all terminate, on
both sides of the valley at or near the Bridge of Roy ; Third, That the bottom of
Glen Spean, in front of Loch Treig, is not only polished with that polish charac-
teristic of glaciers, but is, moreover, scratched transversely,—that is to say, at
right angles to the direction of the valley, by a cause which evidently proceeded
from Loch Treig.

To explain these appearances, it is suggested, that ‘‘ the supposition of a
ereat glacier descending from Ben Nevis, and shutting up the valley of the
Spean, by resting on Moeldhu, which is opposite, combined with the influence
of a glacier from Loch Treig, and which would bar the valley a second time at
that height, would explain all the facts.”

These facts, for an explanation of which this theory was invented, appear to
me not to have been accurately observed. In the first place, the three shelves do
not occupy, as M. Acassiz asserts, ‘‘ all the sinuosities of the lower part of Glen
Spean, and of the whole of Glen Roy.” It is only the lowest of the three shelves,
which occurs in Glen Spean and in the lower part of Glen Roy. The two upper-
most shelves stop short of the mouth of Glen Roy, by about 2 miles; so that, if
the Lake in Glen Roy was dammed back by a terminal moraine, that moraine
could not have rested on Moeldhu, at the foot of Glen Roy; but must have been
pushed up that valley, before the Ben Nevis glacier, 2 miles farther,—an opera-
tion which the levels, distance, and direction of the valley would have rendered
impossible.

In the second place, the shelves do not, as M. AGassiz says, ‘‘ terminate at
the same point,’’—viz., at Moeldhu, where he supposes the terminal moraine of
the Nevis glacier to have been. The two uppermost shelves (as just stated) do
not come within two miles of this point; and the lowermost shelf, instead of
terminating there, runs, as formerly explained, several miles northwards, on both
sides of the valley, towards Unachan, where they are4 miles apart. It is scarcely
necessary to say, that a moraine in this low district, which is not connected with
any Ben Nevis valley, and considering its required height and length, is incon-
ceivable.

In the third place, as to the existence of transverse scratches on the rocks in
Glen Spean, which are said to indicate the movement of some body from Loch
Treig, I could see no such scratches, though I twice surveyed the ground, and
narrowly inspected the rocks, especially at the outlet from Loch Treig. Indeed,
the supposition that any glacier flowed out of Loch Treig seems to be almost ex-
cluded by the fact, that a shelf, perfectly horizontal, exists on both sides of the

VOL. XVI. PART III. 5 M

412 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

narrow outlet from Loch Treig, and continuously into Glen Spean. Such a shelf
could not have been formed, and would have been obliterated by any glacier mov-
ing out of Loch Treig.

(2.) But assuming all these facts to be as M. Acassiz states them, do they
present unequivocal proofs of the movement of glaciers, and the formation of mo-
raines? Scratches on polished rocks, may be made by various causes; and if a
moraine existed on Moeldhu, surely some trace of it, or of the great blocks which
generally accompany moraines, would have been particularly observable there ;—
whereas there is scarcely a block or a patch of gravel to be seen in that part of
the valley.

Farther, I would observe, that the valley supposed to have been the birth-
place of the glacier, which produced this Moeldhu Moraine, is about two miles
distant from Moeldhu, with an undulating country between them, which is most
unlikely to have formed the channel or bed of a glacier. Dr BuckLanp and M.
Acassiz speak of this glen, as connected with Ben Nevis. But here, again, there
is apparently some mistake. The valley in question is Larich Leachich, and runs
up, not in a NW. direction towards Ben Nevis, but in a SW. direction towards the
head of Loch Treig. It is an extremely short glen, and rises to no great height.

Finally, supposing, that if, in spite of all these objections, it were allowed that
a glacier had moved down this little valley, and across the very uneven country
to Moeldhu, so as to block up Glen Roy and Glen Spean, it would still remain to
explain the blockage of Glen Gluoy, which, by no possibility, could be accounted
for by a moraine at or near Moeldhu.

That there are certain appearances in the valleys of Lochaber, which must
have been produced by attrition of some kind, I am free to admit. Water, ac-
companied by gravel and other detritus, appears, however, to have been the agent,
and not ice. At the Monessie Falls, the valley is compressed to a narrow gorge,
and the rocks forming the east side, present evident marks of attrition on a large
scale, the rough faces of the rock being all down the vallev. The rocks are here
covered by sand and gravel, which indicate the flowing of water and of drift at that
height, when these rocks were worn down. In like manner, at the outlet of Loch
Treig, there are immense expanses of rock, all smoothed and rounded on the sides
facing the SW. or WSW. by compass.* These smoothed rock-faces prevail to a
height of about 786 feet above the lake, and 1680 feet above the sea, above which
level they are no longer visible. There are many boulders lying on these
smoothed surfaces, all of rounded forms. That these boulders have come from

* The general line or axis of the lake is north and south by compass, the upper part being to-
wards the south, so that the motion of a glacier down this valley would have smoothed all the south
faces of the rocks. It is also important to remark, that, on the west side of the lake, the rocks
facing the lake are, as compared with those on the other side, exceedingly rough, shewing still more
clearly that. the smoothing agent had crossed. the valley of Loch Treig, in a direction not parallel
with its longer axis, but obliquely to it.

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 418

the west, is evident from the nature of them; several of a pink coloured felspar.
having been traced by me toa dyke of the same peculiar rock a few hundred yards
to the west, from which they had evidently been derived. Another circumstance
proved this still more strikingly. In one place, a few hundred feet above Loch
Treig, I observed a series of rocky knolls, in an east and west line. The parts of
these knolls which were smoothed and worn down were uniformly to the west.
whilst their rough faces were all to the east, thus—

It was clear, on an inspection of these knolls, that they had been worn down on
their west sides; and the smoothed sides a were so close to the knolls respectively
to the west of them, that nothing except some fluid, charged, it may have been,
with drift, could have possibly reached and acted on them.

This last point was still more palpable, in several places, where there were
narrow smooth-sided troughs, more or less steep, on the sides of hills. These
troughs had apparently been natural fissures in the rocks, which had been smoothed
by the long-continued action of water; for the notion that ice could have entered
and rubbed them, was entirely precluded by their narrowness, situation, direction,
and other circumstances.

M. Acassi1z, in the paper before alluded to, says that he will never forget the
impression he experienced “ at the sight of the terraced mounds of blocks which
occur at the mouth of the valley of Loch Treig, where it joins Glen Spean. It
seemed to me (he adds) as if I were looking at the numerous moraines of the

neighbourhood of Tines, in the valley of Chamounix.” These terraces of blocks,

thus likened to moraines, are, I presume, the accumulations of blocks on the lower-
most horizontal shelf, which is very conspicuous at the entrance to Loch Treig on
both sides of the valley. On this shelf there are multitudes of blocks, just as im
many other parts of the valleys, where this shelf and the others occur. But this
fact is perfectly consistent with the theory, that these shelves were formed by
water, and, indeed, can be explained on no other, when it is considered that they
form at Loch Treig, as at every other place, a line absolutely horizontal,—a quality
which, I presume, no moraine ever possesses.

The only place where I observed an accumulation of blocks, at all resembling
a moraine, is on the east side of Glen Spean, near a place called the Rough Burn,

Al4 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

about three or four miles to the north of Loch Laggan. The accumulation is enor-
mous. Blocks are piled over each other, to sucha height as to render the general
surface of the moor, over a wide extent, quite undistinguishable. This accumu-
lation occurs not at the mouth of any valley. On the contrary, the hills near these
blocks on the east side, are not much furrowed even by mountain torrents, and
present a somewhat steep and high wall face to the west. On looking round for
any possible explanation of the occurrence in this spot of so unusual a quantity
of boulders, consisting almost entirely of grey granites, whilst the rocks on which
they lie are different, I could not help noticing that the valley on the opposite or
west side presented an opening or depression, though at the distance of 2 miles.
This opening is the outlet of Loch Treig, and bearing about WSW. by compass.
The appearance of the locality at once suggested the probability that the blocks
had in some way issued through this opening, and had been transported across
the valley to their present situation, where their farther progress was arrested
by the lofty hills forming here the east side of Glen Spean.

I have already stated reasons for thinking that no glacier issued from Loch
Treig. The only alternative seems to be the agency of water.

I proceed now to shew that the lake theory of the Lochaber shelves, and the
principles on which I have endeavoured to account for the formation of lakes, and
the eventual depression and drainage of them, are not inconsistent with any esta-
blished geological truths,—but, on the contrary, receive support. from collateral
considerations.

1. The first circumstance which I shall notice, ¢s the occurrence of Parallel Roads
m other valleys similar to those of Lochaber, the formation of which canbe attributed
to no other cause than lakes. :

[ have the less hesitation in availing myself of this argument, when I find
Mr Darwin adverting to traces of shelves at Kilfinnin, and in the valley of the
Spey, in support of his theory.

But if Mr Darwin’s views are sound, traces of shelves should not be confined
to the two localities just mentioned ; they should be visible in other parts of the
country of equal height as the Lochaber mountains. i

On the other hand, if it should appear that there are in many valleys, distinct
beach lines, all horizontal, and presenting no uniformity of height above the sea,
the argument against a sea theory will be strengthened, whilst a strong analogy
will arise to favour the lake theory,—if these beach lines, precisely similar in all
essential features to those of Lochaber, can, from their inland situation, and other
circumstances, be clearly shewn to have been produced by the waters of lakes.

I proceed therefore to mention a few localities out of many, where phenomena
similar to those of Glen Roy are observable.

(1.) At Inverournan (about 40 miles SW. of Lochaber) there is a lake called

MR MILNE ON THE PARALLEL ROADS OF LOCHABER. 415

Loch Tulla, about 3 miles in length, and 1 in breadth. A stream enters from its
east and west ends. Its surplus waters are discharged from its south side, by the
river Urchay.

Two years ago, I discovered all round this lake indications of three levels at
which its waters had stood, the lowest being about 183} feet, the second 277 feet,
and the highest 474 feet, above their present level.* Loch Tulla I roughly esti-
mated at 540 feet above the sea. This lake, therefore, extending originally to
about 6 miles in length and half a mile in breadth, had sunk 197 feet,—at which
level it had stood long enough to form the second shelf; it next sunk 933 feet,
—when the third shelf was formed ; after which it sunk 1834 feet,—viz., to the
present level of the lake.

It is unnecessary for me to enter into the proofs, that what I am now describ-
ing are really beach lines. Their perfect horizontality, which I ascertained by a
spirit-level, looking at them from 12 or 15 different places along the banks of the
lake,—their general conformity in sweeping round headlands, and retiring into
valleys or burn-courses,—and the extent of flat surface at the levels of the different
shelves, afford convincing and irrefragable proofs.

The difficulty here, as in other similar cases, is to discover, what could have
dammed up the lake so much above its present level. The blockage, whatever
it was, must have existed somewhere in the valley, through which the river Urchay
flows. The country, on all other sides of Loch Tulla, rises much higher than 500
feet above its present level. The two lowest shelves are traceable for some dis-
tance down the valley of the Urchay,—the middle shelf for about half a mile, and
the lowest considerably farther. My notion is, that this valley had been formerly
filled with a great accumulation of gravel and diluvial debris, which was gradually
eat away and lowered by the stream which issued from the loch. Accordingly,
there exist still, at and near Urchay Bridge, great heaps of unstratified gravel,
which clearly present only a remnant of what must have formerly existed. The
valley at this place, is a quarter of a mile wide; and its sides rise far above the
required level. |

(2.) In the valley, at the head of which Tyndrum is situated, there are very
manifest indications of the beaches of an ancient lake, although the valley is now
occupied by only an insignificant stream. At Strathfillan church, the lowest
terrace is about 50 or 60 feet above the stream, and may be traced continuously
for at least a mile down the valley. The stream has cut through this old lake
bottom, exhibiting beds of gravel, sand, and clay, which have been deposited and
arranged by the water. About 237 feet above this flat, there are, on the sides of
the hills on both sides of the valley, traces of a horizontal shelf, which can be
distinctly followed with the spirit-level from above Tyndrum village, down the
valley by Auchreach farm-houses, Enich farm-houses, and as far as Crianlarich

* These measurements were made by a mountain barometer, checked by the sympiesometer.
VOL. XVI. PART III. SN

416 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

toll. At several places, boulders appear to have accumulated on this higher shelf.
Tyndrum is about 740 feet above the sea.

(3.) Along the margin of Loch Awe, and particularly near Dalmally, there
is a flat or terrace about 40 feet above the present level of the lake; and which
manifestly indicates a subsidence of its waters to that depth.

(4.) Along the margin of Loch Lubnaig, in like manner, there is a flat or
terrace about 40 feet above the lake, and which is very visible on both sides. Here
as well as in the former case, the flat runs back from near the margin of the lake
to the mountains forming one side of the valley; and the steep sides of which,
contrast most significantly with the almost horizontal flatness of the ancient and
exposed bottom.

At Loch Lubnaig, the flat can be traced for a considerable way on both sides
of the valley, beyond the point where the lake now discharges itself, and, indeed,
almost as far as Leny. At this place, as well as at Callendar, there exist. indica-
tions of enormous quantities of gravel, which, before being cut down and carried
away by rivers, afforded ample means of blocking up the waters of Loch Lub-
naig to a higher level. The quantity of gravel which formerly existed hereabouts,
may be inferred from the existence of the following remnants.

About + mile west of Callendar, there is a ridge of gravel and sand about
100 yards long, and from 40 to 50 feet high. Near it, there is a conical mound
of the same materials, and about the same height, bearing a thriving planta-
tion. The ridge of gravel to the east of Callendar, designated in guide-books as
the Roman Camp, is merely a remnant of the ancient gravel-bed with which
the whole valley was filled; and when it contained a lake, of which there are
abundant indications, it is probable, that, when Loch Lubnaig stood 40 feet
above its present level, its waters were discharged into a lower lake, of which the
eastern margin may be seen near the Lodge of Gart-House. Ultimately the gra-
vel heaps which held in this Callendar lake on the east, had been cut through,
so as to allow of its drainage; and, accordingly, there are, on each side of the
river Teith at this place, gravel banks and cliffs from 70 to 80 feet high.

After the Callendar lake was drained, the waters which flowed out of Loch
Lubnaig would acquire fresh cutting power, and would rapidly eat away the bar-
rier which dammed back the lake to the higher level before referred to.

Callendar is about 270 feet above the sea.

(5.) In the valley in which the town of Huntly stands, there are two ter-
races, the one about 32 feet above the other, which are very clearly the beaches
of a lake, which has sunk from the one to the other, and latterly been drained
off.

(6.) A few miles south of Inverury, there are distinct traces of a lake which
formerly filled the valley. The burgh of Kintore has been built in the ancient bot-
tom of the lake. There are two well-marked beach-lines round the whole valley ;

MR MILNE ON THE PARALLEL ROADS OF LOCHABER: 417

the one about 78 feet, and the other 50 feet, above the channel of the united
streams of Don and Urie, which flow through the centre of the valley. The an-
cient bottom of the lake has been cut up by rivulets at the sides of the valley
into separate fragments, some of them of so unusual a form as to have suggested
a notion that they are artificial; and, accordingly, in the guide-books, and even
in the recent statistical accounts of the parish, they are so described. Two of
these alleged remains of antiquity are known by the names of Bass and Konin
Hillock; and are variously conjectured to have been formed for sepulchral or judi-
cial purposes. A similar mistake has been made with the hills of Dunipace.
near Falkirk, which are represented by historians as formed to celebrate and re-
cord a peace between the Romans and the natives of Scotland. They are detri-
tal remnants fashioned into conical shapes by the action of streams.

(7.) In the valley of the Leader (Berwickshire), there will be found terraces on
the hill sides, which clearly shew the action of water. Three very distinct mark-
ings of this nature are traceable near Dodds’ Mill, at Hounslow, at Carfrae Mill.
and at Annfield near Channelkirk. The terraces at these different places, judging
by the sympiesometer, seem to be all very nearly on a level; and if, on a more
minute survey, they really prove to be so, it would follow, that the whole of Lau-
derdale had formerly been one vast lake, with a blockage at or near Chappel.
The height of these shelves is about 800 feet above the sea.

It is scarcely necessary to advert to the inland situation, and other circum-
stances characteristic of the various beach-lines now mentioned, to shew that they
could not have been formed by the sea, but must have been produced by lakes
which filled the valleys, and which sunk at different periods,—in most cases, dis-
appearing altogether.

If, then, the existence of lake-beaches be so common in the valleys of Scot-
land, there will be the less hesitation in ascribing the Lochaber shelves to the
same cause,—established as that cause has been separately by local evidence.

That the occurrence of lake-beaches in the valleys of Scotland should be fre-
quent, is only what every geologist must be prepared to expect, who considers
the proofs which may be adduced, of the gradual emergence of the land out of
the sea. Some of these proofs, in so far as afforded by Scotland, I shall imme-
diately notice; but assuming that Scotland was, to the depth of 1300 feet or
more, submerged beneath the waters of the ocean,—as it rose out, there would be
lakes in every inland hollow, each, of course, having its river to carry off to the
sea, the rain falling on its surface and that of the adjoining mountains. The
stream thus issuing, would gradually wear down the detritus whick formed a bar-
rier at one end of the lake; and the cutting power of the stream would be gra-
dually increased, as the elevation of the land proceeded ; so that in most cases
the blockage of lakes would, in the course of time, be extensively undermined

418 MR MILNE ON THE PARALLEL ROADS OF LOCHABER.

and worn down, and sudden depressions of lakes would take place, leaving marks
of horizontal shelves along the sides of valleys.

The progress of these important changes is indicated, in many parts of the
country, by the existence of haughs or river-flats, far above the present channels
of the streams, and which evidently had been formed when they flowed at a
much higher level.

Thus, from Perth up to Loch Tay, a number of isolated flats or terraces oc-
cur, forming a pretty uniform level, rising gently inland, and at a rate rather
faster than the slope of the river. Near Perth, these old haughs are from 90 to
100 feet, and at Dunkeld about 110 feet, above the river. This old haugh at Dun-
keld may be traced on both sides of the valley,—Dr Fisher’s house being on it at
the east side, and Claypotts farm-house on it at the west side. It may even be
traced a considerable distance up both sides of the Braan, where it slopes a little
to the eastward.

There is a low haugh at Dunkeld which is only about 20 feet above the pre-
sent bed of the river, and is, therefore, quite distinct from the higher terrace
above described. The ground is now cultivated and enclosed; so I suppose that
the floods never rise to a level with it now.

On the Tweed, in like manner, the remains of ancient haughs can be traced
in many part of its course. About half a mile above Berwick Bridge, one may
be seen on the south side, from 30 to 32 feet above the sea. At Gainslaw, it is
44 feet ; opposite to Finchie, it is 55 or 56 feet ; opposite to Paxton, it is 58 feet ;
at Norham, it is 93 feet above the sea.

At New Rattray (in the parish of Blairgowrie) I observed an extensive flat, or
ancient haugh, with its cliff or bank about 80 feet above the River Ericht.

On the Isla, above Airley Castle, there is haugh land, on both sides, about 30
feet above the present level of the river.

On the River Garry, about 34 miles north of Blair, there are on the east side
two terraces, the one about 30 and the other about 50 feet above the river; but
whether they are the remains of ancient haughs, or the beaches of a lake, it is
difficult to determine.

(waters

XXVITI.—Memoir of Dr THomas CuHaRLEs Hope, late Professor of Chenustry m the
University of Edinburgh. By THomas Stewart Trait, M.D., F.R.S.E., Pro-
_ fessor of Medical Jurisprudence in the University of Edinburgh.

(Read December 6, 1847.)

It is presumed that a notice of the life and labours of oNE, who was, for
more than fifty years, a most skilful and successful teacher of chemistry in the
Universities of Scotland, where he was the instructor of more than 15,500 pupils;
who initiated in that interesting science many who now hear me; who long filled
the office of vice-president amongst us, will not be unacceptable to the Royal
Society of Edinburgh.

Tuomas CHARLES Hore was a son of Dr Joun Hops, the first Regius Professor
of Botany in the University of Edinburgh, and of Jutiana STEvENson, daughter
of an eminent physician in that city.

Professor Joun Horr was a grandson of Lord RANKEILLOR, an eminent Scottish
judge in the early part of the last century, and son to Mr Roperr Horr, a respect-
able surgeon in Edinburgh. Professor Hope died in 1786, at the age of 62.
His family consisted of four sons and a daughter. Rosert, the eldest, was bred
to the bar, but died in early life; Marianne married JAMES WaLKER, Esq., of
Dalry, and died in 1837, leaving an only daughter, who became the wife of Sir
JoHN WALL; JOHN, a Major in the army, who died in 1840; THomas CHar es, the
subject of this memoir, who was born on the 21st of July 1766, and died on the
13th of June 1844 ; James, a writer to the Signet, who died in 1842, leaving several
children.

Tuomas CHARLES, the third son of Dr Joun Hope, received the elements of
his classical education in the High School of Edinburgh, to which he was sent in
1772; but in 1778 he was removed to a school at Dumfries, and was, 1779,
entered as a student of general literature in this University, at the early age of
thirteen ; a practice still too common in this country. There he pursued the
usual curriculum of general study, before he began to apply to medicine.

As was natural, he had devoted much attention to Botany, and, under his
able father, had made such proficiency, that on the death of the latter in 1786,
he aspired to the Botanical Chair; and, though supported by the influence of Sir
JosePH Banks, Sir GrorGE Baker, and even by the favour of Royalty, the all-
powerful influence of Mr Dunpas prevailed, and he was unsuccessful. In June
1787, he obtained the degree of Doctor in Medicine at our University. Dr Irvine,
who held the Lectureship of Chemistry in the University of Glasgow, having
died in the following month, Dr Horr was appointed to fill the vacant chair, on

VOL. XVI. PART IV. 50

420 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

the 10th of October of the same year; and thus a new field was opened to his
ambition.

It was no easy task with which young Hope had to grapple. The Glasgow
Lectureship had been successively held by men of consummate abilities, and
high chemical acquirements. The immediate predecessors of Dr Irvine, had
been Dr Ropison, Dr Buack, and Dr CuLLEN; men whose names will ever stand
conspicuous in the science of Scotland. Instead of acting as a discouragement,
this consideration only stimulated Dr Horr to make every effort to prove himself
no unworthy successor of these eminent teachers of chemical science. With
the general doctrines of chemistry he was well acquainted; he possessed
ingenuity in devising illustrative experiments, and a rare delicacy in chemical
manipulation. Yet, as he has confessed to the writer of this memoir, from the
shortness of the period for preparation, the scantiness of his apparatus, and the
utter want of assistance in his laboratory, he regarded his first course of chemistry
as very imperfect. But the novelty of his mode of teaching, and the neatness
of his experiments, seem to have won the approbation of his auditory.

He was, at that period, a strenuous supporter of the then generally received
doctrines of Srani—that inflammable bodies owed that quality to the presence ofa
principle which was termed phlogiston, and of course taught that doctrine in
this his first course of lectures. But his conversion to the Lavoiserian or French
theory of chemistry was at hand.

It is generally known, that from 1777, Lavoisier had doubted the existence
of such a principle as phlogiston, and in 1785 proposed the antiphlogistic theory,
supported by such facts and decisive experiments, that his views were speedily
adopted by his own countrymen ; though for a considerable time afterwards, they
were not received in Britain.

The late Sir James Hatt happened to pass the winter of 1787 in Paris, and
was much in the society of Lavoisier, who showed great anxiety to make a con-
vert of Sir James, and, through him, to spread his doctrines among British
chemists. For this purpose he not only gave Sir James free access to his papers.
but exhibited to him several verv important experiments, even before they had
been communicated to the Academy of Sciences, or made known to the chemical
world in general. Sir James Hatz returned to Scotland in the autumn of 1787, well
versed in the new doctrines, of which he became an able and zealous propagator.

_He had many long discussions on this subject with Dr Horr, who was then a
keen supporter of the phlogistic hypothesis, but was soon convinced by the argu-
ments and facts communicated by his friend ; and next winter he taught them
to his class, the first occasion on which the Lavoiserian doctrines were introduced
in a public course of lectures in Great Britain.

In the beginning of 1783 Dr Horr was admitted as a Fellow of this Society ;
and soon after he resolved to pass the summer vacation in Paris.

MEMOIR OF THE LATE DR THOMAS CHARLES HOPE. 421

In his way to the French capital, he made a short stay in London, where he
was very kindly received by Sir JosepH Banxes ; and he had the high gratifica-
tion of being introduced to CavEeNbisH, BLacpEN, HeErscHEL, and several
other English philosophers.

At Paris he experienced marked attention from LAvoIsiER and BERTHOLLET ;
which he ascribed partly to his having been a pupil of Dr Buack ; but was princi-
pally, I believe, owing to his having been the first chemist who had publicly
taught the new French doctrines in Great Britain.

Dr Hore considered this an important era in his life, as introducing him to
men whose names were then becoming celebrated over Europe for their skill in
a science to which he was ardently devoted. The amiable manners and great
abilities of LavoisiIER made a deep and lasting impression on the Scottish profes-
sor; and few persons more sincerely deplored the sad fate of that accomplished
man, from whom he had received the most flattering attentions.

During his connection with the University of Glasgow, Dr Horr enumerated
as his colleagues and hisfriends, Dr Tuomas Rep, the celebrated Professor of Moral
Philosophy ; the eminent Mr Jonn Mitisr, Professor of Law; and Mr Grorce
JARDINE, Professor of Logic.

Dr Hore, for some years, entertained the wish to join the practice of
medicine with his chemical labours; and in 1789, sought and obtained the
appointment of assistant Professor of Medicine, and successor to his uncle Dr
STEVENSON in the University of Glasgow. For two years he taught the Theory
and Practice of Medicine, at the same time with Chemistry. On the death of his
uncle, in 1791, Dr Horr became the sole Professor of Practical Medicine, and
then resigned the office of Lecturer on Chemistry ; but he continued his private
researches in his favourite study, the first result of which was his masterly
paper ‘“ On a new mineral from Strontian.”

This was communicated to the Royal Society of Edinburgh on the 4th Nov.
1793; and it proved, what indeed had been previously conjectured by others,
that this mineral contained a new earth, differing decidedly in its qualities from
Barytes, to which it bears the greatest affinity. To this earth Dr Hore gave the
name of Strontites, from the place at which it had then only been found. From
the appearance of this mineral, which had been, I believe, first noticed, about six
years before, by Dr Waker, Professor of Natural History in Edinburgh, it was
generally supposed to be a variety of heavy-spar, or perhaps might contain a new
ingredient. Yet Kirwan, in the Second Edition of his Mineralogy, published
late in 1794, takes no notice of Strontites; except we may consider such, his
statement, “that he had heard of the discovery of Larolite, or aerated Barytes in
Argyleshire ;” and ScuMmEisser, whose “ Mineralcgy” appeared in London two
years after the reading of Dr Hopr’s paper, disingenuously passing over his ex-
periments, states, “by analysis I found it yielded 68 of Strontian earth, 30 of

422 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

carbonic acid, 1 of calcareous earth, and a little of phosphate of iron and man-
ganese, which probably gives it colour.” This would lead the unsuspicious
reader to infer that ScumeEIssEeR had been the discoverer of the new earth, which
is certainly not the case; but this is only one of the many plagiarisms of this
writer. The only chemist who has the slightest claim to the merit of an original
detecter of Strontian earth, besides Dr Horr, is M. KiarrotH; who, in the
Chemische Annalen for 1793-94, compared Strontianite with Witherite. In his
first paper, KLAPRoTH conjectured that the two minerals differed in composition,
because the salts of Strontian colour the flame of combustibles red, while those
of Barytes do not; and this conclusion was afterwards confirmed by some expe-
riments of SutzeEr and Brumenspacu. Neither Kiaproru nor Hore seem to
have been aware of what the other had discovered, and both may therefore be
considered as original discoverers, but the first full investigation of the subject is
undoubtedly due to Dr Hope. .

The success of these investigations, and the popularity of Dr Hopr’s Chemical
Lectures at Glasgow, suggested to the celebrated Dr Brack, then in declining
health, the idea of having his promising pupil Dr Horr associated with him, as
his assistant and successsor in the Chemical Chair. He accordingly made the
proposal to Dr Hore in 1795, obtained the concurrence of the Patrons, and on
the 4th of November of that year, the latter body chose Dr Hore in that capacity.
In that session but a few of the lectures were delivered by Dr Hore: But in the
session of 1796-97, after Dr Buack had concluded his admirable Lectures on
Heat (as I find from M.S. notes of a friend who attended that course), the
venerable Professor introduced Dr Hore to the class in the following terms :—
“‘ After having, for between 30 and 40 years, believed and taught the chemical
doctrines of Staut, I have become a convert to the new views of chemical
action; I subscribe to almost all M. Lavorsrer’s doctrines; and scruple not to
teach them. But they will be fully explained to you by my colleague and friend
Dr Horr, who has had the advantage of hearing them from the mouth of their
ingenious author.” Accordingly, Dr Hore delivered a considerable portion of that
wintercourse to a large audience; and in the summer of the year 1797, he also
gave a three months’ course of Chemistry.

The eminent men who were at that time the ornaments of our University,
were Professors Monro secundus, BLAcK, GREGORY, Rogpison, DucaLD STEWART,
and PLayrair—and Hore always remembered with much satisfaction his earlier
intercourse with Principal Ropertson, ApAmM Smits, and especially with
Hutton the geologist—a constellation of names that shed a lustre on the society
of Edinburgh at hat period.

It would seem that the subject of our memoir still intended to conjoin the
practice of medicine with his academical duties. For this purpose, he became a
Fellow of the Royal College of Physicians in November 1796; and, until some

ei

{os =. 2

MEMOIR OF THE LATE DR THOMAS CHARLES HOPE. 423

time after the beginning of this century, regularly took his share of the duties of
Clinical Professor of Medicine.

Dr Biack, who was always of a most delicate constitution, did not feel him-
self able to lecture after the session of 1796-97 ; but the life of this truly great
philosopher and most accomplished teacher, was protracted to the 14th of
November 1799. On his death Dr Hore became the sole Professor of Chemistry
in our University. ;

It was in the Session of 1798-99, that the writer of this memoir first became
Dr Hore’s pupil ; and he remembers, with gratitude, that it was from the clear and
able prelections, and most happy experimental illustrations of the leading principles
of the science by Professor Horr, he imbibed that predilection for chemical pur-
suits, which long formed his chief relaxation from the severer duties of his pro-
fessional life ; and which, he hopes, will continue to afford interest and amusement
to his declining years.

I may here remark, that Dr Horr had become, from the variety and excellence
of his illustrations, and dexterity in chemical manipulations, the most popular
teacher of the science that had ever appeared in Great Britain. Not only was
his lecture-room crowded with medical students from every part of the British
dominions, but numerous foreigners resorted to Edinburgh, and became his pupils.
Many of our nobility at that time were among his students. During one of the
winters that I attended his class, among my fellow-students were the late Earl
of LAUDERDALE, the present Earl (then Lord Mairuanp), Lord Sempiuy, and
the late Lord Asupurron. The large class-room was filled to overflowing ;
and he who was not there before the commencement of the lecture had no
chance of a seat.

The rage for chemistry continued for several years; and certainly no chemist
ever had larger audiences than Dr Horr. I find that the average number of chemical
pupils here, during the six years preceding Dr Hore’s appointment as Dr Biack’s
assistant and successor, was 225. When I attended him in the end of the last
century and beginning of this, his annual pupils were above 400; in 1813 they had
risen to 500, and in 1827 they had actually amounted to 575.

While Hore lectured at Glasgow, the total number of his pupils amounted to
about 300. After his removal to Edinburgh, his chemical lectures were attended
by 15,500 persons, and the number of tickets issued for his chemical class was no
less than 16,800.

His reputation as a lecturer induced a number of the Faculty of Advocates
to request him to give a summer course of chemistry in 1800; which was also
attended by many gentlemen engaged in other pursuits.

-I shall now offer some remarks on the original investigations in which Dr
Hore at different times engaged, after his paper on Strontites.
It is well known that Boye, Mariorre, and other philosophers, ascertained
VOL. XVI. PART IV. 5P

424 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

experimentally, that the diminution of bulk in atmospheric air is always propor-
tional to the compressing force ; or its volume is inversely as the pressure which
it sustains; and philosophers had generally, from analogy, inferred the same of
other gases.

I find, from some notes of Dr Hops, that in 1803 he instituted a series of
experiments to ascertain “ whether the principal permanently elastic fluids, viz..
oxygen, nitrogen, hydrogen, and carbonic acid, observe the same law of compres-
sibility from pressure which air does.”

In these experiments the compression was obtained by means of a column of
mercury in a siphon tube, in the same manner as in the experiments of BoyLe,
and of later experimentalists. The result was, that they all follow the same
law of compression.

On the 9th of January 1804, Dr Hore read a memoir to the Royal Society of
Edinburgh, “ On the contraction of water by heat, at low temperatures,” which
appeared in the 5th volume of the Transactions, in 1805, p. 379.

The Florentine Academicians had published, in 1667, the singular fact, that
water expands as it cools towards its freezing point; and in 1683, the same was
stated to the Royal Society of London by Dr Croune, the Gresham lecturer.
His experiments shewed that water, when cooling, begins to expand as its
temperature sinks, from several degrees above the freezing point, untilit begins
to congeal. Several subsequent writers endeavoured to confirm these observations,
but differed as to the point at which water attains its maximum density; some
contending for the 40° or 41° of Fahrenheit ; others for the 42° or 43°. All those
experiments were made ih tubes with large bulbs at one extremity, resembling
in form the glass of a thermometer, but on a larger scale.

On the reading of CRouNE’s paper, it was contended by Dr Hooks, one of the
most acute but most disputaceous philosophers of his age, that this expansion
was apparent, not real; arising from the sudden contraction of the material of
the bulb, on the application of cold. This opinion has since been maintained by
several very eminent men; among whom we may mention DaLron, whose experi-
ments on this subject are most ingenious, and who, in a private letter, drew Dr
Horr’s attention to this curious phenomenon. It occurred to Dr Hors, that this
point might be decided by experiments, in which a change in the capacity of the
containing vessels could have no influence on the result.

He took a cylindrical glass vessel, 85 inches deep and 44 inches wide, which
was filled with water at the freezing point, 32°. Two delicate thermometers were
suspended in the axis of the jar, so that the bulb of one was half an inch below
the top of the liquid, and that of the other as far from its bottom. This apparatus
was placed inaroom at a temperature 60°, and the progressive temperature of the
water was carefully noted, as indicated by both thermometers. The result was,
that up to 38°, the lower thermometer was invariably one degree higher than the

MEMOIR OF THE LATE DR THOMAS CHARLES HOPE. 425

upper; a proof that, as its temperature rose from 32° to 38°, the water had
become more dense. On reversing this experiment, by placing water at 53° ina
medium cooled to 32°, he found, while the temperature of the water descended to
40°, that the water at the bottom was always the coldest, and that this difference
between upper and lower thermometers was sometimes as much as 7° or 8°; but
that in cooling from 40° to the freezing point, the thermometer at the bottom
remained higher than that near the surface of the liquid. |

The experimentsof Dr Hore, which were varied in different modes, led him to
fix the point of greatest density of water at the temperature of 39°°5 Fahrenheit.

These well-devised though simple experiments are perfectly conclusive on
the question of the greatest density of water being several degrees above its
freezing point ; and Mr Darron, the most able advocate of the opposite doctrine,
afterwards admitted the general correctness of the observation, though he con-
sidered that the greatest density was not at so high a point as Dr Hore supposed.
There are, however, many facts which would lead us to infer, that the greatest
density of water cannot be far from the point assigned by HopE—as, for instance,
the remarkable uniformity of temperature in deep alpine lakes, which is about
40°, according to the observations of Picrrr and others.

From a long note attached to this paper of Dr Hopr*® we also learn, that at
an early period he had experimentally proved the fallacy of Count Rumrorp’s
assertion, that liquids were absolute non-conductors of heat. This philosopher
had alleged, that when heat was applied to the upper surface of a fluid, the heat
could only affect a thermometer placed below the surface of the liquid, by trans-
mission downwards through the medium of the sides of the containing vessel ;
because, according to him, the particles of fluids communicate none of the caloric
they receive to the contiguous particles (as takes place in solids), and that when
heat is applied below, they become heated only by currents set in motion by the
diminished gravity of the heated particles.

In these experiments, Dr Hop employed a wide glass jar to contain the
liquid to be the subject of trial, and applied heat to the surface of the liquid in a
vessel 11 inches in diameter. The bulb of a delicate thermometer was placed
half an inch below the surface of the liquid ; and all conduction by the sides of
the vessel was prevented, by keeping it immersed in water equally cold as high
as the surface of the liquid within the vessel. Notwithstanding these precautions,
the thermometer, in several experiments, slowly rose. The liquids subjected to
such trials were water, olive-oil, and mercury.

Other experimerfts were conducted in a different manner. Equal portions
of liquids, such as alcohol, were rapidly mixed together at different tempera-
tures ; and the mixture immediately indicated a mean temperature—which Hors

* Trans. R. Soc. Edin. V., p. 394.

426 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

contended could not have happened, if liquids had been absolute non-conductors
of caloric.

These experiments seem sufficiently conclusive; but Count RumForp still
insisted, that the rise of the thermometer was only owing to the conduction by
the sides of the containing vessel, in Hopr’s experiments, as well as in the
analogous investigations of THomson, NicHonson, and Darton.

This objection suggested to the late Dr Joun Murray the ingenious idea of
employing a hollow cylinder of ice as the containing vessel ; which, as its tem-
perature could not rise above 32°, could not conduct or communicate any heat to
the thermometer. Water could not be employed in this apparatus, on account
of its anomaly in expanding by cold near its freezing point; but olive-oil,
cooled to 32°, was used; and in experiments made by suspending the heating
cause in contact with the surface of the oil, the thermometer rose, in a longer or
shorter interval, in proportion to the greater or less depth of the instrument below
the surface of the oil~—(Wicholson’s Journal, 8vo series, I. 425.)

In considering these experiments and the objections stated, it occurred to
me, that if the same apparatus were employed with different fluids, did the rise
of the thermometer depend on the conduction of the sides of the vessel, that rise
should be nearly equal, whichever liquid was employed. I tried this with ten
different Jiquids; and though the apparatus was the same, and the distance
between the source of heat and the thermometer similar, yet the time required to
raise the thermometer to the same point, was very different with the different
liquids: this I ascribed to the difference in the conducting power of each liquid.— —
(Nicholson’s Journal, XII. 137, for 1805.)

All these investigations confirmed the view taken by Hops, that though
liquids were very slow conductors of caloric, they could not be considered, as was r
alleged by Rumrorp, absolute non-conductors. | '

Dr Hore’s reputation as a teacher of chemistry, arising from the causes —
already noticed, and his tact in exciting in his hearers his own enthusiasm for ‘
the study, long continued to attract vast crowds of pupils. His honours kept
pace with his reputation.

In 1810 he was elected a Fellow of the Royal Society of London ; in 1815 he ©
was chosen President of the Royal College of Physicians of Edinburgh, an office
which he continued to fill for four successive years; in 1820 he was admitted an
honorary member of the Royal Irish Academy ; and in 1823 he became one of the
Vice-Presidents of this Society, an office which he held until his death. During his
connection with the College of Physicians, he took an activé part in the prepara- ;
tion of the ninth and tenth editions of their Pharmacopeeia, especially in that
published in 1817. For several years, besides his duties as a Professor of Che-
mistry, Dr Hore gave an annual course of Clinical Medicine in this University,
which was also numerously attended. But for many years before his death, he

.

MEMOIR OF THE LATE DR THOMAS CHARLES HOPE. 427

resigned to his younger brethren the duties of the Infirmary, and of Clinical
instruction.

Dr Hore is the author of a decided improvement on the Eudiometer of
ScHEELE, which, by permitting the convenient agitation of the included air with
the liquid that absorbs the oxygen, expedites and simplifies that process; and
is described in most elementary works on Chemistry.—(See Nicholson’s Journal,
mol. VI.)

The establishment of Mechanics’ Institutions, or Schools of Art for the
instruction of the humbler classes, gave to that rank of society means of acquiring
information beyond that usually obtained by many of the wealthier classes; and,
in the opinion of some, diminished the respect of mechanics for individuals less
knowing than themselves. The system of courses of popular lectures on scientific
subjects for hoth sexes, which had prevailed for many years in various parts of
England, was comparatively little practised in Scotland, when Dr Hore delivered,
in the spring of 1826, a short course of chemical lectures to Ladies and Gentle-
men. His vast lecture-room was crowded with what he described to me as
a ‘“‘most brilliant audience ;” and his example was soon followed by more than
one of his colleagues in the University, and by several of the eminent men who
then taught different branches of natural science in their private establishments ;
undoubtedly with no small benefit to the rising generation, and the more general
diffusion, among all ranks, of interesting subjects of contemplation, and of con-
versation. Even admitting that the knowledge thus diffused is not deep, it has
imparted to social intercourse, a vigour and variety that contrasts favourably with
the former insipidities and frivolities of fashionable society.

Dr Hors had always endeavoured to impress his pupils with the importance
of Practical Chemistry, and introduced into the University classes for the cultiva-
tion of that branch of study; but, from increasing years, and love of ease, this
department he soon almost wholly abandoned to his assistants.

In 1828, to encourage the study of chemistry among the students in the
University, particularly in the practical department, he instituted a chemical
prize ; and, for this purpose, presented to the Senatus Academicus a sum of £800,
as a fund, the interest of which should, annually or triennially, be given as a
prize to the author of the best essay on a given chemical subject, illustrated by
experiment. It should be observed, that money thus liberally bestowed, was the
sum which Dr Hore had received for his popular lectures on chemistry, which he
appears from the beginning to have destined for this purpose.

For many years Dr Hore appears to have abandoned the pursuit of original
research, with which he had so auspiciously commenced his chemical career, and
to have confined his efforts to the improvement of his lectures, and the devising
of striking experimental illustrations.

I find no original paper of his, from the publication of his investigations on

VOL. XVI. PART IV. 5Q

428 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

the conducting power of fluids, until the 18th January 1836, when he read, to
the Royal Society of Edinburgh, the first part of a paper entitled, “Observations and
Experiments on the coloured and colourable matters in leaves and flowers of plants, upon
which acids and alkalies act in producing red, yellow, or green colours.” A second
part of this paper was laid before the Society on the 21st of the following March.

Although chemists have at all times used coloured vegetable infusions for
indicating the presence of acids and alkalies, no researches appeared to have been
made on the peculiar vegetable principle on which the acid and alkali acted ; and it
was generally taken for granted that both descriptions of agents acted on one and the
same principle. Dr Horr endeavoured to shew, by various experiments on the gene-
ral colouring matter of plants, that vegetable infusions, which became red by the
addition of an acid, and green or yellow by an alkali, contained two distinct prin-
ciples, on one of which acids acted, and alkalies on the other. To the former he
proposed the name of Lrythrogene, and for the latter that of Xanthogene. DEcAN-
DOLLE had distinguished the colouring matter of flowers by the name of Chromule ;
and Exxis speaks of the substance which may become green, red, or yellow, under
different circumstances, as the colowrable matter of plants. The object of Dr Horr’s
researches was to prove, that this matter was not an individual substance, but
consisted of two distinct vegetable principles, which exist either separate or com-
bined in different plants. He illustrated this by many experiments on different
sorts of plants, and gave the results in eight tables. He shewed that all green
leaves, all white and yellow flowers, contain only one of these principles, viz.,
Xanthogene, that all red and blue flowers, also all leaves with red colours, contain
both Xanthogene and Erythrogene (with the single exception of Litmus, which
contains no Xanthogene), and that red flowers abound in Erythrogene. The
distinct nature of these proximate principles of vegetables he inferred from the
different modes in which they are affected by chemical re-agents.

In the same year Dr Hore made a communication to the Society “ On the
Chemical Nomenclature of Inorganic Compounds.” He pointed out the disadvan-
tages of the want of a discriminating and uniform nomenclature among teachers
and writers on chemistry; and stated certain changes which he had for some
time employed in his lectures.

The changes proposed were—

1. To discard the prefixes proto, per, super, sub, for compounds.

2. To adopt rigidly the happy suggestion of Dr THomson, viz., to employ the
Greek numerals to denote the number of atoms or equivalents of the base of a
compound, and the Latin numerals for the number of atoms of the oxygene
or acid.

3. To avoid as much as possible the intermixture of Greek and Latin in
numerical indications.

.

.

MEMOIR OF THE LATE DR THOMAS CHARLES HOPE. 429

He added examples thus—

1 atom of base to 1 of oxygene, oxide of base.

1 Bile 2 aati bis oxide.

1 vee 3 ses ter oxide.

2 atoms of base to 1 of oxygene, dis oxide.
3 tee 1 ate tris oxide.

2 ane 3 a dis-ter oxide.

and so forth.

The general adoption of some such nomenclature, he conceived, would give
a desirable accuracy to chemical language.

In a conversation with Dr Hopr in the early part of 1837, I noticed the dis-
cordant opinions held by various philosophers on the maximum density of sea-
water, and asked whether he had applied to this fluid the same beautiful and
simple investigations by which he had ascertained the point of greatest density
in fresh water. He replied in the negative. I strongly recommended the subject
to his notice; because, as it appeared to me, several geologists and hydro-
eraphers had deduced erroneous explanations of certain phenomena in the ocean
from this undecided point. I added, that I should long ago have attempted to
solve it, had I not considered that it would have been an interference with a sub-
ject he had already so ably discussed. He thanked me for the hint, and the
consequence was, the completion of the series of experiments, which he commu-
nicated on the 2d of April 1838, to the Society, in an “ Inquiry whether sea-water
has its maximum density at some degrees above its congealing point, after the manner
of fresh water.” Most philosophers seem to have assumed, that sea-water followed
the same law in cooling as fresh water; and its greatest density was generally
considered to be at temperature 363° F.

Dr Hore first tried the effect of cooling sea-water from 40° in vessels shaped
like large thermometers, and found that it continued to shrink, by a diminution
of temperature, like other bodies. He afterwards employed the same apparatus
with which he had examined the peculiarity in fresh water; and he found, that
in cooling from 40° to its freezing point, the coldest water was invariably at the
bottom of the vessel. Therefore, the striking anomaly which so remarkably dis-
tinguishes the cooling of fresh water, does not take place in sea-water. The
importance of this conclusion will be manifest to those who have examined the
theories of oceanic currents, and the remarkable fact, that the existence of banks
or shoals in the ocean is marked by a fall in the temperature of the superin-
cumbent water.

Dr Hore reserved the examination of the precise point of the maximum
density of sea-water for a future communication—which was never made.

In 1848, the Society had two communications from Dr Horz. The first
was—“ Observations on the Flowers of the Camellia Japonica, Magnolia Grandi-

. flora, and Chrysanthemum Leucanthemum.” This paper was read on two evenings,

430 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

the first on the 23d of January, the last on the 3d of April. The author, from
the action of different re-agents on infusions of these flowers, established the
existence in each of a distinct proximate principle, which, however, he had been
unable to exhibit in a separate state; to these he gave the name of Camelline,
Magnoline, and Chrysanthemine. He shewed, also, that notwithstanding the fine
white of the petals of Camellia Japonica, they contained much iron.

The second paper, his last communication, was read on the 1st of May 1843,
the very last time that Dr Hore was ever at the meetings of our Society. It
is styled “An Attempt to explain the Phenomena of the Freezing Cavern at .
Orenburg.”

This cavern is described by Sir Ropertck Murcuison, as one of several
occurring in a low hill of Gypsum. In winter, the air of this cavern feels warm
to those who enter it; but in summer an intensely cold air issues from it. This
has been explained by Sir Jonn HERscHEL, as being produced by the long time
the waves of heat and of cold take to penetrate to the interior of the cavern—
each requiring six months to penetrate to that depth; just as SAussuRE found,
that it required, at Geneva, six months for the heat of summer, or the cold of
winter, to penetrate to the depth of 294 feet. While admitting this general ex-
planation, Dr Hore considered that it would require something more to explain
the forcible issue of such cold air during the summer months; and he makes an
ingenious conjecture, on the part performed by the air cooled in the fissures,
described as existing in the inmost recesses of the cavern, in producing that
phenomenon.

The subject is very interesting though obscure ; but I may observe that such
streams of cold air are not peculiar to the Orenburg cave. Streams of air, cooled
from 15° to 34° below the external air in the shade, are known to issue from the
crevices of the small artificial hill at Rome, named Monte Testaccio ; from the
limestone grottos of Cesz, in the Roman states, so well described by Saussure, in
Journal de Physique for 1776; from the caves in the sandstone hill, on which is
perched the miniature republic of San Marino ; from the Cantines in the potstone
rock near Chiavenna; from the caverns of Caprio, on the Lake of Lugano;
and from the calcareous caves of Hergisweil, at the base of Mont Pilate, nearly
opposite to Lucerne. What is still more extraordinary, such cold caves exist in
countries the seats of not yet extinguished volcanic fire. Sir Wir~1Am HAMILTON
describes the cold winds issuing from the cave of Ottajano, at the base of Vesuvius;
and in the Isle of Ischia, the air which issues from the Ventarola of Funera is as
cold as 48° F., when a thermometer in the shade, without the cavern, is at 58°—
(See Saussure, Voyages dans les Alpes, IIT. 1405.)

Such are the chief contributions of Dr Hors to physical science.

It has been alleged that they are fewer and less important than we had
reason to expect, from the long period during which he filled the Chemical Chair,

MEMOIR OF THE LATE DR THOMAS CHARLES HOPE. 431

his acknowledged skill in experiment, and the brilliant path then opening for im-
portant discoveries in chemistry, which have immortalized the contemporary
names of BLAck, PriESTLEY, Davy, WOLLASTON, DALToNn, and FARADAY among
ourselves—of LAVOISIER, BERTHOLLET, VAUQUELIN, GAy Lussac, Voura, Kuar-
ROTH, BERZELIUS, and Lirpic on the Continent. That there is foundation for
this criticism, I will not attempt to deny: and, indeed, Dr Hore seems to have
anticipated it, by some observations he once made verbally to myself, and has
stated in a paper now in my possession, as his apology. <“‘ Those,” says he, “who
devote themselves to the science of chemistry, may be divided into two classes—
lst, Those whose labours are employed in original researches, to extend our
knowledge of the facts and principles of the science. 2dly, Of those whose busi-
ness it is, from university or other appointments, to collect the knowledge of all
that has been discovered, or is going forward in the science, to digest and arrange
that knowledge into lectures, to contrive appropriate and illustrative experiments,
and devise suitable apparatus for the purpose of communicating a knowledge of
chemistry to the rising generation, or others who may desire to obtain it.
From my professional situation, I consider myself, as Dr Buack had done
before me, as belonging to the second class of chemists. 1 consider my vocation
to be the teaching the science.”

It is true that itis the paramount duty of one appointed to teach a science to
make that his principal object; but this, [ humbly conceive, is quite consistent
with most extensive original research. It may be that the regular recurrence of
the labour of teaching the elements of a science, requiring several hours of daily
personal exertion, may sometimes indispose a lecturer to experimental investiga-
tions of a similar kind; but such has not been its effects on Davy, THomson,
Berzeuius, or Lirepic; all of whom have combined the business of teachers of
chemistry with the most valuable and laborious original researches. Dr Buack had
certainly made all his great discoveries before he was Professor in the University
of Edinburgh; but his health was always very delicate, and his example can
scarcely be pleaded for one who enjoyed such uninterrupted and vigorous health,
that he never was a single day prevented from lecturing by indisposition, for a
period of more than fifty years.

Dr Horr undoubtedly fulfilled admirably the duty of a public teacher of
chemistry, as we have already stated. His mode of lecturing was methodical and
clear, though his style was occasionally too laboured; he scarcely ever failed in
the performance of the nicest and most difficult experiments, which he introduced
to an extent previously never attempted in chemical prelections ; and he possessed
the faculty of impressing his hearers with just notions of the importance and
interest of the science. Still it is to be regretted, that one so well qualified to
advance the boundaries of the study, had limited his ambition and his exertions

VOL. XVI. PART IV. : 5 R

432 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

almost so exclusively to the business of methodizing and detailing the discoveries
of others.

We may here remark, that besides the eminent philosophers already men-
tioned as his friends, Horr was on terms of very friendly intercourse with Warr,
Daron, Wottaston, and Davy. His acquaintance with the latter began in 1799,
ere that illustrious man had yet risen to celebrity. In passing through Bristol,
Hope visited the Pneumatic Institution of Dr Beppors, and was much struck with
the originality and inventive genius of young Davy. Soon afterwards, a lecturer
of talent was wanted to fill the Chemical Chair in the Royal Institution esta-
blished in London, under the management of Count Rumrorp. Dr Hope was
consulted ; he strongly recommended Davy to the notice of the Count; and in
1801, the young chemist was established in the Royal Institution. This anec-
dote, which I have extracted from the original correspondence, once in my hands,
is honourable to the discernment of Horr, who thus early recognised that energetic
genius, which was destined to win the proudest laurels in the career of physical
discovery.

Among Dr Hore’s most intimate friends in Scotland, were Dr Hutton, the
geologist, and Sir James Hatu. From the intercourse with these eminent men,
he had early imbibed their geological tenets; and for many years he was the only
public teacher of science in this country, who inculcatedthe doctrines of the
Plutonic theory of the earth. During the many years of my studies in this Uni-
versity, Hore regularly gave several interesting lectures on geology in his chemical
course, and was a strenuous assertor of the truth of the Huttonian theory, which
he continued annually to teach in many subsequent years ; while the rival Wer-
nerian doctrines were most ably, and no less strenuously maintained, by my
friends, Professor JAMESON, and the late most eminent and eloquent lecturer Dr
JoHN Murray. At that time the chemical history of mineral bodies formed no
inconsiderable part of a course of chemistry; and it was in introducing the
mineral kingdom to the notice of his pupils, that Dr Horr exhibited many of the
proofs of the igneous formation of stony bodies; which was also illustrated by a
well-selected series of rocks, chiefly collected by himself in different excursions
in the Highlands and Western Isles, and in various other parts of the United
Kingdom.

For many years Dr Hore enjoyed uncommon health, and continued to
discharge the duties of the Chemical Chair with his usual success, until within a
year of his death.

A few years before that event, he complained to me of inability to read by
candlelight, and of suffering severe pain in his eyes on making the attempt. On
examining his eyes, I discovered on each cornea those minute depressions like the
marks of the point of a pin, which have been described by some authors as abrasion,

MEMOIR OF THE LATE DR THOMAS CHARLES HOPE. 433

or commencing ulceration of the cornea. The daily use of a weak solution of
nitrate of silver gradually removed the disease ; but, after some months, it recurred
in a less violent degree, and again yielded to the same remedy.

In 1838, on completing the fiftieth year of his career as a Professor of
Chemistry, Dr Horr was invited to a public dinner by a numerous body of his
former pupils. The meeting was attended by many philosophers from a distance,
as well as by a great number of the inhabitants of Edinburgh. It was on this
gratifying occasion that he stated, among other causes of thankfulness, that he
never had been for a single day, either as a student or as a teacher, detained from
the duties of his class.

Dr Hore had continued his lectures in the University until the conclusion of
the winter session in 18438. It was observed, that his voice was feeble, and
although his experiments were, as usual, neatly performed and successful, that
he had lost something of his wonted energy. Increasing debility induced him, in
the autumn of that year, however, to resign his Professorship, rather unexpectedly,
a short time before the commencement of the session of 1843-44; so that the
Patrons had not sufficient time to deliberate on the choice of a successor in this
important Chair. In the mean time, it was very necessary for the interest of the
University, that a course of chemistry should be there delivered as usual. I was
then in England; but, at the earnest request of the Senatus Academicus and the
Patrons, after some hesitation, I undertook the duty, and taught the chemical
class during the session of 1843-44. I know that Dr Hope also was gratified by
my undertaking the task. He not only freely gave me the use of his manuscript
lectures, which were fairly and fully written out, and of his whole apparatus,
but relinquished, in my favour, that portion of the emoluments of the class which
had been secured to him as an annual retiring allowance, by the terms of his
resignation.

It is but justice to Dr Hops to state, that I found his lectures far more nearly
written up to the advanced state of chemistry at that period, than I had been led
to expect ; and although it was necessary to make various alterations and additions,
especially in the disquisitions on organic chemistry, these alterations and additions
were less extensive than I had anticipated. Whether he had employed the interval
between his last course and mine in improving his manuscript, I cannot tell; but
the fact I have mentioned ought to be recorded. During that winter I had much
intercourse with Dr Horr. He was pleased to express a strong interest in my
exertions, and said, that he had frequently enquired from others how I carried
on the duties of the chemical class.

In the end of 1843 and beginning of 1844, he seemed rather more vigorous
than in the preceding autumn; but as the spring advanced, his strength began very
visibly to fail, and he spoke of his gradual decay with firmness and resignation.

434 MEMOIR OF THE LATE DR THOMAS CHARLES HOPE.

During the month of May, he was much in bed ; yet even then he took an
interest in general conversation, and warmly congratulated me on the termination
of my chemical labours.

A few days before his death I saw him for the last time, and although
apparently not in suffering, he took leave of me as if we should meet no more.

He quietly expired on the 13th of June 1844, in the 78th year of his age.

Dr Hore was never married. An excellent portrait of him, by the late
Sir Henry Raxrpurn, which has been engraved, is in the possession of his
family; anda fine bust of him by our eminent artist STEELL was presented to
the University. ;

XXIX.—On the Colouring Matter of the Morinda citrifolia. By Tuomas
ANDERSON, Esq., M.D.

(Read 17th April 1848.)

_ The chemistry of the colouring matters has, perhaps, scarcely as yet met with
the extended and complete investigation which the importance of the subject, in
a theoretical and practical point of view, appears to deserve. The attention of
chemists has been almost exclusively directed to the study of a comparatively
small number of these substances, such as indigo, logwood, and the colouring
matters of the lichens, which have been well and completely investigated; while
the remaining, and by far the more extensive class, has received only a very par-
tial and imperfect examination. To the latter, however, belong some of the most
important of our dyes ; and among others, the most valuable and indispensable
of all, madder namely, the chemistry of which forms a problem as yet very far
from being solved, but which chemists have shewn little disposition to submit to
a thorough and searching investigation ; and this disinclination seems to con-
tinue, notwithstanding that ground has been broken on the subject by the im-
portant observations of RopiqurT, KunLMANN, RunGs, and others, which, though
extremely incomplete, serve at least to indicate the importance of the results it is
likely to afford, and to clear away the preliminary difficulties by which the com-
mencement of such an investigation is surrounded.

But madder is only one member of an extensive class of dye-stuffs, each of
which contains one or more colouring matters, the chemical constitution and rela-
tions of which are almost entirely unknown; and it may seem surprising that,
with the important results obtained from those already examined before them,
chemists should not have attempted to work out more completely than has yet
been done, the rich mine of facts which they present, and the full exploration of
which is equally important to theoretical chemistry and to its practical applica-
tions. The reason, however, in all probability is, that they have been deterred
from the investigation by the small quantity of actual colouring matters which
most of these substances contain, and the tedious and complicated processes re-
quisite for their preparation. In indigo, and those which have been fully inves-
tigated, the colouring matters are supplied to us in the arts in any quantity, and
in a state approaching, at least, to purity; but in roots and plants, the case is
very different, as they there constitute only a minute fraction of the whole mass,
from which their separation is always attended by difficulties, and necessitates

VOL. XVI. PART. IV. os

436 DR ANDERSON ON THE COLOURING MATTER

operations on a larger scale than is either convenient or customary in a chemical
laboratory.

I have experienced this difficulty to a considerable extent in the investigation
of the colouring matter to be treated of in the following communication, which
has been somewhat restricted by the limited quantity of the substance at my dis-
posal. I do not, therefore, present it to the Society as completely exhausting the
subject, which I still leave open for further researches, but principally because the
colouring matter in question differs in certain remarkable points from any hitherto
described, and constitutes the type of an entirely new class, the existence of which
is likely to throw light on some obscure points of Technical Chemistry.

The subject of these experiments was imported into Glasgow, some time since,
under the name of Sooranjee, with the intention of introducing it as a substitute
for madder in the art of dyeing. For this purpose it was, on its arrival, submit-
ted for trial to some of the most experienced and skilful calico-printers in Glas-
gow, all of whom concurred in declaring it not to be a dye at all, and to be totally
destitute of useful applications. My friend Professor BaLrour happening to hear
of this circumstance, was so good as to obtain for me a quantity of the root, which
has enabled me to submit it to a chemical investigation. At the time I received
the substance, no information could be got with regard to the plant from which
it was obtained ; but at the request of Dr Batrour, the importers took the trouble
of writing to their correspondents in Bombay, for the purpose of obtaining speci-
mens of the plant or its seeds. The result of this application was, that we soon
received a small packet of seeds, the label of which bore that they were those of
the sooranjee or soorinjee plant, the Morinda citrifolia of botanists. As this plant
has been long and familiarly known as yielding one of the most extensively em-
ployed native Indian dyes, and as no authority was given with the seeds for the
determination of the species, it was considered desirable to substantiate it by
growing them, and examining the plant itself. They were accordingly sown,
both in the Botanic Garden, and in the garden of Professor Syme at Milbank;
unfortunately, however, not a single seed germinated, and we were compelled to
content ourselves with the less satisfactory process of determining the plant by
the characters of the seed itself. By a comparison with the plates of Garrner’s*
work, they are found to agree very closely with his figures of the seeds of the
Morinda citrifolia, and certainly belong to a species of the genus. Of this genus
six or seven species are known to produce dyes,t but of these two only are im-
portant, the 17. citrifolia of Linnasus, and the I. tinctoria of Roxpureu, both
of which are extensively cultivated in various parts of India, for the sake of

* De Fructibus et Seminibus Plantarum, vol. i., p. 144,

In addition to those above mentioned, colouring matters are contained in Morinda multifida,
5

angustifolia, chachuca, and umbellata,

ra

OF THE MORINDA CITRIFOLIA. 437

the dye they contain. According to Dr Batrour, however, some confusion exists
with regard to these two species, which differ so slightly, that it is doubtful
whether they ought not to be conjoined, the sole difference consisting in the leaves,
which are shining in the céérifolia, and not shining in the ¢éenctoria, in the former
oval, in the latter oblong. All things taken into consideration, Dr Baurour is of
opinion that we are perfectly safe in referring the sooranjee to the Morinda citri-
folia, which has been long described as the source of the native dye.

The JMorimda citrifolia has been described by KHEEDE* under the name of
Cada pilava, and is referred by botanists to the Bancudus lutifolia of Rumpuivs,+
though it is curious that he expressly states that the roots of this species possess
no dyeing properties, while he is very explicit regarding those of his Bancudus
angustifolia, the M. umbellata of modern botanists, and the Wongkudu of the Ja-
vanese dyers, by whom it is employed to produce a beautiful scarlet. <A detailed
account of the cultivation of the MW. citrifolha, and its employment as a dye, is
given by Mr Hunver,+ who states that it is known by the name of Aal in Ma-
Jawa, and of Atchy in Oude. No experiments, so far as I know, have been made
on the chemistry of its colouring matter, unless we except some observations of
Dr Bancrort,§ on a root sent from India under the name of Aurtch, resembling
madder in its external appearance, and which, from the analogy of the native
names, he conjectures to be the WW. citrifolia ; no definite proof, however, is given,
as Dr Banorort had not seen the plant, and I am inclined to doubt their iden-
tity, as the characters he ascribes to it do not agree with those of the substance
I have examined. With regard to the term Sooranjee, I have been able to obtain
no information in any of the works on the natural productions of India, nor is
any one of whom I have had an opportunity of inquiring acquainted with the
name.

Sooranjee is the root of the plant, and is imported cut up into pieces from one
to four inches in length, and varying in diameter from half down to nearly an
eighth of an inch. On the small pieces the bark is thick, and forms a large pro-
portion of the whole root, but on the larger fragments it is much thinner. Its
external colour is pale greyish-brown; but when broken across, it presents colours
varying from fine yellow into brownish-red, and confined principally to the bark.
The wood itself has only a slight yellowish shade, deepest in the centre, and
scarcely apparent close to the bark ;|| but it is coloured dark red by alkalies, in-

* Ruxepe, Hortus Malabaricus, vol. 1., p. 97.

; Rumeuntivus, Herbarium Amboinense, hb. v., cap. 13.

j Asiatic Researches, vol. iv., p. 35.

§ Philosophy of Permanent Colours, vol. i1., p. 308.

|| This is also mentioned by Rumputus as a character of the woody part of the roots and stem
of his Bancudus angustifolia.

438 DR ANDERSON ON THE COLOURING MATTER

dicating the presence of a certain quantity of colouring matter in it. The bark is
readily detached, and its inner surface, as well as that of the wood, has a peculiar
silvery appearance, most apparent on the large pieces, and almost entirely absent
in the smaller. Boiled with water, it gives a wine-yellow decoction, and with
alcohol a deep red tincture.

Morindine.

For the preparation of the colouring matter of sooranjee, to which I give the
name of Morindine, I at first attempted the use of boiling water, in which my
preliminary experiments had shewn it to be pretty soluble; I found, however,
that this method was inapplicable, as the decoction contains a quantity of muci-
laginous matter which hinders the filtration of the fluid. The use of alkalies, in
which the colouring matter is rapidly dissolved, likewise proved abortive, and I
had finally recourse to alcohol, which succeeded perfectly. The bark of the root,
separated from the woody portions and ground to fine powder, was boiled with
six times its weight of rectitied spirit, and the tincture filtered boiling hot. Its
colour was deep brownish-red, and, on cooling, it let fall the greater quantity of
the colouring matter as a brown flocculent precipitate, containing the morindine,
contaminated by another red colouring matter which exists in the root in small
quantity only. A second decoction, with an equal quantity of spirit, gave a paler
solution, from which morindine was deposited with a much smaller quantity of
the red colouring matter. This treatment was repeated over and over again, as
long as the tincture deposited anything on cooling, and every successive boiling
produced it purer than the preceding, until at length, from the final decoctions,
it made its appearance in the form of minute radiated crystals of a yellow colour.
By successive crystallizations from alcohol of 50 per cent., the red matter with
which it was mixed was entirely removed, and the morindine obtained of a fine
yellow colour. It was still, however, impure, and contained a quantity of ash,
amounting, in one experiment, to 0:47, in another to 0°32 per cent. The separa-
tion of this could not be effected by crystallizations from alcohol alone; but after
some trouble I succeeded in removing it completely by solution in alcohol slightly
acidulated by hydrochloric acid, from which it crystallized in a state of purity.

Morindine is deposited from alcohol in minute needles, which, if the solution
be dilute, make their appearance in radiated circles attached to the glass, and re-
sembling, in their arrangement, the crystals of wavellite. They are extremely
soft, and, on being detached, collected on a filter, and dried, mat together into a
a mass, presenting a rich sulphur-yellow colour, and satiny lustre. These crystals
are sparingly soluble in cold alcohol, much more so in boiling spirit, especially if
dilute ; and the fluid on cooling is filled with a mass of bulky needles, which, when
dried, shrink into a very small bulk. They are much less soluble in absolute al-

OF THE MORINDA CITRIFOLIA. 439

cohol, and totally insoluble in ether. Water dissolves morindine in the cold very
slightly. although sufficiently to communicate a yellow colour to the fluid; at the
boiling temperature, however, it is readily taken up, and again deposited, on cool-
ing, as a gelatinous mass, destitute of all traces of crystallization, which stops up
the pores of the filter, and prevents the separation of the mother liquor. It dis-
solves in solutions of the alkalies, with a fine orange-red colour. With concen-
trated sulphuric acid it gives a deep purple, which is violet in thin layers. After
twenty-four hours’ contact, the solution, on being diluted, deposited yellow flocks
of the colouring matter in an altered condition, as it was now totally insoluble in
cold water, and gave, with ammonia, a violet and not an orange solution. Nitric
acid, sp. gr. 1°38, dissolves morindine slowly in the cold, with a deep brownish-
red colour. The application of heat immediately produces violent action, the
brown colour disappears, and nitrous acid fumes are evolved. The fluid, after
long-continued boiling with the acid, and neutralisation with ammonia, gave no
precipitate with salts of lime.

Solution of morindine gives, with subacetate of lead, a precipitate depositing
itself in crimson flocks, which is extremely unstable, and cannot be washed with-
out losing colouring matter. With solutions of baryta, strontia, and lime, it
gives bulky red precipitates, sparingly soluble in water. Perchloride of iron pro-
duces a dark brown colour, but no precipitate. When its ammoniacal solution is
added to that of alum, the alumina precipitated carries down with it the morin-
dine as a reddish lake, and, when added to perchloride of iron, a brown precipi-
tate is thrown down, which cannot be distinguished from pure peroxide of iron,
but which contains morindine, as the supernatant fluid is colourless.

Heated in close vessels, morindine melts into a deep brown fluid, and boils at
a high temperature, with the evolution of an exceedingly beautiful orange vapour
resembling that of nitrous acid, which deposits itself on cold substances in fine
red needles of considerable length. A bulky charcoal remains in the vessel.

The analyses of morindine were performed with oxide of copper, and upon sub-
stance which had been carefully dried for a long time at 212°. The results were
as follows:

13:028 --- carbonic acid, and

6:406 grains of morindine gave
:
2:990 .-- water.

12:100 =: —_ carbonic acid, and

5:956 grains of morindine gave
le
2°699 «+ water.

III { 4-564 grains of morindine gave
9°270 see carbonic acid.
VOL. XVI. PART IV. our

440 DR ANDERSON ON THE COLOURING MATTER '

Ti 106 ai.
Carbon, irc tie WOO EG 55°40 55°39
Hydrogene in LO 5°03 .
Oxygen, 2 gs, OOOO 39°57
100-00 100-00

These analyses give the formula C,,H,;0,,, which agrees perfectly with the
mean of the experimental results, as is shewn by the following calculation.

Calculation. Mean of Experiment.
SS
28 Equivalents Carbon, . . . 2100°0 55°44 55°41
15 vs Hydrogen,) 2*) 21675 4:95 511
15 wee Oxygen, /)/ 2/1 F500 39°61 39°48
3787'5 100-00 100-00

The formula thus ascertained brings out an interesting relation between mo-
rindine and the colouring matters of madder, and more especially that one which
is obtained by the sublimation of madder purple. From his analysis of this sub-
stance, ScHIEL* deduces the formula C, H,O,. As this, however, is no more than
the simplest expression of the analytical results, and as all the other madder
colouring matters examined contain 28 equivalents of carbon, we are justified in
supposing its real constitution to be represented by quadruple of that formula, or
C.,H,,O,,. which differs from that of morindine by a single equivalent of water
only. The unsublimed madder purple is also connected, though more remotely,
with morindine, and differs only by containing 5 equivalents of hydrogen less,
its formula, according to ScHzEL, being C,; Hy) O.;.

Moreover, this similarity is not confined to their formule only, but extends
itself over all their physical and chemical properties, which approximate very
closely, although they are sufficiently distinct to preclude the possibility of their
being confounded with one another. And this isa point well worthy of observa-
tion, as illustrating the similarity in chemical constitution of plants so nearly re-
lated in the botanical system; the morinda belonging to the natural family Cin-
chonaceze, which, by many botanists, is considered as merely a section of the Ru-
biaceze, of which madder is the type.

This similarity, however, does not extend itself to their properties as dyes, in
which respect they differ in a very remarkable manner. I have already men-
tioned that the calico-printers had entirely failed in producing a colour by means
of sooranjee; and this I have fully confirmed as regards the common mordants.
I digested morindine for a long time, in a gradually increasing heat, with small
pieces of cloth mordanted with alumina and iron, but nothing attached itself, and

* Annalen der Chimie und Pharmacie, vol. lx., p. 74.

OF THE MORINDA CITRIFOLIA. 44]

the mordants, after boiling for a minute or two with soap, were found to be un-
changed. Even with the root itself, alum mordant only acquired a slight reddish-
grey shade, and iron became scarcely appreciably darker in colour. The case
was different, however, when cloth mordanted for Turkey-red was employed. I
obtained from Glasgow pieces of calico prepared for Turkey-red both by the old
and new processes, and I found that both acquired, with morindine, in the course
_ of a couple of hours, or even less, a dark brownish-red colour, devoid of beauty,
but perfectly fixed. These observations agree with the account given by Mr
Hunter of the method of dyeing with the MW. citrifola employed by the Hindoos.
The cloth is first soaked in an imperfect soap made by mixing the oil of the Sesu-
mum orientale with soda ley. After rinsing and drying, it is treated with an in-
fusion of myrobalans (the astringent fruit of the Terminalia chebula), and exposed
for four or five days in the sun. It is then steeped in solution of alum, squeezed,
and again exposed for four or five days. On the other hand, the powdered roots
of the morinda are well rubbed with oil of sesamum, and mixed with the flowers
of the Lythrum fruticosum (ROXBURGH), or a corresponding quantity of purwus
(the nut-gall of a species of mimosa). The whole is introduced along with the
cotton into a large quantity of water, and kept over a gentle fire for three hours,
when the temperature is brought to the boiling point. The red colour so obtained
is, according to Mr Hunter, more prized for its durability than its beauty. ‘This
is simply a rude process of Turkey-red dyeing. He also mentions that, by means
of iron mordant, a lasting purple or chocolate is obtained, but in this case the colour
is probably affected by the tannin of the astringent matters employed in the
process.

Morindone.

It has been already mentioned that morindine, when heated, is entirely altered,
a quantity of carbonaceous matter being left, and a crystallizable principle sub-
limed, differing in its properties from the original substance. To it I give the
name of Morindone.

Morindone is obtained by sublimation in the form of long needles, which, un-
der the microscope, are found to be four-sided prisms, terminated by a single
oblique face, and of an exceedingly rich and beautiful red colour. They are to-
tally insoluble in water both hot and cold, but dissolve readily in alcohol and
ether, and the solutions by slow evaporation deposit crystals. The alkalies dis-
solve it with a magnificent violet colour. In strong sulphuric acid it is also so-
luble, with the same intense violet colour, and it is precipitated on diluting the
acid. Its ammoniacal solution gives a fine red lake when added to solution of
alum. and a cobalt-blue precipitate with baryta water. The quantity of morin-
done which I was able to obtain for analysis was too small to admit of accu-
rate results, or of all the precautions for its purification which would have been

442 DR ANDERSON ON THE COLOURING MATTER

resorted to had I possessed a larger quantity. The sublimed crystals were simply
washed with ether, in order to remove empyreumatic matters, and then dried at
212°. Analysis gave the following results :

3°931 eee carbonic acid, and

1:629 grains of morindone gave
0-614 ~~... ~~ water,

which approximates most nearly to the formula C,, H,,0,, as is shewn by the fol-
lowing comparison.

Experiment. Calculation.
——orr ee
Carbon.) eae Gs: ol 65:11 Cog 2100-0
Hydrogen, . . 4:18 3°87 daly 125-0
Oxygen, . . . 30°01 31:02 0, 1000-0
100:00 100-00 3225-0

Of course, it is impossible to consider a formula as established by a single ana-
lysis upon so small a quantity. I think it probable, however, that that given
above may be the true one, and that the excess of carbon was due to imperfect
separation of empyreumatic matters, as, to avoid loss by solution, I washed with
the smallest possible quantity of ether. That morindone is formed from morin-
dine by the elimination of water, derives confirmation from the change which the
latter substance undergoes in contact with sulphuric acid. As already mentioned,
it then becomes insoluble in water, and gives a violet colour with alkalies similar
to that produced by morindone, and as sulphuric acid in general acts by removing
water, the probability is, that it has deprived the morindine of 5 equivalents, and
converted it into morindone; at the same time this is a point which can only be
determined by analysis, and the quantity which I obtained was not nearly suffi-
cient for that purpose. Should further experiments establish C,,H,,0,, as the
true formula of morindone, we have another simple relation with the madder
colouring matters, as it would differ from madder red by a single equivalent of
water, the formula for that substance, according to the analysis of ScurEL, being
C,,H, O,. It would also be polymeric with gentianin, for which BaumErt* has
established the formula C,, H: O,.

Morindone is a true colouring matter, and is capable of attaching itself to
common mordants. It gives with alumina a deep rose-red, and with iron violet
and black; but the colours are not very stable, and it has a strong tendency to
attach itself to the unmordanted parts of the cloth, and to degrade the white.
Morindine, after treatment with sulphuric acid, is capable of attaching itself to
ordinary mordants.

The discovery of a peculiar colouring matter capable of fixing itself exclu-.

* Annalen der Chimie und Pharmacie, vol. Ixii., p. 106.

OF THE MORINDA CITRIFOLIA. 443

sively on Turkey-red mordant, is of interest, as establishing the existence of a
peculiar class of dyes hitherto totally unsuspected,—a class which may be exten-
sive, and may yield important substances. It may serve also, in some respects,
to clear up the rationale of the process of Turkey-red dyeing, which has long been
a sort of opprobrium of chemistry. Although that process has been practised for a
century in Europe, and has undergone a variety of improvements, no clear expla-
nation of it was for a long time given, but it was supposed that, by the action of the
dung, of which large quantities are employed, the cloth underwent a species of
animalisation, as it was called, by which it acquired the property of receiving a
finer and more brilliant colour than could be attached to it by purely mineral
mordants. Recent experiments have, however, shewn that the oil, which is
largely employed in the process, undergoes decomposition by long exposure to the
air in contact with decomposing animal matter, and is converted into a sort of
resinous matter, which constitutes the real mordant for Turkey-red. This has
been pretty clearly made out by the experiments of WeIssceRBER.* He found
that when cloth had been treated with oil, so as to give, when dyed, a fine rose-
red colour, he could, by digestion with acetone, extract from it the altered oil;
and as it was removed, the cloth gradually lost the power of attracting the colour-
ing matter of madder, until, when it was entirely separated, the cloth passed
through the dye without acquiring any colour. On the other hand, he found that,
by applying the substance extracted by acetone in sufficient quantity to cloth, he
could obtain the richest and deepest colours with madder, without the addition
of any other substance whatsoever. These observations receive additional confir-
mation from the experiments detailed in the present paper, as it must be suffi-
ciently obvious that the dark red colour obtained on Turkey-red mordant with
morindine, must be entirely irrespective of the alumina, on which that substance
is incapable of fixing.

I fully agree with the opinion expressed by PErsoz that the use of alum mor-
dant, which is at present always employed in Turkey-red dyeing, will be entirely
abandoned so soon as calico-printers have learned the method of modifying at
will the oil which they employ, so as to bring it at once into the state in which it
acts asa mordant. Some steps have been made in this direction, by making use
of some chemical agents, as nitric acid and chloride of lime, for the purpose of
acting on the oil; but the improvements which have been effected stop far short
of what I believe will eventually be effected, when the system of pure empiricism
which has been all along employed in this particular process of dyeing is aban-
doned, and the subject submitted to really scientific investigation. It is understood
that M. Cuevreut has entered upon the inquiry, and in his hands there is little
doubt but that it will meet with a satisfactory solution.

* Persoz, Sur l’Impression des Tissus, vol. i., p. 176.

VOL. XVI. PART IV. 5U

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( 445 )

XXX.— Notice of the Orbit of the Binary Star a Centauri, as recently determined by
Captain W. S. Jacos, Bombay Engineers. By Professor C. Piazzr Smytu,
F.R.S.E.

(Read, April 5, 1848.)

The object of this short notice is merely to submit to the Society some astro-
nomical results which were recently communicated to me in a letter from my
friend Captain Jacos, as they appeared not only to be of a highly interesting
nature in themselves, but imperatively to require being followed up farther, and
as the observer has lately been obliged by bad health to resign his situation in
India, it seemed advisable, for the purpose of procuring attention to the subject
elsewhere, to make its peculiarly interesting features as generally known as pos-
sible amongst scientific men ; and as a Centauri is already in a manner identified
with Scotland, through the researches of the late Professor HENDERSON, and his
determination of the parallax, no medium can be more appropriate than the
Transactions of the Royal Society of Edinburgh.

The star a Centauri, situated in 14° 29™ A.R., and 150° 12’ N.P.D., is in many
respects a notable object, and though its greatest claims to attention have all
arisen within the last few years, under the applications of the advanced astro-
nomy of the present day, yet even to the naked eye it has much to raise it above
the general crowd. It is a star of the first magnitude, and one of the brightest
indeed of that class, and is situated in a peculiarly splendid region of the sky,
the same as that occupied by the Southern Cross; a constellation, by the way,
which, on account of its small dimensions, and the few stars it contains visible
to the naked eye, is by no means entitled to the too warm encomiums so lavishly
bestowed upon it so generally by the early Southern navigators and travellers.
(And here I may be perhaps allowed to point out an error in Purpy’s Hydro-
_graphy, where, amongst other fine qualities attributed to the Cross, he adds that
of its forming always a sort of clock to the inhabitants of the Southern hemi-
sphere ; for the longer diameter of the Cross standing vertical, as he says. at mid-
night, persons may always judge by the inclination of the Cross to the one side
or the other, when the middle of the night may have passed. Now the two stars
at either end of the longer diameter having the same right ascension, will cer-
tainly stand in a vertical line when on the meridian, but will of course only be
on the meridian above the pole at midnight, once in the course of the year.) The
region of the Cross, however, abundantly compensates for the poverty of the con-
stellation itself, for such is the general blaze of star-light from that part of the
sky, that a person is immediately made aware of its having risen above the hori-

id

VOL. XVI. PART IV. dX

446 NOTICE OF THE ORBIT OF THE

zon, though he should not be at the time looking at the heavens, by the increase
of general illumination of the atmosphere, resembling the effect of the young
moon.

This excessive splendour is caused not only by the profusion of first, second,
and third magnitude stars in the neighbourhood, but by the extraordinary general
breadth and brightness of the Milky Way thereabouts; for, separating into so
many distinct luminous clouds, as it were, and exhibiting between them void
black spaces unchequered by a single luminous object of any kind whatever,
it forcibly impresses the idea of our being situated there near the confines of the
sidereal system, or in the southern side of the vast ring in which the generality of
the stars are arranged. The superior brightness of so large a proportion of the
stars is then naturally accounted for by their greater proximity to us; and this
fact was actually proved by my predecessor, who found from his own observations
of a Centauri, an annual parallax of the large amount of 1", 7.e., that at the dis-
tance of this star, the radius of the earth’s orbit, or 95 million of miles, subtended
an angle of 1”; the greatest quantity previously found for any star in the Northern
hemisphere being only 0°23".

Professor HeNDERson’s results were fully confirmed by a very much longer
series of observations subsequently made at the Cape Observatory by different
observers, and with different instruments, and he then computed his old observa-
tions of the other principal stars in that region, and finding a considerable num-
ber* which shewed also indications of a sensible parallax, he immediately sent
out a notice of the results to the present energetic Director of the Cape Observa-
tory, for the purpose of procuring from him a greater number of observations of
those suspicious stars. Such a series was accordingly commenced, and is still
going on, and we may expect before long to hear of trustworthy results having
been obtained, and there is little doubt that these labours will still more strongly
tend to establish the proximity of that part of the sky.

On the application of the telescope to a Centauri, it proves to be composed of
two stars, one very much brighter than the other, but still both may be placed in
the list of first magnitude, the smaller occupying the lowest possible step in that
grade. Early observers have indeed assigned it a much smaller rank, and in the
British Association Catalogue published only two years ago, and intending to
apply to the year 1850, it is actually made as low as the fourth magnitude ; this,
however, is manifestly an error, for the present epoch, as I can state from the
experience derived from making the observations which served to confirm Pro-

* 6 Hydri. n Argus. € Centauri.
a Phenicis. a Crucis. a Trianguli Austr.
a Eridani. ry Crucis. & Trianguli Austr.
a Columbe. 8 Crucis. a Pavonis.
e Argus. 8 Centauri. a Gruis.

BINARY STAR a CENTAURI. 447

fessor HENDERSON’s parallax ; for, during the whole year, there was not a single
day when, if the larger star was seen at all, the smaller one was not abundantly
visible also; and during that part of the year when they transited the meridian
by daylight, they were even then invariably seen with the mural circle telescope.
whatever the state of the atmosphere, unless actual clouds intervened. But that
the smaller star was never in ages past as low as the fourth magnitude, the mar-
vellous change which has occurred in the case of 7 Argus in our own times, would
render a most hazardous assertion.

A proper motion of the large amount of 3°58" is participated in by both the
stars, a fact which pretty clearly proves a physical connection between them ; for
while they are now very nearly in the position they were in 100 years ago, when
observed by the Abbé LacaiLuz, they would have separated by this time upwards
of five minutes, if one only was pursuing this anomalous path amongst the rest
of the stars.

The first person to remark on this physical connection was Professor HENDER-
son, who, in the concluding paragraph of his memoir on the parallax, says,

“ The two stars appear to be approaching each other. The earliest observa-
tions of a Centauri made with a telescope which I have found, are those of
RicHEr at Cayenne in 1673, but neither he nor Hattey, who observed it at St
Helena in 1677, mentions it as being double. Their telescopes were of course
anachromatic, and probably not of much power. FEULLEE appears to have been
the first person who observed the star to be double, as he mentions in the journal
of his voyage in South America in July 1709. La ConpAmMINE next observed the
star during the scientific expedition to Peru for measuring an arc of the meridian.”
But neither of them made any observations of real service in determining the na-
ture of the physical connection of the two stars. “ From LacatLe’s observations
in 1751-2, the distance of the two stars appears to have been then 22:5". Mas-
KELYNE, who observed them at St Helena in 1761, says (Philosophical Transactions,
1764, p. 383), The bright star in the foot of the Centaur, marked a in the cata-
logues, when viewed through a telescope, becomes divided into two stars, one of
which is about the second and the other the fourth magnitude. They were both ob-
served by the Abbé De Lacaiiiz. I found their distance by the divided object-
glass micrometer, fitted to the reflecting telescope, to be 15” or 16”. [have not found
any observations,” continues Professor HENDERSsoN, “of the distance of the two
stars made between 1761, and the institution of the Paramatta Observatory: there,
in the end of 1825 or the beginning of 1826, the distance was observed to be 23”
(Memoirs of Astronomical Society, Vol. iii., p. 265), since which time it has been
decreasing at the rate of more than half a second per annum. The angle of posi-
tion scarcely appears to have changed since LacarLLr’s time, whence it may be
inferred, that the relative orbit is seen projected into a straight line or very excen-
tric ellipse; that an apparent maximum of distance was attained in the end of

448 NOTICE OF THE ORBIT OF THE

the last or the beginning of the present century; and that about twenty years
hence the stars will probably be seen very near each other, or in apparent con-
tact, but the data are at present insufficient to give even an approximation to the
major axis of the orbit and time of revolution.”

The next authority on the subject is Sir Joan Herscuet, who specially applied
himself to the subject of the Southern double stars when at the Cape, and had
far superior instruments for such a purpose to any of his predecessors; he thus
describes and sums up all that was known to him of this star, in his recently
published work.

“This superb double star, beyond all comparison the most striking object of
the kind in the heavens, and to which the discovery of its parallax by the late
Professor HENDERSON has given a degree of astronomical importance no less con-
spicuous,—consists of two individuals, both of a high ruddy or orange colour,
though that of the smaller is of a somewhat more sombre and brownish cast.
They constitute together a star which to the naked eye is equal or somewhat
superior to Arcturus in lustre”’ After describing the magnitude which he con-
sidered should be assigned to each, and which agrees more nearly with what I
have already stated as being my own opinion, and after giving some optical and
physiological reasons which may tend to explain the under-estimation of former
observers,—Sir John then cites the fact of the remarkable amount of proper mo-
tion of the stars, and says, “ This consideration alone suffices to decide us in ad-
mitting a binary connection between them, and it will therefore be interesting to
see what evidence observation furnishes of orbitual motion round their centre of
gravity. For this, however, the data are somewhat precarious, as we have, until
recently, only catalogued differences of A.R. and Polar distances, from which to
calculate the angle of position and distance at the epochs of observation. ‘This
done, and the results tabulated, together with my own positions and distances,
obtained by direct measurement with the equatorial, we have as follows :”—

Epoch of
Authority. | Observation. Position. Distance.

Lacaille, - 1750 218 44 20:51

(Maskelyne, 1761 15:5)
Fallowes, 1822 209 ~=—36 28:75
Brisbane, 1824 215. 25 22:45
Dunlop. 1825 2138 - 1% 22°45
Johnson, 1830 215 2 19-95
Taylor, | 1831 215 58 22°56
Herschel, 1834-68 17-43

1834-79 218 30
1835-86 219 30
1837-34 220 42
1837-44 16°12

BINARY STAR a@ CENTAURI. 449

I have inserted here the observation of MAsKELYNE in 1761, with which, pro-
bably, Sir J. HerscurL was unacquainted; it makes an apparently bad figure
among the rest, but is by no means to be left out on that account merely, seeing
the care and the superior means for that day with which the measures were made.

‘“‘Mr Fattowss’ determinations,” continues Sir Joun, “in this series, are open
to objection, from the decidedly inadequate instrumental means by which they
were furnished (a small altitude and azimuth circle). Mr Tayuor’s results also
rest on so few observations, as to entitle them to little weight.

“ Though it is obviously impracticable to deduce any elliptic elements from
such a series, there are some features which it is impossible not to recognise.
There can be no doubt that the distance has gone on decreasing since 1822 at
least ; and the comparison of the measures least open to objection leads us to con-
clude that, for the ten years previous to 1838, the rate of decrease was j4, or a
little more than half a second per annum, which, if continued, will bring on an
occultation, or exceedingly close appulse, about the year 1867. The small amount
of variation in the angle of position shews that the plane of orbitual motion passes
nearly, but not quite through our system, while its actual tendency to increase
exemplifies the general law of increase of angular velocity, with diminution of
distance. Mr Fattowes’ distance is probably too great by 3” or 4’; but in the
long interval between 1750 and 1822 (at the former of which epochs the distance
must have been on the increase), there is room for a very much greater excursion
of the small star towards its apparent aphelion, so that, although we are sure that
the major axis of the real orbit must materially exceed 24”, it is impossible to say
how much it may exceed that limit. Taking, therefore, the co-efficient of parallax
for a Centauri, as determined by Professor HENDERSON, at 1”, it will follow from
what has been said, that the real orbit of one star about the other cannot be so
small as that of the orbit of Saturn about the sun, and exceeds, in all probability,
that of the orbit of Uranus.

“ The plane of the orbit in the case of a Centauri, passing nearly through our
system, my method of approximating to the elliptic elements becomes inapplicable,
and for their determination, measures of the distance of the stars from each other
can alone be relied on. No subject more worthy of continued and diligent inquiry
can possibly be urged on the attention of southern astronomers.”

Thus the result arrived at, both by Professor HENDERSON and by Sir J. HERSCHEL,
and which, though proved since to be erroneous, would have been probably con-
cluded by any one else from the same data, seems to be, that the smaller star
had been employed during the last century in gaining its aphelion, without any
sensible change of angle of position; what the aphelion distance, the diameter
of the orbit, and the period of revolution, might be, no guess could be at-
tempted: but in his address, on the occasion of giving the gold medal to
Besset for his discovery of the parallax of 6 Cygni, Sir Joun HeErscHet stated,

VOL. XVI. PART IV. DY

450 NOTICE OF THE ORBIT OF THE

that the orbit of the smaller star of a Centauri might subtend the large angle of
about 1 minute. As it had been actually observed at an elongation of 28” on one
side of the large star, the very reasonable supposition of a nearly circular orbit,
seen in profile, would, in course of time, give the same distance on the opposite
side. Both authorities also predicted the probability of an appulse of the same
stars somewhere about the year 1867.

At the time of Sir Joun HERsScHEL going to press, he knew of no micrometri-
cal measures subsequent to 1838, but soon after that period, most fortunately for
the interests of sidereal astronomy, Captain Jacos came into the field. On visit-
ing the Cape from India, where he had been engaged in the great Trigonometrical
Survey, he spent most of his time at the Observatory, and not only witnessed,
but took part in the parallax observations of a Centauri. He then ordered a good
achromatic telescope from Dollond, and on its arrival in India, after his return
there, erected a small observatory, and devoted all his spare time with great per-
severance and eminent success to that most difficult species of observation,—viz.
the double stars.

About a year ago, he wrote to me to send him out all the old observations
known of @ Centauri, for the two stars were approaching more and more rapidly,
and his own observations seemed to give a most unexpected orbit. The first docu-
ment which reached him was Professor HENDERSON’s memoir on the parallax,
and then Captain Jacos found that he had been forestalled as to the actual facts of
an appulse being shortly to be expected, though he indeed fixed the time as being
very much closer at hand, bringing it from 1867 to 1851 ; but as to the idea that
the small star had only been gaining its aphelion, without sensible alteration of
angle of position since 1751,—he found, on computing the orbit, that within that
interval it had made a whole revolution, or had altered its angle of position by
360°. The subsequent arrival of Sir J. HerscneEt’s observations fully confirmed
Captain JAcos’s views, who has now recomputed the orbit, including all the
known observations up to the present time; and though this performance is to be
considered but a first approximation, still it will probably not be very much al-
tered by future observations in any of the important elements.

The difficulty that might be started at the first mention of this new opinion,
would be, that supposing the small star, instead of having remained almost sta-
tionary in its orbit for the last 100 years, to have really made a whole revolu-
tion,—how came it to pass that every observer in the interval saw it always in
about the same position on the west, and never on the east of the large star? This
objection is fully met by the extraordinary nature of the orbit, which turns out
much more nearly like that of a comet than of a planet, the greatest distance
being 21°85,” and the least 0-5,” in consequence of which, the small star moves
with such surpassing rapidity at its periaster, actually 2° 40’ per day; that it is
but a very short space of time on the eastern side of its primary, and when at its

BINARY STAR a CENTAURI. 451

aphaster on the west, moves again with proportionate slowness, and so is seen there
for a long period with hardly any sensible alteration of place. The time of revo-
Jution seems to be as short as 77 years; and LaCaitue and MaskELyNe’s' obser-
vations, which had before appeared somewhat anomalous, are fully reconciled, as
belonging to a former revolution; indeed the small star seems to have been al-
most in precisely the same situation with respect to the large one when observed
by MaskELYNE in 1761, as it appeared to Str J. HERSCHEL in 1838; and had ob-
servations been continued for twelve years after MASKELYNE’s time, our know-
ledge of sidereal astronomy might have been almost a century in advance of its
present position.

Captain W. S. Jacob’s Observations of a* and ? Centauri (A.B. 14" 29:5", NPD.
150° 12’), made at Poonah, Lat. 18° 31’ N., Long. 4 55™ 42° H., with a Five
Feet Achromatic Telescope.

Distance
of the
Two
Stars.

Estimated Remarks.
Magnitudes.

Magnifying Power.
| Weight of Observations.
Magnifying Power.

Or

|

= Se | Weight of Observations.

do.
definition tolerable.
daylight; dawning.
daylight; definition tolerable.
d

.

—
Chl oF ©

good.
tolerable.
do.
do.

| |
G9 G9 &9 OD GO CO G9 G2 OD CO Oy OO GO GO O9 OD G9 C9 C9 G9 LD

do.
definition tolerable.
daylight; definition tolerable.
: do.
very good.
do.
fair.
excellent.

|

|

i

do.
slightly tremulous.

|

PEPE EP PRE E EE PE RED A RE ROKRR EP BD | Number of Observations.

Tl eel ee tc I De ee ee
|

|
NOt ty by ©
Oro or or

g
:
§
a
Zi
4
6
5
5
5
7
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5

452 NOTICE OF THE ORBIT OF THE

Captain W. 8S. Jacob’s Orbit of a and? Centauri.

Position of perihelion, er = 26° 24
Inclination to the plane of projection, y = AT “56
Position of ascending node, : oO = Shay
Angular distance of perihelion from ay on the “saab of the orbit, A = 291 22
Kecentricity, d . : : F s ; = + 0:960
Kpoch of perihelion passage, rs = 1851:50 year
Periodic time, : : : t ; P = 77:0 years
Mean motion, ; : : : ; » =) 4e6ro
Semiaxis major, . : : ; : e =) loom

Mass = 3 of the Solar

Apparent Orbit.

21:85" at 207°5°
0:50 ... ay
2° 40’

Maximum distance,
Minimum,
Greatest daily motion,

II

(See Plate XI.)

We thus have here altogether one of the most, if not the most, interesting and
important sidereal system in the heavens; the only one which can compare with
it is y Virginis, and that has been looked upon as being amongst the double stars,
what HALLEy’s comet is amongst comets; but though so well and frequently
observed of late years, it was not instrumentally measured so early as « Centauri,
and it isa much smaller star, with an orbit of only one-fourth the apparent dimen-
sions, and a period of time double the length of its southern rival; so that, while
the actual observation for the purpose of carrving theory with fact would be eight
times more difficult in the case of y Virginis, and loaded with eight times the pro-
bable error of observation, there is the further objection, that on account of the
greater length of the period, but a small portion of the orbit could be determined
by one observer, or even by one instrument.

But the crowning importance of the binary system of a Centauri, is the accu-
rate determination of its parallax or distance from us, by the late Professor
HENDERSON, as we are thereby enabled to speak, not only of the proportions of
the different parts of the orbit, but of their actual size, and the weight of the two
bodies. Thus the least distance of these two suns is only half that of the earth
from the sun, or a little less than that of Venus, while the greatest distance is a
little more than that of Uranus; and the mass of the two stars comes out three-
quarters of that of our sun, their distance from us being 226,100 times our dis-
tance from the sun.

Well, therefore, may Sir J. Herscuex have said, “that no subject more
worthy of diligent and continued inquiry can possibly be urged on the attention
of southern astronomers.”

| el the te 23

BINARY STAR a CENTAURI. 453

But the most interesting part of the orbit is still to come, viz., the periaster in
1851, and that this be well observed is indeed to be earnestly hoped, for the period
will be an eminently crucial one; it proved so in the case of + Virginis, impera-
tively requiring an excessive alteration in all the elements except one, as pre-
viously calculated; and in the case of @ Centauri, the characteristic features of
the orbit are of a much more violently marked nature, besides being represented
altogether on a larger scale.

The extreme importance of obtaining an abundance of observations at that
epoch may be further indicated by the mere statement, that it cannot yet be con-
sidered as fully proven, that the law of gravity extends absolutely unaltered to the
most distant parts of the sky, and the only mode of proof open to us is by ob-
serving the double stars. It is true that most of the orbits yet computed on the
theory of gravity have turned out very near the truth, but still not quite so near,
it must also be confessed, as could have been desired; and in the luciferous case
of y Virginis, every orbit that has been computed for it yet, has persisted in giving
a minimum distance of not less than 0°5”, while observation at the time of the
periastral passage made it certainly much smaller.

I do not, of course, by any manner of means, wish to express any doubt on
these grounds as to the sufficiency of gravity to explain all the observed pheno-
mena; a great part of the onus, or the whole of it, may rest on the excessive diffi-
culty of the species of observation, and their inappropriateness for calculation in
all ordinary manners, caused by the extreme roughness of even the very best
procurable data; resembling, indeed, those of the comet of 1556, whose return,
calculated on such wretched notices of its former perihelion passage, we have
been looking out for in vain so long.

But whatever weight we may attach to the insufficiency of our observations
and methods of calculation,* it is always proper to draw a distinct line of demar-
cation between those things which are proved and those which are merely inferred,
and not seek to enjoy a triumph before the victory has been decidedly achieved.

* In a letter just received from Captain Jacos, he says that he thinks he has fallen on the right

orbit of ty Virginis at last, having obtained one that expresses all the known observations very well,
and gives a minimum distance of 0:23”.

VOL. XVI. PART IV. Se

PLATE A Royal Soc rans. Ea

L584. 4

@
JM

ORBIT OF @CENT
Seale 4° to 1 inch

:

PROPOSED FORM OF THE ANEMOMETER FOR USE

Diameter of the Hemispheres: — 4 Inches

Distance of the centre of ‘cach Hemisphere tom the centre of motion 6%

P 458.

F
B
z
§
Gi d

P4860 Pe SS eee

CED Direction. Ship 15 4 goung to]

SCALES FOR REDUCING THE APPARENT WIND TO THE TRUE
Tray Wea oimsin aie a+; a ——

( 455 )

XXXI.—An Attempt to Improve the present Methods of Determining the Strength and
Direction of the Wind at Sea. By C. P. Smytu, Esq., F.R.S.E., Professor of
Astronomy in the University of Edinburgh. (With a Plate.)

(Read April 3 and 17, 1848. )

Last year, my friend Captain Cocxsurny, R. N., brought to my notice the very
lax method which is usually pursued at sea in determining the strength and di-
rection of the wind ; and said, that he had for many years been trying to contrive
some sort of anemometer that might be useful on board, as well as an easy method
of eliminating the effect of the motion of the ship on the true character of the
wind, but hitherto without success. I undertook, therefore, to endeavour to sup-
ply him with these two desiderata. He thought that they would be useful, in a
practical point of view, in seamanship; and as I considered that they might be of
importance in meteorology, I was the more ready to lend my assistance.

The foundation of meteorology as a science, may be considered to reside in a
knowledge of the general motions of the atmosphere; and these may be far more
correctly determined at sea than on any station on land, where local circumstances
always produce more or less of an artificial climate, circumscribed, perhaps, to a
_ few miles, or even less, and therefore of no moment to the world at large.

But although a ship, traversing the uniform surface of the ocean, of nearly
unvarying temperature, day and night, and winter and summer, is thus naturally
under highly favourable circumstances for advancing the science, still those op-
portunities seem never to have been turned to full account.

The usual mode of entering the wind in the log-book used to be, and may be
still in the greater part of the merchant navy, ‘“‘a hard breeze, or a stiff breeze, or
strong breezes, and squally,” &c., &c.; each person judging by his feelings merely,
and having a nomenclature of his own for those feelings; so that there is no way
of reducing them all to any one uniform natural standard.

On account of the flagrant absurdity of this method, in a scientific point of
view, Admiral Braurort, of the Hydrographical Office, proposed and procured
the general adoption of, in all Her Majesty’s ships, a well-digested table of the
names of different strengths of wind, and of the means of judging of them, in the
terms of the numbers of which table all entries in the log-book were to be made.

Admiral Beaufort's Wind-Table.

0. Calm.
Ee Light air, ......- Or just sufficient to give steerage way.
: Or that in which a well-conditioned
4 ea eee mee man-of-war, with all sail set, ie : re
4 Mod aah ae and clean full, would go insmooth tole ate
: Baer ene water, for ; . ‘

VOL. XVI. PART IV. 6A

456 ON THE DETERMINATION OF THE TRUE STRENGTH

5. Fresh breeze, ... Royals, &c.

6. Strong breeze, or : Single-reefed topsails and top-gallant-sails.

7. Moderate gale. ee Pepa He id justearry | Double-reefed topsails, jib, &c.

8. Fresh gale,...... | ie oS ee 8 : Triple-reefed topsails, &c.

9. Strong gale, ... Close-reefed topsails and courses.

Or that in which she could scarcely bear close-reefed main-top-sail and reefed

10. Whole gale, ... edeadnit.
1d oe Storna,) © reac. Or that which would reduce her to storm-staysails.
12. Hurricane, ...... Or that which no canvass could withstand.

But although this was at the time a great improvement on the old system,
it is by no means sufficient for the requirements of the present day; for so much
is still left to the feelings and experience of each observer, that one officer will say
that the wind should be marked as No. 4; while his companion may say it is
rather No. 5, and another may decide on 3 being the more appropriate expressive
number.

But even supposing that they were all agreed on this point, and said the wind
was 4 in strength, no one has ever attempted to determine what that number, or
any other in the table, really means,—what natural strength of the wind, or what
velocity of the air, it is equal to. A simple inspection of the table shews that the
scale is by no means a uniform one; for, between Nos. 1 and 2, there can hardly
be a difference of 4ib pressure of the wind on the square foot; while between 11
and 12, there may be 20 or 3016 difference.

Now, this is an imperfection in the system of the gravest kind, for if the strength
of the apparent wind be not observed in such terms as are reducible to those in
which the velocity of the ship is measured, the strength of the true wind, or that
which a person would feel if perfectly at rest on the ocean, cannot be determined ;
and the real motions of the atmosphere would be concealed to a great and un-
known extent, by the effects of the movement of the ship.

These defects are of consequence, too, even in ordinary practical matters, as
in trial squadrons; for it is not the whsolute speed of a ship which is wanted, but
the relative speed of it, with regard to the wind; and the winds, blowing at the
same time on the various ships several miles asunder, may be of very different
strengths ; as any one may prove to himself, by noting the capricious streaks, in
which, after a calm, a change sets in on the surface of the water. It is true, that,
by keeping the ships out a long time, a mean may be obtained of all these little
atmospherical currents, but the result will not be satisfactory ; and, as in the cele-
brated case of the three trial brigs, there may be a total difference of opinior on
the absolute merits of each vessel, by reason of the cause of the apparent su-
periority, now of one, and now of another, not being properly understood.

These difficulties are all of the character which would be removed by an instru-

mental method of determining the strength of the wind; and this is not the first

time that the use of an anemometer has been proposed on boardship; but those
which have hitherto been tried would seem to have failed, from not having been
of the appropriate kinds; and partly, indeed, because, in the case of those officers

AND DIRECTION OF THE WIND AT SEA. 457

with whom I have communicated, they seemed to look upon the effect of the
motion of the ship as something insuperable, and in the face of which there was
no need of aiming at any great accuracy.

On beginning to consider the best species of anemometer for the purpose in
question, it appeared to me that something on the principle of the log-line used
for determining the ship’s speed through the water, would be appropriate ; for,
notwithstanding the very scientific and accurate character of numerous instru-
ments invented for the sarme purpose in later years, still they have one by one
‘disappeared, or been forgotten ; and the old log-line has not only continued in ex-
istence from the earliest times to the present, but ninety-nine out of every hundred
ships that now go to sea are furnished with it, and with it alone. This peculiar vi-
tality and power of withstanding the changes of fashions and times, may perhaps
depend partly on this, that the quantity to be observed is measured on so very large
a scale, that the clumsiest person can read it off to sufficient accuracy ; while,
with the more modern methods, the accuracy of a person accustomed to delicate
observation, is necessary for any trustworthy determination at all. '

The case in anemometry, perfectly parallel to the log-line, would be,—to have
a float of some sort suspended in the air, and to note how many feet of line it ran
out in a certain length of time, under the combined influence of the movements of
the air and the ship. But though so perfect an imitation as this is prevented by
the rarity of the atmosphere, yet the vane of a horizontal windmill is an approach
to the same thing; where the float is supported in the air on a horizontal arm
fixed to a vertical axis; and the distance run out, is measured by noting the nuin-
ber of revolutions, and the magnitude of the circle described by the vane or float.

The small motive power, however, of a horizontal windmill, only one-twelfth,
according to SMEATON, of the vertical construction, together with the necessity of
having a moveable screen to cover up one-half of the wheel from the action of the
wind, has prevented the adoption of such a machine as completely for scientific
as for industrial purposes.

The vertical windmill, again, though it gains a far greater degree of mechani-
cal power, is also inappropriate for our purpose, on account of the very different
amounts of glancing off of the wind, at different velocities, from the inclined surface
of the sail ; the unavoidable twisting of the necessarily light arms, which prevents
the angle of the sail being perfectly constant; and the impossibility of fixing one
uniform standard for the shape, size, and angle of the sail; as well as the neces-
sity of having the plane of the sail-wheel always turned toward the direction of
the wind.

All these objections have, however, been very happily removed by a novel
windmill, of the horizontal form, invented by Mr EpGrwortu, which requires no
screen, but revolves by virtue of the shape of the float-boards ; which shape being
a constant quantity in all strengths and directions of the wind, the revolution goes

458 ON THE DETERMINATION OF THE TRUE STRENGTH

on in the same direction from whatever quarter the wind may come, and increases
in rapidity exactly in proportion to the strength of the wind.

Mr Epcrworts had proved many years ago the increased effect of wind
on a concave surface to a flat one, by taking a sheet of tin, and shewing that;
when bent into so very concave a form as to present considerably less area than
inits flat condition, to a current of wind blowing straight upon it, that still it ex-
perienced a greater degree of pressure. But it was only very recently that he
carried the principle farther into a practical form ; and the first notice of this is
found in Dr Rozinson’s communication to the British Association at Southampton, ’
descriptive of the application to a Whewell’s anemometer of one Mr EpGEworTH’s
horizontal vane wheels, where each vane consisted of a hemisphere, and the con-
cavities being all turned in one direction, and experiencing one-third more resist-
ance than the convex sides, the whole revolves from the concave as it were to
the convex sides, at one-third the rate of the wind.

This, then, seemed to be eminently the sort of anemometer for use on board-
ship.

No particulars of size or construction were given, only the important prin-
ciple involved was mentioned ; and as the first instrument which I had made, did
not prove sufficiently sensitive, I entered on a course of experiments to ascertain
the best sizes of the machine, and shape of the floats; and being greatly assisted
therein by the practical skill and ingenious methods of Mr Mixing, the artist em-
ployed, was at last enabled to fix definitively on the instrument figured in the ac-
companying plate as the one which combines the greatest number of advantages,
and forms altogether the best standard, perhaps, that can be adopted.

There are 4 hemispherical floats, 4 inches each in diameter, and 1 foot apart
from centre to centre: an endless screw, on the axis of the vane-wheel, gives
motion to a train of wheels and pinions, which serve to measure the number of
revolutions made; 13 grain, in the centre of one of the floats, is sufficient to pro-
duce motion. (See Plate XI.)

If the instrument be made on too small a scale, then it will have to overcome so
much larger a proportion of the friction of surface than a larger one, that the floats
will not move at one-third the velocity of the wind ; but as much of this friction
and resistance depends on the linear measure of the parts, while the motive power,
which is as the area of the float, increases as the square of the dimensions, it is
evident that increased velocity may be obtained by adopting a larger instrument.
There is, however, a danger of passing the proper medium again in this way ; for,
as some of the sources of friction increase according to the weight of the moving
parts, or as the cube of the linear dimensions, these may soon surpass the motive
power, which increases as the square only. There is another objection also to
having a vane-wheel with much mass, or vis inertiw; for although we wish in
this inquiry to get a mean, or the total sum, of all the little separate gusts of

AND DIRECTION OF THE WIND AT SEA. 459

which any particular wind is made up; and although, in a mere mechanical poing
of view, a wheel of great weight would tend to equalize and mean all the cur-
rents of different intensity, still it can only do so with a certain amount of loss,
and with the total omission of all very light impulses; and the only way accu-
rately to sum up all those separate little quantities, is to employ an instrument
which shall be as sensible as a feather, and take full and immediate account of
the slightest motion of the atmosphere.

After trial of floats 2, 3, 34, 4, and 6, inches in diameter, the 4-inch ones were
considered as being the best; and the hemispherical shape was also preferred,
as giving the greatest per centage of velocity with the least weight of material
and smallest side resistance, as well as offering the shape, of all others, of the
easiest and truest execution, and best understood everywhere.

Various experiments were tried, of making the floats more or less conical, in
order to diminish the pressure of the wind on their backs; but though that point
was most eminently obtained, still the advantage was outweighed by the neces-
sary increase of weight accompanying the increase of surface, the greater side
resistance to the wind, and the diminished pressure on the concave side.

In the month of January this year, I had the opportunity of trying the value
of the revolutions of this anemometer, in company with Captain CockBurn. The
instrument was mounted on the top of a cab, clear of the driver’s head, and
driven at a pretty uniform speed of above seven miles an hour, first forwards
and then back, on two miles of the London Road; the object being to measure
the artificial wind produced by the motion of the vehicle, which would of course
be equal to a natural wind blowing with the same velocity in the contrary
direction. The first day there was a rather strong breeze, which would have
completely vitiated the experiments, but that, as it was blowing almost exactly
in the direction of that part of the road which was traversed, we expected to be
able to eliminate its effects by taking a mean of the numbers given in going and
returning.

When going, having the wind with us, the instrument, which measured then
only the difference between the velocities of the wind and the cab, made 209
revolutions in one mile; but in returning, measuring the sum, it gave 921 revolu-
tions in the same distance. The mean of these, or 565, when multiplied by 3:1415
feet, or the space described by the centre of the float in one revolution, gives

a velocity not exactly 4, but aa of that of the wind.

The second day was all but perfectly calm; it was at the commencement of
the long-continued frosty weather; and a proof of the general stillness of the air
was offered in the dense, unnatural manner in which the smoke was accumulated
and remained suspended over the city. In going out, 558 revolutions were made in
one mile; and in coming back, 55). The mean of these, or 555, gives a velocity

VOL. XVI. PART IV. 4 6B

460 ON THE DETERMINATION OF THE TRUE STRENGTH

of the floats of a and the mean of both days makes it =. or almost exactly

what Dr Rosinson stated that it should be from theoretical investigation.

The result was, so far, perfectly satisfactory, and seemed to shew that the
instrument was fully entitled to be tried at sea, as giving a good and convenient
measure of the velocity of the wind. The particular proportion mentioned (4)
might probably not obtain equally under all velocities of wind, but it has not
been thought worth while to try the instrument at other velocities on shore ; because
there are much more powerfully modifying circumstances in the rolling motion
of the ship, the full effect of which can only be determined by actual experiment
at sea. But whatever alteration of the value of the revolutions takes place under
such conditions, naval officers may be assured of this, that a certain physical
connection between the velocity of the air and the revolutions of the anemometer
exists, and its exact nature may be easily investigated and discovered, and the
strength of the wind may then be entered in the log-book, in numbers expressive
of the velocity of the air in knots per hour, or in the same terms as the motion
of the vessel; and as the direction of the wind is already sufficiently well observed
by the different vanes at present in use on board ship, all the elements of the
apparent wind may, with the assistance of this anemometer, be looked upon as
satisfactorily obtained.

This apparent wind being, however, the combined effect of the motions of
the ship and of the air, may be very different from the true wind, both in di-
rection and in strength. When the ship is going with the wind, the velocity of
the true wind will be equal to the sum of the velocities of the ship and of the
apparent wind; and when going against the wind it will be equal to their
difference, without alteration of direction in either instance. But in almost
every other possible case both the velocity and the direction will be changed, the
problem being a particular application of the well known and important theorem
in mechanics of the parallelogram of forces; the velocity of the ship observed
forming one side, the velocity of the apparent wind—also obtained from obser-
vation—being the diagonal, and the true wind to be determined, another side.

This may be illustrated familiarly as follows:—Let the line A B (Plate XI.)
represent the motion of the ship, the length of the line shewing the velocity in
knots per hour as determined by the log-line, and the position of the line shewing the
vessel’s course, or the direction to which the vessel is proceeding, obtained by refe-
rence to the vanes and the compass. Similarly, let the lines A C or B D represent
the true wind, or the wind which a person at rest would feel to be blowing over
the sea during the time that the ship passed from A to B. The length of the
lines A C and B D shew the velocity of the wind in knots per hour, given by the
- anemometer, and the position of the lines gives the direction from which the wind
is coming.

Under such circumstances, what will be the apparent wind, or, in other words,

AND DIRECTION OF THE WIND AT SEA. 461

what will be the direction and the velocity of the wind which a person in the
ship will feel ?

Now, the motion of the ship from A to B being equivalent to a wind moving
with equal velocity in a contrary direction, or from B to A, then any particle
of air at rest at A will be driven, if acted on by the impact of this adventitious
wind only, to a distance, equal to AB, beyond A, and in the same direction, or
to E; but if acted on only by the natural wind, the particle will receive a velo-
city and a direction equal to that, and be driven from A to F; but as the particle
is acted on instantaneously by both forces, it will neither go to E nor to F, but in
an intermediate direction, and closer to one or other according to the relative
strength to the two forces, or in the diagonal of the parallelogram of which A F
and A E form two sides. AG, therefore, in the parallelogram AE FG, repre-
sents, by its length and position, the distance to which, and the direction in
which, a particle at A will be driven under the united influence of the natural
wind blowing over the sea, and the artificial wind caused by the motion of the
ship; i.e, AG represents the apparent wind, or that which a sailor would
observe.

For convenience of illustration we may complete the parallelogram A BDC,
which is similar to the parallelogram A EK FG, and where A D is consequently
equal to AG; and we may now, for the purposes of calculation, omit all but the
triangle A B D, in which the sides A B, A D, being given by observation, and the
included angle B A D being obtained from the difference of the observed directions
of the ship and of the apparent wind, we have merely to compute by the usual
rules for plane triangles, the length of the side B D, or the velocity of the true
wind; and the angle ABD, which, being added on to the course of the ship,
gives the direction of the true wind.

Considering, however, the necessary length of time which such a computation
must occupy in the hands even of the most expert (the mere preparation of the
angles for computation would of itself be no small matter, on account of the
rough character of the subtraction of the course of the ship from the direction of
the wind—both observed by compass points—the reduction of this to degrees,
then the re-reduction of the resulting angle into points, and the addition of them
to the course of the ship): considering, also, the almost infinite number of times
the calculations would have to be gone through in any voyage, and the extreme
improbability of any amateur undertaking so large a quantity of an unimproving
sort of labour, I have had a set of scales made for solving the problem by
inspection, and the entry being made with the velocities and directions observed,
the velocity and direction of the true wind are immediately given.

These scales, which are represented in Plate XI, are formed of two ordinary
jointed rulers, having moveable circles marked with the points of the compass on
the joints, and three sets of divisions on the legs, to include all possible velocities

462 ON THE STRENGTH AND DIRECTION OF THE WIND AT SEA.

of the wind and ship, from 1 mile to 100 per hour, each mile being capable of
subdivision into tenths.

A leg of each scale being made to slide one upon another, with the joint of
each turned outwards, the centres of these joints are to be placed at such a
distance apart as corresponds to the velocity of the ship in terms of any one of
the three sets of divisions on the legs. Both circles are then turned, so as to
shew on one edge of that double leg the observed direction of the ship’s course;
the single projecting leg of one scale being then placed in the observed direction
of the apparent wind, and the projecting leg of the other moved until one edge of
it cuts on the first, the divisions indicating the velocity of the apparent wind ;
then the length of the intercepted portion of that second leg shews the velocity of
the true wind, and its reading on its own circle gives the direction.

The circles are graduated to degrees as well as to points of the compass, so
as to be capable of solving all ordinary cases of plane triangles, as well as those
immediately contemplated, and to suit the instances sometimes found of the
more exact determination of the direction of the wind in degrees instead of
points.

As the scales stand at present, they require, when the significant numbers
of the anemometer shall have superseded the present unmeaning ones entered in
a ship’s log, no new data from observation; but by merely running down, scale
in hand, the columns of “Directions and Velocities of the Ship, and Apparent
Wind,” as entered in the book for the ordinary purposes of navigation, the direc-
tion and velocity of the true wind may be rapidly entered in a couple of adjacent
columns; and the importance of making this correction before beginning to reason,
from the data at present afforded by ships, on the general character of the winds
on the surface of the ocean, may be seen in the accompanying supposed extract
from the journal of a man-of-war or a steamer; where, though the true wind was
the same during the whole interval, yet, on account of the different courses
pursued, and velocities attained, by the ship at the various hours, the wind did alter
to those on board at times, almost of 90° in direction, and from 9 knots to 23 knots
in velocity.

Date. Ship’s Apparent Wind. True Wind.
Tote silk: cas JRA. CRWRLLEOS ri
Course : Direction ‘ Direction ae
1848. Hour. (to) Velocity. (from) Velocity. (from) Velocity.
Knots. | Knots. | Knots.
N 10°5 WSW 12-1 SW. by S 19:3

April 17

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( 463 )

XXXII. On the Products of the Destructive Distillation of Animal Substances.
Part I. By THomas AnpErson, Esq., M.D.

(Read 3d April 1848.)

In April 1846, I communicated to the Royal Society a paper on a new organic
base, to which I gave the name of Picoline, and which occurs in coal-tar, asso-
ciated with the Pyrrol, Kyanol, and Leukol of Runce. In that paper I pointed out
that the properties of picoline resembled, in many respects, those of a base which
UNVERDORBEN had previously extracted from DippeEt’s animal oil, and described
under the name of Odorine; and more especially mentioned their solubility in
water, and property of forming crystallisable salts with chloride of gold, as cha-
racters in which these substances approximated very closely to one another. And
further, I detailed a few experiments on the odorine of UNVERDORBEN extracted
from Drerev’s oil, with the view of ascertaining whether or not they were ac-
tually identical, but on too small a scale to admit of a definite solution of the
question.

These observations, coupled with the doubts which had been expressed by some
chemists, and more especially by REIcHENBAcH, as to the existence of the bases
described by UNVERDORBEN, induced me to take up the whole subject of the pro-
ducts of the destructive distillation of animal substances, which has not yet been
investigated in a manner suited to the requirements of modern chemistry. In
fact, UNVERDORBEN is the only person who has examined them at all, and his
experiments, contained in the 8th and 11th volumes of PocGEnporr’s Annalen,
constitute the whole amount of our knowledge on the subject ; and his observa-
tions, though valuable, and containing perhaps as much as could easily be deter-
mined at the time he wrote, are crude and imperfect, when we come to compare
them with those which the present state of the science demands. Since his time,
the methods of investigation in organic chemistry have undergone an entire
change: the simplifications of the process of organic analysis had not then been
made, or at least had not come into daily use as the auxiliary of investigation,
and UNVERDORBEN, who belonged to the old school, and contented himself with
the observation of reactions only, was necessarily led, as I shall afterwards more
particularly shew, to confound together substances, the reactions of which approxi-
mate so ‘closely that it is impossible, or at least very difficult, to distinguish them
by such means alone. The errors, however, lay with the method, and not with

the observer ; for UNVERDORBEN’s experiments, so far as they go, I have found to
VOL. XVI. PART IV. 6c

464 DR ANDERSON ON THE PRODUCTS OF THE

be correct in the main, notwithstanding their having been called in question by
REICHENBACH, whose numerous researches on the kindred subject of the products
of the destructive distillation of vegetable substances, gave weight to his opinion,
and have indeed been the principal cause of the doubts expressed by others on
the subject.

The investigation of these products has occupied me pretty continuously since
the publication of the paper before alluded to; and my researches have now ex-
tended themselves over a large part of the subject, although, from its branching
off into so many subdivisions, and embracing the consideration of so large a num-
ber of substances belonging to almost every class of organic compounds, some
time must still elapse before it is complete in all its parts. It is my intention,
therefore, as the subject naturally divides itself into several sections, to take up
the consideration of these in a succession of papers, of which the present is the
first, and in which I propose to consider the general properties of the crude pro-
duct employed in my experiments, and those of certain of the organic bases con-
tained in it.

The products of the destructive distillation of animal matters were long since
employed in medicine, and were obtained from all parts of the body, and from
almost every section of the animal kingdom; but these afterwards entirely gave
way to the Oleum Cornu Cervi, which, as hartshorn is entirely free from fatty
matters, must necessarily be the pure product of decomposition of the gelatinous
tissues. The more volatile portions of this oil, separated by distillation with
water, and purified by numerous rectifications, constituted the Oleum Animale
Dippellii of the older pharmacopceias. These substances would, in all probability,
have been the most convenient crude materials for my experiments; but as they
have long since ceased to be employed, and cannot now be obtained except by
going through the tedious and disagreeable process for their preparation, I have
made use of the bone-oil of commerce, which is prepared on the large scale by
the distillation of bones in iron cylinders, and can be had in any quantity from
the manufacturers of ivory-black. This oil appears to differ in no respect from
the true Oleum Cornu Cervi, and, like it, is the product of decomposition of the
gelatinous tissues only ; for previous to distillation the bones are boiled in a large
quantity of water, by which means both the fatty matters and also a certain pro-
portion of the gelatine are separated. They are then dried, packed in the cylin-
ders, and distilled at a heat which is gradually raised to redness. The oily pro-
duct of this distillation is separated from the watery portion, and, after rectifica-
tion, forms the bone-oil of commerce; though in some instances this latter dis-
tillation is dispensed with, and the product of the first made use of without any
further purification.

Bone-oil, as supplied by the manufacturer, has a dark-brown, almost black co-
lour, with a somewhat greenish shade, and perfectly opaque in the mass: but when

DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 465

spread in a thin layer on a glass plate, it is seen to be brown by transmitted light.
Its specific gravity is about 0:970. Its smell is peculiarly disagreeable, and is mixed
with that of ammonia, which is always present, though sometimes in so small
quantity that its odour is disguised by that of the oil itself, and is only rendered
apparent by distillation. A piece of fir-wood moistened with hydrochloric acid,
and held over the mouth of a vessel containing it, rapidly acquires the dark red-
dish-purple colour which is characteristic of the pyrrol of Runer. Acids agitated
with the oil acquire a brown colour, especially on standing, and extract the bases
contained in it; but if the quantity of the acid be large, and in a pretty concen-
trated state, a nonbasic oil is also dissolved, which, on standing for some time,
and more rapidly if heated, undergoes decomposition, and the fluid becomes filled
with orange-yellow flocks of a resinous substance, which acquires a dark colour
by exposure to the air ; this change is produced by the stronger vegetable as well
as the mineral acids. Alkalies extract an acid oil, and a considerable quantity
of hydrocyanic acid, which, on the addition of an acid to the alkaline solution,
and distillation, can be distinguished in the product by its smell, as well as by
_ Its reaction with the salts of iron.

Previous to the seperation of the bases, the crude oil was again rectified in
portions of about fifteen pounds each, in an iron retort,—an operation attended
with some trouble, as the fluid is apt to froth up and boil over in the early part
of the process, so that the retort must not be more than half full, and the heat
requires to be applied in a very gradual manner. At first a watery fluid distils,
containing in solution ammonia, and a small quantity of the most volatile bases.
This is accompanied by an oil of a pale yellow colour, limpid and very volatile,
which after a time comes over without water, and with an increased though by no
means dark colour. The distillation proceeds in a perfectly steady and gradual
manner, until about two-fifths of the oil have passed over, when a point is attained
at which the temperature requires to be considerably raised, in order that the dis-
tillation may continue uniformly, and the product becomes much thicker and
more oily in its appearance. At this point the receiver was changed for the pur-
pose of collecting the less volatile portion apart, and the distillation continued
until the bottom of the retort reached a red heat. The latter portions of these
products were obviously altered during the distillation, for a bulky porous char-
coal remained in the retort ; the oil which passed over smelt strongly of ammonia,
crystals of carbonate of ammonia made their appearance in the neck of the re-
tort, and a certain quantity of water collected in the receiver. The oil also be-
came gradually darker in colour, and more viscid in its consistence. By collect-
ing in a succession of receivers, I had an opportunity of observing a great number
of curious optical phenomena at different epochs of the distillation. The oils fre-

| quently presented well-marked appearances of epipolic dispersion, and the very

last portion exhibited a curious species of dichroism, its colour being dark reddish-

466 DR ANDERSON ON THE PRODUCTS OF THE

brown by transmitted, and green, with the effect of opacity, by reflected light.
All these appearances, however, were very evanescent, and are only seen in the
newly distilled oil, for after a few days it becomes very dark coloured, and they
are then no longer visible.

Both the more and the less volatile oils contain a variety of bases, and were
separately treated for their extraction. In neither, however, is the quantity
large. I obtained from the more volatile portion of three hundred pounds of
bone-oil less than two pounds of the mixed bases; but as, in the course of the
various processes to which it was submitted, some small portions were lost, the
whole may perhaps amount to about three-fourths per cent. of the total quantity
of oil. The less volatile portion yields a larger quantity, which may be estimated
at two or three per cent. of the crude oil. These, of course, are only rough esti-
mates, but they may serve to give an idea of the quantity of the products.

Preparation of the Bases.

For the preparation of the bases precisely the same processes were followed
throughout for both portions into which the oil was separated by distillation ; and
as the bases to be described in the present paper were contained in the more vo-
latile portion, I shall detail the steps followed in reference to that quantity only.
The oil was mixed in a cask with sulphuric acid diluted with about ten times its
weight of water, and the fluids left in contact for a week or two, during which
time they were frequently agitated. More water was then added, and the whole
drawn off, and the process repeated with fresh quantities of sulphuric acid as long
as any bases were extracted. The solution, which had a reddish and sometimes
very dark brown colour, contained the bases, along with a quantity of nonbasic
oil and of pyrrol. It was mixed with an additional quantity of sulphuric acid,
introduced into a glass distilling apparatus, and heat applied. As the fiuid ap-
proached the boiling point, a quantity of the red resinous matter before alluded
to began to separate, and occasioned succussions of so violent a character as to
endanger the safety of the vessel, and render it necessary to interrupt the process
for the purpose of filtering it off, after which the distillation proceeded without
difficulty. A small quantity of oil distilled over, and the water which accompa-
nied it had exactly the smell of the water in a gas-meter, and contained pyrrol,*
which continued to pass over for a long time, during the whole of which the dis-
tillation was continued. This distillation I had recourse to at first, from a sus-
picion that some of the bases were separated from the acid, and volatilised during
the process; but so soon as I had ascertained that this was not the case it was

* These odours were so exactly alike, that I was induced to seek for pyrrol in the water of gas-
meters, and I found that when mixed with sulphuric acid and distilled, the product gave the cha-
racteristic reaction of pyrrol with fir-wood. Ammonia remained in combination with the sulphuric

acid.

DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 467

dispensed with, and the fluid boiled down in porcelain or copper evaporating
basins, water being added, and the distillation continued until, by taking a small
quantity of the fluid and distilling off a few drops in a retort, they were found to
be free from pyrrol. Even this precaution soon became unnecessary, for a little
experience enabled me to know when the evaporation had been sufficiently pro-
longed.

. The dark-brown fluid which remained in the basins was once more strained,
in order to get rid of such resinous matters as might have separated during the
evaporation, and then distilled in a large glass balloon connected with a condenser,
after the acid had been previously supersaturated by a base. For this purpose,
potass, soda, and lime were indifferently made use of: the latter answers ex-
tremely well, but, owing to the large quantity of sulphate of lime separated, the
distillation requires to be carried on in the chloride of calcium or oil bath. When
the alkali is added in sufficient quantity, an oil floats up to the surface of the
fluid, and a strong pungent odour is given off, in which that of ammonia is appa-
rent, along with another which can be compared to nothing but the smell of stink-
ing lobsters. At the first part of the distillation a transparent and colourless
watery fluid passed over, which contained the bases in solution; but after this
had continued for some time, an oil made its appearance running in globules
down the tube of the condenser, and dissolving immediately in the fluid which
had already distilled. When the bases ceased to distil in quantity, the receiver
was changed, and a small quantity of oil heavier than water was obtained by con-
tinuing the distillation for some time. At the end of the process an oil remained
floating upon the concentrated fluid in the balloon, the quantity of which is very
variable, and depends on the distillation of the crude bone-oil, having been con-
tinued too long before changing the receiver. In fact, it contains some of the
bases of the less volatile oil, and will come to be considered in an after part of
the investigation.

To the product of the distillation sticks of caustic potass were added, and, as
these dissolved, the oily bases separated from the fluid in a manner exactly similar
to that which was observed in the preparation of picoline, as detailed in the paper
to which reference has already been made. The alkaline solution was drawn off
by means of a siphon, and more potass added as long as water was separated. In
this way the greater part of the base was obtained, but a small quantity of the
most volatile of all still remains in the alkaline solution, and cannot be separated
except by the addition of a very large quantity of potass. It was, however,
readily obtained by distilling the fluid, and collecting only the first portion of
the product, from which it was separated by a comparatively small expenditure
of potass. The small quantity so obtained was preserved separately from the
large mass.

VOL. XVI. PART IV. 6D

468 DR ANDERSON ON THE PRODUCTS OF THE

The product of this operation was found to be extremely complex, and to con-
sist of a mixture of four or five different bases, exclusive of ammonia. For the
purpose of obtaining these in a separate state a great variety of processes was
attempted, but none were found to answer so well as fractionated distillation,
although it is an extremely tedious method of separation, and occasions a consi-
derable loss of substance, which is very annoying when the quantities obtained
are so small. When the mixed bases were distilled with a thermometer, ammo-
nia began to escape at a very low temperature; but at 160° Fahr. the fluid entered
into steady ebullition, and a perfectly transparent and limpid oil began to distil.
A small quantity of oil passed over between this temperature and 212°, which was
received by itself, and the after products collected in a succession of receivers,
which were changed at every ten degrees which the thermometer rose. The fluid
continued in steady and rapid ebullition, and the thermometer ascended rapidly
to 240°; and between that and 250° a considerable quantity was collected. It
then again went up pretty rapidly, and another large quantity was obtained be-
tween 270° and 280°; after which the distillation proceeded more slowly until
the temperature rose to 305°, at which point the characters of the products under-
went a complete change. All the substances obtained at lower temperatures dis-
solved instantaneously in water ; but that which now distilled floated on the sur-
face, and only dissolved on agitation with a considerable quantity of water. Dis-
tillation now continued with somewhat greater rapidity, till the thermometer rose
to about 355°, when a drop of the product allowed to fall into a solution of chlo-
ride of lime immediately gave the reaction of aniline. When this was observed,
the whole remaining products, which formed only a small fraction of the whole,
were collected together. They consisted chiefly of aniline.

The products of these different distillations were repeatedly rectified, and by
this means bases were obtained, corresponding to the points at which the ther-
mometer was found to remain longest in the first distillation. Of these I have
as yet examined only the most volatile, and that which boiled at about 270°.

Petinine.

The most volatile portion of the bases obtained by the fractionated distillation,
was mixed with the small portion which was separated with difficulty from the
potash solution, and had been kept separate from the large quantity. The mixed
fluid still contained a large quantity of ammonia, for the separation of which it
was again rectified several times in succession, and fractionated in a small retort,
the receiver being kept carefully cool. After this process has been repeated until

it is properly purified, it constitutes the base to which I give the name of Petin-

ine (from zerenos, volatilis), in allusion to its volatility, which is greater than that of
any base yet known, with the exception, of course, of ammonia. The quantity of
this substance contained in the bone-oil is excessively small, as I obtained from

DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 469

three hundred pounds no more than was sufficient for the determination of its
constitution, and the leading characters of a few of its compounds. It is probable,
however, that some loss was incurred in the preliminary processes, as, from not
anticipating the presence of so volatile a base, I did not take any precautions for
producing complete condensation of the products, by means of freezing mixtures
or otherwise; and a considerable quantity was also lost owing to my anxiety to
expel completely the ammonia which it might retain.

Constitution of Petinine.

The petinine employed for analysis was very carefully dried over caustic
potass, the fluid poured off after some days’ contact, and distilled in the water-
bath at a very gentle heat; a precaution which is rendered necessary by its dis-
solving a certain quantity of potass. I did not possess a sufficient quantity to
make a determination of the nitrogen, but took it for granted that oxygen was
absent; an assumption which is justified by the analogy of all the other volatile
bases, as well as by the perfect coincidence of the experimental results with the
calculated formule. It was analysed with oxide of copper in a very long tube,
and gave the following results :

16:°286 ... carbonic acid, and

6°663 grains of petinine gave
8°382 ... water;

corresponding exactly with the formula C,H,,N, as is shewn by the following
comparison :

Experiment. Calculation.
EO
Carbon, ee 66:66 66°66 Cz 600-0
Hydrogen, . . . 13:97 13°88 io 125-0
Nitrogen, eee tel 823K 19°44 N 175-0
100-00 100-00 900-0

In order to ascertain the atomic weight of petinine, I prepared its compound
with chloride of platinum, and made the following determinations of the platinum
contained in it :

I { 6°351 grains of chloride of platinum and petinine gave
"(2-245 ... platinum = 35°34 per cent.

i { 3'860 grains of chloride of platinum and petinine gave
‘(1372 ....__ platinum = 35-54 per cent.

Ill { 2°844 grains of chloride of platinum and petinine gave
‘(1010 ... platinum = 35:51 per cent.

470 DR ANDERSON ON THE PRODUCTS OF THE

The atomic weights deduced from which agree very closely with the calculated
results :

I. Atomic weight, by experiment, ‘ : 910°3
IT. we es se : é 5 891-2
EE. Ags oe ies ; : ‘ 894-2
Mean, ; : 7 : : : : 898°5
Calculation, . : ; : 5 Z : 900-0

The mode in which this base is formed during the decomposition of gelatine,
it is, of course, impossible at present to perceive. In its chemical relations it is,
however, in all probability, related to the butyric series; and it is even possible that
we may obtain it by artificial processes. Some time since, Korpe* published some
researches on the galvanic decomposition of valerianic acid, among the products
of which he discovered a carbo-hydrogen, having the formula C,H,. Now, by
treating this substance in the same manner as benzine is acted upon for the pre-
paration of aniline, we ought to obtain from it, if not petinine, at least an iso-
meric compound, as may be easily seen by comparing the formule of the different
substances :

Benzine, . . . Cy He, C; Hy Ko.sz’s carbo-hydrogen..
Nitro-benzide, . Cy H;(NO,) C;H,;(NO,) Action of nitric acid.
Aniline, . . . Cy, N Cs Hy) N Petinine.

I have not yet had an opportunity of determining whether the change which
theory would lead us to expect actually takes place, but there is every reason to
suppose that it would.

Properties of Petinine.

Petinine is a transparent colourless fluid, limpid as ether, and possessing a high
refracting power. It has an excessively pungent odour resembling that of am-
monia, and yet quite distinct, for when the effect of its pungency has gone off, or
it-is smelt in a dilute state, its smell is disagreeable, and somewhat similar to that
of decayed apples. Its taste is hot and very pungent. It boils at a temperature
of about 175° F.; but the quantity which I possessed was too small to admit of
an accurate determination either of this point, or of its specific gravity, although
the latter is certainly less than that of water. Petinine is a very powerful base,
and immediately restores the blue colour of reddened litmus, and gives abundant
fumes, when a rod dipped in hydrochloric acid is held over it. It unites with the
concentrated acids, with the evolution of much heat. It dissolves in all propor-_
tions in water, alcohol, ether, and the oils; and is also soluble in dilute solution
of potass, but not in concentrated. Petinine gives double salts with bichloride of —

* Memoirs of the Chemical Society of London, Part xxi.

DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 471

platinum and corrosive sublimate, both of which are soluble in water. With chlo-
ride of gold it gives a pale yellow precipitate, which does not dissolve on boiling
the solution, and is not deposited in crystals. Petinine throws down peroxide of
iron from its compounds. It also precipitates salts of copper, and the oxide
thrown down dissolves in excess of the base with a fine blue colour.

These properties agree with those of none of the bases described by UNVER-
DORBEN ; and, in fact, it is certain that petinine could not have been present in
the mixture to which he applies the name of odorine, for he expressly states that
it commenced boiling at 212°. And it is easy to see why he did not obtain it,
because, in separating the bases from the acid by which they were extracted from
the crude oil, he took care to add a quantity of potass just so great that the oily bases
were liberated, and not the ammonia; and as his object in doing so was to get
rid of the latter substance, and there being no means of doing this exactly, it is
probable that he did not fully separate the bases, but the most volatile, which is
also the most powerful, remained in combination with the acid along with the
ammonia.

Compounds of Petinine.

The minute quantity of petinine which I obtained has necessitated a very cursory
examination of its salts, which are interesting, both from the facility with which
they crystallise, and their great stability. None of them undergo change in the
air, but may be left exposed for any length of time without acquiring colour.
They are all soluble in water, and those with the volatile acids sublime without
decomposing, and are deposited in crystals upon cold surfaces.

Sulphate of Petinine, is obtained by adding petinine to dilute sulphuric acid
until the fluid is neutral. On evaporating, petinine is given off, and the solution,
when concentrated to a syrup, concretes on cooling into a foliated mass of crys-
tals of an acid sulphate. These crystals are strongly acid to test-paper, extremely
soluble in water, and slightly deliquescent in moist air.

Nitrate of Petinine—The solution of petinine in nitric acid, evaporated to
_ dryness, and gently heated on the sand-bath, gives a sublimate of the nitrate in
fine woolly crystals.

Hydrochlorate of Petinine—Hydrochloric acid combines with dry petinine,
with the evolution of much heat, and the formation of a salt which is extremely
soluble in water, and sublimes in fine needle-shaped crystals.

Chloride of Platinum and Petinine—If bichloride of platinum be added to a
dilute solution of hydrechlorate of petinine, the salt formed remains in solution ;
but when both substances are concentrated, it falls as a pale yellow precipitate,
which was purified by crystallisation from hot water. On cooling, the fluid, if
sufficiently concentrated, becomes entirely filled with exceedingly beautiful golden-
yellow plates, resembling those of crystallised iodide of lead. Jt ispretty soluble

VOL. XVI. PART IV. 6E

472 DR ANDERSON ON THE PRODUCTS OF THE

in cold water, extremely so in hot, and is not decomposed by boiling the solution.
It is also soluble in alcohol.

5930 ... carbonic acid, and

9°552 grains of chloride of platinum and petinine gave
S000, | ...4 Water,

By three determinations of platinum, the details of which have been already
given, the mean per-centage of platinum was found to be = 35-46.
These results correspond with the formula C, H,, N, H Cl, Pt Cl..

Experiment. Calculation.

——
Carbon.) t on 16°93 17:26 C; 600:0
Hydrogen;) .)/).) sa 4:17 3°96 Ay 137°5
Nitrogen) op) b if 5°04 N 175-0
Chloning,, 24. 6 a 38:29 Cl, 1330°4
Platnum, . . . 35°46 35°45 PE 1232°0

100:0 3474-9

Chloride of Mercury and Petine.—A solution of petinine in water, added to a
solution of corrosive sublimate, gives a white precipitate, which dissolves in a
considerable quantity of hot water, from which it is again deposited in crystals.
It is much more soluble in alcohol; and the boiling solution gives a deposit of
beautiful silvery plates on cooling. It is decomposed by boiling its watery solu-
tion, petinine being driven off, and a white powder deposited. It is readily so-
luble in the cold in dilute hydrochloric acid, probably with the formation of ano-
ther double salt.

Products of Decomposition of Petinine.

The want of substance, which prevented the full investigation of the salts,
has likewise curtailed this branch of the subject to a very few observations, which
is the more to be regretted, as the general properties and low atomic weight of
petinine give promise of definite products, which might enable us fully to deter-
mine its position in the chemical system.

When treated with concentrated nitric acid, it dissolves without any remark-
able phenomena, and, on boiling, a feeble evolution of nitrous fumes takes place;
but the petinine is attacked only to a very small extent, for, after being kept
boiling for a long time, and then supersaturated with potass, it evolved the smell

of the base apparently unchanged. Solution of chloride of lime immediately acts —

upon it in the cold, and developes a highly irritating odour, and some compound
is manifestly produced; the solution remains colourless. Bromine water dropped
into an aqueous solution of petinine occasions the precipitation of a yellow oil

DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 473

heavier than water, and insoluble in acids,—the solution contained hydrobromate
of petinine. From the analogy of the other volatile bases, we should expect this
to be tribromopetinine, C,H, Br, N. My material being exhausted, I was not able
to extend these observations further.

Picoline.

Having determined the properties of petinine, I next turned my attention to
that portion of the mixed bases which boiled between 270° and 280°, where I had
every reason to expect the presence of picoline. After several rectifications, in
each of which the first and last portions of the product were separated, I obtained
a fine colourless transparent oil, possessed of all the properties of that substance.
It dissolved readily in water: gave, with chloride of gold, a fine yellow compound
depositing in needles from the hot solution, and with bichloride of platinum, a salt
crystallizing in orange-yellow needles, analogous in all its properties to that of
picoline. This identity was confirmed by analysis, which gave the following
results:

5°648 grains of picoline from bone-oil gave

15°990 ... carbonic acid, and
3°998 ... water.
Carbon Erie is wae TT ol 7741 Cre 900-0
HHydroreny) ss. vt%) 7:86 7-53 H, 87:5
Nitrogen, . . . . 14:98 15:06 N 1750
100-00 100-00 1162°5

For still further security, a determination of the platinum in its double salt
with the chloride was made :

{ 12-784 grains of chloride of platinum and picoline gave
4204 .., platinum.

This corresponds to 32°88 per cent., and the calculation gives 32:94.

The suspicion, then, of the occurrence of picoline in the odorine of UNVER-
DORBEN turns out to be perfectly correct; at the same time my experiments have
clearly shewn, that odorine is a mixture of picoline, with at least one other base,
the properties of which will be detailed in the second part of this investigation. The
quantity of picoline contained in bone-oil is considerable, and it can be more readily
prepared from that substance than from coal-tar naphtha; in fact, I obtained from
three hundred pounds of bone-oil a larger quantity of picoline than that employed
in my examination of it, which was obtained from some hundred gallons of coal-
tar naphtha; and by means of it, I shall be enabled to trace out the products of
its decomposition, which I was unable to pursue in my former communication

474 DR ANDERSON ON THE DISTILLATION OF ANIMAL SUBSTANCES.

The presence of aniline in bone-oil I have already alluded to, and its quantity,
though small, is by no means inconsiderable, when compared with that of the
other bases. I did not think it necessary to take any further means for its iden-
tification than its highly characteristic reactions with chloride of lime and nitric
acid.

The investigation of the other bases is not yet in a sufficiently advanced state —
for publication. The sparingly soluble one has been especially troublesome, and
its purification is attended by difficulties which I have not yet fully overcome.
The consideration of these will be taken up in the second part of this investiga-
tion.

( 475 )

XXXIIT—On the Action of the Dry Gases on Organic Colouring Matters, and its
relation to the Theory of Bleaching. By Grorce Witson, M.D., Lecturer on
Chemistry, Edinburgh.

(Read, April 17, 1848.)

I. Preliminary Remarks.

The remarkable power which chlorine possesses, of destroying all colours of
organic origin, has long been an object alike of speculative and practical interest.
The theory of bleaching, however, has hitherto remained imperfect, in conse- .
quence chiefly of the observation of Sir H. Davy, that chlorine loses the power of
decolorising when deprived of water. So striking is the difference, in this respect,
between wet and dry chlorine, that it led the distinguished chemist mentioned, to
deny to this gas the character of being essentially, or per se, a bleacher. He re-
garded as the true decolorising agent the oxygen of the water, which must be
associated with chlorine before the latter can bleach. The late Dr TurNsr has
stated Davy’s view so shortly and clearly, that I quote his abstract in preference
to any statement of my own. ‘ Davy,” says he, “ proved that chlorine cannot
bleach, unless water is present. Thus dry litmus suffers no change in dry chlo-
rine; when water is admitted the colour speedily disappears. It is well known
also, that hydrochloric acid is always generated when chlorine bleaches. From
these facts, it is inferred that water is decomposed during the process; that its
hydrogen unites with the chlorine, and that decomposition of the colouring mat-
ter is occasioned by the oxygen which is liberated. The bleaching property of
binoxide of hydrogen, and of chromic and permanganic acids, of which oxygen is
certainly the decolorising principle, leaves little doubt of the accuracy of the
foregoing explanation.’’*

The opinions of chemists on this point have now entirely changed. Chlorine
is reinstated in the place it formerly held as the possessor of positive and intrinsic
bleaching powers, and is looked upon as exerting these even when water is pre-
sent. I quote Sir Ropert Kane’s views on this subject, as more fully expressed
than the statements of most of our chemical authorities, and because he has de-
monstrated experimentally the falsity of Davy’s conclusion. ‘‘ The theory,”
says he, in allusion to bleaching, ‘‘of this action of chlorine, which had been
formerly thought to depend upon a mere oxidation of the colouring matter, water
being decomposed, has been shewn by my results with orceine, and confirmed by
those of ErpMAN on indigo, to consist in the formation of new substances con-

* Elements of Chemistry, 7th edit., p. 275.
VOL. XVI. PART IV. 6F

476 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

taining chlorine. The chlorine in some cases replaces hydrogen; in others, it
combines directly with the colouring matter; in others, again, water is decom-
posed, and the product, besides containing chlorine, is also more highly oxi-
dised.’’*

Beautiful, however, and satisfactory as the investigations of Kanr, ErpMAN,
Dumas, Laurent, and others are, they leave unconsidered the question, why has
chlorine, which so rapidly and permanently destroys the colour of organic com-
pounds when moist, no action on them when dry ?

The object of the researches I am about to detail, is to supply, in part at least,
this defect in the theory of bleaching, by endeavouring to shew how the removal
of water from chlorine arrests or suspends its decolorising power. Before enter-
ing at length into this question, however, I would observe, that Davy’s conclu-
sion, that oxygen is the efficacious bleaching constituent of moist chlorine, cannot
be regarded as marked by the felicity which generally characterised that great
chemist’s interpretations of obscure or complicated phenomena.

1. His view assumed, against all probability, that the acknowledged great
affinity of chlorine for hydrogen would be exerted solely towards the hydrogen
of water, but not towards that present in a colouring matter; or at all events,
that the affinity in question would be efficacious only in relation to the elements
of water. We certainly must set aside, as entirely arbitrary, the notion, if that
were implied in Davy’s statement, that chlorine in the presence of two bodies—
water and a colouring matter—each containing hydrogen, would be indifferent to
that element, as a constituent of the one, but eager to unite with it as present in
the other. Although free chlorine, however, must be regarded as equally ready
to unite with the hydrogen of every compound which comes within the sphere of
its affinity, it does not follow that it will obtain that element with equal ease
from every substance containing it. On the other hand, we may be certain, that
those more unstable compounds which part most readily with their elements,
will be the first to have the hydrogen removed from them by chlorine, whilst
less easily decomposed substances may resist its action altogether. Davy’s view,
however, gains nothing from this acknowledgment; for it represents water, an
enduring compound of but single equivalents of two elements, as compelled to
abandon its hydrogen to chlorine, whilst the proverbially fading colouring prin-
ciple of a flower or an insect—a frail combination of many equivalents of three
or more elements—is assumed to be able to retain its hydrogen unaffected by
chlorine. In the justice of such a conclusion, no chemist could concur.

2. Again, DAavy’s argument proved too much, and was in truth, self-destruc-
tive; for if chlorine be denied the character of a positive bleaching agent, be-
cause it does not bleach when dry, then oxygen, judged by the same rule, must

* Elements of Chemistry, p. 1054,

ON ORGANIC COLOURING MATTERS. 477

be refused that character also, for when the latter gas is deprived of moisture, it
is more indifferent to colouring matter than even chlorine. Davy’s reasoning,
then, if pushed to its logical consequences, conducts us to the strange conclusion
that since, when moist chlorine bleaches, the chlorine and oxygen are not the
active agents, and the only other body present except the colouring matter is
hydrogen, which certainly does not decolorise when dry, bleaching must be re-
garded as an inexplicable phenomenon, an effect without a cause.

It would not be difficult to point out other objections to the consistency of
Davy’s opinion; but those given may suffice to prove that, before the analysis of
the products of chlorine-bleaching shewed the erroneousness of his conclusion,
its inherent untenableness admitted of easy illustration. ~

Il. Influence of Sunlight on the Bleaching Action of Dry Chlorine.

The chief object of the experiments which this paper details was, to ascertain
the cause of the indifference of chlorine when free from moisture to anhydrous
organic colouring matters. But before entering on this inquiry, it occurred to
me to doubt, whether Davy’s original proposition, that dry chlorine does not
bleach dry colours (which seems to have been universally assented to by his suc-
cessors), could be admitted without limitation.

A repetition of his experiments appears, at first sight, to justify uncondition-
ally his conclusion. Among the specimens which accompany this communica-
tion are two sealed tubes, containing blue and red litmus-paper shut up in an
atmosphere of chlorine. The paper was first dried in a current of air previously
passed through chloride of calcium. A stream of carefully desiccated chlorine was
then sent over the paper for five minutes, and the tube, whilst full of gas, sealed
at the blow-pipe. The coloured papers were thus exposed, in the first place, to
the bleaching action of some sixty cubic inches of chlorine; and have, in addi-
tion, remained in contact with that gas since the 28th of July 1847, a period
of more than eight months, yet they still retain their original tints, though
somewhat faded. Had water been present in these experiments, the colours
would have been irrecoverably destroyed in a few seconds, or minutes at the
farthest.

Striking as these results are in supplying confirmation of Davy’s views, they
are curiously contradicted, or rather qualified, by other experiments, differing,
from those just mentioned, as to mode of trial, only in one particular.

The affinity of chlorine for hydrogen, when both gases are free, is greatly mo-
dified by the action of sunlight, so that whilst in perfect darkness they may be
kept mingled without combining, they unite with explosion if exposed to the
direct rays of the sun, and more or less rapidly in diffuse daylight, according to its
intensity. So faithfully, indeed, do free chlorine and hydrogen obey what natural

478 DR GEORGE. WILSON ON THE ACTION OF THE DRY GASES

philosophers and chemists have agreed to call the actinic influence of the sun-
beam, that the mixed gases contained in a graduated tube over water are found
to form a delicate actinometer, the intensity of the actinism being measured by
the rapidity with which the water rises in the tube, as it dissolves the hydrochlo-
ric acid produced by the union of the gases.* This actinic exaltation of affinity,
so striking when both gases are free, continues to manifest itself, though less
powerfully, when chlorine is in contact with substances containing hydrogen,
although the latter is in a state of combination.

Chlorine water remains unchanged in the dark, but is rapidly converted by
sunlight into hydrochloric acid, and free oxygen. Dutch liquid, chloroform, and
chloric ether, besides various other bodies, are known to give up their hydrogen
to chlorine much more swiftly when exposed to the direct rays of the sun than
if shaded from them. It seemed in the highest degree probable that the hydro-
gen of organic colouring matters would, in like manner, resist the action of dry
chlorine for a much shorter period in sunlight than in diffuse daylight, or in
darkness. To determine this point, the following experiment was tried. A wide
glass-tube, open at both ends, was constricted in the middle so as to present a
narrow central canaJ, like that of an hour-glass. Pieces of blue and of red
litmus-paper were then placed on either side of the constricted portion, and the
open ends of the tube drawn out at the blow-pipe, so as to admit of their being
put in communication, by means of caoutchouc connectors, with an arrangement
for drying the paper, and furnishing chlorine. After the paper had been ex-
posed to a current of dried air at the temperature of 220° Fahr. for three hours,
washed chlorine, transmitted through Nordhausen sulphuric acid, and a tube
three feet long containing fused chloride of calcium, was sent along the double
tube containing the papers, for five minutes. The ends of the tube were then
sealed whilst it remained full of gas, and the constricted middle portion closed
and divided at the blow-pipe, so that the double tube was converted into two
single hermetically sealed ones, each containing dried litmus-paper mm an atmo-
sphere of chlorine. In this way two tubes were procured, each containing por-
tions of the same coloured paper, which had been dried in the same current of
air, and exposed in exactly similar circumstances to the same stream and the
same amount of dry chlorine.

The one of these twin tubes was hung up inside a window, with a western
exposure, on or about the 31st of July 1847. The other was laid aside in a cup-
board, out of reach of the direct rays of the sun, but not protected from the influ-
ence of dull daylight. It was frequently brought out, moreover, to be examined,

and was at no time during the day in absolute darkness. I shew the Society 3

this tube after remaining in the circumstances described for more than eight

* Lond. and Edin. Phil, Mag., 1844, vol. xxv. . 2-3.
g > Pp

ON ORGANIC COLOURING MATTERS. 479

months. ‘The inclosed papers still retain their original colours little altered; and
in perfect darkness would, in all probability, have retained them still better.
Side by side with this tube I have placed its twin, which was exposed to full sun-
shine, and the papers in which are bleached to the purest white. In how short
atime his change occurred I cannot precisely say, as absence from town be-
tween the Ist of August and the 16th of September 1847 prevented me from watch-
ing the progress of the actinic bleaching. But, on the last-mentioned date, I found
the paper completely decolorised, so that six weeks of sunshine sufficed totally to
bleach paper in dry chlorine, whilst that gas excluded from direct sunlight has
failed to produce the same effect in eight months and a half.* In another quite
similar experiment, the results were much less striking. A tube with dry chlo-
rine and litmus-paper has hung since 1st August 1847 in a western exposure,
yet, at the date of my writing, (April 13, 1848), the litmus-paper, though much
faded, as appears when it is contrasted with the contents of the twin tube which
was kept out of sunshine, is far from being entirely bleached. This difference
in result leads to the suspicion, that in the experiment first recorded, the chlo-
rine or the paper may not have been so dry as both were in the second trial.
Great precautions (the same in both cases) were taken to secure absence of mois-
ture from the gas and the paper, but I know of no test of perfect dryness appli-
cable to gases, and I cannot. affirm that, in either case, the chlorine or the colour-
ing matter was absolutely anhydrous. Nor does it admit of doubt that the pre-
sence of even a trace of water would sensibly quicken bleaching under sunlight,
which rapidly decomposes chlorine-water. Yet every chemist will acknowledge
that chlorine, which could be retained over litmus without bleaching it for
nearly nine months, must have made a close approximation to perfect dryness.
We are as yet, moreover, too ignorant of the laws and conditions of actinic action,
to know well how to dispose of apparent discrepancies in its effects.

I could not try more than the two experiments recorded, last summer, and I
did not think it desirable to attempt a repetition of them during the clouded
season of the year. Meanwhile, different as is the testimony these experiments
afford, as to the rapidity of actinic chlorine-bleaching, they agree in proving that
darkness, as well as dryness, is essential to the preservation of organic colours
from destruction by chlorine, and that this gas, at least when assisted by sun-
light, is a positive bleacher. Davy’s original proposition must be accepted with
this qualification.

I close my remarks on this subject, with the observation, that in bleaching on
the large scale it should make a sensible difference on the rapidity of the process,
whether it be carried on in open sunlight, or in exclusion from it. Our present
bleaching process is as rapid as could well be wished, so that it is not in the direc-

* The papers shut up with chlorine, and kept in darkness, have not become bleached by two
months’ longer retention in the gas June 19, 1848
VOL. XVI. PART IV. 6G

480 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

tion of quickening his methods, that the practical bleacher probably desires im-
provement. One may expect, however, that the same amount of chlorine, espe-
cially if moist, should be more efficacious in bleaching, if assisted by sunlight,
than if debarred from it; or what comes to the same thing, that a small amount
of chlorine should, in practice on the great scale, bleach as powerfully in sunshine,
as a larger one in darkness. It might be possible, accordingly, to economise chlo-
rine, or chloride of lime, in this country, in the brighter seasons of the year, and
at all times in sunny climates, if the bleaching operations were carried on in the
open air.

Ill. Influence of Water over the Bleaching Action of Oxygen, Sulphurous Acid, and
Sulphuretted Hydrogen.

The fact that actinised chlorine bleaches, though dry, supplies no explanation
of the function which water performs, when it invests that gas with decolorising
power. With a view to solve this problem, I made two series of experiments ;
1st, The object of the one was to observe to what extent other bleaching gases
resemble chlorine in being dependent for bleaching power on the presence of
water, and likewise to ascertain whether the acid gases and the volatile alkali,
when made anhydrous, lose that power of changing the tints of dry organic colour-
ing matters, which characterises them when moist. These experiments promised
to shew whether the action of dry chlorine on colours is exceptional and anoma-
lous, so as to demand a special explanation, such as Davy gave, or but a parti-
cular case of a general law, to which all elastic fluids are obedient.

2d, The object of the other set of trials was to determine, whether bleaching
power can be conferred upon dry chlorine, by dissolving it and anhydrous colouring
matters in liquids containing no oxygen. I begin with the experiments first re-
ferred to.

Five gases besides chlorine have marked bleaching powers when in the condition
of perfect elastic fluidity, and not anhydrous, viz., chlorous acid, hypochlorous
acid, sulphurous acid, sulphuretted hydrogen, and oxygen.* To these may be
added provisionally, the curious body ozone, which Berzetius regards as an allo-
tropic form of oxygen, and SCHOENBEIN as a volatile peroxide of hydrogen. I have
made no experiments with this substance, because, in the present state of our
knowledge concerning it, it could not supply crucial results. Chlorous acid is too
explosive to admit of satisfactory researches being made with it. The same re-
mark applies with limitation to hypochlorous acid, a substance so interesting, from
its high bleaching power, and its containing, like chlorous acid, the two most im-
portant bleaching agents, chlorine and oxygen. I have made no experiments with ~
this substance, but PELouzE has quite recently supplied us with a new and much

* T omit from this list hydrogen, because, although it bleaches powerfully in the nascent state, it has
no sensible bleaching action, whether moist or dry, after it has attained the condition of perfect gaseity.

ON ORGANIC COLOURING MATTERS. 481

more manageable process for preparing it, by means of which we may hope to
make researches as to its action on colours.* My experiments have been limited
to sulphurous acid, sulphuretted hydrogen, and oxygen. I begin with the last as
the chief rival in bleaching power of chlorine.

Oxygen.

I have not thought it necessary to make many experiments with oxygen, as to
its relative bleaching power when moist and dry. Test papers can be preserved
for years, without sensibly changing tint in air, 2.e¢., diluted oxygen, only mode-
rately dry, especially if free exposure to light be avoided. The general experience
of mankind has led to the same conclusion, in reference to the comparative per-
manence of tint, of dyed. tissues kept in the shade. I have exposed coloured
papers for four and five hours to a current of dry air, without permanently alter-
ing their hue. The paper in such trials always exhibits a duller tint at the
end than at the beginning of the experiment; but that this is the result merely
of its loss of water, is evident from the fact that, on moistening the paper,
the original brightness of tint is restored. No one, probably, will dispute the
conclusion, that dry oxygen does not, at least in darkness, bleach more than dry
chlorine.

The effect, on the other hand, of the addition of water to oxygen in increasing
its decolorising power, is so strikingly demonstrated by the practical experience
of the domestic bleacher, that experiments on the small scale did not seem neces-
sary to prove the fact. No point is more attended to, in the familiar practice of
bleaching cloth by free exposure to rain, wind, and sun, than the constant keep-
ing of the tissue wet. Iam far from affirming that other important agencies,
such as the actinic, concerned in the bleaching, are not affected by the presence
of water; yet I think no one will doubt, that one important function it serves, is
the increasing (I do not at present say how) the bleaching action of the oxygen of
the atmosphere.

The unquestionable decolorising power of peroxide of hydrogen, chromic, and
permanganic acids, to which Dr Turner refers as confirming Davy’s view re-
garding the bleaching action of moist chlorine, only demonstrates that nascent
oxygen bleaches, and is of no service in proving that that gas, when in its state
of perfect elastic fluidity, possesses bleaching powers. The nascent hydrogen of
decomposing water bleaches readily; so that, if Dr TuRNER’s view were accepted
as valid in relation to oxygen, a theory of chlorine-bleaching might, with some
plausibility, be defended, in which hydrogen, instead of, or as well as, oxygen,
should be represented as the positive bleaching agent in chlorine-water.

* It would be peculiarly interesting to observe the effect of drying this gas in modifying its action
on colouring matters. Should it lose its bleaching power when dry, it would be curious to watch the
effect of exploding it in the presence of an anhydrous colouring matter. The result would shew whether
nascent oxygen and chlorine bleach as powerfully when dry as moist.

482 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

Sulphurous Acid.

The bleaching power of moist sulphurous acid is so well known, and has so
long been turned to account in the arts, that I need enter into no details in proof
of the gas possessing this property. With a view to determine whether it loses
its bleaching power when made anhydrous, I passed washed sulphurous acid, ob-
tained by the action of mercury on oil of vitriol, through strong sulphuric acid,
and over chloride of calcium, so as to deprive it of moisture. The gas was then
made to stream for five minutes through a tube containing blue litmus-paper,
carefully dried, and the tube hermetically sealed while full of the gas. This ex-
periment was made on March 31, 1848. The paper was not altered in tint dur-
ing the passage of the gas, and at the present date (April 17) it remains un-
changed.* I made a similar experiment on the 10th of July 1847, only the
sulphurous acid, being obtained by the action of charcoal on oil of vitriol, was
mingled with carbonic acid. The mixed gases were passed dry over blue litmus-
paper for seven minutes, but did not change its tint in the slightest; the tube
was then sealed, and is included among the specimens laid before the Society.
After the lapse of nearly nine months, the paper continues not appreciably altered.
Gaseous sulphurous acid, then, is no better bleacher when dry than chlorine.

Sulphuretted Hydrogen.

The other remarkable properties of sulphuretted hydrogen have prevented its
bleaching power from attracting very much attention; nevertheless, it has long
been recognised. Nascent sulphuretted hydrogen bleaches powerfully. An aci-
dulated infusion of litmus has its colour rapidly destroyed by the addition to it of
a metallic sulphuret, such as that of calcium, barium, or iron. The free gas
bleaches much less distinctly, yet its action is tolerably rapid. In proof of this,
I have sent with this communication a tube, which, after the blue litmus-paper
contained in it had been dried, was opened for a few seconds to the atmosphere,
in consequence of a derangement of the apparatus. The paper was thus exposed
for a very short period to the amount of vapour which is diffused through air at
the temperature of about 60° F. - Immediately after this accident, carefully-dried
sulphuretted hydrogen was passed over the litmus for five minutes, and the tube
sealed. The paper was distinctly, though faintly, reddened during the passage of
the gas, and after the lapse of about twenty hours the colour was found almost
completely gone. In contrast with this result obtained with slightly moist sul-
phuretted hydrogen, I shew the Society a tube containing dry blue litmus-paper,
and brown-red rhubarb paper, which were exposed to the action of equally dry

sulphuretted hydrogen for six minutes. The papers were not altered in tint. | |

* The colours are still unaltered ; a remark which applies also to the experiment next recorded,

June 19, 1848.

ON ORGANIC COLOURING MATTERS. 483

Thev have remained sealed up in the tube, in an atmosphere of the gas in ques-
tion, since July 9, 1847, when the experiment was made. No decided change
was observed in the tints of the papers up to July 30, when I ceased to make
notes of their appearance. The rhubarb paper is now little altered, but the blue
has, here and there, a few small red spots, some with white borders upon them.
Both tints, however, are still, after so many months’ exposure to the gas, very
slightly affected.* I shew the Society also tubes containing blue paper, which
were exposed for five minutes to dry sulphuretted hydrogen on the 25th March
1848, and have since remained shut up in the gas. They exhibit, at the present
date (April 17), no sensible change in tint.| Sulphuretted hydrogen, then, has
its bleaching power arrested by depriving it of water.

IV. Action of the Acid Gases and of Ammona on Organic Colours.

I pass now to the acid gases and ammonia, which so characteristically alter
the tints of organic colouring matters, when water is present. The gases I tried
were, sulphurous acid, carbonic acid, sulphuretted hydrogen, and hydrochloric
acid, in addition to the volatile alkali.

Sulphurous Acid.

I need not say anything further concerning sulphurous acid, as it is implied
in what was stated as to its negative action on vegetable blues, that its redden-
ing action is as much arrested as its bleaching one by depriving it of water. Dry
sulphurous acid, I also find, does not change alkalised turmeric or rhubarb paper
to yellow.

Carbonic Acid.

I have already referred to the retention of its full blue tint, by dry litmus-
paper, exposed for many months to a mixture of anhydrous carbonic and sul-

* The papers have not sensibly altered after the lapse of two additional months ; nor is there
any change in the litmus-paper referred to in the next experiment, June 19, 1848.

+ One of the arguments in favour of the “ Binary Theory of Salts” is the fact, that the so-
called oxygen acids do not affect vegetable colours unless associated with water, which they are
assumed to decompose, so as to become by appropriation of its elements hydracids of new radicals.
The experiments recorded in the text, however, shew that one hydracid, at least, has its action on
colouring matter as much negatived by the withdrawal of water as any oxyacid. It does not follow
that the rationale of the change is the same in both cases; but the fact that anhydrous gaseous
hydrosulphuric acid does not redden vegetable blues, lessens the value of the argument alluded to.
In the great majority of cases, the rendering of an oxyacid anhydrous implies its alteration from the
liquid state to the solid or gaseous one. This change in condition is of itself sufficient to alter most
materially the influence of a reagent. It appears, however, to have been altogether overlooked in
explaining the indifference of a dry oxyacid to organic colours. The phenomena recorded further
on, as observed with gaseous hydrochloric acid and liquefied sulphurous acid, bear upon this point,
but it cannot be discussed at length here.

VOL. XVI. PART IV. 6H

484 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

phurous acid gases. Pure carbonic acid is equally negative in its action on vege-
table blues and browns.

Sulphuretted Hydrogen.

Sulphuretted hydrogen, even when moist, does not change organic colours to
so great an extent as the stronger acids do. Solutions of litmus, ev. gr., become,
under its action, only of a purple-red tint, like that which carbonic and boracic
acids give them, whilst the more powerful acids destroy all shade of blue. If I
may judge from the few experiments I have made on this subject, the reddening
power of sulphuretted hydrogen is more dependent than its bleaching action on
the presence of water. At all events, it is equally dependent on moisture, for
blue litmus has been reddened very slightly by eight months’ exposure to the dry
gas, neither has brown rhubarb paper become yellow, or appreciably grown paler.

Hydrochloric Acid.

No acid excels hydrochloric in full and rapid action on organic colours ; nor is
any one, according to the prevailing opinions of chemists, less likely to be indebted
to association with water for its characteristic properties. It is the simplest type
of a perfect acid, and as such, might be expected to exhibit, even when gaseous
and anhydrous, the same relation to organic colours which it does when moist.
_ I looked upon hydrochloric acid, therefore, as the most interesting of the acid
gases with which experiments could be made.

I have not hitherto referred particularly to the method followed for drying
the gases, because none of those I have yet mentioned present great difficulties
in the way of rendering them,—I will not say certainly anhydrous,—but at least
sufficiently dry not to affect colours. It is otherwise with hydrochloric acid. I
have failed more frequently than I have succeeded, in rendering this gas, by dry-
ing, indifferent to colours; nor have I been able to preserve blue litmus for any
length of time unchanged in an atmosphere of the dry gas. It is necessary, there-
fore, to be more particular in describing the process for drying, which was fol-
lowed with hydrochloric acid; although it differed in no respect from that pur-
sued with the majority of the other gases.

The general arrangement, especially in the later and more perfect trials, was
the following:—The thinnest India letter-paper was stained with an infusion
or tincture of the colouring matter intended to be used, and afterwards dried at
the temperature of the air. Slips of the paper were introduced into a tube, vary-
ing in different cases from half an inch to one inch in diameter, and from six to
eighteen inches in length. The tube was then hermetically sealed at one extre-
mity, and drawn out at the other into a narrow canal, which was left open. A

=
Sees AR awe

in

ON ORGANIC COLOURING MATTERS. 485

smaller open tube was afterwards attached to each side of the larger one, near to
its shut end, so as to communicate with its cavity. These lateral tubes projected
for a short distance at right angles to the long axis of the larger tube, and then
ran parallel to it, with their open mouths pointing in the opposite direction from
that of the single canal at the other end of the tube. To prevent confusion, I
shall call the lateral appendages which I have described, the horns of the tube.

When the latter was arranged for an experiment, the narrowed termination
at one end was placed in communication with a short tube filled with chloride
of calcium, by means of a caoutchouc connector. The free extremity of this tube
was bent at right angles, and dipped into oil, so as to cut off communication with
the outer air. To each of the open horns, also, a chloride of calcium tube, three
feet in length, was attached. The one of these tubes was intended to convey,
and render anhydrous, a current of air, which should dry the paper. The other,
in like manner, was to carry and dry the gas, which should be brought in contact
with the paper, when the latter was deprived of moisture. At the beginning of
an experiment, the tube through which the gas subsequently passed, after being
connected with one of the horns, was sealed at the end furthest from the paper.
Its presence from the first was essential, because otherwise the dried paper must
have been put in communication with the moist outer air, when a fresh chloride
of calcium tube to carry the gas was substituted for that which previously con-
veyed the air: for if the same tube in whole, or in part, had been employed, first
to dry the air, and then the gas, the freedom of the latter from moisture could
not have been counted upon.

I found, after trying various devices, a pair of common bellows the most con-
venient instrument for furnishing a current of air. The air was first passed
through a bulbed tube, immersed in a freezing mixture, and then through the
chloride of calcium tube into the one containing the paper; from which it escaped
through the smaller drying tube that dipped into oil, as already mentioned. The
paper was maintained by gas lights at a temperature of about 220° Fahr., and
the air was kept passing over it, for at least two, generally for three, hours.

When the paper appeared perfectly free from moisture, the lateral horn, by
which the air reached it, was sealed at the blow-pipe, and the drying apparatus
detached. The shut end of the other long chloride of calcium tube was then
opened, and connected with an apparatus for furnishing the gas to be used in the
experiment.

The woodcut on the following page will make the description more intelligible.
Only the more essential parts of the arrangement are represented in the dia-
gram; the bellows and connecting flexible tube on the one hand, and the retort
in which the gas was generated on the other, as well as the washing bottles, &c.,
being omitted.

486 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

A, Tube in which coloured paper was placed.

a, Narrow canal, communicating by a caoutchoue collar, with small tube containing chloride of calcium.

b and c, Lateral appendages or horns, communicating with long drying tubes, C and D.

B, Small drying tube, dipping into oil, through which the elastic fluids, after passing over the paper,
escaped into the air.

C, Long drying tube, which was sealed at ¢, at the commencement of an experiment, but opened when
the paper had been dried, and employed to convey the gas which was to act on it.

D, Second long drying tube employed to carry air, to render the paper in A anhydrous. When the
paper was dried, the horn c was sealed at the blow-pipe, and D detached. Gas was then trans-
mitted through C.

The arrangement I have described was followed with all the gases except
ammonia. Chlorine and sulphurous acid were sent through oil of vitriol before
reaching the chloride of calcium tube. The other gases were generally passed
simply through a bulb immersed in a freezing mixture, before being transmitted
through the drying tube. I found it essential to success in the experiments re-
corded to dispense with corks, asbestos, and cotton, in connecting or loosely stop-
ping the tubes, as these bodies retained moisture with the greatest obstinacy.
Caoutchouc collars were used in every case to unite the detached portions of the
apparatus. The special devices followed in particular cases are mentioned under
the gases which called for them.

I procured hydrochloric acid gas by the action of Nordhausen sulphuric acid on
common salt previously fused. Theoretically, the gas should carry with ita

‘mere trace of moisture, yet in spite of the apparently effectual drying apparatus
made use of, the acid, in the majority of trials, changed the tint of blue litmus
as soon as it came in contact with it, giving it a dark lilac or deep wine-red
colour. Nevertheless, on three occasions I was able to pass a current of dried
hydrochloric acid for five minutes over blue litmus-paper, without sensibly alter-
ing its tint, according to the judgment of four persons besides myself, who were
witnesses of the experiments. These positive results outweigh the negative
ones already referred to. The majority of the latter, moreover, were only partial
failures, and went the length, at least, of proving that the removal of moisture
from hydrochloric acid gas delays, if it does not prevent, its characteristic action
on organic colours. In the successful experiments mentioned above, the negative
action of the acid was only transient; for when the tubes containing the

gas and paper were sealed and set aside, the colour invariably passed from its —

original blue tint to a more or less decided red. In several trials, however, the
ultimate effect of the hydrochloric acid fell far short of the full reddening which

eh ee aT

ON ORGANIC COLOURING MATTERS. 487

even the slightly moist gas produces. I shew the Society a tube, containing lit-
mus-paper, which withstood, without change, a current of hydrochloric acid
passed over it for five minutes. The experiment was made on 23d February
1848 ; and the paper is at this date not a bright red, but only a dark lilac.

Three explanations suggest themselves as to the ultimate though imperfect
reddening of the blue litmus. 1. The gas may not have been quite dry. 2.
Hydrogen acids, though perfectly dry, may, unlike the so-called oxygen acids, be
able to modify the tints of colours. 3. Hydrochloric acid, which has a great affi-
nity for water, can compel its elements to unite to form it, so that the gas may
combine with the liquid. Hydrogen and oxygen are present, both in the colour-
ing matter and in the paper. In the paper, indeed, they are present in the pro-
portion to form water. This solvent, therefore, may be slowly generated within
the sealed tube, and be the cause of the gradual reddening of the blue paper.

As to the first of these views, I can neither disprove nor confirm it. It is pro-
bably as difficult to render a gas absolutely anhydrous, as it is to produce a per-
fect vacuum. Moreover, as I have stated already, we have no test of absolute
dryness, applicable to a gas. It would interrupt the argument, however, to con-
sider this question at length here; I have devoted, accordingly, the section which
succeeds this to its discussion.

Of the second explanation, I would say much the same as I have said of the
first. It is highly probable that a powerful hydracid like the hydrochloric should
retain, more or less, as a gas, its characteristic action on organic colours.

I would speak most positively of the third view. The power of bodies which
have a great affinity for water, to compel its formation and separation, is so great,
that I ventured to predict, that it would be impossible to preserve, for any length
of time, blue litmus unchanged in tint in the driest hydrochloric acid. I do not
dwell at length, however, on the cause of the ultimate reddening, as the fact that
the paper was only slowly and imperfectly reddened, is sufficient for my present
purpose. At lowest, the experiments I have detailed demonstrate that the re-
moval of water from hydrochloric acid gas delays its action on colours.

Ammonia.

The last of the gases I tried was ammonia. According to KANnz,* when dry
it has no action on organic colours, although no body, when moist, affects these
substances more powerfully. I might content myself with adducing this distin-
guished chemist’s statement as to the negative action of dry ammonia, and add it
to the list of gases which have their action on colouring matter arrested by the
removal of moisture. My own experiments, however, have been so much less deci-
sive than KaNr’s statement led me to expect they would be, that I cannot, without
comment, avail myself of his evidence. ‘The difference between his results and

* Elements of Chemistry, p. 852.
VOL. XVI. PART. IV. 61

488 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

mine is probably sufficiently accounted for by the supposition, that I did not
thoroughly dry the ammonia. This gas is more difficult to render anhydrous
‘than even hydrochloric acid; not so much, perhaps, because it has a greater affi-
nity for water, but because our most powerful desiccating agents, such as the
deliquescent chlorides and oil of vitriol, cannot be employed to dry it. We are
restricted, accordingly, to substances much less hygrometric, such as unslaked
lime, hydrate of potass, and its fused carbonate.

It would serve no purpose to record a series of unsuccessful experiments: |
merely mention, therefore, that I have never been able to obtain ammonia in a
condition in which it did not change the tint of reddened litmus and of yellow
turmeric paper as soon as it came in contact withthem. Ihave found its action on
colouring matter, however, sensibly reduced by passing it over the hygrometrics
last referred to. Reddened litmus, for example, became only purple when it first
encountered dried ammonia, and did not acquire a bright-blue tint, when left in
the gas, till after the lapse of some hours.* For the reasons mentioned above, I
do not, in the meanwhile, feel myself at liberty to say more than that the pre-
sence of water greatly quickens the action of ammonia on colours.

It would appear, then, from the results I have detailed, that there is little, if
anything, anomalous or exceptional in the negative bleaching of dry chlorine.
Oxygen, sulphurous acid, and sulphuretted hydrogen, are equally powerless as
bleachers, when deprived of moisture, as that gas. Sulphurous and carbonic acids
are probably more indebted than chlorine to water for their power of modify-
ing colouring matters, both as regards changing and destroying their tints. Hy-
drochloric acid and ammonia have their influence on colours at least temporarily
arrested by the absence of water; and, after all, it is a question with the whole
of the gases referred to, only of degree. It is not likely that even in absolute
darkness chlorine has no action on anhydrous colouring matter. If this be con-
ceded, the whole of the gases referred to may be included in one category, as hay-
ing their modifying action on organic colours accelerated by the presence and re-
tarded by the absence of water. I trust to supply an additional datum towards
the settlement of this question, by observing the difference which exposure to sun-
light makes, in relation to the action of all the gases with which experiments were
tried.

* In the experiment which yielded the most successful result, the ammonia was first passed
through a bulb immersed in a freezing mixture, and afterwards through long tubes containing lime,
caustic potass, and its fused carbonate. The gas was then allowed to flow through a tube for some
minutes till it had expelled the air, and the tube was sealed. The one end of this tube had been
previously expanded into a large ball, which was filled with fragments of the hygrometrics just men-
tioned: in the other end of the tube a small sealed bulb was placed, containing a piece of carefully
dried red litmus-paper. The ammonia was left in contact with the drying agents for a week, when the
tube was shaken till the bulb broke, and allowed the gas and the paper to meet. The latter, as men-
tioned in the text, immediately became purple, and after some hours bright blue.

i]

ON ORGANIC COLOURING MATTERS. 489

Before proceeding to detail the second series of researches, I have thought it
desirable to offer some observations on the processes employed for drying gases.

V. On the Methods applicable to the Drying of Guses.

The methods at present in use for drying gases cannot be considered as yield-
ing more than an approximation to absolute dryness in the case of any elastic
fluid. The processes employed are inherently defective, both mechanically and
chemically. When chloride of calcium and pumice-stone, steeped in oil of vitriol,
are employed as the desiccating agents, they cannot be made use of except in frag-
ments of considerable size, otherwise the containing tubes become choked, and
the gas does not pass. Interstices, accordingly, comparatively speaking large,
occur between the separate fragments of the drying agent; and the gas, in moving
along, has a certain portion of its mass not in physical contact with the hygro-
metrics, or directly exposed to their desiccating action. In like manner, when a
gas is sent through a column of oil of vitriol, only the surface of each bubble
is in contact with the liquid, and the gas-bells rise very rapidly through so dense
a fluid, so that they can be dried only imperfectly during their ascent.

Those defects admit only of partial remedy, by extending the surface of chlo-
ride of calcium or pumice-stone, or by multiplying the columns of oil of vitriol
through which the gas shall pass. A practical limit is set to such devices by the
obstruction which they offer to the passage of elastic fluids. This can be over-
come only by increasing the pressure at which the gas is delivered, and it is not
easy to regulate this, so that the gas shall not flow in too swift a current, and so
neutralise, by the rapidity of its passage, the benefit which would otherwise result
from its coming in contact with an extended hygrometric surface.

The imperfections just alluded to are not, perhaps, beyond the reach of suit-
able mechanical contrivances; but even if they were all remedied, the important
question still remains, will the protracted and complete contact of a gas contain-
ing water-vapour with the most powerful hygrometrics, suffice entirely to de-
prive the gas of moisture? With a view to determine this point, I shut up mu-
riatic acid gas, previously passed through a freezing mixture, and over chloride
calcium, within a glass tube containing fragments of the same salt. It was left
for a week in contact with the chloride, and then allowed to meet carefully dried
blue litmus-paper, enclosed along with it at the commencement of the experi-
ment, in a small sealed bulb of thin glass, which was readily broken by shaking
the tube. The paper began to change tint as soon as it met the gas; and if this
alteration in colour be accepted as an evidence of moisture being present in the
muriatic acid, then the latter was not dry. A similar experiment, with a like
result, has already been related in reference to ammonia.

These results, however, are not decisive of the point whether the gas was an-
hydrous or not, for the change in tint of the litmus may possibly be accounted

490 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

for otherwise than by assuming the presence of water; and the fault, moreover,
even if water were present, may have lain with the coloured paper, not with the
gas. The same objection does not apply to the following observation. If air at
the temperature of 60° F. be sent through a long tube filled with fused chloride
of calcium, it parts with moisture, which the chloride absorbs and combines with.
If this dried air be thereafter transmitted over moist chloride of calcium, the lat-
ter becomes, to appearance, speedily dry. Here we have the apparently contra-
dictory results of chloride of calcium drying air, and air drying chloride of calcium.
The inference seems unavoidable, that there must be a neutral point where the
chloride of calcium and air will be mutually indifferent, so that neither shall be
able to deprive the other of moisture. This point will vary in reference to, 1. the
relative quantities of the hygrometric salt and air acting on each other; 2. the re-
lative dryness of the gas and solid; and, 3. the temperature at which the trial is con-
ducted. Experiments on gases are generally made in apartments having an average
temperature of or about 60° F., at which the tension of water-vapour is probably
great enough to resist, so far as complete condensation is concerned, the absorb-
ing power, and affinity for it, of all hygrometrics. This remark leads directly to
the observation, that reduction of temperature is probably the most effectual of
all processes for drying a gas. It has been employed with great success by
Farapay, in his later researches on the liquefaction of the gases ;* and I was in-
duced, in consequence, to make use of it in my experiments. The value of the
method admits of easy demonstration. The great obstacle to rendering a gas an-
hydrous, is the tension which heat confers on the water-vapour diffused through !
it. We generally endeavour to overcome this tension by opposing to it the con-
densing force of porous hygrometrics, and the chemical affinity of substances
which combine readily with water; yet it is not at all certain that these forces
have the maximum condensing power attributed to them. On the other hand, it
is certain, that the tension of water-vapour is exceedingly small at zero, and
rapidly decreases as we descend the thermometric scale.

FaRADAY’S discovery, moreover, of the existence of a limit to vaporisation,
teaches that there must be a temperature at which ice abruptly ceases to give off
vapour. If this point be within reach of our frigorific appliances, and were as-
certained, we should possess, in the reduction of gases to this temperature of no
vapour, a theoretically perfect process for rendering gases anhydrous. It would
be applicable, however, only to the less condensible elastic fluids, for the more.
easily liquefied ones would become liquid before the temperature of no-water va-
pour had been attained. It is further to be noticed, and the remark is important,

that all volatile bodies have their vaporising point lowered in the presence of |

bodies more volatile than they are. The fact is familiar to every chemist. The

* Phil. Trans., 1845. Part I., p. 155.

i

ON ORGANIC COLOURING MATTERS. 491

essential oils, ea. g., whose boiling points are much above that of water, are en-
tirely dissipated in vapour if mingled with water raised only to the temperature
of 212° F. Even bodies ranked, when anhydrous, among fixed substances, such
as common salt, nitre, and boracic acid, rise with the vapour of water below its
boiling point. It cannot be doubted that, in like manner, a temperature suffi-
ciently low to hinder ice from volatilising in vacuo, or in still air, would not pre-
vent it yielding a continuous stream of vapour in a current of gas. This power,
indeed, of gases, as the more volatile bodies, to solicit and compel water-vapour
to accompany them, is, at all temperatures, but especially at high ones, a formi-
dable obstacle to rendering elastic fluids anhydrous. On the other hand, this dif-
fusive power greatly increases the desiccating effect of gases, even not absolutely
dry, when sent in currents over moist solids.

How near an approximation may be made to perfect dryness in the case of
gases, cannot be determined till we have a test of the anhydrous state applicable
to elastic fluids. A criterion of some value would be the passage of a consider-
able volume of the gas (ammonia excepted), through a weighed tube containing
chloride of calcium, which should not increase in weight if the gas were anhy-
drous; but, if the preceding observations are well founded, this test would cease
to act before the gas was quite dry.

[ have tried whether the change of tint which the so-called s mpathetic inks
(solutions of the salts of cobalt and nickel) undergo when deprived of water, would
Serve as an indication of dryness on the part of gases; but I find that it is a test
of no delicacy.

Indifference to colouring matter will certainly be found a negative indication
of some value. Chlorine, ew. gr., which immediately bleaches, and sulphurous or
carbonic acid, which reddens litmus, cannot be dry. This test, of necessity, is
limited to the gases which affect organic colours, and would be useless in the
case of oxygen, nitrogen, hydrogen, the carburetted hydrogens, &c. &c.

A convenient way of examining the dryness of gases by means of colouring
matters is to prepare, by blowing at short distances along a thin glass-tube, a
series of small bulbs, in each of which a piece of litmus-paper may be placed.
The papers are then to be dried in a current of air, passed through oil of vitriol
and over chloride of calcium, and each bulb sealed off separately. In this way, a
large number of bulbs can be prepared at the same time, and kept ready for use
when required. One of these is to be placed in a tube forming part of the ar-
rangement employed in the particular experiment, so that it shall be enveloped
in the gas whose dryness is to be tested. By a sharp tap on the tube, the en-
closed bulb is easily broken, and the gas and paper allowed to meet. There is no
difficulty in making the bulbs thick enough to bear handling, and yet sufficiently
thin to give way when required.

In the preceding remarks, I have chiefly referred to the difficulty experienced
VOL. XVI. PART IV. 6K

492 DR GEORGE. WILSON ON THE ACTION OF THE DRY GASES

in drying gases. But organic solids, such as litmus and colouring matter, though
probably more readily dried than gases, are certainly with difficulty rendered an-
hydrous. The difficulty is too familiar to every chemist who has made organic
analyses, to call for any illustration or proof. Reference has already been made
to the desiccating power of currents of air, and to the likelihood of a solid being
more effectually dried by a gas than a gas by a solid. If, however, it is impos-
sible to supply a current of perfectly dry air, it may be doubted whether it is pos-
sible to render a solid anhydrous by passing air over it. It is difficult to imagine
that air, containing ex hypothesi some moisture, should make a solid absolutely
dry, drier than the air itself is; yet it is not impossible that it should. The ten-
sion which heat gives to water-vapour ; its great dilatation when present in small
quantity ; and its diffusion through a large volume of gas, may more than balance
any power on the part of the solid to attract or condense it. There may bea limit
to condensation, as well as to vaporisation.

Notwithstanding all that has been urged in this section, in reference to the
difficulty of rendering gases absolutely dry, it will not, I think, be questioned, that
in the experiments I have recorded, a close approximation to actual dryness was
attained in many of the trials. And, conceding that traces of moisture may have
been present, | may, nevertheless, with some justice, argue, that if the removal
of a certain amount of water from gases arrests for months their action on colours,
a fortiori, the total abstraction of moisture would still more decisively negative
that action. |

VI. On the Action on Dry Organic Colouring Matters of the liquefied Anhydrou

Gases, and of Chlorine dissolved in liquids containing no Oxygen.

The second series of experiments, as I have already mentioned, was made with
the view of ascertaining in what way water acts, when it accelerates the action
on colouring matter of the gases referred to, but particularly of chlorine. Accord-
ing to the prevailing theories of chemists, when water meets dry carbonic and
sulphurous acid, or dry ammonia, it does not merely dissolve them, but allows
its elements to be appropriated by each of these gases, which become, in conse-
quence, compounds possessed of new relations to bases, acids, colouring matters,
and the like. I shall therefore set these gases aside, as not admitting of direct
comparison with chlorine, which chiefly concerns us. There is no reason, on the
other hand, for supposing that water does more than merely dissolve oxygen,
sulphuretted hydrogen, and hydrochloric acid, so that that liquid may be sup-
posed to change their relation to colours in the same way as it does that of
chlorine.

The older chemists held by the axiom, “Corpora non agunt nisi soluta,’ and
by means of it could fully have accounted for the difference in action on colours

ON ORGANIC COLOURING MATTERS. 493

of the dry and moist gases. In our own day, however, the problem takes a
somewhat different shape, for we have learned to liquefy the gases without the
intervention of a solvent. Three of the four gases last referred to, which simply
dissolve in water, viz., chlorine, sulphurous acid, and sulphuretted hydrogen,
admit of liquefaction, although quite anhydrous. It has been held, accordingly,
that the liquefaction of a gas changes its properties, in the same way as dissolving
it in water would.

With a view, so far at least, to examine this point, I exposed carefully dried
blue litmus-paper to the action of liquid bromine (which is equivalent to a lique-
fied gas), repeatedly rectified from chloride of calcium, and supposed to be an-
hydrous. Ultimately the paper was quite bleached; but the decolorising action
was slow, certainly much slower than that of hydrated bromine. Specimens ac-
company this paper. The dark colour, however, of that element makes it an
unsatisfactory substance to work with, in relation to changes of tint in the bodies
upon which it acts. From experiments such as I have described, as well as from
theoretical observations, it has been inferred that the function of water in rela-
tion to the gases I have been considering is simply to effect their mediate lique-
faction, and thereby to bring them into closer physical contact with the colouring
matters than their elastic condition permits. So general a conclusion, however,
as this, which would imply that a liquefied gas has the same properties as a dis-
solved one, is certainly in the meanwhile without proof, and is probably unten-
able. So far as they have been examined, the liquefied gases present properties
very different from those exhibited by the same bodies when in aqueous solution,
although their action on colouring matters has been less inquired into than might
have been expected.

There is, moreover, this manifest distinction between the action on a colouring
matter of a liquefied gas, and of an aqueously dissolved one, that in the former
case the gas only is in the liquid form, the colouring matter remaining solid,
whilst in the latter the water dissolves alike the colouring principle and the gas,
and brings both into a condition far more favourable to chemical action than
where the one only is liquid.

It is further certain that much must depend on the force of the adhesive
attraction of the liquidised gas for the dry colour. A liquid which cannot wet a
solid will exert little, perhaps no chemical action upon it, although it may pro-
duce a marked effect when both are dissolved in water.

Again, if the liquidised gas can dissolve the colouring matter, we may be cer-
tain that, sooner or later, it will affect it; but if it cannot dissolve it, the latter
may be totally unaltered by its presence. The slow action of dry bromine is
probably related, either to incapacity of quickly wetting, or of dissolving litmus;
perhaps to both.

In connection with this subject, I tried an experiment with liquefied anhydrous

494 DR GEORGE WILSON ON THE ACTION OF THE DRY GASES

sulphurous acid, which yielded a result so interesting, that I mention it particu-
larly. A piece of blue litmus-paper was exposed for three hours to a current of
dry air, and then sealed up in the narrow tube in which it had been dried. The
sealed bulb, containing the paper, was placed in a tube immersed in a mixture of
pounded ice and salt, and carefully dried sulphurous acid transmitted through
the arrangement. As soon as a sufficient quantity of the gas had assumed the
liquid form, at the low temperature to which it was exposed, the open ends of the
tube were sealed, and it was shaken till the bulb within broke, and allowed the
paper and the liquefied gas to come in contact with each other. The paper was
instantaneously soaked through, and completely wetted, but its blue colour re-
mained totally unaltered, whilst an aqueous solution of sulphurous acid would
have instantly reddened it. The liquidised gas acquired no colour itself, even
after a fortnight’s contact with the litmus-paper. It appeared to wet it without
dissolving anything from it.

The retention of the blue tint on the part of the paper was, however, only
temporary. In an hour and a quarter it had become dark purple, and the blue
slowly faded, till, in twenty hours, the paper was bright red. No indication of
bleaching action appeared.

1 attribute the final reddening to the production of water, generated out of its
elements in the litmus or paper, or both, by the influence of the sulphurous acid.
For, if anhydrous liquid sulphurous acid possessed the power, per se, of redden-
ing vegetable blues, there seems no reason why its action should be so long de-
layed, when it wetted the coloured paper so readily. And it could not owe its
reddening power to water present in it, ready formed from the first, otherwise
it would have reddened instantaneously.

I set aside, therefore, as at least unproven, and, further, as not probable, the
dogma, that the mere passage of an elastic fluid, such as chlorine, from the state
of gaseity to that of liquidity, is the whole cause of its accelerated action on
colours, when dissolved in water. It seemed to me, indeed, that the acceleration
of action was as much owing to the water liquefying the colouring matter as to its
liquefying the gas, and that one might venture, in the spirit of the elder chemists’
motto already quoted, to infer, that any liquid which dissolves alike the gas and
the colouring matter, would be as efficacious as water in determining the destruc-
tion or modification of the colour. But, I have learned by experiment, that this
also is too general a conclusion, and that it is quite possible for a liquid to dissolve
simultaneously a colouring matter and a gas, and yet not exhibit the results
which it would present if water were the solvent of both.

So far as this branch of the inquiry is concerned, I have been compelled, by want _

of leisure and opportunity, to limit myself almost entirely to chlorine. This gas
is dissolved by chloroform, by bisulphuret of carbon, and by the volatile oils of the
type of spirit of turpentine (C’ H’). None of these liquids, when pure, contain

ON ORGANIC COLOURING MATTERS. 495

oxygen, and all of them dissolve several colouring matters. Yet, not only dry,
but moist chlorine may be passed through solutions of the colouring principle of
false alkanet root (anchusa tinctoria), in the solvents mentioned, without bleaching
occurring.

On the other hand, solutions of blue litmus, in chloroform and bisulphuret of
carbon, are bleached instantaneously by dry chlorine. I took the greatest precau-
tions in these trials to exclude moisture. Paper was dispensed with. A solu-
tion of blue litmus was dried up in a glass tube, and desiccated in a current of
air. The chloroform, or sulphuret of carbon, was repeatedly rectified over
chloride of calcium, and finally distilled into a bulb communicating with the
outer air, through a narrow tube filled with the same hygrometric salt. The
bulb was then sealed, and placed within the tube containing the litmus at the
commencement of the experiment. Chlorine was ultimately passed over the
colouring matter for some minutes, in order to make certain that the gas was too
dry to act unaided on the colour. The tube was then sealed, full of chlorine, and
shaken till the bulb broke. The blue colour immediately disappeared, and the
liquid became of a pale yellow tint.

The tincture of alkanet in chloroform or sulphuret of carbon retained its
bright red colour, if kept in darkness; but less than an hour’s exposure in the
open air, though the sky was clouded, sufficed to turn the scale in favour of
bleaching, and the colour disappeared.

From these results it appears that, contrary to Davy’s view, chlorine can
bleach though oxygen be absent, for chloroform contains none; and that neither
of the elements of water is essential to its bleaching action, for sulphuret of car-
bon is devoid of both. The further conclusion seems unavoidable, that neither
water nor any other liquid is essential to the decolorising action of chlorine,
otherwise than as enabling the gas and the colour to come within the sphere of
chemical action, by dissolving both. This function, water probably performs
better than any other liquid, in virtue of its solvent power for most substances
exceeding that of almost all other fluids.

A similar conclusion, mutatis mutandis, may be extended to oxygen, sulphur-
ous, hydrosulphuric, and hydrochloric acids, but with this qualification, that
specific differences may be expected to occur with all the gases named, as to
their action on any one colouring matter, and with different colouring matters, as
to their deportment with any one of the gases.

VOL. XVI. PART IV. 2 6

( 497 )

XXXIV.—A Biographical Notice of the late Tuomas Ouatuers, D.D. § LL.D.
By the Very Reverend E. B. Ramsay, M.A., F.R.S.E.

(Read 4th March 1849.)

Mr PreEstDENT,—It has been a practice from the foundation of the Royal
Society of Edinburgh, to commemorate its deceased distinguished members by me-
moirs or biographical notices, read at the ordinary meetings of the Society. Some
of these have been printed in the Transactions ; and our published volumes are
enriched by papers of DucaLp Stewart, Professor PLAYFAIR, Sir JOHN MAcngEIL,
and Dr Trait, on the characters and writings of Apam Smrru, Dr Huron, Pro-
fessor Rosison, Sir CHARLES Beuu, and Dr Hore. A biographical notice is now
due to the memory of a distinguished countryman, late Vice-President of the
Royal Society ; and the following remarks will, in attempting that object, make a
deviation from those more severe discussions with which the time of the Society
is usually occupied, in connection either with pure mathematics, natural philoso-
phy, or natural history.

I consider it scarcely becoming for the reader of a paper to occupy the time
of the Society, by details or explanations which are merely personal. I would,
however, ask permission to state, that I did not enter upon this office till I knew
that it had been declined by one far better qualified for its performance ; one who,
if named, would, I am confident, be recognised as the individual of our body best
calculated to do justice to the subject.

I feel assured, however, that, from those whom I have the honour to address, I
shall receive every sympathy and indulgence in the few observations which I pro-
pose to offer in attempting to delineate those literary characteristics—those efforts
of practical benevolence—by which the subject of this brief notice was distinguished
during the many years which, as a public man, he came before his contemporaries.

THoMAS CHALMERS was born at Anstruther, 17th March 1780, and at its paro-
chial school received his early education. He studied at the University of St An-
drews the usual course of eight years, from 1791 to 1799. He received licence from
the Presbytery of St Andrews, 31st July 1799. During the sessions 1799-1800,
1800-1801, he studied at Edinburgh under Professors Ropison, Stewart, and Hope.
He commenced his clerical life as assistant at Cavers, December 1801—was in-
stituted to the Parish of Kilmany, Fife, 12th May 1803—removed to Glasgow, 1815
—to St Andrews, as Professor of Moral Philosophy, 1823. He came to Edinburgh
as Professor of Divinity, 1828, and filled that chair till the Disruption in 1843. In
February 1834 he was elected a Fellow of the Royal Society, Edinburgh—in 1835
a Vice-President. In January 1834, he was elected a corresponding member of the
Institute of France, before which distinguished body he read, in 1838, a paper, in

VOL. XVI. PART V. 6M

498 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

English, on the distinction between legal charity for the relief of indigence, and
legal charity for the relief of disease. At the annual commemoration of Oxford,
Ist July 1835, he received the honorary degree of LL.D. In that ancient and
Episcopal seat of learning this degree was conferred upon the Presbyterian Pro-
fessor amidst enthusiastic acclamations, without one dissenting voice. His death
took place, 31st May 1847, at the age of 67: He was buried, 4th June 1847.

Of a life solong extended, and embracing so many subjects of active exertion,
it is evident such a paper as the present can include only a very abridged and
limited notice. It is not intended to embrace those points which belong to mere
personal and private biography, or to details of questions on which there existed
special and peculiar relation to his own religious communion. There is, I believe,
in preparation a full Life of Dr CuauMers, which will include a publication of his
private memoirs, of his correspondence, and other personal biographical expositions.
We have now to consider Dr CHALMERS as he came before the world, as he occu-
pied a distinguished place in the observation of mankind ; for his reputation was
not merely Scottish, or merely British,—it was European. In this view, then, I
think we may at once, for the sake of preserving something like method and order
in our remarks, consider his public character under three heads:

1. Asan Author.

2. As a Political Economist.

3. As a Speaker.

First, One thing strikes us at first approaching the subject of Dr CHALMERS’
writings, and that is, the great industry which must have marked his literary la-
bours. When we look at the array of volumes published during his lifetime; when
we consider the manuscripts which he left behind ; and, in addition to all this, take
into account that these volumes were not written in the retired cloisters of a college,
or the quiet of a country parsonage, but that he wrote in the bustle of numerous en-
gagements, of meetings to be attended, of lectures and examinations for his classes,
of correspondence to be maintained, and perhaps, above all, amidst lavish encroach-
ments made upon his time by strangers; we must be struck with his economy of
time, and with the perseverance of his mental efforts. How many might say of
him, as the Younger Puiny wrote of his uncle, the Elder Puiny, “ Erat incredibile
studium summa vigilantia. Itaque soleo ridere, cum me quidam studiosum vocant ;
qui si comparer illi sum desidiosissimus.”* Dr CHALMERs was far from being, in the
classical or scholastic sense of the term, a /earned man, or a great scholar. His early
education, his habits, and pursuits through life, prevented it.; But itis a pleasing

* Plin. Epist. mi. 5.

+ In his Lectures on the Romans, he makes no reference to an exegetical or critical view of the
passages, though in that Epistle there is a great temptation to do so. He takes the statements of

the Apostle in their broadest and most general acceptation. His mind did not rest on the niceties of
philological distinctions.

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 499

view of his character to find how much he admired and respected learning in
others. He never undervalued an attainment because he did not possess it him-
self. He impressed his students with the value and importance of learning in
Theology, and revered what he called the “ massive erudition” of divines of the
English Church. In describing the peculiarities of his mental constitution, we are
at once led to the conclusion of a remarkable predominance of one, and that is an
extraordinary abundance of the imaginative faculty,—the power of illustrating his
ideas, and of setting forth his subjects of discussion with never-ending variety of
imagery, comparison, and analogy. In some of his works it seems as if he
could not tear himself away from the pleasure of reproducing some great truth,
which he enforces under all the different garbs and attitudes with which he
can invest it. There is no question that this is a very effective and important
method of handling subjects, when the particular bent of the author’s genius
enables him to pursue it effectually, and is specially adapted for leaving a
clear, distinct, and vivid impression upon the mind. In the case of Dr CHALMERS,
attachment to science, and early pursuits in astronomy, chemistry, and other
branches of physical science, gave him a great advantage in furnishing types
for analogy and illustration. These he used on some occasions with happy
effect. Indeed, he never lost his interest in the exact sciences; and, had the cir-
cumstances of life been favourable to their pursuit, would, no doubt, have
been distinguished in the branches of mathematical pursuits. His mind was
always alive to scientific subjects. In 1838, when introduced to the present
Bishop of Nova Scotia, he heard, with much interest, the Bishop’s description of
the Bay of Fundy (which is in his diocese), and the enormous roll of tide com-
ing in with a front 70 feet in height; next day Dr CHaLMErs wrote a letter to the
Bishop, proposing the experiment of having a delicate pendulum placed on the
shore, and to watch the effect of the mass of water upon it, as they came into the
bay, similar to Dr MAsKELYNE’s celebrated experiment at Schehalion, to test the
effect of gravity, but, with the advantage over Dr MAsKELynez, that the waters
would form a homogeneous mass of matter, and the result be more striking, from
marking the effect of the mass approaching the pendulum.* When I said, there-
fore, that, in Dr Cuautmers, the faculty of imagination was an abounding and pro-
minent endowment, I was far from meaning that this implied a poverty of the
reasoning faculties, or defect in other mental qualities. On the contrary, he had
a mind remarkably adapted for the apprehension of great principles, of broad and
profound truths. He delighted to grasp primary and fundamental elements.
He expatiated, with the fullest enjoyment, on reasonings of such authors as Bishop
Buruter, Bacon, Newton. His admiration of BurLER was intense: as an ex-
pounder of great elementary truths, he placed him in the first and highest class

* This experiment, [ find, had been suggested by Professor Roxzison, in his Elements of
Mechanical Philosophy, § 474.

500 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

of human intellects. In the dedication of his Bridgewater Treatise to the BisHop
of Lonpon, he thus expressed his admiration: ‘I have derived greater aid from
the views and reasonings of Bishop Butter, than I have been able to find besides
in the whole range of our existent authorship.” On one occasion, when some
person present was animadverting upon the wealth of the Church of England, and
gave, as an example of its over-abundance, the revenues of the See of Durham, the
Doctor exclaimed, with characteristic eagerness, “Sir, if all that has been re-
ceived for the Bishopric of Durham since the foundation of the See, were set down
as payment for BuTLer’s Analogy, I should esteem it a cheap purchase.” We are
not to consider his admiration of BuTLER’s works as proceeding from the same-
ness or resemblance of their mode of reasoning, but rather from the difference.
ButLer excogitated masses of profound thought, and left them nearly as raw ma-
terial, costly indeed, but not elaborated for use, except for the purpose of furnishing
him with examples of analogy between natural and revealed theology. CHALMERS
found, in this storehouse, abundant substance for practical application to the busi-
ness and improvement of life. He polished and carved, and adjusted the stone
which he had dug from the quarry. And thus, both as an able quarryman, and
as an accomplished dresser, he has erected graceful, durable, and useful edifices
for mankind. His method of exhibiting truths, in so many and in such attractive
positions, has deeply impressed the minds of thousands, not only of those who
were amongst his stated hearers as pupils, but amongst readers of his works ge-
nerally. Although Dr CHaumers’ mode of treating his subjects was such as I
have described, and though his usual mode of handling was to exhibit one great
and leading topic, illustrated and enforced with all the profusion and imagery of
a rich fancy and a powerful imagination, we should, at the same time, observe
that the method is frequently applied with great ability, and with great effect in
bringing forward two ideas where one is required to check or modify an exclusive
attention to the other. Thus, for instance, in his Sermons, though he dwells upon
the doctrine of the corruption of human nature, and the utter insufficiency of all
mere natural efforts to merit the Divine favour, and to claim a reward at God’s
hand, he runs, as it were, parallel with this great truth another truth, equally im-
portant and equally authoritative, viz., that virtue in itself is beautiful, that the
generous affections and good feelings must not be undervalued or depreciated,
but are, in fact, desirable and estimable in their own place and their own charac-
ter, and require only the right motives to render them acceptable. I know no
writer who has more successfully elaborated this important subject. He has shewn
the harmony and consistency of the two doctrines. He has upheld and vindicated
the dignity and the loveliness of virtue. He has cut away all ground of merit and of
human dessert before God. In the same manner, as a predestinarian, he has ably
and powerfully (in some instances sternly) put forward the proofs of God’s pre-
science and omnipotence over all his works; but, in conjunction with that great
truth, he has upheld, with unflinching fidelity, the necessity of human exertion,

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 501

and he has illustrated the agency of man’s own endeavours as fully and as freely as
if he had been the champion ofa free will entire and uncontrolled. Thus it is always
in his writings. He is urging and reiterating, with all the fervency of an ardent
eloquence, a great and important principle, or he is running the parallel between
two essential truths. He is sustaining, singly and conjunctly, the position of two
considerations, both of which are to be of supreme authority. The action of both is
requisite for man’s moral and spiritual wellbeing; at times they may, in theory, ap-
pear to be incompatible, but in action are never inconsistent. He is not, therefore, a
writer of subdivisions or details. He is copious, but copious in illustrating great pro-
positions. He offers, in this respect, a remarkable contrast to a great writer, Dr
Isaac Barrow, whose strength isin division. Of him it was said, that he “exhausted
his subject.” Caumers also exhausted his subject. But then one exhausted the
practical application and minute enforcement of a truth, in all its results and con-
sequences; the other exhausted the various forms and illustrations by which that
truth itself could be enforced upon the human mind. There is nothing of the
analytical method in his treatment of a subject. It is almost purely deductive.
He sets out with a great principle, and shews, in a thousand shapes, its application
and appropriation. One remark, however, we would make on this subject. Al-
though the handling is so copious and diffusive, it is seldom deficient in strength
and pungency. It would frequently be difficult to abbreviate without injury; and
we find expressions constantly occurring of great force and point. It was said of
Dr Cuaumers by Rosert Hatt, after hearing him preach, that his sermon went
on hinges, not on wheels. Images are sometimes dangerous coadjutors. A dis-
course on wheels may run off the course; but a discourse on hinges must, at any
rate, retain the speaker in his place, and make him exhibit the various forms and
phases of his subject, by turning it in every direction to his audience.

The style of Dr CuaLmers’ writing partakes of the character of his mind.
It is copious and overflowing; cumbrous, perhaps, at times, for the more minute
detail of a subject; but the phraseology (though occasionally somewhat eccen-
tric) is often powerful and beautiful in the highest degree. It is impossible to
illustrate these peculiarities without examples. I shall only select a few.
Thus, to express the quick passage of time: “ Time, with its mighty strides,
will soon reach a future generation, and leave the present in death and in for-
getfulness behind it.” To express that the world occupies our thoughts: “ Its
cares and its interests are plying us every hour with their urgency.” A man
of shallow views in religion is a ‘‘man whose threadbare orthodoxy is made up of
meagre and unfruitful positions.” The external marks of piety: ‘“ A beauty of
holiness, which effloresces on the countenance, and the manner, and the outward
path.” To say that the repentance of a sinner interests the angels, is thus worded :
“His repentance would, at this moment, send forth a wave of delighted sensibility
throughout the mighty throng of their innumerable legions.” Persons who take

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their opinions from a partial adoption of Scripture truth, are persons who, “ re-
tiring within the entrenchment of a few verses of the Bible, will defy all the
truth and all the thunder of its warning denunciations.”

His style, with all its peculiarities, was His own. It may be called man-
nerism ; but it is the mannerism of a powerful mind striving to express its own
conceptions without regard to rules of rhetoric or the discipline of schools. It is
the mannerism of genius,—one leading characteristic of which is to invest known
truths and ordinary objects with new and untiring interest, and with constantly-
fresh attraction; and, on this ground, it is characteristic and becoming, because
it 1s his own; and, accordingly, these peculiarities of style pervaded his ordinary
conversation and his familiar letters, just as much as they marked his more ela-
borate compositions; and in the ordinary intercourse of life, expressions con-
stantly recurred to remind one of his writings. In fact, his language is merely
the vehicle or medium of expressing and communicating his ideas; and we may
almost say he could not help it. There is a danger with him (as there is with all
imaginative writers) of his style being considered imaginative only. To many
minds declamation is irksome and wearisome in the highest degree,—to them it
conceals rather than develops the mental power which lies below the surface;
and, not unfrequently, practical wisdom and sound argument are not duly esti-
mated, simply because there is a play of imagination around them,—the lustre and
richness of the setting obscures the pearls. Such authors are not unfrequently a
snare to their admirers. Mannerism in authors may be easily caught by those
who have no inspiration of their genius. Hence, of all writers and speakers Dr
CHALMERS was one most dangerous for imitators (and amongst young and inju-
dicious students he had imitators). What was natural to him was constraint or
affectation in them. In fact, they became copyists more than imitators. Their
taking his style and manner becomes a literary larceny, rather than an honourable
and fair obligation. It is miserable to see men borrowing fine clothes which they
know not how to wear,—affecting a glow of eloquence to cover a vapid and com-
monplace conception of their subject.

Secondly, As affecting the happiness of mankind, and as bearing upon their
best and highest interests for time and for eternity, Dr CHaLMERs was, during the
whole of his public career, much occupied with the theories of Political Economy.
In all ages of the world, how much of the misery of mankind may be traced to
the errors and mistakes of erroneous legislation. Bad laws on excise,—on poor
management, —on taxation,—on police or criminal jurisprudence, proceeding from
false views of political economy, have been the most fruitful sources of crime, of
misery, and degradation. The energetic and benevolent spirit of CHALMERS saw
and felt the connection between a well-doing and a well-living population. He
felt how much, under the Divine blessing, might be done by rulers and statesmen

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 903

to make or mar human happiness, and he took a very prominent position amongst
the Christian economists of the day. Into the general question of political econo-
my as a theory, whether of population, free trade, balance of trade, capital, taxes
or tithes, Ido not pretend to enter. On these points Dr CuHaLMers wrote with
much power and acuteness. His views on most points generally coincided with
Apam Smit, Matrnuus, Tooxs, and authors of that school. But in one depart-
ment of political economy, he took that position which has added lustre to his
name, and which exhibits him to the world as the true Christian philanthropist,
and the best friend of human nature. Speculations on theory and doctrine in
political economy were not sufficient for one who constantly sought to do good
to those who most needed the help and guidance of their fellow-Christians. We
have to consider CHALMERS, then, as a practical economist; as one who, not sa-
tisfied to reason and to speculate in his study upon the best methods of improv-
ing the conditions of mankind, went forth into the cottages, the hovels, and
crowded habitations of the poor, to improve their temporal, moral, and religious
condition. The agencies on which he depended for improving mankind were the
school, the Bible, the visitor, the pastor. Hence the titles of his works and
articles on this subject, indicate what were the objects and purposes he had
in view: for instance, we have “ The Civic and Christian Economy of Great
Towns ;” “The Christian and Eccnomic Polity of a Nation ;” ‘* Sabbath Schools ;”’
“‘ Bearing of Christian Economy upon Pauperism,” &e. In his “ Civic and Chris-
tian Economy of Large Towns,” he lays down some of the most valuable and
practical principles of useful charity. It is a dreary and heart-sickening prospect
which the Christian philanthropist encounters when he enters upon the charity of
great cities; and not only did Dr Cuaumers zealously promote amendment in
that field of our erring, and destitute, and suffering countrymen, by suggesting
sound principles of management, but he threw his whole energy, his persuasive
eloquence, and his personal superintendence into the work.*

In 1815 he had been called to take the pastoral charge of a parish in
Glasgow, a city where he knew there would be abundant opportunities for
verifying his opinions and employing his resources. He commenced the pub-
lication of The Civic and Christian Economy, as a small periodical, and took the
lead in directing the attention of the nation to the absolute necessity of ex-
tending, in our city population, means of education, of pastoral superintendence,
and spiritual instruction, similar to what prevailed through the country parishes

* It is pleasing to remember how the last mortal days of such a man were engaged with plans
of instruction for the benefit of this very class. He had for some time been entirely taken up with
a School and Church, in the worst locality of the Old Town of Edinburgh. The man of high specu-
lation became a teacher of ragged children. The Professor of Theology descended from his chair to
impress the first rudiments of Christian truth upon the rude minds of a congregation the most igno-
rant and most neglected.

504 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

of Scotland. However ample and effective had been the supply of these elements
of human improvement in the agricultural parishes and districts, the commercial
and manufacturing population had quite outgrown them, and the work required to
be recommenced, and taken in hand in good earnest. He was, therefore, a strenu-
ous and constant advocate for carrying out the system of TERRITORIAL SUBDIVISION.
There was a vitally important principle in the accomplishing this great end, and
one which Dr Cuatmers established with great ability: it was the principle of
providing for the work being efectually done, in the particular portions or dis-
tricts chosen—not only the taking in hand the worst localities, but in every one
of these laying a sufficient foundation or substratum of good, so far as you go.
I think this principle was first taken up by Dr Cuatmers. It is of immense im-
portance, and I know was adopted from Dr Cuatmers by the Bisnor of Lonpon,
in consequence of consultation with him regarding the plans for providing churches,
schools, and parsonages, for the recently-formed masses of the destitute popula-
tion of the great metropolis. The experiment was tried in Bethnal Green, where
ten new parishes were formed, dividing the population into sections manageable
by a pastor, and curate, and school. For want of attending to this principle, a
grant of a million of money for church-building in England had been rendered
comparatively ineffective. Churches and schools were set down here and there ;
lost in the mass of surrounding poverty and destitution, their influence was little
felt,—in some cases almost unnoticed.*

I have now to notice, in connection with the political economy of Dr CHALMERs,
an important incident of his life. And I must allude to an achievement which
exercised the greatest influence upon his own views of the parochial system and
management of the poor, and which excited astonishment, admiration, and scep-
ticism amongst his contemporaries. I refer to the remarkable effects produced by
management of the poor in St John’s Parish, Glasgow, under his direction and su-
perintendence. I will endeavour to make a plain and distinct statement of the
FACTS, as established by the evidence of the parties concerned in the operation.

It is well known how exceedingly Dr CHALMERs was opposed to the support of
the poor by a compulsory assessment ; that is to say, the ordinary wants and the
ordinary support of the poor. He approved of assessments for disease and casu-
alties, for supporting infirmaries, dispensaries, and lunatic asylums, also for ex-
traordinary emergencies of famine, pestilence, or catastrophe; but general poor-

* This principle of territorial subdivision, for which Dr Cuaumers, as a Christian philanthropist,
so long contended, is at last acknowledged as the essential preparation for bringing spiritual instruction
to bear upon the worst portions of our crowded and demoralised population. Lord Asutery, the en-
lightened friend of the poor, has, with the full approbation of the Premier, moved for a commission
to inquire into the best method of dividing all parishes in England which contain a population of
10,000 or upwards.

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 505

laws he utterly condemned. He had termed the system a “ legalised enormity.”
He had ascribed to the action of those laws in England all the evils under which
the country suffered from pauperism. He considered them to be the bane of
Christian charity, and the curse of all connected with them. It remained, then,
to test by experience, when he had a proper field, an opposite system ; and this he
was determined to do in Glasgow. When, in the year 1815, he took charge of the
Tron Church Parish in Glasgow, the system of management for the poor through-
out the city was somewhat peculiar. The whole funds raised for the poor, whether
in the shape of assessments or collections at the church-doors, were under the
administration of two bodies, one called the General Session, consisting of the
elders and clergy of all the parishes, and the other called the Town-Hospital, which
had pensioners within its walls, and owé-pensioners residing in the city. The
whole expense of poor support had been on the increase. In 1803 it amounted
to about £4000; in 1818, to about £11,000; in 1820, to £13,000. His determination
was, from the first, to manage his district without assessment. In this wild and
extravagant scheme, as it was considered, he was opposed by the General Session,
by the Magistrates, by the Town-Hospital, and by the Presbytery. Indeed, the
Presbytery had carried up a case against him to the General Assembly ; accord-
ingly, he was glad to be transferred to St John’s Parish, which took place in 1819,
and where the same obstacles and impediments to his experiment did not exist.
The population was 10,000; the people, with very few exceptions, of the poorest
class of manufacturers. According to the due proportion of population and pau-
perism, the expenditure for St John’s had been about one-tenth of the expendi-
ture for all Glasgow, or upwards of £1400 annually. His first step was to release
the General Session and the Town-Hospital from all obligation to support the
St John’s poor, and he undertook, with his own church-door collection, to meet
their wants. This collection averaged £400 a-year. With £400 a-year, there-
fore, he began the work. Now, of this sum, £225 were already pledged for
regular cases permanently settled upon parochial relief, so that, from this col-
lection fund of £400, £175 only remained as a surplus to meet and to provide for
new cases of pauperism. But, besides the £400—the result of day collections at
the church-door—there was another and an evening collection made by a very
poor congregation, chiefly in halfpence, which amounted to about £80 a-year. Out
of this £80 he resolved to provide for new cases of paupers coming upon the
parish, and to leave the £400 collection to take care of the old paupers. He had
previously made a minute district subdivision of the parish, and secured the as-
sistance of zealous and intelligent deacons as visitors, one for each district. What,
then, was the result of the system, and the degree of success with which it was
accompanied? The £80 covered the whole expense of the new pauperism, which
did not require more than £66, 6s. The £400 were, in the mean time, increasing
in the hands of the kirk-session by old paupers dropping off, and by the surplus
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of £175 not being required. This command of money in the hands of the kirk-
session Dr CHALMERS considered to be a snare and a danger; accordingly, as he
expressed it with considerable nazveté, he sought to provide “a safe and salutary
absorbent” to take off this plethora of pecuniary oppression, and this he did by
expending it all in the permanent endowment of a school. Thus the system
worked, and the only disturbing force seems to have been the occasional indis-
creet and injudicious introduction of charitable contributions from without : And
certainly here is a marvellous result,—the poor of a parish absolutely managed
with a success varying inversely as the pecuniary resources at the command of
the managers. But neither the principal mover of this scheme, nor his colleagues
in the work, seemed to consider it a mystery or a miracle; their solution of the
problem was ; 1st, that former applicants who were conscious that they did not
require or deserve support withdrew, and the idea of legal right ceasing, no cases
but those of absolute necessity were left; but, 2d, and chiefly, that the sym-
pathies of the poor themselves were thus called forth, and no one allowed his
neighbour to starve so long as he could spare a morsel, and when he knew that
neighbour was deprived of other resources on which he could depend. The
poor, in short, helped each other through their difficulties when no one else would.
The artificial channels of charity being closed, a more copious and more permanent
supply flowed through the natural channels of relationship and vicinage. Such
was the theory; the results were indisputable. The world was still sceptical, and
two solutions were offered to account for the success of a scheme which would
support poor people without poor-laws. It was said, in the first place, that the
system was so hard upon the people that the poor were driven out of St John’s
parish, and took refuge in other parishes, where more money was expended. It was
said, in the second place, that the success was the consequence of Dr CHALMERS’ per-
sonal influence and powers. That what he accomplished in St John’s, another man
could not accomplish in St Luke’s; and that, with the man, the scheme would die
out. To both of these objections an answer was ready. To the first objection it
was declared, that the balance of migratory pauper population was fully in favour
of St John’s; and, to come to greater exactness, it was stated that a correct ac-
count was kept of poor leaving St John’s, and poor coming in to St John’s: the
result was the imports exceeded the exports by fourteen souls. The exchange, in
fact, was against them, and this they considered a conclusive answer to the charge
of harsh treatment of paupers. To the second objection it was replied, that the
system worked for many years after Dr Cuatmers’ departure from Glasgow, and
succeeded also in other manufacturing parishes of Scotland where it was tried—
the Gorbals of Glasgow and Langholm being cited as favourable examples. How
it was that, in the face of an experiment apparently so successful, detailed by
himself in evidence before a parliamentary Committee, a more stringent enactment
of poor-laws for Scotland should have been made, and the system be adopted for

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 507

Ireland ; or how, in the public mind, it did not produce a stronger feeling against
compulsory charity in general, 1am not competent to decide. The facts are indis-
putable, and were, during the whole of Dr Cuatmers’ lifetime, after he left Glas-
gow, referred to in corroboration of the correctness of his theory, and as a standing
proof that charity, if left to itself, would supply means for the maintenance of the
poor, and a maintenance of a more suitable and effective nature than could be
done by a compulsory assessment. In all his treatises on Management of the
Poor, he alludes with unshaken confidence to the great Glasgow experiment.

The complete and detailed account of the experiment will be found in four
articles, forming the general Appendix on Pauperism, in the sixteenth volume of
his collected Works, including his own evidence before the Committee of the House
of Commons on the subject of a poor-law for Ireland. Great prejudice existed
(in England especially) against the whole system, as harsh, and severe, and
cruel, and numerous objections were urged against the possibility of success.
One objection brought by the writers of articles on Poor-laws in the Quarterly
Review, against the plan of withholding an assessment for supporting the poor,
and throwing them on the natural or voluntary principle of charity, was an un-
just one, and indicated a misapprehension of the whole system upon which that
method was grounded. It was said that the principles advocated by Dr Cua.-
MERS were an encouragement to vagrancy and mendicity. Therefore, according
to this view, it was merely a question whether we were to have parish paupers or
highway and street beggars. But the writers of those articles did not consider
that on no point was Dr CHALMERS’ views of pauperism more decided than on the
discouragement of relief to common vagrants and beggars. The principles on which
the Glasgow experiment was accomplished, when carried through, would have
entirely put down common beggars; and Dr CHaLMERs drew an ingenious and
novel argument agaist promiscuous charity from the example of our Lord, as re-
corded in the four Gospels. He healed all diseases and sickness in those who
came to him ; but only on two occasions did he supply by miracle the multitudes
with food. These were occasions of urgency ; and when he found that they came
to him idly and on account of food, he firmly withheld it.

But, Sir, | would now turn to another subject connected with the great ques-
tion of a nation’s civic economy—and that is the Endowment of its Church and
Universities. On these points Dr CuauMers has written with remarkable force
and much enthusiasm. And he has propounded the compulsory endowment
theory for ecclesiastical and educational objects as vigorously as he has disclaimed
it for sustaining the poor. His essay “On Ecclesiastical and Academical Endow-
ments” has been described in the Quarterly Review (vol. xliv., p. 527) “as one
of the most vigorous and eloquent defences of such endowments that ever pro-
ceeded from the press—a treatise which would alone have been sufficient to im-
mortalize its author.” This is high praise from such a quarter: But I think it is

508 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

deserved, and fully deserved. There is great power of argument, felicitous illus-
tration, and a glowing enthusiasm of admiration, for the theological literature,
and the erudition, and the learning, and the eminent men produced by the eccle-
siastical and academical endowments of England. In reference to the Church of
England he writes :—‘“ There are many who look with an evil eye to the endow-
ments of the English Church, and to the indolence of her dignitaries. But to
that Church the theological literature of our nation stands indebted for her best
acquisitions ; and we hold it a refreshing spectacle, at any time that meagre
Socinianism pours forth a new supply of flippancies and errors, when we behold,
as we have often done, an armed champion come forth in full equipment, from
some high and lettered retreat of that noble hierarchy; nor can we grudge her
the wealth of her endowments, when we think how well, under her venerable
auspices, the battles of orthodoxy have been fought,—that in this holy warfare
they are her sons and her scholars who are ever foremost in the field—ready at
all times to face the threatening mischief, and by the weight of their erudition to
overturn it.”

In the same work, ‘‘On the Use and Abuse of Literary and Ecclesiastical
Endowments,’’ he thus writes of Oxford and Cambridge:

“We cannot conclude this passing notice of the Universities of England, with-
out the mention of how much they are ennobled by those great master-spirits,
those men of might and of high achievement,—the Newtons, and the Miltons, and
the Drydens, and the Barrows, and the Addisons, and the Butlers, and the Clarkes,
and the Stillingfleets, and the Ushers, and the Foxes, and the Pitts, and Johnsons,
who, within their attic retreats, received that first awakening, which afterwards
expanded into the aspirations and the triumphs of loftiest genius. This is the
true heraldry of colleges. Their family honour is built on the prowess of sons,
not on the greatness of ancestors; and we will venture to say, that there are no
seminaries in Europe on which there sits a greater weight of accumulated glory,
than that which has been reflected, both on Oxford and Cambridge, by that long
and bright train of descendants who have sprung from them. It is impossible to
make even the bare perusal of their names without the feeling, that there has
been summoned before the eye of the mind the panorama of all that has upheld
the lustre, whether of England’s philosophy, or of England’s patriotism, for cen-
turies together. We have often thought what a meagre and stinted literature we
should have had without them; and what, but for the two Universities, would
have been the present state of science or theology in England! These rich semi-
naries have been the direct and the powerful organs for the elaboration of both;
and both would rapidly decline, as if languishing under the want of their needful
aliment, were the endowments of colleges swept away. It were a truly Gothic
spoliation ; and the rule of that political economy which could seize upon their
revenues, would be, in effect, as hostile to the cause of sound and elevated learn-

he

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 509

ing in Britain, as would be the rule of that popular violence which could make
havoc of their architecture, and savagely exult over the ruin of their libraries
and halls.”

Now, throughout the whole of this Essay on Endowments, and in the lectures
which he delivered with so much success in London before Princes of the Blood
Royal, Peers, Bishops, Ministers of State—the highest and the most intelligent of
the land—it will be observed that he constantly advocated compulsory enactment
or permanent endowment for support of the objects on which he lectured. He
maintains this opinion chiefly on the ground, that individuals are not in all cases
the best judges of their own interests, and will not always voluntarily employ
their means in that way which is most conducive to their own benefit and that
of society. In religion the supply must not be delayed till the demand come
forth to claim it. The demand is, in fact, to be created, for there is no natural
appetency for religious instruction; and so, as he himself declares, “the great
argument for literary endowments is founded on the want or weakness of the
natural appetency for literature.” Now the difficulty which most people have in
following Dr CHALMERS’ views on pauperism, arises out of this very argument of
his own in defence of academical and ecclesiastical endowments. For may it not
be urged, if the principle of provision by compulsory payment be so clear and
applicable to the case of sustaining ecclesiastical and academical institutions,
why is it not equally applicable to provision for maintaining the poor? The
natural appetency for charity is frequently quite as dull and torpid as natural
appetency for religious or literary instruction. Asa high and moral obligation,
should it not therefore also be compulsory equally with the others? But the poor
do assist each other in their poverty. But then, again, it may be asked, why
should the support of the poor be confined to the poor? They see their brethren
suffer, and charity is forced upon them. The more wealthy neighbours live at a
distance. If human distress were forced upon thezr notice, they too would help.
But they do not witness suffering at their doors, and so they forget it. But ought
they to be allowed to forget it ? Whatever force there may be in these or similar
arguments, one thing is clear, the Glasgow experiment did not practically con-
vince the Legislature that they might now abandon all compulsory assessment
for the poor, and throw themselves upon the natural charity of mankind for better
attaining, wrthout compulsion, the same object. This, however, be it remem
bered, is no real argument either against the truth of the statement or the sound-
ness of the theory. The highest exercise of Christian charity is undoubtedly the
voluntary ; indeed, giving to the poor except voluntarily, is not charity at all. The
principle may be pure and right, but human nature is not perhaps yet fitted to
receive it, or capable of acting upon it. A time may come when the world will
discern and receive it, when the outpourings of Christian love to the brethren will
50 promptly and so amply supply all the wants of the poor, that assessments will

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510 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

be unheard of. Men will do that on principle which now they must do by legal
enactment. Such a state of things would follow the universal prevalence of
Christian charity in men’s hearts, and is not therefore to be considered a mere
chimera. Should this triumph of principle and of love ever be achieved amongst
mankind, what will be said and thought in those days of the mind that, amidst
scepticism and ridicule, had resolutely maintained the principle, nay, which had
in its own sphere of action practically worked out its successful application ?

Thirdly, And now, Sir, we have to consider Dr CHALMERS as an orator. He was
distinguished as a preacher, as a speaker at public meetings, and as a member of
ecclesiastical courts. We attribute to him in all these positions, especially in the
pulpit, the quality of a high and a peculiar eloquence, and we have the utmost con-
fidence in the correctness of this estimate; for if CHALMERS were not eloquent,
where, we may ask, is eloquence to be found? Judge by the effects upon men’s ;
minds, and say, is not that eloquence which captivates and enchains the hearers ? 7
Is not that eloquence which delights all classes of mankind, all ages, all situations :
of life? Is not that eloquence which ensures an interest and admiration unbroken,
and which to the last attend every appearance of the speaker in public? Nor was
this attraction the result of art, or the merely artificial embellishments of oratory. Bs
It was not in graceful and studied action. It was not in musical and practised |
intonation. It was not in the purity and beauty of the accent. All these were |
plain, homely, to some hearers quite unusual; and yet how extraordinary were __
the effects of his eloquence! Such effects, then, being the result, not of artificial
embellishments or natural grace of manner, tones of voice or skilful action, are :
attributable to the power and energy of the preacher’s own spirit, to the vivid
pictures which he brought before his hearers, the fervid oratory with which he
took captive the heart and understanding. One important element of his success
as a preacher, I think, was the impression of earnest truth and sincere conviction
existing in hisown mind. As to the mode of arguing and the style of composi-
tion, the remarks already made upon Dr CHALMERS as an author, apply to him
as a preacher. indeed, all his writings seem as if composed for spoken communi-
cation, and the method is favourable to producing one vivid and powerful effect
upon the mind. No one indeed, who has not heard Dr CuaLMers in his day of
vigour, can form a correct idea of his power as a pulpit orator. It is now thirty
years since his Astronomical Sermons were delivered, and though I suppose no
discourses ever produced a greater effect, the nature of that effect must be little
known to the younger members of the present generation. The fame of a preacher
mainly depends (like the fame of an actor or singer) upon traditionary descrip-
tion. In many cases, the perusal of written discourses gives little notion of the
effect in delivery; in some cases, as of WHITFIELD, Dean Kirwan, and other emi-
nent preachers, who, in their day, produced marvellous sensations, they give no

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. oll

notion at all ; the effect must have arisen entirely from the manner. And when
we consider how much pleasure the printed Sermons of Dr CuAaLMErs now afford
to the intelligent reader, we may easily imagine the delight with which they must
have been heard, coming with all their novelty and fervour, fresh from the
preacher’s lips. To enter into any description or analysis of compositions so well
known as these published Sermons, would be here quite out of place. I may per-
haps refer to one or two passages as specimens, and favourable illustrations of
his own peculiar manner. In his sermon “ On Cruelty to Animals” (preached in
consequence of an endowment), he has occasion to shew that suffering is often in-
flicted on the inferior creatures by man, not for the purpose of torment, but that it
follows whilst he is occupied with other considerations and excitements ; and as
an example, to illustrate the absence of any cruel purpose for the mere infliction of
pain, he described in glowing colours the excitement and the interest of an English
hunting-field, and he terms it “ this favourite pastime of joyous old England, on
which there sits a somewhat ancestral dignity and glory.” And he described the
“assembled jockeyship of half a province,” the assemblage “ of gallant knight-
hood and hearty yeomen,” and he spake of “the autumnal clearness of the sky,”
and “ the high-breathed coursers,” and ‘“ the echoing horn”—“ the glee and fer-
vency of the chace,”—“ the deafening clamour of the hounds,” and “the dying
agonies of the fox,” in such a strain of animation, that Lord Eicuo’s huntsman,
who was present, declared that he had difficulty in restraining himself from get-
ting up and giving a vue-holla.

Of a far different character was the scene he drew in the conclusion of a sermon
preached for the benefit of a Society in aid of Orphan Children of Clergymen. He
described the sons and daughters ofa Scottish pastor obliged, at their father’s death,
to leave the peacefulness of their father’s dwelling, and appealed to his hearers for
their assistance in behalf of those who were so friendless and so dependent.
«« With quietness on all the hills, and with every field glowing in the pride and
luxury of vegetation, when summer was throwing its rich garment over this goodly
scene of magnificence and glory, they think, in the bitterness of their souls, that
this is the last summer which they shall ever witness smiling on that scene which
all the ties of habit and affection have endeared to them; and when this thought.
melancholy as it is, is lost and overborne in the far darker melancholy of a father
torn from their embrace, and a helpless family left to find their way unprotected
and alone, through the lowering futurity of this earthly pilgrimage.” I heard
that sermon, and the tears of the father and the preacher, fell like rain-drops on
the manuscript.

In his Sermon on the Death of Dr Tuomson, describing in a picturesque point
of view, the proximity of tenderness and power, of gentleness and strength, in the
same human character, he added this happy illustration: “ This is often exem-
plified in those alpine wilds, where beauty may at times be seen embosomed in

a12 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

the lap of grandeur, as when, at the base of a lofty precipice, some spot of verdure
or peaceful cottage home seems to smile in more intense loveliness, because of
the towering strength and magnificence which are behind it.”

In a very striking Sermon on the “ Paternal Character of God,” when draw-
ing “ the picture of moral and pleasing qualities of mind and affections, apart
from the love of God, or from the influence of divine grace upon the soul,”’ he adds
this beautiful illustration: ‘“ There is beauty in the blush of a rose, and there is
beauty of a higher character in the blush that mantles the cheek of modesty, and
yet there may be just as little of loyalty to God in the living as in the inanimate
object.”

Of his speaking at public meetings, I had fewer opportunities of judging than
I have had of his pulpit discourses. On some of those occasions, he produced
great impression. But, perhaps, the most distinguished of such appearances was
on occasion of a public meeting held in Edinburgh, in the year 1829, on the sub-
ject of a bill then pending in Parliament, commonly called the Catholic Emanci-
pation Bill. Dr Caters, in opposition to the views of the generality of those
with whom he usually acted in public affairs, civil and ecclesiastical, was in
favour of that emancipation, and of the admission of Roman Catholics, Peers and
Commoners, into the two Houses of Parliament. The effects of that speech have
been described as something very remarkable. An excitement and enthusiasm per-
vaded the large and closely-crowded assemblage, seldom witnessed in modern times.
I heard our most distinguished Scottish critic, who was present on the occasion,
give it as his deliberate opinion, that never had eloquence produced a greater effect
upon a popular assembly, and that he could not believe more had ever been done
by the oratory of DEmosTHENES, CicERO, Burke, or SHERIDAN. And this was a case
simply of eloquence. For the speech delivered was not remarkable either as to
argument or literary composition. It was reported in the newspapers at the time,
but has not been deemed worthy of being included in his collected Works. I shall
refer to one incident only connected with his speaking in the General Assembly,
—and the result was the more remarkable as the reply must have been unpreme-
ditated. He had spoken very strongly against the principle of a clergyman hold-
ing the two offices of Professor and Pastor. It was alleged against him that such
opinions were, at any rate, inconsistent in him, inasmuch as he had himself been
an aspirant for the Chair of Mathematics, and justified the union of professional
and pastoral duty. His answer to the charge was striking,—“ I feel obliged,” he
said, “I feel obliged to the Reverend Gentleman for reviving my pamphlet, and
for bringing me forward to make my public renunciation of what is there written.
I now confess myself to have indeed been guilty of a heinous crime, and I now
stand a repentant culprit before the bar of this Venerable Assembly.” After stat-
ing that he had then certainly maintained that a devoted and exclusive attention

BIOGRAPHICAL NOTICE OF THE LATE REV DR. CHALMERS. 513

to the study of mathematics was not dissonant to the proper habit of a clergyman,
he thus concluded :—

“* Alas! Sir, so I thought in my ignorance and pride. I have now no reserve in
saying that the sentiment was wrong, and that, in the utterance of it, I penned
what was most outrageously wrong. Strangely blinded that Iwas! What, Sir,
is the object of mathematical science? Magnitude, and the proportions of mag-
nitude. But then, Sir, I had forgotten two magnitudes, I thought not of the little-
ness of Time,—I recklessly thought not of the greatness of Eternity.”

An important class of productions and of labours come under this head, and
occupy a place somewhat intermediate between the pulpit and the public meeting.
T refer to his Lectwres on Moral Philosophy,—on Evidences,—and on Theology. These
lectures were all composed and written with great care; but he introduced, paren-
thetically, further explanations and illustrations extempore. The remarks made,
on his manner of discussion in the pulpit, apply also to his manner of discussion
in the Chair. The same fulness of illustration, the same energetic and irresistible
enforcement of some leading and fundamental truth,—the same fervour, and the
same sincerity. These did not fail to secure the attention, and to engage the af-
fections, of his class. Many persons, not intended for the ministry, attended these
lectures ; and we have reason to believe that his discussions on Evidences, on Bur-
LER’S Analogy, and on Natural Theology, have, in this generation, exercised con-
siderable influence upon the supposed sceptical tendencies of the northern mind.
I will only adduce one passage in illustration of his lecture style. In his Lectures
on Natural Theology, he draws an argument in favour of an unquestionable act of
Gop in creation, from the geological appearances of the world. The commencement
of the present economy, after the destruction of the previous economy, is a convincing
argument against the eternity of creation. The whole reasoning is ably and inge-
niously conducted, and, at the same time, clothed in language of a high and ima-
ginative eloquence. He thus asks, How could the present world, after former de-
struction, be produced otherwise than by a new and palpable act of creation?
“Is there ought in the rude and boisterous play of a great physical catastrophe
that can germinate those exquisite structures, which, in our yet undisturbed eco-
nomy, have been transmitted in pacific succession to the present day? What is
there in the rush and turbulence, and mighty clamour of such great elements of
ocean, heaved from its old resting-place, and lifting its billows above the Alps and
the Andes of a former continent? What is there in this to charm into being the
embryos of an infant family, wherewith to stock and to people a now desolate
world ? We see, in the sweeping energy and uproar of this elemental war, enough
to account for the disappearance of all the old generations, but nothing that might
cradle any new generations into existence, so as to have effloresced on ocean’s de-
serted bed, the life and the loveliness which are now before our eyes. At no junc-
ture, we apprehend, in the history of the world, is the interposition of Deity more

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514 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

manifest than at this; nor can we better account for so goodly a creation, emer-
ging again into new forms of animation and beauty from the wreck of the old one,
than that the Srrrrit of Gop moved on the face of the chaos; and that nature,
turned by the last catastrophe into a wilderness, was again repeopled at the ut-
terance of His word.”

We naturally feel an interest about the appearance and address, the personal
habits and peculiarities, of those who have been distinguished in their day and
generation. Such peculiarities, in the subject of this biographical notice, must
have been familiar to many now present. For upwards of twenty years I
enjoyed the privilege of friendly intercourse; and it is a pleasing, though melan-
choly office of memory to recall those traits which rendered his society so inter-
esting, and so delightful. I think I can safely say I never left his company
without having some sentiments or expressions in my mind which I felt were
worthy to be remembered. There was a mixture of guileless simplicity and acute-
ness, of playful humour and vigorous conversation, of urbanity and earnestness,
which cannot be forgotten. His face was at times radiant with benevolence and
kindly feeling. Like many powerful and striking countenances, the expression
was chiefly in the mouth. The eye was dull, and often inanimate,—this, in com-
bination with the massive brow, rendered the play of the lower part of the face
the more striking ;—on those occasions especially, when, after being silent and
apparently abstracted, he would burst forth into some strain of admiration, or
some strong expression of his opinion regarding the topic of conversation, or not
unfrequently some humorous or ludicrous combination of thought. His habits
were social—he was hospitable, and enjoyed the hospitality of his friends.
Though, in his whole demeanour, utterly inartificial, he was eminently courteous
and pleasing in his address. Though as plain and unpretending in his manners
as possible, no man had a more acute perception of refinement of manners in
others. I recollect his enthusiastic admiration of the polished and refined man-
ners of an English dignitary of high birth and station, in whose company we had
been.

In his ordinary conversation, there was constantly occurring some appro-
priate and striking expression. In fact he neverexpressed himself exactly like other
people, and yet without any straining or affectation of effect. No man could have
been more conscientiously and sincerely attached to his own Church, both from
argument and from those numerous national associations and social feelings
which are sometimes more binding even than convictions of reason. He was yet
quite free from intolerance and bigotry, and illiberal prejudice. He admired and
loved what was great and amiable in those from whom he differed, and differed in
many important principles. Thus, as appears from passages I have quoted, he
spoke with enthusiasm of the learning and the position of the Church of England.
He gloried in the grandeur of her Gothic architecture, as much as any of her own

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 515

children could do. On one occasion I recollect his describing, with much interest,
a Sunday he passed at Winchester, when a guest of the Bishop, and dilating on
the services and “ staff of the Cathedral,” as he called them; the question was
put, evidently expecting an unfavourable reply, ‘‘ But, Doctor, what did you think
of the chanting?’ His immediate answer was, “ Very grand, Sir!” He could dis-
cern what was good, and exercise kindness and forbearance towards those from
whom he differed far more widely than he did from the Church of England.
Thus, when told of a purpose on the part of Roman Catholics to establish in the
old town a system of visiting the poor by Sisters of Charity, similar to the visiting
in Paris and other continental cities, he exclaimed he was glad to hear it, as it might
induce a similar plan of visits from Protestant Sisters of Charity. In his examina-
tion before the Committee of the House of Commons respecting his management
of St John’s, Glasgow, the question was put, “ Did you meet with any contradic-
tion on the part of the Roman Catholic clergy of Glasgow?” He replied, “ Not
in the least; for the clergyman was a party in the negotiation. He attended our
meetings, and there was mutual understanding between the clergyman and the
members of the committee.” (This mutual understanding was, that there should
be no attempts on either side at proselytizing, but simply to give education with
reading of Scripture. There was this compromise made regarding schools with
Roman Catholic children: The Roman Catholic clergyman consented to the use
of the Bible as a school-book, according to the authorised version ; the Protestants
consenting to have Roman Catholic teachers). He had before said to the Com-
mittee that he attended at a Roman Catholic school from the delight he had in
witnessing the display of native talent among the young Irish, and that he was re-
ceived with welcome and respect by the Roman Catholic master, who asked him to
address the children. Having done so freely, and according to his views, the master
thanked him most cordially—and then he added, “ This convinced me that a vast
deal might be done by kindness, and by discreet and friendly personal intercourse
with the Roman Catholics. I may also observe that, whereas it has been alleged
that, under the superintendence of a Roman Catholic teacher, there might be a
danger of only certain passages of Scripture being read to the exclusion of others,
so far as my observation extended, he read quite indiscriminately and impartially
over Scripture.”

Dr CHALMERS going to the Roman Catholic schools to witness “ display of
native talent amongst the young Irish,” reminds me ofa trait in his character not
generally perhaps understood, but which was on occasions very marked ; I mean
his turn for humour and keen sense of the ridiculous. At times he could not
control his merriment at ludicrous and grotesque combinations ; and I can easily
imagine his exquisite enjoyment of answers from the half-naked little Irish urchins.
Their odd mixture of acuteness and self-possession, with random confusion of
| ideas, would be to him irresistibly comic. He had an instinctive sense of the

516 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

ludicrous combination of circumstances, and narrated them with great effect.
One of the most amusing scenes I remember, was his own description of what
happened at Manchester when he had consented to preach a sermon for some
public object at a large chapel in that town. He had not been thinking about
the matter after he had given his consent to preach ; but his eye was attracted by
seeing his own name in a printed paper, like an immense play-bill, posted on the
walls all about the town. This was a programme of the ceremonial for the day.
There were to be prayers, anthems, choruses from Handel’s Oratorios, and a sermon
by the celebrated Dr CHatmers of Edinburgh! Excessively annoyed at all this
display he refused to take any part, or to preach on the occasion. The directors
expostulated, and represented what would be the effects of his withdrawal, and
the disappointment of the public. The matter was compromised, and Dr
CHALMERS was to sit in the vestry till the proper time for him to come out and
preach his sermon. But his troubles then only began, for, unfortunately, an an-
them, with full instrumental accompaniments, was appointed to follow the ser-
mon. The orchestra being placed immediately behind the pulpit, and more occu-
pied with anticipations of their own performance than with anything else, the
musicians annoyed and disturbed the preacher through the whole sermon by their
preparations and preliminaries for the grand chorus, “ actually,” as the Doctor
exclaimed, “ tuning their very trombones close at my ear before I had finished.”
One other feature of mental constitution, and one only I will refer to; and
it is an important one, as having its influence not only upon the imagery and orna- __
ment of his literary compositions, but, in some instances, upon the general cur-
rent of his opinion and speculations, and that is his deep admiration of the beauti- |
ful in the material universe. This admiration was intense, it amounted to a
passion, and he evidently had exquisite enjoyment in the contemplation of Nature’s
works, or rather, I should say, of the goodness and wisdom of the Creator, whether
displayed in the wildness or loveliness of natural scenery, the delicate tints and
texture of a flower, or the magnificence of the starry heavens. Hence, although
no artist himself, he had the greatest interest and enjoyment in the society and
conversation of artists. He delighted to hear their remarks on subjects of taste
in connection with scenery; on the tints of the landscape, the sky, the ocean, the
forms and varieties of clouds, the appearances most suitable for picturesque re-
presentation, and the practical rules observed in transferring to the canvas imi-
tations of what is in nature. Hence in his moral reasoning we find all his refer-
ences, in the way of analogy or illustration, to the beauties and appearances of the
natural world, expressed with so much freshness and feeling of reality. He
always seems to be impressed with the conviction that, though a fallen world, the
fall has chiefly affected the moral and spiritual nature of man himself; that, though
the ground was cursed for man’s transgression, and so lost the power of support-
ing the species without toil and labour ; yet that, in the material world around us,

BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS. 517.

there remains an impress of primeval beauty,—that there are forms unscathed by
the penalties of the primeval curse, and flowers as delicate and fair as those that
bloomed in paradise. These sentiments of intense admiration for an external
and material world, exercised, I think, considerable influence in modelling his
views, and shaping his arguments for Natural Theology. We ever delighted in
tracing the lineaments of God’s moral character in the mirror of the material
world, as reflecting his attributes, and as displaying the nature of his handiwork.
He deprecated the notion of any essential connection between materialism and
sin; and as the abode of man in innocence was a terrestrial one, so he believed
that in glory there would be provided a new heaven and a new earth, with visible
magnificence and material splendour, to be a fitting habitation, and to furnish fit-
ting occupations and enjoyments, for the new and glorified bodies of the redeemed.

I have now, I think, touched upon all those points of character, and all those
public acts and deeds, of which I have been capable of forming a judgment, and
which have occurred to me as strictly coming within the province of such a paper
as the present. In these remarks I have endeavoured to look upon Dr CHALMERs,
not as a private friend, but as a public character. I have sought to give a fair
transcript of the man as he appeared before us, with no undue partiality arising
from those personal feelings of regard and admiration which I am proud to ac-
knowledge. Lamcertain that those who knew him best esteemed him most. His
character bore investigation; and, I think, whatever opinion, in a literary or cri-
tical point of view, the world may form of the posthumous volumes, on Scripture
Reading, which have been laid before them, it must be allowed that they furnish
unequivocal indications of a mind constantly and habitually occupied with sacred
things,—of private thoughts and of retired meditations, ever conversant with
God and with His holy word.

And now, Sir, to conclude. It will hardly be supposed that I should expect
unanimity of opinion in all those questions by which the name of our late distin-
guished Vice-President has been brought before the notice of his contemporaries.
On every subject, indeed, where there are not positive moral precepts or mathe-
matical demonstration, the different tastes and habits of mankind will lead to a
difference in their judgments. Different styles of writing, for instance, are con-
genial with different mental constitutions. The eloquence which affects and even
overpowers one man, has little charm or influence over the mind and feelings of
another. ‘The early associations of individuals,—the various points of view from
which they contemplate the actions of public men, almost inevitably lead to dif-
ferences in their decisions. In great questions of national or ecclesiastical policy,
the conduct utterly condemned by one party, will often be extravagantly lauded
by another. It was impossible for any one to take so prominent a position in that

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518 BIOGRAPHICAL NOTICE OF THE LATE REV. DR CHALMERS.

recent movement of our country,—the Disruption of a National Church, with all
its accompanying excitements,—its breaking up of old associations,—its contend-
ing opinions and hasty sayings,—without running counter to the opinions of many
early admirers, without partially, at least, alienating himself from former friends,
and separating himself from former coadjutors. On such points it were vain to
expect a concurrent judgment on all he has done and said. But of this I feel as-
sured, that none who have had favourable opportunities of personal acquaintance
with his character and disposition,—that none who have deeply entered upon a
study of his writings, so as fully to appreciate the lofty and benevolent spirit of
their sentiments and tendencies, will hesitate to admit that he was both a good
and a great man,—that he was imbued with the spirit of Christian philanthropy,
—that he had a fervent mind, keen sensibility, and indomitable energy. His
highest praise, but, at the same time, his just eulogium is, that his fervency of
spirit, his sensibility, and his energy, were all exercised’ and called forth in the
one great and magnificent cause,—promoting the glory of Gop and the welfare of
Mankind. In all his meditations, and in all his labours, he had ever distinctly
before his eyes the advancement of his fellow-creatures, in their best and truest
relations to this world and the world to come.

His greatest delight was to contrive plans and schemes for raising degraded
human nature in the scale of moral being,—the favourite object of his contempla-
tion was human nature attaining the highest perfection of which it is capable:
and, as that perfection was manifested in saintly individuals, in characters of great
acquirement adorned with the graces of Christian piety. His greatest sorrow was
to contemplate masses of mankind hopelessly bound to vice and misery by chains
of passion, ignorance, and prejudice. As no onemore firmly believed in the power
of Christianity to regenerate a fallen race,—as faith and experience both conspired
to assure him that the only effectual deliverance for the sinful and the degraded
was to be wrought by Christian education, and by the active agency of Christian
instruction penetrating into the haunts of vice and the abodes of misery ;—these
acquisitions he strove to gain for all his beloved countrymen ; for these he laboured,
and for these he was willing to spend and be spent. From the fields of earthly
toil and trial he has been removed, and he has entered into his rest. The great
business of Christian benevolence, and the contest with ignorance and crime, are
left in other hands. But Ats memory will not die, nor his good example in these
things be forgotten. His countrymen will do his memory justice. Of the thou-
sands who were assembled to witness the funeral procession which conveyed his
earthly remains to the tomb, all felt conviction on that day that a Great Man had
fallen in Israel,—that a Scotchman had gone to the grave, of whom Scotland

might be proud,—a Scotchman who had earned a name in his country’s annals, _ :

and a place in his country’s literature, which will not pass away.

fegsbllObes)

XXXV.—On the Theory of Rolling Curves. By Mr James CLerK MAXWELL.
Communicated by the Rev. Professor KELLAND.

(Read, 19th February 1849.)

There is an important geometrical problem which proposes to find a curve
having a given relation to a series of curves described according to a given law.
This is the problem of Trajectories in its general form.

The series of curves is obtained from the general equation to a curve by the
variation of its parameters. In the general case, this variation may change the
form of the curve, but, in the case which we are about to consider, the curve is
changed only in position.

This change of position takes place partly by rotation, and partly by trans-
ference through space. ‘The rolling of one curve on another is an example of
this compound motion.

As examples of the way in which the new curve may be related to the series
of curves, we may take the following :—

1. The new curve may cut the series of curves at a given angle. When
this angle becomes zero, the curve is the envelope of the series of curves.

2. It may pass through corresponding points in the series of curves. There
are many other relations which may be imagined, but we shall confine our atten-
tion to this, partly because it affords the means of tracing various curves, and
partly on account of the connection which it has with many geometrical problems.

Therefore the subject of this paper will be the consideration of the relations
of three curves, one of which is fixed, while the second rolls upon it and traces the
third. The subject of rolling curves is by no meansanew one. The first idea of the
_ eycloid is attributed to ARISTOTLE, and involutes and evolutes have been long known.

In the “ History of the Royal Academy of Sciences” for 1704, page 97, there
is amemoir entitled “ Nouvelle formation des Spirales,” by M. Varianon, in which
he shews how to construct a polar curve from a curve referred to rectangular co-
ordinates by substituting the radius vector for the abscissa, and a circular arc for
the ordinate. After each curve, he gives the curve into which it is “ unrolled,”
by which he means the curve which the spiral must be rolled upon in order that
its pole may trace a straight line; but as this is not the principal subject of his
paper, he does not discuss it very fully.

There is also a memoir by M. pE La Hire, in the volume for 1706, Part I.,
page 489, entitled,—“ Methode generale pour réduire toutes les Lignes courbes a
des Roulettes, leur generatrice ou leur base étant donnée telle qu’on voudra.”

M. pE LA Hire treats curves as if they were polygons, and gives geometrical
constructions for finding the fixed curve or the rolling curve, the other two being
given ; but he does not work any examples.

op)
n

WiOli XV. PART, Vi,

520 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

In the volume for 1707, page 79, there is a paper entitled,‘ Methode gene-
rale pour déterminer la nature des Courbes formées par le roulement de toutes
sortes de Courbes sur une autre Courbe quelconque.” Par M. Nicoxz.

M. NicoLe takes the equations of the three curves referred to rectangular co-
ordinates, and finds three general equations to connect them. He takes the tracing-
point either at the origin of the co-ordinates of the rolled curve or not. He then
shews how these equations may be simplified in several particular cases. These
cases are,—

Ist, When the tracing-point is the origin of the rolled curve.
2d, When the fixed curve is the same as the rolling curve.
3d, When both of these conditions are satisfied.

4th, When the fixed line is straight.

He then says, that if we roll a geometric curve on itself, we obtain a new
geometric curve, and that we may thus obtain an infinite number of geometric
curves.

The examples which he gives of the application of his method are all taken
from the cycloid and epicycloid, except one which relates to a parabola, rolling on
itself, and tracing a cissoid with its vertex. The reason of so small a number of ex-
amples being worked may be, that it is not easy to eliminate the co-ordinates of
the fixed and rolling curves from his equations.

The case in which one curve rolling on another produces a circle is treated
of in Wituis’s Principles of Mechanism. Class C. Rolling Contact.

He employs the same method of finding the one curve from the other which
is used here, and he attributes it to EULER (see the Acta Petropolitana, vol. v.).

Thus, nearly all the simple cases have been treated of by different authors;
but the subject is still far from being exhausted, for the equations have been ap-
plied to very few curves, and we may easily obtain new and elegant properties
from any curve we please.

Almost all the more notable curves may be thus linked together in a great
variety of ways, so that there are scarcely two curves, however dissimilar, be-
tween which we cannot form a chain of connected curves.

This will appear in the list of examples given at the end of this paper.

Let there be a curve KAS, whose pole is at C.

Let the angle DCA=0, and CA=r, and let

4, =9 (7)
Let this curve remain fixed to the paper.

Let there be another curve BAT, whose pole is B.
Let the angle MBA=@,, and BA=r,, and let

, = op) (12).

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 521

Let this curve roll along the curve KAS without slipping.
Then the pole B will describe a third curve. whose pole is C.
Let the angle DCB=9,, and CB=r;, and let

63 = 03 (73).

M

We have here six unknown quantities, 6, 0, 0,7, 7,73; but we have only
three equations given to connect them, therefore the other three must be sought
for in the enunciation.

But before proceeding to the investigation of these three equations, we must
premise that the three curves will be denominated as follows :—

The Fixed Curve, Equation, 4,=9, (7,)
The Rolled Curve, Equation, #,=0,) (72)
The Traced Curve, Equation, §;=¢9; (75)

| When it is more convenient to make use of equations between rectangular
| co-ordinates, we shall use the letters 7, 4%, a y, x;y; We shall always employ

522 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

the letters s, s. s; to denote the length of the curve from the pole, p: p, p; for the
perpendiculars from the pole on the tangent, and q 9 9; for the intercepted part
of the tangent. :

Between these quantities, we have the following equations :—

= Sri
r= a +H Stan y
x =r cos é = ¢ sin 6
Meo t e af
= 2 ele. dé = LP l
c= Ves Gi) = fu @
bape is Ao _ _yda—ady
oe) oe Ny P= (dx)? + dy?
dé
rar
dé be adxt+ydy
sei SY 1 V@a+ Gy
2 d 2\ 3
nx (22)')3 (a+ (22)')5
dé R dx
R= 2 Fp a @ y
ey yeae eee Py
re has de dx

We come now to consider the three equations of rolling which are involved
in the enunciation. Since the second curve rolls upon the first wethout slipping,
the length of the fixed curve at the point of contact is the measure of the length
of the rolled curve, therefore we have the following equation to connect the fixed
curve and the rolled curve,—

8, =,

Now, by combining this equation with the two equations
= (%) = y
(HERS pon BEE GO)

it is evident that from any of the four quantities 0, 7, 6, 7, or %, y, &, y,, We can
obtain the other three, therefore we may consider hese Gun fies as known fune- |
tions of each other. ?

Since the curve rolls on the fixed curve, they must have a common tangent. —

Let PA be this tangent, draw BP, CQ perpendicular to PA, produce CQ, and
draw BR perpendicular to it, then we have CA=r, , BA=r,, and CB=r,; CQ=p,,
PB=p,, and BN=p,; AQ=q,, AP=9, and CN =q,.

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 523

Also, r,” = CB? = CR? + RB? = (CQ + PB) + (AP — AQ)?
= (P, + Be)” + (Ge — %)?
= py + 2p, By + Py” + 72” — Py” —~29%% +7, — By
ry = 7 + 7 + 2p, Py — 2% %
Since the first curve is fixed to the paper, we may find the angle 6,

Thus é, = DCB = DCA + ACQ + RCB
RB
=o + tant + tan 5

é, = 6, + tan — + tan7! sr

Thus we have found three independent equations, which, together with the
equations of the curves, make up six equations, of which each may be deduced
from the others. There is an equation connecting the radii of curvature of the
three curves which is sometimes of use.

The angle through which the rolled curve revolves during the description of
the element d s,, is equal to the angle of contact of the fixed curve and the rolling
curve, or to the sum of their curvatures,

as, + d 8»
R,

il

But the radius of the rolled curve has revolved in the opposite direction
through an angle equal to d 6,, therefore the angle between two successive posi-

, : d s: < :
tions of 7, is equal to —d%, Now this angle is the angle between two suc-
2

cessive positions of the normal to the traced curve, therefore, if O be the centre
of curvature of the traced curve, it is the angle which d s, or d s, subtends at O.
Let OA=T, then

ds, r, d 6, ds. ds, as
s OE Phy i ae aia,

RA eee 7 Aas tacit

ab, 1 i 1 dé

7? —_2 = + — 7 eal

d 8, Ja R, R, 4 So

Ge eae i

PANGS Gare Sheen? Ytare

As an example of the use of this equation, we may examine a property of
the logarithmic spiral.

In this curve, p = mr, and R = -, therefore if the rolled curve be the
logarithmic spiral

VOL. XVI. PART V. OF

524 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

(iat 5 ail nan
sae NA roe aa R, si Fe
it She
ao) Re
‘ AO
therefore AO in the figure = m R,, and R7™

1

Let the locus of O, or the evolute of the traced curve LYBH, be the curve
OZY, and let the evolute of the fixed curve KZAS be FEZ, and let us consider
FEZ as the fixed curve, and OZY as the traced curve.

Then in the triangles BPA, AOF, we have OAF = PBA, and a == —

therefore the triangles are similar, and FOA = APB = 2 therefore OF is perpen-
dicular to OA, the tangent to the curve OZY, therefore OF is the radius of the
curve which when rolled on FEZ traces OZY, and the angle which the curve makes
with this radius is OFA = PAB = sin™ m, which is constant, therefore the curve,
which, when rolled on FEZ, traces OZY, is the logarithmic spiral. Thus we have
proved the following proposition: ‘“ The involute of the curve traced by the pole
of a logarithmic spiral which rolls upon any curve, is the curve traced by the
pole of the same logarithmic spiral when rolled on the involute of the primary
curve.”

It follows from this, that if we roll on any curve a curve having the property
p, = m,7,, and roll another curve having p, = m, 7, on the curve traced, and so
on, it is immaterial in what order we roll these curves. Thus, if we roll a loga-
rithmic spiral, in which p = mr, on the nth involute of a circle whose radius is a,
the curve traced is the n + 1th involute of a circle whose radius is / 1 — m’.

Or, if we roll successively m logarithmic spirals, the resulting curve is the
n + mth involute of a circle, whose radius is

aJl1—m? J/1—m,? J ete.

We now proceed to the cases in which the solution of the problem may be
simplified. This simplification is generally effected by the consideration that the
radius vector of the rolled curve is the normal drawn from the traced curve to the
fixed curve.

In the case in which the curve is rolled on a straight line, the perpendicular
on the tangent of the rolled curve is the distance of the tracing point from the
straight line ; therefore, if the traced curve be defined by an equation in «, and y,.

Us SF aero ond a BG 2)

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 525

ee eee eaten SPN BIRD

)

By substituting for r, in the first equation, its value, as derived from the

second, we obtain
= Gy LG8)' 1-09)
3 d Ys dy, ad 6,
oes

2
If we know the equation to the rolled curve, we may find ( aa ) in terms
of r,, then by substituting for 7, its value in the second equation, we have an
: tA d 5 “
equation containing w, and aa from which we find the value of a in terms
3 3

of w,, the integration of this gives the equation of the traced curve.
As an example, we may find the curve traced by the pole of a hyperbolic
spiral which rolls on a straight line.

The equation of the rolled curve is 6, = =

dx.\ 2 dxz.\? Lat dx.\ ” 2
ee Mead Cat bet a coe
“ (75) Ge) +1]=3(G2 +1]
d2.\ ? dx.\?
aS =«3[ 5) +1]
dy, : d ¥;

d x, = 45

dy; es ne a =u ae
This is the differential equation of the tractory of the straight line, which is
the curve traced by the pole of the hyperbolic spiral.
By eliminating w, in the two equations, we obtain

dr, d x,
ce)
This equation serves to determine the rolled curve when the traced curve is
_ given.
As an example we shall find the curve, which being rolled on a straight line,
traces a common catenary.
Let the equation to the catenary be

Then tama his —1.

526 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

dr, PEM Se er aie
d 6, a. on)" 2
2

7
d é,
dr, 5 A ee
Maa ae. =
dr, 2 34
= 4. —a
(aH 2 (r—a)
do 1
r ik then by integration
TN a
@ = cos* (=* _1)
F:
ee i sal
~ 1 + cos 6

This is the polar equation of the parabola, the focus being the pole, therefore,
if we roll a parabola on a straight line, its focus will trace a catenary.

The rectangular equation of this parabola is «* = 4 a y, and we shall now
consider what curve must be rolled along the axis of y to trace the parabola.

By the second equation (2.),

eee
= wile aad but 27, = Pp,
3

r= NN 4a +p?

De ao ae 2
Yr, =p, =4a

2a= Nt." — py? = %

but g, is the perpendicular on the normal, therefore the normal to the curve al-
ways touches a circle whose radius is Q a, therefore the curve is the involute of
this circle.

Therefore we have the following method of describing a catenary by continued
motion.

Describe a circle whose radius is twice the parameter of the catenary ; roll a
straight line on this circle, then any point in the line will describe an involute
of the circle; roll this curve on a straight line, and the centre of the circle will
describe a parabola; roll this parabola on a straight line, and its focus will trace
the catenary required.

We come now to the case in which a straight line rolls on a curve.

When the tracing-point is in the straight line, the problem becomes that of in-
volutes and evolutes, which we need not enter upon, and when the tracing-point is

‘
3
:

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 527

not inthe straight line, the calculation is somewhat complex, we shall therefore con-
sider only the relations between the curves described in the first and second cases.

Definition.—The curve which cuts at a given angle all the circles of a given
radius whose centres are in a given curve, is called a tractory of the given curve.

Let a straight line roll on a curve A, and let a point in the straight line de-
scribe a curve B, and let another point, whose distance from the first point is },
and from the straight line a, describe a curve C, then it is evident that the curve
B cuts the circle whose centre is in C, and whose radius is 6, at an angle whose

sine is equal to x therefore the curve B is a tractory of the curve C.

When a = 8, the curve B is the orthogonal tractory of the curve C. If tan-
gents equal to a be drawn to the curve B, they will be terminated in the curve C;
and if one end of a thread be carried along the curve C, the other end will trace
the curve B.

When. a = O, the curves B and C are both involutes of the curve A, they are
always equidistant from each other, and if a circle, whose radius is 6, be rolled on
the one, its centre will trace the other.

If the curve A is such that, if the distance between two points measured along
the curve is equal to ), the two points are similarly situate, then the curve B is
the same with the curve C. Thus, the curve A may be a re-entrant curve, the
circumference of which is equal to 0.

When the curve A is a circle, the curves B and C are always the same.

The equations between the radii of curvature become

When a = O, T = O, or the centre of curvature of the curve B is at the point
of contact. Now, the normal to the curve C passes through this point, therefore—

“The normal to any curve passes through the centre of curvature of its trac-
tory.”

In the next case, one curve, by rolling on another, produces a straight line.
Let this straight line be the axis of y, then, since the radius of the rolled curve is
perpendicular to it, and terminates in the fixed curve, and since these curves have
a common tangent, we have these equations,

If the equation of the rolled curve be given, find = in terms of ,, substitute

VOL, XVI. PART V. 6U

528 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

d
«, for r,, and multiply by «,, equate the result to = , and integrate.

Thus, if the equation of the rolled curve be

—>Ar”+4 ete. + Kr?24+Lr + Mlogr + Nr + ete. + Zr”

=n Ar — ete 2K — Lr +MrouNiete tn Zr

r

oY =n Ae — etc. 2K 2? —- Let + M+Natete +nZer

x

t= Ag sete, +2Kat—Llog#++ Me+4N a + ete. + BS ee
a n+

which is the equation of the fixed curve.

; : Cy.
If the equation of the fixed curve be given, find 7. in terms of x, substitute

ry for x, and divide by v, equate the result to ae and integrate.

Thus, if the fixed curve be the orthogonal tractory of the straight line, whose
equation is

this is the equation to the orthogonal tractory of a circle whose diameter is equal
to the constant tangent of the fixed curve, and its constant tangent equal to half
that of the fixed curve.

This property of the tractory of the circle may be proved geometrically, thus—
Let P be the centre of a circle whose radius is PD, and let CD be a line constantly
equal to the radius. Let BCP be the curve described by the point C when the
point D is moved along the circumference of the circle, then if tangents equal
to CD be drawn to the curve, their extremities will be in the circle. Let ACH
be the curve on which BCP rolls, and let OPE be the straight line traced by the
pole, let CDE be the common tangent, let it cut the circle in D, and the straight
line in E.

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 529

A

Then CD=PD .:. =~ DCP = —DPC, and CP is perpendicular to OE,
.'. <CPE=2 DCP+=_DEP. Takeaway — DCP=— DPC, and there remains
DPE— DEP .-. PD = DE.: CE=2 PD.

Therefore the curve ACH has a constant tangent equal to the diameter of the
circle, therefore ACH is the orthogonal tractory of the straight line, which is the
tractrix or equitangential curve.

The operation of finding the fixed curve from the rolled curve is what Sir
JoHN LESLIE calls “ divesting a curve of its radiated structure.”

The method of finding the curve which must be rolled on a circle to trace a
given curve is mentioned here because it generally leads to a double result, for
the normal to the traced curve cuts the circle in two points, either of which may
be a point in the rolled curve.

Thus, if the traced curve be the involute of a circle concentric with the given
circle, the rolled curve is one of two similar logarithmic spirals.

If the line traced be a tangent to the circle, the rolled curve is either of the
parts of the polar catenary.

If the curve traced be the spiral of ARCHIMEDES, the rolled curve may be either
the hyperbolic spiral or the straight line.

In the next case, one curve rolls on another and traces a circle.

Since the curve traced is a circle, the distance between the poles of the fixed
curve and the rolled curve is always the same ; therefore, if we fix the rolled curve
and roll the fixed curve, the curve traced will still be a circle, and, if we fix the
poles of both the curves, we may roll them on each other without friction.

Let a be the radius of the traced circle, then the sum or difference of the radii

930) MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

of the other curves is equal to a, and the angles which they make with the radius
at the point of contact are equal,

d 6, d 4, :
n= a @ Serj) ands, 5 oe moe
i

as, eee if
am a dr, .

: dé,.
If we know the equation between 0, and 7,, we may find es in terms of 7,,
1

= T»)

substitute + (4+ 7,) for 7,, multiply by , and integrate.

Thus, if the equation between @, and 7, be
7, = asec 4,

which is the polar equation of a straight line touching the traced circle whose
equation is 7” = @,
then

Ct ee a
a7 ie (7) a) 72 +2 7,
a

Now, since the rolling curve is a straight line, and the tracing point is not in
its direction, we may apply to this example the observations which have been made
upon tractories.

Let, therefore, the curve * = 2; be denoted by A, its involute by B,
and the circle traced by C, then e is ae tractory of C; therefore the involute

2 : : 5 = ee
of the curve r = == is the tractory of the circle, the equation of which is

slave 2 5 : 2a
0 = COs? | ef “—1. The curve whose equation is 7 = z_y Seems to be
among spirals what the catenary is among curves whose equations are between
rectangular co-ordinates ; for, if we represent the vertical direction by the radius

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 531

vector, the tangent of the angle which the curve makes with this line is proportional
to the length of the curve reckoned from the origin; the point at the distance a from
a straight line rolled on this curve generates a circle, and when rolled on the cate-
nary produces a straight line; the involute of this curve is the tractory of the circle,
and that of the catenary is the tractory of the straight line, and the tractory of the
circle rolled on that of the straight line traces the straight line ; if this curve is
rolled on the catenary, it produces the straight line touching the catenary at its
vertex ; the method of drawing tangents is the same as in the catenary, namely,
by describing a circle whose radius is a on the production of the radius vector, and
drawing a tangent to the circle from the given point.

In the next case, the rolled curve is the same as the fixed curve. It is
evident that the traced curve will be similar to the locus of the intersection of
the tangent with the perpendicular from the pole; the magnitude, however, of
the traced curve will be double that of the other curve; therefore, if we call
r, = p, 8, the equation to the fixed curve, 7, = ¢, 6, that of the traced curve, we
have,

r, = 2p, = 6 — cos 10 = by — 7 + sino
Op 2 To
also, 41 = 7%
Lf th

1 0

2 2
Similarly, r, = 2p,=2r,2¢= 47% ay, (7), # = 6 — 2 cosh
: 79 " "9 "0

Similarly, (Bee 7) ie aa etc. = 27, a
1) vo

and Pn — Po
vr %o
—1 Po

0

-1 Pn

§, = 8 — m COS

Now, cos" is the complement of the angle at which the curve cuts the radius

VOL. XVI. PART V. 6x

»

532 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

1
= is the variation of this angle when @, varies
n

— cos

vector, and cos *"

n

by an angle equal to a. Let this variation = ?; then if 0,— 0,'=6

Now, if ~ increases, @ will diminish; and if m become infinite,

a = + at = 0 when « and 8 are finite.

Therefore, when mw is infinite, @ vanishes; therefore, the curve cuts the radius
vector at a constant angle; therefore the curve is the logarithmic spiral.

Therefore, if any curve be rolled on itself, and the operation repeated an
infinite number of times, the resulting curve is the logarithmic spiral.

Hence we may find, analytically, the curve which, being rolled on itself,
traces itself.

For the curve which has this property, if rolled on itself, and the operation
repeated an infinite number of times, will still trace itself.

But, by this proposition, the resulting curve is the logarithmic spiral; there-
fore the curve required is the logarithmic spiral. As an example of a curve
rolling on itself, we will take the curve whose equation is

6 n
f(=tena (cos ‘)

n

H a (sin 4 (cos oy
a d a " : ~) *)
r) 2n
22” a2 (cos *)
ao 22 py _——_—-
as ae?) 2 6 2n—2
a/ 920 a’ (cos i) ana + 22” @ (sin 2) (cos 2)
n n

f) ntl
2-4 (cos *)
n st 6 nt+1
2 me eae a (cos *)
NA (cos *) + (sin “) ie
n n

i

6 6
Now 6, — 4 = — cos! 22 = '= cos! cop =
‘o n n
n
5 Se
‘ eon

substituting this value of 6, in the expression for r,

x A
n+1 n+1
C52 a{ cos a
m+

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 533

similarly if the operation be repeated m times, the resulting curve is

t

f) n+m
i Dr+rm a cos ™
n+m

When n = 1, the curve is

r=2acos é

the equation to a circle, the pole being in the circumference.
When n = 2, it is the equation to the cardioid.

r=4a (cos 5)
2

In order to obtain the cardioid from the circle, we roll the circle upon itself,
and thus obtain it by one operation ; but there is an operation which, being per-
formed on a circle, and again on the resulting curve, will produce a cardioid, and
the intermediate curve between the circle and cardioid is

ee (cos)!
B

+

9

As the operation of rolling a curve on itself is represented by changing 7 into
n + 1 in the equation, so this operation may be represented by changing » into

n+ 4.
Similarly there may be many other fractional operations performed upon the
curves comprehended under the equation

r= a (cos —)
n

We may also find the curve, which, being rolled on itself, will produce a given
curve, by making n = — 1.

We may likewise prove by the same method as before, that the result of per-
forming this inverse operation an infinite number of times is the logarithmic
spiral.

As an example of the inverse method, let the traced line be straight, let its
equation be

r, = 2a sec 0,

534 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

therefore suppressing the suffix,

the polar equation of the parabola whose parameter is 4 a.

The last case which we shall here consider, affords the means of constructing
two wheels whose centres are fixed, and which shall roll on each other, so that
the angle described by the first shall be a given function of the angle described
by the second.

dé r
Let B09 Oe RE a ee aaa as es
uM d (9 4,) r,
; d 6, 7 ty

Let us take as an example, the pair of wheels which will represent the angu-
lar motion of a comet in a parabola.

é d ¢ 1 r
1 é,=tan— .°. — = ——e=
I ere 2 9 d 6, cos? 4, ere r,
2
r 1

lye US lat 2
a 2+ cosé,
therefore the first wheel is an ellipse, whose major axis is equal to = of the dis-

tance between the centres of the wheels, and in which the distance between the
foci is half the major axis.

Now, since 6, =2 tan 6, and7, =a— 7,
ea Sil “
a 2(2 — 6)
aoe
27r —2

which is the equation to the wheel which revolves with constant angular velocity.

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 535

Before proceeding to give a list of examples of rolling curves, we shall state
a theorem which is almost self-evident after what has been shewn previously.

Let there be three curves, A, B,and C. Let the curve A, when rolled on itself,
produce the curve B, and when rolled on a straight line let it produce the curve
C, then, if the dimensions of C be, doubled, and B be rolled on it, it will trace
a straight line.

A Collection of Examples of Rolling Curves.

lst. Examples of a curve rolling on a straight line.

Ex. 1. When the rolling curve is a circle whose tracing-point is in the circum-
ference, the curve traced is a cycloid, and when the point is not in the circum-
ference, the cycloid becomes a trochoid.

Ex. 2. When the rolling curve is the involute of the circle whose radius is
2 a, the traced curve is a parabola whose parameter is 4 a.

Ex. 3. When the rolled curve is the parabola whose parameter is 4 a, the
traced curve is a catenary whose parameter is a, and whose vertex is distant a
from the straight line.

Ex. 4. When the rolled curve is a logarithmic spiral, the pole traces a straight
line which cuts the fixed line at the same angle as the spiral cuts the radius vector.

Ex. 5. When the rolled curve is the hyperbolic spiral, the traced curve is the
tractory of the straight line. |

Ex. 6. When the rolled curve is the polar catenary

gat of p24
r

the traced curve is a circle whose radius is a, and which touches the straight line.
Ex. 7. When the equation of the rolled curve is

rt x2 4 2
pang (VE-1+ 2) — or (YBa 2)

the traced curve is the hyperbola whose equation is
ye =a + @
2d. In the examples of a straight line rolling on a curve, we shall use the
letters A, B, and C to denote the three curves treated of in page 555.
Ex. 1. When the curve A is a circle whose radius is a, then the curve B is
the involute of that circle, and the curve C is the spiral of Archimedes, 7 = a 0.
Ex. 2. When the curve A is a catenary whose equation is

VOL. XVI. PART V. 6¥

536 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

the curve B is the tractory of the straight line, whose equation is

x eth ee
y = a log ————— + V@ 2
4 nN ee ue ss

and Cis a straight line at a distance a from the vertex of the catenary.
Ex. 3. When the curve A is the polar catenary

(ce NG eee
r

the curve B is the tractory of the circle
ca aie Oe / a
é = cos iz mR it

and the curve C is a circle of which the radius iss.

3d. Examples of one curve rolling on another, and tracing a straight line.
Ex. 1. The curve whose equation is

6=Ar”+ ete. + Kr? + Lr + Milogr+Nr+ete.+ Zr
when rolled on the curve whose equation is

pees Aaz'”+ ete. +2K24-—Llog2+M2xzi+iN 2’ + ete. + —_ Zgntt
n—1 n+1
traces the axis of y.
Ex. 2. The circle whose equation is 7 = a cos @ rolled on the circle whose
radius is a traces a diameter of the circle.

Ex. 3. The curve whose equation is
a= Rie — 1 — versin-? —
ip a

rolled on the circle whose radius is @ traces the tangent to the circle.

_ Ex. 4. If the fixed curve be a parabola whose parameter is 4 a, and if we
roll on it the spiral of Archimedes 7 = a @, the pole will trace the axis of the para-
bola.

Ex. 5. If we roll an equal parabola on it, the focus will trace the directrix of ; |

the first parabola.
Ex. 6. If we roll on it the curve r = =
the vertex of the parabola.

Ex. 7. If we roll the curve whose equation is

ts Co)
7 = a COS b

the pole will trace the tangent at

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

on the ellipse whose equation is

the pole will trace the axis 0.
Ex. 8. If we roll the curve whose equation is

aé _aé
b a
r= a eex
2

on the hyperbola whose equation is

the pole will trace the axis 0.
Ex. 9. If we roll the lituus, whose equation is

a’
li nie
Srey,
on the hyperbola whose equation is
Ly=a@

the pole will trace the asymptote.
Ex. 10. The cardioid whose equation is

r= a(l + cos @)
rolled on the cycloid whose equation is
y = aversin "= + V2ax— x
traces the base of the cycloid.
Ex. 11. The curve whose equation is
zh Moray 2a
§ = versin flag 2 | A
rolled on the cycloid traces the tangent at the vertex.
Ex. 12. The straight line whose equation is

r=asec é

537

rolled on a catenary whose parameter is @, traces a line whose distance from the

vertex iS a.
Ex. 13. The part of the polar catenary whose equation is

je eg 2
;

rolled on the catenary traces the tangent at the vertex.
Ex. 14. The other part of the polar catenary whose equation is

4 Eee
a

rolled on the catenary traces a line whose distance from the vertex is equal to

2a.

538 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

Ex. 15. The tractory of the circle whose diameter is a, rolled on the tractory
of the straight line whose constant tangent is a, produces the straight line.
Ex. 16. The hyperbolic spiral whose equation is

(==

2/8

rolled on the logarithmic curve whose equation is
x
y =alog a

traces the axis of y or the asymptote.
Ex. 17. The involute of the circle whose radius is a, rolled on an orthogonal
trajectory of the catenary whose equation is |

EN rama ig ( x? x
y=5,V% a” + 5 log Np acre

traces the axis of y.
Ex. 18. The curve whose equation is

nia, es: Gg
s=(S41) 2241
rolled on the witch, whose equation is
¥y = 2 a SSS 1
traces the asymptote.
Ex. 19. The curve whose equation is

7 = a tan @

rolled on the curve whose equation is

r= $oe(S—2)
traces the axis of y.
Ex. 20. The curve whose equation is
2r
ya.

rolled on the curve whose equation is

6

a?

=i Or 7 = ata 8
Va? — x

y=
traces the axis of y.
Ex. 21. The curve whose equation is

r = a (sec 6 — tan @)

rolled on the curve whose equation is
2

y=alog (5 4 1)

traces the axis of y.

MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES. 539

4th. Examples of pairs of rolling curves which have their poles at a fixed
distance = a

The straight line whose equation is @= sec —
x, 1. Sawa I
The polar catenary whose equation is = J = 4
Bix. 2. Two equal ellipses or hyperbolas centred at the foci.
Ex. 3. Two equal logarithmic spirals.
Circle whose equation is r= 2a cos 0.
Ex. 4. . ears
Curve whose equation is aR 2° — 1 + versin
t
Cardioid whose equation is r= 2a(1 + cos 4.)
Ex. 5 yan
is Curve whose equation is j= fine oe log Z
og a—r?+ta
Conchoid, r = a (sec 6 — 1.)
Ex, 6. 2
Curve, a a se “ at seo}
Spiral of Archimedes, r=aé
Ex. ve Curve, = a ae log —
a a
Hyperbolic spiral, r= =
Ex. 8.
Curve, SAI
Ellipse whose equation is, Ap armenay,
Ex. 9. l
Curve, r=@ (1 = »)
| Involute of circle, j= Rs is SWsee =
Ex. 10. et 1 ———
Curve, a mE (F1 1/5027)
a~ a a a a

5th. Examples of curves rolling on themselves.
Ex. 1. When the curve which rolls on itself is a circle, equation

r= acosé

the traced curve is a cardioid, equation 7 = a (1 + cos 8).
Ex. 2. When it is the curve whose equation is

f) n
a aa( cos =)
i

the equation of the traced curve is
4 . +1
n +1

VOL. XVI. PART V. 6 z

72 fom Pea) a( cos

540 MR CLERK MAXWELL ON THE THEORY OF ROLLING CURVES.

Ex. 3. When it is the involute of the circle, the traced curve is the spiral of
Archimedes.

Ex. 4. When it is a parabola, the focus traces the directrix, and the vertex
traces the cissoid.

Ex. 5. When it is the hyperbolic spiral, the traced curve is the tractory of the
circle.

Ex. 6. When it is the polar catenary, the equation of the traced curve is

2a F r
=f S] = reea
r . a

Ex. 7. When it is the curve whose equation is
he rs) Ee ae:
ae ee ~tog(/1 + 5-5)

the equation of the traced curve is, 7 = @ ¢—eé-‘).

( 541)

XXXVIL—An Account of Carnot’s Theory of the Motive Power of Heat ;* with
Numerical Results deduced from Ruenavyt’s Experiments on Steam.t By
Witu1am Tuomson, Professor of Natural Philosophy in the University of
Glasgow.

(Read January 2, 1849.)

1. The presence of heat may be recognised in every natural object ; and there
is scarcely an operation in nature which is not more or less affected by its all-
pervading influence. An evolution and subsequent absorption of heat generally
give rise to a variety of effects; among which may be enumerated, chemical
combinations or decompositions ; the fusion of solid substances; the vaporisation
of solids or liquids; alterations in the dimensions of bodies, or in the statical
pressure by which their dimensions may be modified ; mechanical resistance over-
come; electrical currents generated. In many of the actual phenomena of na-
ture, several or all of these effects are produced together; and their complication
will, if we attempt to trace the agency of heat in producing any individual effect,
give rise to much perplexity. It will, therefore, be desirable, in laying the foun-
dation of a physical theory of any of the effects of heat, to discover or to imagine
phenomena free from all such complication, and depending on a definite thermal
agency ; in which the relation between the cause and effect, traced through the
medium of certain simple operations, may be clearly appreciated. Thus it is
that Carnot, in accordance with the strictest principles of philosophy, enters upon
the investigation of the theory of the motive power of heat.

2. The sole effect to be contemplated in investigating the motive power of
heat is resistance overcome, or, as it is frequently called, “work performed,” or
«mechanical effect.”’ The questions to be resolved by a complete theory of the
subject are the following :

(1.) What is the precise nature of the thermal agency by means of which
mechanical effect is to be produced, without effects of any other kind ?

* Published in 1824, in a work entitled, <‘ Réflexions sur la Puissance Motrice du Feu, et sur
les Machines Propres 4 Déveloper cette Puissance. Par S. Carnot.” An account of Carnot’s Theory is
also published in the Journal d’ Ecole Polytechnique, vol. xiv., 1834, in a paper by Mons. Crareyron.

+ An account of the first part of a series of researches undertaken by Mons. Recnavtt, by order
of the late French Government, for ascertaining the various physical data of importance in the
theory of the steam-engine, has been recently published (under the title, “ Relation des Expériences,”’
&c.) in the Mémoires de V Institut, of which it constitutes the twenty-first volume (1847). The
second part of these researches has not yet been published.

VOL. XVI. PART V. C&

542 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

(2.) How may the amount of this thermal agency necessary for performing
a given quantity of work be estimated ?

3. In the following paper I shall commence by giving a short abstract of the
reasoning by which Carnot is led to an answer to the first of these questions; I
shall then explain the investigation by which, in accordance with his theory,
the experimental elements necessary for answering the second question are indi-
cated; and, in conclusion, I shall state the data supplied by ReaNnautt’s recent
observations on steam, and apply them to obtain, as approximately as the pre-
sent state of experimental science enables us to do, a complete solution of the
question.

I. On the nature of Thermal agency, considered as a motive power.

4. There are [at present known] two, and only two, distinct ways in which
mechanical effect can be obtained from heat. One of these is by means of the
alterations of volume which bodies may experience through the action of heat ;
the other is through the medium of electric agency. SrEBEcK’s discovery of
thermo-electric currents enables us at present to conceive of an electro-magnetic
engine supplied from a thermal origin, being used as a motive power: but this
discovery was not made until 1821, and the subject of thermo-electricity can
only have been generally known in a few isolated facts, with reference to the
electrical effects of heat upon certain crystals, at the time when Carnor wrote.
He makes no allusion to it, but confines himself to the method for rendering
thermal agency available as a source of mechanical effect, by means of the ex-
pansions and contractions of bodies.

5. A body expanding or contracting under the action of force, may, m gene-
ral, either produce mechanical effect by overcoming resistance, or receive mecha-
nical effect by yielding to the action of force. The amount of mechanical effect
thus developed will depend not only on the calorific agency concerned, but also
on the alteration in the physical condition of the body. Hence, after allowing the
volume and temperature of the body to change, we must restore it to its original
temperature and volume; and then we may estimate the aggregate amount of
mechanical effect developed as due solely to the thermal origin.

6. Now the ordinarily-received, and almost universally-acknowledged, prin-
ciples with reference to “ quantities of caloric” and “latent heat,” lead us to con-
ceive that, at the end of a cycle of operations, when a body is left in precisely its
primitive physical condition, if it has absorbed any heat during one part of the
operations, it must have given out again exactly the same amount during the
remainder of the cycle. The truth of this principle is considered as axiomatic by
CaRNOoT, who admits it as the foundation of his theory; and expresses himself in
the following terms regarding it, in a note on one of the passages of his treatise.*

* Carnot, p. 37.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 543

“In our demonstrations we tacitly assume that after a body has experienced
a certain number of transformations, if it be brought identically to its primitive
physical state as to density, temperature, and molecular constitution, it must
contain the same quantity of heat as that which it initially possessed; or, in
other words, we suppose that the quantities of heat lost by the body under one set
of operations are precisely compensated by those which are absorbed in the others.
This fact has never been doubted ; it has at first been admitted without reflection,
and afterwards verified, in many cases, by calorimetrical experiments. To deny
it would be to overturn the whole theory of heat, in which it is the fundamental
principle. It must be admitted, however, that the chief foundations on which the
theory of heat rests, would require a most attentive examination. Several expe-
rimental facts appear nearly inexplicable in the actual state of this theory.”

7. Since the time when Carnot thus expressed himself, the necessity of a
most careful examination of the entire experimental basis of the theory of heat
has become more and more urgent. Especially all those assumptions depending
on the idea that heat is a substance, invariable in quantity ; not convertible into any
other element, and incapable of being generated by any physical agency; in fact
the acknowledged principles of latent heat; would require to be tested by a most
searching investigation before they ought to be admitted, as they usually have
been, by almost every one who has been engaged on the subject, whether in com-
bining the results of experimental research, or in general theoretical investigations.

8. The extremely important discoveries recently made by Mr Jou of Man-
chester, that heat is evolved in every part of a closed electric conductor, moving
in the neighbourhood of a magnet,* and that heat is generated by the friction of
fluids in motion, seem to overturn the opinion commonly held that heat cannot
be generated, but only produced from a source, where it has previously existed
either in a sensible or-in a latent condition.

* The evolution of heat in a fixed conductor, through which a galvanic current is sent from any
source whatever, has long been known to the scientific world; but it was pointed out by Mr Jou.e
that we cannot infer from any previously-published experimental researches, the actual generation of heat
when the current originates in electro-magnetic induction ; since the question occurs, is the heat which is
evolved in one part of the closed conductor merely transferred from those parts which are subject to the
inducing influence? Mr Jouve, after a most careful experimental investigation with reference to
this question, finds that it must be answered in the negative-—(See a paper ‘* On the Calorific Effects
of Magneto-Electricity, and on the Mechanical Value of Heat; by J. P. Journ, Esq.’ Read before
the British Association at Cork in 18438, and subsequently communicated by the Author to the
Philosophical Magazine, vol. xxiil., pp. 263, 347, 435.)

Before we can finally conclude that heat is absolutely generated in such operations, it would be
necessary to prove that the inducing magnet does not become lower in temperature, and thus com-
pensate for the heat evolved in the conductor. I am not aware that any examination with reference
to the truth of this conjecture has been instituted; but, in the case where the inducing body is a
pure electro-magnet (without any iron), the experiments actually performed by Mr Jouve render
the conclusion probable that the heat evolved in the wire of the electro-magnet is not affected by
the inductive action, otherwise than through the reflected influence which increases the strength of
its own current.

544 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

In the present state of science, however, no operation is known by which heat
can be absorbed into a body without either elevating its temperature, or becoming
latent, and producing some alteration in its physical condition; andthe fundamental
axiom adopted by Carnot may be considered as still the most probable basis for an
investigation of the motive power of heat ; although this, and with it every other
branch of the theory of heat may ultimately require to be reconstructed upon an-
other foundation, when our experimental data are more complete. On this un-
derstanding, and to avoid a repetition of doubts, I shall refer to Carnot’s funda-
mental principle, in all that follows, as if its truth were thoroughly established.

9. We are now led to the conclusion that the origin of motive power, de-
veloped by the alternate expansions and contractions of a body, must be found in
the agency of heat entering the body and leaving it; since there cannot, at the
end of a complete cycle, when the body is restored to its primitive physical condi-
tion, have been any absolute absorption of heat, and consequently no conversion
of heat, or caloric, into mechanical effect ; and it remains for us to trace the pre-
cise nature of the circumstances under which heat must enter the body, and
afterwards leave it, so that mechanical effect may be produced. As an example,
we may consider that machine for obtaining motive power from heat with which
we are most familiar-—the steam-engine.

10. Here, we observe, that heat enters the machine from the furnace, through
the sides of the boiler, and that heat is continually abstracted by the water em-
ployed for keeping the condenser cool. According to Carnot’s fundamental prin-
ciple, the quantity of heat thus discharged, during a complete revolution (or double
stroke) of the engine must be precisely equal to that which enters the water of
the boiler ;* provided the total mass of water and steam be invariable, and be re-
stored to its primitive physical condition (which will be the case rigorously, if the
condenser be kept cool by the external application of cold water, instead of by in-
jection, as is more usual in practice), and if the condensed water be restored to
the boiler at the end of each complete revolution. Thus, we perceive, that a cer-
tain quantity of heat is let down from a hot body, the metal of the boiler, to ano-
ther body at a lower temperature, the metal of the condenser; and that there
results from this transference of heat, a certain development of mechanical effect.

11. If we examine any other case in which mechanical effect is obtained
from a thermal origin, by means of the alternate expansions and contractions of
any substance whatever, instead of the water of a steam-engine, we find that a
similar transference of heat is effected, and we may therefore answer the first
question proposed, in the following manner :—

The thermal agency by which mechanical effect may be obtained, is the trans-
Jerence of heat from one body to another at a lower temperature.

* So generally is Carnor’s principle tacitly admitted as an axiom, that its application in this
case has never, so far as I am aware, been questioned by practical engineers.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 545

II. On the measurement of Thermal Agency, considered with reference to its
equivalent of mechanical affect.

12. A perfect thermo-dynamic engine of any kind, is a machine by means of
which the greatest possible amount of mechanical effect can be obtained from a
given thermal agency ; and, therefore, if in any manner we can construct or ima-
gine a perfect engine which may be applied for the transference of a given quan-
tity of heat from a body at any given temperature, to another body, at a lower
given temperature, and if we can evaluate the mechanical effect thus obtained,
we shall be able to answer the question at present under consideration, and so to
complete the theory of the motive power of heat. But whatever kind of engine
we may consider with this view, it will be necessary for us to prove that it is a
perfect engine; since the transference of the heat from one body to the other may
be wholly, or partially, effected by conduction through a solid,* without the de-
velopment of mechanical effect; and, consequently, engines may be constructed
in which the whole, or any portion of the thermal agency is wasted. Hence it is
of primary importance to discover the criterion of a perfect engine. This has
been done by Carnot, who proves the following proposition :—

13. A perfect thermo-dynamic engine is such that, whatever amount of mecha-
nical effect it can derive from a certain thermal agency ; if an equal amount be spent
in working it backwards, an equal reverse thermal effect will be produced.+

14. This proposition will be made clearer by the applications of it which
are given below (§ 29), in the cases of the air-engine and the steam-engine, than it
could be by any general explanation; and it will also appear, from the nature
of the operations described in those cases, and the principles of CarNnot’s reason-
ing, that a perfect engine may be constructed with any substance of an in-
destructible texture as the alternately expanding and contracting medium.
Thus we might conceive thermo-dynamic engines founded upon the expansions

* When “ thermal agency” is thus spent in conducting heat through a solid, what becomes of
the mechanical effect which it might produce? Nothing can be lost in the operations of nature—
no energy can be destroyed. What effect then is produced in place of the mechanical effect which is
lost? A perfect theory of heat imperatively demands an answer to this question; yet no answer can
be given in the present state of science. A few years ago, a similar confession must have been made
with reference to the mechanical effect lost in a fluid set in motion in the interior of a rigid closed
vessel, and allowed to come to rest by its own internal friction; but in this case, the foundation of a
solution of the difficulty has been actually found, in Mr Jovtz’s discovery of the generation of heat,
by the internal friction of a fluid in motion. Encouraged by this example, we may hope that the
very perplexing question in the theory of heat, by which we are at present arrested, will, before long,
be cleared up.

It might appear, that the difficulty would be entirely avoided, by abandoning Carnot’s funda-
mental axiom ; a view which is strongly urged by Mr Jouxe (at the conclusion of his paper “ On
the Changes of Temperature produced by the Rarefaction and Condensation of Air.” Phil. Mag.,
May 1845, vol. xxvi.) If we do so, however, we meet with innumerable other difficulties—insuper-
able without farther experimental investigation, and an entire reconstruction of the theory of heat,
from its foundation. It is in reality to experiment that we must look—either for a verification of
Carnot’s axiom, and an explanation of the difficulty we havé been considering ; or for an entirely new

basis of the Theory of Heat.
+ For a demonstration, see § 29, below.

VOL. XVI. PART Y.

a |

546 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

and contractions of a perfectly elastic solid, or of a liquid; or upon thealtera-
tions of volume experienced by substances, in passing from the liquid to the solid
state,* each of which being perfect, would produce the same amount of mechanical
effect from a given thermal agency; but there are two cases which Carnot has
selected as most worthy of minute attention, because of their peculiar appropriate-
ness for illustrating the general principles of his theory, no less than on account
of their very great practical importance ; the steam-engine, in which the substance
employed as the transferring medium is water, alternately in the liquid state, and
in the state of vapour ; and the air-engine, in which the transference is effected
by means of the alternate expansions and contractions of a medium, always in
the gaseous state. The details of an actually practicable engine of either kind
are not contemplated by Carnot, in his general theoretical reasonings, but he con-
fines himself to the ideal construction, in the simplest possible way in each case,
of an engine in which the economy is perfect. He thus determines the degree of
perfectibility which cannot be surpassed; and, by describing a conceivable method
of attaining to this perfection by an air-engine or a steam-engine, he points out
the proper objects to be kept in view in the practical construction and working of
such machines. I now proceed to give an outline of these investigations.

Carnot’s Theory of the Sieam-Engine.

15. Let CDF, E, be a cylinder, of which the curved surface is perfectly imper-
meable to heat, with a piston also im-
permeable to heat, fitted in it; while
the fixed bottom C D, itself with no ca-
pacity for heat, is possessed of perfect
conducting power. Let K be an im-
permeable stand, such that when the
cylinder is placed upon it, the con-
tents below the piston can neither gain

La

ij
iS}
Ms

a3
Ld

As>|

WM

VIE EEE

nor lose heat. Let A and B be two
bodies permanently retained at con-

YY

stant temperatures, S° and T°, respec- 7 Or
tively, of which the former is higher

than the latter. Let the cylinder, i
placed on the impermeable stand, K, x
be partially filled with water, at the ]

Y
temperature S, of the body A, and
(there being no air below it) let the 7/ //
piston be placed in a position E F, 7/
Y
near the surface of the water. The da

ai A case minutely examined in another paper, to be laid before the Society at the present
meeting.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 547

pressure of the vapour above the water will tend to push up the piston, and
must be resisted by a force applied to the piston,* till the commencement of the
operations, which are conducted in the following manner.

(1.) The cylinder being placed on the body A, so that the water and vapour
may be retained at the temperature S, let the piston rise any convenient height
EE,, to a position E, F,, performing work by the pressure of the vapour below it dur-
ing its ascent.

[During this operation a certain quantity, H, of heat, the amount of latent heat in the fresh
vapour which is formed, is abstracted from the body A.]

(2.) The cylinder being removed, and placed on the impermeable stand K,
let the piston rise gradually, till, when tt reaches a position KE, F,, the temperature of
the water and vapour is T, the same as that of the body B.

[During this operation the fresh vapour continually formed requires heat to become latent ;
and, therefore, as the contents of the cylinder are protected from any accession of heat, their tem-
perature sinks. |

(3.) The cylinder being removed from K, and placed on B, let the piston be
pushed down, till, when it reaches the position E; ¥;, the quantity of heat evolved and
abstracted by B amounts to that which, during the first operation, was taken from A.

[During this operation the temperature of the contents of the cylinder is retained constantly at
T°, and all the latent heat of the vapour which is condensed into water at the same temperature, is
given out to B.]

(4.) The cylinder being removed from B, and placed on the impermeable
stand, let the piston be pushed down from E; F, to its original position EF.

[During this operation, the impermeable stand preventing any loss of heat, the temperature of
the water and air must rise continually, till (since the quantity of heat evolved during the third ope-
ration was precisely equal to that which was previously absorbed), at the conclusion it reaches its
primitive value, S, in virtue of Carnot’s fundamental axiom.]

16. At the conclusion of this cycle of operations} the total thermal agency
has been the letting down of H units of heat from the body A, at the temperature
S, to B, at the lower temperature T; and the aggregate of the mechanical effect
has been a certain amount of work produced, since during the ascent of the piston
in the first and second operations, the temperature of the water and vapour, and
therefore the pressure of the vapour on the piston, was on the whole higher than
during the descent, in the third and fourth operations. It remains for us actually
to evaluate this aggregate amount of work performed; and for this purpose the

* Tn all that follows, the pressure of the atmosphere on the upper side of the piston will be in-
cluded in the applied forces, which, in the successive operations described, are sometimes overcome by
the upward motion, and sometimes yielded to in the motion downwards. It will be unnecessary, in
reckoning at the end of a cycle of operations, to take into account the work thus spent upon the atmo-
sphere, and the restitution which has been made, since these precisely compensate for one another.

{ In Carnor’s work some perplexity is introduced with reference to the temperature of the
water, which, in the operations he describes, is not brought back exactly to what it was at the com-
mencement ; but the difficulty which arises is explained by the author. No such difficulty occurs
with reference to the cycle of operations described in the text, for which I am indebted to Mons.
CLAPEYRON.

348 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

following graphical method of representing the mechanical effect developed in the
several operations, taken from Mons. CLAPEYRON’s paper, is extremely convenient.

17. LetO X and O Y be two lines ,
at right angles to one another. Along
O X measure off distances O N,, N N,,
N.N;, N; O, respectively proportional
to the spaces described by the piston
during the four successive operations
described above; and, with reference
to these four operations respectively,
let the following constructions be
made :—

(1.) Along O Y measure a length O A, to represent the pressure of the satu-
rated vapour at the temperature S; and draw A A, parallel to O X, and let it meet
an ordinate through N,, in Ao.

(2.) Draw a curve A,P A such that, if ON represent, at any instant during
the second operation, the distance of the piston from its primitive position, N P
shall represent the pressure of the vapour at the same instant.

(3.) Through A, draw A, A; parallel to O X, and let it meet an ordinate
through N; in As.

(4.) Draw the curve A; A such that the abscissa and ordinate of any point in
it may represent respectively the distances of the piston from its primitive posi-
tion, and the pressure of the vapour, at some instant during the fourth operation.
The last point of this curve must, according to Carnot’s fundamental principle,
coincide with A, since the piston is, at the end of the cycle of operations, again
in its primitive position, and the pressure of the vapour is the same as it was at
the beginning.

18. Let us now suppose that the lengths, ON,, N, N,, N.N;, and N30, repre-
sent numerically the volumes of the spaces moved through by the piston during
the successive operations. It follows that the mechanical effect obtained during
the first operation will be numerically represented by the area A A, N,O; that is,
the number of superficial units in this area will be equal to the number of “ foot-
pounds ”’ of work performed by the ascending piston during the first operation.
The work performed by the piston during the second operation will be similarly
represented by the area A, A, N,N;. Again, during the third operation a certain
amount of work is spent on the piston, which will be represented by the area
A, A;N;N,; and lastly, during the fourth operation, work is spent in pushing the
piston to an amount represented by the area A; AO N3. |

19. Hence the mechanical effect (represented by the area O A A, A, N.) which
was obtained during the first and second operations, exceeds the work (repre-
sented by N, A, A; AO) spent during the third and fourth, by an amount repre-
sented by the area of the quadrilateral figure AA, A, A;; and, consequently, it

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 549

only remains for us to evaluate this area, that may determine the total mechani-
cal effect gained in a complete cycle of operations. Now, from experimental
data, at present nearly complete, as will be explained below, we may determine
the length of the line A A, for the given temperature 8, and a given absorption
H, of heat, during the first operation ; and the length of A, A; for the given lower
temperature T, and the evolution of the same quantity of heat during the fourth
operation: and the curves A, PA,, A; P’A may be drawn as graphical representa-
tions of actual observations.* The figure being thus constructed, its area may be
measured, and we are, therefore, in possession of a graphical method of determin-
ing the amount of mechanical effect to be obtained from any given thermal agency.
As, however, it is merely the area of the figure which it is required to determine, it
will not be necessary to be able to describe each of the curves A, P A, A; P’A, but
it will be sufficient to know the difference of the abscissas corresponding to any
equal ordinates in the two; and the following analytical method of completing
the problem is the most convenient for leading to the actual numerical results.
20. Draw any line P P’ parallel to O X, meeting the curvilineal sides of the
quadrilateral in P and P’. Let ~ denote the length of this line, and p its distance
from OX. The area of the figure, according to the integral calculus, will be de-

noted by the expression
Pi
ae 3 $ ae;

where p,, and p; (the limits of integration indicated according to Fourrer’s nota-
tion) denote the lines O A, and N; A;, which represent respectively the pressures
during the first and third operations. Now, by referring to the construction de-
scribed above, we see that < is the difference of the volumes below the piston at
corresponding instants of the second and fourth operations, or instants at which
the saturated steam and the water in the cylinder have the same pressure p, and,
consequently, the same temperature which we may denote by#. Again, through-
out the second operation the entire contents of the cylinder possess a greater
amount of heat by H units than during the fourth ; and, therefore, at any instant
of the second operation there is as much more steam as contains H units of latent
heat, than at the corresponding instant of the fourth operation. H ence, if k de-
note the latent heat in a unit of saturated steam at the temperature ¢, the volume

of the steam at the two corresponding instants must differ by = Now, if « de-

note the ratio of the density of the steam to that of the water, the volume * of
: H

steam will be formed from the volume *7 of water ; and, consequently, we have

* See Note at the end of this Paper.
VOL. XVI. PART V. 7 Oo

550 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

for the difference of volumes of the entire contents at the corresponding instants,
H
g = (1— 6) via

Hence the expression for the area of the quadrilateral figure becomes

p
af (1-0) ap.
P
3

Now, », &, and p, being quantities which depend upon the temperature, may be
considered as functions of ¢; and it will be convenient to modify the integral so
as to make ¢ the independent variable. The limits will be from ¢=T to ¢=S, and,
if we denote by M the value of the integral, we have the expression

dp

laa
M=H/ -9pae emhin abt wena

for the total amount of mechanical effect gained by the operations described
above.
21. If the interval of temperatures be extremely small; so small that
op
(1—o) = will not sensibly vary for values of ¢ between T and S, the preceding ex-

presssion becomes simply
dp
M=(-)5*. H(S-T) .. .. @

This might, of course, have been obtained at once, by supposing the breadth of
the quadrilateral figure A A, A, A to be extremely small compared with its length,
and then taking for its area, as an approximate value, the product of the breadth
into the line A Aj, or the line A; A,, or any line of intermediate magnitude.
The expression (2) is rigorously correct for any interval S—T, if the
dp

mean value of (1— 0) for that interval be employed as the coefficient of H (S—T).

Carnot’s Theory of the Air-Engine.

22. In the ideal air-engine imagined by Carnot four operations performed
upon a mass of air or gas enclosed in a closed vessel of variable volume, consti-
tute a complete cycle, at the end of which the medium is left in its primitive phy-
sical condition; the construction being the same as that which was described
above for the steam-engine, a body A, permanently retained at the temperature
S, and B at the temperature T; an impermeable stand K ; and a cylinder and
piston, which, in this case, contains a mass of air at the temperature S, instead of

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 551

water in the liquid state, at the beginning and end of a cycle of operations. The
four successive operations are conducted in the following manner :—

(1.) The cylinder is laid on the body A, so that the air in it is kept at the
temperature S; and the piston is allowed to rise, performing work.

(2.) The cylinder is placed on the impermeable stand K, so that its contents
can neither gain nor lose heat, and the piston is allowed to rise farther, still per-
forming work, till the temperature of the air sinks to T.

(3.) The cylinder is placed on B, so that the air is retained at the tempera-
ture T, and the piston is pushed down till the air gives out to the body B as much
heat as it had taken in from A, during the first operation.

(4.) The cylinder is placed on K, so that no more heat can be taken in or
given out, and the piston is pushed down to its primitive position.

23. At the end of the fourth operation the temperature must have reached tts
primitive value S, in virtue of CARNOT’S axiom.

24. Here, again, as in the former case, we observe that work is performed
by the piston during the first two operations; and, during the third and fourth.
work is spent upon it, but to a less amount, since the pressure is on the whole less
during the third and fourth operations than during the first and second, on ac-
count of the temperature being lower. Thus, at the end of a complete cycle of
operations, mechanical effect has been obtained; and the thermal agency from
which it is drawn is the taking of a certain quantity of heat from A, and Jetting
it down, through the medium of the engine, to the body B at a lower temperature.

25. To estimate the actual amount of effect thus obtained, it will be con-
venient to consider the alterations of volume of the mass of air in the several
operations as extremely small. We may afterwards pass by the integral calcu-
lus, or, practically, by summation, to determine the mechanical effect whatever
be the amplitudes of the different motions of the piston.

26. Let dq be the quantity of heat absorbed during the first operation, which
is evolved again during the third; and let dv be the corresponding augmentation
of volume which takes places while the temperature remains constant, as it
does during the first operation.* The diminution of volume in the third ope-
ration must be also equal to dv, or only differ from it by an infinitely small

ee lhnie. = will be the partial differential coefficient, with respect to v of that function of
Vv

v and ¢, which expresses the quantity of heat that must be added to a mass of air when in a “ stan-
dard’’ state (such as at the temperature zero, and under the atmospheric pressure), to bring it to the
temperature t, and the volume v. That there is sucha function, of two independent variables v and ¢,
is merely an analytical expression of Carnot’s fundamental axiom, as applied to a mass of air. The
general principle may be analytically stated in the following terms :—If M dv denote the accession of
heat received by a mass of any kind, not possessing a destructible texture, when the volume is in-
creased by dv, the temperature being kept constant, and.if N dt denote the amount of heat which
must be supplied to raise the temperature by d ¢, without any alteration of volume; then M dvu+N dt
must be the differential of a function of v and ¢.

552 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

quantity of the second order. During the second operation we may suppose
the volume to be increased by an infinitely small quantity 9; which will oc-
casion a diminution of pressure, and a diminution of temperature, denoted re-
respectively by » and 7. During the fourth operation there will be a diminution
of volume, and an increase of pressure and temperature, which can only differ, by
infinitely small quantities of the second order, from the changes in the other di-
rection, which took place in the second operation, and they also may, therefore,
be denoted by 9, », and 7, respectively. The alteration of pressure, during the first
and third operations, may at once be determined by means of MariorTe’s law,
since, in them, the temperature remains constant. Thus, if, at the commence-
ment of the cycle, the volume and pressure be v and p, they will have become

v+dvand p — at the end of the first operation. Hence the diminution of
‘ {pate e d :
pressure, during the first operation, is p—p ae or p ae and, therefore, if we

neglect infinitely small quantities of the second order, we have p a for the dimi-

- nution of pressure during the first operation; which, to the same degree of ap-
proximation, will be equal to the increase of pressure during the third. Ifé+7
and ¢ be taken to denote the superior and inferior limits of temperature, we shall
thus have for the volume, the temperature, and the pressure at the commence-
ments of the four successive operations, and at the end of the cycle, the following
values respectively :—

Go v, t+r, Pp;

(2.) v+dv, t+r, pa-@ ;
wo

(3.) v+dvu+o, tt, pGQ-@)-s:
o

(4.) o+9, & p-—®;

(5.) v, t+r, p-

Taking the mean of the pressures at the beginning and end of each operation, we
find
dv
(1, p(i-:2)
dv .
(2.) p(i—“2)-48

(3.) p (1-3 )-«

(A.) | P— 24,

which, as we are neglecting infinitely small quantities of the second order, will be

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 553

the expressions for the mean pressures during the four successive operations.
Now, the mechanical effect gained or spent, during any of the operations, will be
found by multiplying the mean pressure by the increase or diminution of volume
which takes places; and we thus find

(1.) P (1-22 )av

ee eee
(3) {ri eat hae
(4.) (p—#4) 9

for the amounts gained during the first and second, and spent during the third and
fourth operations; and hence, by addition and subtraction, we find

wdv—p o2, or (v w—p9@) =

for the aggregate amount of mechanical effect gained during the cycle of opera-
tions. It only remains for us to express this result in terms of dq and 7, on which
the given thermal agency depends. For this purpose, we remark that 9 and » are
alterations of volume and pressure which take place along with a change of tem-
perature 7, and hence, by the laws of compressibility and expansion, we may
establish a relation* between them in the following manner.

Let p, be the pressure of the mass of air when reduced to the temperature
zero, and confined in a volume v,; then, whatever be v,, the product p, v, will, by
the law of compressibility, remain constant; and, if the temperature be elevated
from 0 to ¢+7, and the gas be allowed to expand freely without any change of
pressure, its volume will be increased in the ratio of 1 to 1+ E (¢+7), where E is
very nearly equal to ‘00366 (the centigrade scale of the air-thermometer being re-
ferred to), whatever be the gas employed, according to the researches of REGNAULT
and of Macnus on the expansion of gases by heat. If, now, the volume be altered
arbitrarily with the temperature continually at ¢+7, the product of the pressure
and volume will remain constant; and, therefore, we have

PV=Po Yo {1+E (¢+1)}.
Similarly (p—4) (V+ 9)=Po % {1+ Es}.
Hence, by subtraction, we have
; va—pot+wo=p, v, Er,

or, neglecting the product » 9,
vo—po=p, v, Er.

* We might also investigate another relation, to express the fact that there 1s no accession or
removal of heat during either the second or the fourth operation ; but it will be seen that this will not
affect the result in the text ; although it would enable us to determine both g and w in terms of r.

cD

VOL. XVI. PART Vi.

554 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

Hence, the preceding expression for mechanical effect. gained in the cycle of ope-
rations, becomes

d oe
Po Vo. Fg
vo?
Or, as we may otherwise express it,
Ep,
dv

Hence, if we denote by M the mechanical effect due to H units of heat descending
through the same interval r, which might be obtained by repeating the cycle of

operations described above, tie times, we have

27. If the amplitudes of the operations had been finite, so as to give rise to
an absorption of H units of heat during the first operation, and a lowering of
temperature from S to T during the second, the amount of work obtained would
have been found to be expressed by means of a double definite integral, thus ;*—

staf, ag fai Beem |

"do T aciy dupenittes@ car tae Ae
or ay i PL de. fee

™ ty vdq
this second form being sometimes more convenient.

28. The preceding investigations, being founded on the approximate laws of
compressibility and expansion (known as the law of Mariorre and Boy e, and
the law of Datron and Gay-Lussac), would require some slight modifications, to
adapt them to cases in which the gaseous medium employed is such as to present
sensible deviations from those laws. REGNAULT’s very accurate experiments
shew that the deviations are insensible, or very nearly so, for the ordinary gases
at ordinary pressures; although they may be considerable for a medium, such as

* This result might have been obtained by applying the usual notation of the integral calculus
to express the area of the curvilinear quadrilateral, which, according to CLapryron’s graphical con-
struction, would be found to represent the entire mechanical effect gained in the cycle of operations
of the air-engine. It is not necessary, however, to enter into the details of this investigation, as the
formula (3), and the consequences derived from it, include the whole theory of the air-engine, in

the best practical form ; and the investigation of it which I have given in the text, will probably give — Ps

as clear a view of the reasoning on which it is founded, as could be obtained by the graphical method,
which, in this case, 1s not so valuable as it is from its simplicity m the case of the steam-engine.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 555

sulphurous acid, or carbonic acid under high pressure, which approaches the phy-
sical condition of a vapour at saturation ; and therefore, in general, and especially
in practical applications to real air-engines, it will be unnecessary to make any
modification in the expressions. In cases where it may be necessary, there is no
difficulty in making the modifications, when the requisite data are supplied by
experiment.

29.* Either the steam-engine or the air-engine, according to the arrangements
described above, gives all the mechanical effect that can possibly be obtained from
the thermal agency employed. For it is clear, that, in either case, the operations
may be performed in the reverse order, with every thermal and mechanical effect
reversed. Thus, in the steam-engine, we may commence by placing the cylinder
on the impermeable stand, allow the piston to rise, performing work, to the posi-
tion EK, F;; we may then place it on the body B, and allow it to rise, performing
work, till it reaches E, F,; after that the cylinder may be placed again on the
impermeable stand, and the piston may be pushed down to EH, F,; and, lastly,
the cylinder being removed to the body A, the piston may be pushed down to its
primitive position. In this inverse cycle of operations, a certain amount of work
has been spent, precisely equal, as we readily see, to the amount of mechanical
effect gained in the direct cycle described above; and heat has been abstracted
from B, and deposited in the body A, at a higher temperature, to an amount pre-
cisely equal to that which, in the direct cycle, was let down from A to B. Hence
it is impossible to have an engine which will derive more mechanical effect from
the same thermal agency, than is obtained by the arrangement described above ;
since, if there could be such an engine, it might be employed to perform, as a
part of its whole work, the inverse cycle of operations, upon an engine of the kind
we have considered, and thus to continually restore the heat from B to A, which
has descended from A to B for working itself; so that we should have a complex
engine, giving a residual amount of mechanical effect without any thermal agency,
or alteration of materials, which is an impossibility in nature. The same reason-
ing is applicable to the air-engine; and we conclude, generally, that any two en-
gines, constructed on the principles laid down above, whether steam-engines with
different liquids, an air-engine and a steam-engine, or two air-engines with differ-
ent gases, must derive the same amount of mechanical effect from the same ther-
mal agency.

30. Hence, by comparing the amounts of mechanical effect obtained by the
steam-engine and the air-engine from the letting down of the H units of heat
from A at the temperature (¢+7) to B at ¢, according to the expressions (2) and
(3), we have

* This paragraph is the demonstration referred to above, of the proposition stated in § 13; as it
is readily seen that it is applicable to any conceivable kind of thermo-dynamic engine.

556 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

dp
M=(-9-— Hea Ebete He pe Re STE,
: sie

If we denote the coefficient of H z in these equal expressions by «, which may be
called ‘“‘ Carnot’s coefficient,” we have

dp
fa ie
e=(Sn = anes epbehiuadas evel (Gp)

and we deduce the following very remarkable conclusions :—
(1.) For the saturated vapours of all different liquids, at the same tempera-

ture, the value of
dp

(1) di

must be the same.
(2.) For any different gaseous masses, at the same temperature, the value of

must be the same.

(3.) The values of these expressions for saturated vapours and for gases, at
the same temperature, must be the same.

31. No conclusion can be drawn @ prior? regarding the values of this coeffi-
cient » for different temperatures, which can only be determined, or compared, by
experiment. The results of a great variety of experiments, in different branches of
physical science (Pneumatics and Acoustics), cited by Carnot and by CLAPEYRON,
indicate that the values of « for low temperatures exceed the values for higher tem-
peratures; aresult amply verified by the continuous series of experiments performed
by Reenavtt on the saturated vapour of water for all temperatures from 0° to
230°, which, as we shall see below, give values for » gradually diminishing from
the inferior limit to the superior limit of temperature. When, by observation, «
has been determined as a function of the temperature, the amount of mechanical
effect. M, deducible from H units of heat descending from a body at the tempera-
ture S to a body at the temperature T, may be calculated from the expression,

S
M=H CBG: Or Ee ett ale 7
af @) P

“which is, in fact, what either of the equations (1) for the steam-engine, or (4) for

the air-engine, becomes, when the notation », for CarNnot’s multiplier, is intro-
duced.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 557

The values of this integral may be practically obtained, in the most con-
venient manner, by first determining, from observation, the mean values of «
for the successive degrees of the thermometric scale, and then adding the values
for all the degrees within the limits of the extreme temperatures S and T.*

32. The complete theoretical investigation of the motive power of heat is thus
reduced to the experimental determination of the coefficient «; and may be con-
sidered as perfect, when, by any series of experimental researches whatever, we
can find a value of » for every temperature within practical limits. The special
character of the experimental researches, whether with reference to gases, or with
reference to vapours, necessary and sufficient for this object, is defined and re-
stricted in the most precise manner, by the expressions (6) for 4, given above.

33. The object of ReGNAuLT’s great work, referred to in the title of this
paper, is the experimental determination of the various physical elements of the
steam-engine ; and when it is complete, it will furnish all the data necessary for
the calculation of ». The valuable researches already published in a first part of
that work, make known the latent heat of a given weight, and the pressure, of
saturated steam for all temperatures between 0° and 230° cent. of the air-thermo-
meter. Besides these data, however, the density of saturated vapour must be
known, in order that &, the latent heat of a unit of volume, may be calculated from
REGNAULT’s determination of the latent heat of a given weight.| Between the
limits of 0° and 100°, it is probable, from various experiments which have been
made, that the density of vapour follows very closely the simple laws which are
so accurately verified by the ordinary gases;{ and thus it may be calculated from
ReEGNAULT’s table giving the pressure at any temperature within those limits.
Nothing as yet is known with accuracy as to the density of saturated steam between
100° and 230°, and we must be contented at present to estimate it by calculation
from REGNAULT’s table of pressures; although, when accurate experimental re-
searches on the subject shall have been made, considerable deviations from the
laws of Boye and Daron, on which this calculation is founded, may be disco-
vered.

* The results of these investigations are exhibited in Tables I. and II. below.

+ It is, comparatively speaking, of little consequence to know pecmnately the value of o, for the
factor (l—c) of the expression for yw, since it is so small (being less than 7755 for all temperatures
between 0° and 100°) that, unless all the data are known with more accuracy than we can count

dp

upon at present, we might neglect it altogether, and take ai simply, as the expression for 4, with-

out committing any error of important magnitude.
{ This is well established, within the ordinary atmospheric limits, in Reanavu.t’s Etudes Mé-
téorologiques, in the Annales de Chimie, vol. xv., 1846.

VOL. XVI. PART V. . 7E

558 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

34. Such are the experimental data on which the mean values of » for the
successive degrees of the air-thermometer, from 0° to 230°, at present laid before
the Royal Society, is founded. The unit of length adopted is the English foot;
the unit of weight, the pound; the unit of work, a “foot-pound;” and the unit
of heat that quantity which, when added to a pound of water at 0°, will produce
an elevation of 1° in temperature. The mean value of »« for any degree is found

citing Ae ope d :
to a sufficient degree of approximation, by taking, in place of >, and k ; in the

ex pression

the mean values of those elements; or, what is equivalent to the corresponding
accuracy of aproximation, by taking, in place of « and & respectively, the mean
of the values of those elements for the limits of temperature, and in place of

d ‘ eae
= the difference of the values of p, at the same limits.

35. In REGNAULT’s work (at the end of the eighth Mémoire), a table of the
pressures of saturated steam for the successive temperatures 0°, 1°, 2°, . . . 230°,
expressed in millimetres of mercury, is given. On account of the units adopted
in this paper, these pressures must be estimated in pounds on the square foot,
which we may do by multiplying each number of millimetres by 2°7896, the
weight in pounds of a sheet of mercury, one millimetre thick, and a square foot
in area.

36. The value of k, the latent heat of a cubic foot, for any temperature ¢, is
found from 4, the latent heat of a pound of saturated steam, by the equation

pee 1+ 00366 x 100
760 © 14 °00366 x z
where p denotes the pressure in millimetres, and 4 the latent heat of a pound of
saturated steam ; the values of 4 being calculated by the empirical formula*
A= (606-5 + 0°305 ¢)— (¢ + -00002 ¢? + 0:000000 2°),
given by REGNAULT as representing, between the extreme limits of his observa-
tions, the latent heat of a unit weight of saturated steam.

. x 036869 . a,

* The part of this expression in the first vinculum (see ReGnautr, end of ninth Mémoire) is
what is known as “the total heat’’ of a pound of steam, or the amount of heat necessary to convert
a pound of water at 0° into a pound of saturated steam at ¢°; which, according to ‘“ Wart’s law,”
thus approximately verified, would be constant. The second part, which would consist of the single
term ¢, if the specific heat of water were constant for all temperatures, is the number of thermic
units necessary to raise the temperature of a pound of water from 0° to ¢°, and expresses empirically
the results of RegnavuLt’s experiments on the specific heat of water (see end of the tenth Mémoire),

described in the work already referred to.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 559

Explanation of Table I.

37. The mean values of » for the first, for the eleventh, for the twenty-first,
and so on, up to the 231st* degree of the air-thermometer, have been calculated in
the manner explained in the preceding paragraphs. These, and interpolated re-
results, which must agree with what would have been obtained, by direct calcu-
lation from ReGNautt’s data, to three significant places of figures (and even for
the temperatures between 0° and 100°, the experimental data do not justify us in
relying on any of the results to a greater degree of accuracy), are exhibited in
Table I.

To find the amount of mechanical effect due to a unit of heat, descending from
a body at a temperature S to a body at T, if these numbers be integers, we have merely
to add the values of » in Table I. corresponding to the successive numbers.

aL 2, othe ee Loy Bee ek,

Explanation of Table I.

38. The calculation of the mechanical effect, in any case, which might al-
ways be effected in the manner described in § 37 (with the proper modification
for fractions of degrees, when necessary), is much simplified by the use of Table
II., where the first number of Table I., the sum of the first and second, the sum
of the first three, the sum of the first four, and so on, are successively exhibited.
The sums thus tabulated are the values of the integrals

Hibs zi, ys 231
fonds fiwas frwas . 2. [mars

and, if we denote va ; # dt by the letter M, Table II. may be regarded as a table
of the values of M.

To find the amount of mechanical effect due to a unit of heat descending from a
body at a temperature S to a body at T, if these numbers be integers, we have merely

to subtract the value of M, for the number T + 1, from the value for the number S,
given in Table IT.

* In strictness, the 230th is the last degree for which the experimental data are complete ; but
the data for the 231st may readily be assumed in a sufficiently satisfactory manner.

560 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

Taste 1.* Mean Values of pw for the successive Degrees of the Air-Thermometer
from 0° to 230°.

O°

OCOntouarh wd eH

* The numbers here tabulated may also be regarded as, the actual values of w for t=}, t=13,
¢=21, ¢=381, &.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 561

Taste Il. Mechanical Effect in Foot-Pounds due to a Thermic Umit Centigrade,
passing from a body, at any Temperature less than 230° to a body at 0.

Superior Superior Superior Superior Superior

Limit of | Mechanical || Limit of} Mechanical |) Limitof} Mechanical |} Limit of} Mechanical || Limit of | Mechanical

Tempe- Hffect. Tempe- Effect. Tempe- Effect. Tempe- Effect. Tempe- Effect.

rature. rature. rature. rature. rature.

Foot-pounds. Foot-pounds. Foot-pounds. Foot-pounds. Foot-pounds.

i 4-960 48° | 223-487 | 94° | 412:545 140° | 582°981 186° | 740-310
2 9-906 49 | 227-842 | 95 | 416-425 141 | 586-524 187 | 743:614
3 14838 50 | 232:185 | 96 | 420-296 142 | 590-061 188 | 746-914
4 19-756 51 | 236-516 | 97 | 424159 | 143 | 5938-592 189 | 750:209
5 24:661 52 | 240835 | 98 | 428-0138 144 | 597-117 190 | 753-500
6 29°553 53 | 245143 | 99 | 431-858 145 | 600-636 191 | 756°787
q 34:431 54 | 249-489 | 100 | 435-695 146 | 604:099 192 | 760:069
8 39°296 55 | 263-724 101 | 439-524 147 | 607°656 193 | 763:347
9 44-148 56 | 257:997 102 | 443-344 148 | 611:157 194 | 766-621

10 48°987 57 | 262-259 1038 | 447-156 149 | 614:652 195 | 769890
ai! 53°813 08 | 266-509 104 | 460-960 150 | 618-142 196 | 7738-155
12 08°625 59 270-748 105 | 454-756 151 | 621:626 197 | 776-416
13 63°424 60 | 274:975 106 | 458:544 152 | 625:105 198 | 779-673
14 68-210 61 279-191 107 | 462-324 153 | 628°578 199 | 782-926
15 72°983 62 283°396 108 | 466-096 154 | 632-046 200 | 786-175
16 77:7438 63 | 287.590 109 | 469-860 155 | 635-508 201 | 789-420
17 82-490 64 | 291-773 110 | 473-617 156 | 638:965 202 | 792-661
18 87.225 65 | 295-945 111 | 477-366 157 | 642-416 203 | 795°898
19 91:947 66 300°106 112 | 481:107 || 158 | 645-862 204 | 799-131
20 96°656 67 304:256 113 | 484-3841 159 | 649°302 205 | 802°360
21 101-353 68 | 308-396 114 | 488:567 | 160 | 652-737 206 | 805-585
22 106:°037 69 | 312°525 115 | 492-286 | 161 | 656-167 207 | 808°806
23 110-709 70 | 316-644 116 | 495:998 | 162 | 659-591 208 | 812-023
24 115°368 va! 320°752 117 | 499-702 | 163 | 663-010 209 | 815:236
25 120-014 72 324°851 118 | 503-399 164 | 666°424 210 | 818-446
26 124-648 73 328°939 119 | 507:088 | 165 | 669°833 211 | 821-652
27 129:269 } 74 333°017 120 | 510:770 | 166 | 673°237 212 | 824°854
28 133-878 75 | 337-084 121 | 514-445 167 | 676°636 213 | 828°052
29 138-474 76 341:141 122 | 518113 | 168 | 680-030 214 | 831-247
30 | 143-058 77 345'188 123 | 521-174 169 | 683°419 215 | 834:438
3l 147-630 78 | 349-225 124 | 525428 | 170 | 686-803 216 | 837-626
32 152°189 79 300'253 125 | 529:075 | 171 | 690:183 217 | 840-810
33 156°736 80 | 3857-271 | 126 | 532:715 | 172 | 693°558 218 | 843:990
34 161-271 81 361:280 | 127 | 536:348 | 173 | 696:928 219 | 847-167
30 165°793 82 | 365-279 || 128 | 589-975 174 | 700:2938 220 | 850:340
36 170°303 83 369-269 | 129 | 548-595 175 | 703°654 221 | 853-509
37 174801 84 373°249 | 1380 | 547-209 176 | '707°010 222 | 856-674
38 179:287 85 | 377:220 131 | 550-816 Wig “GLO SGes 223 | 859:°836
39 183-761 86 381-181 132 | 564:417 178 | 713°707 224 | 862:994
40 188-223 87 | 385°133 133 | 558-051 179 | 717-049 225 | 866:149
41 192-673 88 | 389-076 134 | 561:597 180 | 720°386 226 | 869-300
42 TS (taal 89 393°010 135 | 565-176 | 181 | 723-718 227 | 872-448
43 201:537 90 396°935 1386 | 568-749 | 182 | 727-046 228 | 875-592
dt 205°951 91 400°851 | 187 | 572:316 | 183 | 730-369 229 | 878:733
45 210°353 92 | 404-758 138 | 576°877 184 | 733°687 230 | 881:870
46 | 214°743 93 | 408656 | 139 | 579-432 185 | 737-001 231 | 885-004
47 219°121 | ;

VOL. XVI. PART. V. iF

562 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

Note.—On the curves described in CLAPEYRON’s graphical method of exhibit-
ing Carnov’s Theory of the Steam-Engine.

39. At any instant when the temperature of the water and vapour is ¢, dur-
ing the fourth operation (see above, § 16), the latent heat of the vapour must be
precisely equal to the amount of heat that would be necessary to raise the tem-
perature of the whole mass, if in the liquid state, from ¢ to S.* Hence, if 7 de-
note the volume of the vapour, c the mean capacity for heat of a pound of water
between the temperatures S and ¢, and W the weight of the entire mass, in pounds,
we have

kv=c (S—2) W.

Again, the circumstances during the second operation are such that the mass of
liquid and vapour possesses H units of heat more than during the fourth; and
consequently, at the instant of the second operation, when the temperature is 2,
the volume v of the vapour will exceed 7 by an amount of which the latent heat
is H, so that we have

40. Now, at any instant, the volume between the piston and its primitive
position is less than the actual volume of vapour by the volume of the water eva-
porated. Hence, if z and a denote the abscissze of the curve at the instants of
the second and fourth operations respectively, when the temperature is 7, we have

L=v—6v, xe =vV—oN,
and, therefore, by the preceding equations,

i

7 {H+¢ (S—4 W} er a)

vatZte(S—-)W ern aah (Gl

These equations, along with
eof py. VG ed... Ree oee)

enable us to calculate, from the data supplied by ReGnauut, the abscissa and
ordinate for each of the curves described above (§ 17), corresponding to any as-

* For, at the end of the fourth operation, the whole mass is liquid, and at the temperature ¢.
Now, this state might be arrived at by first compressing the vapour into water at the temperature ¢,
and then raising the temperature of the liquid to 8; and however this state may be arrived at, there
cannot, on the whole, be any heat added to or subtracted from the contents of the cylinder, since,
during the fourth operation, there is neither gain nor loss of heat. This reasoning is, of course,
founded on Carnot’s fundamental principle, which is tacitly assumed in the commonly-received ideas
connected with ‘“‘ Watt’s law,” the “latent heat of steam,” and “ the total heat of steam.”

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 563

sumed temperature ¢. After the explanations of S§ 33, 34, 35, 36, it is only ne-
cessary to add that ¢ is a quantity of which the value is very nearly unity, and
would be exactly so were the capacity of water for heat the same at every tem-
perature as it is between 0° and 1°; and that the value of c (S—2), for any assigned
values of S and #, is found, by subtracting the number corresponding to ¢ from
the number corresponding to s, in the column headed ‘“ Nombre des unités de
chaleur abandonnées par un kilogramme d'eau en descendant de T° a 0°”, of the last
table (at the end of the Tenth Mémoire) of Reanavuut’s work. By giving S the
value 230°, and by substituting successively 220, 210, 200, &c., for z, values for
X,Y, Z, y, have been found, which are exhibited in the following Table :—

Volumes from the primi-
tive position of the piston | Pressures of saturated

Volumes to be de-
scribed by the piston,
to complete the
fourth operation.

to those occupied at steam, in pounds
instants of the second on the square foot.
operation.

Temperatures.

nae y=y =p
w+ 6:409.H 12-832
25:°567
48°514
88:007
153°167
256°595
415-070
650°240
989-318
1465-80
2120°11
2999-87
4160:10
5663°70
758115
9990-26
12976-2
16630°7
21051°5
26341°5
32607-7
39960°7
; 48512-4
°002643.H 58376-6

564 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

Appendix.

(Read April 30, 1849.)

41. In p. 30, some conclusions drawn by Carnot from his general reasoning
were noticed; according to which it appears, that if the value of uw for any
temperature is known, certain information may be derived with reference to the
saturated vapour of any liquid whatever, and, with reference to any gaseous mass,
without the necessity of experimenting upon the specific medium considered.
Nothing in the whole range of Natural Philosophy is more remarkable than the
establishment of general laws by such a process of reasoning. We have seen,
however, that doubt may exist with reference to the truth of the axiom on
which the entire theory is founded, and it therefore becomes more than a matter
of mere curiosity to put the inferences deduced from it to the test of experience.
The importance of doing so was clearly appreciated by Carnot; and, with such
data as he had from the researches of various experimenters, he tried his con-
clusions. Some very remarkable propositions which he derives from his Theory,
coincide with Dutone and Petit’s subsequently-discovered experimental laws with
reference to the heat developed by the compression of a gas; and the experimen-
tal verification is therefore in this case (so far as its accuracy could be depended
upon) decisive. In other respects, the data from experiment were insufficient,
although, so far as they were available as tests, they were confirmatory of the
theory.

42. The recent researches of RecnauttT add immensely to the experimental
data available for this object, by giving us the means of determining with consi-
derable accuracy the values of 4 within a very wide range of temperature, and so
affording a trustworthy standard for the comparison of isolated results at different
temperatures, derived from observations in various branches of physical science.

In the first section of this Appendix the Theory is tested, and shewn to
be confirmed by the comparison of the values of » found above, with those
obtained by Carnot and CLapeyron from the observations of various experi-
menters on air, and the vapours of different liquids. In the second and third
sections some striking confirmations of the theory arising from observations
by Dutone, on the specific heat of gases, and from Mr JouLE’s experiments
on the heat developed by the compression of air, are pointed out; and in con-

~~

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 565

clusion, the actual methods of obtaining mechanical effect from heat are briefly
examined with reference to their economy.

I. On the values of pb derived by Carnot and Clapeyron from observations on Air, and on the
Vapours of various liquids.

43. In Carnot’s work, p. 80-82, the mean value of u between 0° and 1° is
derived from the experiments of DeELARocHE and BERARD on the specific heat of
gases, by a process approximately equivalent to the calculation of the value of
10} Eon et

lay

°F
of the values of u from observations on the vapours of alcohol and water; but a
table given in M. CLapEyRon’s paper, of the values of » derived from the data
supplied by various experiments with reference to the vapours of ether, alcohol,
water, and oil of turpentine, at the respective boiling-points of these liquids, afford
us the means of comparison through a more extensive range of temperature. In
the cases of alcohol and water, these results ought of course to agree with those of
Carnot. ‘There are, however, slight discrepancies which must be owing to the
uncertainty of the experimental data.* In the following table, CarNovt’s results
with reference to air, and CLAPEYRON’S results with reference to the four different
liquids, are exhibited, and compared with the values of uw which have been given
above (Table I.) for the same temperatures, as derived from REGNAULT’s observa-
tions on the vapour of water.

v a t : ,
* for the temperature 4°. There are also, in the same work, determinations

Values of « de-
duced from
Regnault’s

Observations.

Names of the Media. Temperatures. Values of « Differences.

Air, . 0°5 (Carnot) 4-377 4-960

Sulphuric Ether, (Boiling point) 85°5 |(CLapzyron) 4° Eas 4:510
Alcohol, . 78°8 4:030
Water, : 4 | 3°337
Essence of Turpentine, ; : 3449

44. It may be observed that the discrepancies between the results founded on
the experimental data supplied by the different observers with reference to water
at the boiling-point, are greater than those which are presented between the re-
sults deduced from any of the other liquids, and water at the other tempera-
tures ; and we may therefore feel perfectly confident that the verification is com-

* Thus, from Carnovt’s calculations, we find, in the case of alcohol, 4:035; and in the case of
water, 3°648, instead of 3:963, and 3°658, which are CLApEYRon’s results in the same cases.

VOL. XVI. PART V. 7G

566 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

plete to the extent of accuracy of the observations.* The considerable discrepancy
presented by Carnor’s result, deduced from experiments on air, is not to be
wondered at when we consider the very uncertain nature of his data.

45. The fact of the gradual decrease of y, through a very extensive range of
temperature, being indicated both by ReGNAULT’s continuous series of experiments,
and by the very varied experiments on different media, and in different branches
of Physical Science, must be considered as a striking verification of the theory.

II. On the Heat developed by the compression of Air,

46. Let a mass of air, occupying initially a given volume V, under a pres-
sure P, at a temperature ¢, be compressed to a less volume V, and allowed to
part with heat until it sinks to its primitive temperature ¢. The quantity of heat
which is evolved may be determined, according to Carnovt’s theory, when the
particular value of u, corresponding to the temperature ¢, is known. For, by
equation § 30, equation (6), we have

dq Ep, »,
” ibn eae
where d q is the quantity of heat absorbed, when the volume is allowed to in-
crease from v to v + dv; or the quantity evolved by the reverse operation.
Hence we deduce
Ep,v, dv

dg=
Cc aamrentio

(8),

Ep

oD ° . A
Now, —~°—° is constant, since the temperature remains unchanged ; and
fe

therefore, we may at once integrate the second number. By taking it between
the limits V’ and V, we thus find

E p, % Vv

where Q denotes the required amount of heat, evolved by the compression

from V to V’. This expression may be modified by employing the equations
PV=P’ V’=p, uv, (1+ E ¢); and we thus obtain

EP V Vv EP’ V’ V

* A still closer agreement must be expected, when more accurate experimental data are afforded
with reference to the other media. Mons. Recnavir informs me that he is engaged in completing
some researches, from which we may expect, possibly before the end of the present year, to be fur-
nished with all the data for five or six different liquids which we possess at present for water. It
is therefore to be hoped that, before long, a most important test of the validity of Carnor’s theory
will be afforded.

+ The Napierian logarithm of =. is here understood.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 567

From this result we draw the following conclusion :—

47. Equal volumes of all elastic fluids, when compressed to smaller equal
volumes, disengage equal quantities of heat.

This extremely remarkable theorem of CArRNnot’s was independently laid down
as a probable experimental law by Dutone, in his “ Recherches sur la Chaleur
Spécifique des Fluides Elastiques,” and it therefore affords a most powerful con-
firmation of the theory.*

48. In some very remarkable researches made by Mr JouLE upon the heat
developed by the compression of air, the quantity of heat produced in different
experiments has been ascertained with reference to the amount of work spent in
the operation. To compare the results which he has obtained with the indi-
cations of theory, let us determine the amount of work necessary actually to pro-
duce the compression considered above.

49. In the first place, to compress the gas from the volume v+d v¢ to z, the
‘work required is pdv, or, since pv=p, v, (1+ Ed,

dv
Po % 1+ HA) ea

Hence, if we denote by W the total amount of work necessary to produce the
compression from V to V’, we obtain, by integration,

W=p, % (1+E 2) log Y,,

Comparing this with the expression above, we find

go = t) (11)

50. Hence we infer that

(1.) The amount of work necessary to produce a unit of heat by the compres-
sion of a gas, is the same for all gases at the same temperature.

(2.) And that the quantity of heat evolved in all circumstances, when the

temperature of the gas is given, is proportional to the amount of work spent in
the compression.

* Carnor varies the statement of his theorem, and illustrates it in a passage, pp. 52, 53, of
which the following is a translation :—

“ When a gas varies in volume without any change of temperature, the quantities of heat absorbed
or evolved by this gas are in arithmetical progression, if the augmentation or diminutions of volume
are in geometrical progression.

« When we compress a litre of air maintained at the temperature 10°, and reduce it to half
a litre, it disengages a certain quantity of heat. If, again, the volume be reduced from half a litre
to a quarter of a litre, from a quarter to an eighth, and so on, the quantities of heat successively
evolved will be the same.

“« Tf, in place of compressing the air, we allow it to expand to two litres, four litres, eight litres,

&c., it will be necessary to supply equal quantities of heat to maintain the temperature always at the
same degree.”

568 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

51. The expression for the amount of work necessary to produce a unit of.

heat is :
M(1+E¢4)
E bl

and therefore REGNAULT’s experiments on steam are available to enable us to cal-
culate its value for any temperature. By finding the values of p at 0°, 10°, 20°,
&c., from Table I., and by substituting successively the values 0, 10, 20, &c., for
t, the following results have been obtained.

Table of the Values of pies

Work requisite to Work requisite to

produce a unit of Temperature of produce a unit of Temperature of

Heat by the com- the Gas. Heat by the com- the Gas.

pression of a Gas. pression of a Gas.
Ft.-lbs. - Ft.-lbs. ss
1357°1 0 1446°4 ; 120
1368-7 10 1455°8 130
13790 20 1466°3 140
1388-0 30 14758 150
1395°7 40 1489-2 160
1401°8 50 1499-0 170
1406°7 60 1511°3 180
1412-0 70 1523°5 190, *
1417-6 80 1536°5 200
1424-0 90 1550-2 | 210
1430°6 100 1564-0 | 220
1438-2 110 15778 230

Mr JouLe’s experiments were all conducted at temperatures from 50° to
about 60° Fahr., or from 10° to 16° cent.; and, consequently, although some irre-
gular differences in the results, attributable to errors of observation inseparable
from experiments of such a very difficult nature are presented, no regular depend-
ance on the temperature is observable. From three separate series of experi-
ments, Mr JouLe deduces the following numbers for the work, in foot-pounds,
necessary to produce a thermic unit Fahrenheit by the compression of a gas.

820, 814, 760.
Multiplying these by 1:8, to get the corresponding number for a thermic unit

centigrade, we find
1476, 1465, and 1368.

The largest of these numbers is most nearly conformable with Mr Jouun’s
views of the relation between such experimental “ equivalents,” and others which
he obtained in his electro-magnetic researches; but the smallest agrees almost
perfectly with the indications of Carnor’s theory; from which, as exhibited in
the preceding Table, we should expect, from the temperature in Mr JouLE’s expe-
riments, to find a number between 1369 and 1379 as the result.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 569

Ill. On the Specijfic-Heats of Gases.

52. The following proposition is proved by Carnot as a deduction from his
general theorem regarding the specific heats of gases.

The excess of the specific heat® under a constant pressure above the specific heat
at a constant volume, is the same for all gases at the same temperatureand pressure.

53. To prove this proposition, and to determine an expression for the “ ex-
cess” mentioned in its enunciation, let us suppose a unit of volume of a gas to be
elevated in temperature by a small amount, ;. The quantity of heat required to
do this will be Az, if A denote the specific heat at a constant volume. Let us
next allow the gas to expand without going down in temperature, until its pres-
sure becomes reduced to its primitive value. The expansion which will take

place will be ees if the temperature be denoted by ¢; and hence, by (8), the

quantity of heat that must be supplied, to prevent any lowering of temperature,

2 Ep, % Er E? p
wil be py eee Uta Ba

Hence, the total quantity added is equal to

EK? p
aaa (1+Es?"
But, since B denotes the specific heat under constant pressure, the quantity of
heat requisite to bring the gas into this state, from its primitive condition, is
equal to B;; and hence we have
FE

= P
a (+E? °

(12)

IV. Comparison of the Relative advantages of the Air-Engine and Steam-Engine.

54. In the use of water-wheels for motive power, the economy of the engine
depends not only upon the excellence of its adaptation for actually transmitting
any given quantity of water through it, and producing the equivalent of work, -
but upon turning to account the entire available fall; so, as we are taught by
Carnot, the object of a thermodynamic engine is to economize in the best pos-
sible way the transference of all the heat evolved, from bodies at the temperature
of the source, to bodies at the lowest temperature at which the heat can be dis-
charged. With reference then to any engine of the kind, there will be two points
to be considered.

(1.) The extent of the fall utilised.

(2.) The economy of the engine, with the fall which it actually uses.

55. In the first respect, the air-engine, as Carnot himself points out, has a

* Or the capacity of a unit of volume for heat.
VOL. XVI. PART V. 7H

570 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

vast advantage over the steam-engine ; since the temperature of the hot part of
the machine may be made very much higher in the air-engine than would be
possible in the steam-engine, on account of the very high pressure produced in
the boiler, by elevating the temperature of the water which it contains to any
considerable extent above the atmospheric boiling point. On this account, a
“ perfect air-engine” would be a much more valuable instrument than a “ per-
fect steam-engine.” *

Neither steam-engines nor air-engines, however, are nearly perfect ; and we
do not know in which of the two kinds of machine the nearest approach to per-
fection may be actually attained. The beautiful engine invented by Mr Srir-
LING of Galston, may be considered as an excellent beginning for the air-engine ;+
and it is only necessary to compare this with Newcomen’s steam-engine, and
consider what Watt has effected, to give rise to the most sanguine anticipations
of improvement.

V. On the Economy of actual Steam-Engines.

56. The steam-engine being universally employed at present as the means
for deriving motive power from heat, it is extremely interesting to examine, ac-
cording to Carnov’s theory, the economy actually attained in its use. In the first
place, we remark that, out of the entire “ fall” from the temperature of the coals to
that of the atmosphere, it is only part—that from the temperature of the boiler to
the temperature of the condenser—that is made available ; while the very great
fall from the temperature of the burning coals to that of the boiler, and the com-
paratively small fall from the temperature of the condenser to that of the atmo-
sphere, are entirely lost as far as regards the mechanical effect which it is desired
to obtain. We infer from this, that the temperature of the boiler ought to be
kept as high as, according to the strength, is consistent with safety, while that of
the condenser ought to be kept as nearly down at the atmospheric tempera-
ture as possible. To take the entire benefit of the actual fall, Carnot shewed
that the “ principle of expansion’? must be pushed to the utmost.t

* Carnot suggests a combination of the two principles, with air as the medium for receiving
the heat at a very high temperature from the furnace ; and a second medium, alternately in the state
of saturated vapour and liquid water, to receive the heat, discharged at an intermediate temperature
from the air, and transmit it to the coldest part of the apparatus. It is possible that a complex
arrangement of this kind might be invented, which would enable us to take the heat at a higher
temperature, and discharge it at a lower temperature than would be practicable in any simple
air-engine or simple steam-engine. If so, it would no doubt be equally possible, and perhaps
more convenient, to employ steam alone, but to use it at a very high temperature not in contact
with water in the hottest part of the apparatus, instead of, as in the steam-engine, always in a satu-
rated state.

+ It is probably this invention to which Carnor alludes in the following passage (p. 112) :—
“ Tl a été fait, dit-on, tout recemment en Angleterre des essais heureux sur le développement de la
puissance motrice par l’action de la chaleur sur l’air atmosphérique. Nous ignorons entiérement
ne quoi ces essais ont consisté, si toutefois ils sont réels.”’

{ From this point of view, we see very clearly how imperfect is the steam-engine, even after all
Warr’s improvements. For to “‘ push the principle of expansion to the utmost,’’ we must allow the

j
!
]

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. O71

57. To obtain some notion of the economy which has actually been obtained,
we may take the alleged performances of the best Cornish engines, and some
other interesting practica cases as examples. *

(1.) The engine of the Fomwey Consols mine was reported, in 1845, to have given
125,089,000 foot-pounds of effect, for the consumption of one bushel or 94 Ibs. of
coals. Now, the average amount evaporated from Cornish boilers, by one pound
of coal, is 8} lbs. of steam ; and hence, for each pound of steam evaporated 156,556
foot-pounds of work are produced.

The pressure of the saturated steam in the boiler may be taken as 34 atmo-
spheres ;+ and, consequently, the temperature of the water will be 140°. Now
(ReGNAULT, end of Memoire X.), the latent heat of a pound of saturated steam at
140° is 508, and since, to compensate for each pound of steam removed from the
boiler in the working of the engine, a pound of water, at the temperature of the
condenser, which may be estimated at 30°, is introduced from the hot well; it
follows that 618 units of heat are introduced to the boiler for each pound of water
evaporated. But the work produced, for each pound of water evaporated, was
found above to be 156,556 foot-pounds. Hence, “*, or 253 foot-pounds is the
amount of work produced for each unit of heat transmitted through the Fowey Con-
solsengine. Now, in Table II., we find’583:0 as the theoretical effect due to a unit
descending from 140° to 0°, and 143 as the effect due to a unit descending from
30° to 0°. The difference of these numbers, or 440,{ is the number of foot-pounds
of work that a perfect engine with its boiler at 140°, and its condenser at 30°
would produce for each unit of heat transmitted. Hence, the Fowey Consols en-
gine, during the experiments reported on, performed 2 of its theoretical duty, or
574 per cent.

(2.) The best duty on record, as performed by an engine at work (not for
merely experimental purposes), is that of TayLor’s engine, at the United mines,
which, in 1840, worked regularly, for several months, at the rate of 98,000,000 foot-
pounds for each bushel of coals burned. This is =, or -784 of the experimental

steam, before leaving the cylinder, to expand until its pressure is the same as that of the vapour in
the condenser. According to “ Wart’s law,” its temperature would then be the same as (actually a
little above, as Recnautt has shewn) that of the condenser, and hence the steam-engine worked in
this most advantageous way, has in reality the very fault that Warr found in Newcomen’s engine.
This defect is partially remedied by Hornsiower’s system of using a separate expansion cylinder,
an arrangement, the advantages of which did not escape Carnot’s notice, although they have not been
recognised extensively among practical engineers, until within the last few years.

* I am indebted to the kindness of Professor Gorpon of Glasgow, for the information regard-
ing the various cases given in the text.

+ In different Cornish engines, the pressure in the boiler is from 23 to 5 atmospheres; and,
therefore, as we find from Reanautr’s table of the pressure of saturated steam, the temperature of
the water in the boiler must, in all of them, lie between 128° and 152°. For the better class of
engines, the average temperature of the water in the boiler may be estimated at 140°, the corre-
sponding pressure of steam being 34 temperatures.

{ This number agrees very closely with the number corresponding to the fall from 100° to 0°,
given in Table II. Hence, the fall from 140° to 30° of the scale of the air-thermometer is equiva-
lent, with reference to motive power, to the fall from 100° to 0°.

572 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF

duty reported in the case of the Fowey Consols engine. Hence, the best useful
work on record, is at the rate of 198°3 foot-pounds for each unit of heat transmit-
ted, and is %”, or 45 per cent. of the theoretical duty, on the supposition that the
boiler is at 140°, and the condenser at 30°.

(3.) French engineers contract (in Lille, in 1847, for example) to make en-
gines for mill power which will produce 30,000 metre-lbs., or 98,427 foot-lbs. of
work for each pound of steam used. If we divide this by 618, we find 159 foot-
pounds for the work produced by each unit of heat. This is 36:1 per cent. of
440, the theoretical duty. *

(4.) English engineers have contracted to make engines and boilers which
will require only 34 Ibs. of the best coal per horse-power per hour. Hence, in
such engines, each pound of coal ought to produce 565,700 foot-pounds of work,
and if 7 lbs. of water be evaporated by each pound of coal, there would result
80,814 foot-pounds of work for each pound of water evaporated. If the pressure
in the boiler be 35 atmospheres (temperature 140°) the amount of work for each
unit of heat will be found, by dividing this by 618, to be 130-7 foot-pounds, which
is or 29°7 per cent. of the theoretical duty.

(5.) The actual average of work performed by good Cornish engines and
boilers is 55,000,000 foot-pounds for each bushel of coal, or less than half the ex-
perimental performance of the Fowey Consols engine, more than half the actual
duty performed by the United Mines engine in 1840; in fact about 25 per cent. of
the theoretical duty.

(6.) The average performances of a number of Lancashire engines and boilers
have been recently found to be such as to require 12 lbs. of Lancashire coal per
horse-power per hour (7. ¢., for performing 60 x 33,000 foot-pounds) and of a num-
ber of Glasgow engines, such as to require 15 lbs. (of a somewhat inferior coal)
for the same effect. There are, however, more than twenty large engines in Glas-
gow at present, {| which work with a consumption of only 64 Ibs. of dross, equiva-
lent to 5 lbs. of the best Scotch, or 4 Ibs. of the best Welsh coal, per horse-power

* It being assumed that the temperatures of the boiler and condenser are the same as those of
the Cornish engines. If, however, the pressure be lower, two atmospheres, for instance, the num-
bers would stand thus: The temperature in the boiler would be only 121. Consequently, for each
pound of steam evaporated, only 614 units of heat would be required; and, therefore, the work
performed for each unit of heat transmitted would be 160-3 foot-pounds, which is more than according
to the estimate in the text. On the other hand, the range of temperatures, or the fall utilised, is
only from 131 to 30, instead of from 140 to 30°, and, consequently (fable II.), the theoretical duty
for each unit of heat is only 371 foot-pounds. Hence, if the engine, to work according to the speci-
fication, requires a pressure of only 15 lbs. on the square inch (i. ¢., a total steam pressure of two at-
mospheres), its performance is 47’, or 43:2 per cent. of its theoretical duty.

+ If, in this case again, the pressure required in the boiler to make the engine work according
to the contract were only 15 Ibs. on the square inch, we should have a different estimate of the eco-
nomy, for which, see Table B, at the end of this paper.

{ These engines are provided with separate expansive cylinders, which have been recently added
to them by Mr M‘Naueur of Glasgow.

CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 973
per hour. The economy may be estimated from these data, as in the other cases,
on the assumption which, with reference to these, is the most probable we can
make, that the evaporation produced by a pound of best coal is 7 Ibs. of steam.

58. The following Tables afford a synoptic view of the performances and
theoretical duties in the various cases discussed above.

In Table A the numbers in the second column are found by dividing the
numbers in the first by 83 in cases (1.), (2.), and (5.), and by 7 in cases (4.), (6.),
and (7.), the estimated numbers of pounds of steam actually produced in the dif-
ferent boilers by the burning of 1 Ib. of coal.

The numbers in the third column are found from those in the second, by
dividing by 618, in Table A, and 614 in Table B, which are respectively the
quantities of heat required to convert a pound of water taken from the hot well
at 30°, into saturated steam, in the boiler, at 140° or at 121°.

With reference to the cases (3.), (4.), (6.), (7.), the hypothesis of Table B is
probably in general nearer the truth than that of Table A. In (4.), (6.), and (7.),
especially upon hypothesis B, there is much uncertainty as to the amount of eva-
poration that will be actually produced by 1 1b. of fuel. The assumption on which
the numbers in the second column in Table B are calculated, is, that each pound
of coal will send the same number of units of heat into the boiler whether hypo-
thesis A or hypothesis B be followed. Hence, except in the case of the French
contract, in which the evaporation, not the fuel, is specified, the numbers in the
third column are the same as those in the third column of Table A.

TaBLe A. Various Engines in which the temperature of the Boiler is 140°, and
that of the Condenser 30°.

Theoretical Duty for each Unit of Heat transmitted, 440 foot-pounds.

Work produced] Work produced] Work produced|Per cent-
for each pound |for each pound | for each unit | age of
of coal con- | of water eva- | of heat trans- |theoreti-

(1.) Fowey Consols Experiment, reported in 1845,
(2.) Taylor’ s Engine at the United Mines, work- S|

ing in 1840, :
(3.) French Engines, according to contrat
(4.) English Engines, according to contract,
(5.) Average actual performance of Cornish Engines,
(6.) Common Engines, consuming 12 lbs. of best
coal per hour per horse-power,
(7.) Improved Engines with Expansion Cylinders,
consuming an equivalent to 4 Ibs. of best
coal per horse-power per hour, |

VOL. XVI. PART V.

sumed.

Foot-Pounds.
1,330,734

1,042,553

* * K *¥

565,700
585,106

165,000

495,000

porated.

Foot-Pounds.

156,556
122,658

98,427
80,814
68,836

23,571

70,710

mitted.

Foot-Pounds.

253
198-4

159
130°8
111°3

381

114-4

~I
coal

cal duty.

57°5

| 4541

36:1
29:7
25:3

8-6

26

574 CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT.

TaBLe B. Various Engines in which the Temperature of the Boilers is 121,* and
that of the Condenser 30°.

Theoretical Duty for each Unit of Heat transmitted, 371 foot-pounds.

Work produced] Work produced |Work produced/Per cent-
for each pound | for each pound | for each unit | age of
of coal con- of water eva- | of heat trans- |theoreti-
sumed, porated. mitted. cal duty.
Foot-Pounds. | Foot-Pounds. | Foot-Pounds.
+e + 98,427| 160-3 | 43-2
565,700 |&14 x 80,814 130°8 35
&
6

iH
14 x 23,571 38-1 10-3

(3.) French Engines, according to contract,

(4.) English Engines, according to contract,
(6.) Common Engines, consuming 12 lbs. of coal 165,000
per horse-power per hour, :

(7.) Improved Engines with expansion cylinders,
consuming an equivalent to 4 Ibs. best coal 495,000 |&4 x 70,710 114-4 30:7

per horse-power per hour,

* Pressure 15 lbs. on the square inch.

( 575)

XXXVII.—Theoretical Considerations on the Liffect of Pressure in Lowering the
Freezing Point of Water. By James Tuomson, Esq., of Glasgow. Commu-
nicated by Professor W1LL1AM THOMSON.

(Read 2d January 1849.)

Some time ago my brother, Professor WiLL1am THomson, pointed out to mea
curious conclusion to which he had been led, by reasoning on principles similar to
those developed by Carnot, with reference to the motive power of heat. It was,
that water at the freezing point may be converted into ice by a process solely mecha-
mcal, and yet without the final expenditure of any mechanical work. This at first
appeared to me to involve an impossibility, because water expands while freezing ;
and, therefore, it seemed to follow, that if a quantity of it were merely enclosed
in a vessel with a moveable piston, and frozen, the motion of the piston, conse-
quent on the expansion, being resisted by pressure, mechanical work would be
given out without any corresponding expenditure; or, in other words, a per-
petual source of mechanical work, commonly called a perpetual motion, would
be possible. After farther consideration, however, the former conclusion ap-
peared to be incontrovertible; but then, to avoid the absurdity of supposing that
mechanical work could be got out of nothing, it occurred to me that it is neces-
sary farther to conclude, that the freezing point becomes lower as the pressure. to
which the water is subjected 1s increased.

The following is the reasoning by which these conclusions are proved. Let
there be supposed to be a cylinder, and a piston fitting water-tight to it, and
capable of moving without friction. Let these be supposed to be formed of a
substance which is a perfect non-conductor of heat; also, let the bottom of the
cylinder be closed by a plate, supposed to be a perfect conductor, and to possess
no capacity for heat. Now, to convert a given mass of ice into water without the
expenditure of mechanical work, let this imaginary vessel be partly filled with air
at 0° C., and let the end of it be placed in contact with an indefinite mass of
water, a lake for instance, at the same temperature. Now, let the piston be
pushed towards the bottom of the cylinder by pressure from some external reser-
voir of mechanical work, which, for the sake of fixing our ideas, may be supposed
to be the hand of an operator. During this process the air in the cylinder would
tend to become heated on account of the compression, but it is constrained to re-
main at 0° by being in communication with the lake at that temperature. The
change, then, which takes place is, that a certain amount of work is given from
the hand to the air, and a certain amount of heat is given from the air to the
water of the lake. In the next place, let the bottom of the cylinder be placed in

VOL. XVI. PART V. y Ga

576 JAMES THOMSON, ESQ., ON THE EFFECT OF PRESSURE

contact with the mass of water at 0°, which is proposed to be converted into ice,
and let the piston be allowed to move back to the position it had at the com-
mencement of the first process. During this second process, the temperature of
the air would tend to sink on account of the expansion, but it is constrained to
remain constant at 0° by the air being in communication with the freezing water,
which cannot change its temperature so long as any of it remains unfrozen.
Hence, so far as the air and the hand are concerned, this process has been exactly
the converse of the former one. Thus the air has expanded through the same
distance through which it was formerly compressed; and, since it has been con-
stantly at the same temperature during both processes, the law of the variation
of its pressure with its volume must have been the same in both. From this it
follows, that the hand has received back exactly the same amount of mechanical
work in the second process as it gave out in the first. By an analogous reason it
is easily shewn, that the air also has received again exactly the same amount of
heat as it gave out during its compression ; and, hence, it is now left in a condi-
tion the same as that in which it was at the commencement of the first process.
The only change which has been produced, then, is, that a certain quantity of heat
has been abstracted from a small mass of water at 0°, and dispersed through an in-
definite mass at the same temperature, the small mass having thus been converted into
ice. This conclusion, it may be remarked, might be deduced at once by the appli-
cation, to the freezing of water, of the general principle developed by Carnov,
that no work is given out when heat passes from one body to another without a
fall of temperature ; or rather by the application of the converse of this, which of
course equally holds good, namely, that no work requires to be expended to make
heat pass from one body to another at the same temperature.

Next, to prove that the freezing point of water is lowered by an increase of
the pressure to which the water is subjected :—Let a cylinder, of the same ima-
ginary construction as that used in the foregoing demonstration, contain some
air at 0° C. Let the bottom of the cylinder be placed in contact with the
water of an indefinitely large lake, of which the temperature is above 0° by an
infinitely small quantity; and let the air be subjected to compression by pressure
applied by the hand to the piston. A certain amount of work is thus given from
the hand to the air, and a certain amount of heat is given out from the air to the
lake. Next, let the bottom of the cylinder be placed in communication with a
small quantity of water at 0°, enclosed in a second imaginary cylinder similar in
character to the first ; and let this water be, at the commencement, subject merely
to the atmospheric pressure. Let, however, resistance be offered by the hand to
any motion of the piston of this second cylinder which may take place. Things
being in this state, let the piston of the cylinder containing the air move back to
its original position. During this process part of the heat of the air becomes latent
on account of the increase of volume. Thus the temperature of the air, from being

IN LOWERING THE FREEZING POINT OF WATER. 577

above 0°, by an infinitely small quantity, instantly becomes absolutely 0°; and
afterwards, as the motion of the piston continues, the air absorbs heat from the
mass of water in the second cylinder, part of the mass passing at the same time
into the state of ice. Hence the whole mass expands; and therefore, on account
of the resistance offered by the hand to the motion of the piston of the cylinder
containing the mass, the internal pressure is increased, and a quantity of work,
not infinitely small, is given out by the piston, and is received by the hand. To-
wards the end of this process, let the resistance offered by the hand gradually de-
crease till, just at the end (that is, when the piston of the air-cylinder has resumed
its first position) it becomes nothing, and the pressure within the water-cylinder
thus becomes again equal to that of the atmosphere. The temperature of the
mass of partly frozen water must now be 0°, and the air in the other cylinder
being in communication with this, must have the same temperature. The air is
therefore, infinitely nearly at its original temperature, and it has its original
volume. Hence it is now left in a state infinitely nearly the same as that in which
it was at first. Farther, let the ice, which has been formed by the freezing of
the water, be placed in contact with the lake till it melts, which it will really do
since the lake is warmer than 0°, though only by an infinitely small quantity.
Thus the mass of water is left in its original state, and it has been already shewn
that the air is left infinitely nearly in its original state. Hence no work, except
an infinitely small quantity, can have been absorbed or developed by any change
on the air and water, which have been used. But a quantity of work not infi-
nitely small has been given out by the piston of the water-cylinder to the hand ;
and therefore an equal quantity* of work must have been given from the hand
to the air-piston, as there is no other way in which the work developed could
have been introduced into the apparatus. Now, the only way in which this can
have taken place is by the air having been colder, while it was expanding in the
second process, than it was while it was undergoing compression during the first.
Hence it was colder than 0° during the course of the second process; or, in other
words, while the water was freezing, under a pressure greater than that of the
atmosphere, its temperature was lower than 0.

The fact of the lowering of the freezing point being thus demonstrated, it be-
comes desirable, in the next place, to find what is the freezing point of water for
any given pressure. ‘The most obvious way to determine this would be by direct
experiment with freezing water. I have not, however, made any attempt to do so
in this way. The variation to be appreciated is extremely small, so small, in fact,
as to afford sufficient reason for its existence never having been observed by any
experimenter. Even to detect its existence, much more to arrive at its exact
amount by direct experiment, would require very delicate apparatus which would

* In saying ‘an equal quantity’’ I, of course, neglect infinitely small quantities in comparison
to quantities not infinitely small.

578 JAMES THOMSON, ESQ., ON THE EFFECT OF PRESSURE

not be easily planned out or procured. Another, and a better, mode of proceeding
has, however, occurred to me: and by it we can deduce, from the known expansion
of water in freezing, together with data founded on the experiments of REGNAULT
on steam at the freezing point, a formula which gives the freezing point in terms
of the pressure ; and which may be applied for any pressure, from nothing up to
many atmospheres. The following is the investigation of this formula :—

Let us suppose that we have a cylinder of the same imaginary construction
as that of the one described at the commencement of this paper ; and let us use it
as an ice-engine analogous to the imaginary steam-engine conceived by Carnot,
and employed in his investigations. For this purpose, let the entire space en-
closed within the cylinder by the piston be filled at first with as much ice as
would, if melted, form rather more than a cubic foot of water, and let the ice
be subject merely to one atmosphere of pressure, no force being applied to the
piston. Now, let the following four processes, forming one complete stroke of the
ice-engine be performed.

Process 1. Place the bottom of the cylinder in contact with an indefinite lake
of water at 0°, and push down the piston. The effect of the motion of the piston
is to convert ice at 0° into water at 0°, and to abstract from the lake at 0° the
heat which becomes latent during this change. Continue the compression till one
cubic foot of water is melted from ice.

Process 2. Remove the cylinder from the lake, and place it with its bottom on
a stand which is a perfect non-conductor of heat. Push the piston a very little
farther down, till the pressure inside is increased by any desired quantity which
may be denoted, in pounds on the square foot, by p. During this motion
of the piston, since the cylinder contains ice and water, the temperature of the
mixture must vary with the pressure, being at any instant the freezing point
which corresponds to the pressure at that instant. Let the temperature at the
end of this process be denoted by —t¢° C.

Process 3. Place the bottom of the cylinder in contact with a second inde-
finitely large lake at —¢°, and move the piston upwards. During this motion the
pressure must remain constant at p above that of the atmosphere, the water in
the cylinder increasing its volume by freezing, since, if it did not freeze, its pres-
sure would diminish, and therefore its temperature would increase, which is im-
possible, since the whole mass of water and ice is constrained by the lake to remain
at—z°. Continue the motion till all the heat has been given out to the second
lake at —¢°, which was taken in during Process 2, from the first lake at 0°.*

* This step, as well as the corresponding one in Carnort’s investigation, it must be observed, in-
volves difficult questions, which cannot as yet be satisfactorily answered, regarding the possibility of the
absolute formation or destruction of heat as an equivalent for the destruction or formation of other
agencies, such as mechanical work ; but, in taking it, I go on the almost universally adopted suppo-
sition of the perfect conservation of heat.

IN LOWERING THE FREEZING POINT OF WATER. 579

Process 4. Remove the cylinder from the lake at—?¢’, and place its bottom
again on the non-conducing stand. Move the piston back to the position it occu-
pied at the commencement of Process 1. The temperature and pressure, during
this process, must vary with one another, as they did in Process 2. Also, since
as much heat has been given out as was taken in; and since the volume is the
same as at the commencement of Process 1, the physical state of the mass con-
tained in the cylinder must be now in every respect the same as it was at that
time.

By representing graphically in a diagram the various volumes and corre-
sponding pressures, at all the stages of the four processes which have just been
laid down, we shall arrive, in a simple and easy manner, at the quantity of work
which is developed in one complete stroke by the heat which is transferred during
that stroke from the lake at 0° to the lake at—7¢°. For this purpose, let E be
the position of the piston at the beginning of Process 1; and let some distance,
such as EG, represent its
stroke in feet, its area be-
ing made a square foot,
so that the numbers ex-
pressing, in feet, distances
along EG may also ex-
press, in cubic feet, the
changes in the contents of A
the cylinder produced by
the motion of the piston. Now, when 1:087 cubic feet of ice are melted,
one cubic foot of water is formed. Hence, if EF be taken equal to -087 feet,
F will be the position of the piston when one cubic foot of water has been melted
from ice, that is, the position at the end of Process |, the bottom of the cylinder
being at a point A distant from F by rather more than afoot. Let e¢/ be parallel
to EF, and let E ¢ represent one atmosphere of pressure ; that is, let the units of
length for the vertical ordinates be taken such that the number of them in Ee
may be equal to the number which expresses an atmosphere of pressure. Also
let gh be parallel to EF, and let fm represent the increase of pressure produced
during Process 2. Then the straight lines ¢/and gh will be the lines of pressure
for Processes 1 and 2; and for the other two processes, the lines of pressure will
be some curves which would extremely nearly coincide with the straight lines /g
and he. For want of experimental data, the nature of these two curves cannot
be precisely determined ; but, for our present purpose, it is not necessary that
they should be so, as we merely require to find the area of the figure ¢ fg h, which
represents the work developed by the engine during one complete stroke, and this
can readily be obtained with sufficient accuracy. For, even though we should

VOL. XVI. PART V. tals

580 EFFECT OF PRESSURE IN LOWERING FREEZING POINT OF WATER.

adopt a very large value form, the change of pressure during Process 2, still
the changes of volume gm and hn in Process 2 and Process 4 would be ex-
tremely small compared to the expansion during the freezing of the water; and
from this it follows evidently that the area of the figure ¢fg h is extremely nearly
equal to that of the rectangle efmn, but fe is equal to F E, which is -087 feet.
Hence the work developed during an entire stroke is ‘087 < p foot-pounds. Now
this is developed by the descent from 0° to—¢ of the quantity of heat neces-
sary to melt a cubic foot of ice; that is, by 4925 thermic units, the unit being the
quantity of heat required to raise a pound of water from 0° to 1° centigrade.
Next we can obtain another expression for the same quantity of work; for, by
the tables deduced in the preceding paper from the experiments of REGNAULT,
we find that the quantity of work developed by one of the same thermic
units descending through one degree about the freezing point, is 4-97 foot-pounds.
Hence, the work due to 4925 thermic units descending from 0° to—¢ is 4925 x
4:97 x ¢ foot-pounds. Putting this equal to the expression which was formerly
obtained for the work due to the same quantity of heat falling through the same
number of degrees, we obtain

4925 x 4:97 x t = 087 x p.
Hence,

¢=00000855 p.0 ob aoe et

This, then, is the desired formula for giving the freezing point —¢ centigrade, which
corresponds to a pressure exceeding that of the atmosphere by a quantity p,
estimated in pounds on a square foot.

To put this result in another form, let us suppose water to be subjected to one
additional atmosphere, and let it be required to find the freezing point. Here
p = one atmosphere = 2120 pounds on a square foot; and, therefore, by

(r) = 00000355 x 2120.
or ¢ = ‘0075.

That is, the freezing point of water, under the pressure of one additional atmo-
sphere, is—-0075 centigrade; and, hence, if the pressure above one atmosphere
be now denoted in atmospheres,* as units by n, we obtain ¢, the lowering of the
freezing point in degrees centigrade, by the following formula—

t= -0075 n. cong yee 2)

* The atmosphere is here taken as being the pressure of a column of mercury of 760 milli-
metres ; that is 29-92, or very nearly 30 English inches.

( 581 )

XXXVIII—On the Gradual Production of Luminous Impressions on the Eye, and
other Phenomena of Vision. By WitLiam Sway, F.R.S.E.

(Read March 19, 1849.)

It is well known that a luminous object is seen for some time after its light
has ceased to fall on the retina; but less attention seems to have been paid to the
fact, that light requires a certain time to produce its full impression on the eye.
Accordingly, while it is stated in most treatises on optics, that the sensation of
vision continues after the action of light has ceased, only a few writers have
mentioned that the total effect of light on the eye is not produced instantaneously,
but that a certain time is required for its complete development.

The merit of having first noticed this phenomenon of vision is probably due
to Lord Bacon, who observes, that notwithstanding the rapidity of the act of vision,
a certain time is required for its exercise, which is proved by certain objects, such
as a musket-ball, being invisible on account of the velocity of their motion. For
the flight of the ball, he remarks, is too swift to allow an impression of its figure
to be conveyed to the sight.*

While succeeding writers have devoted much attention to other departments
of the physiology of vision, they have not, so far as Iam aware, added a single
fact to our knowledge of this part of the subject, which remains, therefore, pre-
cisely as it was left by Lord Bacon.+

* “ At in visu (cujus actio est pernicissima) liquet etiam requiri ad eum actuandum momenta
certa temporis : idque probatur ex iis, quae propter mottis velocitatem non cernuntur; ut ex latione
pilae ex sclopeto. Velocior enim est praetervolatio pilae, quam impressio speciei ejus quae deferri
poterat ad visum.””—(Novwm Organum, lib. 1., Aph. xlvi. Bacon's Works, vol.i., p. 370. Lond. 1711.)

{ This appears from the following passages, which will be found to contain little more than a
repetition of Lord Bacon’s statement :—

“Tl est un fait auquel on a généralement accordé peu d’attention, quoiqu’il ait été remarqué
(voyez Essai d’wn Cours Elémentaire et Général des Sciences Physiques, par M. Beupant : Partie Phy-
sique, p. 489 de la 3me edition), c’est que les impressions directes ewigent un certain temps pour se dévelop-
per sur la rétine. Pour se convaincre de la réalité de ce fait, qui devait naturellement se prévoir a priori,
il suffit de se rappeler qu’un objet qui passe trés rapidement devant l’cil, ne se voit pas, ou s’aper-
coit 4 peme. On peut encore prouver la chose par l’expérience suivante. Si l’on fait mouvoir cir-
culairement, devant un fond noir, un petit morceau de papier blanc, avec une vitesse telle que
Vanneau apparente qu’en resulte présente une teinte parfaitement uniform et tranquille, cet anneau
ne paraitra pas blanc, mais gris. Or il suit de l’uniformité de la teinte, que pendant le petit inter-
valle de temps qui sépare deux passages successifs de l’objet au méme point, l’impression ne décréit pas
d’une quantité sensible: il faut done nécessairement admettre que cette impression n’est pas blanche,
comme celle qui est produite par l’objet en repos, mais qu’elle est grise, c’est-a-dire d’une blancheur
imparfaite, ou enfin qu’a raison du temps extrémement court que l’objet emploie a passer devant l’ceil,
il ne produit qu’une impression incomplete. I] est inutile d’ajouter qu’on obtiendra des resultats
analogues en employant un objet d’une couleur quelconque: toujours l’anneau paraitra plus sombre
que l’objet en repos. L’éclat de l’anneau sera d’ailleurs d’autant moins éloigné de celui de l’objet en

VOL. XVI. PART V. 7M

582 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

Before I was aware that any one had noticed the gradual action of light on
the eye, my attention was accidentally directed to that subject about eighteen
months ago, by observing that the light of the sky seen immediately over a ball
in its descent through the air, seemed less bright than at those parts of the retina
where the action of the light had not been interrupted by the passage of the dark
body. Itimmediately occurred to me, that this appearance was caused by the por-
tion of the retina over which the image of the ball had passed, not having had time
to be fully impressed with the light of the sky at the instant when the passage of
the ball again exposed it to theaction of that light.* Such an observation as this
does not admit of easy repetition, but a more convenient method of exhibiting the
gradual production of luminous impressions will be afterwards described.

It may be necessary here to anticipate an objection to the supposition, that
light requires a sensible time to produce its full effect on the retina, founded on
the observations of Professor WHEATSTONE, whose experiments prove, that “ the
light of electricity of high tension has a less duration than the millionth part of a
second ;” and that ‘the eye is capable of perceiving objects distinctly which are
presented to it during the same small interval of time.” +

It is obvious, however, that these statements are perfectly consistent with the
gradual action of light on the eye. For, although light may produce a certain effect

repos, ou, en d’autres termes, l’impression approchera d’autant plus d’étre compléte, que cet objet
aura plus de largeur, et que par suit il emploiera, dans son mouvement, un temps moins court 4 passer
devant l’wil : ainsi l’expérience, que nous venons de décrire, conduit de plus a cette conséquence facile
i prévoir que le développement de V' impression directe est progressive quoique trés rapide.’ —( Essai dune
Theorie Génerale comprenant Vensemble des Apparences Visuelles, &c. par J. PuatEau, p. 53. Nou-
veauz Memoires de ’ Academie Royale des Sciences et Belles Lettres de Brumelles, tome vui., 1834.)

A statement almost identical with this will be found in Piatgeau sur la Persistance des Impres-
sions de la Rétine. Supplement au Traité de la Lumiére de Sir J. F. W. Herscner. Par A. QuETELET.
p. 474, 1833. See also Mutusr’s Physics, p. 274. London, 1847.

The following is the passage in Brupant Cours de Physique, to which M. Puatzav refers :—“ C’est
aussi parce que l’impression d’un objet sur notre ceil ne se fait pas instantanément, que nous ne
pouvons apercevoir un corps qui se meut avec une extréme vitesse. Ainsi par example, un boulet de
canon laneé par une bouche a feu, est invisible pendant une grande partie de sou mouvement, parce
qwil ne reste pas assez de temps dans un méme lieu, pour qu’on ait celui de l’apercevoir.”

M. Prareav observes, in the passage which has just been quoted, that it was easy to foresee a
priori that the development of the impression of light on the eye is progressive, although very rapid.
With reference to this opinion, while it may be admitted that it is quite natural to suppose that the
action of light on the eye is not absolutely instantaneous ; yet, certainly, no one would be entitled to
conclude a priori that a sensible time is required to produce impressions on the eye. I have, therefore,
much satisfaction in availing myself of the present opportunity of directing attention to Lord Bacon’s
prior claim to the merit of pointing out the curious and interesting fact, that light requires an ap-
preciable time to produce visual impressions on the eye.

* It may be supposed that a different explanation of this effect might be afforded by the persist-
ence of the impression of the image of the ball on the eye. That this explanation is identical with
that given above, is evident from the image of the ball when seen projected upon the sky, being sen-
sibly black. For, since blackness is the negation of light, the persistence of a black impression is
but a want of light on that portion of the retina where the impression is perceived ; and the existence
of such an impression, or a want of luminosity after the eye is fully exposed to light, clearly proves
that its action on that organ is not instantaneous.

+ Philosophical Transactions, 1834, p. 591.

LUMINOUS IMPRESSIONS ON THE EYE. 583

on that organ in the millionth part of a second, it by no means follows that this
is its full effect; and thus, while the electric spark renders objects distinctly
visible which are seen for less than the millionth part of a second, it may still be
true that the apparent brightness of those objects would increase if the duration
of the light could be prolonged.

Having found only very brief and general references, to the gradual action
of light on the eye, in any authors to whose works I have had access, I resolved
to investigate the subject experimentally; and the object of this paper is to de-
scribe a series of experiments undertaken for the purpose of ascertaining the con-
nexion between the brightness of the impression produced by light on the retina,
and the time during which it acts on the eye.*

Before entering upon the narrative of my experiments it may be proper to
premise, that if, in some cases, I seem to assume that the results obtained by
experiments on my own eyes, are to be regarded as universal phenomena, I do
so merely to avoid circumlocution; and I believe I may plead the example of
most writers who describe experiments on vision in justification of such an ap-
parent assumption.

In several cases, however, some of which will be afterwards noticed, the ex-
periments have been witnessed by others, whose concurrent testimony has proved
that the results were not dependent upon any idiosyncrasy of vision on my part.

I may also have made use of expressions which seem to involve the assump-
tion that the brightness with which a luminous object is seen at any instant, is
the same as the apparent brightness of its image on the retina at that instant ; or,
in other words, that the impression of light on the retina is perceived by the mind
instantaneously. Such expressions, however, are employed simply for the sake of
brevity. The principal object of my investigation is to determine the brightness of
an impression made on the retina by a light of a given intensity, acting for a
given time; and it will be found in the sequel that the method I have devised for
measuring the time during which the light acts, and the intensity of the resulting
impression, does not depend for its accuracy on the settlement of the question,
whether or not the impressions of light on the retina are instantaneously per-
ceived by the mind.

I. Method of Observation.

In order to examine the phenomena presented by luminous impressions of
short duration, I made use of the following method of observation. If a disc of

* Additional proof that almost no attention has hitherto been paid to this subject, may be
derived from the fact, that no notice is taken of it in Mutuzr’s Physiology, London 1839, nor in
the Supplement to that work by Baty, London 1848. M. Prarzav also observes: “‘ Personne n’a
essayé de mésurer le temps nécessaire 4 la production compléte de impression.” Prareav Sur la
Persistance des Impressions. (Supplément au traité de la Lumiere de Sir J. F.W. Herscner. Par
A. Queretet, p. 474, 1833.)

584 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

pasteboard (see Fig. 4, Plate XII.), or other convenient material, having a portion of
a sector ABCD, cut out from its circumference, be made to revolve, in a plane
perpendicular to the line of vision, between the eye and a luminous object, the ob-
ject may be placed so as to be seen through the sector at each revolution of the
disc. In this manner a succession of luminous impressions will be obtained ; and
the time during which the light acts on the eye at each impression will depend
partly on the velocity of the rotation of the disc, and partly on the ratio of the
arc of the sector to the whole circumference.

Let ABG (Fig. 1) represent the disc, A C B the sector cut out of it, and E D
the section, by the plane of the disc, of the pencil of rays proceeding from the
luminous object to the eye. Then, if 6 =the angle ACB, and ¢ = the time in
which the disc makes one revolution; the time in which the line AC revolves

from its present position to the position BC will evidently be s

Now, if a ray proceeding from any point in the luminous surface is just
emerging at F, the point from which it emanates will remain visible until A C

comes to the position BC, or during the time > . Since this is obviously true of

any other element of the surface, it follows that every part of the surface remains
visible for the same time.

The interval of time between the first appearance of the object and its final
disappearance is obviously greater than that during which each element of its
surface is visible. For, if E and D be sections of the rays proceeding from the
points in the luminous surface which are first and last visible, some part of the
surface will be seen during the interval of time between the instant in which C B
coincides with CE, and that in which AC coincides with CD, or during the time
in which the line AC revolves through the sum of the angles ECD, ACB. De-

noting ECD by A, this time will be Z whe ,
If the luminous object is won and the axis of the pencil of rays proceed-
ing to the eye is perpendicular to the plane of the disc, putting
s=the radius of the luminous circle,
d=its distance from the eye,
d’=the distance of the disc from the eye,
c=the distance of the axis of the pencil of rays from the centre

of the disc, it will be found that A\=2 sin — ; and therefore the time which
elapses between the first appearance and the final disappearance of the luminous
circle, is

oq (2sin 15 ane + 0)

From this expression it will be seen that the time during which the eye re-

es

PLATE A, Royal Soe. trans. Edin. Vol. XU p. 5 84:

Weare ne a

* Projection of observations of the brightness of impressions, with the times during which light acted on the eye .

O16 0102 0:0
Time during which light acted on the eye

je iS. ol Ee SS Sa eS AE ee |
25 0108 01065 0.04

a eee |
WEAK. Johnston, Fatt

LUMINOUS IMPRESSIONS ON THE EYE. 585

ceives light at each revolution of the disc may be varied, by altering the diameter of
the luminous circle, or its distance from the eye, or from the disc, or by changing
the distance of the pencil of transmitted rays from the centre of the disc. But
in the experiments to be afterwards described, these elements remained constant,
and the effect was modified only by altering the angles of the sectors, or the rate
of revolution of the discs. It may, however, be proper to observe that, as the time
during which each element of the surface remains visible is independent of the
magnitude of the luminous object; so also, as might be anticipated, the apparent
brightness of the surface is independent of the ratio which the portion visible at
once through the sector bears to the whole area. For, in repeating the same ex-
periments with circular luminous objects of different diameters, while the angle
of the sector and the velocity of the disc were constant, it was found that the
apparent brightness of the luminous circle was not sensibly affected by varying
its diameter.

In order to compare the brightness of the impressions produced by light
seen through the sectors of revolving discs, in the manner now described,
with its brightness when seen by uninterrupted vision, the following arrangement
was devised, which, for the sake of convenient reference, may be termed a
selaometer (from «Aas, brightness), to indicate its use in measuring the brightness
of luminous impressions. This apparatus, represented in Fig. 2, is supported on
a stout plank AB. AC and BD are screens with circular apertures C, D, an inch
in diameter, to which are fitted pieces of ground glass, cut from the same plate,
in order to secure similarity of surface. The apertures C, D, are illuminated by
the gas-burners, L, S,* which are supplied by flexible tubes, so that their dis-
tances from the screens can be varied at pleasure by sliding their supports M, M,
along the plank A B, in a groove cut in it for that purpose. An axis EH, carry-
ing the disc I K, revolves between conical points in supports, one of which EF is
seen in the figure. This axis is put in motion by a band passing over the pulley
Q, and over a wheel driven by means of a winch; and it is made of sufficient
length to admit of a second disc revolving in front of the screen AC simultaneously
with the disc IK. The brightness of the apertures in the screens is observed by
means of a rectangular prism of glass NO, placed half-way between them, with
its faces inclined at angles of 45° to the line CD joining their centres. By this
means the light passing through the apertures, and dispersed by the ground-
glass, is reflected from the faces of the prism to the eye at P, and the images of
the apertures being seen in apparent contact, as represented at C’, D’, their rela-
tive brightness can be compared with great nicety.;+ The driving-wheel is made

* The gas-light used in all the experiments described in this paper, was that of coal-gas

burned by a No. 2 swallow-tail jet. It will be seen that the numerical results, afterwards obtained,
do not depend on the absolute brightness of this light,

+ Screens covered with black paper, which are not represented in the figure, were used to pro-
tect the eyes from the action of extraneous light, and also to intercept any rays, whose influence might
have otherwise affected the accuracy of the experiments.

VOL. XVI. PART V. 7N

586 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

to revolve in time with a metronome adjusted to beat seconds; so that, by ascer-
taining the number of revolutions which the pulley, Q, makes during each revolu-
tion of the driving-wheel, the time of asingle revolution of the disc is readily de-
termined. This time multiplied by the ratio of the arc of the sector to the whole
circumference of the disc, gives the length of each luminous impression. Thus,
if the driving-wheel revolves m times in a second, and the disc times during
each revolution of the driving-wheel, the time of revolution of the disc, ex-

pressed in seconds, is seal: and if 6 be the angle of the sector, the time during
which the eye receives light from each element of the luminous surface at every

P een, 6
revolution of the disc is Tee

In order to compare the brightness of the aperture D, seen by uninterrupted
vision, with its brightness as seen during the revolution of the disc, the illumina-
tion of the apertures is first made equal by varying the distance of the flame L
from the screen AC, until both apertures seen by reflexion in the prism appear
equally bright. When the disc is then made to revolve, the apparent brightness
of the aperture D immediately diminishes, and the equality of the brightness of
the apertures is again restored by withdrawing the light L, to a greater distance
from the screen AC.* Since the distance of the light S, from the screen B D, re-
mains constant during this operation, the ratio of the apparent brightness of the
aperture D, seen by uninterrupted vision, to its apparent brightness during the
revolution of the disc, will be that of the square of the distance of the light L, from
the screen A C, before the disc has begun to revolve, to the square of its distance
during the revolution of the disc. For since the intensity of the light incident on
the face O, of the prism is constant, we may conceive that face of the prism as the
source of light of a constant intensity. Let 6,=the apparent brightness of this
light seen by uninterrupted vision; b,=its apparent brightness seen during the
revolution of the disc. Then if 7=the intrinsic brightness of the flame L, d, and
d, its distances from the screen before and during the revolution of the disc, a,
the ratio of the brightness of the light transmitted by the glass in the aperture
C’, to that incident upon it, and 7, the ratio of the brightness of the reflected light
to the light incident upon the face N, of the prism; the apparent brightness of the

aperture C, when the light L, is at the distance d,, will be a and at the dis-
1

ari

ay

of both apertures is made equal, we have

tance d, its apparent brightness will be Now since the apparent brightness

* This is conveniently done by means of a pulley and cord. When the apertures are being made
equally bright before the dise is made to revolve, it is necessary that the aperture D should be fully
exposed. Where the sector is too narrow to admit of the whole aperture being seen at once, another
sector is cut in the dise for this purpose, which admits of being closed by a slider of pasteboard be-
fore the disc is made to revolve.

LUMINOUS IMPRESSIONS ON THE EYE. 587

ard

2 2
Ceres
6, ant x

d,?

It has here been assumed that the brightness of the gas-flame remains con-
stant during the experiment, a condition which is not fulfilled in practice, owing to
the variable pressure of the gas in the pipes. It is probable, however, that the
brightness of both flames will vary nearly in the same proportion, so that the
distances necessary to equalise the apparent brightness of the apertures in the
screens will remain almost unaltered ; and it is obvious also, that any residual
error, arising from a gradual change in the brightness of the flames, will be nearly
eliminated by taking the mean of a series of observations immediately succeeding
each other, and conducted in the manner now described.

Il. Proof of the Gradual Action of Light on the Eye.

If a disc, with a sector of a small angle, is made to revolve between the eye
and a luminous object, a flash of light is seen at each revolution ; but as the velo-
city of rotation increases, the brightness of the flashes diminishes, which shews
that the apparent brightness of a luminous object diminishes as the time during
which it is visible becomes shorter. A similar result is obtained by placing two
discs with sectors of different angles before the screens of the selaometer, and
observing the relative intensity of the simultaneous flashes of light when the discs
are made to revolve. It will always be found that although the apertures in the
screens are equally bright, when seen by uninterrupted vision, the disc whose
sector has the greater angle produces the brighter flash. Now as both discs re-
volve with the same velocity, the length of the luminous impressions will be pro-
portional to the angles of the sectors; so that, by this experiment also, the ap-
parent brightness of the light is shewn to increase with the time during which it
continues to act upon the eye. A convenient selascope, which exhibits this phe-
nomenon in a striking manner may be made by causing a disc with a sector of
the form EF GH (Fig. 4), to revolve before a luminous aperture. The flash pro-
duced by the wide part of the sector E F, greatly exceeds in brightness that pro-
duced by the narrow part G H.

The experiment of causing a disc, with a sector cut in it, to revolve before a
luminous aperture, also affords a simple proof of the duration of luminous impres-
sions on the retina. At about seven revolutions in a second the luminous impres-
sion becomes continuous, so that the aperture always appears visible, even during
the dark interval between the successive passages of the sector between it and the
eye; but a considerably higher velocity, about twenty revolutions in a second,
is required in order to produce a sensibly uniform impression. These velocities
are not meant to be stated with great exactness. They were obtained by experi-

088 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

ments with discs having sectors varying from 60° to 7°30’, and did not appear to
differ very sensibly in different cases ; but it seems probable that the velocity re-
quired to produce a continuous or a uniform impression should be sensibly af-
fected by greatly altering the angle of the sector.

Ill, Effect of combined Luminous Impressions on the Eye.

So long as the rotation of the disc is so slow as to allow each flash to be seen
separately, the brightness of the flashes diminishes as the velocity of rotation
increases, until, at about twenty revolutions in a second, the flashes become
blended into a nearly uniform impression. Whenever this takes place, no
farther increase of the velocity of the disc diminishes the intensity of the impres-
sion in the smallest perceptible degree. This result is evidently produced by the
increased number of luminous impressions in a given time compensating for their
diminished intensity; but it is remarkable that the one effect should so exactly
compensate for the other. Having found that this compensation took place at
velocities varying from twenty to forty revolutions in a second, I was anxious to
ascertain whether it continued unimpaired at higher velocities. For this purpose
a disc of pasteboard 4:5 inches in diameter, with a sector of 2° 30’ cut out of its
margin, was fitted to the axle of a clockmaker’s wheel-cutting engine. It was
found by a previous careful trial, that the disc made exactly 100 revolutions for
each revolution of the driving-wheel; and as the latter, at its greatest velocity,
made thirteen revolutions in ten seconds, the disc ought to have revolved 130 times
inasecond. But to avoid the chance of errors arising from the driving-bands slip-
ping at so high a velocity, I availed myself of Professor WHEATSTONE’s Ingenious
method of ascertaining the velocity of a rapidly-revolving axle, described in his
paper in the Philosophical Transactions for 1834, to which I have already re-
ferred. This consisted in observing the pitch of the note produced by the rapid
percussion of a pin, fixed in the revolving axle, upon a piece of paper held in con-
tact with it. The highest note produced during the experiment was rather less
than an octave below C of the tenor clef, which corresponds to above 128 vibra-
tions ina second. This result agrees almost exactly with the calculation founded
on the observed rotation of the disc at low velocities; and it may, therefore, be
concluded, that the disc made above 128 revolutions in a second. Since the are
of the sector was ;4q of the circumference, the light from a luminous point placed
behind the disc would, at each revolution, act on the eye for only 7433 of a second.
A lighted candle being placed behind the disc, the machine was put in motion, and
the velocity gradually increased until the driving-wheel made thirteen revolutions
in ten seconds, after which it was allowed to come to rest spontaneously. It was
found that the brightness of each successive flash diminished as the velocity of
the disc increased, until the impression on the eye became uniform, at a velocity of

LUMINOUS IMPRESSIONS ON THE EYE. 589

about twenty revolutions in asecond. After this no increase of velocity, up to 128
revolutions in a second, produced the slightest farther diminution of the apparent
brightness of the light; and again, as the speed diminished the light continued
uniformly bright, until the motion became so slow as to allow the eye to perceive
the impressions separately, after which they gradually increased in intensity until
the disc stopped. The same experiment was repeated, substituting for the flame
of the candle an illuminated aperture in a screen, covered with tissue paper. The
apparent brightness of this aperture, when the disc revolved, was compared, in the
manner already described at p. 585, with that of another similar aperture seen by
uninterrupted vision, and the result was perfectly in accordance with that ob-
tained in the previous experiment. The same phenomena were also observed
when a disc with a sector of 30° was substituted for that with a sector of 2° 30 .*

A similar result was obtained by varying the form of the experiment, in the
following manner :—Two discs, one with a sector of 30°, and the other with two
sectors of 15°, suchas ABCD, abcd (Fig. 4), at opposite extremities of its dia-
meter, were placed in the selaometer, and made to revolve simultaneously. In
both discs the ratio of the duration of the flashes to that of the dark intervals,
is obviously the same; but when the discs revolve simultaneously, for each flash
produced by the disc with the sectors of 30°, there are two flashes of half the
duration produced by the disc with two sectors of 15°. The disc with two sec-
tors of 15°, revolving at a given velocity, is, therefore, precisely identical in its ac-
tion to the disc with a single sector of 30° revolving at double the velocity. The
apertures in the screen being made equally bright before the discs revolved, the
equality of their brightness remained unaltered when the discs revolved so rapidly
as to produce a uniform impression upon the eye. In the same manner, the
brightness of the apertures remained equal when any disc, in the first part of
the following table, revolved simultaneously with the corresponding disc in the
second part, at such a velocity as to produce a uniform impression on the eye.
——<—<$<$<

Number of Sectors.t Angle of Sectors. Number of Sectors. Angle of Sectors.

2 15° 1 30°
4 7° 30’ 1 30°
2 7° 30 1 15°
2 30° 1 60°
3 30° 1 90°
4 30° 1 120°

In all these cases, the duration of each flash was inversely as the number of

* I was enabled to make this experiment by the kindness of Mr ALgxanper Bryson, who,
along with Mr Joun Turnsutt, W.S., witnessed the results above described.
+ In all experiments in which the discs had more than one sector, the sectors were arranged
round the circumference at equal distances from each other.
VOL. XVI. PART V. 70

590 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

flashes in a given time; and these experiments, therefore, confirm the result ob-
tained by varying the velocity of a disc with a sector of a given angle. We may..
therefore, infer, |

lst, That if the number of flashes, in a given time, succeeding each other so
rapidly as to produce a uniform impression on the eye is inversely as the duration
of each flash, their aggregate effect on the eye will be constant.

2dly, This compensation of the diminished intensity, by the increased fre-
quency of the flashes, is independent of the interval of time betweeen each im-
pression, within the limits of the observations; that is, with intervals varying from
goth to zgth of a second.

3dly, The effect is also independent of the ratio of the duration of the lumi-
nous to that of the dark intervals.

It is thus shewn that, after a uniform impression is produced, increasing the
number of flashes in a given time, compensates for their diminished intensity.
This naturally leads to the inquiry, at what rate would the brightness of the
resulting impression increase with the number of flashes in a given time, sup-
posing the intensity of the flashes to remain constant? In order to ascertain the
connexion between the number of flashes of a given intensity in a given time, and
the intensity of their combined effect on the eye, I made the following experi-
ments :—

1. Two discs, one with a sector of 15°, and the other with two equidistant
sectors of 15°, as ABCD, abcd, Fig. 4, were placed in the selaometer, and the
screens were equally illuminated by carefully adjusting the distances of two simi-
lar spermaceti candles placed behind them. When the discs were made to re-
volve so rapidly as to produce a uniform impression, a second candle placed be~
hind the screen, whose disc had a single sector of 15°, restored the equality of the
apparent brightness of the apertures, and a similar rest was obtained when
discs with single sectors of 30° and 7° 30’, were compared with discs having two
sectors of the same angles.

2. To vary the experiment, the flame of a gas burner was placed 10 inches
behind the screen, whose disc had two sectors of 30,° and a similar flame was ad-
justed behind the screen, whose disc had a single sector of 30°, so as to illuminate
the apertures in the screens equally. When the discs revolved rapidly, the flame
behind the disc with two sectors was withdrawn to 14:1 inches (10 / 2): so as
to halve the intensity of the light incident on the screen, and the illumination of
the apertures appeared to be perfectly equal. In like manner, when the light was
first placed at 20 inches from the screen, after the discs revolved, the screens
seemed equally illuminated when it was withdrawn to 28-2 inches.

3. A disc with a single sector of 7 30, and another with two sectors of the
same angle, were placed in the selaometer. The illumination of the screens was
then made equal by adjusting the distance of the light behind the disc with two

LUMINOUS IMPRESSIONS ON THE EYE. 591

sectors. The distance of this light was noted, and, when the discs revolved ra-
pidly, the light was withdrawn until the apertures seemed again equally bright.
The degree in which the brightness of the light required to be diminished, by with-
drawing the flame from the screen, in order to equalise the brightness of the im-
pressions produced by the two discs, was taken as a measure of the ratio of the
brightness of those impressions when the screens were equally illuminated. Four
experiments were made, and, as formerly, putting ¢,, and d, to denote the dis-
tances of the light from the screen before and after the disc had been made to
revolve, and ¢ to denote the ratio of the apparent brightness of the apertures seen
during the revolution of the discs when their illumination was actually equal, the
mean values of those quantities was found to be

d, =13°82; d,=2013; @=2-122.
In a second set of four experiments,

d,=4:075 ; d,=5'95; 9=2°132.

4, When a disc with three equidistant sectors of 7° 30’ was compared with

a disc having a single sector of 7° 30’, the mean of four experiments gave
d,=14:15; d,=24175; 9 =2:920.
In other four experiments,
d,=41; d,=715; o=3-041.

5. A disc with two sectors of 30°, compared four times with a disc having a

single sector of 30°, gave

d,=4:05; d,=61; 9=2-269.
and a second set of four experiments,

d,=13-95; d,=20; 0=2°056.

6. A disc with four sectors of 30°, compared four times with a disc having a

single sector of the same angle, gave

d,=3-95 ; dy=7-925; 0 = 4-026,
and a second trial of four experiments,

@,=141; ¢d,=29°-4; Q =4:348.

In all these experiments, the discs revolved so rapidly, as to produce a uni-
form impression on the eye, but the equality of illumination, when once obtained,
was not affected by increasing the velocity; and from the variation of the quan-
tity d, in the different experiments, it will be seen that the results are inde-
pendent of the intrinsic brightness of the light incident on the screen.

The following table exhibits the mean values deduced from experiments
No. 3 to No. 6 inclusive, and shews that the brightness of the impression pro-
duced by rapidly succeeding flashes of light of a given intensity, is sensibly pro-
portional to the number of flashes in a given time.

592 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

Number of Flashes in Brightness of
a Second. Impression.

In these experiments it is assumed, that when the light is withdrawn from the
screen, so as to diminish the intensity of its illumination, the brightness of a flash
of short duration will be diminished in the same ratio. This will only be true,
provided lights of different intensity produce impressions of proportional inten-
sity in equal times; but if it be afterwards proved, independently of these obser-
vations, that such is really the case, the conclusion which has now been drawn
from the experiments will be perfectly correct. In order to avoid this assumption,
the brightness of the impressions produced by the revolution of the different discs
was next compared with the impression of uninterrupted light.

1. A disc, with a single sector of 30°, was placed in the selaometer, with a gas-
flame at a constant distance of 6 inches from its screen. In order to render the
illumination of the screens equal, the other light had to be placed at a distance of
59 inches from the second screen. When the disc revolved 20 times in a second,
the latter light was gradually withdrawn until the apertures in the screens again
appeared equally bright. The distance of that light was now found to be 22-2 inches.
This experiment, eight times repeated, gave the following mean values :—

d, = 578; d, = 22-21; 6, = 006773.

where 6, denotes the brightness of the impression produced during the revolution
of the disc. In like manner, a disc, with two sectors of 30°, treated in precisely
the same manner, gave the following mean values of eight trials :—

d, = 561; d, = 15-22; 6, = 0-1859.

6, denoting the brightness of the impression produced by the revolution of this
disc. From this experiment, the ratio of the brightness of the impressions pro-

duced by the revolution of the two discs, or os will be found to be 2°006.
if

2. A disc, with three sectors of 30°, was compared with direct light in the
same manner. The mean of eight experiments gave

d, = 561; d, = 12-11; 6,= 0-2164.

From which the ratio of the brightness of the impression produced by means
of this disc, with three sectors, to that produced by means of the disc with a single

(Dees
sector, or 9 is 3°169.

LUMINOUS IMPRESSIONS ON THE EYE. 593

3. The mean of a similar set of experiments made with two discs, one having
asingle sector, and the other two sectors of 15°, gave 2 = 2:099.

4. Two discs, one having a single sector, and ie other two sectors of
7 °30' were compared, and it was found that 2 = 1°851.

1
The results of the experiments in the last four sections are shewn in the ac-

companying Table.

Number of Brightness
Flashes in a of Impres-
Second. sion.
20 1-000
40 2-006
40 1-851
60 3°169

In this table, as in the last, the corresponding numbers in the opposite columns
will be seen to be almost exactly proportional ; and both sets of experiments there-
fore, lead to the following results :-—

1. The brightness of the impression produced by equal flashes of light, which
succeed each other so rapidly as to produce a uniform impression on the eye, is
exactly proportional to the number of flashes in a given time.

2. Within the limits of the different velocities of the discs in the experiments,
the effect of the combination of the flashes is not sensibly affected by the length
of the dark intervals between them.

3. With the same limitation, the effect is also independent of the time of
duration of the flashes.

IV. On the connexion between the apparent Brightness of Light and the time during which

at continues to act on the Eye.

It has thus been proved that the brightness of the impression produced by
rapidly succeeding flashes of light is proportional to the number of flashes in a
given time, provided the brightness of the flashes remains constant. Hence, if a
rapidly revolving disc, with a sector of a given angle, has its velocity doubled,
and, consequently, the number of flashes produced by it in a given time also
doubled, if the brightness of the flashes remains unaltered, the brightness of the
impression produced by them will be twice as great as at first. But, instead of
the brightness of the impression increasing, it has been found to continue un-
changed, notwithstanding the increased velocity. It is, therefore, evident that
when the velocity of the disc is doubled, and, consequently, the duration of each
flash is half as great as at first, its brightness is also half as great as at first.
Thus, if the disc first revolves 20 times in a second, and then 40 times in a second,

VOL. XV i. PART V. (EP

594 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

the intensity of the impression is precisely the same in both cases. But at the
velocity of 40 revolutions in a second, there are twice as many flashes in a given
time as there are at the first velocity; and if the brightness of the flashes was
the same as at the first velocity, the brightness of the impression produced by
them would be doubled. Since, therefore, the impression, instead of being doubly
bright, remains the same as at first, each flash at 40 revolutions in a second must
only be half as bright as at 20 revolutions in a second. In like manner, by sup-
posing the velocity increased to 80 revolutions in a second, it might be shewn
that the brightness of the flashes is again halved. But the effect of doubling the
velocity is to halve the duration of the flashes, therefore the brightness of the flashes
is proportional to their duration. This law of vision may be thus stated: When
light of a given intensity acts on the eye for a short space of time, the apparent
brightness of the luminous impression on the retina is exactly proportional to the
time during which the light continues to act. From the velocities of the discs,
and the angles of the sectors used in the experiments, it will be seen that this
law is true for impressions lasting from -1., to of a second; and it will

18432 “" 120
presently be shewn to be true for impressions of longer duration.

V. Observations of the apparent Brightness of Luminous Impressions of short duration.

In almost all the experiments hitherto described, the phenomena of vision
which have been investigated have been derived from the observation of the
aggregate effect of luminous impressions succeeding each other so rapidly as to
produce a continuous impression on the eye. It is obvious, that such expe-
riments afford no information regarding the absolute brightness of the sepa-
rate impressions which are thus blended together. I adopted the indirect
mode I have now described of ascertaining the connexion between the duration
and apparent brightness of luminous impressions, from an apprehension of the
difficulty of comparing the brightness of a constant light with that of an isolated
flash. But repeated trials satisfied me that my fears were groundless; and the
succeeding experiments prove that, with a little practice, the eye is perfectly capa-
ble of making this comparison. Such experiments cannot, however, be long con-
tinued without fatiguing the eye, and a considerable effort of attention is re-
quired for their successful performance.

In order to find the intensity of separate impressions of short duration, I
used a disc of wood two feet in diameter, revolving once in a second; so that a
sector, whose arc had a known ratio to the circumference of the disc, passed at
each revolution before the aperture in one of the screens of the selaometer. In
this manner, a series of perfectly isolated impressions was obtained; and the
intensity of each could be compared with that of a light seen by continuous
vision in the manner already described. The different sectors were cut in paste-
board, and placed over an aperture in the disc. The following experiments were
made :—

LUMINOUS IMPRESSIONS ON THE EYE. 595

1. The fixed light was placed six inches behind the screen before which the
disc revolved. The sector had an angle of 0° 27’, or 34, of the circumference of
the disc; and the disc revolved once in a second. To equalise the brightness of
the apertures in the screens, when both were seen by continuous vision, the light
behind the second screen was placed at a distance (d,) of 5:3 inches. But,
when the disc revolved, this light had to be withdrawn to a distance (d,) of 46:3
inches. This experiment was repeated ten times, with the following mean
results: d,=5:11; d,=50'29; and the brightness of the flashes 6 =0:0103, the
brightness of the light seen by continuous vision, being unity.

2. A sector of 0°54’, or 4. of the circumference, was next used, and ten

400
experiments made as before, from which

d, = 5:23; d,= 35°24 and 6=0:022.
3. With a sector of 1° 48’, or ,3, of the circumference,
d,=5:19; d,=23'52; 6=0-0487.
4. With a sector of 3° 36’, or ;3, of the circumference,
d,=4:9; d,=15-08; 6=0-1056.
. With a sector of 7° 12’, or 2, of the circumference,
d,=5'13; d,=11-3; 6=0-2061.
6. With a sector of 15°, or 3, of the circumference,
d,=5:02; d,=764; 6=0-4317.

or

With each sector, the mean of ten results was taken; and at each successive
trial, the flame was alternately drawn from the screen, or pulled towards it in
equalising the apparent brightness of the apertures in the screens. The following
Table contains the results of these experiments, the brightness of the light seen
by continuous vision being expressed by unity :—

Duration of Flash} Brightness of
in Seconds. Impression.

0:00125 0:0103
0:00250 0:0220
0:00500 0:0487
0:01000 0-1056
0:02000 0:2061
0:04167 0:4317

The results of these experiments are shewn in fig. 3, where the observed
intensities of the light, denoted by small circles, are projected with the corre-
sponding times during which it acted on the eye; and it will be observed, that the
line a ¢ 6, shewing the increase of the apparent brightness of the object, with the
time during which it remains visible, is very nearly straight; which proves that

596 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

within the limits of the observations the brightness of the light increases in exact
arithmetical proportion with the time during which it acts on the eye. Since the
observed intensities of the lights when projected, as in the figure, are all nearly
included in a straight line passing through the origin, it may naturally be in-
ferred, that the impression of light commences at the instant of its incidence
on the retina. This conclusion is strengthened, when it is recollected that the
preceding experiments prove that light, which is incident on the eye only IP
of a second, produces a distinct impression, while, according to Professor WHEat-
STONE, less than the millionth part of a second is necessary for this effect. It has
also been proved (see p. 594), that up to ;,1,, of a second, the impression produced
by light is proportional to its duration. It seems, therefore, highly probable, that
from 0” up to 0:05, the brightness of a luminous impression is exactly proportional
to the teme during which the light has acted on the eye.*

These experiments, therefore, confirm, in a very satisfactory manner, the
inference which has already been drawn from the previous investigation, as the
observed intensities of the flashes are very nearly proportional to their duration ;
while, at the same time, they exhibit the actual numerical ratio of the apparent
brightness of a flash of a certain duration, to that of the light which preduces it
acting continuously on the eye.

VI. The time required for the complete production of Luminous Impressions is independent

of the apparent intrinsic brightness of the light.

The following series of experiments was made partly to confirm the result al-
ready obtained ; but more especially in order to ascertain whether the time re-
quired for the complete development of luminous impressions varies with the
brightness of the light by which they are produced. In this set of experiments, the
same sectors were used as in the last ; and the circumstances were identical, except
that the fixed light was placed 8°5 inches (64/ 2) from the screen, so that the
brightness of the incident light was reduced to half its former intensity. The fol-
lowing Table exhibits the mean of ten observations with each sector; the bright-
ness of the light seen by continuous vision, being expressed by unity.

Duration of Brightness of
Flash. Flash.

0-00125 0-0130

0:00250 0:0275
0-00500 0:0508
0:01000 0:0991
0:02000 0:2240

* In an experiment made since this paper was read, I have found that the same law extends to
impressions lasting for ~,th of a second, of which the observed brightness was 06118.

:
ik

LUMINOUS IMPRESSIONS ON THE EYE. 597

In fig. 3, the line ae contains the projections of these observations, which are
denoted by crosses ; and it nearly coincides with the line a 6, containing the projec-
tions of the observations in the last Table, shewing that the ratio of the brightness
of an impression of given duration to that of the absolute brightness of the light
which produces it, is almost exactly the same in both sets of experiments. On
thus comparing the apparent intensities of the flashes exhibited in the above Table
with the similar results in the preceding one, it will be seen that although the ab-
solute intensity of the light is only half as great as formerly, the time required for
the propagation of the luminous impression on the eye remains unaltered ; while
both sets of experiments prove that the brightness of a luminous impression caused
by a light of given intensity is proportional to the time during which the light
acts on the eye.

On repeating the experiment with the sector of th of the circumference, re-
volving once in a second, with the fixed light 24 inches from the screen, the mean
of ten trials gave

d, = 22-27; d, = 48-46; 6 = 0-2112.

The ratio of the apparent brightness of the flashes to that of the light seen
by continuous vision is, in this case, almost exactly the same as in the preceding
experiments, as will be seen from the following comparative view :—

Time during which | Xatio of the bright-
Distance of | Intensity of aera 7 ness of Flashes
y Light acted on

Light. Light. the Hye. to that of the Light
seen continuously.

6:0 1:0000 0”:02 0:2061
8:5 0-5000 0”-02 0:2240
24:0 0:0625 0”:02 0.2112

The conclusion to be derived from these results will be distinctly apprehended
by reference to fig. 3, where the ordinates e/, cf, and df, represent the ap-
parent intensities of the lights shewn in the above table. In order to pre-
vent misunderstanding, it is necessary to observe, that although the absolute
brightness of the lights used in the three experiments given in the table are in
the ratio of the numbers 1, 2, and 16, they are all represented in the figure by
the same line ag; and since the lines ef, cf, df, are nearly equal, they may be
regarded as having the same ratio to ag, the slight differences between them ob-
viously resulting from errors of observation. It thus appears that after an inter-
val of ath of a second, the three lights of very different intensity have all pro-
duced the same portion of their total effect on the eye; the impression in each case
having nearly 1th of the absolute brightness of the light.

Lights of different intensity, therefore, produce like portions of their total effect

VOL. XVI. PART y. iQ

098 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

on the eye in equal times ; from which it obviously follows, that the brightness of
an impression on the eye increases nith a rapidity exactly proportional to the bright-
ness of the light which produces it.

This conclusion seemed so remarkable, that I determined to try whether the
direct light of the sun produced a given portion of its impression on the eye with
no greater rapidity than ordinary artificial light. For this purpose I made use of
a selaometer, represented in fig. 5, where K L represents a plate of brass with
two apertures A B, 4th of an inch in diameter, and half an inch distant. A plate
of ground glass is placed before the apertures, and behind the aperture B, a
tube B C is fixed, in which is placed a Nicow’s polarizing prism. A longer tube
BD, is fitted so as to turn freely upon the outside of the tube C D, and another
Nicow’s prism is placed in its further extremity, so that, by turning round the
tube B D, the illumination of the aperture B can be varied at pleasure. A disc
EF, with a sector of 7° 30 revolves rapidly in front of the plate, by means of the
band HI passing over the pulley G, so as to project beyond the aperture A, which
is only visible when the sector passes before it at each revolution of the disc.* The
apertures were first illuminated by gas-light, and the disc being made to revolve
so rapidly as to produce a continuous impression, the apparent brightness of the
apertures was made equal by turning one of the prisms. When the apparatus
was next illuminated by the direct light of the sun at noon, and the disc made
to revolve so as to produce a uniform impression, the apertures were still equally
bright, although the position of the prisms remained unaltered. This experiment
was repeated several times with the same result, and a similar result was ob-
tained when moon-light was compared with gas-light. Now the effect of turning
round the prism is to diminish the brightness both of the sun-light and gas-light
in the same proportion. Since, therefore, the two apertures were always equally
bright, it follows, that the apparent brightness of the aperture behind the revolv-
ing disc, had also, in both cases, the same ratio to that of the light seen by unin-
terrupted vision. But the ratio of the apparent brightness of the aperture behind the
revolving disc to that of the direct light, evidently depends on the rapidity with
which the light acts on the eye at each passage of the sector before the luminous
aperture. Hence it is obvious, that if the sun-light and gas-light required dif-
ferent times to produce like portions of their total effect on the eye, the apparent
brightness of the fiashes produced by the revolving disc would have different ratios

* By means of this arrangement, the brightness of the impressions produced during the revolu-
tion of the disc, can be compared with the light transmitted through the aperture B. Since the in-
tensity of a ray of polarized light when transmitted through a doubly-refracting crystal, varies as the
square of the cosine of the inclination of the principal section of the crystal to the plane of polariza-
tion of the ray ; by attaching an index to the tube B D, so as to measure the angle through which it
has been turned, the intensity of the transmitted light might be estimated, and thus the brightness
of the impressions produced by the revolving disc might be determined. (See Supplément au Traité
de la Lumiére de Sir J. F. W. Herscner. Par A. QuerExer, p. 595.)

LUMINOUS IMPRESSIONS ON THE EYE. 599

to that of the uninterrupted light, according as the apparatus was illuminated by
sun-light or by gas-light. Therefore, since it has been shewn that this was not the
case, it is evident, that the sun-light and gas-light produced similar portions of
their complete impressions on the eye with the same rapidity.

It has thus been proved, that, when light acts on the eye for short intervals
of time, the rapidity of the development of its impression is independent of its ac-
tual brightness ; and it seems highly probable that this law extends to the whole
time required for the complete production of luminous impressions. For, when
it has been found, that lights of very different intensity acting on the eye during
zoth of a second, all produce impressions, having almost exactly }th of the ab-
solute brightness of the lights, it seems natural to conclude, that they will also
produce their complete effect on the eye in exactly equal times.

I hoped to have been able in this paper to exhibit the results of some experi-
ments upon the intensity of impressions of short duration, repeated by different
individuals, in order to ascertain whether the rapidity of the production of visual
impressions varies much in different eyes. I have only obtained one comparison
of this kind, through the kindness of Mr AtexanpER Wattace, of the Royal Ob-
servatory, Edinburgh, who observed the impression produced on his eye by a disc
with a sector of 7° 30, revolving 20 times in a second. The following result is
the mean of three trials,

d, =4°39 ; d,=42°5 ; 6=0:01067.

The result of my own experiments gives b=0:0137 : which agrees very well
with Mr Wattace’s observations. I trust to be able to obtain some more com-
parisons of this kind, in order to ascertain whether the agreement between Mr
WALLACE’s result and my own is to be regarded as proving that visual impressions
in the eyes of different individuals, are propagated with nearly equal rapidity.

VII. On the time which Light requires to produce a full impression on the Eye.

I have found, by means of a disc revolving once in a second (see p. 594), that
impressions produced by a light acting on the eye for 1th of a second, have very
nearly the same brightness as the light seen by continuous vision ; but that when
light acts on the eye for a shorter time, its apparent brightness is sensibly di-
minished. As the brightness of the impression produced by light increases by in-
sensible degrees, until, at length, it attains its full intensity, it is obviously al-
most impossible, by direct observation, to assign the exact instant when this
takes place. The experiments in Sections V. and VI. have proved, that, up to 1th
of a second, the brightness of a luminous impression is strictly proportional to the
time during which light has acted on the eye, and also, that the impression produced
iN zAoth of a second, has almost exactly jth of the brightness of a full impres-

600 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

sion. If this proportionality between the duration and the apparent brightness of a
light be supposed to extend beyond the limits of the experiments, so as to include
nearly the whole time required for the production of a complete impression, it
would obviously follow that light requires about th of a second to produce its
full effect on the eye; and this conclusion, it will be observed, agrees with the
result of direct observation.

The following inferences may be derived from the laws of vision which
have now been investigated.

1. Personal Equation in Astronomy.

It is well known, that different observers assign different times to the occur-
rence of the same astronomical phenomenon ; as, for example, the passage of a
star across the meridian wire of a transit instrument. The correction to be ap-
plied to reduce the observations, or personal equation, as it is termed, frequently
amounts to a considerable quantity.

It might at first be supposed, that this discrepancy between the results of
different observers, may be occasioned by light acting on their eyes with unequal
degrees of rapidity. But on considering the manner of observing the transit of a
star, it will appear that this explanation is insufficient. In order to estimate the
exact time at which the star passes one of the wires, the observer endeavours to
recollect the position of the star on one side of the wire, at the instant when he
heard the clock beat. At the next beat of the clock, the star has passed to the
other side of the wire; and the observer then, by the eye, subdivides into equal
parts the space between the positions occupied by the star at the successive beats
of the clock, and estimates how many of those parts are contained in the interval
between the wire and the first position of the star. The magnitude of that interval
estimated in this manner, determines the fraction of a second to be added to the
time given by the clock. If, then, the discrepancy between the results of different
observers is to be regarded as a phenomenon of vision, it must depend upon some
cause which displaces the image of the star, and thereby alters its apparent dis-
tance from the wire. Now as the star passes across the field of the telescope, its
light falls successively upon different parts of the retina, illuminating each portion
for a very small space of time ; and if light acted on the eye of one observer more
rapidly than on that of another, the obvious consequence would be that the
image of the star would appear brighter to the person whose retina was most
quickly impressed by light. The only other effect which the gradual action of
light on the eye seems capable of producing, is to render the advancing edge
of the image of the star so faint, owing to the extremely short time during
which its light acts on the eye, as to become imperceptible when contrasted with
the succeeding parts of the image: for these fall upon points of the retina over

LUMINOUS IMPRESSIONS ON THE EYE. 601

which a portion of the image has already passed, and on which the light has had
time to develop a distinct impression. In this manner, it may be conceived, that
the breadth of the image will be diminished on the side towards which it moves,
while it will be increased on the other side by the persistence of the impression
of light on the eye; and, consequently, the image of the star will appear behind
its true position. It is obvious, however, that the retardation of the advancing
edge of the image cannot exceed the breadth of the extremely minute disc with
which a star appears in a good telescope, otherwise it would amount to a total
extinction of the light; and, on the other hand, the image cannot be prolonged
by the persistence of its impression on the retina, by a greater quantity than its
advancing edge is retarded, without becoming perceptibly elongated. Any dif-
ference in the amount of retardation due to such causes, in different eyes, must
therefore be confined within extremely narrow limits, and seems quite inadequate
to account for the personal equation which, in some instances, amounts to a large
fraction of a second.*

2. Rays of Light of diferent Refrangibility act on the Eye with the same rapidity.

In the observations made with a rapidly revolving disc, where each flash lasted
only zs435 of a second, not the slightest alteration in the colour of the luminous
object was perceptible. The blue part of a gas flame, indeed, became invisible ; but
this was evidently due to the great reduction of the intensity of the light render-
ing the blue rays incapable of producing a sensible impression on the eye, already
affected by the more luminous rays. From this it follows, that rays of light of
different refrangibility act on the eye with equal rapidity. For if we suppose some
of the rays which constitute white light to act on the eye more rapidly than
others, the effect of shortening the luminous impressions would be quite analogous
to that produced by the interposition of some medium, such as red glass, which
absorbs the rays unequally; and the eye would be affected with the complemen-
tary colour of the deficient rays.

That there is no sensible difference in the rapidity of the action of lights of
various colours on the retina, appears also from the fact, that when the eye is sud-
denly directed to a luminous object, the first impression of its colour remains
afterwards unaltered. This could not be always the case if there was any great
inequality in the rapidity with which the different rays produce their effect on
the eye. If, for example, we suppose the blue rays to act more rapidly than
the yellow rays, green objects would, at first sight, appear to have moré of a bluish
tinge than after the eye had continued to regard them for a short time.

* As my object here is simply to discuss the possibility of explaining the personal equation by
the gradual action of light on the retina, I have intentionally refrained from entering upon any ex-
planation of that phenomenon which may be derived from the supposition that time is required for
the transmission of impressions from the organs of sensation to the mind.

VOL. XV. PART, V. TR

602 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF

3. On the Difference between the Apparent and the Intrinsic Brightness of the Flash
produced by Electricity of high tension.

Professor WHEATSTONE, as was already noticed, has proved that the light of
electricity of high tension has a less duration than the millionth part of a second.
Now, since it has been shewn that lights of every intensity produce their impres-
sions on the eye in equal times,* and that the brightness of an impression is
exactly proportional to its duration ; it follows, that if the electric spark could be
made to last for the hundredth part of a second, which is 10,000 times its actual
duration, its apparent brightness would also be increased 10,000 times. But the
results already recorded (see Table, p. 595), shew that the apparent intensity
of light lasting for the hundredth part of a second scarcely exceeds a tenth of its
real intensity. Hence, if the duration of the electric spark could be prolonged so as
to render its light continuous, its apparent brightness would probably be increased
about 100,000 times.

From the nature of the experiments on which this conclusion is founded, it is
perhaps only strictly applicable to the case where the electric spark is seen by the
eye already acted on by light of moderate intensity ; for in other cases its apparent
brightness is no doubt greatly increased by the contrast with previous darkness ;+
but however remarkable the conclusion may appear, it seems perfectly consistent
with the estimate of the intrinsic brightness of the electric spark, which arises
from reflecting on the extremely short space of time in which its powerful im-
pression on the eye is produced.

Dr Faraday observes, that “the beautiful flash of light attending the dis-
charge of common electricity, rivals in brilliancy, if it does not even very much
surpass, the light from the discharge of voltaic electricity ;’ + and again he states,
that when a battery of 15 jars was discharged through a wet string, “ the spark
was yellowish, flamy, and having a duration sensibly longer than if the water
had not been interposed.” Now the effect of discharging the battery through a
bad conductor, would be greatly to diminish the tension of the electricity, while
it augmented the duration of the spark. If, therefore, the intrinsic brightness
of the spark had remained the same as before, the intensity of the impression on
the eye should have been increased ; but the reverse seems to have been the case.
Hence it follows, that the brightness of the electric spark increases with the tension
of the electricity. A similar conclusion may obviously be derived from a compa-

* The electric spark is a light whose intensity places it undoubtedly within the limits of the
experiments on this point, as its brightness is inferior to that of sun-light. According to Sir Jonn
Herscuet, the lime-ball light appears only as a black spot on the disc of the sun when held between
it and the eye.—(See Treatise on Astronomy, Larpner’s Cyclopedia, p. 210. London, 1835.)

I have observed that, in like manner, the spark produced by a strongly-charged Leyden phial,
is absolutely invisible when it passes between the eye and the sun’s disc.

+ See Light. Encyclopedia Metropolitana, Art 58.

{ Experimental Researches in Electricity, vol. 1., sec. 333. Lond. 1839.

LUMINOUS IMPRESSIONS ON THE EYE. 603

rison of the nearly instantaneous electric spark of high tension, with the apparently
continuous light of voltaic electricity. For since the latter light, notwithstand-
ing its sensible duration, does not appear brighter than the former, it must
obviously be greatly inferior in intrinsic brightness.

It may now be useful to recapitulate the principal results of the experiments
described in this paper.

1. When the eye receives a succession of flashes of equal duration from
a light of constant intensity, which succeed each other so rapidly as to produce a
uniform impression, the intensity of this aggregate impression will also be con-
stant, provided the number of flashes in a given time varies inversely with the
duration of each.

2. The brightness of the impression produced by flashes of light of a given
intensity, which succeed each other so rapidly as to produce a uniform impres-
sion on the eye, is proportional to the number of flashes in a given time.

3. When light of a given intensity acts on the eye for a short space of time,
the brightness of the luminous impression on the retina is exactly proportional to
the time during which the light continues to act. This law has been proved to
be true for impressions lasting from ;,4,, to i, of a second.

4. The intensity of the impression produced by light which acts on the eye for
169 Of a second is almost exactly th of the apparent brightness of the light
when seen by uninterrupted vision ; and the time required for light to produce its
full effect on the eye seems to be about 3th of a second.

5. Lights of different intensities produce their complete impressions on the
eye in equal times, so that the light of the sun requires the same time as common
artificial light to produce its impression on the eye.

6. The brightness of an impression on the eye increases with a rapidity
exactly proportional to that of the light by which it is produced.

7. Rays of different refrangibility act on the eye with equal rapidity.

8. The apparent brightness of the spark produced by electricity of high ten-

sion is only about zgdg00th of what its apparent brightness would become if its

duration were prolonged to 75th of a second; and the brightness of electric light
increases with the tension of the electricity.

PROCEEDINGS

OF THE

EXTRAORDINARY GENERAL MEETINGS,

LISTS OF MEMBERS ELECTED AT THE ORDINARY MERTINGS,

SINCE NOVEMBER 25, 1844.

VOL, DVL. PART V-.

PROCEEDINGS, &.

OOO

Monday, November 25, 1844.

At a Statutory General Meeting, held for the purpose of appointing Office-Bearers for
the ensuing Session, The Right Honourable Earl CaTHcaARtT, Vice-President, in the Chair,
the Ballot was taken in the usual way, and the following Gentlemen were declared to be

duly elected, viz. :—

Sir T. Maxpoveart BrisBane, Bart., President.
Sir Witt1am Miter, Bart.,
Sir Davip Brewster, K.H.,
Earl Catucart,
Very Reverend Principal Lez,
Sir Gzorce 8. Mackenziz, Bart.,
Right Reverend Bishop Terror,
Professor Forses, General Secretary. —
Davip Mitnz, Esq.,
Dr Grecory,
Joun Russet1, Esq., Treasurer.

Vice-Presidents.

} Ordinary Secretaries.

Dr Traitz, Curator of Library.
Joun Srark, Esq., Curator of Museum.

COUNSELLORS.
Dr ParneLt. Dr Craicte.
Dr Carson, Professor Minter.
Sir Jonn M‘Nerit. Professor PILLANs.
Sir Tuomas D. Lauper, Bart. Professor KELLAND.
Azan Stevenson, Esq. Dr Curistison.
James T. Greson-Cratc, Esq. Dr Ner11.

Dr CHRISTISON, as acting General Secretary, read the following Resolution from the
Minutes of the Council :—“ 18th November 1844.—The Council unanimously resolved, That it
was expedient to allow a Salary of £100 annually to the General Secretary, on the understanding
that the duties of the Office should, henceforth, include the charge of publishing the Society's
Proceedings, and that the proposed arrangement should be considered as an experimental

608 PROCEEDINGS OF GENERAL MEETINGS,

one, which might be altered in the event of its not being found to answer the Council’s ex-
pectations, or of the Society’s funds proving inadequate.” Dr CHRISTISON having explained
the views which had led the Council to this opinion, Lord Murray moved, seconded by
James L’Amy, Esq., That the Resolution of the Council be adopted by the Society ; which
motion was agreed to by the meeting, with one dissentient.

On the motion of the Treasurer, the Council-Committee on the Funds were appointed to
audit his accounts.

Mr RUSSELL moved, seconded by Dr GREVILLE, That the Royal Society, in consideration
of the able and efficient manner in which Dr CHRISTISON, in the absence of Professor FORBES,
has, during the last twelvemonth, discharged the duties of General Secretary to the Society,
hereby tender their warmest thanks to him for these and all his other valuable services.
This motion being carried unanimously, Earl CATHCART conveyed the thanks of the Society
to Dr CHRISTISON.

(Signed) C. H. Tarrot, V.P.

Monday, November 24, 1845.

At a Statutory General Meeting, Right Reverend Bishop TERROT in the Chair, the fol-
lowing Office-Bearers were duly elected :—

Sir T. M. Brispane, Bart., G.C.B., President.
Sir Witi1am Mitter, Bart.,
Sir D. Brewstsr, K.H.,
Very Reverend Principal Lez,
Sir G. S. Mackenziz, Bart.,
Right Reverend Bishop Trrror,

Vice- Presidents.

Dr CuristTIson,

Professor Forses, General Secretary.
D. Ming, Esq., g ; :

Me Cecone: ecretaries to Ordinary Meetings.
Joun Russet, Esq., Treasurer.

Dr Trar11, Curator of Library.

JoHN Stark, Esq., Curator of Museum.

COUNSELLORS,
Azan STEVENson, Esq. Dr NEItt.
J. T. Greson-Cratc, Esq. Dr FLeMine.
Dr CRaiciz. Mr Aopte,
Professor MILER. Lord Murray.
Professor KELLAND. Dr Brunton.
Professor PrnLans. G. Forszs, Esq.

The following Committee was appointed to audit the Treasurer’s accounts :—

Sir H. Jarpine. James Gipson-Cratc, Esq. Georce Forges, Esq.

AND LIST OF MEMBERS ELECTED. 609

Part of the Minute of Council of the 19th November having been read. relative to the
Salary of the General Secretary, it was moved by Dr MAcLAGan, “ That the Royal Society
having considered the recommendation of the Council of the 19th November, that the Salary
of £100 should be continued to Professor FORBES, as General Secretary, unanimously approve
of the said recommendation, and resolve that the said Salary of £100 shall be continued to
Mr Forsss ;” which motion having been seconded by Mr CADELL, was unanimously
agreed to.

It was farther moved and seconded, and unanimously agreed to, That, in conformity to a
recommendation by the Council, the name of JAMES SKENE, Esq. of Rubislaw, now returned
from the Continent, shall (if agreeable to him) be replaced in the list of Fellows of the

Society.
(Signed) G. S. MackEnzizn, V.P.

Monday, November 23, 1846.

At a Statutory General Meeting, Sir G. S. MAcKENzIE, Bart., V. P., in the Chair, the
following Office-Bearers were duly elected :—

Sir T. Maxpoucatt Brispane, Bart., G.C.B., G.C.H., President.
Sir D. Brewster, K.H.,
Right Hon. Earl Carucart,
Very Rev. Principal Lez, ? ;
Sir Gzeorce S. Mackenzin, Bart., Beersieeetent,
The Right Rev. Bishop Trrrot,

Dr CuristIson,

Professor Forses, General Secretary.

Davip Mitnz, Esq., : . ;

De Ceo Secretaries to the Ordinary Meetings.
Joun Russexz, Esq., Treasurer.

Dr Traitt, Curator of Library and Instruments.

Joun Stark, Esq., Curator of Museum.

COUNSELLORS.
Professor KELLAND. Rev. Dr Brunton.
Professor PILLANs. Grorce Forses, Esq.
Dr NEILL. W. A. Cavett, Esq.
Rey. Dr FiLEmine. Sir Wo. Scort, Bart.
A. Avie, Esq. Dr J. H. Barrour.
Hon. Lord Murray. Henry Marsuatt, Esq.

On the motion of Sir G. S. MACKENZIE, it was resolved, unanimously, That the name of
Earl CatTucaRtT be replaced according to his former standing in the List of Vice-Presidents.
The following gentlemen were named a Committee to audit the Treasurer’s Accounts :—

Gerorce Fores, Esq. D. Smitu, Esq. J. T. Gisson-Craie, Esq.

The Meeting then adjourned.
(Signed) C. H. Terrot, V.P.

VOL. XVI. PART V. 77

610 PROCEEDINGS OF GENERAL MEETINGS,

Monday, November 22, 1847.

At a Statutory General Meeting, Bishop TERROT in the Chair, the following Office-
Bearers for the ensuing Session were duly elected :—

Sir T. Maxpovueatt Brispane, Bart., G.C.B., G.C.H., President.
Sir D. Brewster, K.H.,
Right Hon. Earl Carucart,
Very Rev. Principal Lzz, Srifioeaals aiate
Sir Georce S. Mackenzie, Bart., :
Right Rev. Bishop Tzrror,

Dr CurisTIson,

Professor Forzes, General Secretary.

Dep Prete Secretaries to the Ordinary Meetings.
Dr GREGORY,

Joun Russert, Esq., Treasurer.

Dr Trart1, Curator of Library and Instruments.

Joun Srark, Esq., Curator of Museum.

COUNSELLORS.
A. Apis, Esq. Dr J, H. Barrour.
Hon. Lord Murray. Henry Marsuatt, Esq.
Rev. Dr Brunton. Sir Wn. Jarpine, Bart.
GzorGE Forszs, Esq. Prof. C. Piazzi1 Smytu.
W. A. Cavett, Esq. Rev. Dr Ropertson.
Sir Wo. Scorr, Bart. C. Macraren, Esq.

The following gentlemen were appointed to audit the Treasurer’s Accounts :—

GeorGce Forsess, Esq. Davip Smiru, Esq. James T. Greson-Craice, Esq.

The Meeting then adjourned.
(Signed) C. H. Terror, V.P.

Memorandum.—February 21, 1848.—At an Ordinary Meeting of the Royal Society, on
the 21st February, the following motion for a change of Law, was proposed by Mr RuSSELL,
Treasurer, the motion itself having been announced from the Chair on the 17th January, and
printed in the Billets of the 7th and 21st February, viz :—

“That Law IV. shall be altered, and stand as follows :—

“TV. The Fees of Admission of an Ordinary Non-Resident Fellow shall be £26, 5s.,
payable on his admission ; and in case of any Non-Resident Fellow coming to reside at any
time in Scotland, he shall, during each year of his residence, pay the usual Annual Contri-
bution of £3, 3s. payable by each Resident Fellow ; but after payment of such Annual Con-
tribution for eight years, he shall be exempt from any farther payment.”

The motion was seconded by Dr TRAILL, and was adopted.

(Signed) C. Hi. Terror, Vue:

AND LIST OF MEMBERS ELECTED. 611

Monday, November 27, 1848.

At a Statutory General Meeting, Right Rev. Bishop Tmrrot V-P., in the Chair, the fol-
lowing Office-Bearers for the ensuing year, were duly elected :—

Sir T. Maxpoveatt Brispane, Bart., G.C.B., G.C.H., President.
Sir D. Brewster, K.H.,
Right Hon. Earl Carucarr,
Very Rev. Principal Les,
Right Rev. Bishop TERxor,
Dr Curisrison,

Dr Atison,

Vice-Presidents.

Professor Fores, General Secretary.
Dr GREGORY

: Secretaries to the Ordinary Meetings.
Professor C. P. Smytu, eee : :
Joun Russexz, Esq., Treasurer,
Dr Trait1, Curator of Library and Instruments.

Joun Stark, Esq., Curator of Museum.

COUNSELLORS.
W. A. Cavett, Esq. C. Macuaren, Esq.
Sir Wm. Scort, Bart. D. Minne, Esq.
Dr J. H. Barrour. J. T. Grpson-Craie, Esq.
Henry Marsuatt, Esq. Dr Grorce WILSON.
Sir Wn. Jarpine, Bart. Sir Joun Macnernz, G.C.B.
Rev. Dr Rozerrson. James Datmanoy, Esq.

The following Committee was named to audit the Treasurer’s Accounts.

Dr NEILL. James T, Gisson-Craice, Esq. James Witson, Esq.

The Meeting then adjourned.

MEMBERS ELECTED.

January 6, 1845.

James AnpREw, M.D. Grorce Witson, M.D.

February 3, 1845.
Joun G. M. Burt, M.D. Tuomas AnpERson, M.D.

January 5, 1846.
A. Taytor, M.D., Pau. S. A. Pagan, M.D.

February 2, 1846.

Rev. Dr James RoBertson. ALEXANDER J. ApIE, Esq.

612 PROCEEDINGS OF GENERAL MEETINGS,

February 16, 1846.

WitiiaM Murray, Esq., of Henderland.

March 16, 1846.

GzroRGE TURNBULL, Esq. GzEorGE J. Gorpon, Esq.
Dr L. Scumrrz, Rector of High School.

December 7, 1846.

Cuar.es Prazzi Smytu, Esq., Professor of Astronomy.

January 4, 1847.
Gzorce Maxeitz, Esq.
Davip Gray, Esq., Professor of Nat. Philosophy, Marischal College, Aberdeen.

February 1, 1847.
Wittiam THomson, Esq., Prof. of Nat. Philosophy, Glasgow. J. H. Burton, Esq., Advocate.

March 1, 1847.

James Nicot, Esq., London.

April 19, 1847.

W. MacponaLp Macponatp, Esq., of St Martins. Rozsert Hanpysive, Esq., Advocate.
ALEXANDER CuristIz, Esq.

December 20, 1847.

Joun Wixson, Esq., Cirencester. Moszs StEvEN, Esq., of Bellahouston.

January 17, 1848.
James Top, Esq., W.S.

March 6, 1848.

Tuomas STEVENSON, Esq., C.E. James ALLAN, M.D., Haslar Hospital.
Joun Hatt Maxwext, Esq., Younger of Dargavel.

March 20, 1848.

Rev. Joun Hannan. Henry Davinson, Esq.

April 17, 1848.

Patrick Newsieeine, M.D. Witiiam Sway, Esq.

December 4, 1848.

Rev. Francis GARDEN.

December 18, 1848.

Patrick JAMES STIRLING, Esq.

AND LIST OF MEMBERS ELECTED. 613

January 2, 1849.

Wiiiam Srirxine, Esq., of Keir, D. R. Hay, Esq.
Joun Tuomson Gorpon, Esq., Sheriff of Mid-Lothian. Wit1am Tuomas Tuomson, Esq.
Rt. Hon. Anprew RutHERFuRD, Lord Advocate for Scotland. Honourable Lorp Ivory.

February 5, 1849.
Apam Anperson, Esq., Advocate.

February 19, 1849.

Wittram E. Ayroun, Esq., Professor of Rhetoric and Belles Lettres, University, Edinburgh.
W.#H. Lowe, M.D.

March 19, 1849.
Hon. B. F. Primrose. Joun Srenuouse, M.D., Glasgow.
Davin Anperson, Esq., of Moredun.
April 2, 1849.

W. R. Pirriz, M.D., Professor of Surgery, Marischal College, Aberdeen.
Right Hon. The Ear of Minto,

April 16, 1849.
Right Hon. The Earz of ABERDEEN. Right Hon. The Earx of Happineron.

VOL. XVI. PART VY. éU

Crean)

LIST OF THE PRESENT ORDINARY MEMBERS,

IN THE ORDER OF THEIR ELECTION.

Major-General Sir THOMAS M. BRISBANE, Bart., G.C.B., &., F.R.S, Lond.,
PRESIDENT.

Date of
Election.

1798 Alexander Monro, M.D.
1799 Robert Jameson, Esq., Professor of Natural Mistory.
1805 Thomas Thomson, M.D., F.R.S. Lond., Professor of Chemistry, Glasgow.
George Dunbar, Esq., Professor of Greek.
1807 John Campbell, Esq., of Carbrook.
Thomas Thomson, Esq., Advocate.
1808 James Wardrop, Esq.
Sir David Brewster, K.H., LL.D., F.R.S. Lond., St Andrews.
1811 Major-General Sir Thomas Makdougall Brisbane, Bart., G.C.B., G.C.H., F.R.S. Lond.
James Jardine, Esq., Civil Engineer.
J. G. Children, Esq., F.R.S. Lond.
Alexander Gillespie, Esq., Surgeon.
W. A. Cadell, Esq., F.R.S. Lond.
James Pillans, Esq., Professor of Humanity.
1812 Sir George Clerk, Bart., F.R.S. Lond.
1813 William Somerville, M.D., F.R.S. Lond.
1814 Sir Henry Jardine.
Patrick Neill, LL.D., Secretary to the Wernerian and Horticultural Societies.
Right Honourable Lord Viscount Arbuthnot.
John Fleming, D.D.., Professor of Natural Science, New College.
Alexander Brunton, D.D.
1815 Robert Stevenson, Esq., Civil Engineer.
Henry Home Drummond, Esq., of Blair-Drummond.
William Thomas Brande, Esq., F.R.S. Lond., Professor of Chemistry in the Royal
Institution.

Date of
Election.

1816

1817

1818

1819

1820

1821

1822

LIST OF ORDINARY MEMBERS. 615

Leonard Horner, Esq., F.R.S. Lond.

Henry Colebrooke, Esq., Director of the Asiatic Society of Great Britain.
Honourable Lord Fullerton.

Right Honourable Earl of Wemyss and March.

John Wilson, Esq., Professor of Moral Philosophy.

Alexander Maconochie, Esq., of Meadowbank.

Sir David James Hamilton Dickson, M.D., Clifton.

William P. Alison, M.D., Professor of the Practice of Physic.
Robert Bald, Esq., Civil Engineer.

Robert Richardson, M.D., Harrowgate.

Patrick Miller, M.D., Ezeter.

John Watson, M.D.

Right Honourable John Hope, Lord Justice-Clerk.

Sir Patrick Murray, of Simprim.

James Muttlebury, M.D., Bath.

Thomas Stewart Traill, M.D., Professor of Medical Jurisprudence.
Alexander Adie, Esq.

Marshall Hall, M.D., London.

Richard Philips, Esq., F.R.S. Lond.

Reverend William Scoresby, Hweter.

George Forbes, Esq.

Right Honourable David Boyle, Lord Justice-General.

James Keith, Esq., Surgeon.

Charles Babbage, Esq., F.R.S. Lond.

Thomas Guthrie Wright, Esq., Auditor of the Court of Session.
Sir John F. W. Herschel, Bart., F.R.S. Lond.

John Shank More, Esq., Professor of Scots Law.

Robert Haldane, D.D., Principal of St Mary's College, St Andrews.
Sir John Mead, M.D., Weymouth.

Dr William Macdonald.

Sir John Hall, Bart., of Dunglass.

Sir George Ballingall, M.D., Professor of Military Surgery.
Sir James M. Riddell, Bart., of Ardnamurchan.

Archibald Bell, Esq., Advocate.

John Clerk Maxwell, Esq., Advocate.

John Lizars, Esq., Surgeon.

John Cay, Esq., Advocate.

Robert Kaye Greville, LL.D.

Robert Hamilton, M.D.

A. R. Carson, Esq., LL.D.

James Smith, Esq., of Jordanhill, F.R.S. Lond.

William Bonar, Esq.

George A. Walker-Arnott, Esq., LL.D., Professor of Botany, Glasgow.
Very Reverend John Lee, D.D., Principal of the University.

616 LIST OF ORDINARY MEMBERS.

Date of
Election.

1822 Sir James South, F.R.S. Lond.
Lieutenant-General Martin White.
Walter Frederick Campbell, Esq. of Shawy/ield, M.P.
Sir W. C. Trevelyan, Bart., Nettlecombe, Somersetshire.
Sir Robert Abercromby, Bart., of Birkenbog.
Dr Wallich, Calcutta.
John Russell, Esq., P.C.S.
John Dewar, Esq., Advocate.

1823 Sir Edward F french Bromhead, Bart., A.M., F.R.S. Lond. Thurlsby Hall.
Captain Thomas David Stuart, of the Hon. East India Company’s Service.
Andrew Fyfe, M.D., Professor of Medicine and Chemistry, King’s College, Aberdeen.
Robert Bell, Esq., Advocate.

Captain Norwich Duff, R.N.
Warren Hastings Anderson, Esq.
Alexander Thomson, Esq. of Banchory.
Liscombe John Curtis, Esq., Ingsdon House, Devonshire.
Robert Christison, M.D., Professor of Materia Medica.
John Gordon, Esq., of Cairnbulg.
1824 Dr Lawson Whalley, Lancaster.
Alexander Wilson Philip, M.D., London.
Sir Charles Adam, R.N.
Robert E. Grant, M.D., Professor of Comparative Anatomy, Univ. Coll., London.
Rev. Dr William Muir, one of the Ministers of Edinburgh.
W. H. Playfair, Esq., Architect.
John Argyle Robertson, Esq., Surgeon.
James Pillans, Esq.
James Walker, Esq., Civil Engineer.
Sir William Newbigging, Surgeon.
William Wood, Esq., Surgeon.
1825 The Venerable Archdeacon John Williams.
W. Preston Lauder, M.D., London.
Right Honourable Lord Ruthven.
Sir William Jardine, Bart., of Applegarth.
Honourable Lord Wood.
1826 Sir David Hunter Blair, Bart.
John Stark, Esq.
Dr John Macwhirter.
1827 John Gardiner Kinnear, Esq.
James Russell, M.D.
Rev. Dr Robert Gordon, one of the Ministers of Edinburgh.
James Wilson, Esq.
Very Rev. Edward Bannerman Ramsay, A.M., Camb.
George Swinton, Esq.
1828 Erskine Douglas Sandford, Esq., Advocate.

LIST OF ORDINARY MEMBERS. 617

Date of
Election.

1828 David Maclagan, M.D.
Sir William Maxwell, Bart.
John Forster, Esq., Architect, Liverpool.
Thomas Graham, A.M., Professor of Chemistry, London University.
David Milne, Esq., Advocate.
Dr Manson, Nottingham.
William Burn Callender, Esq., of Prestonhall.
1829 A. Golyar, Esq.
William Gibson-Craig, Esq., M.P.
James Ewing, LL.D., Glasgow.
Duncan M‘Neill, Esq., Dean of Faculty.
Ven. Archdeacon Sinclair, Kensington. 4
Arthur Connell, Esq., Professor of Chemistry, St Andrews.
Bindon Blood, Esq., M.R.I.A.
James Walker, Esq., W.S.
William Bald, Esq., M.R.1.A.
1830 J. T. Gibson-Craig, Esq., W.S.
Archibald Alison, Esq., Sheriff of Lanarkshire.
Honourable Mountstuart Elphinstone.
James Syme, Esq., Professor of Clinical Surgery.
Thomas Brown, Esq., of Lanjine.
James L’Amy, Esq., Sheriff of Forfarshire.
Thomas Barnes, M.D., Carlisle.
1831 James D. Forbes, Esq., F.R.S. Lond., Professor of Natural Philosophy.
Right Honourable Lord Dunfermline.
Donald Smith, Esq.
Captain Sir Samuel Brown, R.N.
O. Tyndal Bruce, Esq., of Falkland.
David Boswell Reid, M.D., London.
T. S. Davies, Esq., A.M., Woolwich.
1832 John Sligo, Esq. of Carmyle.
James Dunlop, Esq., New South Wales.
James IF’. W. Johnston, A.M., Professor of Chemistry in the University of Durham.
William Gregory, M.D., Professor of Chemistry.
Robert Allan, Esq., Advocate.
Robert Morrieson, Esq., Hon. #.L.C. Civil Service.
Montgomery Robertson, M.D.
1833 Captain Milne, R.N.
His Grace the Duke of Buccleuch.
A. T. J. Gwynne, Esq.
David Craigie, M.D.
George Buchanan, Esq., Civil Engineer.
Sir John Stuart Forbes, Bart., of Pitsligo.
Alexander Hamilton, Esq., LL.B., W.S.
VOL. XVI. PART V. 7x

618 LIST OF ORDINARY MEMBERS.

Date of
Eection.

1833 Right Honourable Earl Cathcart.
1834 Mungo Ponton, Esq., W.S.
Isaac Wilson, M.D., F.R.S. Lond.
David Low, Esq., Professor of Agriculture.
Patrick Boyle Mure Macredie, Esq., Advocate.
John Davie Morries Stirling, Esq.
Thomas Jameson Torrie, Esq.
William Copland, Esq., of Colliston. .
John Steuart Newbigging, Esq., W.S.
John Haldane, Esq., Haddington.

1835 John Hutton Balfour, M.D., Professor of Botany.
William Sharpey M.D., Professor of Anatomy, University College, London.
Right Honourable Lord Campbell.
William Brown, Esq., F.R.C.S.
Reverend Edward Craig.
R. Mayne, Esq.

1836 David Rhind, Esq., Architect.
Archibald Robertson, M.D., F.R.S. Lond.
Sir J. Macpherson Grant, of Ballindalloch.
Alexander Gibson Carmichael, Esq.

1837 John Archibald Campbell, Esq., W.S.
John Scott Russell, Esq., A.M.
Charles Maclaren, Esq.
A. Smith, Esq., M.A. Camb., Lincoln’s Inn, London,
Richard Parnell, M.D.
Peter D. Handyside, M.D., F.R.C.S.

1838 William Nicol, Esq.
William Scott, Esq., H.EI.C. Service.
Thomas Mansfield, Esq., Accountant.
Alan Stevenson, Esq., Civil Engineer.

1839 James Auchinleck Cheyne, Esq., of Kilmaron.

David Smith, Esq., W.S.

Adam Hunter, M.D.

Rev. Philip Kelland, A.M., Professor of Mathematics.

Henry Marshall, Esq., Dep. Inspector-General of Army Hospitals.
William Alexander, Esq., W.S.

F. Brown Douglas, Esq., Advocate.

Lieutenant-Colonel Swinburne.

1840 Alan A. Maconochie, Esq., Professor of Civil Law, Glasgow.

Martyn J. Roberts, Esq.
Robert Chambers, Esq.
James Forsyth, Esq.

Sir John M‘Neill, G.C.B.
John Cockburn, Esq.

Date of
Election.

1840

1841

1842

1843

1844

1845

1846

LIST OF ORDINARY MEMBERS.

Sir William Scott, Bart., of Ancrum.

Right Rev. Bishop Terrot.

Robert Bryson, Esq.

Edward J. Jackson, Esq.

John Learmonth, Esq., of Dean.

John Mackenzie, Esq.

John Anstruther, Esq., W.S.

Colonel Morison, C.B., Madras Artillery.

John Miller, Esq., Civil Engineer.

George Smyttan, M.D.

James Dalmahoy, Esq.

James Thomson, Esq., Cevél Engineer, London.
John Davy, M.D., Inspector-General of Hospitals.
Robert Nasmyth, Esq., F.R.C.S.

Sir James Forrest, Bart., of Comiston.

James Miller, Esq., Professor of Surgery.

John Adie, Esq.

John Goodsir, Esq., Professor of Anatomy.

A. D. Maclagan, M.D., F.R.C.S.

John Rose Cormack, M.D., F.R.C.P., Putney.
Allen Thomson, M.D., Professor of Anatomy, Glasgow.
Joseph Mitchell, Esq., Civil? Engineer, Inverness.
Duncan Davidson, Esq., of Tulloch.

Andrew Coventry, Esq., Advocate.

John Hughes Bennett, M.D., F.R.C.P., Professor of Physiology.

D. Balfour, Esq., Younger of Trenaby.

Henry Stephens, Esq.

The Honourable Lord Murray.

Arthur Forbes, Esq., of Culloden.

J. Burn Murdoch, Esq., Advocate.

Archibald Swinton, Esq., Professor of Civil Law.
James Begbie, M.D., F.R.C.S.

James Y. Simpson, M.D., Professor of Midwifery.
David Stevenson, Esq., Ccvil Engineer.

Thomas R. Colledge, M.D., F.R.C.P.E.

James Andrew, M.D.

George Wilson, M.D.

John G. M. Burt, M.D.

Thomas Anderson, M.D.

A. Taylor, M.D., Pau.

8. A. Pagan, M.D.

Rev. Dr James Robertson, Professor of Divinity and Ecclesiastical History.

619

620

Date of

LIST OF ORDINARY MEMBE}

Election.

1846

1847

Alexander J. Adie, Esq., Civil Engineer.

William Murray, Esq., of Henderland.

George Turnbull, Esq.

George J. Gordon, Esq,

Dr L. Schmitz, Recor of High School.

Charles Piazzi Smyth, Esq., Professor of Practical Astronomy.

George Makgill, Esq., of Kemback.

David Gray, Esq., Professor of Natural Philosophy, Marischal College, Aberdeen.
William Thomson, Esq., M.A., Camb., Professor of Natural Philosophy, Glasgow.
J. H. Burton, Esq., Advocate.

James Nicol, Esq., Assistant Secretary of the Geological Society, London.

W. Macdonald Macdonald, Esq., of St Martins.

Robert Handyside, Esq., Advocate.

Alexander Christie, Esq.

John Wilson, Esq., Agricultural College, Cirencester.

Moses Steven, Esq., of Bellahouston.

1848 James Tod, Esq., W.S., Secretary to the Royal Scottish Society of Arts.

1849

Thomas Stevenson, Esq., C.E.

James Allan, M.D., Haslar Hospital.

John Hall Maxwell, Esq., Younger of Dargavel.

Rev. John Hannah, Rector of the Edinburgh Academy.

Henry Davidson, Esq.

Patrick Newbigging, M.D.

William Swan, Esq.

Rev. Francis Garden.

Patrick James Stirling, Esq.

William Stirling, Esq., of Keir.

John Thomson Gordon, Esq., Sheriff of Mid-Lothian.

Right Honourable Andrew Rutherfurd, Lord Advocate for Scotland.
D. R. Hay, Esq.

William Thomas Thomson, Esq.

Honourable Lord Ivory.

Adam Anderson, Esq., Advocate.

William EK. Aytoun, Esq., Professor of Rhetoric and Belles Lettres.
W. H. Lowe, M.D., Balgreen.

Honourable B. F. Primrose.

John Stenhouse, M.D., Glasgow.

David Anderson, Esq., of Moredun.

W. R. Pirrie, M.D., Professor of Surgery, Marischal College, Aberdeen.
Right Honourable The Earl of Minto.

Right Honourable The Earl of Aberdeen.

Right Honourable The Earl of Haddington.

LIST OF NON-RESIDENT AND FOREIGN MEMBERS,

ELECTED UNDER THE OLD LAWS.

NON-RESIDENT.

Sir James Macgrigor, Bart., M.D.
Richard Griffiths, Esq., Civil- Engineer.

FORHIGN.
Dr S. L. Mitchell, New York.

M. P. Prevost, Geneva.

LIST OF HONORARY FELLOWS.

His Majesty the King of the Belgians.

His Imperial Highness the Archduke John of Austria.
His Royal Highness the Archduke Maximilian.

His Royal Highness Prince Albert.

BRITISH SUBJECTS (LIMITED TO TWENTY, BY LAW X.)

J. C. Adams, Esq.,
G. B. Airy, Esq.,

St Johi’s College, Cambridge.
Greenwich.

Robert Brown, Esq., London.

Sir M. I. Brunel, Do.

Dr Faraday, Do.

Sir John Franklin, Do.
Professor Graham, Do.

Henry Hallam, Esq., Do.

Sir W. R. Hamilton, Dublin.

Sir John F. W. Herschel, Bart., Collingwood.
Sir William J. Hooker, Ken.
William Lassell, Esq., Starfield, Liverpool.
Dr Lloyd, Dublin.

Sir Charles Lyell, London.

Sir Roderick I. Murchison, Do.
Richard Owen, Esq., Do.

Sir W. E. Parry, Do.

Earl of Rosse, Pres. R.S. Lond., Parsonstown.
Rev. Dr Whewell, Cambridge.
William Wordsworth, Esq., © Rydal.

VOL. XVI. PART VY.

622 LIST OF HONORARY FELLOWS.

FOREIGNERS (LIMITED TO THIRTY-SIX.)

M. Arago, Paris.

M. Biot, Do.

M. de Hammer, Vienna.
M. de Humboldt, Berlin.

M. Gay-Lussac, Paris.

M. Agassiz, Neufchatel.
M. Audubon, United Staies.
Sir Henry Bernstein, Berlin.

M. de Buch, Do.

M. Cauchy, Paris.

M. de Charpentier, Bex.

M. Cousin, Paris.

M. Degerando, Do.

M. Charles Dupin, Do.

M. Ehrenberg, Berlin.

M. Elie de Beaumont, Paris.

M. Encke, Berlin.

M. Flourens, Paris.

M. Gauss, Gottingen.
M. Guizot, Paris.

M. Haidinger, Vienna.
M. Hansteen, Christiania.
M. Hausmann, Gottingen.
M. Jacobi, Konigsbera.
M. Lamont, Munich.
M. Leverrier, Paris.

M. Liebig, Giessen.
M. Melloni, Naples.

M. Mitscherlich, Berlin.

M. Miiller, Do.

M. Neander, Do.

M. Necker, Geneva.
M. Oersted, Copenhagen.
M. Plana, Turin.

M. Quételet, Brussels.
M. Gustav Rose. Berlin.

M. Schumacher, Altona.

M. Struve, Pulkowa.
M. Thenard, Paris.

M. Tiedemann, Heidelberg.

LIST OF FELLOWS DECEASED, RESIGNED, AND CANCELLED,

FROM JULY 1844 To 1849.

HONORARY FELLOWS.

M. Bessel, Konigsberg.
M. Alexandre Brongniart, Paris.
M. le Baron Berzelius, Stockholm.

ORDINARY FELLOWS DECEASED OR RESIGNED.

John Borthwick, Esq., of Crookston.
Dr George Cook.

Professor George Glennie.

Dr Robert Graham.

Professor Thomas Henderson.
Dr James Home.

James Hunter, Esq., of Thurston.
A. Kinnear, Esq.

Colonel Robertson Macdonald.
Sir D. Milne.

Rev. Dr Welsh.

Henry T. Witham, Esq.

Rev. Dr Bennie.

Dr John Clark.

William Rennie, Esq., W.S.
Claud Russell, Esq.

Dr John Thomson.

Sir William Miller, Bart., of Glenlee.
Hugh Murray, Esq.

Sir Archibald Campbell, Bart.
Dr A. Anderson.

His Grace The Duke of Argyll.
Captain D. Boswall, R.N.

Rey. Dr Chalmers.

Dr Davidson.

Sir G. Macpherson Grant.
Professor Macvey Napier.

James Nairne, Esq., W.S.

Rev. Dr Traill.

Sir Thomas Dick Lauder, Bart.
Sir George Stuart Mackenzie, Bart.
Sir Charles G. Menteath, Bart.
James Kinnear, Esq., W.S.

624

LIST OF MEMBERS RESIGNED AND ELECTIONS CANCELLED.

RESIGNATIONS.

William Burn, Esq.

Nicholas Grut, Esq.

A. Earle Monteith, Esq., Advocate.
James Stark, M.D.
Lieutenant-Colonel Low.

Robert Paul, Esq.

William Fergusson, Esq.

J. P. Muirhead, Esq., Advocate.

ELECTIONS CANCELLED.

J. Anderson, Esq., C. E.
W. Bell, Esq.

Dr Couper.

Dr W. Ferguson.
William Paul, Esq.

Dr Reid Clanny.

James Hamilton, Esq.
Dr Knox.

W. H. Norie, Esq.

( 625 )

LIST OF DONATIONS.

(Continued from Vol. XV., p. 722.)

December 2, 1844.

DONATIONS.

Transactions of the American Philosophical Society, held at Philadelphia, for Pro-
moting Useful Knowledge. Vol. ix., Part 1.

Bulletin de la Société Géologique de France. Tome xiii.

Memoirs and Proceedings of the Chemical Society. Parts 7, 8, 9.

Journal of the Statistical Society of London. Vol. vii., Parts 1, 2, 3.

Journal of the Asiatic Society of Bengal, 1843. No. 142.

Det Kongelike Danske Vindenskabernes Selskabs Naturvidenskabelige og Mathe-
matiske Afhandlingar. eels ix. and x.

A System of Mineralogy, comprising the most recent Discoveries. By J. D. Dana.

The Journal of Agriculture, and the Transactions of the Highland and Agricul-
tural Society of Scotland, 1844, July and October.

Scheikundige Onderzoekingen, gedaan in het Laboratorium der Utrechtsche Hooge-
school. Deel. ii., Stuk. 5.

Report of the Thirteenth Meeting of the British Association for the Advancement
of Science, held at Cork in August 1843.

The Eleventh Annual Report of the Royal Cornwall Polytechnic Society, 1843.

The Journal of the Royal Geographical Society of London. Vol. xiv., Part 1.

Proceedings of the Royal Astronomical Society. Vol. vi., Nos. 1-6.

The Electrical Magazine, conducted by Mr Charles V. Walker. Vol. i., No. 5.

Journal of the Asiatic Society of Bengal. No. 143.

Journal of the Bombay Branch Royal Asiatic Society. Nos. 5 and 6.

Annales des Sciences Physiques et Naturelles, d’Agriculture et d' Industrie, pub-
liées par la Société Royale d’Agriculture, &c., de Lyon. Tome vi.

Geologische Bemerkungen iiber die Gegend von Baden bei Rastadt. Von J. F. L.
Hausmann.

Mémoire sur le Daltonisme. Par Elie Wartmann.

Astronomische Nachrichten, herausgegeben von H. C. Schumacher.

Versuch einer objectiven Begrundung der Lehre von den drei Dimensionem des
Raumes. Von Dr Bernard Bolzano.

Magnetische und Meteorologische Beobachtungen zu Prag. Von Karl Kreil—
(vierter Jahrgang).

Astronomical Observations made at the Royal Observatory, Greenwich, in the
year 1842, under the direction of George Biddell Airy, Esq., M.A., Astro-
nomer-Royal. ,

VOL. XVI. PART V.

DONORS.
The Society.

The Society.
Ditto.
Ditto.
Ditto.

Ditto.
The Author.

The Society.
The Editors.

The Association.

The Society.
Ditto.
Ditto.

The Editor.

The Society.
Ditto.
Ditto.

The Author.
Ditto.

The Editor.

The Author.

Ditto.

Royal Observatory.

tod

626 LIST OF DONATIONS.

DONATIONS. DONORS.
Catalogue of the Places of 1439 Stars, referred to the 1st of January 1840; de- Royal Observatory.
duced from the Observations made at the Royal Observatory, Greenwich, from
1836, January 1, to 1841, December 31.

Proceedings of the Geological Society of London. No. 98. The Society.

Mémoires de la Société Géologique de France. (2™e Série). Tome i., 1'¢ Partie. Ditto.

Sixth, Seventh, and Kighth Letters on Glaciers. By Professor Forbes. The Author.

Proceedings of the Zoological Society of London. Nos. 120 to 134. The Society.

Abhandlungen der Konig]. Akademie der Wissenschaften zu Berlin aus dem Jahre The Academy.
1842.

Bericht iiber die zur Bekantmachung geeigneten Verhandlungen der Konigl. Preuss. Ditto.

Akademie der Wissenschaften zu Berlin. Juli 1843 bis Juni 1844.

Tijdschrift voor Natuurlijke Geschiedenis en Physiologie—Uitgegeven door J. van The Editors.
der Hoeven & W. H. D. Vriese, M.D. Deel. xi., St. 2.

Archief voor Geneeskunde. Uitgegeven door Dr J: P. Heije. Deel. iii., St. 4. | The Editor.

Het Instituut of Verslagen en Mededeelingen, uitgegeven door de vier Klassen van Royal Institute of
het K. Nederlandsche Instituut van Wetenschappen, Letterkunde en Schoone Holland.
Kunsten over den Jahre 1842, St. 4. 1848, St. 1, 2, 3.

Nieuwe Verhandelingen van het Bataafsch Genootschap, der Proefondervindelijke The Society.
Wijsbegeerte te Rotterdam. Deel. ix., St. 1, 2, 3.

Mémoire de |’Académie Impériale de Sciences de St. Pétersbourg—(Sciences ‘The Imperial

Politiques, &c.) Tome vi., Liv. 4, 5, 6. Tome vii., Liv. 1, 2, 3. Academy.
(Sciences Mathématiques. ) Tome , Liv. 4, 5, 6. Tome Vie, duiy: Ditto.
Recueil des Actes de la Séance Publique de I’ Académie Impériale de Seicnees de St. Ditto.

Pétersbourg, tenue le 29. Dec. 1843.
Nouveaux Mémoires de la Société Helvétique des Sciences Naturelles. Tomei.—vi. The Society.

Actes de la Société Helvétique des Sciences Naturelles. Ditto.
Verhandlungen der Schweizerischen Naturforschenden Gesellschaft bei ihrer Ver- Ditto.
sammlung zu Zurich, 1841.
zu Altdorf, 1849, Ditto.
Specimens of Printing-Types in the Establishment of Neill & Co., Printers, Edin: Messrs Neill & Co
burgh.

Comptes Rendus Hebdomadaires des Séances de l’ Académie des Sciences.. Tome The Academy.
xvill., Nos. 15-26, and Tome xix., Nos.. 1-16.
Maps of the Irish Ordnance Survey, containing the County of Limerick, 62 sheets. The Lord Lieu-
‘ tenant.

December 16, 1844.

Annuaire de ’Académie Royale des Sciences et Belles Lettres de Bruxelles, 1844. The Academy.

Bulletin de l’Académie Royale de Bruxelles. Tome x., Nos. 8-12. Tome xi., Ditto.
Nos. 1-8.

Mémoires Couronnées et Memoires des Savants Etrangers, publi¢es par |’ Académie Ditto.
Royale des Sciences et Belles Lettres de Bruxelles. Tome xvi.

Annales de l’Observatoire Royale de Bruxelles. Par A. Quételet. Tome iii. Ditto.

Annuaire de l’Observatoire Royale de Bruxelles. Par A. Quételet, 1844. The Author.

Recherches Statistiques. Par A. Quételet, Ditto.

Notices sur Pierre Simons, Alexis Bouvard, et Antoine Reinhard Falck. Par A. Ditto.
Quételet.

Bulletin'de la Societé Géologique de France. Tomei. Feuilles 28-33. The Society.

Novi Commentarii ee dora Scientiarum Instituti Bononiensis.. Vols. i., ii., iii., The Academy.
vee Vv.

Opere Edite et Inedite del eee Luigi Galvani, raccolte e pubblicate per cura The Academy.
dell’ Accademia delle Scienze dell’ Institute di Bologna.

On the Excision of the Eyeball in cases of Melanosis, Medullary Careinoma, and The Author.
Carcinoma, with Remarks by J. Argyll Robertson, M.D., F.R.S.E.

LIST OF DONATIONS.

DONATIONS,

January 6, 1845.

The Journal of Agriculture, and the Transactions of the Highland and Agricul-
tural Society of Scotland, for January 1845.

Arsberattelse om Zoologiens Framsteg under aren 1840-42. Af S. Loven.

Arsberittelse om Framstegen i Kemi och Mineralogi afgiven den 31 Mars 1844.
Af Jac. Berzelius.

Arsberittelse om Botaniska STESRE och Upptackter for ar. 1838.
Wikstrom.

Kongl. Vetenskaps-Academiens Handlingar, for ar. 1842.

Ofversigt af Kongl. Vetenskaps-Academiens Forhandlingar, 1844. Tes toms.

The Journal. of the Royal Asiatic Society. No. 15, Parts 1, 2.

Observations Météorologiques faites 4 N jjne-Taguileh (3 (Monts Oural) cies
de Perm. Année 1842. ;

Mittlere Oerter von 12,000 Fix Sternen, von Carl Rumker.

Af J. E.

Part 1, pp. 1247,

January 20.

Journal of the Royal Asiatic Society of Bengal. Nos. 144, 145.

On the Nature of the Nervous Agency. By James Stark, M.D., F.R.S.E.

Researches on the Brain, Spinal Cord, and Ganglia, with Remarks on the Mode
by which a continued flow of Nervous Agency is excited in, and transmitted
from, these Organs. By James Stark, M.D., F.R.S.E,

Philosophical Transactions of the Royal Society of London for 1844. .

Proceedings of the Royal Society of London. No, 59.

Magnetical and Meteorological Observations made at the Royal Observatory,
Greenwich, in the year 1842, under the direction of George Biddell Airy,
Esq., M.A., Astronomer-Royal.

Outlines of Oneeesee te the use of Students. By William Gregory, M.D.

February 3.

The Electrical Magazine, conducted by Mr Charles V. Walker, for October 1844.
Memoir of Francis Baily, Esq., D.C.L., Oxford and Dublin. By Sir John F. W.
Herschel, Bart.

Inest de Stella Lyre variabili Disquisitio. Per F. G. A, Argelander.

Description of Bones, &c., found near the River Ohio, 1786, with an Engraving,

and Observations on the Annual passage of Herrings.
From the Columbian Magazine, December 1786.
Three Volumes, in the Chinese Character, on Astronomy and Geography.

By Mr John Gilpin.

February 17.

List of Specimens of Birds in the Collection of the British Museum. Parts 1 and 3.
Accipitres, Gallinz, Gralle, and Anseres.

List of the Specimens of Lepidopterous Insects in the Collection of the British

_ Museum. | Part 1.

List of the Specimens of Myriapoda in the Collection of the British Museum.

Catalogue of the Tortoises, Crocodiles, and Amphibenians, in the Collection of the
British Museum.

The Electrical Magazine, conducted by Mr Charles We Walker... «Vol., 15, 0Nos"72

Tijdschrift voor Naturlijke Geschiedenis en Physiologie—Uitgegeven door J. van
der Hoeven, M.D., & W. H. de Vriese, M.D., Deel. xi. St. 3, 4.

Cast of the Bust of the late Professor Playfair, warn was executed by the late Sir
Francis Chantrey.

Fifteenth Report of the Scarborough Philosophical Bice,

DONORS.

The Society.

The Academy.
Ditto.

The Academy.

Ditto.
Ditto.
The Society.
Sir Thomas M.
Brisbane.
Ditto.

The Society.
The Author.
Ditto.

The Royal Society.
Ditto.
Ditto.

The. Author.

The Editor.

The Royal Astro-
nomical Society.
Ditto.

Anonymous.

Professor Forbes.

The Trustees of the
British Museum.
Ditto.

Ditto.
Ditto.

The Editor.
The Editors.

Sir George Mac-
kenzie, Bart.
The Society.

628 LIST OF DONATIONS.

DONATIONS.

March 3, 1845.

The Journal of the Royal Agricultural Society of England. Vol. v., Part 2.

Transactions of the Society for the Encouragement of Arts, Manufactures, and
Commerce. Vol. lv.

Memoirs and Proceedings of the Chemical Society. Part ii.

The Journal of Agriculture, and the Transactions of the Highland and Agricul-
tural Society of Scotland, for March 1845.

Fifteenth Report of the Scarborough Philosophical Society, for the year 1844.

March 17.

Anatomical and Pathological Observations. By John Goodsir, F.R.S.E., and
Harry D. S. Goodsir, M.W.S.
The American Journal of Science and Arts, conducted by Professor Silliman, for

January 1845.

April 7.

Scheikundige Onderzoekingen, gedaan in het Laboratorium der Utrechtsche Hooge-
school, 24 Deel. 64 Stuk.

The Journal of the Royal Geographical Society of London.
and Vol. xiv., Part 2.

The London University Calendar 1845.

Account of the Northumberland Equatorial Dome attached to the Cambridge Ob-
servatory.

Observations made at the Magnetical and Meteorological Observatory at Toronto
in Canada, printed by order of Her Majesty’s Government under the super-
intendence of Lieut.-Col. Edward Sabine, of the Royal Artillery.

Memoir of Thomas Henderson, Esq., Professor of Practical Astronomy in the Uni-
versity of Edinburgh. By Thomas Galloway, Esq.

The Grasses of Britain. Part 2. By Richard Parnell, M.D., F.R.S.E.

On the Chemical Constitution of the Bones of the Vertebrated Animals. By James
Stark, M.D., F.R.S.E.

Memoirs and Proceedings of the Chemical Society. Part 12.

The Fifth and Ninth Letters on Glaciers. By Professor Forbes, F.R.SS.L. & E.

On the Medicinal properties of Bebeerine. By Douglas Maclagan, M.D., F.R.S.E.

Remarks on the Improvements of Tidal Rivers. Dy David Stevenson, C.E.

On a possible explanation of the Adaptation of the Kye to distinct Vision at differ-
ent distances. By Professor Forbes, F.R.SS.L. & E.

Vol, xiii. Part 2,

April 21.
Journal of the Statistical Society of London. Vol. viii., Part 1.
The Electrical Magazine. Conducted by Mr Charles V. Walker.
Memoir of Francis Baily, Esq., D.C.L. Oxford and Dublin.
Herschel, Bart.
Bulletin de la Société de Géographie. (2me Série.) Tome xvi., xvii., xviii.
Comptes Rendus Hebdomadaires des Séances de |’ Académie des Sciences. Tome xix.,
Nos. 17-27. Tome xx., Nos. 1-11.

Vol. i., No. 8.
By Sir John F. W.

December 1.

Vestiges of the Natural History of Creation.

Report of the Fourteenth Meeting of the British Association for the Advancement
of Science, held at York, in September 1844.

De l’Influence Curative du Climat de Pau et des Eaux Minérales des Pyrenées.
Par M. A. Taylor, M.D.

A Catalogue of the Library of the Atheneum.

DONORS.

The Society.
Ditto.

Ditto.
The Society.

Ditto.

The Authors.

The Editor.

The Editors.
The Society.

The University.

Duke of Northum-
berland.

The British Go-

vernment.

The Author.

Ditto.
Ditto.

The Society.
The Author.
Ditto.
Ditto.
Ditto.

The Society.
The Editor.
The Author.

The Society.
The Academy.

The Author.
The Association.

The Author.

The Athenzum.

LIST OF DONATIONS.

DONATIONS.

The Transactions of the Royal Irish Academy. Vol. xx.

Journal of the Statistical Society of London. . Vol. viii., Parts 2, 3.

Memoirs and Proceedings of the Chemical Society. Parts 13, 15.

Outlines of Chemistry, for the Use of Students. Part 2. By William Gregory, M.D.

Geschiedenis der Ioden in Nederland. Door M. H. J. Koenen.

Over Het Onmatig Gebruik van Sterken Drank en de Middelen om Helzelve te
Keer te Gaan. Door A. W. F. Herckenroth.

Het Gebruik en Misbruik der Geestrijke Dranken. Door H. M. Duparc.

De Uitoefening de Geregtelijke Geneeskunde in Nederland. Door J. C. Van Den
Broecke.

Uitkomsten der Meteorologische Waarnemingen, gedaan te Utrecht, in de Jaren
1839-43.

Natuurkundige Verhandelingen van de Hollandsche Maatschappij der Wetenschap-
pen te Haarlem.

The American Journal of Science and Arts, conducted by Professor Silliman and
Benjamin Silliman jun., for April, July, and October.

A Physiological Essay on the Thymus Gland. By John Simon, Esq., F.R.S.

On the Comparative Anatomy of the Thyroid Gland. By John Simon, Esq., F.R.S.

Astronomical Observations made at the Royal Observatory, Greenwich, in the year
1843, under the direction of George Biddell Airy, Esq., Astronomer-Royal.

Reduction of the Observation of Planets, made at the Royal Observatory, Green-
wich, from 1750 to 1830; computed by order of the Lords Commissioners
of the Treasury, under the superintendence of George Biddell Airy, Esq.,
Astronomer-Royal.

Philosophical Transactions of the Royal Society of London for the year 1845. Pt. 1.

Proceedings of the Royal Society, 1844. No. 60.

Transactions of the Geological Society of London. (2d Series.) Vol. vii., Parts 1, 2.

Proceedings of the Geological Society of London. Nos. 99, 100, and 101.

Annuaire Magnétique et Météorologique du Corps des Ingénieurs des Mines de
Russie. Par A. T. Kupffer. 1842. Nos. 1, 2.

Etudes sur la Mortalité dans les Bagnes et dans les Maisons Centrales de Force et
de Corrections de France depuis 1822 jusqu’ a 1837. ParM.R.Chassinat,M.D.

Resultats des Observations Magnétiques faites 4 Genéve dans les années 1842 et
1848. Par E. Plantamour, Professeur d’ Astronomie a |’ Académie de Genéve.

Astronomische Nachrichten herausg. von H. C. Schumacher. Nos. 536, 537, 538.

The Electrical Magazine, conducted by Mr Charles V. Walker. Vol. ii., No. 9.

Journal of the Asiatic Society of Bengal, edited by the Secretary. Nos. 146 to 154.

Carte Géologique du Globe. Par M. A. Boué.

The Twelfth Annual Report of the Royal Polytechnic Society, 1844.

Address to the Ethnological Society of London, delivered at the Anniversary Meet-
ing. By Richard King, M.D.

Scheikundige Onderzoekingen, gedaan in het Laboratorium der Utrechtsche
Hoogeschool. Deel. iii., St. 1, 2.

Tijdschrift voor Natuurlijke Geschiedenis en Physiologie. Uitgegeven door J. Van
der Hoeven, M.D., & W. H. D. Vriese, M.D. Deel. xii., St. 1, 2.

On the Vision of Objects on and in the Eye. By William Mackenzie, M.D.

Journal of the Bombay Branch Royal Asiatic Journal. April and October 1843.

Bulletin de la Société de Géographie (2™¢ Série), Tomes xvi., xvii., xvili., xix.,
and xx.; and Tomes i., ii. (8™°® Série.)

Mémoires de la Société de Physique et d’Histoire Naturelle de Genéve. Tomex.,
tie. 2.

Moma della Reale Accademia delle Scienze di Torino. Vol. xxxix.

Handbuch der Mineralogie. Von J. F. L. Hausmann, Zweite Theil.

Transactions of the Zoological Society of London. Vol. ii., Parts 2, 3, 4, 5; and
Vol. iii., Parts 1, 2, 3.
VOL. XVI. PART V.

DONORS.
The Society.
Ditto.
Ditto.
The Author.

The Directors of
the Provincial
Society of Arts
and Sciences at
Utrecht.

The Society.
The Editors.

The Author.
Ditto.
The Royal Society.

Ditto.

The Royal Society.
Ditto.
The Society.
Ditto.
The Author.

Ditto.
Ditto.

Ditto.
Ditto.
The Society.
The Geological So-
ciety of France.
The Society.
The Author.

The Editors.
The Editors.
The Author.
The Society.
Ditto.
Ditto.
Ditto.
The Author.
The Society.

8 4

630 LIST OF DONATIONS.
DONATIONS.

Proceedings of the Zoological Society of London.

Abhandlungen der Konig. Gesellschaft der Wissenschaften zu Gottingen. Band 2,

Nieuwe Verhandelingen der Eerste Klasse van het Koninkl. Nederlandsche Instituut
van Wetenschappen, Letterkunde en Schoone Kunsten te Amsterdam. Deel. ii.

Annales des Sciences Physiques et Naturelles d’ Agriculture et d’Industrie, Publiées
par la Société Royale d’ Agriculture, &c., de Lyon. Tome vii.

Pilote Francais ; comprenant les Cotes Septentrionales de France depuis les Roches
de Porsal jusqu’ au Phare des Heaux de Brehat. 6™e Partie.

Pilote Frangais; Instructions Nautiques (Partie des Cotes Septentrionales de
France comprise entre la Pointe de Barfleur et Dunkerque et entre les Cas-
quets et la Pointe de Barfleur Environs de Cherbourg), Redigées par M. Givry.
2 Parties, 4to.

Proceedings of the Geological Society of London. No. 103.

Proceedings of the American Philosophical Society. Nos. 30 and 31.

A Public Discourse in commemoration of Peter S. Du Ponceau, LL.D., late Presi-
dent of the American Philosophical Society. By Robley Duglison, M.D.
Archeologia, or Miscellaneous Tracts relating to Antiquity, published by the So-
ciety of Antiquaries of London. Vols. i., ii., xi., xii., xiv., Xvi., Xvil., xviil.,
MIX.; MX, RKL., Mls, AKL, Rive RAV, RMS, KVL, RAVI.) ORES ome oO

Index.

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631

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VOL. XVI. PART. V. SB

633

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Address delivered at the opening of the New Hall of the Royal College of Physi-
cians, Nov. 27, 1846. By William Beilby, M.D., President. 8vo.

Journal of the Royal Asiatic Society. Vol. x., Part 2. 8vo.

Comptes Rendus Hebdomadaires des Séances de |’ Académie des Sciences. Tome xx.,
No. 12. Tome xxiv., No. 10. Ato.

On the Polarization of the Atmosphere (from Johnston's Physical Atlas), With a
Plate. One leaf folio.

Drawing Illustrative of a Geological Section on the Caledonian Railway, two miles
from Edinburgh. By Sir G. S. Mackenzie, Bart.

May 3.

Memoirs and Proceedings of the Chemical Society. Part 20. 8vo.

The American Journal of Science and Arts. Conducted by Professors Silliman
and J. D. Dana. For March 1847. 8vo.

On three several Hurricanes of the Atlantic, and their relations to the Northers of
Mexico and Central America, with notices of other Storms. By W. C. Red-
field. 8vo.

Proceedings of the American Academy of Arts and Sciences. May 26, 1846. 8vo.

The Fourteenth Annual Report of the R. Cornwall Polytechnic Society, 1846. 8vo.

Magnetical and Meteorological Observations made at the Royal Observatory, Green-
wich, in the year 1844, under the direction of George Biddell Airy, Esq.,
M.A., Astronomer-Royal. 4to.

December 6.

Annals of the Lyceum of Natural History of New York. Vol. iv., No. 67. 8vo.

Address delivered at the Anniversary Meeting of the Geological Society of London,
on the 19th February 1847. By Leonard Horner, V.P.R.S. 8vo.

Proceedings of the American Philosophical Society. Vol. iv., No. 34. 8vo.

Transactions of the American Philosophical Society, held at Philadelphia, for Pro-
moting Useful Knowledge. Vol. ix., Part 3.

A Treatise on Atmospheric Phenomena. By Edward Joseph Lowe, Esq. 8vo.

Annales de |’Observatoire Royale de Bruxelles. Tom. v.

Mémoires Couronnées et Mémoires des Savants Etrangers, par l’ Académie Royale
de Bruxelles. Tom. ix., 1845 et 1846; Tom. xx., 1846, 2 Part.;
Tom. xxi., 1846. 4to. Y

VOL. XVI. PART V.

637

DONORS.
The Academy.
The Institute.

Ditto.

The Author.
The Author.

The Author.
Ditto.

Royal College of
Physicians.

The Society.

The Academy.

The Author.

Ditto.

The Society.
The Editors.

The Author.
The Academy.

The Society.
Royal Society.

The Society.
The Author.

The Society.
Ditto.

The Author.

M. A. Quételet.
The Academy.

8c

638 LIST OF DONATIONS.

DONATIONS.
Nouveaux Mémoires de l’Académie Royale des Sciences et Belles Lettres de
Bruxelles. Tom xix. 4to.
Mémoires de |’Académie Royale des Sciences, des Lettres, et des Beaux Arts de
Belgique. Tom. xx. 8vo.

Bulletin de l’Académie Royale des Sciences, des Lettres, et des Beaux Arts de
Belgique. Tom. xiii. (compléte) et Tom. xiv., Nos. 1, 2, 3, 4, 5, 6. 8vo.

Bulletin de la Commission Centrale Satistique de Belgique. Ext. de Tom. iii., sur
les Anciens Recensements de la Population Belge, par M. Quételet; et la
méme livraison, De |’Influence du Libre Arbitre de |'Homme sur les Faits
Sociaux. Par M. A. Quételet. 8vo.

Bulletin de la Société, Impériale des Naturalistes de Moscou. Nos. 3, 4, (1846) ;
No. 1 (1847). 8vo.

Séance Extraordinaire de la méme Société, du 22 Février 1847. 8vo.

Berichte Uber die Mittheilungen von Freunden der Naturwissenschaften in Wien.
Von W. Haidinger. Band i., Nos. 1—6, und Subscriptions Liste. 8yo.

Bulletin der Konig]. Akademie der Wissenschaften zu Berlin. Nos. 1-77. 8vo.

Gelehrte Anzeigen, von der Akad. der Wissenschaften zu Berlin. Bde. 16-23. 8vo.

Abhandlungen der Mathematisch-Physikalischen Classe der Konig]. Bayerischen
Akademie der Wissenschaften. 4 Band. 3 Abtheilung, 4to.

Uber das Studium der Griechischen und Rémischen Alterthiimer.
von Lasaulx. 8vo.

Von Ernest

Uber die Ordealien bei den Germanen in ihrem Zusammenhange mit der Religion.
Von Georg Phillips. 8vo.

Die Uberbleibsel der Altegyptischen Menschenrace. Von Dr Franz Pruner. 8vo.

Almanach der Akademie der Wissenschaften zu Gottingen, fiir 1847. 8vo.

Annuaire de l’ Académie Royale de Belgique, 1846 et 1847. 8vo.

Annuaire de l’Observatoire Royale de Bruxelles. Par M. Quételet. 1847.

Journal of Agriculture, and Transactions of the Highland and Agricultural Society

of Scotland. No. 17 (July), and No. 18 (October) 1847. 8vo.
Journal of the Statistical Society of London. Vol. x., Part 3. 8vo.
Quarterly Journal of the Geological Society. No, 2 (August). 8vo.

Monthly Journal of Medical Science. No. 81 (September). 8vo.

Thirteenth Annual Report of the Royal Cornwall Polytechnic Society. 8vo.
Journal of the Royal Asiatic Society. Vol. x., Parts 2 and 3. 8vo.
Journal of the Asiatic Society of Bengal. Edited by the Secretary. Nos. 171,
172, 173. 1846. 8vo.
Do. do. Edited by the Secretaries. New Series. Nos. 174,

175, 176, and 181; with Supplementary Number published January 1847.
8yvo.

American Journal of Science and Arts. Conducted by Professors Silliman and
Dana. Second Series. Nos. 5, 8,9, 10,11. 8vo.

Philosophical Transactions of the Royal Society of London. Part 1, 1847. 4to.
Kongelike Danske Videnskabernes Selskabs Naturvidenskabelige og Mathematiske
Afhandlinger. Tolvte Deel. 4to.

Flora Batava. No. 147. to.

Handbuch der Mineralogie. Von J. F.L. Hausmann. 2 Theil. 8vo.

Astronomische Beobachtungen der Konig]. Universitats-Sternwirte in Kénigsberg.
Von F. W. Bessel. 19 und 21 Abtheilung. Fol.

Annales de la Société Royale d’Agriculture de Lyon. Tom. viii. 1845. to.

Recherches sur les Mouvements de Ja Planéte Herschel. Par M. Le Verrier.
1846. 8vo.

Ankuendigung und Probe einer Neuen Kritischen Ausgabe, und Neuen Ueberset-
zung der Syrischen Chronik, des Gregor Bar-Hebraeus. Von G. H. Bernstein.
1847. 8vo.

DONORS.
The Academy,

Ditto.
Ditto.

The Author.

The Society.

Ditto.
The Author.

The Academy.
Ditto.
Ditto.

The Author.
Ditto.

Ditto.
The Academy.
Ditto.
The Author.
The Society.

Ditto.
Ditto.
The Editor.
The Society.
Ditto.
The Editor.

The Editors.

Ditto.

The Society.
The Society.

The King of the
Netherlands.

The Author.
Ditto.

The Society.
The Author.

Ditto.

LIST OF DONATIONS.

DONATIONS.

Sur la Publication des Monuments de la Géographie. 8vo.

Satistique Générale. Rapport au Ministre de l’Intérieur sur les Travaux de la
Commission Centrale, et des Commissions Provinciales de Satistique. 4to.

Rapport sur les Travaux de l’Académie Royale des Sciences et Belles Lettres de
Bruxelles, pendant l’année 1842-43. Par A. Quételet. 8vo.

Rapport sur les Travaux et les Titres Scientifiques de M. Duponchel, lu a la Société
des Enfants du Nord. 2 copies. 8vo.

Bulletin des Séances de la Société Vaudoise des Sciences Naturelles. Nos. 14
et 15. 8vo.

Censura Commentationum Soc. Reg. Danice Scientiarum, anno 1846, ad premum
reportandum oblatarum.

Ofversigt dver det Kongelike Danske Videnskabernes Selskabs Forhandlinger, og

dets Medlemmers Arbeider i Aaret, 1846, af H. C. Orsted. 8vo.
On the Nucleus of the Animal and Vegetable ‘‘Cell.””’, By Martin Barry, M.D. 8vo.
Memoirs and Proceedings of the Chemical Society. Part 21. 8vo.
On the Origin of Continents. By James D. Dana.
Origin of the Grand Outline Features of the Earth. By James D. Dana. 8vo.
Greenwich Astronomical Observations. 1845. 4to.
Medico-Chirurgical Transactions. Vol. xili. 8vo.
Everest’s Measurements of the Meridional Arc of India. With Plates. 4to.

Results of Astronomical Observations at the Cape of Good Hope. By Sir
J. F. W. Herschel, Baronet. 8vo.

Researches for a Remedy against Communism. By Baron Dersenyis. 8vo.

Turner’s Chemistry. 8th Edition. By Liebig and Gregory. 8vo.

Description and Conquest of Ceylon. By Henry Marshall. 8vo.

Elements of General and Pathological Anatomy. 2d Ed. By David Craigie, M.D. 8vo.

Observations on the Famine of 1846-7 in the Highlands of Scotland and in Ivre-
land. By W. P. Alison, M.D. 8vo.

The Acts of the Parliaments of Scotland. Vol. i. (1124-1423.) Fol.

Acta Dominorum Concilli. Oct. 5, 1478 ad Nov. 15, 1495. Fol.

Acta Dominorum Auditorum. Oct. 9, 1466 ad Dec. 16, 1494. Fol.

Proceedings of the Royal Society. No. 67, 1846, and No. 68, 1847. 8vo.

Memorie della Reale Academia delle Scienze di Torino. Ser. Seconda. Tom. iii.,
1v., V., Vi. 4to.

Memoirs and Proceedings of the Chemical Society. Part 22. to.

Journal of the Statistical Society of London. Vol. x., Part 4. 8vo.

Observations on the Temple of Serapis. By Ch. Babbage. 8vo.

Bulletin de la Société de Géographie. 3ieme Série, Tome vii, 8vo.

Etudes d’Astronomie Stellaire. Par M. Struve. 1847. 8vo.

Die Cephalopoden des Salzkammergutes, aus der Sammlung Seiner Durchlaucht
Fiirsten Von Metternich. Von F. R. Von Hauer. 4to.

Journal of the Asiatic Society of Bengal. Nos. 178 and 179, for May and June
1847 ; and Index to Vol. xv. 8vo.

Proceedings of the Zoological Society of London. Nos. 155,177. 8vo.

Reports of Council and Auditors of the Zoological Society of London, for April
1847. 8vo.

A List of the Fellows, &c., of the Zoological Society of London, for April 1847.

Transactions of the Zoological Society of London. Vol. iii., Part 4.

A large Collection of Admiralty Charts of Great Britain.

639

DONORS.
The Author.
M. A. Quételet.

The Author.
The Society.
Ditto.

Ditto.
The Author.

Ditto.
The Society.
The Author.
Ditto.
Royal Society.
The Editor.
Directors of East
India Company.
The Duke of
Northumberland.
The Author.
The Editors.
The Author.
Ditto.
Ditto.

The Lords Com-
missioners of
the Treasury.

The Society.

The Academy.

The Society.
Ditto.

The Author.

The Society.

The Author.

Prince Metternich.

The Society.

Ditto.
Ditto.

Ditto.

Ditto.
The Lords Com-
missioners of the

Admiralty.

640 LIST OF DONATIONS.

DONATIONS.

December 20, 1847.

Emploi de I Airain a défaut du Fer chez la plupart des peuples des cing parties du
monde, &c. Notice intéressant les Peintres d'Histoire et les Archéolo-
giques, Extraite du livre intitulé, Découvertes dans la Troade. Par A. F.
Mauduit. 3 copies. 8vo.

Défense de feu Le Chevalier, et du feu Comte de Choiseul Gouffier contre M. P.
B. Webb. Par M. Mauduit. 4 copies.

Appendices du livre Découvertes dans la Troade, publié en 1840 par M. Mauduit ;
Défense de Le Chevalier et du Comte Choiseul Gouffier, &c. 4to.

Verhandlungen der Schweizerischen Naturforschenden Gesellschaft bei ihrer Ver-
sammlung zu Chur, 1844. 4to.

Actes de la Société Helvétique des Sciences Naturelles. Trentiéme Session. 4to.

Journal of the Asiatic Society of Bengal; Edited by the Secretaries. September,
No. 182. 8vo.

Scheikundige Onderzeekingen, gedaan in het Laboratorium der Utrechtsche
Hoogeschool. 4de Deel, 4de Stuk. 4to.

Mittheilungen der Naturforschenden Gesellschaft in Bern, aus dem Jahre 1844
46. Nos. 138-388, 57-86. 8vo.

Bulletin de la Société des Sciences Naturelles de Neuchatel. 1844-46. Tomei. 8vo.

Mémoires de la Société des Sciences Naturelles de Neuchatel. Tom. i., ii., iii. 4to.

Abhandlungen der Kénigl. Akademie der Wissenschaften zu Berlin, aus dem
Jahre 1845. Ato.

Bericht iiber die zur Bekanntmachung geeigneten Verhandlungen der Kénigl.,
Preuss. Akademie der Wissenschaften zu Berlin. Juli—December 1846,
und Januar—Juni 1847. Ato.

Bemerkungen iiber Gyps und Karstenit. Von J. F. L. Hausmann. 4to.

Nachrichten von der Georg-Augusts- Universitat und der Konig]. Gesellschaft der
Wissenschaften zu Gottingen. 1846. 8vo.

Tradescant der Aeltere 1618 in Russland. Von Dr J. Hamel. 4to.

Annuaire Magnétique et Météorologique du Corps des Ingénieurs des Mines de
Russie, ou Recueil d’Observations Magnétiques et Météorologiques, par
A. T. Kupffer. Année 1844. Nos. 1 and 2. 4to.

An Engraving of the late Principal Robertson.

January 3, 1848.

The American Journal of Science and Arts, conducted by Professors Silliman and
Dana. Vol. IV., No. 12. November, 1847. 8vo.

The Journal of Agriculture. N.S. No. 19. January, 1848. 8vo.

On certain Laws of Cohesive Attraction. By James D. Dana. 8vo.

A General Review of the Geological Effects of the Earth’s Cooling from a State of
Igneous Fusion. By James D. Dana. 8vo.

Conspectus Crustaceorum. Auctore Jacobo D, Dana. 8vo.

Leeds Philosophical and Literary Society. Annual Report. 1846, 1847. 8vo.

The Mathematical Analysis of Logic. By George Boole. 8vo.

Konig]. Vetenskaps Handlingar, for Ar. 1845. Hft. 1 and 2. Stockholm, 1847. 8yo.

Ofversigt af Konig]. Vetenskaps-Akademiens Forhandlingar. 1846, Nos. 7—

> 10. 1847. Nos. 1-6. Stockholm. 8vo.

Arsberattelse om Zoologiens Framsteg under Aren 1843, 1844. Af C.J.Sunderall.
Stockholm, 1846. 8vo.

Tal Hallet vid Praes. Nedliggande uti Kénigl. Vetenskaps-Akademien, den 7
April 1841. Af N.G. Sefstrém. Stockholm, 1846. 8vo.

DONORS.
The Author.

Ditto.
Ditto.
The Society.

Ditto.
Ditto.

The University.

The Society.
Ditto.
Ditto.

The Academy.
Ditto.

The Author.

The Society.

The Author.
The Editor.

John Russell, Esq.,
W.S.

The Editors.

The Publishers.
The Author.
Ditto.

The Author.
The Society.
The Author.
The Academy.
Ditto.

The Editor.

Ditto.

LIST OF DONATIONS.

DONATIONS.

Berattelse om Framstegen i Fysik, aren 1848, 1844, afgiven till Konigl.
Vetenskaps-Akademien, af A. F. Svanbergoch, och P. A. Siljestrém.
Stockholm, 1847. 8vo.

Memoirs of the Royal Astronomical Society. Vol. xvi. 4to.

Proceedings of the Royal Astronomical Society. Vol. vii., Nos. 1-17.

Monthly Journal of Medical Science, No. 85. January, 1848, 8vo.

8vo.

January 17, 1848.

Ordnance Survey. Account of the Measurement of the Lough Foyle Base in

Treland. By Capt. William Yolland. 4to.

Natural History of New York. (Botany.) By John Torrey. Vol. i., Part 2.
Vol. it, Part. 2. 4to.
Ditto Ditto. (Agriculture.) By E. Emons. Part 5. 4to.

Flora Batava, Parts 148 and 149. 4to.

Journal of the Asiatic Society of Bengal, No. 183. October, 1847. 8vo.

A Collection of Fossil Plants from the Newcastle Coalfield.

February 7.

Observations made at the Magnetical and Meteorological Observatory at St Helena.

Vol. i. 1840-43. 4to.
Fusinieri (A.) Sulle Ipotesi del Signor Melloni circa il Calore Raggiante. 4to.
Astronomical Observations made at the Royal Observatory, Edinburgh. By the

late T. Henderson. Reduced and Hdited by C.P. Smyth. Vol.vii.for 1841. 4to.
Fellenberg (L. R. de), Fragmens de Recherches comparées sur la Nature con-
stitutive de différentes sortes de Fibrine du Cheval dans l'état Normal et Pa-
thologique. 8vo.
Analyse de Eau Minérale de Weissenburg. 8vo.
Ueber die bei der Consolidation des Faserstoffes stattfindenden Verdnderun-
gen der elementar-analytischen Bestandtheile desselben. 8vo. !
Bulletin des Séances de la Société Vaudoise des Sciences Naturelles. No. 13. 8vo.
Journal of the Royal Geographical Society of London. Vol. xvii., Pt. 2. 1847. 8vo.
The London University Calendar for 1848. 12mo.
Acta Acad. Cesarze Leopoldino-Caroline Nature Curiosorum. Vol. xxi., Pars 2. 4to.

February 21.

An Attempt to discover some of the Laws which govern Animal Torpidity and

Hibernation. By Peter A. Browne, LL.D. 8vo.
Cambridge and Dublin Mathematical Journal. Nos. 13 and 14. 8vo.
Journal of the Asiatic Society of Bengal. No. 184. 8vo.
Journal of the Indian Archipelago and Eastern Seas. Nos. 1, 2, 3. 8vo.

Guyot(A.) Note sur la distribution de Roches dans le Bassin Erratique du Rhone. 8vo.

Note sur le Bassin Erratique du Rhin. 8vo.

— Note sur le Topographie des Alpes Pennines, &. 8vo.
March 6.

Lalande’s Catalogue of Stars. 8vo.

Lacaille’s Catalogue of Stars. 8vo.

VOL. X<Vi. PART V.

641

DONORS.
The Editors.

The Society.
Ditto.
The Editors.

The Honourable
Board of Ord-
nance.

The State of New
York.

Ditto.

The King of the
Netherlands.

The Secretaries.

Sir G. S. Macken-

zie, Bart.

Her Majesty’s Go-
vernment,

The Author.

The Observatory.

The Author.

Ditto.
Ditto.

The Society.
Ditto.

The University.

The Academy.

The Author.

The Editor.
The Society.
The Editor.
The Author.
Ditto.
Ditto.

The British Asso-

ciation.

8D

642 LIST OF DONATIONS.

DONATIONS. DONORS.
The Journal of Agriculture, and Transactions of the Highland and Agricultural The Society.
Society of Scotland. No. 20, March 1848. 8vo.

March 20, 1848.

First Report on the Coals suited to the Steam Navy. By Sir Henry De la Beche Sir Henry
and Dr Lyon Playfair. Folio. De la Beche.

April 3.

The American Journal of Science and Arts. Conducted by Professors Silliman The Editor.
and Dana. Second Series. January 1848, No. 13. 8vo.

Bouet Villaumez (Le Comte E.) Description Nautique de l’ Afrique Occidentale. 8vo.

Petit-Thouars (Abel du). Voyage auteur du Monde sur la Frégate la Vénus. Tom.
vi., Vil., viii., ix.,x. (Physique, par U.de Tessan. Tow. i., ii., iii., iv.,v.) 8vo.

Petit Atlas Hydrographique du méme. Imp. Fol.

Collection des Cartes des Cotes de France. Imp. Fol. (In sheets.)

Beyat (P.) Traité de Géodésie a ’usage des Marins. 8vo.

Exposé des Opérations Géodésiques. 1839. 4to.

Le méme. 1844. 4to.

Jehenne (M.) Renseignements Nautiques sur Nossi-Bé, Nossi-Mitsiou, Bavatoubé,
&c. 8vo.

Urville (J. Dumont d’) Voyage au Pole sud, et dans 1’Océanie, sur les Corvettes
L’ Astrolabe et la Zelée. 8vo.

Daussy (M.) Nouvelle Méthode pour calculer la Marche des Chronométres. 8vo. | The French Go-

Table des Positions Géographiques des principaux lieux du Globe. 8vo. vernment, Marine

Brossay (M. Chiron du). Instructions Nautiques sur l’ Attérrage et la Navigation} Department.
de la Platte. 8vo.

Macroix (M. D’Estromont de). Note sur le Bane de Feroé. 8vo.

Moutravel (L. Tarly de). Instructions pour naviguer sur la Céte Septentrionale
du Brésil et dans le fleuve des Amazones. 8vo.

Condé (M. de Maussion). Notice sur le Golfe de Honduras. 8vo.

Bourdieu (L. du). Notes sur quelques Ports de He de Haiti. 8vo.

Keller (F. A. E.) Des Ouragans, Tornados, Typhons, et Tempétes. 8vo.

Périer (M. du). Notes sur l’Attérrissage du Rio de la Plata. 8vo,

Kerhallet (Charles P. de). Instruction pour remonter la Céte du Brésil. 8vo,

Jehenne (M.) Renseignements Nautiques sur Ile Mayotte. 8vo.

Lartigue (M.) Exposition du Systéme des Vents. 8vo.

Pagel (Louis). La Latitude par les Hauteurs hors de Méridien. 8vo.

Spittal (Robert), M.D. Introductory Discourse on Pathology and the Practice of The Author.
Medicine. 12mo.

First Report on the Coals suited to the Steam Navy. By Sir Henry De la Beche Sir Henry
and Dr Lyon Playfair. 8vo. De la Beche.

Journal of the Statistical Society of London. Vol.ii., Partl. March 1848. 8vo. The Society.

April 17.

Greenwich Magnetical and Meteorological Observations, 1845. 4to. The Observatory.
Annales des Sciences Physiques et Naturelles, d’ Agriculture et d’Industrie, publiées The Society.
par la Société Royale d’ Agriculture, &e., de Lyon. Tom. ix. 1846. 8vo.
Abhandlungen der Kénigl. Gesellschaft der Wissenschaften zu Gottingen. 3Bde. The Society.
1845-47. to.
Philosophical Transactions of the Royal Society of London, for 1847. Pt. ii. 4to.

List of Fellows of the Royal Society. 4to. } The Society.

LIST OF DONATIONS.

DONATIONS.
Proceedings of the Royal Society. 1847, No. 69. 8vo.
Proceedings of the American Academy of Arts and Sciences.
Jan. 4, 1848, 8vo.
Thoughts on the Principles of Taxation, with reference to a Property Tax, and its
Exceptions, By Charles Babbage, Esq. 8vo.
Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences.
xxiv., No. 11, to Tom. xxvi., No. 11. 4to.

Jan. 27, 1847—

Tom.

December 4, 1848.

Ancient Sea-Margins. By Robert Chambers, Esq. 8vo.

Account of the Skerryvore Lighthouse ; with Notes on the Illumination of Light-
houses. By Alan Stevenson, LL.B. 4to.

Reduction of Greenwich Lunar Observations, under the superintendence of G. B.
Airy, Esq. 1750-1830. Vols. i. and ii. 4to.

Modern Languages ; their Historical Development and Claims, as a branch of Aca-
demical Study. By Sigismund Wallace, Ph. D. 12mo.

Mémoires de la Société de Physique, et d’Histoire Naturelle de Genéve.
xi., 2me Partie. 4to.

Scheikundige Onderzoekingen, gedaan in het Laboratorium der Utrechtsche
Hoogeschool. 44¢ Deel, 54¢ Stuk. 8vo.

Transactions of the American Philosophical Society. N.8S., Vol. x., Part 1. 4to.

Proceedings of the American Philosophical Society. Vol. iv., Nos. 836-39. 8vo.

American Journal of Science and Arts. Conducted by Professors Silliman and
Dana. 2d Ser., No. 14. 8vo.

Annals of the Lyceum of Natural History of New York. Vol. iv., Nos. 8 and 9. 8vo.

Journal of the Asiatic Society of Bengal. dited by the Secretaries. Nos. 185,
186, 187; (N.S., Nos. 12, 18, 14.) 8vo.

Journal of the Indian Archipelago and Eastern Asia. Vol. i., Nos. 4-6. Vol. ii.,
Nos, l and 2. 8vo.

Quarterly Journal of the Chemical Society of London. Edited by Edmund Ronalds,
Ph. D. No. 182. 8vo.

Memoirs and Proceedings of the Chemical Society. Part 23. 8vo.

Journal of the Statistical Society of London. Vol. xi., Part 2. May 1848. 8vo.

Quarterly Journal of the Geological Society. No. 14. 8vo.

Journal of the Royal Geographical Society of London. Vol. xviii., Pt. 1. 1848. 8vo.

Fifteenth Annual Report of the Royal Cornwall Polytechnic Society. 1847. 8vo.

Journal of Agriculture, and Transactions of the Highland and Agricultural Society
of Scotland. No. 21,N.8. July 1848. 8vo.

Address delivered at the Anniversary Meeting of the Geological Society of London,
18th February 1848. By Sir H. T. De La Beche. 8vo.

Memoirs of the Literary and Philosophical Society of Manchester. N.S. Vol. viii. 8vo.

Histoire des Révolutions de la Philosophie en France. Par le Duc De Caraman.
Paris, 1845-8. 3tom. 8vo.

Flora Batava. Parts 144, 145,146. 4to.

Transactions of the Royal Irish Academy. Vol. xxi., Part 2. 4to.

Report of the British Association for the Advancement of Science for 1847. 8vo.

Astronomical Observations made at the Royal Observatory, Greenwich, in the
year 1846, under the superintendence of G. B. Airy, Esq. 4to.

Journal of the Asiatic Society of Bengal. Edited by the Secretaries.
Nos. 15 and 16. 8vo.

Journal of the Royal Asiatic Society of Gt. Britain and Ireland, 1848. No. 18. 8vo.

Geology of the Silurian Rocks in the Valley of the Tweed. By James Nicol. 8vo.

Annals of the Lyceum of Natural History of New York. Vol. iv. Nos. 10, 11. 8vo.

Tom.

NeS.,

643

DONORS.

The Society.

The Society.
Ditto.

The Author.

The Author.
Ditto.

The Observatory.

The Author.

The Society.

The University.

The Society.
Ditto.

The Editors.

The Lyceum.
The Editors.

Ditto.
The Society.

Ditto.
Ditto.
Ditto.
Ditto.
Ditto.
Ditto.

Ditto.

Ditto.
The Author.

King of Holland.
The Academy.

The Association.
The Observatory.

The Editors.
The Society.

The Author.
The Lyceum,

644 LIST OF DONATIONS.

DONATIONS.

Journal of the Statistical Society of London. Vol. xi., Part 3. 8vo.
Flora Batava. Parts 152 and 153. 4to. .

Philosophical Transactions, Royal Society of London. Part. 1. 4to.
Annales de l’Observatoire Royale de Bruxelles. Tom. vi. 4to.

Mémoires Couronnées et Mémoires des Savants Etrangers, publiées par Académie
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Mémoires de |’ Académie Royale des Sciences, &c., de Belgique. Tom. xxi. and
xxii. 1848. 4to.

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Address of the Marquis of Northampton to the Royal Society, June 9, 1848. 8vo.

Observations des Phénoménes Périodiques. (Acad. R. de Belgique, Extrait du
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Du Systéme Social et des lois qui le régissent, par Ad. Quételet. Paris, 1848. 8vo.

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Atheneum (London) Rules and Regulations, List of Members, and Donations to
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June 1848. 8vo.

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The Ethnological Journal. No. 5. October 1848. 8vo.,

Reprint of the Report of the Trustees of the Massachusetts General Hospital, with
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Magnetical and Meteorological Observations made at the Royal Observatory, Green-
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Proceedings of the Literary and Philosophical Society of Liverpool, during the
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On the Manufacture of Artificial Stone with a Silica Base. By F. Ransome. 8vo.

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The Ethnological Journal. No. 6. 8vo.

Conducted by Professors Silliman and

Supplement to No. vi. of

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Astronomical Observations made at the Observatory of Cambridge, by Rev. J. Challis.
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Résumés des Observations Météorologiques faites dans l’entendue de l’Empire de

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Troisiéme, Cinquiéme, Sixiéme, et Septiéme Mémoires sur |’Induction.
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Dargestellt von der Physikalischen

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January 2, 1849.

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Description de l’Observatoire Astronomique Central de Pulkova.
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Uber die Flicheninhalt der 87 Westlichen Gouvernements und Provinzen des
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Etudes d’Astronomie Stellaire. Par F. G. W. Struve. 1847, 8vo.
VOL. XVI. PART V. SE

645

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646 LIST OF DONATIONS.
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Resultate aus Beobachtungen des Polarsterns am erstelschen vertikalkreise der
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_.. Anziehungen der Sonne, &. Von Dr C. A. F. Peters. 4to.

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Mémoires de l’Académie Imp. des Sciences de St Pétersbourg. 6™¢ Série.
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Notiser ar Siillskapets pro Fauna et Flora Fennica Forhandlingar. 1 Haftet. 4to.

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Abhandlungen der K, Akademie der Wissenschaften zu Berlin.

Monatsbericht der K. Akademie der Wissenschaften zu Berlin.
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1846. to.
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January 15, 1849.

The Quarterly Journal of the Chemical Society. No. 4. 8vo.

Railway Economy: An Exposition of the advantages of Locomotion by Locomotive
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Memoirs of the American Academy of Arts and Sciences. N.S. Vol. iii. 4to.

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Remarks on the Improvement of Tidal Rivers, illustrated by reference to works
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LIST OF DONATIONS.
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February 19, 1849.

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8vo.

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Magnetische und Meteorologische Beobachtungen zu. Prag. 1841-1848. 4to.

Magnetische und Geographische Ortsbestimmungen Bohmen in dem Jahren 1843-5.
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staate. Erster Jahrgang. 1846. 4to.

March 19.

The London University Calendar for 1849.
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8vo.

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647

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648 LIST OF DONATIONS.

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April 80.

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Ethnological Journal. No. 11. 8vo.

Passages in the History of Geology. By Andrew C. Ramsay, F.G.S. 8vo.
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INDEX TO VOL. XVI.

A

Adaptation of the Eye to distinct Vision at different Distances, 1.

Aviz (Jou). On the advantages to be derived from the use of metallic reflectors for sextants and
other reflecting instruments ; and on the methods of directly determining the errors in mirrors
and sun-shades used in reflecting instruments, 61.

Axtson (Witxi4m P.) M.D. Observations on the principles of vital affinity, as illustrated by recent
discoveries in organic chemistry, 305.

Anperson (THomas), M.D. On the constitution and properties of picoline, a new organic base from
coal-tar, 123. On certain products of decomposition of the fixed oils in contact with sulphur, 363.
On the colouring matter of the Morinda citrifolia, 435. On the products of the destructive dis-
tillation of animal substances, 463.

Animal Substances, on the products of the destructive distillation of, 483.

Atlantic and German Oceans, force of the waves of the, 23.

B

Balance Magnetometer, and its temperature corrections, 67.

Barometer, mean height of the, at the level of the sea, 237.

Binary Star «a Centauri, notice of the orbit of the, 445.

Bleaching, on the action of dry gases on organic colouring matters, and its relation to the theory of, 475.

Blood and Milk, observations on, 53. :

Bones, on the extraction of phosphoric acid from, 47.

Brewster (Sir Davip). On the modification of the doubly refracting and physical structure of
topaz by elastic forces emanating from minute cavities, 7. On the existence of crystals with
different primitive forms and physical properties in the cavities of minerals, 11. On the de-
composition and dispersion of light within solid and fluid bodies, 111.

Broun (Joun A.) On the relation of the variations of the earth’s magnetism to the solar and lunar
periods, 99, 137. On the balance magnetometer, and its temperature corrections 67.

C
Calcium, on the solubility of fluoride of, in water, 145.
CaLpEcot (JoHN). Observations on the temperature of the ground at Trevandrum, in India, from
May 1842 to December 1845, 379.
Carnot’s theory of the motive power of heat, 541.
Cuatmers (Tuomas) D.D. & LL.D. Biographical notice of the late, 497.
Cockburnlaw, and the adjoining district, im Berwickshire, geology of, 33.
ConnELL (ArTHUR). On the reaction of natural waters with soluble lead salts, 357.
Crystals in the Cavities of Minerals, on the existence of, 11.
Curves, theory of rolling, 519.

D
Davy (Joun) M.D. Miscellaneous observations on blood and milk, 53.
Decomposition of the fixed Oils in contact with Sulphur, on certain products of, 363.
VOL. XVI. PART V. SF

650 INDEX.

Differentiation, on general, 241.

Digits of Numbers, on the sums of the, 87.

Distillation of Animal Substances, on the products of the destructive, 463.
Dry gases on organic colouring matters, on the action of the, 475.

EK
Earth, on the temperatures of the, 189.
Earth’s magnetism, the relation of the variations of the, to the solar and lunar periods, 99, 137.
Eye, possible explanation of the adaptation of the, to distinct vision at different distances, 1.
Eye, and other phenomena of vision, on the gradual production of luminous impressions on the, 581.

F

Finite Divisibility of Matter, 79.

Fluoride of calcium, on the solubility of, in water, 145.

Forzes (James D.) On a possible explanation of the adaptation of the eye to distinct vision at dif-
ferent distances, 1. Account of some experiments on the temperature of the earth at different
depths, and in different soils, near Edinburgh, 189. Remarks on Mr Caldecot’s observations
on the temperature of the ground at Trevandrum, in India, 392.

Freezing Point of Water, effect of pressure in lowering the, 575.

Fund, account of the Keith, i.

G
Gases, the action of dry, on organic colouring matters, 475.
Goniometry, an attempt to elucidate and apply the principles of, 345.
Grecory (Witt1am) M.D. On the extraction of pure phosphoric acid from bones, and on a new and
anomalous phosphate of magnesia, 47.

H
HansTEen (Curisropuer.) On a formula representing the mean height of the barometer at the level
of the sea, 237.
Heat, Carnot’s theory of the motive power of, 541.
Horr (Tuomas Cuartes) M.D. Memoir of, 49.

I

Iceland Spar, experiments on the ordinary refraction of, 375.

kK
Keith Fund, account of the, 1.
KeExianp (Rev. Pirie) M.A. On general differentiation, 241.

: L
Light, the decomposition and dispersion of, within solid and fluid bodies, 111.
Lochaber, on the parallel roads of, 395.
Luminous Impressions on the Eye, and other Phenomena of Vision, on the gradual production of, 581.
Lunar and Solar Periods, the relation of the variations of the earth’s magnetism to the, 99, 137.

INDEX. 651

Magnesia, on a new and anomalous phosphate of, 47.

Magnetometer, Balance, and its mean corrections, 67.

Matter, finite divisibility of, 79.

Milk and Blood, observations on, 53.

Maxwet1 (JAMES CrzrK). On the theory of rolling curves, 519.

Metallic Reflectors for sewtants and other reflecting mstruments, on the use of, 61.

Minx (Davin). On the parallel roads of Lochaber, with remarks on the change of relative levels
of sea and land in Scotland, and on the detrital deposits in that country, 395.

Minerals, on the existence of crystals with different primitive forms and physical properties in the
cavities of, 11.

Morinda citrifolia, on the colouring matter of the, 435.

N

Negative quantites, on the square roots of, 345.
Numbers, on the sums of the digits of, 87.

O

Oils, decomposition of the fixed, in contact with sulphur, on certain products of, 363.

iP

Parallel Roads of Lochaber, on the, 395.

Phosphate of Magnesia, on a new and anomalous, 47.

Phosphoric Acid from Bones, on the extraction of 47.

Picoline, a new organic base from coal-tar, on the constitution and properties of, 123.

Pressure in Lowering the Freezing Point of Water, theoretical consideration on the effects of, 575.

R

Ramsay (Rev. E. B.) Biographical notice of the late Thomas Chalmers, D.D., & LL.D., 497.
Reaction of natural waters with soluble lead salts, on the, 357.

Reenavut’s Experiments on steam, numerical results deduced from, 541.

Roads of Lochaber, on the parallel, 395.

Rolling Curves, on the theory of, 519.

S

Salts, on the reaction of natural waters with soluble lead, 357.

Sextants and other reflecting instruments, on the advantages to be derived from the use of metallic
reflectors for, 61.

Smytu (C. Prazz1). Notice of the orbit of the binary star « Centauri, as recently determined by Capt.
W. S. Jacob, Bombay Engineers, 445. An attempt to improve the present methods of deter-
mining the strength and direction of the wind at sea, 455.

Solar and Lunar Periods, the relation of the variations of the earth’s magnetism to the, 99, 137.

Solid and Fluid Bodies, the decomposition and dispersion of hight within, 111.

Spar, experiments on the ordinary refraction of Iceland, 375.

Star, notice of the orbit of the binary, a Centauri, 445.

652 INDEX.

Steam, numerical results deducted from Regnault’s experiments on, 541.

Srevenson (Tuomas) C.E. Account of experiments upon the force of the waves of the Atlantic
and German Oceans, 23.

Srevenson (Witi1aAM). On the geology of Cockburnlaw, and the adjoining district, in Berwick-
shire, 33.

Swan (Witt1am). Experiments on the ordinary refraction of Iceland spar, 375. On the gradual
production of luminous impressions on the eye, and other phenomena of vision, 581.

-

Temperature of the Earth, on the, 189.

Temperature of the Ground at Trevandrum, in India, observations on the, 379.

Terror (Right Rev. Bishop). On the sums of the digits of numbers, 87. An attempt to elucidate
and apply the principles of goniometry, as published by Mr Warren in his Treatise on the
Square Roots of Negative Quantities, 345.

Tuomson (Jamzs). On the effect of pressure in lowering the freezing point of water, 575.

Tuomson (Witt1am). An account of Carnot’s theory of the motive power of heat; with numerical
results deduced from Regnault’s experiments on steam, 541.

Topaz, modification of the doubly refracting and physical structure of, 7.

Traitu (Tuomas S.) M.D. Memoir of Dr Thomas Charles Hope, late Professor of Chemistry in
the University of Edinburgh, 419.

Trevandrum, observations on the temperature of the ground at, 379.

V
Vision, on the gradual production of luminous impressions on the eye, and other phenomena of,
581.
Vital Afinity, observations on the principle of, 165.

W

Warren’s Treatise on the Square Roots of Negative Quantities, 345.

Water, effect of pressure in lowering the freezing point of, 575.

Waves of the Atlantic and German Oceans, force of the, 23.

Witson (Gzorce) M.D. On Wollaston’s argument from the limitation of the atmosphere, as to
the finite divisibility of matter, 79. On the solubility of fluoride of calcium in water, 145. On
the action of the dry gases on organic colouring matters, and its relation to the theory of
bleaching, 475.

Wind at Sea, method of measuring the strength and direction of the, 455.

Wottaston’s argument from the limitation of the atmosphere, as to the finite divisibility of matter, 79.

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