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THE
LONDON, EDINBURGH, and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
CONDUCTED BY
SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L.&E. &c.
RICHARD TAYLOR, F.L.S. G.S. Astr.S. Nat.H.Mosc.&c.
SIR ROBERT KANE, M.D. M.R.I.A.
WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S.
" Nee aranearum sane textus ideo melior quia ex se fila gignunt, nee noster
vilior quia ex alienis libamus ut apes." Just. Lips. Polit. lib. i. cap. 1. Not.
VOL. II.— FOURTH SERIES.
JULY— DECEMBER, 1851.
LONDON.
RICHARD TAYLOR, RED LION COURT, FLEET STREET,
Printer and Publisher to the University of London;
SOLD BY LONGMAN, BROWN, GREEN, AND LONGMANS ; SIMPKIN, MARSHALL
AND CO.; s. highley; whittaker and co.; and sherwood,
GILBERT, AND PIPER, LONDON : BY ADAM AND CHARLES
BLACK, AND THOMAS CLARK, EDINBURGH; SMITH AND SON,
GLASGOW ; HODGES AND SMITH, DUBLIN ; AND
WILEY AND PUTNAM, NEW YORK.
** Meditationis est perscrutari occulta; contemplationis est admirari
perspicua Admiratio generat quaestionem, quaestio investigationem,
in\restigatio inventionem." — Hugo de S. Victore.
— " Cur Spirent venti, cur terra dehiscat.
Cur mare turgescat, pelago cur tantus amaror,
Cur caput obscura Phoebus ferrugine condat,
Quid toties diros cogat flagrare cometas ;
Quid pariat nubes, veniant cur fulmina coelo.
Quo micet igne Iris, superos quis conciat orbes
Tarn vario motu."
J. B. Pinelli ad Maxonium,
CONTENTS OF VOL. II
(FOURTH SERIES.)
NUMBER VIII.— JULY 1851.
Page
M. R. Clausius on the Moving Force of Heat, and the Laws re-
garding the Nature of Heat itself which are deducible there-
from 1
Mr. H. J. Brooke on the Beudantite of Levy 21
M. C. F. Schoenbein on the joint Influence exerted by Light
and the Oxidability of certain substances upon common
Oxygen 22
Dr. Tyndall's Reports on the Progress of the Physical Sciences :
1. Prof. Dove on the Reversion-prism, and its application
as ocular to the Terrestrial or Day-Telescope 26
2. Prof. Dove's Description of several Prism-stereoscopes,
and of a simple Mirror-stereoscope 27
3. Prof. Knoblauch on the Deportment of Crystalline
Bodies between the Electric Poles 33
Mr. W. J. M. Rankine on the Theory of Sound 36
Mr. T. G. Bunt's Pendulum Experiments 37
Mr. P. J. Martin on the Anticlinal Line of the London and
Hampshire Basins 41
Mr. G. P. Bond's Historical Sketch of the progress of improve-
ment in the application of Electro-Magnetism to Geodetical
and Astronomical purposes 51
Prof. Donkin on certain Questions relating to the Theory of
Probabilities. — Part III. 55
Prof. Stokes on the Principles of Hydrodynamics 60
Mr. W. J. M. Rankine on the Mechanical Theory of Heat. . . 61
Mr. T. S. Hunt's Description and Analysis of Loganite, a new
Mineral Species 65
Notices respecting New Books : — Prof. Airy's Six Lectures on
Astronomy delivered at the Meetings of the Friends of the
Ipswich Museum 68
Proceedings of the Royal Society 71
Postscript to Mr. T. G. Bunt's Pendulum Experiments 81
On the Total Eclipse of the approaching 28th of July, by M.
Faye 81
Meteorological Observations for May 1 85 1 83
Meteorological Observations made by Mr. Thompson at the
Garden of the Horticultural Society at Chiswick, near
London ; by Mr. Veall at Boston ; by the Rev, W. Dunbar at
Applegarth Manse, Dumfries -shire ; and by the Rev. C.
Clouston at Sand wick Manse, Orkney 84
iv CONTENTS OF VOL. II. FOURTH SERIES.
NUMBER IX.— AUGUST.
Page
Mr. I. B. Cooke on the Measurement of Chemical Affinity . . 85
Prof. Boole's Further Observations on the Theory of Probabi-
lities 96
M. R. Clausius on the Moving Force of Heat, and the Laws
regarding the Nature of Heat itself which are deducible there-
from 102
Mr. R. P. Greg's Descriptionof Matlockite, anew Oxychloride
ofLead 120
Prof. O'Brien on Symbolical Mechanics 121
Mr. P. J. Martin on the Anticlinal Line of the London and
Hampshire Basins (continued) 126
Messrs. Galbraith and Haughton on the Apsidal Motion of a
freely suspended Pendulum 134
M. R. Clausius* Reply to a Note from Mr. W. Thomson on
the Effect of Fluid Friction, &c 139
Mr. J. J. Sylvester on a certain Fundamental Theorem of De-
terminants 142
Proceedings of the Royal Astronomical Society 145
• Royal Society 149
Pendulum Experiments, by Thomas G. Bunt 158
Pendulum Experiments : — Formula for Calculating the Apsidal
Motion, by A. Thacker 159
On Atmospheric Shadows, by Prof. E. Wartmann 160
On the Artificial Formation of Corundum and Diaspore by the
Wet Method, by M. H. De Senarmont 161
The Theory of Sound 162
Meteorological Observations for June 1851 163
* Table 164
NUMBER X.— SEPTEMBER.
Dr. Tyndall on Diamagnetism and Magnecrystallic Action .... 165
Mr. P. J. Martin on the Anticlinal Line of the London and
Hampshire Basins (continued) 189
Mr. C. L. Dresser's Experiments on the Conducting Powers of
Wires for Voltaic Electricity 198
Mr. M.Donovan's Suggestions for the Preparation of Phosphorus 202
The Rev. A. Weld's Account of a remarkable Flood at Chipping
in Lancashire 209
Messrs. Gladstone on the Growth of Plants in various Gases. . 215
Mr. J. J. Sylvester on Extensions of the Dialytic Method of
Elimination 221
Mr. R. Phillips on the Magnetism of Pewter Coils 230
Proceedings of the Royal Society 238
On the Artificial Production of Crystallized Minerals, by M.
Ebelmen 246
CONTENTS OF VOL. II. FOURTH SERIES. V
Page
Further researches upon Crystallization by the Dry Method, by
M. Ebelmen 248
New Static and Dynamic Theory of Ultimate Particles, by
M. Zantedeschi 249
Meteorological Observations for July 1851 251
Table 252
NUMBER XL— OCTOBER.
Mr. F. Claudet on a Class of Ammoniacal Compounds of Cobalt 253
Mr. C. T. Beke's Summary of recent Nilotic Discovery 260
Dr. Woods on the Heat of Chemical Combination 268
Prof. Thomson's Second Note on the Effect of Fluid Friction in
Drying Steam which issues from a High-pressure Boiler into
the open Air 273
The Rev. A. Thacker on the Motion of a Free Pendulum 275
Mr. P. J. Martin on the Anticlinal Line of the London and
Hampshire Basins {continued) 278
Mr. J. Cockle on the Solution of certain Systems of Equations 289
Prof. Muspratt and Mr. J. Danson on Carmufellic Acid 293
Dr. Beer on the deduction of Fresnel's construction from the
formulae of Cauchy for the Motion of Light 297
The Rev. J. A. Coombe on the Motion of the Apse-Line in the
Pendulum Oval 303
Mr. J. P. Joule's Account of Experiments demonstrating a limit
to the Magnetizability of Iron 306
Notices respecting New Books : — M. F. Woepcke's L'Algebre
d'Omar Alkhayyami; Mr. R. J. Bingham on Photogenic
Manipulation 315
Proceedings of the Royal Society 316
Royal Astronomical Society 321
On the Production of Sugar in the Liver of Man and Animals,
by Claude Bernard 326
On the Crystallization of Cymophane, by M. Ebelmen 330
On the Presence of Ammonia in Hail-stones, by M. M^ne. ... 331
On the Application of Rectified Oil of Coal-Tar to the Preser-
vation of Meat and Vegetables, by M. Robin 331
Meteorological Observations for August 1851 331
Table 332
NUMBER XIL—NOVEMBER.
Dr. Tyndall on the Polarity of Bismuth, including an Examina-
tion of the Magnetic Field ... 333
Mr. T. J. Herapath on the Combination of Arsenious Acid with
Albumen 345
VI CONTENTS OF VOL. II. — FOURTH SERIES.
Page
Prof. Boole'8 Account of the late John Walsh of Cork. In a
letter to Professor De Morgan 348
Mr. H. E. Strickland on the Elevatory Forces which raised the
Malvern Hills. (With a Plate.) 358
Mr. P. J. Martin on the Anticlinal Line of the London and
Hampshire Basins (continued) 366
Mr. S. Tebay on the Motion of a Pendulum affected by the
Earth's Rotation 376
The Rev. R. R. Anstice on the Motion of a Free Pendulum . . 379
Capt. E. M. Boxer on the Effect of the Rotation of the Earth
upon the Flight of a Projectile 386
Dr. A. Krantz on a new Mineral named Orangite 390
Mr. J. J. Sylvester on a remarkable Discovery in the Theory of
Canonical Forms and of Hyperdeterminants 391
Mr. J. Lamprey and Lieut. H. Schaw's Account of Pendulum
Experiments made at Ceylon 410
The Rev. A. Thacker on Formulae connected with the Motion
of a Free Pendulum 412
Notices respecting New Books : — Dr. Latham on the Ethno-
logy of the British Colonies and Dependencies ; Man and his
Migrations ; De Morgan's Elements of Arithmetic and of
Algebra 413
Proceedings of the Cambridge Philosophical Society 419
On Foucault's Pendulum Experiment, by Alexander Gerard, Esq. 422
Pendulum Experiments at the Philosophical Institution, Bristol,
by Thomas G. Bunt, Esq 424
Meteorological Observations for September 1851 427
Table 428
NUMBER XIII.— DECEMBER.
Prof. Thomson on the Mechanical Theory of Electrolysis .... 429
Mr. T. S. Davies on Geometry and Geometers. No. VIII. o . 444
Mr. J. P. Joule's Account of Experiments demonstrating a limit
to the Magnetizability of Iron 447
Dr. Anderson on the products of the Destructive Distillation of
Animal Substances. — Part II 457
Mr. P. J. Martin's Postscript to a Paper on the Anticlinal Line
of the London and Hampshire Basins 471
The Rev. B. Bronwin on the Integration of Linear Differential
Equations 477
M. R. Clausius on the Theoretic Connexion of two Empirical
laws relating to the Tension and the Latent Heat of different
Vapours 483
Dr. Fyfe on the Detection of Arsenic 487
Proceedings of the Royal Society 491
Cambridge Philosophical Society 500
CONTENTS OF VOL. IT. — FOURTH SERIES. Vll
Page
On the Constitution of the Atmosphere, by M. Lewy 500
On the Magnetism of Gases, by M. PlUcker 503
On the Formation of Dolomite by the action of Magnesium
Vapours, by M. Durocher 504
New Photographic Process upon Glass, by M. J. R. Le Moyne 505
Reflexion of Light from the Surface of Liquids, by M. Jamin. . 507
Meteorological Observations for October 1851 507
Table 508
NUMBER XIV.— SUPPLEMENT TO VOL. IL
Mr. W. J. M. Rankine on the Centrifugal Theory of Elasticity,
as applied to Gases and Vapours 509
M. W. Hankel's Account of some Experiments upon the Elec-
tricity of Flame, and the Electric Currents thereby originated 542
M. R. Clausius on the Influence of Pressure upon the Freezing
of Fluids 548
Prof. Thomson's Applications of the Principle of Mechanical
Eff'ect to the Measurement of Electro-motive Forces, and of
Galvanic Resistances, in absolute Units 551
Proceedings of the Royal Society 562
On the Hypotheses relating to the Luminous ^ther, and an
experiment which appears to demonstrate that the Motion of
Bodies alters the velocity with which Light propagates itself
in their interior, by M. H. Fizeau 568
On the Formation of Anhydrous Crystallized Alum, by the
Prince of Salra-Horstmar 573
On the Composition of the Gases evolved on the production of
Coke from Coal, by M. Ebelmen 573
Magnecrystallic property of Calcareous Spar, by Prof. Thomson 574
Observations upon the Radiation of Luminous Bodies, by M.
Baudrimont 575
Index , 576
ERRATA IN VOL. I. .
Page 616, line 11 from bottom, for The first were extinguished; read
The first being extinguished,
— 516, note, hne 5 from bottom, /or from that planet read from that
body.
ERRATA IN VOL II.
Page 144, line 17 from top, /or
read
Page 270, line 23 from top, /or zinc read hydrogen.
— 420, — 14 from bottom, /or level-edged reorf bevel-edged.
— 421 , — 6 from bottom, for observing media read absorbing media.
PLATE.
Illustrative of Mr. H. E. Strickland's Paper on the Elevatory Forces
which raised the Malvern Hills.
THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
JULY 1851.
I. On the Moving Force of Heat, and the Laws regarding the
Nature of Heat itself which are deducible therefrom. By
R. Clausius*.
THE steam-engine having furnished us with a means of con-
verting heat into a motive power, and our thoughts being
thereby led to regard a certain quantity of work as an equivalent
for the amount of heat expended in its production, the idea of
establishing theoretically some fixed relation between a quantity
of heat and the quantity of work which it can possibly produce,
from which relation conclusions 4'egarding the nature of heat
itself might be deduced, naturally presents itself. Already, in-
deed, have many instructive experiments been made with this
view ; I believe, however, that they have not exhausted the sub-
ject, but that, on the contrary, it merits the continued attention
of physicists ; partly because weighty objections lie in the way
of the conclusions already drawn, and partly because other con-
clusions, which might render eificient aid towards establishing
and completing the theory of heat, remain either entirely unno-
ticed, or have not as yet found sufficiently distinct expression.
The most important investigation in connexion with this sub-
ject is that of S. Camotf. Later still, the ideas of this author
have been represented analytically in a very able manner by
Clapeyronf. Carnot proves that whenever work is produced by
heat, and a permanent alteration of the body in action does not
at the same time take place, a certain quantity of heat passes
* Translated from PoggendorfF's Annalen, vol. Ixxix. p. 368.
t Reflexions sur la puissance motrice dufeu, et sur les Machines propres
a developer cette puissance, par S. Carnot. Paris, 1824.
X Journ. deVEcole Polytechniqy.e, vol. xix. (1834); and Taylor's Scien-
tific Memoirs, Part III. p. 347.
Phil, Mag, S. 4. Vol. 2. No. 8. July 1851 . B
^f
2 M. R. Clausius on the Moving Force of Heat,
from a warm body to a cold one ; for example, the vapoui- which
is generated in tne boiler of a steam-engine, and passes thence
.to the condenser where it is precipitated, carries heat from the
fireplace to the condenser. This transmission Carnot regards as
the change of heat corresponding to the work produced. He
says expressly, that no heat is lost in the process, that the quan-
tity remains unchanged ; and he adds, " This is a fact which
has never been disputed ; it is first assumed without investigation,
and then confirmed by various calorimetric experiments. To
deny it, would be to reject the entire theory of heat, of which it
forms the principal foundation."
I am not, however, sure that the assertion, that in the pro-
duction of work a loss of heat never occiu's, is sufficiently esta-
blished by experiment. Perhaps the contrary might be asserted
with greater justice ; that although no such loss may have been
directly proved, still other facts render it exceedingly probable
that a loss occurs. If we assume that heat, like matter, cannot
be lessened in quantity, we must also assume that it cannot be
increased ; but it is almost impossible to explain the ascension
of temperature brought about by friction otherwise than by
assiuning an actual increase of heat. The careful experiments
of Joule, who developed heat in various ways by the application
of mechanical force, establish almost to a certainty, not only the
possibiUty of increasing the quantity of heat, but also the fact
that the newly-produced heat is proportional to the work ex-
pended in its production. It may be remarked further, that
many facts have lately transpired which tend to overthrow the
hypothesis that heat is itself a body, and to prove that it con-
sists in a motion of the ultimate particles of bodies. If this be
so, the general principles of mechanics may be applied to heat ;
this motion may be converted into work, the loss of vis viva in
each particular case being proportional to the quantity of work
produced.
These circumstances, of which Camot was also well aware, and
the importance of which he expressly admitted, pressingly de-
mand a comparison between heat and work, to be imdertaken
with reference to the divergent assumption that the production
of work is not only due to an alteration in the distribution of
heat, but to an actual consumption thereof; and inversely, that
by the consumption of work heat may be produced.
In a recent memoir by Holtzmann*, it seemed at first as if the
author intended to regard the subject from this latter point of
view. He says (p. 7), " the effect of the heat which has been
communicated to the gas is either an increase of temperature
* Ueber die Wdrme und Elasticit'dt der Gase und Diimpfe, von C. Holtz-
mann. Manheim, 1846. Also Taylor's Scientific Memoirs, Part XIV.p. 189.
and the Laws regarding the Nature of Heat. 3
combined with an increase of elasticity, or a mechanical work_,
or a combination of both ; a mechanical work being the equiva-
lent for an increase of temperature. Heat can only be measured
by its effects; and of the two effects mentioned, mechanical
work is peculiarly applicable here, and shall therefore be chosen
as a standard in the following investigation. I name a unit of heat,
the quantity which, on being communicated to any gas, is able
to produce the quantity of work a; or to speak more definitely,
which is able to raise a kilogrammes to a height of one metre.'^
Afterwards, at page 12, he determines the numerical value of the
constant a, according to the method of Meyer*, and obtains a
number which completely agrees with that obtained in a manner
totally different by Joule. In carrying out the theory, however,
that is, in developing the equations by means of which his con-
clusions are arrived at, he proceeds in a manner similar to Cla-
peyron, so that the assumption that the quantity of heat is con-
stant is still tacitly retained.
The difference between both ways of regarding the subject has
been laid hold of with much greater clearness by W. Thomson,
who has applied the recent discoveries of Regnault on the tension
and latent heat of steam to the completing of the memoir of
Carnotf. Thomson mentions distinctly the obstacles which lie
in the way of an unconditional acceptance of Carnof s theory,
referring particularly to the investigations of Joule, and dwelling
on one principal objection to which the theory is liable. If it be
even granted that the production of work, where the body in
action remains in the same state after the production as before,
is in all cases accompanied by a transmission of heat from a warm
body to a cold one, it does not follow that by every such trans-
mission work is produced, for the heat may be carried over by
simple conduction ; and in all such cases, if the transmission
alone were the true equivalent of the work performed, an abso-
lute loss of mechanical force must take place in nature, which is
hardly conceivable. Notwithstanding this, however, he arrives
at the conclusion, that in the present state of science the prin-
ciple assumed by Carnot is the most probable foundation for an
investigation on the moving force of heat. He says, " If we
forsake this principle, we stumble immediately on innumerable
other difficulties, which, without further experimental investiga-
tions, and an entirely new erection of the theory of heat, are
altogether insurmountable.^'
I believe, nevertheless, that we ought not to suffer ourselves
to be daunted by these difficulties ; but that, on the contrary, we
must look steadfastly into this theory which calls heat a motion,
as in this way alone can we arrive at the means of establishing
* Ann. der Chim. und Pharm., vol. xlii. p. 239.
t Transactions of the Royal Society of Edinburgh, vol. xvi.
4 M. R. Clai\sius on the Moving Force of Heat,
it or refuting it. Besides this, I do not imagine that the diffi-
culties arc so great as Thomson considers them to be ; for although
a certain alteration in our way of regarding the subject is neces-
saiy, still I find that this is in no case contradicted by proved
facts. It is not even requisite to cast the theory of Carnot over-
board ; a thing difficult to be resolved upon, inasmuch as expe-
rience to a certain extent has shown a surprising coincidence
therewith. On a nearer view of the case, we find that the new
theory is opposed, not to the real fundamental principle of Carnot,
but to the addition "no heat is lost;" for it is quite possible
that in the production of work both may take place at the same
time ; a certain portion of heat may be consumed, and a further
portion transmitted from a warm body to a cold one ; and both
portions may stand in a certain definite relation to the quantity
of work produced. This will be made plainer as we proceed ;
and it will be moreover shown, that the inferences to be drawn
from both assumptions may not only exist together, but that
they mutually support each other.
1. Deductions from the principle of the equivalence of heat and
work.
We shall forbear entering at present on the nature of the
motion which may be supposed to exist within a body, and shall
assume generally that a motion of the particles does exist, and
that heat is the measure of their vis viva. Or yet more general,
we shall merely lay down one maxim which is founded on the
above assumption : —
Li all cases where work is produced by heat, a quantity of heat
proportional to the work done is eapended; and inversely, by the
expenditure of a like quantity of work, the same amount of heat
may be produced.
Before passing on to the mathematical treatment of this maxim,
a few of its more immediate consequences may be noticed, which
have an influence on our entire notions as to heat, and which are
capable of being understood, without entering upon the more
definite proofs by calculation which are introduced further on.
We often hear of the total heat of bodies, and of gases and
vapours in particular, this tei-m being meant to express the sum
of the sensible and latent heat. It is assumed that this depends
solely upon the present condition of the body under considera-
tion; so that when all other physical properties thereof, its
temperature, density, &c. are known, the total quantity of heat
which the body contains may also be accurately determined.
According to the above maxim, however, this assumption cannot
be admitted. If a body in a certain state, for instance a quan-
tity of gas at the temperature t^ and volume Vq, be subjected to
various alterations as regards temperature and volume, and
and the Laws regarding the Nature of Heat. 5
brought at the conclusion into its original state, the sum of its
sensible and latent heats must, according to the above assump-
tion, be the same as before ; hence, if during any portion of the
process heat be communicated from without, the quantity thus
received must be given off again during some other portion of
the process. With every alteration of volume, however, a certain
quantity of work is either produced or expended by the gas ; for
by its expansion an outward pressure is forced back, and on the
other hand, compression can only be effected by the advance of
an outward pressure. If, therefore, alteration of volume be
among the changes which the gas has undergone, work must
be produced and expended. It is not, however, necessary that at
the conclusion, when the original condition of the gas is again
established, the entire amount of work produced should be exactly
equal to the amount expended, the one thus balancing the other ;
an excess of one or the other will be present if the compres-
sion has taken place at a lower or a higher temperature than the
expansion, as shall be proved more strictly further on. This
excess of produced or expended work must, according to the
maxim, correspond to a proportionate excess of expended or pro-
duced heat, and hence the amount of heat refunded by the gas
cannot be the same as that which it has received.
There is still another way of exhibiting this divergence of our
maxim from the common assumption as to the total heat of bodies.
When a gas at /q and Vq is to be brought to the higher tempera-
ture ^j and the greater volume Vj, the quantity of heat necessary to
effect this would, according to the usual hypothesis, be quite in-
dependent of the manner in which it is communicated. By the
above maxim, however, this quantity would be different according
as the gas is first heated at the constant volume v^ and then per-
mitted to expand at the constant temperature t-^, or first expanded
at the temperature ^q and afterwards heated to t^ ; the quantity
of heat varying in all cases with the manner in which the altera-
tions succeed each other.
In like manner, when a quantity of water at the temperature
tQ is to be converted into vapour of the temperature t^ and the
volume ^1, it will make a difference in the amount of heat neces-
sary if the water be heated first to t^ and then suffered to evapo-
rate, or if it be suffered to evaporate by t^ and the vapour heated
afterwards to t^ ; or finally, if the evaporation take place at any
intermediate temperature.
From this and from the immediate consideration of the maxim,
we can form a notion as to the light in which latent heat must
be regarded. Referring again to the last example, we distin-
guish in the quantity of heat imparted to the water during the
change the sensible heat and the latent heat. Only the former
of these, however, must we regard as present in the produced
6 M. R. Clausius on the Moving Force of Heat,
steaui ; the second is, not only as its name impoi-ts, hidden from
our perceptions, but has actually no existence -, during the altera-
tion it has been converted into work.
We must introduce another distinction still as regards the
heat expended. The work produced is of a twofold nature. In
the first place, a certain quantity of work is necessaiy to over-
come the mutual attraction of the particles, and to separate them
to the distance which they occupy in a state of vapour. Secondly,
the vapour during its development must, in order to procure
room for itself, force back an outer pressure. We shall name
the former of these interior work, and the latter exterior work,
and shall distribute the latent heat also under the same two heads.
With regard to the interior work, it can make no difference
whether the evaporation takes place at /q or at /j, or at any other
intermediate temperature, inasmuch as the attraction of the par-
ticles must be regarded as invariable*. The exterior work, on
the contraiy, is regulated by the pressure, and therefore by the
temperature also. These remarks are not restricted to the ex-
ample we have given, but are of general application ; and when
it was stated above, that the quantity of heat necessary to bring
a body from one condition into another depended, not upon the
state of the body at the beginning and the end alone, but upon
the manner in which the alterations had been carried on through-
out, this statement had reference to that portion only of the
latent heat which corresponds to the exterior work. The re-
mainder of the latent heat and the entire amount of sensible heat
are independent of the manner in which the alteration is effected.
WTien the vapour of water at t^ and t?, is reconverted into
water at /q, the reverse occurs. Work is here expended, inasmuch
as the particles again yield to their attraction, and the outer
pressure once more advances. In this case, therefore, heat must
be produced ; and the sensible heat which here exhibits itself does
not come from any retreat in which it was previously concealed,
but is newly produced. It is not necessary that the heat developed
by this reverse process should be equal to that consumed by the
other ; that portion which corresponds to the exterior work may
be greater or less according to circumstances.
We shall now turn to the mathematical treatment of the sub-
ject, confining ourselves, however, to the consideration of per-
* It must not be objected here that the cohesion of the water at t^ is less
than at f^, and hence requires a less amount of work to overcome it. The
lessening of the cohesion implies a certain \york performed by the warming
of the water as water, and this must be atlded to that produced by evapo-
ration. From this it follows, that of the heat which the water receives from
without, only one portion must be regarded as sensible, while the other
portion goes to loosen the cohesion. This view is in harmony with the
fact, that water possesses a so much greater specific heat than ice, and pro-
bably than steam also.
and th^ Laws regarding the Nature of Heat. 7
manent gases, and of vapours at their maximum density ; as
besides possessing the greatest interest, our superior knowledge
of these recommends them as best suited to the calculus. It
will, however, be easy to see how the maxim may be applied to
other cases also.
Let a certain quantity oi permanent gas, say a unit of weight,
be given. To determine its present condition, three quantities
are necessary ; the pressure under which it exists, its volume^
and its temperature. These quantities stand to each other in a
relation of mutual dependence, which, by a union of the laws of
Mariotte and Gay-Lussac*, is expressed in the following equation:
|?i;=R(« + 0, (I.)
where p, v, and t express the pressure, volume, and temperature
of the gas in its present state, a a constant equal for all gases,
and R also a constant, which is fully expressed thus, ^^ ^, where
Poy ^oj ^^d ^0 express contemporaneous values of the above three
quantities for any other condition of the gas. This last constant
is therefore different for different gases, being inversely propor-
tional to the specific weight of each.
It must be remarked, that Regnault has recently proved, by a
series of very careful experiments, that this law is not in all
strictness correct. The deviations, however, for the permanent
gases are very small, and exhibit themselves principally in those
cases where the gas admits of condensation. From this it would
seem to follow, that the more distant, as regards pressure and
temperature, a gas is from its point of condensatioij, the more
correct will be the law. Its accuracy for permanent gases in
their common state is so great, that it may be regarded as per-
fect ; for every gas a limit may be imagined, up to which the
law is also perfectly true ; and in the following pages, where the
permanent gases are treated as such, we shall assume the exist-
ence of this ideal condition.
The value - for atmospheric air is found by the experiments
both of Magnus and Regnault to be =0-003665, the tempera-
ture being expressed by the centesimal scale reckoned from the
freezing-point upwards. The gases, however, as already men-
tioned, not following strictly the law of M. and G., we do not
always obtain the same value for - when the experiment is re-
peated under different circumstances. The number given above
is true for the case when the air is taken at a temperature of (f
under the pressure of one atmosphere, heated to a temperature
* This shall be expressed in future briefly thus — the law of M. and C^. j
and the law of Mariotte alone thus — the law of M.
8
M. R. Clausius on the Moving Force of Heat,
of 100°, and the increase of expansive force observed. If, how-
ever, the pressure be allowed to remain constant, and the increase
of volume observed, we obtain the somewhat higher value
0*003670. Further, the values increase when the experiments
are made under a pressure exceeding that of the atmosphere, and
decrease when the pressure is less. It is clear from this, that
the exact value for the ideal condition, where the differences
pointed out would of course disappear, cannot be ascertained.
It is certain, however, that the number 0*003665 is not far from
the truth, especially as it very nearly agrees with the value found
for hydrogen, which, perhaps of all gases, approaches nearest the
ideal condition. Retaining, therefore, the above value for -, we
have
«=273.
One of the quantities in equation (I.), for instance p, may be
regai-ded as a function of the two others ; the latter will then be
the independent variables which determine the condition of the
gas. We will now endeavour to ascertain in what manner the
quantities which relate to the amount of heat depend upon v
and t.
When any body whatever changes its volume, the change is
always accompanied by a mechanical work produced or expended.
In most cases, however, it is impossible to determine this with
accuracy, because an unknown interior work usually goes on at
the same time with the exterior. To avoid this difficulty, Carnot
adopted the ingenious contrivance before alluded to : he allowed
the body to undergo various changes, and finally brought it into
its primitive state ; hence if by any of the changes interior work
was produced, this was sure to be exactly nullified by some other
change ; and it was certain that the quantity of exterior work
which remained over and above was the total quantity produced.
Clapeyron has made this very evident by means of a diagram :
we propose following his method with permanent gases in the
first instance, introducing, however, some slight modifications
rendered necessai-y by our maxim.
In the annexed figure let oe
represent the volume, and ea the
pressure of the unit weight of
gas when its temperature is t ;
let us suppose the gas to be
contained in an expansible bag,
with which, however, no ex-
change of heat is possible. If
the gas be permitted to expand,
no new heat being added, the
temperature will fall . To avoid
and the Laws regarding the Nature of Heat. 9
this, let the bag during the expansion be brought into contact
with a body A of the temperature t, from which it shall receive
heat sufficient to preserve it constant at the same temperature.
While this expansion by constant temperature proceeds, the
pressure decreases according to the law of M., and may be repre-
sented by the ordinate of a curve ah, which is a portion of an
equilateral hyperbola. When the gas has increased in volume
from oe to of, let the body A be taken away, and the expansion
allowed to proceed still further without the addition of heat ;
the temperature will now sink, and the pressure consequently
grow less as before. Let the law according to which this pro-
ceeds be represented by the curve be. When the volume of the
gas has increased from of to og, and its temperature is lowered
from t to T, let a pressure be commenced to bring it back to its
original condition. Were the gas left to itself, its temperature
would now rise ; this, however, must be avoided by bringing it
into contact with the body B at the temperature r, to which any
excess of heat will be immediately imparted, the gas being thus
preserved constantly at t. Let the compression continue till
the volume has receded to h, it being so arranged that the de-
crease of volume indicated by the remaining portion he shall be
just sufficient to raise the gas from r to t, if during this decrease
it gives out no heat. By the first, compression the pressure in-
creases according to the law of M., and may be represented by a
portion cd of another equilateral hyperbola. At the end the in-
crease is quicker, and may be represented by the curve da. This
curve must terminate exactly in a ; for as the volume and tem-
perature at the end of the operation have again attained their
original values, this must also be the case with the pressure,
which is a function of both. The gas will therefore be found in
precisely the same condition as at the commencement.
In seeking to determine the amount of work performed by
these alterations, it will be necessary, for the reasons before
assigned, to direct our attention to the exterior work alone.
During the expansion, the gas produces a work expressed by the
integral of the product of the differential of the volume into the
corresponding pressure, which product is represented geometri-
cally by the quadrilaterals ea, bfandfbcg. During the com-
pression, however, work will be expended, which is represented
by the quadrilaterals gcdh and hdae. The excess of the former
work above the latter is to be regarded as the entire work pro-
duced by the alterations, and this is represented by the quadri-
lateral abed.
If the foregoing process be reversed, we obtain at the conclu-
sion the same quantity abed as the excess of the work expended
over that produced.
10
M. R. Clausius o?i the Moving Force of Heat,
I
^
In applying the foregoing Fig. 2.
conaideratious analytically, we
will assume that the various
alterations which the gas has
undergone have been infinitely
small. We can then consider
the curves before mentioned
to be straight lines, as shown
in the accompanying figure.
In determining its superficial
content, the quadrilateral abed ^ € h f
may be regarded as a parallelogi-am, for the error in this case can
only amount to a differential of the third order, while the area
itself is a differential of the second order. The latter may there-
fore be expressed by the product ef.bk, where k marks the point
at which the ordinate 6/* cuts the lower side of the parallelogram.
The quantity bk is the increase of pressure due to the raising of
the constant volume of from t to t, that is to say, due to the
differential t—T=dt. This quantity can be expressed in terms
of V and t by means of equation (I.), as follows :
dp=z
Rrf/
If the increase of volume ef be denoted by dv, we obtain the
content of the quadrilateral, and with it
TTie work produced = (1 .)
We must now determine the quantity of heat consumed during
those alterations. Let the amount of heat which must be im-
parted to change the gas by a definite process from any given
state to another, in which its volume is =« and its temperature
= /, be called Q ; and let the changes of volume occurring in
the process above described, which are now to be regarded sepa-
rately, be denoted as follows : efhy dv, hg by dJv, eh by 8u, and
fg by h'v. During an expansion from the volume oe=zv to
of=^V'\-dvy at the constant temperature /, the gas must receive
the quantity of heat expressed by
and in accordance with this, during an expansion from vhzszv-\-hv
to og=iV-{-hv-\-d!v at the temperature t—dt, the quantity
and the Laws regarding the Nature of Heat. 11
In our case, however, instead of an expansion, a compression
has taken place ; hence this last expression must be introduced
with the negative sign. During the expansion from of to og,
and the compression from oh to oe, heat has been neither
received nor given away -, the amount of heat which the gas has
received over and above that which it has communicated, or, in
other words, the quantity of heat consumed, will therefore be
The quantities Sv and d'v must now be eliminated ; a conside-
ration of the figure furnishes us with the following equation :
dv + B'v =Bv + d'v.
During its compression from oh to oe, consequently during its
expansion under the same circumstances from oe to oh, and
during the expansion from of to og, both of which cause a de-
crease of temperature dt, the gas neither receives nor communi-
cates heat : from this we derive the equations
[(f)-i(§W»'-[(f)+£(§)*>»;
From these three equations and equation (2.) the quantities
d'v, 8v and B'v, may be eliminated ; neglecting during the pro-
cess all diiferentials of a higher order than the second, we obtain
nekeate^en,ed=[^(§)-i{§)],.d, . (3.)
Turning now to our maxim, which asserts that the production
of a certain quantity of work necessitates the expenditure of a
proportionate amount of heat, we may express this in the form
of an equation, thus :
The heat expended __ , ,..
The work produced "~ ^
where A denotes a constant which expresses the equivalent of heat
for the unit of work. The expressions (1.) and (3.) being intro-
duced into this equation, we obtain
a(2)-£(g)]"-_.
B^.dvdt
or
dt
^/^Q\ d /dQ\^ A.R ,jj.
it\dv) dv\dt) v ^ *^
12 M. R. Clausius on the Moving Force of Heat,
This equation may be regarded as the analytical expression
of the above maxim applicable to the case of permanent gases.
It shows that Q cannot be a function of v and t as long as the
two lattei* are independent of each other. For otherwise, ac-
cording to the known princij)le of the differential calculus, that
when a function of two variables is differentiated according to
both, the order in which this takes place is matter of indiffer-
ence, the right side of the equation must be equal 0.
The equation can be brought under the form of a complete
differential, thus :
dQ=dV-{-A.U''-^dv, .... (Lla.)
where U denotes an arbitrary function of v and t. This differ-
ential equation is of course unintegrable until we find a second
condition between the variables, by means of which t may be
expressed as a function of v. This is due, however, to the last
member alone, and this it is which corresponds to the exterior
work effected by the alteration ; for the differential of this work
is pdvj which, when j!> is eliminated by means of (I.), becomes
V
It follows, therefore, in the first place, from (II«.), that the
entire quantity of heat, Q, absorbed by the gas during a change
of volume and temperature may be decomposed into two portions.
One of these, U, which comprises the sensible heat and the heat
necessary for interior work, if such be present, fulfils the usual
assumption, it is a function of v and /, and is therefore determined
by the state of the gas at the beginning and at the end of the
alteration ; while the other portion, which comprises the heat
expended on exteiior work, depends, not only upon the state of
the gas at these two limits, but also upon the manner in which
the alterations have been effected throughout. It is shown above
that the same conclusion flows directly from the maxim itself.
Before attempting to make this equation suited to the deduc-
tion of further inferences, we will develope the analytical expres-
sion of the maxim applicable to vapours at their maximum density.
In this case we are not at liberty to assume the correctness of
the law of M. and G., and must therefore confine ourselves to the
maxim alone. To obtain an equation from this, we will again
pursue the com'se indicated by Camot, and reduced to a diagram
by Clapeyron." Let a vessel impervious to heat be partially filled
with water, leaving a space above for steam of the maximum
density corresponding to the temperature t. Let the volume of
both together be represented in the annexed figure by the
and the Laws regarding the Nature of Heat.
13
owt
abscissa oe, and the pressure of ria^di ^d VfiFig^i'SJK^'P^ erilT
the steam by the ordinate ea. Let ^IdBiiiqtjs laimm »vod*? ad* 1<>
the vessel be now supposed to r
expand, whilebothfluidand steam
are kept in contact with a body
A of the constant temperature < Ik rtJ^v ov/
t. As the space increases, more t ijijt rijuli^
fluid is evaporated, the necessary 'fjf'p') '^f t V' -^l
amount of latent heat being sup-
plied by the body A ; so that the
temperature, and consequently
the pressure of the steam, may remain unchanged. "When the
entire volume is increased in this manner from oe to o/, an ex-
terior work is produced which is represented by the rectangle ea
bf. Let the body A be now taken away, and let the vessel con-
tinue to expand without heat being either given or received.
Partly by the expansion of the steam already present, and partly
by the formation of new steam, the temperature will be lowered
and the pressure become less. Let the expansion be suiFered to
continue until the temperature passes from t to r, and let og
represent the volume at this temperature. If the decrease of
pressure during this expansion be represented by the curve he,
the exterior work produced by it will be represented by fbcg.
Let the vessel be now pressed together so as to bring the fluid
and vapour to their original volume oe, and during a portion of
the process let the vessel be in contact with a body, B, of the
temperature t, to which any excess of heat shall be immediately
imparted, and the temperature of the fluid and vapour kept con-
stant at T. During the other portion of the process, let the body
B be withdrawn so that the temperature may rise ; let the first
compression continue till the volume has been reduced to oh, it
being so arranged that the remaining space he shall be just suf-
ficient to raise the temperature from r to t. During the first
decrease of volume the pressure remains constant at gc, and the
quantity of exterior work expended is equal to the rectangle ^c dh.
During the last decrease of volume the pressure increases, and
may be represented by the curve da, which must terminate exactly
in the point a, as the original temperature t must again corre-
spond to the original pressure ea. The exterior work expended
in this case is :=-hdae.
At the end of the operation both fluid and vapour are in the
same state as at the commencement, so that the excess of the
exterior work produced over the amount expended expresses the
total amount of work accomplished. This excess is represented
by the quadrilateral ahcd, the content of which must therefore
be compared with the heat expended at the same time.
^
14 M. R. Clausius on the Moving Force of Heat,
For this purpose let it be as- Fig. 4.
sumed, as before, that the de-
scribed alterations are infinitely
small, and under this view let
the process be represented by
the annexed figure, in which the
curves ad and be shown in fig. 3
have passed into straight lines.
With regard to the content of
the quadrilateral abed, it may be -
again regarded as a parallelogram,
the area of which is expressed by the product ef. bk. Now if,
when the temperature is /, the pressure of the vapour at its
maximum tension be equal to p, and the difierence of tempera-
ture /— T be expressed by dt, we have
bk^^dt)
at
ef is the increase of volume caused by the passing of a certain
quantity of fluid represented by dm into a state of vapour. Let
the volume of the unit of steam at its maximum density for the
temperature t be called s, and the volume of the same quantity
of fluid at the temperature t be called a ; then is
ef^{s—(T)dm\
and hence the content of the rectangle, or
The work produced
(s— o") -jidm dt.
(5.)
To express the amount of heat, we will introduce the following
notation : — Let the quantity of heat rendered latent by the pas-
sage of a unit weight of fluid at the temperature /, and under a
corresponding pressure into a state of vapour, be called r, and
the specific heat of the fluid c; both of these quantities, as
dp
Finally,
also the foregoing s, a, and -^, being functions of t.
let the quantity of heat which must be communicated to a unit
weight of vapour of water to raise it from the temperature t to
t + dt, — the vapour being preserved by pressure at the maximum
density due to the latter temperature without precipitation, — be
called hdt, where h likewise represents a function of t. We shall
refer the question as to whether its value is positive or negative
to future consideration.
If we name the mass of fluid originally present in the vessel
fi, and the mass of the vapour m ; further, the mass evaporated
during the expansion from oe to of, dm, and the mass precipi-
tated by the compression from off to oh, d'm, we obtain in the
and the Laws regarding the Nature of Heat, 15
first case the quantity
rdm
of latent heat which has been extracted from the body A ; and
in the second case, the quantity
hP')
d'm
of sensible heat which has been imparted to the body B. By
the other expansion and contraction heat is neither gained nor
lost ; hence at the end of the process we have
The heat eocpended = rdm ~ ( ^ ~" jT ^M d^i^. . (6.)
In this equation the differential d^m must be expressed through
dm and dt ; the conditions under which the second expansion
and the second contraction have been carried out enables us to
do this. Let the mass of vapour precipitated by the compression
from oh to oSj and which therefore would deyelope itself by expan-
sion from oe to oh, be represented by hm, and the mass developed
by the expansion from of to og by am ; then, as at the conclu-
sion of the experiment the original mass of fluid and of vapour
must be present, we obtain in the first place the equation
dm + 8'm = d^m + hm.
Further, for the expansion from oe to oh, as the temperature
of the fluid mass /a and the mass of vapour m must thereby be
lessened the quantity dt without heat escaping, we obtain the
equation
rBm—fi . cdt—m . hdt = 0 ;
and in like manner for the expansion from of to og, as here we
have only to set fi—dm and m + ^m in the place of jm andm, and
h^m in the place of hm, we obtain
rh^m — (ft — dm) cdt ■— (m + dm) hdt = 0.
If from these three equations and equation (6.) the quantities
d^m, hm and S'm, be eliminated, and all diff'erentials of a higher
order than the second be neglected, we have
The heat expended — ijr -{-c—h\dmdt. . . (7.)
The formulae (7.) and (5.) must now be united, as in the case
of permanent gases, thus :
e--)
—a)^dmdt
dmdt
=A
16 M. R. Clausius on the Moving Force of Heat,
and hence we obtain, as the analytical expression of the maxim,
apphcablc to vapours at their maximum density, the equation
J+o-A=A(,-<.)f (III.)
If, instead of the above maxim, the assumption that the quan-
tity of heat is constant be retained, then, according to (7.), in-
stead of equation (III.) we must set
|+^-*=o- («•)
And this equation, although not exactly in the same form, has
been virtually used heretofore to determine the value of the quan-
tity h. As long as the law of Watt is regarded as true, that the
sum of the latent and sensible heat of a quantity of steam at its
maximum density is the same for all temperatures, and conse-
quently that
It +'=*''
it must be inferred that for this fluid k also is equal 0 ; this,
indeed, has been often asserted, by saying that when a quantity
of vapour at its maximum density is compressed in a vessel im-
pervious to heat, or suffered to expand in the same, it will remain
at its maximum density. As, however, Regnault* has corrected
the law of Watt so that we can set with tolerable accuracy
^+c=0'305,
the equation (8.) gives for h also the value 0*305. It follows
from this, that a portion of the steam in the impermeable vessel
must be precipitated by compression, and that it cannot retain
its maximum density after it has been suffered to expand, as its
temperature does not decrease in a ratio corresponding to the
decrease of density.
Quite otherwise is it if, instead of equation (8.), we make use
of equation (III.). The expression on the right-hand side is
from its nature always positive, and from this follows in the first
place that h is less than 0'305. It will be shown further on
that the value of the said expression is so great that h becomes
even negative. Hence we must conclude that the above quan-
tity of vapour will be partially precipitated, not by the compres-
sion, but by the expansion ; when compressed, its temperature
rises in a quicker ratio than that corresponding to the increase
of density, so that it does not continue at its maximum density.
This result is indeed directly opposed to the notions generally
* M^, de VAcad.y vol. xxi. 9th and 10th Memoirs,
and the Laws regarding the Nature of Heat. 17
entertained on this subject ; I believe_, however, that no experi-
ment can be found which contradicts it. On the contrary, it
harmonizes with the observations of Pambour better than the
common notion. Pambour found* that the steam issuing from
a locomotive after a journey always possesses the temperature
for which the tension observed at the same time is a maximum.
From this it follows that h is either 0, as was then supposed,
because this agreed with the law of Watt, which was considered
correct at the time, or that h is negative. If h were positive, then
the temperature of the issuing steam must have been too high
in comparison with its tension, and this could not have escaped
Pambour. If, on the contraiy, in agreement with the above, h be
negative, too low a temperature cannot occur, but a portion of the
vapour wdll be converted into water so as to preserve the remainder
at its proper temperature. This portion is not necessarily large,
as a small quantity of vapour imparts a comparatively large
quantity of heat by its precipitation ; the water thus formed is
probably carried forward mechanically by the steam, and might
remain unregarded ; the more so, as, even if observed, it might
have been imagined to proceed from the boiler.
So far the consequences have been deduced from the above
maxim alone, without any new assumption whatever being made.
Nevertheless, by availing ourselves of a very natural incidental
assumption, the equation for permanent gases (II«.) may be ren-
dered considerably more productive. Gases exhibit in their de-
portment, particularly as regards the relations of volume, tem-
perature and pressure, expressed by the laws of M. and G., so
much regularity as to lead us to the notion that the mutual
attraction of the particles which takes place in solid and fluid
bodies is in their case annulled ; so that while with solids and
fluids the heat necessary to efi*ect an expansion has to contend
with both an inner and an outer resistance, the latter only is
effective in the case of gases. If this be the case, then, by the
expansion of a gas, only so much heat can be rendered latent as
is necessary to exterior work. Further, there is no reason to
suppose that a gas, after it has expanded at a constant tempera-
ture, contains more sensible heat "than before. If this also be
admitted, we obtain the proposition, when a permanent gas ex-
pands at a constant temperature, it absorbs only as much heat as is
necessary to the exterior work produced by the expansion ; a pro-
position which is probably true for all gases in the same degree
as the law of M. and G.
From this immediately follows
■«\-A.Ki±i, (9.)
o-
* Traite des locomotives, 2nd edit., and Theorie des machines a vapeur,
2nd edit.
Phil, Mag, S. 4. Vol. 2, No. 8. July 1851. C
18 M. R. Clauaiua on the Moving Force of Heat,
for, SB already mentioned, R dv represents the quantity yf
exterior work produced by the expansion dv. According to this,
the function U, which appears in equation (Ha.), cannot contain
V, and hence the equation changes to
rfQ=crf/ + AR^rft;, .... (lib.)
wherein e can only be a function of / ; and it is even probable
that the quantity c, which denotes the specific heat of the gas at
a constant volume, is itself a constant.
To apply this equation to particular cases, the peculiar con-
ditions of each case must be brought into connexion therewith,
80 as to render it integrable. We shall here introduce only a
few simple examples, which possess either an intrinsic interest,
or obtain an interest by comparison with other results connected
with this subject.
In the first place, if we set in equation (11^.) v= const, and
/)s=: const., we obtain the specific heat of the gas at a constant
volume, and its specific heat under a constant pressure. In the
former case dv=iO, and (116.) becomes
f =^ ao-)
In the latter case, from the condition p = const., we obtain with
help of equation (I.),
, ndt
av= ,
P
or
. :■< , dv dt
V a-ht'
which placed in (lib.), the specific heat under a constant pressure
being denoted by c/, gives us
^=c'=c + AR (10a.)
From this it may be inferred that the difference of both specific
heats for every gas is a constant quantity AR. But this quantity
expresses a simple relation for different gases also. The com-
plete expression for R is ^^ ^ , where Pq, Vq,] and /q denote the
contemporaneous values of ^, v, and t for a unit of weight of the
gas in question ; and from this follows, as already mentioned in
expressing equation (I.), that R is inversely proportional to the
specific heat of the gas ; the same must be tme of the difference
cr-ocs AR, as A i» for all gases the same.
and the Laws regarding the Nature of Heat, 19
If it be desired to calculate the specific heat of the gas, not by
the unit of weight_, but by the method more in use, the unit of
volume, say at the temperature ^q and the pressure jOq, it is only
necessary to divide c and c' by Vq. Let these quotients be ex-
pressed by y and y, and we obtain ^>^ s-^'
In this last expression nothing appears which is dependent on
the peculiar nature of the gas ; the difference of the specific heats
reckoned according to the unit of volume is therefore the same
for all gases. This proposition has been deduced by Clapeyron
from the theory of Carnot ; but the constant found above .is
not given by the difference d —c, the expression found for it
having still the form of a function of the temperature.
Dividing both sides of equation (11.) by 7, we obtain
wherein k is set for shortness' sake in the place of — . This is
equal to the quotient - ; and through the theoretic labours of
Laplace on the transmission of sound through air, has attained
a peculiar interest in science. The excess of this quotient above
unity in the case of different gases is therefore inversely propor-
tional to their specific heats, reckoned according to the unit of
volume when the latter is constant. This proposition has been
proved experimentally by Dulong* to be so nearly correct, that
its theoretic probability induced him to assume its entire truth,
and to use it in an inverse manner in calculating the specific
heat of various gases, the value of k being first deduced from
observation. It must, however, be remarked, that the propo-
sition is theoretically safe only so far as the law of M. and G.
holds good ; which, as regards the various gases examined by
Dulong, was not always the case to a sufficient degree of accuracy.
Let us suppose that the specific heat c of the gases by constant
volume is constant, which we have already stated to be very pro-
bable ; this will also be the case when the pressure is constant,
c
and hence the quotient of both specific heats — =k must be also
constant. This proposition, which Poisson, in agreement with
the experiments of Gay-Lussac and Welter, has assumed to be
correct, and made the basis of his investigations on the tension
* Ann. de Chim. et de Phys,, xli. ; and Pogg. Ann., xvi.
C3
20 M . R. Clausius on the Moving Force of Heat.
and heat of gases*, harmonizes very well with our present theory,
while it is not possible to reconcile it with the theory of Camot
as heretofore treated.
In equation (116.) let Q=: const., we then obtain the following
equation between v and / :
cdt + A.n^^dv=:0; .... (13.)
V
from which, when c is regarded as constant, we derive
V • (a + t)= const. ;
AT? /^ *
or, since according to equation (10a.), = -— I==A— 1,
v*~*(fl + ^)= const.
Let three corresponding values of v, / and p, be denoted by g^
tQsmdpQ} we obtain from this igsWxs
a + tQ \v/ ^ ^
By means of equation (I.) let the pressure p, first for v and
then for /, be introduced here, we thus obtain
m-(B'- (-)
fe-fe)" <«•'
These are the relations which subsist between volume, tempe-
rature and pressure, when a quantity of gas is compressed, or is
suffered to expand in a holder impervious to heat. These equa-
tions agree completely with those developed by Poisson for the
same casef, the reason being that he also regarded k as constant.
Finally, in equation (lib.) let /= const., the first member at
the right-hand side disappears, and we have remaining
d(i=AU^-^dv; (17.)
V
from which follows
Q= AR(a + /) log i; 4- const. ;
or when the values of v, p, t and Q, at the commencement of
the experiment, are denoted by Vq,Pq, ^q and Qo,
Q-Qo=AR(«.F/o)logf. . . . (18.)
* Traiti de M^canique, 2nd edit. vol. ii. p. 646.
t Traits de M^canique, vol. ii. p. 647.
Mr. H. J. Brooke on the Beudantite of Levy. 21
From this, in the first place, we derive the proposition deve-
loped also by Carnot ; whe7i a gas, without alteration of tempera-
ture, changes its volume, the quantities of heat developed or absorbed
are in arithmetical progression, while the volumes are in geometrical
progression. ^^.
Further, let the complete expression for R= ^-^-^ be set in
equation (18.), and we obtain , .
Q-Qo=Ai,o''olog-. . . .' .' (19.)
If we apply this equation to diiferent gases, not directing our
attention to equal weights of the same, but to such quantities as
at the beginning embrace a common volume Vq, the equation
will in all its parts be independent of the peculiar nature of the
gas, and agrees with the known proposition to which Dulong,
led by the above simple relation of the quantity ^ — 1, has given
expression : that when equal volumes of different gases at the same
pressure and temperature are compressed or expanded an equal
fractional part of the volume, the same absolute amount of heat is
in all cases developed or absorbed. The equation (19.) is however
much more general. It says besides this, that the quantity of
heat is independent of the temperature at which the alteration of
volume takes place, if only the quantity of gas applied be always
so determined that the original volumes Vq at the diiferent tem-
peratures shall be equal; further, that when the original pressure
is in the different cases different, the quantities of heat are thereto
proportional.
[To be continued.]
II. On the Beudantite of Levy. By H. J. Brooke, F.R.S."^
HAVING had the pleasure last week of a personal commu-
nication with M. Des Cloizeaux, and having shown him
Levy's specimen of this mineral, he at once stated that it differed
entirely from that examined by himself and M. Damouras Beu-
dantite, as well as from every other specimen under the same
name which he had seen. He said that he was not aware of the
existence of any mineral resembling Levy's in any collection on
the Continent, and that he was inclined with Levy to regard his
specimen as belonging to a separate species. The mineral known
as Beudantite on the continent appears to be only an impure
variety of cube ore of the usual form.
June 9, 1851.
* Communicated by the Author.
[ 22 ]
III. On the joint Influence exerted by Light and the Oxidability
of certain substances upon common Oxygen. By C. F. Schosn-
BEIN*.
My dear Faraday,
SINCE I wrote to you last, I have been engaged in making
researches on the different ways of exalting the chemical
affinities of oxygen at the common temperature, and trust that
the labour bestowed upon the subject will have been not entirely
lost.
You know that I was inclined to consider phosphorus as the
type of all the substances that are capable of undergoing oxida-
tion in atmospheric air or oxygen at the common temperature,
f. e. that I thought common oxygen unfit to unite chemically to
any body ; or to speak still more distinctly, I was disposed to
conjecture that the slow oxidation of any substance is always
preceded by a change of condition, or, if you like, an allotropic
modification of the oxygen causing that oxidation. To be able
to test the correctness of that conjecture, I wanted a substance
which was not affected by common oxygen, but readily oxidized by
ozonized or excited oxygen, and at the same time such as to
allow perceiving easily and surely its oxidation. Such a matter
I think is indigo dissolved in sulphuric acid, i. e. common indigo
solution, whose colour cannot be discharged by common oxygen,
but very easily by means of oxygen in the ozonic condition.
Now I reasoned thus : if any mJitter (undergoing oxidation in
atmospheric air at the common temperature) should have the
power of effecting, previously to its oxidation, an allotropic mo-
dification of the common oxygen, indigo solution being mixed
with that matter and bi'ought in contact with atmospheric air
ought to be oxidized conjointly with the oxidable substance, just
in the same way as the colour of indigo solution placed in con-
tact with phosphorus and atmospheric air, is discharged whilst
phosphorus is undergoing oxidation.
My anticipations have, I think, been confirmed by the results
of numerous experiments ; for I have ascertained that a series of
organic and inorganic matters, capable of oxidation at the common
temperature, have indeed the power of discharging the colour of
indigo solution, and exhibit in this respect a befiaviour exactly
like that of phosphorus. But, before I proceed further, I must
not omit to mention tliat that power is vei-y small in the dark,
and, comparatively speaking, strong in direct solar light.
The organic matters as yet tested are-^spirit of wine, spirit of
wood, linseed oil, tartaric acid, nitric acid, formic acid, acetic
* Communicated by Prof. Faraday.
On the Influence exerted by Light upon common Oxygen. 23
acid, wine and beer; the inorganic ones are — sulphuretted,
arseniuretted, antimoniuretted hydrogen, sulphurous acid.
The most distinguished of the first series is tartaric acid, of
the second series, sulphurous acid.
I put into a spacious bottle (charged with atmospheric air)
100 grammes of water, 10 grammes of tartaric acid, and one
gramme of my standard indigo solution, continually shaking the
whole exposed to strong sunlight, and within forty minutes the
colour of the liquid appeared to be discharged. In this way I
have already destroyed 50 grammes of indigo solution by the 10
grammes of the acid, without having as yet exhausted its dis-
charging power.
A strip of linen cloth rather strongly dyed by indigo solution,
drenched with a solution of tartaric acid, continually kept moist
by water and exposed to the joint action of a strong sun and
atmospheric air, was completely bleached within five hours. In
the dark, under the same circumstances, the bleaching of the
dyed cloth, or the discharge of the colour of the indigoferous
tartaric acid solution, takes place very slowly. I have kept these
last four weeks a bit of moist blue linen impregnated with a solu*
tion of tartaric acid in a dark room, and now it appears certainly
to be a shade lighter than it was in the beginning ; but it is still
very blue.
To test the discharging power of the other otganic matters
named, I put 10 grammes of the one or the other of them into
a spacious white bottle filled with air, add to it 100 grammes of
water, and 1 gramme of the standard indigo solution, expose
the mixture to the action of light, and shake the whole as often
as I can, taking care to renew now and then the air of the bottle.
Experimenting in this way, the discharging power of the sub-
stances mentioned and that of others is easily ascertained.
As to the hydrogenated compounds of sulphur, selenium,
arsenic and antimony, I mix them with atmospheric air, putting
some water on the bottom of the vessel holding the mixture,
suspend within it a moist strip of linen dyed with dilute indigo
solution, and expose the whole to the action of solar light. The
bleaching of the cloth does not take place very rapidly in those
gaseous mixtures ; for instance, in that of sulphuretted hydrogen
the strip had to remain for a week before its colour was entirely
discharged. In the mixture of arseniuretted or antimoniuretted
hydrogen and atmospheric air, the cloth becomes brown in con-
sequence of metallic arsenic or antimony being deposited upon
the strip.
By far the most interesting oxidable inorganic substance, as
to its indirect bleaching power, is sulphurous acid. This acid,
as well as the other oxidable matters mentioned, when deprived
24: M. C. F. Schocnbein on the joint Influence exerted by Light
of any free oxygen, has no appreciable action upon the indigo
solution ; for you may keep them together any length of time
(even in sunlight) without being able to perceive any diminution
or change of colour. So soon, however, as you permit oxygen
or atmospheric air to enter, an action will ensue, very slow in
the dark ; comparatively speaking, very rapid in solar light.
The simplest way of exhibiting the action is this : suspend
moist strips of linen dyed with indigo solution in a mixture of
gaseous sulphurous acid and oxygen gas or atmospheric air.
When placed in the dark, such strips require many weeks to
become entirely white, whilst a strong noon^s insolation of one
and a half, or at most two hours' duration, will completely bleach
them.
As a matter of course, the colour of aqueous sulphurous acid
mixed up with some indigo solution and shaken with oxygen
or atmospheric air, \vill also be much more rapidly discharged in
solar light than it is in the dark. 100 grammes of a weak sul-
phui'ous acid, coloured by 1 gramme of the standard indigo
solution, on being continually shaken with atmospheric air and
exposed to a strong sun, lost the colour within twenty minutes.
It is hardly necessary to mention, that the bleaching power is
exerted as long as there is free oxygen and sulphurous acid ; for
no sooner has the latter disappeared, i. e. been transfoi-med into
sulphuric acid, than the action ceases to take place in a per-
ceptible degree.
I w^as curious to see how much of my standard indigo solution
could be destroyed by a given weight of pure sulphurous acid.
Five grammes of the latter, mixed up with 200 grammes of water,
were therefore put into a bottle holding about two litres and
filled with atmospheric air,, then 50 grammes of the standard
indigo solution added, the whole exposed to the action of solar
light, repeatedly shaken, and the atmospheric air now and then
renewed. There being little sunshine, the colour of the liquid
was discharged within a couple of days, and in the course of six
weeks (very deficient in sunshine) I have been able to destroy
600 grammes of the standard indigo solution, and find that there
is still a very perceptible quantity of sulphurous acid in the
mixture. The discharging power is therefore not yet exhausted.
Now to discharge the colour of 600 grammes of my indigo
solution, I require nearly 1 1 grammes of the strongest nitric acid
(the monohydrate), or fully 18 grammes of good chloride of lime ;
and 5 grammes of pure sulphurous acid having already done the
same work, and being able to do still more, we see that sulphu-
rous acid enjoys a most extraordinary indirect oxidizing power.
I say " indirect,'' because the acid itself has nothing to do with
the oxidation of indigo; the only part it performs conjointly
and the Oxidability of certain substances upon common Oxygen. 25
with light is^ to exalt the chemical affinities of free common
oxygen to such an extent as to render that element capable of
destroying indigo just as well as ozone does. I have reason to
believe that indigo is not the only organic substance which is
indirectly oxidized by sulphurous acid^ for I have succeeded in
destroying some very strongly coloured organic matters by the
joint agency of light, sulphurous acid and common oxygen.
It is worthy of remark, that the amount of the exalting effects
produced by light conjointly with sulphurous or tartaric acids,
&c. upon oxygen far surpasses the sum of the effects brought
about singly by those agents. Insolated oxygen or air of itself
certainly is capable of discharging the colour of indigo solution,
and so is oxygen placed under the exciting influence of sulphu-
rous acid, tartaric acid> &c. unassisted by light ; but in both cases
the action is very slow, whilst it is rapid if both causes be work-
ing together. The facts, that linseed oil, on being shaken with
copper filings and atmospheric air in sunlight, soon turns green,
brass in contact with fatty matters assumes the same colour,
mercury contained in a divided state in the unguentum mercu-
riale is gradually transformed into the protoxide, fibrous mat-
ters impregnated with oils are now and then spontaneously set
on fire, &c., seem to be connected with the exciting influence
exerted by oxidable matters upon ordinary oxygen.
If, according to Berzelius and others, ozone be but an allo-
tropic modification of common oxygen, we must admit that phos-
phorus, like electricity, has the power of causing that extraordi-
nary change of condition in common oxygen, and are led to sup-
pose that phosphorus stands not alone in this respect. Indeed,
my late researches on oil of turpentine, &c. show that many other
substances make oxygen act (even independently of light) as
phosphorus does.
Now these facts seem to give room to the conjecture, that
many oxidable matters and oxygen, on being put in contact with
one another, exert a peculiar influence upon each other previous
to their chemically uniting with one another. As to phosphorus,
oil of turpentine, &c., it seems as if the first action produced
upon common oxygen be the allotropification of that body, and
the oxidation of phosphorus the sequel, and not the cause of the
formation of ozone. I therefore think it not impossible, that at
least some of those strange chemical phsenomena, called cata-
lytic, may be connected with an action similar to that pro-
duced by phosphorus, oil of turpentine, &c. upon oxygen, i. e.
depend upon allotropic modifications of elementary bodies brought
about by the mere contact of certain substances. Certainly we
do not know as yet in what the allotropic modifications consist,
and how they are effected ; but whatever they may depend upon
26 Dr. Tyndall on the Progress of the Physical Sciences :
they are facts ; and facts, too, which in my opinion will, if once
better understood than they are now, throw floods of light upon
the thick darkness with which the chemical world is as yet
covered. And I am inclined to think so, because it is very
likely that the so called catalytical phfenomena reveal the very
clementai-y, and on that account the most important, actions or
functions of matter.
I am, my dear Faraday,
Yours most truly,
BAle, May 1, 1851. C. P. Schcenbein.
IV. Reports on the Progress of the Physical Sciences.
By John Tyndall, Ph.D., Marburg.
1. The Reversion-prism, and its application as oculaf to the Terrestrial
or Day-Telescope, by H. W. Dove.
2. Description of several Prism-stereoscopes, and of a simple Mirror^
stereoscope, by H. W. Dove.
3. On the deportment of Crystalline bodies between the electric poles, by
II. Knoblauch.
FOR the manuscript of the first two papers I am indebted to
the kindness of Professor Dove. The reversion-prism will
probably come into practical use both in England and Germany.
In leveling instruments, for example, the inconvenience of the
common telescope led to Gravatt^s invention of the dumpy-level ;
but the inversion of the figures upon the leveling- staves consti-
tutes an objection in the eyes of many. M. Dove's invention
removes this objection; the reversion-prism sets the figures
again erect without rendering a lengthening of the instrument
necessary. The application of the invention will render the day-
telescope in genei-al a more convenient instrument.
The stereoscopic apparatus and phsenomena described in the
second paper are strikingly simple and beautiful. I would
recommend the reader to furnish himself with a pair of prisms
and a few stereoscopic drawings ; with their aid the paper will
be much more intelligible.
The paper by Professor Knoblauch has also been handed to
me in manuscript. It is highly interesting to observe the par-
allelism between electricity and magnetism in the production
of phsenomena. The author has demonstrated the action of
electricity on crystalline substances in a very convincing manner,
and seems to have succeeded in tracing the phsenomena-to the
same cause as that to which magneto-optic action has been
referred by him and the writer, namely, to peculiarity of aggre-
gation. In the ' Report ' the translation of the manuscript is
slightly abbreviated.
Prof. Dove on the Reversion-prism ^ 37
\'l'Th6 'R^'ii&rdon-prism, and its application as ocular to the Ter- ,
restrial or Day -Telescope, and to the measurement of angles.
When rays fall upon the side surface of a prism whose ends
are right-angled isosceles triangles^ and parallel to the hypo-
thenuse surface of the same, they issue from the other side, after
having endured two refractions and one total reflexion.
An object observed through such a prism appears unaltered
in shape and magnitude, but it has changed sides in the same
manner as the image of an object in a looking-glass. The con-
ditions of achromatism are strictly fulfilled, for all rays which
were parallel before their entrance remain so after their exit. If
the hypothenuse surface lie horizontal, so that its production
shall intersect the object in a horizontal line, then the image is
obtained by letting fall from all points of the object perpendi-
cularfe upon this line, and producing them until their parts above
and below the horizontal line are equal to each other. .The ends
of the productions taken all together form the image of the
object.
If therefore a vertical line be intersected in the centre by the
above horizontal line, the former line and its image will coincide,
its position being reversed. If the line make an angle of 45°
with the produced hypothenuse surface, then the image will be
perpendicular to the object. Now as an inclination of 45° on
the part of the line which was first considered vertical, the prism
remaining fixed, has the same efi'ect as if the line remained fixed
and the prism were turned 45° in the opposite direction, the
image must rotate with double the velocity of the plane of refrac-
tion of the rotating prism.
As the rays which emerge from this first prism with regard
to a second similar one may be considered as proceeding direct
from an object which occupies the position of the image, it
follows, —
If the hypothenuse surfaces of two equal prisms lie in the
same plane, their corresponding edges being parallel, then an
object viewed through both will appear altogether unchanged ;
for the second prism reverses the image delivered by the first
prism, or in other words, it undoes the work of the latter and
restores things to their primitive condition. If, on the contraiy,
the first prism remain fixed and the second be turned, so that the
planes of refraction of both prisms are perpendicular to each
other, the object then appears completely reversed. The first
prism reverses it with regard to right and left, and the second
with regard to top and bottom. As, however, a reversion is
equivalent to a turning of the object through an angle of 180°,
it follows, —
28 Dr. Tyndall on ike Prop-ess of the Physical Sciences :
Through two prisms situated so that the hypothcnusc edges
form a straight line, an ohject appears unchanged in size and
shape, but inchned at an angle which is twice as large as that
inclosed by the planes of refraction of the two prisms. For it is
clear that the double re^ crsion takes place in the same manner,
whether the two lines in which the productions of the hypo-
thenuse surfaces of the prism cut the object form a right or an
acute angle with each other. Everybody will admit>that when a
plane is turned 180° round an arbitrary line which lies in it,
and then 180° round another arbitrary line which also lies in it,
the appeai*ance of the plane as regards shape and size is the
same ; but if the lines do not cross each other at a right angle,,
the position of the plane will be oblique.
At whatever stage of the rotation the prisms may stand, if
they be both turned together, that is to say, if the case which
incloses them be caused to rotate, the image continues fixed.
For, as the image of the first prism moves with twice the velo-
city of the second prism, the motion, however, being equivalent
to a motion of the prism in the opposite direction, the second
prism win therefore cany the image back with exactly the same
velocity as the first prism carries it forward.
A system of two such prisms is named by the inventor a
reversion^prism. If the reversion -prism be screwed before the
ocular of an astronomical telescope, then if the planes of refrac-
tion of the prisms stand perpendicular to each other, the tele-
scope is converted into a terrestrial one. An ocular so constructed
is named by the inventor a terrestrial prism-ocular. The prisms
are made fast in a cylindrical collar, the second being capable of
rotating while the first remains fixed. The periphery of the
piece which turns is divided into degrees like the head of a
micrometer-screw ; and upon the cylindrical collar, two strokes
which stand opposite to each other denote the position of the
plane of refraction of the fixed prism. The zero of the gradua-
tion corresponds to the plane of refraction of the moveable prism.
When the planes of refraction inclose the angle 0, the telescope
is astronomical ; when they inclose an angle of 90°, the telescope
is terrestrial. If the planes inclose an acute angle, the observed
object will appear turned through twice the angle formed by the
planes of refraction, and will remain thus inclined when the tele-
scope is turned round its axis.
Owing to the shortness of the prism-ocular, a terrestrial tele-
scope thus constructed is much shorter than the common one,
and may therefore be used with advantage in the naval or mili-
tary service. It is to be screwed like a shade before the ocular
of the astronomical telescope. If it be applied as a terrestrial
ocular only, it is best to fasten both prisms together, so that
Prof. Dove on several Prism-stereoscopes, 29
their planes of refraction shall be constantly perpendicular to
each other. In the reading of numbers we thus avoid the un-
pleasantness of an inversion.
The application to the measurement of angles of inclination is
as follows : — The prisms being set at an angle of 90° in the tele-
scope, so that objects appear in their natural position,, the tele-
scope is turned round its axis until the vertical cross-wire covers
the line, the inclination of which is to be determined; The
forward prism is now turned until the vertical wire and the line
which it covers coincide with a plummet-line suspended before
the telescope. The angle of rotation is equal to half the com-
plement of the angle of inclination sought. The reversion-prism
can also be placed within the telescope or before the object-glass
of the instrument, its size being so chosen that an object can be
seen through the prism and through the uncovered portion of
the object-glass at the same time. The two lines whose inclosed
angle is to be determined are brought to coincidence ; the one
seen through the uncovered object-glass, and the other through
the prism. If the reversion -prism be set in the interior of the
telescope, then the terrestrial instrument is of the same length
as the astronomical, the entire length of the terrestrial ocular
being thus spared. If in this case it be required that the prism
should be capable of being turned round, the tube of the tele-
scope may be composed of two parts, one of which fits into the
other ; in one part the fixed prism is to be set, and in the other
part the rotating prism.
In all isosceles triangles the condition of total reflexion is ful-
filled for those rays which fall parallel to the base and near it.
That which has been heretofore affirmed regarding right-angled
triangles, is true of isosceles triangles generally. The number
of rays, however, which after their first refraction reach the base,
decreases as the angle at the vertex becomes more acute. In
each particular case, therefore, where another than the right-
angled triangle is applied, the angle must be determined which
permits of the whole of the rays falling upon the first surface
being totally reflected. With an acute angle, the length of the
ocular decreases and the light intensity increases. To adjust the
prisms, the common method of turning the telescope round its
axis, and observing that the position of any chosen point remains
fixed, is to be applied. >; -. << "i; '^
, 2. Description of several Prism-stereoscopes, and of a simple ^s
1 1 ■:. MiiTor-stereoscope. ■. ^'
When stereoscopic di-awings are executed in white lines upon
a black ground, a weak image arising from the reflexion which
takes place at the uncovered forward surface of the glass often
so Dr. Tyndall on the Progi^ess of the Physical Sciences :
mixes itself with the principal image reflected from the silvered
surface behind. To prevent the appearance of such images,
total or metallic reflexion is necessary. In stereoscopic investi-
gations, where the contours of the images do not exactly coin-
cide, a doubt may arise whether this be not due to the imperfec-
tion of the drawings made use of. The desire to set aside this
possible source of error has led to the construction of the follow-
ing stereoscopes.
a. Prism-stereoscope J consisting of one Prism and one Drawing
intended for a single eye.
The condition of complete identity can only be fulfilled when
one object, and not two, is observed. An object seen in a look-
ing-glass appears reversed as regards right and left. In all
stereoscopic drawings, which difiier only in the circumstance that
one is a reflected image of the other (and to this class belong the
greatest number, even the most complicated of those hitherto
executed), the reflected image of the object can take the place of
the second drawing. Such drawings may be named simple rever-
sions, in contradistinction to those in which a plane perpendicular
to the line which joins both eyes and passing through the centre
of the body does not divide the latter symmetrically. If an erect
object be viewed through a prism whose ends are right-angled
isosceles triangles, the prism being so placed that its plane of
refraction is horizontal, that is to say, with its hypothenuse sur-
face vertical, the object will remain erect ; but with regard to
right and left, it will be found to have changed sides. Through
such a prism, therefore, the arranged type in a printer's work-
shop may be read as the page of a common book ; the letters
change places right and left, and thus appear as when they are
printed. In the same way a profile is reversed. If a common
stereoscopic drawing intended for the left eye be viewed by the
right eye through such a prism, then if the projections be simple
reversions of each other, the image will appear as if designed for
the right eye. To the left, or naked eye, the drawing appears
unchanged. It is easy, by turning the prism round one of the
edges which stands perpendicular to the plane of refraction, to
cause both images to coincide ; the moment this takes place, the
relief starts into existence with surprising sharpness.
If the position of the drawing remain unchanged, and the
prism be held before the left eye, then if the object be conceived
to be transparent, so that both its exterior and interior surfaces
are risible, the forward surface will appear converted into the
surface behind, and vice versd. When, on the contrary, a draw-
ing intended for the right eye is viewed through the prism by
the left eye, it will appear exactly as in the first case, always
provided that it is viewed at the same time by the naked right
Prof, Dove on several Prisni'Stereoscopes. 31
eye. If the drawing represents a body, whicli, like a pyramid
or the frustum of a pyramid, appears with regard to the surface
of the paper either as convex or concave rehef, then the said
drawing viewed through the prism with one eye, and with the
other eye naked, will appear in convex relief; when the prism is
held before the other eye, the stereoscopic combination of both
images gives rise to a concave relief. If the drawing be turned
in its own plane while the prism remains before the same eye, a
rotation of 90° causes the coincidence of the images to appear as
a plane projection, A rotation of 180°, on the contrary, changes
it from concave to convex. During the rotation, the hypo-
thenuse surface must stand perpendicular, or nearly so, to the
observed drawing.
With regard to the dimensions of the prism for holding
freely in the hand, an inch in length for the two equal sides of
the isosceles triangle at the end, and three-quarters of an inch
in width, will be found convenient proportions. When fastened
in a cylindi'ical tube attached to a stand, which permits of its
being raised and lowered, a prism will be found sufficiently large
in which the height of the right-angled triangle does not quite
amount to two lines.
b. Prism-stereoscope, consisting of one Prism and two Drawings.
The stereoscope just described fulfils the condition of the
complete identity of both projections, and besides this possesses
the advantage of a total reflexion, by which incidental images are
avoided; but it is applicable to simple reversions only. The
following instrument is free from this limitation. In simple
reversions, two copies of the same drawing are laid side by side.
One of them is viewed through the prism, and the image thus
obtained is projected upon the other which is viewed with the
naked eye. When the drawings are unsymmetrical, that intended
for the right eye is placed right, and viewed through the prism
held before the right eye ; the image thus obtained is projected
upon the second drawing, which is observed by the naked left
eye, and which must be a copy of the looking-glass image of the
drawing intended for the left eye in the common stereoscope.
c. Prism-stereoscope, consisting of a Reversion-prism and two
Drawings.
The reversion-prism reverses an object completely, as well in
respect to right and left as to top and bottom. The unsymme-
trical projections intended for the common stereoscope are placed
in reversed positions beside each other, and the image seen
through the reversion- prism is projected upon the other drawing
which is observed with the naked eye,
d. Prism-stereoscope, consisting of two Prisms and two Drawings.
Two equal isosceles right-angled prisms are held one before
32 Dr. ^yndall on tlte Progress of tlie Physical Sciences :
each eye, so that the hypothenuse surfaces are vertical — best so
that the hypothenuse surfaces face each other — and by inclining
the prisms, the images of the two drawings placed side by side
are brought to coincidence. This stereoscope, like the eye, is
applicable to all drawings ; when the prisms are fixed in cylin-
drical tubes and attached to a stand, the arrangement is exceed-
ingly convenient. , .>
e. Mirror-stereoscope mth two Drawings and a plane metallic
mirror or reflecting prism.
The drawing intended for the left eye is laid horizontal, and
is viewed with the naked left eye. Before the right eye is held
a small metallic mirror or a reflecting prism ; and in the case of
simple figures, another copy of the same drawing is observed in
a vertical plane. For an unsymmetrical figm*e, a drawing which
is the reflected image of that intended for the right eye must be
used.
f. Double-seeing, as Stereoscope.
Those who have accustomed themselves to double-seeing, when
two stereoscopic drawings are laid side by side, can obtain four
images in a direction parallel to a line joining both eyes. The
two central images can be brought to coincidence, the relief
being thus obtained between its two projections. This experi-
ment is, however, so weaiying to the eyes, that its frequent
repetition is not to be recommended. The author has made the
experiment purely on account of its physiological interest. A most
peculiar impression is caused by the union of the two images in
the relief. When brought near, they seem to rush together with
an accelerated velocity as if they more strongly attracted each
other. In a similar manner, when two persons lay their fore-
heads together and look into each other's eyes, each observes the
eyes of the other to run together into one large eye in the centr^.
of the forehead. ^
g. Whi/ does the depth of the concave Relief appear greater
than t/ie height of the Convex ?
In the application of the stereoscopes above described, it is
observed in a sti-iking manner, particularly when the di'awings
are viewed from some distance, that by exchanging the projec-
tions the height of the convex relief appears less than the depth
of the concave. The plane of the paper on which, as ground
surface, the drawing is executed, is seen at the same distance in
both cases. That this is the cause of the phsenomenon is proved
by the fact, that the side surfaces of the frustum of a pyramid,
stereoscopic obseiTcd, seem to be less steeply inclined towards the
base when the top of the frustum is nearest the eye, than when
it falls at the other side of the base, and is viewed through the
hollow prism. The top surface of the frustum is seen in both
Prof. Knoblauch on the Deportment of Crystalline Bodies. 33
cases under the same angle ; but in the second case we imagine
that it lies further away. Hence the idea of a larger surface
seen at a greater distance^ and the apparent diminution of the
inclination.
This explanation is corroborated by the following experiment :
A small gypsum bust was placed before a polished hollow mirror,
so that the reversed image seen with both eyes fell beside the
bust. Without changing the position of the right eye, the left
eye was closed. The image receded immediately to the surface
of the mirror, and appeared much larger ; it was observed under
the same angle, but fancied to be at a greater distance.
In comparative stereoscopic investigations the drawings must
always stand at equal distances. It is a proof that the combina-
tion is good if, when the head is moved slowly to and fro, the
relief is set in slow oscillatory motion.
3. On the Deportment of Crystalline Bodies between the Electric
Poles.
It is well known that crystalline bodies suspended between
the poles of a magnet take up positions which distinguish them
from unciystalline. It will be of interest to examine whether a
similar deportment is exhibited between the electric poles.
As in the case of bodies suspended between the poles of a
magnet, it is here absolutely necessary to annul all action which
might arise from a mere peculiarity of shape. This is done by
converting the substance into circular discs, which arc to be sus-
pended horizontally.
A plate of heavy spar cloven parallel to the plane of most emi-
nent cleavage had the short diagonal of the rhombic base marked
upon it. Suspended between the poles of a dry pile consisting
of 400 pairs of zinc and gold-paper, or of 2000 pairs of silver-
paper and manganese, it set itself so that the short diagonal stood
perpendicular to the line joining the poles.
For the sake of brevity, as in the case of experiments with the
magnet, we shall call this position the equatorial.
A circular disc taken from a gypsum crystal parallel to the
plane of most eminent cleavage, set itself so that a line, which
slightly deviated from the short diagonal of the rhombus inclosed
by the other cleavages, stood equatorial.
These experiments require the greatest caution ; only such
crystals should be used as are entirely free from all traces of
fracture. Seven examples coincided in the deportment just
described. The action is stronger in the following crystals : —
Saltpetre was so cut that the crystallographic axis lay in the
plane of the disc; between the electric poles the axis stood
equatorial.
Phil Mag. S. 4. Vol ». No, 8. July 1851. D
34 Dr. Tyndall on the Progress of the Physical Sciences :
Discs were taken from Iceland spar, carbonate of lime and iron,
and carbonate of iron, so that the axis in each instance lay in
the plane of the disc. The axis in every case turned slowly
into the equatorial position and finally remained there.
A disc of arragonite exhibited the same deportment. The axis
stood equatorial. In this experiment particular precautions are
necessary, which shall be immediately pointed out.
Beryl cut into the form of a shallow cylinder set its axis from
pole to pole. The plane of most eminent cleavage stood con-
sequently equatorial.
A disc of tourmaline set itself so that the line perpendicular to
the axis stood equatorial.
In all non-conducting substances it is known that the induc-
tion which takes place on the approach of an electrified body
continues for some time after the said body is removed. This
fixation of the fluid may be readily demonstrated with a disc of
glass.
In rock-crystal and topaz this polarization is exhibited so
strongly, that if a disc be held for an instant between the two
poles, it will continue to assert this position against an inten-
tional torsion of the suspending fibre.
Although similar phsenomena of polarity were exhibited more
or less by all the crystals examined, still, if we except arragonite,
they never attained to such a degree of intensity as to prevent
the assumption of the positions above described.
If the crystal be a conductor, a continuance of the electric
state is not observed after the exciting cause has been removed.
A cylinder of bismuth, the axis of which was perpendicular to
the plane of most eminent cleavage, always set itself so that the
said plane formed an angle of 90° with the line joining the
poles.
In the investigation on the magneto-optic properties of cry-
stals* carried out by Dr. Tyndall and myself, the position of
crystals between the poles of a magnet is referred to the peculiar
.aggregation of the material particles. The question occurs, Do
not the phsenomena above described permit of being referred to
a similar origin ?
A fine powder of sulphate of barytes was mixed to a paste
with gum- water and pressed together in one direction. From
the mass when dried a circular disc was taken, so that the line
of compression was parallel to the plane of the disc. The direc-
tion of greatest compression takes up between the poles a posi-
tion similar to that assumed by the short diagonal of heavy spar
— it sets equatorial.
* Philosophical Magazine, July 1850.
Prof. Knoblauch on the Deportment of Crystalline Bodies. 35
A disc of carbonate of lime, in which the particles were brought
by pressure more closely together in one direction_, set itself with
the line of compression equatorial. This line therefore corre-
sponds with the axes of arragonite and calcareous spar.
The same coincidence was exhibited between a disc of pow-
dered carbonate of iron and the crystal of the same substance.
The direction of compression, like the axis of the crystal, set
equatorial.
Besides those bodies whose chemical composition is the same
as that of the crystals examined, others of powdered glass, chro-
mate of lead, and phosphate of lime were also submitted to ex-
amination. Of conducting bodies, oxide of manganese, oxide of
iron, antimony and bismuth, were examined; the direction of
compression in all these substances set itself between the electric
poles equatorial.
The decided manner in which these pheenomena are exhibited,
prove to a certainty that those bodies in which the material par-
ticles are not the same distance apart in all directions set between
the poles (when the directing influence of mere shape is annulled),
so that the line in which the particles stand most closely together
stands equatorial.
The coincidence of position of diamagnetic crystals between
the magnetic and the electric poles, and the difference of position
assumed by magnetic crystals, stand in immediate connexion
with the results arrived at by Mr. Tyndall and myself. We have
shown that, in bodies whose particles are unequally separated in
different directions, that direction in which the particles lie most
closely together sets in the magnetic field when the substance is
magnetic from pole to pole ; when the substance is diamagnetic,
equatorial.
Of the crystals mentioned the following are magnetic : — car-
bonate of lime and iron, beryl and tourmaline. In all these
cases, that direction, which, by the action of the magnetic poles,
sets itself axial, between the electric poles sets equatorial.
Of the crystals examined the following are diamagnetic : —
heavy spar, sulphate of lime, saltpetre, Iceland spar, arragonite
and bismuth ; in all these cases, the direction which between
the magnetic pole stands equatorial, takes up the same position
between the electric poles.
The principal results of the inquiry may be expressed as fol-
lows: — 1. Crystals, conductors and non-conductors, under the
influence of the electric poles obey a directive force which is in-
dependent of the form of the mass. 2. The same is the case
with bodies the material particles of which are brought by pres-
sure into unequal distances from each other ; that line in which
the particles lie most closely together being caused to recede
D2
36 Mr. W. J. M. Rankiiie on the Theory of Sound.
from the poles. 3. When the ci-ystal is magnetie, that dii*ection
which between tlie magnetic poles stands axial, between the elec-
tric poles stands equatorial. When the ciystal is diamagnetic,
the positions between the magnetic poles and electric poles arc
coincident. The same holds true for substances artificially com-
pressed.
V. On the Theory of Sound,
By W. J. Macquorn Rankine, F.R.S.E. ^c*
I TRUST that the following brief remarks may remove the
objections still entertained by Professor Potter f to my ex-
planation of Poisson's investigation of the velocity of sound
in air J.
Professor Potter objects that I have asserted, without sufficient
groimds, that the variation of pressure is developable in terms of
the variation of density by means of Taylor's theorem, the coeffi-
cient of the first term being a finite quantity,
e«.,^Vo=l+/8.
Po
My grounds for this assertion are, that if the variation of
pressure is not so developable in tenns of the variation of den-
sity, or if 1+/3 is not a finite quantity, then the variation of
pressure con'esponding to an indefinitely small variation of den-
sity must be either null or infinite ; that is to say, either the
pressure must be a maximum or a minimum with respect to the
density, or the density a maximum or a minimum with respect
to the pressure. But this is not the case, for the pressure varies
continuously with the density ; therefore the variation of pressure
is developable in terms of the variation of density by Taylor's
theorem, and the coefficient 1 +^8 is a finite quantity.
Professor Potter misconceives my meaning when he supposes
that I deny the existence of unsymmetrical waves of sound. My
remarks were intended to apply to waves, which, having been
originally symmetrical, become unsymmetrical as they advance,
like those on the surface of shallow water.
LondoD, June 2, 1851.
* Communicated by the Author.
t Fourth Series, vol. i. p. 476. % Ibid. p. 410.
\\\\\\{y< \\\' \rui:>iV V
[ 37 ]
)t
VI . Pendulum Eooperiments. By Thomas G. Bunt. '^^
To the Editors of the Philosophical Magazine and Journal. ^
Gentlemen, Bristol, June 11, 185T.
THE series of pendulum experiments detailed in my last letter
I have now somewhat extended, and arranged more system-
atically than before. The result of the whole is shown in the
following summary : —
Part of azimuth
circle observed.
Time occupied in
the experiments.
Motion of plane
in azimuth.
Rate per hour.
Oto 20
20... 40
40... 60
60... 80
80... 100
100 ... 120
120... 140
140 ...160
160... 180
min.
224-9
323-8
220-0
177-5
182-6
144-8
2091
200-7
167-1
41-1
63-9
44-4
35-7
36-9
275
45-1
40-2
33-6
10-96-^^^-^^^^
11-84
12-11
1207
13-13
11-39
12-94
12-02
12-06
1850-5
368-4 = 11-945 per hour.
I
fffVl^g
The arc of vibration usually given to the pendulum on starting
it_, was about nine feet^ which in half an hour decreased nearly
one-third. The mean rate of apsidal motion of these arcs, on
their becoming elliptical (as they generally did in the course of
a few minutes), 1 had found to be about y^ths of a degree per
hour to Y^o^h of an inch of ellipticity, or length of half minor
axis. I had assumed that this rate would hold good as the arcs
become shorter, provided both axes diminished in the same ratio^
and consequently that it would increase when the arc shortened
and the ellipticity continued the same. A few experiments on
short arcs (which I had begun to prefer to long ones) soon con-
vinced me that this assumption was directly contrary to the fact ;
and that with a given length of minor axis, the progression of
the apsides was slower as the arc of vibration decreased. This
discovery, together with other manifest advantages attending
short arcs, determined me on confining myself entirely to them
in future ; and I accordingly substituted instead of my old circle,
a new one of only half the diameter. My next improvement
was in the mode of suspension ; a suggestion for which I am
indebted to a scientific friend, who made the apparatus for me.
A brass screw, about li inch long and | inch in diameter,
was sawn through the greater part of its length into four sec-
tions or quadrants, meeting in the axis. The screw was firmly
centred into a brass disc, and before having the thread cut upon
38 Mr. T. G. Bunt on Pendulum Experiments.
it, was tapered so as to be larger towards the disc. The wire
being passed up the middle of this screw, is tightly held between
the four quadrants, which are compressed by a nut. The disc
was then screwed down to the floor and leveled by a spirit-level.
Nearly the whole of the following series of experiments were
made with these new arrangements, and they appear to be in
every respect much superior to those of the former series. The
tendency to elliptic motion in the pendulum-bob was very consi-
derably lessened ; and sometimes it would vibrate for nearly three-
quarters of an hour without any cUipticity at all. After making
and tabulating a mass of experiments, I found the correction for
y^^th of an inch ellipticity, in a mean arc of about three feet, to
be only 0°*43 per hour ; and from several experiments in which
the pendulum was left to vibrate several hours, without receiving
a new impulse, I found the apsidal motion of short elliptic arcs
to be much below this proportion, though their precise law I do
not pretend to determine.
In the following experiments, occupying rather more than
thirty-seven hours, an impulse was usually given to the pendulum
about once in an hour. The degree of the azimuth circle cut by
the plane of vibration, and the amount of the ellipticity, were
usually observed and written down at the end of every quarter
of an hour. Those experiments in which the pendulum was left
unobserved for a whole hour or more are excluded from this
series, and their results given separately. The ellipticities were
seldom permitted to exceed 0*2 inch, and a correction for each
is introduced into the observed motion in azimuth. Care was,
however, taken to make the opposite ellipticities as nearly equal
as possible ; and it will be seen below, that, in taking their sum
(regard being had to the sign of each), they amounted to only
— 0°*32, although they were about 150 in number.
I find that I was in error in saying that the zero of my circle
was in the meridian ; it is not zero, but the division 16° nearly.
In Table I. I have given my experiments in the order in which
they were made, adding just so many together (usually about
four) as would make about the interval of one hour for each
group. With the number of minutes are given the degrees of
motion in azimuth, the con'cction for ellipticity, the part of the
circle observed, and the rate of motion per hour, for each of the
thirty-seven hours through which the experiments extended.
Table II. is deduced from Table L, and shows the mean rate of
the motion in azimuth for every 20°, from 0°to 180°. Table III.
gives the result of experiments with intervals longer than any
contained in Table I., varying from one to four hours, at the
beginning and end of which intervals only the pendulum was
observed.
Mr. T. G. Bunt on Pendulum Experiments,
39
&rw
Table I. — Thirty-seven hours^ motion in Azimuth of Plane of
Vibration, "showing the rate of motion for each hour.
Observed
ElUptic
Part of circle
Rate per
Time.
motion.
correction.
observed.
hour.
Date.
min.
722
14-84
°-o
20 to 33
12-33
May 27.
50-3
10-50
-0-48
57... 69
12-00
28.
70-7
13-92
-0-29
/ 69... 761
1 120... 126/
128... 139
11-57
30.
60-0
11-42
-0-31
11-11
...
47-8
61-4
8-65
12-42
-fO-24
-0-66
/ 140 ...1451
1 122 ...126/
/ 127 ...1351
1 50... 54/
/ 54... 621
' 145 ...148/
148... 161
10-93
11-49
'ii-^f^Y^
61-7
11-90
+0-01
11-58
65-9
1301
-0-29
11-59
31.
510
9-57
+0-37
161... 171
11-70
...
66-5
1245
+0-38
171 ... 180
11-57
...
53-9
10-41
+0-26
180... 9
11-89
...
57-8
11-14
+0-23
9... 20
11-80
64-7
12-80
+0-02
20... 32
11-89
June 2.
' .58-0
1205
-0-17
33... 45
12-29
...
' >^ 601
12-46
+0-25
/45... 511
174... 81/
12-69
...
^^ ;' 633
1318
+0-08
81... 94
12-57
...
^ifi 59-9
12-05
+005
95 ... 107
12-12
3.
,y, 59-3
11-45
-0-13
107... 119
11-45
...
. 71-6
^^' 53-3
13-69
+0-05
119 ...133
11-52
Q'QQ
+0-26
132 ...142
11-17
...
fejr 60-3
1110
-0-04
142... 152
11-01
...
i;j- 69-1
12-60
+0-09
152... 165
11-02
'4.
QQ7
11-95
+0-18
165... 177
10-90
...
61-8
11-56
-0-04
177... 6
11-18
...
65-5
12-26
+0-04
6... 19
11-27
/4.
15.
52-9
10-13
-0-01
19... 28
11-48
61-2
11-98
+0-0
30... 42
11-75
...
56-2
11-06
+0-23
41... 52
12-03
6.
63-9
12-95
-0-23
51... 64
11-94
54-4
11-16
-0-27
65... 75
1202
...
63-6
12-59
•0
75... 88
11-89
...
63-7
1309
-0-15
88... 101
12-19
/6.
17.
62-9
12-34
-0-36
101 ... 114
11-42
62-7
11-77
+ 015
114 ...126
11-41
...
61-2
11-83
+0-13
126... 139
11-73
..a
46-8
9-23
-0-5
139 ...148
11-77
39-8
7-56
+0-14
148 ... 156
11-61
22221
432-73
--32
-0-32
'>Vj~'-
432-41 =
ll°-677 n
lean rate per hou
r.
40 \ Mr. T. G. Bunt on Pendulum Expeninents,
Table II. — ^Mean hourly rate for every 20° of Azimuth,
■ ■ "' ■ ( t 'I'h ' • '
Oto 20
11-56 per hour.
20... 40
11-92 ...
40... 60
1209 ... 1
HO... 80
1208 ... 1
80... 100
12-24 ...
100... 120
11-63 ...
120... 140
11-29 ...
140... 160
11-42 ...
160... 180
11-33 ...
1 11-729 mean of these per hour
Table III, — Eleven Experiments with Long Intervals.
No correction introduced.
May 23.
28.
30.
31.
June 2.
3.
4.
5.
6.
7.
245-7
130-2
118-9
127-4
110-8
121-5
102-8
283-9
165-7
701
162-5
49-45 motion.
23-90 ...
23-00 ...
25-75 ...
21-43 ...
24-80 ...
1702 ...
5813 ...
32-45 ...
14-52 ...
32-18 ...
1638-5 I 322-63 = ir-814 per hour.
ijifiii
All the experiments which I have as yet detailed were made
with my leaden ball, of 53^ lbs. weight. I had previously been
experimenting with an iron half cwt., of a form nearly cylin-
drical ; but finding its motion irregular, I suspected the influ-
ence of magnetism and laid it aside. Two days ago I deter-
mined to suspend it again, and tiy whether its iiTcgular motion
might not have ai-isen from ellipticity, which in my first ex-
periments with this weight I had not recorded, or whether it
must be assigned to some other cause. The rates of motion
I obtained, in inteiTals of about ten or fifteen minutes each, were
the following, viz.
Part of circle observed.
Rate per hour.
359 to °0
0... 1
1... 3
3... 9
6... 18
6-30
6-18
6-88
6-70
8-58
56 ...67
57. ..60
80 ...85
9-75
10-64
12-14
On the Anticlinal Line of the London and Hampshire Basins. 41
About four hours afterwards on the same day I tried again on
the same part of the circle, viz. from 1° to 4°, for fifteen minutes,
and obtained a rate of 12^'4! per hour. The next day, from 5°
to 6°, for twenty minutes, the rate was only 4*^*38 per hour.
Several other similar results were obtained, with which I shall
not trouble you; but these, contrasted with the experiments
made with the leaden ball, in which no such irregularities were
ever observed, render it evident that the iron weight was deflected
by magnetic currents, and that it is utterly impossible to obtain
correct results in these experiments when the pendulum-bob is
made of that metal*. ''^^ ■>/'-
I am, Gentlemen,
,; luxl 4ii / Yours very respectfully; ^'^^ ^
""'■'•" ^;'-i -^-i^^'.. - Thomas G. Bunt.
VII. On the Anticlinal Line of the London and Hampshire
Basins. By P. J. Martin, Esq.
To Richard Taylor, Esq.
My dear Sir, , Pulborough, May 26, 1851.
THE renewed interest which geologists take in the modus
operandi of the great chalk denudation of the Weald since
the advancement of Sir Roderick Murchison^s paper, read to the
Geological Society on the 14th instant, inclines me to request
that you would lend me your assistance for the promulgation of
some thoughts on the same subject, and for the description of
some additional natural appearances strongly illustrative, as I
think, of that phsenomenon.
So long ago as the year 1828 you did me the honour to review
my first publication (see vol. iv. New Series, Phil. Mag.), in
which, as an appendage to a memoir descriptive of Western Sussex,
and taking the geological structure of that district as a type of
the whole, I ventured to bring forward a " Theory of Disruption
and Denudation" as a corollary to Dr. Buckland^s paper on
'^'^^ Valleys of Elevation," published in the Geological Transactions
of the foregoing year. The year following (in 1829) you also
published a paper in which, as further illustrative of the subject,
I made an attempt to restore the lost beds on the dome of the
Weald ; showing that, but for the instrumentality of the con-
comitant flood, the upburst of the Wealden would have produced
an elevation of at least four or five thousand feet, instead of an
excavation of as many hundred, above the sea-level. In a manner,
therefore, by an approximate synthesis as well as analysis, we
were led to the conclusion that the idea first broached by Dr.
Buckland in the before-mentioned paper was the correct one ;
* A Postscript to this paper will be found at p. 81.
42 Mr. P. J. Martin on the Anticlinal Line of
namely, that the basins, as they are called, of London and Hamp-
shire were once united ; or more properly, as I showed in my
" Memoir,'' that these great synclinals had no existence till the
convulsion we then contem})lated raised the ban'ier between them ;
and that they could not therefore be the areas of a marine deposit
posterior to the epoch of •their fonnation.
At the time these speculations were given to the world, men's
minds were fully engaged in the investigation of the formation
and succession of strata, their age and organic contents, and less
to geological stmcture ; and there was a disposition to repress
opinions founded on any appeal to periods of extraordinary
activity. The doctrines of uniformity in geological causation
had then the ascendency, and Sir Charles Lyell advanced his
theory of the gradual erosion of the Weald and the quiet trans-
port of the materials into the adjoining basins*. For several
years after this I was myself otherwise and better employed, and
did nothing in the prosecution of my research ; but from time
to time other observers ventured timidly to differ from Mr. Lyell,
especially when in contemplation of the accidents of water-shed,
and as appearances of violent disruption were occasionally deve-
lopedf. Still, having full confidence in the truthfulness of my
early interpretation of the structural phsenomena ever under my
obsen-ation, and intending some day to satisfy myself with giving
the world a history of the Weald denudation, I made occasional
excursions, as my leisure would permit, into Hampshire and
Wiltshire, believing that the same parallel lines of fracture and
concomitant aqueous denudation would there exhibit (in the
great chalk dome of those counties), mutatis mutandis , the same
or similar features. I say "with a difference," because it could
not be supposed that a country composed of so ductile a material
as the chalk, ever reluctant to disclose the secrets of its dispo-
sition except when great disruptive violence has been used, would
offer the broad and unmistakeable marks of disturbance to be
found in the variable beds ofthe Wealden, — its flexible clays and
its frangible sandstones.
I felt the propriety of resuming the task I had assigned my-
self in this direction on two accounts. First, because I have
always found that, in discussing the affairs of the Weald, even
* This hypothesis took such entire possession of the pubhc mind, and
my opinions fell so much into abeyance, that two or three years after, when
I ventured to repeat them before the Philosophical and Literary Society of
Chichester, I was told that I was " all wrong," — " that Mr. Lyell had given
the true explanation, and Dr. Mantell had confirmed it." I thought that
this hypothesis of Sir C. Lyell had been entirely withdrawn; but I have
been informed that it appears in the latest edition of his Elements.
t See Dr. Fitton's " ueologj- of Hastings," " History of the Beds below
the Chalk," GeoL Traiw.; Dr. ManteU'i Geology of S.E. of England, &c.
the London and Hampshire Basins. 48
persons generally well-informed on the subject found it difficult,
or could never be persuaded to abstract themselves from the
notion, that the Weald denudation was a piece by itself, that it
was to be viewed and spoken of as a district from which certain
removals had been effected, by whatever means, and where changes
had taken place, in which the neighbouring countries did not
share. It was therefore most desirable that Dr. Buckland's
original views of the elevation of the great chalk district should
be restored in the public mind ; and that the idea of a general
denudation of all the south-east part of our island should take
the place of the denudation of the Weald, of which general de-
nudation the latter was only a part. In my Memoir of 1828
the case is so put, and in that sense it was my object to revive
the discussion. Secondly, I was the more inclined to take this
course, because I found that, whilst I was preparing myself for
bringing the elevation and denudation of the Hampshire district
into relation with the other parts of the same parallel, Mr. Hop-
kins was engaged in a review of the Weald in illustration of his
theory of fracture and displacement ; and it was highly desirable
that any agreement in our views, or any discrepancy, if any such
should exist, should stand in juxtaposition. On this account I
put myself in communication with Mr. Hopkins, and brought
forward a paper '^ On the probable Connexion of the Eastern and
Western Chalk Denudations.^^ This paper was read before the
Geological Society in the early part of the session of 1840-41,
and, as I was told, was ordered to be printed ; but when inquiry
was made for it in order to its correction before publication, I
was told " it was lost.'' This was the more to be regretted,
because it ought to have appeared contemporaneously with Mr.
Hopkins^s essay, to which it would have been ancillary; and
because that gentleman did me the honour to borrow it, in order
to bring his own in relation with it, as much as the difference of
our practical or theoretical views would allow. And to myself
it was more a matter of regret, because I lost the opportunity of
explaining some of the discrepancies to which Mr. Hopkins
refers*. But the oubliettes of the council chamber of the Geo-
logical Society are not bottomless ; and two years after the pub-
lication of Mr. Hopkins's paper, or about three years ago, my
MSS. were returned to me without explanation f- I now hand
* Vide Hopkins " On the Geological Structure of the Wealden District/'
passim, Trans, of Geol. Soc, vol. vii. 1845.
t I am willing to believe that the temporary disappearance of my MS.
was the effect of accident, notwithstanding that a large roll of papers, with
six sections of the Ordnance Map along with it, must have occupied some
space ; and notwithstanding that any, the most trivial matter, concerning
a question which has been so long lying at the very doors of the Society
undecided, and about which its two greatest celebrities are now openly at
issue might have challenged more care.
44> Mr. P. J. Martin on the Anticlinal Line of
them to you to be published, if you please, iii your Magazine.
And, with only two corrections, which I had })roposed to make
before their appearance in the Society's publications, I pledge
myself to the general fidelity of the details both of fact and theo-
retical inference. In the last paragraph of my unfortunate paj)er,
you will observe that I propose to myself and to the Geological
Society a continuance of the investigation into other parts of the
great anticlinal line. This I shall now do with your permission ;
and I shall unreservedly and without hesitation finally reproduce
my original proposition of the contemporaneity of upburst and
denuding Hood over an area of at least four degrees of longitude,
from the chalk of the Pas de Calais to where the line of eleva-
tion at Devizes is met by that of the general line extending from
S.W. to N.E. from the Dorsetshire to the Yorkshire coasts. I
should also say, of as many degrees of latitude, but, except as a
speculation of the highest order of probability, I am not prepared
to include the parallel lines of elevation of the Isle of Wight in
this disquisition ; and it would be an area inconveniently large
for the discussion of matters of a practical natm'c.
I am, dear Sir,
Yours very truly,
P. J. Martin.
[Read before the Geological Society, December 16, 1840.]
A paper was read before the Geological Society in 1827,
afterwai-ds enlarged into a small quarto volume, published the
following year, under the title of a '^ Memoir on a part of West-
em Sussex, with some observations on the Weald Denudation,'^
&c. In this paper some new facts and some speculations were
advanced on the construction of the Weald, — its cross fractures,
drainage and other phsenomena, illustrative of the simultaneous
operations of upheaving force, and violent aqueous abrasion.
In pursuance of the subject, some additional remarks were
offered to the public in the Philosophical Magazine for February
1829, on the extent and magnitude of the abraded materials;
and to show also, that although the word " denudation " was
usually restricted to the Weald valley, the chalk country, espe-
cially that of Hampshire and Wiltshire, ought to be included in
the same category ; and, in fine, that the upburst of the Wealden,
and the area comprised in the chalk-boundaries of what was
called '* the great denudation of the Weald,'' did not present any
features attributable to disturbing forces, distinct and separable
from those of the surrounding districts.
The object of the present inquiry is to trace the lines of dis-
turbance from and into the Weald, through the great expanse of
chalk which separates the western parts of the basins of London
the London and Hampshire Basins. 45
and Hampshire^ and their probable connexion with the corre-
sponding lines of the vales of Pewsey, Warminster and Wardour.
The construction and arrangement of the chalk country will
follow ; and the whole will serve, when the drainage and other
geological and geographical features come to be considered, as a
suitable introduction to a reconsideration of the phsenomena of
disturbance and denudation. The district in question, moreover,
forms with the Boulonnais a convenient geological whole, whether
considered apart, or in conjunction with other " lines of eleva-
tion,^' or denuded countries of suspected contemporaneity.
In reference to the connexion of the Weald with the Wiltshire
valleys above mentioned, the sum of our present knowledge may
be gathered from the following passage in Professor Phillips's
^^ Treatise on Geology*/' *^^In England, two lines of subter-
ranean movement have long been known, by which the tertiary
and secondary strata have been raised into anticlinal ridges and
sunk into synclinal hollows. They both range east and west, or
nearly so ; one line, viz. from the Vale of Pewsey, by Kingsclere,
Parnham, Guildford, and through the Weald of Sussex to Bou-
logne, is somewhat parallel to the vale of the Thames, &c." And
in reference to the Vale of Wardour, and its probable connexion
with the western extremity of the W^eald, the latest information
is to be derived from Dr. Fitton's History of the Strata below
the Chalkf. Dr. Pitton says, '' The beds at Harnham Hill, im-
mediately on the south of Salisbury, are inclined to the north
(this should be dip to the north, the inclination southerly), and
about a mile to the west of that hill a curved ridge or horeshoe,
formed of the upper chalk, seems to be the first divarication of
the strata which bound the Vale of Wardour. It therefore
deserves inquiry, whether the continuation of the fissure pro-
duced by an upheaving on the east of this point may not be
discoverable in the space between Salisbury and the head of the
Wealden denudation."
These two quotations will serve for the starting-points of our
inquiry ; and I will anticipate the result so far as to state, that,
as regards the Pewsey line of elevation, a vertical disruption is
traceable from Polkstone along the whole range of the North
Downs (and is mainly instrumental in prescribing their southern
limits), which, entering the chalk near Farnham, passes by, and
does not unite with the Pewsey anticlinal line, as continued on
in the Burghclere Hills and Vale of Kingsclere. And secondly,
in regard to the anticlinal line of Wardour ; that it is continued
across the Avon and the Test, and like the before-mentioned
northern line, passes by and dies out, but does not unite or inos-
* Vol. i. p. 260 (Lardner's Cyclopaedia),
ru 0.1 e ^ Qgj,!^ Tvms., vol. iv. 2nd series, p. 245. '^-' '
46 Mr. P. J. Martin on the Anticlinal Line of
culate with another which is projected westward from the " head
of the Weal den denudation."
On inspecting Mr. GreenougVs map or Dr. Pitton's appended
to the above-mentioned memoir, it will be observed that a direct
point is made by the Vale of Wardour toward the south west
corner of the head of the Weald. And in like manner, an incli-
nation is shown by the Pewsey line of valleys at Kingsclere to
bend toward the north-west corner at Farnham. The axes of
elevation appear to run in these two directions, and the geogra-
phical features of the country are in accordance with them, as
indicated by the high grounds. Nevertheless, the anticlinal lines
which constitute these axes of elevation are distinct and separate,
whether they be contemporaneous or not. The Burghclere Hills
sink down and do not unite with the North Downs; and the
high grounds south of Salisbury, although continued eastward
to the Test, in the neighbourhood of Romsey, decline in a syn-
clinal hollow to rise again in the high hills about Winchester,
which are the proper continuation of the South Downs.
To make out this in detail, I begin at the upper or western
end of the Weald denudation. This district, which Dr. Fitton
has called the *' head of the Weald denudation," is a valley
ranging almost directly north and south, about sixteen or seven-
teen miles in length and (east and west) five or six in breadth.
We may for the sake of brevity call it the Wolmar Valley, Wol-
mar Forest being one of its most prominent features. It is
bounded on the north by the Hogsback, on the south by the
bold eminences of Butser Hill and the South Down range, on
the west by the Alton Hills — these three sides all being of chalk —
and on the east by an elevated platform of the lower greensand,
comprising the Hindhead and Blackdown Hills, with the inter-
vening high grounds of Haslemere. This valley is wholly com-
posed of gait and lower greensand, except a narrow slip of Weald
clay in Hartingcombe, as described by Mr. Murchison*. Of
the cause of this intrusion of the Weald clay I shall have to speak
by and by. Three remarkable anticlinal lines traverse the
Wolmar Valley, entering eastward from the greater expansion of
the Weald. The middle and most important of them is the great
central line of the Weald, which enters the platform above men-
tioned by a well-marked " valley of elevation " and erosion, and
cuts through the lower beds of the lower greensand with much
appearance of disruptive violence at Haslemere. The valley
thus formed is based on Weald clay, and at an elevation of
five or six hundred feet above the level of the sea runs directly
west toward Liphook, and is lost as it opens into the greater
expanse of the Wolmar Valley. In its further progress this cen-
* Geol. Trans., vol. ii. 2nd series, p. 102.
the London and Hampshire Basins. 47
tral line heaves in succession the higher beds of the lower green-
sand and the gait ; and tilting up the malm or upper greensand
beds, it gives them a prominence which they do not elsewhere
assume, and enters the chalk between the salient angles of
Hawksley andWorldham. The central rent is at Selborne, and
the highest point in the chalk hills of this part of the Alton
range is a little south and west of that village.
South of the central anticlinal line another enters the Wolmar
Valley by Trotton and Rogate, and passing by Petersfield enters
the upper greensand and chalk about a mile north of East-meon *.
As this line runs the whole length of Sussex, and then traverses
the Hampshire chalk and crosses the Test, it will merit a more
particular description.
The third anticlinal line which traverses the Wolmar Valley
runs north of the other two, and is more strongly marked in
this part of its course than the one last mentioned, though else-
where its features are by no means so prominent. As this line
is to carry us on towards Pewsey, and is otherwise so remarkable,
I shall give a detailed description of its course from the neigh-
bourhood of Guildford into the chalk hills west of Farnham.
But before we quit the Wolmar Valley I must be allowed to say
a few words more on the Haslemere and Hindhead platform,
particularly as its position is strongly illustrative of the range
and operation of these three principal anticlinal lines. Viewed
from any good central position in the western Weald, as say
Loxwood, Billingshurst or Five Oaks, the platform in question
looks like a high table-land ranging north and south. It swells
a little at each end to form the hills of Hindhead and Blackdown,
and thence declines very gently each way toward the Haslemere
gap in the centre. Its appearance when viewed in this position
is doubly interesting to the geological observer, when he under-
stands that it is sustained on the central line of elevation, with
its two extremities resting on the two lateral parallel linesf.
Turning our attention now to the north side of the Wolmar
Valley, we are arrested by the appearance of a remarkable con-
* I have since seen reason to correct this statement. The anticHnal hne
of Winchester, after passing up the Valley of Chilcomb, takes its progress
eastward in an intumescence of the chalk, forming a range of high grounds
terminating in the Vale of East and West Meon. The synchnal of this
elevation appears to be the Vale of Braradean, a remarkable longitudinal
valley, containing, as to be afterwards noticed, an immense accumulation
of angular flints. Its synclinal character is the more probable, as it gives
rise to an affluent of the Itchin.
t The copious springs that burst out in the fissure West of Haslemere
can only be supplied by the rains that fall on this platform of green sand-
stone ; and the manner in which it is tapped and the water drawn oflP west-
ward, in the direction of the decline of the Weald clay toward the Hamp-
shire chalk, is as curious as it is instructive.
48 Mr. P. J. Martin on the Anticlinal Line of
tortion or in-egiilar saddle, part at' an anticlinal line, which I shall
call the Peasemarsh line. Dr. Fitton having first ])ointed out the
rise of the Weald clay at that ])lace. The sudden dip of the chalk
at the west end of the Hogsback, and the remarkable pre-emi-
nence of the tertiary beds in Farnham Beacon Hill, are produced
by this contortion. The Peasemarsh line is here screwed up, as
it were, hard to the chalk. In its progress eastward into the
broad vale from which it takes its name, it recedes from the chalk
and attains its culminating point, or point of greatest intensity,
at Peasemarsh, and brings the Weald clay to the surface. And
here also, as might be expected, it opens up the transverse fis-
sure by which the river Wey is discharged through the chalk at
Guildford. Further east this anticlinal valley is prolonged toward
Albury and Shire, bringing down one of the tributaries of the
Wey ', the lower greensand hills on either side showing the anti-
clinal disposition, as Dr. Fitton has already pointed out*.
Returning westward to Farnham, the line of disturbance is
found to have changed its character, and it begins to heave the'
gait at Wrackleshamf. Here the anticlinal disposition may be
tested by examination of the sand-hollow on the north side of
the village by the parsonage house, and in the sand-pits a little
further up the stream. A gait saddle succeeds, which, with its
synclinal replication toward the central ridge, produces the broad
expanse of Alice-holt. F'urther west the gait saddle is continued
through Bentley Green, the malm or upper greensand lying on
each side, — southerly in the high grounds of Binstead, and north-
erly in those of Bentley Church and Berry Court. As the syn-
clinal line brings out a great exposure of gait in Alice-holt, so
also it produces a great body of malm in the Binstead country.
Holybourne Froyle and Bentley form the confluence of the malm
or upper greensand, and the line of elevation enters the chalk
by Peacombe and Lower Froyle. The chalk succeeds and attains
its highest altitude near where Shaldon Copse is to be found in
the Ordnance map, and is continued westerly in a broad expanse
of highlands, marked in the Ordnance Map by the names of Lips-
comb, Ellisfield, Dummer and Popham. From this line, the coun-
tiy declines gently northward by South Warnborough, Uptongrey
and Hackwood Park ; and southward into a well-marked syn-
chnal valley running westward from Alton to Axford and Wood-
mancote. At this part of the line Dummer Farm and Popham
Farm are on the top of the ridge % . At Popham Beacon it is inter-
* Trans. Geol. Soc. loc. cit. p. 142.
t If this is not the same hne of contortion as Peasemarsh, losing much
of its intensity west of Farnham, it is a new and independent anticlinal.
But Iprefer the former view of the case.
X This intumescence of the chalk answers very much to that which fol-
lows the Winchester line east of Chilcomb. Vide infra.
the London and Hampshire Basins. 49
sected by the Southampton Railway at the height of 454 feet above
the sea-level ; but at this point it has lost much of its intensity.
Westward from Popham I cannot say that I have made a very
satisfactory exploration. Denudations and river-courses, and
the absence of satisfactory sections just where they are wanted,
make it very puzzling. My impression is, that, keeping the
infant Test in its northern synclinal line, it passes the great gap
in the Burghclere Hills north of Whitchurch, and takes on in
the vicinity of Andover towards Waybill. The stratification of
the chalk-pit on the south side of the town of Andover exhibits
too much dip to have come from the Burghclere line without a
reduplication; and the occurrence of a considerable tract of
country of a tertiary character in Harewood Forest, favours the
supposition of a synclinal arrangement. However this may be,
the superior swell of the Pewsey line of upheaval now throws all
other into shade, and the drainage is sufficient evidence of the
constant slope southward of all the country west of the Popham
heights, and the almost entire extinction of this line of elevation.
au ■ i
^^. ■
At this stage of the inquiry, finding that there was now no
chance of the Peasemarsh running into the Pewsey anticlinal,
and that I was moving in a line parallel with the Burghclere
Hills, eight miles north of Popham, it became a point of much
interest to ascertain the progress of the Pewsey line, and how it
stood in relation to the one I have been describing.
As all the relations of the Vale of Pewsey are well known, and
the history of its anticlinal line has been carried on by Dr. Buck-
land* through the vales of Ham and Kingsclere, it would be
superfluous to repeat them. The great peculiarity in the fea-
tures of this line, after leaving the Pewsey denudation, is its ex-
treme irregularity.
In the Vale of Pewsey the axis of elevation appears to run
nearly in the centre of the denudation, the strata sloping off
with a gentle declination north and south. But in its progress
eastward the northerly dip is much sharper than the southerly f.
The effect of this disposition is to bring the tertiary beds often
almost to the foot of the Burghclere Hills. This is particularly
perceptible after the line emerges from the Vale of Kingsclere.
At the eastern extremity of this valley the chalk is confluent at
Wolverton Farm. East of this confluence a well-marked anti-
clinal chalk valley runs out towards Monk-Sherbourne ; and evi-
dence may be obtained of the northerly dip, in Wolverton chalk-
* Geol. Trans., vol. xi. 2nd series,
t Dr. Buckland, loc. cit.
Phil, Mag, S. 4. Vol. 2, No. 8. July 1851. E
60 On the Anticlinal Line of the London and Hampshire Basins,
pit, in a copse on the left of the hollow way that leads from
Wolverton Park to Hannington. Here the dip heing 30 or 40
degrees, the chalk is sooii lost beneath the tertiary beds ; but
south of this locality it still preserves the character of the Burgh-
clere Hills, sloping away southerly into the broad synclinal hol-
low which intervenes between the high grounds of Hannington
and those of North Waltham, Popham and Dummer, which
belong to the Peasemarsh line.
From the narrow anticlinal chalk valley before spoken of, be-
tween Wolverton Street and Hannington, the elevation is con-
tinued south-easterly and then easterly, till it dies away under
the plastic clay at Old Basing ; and in a great part of that course
it presents a chalk escarpment to the north, with the tertiary
beds, as at Ewhurst and Ramsdell, lying almost at its foot*.
The countiy west of Basingstoke, between Hannington on the
expiring Pewsey line, and Dummer on the Peasemarsh, as before
said, lies a broad synclinal hollow, in which, and apparently pro-
duced by that disposition of the beds, runs the little stream that
supplies the head of the Basingstoke Canal.
Vale of War dour Line.
To trace out the course of this line from where it was left by
Dr. Fitton at Hamham Hill, south of Salisbury, was the next
object of reseai'ch. The chalk beds of Harnham Hill dip north-
ward, and those of the country north of Salisbui-y southward ;
consequently that town stands in a synclinal depression, which
is in part occupied by the tertiary beds. The sexton of Salisbury
Cathedral tells you that the cathedral is founded on a bed of stiff
clay. This has all the character of plastic clay, of which I had
satisfactory evidence from an open grave in the north transept at
my late visit. The river Nadder and its alluvium occupying the
western extremity of the valley, I do not know exactly where it
begins to exhibit signs of the existence of the tertiary beds, but I
found them fully developed at and near Bemerton, within a mile
of Salisbuiy. Crossing the Avon east of that place on the Romsey
road, we find that the hollow, south of Ashley Hill, where the
words dog-kennel occur in the Ordnance Map, is occupied by
* If this line of elevation is renewed east of Basing, it is most probably in
the Isle of Thanet, a chalk "Outlier-by-protrusion" from the Kentish chalk.
Of the manner in which these parallel lines may pasa interruptedly, and
sometimes silently through a country, we have a good example in the less
questionable case of Portsdown Hill in Hampshire, High Down near
Worthing in Sussex, and the cliffs at Seafoi'd in the same county, all ele-
vations of the same character lying in the same line east and west, with a
dip opposed to the prevailing one of the intervening country. An elevatory
force, acting with greater intensity at these points, can alone explain the
coincidence.
Application of Electro -Magnetism to Astronomical purposes. 51
drift ; but the tertiary beds appear at the brick-kilns and Cla-
rendon Lodge_, and advance in importance as we proceed east-
war d^ so as to occupy all the country in which the words Alder-
bury^ Whitmarsh-bottom, Bentley Wood^ Berrywell Wood, and
French Moor are to be found. The chalk on which these tertiary
beds repose emerges at East Grinstead and West Dean, in a low
ridge dipping sharply north; whilst the opposite side of the
anticlinal consists in the strongly-marked feature of Dean Hill*
dipping southerly. Grimstead Fields is a chalk saddle between
these two ridges. Still proceeding eastward, the northern ridge
is gradually intruded upon by the plastic clay, and is lost under
it at Lockerly. The southern, in the line of Dean Hill, still
maintains its importance ; but that also slopes away to the south-
east, and is soon covered up by tertiary formations : Mount
Farm, Butler's Wood, Uphill, Roke, are tertiary or shingle beds
of the Eocene period. Thus the anticlinal line of the Vale of
. Wardour, after a course of about six miles east of the Avon, sinks
under a saddle of the tertiary beds at, or close upon, the Test.
A cursory examination of the country from Michelmarsh and
Timsbuiy on the last-mentioned river, by Anfield toward Otter-
bourne on the Itchin, gave me some idea of a continuation of
this saddle of tertiary sands and clays, with an escarpment in
the high grounds of Toothill and Chilworth on the south. But
of this I cannot speak with confidence. I am, however, quite
assured, that although it may be possible to discover marks of a
continuation of this line of elevation eastward, it is not connected
with that which I am about to describe, and which issues west-
.ward from the south-west corner of the Weald denudation.
These two, like the Pewsey and Peasemarsh lines, pass by and
do not inosculate with each other.
[To be continued.]
VIII. Historical Sketch of the progress of improvement in the ap-
plication of Electro -Magnetism to Geodetical and Astronomical
purposes f. By G. P. Bond J.
THROUGH the kindness of Dr. Bache and Prof. Walker of
the United States Coast Survey, I am enabled to give from
* If Dean Hill had the chalk colour, which it ought to have had, iu
Mr. Greenough's map, as ought also the line of high ground running west
in the course of the words " proposed canal," then the tertiary colour would
have been seen projected north of it, over the localities above specified,
toward Salisbury ; the synchnal line being a trough of tertiary beds, and
the cause of this projection.
t Communicated by the Author.
X The article consists, mainly, of extracts from an official communicatipn
from Prof. Walker to the Superintendent of the United States Coast Survey,
dated April 24th, 1861.
E2
62 . Mr, G. V.Bonii on the application of Electro-magnetism
th^' I'fecorda of that department, the following abstract of the
history of an invention recently brought into use in America,
by which electro-magnetism is introduced as an agent in the
determination of differences of terrestrial longitude, and for
various astronomical purposes in which the exact noting of time
enters as an important element.
On the 9th of June 1844, Capt. Charles Wilkes, U.S.N.,
made the first experiment for detemiining longitudes by means
of the electric telegraph, between AVashington and Baltimore,
with chronometers rated at each place. All subsequent experi-
ments for determining longitudes by the electric telegraph in the
United States, have been made at the expense of the Coast Sur-
vey, and by its officei*s, or by their request, and uod^* their
immediate supervision. ^'^ iioi3L>jiii«no.> -nii .'.*tl .;ij:>bjit>iimjifi:/>
On the 10th of October 1846, star-signals were first ex-
changed between the Washington Observatory and that of the
Central High School of Philadelphia. The outfit of telegraph
junction lines and apparatus was made by the Coast Survey.
The use of the astronomical instruments for the occasion at the
Washington Observatory, had been offered by Lieut. Matthew
F. Maury, U.S.N., superintendent.
The experiment was made under the charge of Sears C. Wal-
ker, Esq., one of the assistants of the Coast Survey, who from
that time to the present, under an appointment from Prof. A. D.
Bache, LL.D., superintendent, has had uninterrupted charge of
this work. The apparatus used this evening was devised and
constructed by Joseph Saxton, Esq. The star-signals, or taps
on a make-circuit finger-key at the instant of the passage of a
star over a wire of a transit instrument, were made that night
by Lieut. J. J. Almy, U.S.N., and were recorded by the ear by
Mr. Walker and Lieut. J. M. Gillin, U.S.N., at Washington, and
Prof. E. O. Kendall, Dii-ector of the Philadelphia High School
Observatoiy at Philadelphia.
The longitude between the two stations by this night's work
agrees within 0*2 second with the average of all the work done
since.
On the 27th of July 1847, coincidence of beats of solar and si-
dereal chronometers were for the first time tried between Phila-
delphia and Jersey city. These coincidences were noted at each
place by comparison of a solar and sidereal time-keeper. The
circuit of the telegraph line was closed temporarily every ten
seconds by the astronomer at one of the stations, and the receiving
magnet beats were heard sensibly at the same instant of absolute
time at both stations. The date of coincidences of these magnet
beats with the stationary clock beats (the one being at solar
the other at sidereal time), were recorded at both stations. This
to Geodetical and Astronomical pwposes. 53
experiment was repeatedly performed that year by Mr. Walker,
assisted at Philadelphia by Prof. E. O. Kendall, Director, and at
Jersey city by Prof. E. Loomis.
In July and August 1848, an extensive series of star-signals
and clock-signals, by coincidences, were exchanged between the
Harvard Observatory at Cambridge, Mass. and the observatory
in the garden of the late Peter Stuyvesant in Ts^ew York city.
The work was under the charge of Mr. Walker, assisted re-
spectively by Wilham Crouch Bond, Esq., Director of the Ob-
servatory at Cambridge, and Prof. E. Loomis at New York city.
During these experiments, Mr. Bond conceived the idea of using
an automatic circuit interrupter, and on the recommendation of
Mr. W^alker, received in July 1848, an order from Prof. Bache,
superintendent, for the construction of a clock for this purpose
in conformity with Mr. Bond^s di-awings, then before the superin-
tendent, t nx.>)3d &f»>inf>£ff)
This clock was completed in 1850, and forms part of the ap-
paratus in use at Cambridge in 1850 and 1851. The work of
1848, in July and August, forms the date of the first connexion
of Mr. Bond and his two sons, Messrs. George P. and Richard
E. Bond, with the use of the magnetic telegraph line for longi-
tude, and with the machinery and apparatus for the same. It
preceded by two months the work between Philadelphia and
Cincinnati of the year 1848, when in the month of October the
attention of Prof. 0. M. Mitchell, and afterwards of Dr. John
Locke, was turned to the subject. The fact that Prof. Bache
had ordered an automatic circuit interrupter of Mr. Bond in the
preceding August, was communicated both to Prof. Mitchell and
Dr. Locke previous to their undertaking similar experiments.
, J On the 26th of October 1848, Prof. 0. M. Mitchell, at the sug>
gestion of Mr. Walker, prepared a circuit interrupter with an
ordinary eight-day clock, and used it to graduate the running
fillets of paper for several days.
It was not used in the work with Philadelphia, clouds having
prevented work on the 27th, proposed for the purpose. The
same mode which Prof. Mitchell used had been proposed by
Joseph Saxton, Esq. in 1846, but has not been adopted by Prof.
Bache and Mr. Walker, from apprehension of injury to the per-
formance of the astronomical clock which must be used for the
purpose. This apprehension we know by experience to have been
groundless.
On the 26th of October 1848, Dr. J. Locke having stated his
objection to Mr. Bond's contrivance of a circuit interrupter, was
requested by Mr. Walker, on behalf of the superintendent, to
undertake experiments to obviate them.
On the 17th of November 1848, Mr. Walker receiving notice
64 Application of Electro-Magnetism to Astronomical purposes.
from Dr. Locke that he and his sous had completed an automa-
tic circuit interrupter, extended a junction- wire from the Cincin-
nati Telegraph Office, so as to embrace Dr. Lockers clock at his
house, fitted up as a circuit breaker, with a tilt hammer struck by
the teeth of the escapement wheel. Mr. Walker also, acting for
the Coast Survey, engaged the use of the line from Louisville to
Pittsburg, to ti-y the experiment with Dr. Locke's contrivance.
No astronomical nor clock-signals were exchanged this evening,
and no attempt was made to determine longitudes. In this
experiment Dr. Locke's clock graduated a fillet of paper as deli-
vered by the Morse register.
In 1849, January 19th, .the first actual experiment of the
automatic imprint of star-signals on a time scale was made be-
tween Philadelphia and Cincinnati. The telegraph line from
Philadelphia to Cincinnati was engaged for use of the Coast
Survey by Mr. Walker. The automatic clock interrupter w as fur-
nished by Dr. Locke at Cincinnati. The star-signals were given
by Prof. Kendall at Philadelphia, and recorded at both places.
The Cincinnati Obsei-vatory, in the absence of Prof. Mitchell,
could not be used for the pui-pose of longitudes.
The longitudes of Cambridge, New York and Philadelphia, were
determined on the 23rd of January 1849 by star-transit signals,
given for the same star as it passed the meridian of these three
stations. These signals were recorded at Washington, Phila-
delphia and Cambridge. The managements were under the
charge of Mr. Walker. The circuit-breaking clock was prepared
by Mr. Walker on Dr. Locke's plan, and located at Philadelphia.
The same clock contained a tilt-hammer interrupter for making
signals by the teeth of the hour-wheel every two minutes. This
instrument was invented in the year 1847 by J. J. Speed, Esq.,
President of the Telegraph Company in Detroit, Michigan.
The detection of a dday in the transmission of the galvanic
inducing wave proportionate to the space traversed, was made
by Mr. Walker immediately after examining and comparing to-
gether the registers of the four stations above mentioned.
The consideration of this phsenomenon led Prof. Walker to the
discovery of the velocity of the galvanic w^ve. His articles on the
subiect have been published in the Proceedings of the American
Philosophical Society for March 1849, in Silliman's Journal of
Science, and in the Astronomische Nachrichten. A velocity of
15,400 miles per second is given by him as the most probable
result.
In the summer of 1849, Prof. Mitchell proposed the use of a
revolving disc of type-metal to receive the records. Mr. Saxton's
plan of receiving the records upon a sheet of paper rolled upon
a cylinder, seems to be that which combines the most practical
On certain Questions relating to the Theory of Probabilities. 55
advantages. Mr. Saxton proposed to break the circuit by a tilt-
hammer struck by a projecting piece of glass from the middle of
the pendulum^ which acts as a circuit-breaker ; he also contrived
an apparatus for making on the sheet the 0, 5, 10, &c. millims.
by the omission of one or two breaks respectively. Mr. Saxton's
apparatus has been in use ever since at the Seaton station ; its
only defect is the want of uniformity in the time of revolution
of the cylinder.
On the 12th of April, Mr. Bond submitted to Prof. Bache a
model of an invention made with a view to remedy this remain-
ing defect. This instrument^ has been named the Spring Go-
vernor. A perfect working instrument was ordered for the use
of the Coast Survey at that time. The model was completed
and reported upon in November 1850. The cylinder, covered
with a paper, revolves once in a minute, and measures time with
the precision of an astronomical clock. The sheet, when taken
off after being graduated by the clock, has the minute columns
vertical. The seconds are marked off horizontally on each mi-
nute scale. The eye seizes on the appropriate hour, minute,
and whole second, as in an ordinary astronomical table of double-
entry ; the fraction of a second may be estimated to a tenth by
the eye, or read to a hundredth by a graduated scale. A yearns
work of an ordinary observatory may be bound up in a volume
of a few hundred pages, and forms a permanent and legible re-
cord of the actual dates of the imprinted transit signals.
By means of the line connecting the observatory at Cam-
bridge with Boston, the time for the use of shipping and for the
railroads throughout New England is now regularly transmitted
by merely passing the circuit through the clock at Cambridge. Its
beats are thus given through a distance of one or two hundred
miles. One o^ clock has been adopted as the hour for these
signals.
The courtesy with which the Telegraph Companies in different
parts of the United States have met applications for the use of
their lines for scientific purposes, deserves particular acknow-
ledgement, as having contributed most effectually to the success
of these operations.
IX. On certain Questions relating to the Theory of Probabili-
ties.—VsiYt III. ByW. F. Donkin, M.A., F.kS., F.R.A.S.,
Savilian Professor of Astronomy in the University of Oxford.
I PROPOSE in this third and last communication, to offer a
few remarks on the method of least squares, chiefly with
reference to Mr. Ellis^s paper on that subject in the Philosophical
Magazine for November 1850.
5^ Prof. Donkiii on certain Questions rclutiny to
If we arc asked what is the method of obtaining; the most pro-
bable result from a system of observations not numerous enough
to justify, as an ai)})rox.huation, the supposition that they are
injinite in number, it is plain that no answer can be given till
we are told whether it is to be assumed that the law or laws of
facility of errors in the individual observations are known, or
unknown ; or, to speak more accurately, until we are told what
is to be assumed as the state of information of the observer con-
cerning the laws in question. For the probability of every
hypothesis depends upon, the state of information presupposed
concerning it.
If the law of facility of eiTors (which we will suppose, for sim-
plicity, the same in all the observations) be assumed as known,
the problem involves no difficulty of principle, though for most
laws the required integrations would be impracticable.
But if the law be wholly or partially unknown, though it is
still easy to indicate the way in which the problem ought, theo-
retically, to be treated, the processes required are, in all actual
cases, entirely beyond the present powers of analysis.
To illustrate this, consider the case in which all the observa-
tions refer directly to a single unknown quantity x. If a, a',
fl", ... be the obseiTcd values, and </> were known to be the func-
tion expressing the law of facility of errors, then the probability
that the true value lies between x and x + dx would be
Q.(f>{x-a)(f>{x'-(^)4>[x-'a^^) ,,.dx, . . . (1.)
where C is determined by the condition that the integral of this
expression, extended to all admissible values of x, shall be
equal to 1.
Now suppose that the function <f> is not known, but may be
of any of the forms <j)^, (fy^, <l>3, - - - and let pi be the probability
that it is <^^.. Then instead of the expression (1.) we should have
X{C.p.(t).{x-a)(P,{x-a') .... dx},
the summation extending to all the actual values of i .
In the ordinary cases occurring in practice, nothing is known
of the form of (f), except that it must satisfy some veiy general
conditions, such as that smaller errors are more probable than
larger, &e. ; the number of supposable forms is therefore infinite,
and the summation indicated in the preceding expression would
depend upon a calculus bearing the same relation to continuous
variation of /or?/?, that the integral calculus does to continuous
variation of value. Such a method, it is needless to say, does
not at present exist ; the calculus of Variations being, with refer-
ence to functional fo?'m, the imperfect analogue, not of the inte-
gral, but of the differential calculus.
the Theory of Probabilities -' ^ '' "^ ^ 57
- ' The proposed problem, therefore, as applying to ordinary ca?es,
has never been, and at present cannot be, solvedi'*'*^ Utj^ji yiUiifJ
But it is to be observed, that if it were solved, that is^ if the^'
summation just mentioned were actually performed, it cannot be
assumed beforehand that the result would not turn out to be of
the forai Q'^{x — a)'^{oo — a!).,.,dx, giving the same relative
probabilitij for any value of x as would be obtained if it were
known that •\/r(^) were the function actually expressing the law of
facility of errors in the individual obse7^ations. Such a result
would involve no prima facie absurdity or difficulty, and it would
not be a valid objection to it to say, that it professed to establish
an independent external reality by a priori mathematical rea-
soning. For to prove that a required probability is to be calcu-
lated as if a certain hypothesis were known to be true, is a per-
fectly different thing from proving that that hypothesis is true,
or from proving anything about the probability of its truth at
all. To take a simple analogous case, suppose a bag contains
an unknown number of balls, of unknown colours ; a ball is
drawn and replaced n times, and is white each time ; now if a
person professes to prove that the probability of di-awing a white
ball at the next trial is , we may object to his proof on oth0?
grounds, but certainly not on the ground that he thereby assumes
this to be the actual ratio of the number of white balls to the
whole number of balls. Of course his answer would be, that he
assumes no such thing, but only asserts that the probability rela-
tive to a certain state of information is the same as it would be
if a certain hypothesis were known to be true. The fallacy con-
sists in assuming, that because two probabilities are equal, the
states of information to which they refer must be identical. •
To return to the subject of observations. If the law of facility
of errors were known, the mean of the observed values would not
be the most probable result, unless the law were expressed by
the well-known exponential function assigned by Gauss in his
first investigation. But the law of facility not being known,
although it has never been proved that the mean is the most
probable result, relative to this state of information, it has cer-
tainly never been proved that it is not : the question is perfectly
open ; and whoever professes to prove the affirmative, ought not
to be charged with pretending to prove that the law of facility
is actually expressed by the function above mentioned. For
anjrthing that has yet been shown to the contrary, that function
may truly express our expectation of the unknown law, and the
true solution of the problem may be obtained by employing this
" provisional '^ law, as if it were a known or " definitive ^' law.
(See an analogous case discussed in the first paper, Phil. Mag.
58 Prof. Bonkin on certain Questionji relating to
for May, §§ 17, 18.) The reader who is acquainted with
Mr. Ellis's paper, will see that I have been here referring to
some parts of his reasoning at pp. 324, 325 ; and is requested
also to observe, that in pointing out the invalidity of a particular
objection against the Edinburgh Reviewer's result, I am not de-
fending his argument, about which I shall say something here-
after.
If it be now asked what positive grounds there are for using
the method of least squares in the case of a moderate number of
observations, beyond motives of mere convenience, I think it
may be answered that the method has been proved by Gauss (in
the Theoria Combinationis Ohsei'vationum, ^c.) to be a very good
method, though it has not been proved to be the best method.
He has not shown that it gives the most probable result ; but he
has shown that it gives a result such, that if the whole system
of obsen atious were repeated an infinite number of times, the
average value of the square of the error would be a minimum.
I presume that Mr. Ellis does not mean to imply more than this
when he says (p. 321) that "Gauss afterwards gave another
demonstration which is perfectly rigorous.'' In fact, Gauss him-
self expressly points out that there is something arbitrary in
assuming the square of the eiTor as the function whose average
value is to be a minimum. (Theor. Comb. § 6.) Perhaps he
might have added, that the assumption is less arbitrary than any
other which could have been made ; but I shall not attempt to
discuss the question how far this fact, supposing it admitted,
would tend to give a demonstrative character to the reasoning,
considered as an attempt to establish the method of least squares
as the best method. The point to be observed is, that though
Gauss rigorously demonstrates what he professes to demonstrate,
he does not profess to demonstrate the method of least squares, in
the sense in which these words would be commonly understood
without explanation.
- I shall conclude with a few general remarks on the other
proofs which have been, or may be offered, of this remarkable
method. And I must remind the reader, that everything which
is here said applies only to the case in which the actual law of
facility of errors is not known.
Since the rigorous solution of the problem is unattainable,
every professed solution which puts on an appearance of demon-
stration must involve an assumption, leading more or less di-
rectly to the employment of a particular law of facility as if it
were known to be the actual law. And it would appear natm*al
to prefer that solution in which the assumed condition should
be most simple, least arbitrary, and most in accordance with
common notions and experience. That all solutions which
the Theory of Probabilities. 59
have any pretensions to these qualifications agree in thfe same
result is certainly a very remarkable circumstance, and one which
can hardly fail to excite some degree of expectation that this
result will turn out to be the true one, if the problem should
ever be really solved. I shall not go through an examination of
instances in illustration of the above remark ; but there are two
which I must mention briefly.
The first is the Edinburgh Reviewer^s proof, commented upon
by Mr. Ellis. Of course it was easy to annihilate it, considered
as a professed demonstration. But if it had only pretended to
be what it really is, a proof founded upon an assumption (of the
independence of errors in directions at right angles to one an-
other) which is simple and not more arbitrary than the assump-
tions made in other proofs, while it leads to the result with
remarkable ease and directness, it would, I think, have deserved
to be treated with respect. It is to be regretted that the Re-
viewer should have failed to see, or at least to point out, its real
character.
The second instance is a proof proposed by myself some years
ago in an Essay published by the Ashmolean Society, and since
abridged in Liouville^s Journal, vol. xv. This proof depended
upon a more complete and systematic development of the analogy
between the balance of evidence and the balance of forces, than
had been before attempted, and was published chiefly on account
of the interest which belongs (at least in my estimation) to all
such analogies. I was therefore not concerned to point out, and
indeed did not till lately clearly apprehend, what was the assump-
tion really involved in it. This assumption is, that the knowledge
gained from a number of observations is the same in kind as that
gained from a single observation. It is easy to make this the
foundation of the theory, treated according to the ordinary
method; to begin, namely, by assuming that the function ex-
pressing the law of facility of error of the mean of two observa-
tions, is of the same form as that which expresses the law for the
individual observations. I am inclined to think this assumption
in itself more simple and natural than any other ; but this is a
matter of opinion.
I may add, that in the first paragraph of the preface to the
English edition of the Essay just mentioned, I committed the
fallacy which I have endeavoured to explain in the former part
of this paper, of confounding the case in which the actual law
of facility is unknown, with the case in which it is known.
Oxford, May 23, 1851.
P.S. Since Part II. of these remarks was printed, I have,
through the kindness of Professor De Morgan, received his
60 Prof. Stokes on the Principles of Hydrodynamics.
second memoir " On the Symbols of Logic/' &c. (Camb. Phil.
Trans., vol. ix.), with which I was not before acquainted. It
contains some investigations on certain applications of the theoiy
of probabilities, to which I ought to have referred. On the
subject of the credibility of testimony, my remarks appear to be
entirely consistent, so far as they go, with those of Professor De
Morgan. But from what he has said in p. 46 of his Memoir, I
am uncertain how far he would agree with my account of the
surprise excited by the accidental occurrence of a symmetrical
event. I shall not, however, enter further into that subject, as
enough has been said to make it intelligible what the question
is ; and any reader who shall have taken the trouble to follow
the reasoning of these papers and of Professor De Morgan's,
will be in a position to form his own judgement upon it.
X. On the Principles of Hydrodynamics.
By Professor Stokes.
To the Editors of the Philosophical Magazine and Journal:. ,\
Gentlemen,
AS I do not see the remotest prospect of agreement between
Professor Challis and myself respecting the principles of
hydrodynamics, I think it time to fulfill the promise which I
have already made you of discontinuing the controversy.
As, how^ever, I have seen nothing to shake the fii'mness of my
conviction, which I have already expressed, that the new equa-
tion is both unnecessary and untrue, I request that you will have
the goodness to record my protest against it. (
As I do not mean to continue the controversy, it would not
become me to discuss the contents of Professor Challis's last
communication. There is, however, one point in a former article
which I will briefly notice. In alluding to the experiments by
which it is (as I conceive) shown that compression does directly
raise the temperature of air, Professor Challis speaks of the heat
developed by compression as " being in the first moment of its
generation in the state of radiant heat.'' (Phil. Mag., S. 4. vol. i.
p. 407.) I do not know what Professor Challis's notions re-
specting the nature of radiant heat may be ; but according to my
own, I cannot understand how the heat developed by compres-
sion can be in the first instance in the state of radiant heat, or
if it were, how the observed effects could be produced.
I remain, Gentlemen,
Yours sincerely,
Pembroke College, Cambridge, G. G. Stokes.
June 12, 1851.
^, , XI. 0^ the Mechanical Theonj of Heatl^'^ ^^^^j!
,., . % W. J. Macquorn Rankine, F.KS.E. &•» ' <**^*'^*
^J, 'To Me Editors of the Philosophical Maaazine and Journah ^^
A S you have announced your intention to publish a translation
•^^ of the memoir of M. Clausius on the mechanical agency
of heat, which appeared last summer in PoggendorfF^s^ww«7ew_,
I beg leave to offer to you the English version of a letter on the
subject of the First Part of M. Clausius^s paper, which was ad-
dressed by me to the editor of that journal, and published in the
9th Number for 1850.
JUnoqri I am, Gentlemen, 'r//
Your most obedient Servant, {
W. J. Macquorn Rankine;~~
30 Great George Street, Westminster, February 11, 1851.
Letter from Mr. Macquorn Rankine to Dr. J. C. Poggendorff*.
Having observed in your Annalen der Physik und Chemie for
April 1850 a very able and interesting paper on the motive power
of heat, by M. Clausius, 1 beg leave to call your attention to a
paper which was presented by me to the Royal Society of Edin-
burgh in October 1849, read on the 4th of February 1850, and
published in the 20th volume of their Transactions, Part First ; in
which paper, among other results, I have arrived at conclusions
respecting the specific heat of gases and vapours, and the latent
heat of evaporation, agreeing with those of M. Clausius, and de-
duced from principles, and by means of a method, which, though
differing in some details from those employed by him, are the
same in their essential points. In doing, so, I have no wish to
detract from the merit of M. Clausius, or to establish any rivalry
bet weep him and myself; on the contrary, I am gratified to find
the results of my investigations confirmed by so eminent an
authority.
It is probable that you have had, or will soon have, an oppor-
tunity of seeing the part of the Edinburgh Transactions to which
I refer; should that not be case, however, I shall be glad to
send you a copy of the paper as soon as I am aware of a conve-
nient and secure means of conveyance. In the meanwhile I
shall give you a summary of its contents. t ,'yiBW ii Yi
It consists of an introduction and four sections.
The introduction explains the general principles of a conjecture
* From Poggendorff 's Annalen der Physik und Chemie for 1850, No, 9.
62 Mr. W. J. M. Rankine on the Mechanical Theory of Heat.
as to the constitution of matter, called the Hypothesis of Mole-
cular Vortices. Its chief suppositions are the following : —
1. That each atom of matter consists of a nucleus or central
physical point enveloped by an elastic atmosphere, which is re-
tained round it by attraction ; so that the elasticity of bodies is
made uj) of two parts, — one arising from the diffused portion of
the atmospheres, and resisting change of volume only ; the other
arising from the mutual actions of the nuclei, and of the portions
of atmosphere condensed round them, and resisting not only
change of volume y but change oi figure also.
2. That the changes of elasticity produced by heat arise from
the centrifugal force of revolutions or oscillations amongst the
particles of the atomic atmospheres, diffusing them to a greater
distance from their nuclei, and thus increasing the elasticity
which resists change of volume only, at the expense of that
which resists change of figure also.
3. That the medium which transmits light and radiant heat
consists of the nuclei of the atoms vibrating independently, or
almost independently, of their atmospheres; absorptionheing the
transference of motion from the nuclei to the atmospheres, and
radiation its transference from the atmospheres to the nuclei.
This last supposition is peculiar to my own researches, the
first two having more or less resemblance to ideas previously en-
tertained by others.
The elasticity of the atomic atmosphere is supposed to vary
according to the law of Marriotte.
The principal results arrived at in this introduction are the
following : —
I. The specific gravities of the atomic atmospheres of all sub-
stances in the state of perfect gas are inversely proportional to
the coefficients of elasticity of those atmospheres.
II. Quantity of heat is the vis viva of the motions of the par-
ticles of the atomic atnaospheres, whether rotations or rectilinear
oscillations.
III. Temperature is proportional to
(the velocity of the rotations)^
the coefficient of elasticity of the atmosphere '
the constant added being the same for all substances in nature. .
IV. The maximum pressure of vapour in contact with its liquid
ia given by the following formula —
where P is the pressure, t the temperature measured from a
point 274*^*6 Centigrade below the freezing-point of water, and
Mr. W. J. M. Rankine on the Mechanical Theory of Heat. 63
at, ft 7 three constants, to be determined empirically for eacli
fluid.
[The comparison of this formula with the experiments of
Regnault and Ure on the vapours of water, alcohol, aether, tur-
pentine, petroleum and mercury, was published in the Edinburgh
New Philosophical Journal for July 1849.]
The first section of the paper contains the general theory of
the mutual conversion of heat and expansive power in all sub-
stances. The most important of the principles laid down is the
following, which is identical with that of M. Clausius : —
If unity of weight of any substance pass through a variety of
changes of temperature and volumCj and at length return to its pri-
mitive volume and temperature j the algebraical sum of the vis viva
expended and produced, whether in the shape of expansion and
compression, or in that of heat, must be equal to zero.
The expression obtained for the quantity of heat produced by
a given compression, or consumed by a given expansion, consists
of three terms.
uThe first depends on the mere change of volume.
I) The second depends on certain changes of molecular arrange-
ment connected with change of volume only.
The sum of those two terms is equivalent, in most cases, to
what M. Clausius calls " aiissere Arbeit"
The third depends on other changes of molecular arrange-
ment, and corresponds to the '^ inner e Arbeit" of M. Clausius.
The second section relates to real and apparent specific heat,
especially in perfect gases, that is to say gases which follow the
laws of Marriotte and Gay-Lussac. Real specific heat is the in-
crease of the vis viva of the atomic atmospheres for a rise of one
degree of temperature in unity of weight, and is equivalent, for
each substance, to a certain depth of fall. Apparent specific
heat is found by adding to the real specific heat that additional
heat which is consumed in producing changes of volume and
molecular arrangement.
The apparent specific heat of a perfect gas at constant volume
is sensibly equal to its real specific heat.
The apparent specific heat of a perfect gas under constant
pressure exceeds the real specific heat in a certain ratio, 1 + N : 1 ;
the fraction N being inversely proportional to the real spe-
cific heat of unity of volume of the gas, and probably a function
of its chemical constitution. The difference of those two specific
heats, ior unity of volume, is the same for all gases (as M. Clausius
also has shown).
The value of 1 + N, as deduced from the velocity of sound,
lies between 1-4 and 1*410 for atmospheric air; for oxygen and
hydrogen, and probably for all simple gases, it is 1*436. «; »
#1 Mr. W, J. M. Rankine on the Mechanical Theory of Heat.
The mechanical value of one Cimtigrade degree in atmospheric
air, as deduced from N, is
238-66 English feet = 72-74 metres.
The mechanical value of one Centigrade degree in liquid
water, as determined by Mr. Joule from experiments on friction,
being
1389-6 English feet = 423*54 metres,
it follows that the real specific heat of unity of weight of atmo^
spheric air is
1389-6 ""^'^'^
and the apparent specific heat under constant pressure
0-1717x1-4=0-2404;
according to De la Roche and Berard it is 0-2669.
I was at first disposed to ascribe this difierence to some un-
known loss of power in Mr. Joule's apparatus ; but now tlia^; I
am better acquainted with his experiments^ I am inclined rather
to believe that the error lies chiefly in the experiments of De la
Roche and Berard.
The apparent specific heat of vapour maintained at its maxi-
mum pressui'e is
Real specific heat x /l 4- N (^1 -^]^) T ,
and is a negative quantity, as M. Clausius has concluded.
The third section applies the principles of the first to the
latent and total heat of evaporation, and it is shown —
• TJiat the total heat of evaporation, where the vapour is sensibly
a perfect gas, increases at a sensibly uniform rate with the tempe-
rature ; and that the coefficient of its increase with tempei'ature is
sensibly equal to the apparent specific heat of the vapour as a gas
under constant pressure.
The value of this coefficient for steam, as determined by Reg-
nault, is
Specific heat of liquid water x 0-305.
This then is also the apparent specific heat of steam as a per-
manent gas under constant pressure. The real specific heat of
steam is
=0-194, and the ratio H-N = l-57.
These values differ slightly from those given in my original
paper, being calculated from Joule's equivalent, instead of the
experiments of De la Roche and Berard on atmospheric air.
The fourth section applies the principles of the second and
third to the theory of the steam-engine, and shows the modifica-
Mr. T. S. Hunt's Description and Analysis of Loyanite. 65
tions required by the practical formulae of Pambour to suit them
to the true mechanical theory of heat. It is proved^ that, from
the nature of the steam-engine, we cannot expect to convert
more than about one-sixth of the heat expended in evaporation
into available power, the remainder escaping into the condenser
or the atmosphere. The actual amount so converted is in many
ordinary engines less than one-twenty -fourth part. The paper
concludes with two tables for practical use, — the first for calcu-
lating the pressure of steam from the volume, and vice versa ;
and the second for computing the effect of expansive working in
steam-engines*.
Glasgow, September 14, 1850.
XII. Desaiption and Analysis of Loyanite, a new Mineral
Species. By T. S. Hunt, Chemist to the Geological Com-
mission of Canada-^.
THIS mineral occurs at Calumet Island on the Ottawa, in a
white crystalline limestone mixed with pale green serpen-
tine, phlogopite, pyrites, and rarely crystals of apatite.
Form very imperfect, but has the appearance of a prism replaced
* A comparison of the results of those formulae and tables with Mr. Wick-
steed's experiments on the Cornish engine at Old Ford is given in the
Edinburgh Transactions, vol. xx. part 2, together Avith a method of deter-
miniu;^' the proportions of an expansive engine which shall perform a given
amount of work at the least possible pecuniary cost.
Subsequently to the publication of the above letter, I became acquainted
with the second part of M. Clausius's paper, the object of which is to adapt
the principle knoA\Ti as Carnofs law to the mechanical theory of heat.
That law, as modified by M, Clausius and Prof W. Thomson of Glasgow,
is as follows : —
When a machine converts heat into expansive power by communicating
heat to a substance at a higher temperature (tj), and abstracting heat from
it at a lower (tq), the maximum proportion of the heat converted into expan-
sive power to the whole heat received is a function of the two temperatures
only, and independent of the nature of the substance.
I have since succeeded in proving, that Carnot's law is not an indepen-
dent principle, but is deducible from the equations given in my original
paper ; and that the function of the temperatures of receiving and emitting
heat, which expresses the maximum value of the fraction of the whole heat
converted into expansive power, is the following : |.
K being a constant, which is the same for all substances in nature. (Trans.
Rov. Soc. Edin., vol. xx. part 2.)
W. J. M.R.
London, Jvme 7, 1861. "^^
t Communicated by the Author.
Phil. Mag. S. 4. Vol. 2, No. 8. July 1851. F
66 Mr. T. S. Hunt^s Description and Analysis of Loganite,
on the acute and obtuse lateral edges, also on the acute solid
angles. The edges are generally rounded, and the secondary
planes not well defined. Cleavage with the sides and base of
the prism distinct, with the macrodiagonal imperfect.
Hardness 3. Specific gravity 2*60 to 2-64. Lustre of the
cleavages vitreous, shining, the surfaces of the crystals generally
dull. Colour clove-brown to chocolate-brown, streak and powder
grayish-white, sub-translucent, brittle, fracture uneven. The
crystals, which are short and thick, are generally small, and so
penetrated with the calcareous gangue, that great care was ne-
cessaiy in selecting specimens for analysis.
The powdered mineral exposed to heat in a tube gives off a
large quantity of water with an empyreumatic odour. Before
the blowpipe it loses its colour, becoming grayish-white, but
does not fuse ; moistened with cobalt solution and ignited, it
becomes blue. Acids take up magnesia, alumina and peroxide
of iron with a small but variable trace of lime, which exists as a
carbonate derived from the gangue, and leave pulverulent silica ;
the decomposition by this means is not, however, complete.
Qualitative analysis showed the presence of no other ingredients
than those already indicated, with the exception of a feeble trace
of manganese. Regard was had in the examination to the de-
tection of the rarer earths, the alkalies, titanic and phosphoric
acids.
The finely pulverized mineral was heated to whiteness, and
the loss thus sustained regarded as water, with the trace of car-
bonic acid, which was so small as to be difficult to determine
directly upon the portions of the mineral which my specimens
afforded me. The further decomposition was effected by fusion
with carbonate of soda, and the silica and bases were separated
by the usual methods. In analyses upon three different speci-
mens were obtained —
Sihca . . .
Magnesia . .
Alumina . .
Peroxide of iron
Water and C0«
Lime . . .
L II. III.
32-84 3214 3317
3512 36-43
13-37 13-00
2-00 2-28
1702 16-83 16-50
•96 -93
101-31 101-61
If we subtract from the loss by ignition the amount of the
carbonic acid requii-ed to form a carbonate with the lime, we
have respectively 16-36 of water and 1*70 of carbonate, and
16*12 of water and 1-64 of carbonate. Calculating the oxygen
ratio between the silica and the bases, we have for the first ana-
a new Mineral Species. -^ ' ^ 'r 57
lysis 17-515 : 34-990, and for the second 17-140 : 35-198. As
it appears from the third analysis that the amount of silica in
the second is rather too low, we may regard the first as ex-
pressing more exactly the ratio, which is just 1 : 2, and which
makes it a protosilicate in the nomenclature of M. Gerhardt,
pertaining to the type Si O^(M^) *.
The composition is very closely expressed according to the
Berzelian notation by 5Si 0^ 12MgO, If AP 0^, ^Fe^ 0^ 12H0,
which may be represented among others by the formula
2(AP 03 Fe^ 03), Si 03 + 4(3MgO, SiO^) + 12H0. *
This affords by calculation the following numbers, which are
compared with the first of the analyses above given, from which
the carbonate of lime has been deducted : —
Calculated. Found.
Silica 33-29 32-84
Magnesia .... 35-50 35*12
Alumina .... 13-31 13-37
Peroxide of iron . . 1-92 2-00
Water 1600 1636
100-02 99-69
vj iThe peroxide of iron is to be regarded as replacing a portion
of the alumina, so that the mineral is essentially a hydrated sili-
cate of magnesia and alumina, which, denoting Alf by Al/9, will
in the notation of Gerhardt be represented by
Si03(Al/8fMgfH|.).
The only mineral hitherto described which approximates to
this in constitution is chlorite, which belongs to the same type,
and is represented* by Si 03(Al/8f Mg| H|) ; the principal dif-
ference in chemical composition being in the proportion of water.
The hardness and other physical characters of this mineral are,
however, such as to distinguish it completely from chlorite, and
seem to warrant its erection into a new species, for which I
propose the name of Loganite, in honour of the distinguished
geologist who is at the head of the Geological Commission of this
province.
Montreal, C.E., Feb. 1,1851.
* Introduction h V^tude de la Chimie par le Systeme Unitaire, par Ch.
Gerhardt, p. 349. He takes for the equivalent of siUcon 87"5 on the oxygen
scale, which will equal 262-5 if we regard silica as Si O^. It is this number
which I have used in the calculation of the analysis. M. Gerhardt repre-
sents silica by SiO, and hence the formula Si 0^(M^)=SiO, 2W 0, corre-
sponds in the Berzelian notation to SiO^, 6M0. , 01^)$%
F2
Gf) [ 68 ]
XIII. Notices respecting New Books.
Six Lectures on Astronomy delivered at the Meetings of the Friends
of the Ipswich Museum. By George Biddell Airy. Astronomer
Royal. London : Simpkin and Marshall. 8vo. pp. 247.
WE wish to call attention to this work, on account of its intrinsic
merits, and the circumstances under which it was produced.
About four years ago, some of the leading inhabitants of Ipswich,
feeling a deep interest in the welfare of the working classes, and
believing that the cultivation of the intellect would tend greatly to
promote their physical and moral improvement, resolved to establish
an institution for this especial object. A museum was formed con-
taining books, scientific instruments, specimens of the fine arts,
natural history, geology, &c., to which admittance twice a week, free
of charge, has been granted to all. From time to time, as oppor-
tunity served, intelligible and untechnical lectures in various branches
of science have been delivered, which have been very numerously
attended. To show the quality of the instruction afforded, it is suf-
ficient to say that the Astronomer Royal, Professors Sedgwick,
Henslow, Owen, E. Forbes, Ansted, Playfair, &c. have been the
lecturers. The museum has been most handsomely supported by
the inhabitants of the town and the neighbouring nobility and gentry,
and is now very rich in several departments. It is not the least
pleasing characteristic of this admirable institution, that it has been
founded and supported by a union of persons of different ranks,
politics and religion, who seem to have felt no difficulty in discover-
ing a wide neutral space in which all good citizens may agree.
Members of the Society of Friends have been most zealous in this
good work ; indeed it is, we believe, to JVTr. George Ransome, one
of the honorary secretaries, that a very large portion of the merit is
due; but two successive Bishops of Norwich have presided at the
harmonious anniversary meetings, and the names we have just cited
as coadjutors show that nothing narrow or exclusive has entered
into the management. It is equally agreeable to state, that the
general good conduct of the j)ersons for whom this institution was
mainly formed has fully equalled the expectations of their well-
wishers. At Ipswich, as in most places where the experiment has
been fairly and judiciously tried, confidence in the people has been
met on their side by a strong sense of self-respect and responsibility.
To assist this excellent institution, the Astronomer Royal, who
had long been intimately connected with some of its principal pro-
moters, offered to deliver a course of lectures on astronomy, which
was gladly accepted. The nature of the lectures was announced in
the following words : —
** To point out simple methods of coarsely observing the funda-
mental phaenomena of astronomy — to describe some of the methods
of an astronomical observatory — to indicate the degrees and kinds of
evidence of the different parts of the received astronomical system—
Notices respecting New Books, 69
and to explain the waj's of measuring the principal dimensions of
the solar and sidereal systems." — P. iv.
The lectures were given on six successive nights, from March 13
to March 18, 1848, at the Temperance Hall, Ipswich, to between
600 and 700 hearers, a large proportion of whom were working men.
Shorthand-writers were engaged to take down the lectures ; and the
fair copy, revised and corrected by the author, forms the present work.
As might be expected from Mr. Airy, these lectures are quite ori-
ginal, and very dissimilar from the greater part of treatises professing
to be popular. He has carefully avoided the introduction of theo-
rems unknown to the majority of his audience, and those common-
places which too many persons think proper food for uneducated
listeners. Any one who has learned to solve a plane triangle by cow-
struction, and a spherical triangle by the globe, and who is able to
give sustained attention to a chain of reasoning, will find no diffi-
culty in comprehending the whole book. But it must not be con-
sidered to be light reading. The truths of astronomy, like most
things worth knowing, demand considerable mental exertion for
their acquisition. Skill in the teacher may make the steps more
easy, and to some extent supply the want of preliminary training ;
but it would be unreasonable to expect that a science, deduced from a
few indisputable phaenomena by strict mathematical reasoning, can be
as easily mastered by a man of plain common sense as by a geometer.
The scope and results of astronomy, a good notion of its methods,
its difficulties and its triumphs, may be obtained' from this book and
from another volume* by the same author, even by those who have
not had the advantage of a mathematical education : and we are of
opinion, that such a course of study would not only convey a large
amount of sound information on an interesting subject, but would
be singularly well adapted to strengthen and chastise the powers 6f
a student irregularly and imperfectly educated. "^
It is indeed to persons of this class that the lectures were more
particularly addresed. " I wish," says the author, "to invite espe-
cially the attention of those who are commonly called working-men,
to the few lectures 1 propose to deliver. The subjects upon which I
have to treat are commonly regarded as rather beyond their reach ; I
take this opportunity of saying that the subjects of the lectures will not
be beyond any working-man's comprehension. Everybody who has
examined the history of persons concerned in the various branches
of science, has been enabled to learn that, whereas on the one hand
those who are commonly called philosophers may be as narrow-
minded as any other class, and as little informed ; so on the other
hand, those who have to gain their daily livelihood by handicraft,
may associate their trades or businesses, whatever they may be, with
accomplishments of the most perfect and the most elevated kind. I
think, then, it is right I should repeat, that these lectures will be
directed in some measure with the object of being perfectly compre-
* Gravitation, an article in the Penny Cyclopiedia, also published in a
separate volume.
70 Notices respecting New Books.
hended by that class of people. It is not my object, however, to
deal with what may be called the picturesque in astronomy. I have
proposed it to myself as a special object, to show what may be com-
prehended, by persons possessing common understandings and ordi-
nary education, in the more elevated operations of astronomical
Bcience. The lectures will be, therefore, of what I may call a mathe-
matical kind. But in speaking of this, I beg that the ladies present
will not be startled. 1 do not mean to use algebra or any other
science, such as must be commonly of an unintelligible character to
a mixed meeting. When I use the word mathematical, I mean that
it will be my object to show how the measure of great things may
be referred to the measure of smaller things ; or to sum up in few
words, it will be my object, in an intelligible way, to show the great
leading stei)s of the process, by which the distance of the sun and
the stars is ascertained by a yard measure — the process by which the
weight of the sun and the planets is measured by the pound weight
avoirdupois. Occasionally I shall be prepared to go into details ;
but my principal business will be to show the great steps upon which
those who wish to study astronomy may enter, and by which they
may attain a general comprehension of the rules which will lead
them from one step to another." — Pp. 3, 4.
This design has been kept steadily in view throughout the course,
but it is not possible to convey any idea of the author's method or
success by extracts. We would however call attention to the ma-
sterly analysis of one problem of considerable intricacy, viz. the de-
termination of the parallax of the sun, and consequently of his di-
stance, by observations of the transit of Venus. As this is the con-
necting link between measures upon the earth's surface and the
dimensions of our system, great pains have been taken to make the
process intelhgible. The further step of investigating the parallax,
and consequently the distance of the fixed stars (where that is prac-
ticable), is also elucidated ; and the author, with evident satisfaction,
thus sums up the several steps. " By means of a yard measure, a
base-line in a survey was measured ; from this, by the triangulations
and computations of a survey, an arc of meridian on the earth was
measured ; from this, with proper obseiTations with the zenith sector,
the surveys being also repeated on different parts of the earth, the
earth's form and dimensions were ascertained ; from these, and a
previous independent knowledge of the proportions of the distances
of the earth and other planets from the sun, with observations of the
transit of Venus, the sun's distance is determined; and from this,
with observations leading to the parallax of the stars, the distance
of the stars is determined. And every step in the process can be
distinctly referred to its basis, that is, the yard measure." — P. 191.
In a similar manner, through the Schehallien and Cavendish
experiments, the density of the earth is ascertained, i. e. that it is
between five and six times as heavy as a corresponding bulk of water ;
and as its dimensions are known, the weight of the earth in pounds
avoirdupois can be readily assigned. Having the dimensions of the
moon's orbit, the space through which the earth draws the moon in
Royal Society, 71
a certain time is easily calculated ; and again, from the dimensions
of the earth's orbit, the space through which the sun draws the
earth in the same time is also found. These data and the well-known
law of gravitation, that the attractive power varies as the mass of
the attracting body divided Jby the square of the distance, assigns
the proportion of the sun's weight to the earth's weight. A similar
method applies to all the planets which have satellites ; and those
which have none are determined, though more imperfectly, by the
effects they produce in disturbing other bodies, planets or comets.
The satellites of Jupiter are weighed by their mutual disturbances.
The mass or weight of the moon is approximated to by several in-
dependent methods which agree well together. The author con-
cludes in the following words ; — " I shall now repeat what I said in
commencing this course of lectures, that I fully believe there is no
part whatever of these subjects of which thQ principle cannot be well
understood, by persons of fair intelligence, giving reasonable atten-
tion to them ; but more especially by persons whose usual occupa-
tions lead them to consider measures and forces ; not without the
exercise of thought, but by the application only of so much thought
as is necessary for the understanding of practical problems of mea-
sures and forces." — P. 247.
XIV. Proceedings of Learned Societies.
jf ROYAL SOCIETY. ,2^;
ri< [Continued from vol. i. p. 574.] ''
ll^pril 10, 1851 — Sir Philip de Malpas Grey Egerton, Bart., V.P.,
in the Chair.
ri'MlE following communication was read :— Extract of a letter
X from Professor Kamtz to Lieut. Colonel Sabine, on " Correc-
tions of the Constants in the general theory of Terrestrial Magnet-
ism." Received April 3, 1851.
Translation.
Dorpat, y% January 1851. .
From the active zeal with which you pursue the phenomena of
terrestrial magnetism, and collect all the facts which can conduce to
the elucidation of this difficult subject, I think that some researches
with which I have occupied myself will not be wholly uninteresting
to you ; and I therefore address you the following lines, which I have
also permitted myself to write in my own language.
Some years ago I employed myself in endeavouring to correct
the constants which Gauss has given for the earth's magnetism.
The process I adopted was by considering the horizontal and verti-
cal components separately ; but when I learned that Erman had the
same work in hand, I left mine unfinished. I did not then possess
the Reports of the British Association, as it was not until this last
summer (1850) that they were obtained here, and when I had seen
7-2
Royal Society.
Erman's results, I at once decided on taking up my work afresh. I
have made use of ail the data I could procure, and have thus been
able to determine the component Z at above HOO places, including
a series of observations which I had myself made from 1847 to 1849
in Liefland, Esthonia, Finland, Norway, and on the route from Arch-
angel to Petersburg. I have as far as possible reduced all determi-
nations to the epoch of 1830. A calculation of the several observa-
tions by the method of least squares would have required an entire
life ; I therefore preferred following the same path as Gauss ; in doing
this, however, I soon discovered that the 5th order could not be
neglected ; and I then obtained the following values : —
^0^ 6-4
^.o=_5r8
ff*fi=-Syz
5rU= 89-8
^2,1 _ __ J40'6
^.1= ii2'3
^.1=. — I03'2
^.ic= —115-1
AU=-i637
g^.2
A2.1=_ 14-1
f^,'2
A3.i= 48-5
,^.2
A4.i=- 1 8-2
(^.2
h^^= 72-8
2-5
-86-9
-41-3
-96-5
A2.2=_37.3
A8.2=-I7'2
A^.2= 43-4
A&.2=-io*o
ff*^= i8-8 A4.3= 1 8-6
^,3= 2*3 ^8.3= _ i'6
5^'^ = 3*9
flf5,5= -o
A^.''=4-3
AM = 2-8
A comparison will show you that these quantities agree much,
better with Gauss's than Erman's do; and this is also true in respect
to the agreement with the observations, especially in the high souths
latitudes. Thus there was found — ■
Latitude.
-69 54
-69 52
Means —69 53
Longitude.
179 55
180 04
180 0
Inclination.
Force.
-84 30 1999
-83 34 1994
-84 02
1996-5
Z=-1985-8 for —70° and 180°; Gauss found —2193-5; Erman?
'^—1781*1 ; my calculation givt^s —2009*3. My constants also still
^*^quire a small correction. I do not however mean to examine
this at present, but propose first to consider the horizontal compo-
nent, in order to satisfy myself previously whether both components
depend upon the same constants or not. The probable error of a ■
single determination is nearly 1 9 ; and to show the degree of agree- ; ;
ment, I subjoin the following table. As in forming it I merely took i '
from my larsje table every 10th observation i.. the order of succes-
sion, you will not be surprised at finding unimportant places, whilst
others of greater note in their vicinity are omitted: it may suflSce
however for the present purpose. The quantities given are the dif-
ferences between the observed and calculated vertical intensity. ,
Royal Society .
Stationsi^H ^i»^-
Lat.N. Long.E. A Z.
m^^m, ^^f ^
ia,iiYnT>]'j
"^ '^^"'f'
3:
43
5:
6]
7]
8]
91
lO]
II]
12]
14]
16]
17:
18]
19]
20]
21]
22]
23]
24]
26]
27:
25
29]
3O]
3-
32]
33^
341
35^
36]
37]
38]
391
40 ]
41
42;
43]
44]
451
46]
47]
48]
49]
53^
Fairliaven, Spitzbergen
Tromsoe
Tukansk, Isl
Grundsat ..,>:..,'.;.£./.'..
Sundsvall M«frA.'i..<wK«.
Abo
Danzig
Doskino
Perm
Tiuraen
Wandiask
Tschuluim
Botowsk
Monachanowa
Nowaja River
Progromnoi
Nalaicha
Chapchaktu
Zackildack
Gaschun
Arki
Sitka
F. Dunvegan
Frog Portage
York Factory
Fort Alexander
Devil's Drum Island ...
Cape Disappointment...
Lac a la Pluie
Fort a la Cloche
Portage Ecarte
Chat Falls
Pointe aux Chenes ...
Lake Nipissing
Waterville
Dubuque's Town
St. Mary's
Detroit
Alleghany Summit ...
Utica
Portland
St. Louis
Paoli
Columbus
Lerwick
Loch Slapin
Braeraar
Edinburgh
Valencia
Enniskillen
York
Calderstone
Castleton
Dublin
Fermoy
Clifton
79 40
69 39
68 4
60 56
62 22
60 27
54 21
56 9
58 1
57 10
66 16
55 6
55 10
50 58
72 7
52 30
47 47
46 2
42 48
44 23
60 6
57 3
55 56
55 28
57 o
50 37
53 19
46 16
48 32
46 7
48 25
45 26
45 37
46 13
44 33
42 29
40 32
42 25
40 27
43 7
43 41
38 38
38 5
39 57
60 9
57 14
"^T I
51 56
54 21
53 58
53 23
54 4
52 7
51 27
II 40
18 55
39 35
" 35
17 16
22 18
18 38
43 34
56 14
65 27
65 10
81 14
105 22
106 29
95 25
III 3
107 18
108 35
114 17
III 19
142 20
224 34
241 26
256 30
267 34
263 39
259 20
236 4
267 4
277 35
270 15
283 28
285 5
280 I
293 23
269 37
275 41
277 o
281 50
284 47
289 40
269 56
273 35
276 57
358 53
353 58
356 35
349 43
352 22
358 54
357 7
355 20
24-1
31-2
39-1
39-8
2-5
157
31-0
32-8
30*0
13-4
27-7
24*6
37
6-8
22*3
11-8
9-8
13-0
13-5
9-8
1*2
2'2
227
9-1
4*9
i3'4
22*7
34*2
19-9
197
4-8
22-8
77
167
11-9
-f- 20-8
+ 31-9
24-0
29*3
27*2
H*5
35-8
307
11-9
46-8
30*4
l6*2
351 44
357 25
8-5
25*6
22'5
177
227
15-2
13*5
i6-4
Sabine,i^^g .hiifift'jul -IIJ
Hansteen. '^^ ^^ fe«OJifi£i
Hansteen. >rfJ \^ 8"OS*
Hansteen. ^d! T ; /ill
Ericksen. ,,,^f ;,^vj
Erman and Hansteen.*
Erman and Hansteen.
Erman and Hansteen.
Erman^i , c vv; ;^
Erman;,> t^'-^ »^ v-t^ .V
Erman. ''''
Hansteen.
Middendorf.
Fuss.
Fuss.
Fuss.
Fuss.
Fuss.
Erman.
Liitke, Erman, Belcher.
Lefroy^,^:^j^^-qxnoa A
Lefroy. . .
Lefroy.*"^'"^'^'^^^ eriJ 03
Lefroy. '' :>bjiiiJBf
Douglas.
Lefroy.
Lefroy.
Lefroy.
Lefroy.
Lefroy.
Lefroy.
Keely.
Locke.
Locke.
Loomis,Younghusband,Locke;
Locke. .. j^. ^;^£Lefroy
Loomis, Lock. ' "* "'?
Locke. - m;:; .:
Locke, Loomis, Nicollet.
Locke. .„,., v,^,.:..^'-:L
Locke. nriicj'iy ^fgnig
Sabind'iJ ^^i^ Vf« ^^^'^
Sabine, Ross^.j-g Ic* aitjrfiO
Phillips, Ross. . .-.
Phillips. ^^^^ ^^^^'^
Phillips.
All Observers.
Sabine.
Lloyd, Ross.
74
Royal Society.
Stations.
541. London
551. Salisbury
561. Dover
571. Fontainebleau ..
581. Nimes
591. Malaga
601. Prague
611. Berne
621. Seelau
631. Rome
641. Mile
651. San Diego
661. At sea
671. At sea
681. At sea
Tcneriffe
691. At sea
701. At sea
711. Socorro Island ..
721. Ulean
731. At sea
741. La Guayra ,
751. Morales
761. At sea
771. St. Thomas 1
Fernando Po >
Isla das Rolhas J
781. At sea
791. At sea
801. Pasto
8ii. At sea
821. At sea
831. Pulo Kumpat
841. Shell Rock
851. Gonzanama
861. At sea
871. Tomependa
881. Huaura
891. At sea
90I. At sea
911. At sea
921. At sea
931. Bow Island
941. At sea
St. Helena
951. At sea
961. At sea «.
Mauritius
971. At sea
981. At sea »....
991. At sea
Lat. N.
51 31
51 4
48 24
43 SO
36 44
50
46 57
49 32
41 54
36 43
32 41
47 7
44 22
30 o
28 27
21 32
23 12
18 43
7 22
8 55
10 36
8
10 7
-a6 25
-21 54
-20 9
■22 41
■22 38
•22 34
Long. £.
359 53
358 12
X 19
2 38
4 20
355 36
14 27
7 25
15 17
12 26
24 27
242 27
346 54
330 54
318 5
343 43
316 43
238 9
249 6
143 57
235 48
292 54
286 o
319 51
7 20
162 59
236 4
282 39
331 9
341 3
no 7
136 21
280 27
223 32
281 24
282 14
324 44
339 50
214 37
251 20
219 7
3^5 5
354 17
49 12
53 o
57 31
69 54
76 10
80 10
AZ.
21*9
i8-3
197
I I'D
3-8
13-4
'5*5
I2"0
21*6
S'°
i9*6
70*6
0-4
i8-3
4'3
0-4
21-3
61-2
28-0
10-8
27-8
2-6
7'o
48-9
- 35-i
8-2
317
13-0
8-4
IO-8
168
1*4
4-5
19-9
lO'l
12-9
52-2
2I'l
9*4
57'o
7*5
207
H7
17-1
20*0
0-5
267
17-4
22*1
Observers.
All Observers.
Lloyd, Ross.
Sabine.
Fox.
Fox, Humboldt.
Norwegian Officers.
Keilhau, Kreil.
Fox.
Kreil.
Humboldt, d'Abadie,Quetelet.
Norwegian Officers.
Belcher.
Sulivan.
Erman.
Sulivan.
r Humboldt, Freycinet, Du.
■< perrey, Sabine, Bethune,
L Wick'ham, Sulivan.
Sulivan.
Erman.
Belcher.
Liitke.
Erman.
Humboldt.
Humboldt.
Sulivan.
The secular change at this
station is uncertain ; I
take the mean of the in-
clinations by Sabine and
Alien; the force at St.
i_ Thomas, from Sabine.
Liitke.
Liitke.
Humboldt and Bousingault.
Erman.
Dunlop.
Belcher.
Belcher.
Humboldt.
Erman.
Humboldt.
Humboldt.
Sulivan.
Dunlop.
Erman.
Liitke.
Belcher.
Sulivan.
All Observers.
Moore and Clerk.
Moore and Clerk.
Duperrey, Fitzroy, Moore and
Dayman. [Clerk.
Dayman.
Dayman.
Royal Society.
75
Stations.
lOO
lOI
1 02
103
104
105
106
107
108
109
no
III
H2
"3
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
132
133
134
135
136
137
138
139
140
1410
141
141:
142
H3
144
1444
. At sea..
. At sea..
. At sea..
. At sea. .
. At sea..
. At sea..
. At sea..
. At sea..
. At sea..
. At sea. .
. At sea
Sydney
At sea
Bay of Islands ..
Valdivia
At sea
At sea
At sea
At sea.....
At sea
Kerguelen Island
At sea
At sea
HobartTown
Bass's Strait
At sea
At sea
At sea
At sea
At sea
At sea
At sea
At sea
At sea
Port Famine
At sea
Falkland Islands
At sea
At sea
At sea
At sea
At sea .
At sea
At sea
At sea
At sea
At sea
At sea
At sea
At sea
At sea
At sea
At sea
Lat. S.
24 17
21 51
^9 S3
38 44
35 48
32 17
38 II
39 16
33 47
35 5
42 35
33 38
35 16
39 53
44 4
37 37
41 47
46 28
48 40
48 41
47 39
47 34
42 53
40 28
41 49
49 23
53 57
54 55
57 54
53 I
58 39
60 21
58 25
53 38
46 o
51 33
61 10
66 33
66 24
60 50
65 9
64 41
61 34
67 14
65 18
67 16
61 15
62 38
70 23
72 58
77 6
77 47
Long. E.
94
268
6
5
313 43
o 16
18 47
29 34
22 o
30 27
III 4
117 56
125 40
163 42
174 o
286 31
312 I
353 36
26 38
52 31
68 58
68 54
103 42
124 43
147 24
151 35
183 41
188 29
6 5
132 50
170 25
205 8
213 17
237 54
279 44
289 2
299 50
301 55
9 5
36 48
40 30
87 41
143 7
162 34
170 40
188 6
191 39
202 13
213 54
212 44
174 50
189 50
192 31
197 25
AZ.
7*5
19-0
i9'3
77
25-8
0-6
- 29-9
- 107
+ 31*3
- 7-1
+ 5^3
+ 39'o
+ 177
- 33*2
- 8-4
+ 41*3
+ 9-1
- 36-3
- 167
- 4*o
- 55-5
- 11-9
- 23-4
— 109*6
+ 41-8
+ 11-5
- i8-3
•o
- 4*1
- 53'8
+ 40*4
- 18.3
- 67
+
i9'o
io*8
4-6
49*2
41*3
15-9
17-5
8-1
lO'I
52-5
IO-5
267
18-4
28-5
30-4
22*2
3 '4
IO*2
21"0
8-0
23*2
Observers.
Moore and Clerk.
Liitke.
Erman.
Dunlop.
Erebus and Terror.
Dayman.
Erebus.
Dunlop.
Dayman.
Moore and Clerk.
Smith.
All Observers.
(British only).
Erebus.
Duperrey, FitzRoy, Erebus.
FitzRoy.
Sulivan.
Dunlop.
Erebus.
Erebus. -Maximum of proba
Erebus. ble error. There
Erebus, are great anoma-
Erebus. lies in this meri-
Erebus.-' dian.
All Observers.
Wickham.
Erebus.
Erebus.
Moore and Clerk.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
King and FitzRoy.
Sulivan.
All Observers.
Moore and Clerk.
Moore and Clerk.
Moore and Clerk.
Moore and Clerk.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
Erebus.
I think the agreement pretty good for a calculation which I still
expect to correct in some degree ; it is also to be remarked that i
H
Royal Society.
have taken the results of all observers, and that their determinations
- often differ considerably from each other at the same place. Un-
fortunately I could not make use of the two important determina-
? tions of the Euphrates Expedition for want of the Inclination.
As you collect everything that can serve towards a final determi-
nation of the elements, I permit myself to subjoin the following data
which are still partly unpublished.
Stations.
Uellenorm
Dorpat* ..
Kardis .....
Bevel
Nawast ...
Werderf ...
Arensburg
KabbU
Pernaw . . .
Tammiss ...
Kurkundt
Helsingfors
Lat.
N.
Long,
E.
Inclination.
Date.
BoUstad
Kyrkstad ....
Lambola
Nukari
Abborfors ....
Gronwick
Wiborg
Turkbauta ....
Tavastebus ....
Wilman strand .
Imatra Fall ....
Huutjarwi ....
Pumala \6i
6i
6i
62
62
62
62
63
59 35
2§ 43
26 44
26 17
*4 43
35^5 34
35^3 40
1522 25
2022 40
2224 32
2i!h 33
8 24 59
1024 57
Webuwarpe
Nyslott
Tjokt
Warkauss-Sluss .
Johannisdal
Kuopio.»
Wa«a§
924
1024
1523
2224
3026
33;^7
4428
5024
024
4'28
1128
28|24
3228
46|22
52,^9
1821
2027
21 21
551^7
5*1
1847.
1847
to
1850.
1847.
1849.
1847.
1849.
1848.
1848.
1848.
1848.
1848.
1848.
1848.
1847.
849.
Ob-
served.
70 9-8
70 507
70
17-1
17-5
17-3
54*4
45-8
Re.
ducedto
1830.
70 38-0
71 19-9
3 .
X
70 48-3
50-171
41-071
3r6'7o
5i-i|7i
9*3l7i
36-3:71
24-570
47-970
21-
I2-0
2-6
22*1
40-3
7*3
55*5
18-9
4737
465-4
471-6
467-1
469*3
Vertical Force.
1396-0
1317-0
1421-9 1347-1
1388-4
1311-2
7
19-7
847.
1847.
847.
1847.
847.
1847.
1847.
1847.
1847.
1847.
55:1847.
2|i847.
1847.
1847.
1847.
1847.
1847.
1847.
1847.
1847.
20-771
30-271
21-9171
28-971
40-317*
19-8:71
3*'3:72
51-6171
14-672
8-4I72
51-872
51-072
2-372
6-472
59'9
43-0
32-4
27*3 73
54*3,73
0-873
517
59*4
51*1
58-1
49-Oi
1*5
20-8'
43*8
37-6
21-0
20-2
31*5
37-1
35-6
29-1
12-2
1-6
56-5
23*5
30-0
454*41384*21311*5
4547!i374*5 ^o^**
484-6I 1385-4 1302-2
455'5ji388-8ii3i6-o
437*61354-81286-1
458-411380-1 1305-9
459-0:1368-81293-6
476*2 1378-711298-0
444*3
7-6
1317-6
1318-0
RhtfH-
323*4 ^;l'
0-6
+ 29-1
446-0 i394-3'i325-o
441*4 1391-41^323-2
442-6 1385-1I1316-2
4427,1393-8,1325-4
44o-8| 1401-8, 1334-3
450'o|i4o6-2| 1335*9
44i*i!i393*i;n25-o
446-2 1360-9 1289-4
425-5 i395-iii332-2
427*61394-711331*1
439'o 1410-2 1344-0
433*6ji4ii-3|i344-8
433-51 1405-8! 1340-9
431-711406-9 ^^--'f'
433*01409-3
437*211414-6
419*4:141 1*7
420-1 1 1400- 1
399-4! 1402-6
4i5*5|i4i3*6
411-711442-0
[342-6
1344-9
1349*1
1351-3
1339*1
1347-9
1354-6
1351-01367-6
* In the garden near ray house, and at different parts of the town and its en-
virons ; including diflfercnces of inclination of more than 1° 1 5'.
t H. F. very anomalous. X Hanstcen, 1825, A Z= — 12-4.
§ Hansteen, 1825, AZ = — 13-3.
Royal Society.
77
Stations.
Sawojarwi
Sundby . .
Aho
Lot.
N.
Long
E.
22;27 13
36122 40
2 26 27
Wirda 63 3727
47 ^7
Salahmi
Kyrola
Tuomala ..
Lassila
Uleaborg*
Wuornos .,
Rautiola ..
Tornea
Haaparandaf
Alkulat
ToluanenJ
Turtolat
KardisLappl.J-"
Kexiswaarat ...
Muonioniscai ...
KatkesuandoJ...
Palajoensu
Kaaressuando ...
Kielli-jarwi
Troms6e§
Hamraerfest II ...
Havosund^
Kielwig Mageroe
Kitai-Insel** ...
Archangel ft ...
Bobrowsk
Kaduish
Plesskaja
Krassnowskaja. . .
Ustwelskoi
Kargopol
Badoshkaja
Wytegra
Gomorowitschi...
Petersburg t J ...
65 52
66 20
66 36
66 42
67 o
67 15
68 o
3
o
23 30
26 o
24 38
25 27
25 26
24 40
23 30
23 30
23 49
23 52
23 40
23 39
23 27
23 42
23
22 45
22
20 40
18 56
4023 45
024 45
26 15
38 30
40 33
41 o
41 30
40 55
40 10
39 12
38 57
37 30
36 28
34 35
30 18
in n
Bate.
1847
1847
1847,
184.7.
1847
1847
1847
1847
1847
1847
1847
1847
1849
1849
1847
1849
1847
1847
1847
1847
1847
1849
1S49
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
1849
" 'inclination.
Ob-
served.
Re-
duced to
o /
72 53*1
73 18-9
24-9
9'4
14*2
24-8
307
73 50'5
74 6-0
74 4*8
74 49*9
74 52-3
48-4
74 50-3
74
28-1
74
21*1
15-2
74 i8-2
74 31*9
74 47*7
75 4*4
75 45*2
75 32*0
31-0
22*3
48-1
54-1
38-6
43*4
54"o
59*9
197
35"2
30*0
19-1
434*6
401*8
407-4
4"*5
408-8
409*0
410*7
408*2
393*2
393*5
377*5
380*2
2*6
19*5 381*4
57*3
47*4
i6'9
33*6
14*4
75 31*5
75 32*1
76 5*7
75 37*1
75 52*4
76 11*4
76 43*8
76 46*1
76 54*6
75 50*6
73 58*8
74 1*5
73 19*6
72 46*7
72 33"5
72 15*3
72 8*2
71 25*3
71 34*2171
71 34*4 71
70 33-270
382*
392*2
3*8
393*0
386*9
381*3
374*3
366*1
364*7
5*6
365*2
359*8
350*0
359*3
355*1
348*1
59*7
1*3
34*9
6*3
21'6
40*6
13*0 344*3
15*3
23-8
9*6
8*3
11*0
29*1
57*2
43*0
25*3
19*2
28*6
48*2
53*0
59*o
336*7
333*7
358*2
405*4
404*5
420*2
429-8
432*8
442-1
444*4
459'o
457*1
450*6
473*1
1511-
1399*4
1427*4
1420*1
1417*2
1432*7
1446*7
1466-9
143 5 "2
1434*7
1437*9
1458*4
1427*0
1452*8
1450*3
H53*9
1452*9
1487*8
1459*1
1440*6
1456*7
1446*6
1455*0
1458*4
1500*2
1471*0
1473*5
1464*6
1468*9
1469-6
1464*5
1451*7
1443*8
1450*6
1448*6
1440-8
1445*9
1425*5
1420*8
Vertical Foi*ce.
1415*0
1343*9
1371*5
1362*6
1360*6
1376-5
1390-7
1412-4
1383-6
1382*4
1390*9
1410*9
1378*1
1401*9
1401*1
1406*1
1407*1
1445*1
1415*7
1397*9
1416*9
1404*3
1414*0
1419-2
1463*0
1434-8
1438*0
1422*0
1413-0
1414*0
1404*1
1387-9
1378-7
1382-8
1380*2
1366*1
1373-6
1354*8
1343*2
31,
1383*0
1375*0
1388*0
1384-6
1386*6
1382*6
1389*8
1393*0
1398-6
1405*3
1405*2
1404*]
1404*]
1410*0
1413*3
1414*5
1418*0
1420*6
1430*2
1430*7
1432*5
1433*7
1439*0
1444*4
1464*0
1466*1
1467*5
1476*7
1439*1
1440-8
1422*8
1408*3
1407*3
1400*4
13957
1381*1
1380-5
1371*0
1347*0
+32-0
-i6-5
— 22*0
— 26*0
— 6*1
0*9
19-4
15*0
22*9
14*3
+ 6*8
— 26*0
- 8*1
— 12*2
- 8*4
— 10*9
+24-5
■14*5
.32*8
• 16*6
•29*4
■25*0
•25*2
• 1*0
■31*3
■29*5
■547
■26-1
•26*8
■18*7
■20*4
■28*6
•17*6
■15*5
•15*0
• 6*9
■16*2
■ 3-8
* Hansteen 1825, /XZ= — 12*0. f Hansteen 1825, ^Z= — 12*1.
X Hansteen 1825, AZ4-o*i; many iron mines in the vicinity; quantities «f-^|
magnetic ironsand on the banks of Tornea river.
I! Sabine, -|-2*8 ; Keilhau, —30*9, ^ Keilhau, -
"H* Reinicke and Mailander, —62*5.
XX Inclination observed by me j force by KupfFer
A Z = — 9* 3 . ^, ii ,^;^^i, ^^isit; iiMSiJ . .
§ Keilhau, AV-f- 3 1*2. ^a
27*4. ** Keilhau, — 3*2.---
; earlier observations gave
?/
78 Royal Society.
In the above table, the Iiorizontal force was obtained by vibrations,
and reduced to 6° Reaumur. Before and after my journey in 184-7,
the force was determined at Dorpat by Gauss's method, and the
needle employed compared therewith and reduced to the intensity in
London = J 37'2. Subsequently I preferred for trying the needles,
PoissOn's method, at least for traveling purposes; but some alterations
require to be introduced in Poisson's formula, as he has overlooked
some things. With the same needle which I employed in both my
journeys, I have made more than 60 determinations of absolute
force at Dorpat, partly in a room and partly in ihe open air, and in
temperatures varying from— 13° 11. to + 25° R., and have found a
very good accordance. I also made several such determinations in
the journeys of 1848 and 1849.
As I do not possess an observatory, and cannot employ a Bifilar
in my dwelling-house, it has not been possible for me to compare
the variations of the force with my determinations ; I have however
made use of the following method : — If X be the magnetism of the
earth and m that of the needle, I seek not X but m ; this latter
quantity depends on the temperature t and the time T, as the needle
is not constant ; but if I combine all the values of m by an equation
of the form
and calculate the constants, the error is about ^^ m. Besides this,
several simultaneous observations with Gauss's apparatus have shown
that the value of m was itself correct.
The Inclinations have in part been determined by two needles
which agreed very well with each other ; they are so balanced that
I can always take the mean of the eight arcs. On the other hand
they are subject to the error of the axle, which I cannot exactly cor-
rect, but which does not however exceed 5'. It was only last sum-
mer, when I examined the subject more closely, that I became aware
you had likewise the idea of loading the needle, and observing in
different azimuths. In our latitudes the best loading is such as will
cause the north pole to be in one set about 10° above, and in a
second set 10° below the horizontal line. Three series which I made
with one needle were calculated by my friend Claussen, who in
doing so was led to a method of entirely eliminating the form of the
axle. Take a well-balanced needle, the axles of which are not cy-
lindrical ; different degrees of magnetic force can be given to it with-
out reversing the poles. Taking the strongest force as unity, it is
not practically advantageous to go to lower ratios than i or ^.
Though vibration experiments with dipping-needles are not gene-
rally advantageous, yet they suffice in this case, as an approximately
correct proportion of the intensities is all that is wanted. It is suf-
ficient to make, with each degree of intensity, the two observations
with the face east and face west, without reversing the needle on its
supports ; if the latter is done, it gives a second determination, af-
fording a check upon the first. You will then find that the mean of
the two observations in one position of the axles is less than the
true inclination, and in the other position greater ; the difference in
Royal Society ^ 79
both cases being more considerable as the intensity of the needle is
weaker. Let Iq, Ii, l^i ^^' be the inclination observed with different
intensities ; To, T^, Tc2j &c. be the times of vibration, which increase
as the index increases ; a small correction is required, which can
be determined in the following manner. — Take either Iq or a some-
what less value (in round minutes) as being nearly correct, and let
lo— Ii = Ali, ; Io-l2=Al2, &c.,
then Al = a;H-T2?/;
X being the correction ; thus I found
Az.O; 1=70 23-8.
Az. 180; 1=71 26-5.
Mean 70 55-1. T= 1-167.
Az.O; 1=70 48-7.
Az. 180; 1=71 44-7.
Mean 71 15-2. T=l-738.
Az.O; 1=66 16-0.
Az. 180; 1=84 16*5.
Mean 75 36'3. T=4-25.
If I take 70° 55'*0 as nearly correct, I obtain the three following
equations ;
0'-l=aj + (M67)-?^ ; 20'-2=^ + (l-738)22/ ; 281 -3= a? + (4-25)2^.
The three equations have not however the same weight, as the di-
rective force is less in proportion as T is larger; in order to give
them all the same weight I divide each by the coefficient oiy, and
thus obtain in logarithms
8-86586=9-86586^+y ; 0-82525 =9*51 990 a? +y ;
M9239=8-74322a;+y.
and hence :r=21'-8 ; and the true dip =70° S3'-2.
I have here taken an imperfect needle, which I also observed" in
Azimuths of 30° to 30° ; in one position of the axles I obtained 70°
39'-5 ; +5'-9 ; and in a second 70°42'-5 ; +5'-4 ; mean 70°41'-0. On
a subsequent day I observed with a second needle and obtained 70°
43'*4 ; but an independent needle gave a dip 2'*6 greater, so that
the two determinations are 70° 42''1, 70° 42'*3, if we add to each
the half difference.
In this method, in which no reversal is needed, the differences of
the partial determinations will appear somewhat large, but you must
not forget that instead of the ordinary eight observations only two
have been taken.
I permit myself one additional remark. In observations on dif-
ferent azimuths, it is usual to take simply cot I. = cot I^ cos a; in
latitudes where the dips are so high as here and in England, this
equation may be employed without much error, as the force in
azimuths perpendicular to the meridian is little less than in the
meridian ; but it is quite otherwise in small dips. With the decrease
of force the possibility of error increases, and hence when the ob-
servations made in different azimuths are combined as by Kupffer,
they have not the same weight. In more exact determinations I
employ the following method.
Let K be the total, H the horizontal, V the vertical force,fand a
the nearly known azimuth; then
V 1
K cos I=H cos a ; K sin I=V ; tan I=iT • rTr~ '
xX COS ct
80 Royal Society.
whence . ^ I=^^7^'^(h;+ K^ ^'^ " * ^ «*
If on the right we substitute foi: cos *I its value, then
,T H«cosa ,/V\ , HV . ,
'As the possibility of error is inversely as the force, I multiply the
equation by K, to give to the different determinations equal weight,
thus
If^T-H^cosa ,/V\^HV . ,
having determined the dips in the customary maimer with the ap-
proximately known values of «, I obtain the values d I, which serve
to find d Itj); ('€. the correction of I. I possess now with my in-
strument six needles, which I Iiope to compare very accurately with
each other in the course of this year ; but some months must first
elapse, as I make all these determinations in the open air, and the
bad autumn we have had has interrupted me in the work. I have
had two of my needles fitted according to Fox's method, with wheels
on their axles ; two others have brass indexes, as was formerly pro-
posed by Bernoulli and Euler (Berlin Trans. 1755), and I can now
determine the absolute intensity with the inclinatorium. I know
Fox's method only from a short notice in the London and Edinburgh
Phil. Mag. ; if I do not mistake, he proposed also to determine the
declination by the same apparatus. With ordinary needles there
remains an uncertainty. If we load the S. end of the needle so that
the N. end is about 10^ above the horizon, the S. end sinks down;
and if we seek the azimuth in which the needle is perpendicular and
then observe at about half a degree of azimuth on either side, the
inclination alters so rapidly with the azimuth, that I have thus been
even able to follow the diurnal variations of the declination ; and
the magnetic meridian may thus be determined for the observations
of absolute declination whilst travelling.
I will not trouble you further as my letter is already so long, and
will only add one request. The Phil. Trans, arrive here rather late,
and the last communications which I have seen of yours contain
Keely's determinations. All the observations of the Erebus and
Terror have not yet appeared ; in the Atlantic I know only the total
intensities but without inclinations or declinations, and yet I am very
anxious for some determinations that have been made between 10°
and 20° of longitude in the higher latitudes to compare my calcula-
tions witli them. If your time permits, I should be very much obliged
to you if you could communicate to me the inclination and force at
some points. In the mean time I will occupy myself with the dis-
cussion of the two horizontal forces ; unfortunately the number of
determinations serving for this purpose is much smaller. For North
America those recorded by Lament in Dove's ' Repertorium ' are
for the most part in comparatively low latitudes.
[ 81 ]
i¥<:'
XV. Intelligence and Miscellaneous Articles.
POSTSCRIPT TO MR. T. G. BUNt's PENDULUM EXPERIMENTS.
June 23. TOURING the last two or three days I have been making
■^-^ some further experiments, with a view to ascertain
more nearly the rate of the apsidal motion, when the arc of vibration
becomes very small. Twelve experiments, averaging about 20 minutes
each, gave 11°'60 for the azimuthal horary motion, when the mean
length of the arc was 11 inches and the ellipticity +0*19 inch;
and seventeen similar experiments gave 11°*39 per hour, when the
ellipticity was —0' 17 inch. The mean length of arc, ellipticity, and
motion in azimuth, for each hour, are as follows : —
Part of Circle
Motion in Azi-
Length of Arc.
Mean Ellipticity.
observed.
muth per hour.
'M
in. in.
inch.
o o
o
12 to 9
+ 0-18
49 ... 62
11-64
13 ... 9
-1- 0-19
62 ... 74
11-88
f4... 9
f 11-90
-j-0-24
74 ...113
\ 11-90
[11-90
14 ... 11
+ 0-22
113 ...127
11-00
14 ... 9
+ 0-27
141 ...156
12-66
14 ... 11
-016
50 ... 63
11-81
14 ... 9
- 0-0/
65 ,.. 89
j 11-50
1 11-50
11-55
15 ... 11
-0-23
90 ...102
16 ... 11
- 013
102 ...113
12-03
14 ... 10
- 0-02
113 ...133
r 11-35
1 11-35
14 ... 10
- 0-13
134 ...144
10-78
15 ... 11
-0-08
127 ...140
Mean...
11-07
• ■\
11-651
^M
1
:*(U&
On leaving the pendulum yesterday evening I gave it an impulse,*
intending to see what would be the motion of the plane during the
night. At 7^ 34"^ p.m. it was vibrating towards the division 1 70°'53,
the arc being 22 inches and the ellipticity — 0*04 inch. This
morning, at 9^* 30™, the plane of vibration cut the circle at 331° '80,
the ellipticity was about — O'Ol inch, and the arc 1*6 inch. The
mean hourly motion during the night had therefore been ll°-576.
I stated in my former letter, that the motion of the plane of vi-
bration, when in proportion to the sine of the latitude of St. Nicholas
Tower, is 11°* 7309 per hour. This is true for an hour of sidereal
time only; for an hour of mean time, the amount will be 11°*763
nearly.
ON THE TOTAL ECLIPSE OF THE APPROACHING 28tH OF JULYi^f
BY M. FAYE. '"*'
A few days ago, through the politeness of Mr, Airy, I received a
remarkable tract published by a committee of the British Association
for the Advancement of Science, in conjunction with the astrono-
mers of Russia, for the purpose of making known the arrangements
which will be requisite for the complete observation of the approach-
ing eclipse. Since the Committee has done me the honour of direct-
Phil, Mag. S. 1. Vol. 2. No. 8. July 1851. , G
8^ Intelligence and Miscellaneous Articles.
ing the attention of astronomers to one of my memoirs upon instru-
mental errors, in which I have incidentally treated of eclipses*, it
may perhaps not be considered amiss for me again to dwell upon
the notions which I published last year.
In accordance with these notions, it would be of importance to
determine the temperature of the atmosphere, and especially its
variations, by means of very delicate thermometers, and at different
elevations above the surface of the earth. If even aeronauts would
consent to make an aerial ascent on the 28th of July, they would un-
doubtedly enjoy during the complete eclipse, a very beautiful spec-
tacle ; they would be certain, at all events, to render their under-
taking of great scientific interest, by carefully determining the vari-
ations of the temperature at an elevation of some thousands of metres.
Probably some very useful information upon the temporary constitu-
tion of the atmosphere during the eclipse might be obtained by mea-
suring several very exact zenithal distances of the sun or the moon,
before, during, and after complete obscuration. M. Otto Struve
has informed me that arrangements will be made, at least at one
station, in conformity with the plan suggested by me, and this
good new^s diminishes my regret at not being able to render my
feeble cooperation in this noble astronomical undertaking. I may,
however, be permitted to recall to the attention of observers a
phaenomenon which the Report of the British Association has omit-
ted to notice, undoubtedly because the phaenomenon has appeared
too doubtful or completely exceptional. But as numerous stations
ought to be arranged in several lines perpendicular to the progressive
motion of the shadow, and as the observers ought to occupy every
possible position within the cone of the shadow, it is probable that
no phaenomenon, however rare and exceptional, will escape attention
when so scientifically directed. I must say a few words here upon
the brilliant points observed by UUoa and M. Valz upon the disc of
the moon. In consequence of an inherent tendency of the mind,
which at first always attributes substance and reality to appearances
by which it is struck, the luminous points have been explained as
material apertures existing in the substance of the moon. But in
my opinion, one and the same theory is sufficient to explain both the
external protuberances and the internal apertures ; this consists in
viewing them as two distinct effects of mirage produced temporarily
in the atmosphere ; and I have pointed out the probable connexion
of these phaenomena, which are so dissimilar in appearance, in the
excellent Astronomical Journal of my learned friend Mr. Gould,
published in the United States f. They both depend upon the distri-
bution of the temperatures of the layers of air parallel to the visual
rays ; except that in the second case, and in consequence of the posi-
tion of the observer, the trajectory presents a point of inflection which
does not exist in tlie case of the external protuberances. These
statements are very reservedly made ; as regards the fact itself, it is
based upon evidence, the entire value of which is known to astrono-
mers. M. Valz must himself have been forcibly struck by it, for
during the occurrence of a partial eclipse here, I have seen him care-
fully seek for the brilliant aperture which he remarked in 1842.
* Comptes Rendus, 1850, Nov. 4.
t Gould's Astronomical Journal, No. 20, p. 167.
Meteorological Observations, 88
As the altitude of the sun will be very different at the various
stations, from Norway to the Black or the Caspian sea, the thickness
of the layers of the atmosphere which must exert some influence
upon the phaenomenon, will vary in a very marked degree. Now,
the height and the brilliancy of the red mountains will depend essen-
tially upon this thickness ; hence it must be expected that the moun-
tains will be larger afld more marked to observers situated towards
the eastern extremity of the band traversed by the shadow, unless a
greater depression of temperature compensates, towards the west,
for the eflTect of a less thickness of the refracting layers of air. It is
here again evident how far the measure of these variations may prove
of interest in regard to the proofs to which it may be condescended
to submit the preceding ideas. The eclipse of the 28th of July will,
I hope, be completely decisive, thanks to the admirable understand-
ing of the astronomers of the two great countries. — Comptes Rendns,
May 19, 1851.
METEOROLOGICAL OBSERVATIONS FOR MAY 1851.
Chiswick. — May 1. Very fine. 2. Clear : fine : slight frost at night. 3. Fine :
rain at noon : cloudy. 4. Cloudy and fine : frosty at night. 5. Cloudy and
cold. 6. Slight rain : cloudy and cold. 7. Fine, but cold. 8. Fine. 9. Fine :
clear. 10, 11. Very fine. 12. Cloudy and fine. 13. Fine : clear. 14. Cloudy :
clear and frosty. 15. Very clear : fine : frosty at night. 16. Very fine : densely
clouded : rain. 17. Densely clouded. 18. Overcast : clear. 19. Cloudy : fine :
clear. 20. Clear and cold : fine. 21. Overcast. 22. Cloudy and warm. 23.
Hazy : fine : clear. 24. Very fine. 25. Cloudy: rain. 26 — 28. Fine. 29 —
31. Very fine.
Mean temperature of the month 51°*16
Mean temperature of May 1 850 51 '14
Mean temperature of May for the last twenty-five years . 54 '13 ^'*
Average amount of rain in May 1*89 inchi ■
Boston. — May 1. Fine. 2. Cloudy : rain p.m. 3. Cloudy: rain a.m. and p.m.
4. Cloudy : rain and hail a.m. and p.m. 5. Cloudy : rain a.m. and p.m. 6. Cloudy :
rain A.M. 7,8. Cloudy. 9. Fine. 10. Cloudy. 11. Cloudy: rain a.m. 12,
13. Cloudy. 14— 16. Fine. 17. Cloudy. 18. Cloudy : rain p.m. 19. Cloudy:
rain A.M. 20— 22. Cloudy. 23,24. Fine. 25. Cloudy. 26. Cloudy : rain and
hail A.M. 27 — 31. Fine.
Applegarlh Manse, Dumfries-shire. — May 1. Frost keen : hail-shower: rain-
shower. 2. No frost, but cold : fair all day. 3. Cold : hail-showers : wind keen.
4. Frost : hail : rain p.m. 5. Cold : dull : quiet. 6. Milder. 7. Mild and slight
showers. 8. Dull and cloudy : rain p.m. 9. Heavy showers. 10. Dry and
parching. 11. Wind high, l)ut fair. 12. Fine: cloudy p.m. 13. Fine day.
14. Very fine all day. 15. Fine : cloudy p.m. 16. Dull : slight showers. 17.
Fine : dull P.M. 18. Wet morning: cleared and fine. 19. Hail-showers fre-
quent. 20. Dull and showery. 21. Dull, but fair. 22. Cloudy : cold wind,
23. Fine clear day and fair. 24, 25. Fine a.m. : slight shower p.m. 26. Fair
and clear. 27. Fair, but chilly. 28. Fair and fine : wind strong. 29. Fair and
fine: wind keen. 30. P'air and fine : very droughty. 31. Fair and fine: verj
warm. , ;
Mean temperature of the month 48°*9
Mean temperature of May 1850 49 'I
Mean temperature of May for the last twenty-nine years ... 50 '9 '
Average rain in May for twenty-four years r89incb. i
Sandwich Manse ^ Orkney. — May 1. Damp: cloudy. 2. Damp: drizzle: showery.
5, 4. Snow-showers. 5. Bright : drops. 6. Damp : drops. 7. Clear : fine :
clear. 8. Bright : cloudy : aurora. 9. Bright: clear. 10. Bright : fine. 11,
12. Cloudy : clear. 13. Fine: hazy. 14, Bright : hazy, 15. Clear : rain. 16.
Fine: clear. 17. Cloudy. 18. Bright: clear. 19. Cloudy: showers. 20.
Bright : drizzle. 21. Hazy. 22, Drizzle : showers. 23. Showers. 24. Fine :
rain. 25. Showers : clear. 26. Bright : fine. 27. Damp : showers. 28. Hazy:
drizzle. 29. Hazy : damp. 30. Showers : hazy. 31. Hazy.
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THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE,
[FOURTH SERIES.]
AUGUST 1851.
XVI. On the Measurement of Chemical Affinitij.
Bij Isaac B. Cooke*.
THE controversy in reference to the source of voltaic electri-
city, appears to be decided, at least in England, in favour
of tlie chemical theory. A voltaic current seems generally ad-
mitted to be nothing else than the circulation, in another form,
of the sum of the chemical affinities developed in the circuit.
Is it not therefore time, since electric currents are susceptible of
minutely accurate measurement, that an attempt was made to
analyse the forces circulating in our batteries, and to assign to
the different substances present the value of the respective affi-
nities they mutually exert, from the united action of which
results that balance of forces constituting the effective power of
the battery ?
Accurately to measure and tabulate the combining force of the
constituents of compound substances, as we now do their com-
bining quantities, specific gravities, &c., would be an important
step in chemical science, and a great addition to our know-
ledge of the natural histoiy of the materials of the globe.
Many attempts have been made roughly to estimate these
forces by purely chemical experiment ; and tables have been con-
structed of the strength of affinities, in which, without nume-
rical values, substances have been arranged, with more or less
accuracy, in the order in which they expel each other from their
combinations. Estimates have also been formed, founded on
other considerations, but with little pretensions to numerical
exactness. Accurate measurements, again, have been made by
several methods, and by various observers, of the intensities of
current developed in different voltaic arrangements, and with
* Communicated by the Author.
Phil Mag, S. 4. Vol, 2. No. 9. Aug. 1851. H
86 Mr. I. B. Cooke on the Measurement of Chemical Affinity,
different substances in action ; but, as far as the writer is aware,
no attempt has yet been made to analyse these intensities, and
to attribute to any two substances the exact amount of force
which their act of combination contributes to the general result.
The inconstancy of the current developed in the simple voltaic
cell, — the reduction of its strength arising from the continuance
of its own action, — if it do not furnish an argument against the
chemical theory, at least seems unfavourable to the attempt to
fix any specific constant force, as due to the mutual affinity of
any two elements of the series. And the apparent complexity
of the more constant forms of electromotors, — the number of ele-
mentary substances concerned in their circuits, — appears to forbid
the hope of analysing the mere balance of such a multitude of
forces, so as to render evident their individual values.
Let us, however, investigate the sources of the inconstancy of
the zinc and copper pair, both immersed in the same fluid. For
this pui-pose we shall require to measure, first, the initial intensity
of the current of the cell before it becomes in the least degree
weakened by its own action; and again, to measure the re-
mainder of constant force which may be left after all the sources
of inconstancy have expended their action, and before any in-
fcrease can be regained by an instant of repose.
The elegant method of compensation devised by M. Poggen-
dorff for the measurement of initial intensities, seems only cal-
culated for the most skilful manipulators. To make a perfect
and conclusive experiment by this method, requires beforehand
a knowledge of the fact which the experiment is intended to
determine. And though the exact compensation may be arrived
at after a few preliminary trials, the time consumed in these
trials, if many cases have to be examined, is inconveniently great ;
since if the elements have been subjected to even a slight action,
they are no longer admissible for a second experiment, and the
whole arrangement must be prepared anew.
Intensities may also be measured by the use of Professor
Wlieatstone's rheostat, and by Ohm's "limit multiplier;" but
these instruments act only by virtue of a continuous current,
and cannot therefore be trusted to determine either initial or
variable intensities. Galvanometers, however, may be constructed
sufficiently sensitive to indicate cun-ents incomparably smaller
than those for which they are usually employed; and as it
seemed probable that the causes of inconstancy in the forces
would diminish more rapidly than the forces themselves, so that
the former would be wholly imperceptible to an instrument which
might yet be sufficiently sensitive to reveal correctly the relative
magnitudes of the latter, an attempt was made in this direction.
So excellent is the conducting quality of metals, that a suffi-
Mr. I. B. Cooke on the Measurement of Chemical Affinity. 87 -
cient resistance could not be obtained for this purpose through
their use, except by a most inconvenient length of wire, even of
the utmost practicable tenuity, and though used as an indepen-
dent resistance, without directive action on the needle. Fluids
could easily be made to oppose the required resistance, but would
introduce new tensions into the circuit, and perhaps additioilal
sources of inconstancy in their electrolysis.
Theoretically, the electrolysis of a salt, between electrodes of
its metal base, should introduce only a balance of affinities into
the circuit ; inasmuch as for every equivalent of the metal thrown
down at the cathode, an equivalent is absorbed at the anode.
But practically, it is almost impossible to place two pieces of the
same metal, in even a solution of their own salt, without a cur-
rent of electricity being generated between them when put in
contact ; and if a current be passed between them from an inde-
pendent source, a reactionary force is generally created. These .
evils we might also perhaps hope to overcome by such a consi-
derable reduction of the quantity of the current, as would leave
merely sufficient to be measured by a galvanometer of the most
sensitive construction.
A glass tube 4 inches long, and about yoth of an inch bore,
was fitted with a copper cap at each end. It was then by means
of a small opening drilled through each cap, filled with a solu-
tion of sulphate of copper, formed of one part of the saturated
solution with ten of water. The openings were then closed tight
by small copper wires screwed in.
When this tube was connected in a vertical position with one
wire of a very sensitive galvanometer, the current from a pair of
zinc and copper plates in rain-water, exposing a surface of 1
square inch and | inch apart, if sent through so as to deposit
copper upon the lower cap, caused a deflection of the needle of 8°,
which was perfectly constant through long -continued action.
The two caps of the tube afterwards showed no tendency to
reaction through the galvanometer. All pairs of zinc and copper
in rain-water, without reference to size, if only not smaller than
the above, gave exactly the same indication through the tube and
galvanometer of 8°; and in all these cases it was perfectly .
constant.
If the copper plate of the electromotive pair was retained at
the standard size of 1 inch, the zinc plate might be considerably
reduced below that limit, without diminishing the maximum de-
flection of 8° ; but however large the zinc plate was made, the
copper plate could not be materially reduced below the standard
size of 1 inch, without reducing the deflection and rendering the
current inconstant.
The resistance furnished by the tube was thus evidently in-
88 Mr. I. B. Cooke on the Measurement of Chemical Affinity »
comparably greater than the sum of all the other resistances of
any circuit of ordinary dimensions and conducting capacity into
which it could be introduced ; and as by its use the sources of
inconstancy could be eliminated from all such circuits, and their
resistances reduced to one conmion standard, the currents they
respectively developed would be obtained at the galvanometer in
direct proportion to their initial unweakened intensities ; or, in
other words, to the balance of the affinities exerted between the
elements present, before those affinities can in any degree be
satisfied by combination.
If, while a cell was thus connected with the resistance tube
and galvanometer, the circuit was additionally completed by a
short thick wire joining the anode and cathode, the deflection of
the needle was of course destroyed ; and after a certain lapse of
time, if the wire was suddenly removed, the first swing of the
needle revealed the amount of diminution of current affinity
caused by the continued unobstructed action of the elements
during that space of time.
In the case of a pair of zinc and copper in rain-water, the
diminution of force was found to vary witli the time of continu-
ance of the connexion, with the resistance of the circuit, and
with the excess in size of the zinc plate over that of the copper.
The current was never reduced to zero, but each individual cell
attained to a diff'erent minimum.
On removal of the short connecting wire, the pair immediately
commenced slowly to recover their original force, which, how-
ever, could almost instantly be fully restored by taking out the
copper plate, and after waving it in the air, replacing it in the
cell. No such result was produced by a similar treatment of the
zinc plate, if efi'ected without disturbance of the copper, or of
the medium in which it was placed.
If the copper plate was much larger than the zinc, and the
pair was placed in a stream of water, the maximum current was
maintained, even after a connexion by a thick wire of some
moments' duration. ,
If a single cell of Smee's batteiy was joined in series with a
pair of zinc and copper in water, the inconstancy of the latter
could be extended to the zero-point ; and indeed, as soon as
bubbles of hydrogen covered the surface of the copper plate, the
cui-rent became reversed, the copper being then slightly positive
to the zinc.
-5 1 In considering the sources of the current in these simple cir-
(!uit8, it appears fair to assume that no affinity is exerted, when,
under favourable circumstances, no combination is efiected.
Thus the development of nascent hydrogen upon the copper plate
is favourable to the combination of the hydrogen and copper.
Mr. I. B. Cooke on the Measurement of Chemical Affinity. 89
As no such product is formed, it may legitimately be assumed
that the mutual affinity of these two substances has no part in
causing the current of the cell. In the same manner, when
water is decomposed between two zinc plates, as the hydrogen is
given off without combining with the zinc, we may conclude that
no affinity between these two elements is concerned in modifying
the strength of the current. The only possible affinities, there-
fore, whose balance of forces can constitute the current of a zinc
and copper pair in water, may be thus enumerated: —
1st. Zinc for the oxygen of the water.
2nd. Copper for the oxygen of the water.
3rd. The hydrogen and oxygen of the water for each other.
4th. The oxygen dissolved in the water, for the other elements
of the circuit.
The only apparent chemical product formed by the action of
this simple circuit is the oxide of zinc. But as no hydrogen is
evolved from the copper, it must either be absorbed in some
way, or the water is not decomposed by the zinc. On the latter
supposition, the action would be merely local, the zinc combi-
ning directly with the dissolved oxygen in its o^vn neighbour-
hood, and no current would be circulated. The action must
therefore be as follows : — First, the zinc attacks the oxygen of
the water, liberating its hydrogen to combine with the oxygen
of the next particle of water ; and thus by successive combina-
tions and decompositions, hydrogen travels on to the copper
plate, when it finally combines with the oxygen held in solution ;
and in addition to the oxide of zinc, water also is a product of
the action. -«■>
The most perfect type of electromotive apparatus would pro-
bably be produced, if two solid conductors, having a powerful
mutual affinity, could be arranged in a fluid electrolyte of which
they should be themselves the constituent ions. The two con-
ductors would be equally active as electromotors, and the current
resulting would be the measure of their combining energy.
The nearest approximation to this type at present known, is
probably the gas battery of Grove, where the two ions, oxygen
and hydrogen, unite to form the electrolyte water; the pla-
tinum plates being merely requisite to serve as odes or door-
ways for the combination of the elements, and for the passage
of the current affinity. All batteries have more or less resem-
blance to this type. The water battery of zinc and copper
differs from it principally in the substitution of the metal zinc
for one of the ions of the electrolyte, viz. hydrogen, for which
it has no affinity, but to the affinities of which its own have
much resemblance. The copper serves as the ode by which
the other ion, viz. the dissolved oxygen, contributes its action,
90 Mr. I. B. Cooke on the Measurement of Chemical Affinity.
and by which the resulting current is transmitted. The copper
and dissolved oxygen tend also to produce an opposing current,
for which the zinc plate would serve as ode ; but this current is
overcome and masked by the much stronger one of the other
pair, and is only manifested by diminishing the force in com-
parison with what it would have been, if a plate wholly indiffer-
ent to the oxygen was substituted for the copper. The foimula
of the force may be thus stated,
z for 0-0 for H + H for 0- (c for 0-0 for H + H for 0) ;
leaving a balance of affinities, after the elimination of equal and
contrary forces, of
(<?— c) for 0.
If this view be correct, the inconstancy of the water battery
must arise from the exhaustion of the dissolved oxygen on the
surface of the copper plate, this being the only element of which
the supply is deficient in quantity ; a conclusion fully warranted
by the above experiments with the resistance tube. And it is to
the abundant supply of this element in the DanielPs battery that
its superior constancy is owing.
The substitution for the copper plate of any other conducting
substance having no affinity for either oxygen or hydrogen, would
destroy the negative portion of the formula {z—c) for 0; and
the deflection of the needle by a current passed through the re-
sistance tube would be then proportional simply to the affinity of
the zinc for bxygen. And thus the relative affinity for oxygen of
all conducting substances, having no affinity for hydrogen, might
be ascertained if such a substitute for the copper plate could be
procured.
Now platinum forms no combination with, and consequently
exercises no affinity sensible to the galvanometer for, either
oxygen or hydrogen when developed in the nascent state on its
surface by electrolysis. Platinum might therefore be supposed
to furnish the required substitute for the copper plate. But
hei-e a difficulty arises, in consequence of the peculiar conditions
of surface which platinum ordinarily assumes. After an electric
cuiTent has passed through water, between two plates of platinum,
they are no longer similar in their electric relations, but are
capable, when closed in circuit, of creating a reactionary current,
until they gradually return to their ordinaiy state of inertness.
Though platinum, therefore, has no affinity for oxygen or hy-
drogen, it is in some way susceptible of different relations to them,
and is in fact extremely inconstant in its value as an electro-
negative substance.
This property of platinum, which is equally shared by gold,
and partially by silver and other electro-negative bodies, has been
Mr. I. B. Cooke on the Measurement of Chemical Affinity. 91
usually classed^ without any very precise definition, as a result
of polarization ; and though it is perhaps thoroughly understood
by many philosophers, has not, as far as the writer is aware,
been clearly explained in any published treatise.
A few experiments with the resistance tube sufficed to demon-
strate the real nature of the phsenomenon. But first, the con-
struction of the tube was improved in accordance with the facts
above deduced, and a form adopted which permitted the measure-
ment of intensities with greater minuteness. A glass tube 13
inches long, and ^th of an inch in internal diameter, of perfectly
even bore, was graduated through its length on the glass into
twentieths of an inch, and these divisions numbered from 1 to
240. It was placed in a tall glass jar about 2 inches in dia-
meter. A coil of copper riband covered the bottom of the jar,
and one end of the riband rose to the surface, and was connected
with one wire of the galvanometer. A piece of copper wire,
rather longer than the tube and thin enough to move easily in
it, was inserted into the tube, and being slightly bent, would
remain at any height at which it might be placed. To its upper
end was attached a long fine copper wire, which could be con-
nected by means of a mercury cup on the table with one of the
metals of any cell, the intensity of which was to be tested ; the
other metal being connected with the second wire of the galva-
nometer. The connexion was always made so as to deposit copper
upon the copper coil. The jar was filled with rain-water, to
which a small quantity of a solution of sulphate of copper was
added ; when it was found that the current of a pair of zinc and
copper, of ordinary dimensions in rain-water, produced a mo-
mentary deflection of 5° in the needle of the galvanometer, the
end of the wire in the tube being raised to the forty-sixth divi-
sion. When the wire was placed at a lower elevation, a greater
deflection was of course obtained. And a permanent deflection of
10° could be maintained for a considerable time without variation,
by any pair of zinc and copper exposing more than a square
inch of surface.
As the intensity of the current is equal to the product of the
quantity into the resistance, the relative intensities of different
circuits would therefore be measured by the product of the de-
flection of the needle into the number of divisions contained
between the end of the wire and the bottom of the tube, pro-
vided the resistance of the tube could be safely taken as the total
resistance of the circuit ; or
1 = 5x46 = 230.
But inasmuch as the coil of the galvanometer is formed of a very
fine long wire, it may be supposed to oppose a sensible resist-
9ji jVJlr.Iv B. Cooke on l/te Measurement of C/temical Affiniij/i
a)ftCC,.>j^LicU cau Imj Cjasily weasuird and allowed for. In fact,
■\,.> >-.l.ul,ui >i: ,..:. ^J[ = 5X:(46 + ^-)>-.
Whietei^'ife'thfe wsistancc rtf the ^galvanometer coil. The wife
was pushed down the tube until an elevation was attained^
at which the momentary deflection of the needle by a zinc and
copper circuit was 10^, which was found to require a resi^tahiijife
oi'twenty-one divisions of the tube, or
^l' ( ■/■' ' I = 10 X (21 + ?•) = 5 X (IG + r),
Gdiisequently^ in ttll?*ttie^8tu'efttients Of intensity, ion^ S^s befeii
added to the number of the divisions of the tube, to allow for the
I'esistance of the coil.
^Measured thus, the intensity of the current from zinc and
copper plates in water, or the affinity of zinc for oxygen, less the
affinity of copper for oxygen,
while the intensity produced by zinc and platinum plates 'itt th6
same fluid
= 5(49 + 4) =265;
leaving, if the platinum be really inert, only 15 for the affinity
of copper for oxygen, or only y^yth pail'jp^; tji^t of xiue fpi*
oxygen.^ ^ . . ^ ' '■■ ^^'i-:-: '' ■ : '' ':i^'-.
Considering the easy oxidation of copper and its fierce decom-
position of nitric acid, this small estimate of its force of affinity
for oxygen does not seem a })robable result, and the platinum
may be fairly suspected of exercising some counteracting influ-
c^CQ. When oxygen is nascent upon the surface of platinum,
even though it be urged in addition to its own affinity by the
current affinity of a thousand cells, no combination is effected.
Can it be that there is a tendency to combine which is sensible
to the galvanometer, but by some hidden influence which is not
sensible to the galvanometer the combination is prevented?
The supposition is inadmissible until no other explanation can
be found.
The attempt was made to ascertain the limit, if there be one,
tb which the polarization of platinum can be carried, and whether
both anode and cathode are equally aiiected. Two platinum
plates aijd one of copper were arranged in a glass of rain-water
without contact with each other. The copper plate was connected
with the galvanometer. The ])air of platinum plates were joined
ifi .series with a battery bv which the water between them was
Ml*. I. B. Cooke on the Measurement of Chemical Affinity. ^3'
electrolyzecl. The wires weiv? so adjusted, that it was easy ii*i'«^
stantaneously to disconnect the battery, and to join either pla-
tinum plate to the resistance tube. As soon as bubbles of
oxygen began to form on the anode platinum, its junction with
the instrument and copper plate was eifected. The swing of the
needle was now 5° when the current was passed through fifty-
nine divisions of the tube, giving an intensity = 5 (59 H- 4) = 315.
The swing could be reproduced several times undiminished with-
out reconnexion with the battery. The total secondary current
between the two platinum plates =5(114 + 4) = 590 ; but this
current was more inconstant than the former, and began imme-
diately to diminish. When the cathode platinum plate was con-
nected with the galvanometer, and the copper plate with the
resistance tube, the intensity was 5(51 4-4) =275, which equals
the difference of the two former numbers ; but was very incon-
stant, and could instantly be reduced almost to zero, by shaking
the platinum plate so as to dislodge all the bubbles of hydrogen.
The anode platinum plate was found to receive its maximum
polarization from the current of two cells of Smee^s battery.
The current of six cells did not increase it. The cathode received
its maximum polarization from three cells, and after being
thoroughly covered with hydrogen, could receive no increase of
force.
The polarization of the cathode plate therefore clearly resulted
from the coating of hydrogen with which it became covered, but
the anode received its greatest charge before a single bubble of
oxygen was formed ; and indeed, since oxygen was already pre-
sent in solution in the water, its additional production by elec-
trolysis was not likely to produce an increased effect. ''
This definite amount of polarization of the anode plate would
be accounted for, if its surface could be supposed to contract
from the atmosphere, in its ordinary condition, a covering of
matter possessing an affinity for oxygen. The current would of
course be affected by this covering at its commencement, as by
an electro-positive element; but as the covering became eaten
away by the oxygen determined to its surface by the force of the
battery, the purified platinum would begin to act simply as con-«
ductor, and wholly indifferent as to afiinity. . ./ '
That platinum and other substances do contract such a' coijer-
ing. Dr. Faraday has proved in his experiments on the catalytic,
deflagration of explosive gases. He has also shown, that expo--
sure at the anode of a battery to the action of nascent oxygen, is
identical in its results with a mechanical purification of the sur-'
faceofplatinmn. ' '^^j':^'!;::'^^
This covering is instantly destroyed by immersi&ri''iii stron^'^
nitric acid ; and it is to this fact probably, more than to the
94 Mr. I, B. Cooke on the Measurement of Chemical Affinity,
excessive facility with which nitric acid yields one out of its five
equivalents of oxygen, that Grove's nitric acid battery owes its
superiority in energy over Daniell's sulphate of copper batteiy.
Since the coating actually exists on the surface of the negative
metal, and since the erosion of such a coating by oxygen suffices
to explain the polarization of the anode plate, it may be accepted
as the true explanation. If a platinum plate, thereforfe, previ-
ously purified from all adhering matter, be taken to serve as
cathode in combination with an electro-positive substance in
water, the quantity of current urged by them through the galvano-
metet*, multiplied by the number of divisions of the resistance tube
through which it is passed, may be taken as the measure of the
affinity of the electro-positive substance for oxygen.
The measurements given in the table were made on this prin-
ciple in the following manner : — Two plates of platinum were
placed in a glass of clean rain-water, and were connected with
the poles of a two-celled Grove's battery. A portion of the sub-
stance whose affinity for oxygen was to be tested was placed in
the same glass, out of contact with the platinum plates. The
anode platinum plate was also permanently connected with the
resistance tube and the wires from the cathode platinum, and
from the substance to be tested, were so adjusted in mercury
cells on the table, that the connexion of the one with the bat-
tery could be destroyed and the other be instantly joined to the
free wire of the galvanometer. The first swing of the needle,
multiplied into the number of divisions + 4 of the tube below
the end of the wire, was recorded as the force of affinity. Each
experiment was repeated several times, and the result confirmed
by placing the wire of the tube at different altitudes, and com-
paring the deflection produced with that calculated.
The measurements are far from the limit of minute accuracy,
of which the method is susceptible with superior instruments, but
are the best which the means and leisure of the writer enable
him to obtain. The current of zinc and copper in water is taken
as the standard unit of force, because, by simple arrangements
on the table, it is capable, at an instant's notice, of easy verifica-
tion. Frequent verification is indeed essential, in consequence
of changes to which the resistance tube is liable. After long-
continued action, the copper electrodes of the tube take on a
very slight amount of polarization. The homogeneity of the
solution in the jar and tube is apt to be slightly disturbed.
Changes of temperature, again, somewhat modify the conducting
capacity of the solution. Any of these sources of eiTor is de-
tected instantly by appeal to the standard electromotor, and
easily remedied or allowed for. The wire of the tube should,
when out of use, be thrust down into contact with the copper
Mr. I. B. Cooke on the Measurement of Chefriical Affinity. 95
riband^ and also connected with it by its wire through the gal-
vanometer. The copper solution should be thoroughly stirred
up by the tube previous to experiment, and the room be kept
during experiment as nearly as possible at a uniform tempera-
ture. With these precautions, measurements may be taken
again and again without the slightest variation. Any great
changes in the temperature will of course necessitate a correction
in the allowance for the resistance of the galvanometer coil.
Table of the Affinity of various Substances for Oxygen.
Zinc — copper (standard) . =1
Hydrogen =2*36
Zinc =2-23
Potassium =3*13
Sodium =2-91
Iron =1*85
Tin =1-75
Lead =1*7
Bismuth =1-29
Antimony =1'29
Copper =1-25
Silver = -85
These affinities do not appear to be affected by changes of
temperature between the range of 50° and 212° F.
It is almost impossible to obtain mercury perfectly free from
traces of impurity ; and however small may be the quantity of
any substance more electro-positive than itself which may be
dissolved in it, the mercury usurps to the full the affinities of
that substance. This property renders its own affinity for oxygen
difficult to determine, but has been made use of to ascertain
those of potassium and sodium, the action of which metals upon
water is otherwise too violent to admit of satisfactory experiment.
A fluid amalgam of either of these metals decomposes water
slowly, especially if the surface exposed be small compared with
the bulk of the "^amalgam, and a deliberate experiment is thus
permitted.
It will be seen from the table, that hydrogen has a higher
number assigned to it than is given to zinc. Why then, it may
be asked, does zinc so easily decompose acidulated water ? The
truth is, that the zinc is retained in its salts generally by a force
fully as strong as that which combines it with oxygen alone,
while hydrogen is held in acidulated water with a considerably
slighter affinity than in pure water. Pure zinc will not decom-
pose pure water if atmospheric air or oxygen be not present.
The principle developed in this paper is probably applicable
96 Prof. Boole on the Theory of Probabilities.
to uiaxiy classes of salts, to sulphurets and other compounds.
Attempts to apply it to the chlorides have hitherto proved un-
successful, chiefly owing to the want of a conducting substance
perfectly iuditierent to chlorine, which even plumbago can
scaixjely be supposed to be.
The galvanometer may perhaps, by this method, shortly be-
come a useful instnmient in qualitative analyses.
Jl'.MliiU : MjtJ Uiil ' ''(i ■ i 'I! iM' I , ■ .■■i;i j I I :^, I I > i--'ii>.' > I ■ • > -I I ......
»lij '>',1H;/ iMl!.:i.'' ! M lit :lMu- t.' t'.i! .v.jf; 'mIt to '^i- ' iffHl./;! ■(llf (1 ' •
m-3^(II. \iFur titer Observations on the Theory ofProbabiliiies.
j;T ■> ' >;• By George Boole.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
SOME commimications which 1 have received since the pub-
lication of my letter on the Theory of Probabilities in the
last Number of your Journal, have led me to think that a little
further explanation of certain points involved in it may be desi-
rable. This explanation I the more readily offer, because it
appears to me that upon one of the points in question, viz. the
prevalent doctrine among mathematicians concerning the inves-
tigation of the probabilities of causes, I have made a statement
which a more careful survey of authorities does not fully warrant.
As the question lies at the foundation of some of the most in-
teresting applications of the theory of probabilities, I am desirous
of stating how it has really been viewed by eminent writers ; and
I shall subsequently notice certain other points suggested to me
in the correspondence above referred to. .,^1 -a jjwi
The problem under discussion was the following :— Given the
probability p of the truth of the proposition. If the condition
A has been satisfied, the event B has not happened. Required
the probability P of the truth of the proposition. If the event
B has happened, the condition A has not been satisfied. And
its correct solution, as given in my letter, is
c[\'-a)-^a[l-pY • • • • ii-i
c and a being arbitrary constants whose interpretation is assigned.
I have remarked that it has generally been erroneously held,
that the solution of the above question is P=jt?. It is to this
point that I desire first to refer.
i^i^The doctrine that P=/? is expressly taught in the Edinburgh
Review (Quetelet on Probabilities). Speaking of a certain com-
bination of phaenomena observed in rock-crystal, the Reviewer
says, " The chances against such a coincidence happening thir-
teen times in succession by mere accident are more than 8000
Prof. Boole oyi the Theory of Probabilities. 97
to 1 ; and this therefore was the probability that some law of
nature, some cause was concerned." 'fq^ ^'i hiqin^tsA
The same doctrine seems to me to be strongly iiiipilied" by
Laplace in the Introduction to his great work on Probabilities.
Discussing the question of a primitive cause, fixing the direction
of rotation of the planets in their orbits, he introduces the object
of his inquiry in the words "pour avoir la probabilite avec^
laquelle cette cause est indiquee." And then having determined,
on the hypothesis of the absence of such determining cause, the
probability against the phrenomenon of rotation in one uniform
direction, he says, " Nous devons done croire au moins avec la
meme confiance qu\me cause primitive a dirige les mouvements
planetaires, surtout si nous considerons que I'inclinaison du plus
grand nombre de ces mouvements a Fequateur solaire est fort
petite." Laplace does not indeed expressly affirm the principle
under consideration, but it appears to me that his language does
in some degree give it sanction.
Mr. De Morgan, in investigating the probability that there is
a cause for the observed phsenomenon that the sum of the incli-
nations of 10 of the planetary orbits is less than 92°, reasons in
the following manner. Having found a calculated probability
•00000013, say q, that the sum of the inclinations would be less
than 92° on the assumption that all inclinations are equally pos-
sible in each orbit, he says, " If there be a reason for the incli-
nations being as described, the probability of the event is 1.
Consequently it is 1 : -00000012 {i. e.l : q) that there was a
necessary cause in the formation of the solar system for the incli-
nations being what they are." The probability of the existence
of such a cause is thus expressed by the fraction
ooiJibnoo i*m li ^ \ "(aiiicifido'iq
hQmir^ii iwii'*'' — i . , ... iiyi)d gjjd A
j^is-fa 9iif il 1+9' I YitiluMoiq ail
I at on^ time thought that this reasoning involved an eri^orvfei^
nearly equivalent to that which I have adverted to in the previous
remarks. But upon examination it appears that Mr. De Morgan^s
result is really a limitation of the general formula (1.) obtained by
assigning particular values to the constants a and c. For in order
to apply that formula to the case considered by Mr. De Morgan,
let us assume A to represent the absence of any determining
cause of the phsenomenon B, viz. of the phsenomenon that the
sum of the planetary inclinations is less than 92°, then will a
represent the a priori probability of the absence of a determining
cause, and c the probability that on the assumption of its exist-
ence the phgenomenon B would result. Mr. De Morgan's rea-
soning then involves the hypothesis that a= -^ and that <:==1,
98 Prof. Boole on the Theory of Probabilities.
Also/? =1—9. If we make these substitutions in the general
value of P, we find
1
2 1
P=
2 2*
There is therefore, I conceive, no error in the reasoning adopted ;
although there may be, as it seems to me (but I state this merely
as an opinion), a serious doubt as to the determination of the
constant a. We are not, I think, at liberty to assume that it is
a priori as likely as not that a sufficient ground for a determi-
nate phsenomenon should exist in nature. All that we can infer
from the general solution is, that unless the existence of such a
ground is a priori highly improbable, then, after frequent expe-
rience of the phsenomenon, there exists a high probability in
favour of the existence of that ground.
I have not at present the opportunity of making further refer-
ences ; but I think the most just inference from what has been
adduced, to be, that while the doctrine objected to has really
been put forth, it has not been held uniformly or universally.
I would suggest also the consideration, that even the passage
quoted from the Edinburgh Review, although certainly conveying
the erroneous notion adverted to, might by the omission of the
word therefore be understood as expressing the result of a train
of reasoning similar to that which Mr. De Morgan has adopted.
For if we granted in that case Mr. De Morgan^s determination
of the constants, the numerical result obtained would be extremely
near to that which the Reviewer has assigned. It seems to me
to be the part of justice, to give to such considerations as these
their full share in estimating the opinions wliich a writer has
expressed. While on the one hand we ought to bring every
statement into comparison with the standard of what is abso-
lutely true and right, we ought on the other hand to be willing
to take into account those possible hjrpotheses upon which there
may be reason to think that an author has proceeded, even
though no mention of them be retained in his conclusions.
Upon the whole, I conceive that the following is the true
theory of that class of questions which has been under considera-
tion : —
1st. That it is not in any case a question whether a particular
phsenomenon which has come under our notice is an effect of
causation or not, but whether or not it is an effect of some single
predominant cause, or simple combination of causes, the conse-
quences of which are in some measure within the reach of our
intelligence.
Prof. Boole on the Theory of Probabilities. 99
2nd. That upon the supposition of the absence of such cause,
or simple combination of causes, certain results- appearing to us
equally probable, the probability of that definite combination of
those results which constitutes the effect observed may be defi-
nitely calculated.
3rd. That if the value thus obtained be expressed by p, then
the formula (1.) will represent the probability of the existence of
such predominant cause or combination of causes. That in that
formula we may, following Mr. De Morgan, justly assume c=l,
but that there appear to be no grounds further than the analogy
of Nature for determining a. [The difficulty here is not that
we are choosing among causes equally probable, but that we are
attempting to assign the a priori probability of the existence of a
condition of things, or in other words, to compare the probabi-
lities of its presence and its absence. Now this is a question,
the conjectural solution of which will vary with our varying
knowledge of the constitution of Nature. Unless, however, we
have reason to suppose that the value in question is very small,
the general formula will still be available for our general guidance,
if not for definite numerical evaluation.]
Quitting this problem, I shall now notice two others, of which
solutions have been given, that appear to me to be defective in
generality from the same cause, viz. the non-recognition of the
requisite arbitrary constants.
1st. Given j9 the probability of an event X,andg' the probability
of the joint concurrence of the events X and Y : required the
probability of the event Y.
The solution of this problem afforded by the general method
described in my last letter is
Prob. ofY = 9 + c(l-jo),
where c represents the unknown probability, that if the event X
does not take place the event Y will take place. Hence it ap-
pears that the limiting probabilities of the event Y are q and
1 + g— JO. The result is easily verified.
The only published solution of this problem with which I am
acquainted is
Prob. ofY=i,
P
a result which involves the supposition that the events X and Y
are independent. This supposition is, however, only legitimate
when the distinct probabilities of X and Y are afforded in the
data of the question.
Given the probabilities p and q of the two premises of the syl-
logism,
All Ys are Xs
AllZsareYs.
100 Prof. Boole (tn the Theory nf Probabilities.
lloquk^il the ])rohiil)ility P of the conclusion ' '"^
*''«*^^ AllZsarcXs. ^
Here, by the probfthility 7? of the premiss all Ys are Xs, is meant;
the probability that any individual of the class represented by Y,
taken at random, is a member of the class Z^ and so in the other
cases. The rcsidting probability of the conclusion afforded bjrjt
the general method is then .»;^
where c is an arbitrary constant expressing the unknown proba-
bility, that if the minor premiss is false the conclusion is true.
The limiting probabilities of thcr conclusioii dr6 thiis
pq and;;(/ + l— ^.
The only published solution of the above problem with which I ^
am acquainted is V=pq, a result which manifestly involves th^*^
hypothesis that the conclusion cannot be true on any other"
grounds than are supplied by the premises. ''' '"' " ' " '
There are also, I have reason to think_, other cases than the
above in which definite numerical results have been assigned; *
either by neglecting the arbitrary constants, or by determining
them upon grounds not sufficiently explained. I do not, how-
ever, purpose to enter into the further consideration of this sub-
ject here, nor do 1 offer the above remarks mth any view to
depreciate the eminent labours of those from whose writings my
illustrations have been drawn. Indeed the results which I have
deduced from the new method might all have been obtained by
the principles of the received theory, with this principal differ-
ence, that the constants, which with their interpretations are •
given by the one method, would require to be assumed in the
other. While I think it right to make this acknowledgement, I
feel it to be just also to say, that it is only to the simpler kind
of problems that the remark appears to me to be applicable.
Granting even a proper assumption of the arbitraiy constants, I
do not see how a solution is to be obtained by the received me-
thods when the data are much involved ; not to mention those
cases in which the number of the data exceeds or falls short of
the number of simple events combined in them, and in the solu-
tion of which cases nevertheless arbitrary constants may not be
required. Restricting our attention to the ordinaiy theoiy, it
appears to me to be certain that the problems which fall under
our notice may be resolved into two great classes ; viz. 1st, those
in which definite numerical solution is attainable from the data
alone, without any determination of arbitrary constants ; 2nd,
those in which the data do not suffice to this end, but in which
we must either introduce arbitraiy constants, as has been done
in this paper, or implicitly determine them as Mr, Be Morgan
Prof. Boole on the Themij of Probabilities. 101
has (lone. And I can conceive of nothing as more likely to in-
spire a rational confidence in the theory of probabilities^ than a
clear and well-marked distinction between these cases^ accom-
panied by a distinct statement of the grounds upon which,
whenever constants are determined, their determination is effected.
The question has been suggested to me by a correspondent =!',
to whom I am indebted for some valuable remarks, whether
the general method described in my last paper involves any
fundamentally different idea of probability from that which is
commonly accepted. He observes, that the results which I
have given are in accordance with the principles of the established
theory. As the same question may present itself to other minds,
I would remark that the theory of probabilities has, in the view
which I have been led to take of it, two distinct but accordant
sources. From whichsoever of these it may be derived, it will
be found to involve the idea of numerical magnitude ; but in the
one case that idea will have reference simply to the relative fre-
quency of the occurrence of events, being in fact the received
ground of the theory ; in the other, to the persistency of certain
forms of thought, which are manifested equally in the operations
of the science of number, and in the reasonings and discourses
of common life. Setting out from either of these grounds, we
may, I conceive, without difficulty attain to a knowledge of the
other. Now it appears to me to be perfectly in accordance with
the nature of probability that this should be the case ; for its
relation to number is not more essential than its relation to the
manner in which events are combined. But while the expression
of the former relation belongs to arithmetic, or more generally
to algebra, that of the latter belongs to logic.
I design, as soon as leisure and opportunity shall permit, to
publish the general theory to which reference has been made in
this and the previous paper. Had it been possible for me to
offer in the space which they have aftbrded a satisfactory state-
ment of its principles, I should have gladly availed myself of the
opportunity of doing so. But for the particular ends here in
view this has been the less necessary to be done, as the results
actually exhibited admit of verification by known methods. Still
I trust that the collateral discussions into which I have entered
have not been altogether without interest or profit, even with
reference to established doctrines. .i .]j?i'iii»[»;u
I remain, Gentlemen, ■n ".t -'-'^no^ipi
^i^offt Your obedient Servant, »• '
ft-- ' George Boolb. i ? i
Lincoln, June 17. 1851. iu^Ih
* W. F. Donkin, M.A., Savilian Professor of AstronoBiy, Oxford- -/pyv/
Phil, Mag, S. 4. Vol. 2. No. 9. Aug. 1851. ,,ui. ... ., • .i|4 ^aW m
[ 102 ]
XVIII. On the Moving Force of Heat, and the Laws regarding
the Nature of Heat itself which are deducible therefrom.
By R. Clausius.
[Concluded from p. 21.]
CARNOT, as already mentioned, has regarded the production
of work as tiie equivalent of a mere transmission of heat
from a warm body to a cold one, the quantity of heat being thereby
undiminished.
The latter portion of this assumption, that the quantity of
heat is undiminished, contradicts our maxim, and must there-
fore, if the latter be retained, be rejected. The former portion,
however, may remain substantially as it is. For although we
have no need of a peculiar equivalent for the produced work,
after we have assumed as such an actual consumption of heat, it
is nevertheless possible that the said transmission may take place
contemporaneously with the consumption, and may likewise stand
in a certain definite relation to the produced work. It remains
therefore to be investigated whether this assumption, besides
being possible, has a sufficient degree of probability to recom-
mend it.
A transmission of heat from a warm body to a cold one cer-
tainly takes place in those cases where work is produced by heat,
and the condition fulfilled that the body in action is in the same
state at the end of the operation as at the commencement. In
the processes described above, and represented geometrically in
figs. 1 and 3, we have seen that the gas and the evaporating water^
while the volume was increasing, received heat from the body A,
and during the diminution of the volume yielded up heat to the
body B, a certain quantity of heat being thus transmitted fi'om
A to B j and this quantity was so great in comparison with that
which we assumed to be expended, that, in the infinitely small
alterations represented in figs. 2 and 4, the latter was a difi*er-
ential of the second order, while the former was a differential of
the first order. In order, however, to bring the transmitted
heat into proper relation with .the work, one limitation is still
necessaiy. As a transmission of heat may take place by con-
duction without producing any mechanical effect when a warm
body is in contact with a cold one, if we wish to obtain the
greatest possible amount of work from the passage of heat be-
tween two bodies, say of the temperatures t and t, the matter
must be so arranged that two substances of different tempep-
tures shall never come in contact with each other. l
It is this maximum of work that must be compared with the
transmission of the heat ; and we hereby find that it may reason-
M.^IR,.' Ciausius on the Moving Force of Heai. 103
ably be assumed_, with Carnot, that the work depends solely upon
the quantity of heat transmitted^ on the temperatures t and t of
both bodies A and B, and not upon the nature of the substance
which transmits it. This maximum has the property, that, by its
consumption, a quantity of heat may be carried from the cold body
B to the warm one A equal to that which passed from A to B during
its production. We can easily convince ourselves of this by con-
ceiving the processes above described to be conducted in a reverse
manner ; for example, that in the first case the gas shall be per-
mitted to expand of itself until its temperature is lowered from
t to T, the expansion being then continued in connexion with B ;
afterwards compressed by itself until its temperature is again t,
and the final compression eff'ected in connexion with A. The
amount of work expended during the compression will be thus
greater than that produced by the expansion, so that on the
whole a loss of work will take place exactly equal to the gain
which accrued from the former process. Further, the same
quantity of heat will be here taken away from the body B as in
the former case was imparted to it, and to the body A the same
amount will be imparted as by the former proceeding was taken
away from it ; from which we may infer, both that the quantity
of heat formerly consumed is here produced, and also that the
quantity which formerly passed from A to B now passes from
# to A.
"^ Let us suppose that there are two substances, one of which is
able to produce more work by the transmission of a certain
amount of heat, or what is the same, that in the performance of
a certain work requires a less amount of heat to be carried from
A to B than the other; both these substances might be applied
alternately ; by the first work might be produced according to
the process above described, and then the second might be applied
to consume this work by a reversal of the process. At the end
both bodies would be again in their original state ; further, the
work expended and the work produced would exactly annul each
other, and thus, in agreement with our maxim also, the quantity
of heat would neither be increased nor diminished. Only with
regard to the distribution of the heat would a diff'erence occur, as
more heat would be brought from B to A than from A to B, and
thus on the whole a transmission from B to A would take place.
Hence by repeating both these alternating processes, without
expenditure of force or other alteration whatever, any quantity
of heat might be transmitted from a cold body to a warm one ;
and this contradicts the general deportment of heat, which every-
where exhibits the tendency to annul differences of temperature,
and therefore to pass from a warmer body to a colder one.
From this it would appear that we are theoretically/ justified in
12
it>4 M. R. Clausius on the Moving Force of Heat,
retaiuing the first and really essential portion of the assumption
of Carnot, and to apply it as a second maxim in connexion with
the fonner. It will be immediately seen that this procedure
receives manifold corroboration from its consequences.
This assumption being made, we may regard the maximum
work which can be effected by the transmission of a unit of heat
from the body A at the temperature t to the body B at the tem-
perature T, as a function of t and t. The value of this function
must of course be so much smaller the smaller the difierence
/ — T is; and nmst, when the latter becomes infinitely small ( = dt),
pass into the product of dt with a function of t alone. This
latter being our case at present, we may represent the work
under the form
wherein C denotes a function of / only.
To apply this result to the case of permanent gases, let us
once more turn to the process represented by fig. 2. During
the first expansion in that case the amount of heat,
passed from A to the gas ; and during the first compression, the
following portion thereof was yielded to the body B,
[(f)*i(S)»-i(S)"]".
or
(S)*-[i(S)-i(S)]"'-
The latter quantity is therefore the amount of heat transmitted.
As, however, we can neglect the differential of the second order
in comparison with that of the first, we retain simply
(S)
dv.
The quantity of work produced at the same time was
V '
and from this we can construct the equation
^dv .dt
(S)
dv
or
mid the Laws regarding the Natare of Heater jLQ^
(§)=^"- ■■i".i
Let us now make a corresponding application to the process
of evaporation represented by fig. 4. The quantity of heat in
that case transmitted from A to B was
rdm-^ i-jr -\-c—h\dmdt'y
for which_, neglecting the differentials of the second order^ we
may set simply
rdm.
The quantity of work thereby produced was
{s—iT)-~-dmdt,
and hence we obtain the equation ,.
{s—o)~~' dm.dt 1
rdm C
or
'•=c.(--)J (V.)
These, although not in the same form, are the two analytical
expressions of the principle of Carnot as given by Clapeyron. In
the case of vapours, the latter adheres to equation (V.), and con-
tents himself with some immediate applications thereof. For
gases, on the contraiy, he makes equation (IV.) the basis of a
further development ; and in this development alone does the
partial divergence of his result from ours make its appearance.
We will now bring both these equations into connexion with
the results furnished by the original maxim, commencing with
those which have reference to permanent gases.
Confining ourselves to that deduction which has the maxim
alone for basis, that is to equation (II«.), the quantity U which
stands therein as an arbitrary function of v and / may be more
nearly determined by (IV.) j the equation thus becomes
dQ=^B + n{^-Ayogv']dt+^'dv, {lie.)
in which B remains as an arbitrary function of t alone.
If, on the contrary, we regard the incidental assumption also
16i M. R. Clausius on the Moving Force of Heat,
as correct, the equation (IV.) will thereby be rendered unneces-
sary for the nearer determination of (Ila.), inasmuch as the same
object is anived at in a much more complete manner by equa-
tion (9.), which flowed immediately from the combination of the
said assumption with the original maxim. The equation (IV.),
however, furnishes us with a means of submitting both princi-
ples to a reciprocal trial. The equation (9.) was thus expressed,
c?Q\_R.A(a4-0
(S)
V
and when we compare this with equation (IV.), we find that
both of them express the same thing ; with this difference only,
that one of them expresses it more definitely than the other. In
(IV.) the function of the temperature is expressed in a general
manner merely, whereas in (9.) we have instead of C the more
definite expression A{a-{-t).
To this surprising coincidence the equation (V.) adds its testi-
mony, and confirms the result that R(fl + 1) is the true expres-
sion for the function C. This equation is used by Clapeyron
and Thomson in determining the values of C for single tempe-
ratures. The temperatures chosen by Clapeyi-on were the boiling-
points of sether, of alcohol, of water, and of oil of turpentine. He
determined by experiment the values of ~, 5 and r, for these
fluids at their boiling-points ; and setting these values in equa-
tion (V.), he obtained for C the numbers contained in the second
column of the following table. Thomson, on the contrary,
limited himself to the vapour of ivater ; but has observed it at
various temperatures, and in this way calculated the value of
C for every single degree from 0° to 230*^ Cent. The observa-
tions of Regnault had furnished him with a secure basis as
regards the quantities -^ and r ; but for other temperatures than
the boiling-point, the value of s is known with less certainty.
In this case, therefore, he felt compelled to make an assumption
which he himself regarded as only approximately correct, using
it merely as a preliminary help until the discoveiy of more exact
data. The assumption was, that the vapour of water at its
maximum density follows the law of M. and G. The numbers
thus found for the temperatm'cs used by Clapeyron, as reduced
to the French standard, are exhibited in the third column of the
foUoTving table : —
and the Laws regarding the Nature of Heatf,.. JQ7
Table I. Tinim^- €
1.
2.
3.
t in Cent, degrees.
C according to Clapeyron.
C according to Thomson.
355
0-733
0-728
78-8
0-828
0-814
100
0-897
0-855
156-8
0-930
0-952
We see that the values of C found in both cases increase, like
those of A(fl + ^), slowly with the temperature. They bear the
same ratio to each other as the numbers of the following series :
1; 1-13; 1-22; 127;
1;1-12; 1-17; ISl;
and when the ratio of the values of K[a-\-t) (obtained by setting
fl = 273) corresponding to the same temperatures are calculated,
we obtain
m: 1; 1-14; 1-21; 1-39.
This series of relative values deviates from the former only so far
as might be expected from the insecurity of the data fi-om which
those are derived : the same will also e:diibit itself further on in
the determination of the absolute value of the constant A.
Such a coincidence of results derived from two entirely differ-
ent bases cannot be accidental. Rather does it furnish an im-
portant corroboration of both, and also of the additional inci-
dental assumption.
Let us now turn again to the application of equations (IV.)
and (V.) ; the former, as regards permanent gases, has merely
served to substantiate conclusions already known. For vapours,
however, and for other substances to which the principle of Carnot
may be applicable, the said equation furnishes the important
advantage, that by it we are justified in substituting everywhere
for the function C the definite expression Kia + t).
The equation (V.) changes by this into
r=^a + t).{s-<T)^', .... (Va.)
we thus obtain for the vapour a simple relation between the tem-
perature at which it is formed, the pressure, the volume, and
the latent heat, and can make use of it in drawing still further
conclusions.
Were the law of M. and G. true for vapours at their maximum
density, we should have
ps^^{a + t) . (20.)
tO^ M. 11. Clausius on the Mov^htg Force of Heat,
By means of this equation let 5 be eliminated from (Va.) ; neg-
lecting the quantity o", which, when the temperature is not
very high, disappears iu comparison with s, we obtain
^' 1 dp ^ r
pTt" Ail(fl +7p*
If the second assumption that r is constant be made here, we
obtain by integration
^;?i" A.R(a + lOO)(a4-0'
where p^ denotes the tension of the vapour at 100°. Let
/-100=T, « + 100=«, and -^^^^^ =^;
we have then
log^ = ^ (21.)
^Pi a + T ^
This equation cannot of course be strictly correct, because the
two assumptions made during its development are not so. As
however the latter approximate at least in some measure to the
tinith, the fonnula expresses in a rough manner, so to speak,
the route of the quantity log — ; and from this it may be per-
Pi
ceived how it is, when the constants « and jS are regarded as
arbitrary, instead of representing the definite values which their
meaning assigns to them, that the above may be used as an em-
pirical formula for the calculation of the tension of vapours,
without however considering it, as some have done, to be cam-
ple tely true theoretically.
Our next application of equation (Ya.) shall be to ascertain
how far the vapour of water, concerning which we possess the
most numerous data, diverges in its state of maximum density from
the law of M. and G. This divergence cannot be small, as car-
bonic acid and sulphurous acid gas, long before they reach their
points of condensation, exhibit considerable deviations.
The equation (Vflf.) can be brought to the following foi-m :
' p dt
Were the law of M. and G. strictly true, the expression at the
left-hand side must be very nearly constant, as the said law
would according to (20.) immediately give
and tJie Laws regarding the Nature of HeaM Wft
A.ps 7=A.R«.
a-i-t
where instead of s we can, with a near approach to accuracy, set
the quantity s^a. By a comparison with its true vahies calcu-
lated from the foi-mula at the right-hand side of (22.), this equa-
tion becomes peculiarly suited to exhibit every divergence from
the law of M. and G. I have carried out this calculation for a
series of temperatures, using for r and p the numbers given by
Regnault*.
With regard to the latent heat, moreover, according to Reg-
naultf the quantity of heat X necessary to raise a unit of weight
of water from 0° to t°, and then to evaporate it at this tempera-
ture, may be represented with tolerable accuracy by the following
formula :
\=606-5 + 0-305^ (23.)
In accordance, however, with the meaning of \, we have
cdt (23«.)
^ 0
For the quantity c, which is here introduced to express the spe-
cific heat of the water, Regnault J has given in another investiga-
tion the following formula :
c=l + 0-00004. if-f 0-0000009. ^2/ ^ ^2Sb.)
By means of these two equations we obtain from (23.) the fol-
lowing expression for the latent heat :
/• = 606-5-0-695. ^-000002. /2_0-000000./3^. . (24.)
Further, with regard to the pressure, Regnault has had recourse
to a diagram to obtain the most probable value out of his nume-
* 3Iem. de VAcad. de VInst. de France, vol. xxi. (1847).
t Ibid. Mem. IX. ; also Pogg. Ann., vol. Isxviii.
X Mem. de VAcad. de VInst. de France, Mem. X.
§ In the greater number of his experiments Regnault has observed, not
so much the heat which becomes latent during evaporation, as that which
becomes sensible by the precipitation of the vapour. Since, therefore, it
has been shown, that if the maxim regarding the equivalence of heat and
work be correct, the heat developed by the precipitation of a quantity of
vapour is not necessarily equal to that which it had absorbed during evapo-
ration, the question may occur whether such differences may not have
occurred in Regnault's experiments also, the given formula for r being thus
rendered useless. I believe, however, that a negative may be returned to
this question ; the matter being so arranged by Regnault, that the precipi-
tation of the vapour took place at the same pressm-e as its development,
that is, nearly under the pressure corresponding to the maximum density
of the vapour at the observed temperature ; and in this case the same quan-
tity of heat must be produced during condensation as was absorbed by
evaporation.
IW M. R. Clausius on the Moving Force of Heat,
rous experiments. He has constructed curves in which the
abscissae represent the temperature, and the ordinates the pres-
sure jo, taken at different intei-vals from —33° to 230°. From
100° to 230° he has drawn another curve, the ordinates of which
represent, not;? itself, but the logarithms of;?. From this dia-
gram the following values are obtained ; these ought to be re-
garded as the most immediate results of his observations, while
the other and more complete tables which the memoir contains
are calculated from formulae, the choice and determination of
which depend in the first place upon these values.
Table II.
p in millimetres,
< in Cent, degree*
of the air-ther-
mometer.
/in r^i^Tlf t^atYvAaa
p in millimetres.
I m i./eut. ue^ees
of the air-ther-
mometer.
according to the
curve of the
according to the
curve of the
numbers.
logarithms*.
-20
0-91
110
1073-7
1073-3
-10
2-08
120
1489-0
1490-7
0
4-60
130
20290
2030-5
10
916
140
2713-0
2711-5
20
17-39
150
35720
3578-5
30
31-55
160
46470
4651-6
40
54-91
170
59600
5956-7
50
91-98
180
75450
7537-0
60
148-79
190
94280
9425-4
70
23309
200
116600
11679-0
80
354-64
210
143080
14325 0
90
525-45
220
173900
173900
100
760-00
230
209150
20927-0
To carry out the intended calculations fi'om these data, I have
first obtained from the table the values of - • ^ for the tempe-
p at ^
ratures —15°, —5°, 5°, 15°, &c. in the following manner. As
the quantity — • -^ decreases but slowly with the increase of
temperature, I have regarded the said decrease for intervals of
10°, that is, from -20° to - 10°, from - 10° to 0°, &c. as uniform,
so that the value due to 25° might be considered as a mean
between that of 20° and that of 30°. As - • ^ = ^^2^', I was
p at at
by this means enabled to use the following formula :
\p ' dt/^iP ' 10 '
* This column contains, instead of the logarithms derived immediately
from the curve and given by Regnault, the corresponding numbers, so that
they may be more readily compared with the values in the column preceding.
and the Laws regarding the Nature of Heat.
Ill
or
\p dt),
log^Jar-logi?;
20°
10. M
(25.)
wherein log is the sign of Briggs's logarithms, and M the mo-
dulus of his system. With the assistance of these values of
— • ~^y and those of r given by equation (24.), as also the value
273 of a, the values assumed by the formula at the right-hand
side of (22.) are calculated, and will be found in the second
column of the following table. For temperatures above 100^,
the two series of numbers given above for p are made use of
singly, and the results thus obtained are placed side by side.
The signification of the third and fourth columns will be more
particularly explained hereafter.
Table III.
1.
* in Cent, degrees
of the air-ther-
Apis-^)^.
4.
2.
3.
Differences.
mometer.
According to the values
According to
observed.
equation (27.).
-15
30-61
30-61
000
- 5
29-21
30-54
-fl-33
5
30-93
30-46
-0-47
15
30-60
30-38
-0-22
25
30-40
30-30
-0-10
35
30-23
30-20
-0-03
45
30-10
3010
0-00
55
29-98
30-00
+0-02
65
29-88
29-88
0-00
75
2976
29-76
0-00
85
29-65
29-63
-0-02
95
29-49
29-48
-001
105
29-47 29-50
29-33
-0-14 -0-17
115
29-16 29-02
2917
-fO-01 +0-15
125
28-89 28-93
28-99
+0-10 +0-06
135
28-88 29-01
28-80
-0-08 -0-21
145
28-65 28-40
28-60
-0-05 +0-20
155
28-16 28-25
28-38
+0-22 +0-13
165
28-02 2819
28-14
+012 -0-05
175
27-84 27-90
27-89
+005 -0-01
185
27-76 27-67
27'Q2
-0-14 -0-05
195
27-45 27-20
27-33
-0-12 +0-13
205
26-89 26-94
27-02
+0-13 +008
215
26-56 26-79
26-68
+0-12 -Oil
225
26-64 26-50
26-32
-0-32 -0-18
We see directly from this table that Ajo(s— c) is not con-
stant, as it must be if the law of M. and G. were valid, but that
tl2 M. R. Clausius on the Moving Force of Heaf,
it decidedly decreases with tlie temperature. Between 35° and
90° this decrease is very uniform. Before 35°, particularly in
the neip^hbourhood of 0 , considerable irregularities take place ;
which, however, are simply explained by the fact, that here the
pressure p and its differential quotient -—; are very small, and
hence the trifling inaccui-acies which might attach themselves to
the observations can become comparatively impoiiant. It may
be added, further, that the cune by means of which, as men-
tioned above, the single values of jo have been obtained, was not
drawn continuously from —33° to 100°, but to save room was
broken off at 0°, so that the route of the curve at this point
cannot be so accurately determined as within the separate por-
tions above and below 0°. From the manner in which the di-
vergences show themselves in the above table, it would appear
that the value assumed for p at 0° is a little too great, as this
would cause the values of Ap(s'^a-) to be too small for the
a "T~ I
temperatures immediately under 0°, and too large for those above
it. From 100° upwards the values of this expression do not
decrease with the same regularity as between 35° and 95°. They
show, how ever, a general coiTCspondence ; and particularly when
a diagram is made, it is found that the curve, which almost
exactly connects the points within these limits, as determined
from the numbers contained in the foregoing table, may be car-
ried forward to 230°, the points being at the same time equally
distributed on both sides of it.
Taking the entire table into account, the route of this curve
may be expressed with tolerable accuracy by the equation
Ap{s~-(T)—-=m—ne'^^; . . . (26.)
in which e denotes the base of the Napierian logarithms, and m,
n, and k are constants. When the latter are determined from
the values given by the curve for 45°, 125° and 205°, we obtain
m=31-549; «= 1-0486; ^=0007138; . (26^.)
and when for the sake of convenience we introduce the loga-
rithms of Briggs, we have
log[31-549-Ajo(5-o-) _^J=00206 + 0-003100^. (27.)
From this equation the numbers contained in the third column
are calculated, and the fourth column contains the differences
between these numbers and those contained in the second.
From the data before us we can readily deduce a formula
and the Laws regarding the Nature of Heat*
\n
which will enable us more definitely to recognize the manner in
which the deportment of the vapour diverges from the law of M.
and Gr. Assuming the correctness of the law, if psQ denote the
value oips for 0^, we must set in agreement with (20.),
ps __a + t
ps'o'^ a '
and would therefore obtain for the differential quotients -j- • ( "^j
a constant quantity, that is to say, the known coefficient of ex-
pansion — = 0*003665. Instead of this we derive from (26.),
when in the place oi s—a we set s itself simply, the equation
ps ^m — n.e^^ a-\-t
m-'n
(38.)
and from this follows
d rps \ 1 in—nll-\-k(a + t)]^^
dt\ pSn J
m—n
(39.)
The differential quotient is therefore not a constant, but a func-
tion which decreases with the increase of temperature, and
which, when the numbers given by (26«.) for m, n and ky are
introduced, assumes among others the following values : —
Table IV.
t.
dt Kpsq)' 1
t.
dt \psoJ
1 .. !
1 1
dt \psj
5
000342
70
0-00307
1 1
1 140
000244
10
0-00.338 1
80
0-00300
1 150
000231
20
000334 i
90
000293
j 160
000217
30
000329 !
100
0-00285
j 170
000203
40
000325
110
000276
i 180
0-00187
50
000319
120
0-00266
i 190
000168
60
0-00314
130
0-00256
I 200
000149
We see from this that the deviations fi-om the law of M. and
G. are small at low temperatures j at high temperatures, how-
ever, for example at 100° and upwards, they are no longer to be
neglected.
It may perhaps at first sight appear strange that the values
found for -rrX — ) are less than 0*003665, as it is known that
dt \psq/ ^
for those gases which deviate most from the law of M. and G.,
as carbonic acid and sulphurous acid, the coefficient of expansion
is not smaller but greater. The differential quotients before
114 M. R. Clausius on the Moving Force of Heat,
calculated must not however be regarded as expressing literally
the same thing as the coefficient of expansion, which latter is
obtained either by suffering the volume to expand under a con-
slant pressure, or by heating a constant volume, and then obser-
ving the increase of expansive force ; but wc are here dealing
with a third particular case of the general differential quotients
-f7\—)f where the pressure increases with the temperature in
the ratio due to the vapour of water which retains its maximum
density. To establish a comparison with carbonic acid, the same
case must be taken into consideration.
At 108^ steam possesses a tension of 1 metre, and at 1.29^°
a tension of 2 metres. We will therefore inquire how carbonic
acid acts when heated to 21^°, and the pressure thus increased
from 1 to 2 metres. According to Regnault*, the coefficient
of expansion for carbonic acid at a constant pressure of 760
millims. is 0*003710, and at a pressure of 2520 millims. it is
0*003846. For a pressure of 1500 millims. (the mean between
1 metre and 2 metres) we obtain, when we regard the increase
of the coefficient of expansion as proportional to the increase of
pressure, the value 0'003767. If therefore carbonic acid were
heated under this mean pressure from 0 to 21|°, the quantity
^ would be thus increased from 1 to 1 + 0003767 x 21-5
=s 1*08099. Further, it is known from other experiments of
Regnault t, that when carbonic acid at a temperature of nearly
0°, and a pressure of 1 metre, is loaded with a pressure of
1*98292 metre, the quantity j^v decreases at the same time in
the ratio of 1 : 0*99146; according to which, for an increase of
pressure from 1 to 2 metres, the ratio of the decrease would be
1 : 0*99131. If now both take place at the same time, the increase
of temperature from 0 to 21^, and the increase of pressure from
1 metre to 2 metres, the quantity ^ must thereby increase
very nearly from 1 to 1*08099 x 0*99131 = 1*071596; andfrom
this we obtain, as the mean value of the differential quotients
d_/pv_\
dt \pvj'
We see, therefore, that for the case under contemplation a value
is obtained for carbonic acid also which is less than 0*003665 ;
* M^m. de VAcad.y vol. xxi. Mem. I. f Ibid. Mem. VI.
and the Laws regarding the Nature of Heat, 115
and it is less to be wondered at if the same result should occur
with the vapour at its maximum density.
If, on the contrary, the real coefficient of expansion for the
vapour were sought, that is to say, the number which expresses
the expansion of a certain quantity of vapour taken at a definite
temperature and in a state of maximum density, and heated under
a constant pressure, we should certainly obtain a value greater,
and perhaps considerably greater, than 0-003665.
From the equation (26.) the relative volumes of a unit weight
of steam at its maximum density for the different temperatures,
as referred to the volume at a fixed temperature, is readily esti-
mated. To calculate from these the absolute volumes with suffi-
cient exactitude, the value of the constant A must be established
with greater certainty than is at present the case.
The question now occurs, whether a single volume may not
be accurately estimated in some other manner, so as to enable
us to infer the absolute values of the remaining volumes from their
relative values. Already, indeed, have various attempts been made
to determine the specific weight of water vapour ; but I believe
for the case in hand, where the vapour is at its maximum den-
sity, the results are not yet decisive. The numbers usually given,
particularly that found by Gay-Lussac, 0'6235, agree pretty well
with the theoretic value obtained from the assumption, that two
measures of hydrogen and one of oxygen give by their combina-
tion two measures of vapour, that is to say, with the value
2x0-06926 + 1-10563 ^q.^qq
These numbers, however, refer to observations made, not at those
temperatures where the pressure used was equal to the maximum
expansive force, but at higher ones. In this state the vapour
might nearly agree wath the law of M. and G., and hence may
be explained the coincidence of experiment with the theoretic
values. To make this, however, the basis from which, by appli-
cation of the above law, the condition of the vapour at its max-
imum density might be inferred, would contradict the results
before obtained ; as in Table IV. it is shown that the divergence
at the temperatures to which these determinations refer are too
considerable. It is also a fact, that those experiments where the
vapour at its maximum density was observed have in most cases
given larger numbers; and Regnault* has convinced himself,
that even at a temperature a little above 30°, when the vapour
was developed in vacuo, a satisfactory coincidence was first ob-
seiTed when the tension of the vapour was 0*8 of that which
corresponded to the maximum density due to the temperature
* Ann. de Chim. et de Phys., 3 ser. vol. xv, p. 148.
]^ M. vg^^pkimus on the Moving Fwce /tfll^i,
existing at the time; with proportionately greater tenBion^Sttei
numbers were too large. The case, however, is not finally set at
rest by these experiments ; for, as remarked by Regnault, it is
doubtful whether the divergence is due to the too great specific
heat of the developed vapour, or to a quantity of water condensed
upon the sides of the glass balloon. Other experiments, wherein
the vapour was not developed in vacuo but saturated a current qf ^
air, gave results which were tolerably free* from these irregulaii-^'
ties ; but neither from these, however important they may be in •
other respects, can a safe conclusion be di'awn as. to the depprt^t
ment of the vapour in vflCMO. '*'"'-"« > \
The following considerations will perhaps feeiliB' to fill up to"
some extent the gap caused by this uncertainty. The table (IV.)
shows that the lower the temperature of the vapour at its max-
imum density, the more nearly it agrees with the law of M. and^
G. ; and hence we must conclude, that the specific weight foi'"
low temperatures approaches more nearly the theoretic value
than for high ones. If therefore, for example, the value of 0*622
for 0° be assumed to be correct, and the corresponding values d
for higher temperatures be calculated from the following equa-
tion deduced from (26.), i -^ \s
^Ai iai t focrao
m—ne
n
Ttf
^rf rijso \8v
tazo
we shall obtain far more probable values than if we had majflrr
use of 0*622 fpr. ^11. temperatures. The follo;\vipg table gives
some of these.
Table V.
t.
0«.
50°.
100*.
150°.
200°.
d.
0622
0-631
0-645
0-666
0-698
ili morii baa
Strictly speaking, however, we must proceed still further. In
Table III. it is seen that the values of Ap{s—(r) — -— , as tli^,;j.
temperature decreases, approach a limit which is not attained^ *
even by the lowest tem])eratures in the table; and not until this '
limit be reached can we really admit the validity of the law of ?.
M. and G., or assume the specific weight to be 0*622. The
question now occurs, what is this limit ? Could we regard the
formula (26.) to be true for temperatures under —15° also, it
would only be necessary to take that value to which it approaches
as an asymptote, tw =31*5 19, and we could then set in the placets
,.,{ ♦ Anv. de Chim. et de Phys., 3 ser. vol. xv. p. 148. r ni nfia
Akd^ihe Laws regarding tlie Nature of Heat :^^^ tfr
of (30.) the equation - <t is :?^r^^x<>
''=0-623.-:^, (31.)
— ne^'
From this we should derive for 0^ the specific weight 0*643(
instead of 0*622, and the other numbers of the above table would
have to be increased proportionately. But we are not yet jus-
tified in making so wide an application of the formula (26.), as
it has been merely derived empirically from the values contained
in Table III.; and among these, the values belonging to the
lowest temperatures are insecure. We must therefore for the
present regard the limit of A (^—cr) — -- as unknown, and con-
tent ourselves with an approximation similar to that furnished
by the numbers in the foregoing table ; so much however we may
conclude, that these numbers are rather too small than too large.
By combining (Ya.) with the equation (III.), which was im-
mediately derived frOm the original maxim, we can eliminate
at a-\-t ^ '
By means of this equation, the quantity A, described above as
negative, can be more nearly determined. For c and r let the
expressions in (23Z>.) and (24.) be substituted, and for a the
number 273 ; we then obtain
I n ons. 606-5-0-695/-0-0000/2-0-0000003^^ ,^^ ,
A=0-305 ^^3-p^ ; (33.)
and from this we derive among others the following values for h :
Table VI.
50°.
-1-9161 -1-465
1
lOQO.
I- 133
150°. 200°.
•0-879 -0-676
In a manner similar to that already pursued in the case of ■
water-vapour, the equation (V«.) might be applied to the vapours
of other fluids, and the results thus obtained compared with each
other, as is done in Table I., with the numbers calculated by Cla-
peyron. We will not, however, enter further upon this application, *
We must now endeavour to determine, at least approximately,
the numerical value of the constant A, or, what is more useful,
the value of the fraction -r- : in other words, to determine the
A ^ -'.'"'*
equivalent of work for the unit of heat. [mufirin
Pursuing the same course as that of Meyer and Holtzmann, we
can in the first place make use of equation {\0a.) developed for
Phil Mag, S. 4. Vol. 2. No. 9. Aug, 1851. K
118 M, R. Clausius on the Moving Force of Heat,
pennanent gases. This equation was
c/rsc + AR;
and when for c the equivalent expression j is introduced, we have
For atmospheric air, the number 0*267, as given by De Laroche
and Berard, is generally assumed for ^ ; and for k, as given by
Duloner, 1-421. For the determination of R= -^r^, we know
that the pressure of one atmosphere (760 millims.) on a square
metre amounts to 10333 kils. ; and the volume of 1 kil. atmo-
spheric air under the said pressure and at the temperature of the
freezing-point is =0*7733 cubic metres. From this follows
and hence
R=128§|^ =39-36,
1_ __ 1*421x29*26 __
A"" 0-421x0*267 -^^"^
that is to say, by the expenditure of one unit of heat (the quan-
tity which raises 1 kil. of water from 0° to 1°) a weight of 370
kils. can be raised to a height of 1 metre. This value, however,
on account of the uncertainty of the numbers 0*267 and 1*421,
is deserving of little confidence. Holtzmann gives as the limits
between which he is in doubt the numbers 343 and 429.
The equation (Va.) developed for vapours can be made use of
for the same purpose. If we apply it to the vapour of water,
the foregoing determinations, whose result is expressed in equa-
tion (26.), may be used. If, for example, the temperature 100°
be chosen, and for p the corresponding pressure of one atmo-
sphere = 10333 kils. be substituted in the above equation, we
obtain
i-=257.(.-<7). .... (35.)
If it now be assumed with Gay-Lussac that the specific weight
of the water-vapour is 0-6235, we obtain s= 1*699, and hence
A
Similar results are obtained from the values of C contained in
Table I., which Clapeyron and Thomson have calculated from
equation (V.). K these be regarded as the values of A (a -fO
and the Laws regarding the Nature of Heat, 119
corresponding to the adjacent temperatures,, a series of numbers
are obtained for -r> all of which lie between 416 and 462.
It has been mentioned above, that the specific weight of the
vapour of water at its maximum density given by Gay-Lussac is
probably a little too small, and the same may be said of the
specific weights of vapours generally. Hence the value of -r-
derived from these must be considered a little too large. If the
number 0*645 given in Table V. for the vapour of water, and
from which we find s = l"638, be assumed, we obtain
which value is perhaps still too great, though probably not
much. As this result is preferable to that obtained from the
atmospheric air, we may conclude that the equivalent of work for
the unit of heat is the raising of something over 400 kits, to a
height of 1 metre.
With this theoretic result, we can compare those obtained by
Joule from direct observation. From the heat produced by
magneto-electricity he found
Ova \o in ]- =460*.
From the quantity of heat absorbed by atmospheric air during
its expansion,
J=438t;
ana as mean of a great number of experiments in which the heat
developed by the friction of water, of mercury, and of cast iron
was observed.
The coincidence of these three numbers with each other, not-
withstanding the difiiculty of the experiments, dispels all doubt
as to the correctness of the principle which asserts the equivalence
of heat and work; and the agreement of the same with the num-
ber 421 corroborates in like manner the truth of Carnot^s prin-
ciple in the form which it assumes when combined with our
original maxim.
* Phil. Mag., vol. xxiii. p. 441. The English measure has been reduced
to the French standard.
t Ibid. vol. xxvi. p. 381. J Ibid. vol. xxxv. p. 534. -^K'
K2
[ 120 ]
XIX. ^ Description of Matlovkite, a new Oxy chloride of Lead,
By R. P. Greg, Jun., Esq.^
MR. WRIGHT of Liverpool has recently obtained from the
old heaps of the level mine at Cromford, near Matlock,
a small number of specimens of the murio-carbonate of lead, or
phosgenite of Haidinger ; and he has also found a few specimens
of another ore of lead, differing in appearance from any of the
known salts of that metal.
At my request this mineral has been examined by Dr. Robert
Angus Smith of Manchester, and his analysis of it has afforded
the following results : —
Chloride of lead .... 55-17^^'
Oxide of lead 44-30()
Moisture -072
99-549
The proportions by theory would be —
Chloride of lead 55-46
Oxide of lead 44*53
99-99
This gives a definite chemical composition of 1 atom of chlo-
ride of lead combined with 1 atom of oxide of lead ; differing in
this respect from Mendipite, in which the proportion of chloride
to that of oxide is as 1 to 2.
The specific gravity of Matlockite is 7*21, and its hardness
2*5 to 3. Colour yellowish, with sometimes a slight greenish
tinge ; its lustre is adamantine, and occasionally pearly, and it
'is transparent and translucent. It cleaves, but not readily,
"^parallel to P. Its fracture is uneven and slightly conchoidal.
It decrepitates in the flame of the blowpipe, but with care is
reduced to a grayish-yellow globule.
It occurs in tabular ciystals, generally thin and superimposed
on each other, and occasionally slightly cuiTcd ; but my friend
Mr. "W. G. Lettsom has a perfect transparent crystal an inch
square and an eighth of an inch thick.
The primitive form is a light square prism ; and the following
figui-e, drawn by Professor Miller of Cambridge, who has also
corrected the mcasurcd angles, represents all the modifications
hitherto observed : —
♦ Communicated by the Author.
Prof. O^Brien on SymhoUcal Mechanics.
121
mfim' — Oil
tiooIjiiM cr
-iCfSiiTroaq^ re
m
uuni limits
mm= 90 "- '■
^c =119 34
= 59 8
= 138 59
= 104 6
= 111 50
ss 43 4ih<iqi.i m ^m
= 97 58 ' ' />
: ' 'i^i'dfessor Miller adds^ '^ A slice parallel to the plane c, 0'0204
incli thick^ being placed in a polarizing instrument having the
planes of polarization of the polarizer and analyser at right
angles to each other^ the angular radius of the first blue ring in
air was found to be 22° 81'/'
Dr. Smith has also analysed a crystal of* the n urio- carbonate
of lead_, and has obtained —
Chloride of lead . . . 51-784
Carbonate of lead . . . 48-215
99-999
corresponding to 1 atom of chloride combined with 1 atom of
carbonate^ which agrees with the proportions given by Klaproth
and Berzelius.
NorclifFe Hall, near Wilmslow, Cheshire.
XX. On Symbolical Mechanics. By the Rev. M. O'Brien, M.A.,
Professor of Natural Philosophy and Astronomy, King's Col-
lege, London, late Fellow ofCaius College, Cambridge"^.
IN the previous paper I pointed out the distinction between
geometrical and mechanical addition ; the former consisting
in the successive tracing of lines, the latter in the simultaneous
action of forces. When + is used in
its geometrical sense, u-\-v, or AB + AC,
denotes the change of position produced
in a tracing point by causing it to de-
scribe the lines AB and BD in imme-
diate succession, BD being parallel and
equal to AC ; but when + has its mechanical signL.ication,
U + V denotes the mechanical effect produced by the simulta-
neous action of the two forces represented by U and V. In this
way it is that AB + AC denotes the line AD, while U -j- V de-
notes the resultant of U and V.
* Communicated by the Author.
1132 Prof. O'Brien on Symbolical Mechanics.
In ordinary mechanics, where addition is in all cases merely
numej'ical, it is immediately obvious that lines may be assumed
to represent forces in magnitude and direction ; but whether the
same mode of representation can be adopted in symbolical me-
chanicS; where -f is used in the two different senses just alluded
to, is a point to be determined. For, if we suppose AB and AC
to represent the forces U and V respectively, AB + AC ought to
represent the force U + V ; that is, AD ought to represent the
resultant of the two forces represented by AB and AC : otherwise
lines cannot be assumed as proper representatives of forces.
Now this immediately leads us to the parallelogram of forces^
and shows that the general representation of forces by lines
assumes the truth of that theorem. In fact, the parallelogram
of forces is a principle which identifies geometrical and mecha-
nical addition, and shows, that, if the lines u and v represent
the forces U and V respectively, in magnitude and direction, then
the geometrical sum u + v will also represent the mechanical sum
or resultant U + V. That u-\-v repesents U + V admits of remark-
ably simple proof by means of the symbolization explained in
the former papers, as I shall now briefly show.
Let a and /& denote units of length, and A and B units of
force parallel respectively to a and y8. Let U=XA, V=YB,
X and Y being the numerical magnitudes of the forces ; then, if
u and V represent U and V, we must have, msbX*, «=Y/3.
Hence
(^,4.v)(UH-V) = X2aA + XY(«B-|-/3A)-f-Y2/9B;
but we have shown that ak, aB + /8A, and /SB are each equal tor'
zero; consequently
(M + t^)(U-HV)=0,
and therefore the force U -f- V is parallel to the line w + v ; that
is, the latter represents the former in direction.
Again, let € and E be imits of length and force in the common
direction oi u-\-v and U-}-V, and let w-f w=re, U + V = RE, r
and R being the magnitudes of w -f- v and U -f V respectively.
Then we have
wU5;:(r€-«;)(RE-V),
or
X««A=rR6E-ryeB-- YR)5E- Y2/3B ;
but a A, eE, and ySB are each zero, and eBss — /8E ; hence
0=rY-RY, orr=R.
It appears, therefore, that u-{-v represents U + V m magnitude
as well as in direction.
I shaU now always use lines to represent forces, and, therefore.
Prof. O'Brien on Symbolical Mechanics. 123
there will no longer be any occasion to distinguish between units
of force and units of length. I shall employ the Greek letters
a, ^, and 7 to represent both,, and substitute them everywhere ^
in place of A, B and C. Hence^ instead of the relations aA=0^.
&c., ^A= — aB, &c., we have the following, viz. ;,^-
/5a=— aft 7/3=— /37, uy=—yu.J
And generally, supposing U and V to be forces parallel and
equal to the lines u and v respectively, I shall substitute the
latter for the former. Now, since ?;U= — wV*, this substitution
leads to the important result, that ,
vu=s--uv; (2*)i>
that is, the factors in the symbolical product uv may be inter-
changed if we change the sign of the product. ' '
If w and V be parallel, uV=0', hence we have another result'
of importance, namely, that the condition of parallelism of two
lines u and v is
uv = 0 . (3.)
It will be remembered that uv denotes the effect produced by
the translation of the line v along the line u, that is, by the
parallel removal of the force represented by v from A to B, AB
being the line u. It will also be remembered that A and B are
supposed to be points in the same rigid body, and that uv is, in
fact, the couple consisting of the forces —v and v acting at A
and B respectively.
All that is here said respecting forces applies equally well to'
impressed velocities.
Units of Translation, — Representation by perpendicular lines. •
If 6 be the angle between u and v, cc and y8 two units drawiir
at right angles to each other anywhere in the plane of u and v ;
and if x and y denote the numerical magnitudes of u and v ; then
it may be shown, that %avM} }i baR
uv = [xy sin 6) up. • ' -• ■ ^^ • " «<-' . ^ T
For, let <^ and -^Ir be the angles which u and v respectively
make with the direction a ; then, by geometrical addition,
u={x cos (f>)u + [x sin </>)/3
?; = (y cos '>^)cx, + {y sin '^)^. ! '
Hence, observing that uu^^^^O, and /5a = —aft we find
uv=xy(cos (j> sin '\/r— sin </> cos yjr)oi^ n .(|t|^ ji
= (^ysin^)aft ^Hibwgji
* For t?U+wV=X'O«+«6p)=0. Ilidgli.
1)6^ lVpt*AOf^ien m^y^i/»*^olkal Mechanic ^
I shall call a^ a unit of translation * ; consequently the nume-
rical magnitude of uv is to be found by multiplying the numerical
magnitude of ii by that of v, and by the sine of the angle which
V makes with w.
From the result just obtained, it appears that all units of
translation in the same plane (or in parallel planes, by former
papers) are equivalent to each other; for, if we suppose a?=lj
y = l, and ^ = 90^, uv becomes a unit of translation anywhere in
the same plane as the unit ayS : since, therefore, these suppo-
sitions reduce the equation just obtained to uv=ia0, it follows that
all units of translation in the same plane are equivalent to each
other. The method employed in statics of representing couples
by their axes, suggests a similar sort of representation here; J
shall therefore assimie a unit of length di'awn at right angles to
the plane of a and ^ to represent the unit of translation otp,
which it will properly do, since it completely defines uff as
i*egards magnitude and plane of translation ; and this is all that
need be defined.
' Let 7 be the unit of length thus drawn ; then I shall put 7
for a(9, or a^ for 7, as the case may require, in any investigation.
Since /9a =—ayS, it follows that ^u is represented by —7.
To determine generally the direction of the unit of length which
represents a unit of translation, I shall adopt the following rule,
viz. Conceive a man to be so placed that his head is in the direc-i
tion of the translated line {ff) and his feet in the opposite
direction, and let him turn round till the direction of translation
(a) points to the right; then I shall assume the direction in
which he looks to be that of the unit (7) which represents the
translation u^. According to this rule, it is easy to see that /3a
is represented by —y; and generally, supposing a, /8, 7 to be
any three units of length at right angles to each other, we have
the following equations, viz.
a^ = 7, ffy-ct, yoizsff, \
/3a=-7, 7/3= -«. «7=-y5.J * • ^ ^^
llic equivalence here implied may be called equivalence of
symbolical definition ; it simply implies that the symbols equated
define the same thing, and may therefore be substituted for each
other in any symbolical equations.
It has been shown that vv=-[ccy^\\\ 6)aj3 ; whence it follows,
.Vv uv = {a;y sin 0)y (5.)
Now xy sin 6 is the area of the parallelogram formed upon u
* The translation of a unit along a perpendicular unit may properly be
called a Unit of Translation.
¥ivl&M(^ m SijniboHcal I^^^ Hi/i
and V as ' sides,, and 7 is at right angles to the plane ^ or ti at
parallelogram ; hence it follows, that the line which sipnboUcaUy
represents uv is equal numerically to the area of the paralleloyram
uv, and is drawn at right angles to its plane.
io ?!tiim iU.tBfiJ a'iJ85q<(F» Hi jbomxijoo uu^ iXu^yi- ^di moil
' " Th^e ^riii^dlfA^s '^feMffi^ieilt td #Me m tii ^a;()^lf ^^^ip^
bolical system here proposed to a variety of cases of considerable
importance. Among others the following may be mentioned as
interesting, because of its connexion with the problem of the
pendulum as a means of exhibiting the earth's rotation; :'^fi.^Js
as follows.
tinn VM
IP-.
^'*If we calculate the indtioh of a particle relatively to the eai.
rorgetting to allow for the earth's rotation, we may complelte'
correct the error by supposing the accelerating force, '"^
dsdt Ik 81 Mi hm { fioitfil?i\ <?/ "^ i.j^baB '.buiixi^Bm ab-isg^'i
. , Jj'jrrrhb -^rf bfjQff
to act on the particle ; o) denotnig a line equal numerically to
the earth's angular velocity and parallel to the polar axis, and u
the distance of the particle frdm the darth's centre; -j- being
mio': . . ' . dt ■,.
t^^oOn the supposition that the earth is fixed. This is the
ixViQ centrifugal force J —(o{ci)u) represents the ordinary statical
centrifugal force in magnitude and direction, and the additional
fffitf^r^^Sii -TT arises from the motion of the particle relatively to
to «lB&»'iq'*i doidw (f) nm- di %} ndi :)d ot «ioo! sd xLoidw
»^;LBy means of this result the trtle equationsdf m6tion'of a' pm-
dulum are obtained with great facility ; they are as follows : —
flfr a dt
'" ' d\j a ^ . ^ dx
-^ .^.,-.^ dt^ a^ dt ..,:>,.;..., .rff
fere X and y are the coordinates of the projection of tli^^^^^r
ting particle on the horizontal plane referred to two horizontal
axes, one of which always lies in the meridian plane, n denotes
the earth's angular velocity, and X the latitude. ' ' " '
It is obvious from these equations, that the effect produced by
the earth's rotation on the pendulum is proportional in every
respect to sin X. .^ ^iufe.ui, y/o7.
[To be continued.]
fid /!i3cp)"ig y«iii )orjj ft io iHniJ&ham^ odT *
[ 126 ]
^XI> On the Anticlinal Line of the London and Hampshire
Basins. By P. J. Martin, Esq., F.G.S.
[Continued from p. 51.]
Anticlinal Line of the Vale of Greenhurst.
ALTHOUGH a description of this line of elevation forms a con-
spicuous feature in my former disquisition on the Weald*,
in resuming this part of my subject I may be supposed to be in-
vading a province which Mr. Hopkins has in some measure made
his own, by the labour he has lately bestowed on it, with which,
however, I was till very recently unacquainted. Of the result
of Mr. Hopkins's investigation into the construction of the body
of the Weald I am entirely ignorant. I have long been familiar
with most of its phsenomena ; and have, since the publication
of my former essays, been waiting for a favourable opportunity
of publishing the results of my observations in the shape of a
" History of the Weald Denudatiou.^^ But as I am not yet
prepared to fill up all the details of such a history, I am better
pleased that an exposition of the construction of the Weald and
the Boulonnais should come from the author of a " Theory of
Elevation."
On looking at the escarpment of the South Downs in No. 9
of the Ordnance Map, it will be observed that there is a remark-
able recession of that escarpment southward, between the salient
angles of Duncton Hill in the west of Sussex, and Wolfstanbury
in the east. In a line parallel with this receded chalk, and at
an average distance of about a mile, lie the Weald-clay valleys
of Greenhurst and Henfeld — ^^ valleys of elevation," — with their
anticlinal escarpments of lower greensand, and their synclinal
reduplications of the same, with the occasional addition of a
trough of gait ; the whole occupying a length and breadth of
country of about eighteen miles by from one to two.
Greenhurst lies on the road between Storrington and Thake-
ham. Mary Hill on the south and Jacquet's Hill on the north
form its scai'ped anticlinal boundaries of lower greensand, show-
ing a dip which varies from 30 to 60 degrees. Here the syn-
clinal line loms in the valley in which Abbingsworth House and
Champion's Farm are situate ; and the beds which dip north at
Jacquet's Hill rise north again in the hollow way to Thakeham.
East of Greenhui-st the northern escarpment breaks ofi" at the
high grounds of Warminghurst, and the valley opens into the
great expanse of the Weald. The anticlinal line is ^then carried
on in a Weald-clay saddle through Ashington, Guesses' Farm
and Horsebridge Common. It next crosses the Adur, and is
* Memoir on Western Sussex, &c.
On the Anticlinal Line of the London and Hampshire Basins. 127
again bordered by anticlinal scarps of greensand^ at New Hall
on the south and Henfield on the north. The synclinal dispo-
sition is well -characterized north of Henfield. From Henfield,
or from the Adur, the line is carried on by a broad Weald-clay
valley as far as Homebush, where the escarpments of lower green-
sand again become confluent. A saddle of gait, another of malm
rock, and then the chalk of Poynings and Wolfstanbury succeed,
and appear to preclude all further progress to this upheaval.
Indeed I formerly thought that the line either terminated here,
or ran out through the chalk at Saddlescombe. But when
Mr. Lyell published his figure of the upheaved chalk at Souther-
ham near Lewes, with his speculations thereon*, I saw distinctly
that the longitudinal fissure of Greenhurst did enter the chalk,
and running out again eastward from Lewes, the probability
was that it would be found in its place, and be again instru-
mental in carrying back the chalk southward, as it had done west
of Wolfstanbury.
These suspicions have since been verified by observation. The
line of elevation as it enters the chalk is the Valley of Piecomb,
Pangdean, and the north side of Stanmere Park. As it ap-
proaches the Ouse below Lewes, a deep denudation marks its
further progress, bounded by the strongly -marked chalk escarp-
ment south-west of Lewes, over Palmer, Kingstone and Iford.
Crossing the Ouse, the quarry in the northern escarpment of
this denudation, before spoken of, at Southerham cornerf^ pre-
sents a northerly dip of 30 or 40 degrees. The southern escarp-
ment becomes the line of the South Downs as they are carried on
towards East Bourne. Under Mount Caburn, and about a
quarter of a mile further east, the line is carried on in the lower
or gray chalk, which is there quarried. To this succeeds a saddle
of upper greensand stretching over from Glynde to Firle ; then
another of gait ; and then obscure indications of the outcrop of
the lower greensand. In this part of Sussex it is well known
that the sand in question thins out, or is in some way so lost to
view, that it might be passed over in a cursory survey of the
country, were it not known to be still certainly present J. Its
course appears to be this : it crops out in the usual order at
* Principles of Geology. First edition.
t So called at Lewes.
X Mantell's Geology of Sussex and Geology of S.E. of England.
I strongly suspect that the obscure outcrop of the greensands in this
part of our island, or rather their immersion, is mainly caused by the ope-
ration of this line of fissure. These beds form so prominent a feature in
all the country west of Lewes, and appear again in such force on the oppo-
site side of the Channel, in the Boulonnais, that it can hardly be supposed
that their obscurity in this intermediate space is the effect of a proper thin-
ning out.
iSS UY/T:t}Mtai!in'd^W:AMclin(tl Line of
Ringmcr north of Lewes, at Ripe it is syncliiial_, and at SehnstdS
and Bcnvick Common anticlinal. Here it appears to be lost }
for a broad saddle of Weald clay succeeds, and its anticlinal and
synclinal arrangement produces several miles of expansion from
Swinesliill Gate through Hailsham and Hellingly, where the fii-st
Wealden sand crops out. ^ . ; . ;. ;
The country becomes now so flat;'thit?l[ fti^e'^ntt^een able
to determine the exact part of the coast at which the anticlinal
line runs out. But the sharp dip of the chalk by the roadside,
and in the chalk-pit at AVillingdon, shows that it is not far off;
and as still more satisfactory evidence, a fine swell of the upper
gi'ecnsand is seen rising out of its synclinal line from under the
Bourne Level in the cliff at Sea Houses, near East Bourne, and
waving away beautifully southward to sink under the chalk
towards Beachey Head*. ; .; ; . i^j ; ! ,.;;
We must now return to tlie west of Susse?^!' •* Frbiti Cfreenhurst
westward, still following the course of the Downs, the disruption
throws back in succession the three members of the lower green -
sand, forming an irregular but well-defined countiy of each, with
its anticlinal and synclinal lines. A trough of gait is exhibited
in the latter of these at Wiggonholt, Hardham, Watersfield and
Tripp Hillf. The line then passes through a saddle of gait
between the last-mentioned place and the Bury New Woods,
and then, bearing north-westerly, and bringing the Chalk Downs
with it, it points towards Midhurst. From Duncton and La-
vington Commons it enters by Selham into the course of the
Bother (the western branch of the Avon), leaves the gait behind
it, and by its synclinal line projects the argillaceous beds of the
lower greensand northward as far as Lodswoi-th and the south
paii; of Cowdry Park J. Then taking its course north of Mid-
hurst, still following the backward course of the Bother, it
emerges from it and appears in great force at Woolbeding. In
a hollow way a few hundred yards north of Woolbeding Farm, a
good section is to be seen of its central and sharpest upshot ;
but to gain a just notion of its importance here, it is necessary
to traverse the hollow ways round about this locality, and observe
the escarpments and tilted sections of the sandhills at Midhurst
and Trotton. At this most northerly part of its course, at WooU
beding, it enters the lowest or Fullei-'s earth beds of the lowei*
* I am not sure that this wave of the upper greensand has not been
noticed somewhere by Dr. Fitton, although I do not find it in his " Strata
below the Chalk," Geol. Trans, loc. ctt.
t This trough of gait is five miles long, and from a quarter to half a
mile wide. •
X There is much obscurity in this part of the line, and but for its ^^ttp-i
])earance at Woolbeding it might be supposed to be worn (mti'" >««J o,"^^ 4
• 1 i>(tnon (iiiio*f
the J^oniioT;^ and Hampshire Basins, :; 129
greensand country-j , ?uid i-uns so l^ard up to the great centraj
fissure of the Weald, as to conspire with it in producing, and is
indeed, in this way, the cause of the exposure of the Weald clay
in Hartingcombe — that projection into the Wolmar Valley, west
of Hindhead and Blackdown, spoken of in the former part of
this memoir. The transverse fissures between Telegraph Hill or
Holder Hill, Stubs Hill and Vining Common, produce prolon-
gations of that exposure of the Weald clay quite down into the
synclinal line, and indeed almost int9 the anticlinal at Iping*^.|
Although in its further progress westward the Greenhurst line
has still an elevation of its own in a saddle of sand-hills, through
Chithurst, Trotton and Rogate, it is very much incorporated in
its upheaving effect, and thus acts in conjunction with the central
anticlinal line ; or, in other words, its synclinal reduplication is
immediately lost in the superior heave of that line towards Has^
lemere. And it is a curious fact, that the chalk, taking advantage,
as it were, of this aberration northward, losing the ordinary dip
of the South Down range, pushes its escarpment forward iuja
l^ypad high talus at South Harting.
I„j From Rogate westward no satisfactory section can be obtained ;
and in its passage on the north side of the town of Petersfield,
little is seen of this line but a broken saddle of sand-hills till it
^ikes the Malm Rock or upper greensand at Langrishf. ,.^|
IjjThe anticlinal disposition is to be seen in an imperfect section
c^j both sides of the East IVIeon road at Langrish ; and to an
unpractised observer it would seem insignificant, if the general
aspect of a broken chalk saddle in the country west of it had
not caused it to be sought for as a nucleus of elevation.
Although trifling of itself, the sweep of the rocks north and
south away from this point marks its character ; and on prq^
ceeding up the valley on the road to Winchester, a chalk -pit in
the gray chalk shows the northerly dip and westward strike of
^:* I am not sure that there is not another and minor contortion of the
Weald group projected into this curious offset of the Weald-clay valleys
It shows itself in the river bank at Baybridge near Knepp Castle. I have
detected it again in the escarpment of the second Wealden sand course at
Andrews Hill south of Billingshurst, and again in a sand-pit at Ebernoe or
Eberknoll, west of Kirdford ; all in a direct line, and pointing toward the
gorge of the valley in question, between Blackdown and Bexley Hill. But
at all these exposures the wave of elevation is very slight. These minor
or local distm'bances will be afterwards considered as belonging to the lesser
contortions, or puckerings of the Wealden strata.
t Subsequent observations incline me to believe that this fault or upcast
at Langrish is not a continuation of the Greenhurst line ; and that there is
no true inosculation of that antichnal with the Winchester hue, unless by
the Meon Valley. It is probable that, with the upcast at Woolbeding, and
the flexm*e at Midhurst mentioned by Mr. Hopkins (Geol. Trans,, vol. vii.
p. 16), the influence of this line of elevation on the escarpment of the
South Downs ceases.— -P. J. M. May 1851.
130 Mr. P. J. Martin on the Anticlinal Line of
that side of the saddle. This little pass is the entrauce of the
long valley of Bramdean, which is in the synclinal line of the
upheaval. The character of this valley is suflBciently well marked,
and it corresponds very curiously with that on the south side of
the Peasemarsh anticlinal line west of x\lton, on the road to
Lassam. For several miles the bottom of the Bramdean Valley
is covered by a thick bed of washed but angular flint. In its
progress westward it soon shows signs of moisture^ and a tribu-
tary of the Itchin rises in it and runs by Titchborne northward.
On the south side of the saddle runs the denudation of East
and West Meon, till it is closed in by the Beacon and Kilmeston
Downs. Bierly, Old Down, Kilmeston, Hinton Ampner, are
in the anticlinal line. From Hinton the saddle spreads wider, and
rises into greater importance ; and the northern synclinal line
falls back into the course of the Itchin, from Alresford to Win-
chester. The elevation increases now in a series of heights to
Easton High Down, where the saddle bursts suddenly open to
form the anticlinal denudation of Chilcomb, at the north-west
comer of which Winchester is situated, and where it is intersected
by the Itchin. St. Giles' and St. Catherine's Hills are anticlinal.
The same disposition might have been observed in the railway
cutting when it was fresh, west of the city. The upper chalk
becomes confluent again at CromwelPs Battery. From this point
the same high and saddle-shaped elevation is continued on in
Pitt and Farley Downs to the Test. In this part of its course
the line is accompanied on its northern side by a continuation
of the synclinal valley which carries the Itchin from Alresford*,
till it is lost at Kings Sombourne in the Valley of the Test.
Viewed from the country north of Winchester, all this line of
elevation gives the idea of a " chalk-bladder," especially as the
denudation of Chilcomb is not there visible. Crossing the Test,
the line of elevation seems to be taken up again by the Broughton
Hills at Bossington. But such a labyrinth of hill and dale
succeeds, owing to the deep denudations (many of them water-
courses) which occupy the countiy north-east of Salisbury, that
in the absence of sections I have not attempted to follow it
further. If it has not died out, and if it still continue its
usual westerly course, it points directly to, and perhaps unites
with, the Warminster anticlinal line. Where it becomes obscure
on the banks of the Test, it passes by the Wardour line, as that
line sinks under the tertiary beds at Timsbury near Michelmarsh.
* A stricter examination of this valley would probably prove it to be a
trough occupied by tertiary dejwsit. There is a patch of this kind on the
northern slope of Easton Down, and the agricultural character of the coun-
try of " the Worthies " (villages so called), and other parishes in the line of
the Itohin, favour the supposition.
the London and Hampshire Basins. 131
Anticlinal Line of Warminster . ' '*
This line enters soutli of Warminster, and heaves the gait and
upper greensand into a dome-like elevation denuded of its chalk,
except the remarkable outlier of Cley Hill, which rests on the
north side of it. The line then runs through Crockerton and
Sutton in a ridge of greensand, as far east as Cortington. At
this point the chalk boundaries approximate so much, that
little else is to be seen but the alluvium of the Wiley, which
takes its course in the line of the rent towards Salisbury. The
anticlinal disposition of the valley in its progress eastward is now
little more than presumptive ; but the presumption is of the
strongest kind. For although no decisive evidence is to be ob-
tained by section, the scarped aspect of the Downs on each side
of the valley, and its undeviating course a little to the south of
east, as far as Wishford, leave little doubt of its true character.
From this last -mentioned place the further course of this line
appears to be along the valley of Stoford Bottom, the river-course
taking off south towards the Nadder at Wilton*. Stoford
Bottom points directly toward the Broughton Hills, and the de-
clining line of the Greenhurst and Winchester denudations. But
I doubt much if a more minute search than I have been able to
make could produce satisfactoryproof of the inosculation of these
two lines, as before stated.
> Central Line of Elevation.
'^It remains now to say something of the central line of the
'5^eald and the Wolmar Valley.
; ' Although its broad expanse and superior importance are very
much enhanced by the reduplication into it of the synclinal
returns of the lateral lines, it no doubt brings with itself many
subordinate contortions of powerful agency f. Assisted by these,
although they no longer make their appearance on the surface,
it heaves the upper greensand between the synclinal valleys of
Bramdean and Alton into a broken but distinctly arched escarp-
ment, forming at least half the elevation of this western boun-
dary of the Wolmar Valley. These beds, and in some places the
chalk in the rear of them, afford many opportunities of observing
the tilting or sudden upward deflection of the truncated edges
* Another instance of drainage transversely to the hne of elevation.
t These minor flexures or puckerings, as they may be called, often run-
ning up into sharp anticlinal faults, are frequently met with in the green-
sand and Wealden districts. Of this kind is the flexure in Grey shot Down,
mentioned by Dr. Fitton, p. 147 of his memoir on the Strata below the
Chalk. The efi'ect of these flexures, like that of the greater anticUnal and
synclinal lines, is always to retard more or less the outcrop of the strata in
which they occur.
Hi Mr. ¥;4imKMtkonlhe AnticHnOl Line of
of Tipbeaved strata, wliich characterizes the entrance of a saddle,
or the extremity of an ('scar{)]nent of any notable elevation, where
the materials are not of the most finable nature. This dispo-
sition, with the gradual decline of force in the line itself, give a
strike to the beds that throws all the water, except a little sur-
face drainage from the chalk marl country, westward towards
Alresford and the Candover Valley. By this test, rather than
by any sections or surface arrangement, we are able to judge of
the prevailing dip.
The highest ])oints of elevation on the central line are in a
nameless ridge a little north-east of Var Down, and the high
grounds about East Fisted and Bentworth, overlooking the syn-
clinal line south of Alton. The importance of this line of elevation
is maintained even beyond the valley of transverse drainage in
which the three Candover villages are situate (the synclinal,
most probably, of the Alton range), and a long succession of
waving hills and high plains (of which the engravings of the
Ordnance Map give no adequate conception) cany it on between
the longitudinal valleys of the Itchin on the south, and the
Mitcheldever River on the north towards the Test, where its
presence is marked by the prominent features of the Stockbridge
Common Down and Longstock Hills. In the middle of this
course, about midway between Mitcheldever and Worthy Down,
it is cut through by the second tunnel of the Southampton Rail-
way at an elevation of 350 feet.
Westward of the Test, the progress and full effect of this line
of elevation becomes very obscure. The central hills which,
bound the remarkable transverse valley* that strikes across, and
forms with the Valley of the Wiltshire Avon the natural limits j
of Salisbury l^lains, lie in its course. Beacon Hill near Ames-
bury is the culminating point of these high grounds ; and in all
probability the strong central line of the Weald denudation is
continued onwards to assist in the support of the high platfonn
of Sahsbury Plains.
The arrangement of the Wiltshire country west of the natural
boundary of the Avon is much more simple than that which has
formed the principal subject of the foregoing paper. By the joint
operation of the Pewsey and Warminster lines, assisted by the faded
influence of those projected from the Weald, this country seems
to be maintained almost in horizontal equilibrium ; the superior
energy of the first mentioned giving to the whole a southerly
bearing, as indicated by the drainage.
The northern limb of the AVardour elevation tilting the south
* See in the Ordnance Map the valley in which the names of Colling-
boume, Kingston, North and South Tidworth, Newton Toney, and Winter-
boume-gunner occur.
'\x\ \J/}^ Lomlon and Hampshire Basins. 133
side of the-long chalk triangle bounded by the Wiley and Nadder,
and the southern limb of the Warminster anticlinal line doing
the same for the north side_, a synclinal trough is Joi'med iix
which I suspect there are relics of tertiary beds. iHt i\%^ ^\oiU9
Of the valleys themselves, a stricter examination w>uld pro*--
bably show that groups of fissures, puckerings, or subordinate
contortions, accompany the great central upheaval. That these
ph?enomena exist in greater force in the Weald Valley is most
probably owing to the great thickness of the Wealden formation.
If a section of the whole Wealden in this great exposure could
be obtained, it would exhibit the appearances we observe in somjB?
ancient schistose formations, and which obtain most probably in
argillaceous deposits of all ages (except the most recent) that
£t^rd the requisite thickness.
j .Of the epoch of these parallel lines. of disruption, and of thaii??
contemporaneity, I propose to treat when the phsenomena of
transverse fissure, drainage, lacerated escarpments, drift, and
other circumstances bearing on the subject of denudation come
to be. considered. Por the present it is sufficient to observe, that
the presence of tertiary beds of the Eocene period in great force
in some parts of the synclinal lines here reviewed, as, for instance,
in that of Salisbury, and the protrusion of the chalk through
them in the anticlinal, bespeak a date posterior to the sera of
those deposits. Of this, stronger evidence is yet to be adduced
from districts of similar structure not now imder review ; as, for
instance^ in the case of Portsdown and its synclinal line of the
Forest of Bere*. Indeed the proposition with which I started,,
the contemporaneity of the acts of elevation and denudation, ne-
cessarily implies an epoch posterior to all the regularly stratified
^^^ %^ districts. ^^j ,^^^^ ^^^^ y^md^^iHA ^o
jfl^ ni hii.F ^ ■ ■ ■ ■ — It- rrfnv tu-o'tvrnrmlff'). '-^jfi v; ■<n»d
*T!'%^aVy 'Already pointed out the obvious connexion of the loii^'^
line of the Greenhurst elevation wdth the escarpment of the
South Downs. And I may briefly call attention to the variable
force of these longitudinal fractures in the different parts *of >
their course. This is a matter of great importance as bearing.
oil the subject of transverse fissure. I have already spoken of
it in the Pewsey line. At one point it scarcely heaves the ter-^^
tiarybeds; at another it is carried on in the chalk; and in; ^''^
third it brings up the greensand on a level with the plastic clay.
In the Peasemarsh line we have seen that the Weald clay rises; '
allowing something for denudation, within a few feet of the chalk
marl at Alton, and a transverse fissure shows itself at the point
* See also Dr. Buckland's raemoii* on " Valleys of Elevation," Geol.
Trans., vol. n. 2nd series, p. 125. ^ ^^^^, ^,^.,, a
PhU. Mag. S. 4. Vol. 3. No. 9. Aug. 1851. ""'^ "-""fi-"™"''
184 Messrs. Galbraith and Haughton on the Apsidal Motion
of greatest tension at Guildford. Then in the Greenhurst line,
we see that where it is exhibited in greatest force, and its fea-
tures are best displayed almost in the axis of the Weald, it brings
up a long line of Weald-clay exposure from Greenhurst to Poyn-
ings. And at this part of its course two notable lines of trans-
verse fissure show themselves*. It heaves the gait in a saddle
at Waltham Park and the New Woods, and throws it back into
a synclinal at Hardham and Wiggonholt. At Bramdean it is a
chalk saddle, and at Winchester an open anticlinal valley of the
lower chalk. All this necessarily implies change of strike, and
of angle of inclination, which cannot take place beyond a certain
point without transverse fracture at the surface.
Having now cleared the way for a recognition of the strict
relations of the chalk dome of Hampshire and Wiltshire with
the Weald denudation, I hope to be able in my next communi-
cation to proceed to the subject of transverse fissure and the
phsenomena of drainage; recapitulating and carrying forward
my former disquisitions on the simultaneous and tumultuous
operations of upheaval and aqueous abrasion.
[To be continued.]
XXII. On the Apsidal Motion of a freely suspended Pendulum. By
Mei^ev. Joseph A. Galbraith and the Rev. Samuel Haughton.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
THE following investigation of the apsidal motion of a freely
suspended pendulum may be interesting to those of your
readers who have been engaged in verifying M. Foucault's ex-
perimental demonstration of the earth^s rotation. Some time
ago we undertook a course of experiments with that view ; and
although we arrived as a general result at a complete verification
of this remarkable experiment, we found considerable deviations
from the law of uniform angular motion. This led us to con-
sider the different disturbing forces, and if possible calculate
their effects, and thus eliminate them from our observations.
The motion of a pendulum may be compared with that of a
point moving in a plane round a centre of force, whose intensity
is directly as the distance, if the amplitude of vibration be inde-
finitely small; but if this be not the case, we must consider the
motion as taking place in a spherical ellipse and disturbed by a
small force directed from the centre, and varying as the third
power of the distance. As the influence of this disturbing force
* Viz. the river course of the Adur, and the Vale of Findon, the line of
the Worthing road.
' ^^Mm of a freely suspended Pendulum. 135
is very considerable in modifying the angular motion^ we send
you a complete investigation of its effects, requesting the favour
of its insertion in your valuable Journal.
We remain, Gentlemen,
Yours, &c.,
Joseph A. Galbraith,
Trinity College, Dublin, Samuel Haughton.
"July 14, 1851.
If a point P move
on the surface of a
sphere under the influ-
ence of a force F, which
acts in the tangent to
the great circle joining
P with a fixed point C
on the sphere, it will
describe a spherical el-
lipse roundC as centre;
if the force F act from
P towards C, and be
equal to g tan r sec^ r,
r being the angle at
the centre subtended by the arc CP, and g the accelerating force
of gravity*.
Let o) be the angle which CP makes with the axis, m the
angle which the semidiameterCM, conjugate to CP, subtends at
the centre, cJ the angle which CM makes with the axis : let also
a and h be the semiaxes major and minor, a and /3 the tangents
of the angles which they subtend at the centre, v the velocity of P,
and p the perpendicular arc, drawn from C to the tangent.
The following fundamental equations connect the motion of P
with the elements of the ellipse :
^ F=^tanr(l+ tan^r)
sin^ rd(o =^ \f g a^ dt
„- ^^«^ I
sin^ J
Let a small force R acting in the direction of the tangent to
CP at P, and outwards, at each instant disturb this elliptic motion^
we may still suppose the point P to move in an ellipse, the mag-
* This elegant theorem is due to Professor Graves, who communicated
it, together with some others connected with the motion of a point on a
sphere, to the Royal Irish Academy, January 24, 1842.
L2
(1.)
136 Messrs. Galbraith and Haugliton on the Apsidal Motion
nitude and dii*ection of whose axes ai-c continually varying. In
order to see how R produces these effects, suppose it resolved
into two components, 11 cos <^ and R sin <^ : the fonner, acting
along the tangent, either accelerates or retards the elliptic velocity;
whilst the latter, acting in the direction of the nomial, increases
or diminishes the angle <^ which the tangent makes with the
radius vector. These variations of <\> and v arc the immediate
effects of the disturbing force. The momentary variations of the
elements of the orbit depend on and may therefore be expressed
in teniis of them, so that by the application of the rules of the
integral calculus we can calculate the total variation of these
elements produced in a given time. '^' ""'"
To fix our ideas, suppose that P is in the fifst quadrant moving
from the apse A towards B, the effect of the tangential compo-
nent is to diminish the velocity in the ellipse, and that of the
normal component to increase the angle which the tangent makes
with the radius vector ; these variations are expressed as follows :
8.= -R cos </,<;< S,^=?^lEi*. . . (3.)
From these and equations (1.), we obtain
e, R cos <f) sin^ r«?a)
tv= J- ^
5., R sin^ <f> sin^ r</G)
«*= — -^^ —
It may be easily shown that
tan^ r sin 2ft) = tan^ m sin 2ft)' (4.)
Differentiate this, considering r constant, and eliminating W by
means of the relation
cosrtan<^= tan (ft) + G)'), (5.)
we obtain after some reduction
(a^— ^^)Sft)=sin2ft)'tanmStanm j
„ ,, . cosM<w + «') 5^^ I ' * ^^'^
+ cos2a)'tan27w ^ . - cos r6<j>
It may be easily proved from equations (1.) that
tan^m= — cos*^ (7.)
By means of this and equations (3.), we may eliminate B tan m and
B^ from (6.), and obtain, finally,
/ O /VJNC* R. 7 sin (ft)' — ft)) g /Q X
(a^—6^)B^= —tsmrdco ... ■; cosV, . . (8.)
^ '^ ^ (/ sm^a^-t-ft))
1
(3.)
\,v\J; lx\\\.v5.i"'/i
of a freelp'mp^ikdd'FMml^h:' ''^''^'^- 'Wn ^
in which -cr is the longitude of the apse measured from a fixed
line CU. JBoqcfwa ^enyiltj *j«)ii.t >/;>)/b : r ^amo
From this equation Sve "can oBtaih the motion of thte ap^e
which results from any radial disturbing force. In order to
apply it to the case of the elliptic vibration of a freely suspended
pendulum^ we suppose the pendulum to be a point moving on a
sphere, and urged towards its lowest point by a force tangential
to the surface = a sin r = — ^=^. We may therefore sup-
^ ^1+tanV ^ ^
pose that the motion takes place in a moveable spherical ellipse,
the disturbing force being radial, acting outwards from the centre,
n tan 7*
and equal to the difference of a tan r(l + tan^r) and ; =,
Q vl+tan^r
or to ~ ^ tan^ r, if the arc r be so small that all powers higher
than the third may be neglected. Substituting, therefore, for
— its value ^ tan^ r, and for cos^ r its approximate value unity,
we obtain
(a^-/3"^)8t^= gtan^r ^!^ "^. "^ da>. . . . (9.)
Let -i/r be an angle which satisfies the equations
acos-xlr;
i-, 2^06
tan r
acos'^/r;
cosa)= — —J lis 06
tan r
and therefore
smo);
cos ft)' = ^, ^fff
tanm
smft)'= -,
tanm
The last equation may be reduced to
E^= ^(l-{.2^^^^CO&2^|r + COB4^P^^d^|r. . (10.)
Let Act- be the total variation in the value of ct, while the angle
'yjrj which varies uniformly with the time, increases from cipher
to any finite value, we have by integrating equation (10.), and
substituting for u and /3 their approximate values j and-^, / being
the length of the pendulum, - ' '^ '' ' '"'■ " ''" '^ ^ '
Sab / , a^ + b^ . J. *1 -y . vA /i-, ^
188 On the Apsidal Motion of a freely suspended Pendulum.
As the last two terms of this expression are periodic, it is evident
that the progression of the apse during one complete vibration
of the pendulum is equal to
2^'-; (13.)
and that for any other period it is equal to
3 area described by central radius vector
4 (length of pendulum)^
(13.)
Let N be the number of degrees described in one hour, then
N =
135 X 1800
sT^
ah
(14.)
In this equation, g, /, a, b arc supposed to be expressed in feet.
The length of the pendulum used in our experiments was 35*4
feet; consequently, assuming gravity to be 32*19 feet, equation
(14.) will become for the pendulum used by us
N = 58-86x«6; (15.)
At the commencement of the experiments, « = 24 inches, ^= 0 ;
at the end of first hour, « = 13 inches, ^ = *134 inch.
The above figures are taken from ten experiments. Taking
the means of the semiaxes at the beginning and end of the hour,
and converting them into feet, we obtain fl6 = *009 square feet.
Hence
N=0°-53. (16.)
The progi*ession of the apse is consequently a little more than
half a degree in the first hour, and of course in the succeeding
hours should be considerably less in consequence of the small
value of the -product ab.
The obseiTcd deviation from 12° per hour (due to the rotation
of the earth, at the latitude of Dublin,) in the ten experiments is
contained in the following table : —
Right-handed motion.
Left-handed motion.
0-60
110
000
020
300
0-50
0-85
100
100
0-50
073 mean.
0-83 mean.
A comparison of the foregoing table with (16.) shows, that
although apsidal motion, of the kind here considered, accounts
M. R. Clausius on the Effect of Fluid Friction, ^c. 139
for the greater part of the observed deviation, it leaves about
three-tenths unaccounted for.
In the account of Mr. Bunt's experiments, contained in the
June Number of the Magazine, the observed deviation of the
apse for every tenth of an inch of semiaxis minor is given for
the pendulum used by him, which was 53 feet in length.
The observed deviation per tenth of inch semiaxis minor is
0*7 of a degree per hour.
On calculating (14.) for this pendulum, we find
N=21-46x«^' (17.)
Substituting in this expression the values 3*5 feet and "1 inch
for a and b (as stated in Mr. Bunt's communication), we obtain
N = 0°-626 (18.)
In this case the formula agrees more nearly with experiment.
In Mr. Bunt's communication in the last Number of the
Magazine, he states as the result of a new set of experiments,
that he found the correction for y^th of an inch ellipticity or
semiaxis minor, in a mean arc of about three feet, to be 0°*43
per hour. If we apply equation (17.) to this case, the result is"
0°'27, which differs much more from observation than Mr. Bunt's
former determination of the correction. From all this it would
appear, that other causes beside the apsidal motion here con-
sidered operate in disturbing the angular motion due to the
earth's rotation.
XXIII. Reply to a Note from Mr. W. Thomson on the Effect of
Fluid Friction, ^c, which appears in the June Number of the
Philosophical Magazine. By B. Clausius*.
THE above-mentioned note of Mr. Thomson refers to an in-
vestigation of mine on the deportment of steam during its
expansion under various circumstances f; and itisstatedinthe note,
that although I determine the work executed by the steam issuing
from a vessel, I have overlooked the mechanical effect, which con-
sists in the circumstance that a certain velocity must be imparted
to the steam, and which must be measured by the vis viva of
this motion, and that on this account my objections against his
reasoning are groundless. I believe, however, that I shall be able
fully to establish the views which I have expressed.
The above mechanical effect was both known to me and taken
into account ; and it is only with regard to the force which
causes the velocity of the steam at a small distance behind the
* Communicated by the Author.
t Pogg. Ann., vol. Ixxxii. p. 263 ; and Phil. Mag. 4th ser. vol. i. p. 398.
J49 M. R. GlausiiwVJ^^fy /ol^i-oif. (Thomson's Note
oritiioe to be much iess than in the orifice itself, and which there-
fore destroys the greater part of the said effect^ that om' views
differ from each othef. > mh }\ )Ci;;/:';H <fiir*i- xit >u :!-infn>M.;ii;
^Mr. Thomson explains this fact by i-feferring it to ^^fthe fric^
tion of the steam as it rushes through the orifice*/' In order
rightly to estimate the ])ossible influence exerted by this friction,
its action must in the first place be more clearly characterized.
This action does not consist in the loss of a velocity which the
steam had already attained, but in the circumstance that the
steam from the commencement never attains the velocity which
it would have done had friction been entirely absent. That ve-
locity, on the contrary, which it possesses in the orifice, and
which it loses further on, cannot be lost by friction. It is in no
way difficult to demonstrate the actual ground of this loss.
For this purpose we will retain the assumption, which, for the
sake of simplifying the matter, I have introduced in my investi-
gation, that the orifice is fui-nished with a widening neck (see
fig. vol. i. p. 403 1), and that up to the point where we suppose
the loss of velocity to have already taken place, th^ steam has
remained unmixed with atmospheric air.
What takes place in the neck may be represented somewhat
more clearly by means of an apparatus of the shape shown in
the figure. AB is a narrow tube f^> > > ^
fastened by means of a closely-fitting K
cork in the w ider tube CDEF, which ■ ■ ii i, mn,! .^-
latter is furnished with a siphon- ^ ^ I II I f ^ .h-cMiol
shaped tube partially filled with fluid,
by means of which the pressure
within may be observed. If we blow
through the narrow tube from A ^
towards B, so that the current of air can expand itself in the
wide tube before it reaches the open atmosphere, it is well known'
that the fluid immediately rises in the leg HG and sinks in HK.
In the vicinity of B a smaller pressure exists than that of the
atmosphere which acts at K and EF. It is this difference of
pressure which destroys so much of the original velocity of the
current of air on its way from B to EF, that the same quantity
of air which passed the orifice B during the imit of time can
during the unit of time fill the cross section EF. Let it be
imagined that a cmTcnt of steam from a high-pressure boiler
passes thi'ough the tube AB instead of the current of air, we
have then in the interior of the wide tube a retarding force,
* Phil. Mag., vol. xxxvii. p. 388.
t In this fiffiire, as already stated in the eiTata to Poggendoi*ff' s Annalen,
the surface GIII must be moved somewhat further from the orifice towards
the centre of the vessel.
-- '^^mthe'EffeS of Flvid Fricti(m},^^c.'^ J^ T41
which is evidfefltiy independent of the small friction whi^h'^&iifS
takes placeJ^i^^ •^■>"''^i'» ^''^^^ '^f"^' '^" ^"'^''f '«'>^'''-''r5 "iii' H/mi«oL a-joi
Inasmuch as the steam between B and E^ taes'the "^rfeMi*
part of the vis viva which it possessed at B, a quantity of heat
equal to that formerly expended in the production of this portion
of the vis viva must be again produced ; this portion of the vis
viva does not therefore at all enter into the calculation of the
entire quantity of heat consumed up to EF ; so that, without
overlooking it, I might leave it altogether unmentioned. ■ -'^"^^^
We must now consider those cases where the orifice is unfil'?-
nished with either a widening neck or a tube such as we have
described,, but where the orifice opens immediately into the atmo-
sphere. And here we will choose an extreme case; that is,
where the orifice is at a tube-end which opens into the free
atmosphere, and the issuing steam has not only the air in front
of it, but is encompassed by it on all sides. ^ i^jn (iikjmfe tu \iAiiH
The current immediately after its exit sets a'ktge ^^ss 6f to
in motion ; not only the air before the opening, but also that
behind the same. For inasmuch as a portion of the air before
the opening is carried forward with the steam, a decrease of den-
sity takes place in the immediate neighbourhood of the orifice,
and thus the air behind will be drawn forwards. This deport-
nient is not only deducible on theoretic principles, but for the
analogous case of a current of w^ater streaming into a reservoir of
the same fluid, it is proved experimentally by Venturi*, Von
Feilitzscht, and recently by Magnus J, so that I may assume it
as known. By this communication of motion the velocity must
naturally diminish in proportion as the mass moved increases ;
inasmuch as the quantity of motion, that is, the product of mass
and velocity, cannot become greater. But if this product remains
constant, the product of the mass and the square of the velocity,
that is, the vis viva, must become smaller ; and we must assume
that the vis viva which thus disappears again makes its appeatf-,
ance as heat. • ' "
All other possible cases with respect to the position of the
orifice, for example, that generally considered where the orifice
is situate in a wide plate, so that the steam after its issue has
the air all around it in front and the plate behind, lie between'
those two already considered. These form, so to say, the tWo
limits ; and by comparison with these we can alw^ays obtain an
approximate idea of the phsenomena under consideration. If it
be even granted that in all other cases the vis viva lost by the
* Recherches Experimentales sur le Principe de la Communication hatf-
rale du Mouvcment dans les Fluides. ^,.^ ',. j^
t Pogg. ^riw., vol. Ixiii. p. 216. . . V*rii>orft
:|: Pogg. Ann,, vol. Ixxx. p. 1 ; and Phil. Mag. 4th ser. vol.'il pi 1'. * '
142 Mr. J. J. Sylvester on a certain
steam is not so completely compensated by heat as in the first
case, I could notwithstanding affirm in my investigation, in
which it was not my design specially to discuss all incidental
circumstances, but which was directed to the establishment of a
principle, that the widening neck was not necessary to the va-
lidity of the reasoning.
I believe I have thus justified the views to which I have given
utterance.
With regard to the friction of the steam as it rushes through
the orifice, I have arrived at the conclusion that it is not neces-
sary to the explanation of the fact adduced by Mr. Thomson.
At the same time, its action, which, according to my view, would
be the reverse of that imagined by Mr. Thomson, and must be
introduced as a loss of lieat into the calculation, is by no means
excluded. In the case of a very small orifice, its influence may
be even considerable. If, however, in such cases as the issuing
of the steam through the safety-valve of a high-pressure engine
I have regarded it as playing a less important part than that
attributed to it by Mr. Thomson, this opinion will not be con-
sidered as groundless by those who understand the subject.
XXIV. On a certain Fundamental Theorem of Determinants,
By J. J. Sylvester, M.A., Dub,^
THE subjoined theorem, w^hich is one susceptible of great
extension and generalization, appears to me, and indeed
from use and acquaintance (it having been long in my posses-
sion) I know to be so important and fundamental, as to induce
me to extract it from a mass of memoranda on the same subject ;
and as an act of duty to my fellow -labourers in the theory of de-
terminants, more or less forestall time (the sure discoverer of
all truth) by placing it without further delay on record in the
pages of this Magazine. Its developments and applications
must be reserved for a more convenient occasion, when the in-
terest in the New Algebra (for such, truly, it is the office of the
theory of determinants to establish), and the number of its dis-
ciples in this country, shall have received its destined augmen-
tation. In a recent letter to me, M. Hermite well alludes to the
theoi-y of determinants as " That vast theory, transcendental in
point of difficulty, elementaiy in regard to its being the basis of
researches in the higher arithmetic and in analytical geometry."
The theorem is as follows : — Suppose that there are two de-
terminants of the ordinary kind, each expressed by a square
array of terms made up of n lines and n columns, so that in each
* Communicated by the Author.
Fundamental Theorem of Determinants. 143
square there are n^ terms. Now let n be broken up in any given
manner into two parts ^ and q^ so that p + qzsn. Let 1°, one
of the two given squares be divided in a given definite manner
into two parts, one containing p of the n given lines, and the
other part q of the same ; and 2°, let the other of the two given
squares be divided in every possible way into two parts, consisting
of q and p lines respectively, so that on tacking on the part con-
taining q lines of the second square to the part containing jo lines
of the first square, and the part containing p lines of the second
square to the part containing q of the first, we get back a new
couple of squares, each denoting a determinant difi'erent from
the two given determinants ; the number of such new couples
will evidently be
n.{n--l) . . . (n—p + l) ,
1.2 ... p '
and my theorem is, that the product of the given couple of deter-
minants is equal to the sum of the products [affected with the proper
algebraical sign) of each of the new couples formed as above de-
scribed. Analytically the theorem may be stated as follows.
Let
r«l «2 • • • «« I /«1 «2 • • • «n 1
\b, b,...bj L^i /e,...^J'
according to the notation heretofore employed by me in the pre-
ceding Numbers of this Magazine, denote any two common de-
terminants, each of the nth order, and let the numbers 6^, 6ci*»*Bn
be disjunctively equal to the numbers 1, 2, ... n andjo + g' = ?z;
then will
\b, b^...bnS i^, )e,.../3j
_^ r«i «2 ... «n "\^r«i «2 ••• ^«1
~\b^ bc^^.bp ^Op+i ffep+2'*»/3en} Xffdi ^e^^.^ep bp+i bp+2*''bn J
The general term under the sign of summation may be repre-
sented by aid of the disjunctive equations
(pi </>2...^^ = l, 2,...n
i^i irc^...ylrn=:l, 2,...n,
under the form of
(a^,.b^ X a^^.b^ x ... a^pbp) {a^^_^^.bp+, x a^^_^^.bp+2 x ...a^^ X)
><{^<Pp+v^9p^y^a^^^^.^9p^^x,.M^^.^eJ{a4,^.0g^Xa^,.l3e,x.^^^
1st. AVhen ^^ (j><.2 • - • 0,='«/^i '^2 • • • '^r, it will readily be
seen, that for given values of <)E)j, <j5)2 . . . <^r; the product of the
144 On a certain Fundamental Theorem of Detei'minants.
third and fourth factors becomes mbstantially identical with the
general term of the determinant - s
and consequently, making the system </>!, <^2 • • • </>p (^^I'i which is
the same thing, its equivalent yjr^, yjr^ . /. i^^) go through all its
jp values, we get back for the sum of the terms corresponding to
the equation 0i </>2 • • ' ^iB='»^i V^2 • • • "^py ^^ product of the
determinant 1/ f ^^ i)^l^nJfeoi
/«i «2 . . . «n\ and ^«' ^2 • • • ««\.
U, b, ...bj 1/9, fi^...pj
2nd. When we have not the equality above supposed between
the 0*8 and the -^^s, let
ffip-h^-^p+k and <j>p+,^^'^p~^'y
the con'csponding term included under the S will contain the
factor
Now leaving <^i, <A2 • • • </*p^ ^^^ '^p '^2' - ^'^p ^^^^^^^^^^t,!^^
may take a system of values ^/, ^2 • - - ^»^ ^^^ch that '^''*' > ^'^
and
and for all other values of q except p + rjj or p — f, ^'^ = 0^.
The corresponding new value of the general term so formed
by the substitution of the 0' for the 6 series, will be identical
with that of the term first spoken of, but will have the contrary
algebraical sign, because the 6' arrangement of the figures
1, 2, 3 . . .p is deducible by a single interchange from the 6 ar-
rangement of the same, the rule for the imposition of the alge-
braical sign plus or minus being understood to be, that the term
in which
^Op+i ^ep+2 . . '^9n; ^9, /902 . . . ^e^
enter into the symbolical forms of the respective derived couples
of determinants, has the same sign as, or the contrary sign to,
that in which
80 enter, according as an odd or an even number of interchanges
is required to transform the an-angement
Op+x 6p+2 • • • ^„> ^i ^2 • • • ^7,
Royal Astronomical Society. 145
into the arrangement ^ ^
[In applying the theorem thus analytically formulized^ it is of
course to be understood that^ under the sign ^, permutations
within the separate parts of a given arrangement,
^Ji i\R d-^ih ^P+^ ^p+^ ' ' • ^p+''' ^i ^2 • • • ^py ■^^
are- irikdmissible, the total number of terms so included being,
restricted to n.{n-l) . . . {n-p + l) -.
1.2 ... p J
I have therefore shown that all the terms arising from the
expansion of the products included under the sign of summation,
for which the disjunctive identity (^j ^2 • • • 0» = '^i '*/^2- • • '^p
does not exist, enter into the final sum in pairs, equal in quan-
tity and differing in sign, which consequently mutually destroy,
and that the terms for which the said identity does exist together
make up the sum ^ ^ ^^^,^, .bobubo . ohnoq-srioa siii
r«, «2 • • • «n "1 ^ r«l «2 • • • ««1 . ^')«t
which proves, upon first principles drawn direct from that notion
of polar dichotomy of permutation systems which rests at the
bottom of the whole theory of the subject, the fundamental,
and, as I believe, perfectly new theorem, which it is the object
of this communication to establish.
The theorem may be extended so as to become a theorem for
the expansion of the product of any number of determinants,
and adapted so as to take in that far more general class of func-
tions known to Mr. Cayley and myself under the new name of
commutants, of which determinants present only a particulaTj,
and that the most limited instance. to tiifli iisrvr
26 Lincoln's-Inn-Fields, ^'''>'Ry'>*||p
•' July 22, 1851. ^.^vf
)n^
XXV. Proceedings of Learned Societies.
ROYAL ASTRONOMICAL SOCIETY.
i; oiat 'iMiff^
April 11,#^N the Measurements of Azimuths on a Spheroid. By
1851. vJ Lieut. A. R. Clarke, R.E.
The author commences his paper with the following words : —
"It is generally assumed in geodetical calculations, that the sum
of the reciprocal azimuths of two stations on a spheroid is the same
as if the stations were on a sphere and had the same latitudes and
difference of longitude. This is based on Dalby's geometrical prgof,
146 Royal Astronomical Society.
that the difference between the two suras in question is very small
if the stations be equally elevated above the surface. It is not, how-
ever (nor can be geometrically), shown that this difference is not
greater than the probable error of observation, and therefore it may
be useful to find an expression for this small difference in terms of
the latitudes and longitudes of the stations, in order to see whether
it may be in any case greater than the probable errors of observation,
and large enough to be worth taking into account."
The author then investigates by accurate formulae of analytical
geometry, as applied to the co-ordinates of points which satisfy the
spheroidal equation, the expressions for the tangents of the angles
of reciprocal azimuths of two stations, and forms the accurate ex-
pression for the tangent of the sum of azimuths, and for the tangent
of the excess of this sum above the sum of corresponding spherical
azimuths. The expression is then cautiously reduced, and it is
found, at length, that the value of this excess is insensibly small ;
amounting only to 0"*000003 X m^n, where m is the number of de-
grees in the distances of the stations, and n the number of degrees
in the difference of latitude. Then the influence of difference of
heights is computed ; and it is shown that, though (in cases which
may arise in practice) it is greater than what has just been found,
yet that it also will be insensible.
At the close of the meeting, Mr. De Morgan made some remarks
upon the Gregorian Calendar, as an instrument for determining the
moon's phases with sufficient accuracy to settle the question of
moonlight. Having been led to examine it in this point of view, for
the purposes of a collection of almanacs which he is preparing for
publication (and which has since been published), he found that it
may be made to give the day of new moon or of full moon right in
three cases out of five, and with an error of only one day in almost
all the other cases ; the error of two days occurring only about once
in 120 results. In order to obtain this amount of accuracy, the rule
is : — Use the Gregorian epact to determine full moons, and that
epact increased by 1 to determine new moons ; both with the well,
known epact-table which appears in all extensive works or articles
on the calendar.
The reason of this rule is as follows : — Clavius constructed the
Gregorian Calendar expressly in such manner that the moon of his
calendar should be always, as well as it could be managed, one day
younger than the moon of the heavens ; the object being, that the
fourteenth day, by which Easter is determined, should follow the
day on which the Jews keep the Passover. And as this was done
with good success, it follows that one day added to the age of the
calendar moon at the beginning of the year (that is, to the Gregorian
epact), gives the same degree of success to the calendar, as a means
of determining the day of astronomical new moon.
If the chronological full moon had been correctly laid down, this
same addition of 1 would have been equally successful as to the full
Royal Astronomical Society. 147
moon. But the chronological full moon is on the fifteenth day of the
moon. Now, half a lunation being, on the average, 14| days, it
follows that, unless the mean new moon happen in the first quarter
of its day, the mean full moon is on the sixteenth day ; so that, in
the long run, the sixteenth is the proper day three times out of four.
Hence there is no occasion to increase the epact by 1 , in order to
determine the astronomical full moon ; which is as correctly deter-
mined as the calendar will do it, by applying the existing epact to the
existing hypothesis of the fifteenth day.
The preceding conclusions as to the probability of truth and error
were obtained from the nineteen years 1828-1846; the following
are the results for 1851, 1852, and 1853 :—
New Moon.
Jan. Feb. Mar. April. May. June. July. Aug. Sept. Oct. Nov. Dec.
1851 2 12+ 1-30+ 30 28+ 28 26 25 24 23 22
1852 21 19+21- 19 19 17 17 15 14- 13 12- 11
1853 10- 8 10- 8 8 6 6 4+ 3 2 1*30 30
Full Moon.
1851 17 16 17 16- 15 14- 13 12- 10 10 8 8
1852 6+5 6 5- 4- 3- 2- 1-30-29- 28- 27- 26
1853 25 23 25 23 23-21 21- 19- 18- 17 16- 15
Here are exhibited the days of new and full moon by the calendar :
when + or — follows the date, the real day is the day after or the
day before. And though in this period of three years tjie errors of
the full moon much exceed in number those of the new moon, there
is no such excess in the long run. The nineteen years 1828-1846
gave 140 cases of new moon true to the day, and 141 cases of full
moon.
May 9. — On the Vibration of a Free Pendulum in an Oval differ-
ing little from a Straight Line. By G. B. Airy, Esq., Astronomer
Royal.
•' In a paper communicated to this Society several years since,
and printed in the eleventh volume of their Memoirs, I investigated
the motion of a pendulum in the case in which it describes an oval
differing little from a circle ; and I showed that, if the investigation
is limited to the first power of ellipticity, and if a is the mean value
of the angle made by the pendulum rod with the vertical, then the
proportion of the time occupied in passing from one distant apse
to the next distant apse, to the mean time of a revolution, is the
proportion of 1 to the square root of 4 — 3 sin^ a. When a is
small, this proportion is nearly the same as the proportion of \ to
1 — ^ sin^ a ; or the time of moving from one distant apse to an-
other distant apse is equal to the time of half a revolution divided
by 1 — |- sin^ a. . This shows that the major axis of the oval is not
stationary, but that its line of apses progresses, and that, while the
ellipticity is small, the velocity of progress of the apses is sensibly
independent of the ellipticity, and may be assigned in finite terms
for any value of the mean inclination of the pendulum-rod.
il|48 Tloyal Astronomical Society.
" This theorem, however, fails totally when the minor axis of
the oval is small. It is then found that the velocity of progress of
the apses is nearly proportional to tlic minor axis. But, although
the movement of the j)endulum in this case may be defined to any
degree of accuracy by infinite series, it does not appear that it can
be expressed in finite terms of any ordinary function of the time.
This is to be expected, inasmuch as, when the problem is reduced
to its utmost state of simplicity by making the minor axis = 0, the
motion of the pendulum can be expressed only by series. The,
utmost, therefore, for which we can hope is, to determine the ge-
neral form of the curve and the rate of progress of its apses, on the
supposition that the minor axis is small, in series proceeding by
powers of the major axis. This might be so extended as to include
higher powers of the minor axis, if it were judged desirable.
" I have thought that an exhibition of the first steps of solution
(carried so far as to include the principal multiplier of the first
power of the minor axis) might be acceptable to this Society, not
purely as a mechanical problem, but more particularly because it
bears upon every astronomical or cosmical experiment in which the
movement of a pendulum is concerned. The difficulty of starting
a free pendulum so as to make it vibrate at first in a plane is ex-
tremely great ; and every experimenter ought to be prepared to
judge how much of the apparent torsion of its plane of vibration is
really a progression of apses due to its oval motion."
After a careful analysis of the problem, when the pendulum de-
scribes an extremely elongated ellipse, the Astronomer Royal ar-
rives at the following conclusion, which is the principal object of
his present investigation. If the length of the pendulum be a,
the semi-major axis of the ellipse described by the pendulum-bob
be b, and the semi-minor axis be c, then the line of the apses of the
ellipse will perform a complete revolution in the time of a complete
double vibration {i. e. the time of describing the ellipse) multiplied
by 5^.
^ Z be
" Thus If a pendulum, 52 feet long (which performs its double
vibration in 8 seconds), vibrates in an ellipse whose major axis is
52 inches and minor axis 6 inches, the line of apses will perform
a complete revolution /rem this cause in 30 hours nearly.
"If a common seconds pendulum (which performs its double
vibration in 2 seconds) vibrates in an ellipse whose major axis is
4 inches and minor axis -^ inch, the line of apses will perform a
complete revolution from this cause in 30 hours nearly.
" The direction of rotation of the line of apses is the same as the
direction of revolution in the ellipse.
'• It is worthy of remark, that the expression which is thus found
for the progression of the apse on the supposition that the minor
axis is much smaller than the major, will, if we make in it c very
nearly equal to b, correspond exactly to the formula cited in the
beginning of this paper, as found by an accurate investigation when
the ellipse approaches very near to a circle. It appears, therefore.
very probable that, while h is moderatel}'- small, the expression for
the progression of the apses is true for all values of c up to h.
" Although the principal object of this paper, as mentioned in
the beginning, was to point out how far an apparent rotation of
the plane of a pendulum's vibration may depend on causes which
would exist if the suspension were perfect, and if the point of
suspension were unmoved and the direction of gravity invariable,
still it may not be uninteresting to point out liow an effect, in some
respects similar, may be produced by a fault in the suspension. If
a pendulum be suspended by a wire passing through a hole in a
solid plate of metal, the orifice of that hole may be oval. If the
wire be part of a thicker rod tapering to the size of the wire, it
may taper unequally on different sides. In either case there will
be two planes of vibration, at right angles to each other, in which,
if the pendulum is vibrating, it will continue to vibrate, and in one
of which the time of vibration is greater, and in the other less, than
in any other plane ; and, the amplitude of vibration being very
small, the coniiplete motion may be found by compounding the vi-
brations corresponding to these two planes."
After investigating the effect of these causes of error, the Astro-
nomer Royal arrives at the following conclusion : — " It appears,
therefore, that the effect of faulty suspension may be sensibly eli-
minated between two experiments in which the azimuths of the
first vibration differ by 45° ; and it may be prudent, in making any
important experiment, thus to change the commencement-azimuth
in successive trials."
ROYAL SOCIETY.
[Continued from p. 80.]
June 19, 1851. — The Earl of Rosse, President, in the Chair.
The following papers were read : —
1. " Resoarehes in Symbolical Phj'sics. On the Translation of a
Directed Magnitude as Symbolised by a Product. The Principles
of Statics established symbolically." By the Rev, M. O'Brien, M.A.,
late Fellow of Caius College, Cambridge, and Professor of Natural
Philosophy and Astronomy in King's College, London. Communi-
cated by W. A. Miller, M.D., F.R,S. &c. Received April 10, 1851.
In this communication the author (starting from the well-known
theorem, that two sides of a triangle are equivalent to the third, when
direction, as well as magnitude, is taken into account) proposes an
elementary step in symbolization whicli consists in representing the
Translatio7i of a Directed Magnitude by a Product. Any magnitude
which is drawn or points in a particular direction, such as a force, a
velocity, a displacement, or any of those geometrical or physical
quantities which we exhibit on paper by arroics, he calls a directed
magnitude. By the translation of such a magnitude he means the
removal of it from one position in space to another tvitkout change
of direction.
U representing any directed magnitude and u any distance, the
Phil Mag. S. 4. Vol. 3. No. 9. Aug. 1851 . M
150 Royal Society*
translation of U to any parallel position in space, in such wise that
every point or element of U is caused to describe the distance m, is
termed the translation of U along u.
This translation consists generally of two distinct changes, one the
lateral shifting of the line of direction of U, and the other the motion
of U along its line of direction. The former is called the trans-
verse effectf the latter the longitudinal effect of the translation of U
along u.
Both these effects are shown to be products of U and u ; the
transverse effect is represented by wU, and the longitudinal by t^.U,
inserting a dot between the factors in the latter for the sake of
distinction.
The author then goes on to apply the principles established to the
proof of the Parallelogram of Forces ^ and the determination of the
effect of any set of forces on a rigid body. In doing this a remark-
able symbolization of the point of application, as well as the direc-
tion and magnitude of a force, is obtained, namely, that the expres-
sion (l+w)U represents a force U acting at a distance u from the
origin.
The principles of statics are deduced with remarkable facility
from the symbolical representation of the translation of a force along
a given distance.
2. " On an Air-Engine." By James Prescott Joule, F.R.S. «&c.
Received May 13, 1851.
The air-engine described in this paper consists of a pump by
which air is compressed into a heated receiver; and a cylinder,
through which the air passes again into the atmosphere. The dif-
ference between the work evolved by the cylinder and that absorbed
by the pump, constitutes the work evolved by the engine on the
whole. Two tables are given ; the first of which contains the pres-
sure, temperature and work absorbed, for various stages of the
compression of a given volume of air. The second table gives the
theoretical duty of the air-engine described, worked at various pres-
sures and temperatures. The temperature recommended to be
adopted in practice is as little below the red heat as possible, which
would involve the consumption of only about one-third the amount
of fuel consumed by the best steam-engines at present constructed.
?/. " Experiments made at York (Lat. 53° 58' N.) on the Deviation
of the Plane ot Vibration of a Pendulum from the meridional and
other vertical planes." By John Phillips, Esq., F.ll.S. Received
June 3, 1851.
The following is the author's account of these experiments.
The experiments, of which the following is a notice, were made
partly in the north-western Tower of the Minster, and partly in a room
of my residence. The latter attempts have only within a few days
acquired sufficient method and consistency to deserve reporting;
nor have the trials in the Minster been uniformly successful.
Mr. Thomas Cooke, an able optician of York, began the experi-
ments in the Minster. On the 30th of April, Mr. Gray and myself
observed the vibration of his pendulum, and found it so accurate as
Hd^diSdcietf/,
151
to justify the belief that it might not only indicate the direction, but
measure the angular value of the deviation of the pendulum plane
from the meridian. Computing this value for an hour to be 12°+,
we watched the result and found the arc passed over to be 13°. When
this observation was recorded, the pendulum was supposed to have
commenced its vibrations on a north and south line ; but that was
an error ; it was really swung from east to west.
In repeating this experiment, I have been more anxious to vary
the conditions, in a few arranged observations, than to accumulate
many simile results. We have observed in four azimuthal planes ;
one of our balls weighed eight pounds, the other twenty pounds :
one was an oblate, the other a prolate spheroid ; suspension was
effected at first by thoroughly softened catgut, afterwards by un-
twisted silk : we have compared small and large arcs, counted the
periodical times of vibration in three planes, noted the direction of
motion in the elliptic path of the pendulum, and estimated the
length of its minor axis. We have recorded results when no ellip-
ticity was remarked, and others in which its injurious effect was
manifest.
The pendulum performs one complete vibration in 8": from
which its length is deduced =52'+ feet. The chord of the arc of
vibration was usually taken at 14« feet, but was on some trials re-
duced to 7 feet. The graduated circle was 12 feet in diameter.
Great care was used in starting the ball, which did not rotate, but
presented the same face to the same quarter of the room, in what-
ever direction it was swung. The apartment was subject to air
currents; the floor from which the suspension was effected though
strong was large ; and there was no method of securing exact verti-
cality in the iron tube which carried the flexible catgut or silk.
From one or all of these causes it happened that ellipticity in the
path was noticed in almost every experiment, and it might exist in
all, and be unobserved if the minor axis did not exceed one-fourth
of an inch. After abandoning several trials in which the minor axis
was observed to increase rapidly, it was thought desirable to deter-
mine by experiment the effect of this elliptical swing on the angular
movement of the pendulum plane (see exp. 5).
J^irst Set. Deviation observed after given intervals of Time. Sail
a prolate spheroid, weighing eight pounds. Suspension softened
catgut.
Direction at origin.
Minutes
of time.
Deviation.
Chord at
origin.
Ellipticity.
Left.
Right.
Direction.
Minor axis.
1. E. andW....
2. N. andS. ...
60
45
1°3
ft.
14
14
None ob
None ob
served,
served.
Supposing no ellipticity to have existed in these experiments, the
results are —
Deviation in one hour from E. and W. line to right 13°*0
N. andS, „ 15°'3
M2
M
Eofjal Socie({/.
Second Set. Time observed when deination amounted to given
angles. Boll an oblate splieroidy weighing ^0 pounds. Suspen-
sion catgut.
Direction at orisin.
3. E.andW.|
4. N. and S. |
Minute* of
a. 15-38
b. 23-40
a. 150
*. 24-44
Demtion.
Left. Right.
Chord at
origin.
ft.
14
14
EUipticity.
Direction. Minor
None ob served.
None ob served.
t
Very mjinute.
Left. \ inch.
Neglecting the ellipticity in these experiments, the results are —
Deviation in one hour fiom
^•"""^^■•""^ "•J^-|}mea„12-2+.
^•'""'S-line «;}|0j„eanl2-0+.
For obvious reasons — the force maintaining the pendulum plane
being greatest in the beginning of the sweep (when the versed sine
of the arc is greatest), and the action of the elliptical swing then
least — the deviations in the first portions of the hour appear likely
to be more correct than the average of the whole hour.
The suspension was now changed from softened catgut to un-
twisted silk. From some disarrangement connected with this change
it happened that ellipticities were generated in every experiment,
and nearly all were abandoned as useless on account of the great
dimensions of the ellipse, which, growing as the arc of vibration
lessened, sometimes acquired a minor axis of above three inches.
Whatever the direction of the movement in the ellipse, its effect was
to rotate the pendulum plane in the same direction ; thus augment-
ing the deviation when the motion in the ellipse was to the right,
and diminishing it when it was to the left. In most azimuths the
elliptical motion was to the left. In the following example its effect
was followed for an hour to the right.
Direction
at origin.
Time.
Deviation.
Ellipse.
Time to
Successive
Accelera-
ting effect
of ellipse.
Left.
Right.
Direction.
Minor axis.
l°from
origin.
times of 3°.
f
m 8
0
7 3
11-23
14 28
16 56
19 58
24 16
27 38
;34 18
42 8
50 36
60 0
0
"li*
3
4i
5
6
8
9
12
15
18
26i*
1
1
t
7
1
1
none,
small.
inches.
none.
small
U
"2"
24
3
3+
3i
3i-
H
Not obs.
m. 8.
4 42].
3 47^
3 13
3 39 •
3 19^
3 2
3 4 J
2 51
2 48
2 48
m. 8,
14 6
11 23
8 35
7 40
6 50
7 50
8 50
m, s.
2 43
5 31
6 26
7 16
6 16
5 36
* Doubtful.
Royal Society. 153
When this experiment was recorded I had but slight expectation
of being able to apply a correction to results which were so largely
influenced by elliptical motion. While making it my attention was
mainly directed to the rather difficult task of correctly estimating the
minor axis of the ellipse (the most important of the elements for de-
termining its rotatory effect), and I only twice recorded the length
of the major axis, viz. at its origin, 14 feet, and, after the expiration
of rather more than half an hour, 7 feet.
The Astronomer Royal, to whom the experiment in the state here
set down was communicated, having kindly furnished me with an
appropriate formula, I have resumed the consideration of what
had appeared to me an unmanageable result. In this formula
( — x~~=n\ a is the length of the pendulum, h and c the semiaxes
of the ellipse, n the number of complete double vibrations of the
pendulum during the period of one rotation due to the ellipse. In
this case eight such vibrations being performed in one minute,
— — =minutes of time to one rotation of the ellipse.
Uc ^
The first 1^° of deviation were performed in 34"* 18^
or at the rate of 360° in 1029
or 17*15 hours,
the ellipse having its major axis varying from 14 to 7 feet, and its
minor axis from 0 to 3J inches. Taking b and c at arithmetical
means of their extreme values (in the case of the major axis this
mean is something too great, and in the case of the minor axis some-
thing too small), we have
^^' - 2547'
and
36c 3 X 5*25 X -0674
= ; whence
1029 2547 1726
360° are performed by the pendulum without ellipticity in 28*75 hours,
and 12°*5 in 1 hour.
We have thus from the Minster experiments, —
a. Uncorrected for Ellipse.
Exp. 2. 4. On N. and S. line l^l±il!i^= 13°-65 in one hour.
1. 3. On E. and W. line ^^'^ + ^^'^ = 12°*60.
2
/3. Corrected for Ellipse* ''\^^ ■
Exp. 5. On E. and W. line ..... 12-50.
i;v>kfm>(J ^
154
Royal Society.
JSxperiments in my House.
After many failures the apparatus became tolerably etficient, with
a pendulum of 68*7 inches, as deduced from the vibrations, 22*64 in
a minute. The balls used were a prolate spheroid weighing 6^ lbs.,
and a globe weighing only K^lb. I have obtained the best results
with the smaller weight. The suspensions have been silk, gutta
percha, and various contrivances of points and sockets of agate, brass
and steel. The best results have been obtained with gutta percha,
and sockets of agate and steel. The arc mostly used was from 16
to 20 inches. The experiments were seldom continued beyond half
an hour. By that time the chord of vibration was reduced to about
7 or 8 inches, and the errors of experiment were thought likely to be
too great, with so short a radius, if longer continued. The ball, in
whatever direction swung, presents the same face to the same side
of the room.
Direction at origin.
Time.
Deviation.
Chord.
Ellipse.
Left.
Right.
Direction.
Minor axifl.
(6). N.E. and S.W. . \
m
0
15
30
0
H
7
in.
18
No
None ob
None ob
ne.
served.
served.
1
(7). N.W. and S.E. |
0
45
18
No
None ob
ne.
served.
8
(8.). N.E. and S.W. •
0
15
30
18
No
None ob
Left.
ne.
served,
■jiyinch.
3
6
4
(9). N.W. and S.E. ■
9
15
30
18
No
None ob
Left.
ne.
served.
Minute.
3
5-55
From these experiments uncorrected for ellipse, we have, —
Exp. 6. 8. On N.E. and S.W.lineii±i?=13°-0inonehour.
7. 9. On N.W. and S.E. linei2^55±iLi? = io°-88.
I have since made a great variety of experiments with this apparatus,
which, notwithstanding the theoretical and practical disadvantage of
working with so short a pendulum, I hope to render accurately
effective, so that the angular deviation of the pendulum-plane may
become an ordinary and easy experiment. It should, however, be
tried in a glass case, and probably in vacuo.
4. " Note on instantaneous Photographic Imaeres." By H. F.
Talbot, Esq., F.R.S. &c.
Having recently met with a photographic process of great sensi-
bility, I was desirous of trying whether it were possible to obtain a
Royal Society, 155
truly instantaneous representation of an object in motion. The ex-
periment was conducted in the following manner. A printed paper
was fixed upon a circular disc, which was then made to revolve on
its axis as rapidly as possible. When it had attained its greatest
velocity, an electric battery, kindly placed at my disposal by Mr.
Faraday, was discharged in front of the disc, lighting it up with a
momentary flash. A camera containing a very sensitive plate of
glass had been placed in a suitable position, and on opening this
after the discharge, an image was found of a portion of the words
printed on the paper. They were perfectly well-defined and wholly
unaffected by the motion of the disc.
As I am not aware that this experiment has ever succeeded, or
indeed been tried, previously, I have thought it incumbent on me to
lay an early account of it before the Royal Society.
5. " The Human Iris ; its Structure and Physiology." By Bernard
E. Brodhurst, M.R.CS. Communicated by Thomas Bell, Esq.,
Sec.R.S. &c. Received May 22, 1851.
The author commences by stating that the iris is an active fibro-
cellular tissue, or that it may be considered to be a transition tissue
from the ordinary fibro-cellular to the organic muscular: that it is a
tissue differing from every other in the body; being possessed of
a motor power exceeding that of any other tissue, yet diff'ering in
construction and appearance of fibre from those other tissues, the
types of motion.
He remarks that the microscope shows that the fibres of the iris
differ essentially from muscular fibre, whether striped or of organic
life : they are pale, easily separable and readily torn ; but they
resemble in no essential particular muscular fibre ; indeed, the
effect of galvanism on the iris is totally opposed to that produced
on muscular fibre.
He observes that the nerves that pass to the iris are derived from
both motor, sensitive and negative nerves ; but voluntary motion is
not supplied, neither sensation. The motions of the iris are wholly
independent of the powers usually deemed motor ; they are influ-
enced primarily by the sympathetic system of nerves, through which
motion is accorded without sensation, motion without design.
In death, the author observes, the iris assumes a median state, the
pupil being neither dilated nor contracted. In health, it is contracted.
Duringsleepit is contracted. During the presence of disease, thepupil
is dilated, and so much dilated beyond its usual state, as the tonicity of
the vegetative system is removed, as the presenceof disease operates on
the nutritive system to diminish not only the power of nutrition, but,
in a like degree, tension of the visceral system ; nutrition and tension
being as cause and effect of the healthy operation of this basic system
of the animal oeconomy. And as it is not essential to the motions of
the iris, either to their performance or that they be understood, that
they partake of many of those peculiarities, the distinguishing fea-
tures of iiiuscular tissue, and as we find that this membrane is
obedient to those laws which are applicable to each organ under
immediate sympathetic influence, and opposed to those phenomena
1^! UifyuL Society .
whicJi result from spinal auU cerebral influence, it may be asserted
that the contractility of the iris is, primo loco, the motor power of
the sympathetic. For the iris is an irritable membrane with power
alone of involuntary motion and tension, its active condition agreeing
in tiiesG respects with vegetative life in general. And as animal
death may be said to ensue when deep sleep takes possession of the
senses, when those systems under spinal and cerebral influence are
rendered inactive, to be fitted for renewed exertion on waking, it
follows, that those organs which still remain active cannot be go-
verned on the same principle, but must necessarily be subject to the
sole remaining power, through which is accorded involuntary mo-
tion, motion which never tires, and tension its active condition.
. The fimbriated edge of the ciliary body floats loosely in the poste-
rior chamber around the lens, to produce, through the to and fro
motion of each process (their aggregate number representing a
circle), a current forwards or towards the iris. The force of this
current is in a ratio to the pupillary opening, being increased as this
b contracted, to produce, iu proportion to its contraction, convexity
of the iris. On the escape of the aqueous humour from the cham-
bers, these |)rocesses fall down to form a serrated border upon the
lens.
6. *' On the Automatic Temperature-compensation of the Force
Magnetometers." By C. Brooke, M.B., F.R.S.
After explaining the necessity of automatic temperature-compen-
sation in these instruments in order to give the highest degree of
accuracy to results deduced from the ordinates of the magnetic
curves, the author infers from a reference to the formula expressing
the conditions of equilibrium of the bifilar magnet, that the interval
between the lower extremity of the suspension lines will be most
advantageously submitted to some mechanical agency governed by
change of temperature.
The object in view has been attained by attaching the lower ends
of the suspension skein to the adjacent ends of two zinc tubes that
are clamped to a glass rod which is attached by its middle point to
the middle of the bar-magnet. When the temperature rises, the
ends of the skein will evidently be approximated to each other by a
quantity that is equal to the diflT?rencc of expansion of the lengths
of zinc and glass intervening between the clamps. The interval
between the clamps is to be approximately determined by calcula-
tion, and corrected by experiment, so that the ratio of the expansion
to the distance between the threads may be equal to the first term
of the temperature coeflScient.
In the balanced magnetometer the compensation is effected by
means of a small thermomettr attached to the magnet, the stem of
which is parallel to the axis of the bar. In this thermometer, the
size of the bulb, its distance from the freezing-point and length of
the scale, nmy be so proportioned to each other, that the second as
well as the first term of the temperature coefficient yf^^^l •^. Repre-
sented in the correction.
Royal Society. rS¥
'-7. "On the Reproduction of the Ascaris Mystax^ By Henry
Nelson, IVLD. Communicated v fey AUeft Thom80fi,'^:MlI>.rF;HiS.
Received May 22, 1851. ' ^ - rr.';.: s
The author commences with a brief anatomical description of the
Ascaris Mystax, found in the intestinal canal of the Domestic Cat ;
with more especial reference to the organs of generation in the two
sexes. Me traces tlie gradual formation of the semen ; originally
thrown off as seminal particles by the ctecal extremity of the tubular
testicle, the exterior of each solid particle enlarges to constitute a
cell, while the interior retains its consistency and forms a nucleus.
The cell then acquires a granular protecting envelope, and in this
state is introduced into the female. The solution of the protective
envelope and the great enlargement of the seminal cell follow, and
its nucleus is now seen to present a granular structure. The exter-
nal granules of the nucleus coalesce to form a membrane, at first
exactly resembling a watch-glass in shape, but by the contraction of
its margin ultimately forming a curved ca3cal tube. This is the
true spermatic particle or spermatozoon, and is set free by the
rupture of the seminal cell.
The generative apparatus of the female, commencing also in caical
extremities, is next treated of, and the author draws particular atten-
tion to a transparent, narrow contractile portion, the oviduct, inter-
vening between the ovary and uterus, as the part in which the ovule
encounters the spermatic particles, and is by tliem fecundated.
The caecal end of the ovary likewise throws off a solid particle,
which enlarging forms a germinal vesicle and spot. As the ger-
minal vesicle travels slowly down the tubular ovary, it acquires a
thick granular investment or yolk, secreted by the ovarian walls.
The ovules now present a flattened triangular shape, are placed side
by side, and form one solid mass. At the commencement of the
oviduct however they become detached, separated from each other,
and propelled singly along its interior. Here the gelatinous ovule
meets the tubular spermatic particles, and is surrounded on all sides
by them. They are at first seen to be merely applied against the
ovule, but by degrees the margin of the latter presents a rupture,
some of the vitelline grannies are displaced, and the spermatic par-
ticles become imbedded in the substance of the yolk itself.
While the penetration of the spermatic particles is going on, a
chorion, secreted by the oviduct, surrounds the ovule, forming a
spherical envelope, within which the germinal vesicle, the granular
yolk, and the imbedded spermatozoa, are enclosed. The spermatic
particles after penetration are seen to svvell, become transparent, and
ultimately to dissolve. The vitelline granules likewise either disap-
pear altogether, or are transformed into others of a different colour ;
and, lastly, the germinal vesicle is destroyed.
By tracing the changes of the ovule in unfecundated females of
the same species, the author finds the disappearance of the vitelline
granules to be dependent upon, while the formation of the chorion
is wholly independent of, the influence exertj^d ^^)y._the spermatic
particles on the ovule. ^ '
168 Intelligence and Miscellaneom Articles.
As soon as the vitelline granules and germinal vesicle have dis-
appeared, the whole interior of the chorion is filled with a clear fluid,
in which a few granules and the germinal spot are seen to remain.
By swelling up this constitutes the embryonic vesicle and spot. A
membrane separates from the interior of the chorion, and contracting
on the granules forms a spherical yolk, in the centre of which is the
embryonic vesicle. This is the perfect ovum. The subsequent di-
visions of the embryonic spot, vesicle and yolk are described ; the
author particularly pointing out the gyrations of the embryonic ve-
sicle immediately after division. As soon as the whole interior of
the e^g has been filled by the subdivisions of the yolk, the external
granules coalesce and form a continuous membrane internal to the
chorioi], which by gradual depression on one of its sides forms first
a fleshy cup, and then, as the membrane of its concavity touches that
of its convex surface, acquires the form of a ring. The ring divides
at some point of its circumference, the extremities become pointed,
and thus the young Ascaris receives its characteristic shape. The
author has frequently repeated his observations with a view to their
verification, and has employed the camera lucida to render the illus-
trative figures as accurate as possible.
XXVI. Intelligence and Miscellaneotis Articles.
PENDULUM EXPERIMENTS. BY THOMAS G. BUNT.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen, Bristol, July 24, 1851.
IN my last letter I gave the particulars of eleven experiments,
each performed with a single impulse of the pendulum> and of from
one to four hours' duration, in which the effect of ellipticity was dis-
regarded, and the mean arc of vibration for the most part less than
eighteen inches. This series of experiments I have since consider-
ably extended ; their average duration has been increased to nearly
twelve hours, and the initial arc reduced to about twelve inches. I
have already stated, that 1 find a reduction of the arc of vibration to
be accomj)anied by a diminution of the elliptic error ; one-tenth of
an inch of ellipticity causing an apsidal motion of 0°'7 per hour on
a mean arc of about seven feet, and only 0°'06 per hour on an arc
of eleven inches. I have also found, that, in the case of my pendulum,
the direction which the elliptic motion assumes in the first quadrant
of the circle is changed, in the second quadrant, into its opposite ;
and that it is almost invariably the same in the same part of the
circle. 'I'hus, between 15° and 70° the elliptic motion is retrograde ;
between 70° and 90° it almost disappears; from 90° to 150° it is
direct; and from 150° to 0° (or 180°) it again becomes nearly imper-
ceptible. Hence it appears, that if the pendulum be set in motion
with a very small arc, and left to vibrate for a period of fourteen or
fifteen hours, the elliptic errors will not only be everywhere incon-
siderable, but will also tend in a great measure to neutralize each
Intelligence and Miscellaneous Articles.
159
other. The advantage of using very small arcs in performing these
experiments is therefore sufficiently apparent.
In the following summary I have brought forward the total of
the eleven experiments given in my last letter, and added to them
thirty others which have been performed since. Four of these ex-
tend through a period of nearly twenty- four hours each.
Date.
Time.
Motion.
Number of
impulses.
Motion per
hour.
May 23 to June 7.
(brought forward).
June 14 to 17.
21 ...26.
26 ... 28.
June 30 to July 2.
July 2 to 7.
8... 9.
14... 16.
h m
|27 18-5
22 27-3
50 30-3
42 38-7
45 14-1
46 13-3
45 16-4
46 52-8
o
322-63
265-52
584-23
502-30
535-40
545-61
52305
557-97
111
5J
7
3
3
6
3
3
0
11-819
11-568
11-778
11-836
1 1-804 -<*
11-553
11-902
326 31-4
3836-71 = ll°-750
Theory.. .., ir-763
per hour.
A few days ago I received an obliging and most interesting letter
from the Rev. J, A. Galbraith, of Trinity College, Dublin, containing
a formula which he has discovered for calculating the apsidal motion
of the ellipses which a pendulum-ball describes. He says, " The value
you gave for the correction for each ^^th of an inch, in the June
Number, viz. 0°-7, agrees very well with it, the formula giving
0°'626." I had there stated, that the mean length of arc in those
experiments was '* about 7 feet," This rough estimation I after-
wards examined more carefully, and altered it long ago in my minute-
book into 7*4 feet. This gives a still better agreement, viz. 0°'66
formula, 0° 70 experiment. It does not agree so well (as Mr. Gal-
braith observes) with what I gave in the July Number, viz, 0°-43 per
hour for a mean arc of 3 feet, the formula giving only 0°'27. The
agreement with what I gave in the postscript to that letter is much
closer. 11°"60 per hour with -J-*19 inch ellipticity, and lP-39 per
hour with — *17 inch, gives 0°-058per hour for each J^^thof an inch
ellipticity ; the formula gives 0°-082 per hour. This important for-
mula I believe Mr, Galbraith intends communicating to your Maga-
zine, together with the calculations from which it is derived,
I am, Gentlemen,
Yours very respectfully,
Thomas G. Bunt.
PENDULUM EXPERIMENTS : FORMULA FOR CALCULATING THE
APSIDAL MOTION.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
The following formula may be of some use in observations like
those of Mr. Bunt on the motion of a pendulum.
166 IntelUf/ence and Mkcellaneom Articles.
If / be the length of the string, and a and b the apsidal distances
of the orbit described by the bay, then the apsidal angle
-\{
3_ ff6 27 oft(«2 4.^«)
8' l^ 256 /« J
and consequently the progression of the apse in one revolution
=,3a=x^*(i + |.-±*:>
i have been informed that a result, not differing much from this,
was given by the Astronomer Royal in a communication read a short
time since before the Astronomical Society. His paper, I believe,
has not yet been printed*.
I am. Gentlemen,
Your obedient Servant,
Trinity College, Cambridge, . A. Thackeb.
Julys, 1851.
ON ATMOSPHERIC SHADOVTS. BY PROFESSOR E. WARTMANN.
In a former Number of this Journal (June 1849), I described an
obsen'ation made at Nyon, by M. Thury, relative to a blue ray which
was seen before sunrise. In my opinion it was only an effect of
shadow. Analogous appearances are frequently observed at sunset,
when the atmosphere is charged with vapours or dust. But it is
easier to study them on heights, from the greater transparency of
the atmosphere and the less absorption which it exercises on the
light : the vicinity of large surfaces of water and of glaciers is par-
ticularly favourable to the development and the study of these optical
illusions. Every one has been able, in the morning, to follow at
considerable distances, in the humid and diaphanous air of the still
dark valleys, the course of the solar rays which border the surround-
ing crests.
A similar phsenomenon was manifested on the 3 1 st of last July,
toward three o'clock in the afternoon. I was on the signal-station of
the Dole, 1680 metres above the sea. The temperature was high.
A thin band of mist extended horizontally on the mass of Mont
Blanc and on the heights of that chain, at a mean height of 2400
metres. Only one cloud was perceptible in the sky, displaced slowly
by the south-east wind, and the image of which was distinctly pro-
jected on the slopes of the mountains of Faucigny. The whole space,
deprived of light by the interposition of this cloud, was depicted in
.transparent grayish- black with great clearness. Thus, the floating
vesicles of vapour, which, reflecting the rays of the sun, whitened
the blue of the sky, existed abundantly at 1!)00 metres above the
lake.
The same day, and at the same hour, I remarked much more cu-
rious shadows. On examining the strata of the air comprised
between my eye and the bottom of the lake, towards the east, I saw
four nearly pai*allel and equidistant bands, which, inclined toward
the sun, appeared to rise from the surface of the water to a height
of about 30 degrees. These sombre but indistinct bands had the
* An abstract of the paper will be found at p. 14/.— Ed.
Intelligence and Miscellaneous Articles. 161
same aspect as the obscure train produced by the cloud in a very
different region of the sky. They were distinguished from it how-
ever by tlieir size, which was much less ; each extended only a
degree in diameter. They were displaced in a perceptible manner
toward the south-east, in proportion as the sun declined toward the
horizon. They continued to be visible at least two hours, to my
comj)anions as to me. But we knew not to what cause to attribute
them. No perceptible obstacle in the immense panorama which we
commanded could produce shadows in their direction, and serve thus
to explain their presence.
The disposition of the atmospheric vapours in layers, may some-
times engender appearances which are confounded with those of
shadows. Long observation, and the variations of tint of the dark
bands, serve to avoid the error. An example of these false shadows
was presented to me two days after from the i:)lateau of the Barillette.
A few minutes before sunset, the ground of the sky assumed a very
marked gray colour, trenched upon by three horizontal bands tole-
rably long, of a more leaden colour, and which converged toward the
east. These bands, which would have presented an inverse distribu-
tion if they had been parts of the space destitute of light, became
gradually of a bright rose colour a few minutes after the twilight
came on. They were therefore only formed by a slight haze, sus-
pended at a great height in the atmosphere. — Bibliotheqiie Univer'
selle, September 1849.
ON THE ARTIFICIAL FORMATION OF CORUNDUM AND DIASPORE
BY THE WET METHOD. BY M. II. DE SENARMONT.
Not long since I laid before the Academy some experiments upon
the artificial production of several kinds of minerals l)y the wet me-
thod, under the combined influences of heat and great pressure ; and
I endeavoured to explain in this manner the formation of a peculiar
class of metalliferous deposits, principally formed from liquid agents.
Various minerals belong to another class of deposits where the
influence of gaseous agents appears to have predominated, where
water, which has played an important part in these phcenomena, must
have acted principally in the state of vapour. It must not, however,
be. expected that we should find a well-marked line of demarcation
between these two kinds of formations. Those substances which
mineralize thermal waters, frequently perhaps spring from depths
below the earth's surface in the form of volatile compounds; the liquid
and gaseous agents have been present in very variable proportions,
and the phsenomena musthave presented numerous intermediate stages
between their two extreme limits. It is moreover very difficult, even
in a chemical point of view, to imagine the action of water to be very
different when filling the same space in the state of a very strongly
heated liquid, or when saturating it in the state of vapour under enor-
mous pressure.
Numerous kinds of minerals must therefore be formed, almost in-
differently, under one or the other of these conditions.
162 Intelligence and Miscellaneous Articles.
If a hydrochloric solution of an oxide of the formula R^ O^ or
RO* be strongly heated, the acid, even when in excess, becomes free
in the solution, and the oxide is separated. The complete precipi-
tation moreover corresponds to a temperature which appears to de-
pend upon the state of dilution and the excess of acid present. In
this manner I have obtained the sesquioxides of iron and chromium
and titanic and stannic acids, in a pulverulent, amorphous and an-
hydrous state ; the latter alone presenting traces of crystallization.
Alumina, on the other hand, crystallizes, under favourable circum-
stances, in the anhydrous state in the form of corundum, and in the
hydrated state in the form of diaspore. The corundum obtained by
heating a dilute solution of hydrochlorate of alumina to a tempera-
ture which must exceed 662° F., is a white crystalline sand, which
scratches the emerald when pressed between two polished plates. It
is insoluble in acids, unalterable by heat, and under the microscope
is seen to be uniformly composed of minute, very distinct, almost
cubic rhombohedra ; they are usually perfect, and more rarely modi-
fied by truncatures tangential to the culminating angles, perfectly
transparent, and acting regularly upon polarized light. These rhom-
bohedric crystals are often accompanied by others, elongated, and in
thin layers, the lateral boundary of which is terminated by two pa-
rallel right lines, and towards each extremity by two obtuse symme-
trical beveled lines. Like corundum, they are insoluble in acids,
but when heated they become changed, and then some of the alu-
mina is dissolved by sulphuric acid ; which singular property M. Da-
mour detected in diaspore. In the natural state they are transpa-
rent, act strongly upon polarized light ; and their neutral lines are,
one parallel and the other perpendicular to their greatest length.
We may convince ourselves, by the aid of the camera lucida, that
the plane obtuse angle of the terminal slopes is nearly equal to 115
degrees. All these characters are those of diaspore, in layers parallel
to the plane of cleavage, and there can be no doubt that the prismatic
crystals belong to this species.
It is worthy of remark, that the natural diaspore almost always
accompanies corundum in its various repositories ; and this associa-
tion is also one of the geological proofs which every means of arti-
ficial production aiming at imitating the processes of nature must
satisfy.
The oxides of iron, chromium, tin and of titanium, are too rapidly
precipitated to assume a regular structure. This separation may be
retarded by rendering the liquid very acid ; but then it strongly cor-
rodes the glass. — Comptes Rendus, May 19, 1851.
THE THEORY OF SOUND.
A further communication on this subject has been addressed to us
by Professor Potter, from which we extract the material portions,
and with which we shall consider the controversy in this Magazine
as closed, all parties having had the fullest latitude in bringing their
views fairly before the public. Mr. Potter observes,
Meteorological Observations, 163
** The expressions used by Poisson in his solution of the problem
are
p =gmh( l+s + ff)
and
(T=fis;
therefore we have
p=gmh(l + (l-^f3)s).
" I have shown in the Philosophical Magazine for April, page 318,
and June, page 476, that no reason has been given which proves
that /3 is finite in value.
" Mr. Rankine asserts in the last Magazine, that I have stated this
of (l-fi^). and then proceeds to argue upon it. He has evidently
considered the arguments applied with respect to the value of j3 to
have been applied with respect to that of 1 +/3."
" In his concluding remark he says, with respect to the popular
view of Laplace's proposal to account for the discrepancy shown by
the Newtonian formula, ' My remarks were intended to apply to
waves, which, having been originally symmetrical, become unsym-
metrical as they advance, like those on the surface of shallow water,' "
which Mr. Potter considers inconsistent with Mr. Rankine's state-
ment in the Magazine for March, page 266, where he says, " as every
wave must consist of a comjjressed and a dilated part, the different
parts of a wave would travel with different velocities, the compression
and dilatation existing from the beginning."
METEOROLOGICAL OBSERVATIONS FOR JUNE 1851*.
Chiswick. — June 1, 2. Very fine. 3. Fine: cloudy. 4. Cloudy: fine : clear:
cold at night. 5. Densely clouded : rain. 6. Boisterous : cloudy and fine.
7. Densely overcast : slight rain. 8, Boisterous. 9. Drizzly. 10. Uniformly
overcast : rain. 11. Very fine. 12. Densely clouded : showers. 13. Overcast:
densely clouded : rain. 14. Fine : heavy clouds : slight rain. 15. Cloudy : rain.
16. Boisterous. 17. Cloudy and fine. 18. Very fine : boisterous. 19 — 21.
Very fine. 22. Cloudy : clear. 23. Fine : clear and cold at night. 24, 25. Very
fine. 26, 27. Hot and very dry. 28, 29. Hot and dry. 30. Slightly clouded.
Mean temperature of the month 59°'21
Mean temperature of June 1850 59*26
Mean temperature of June for the last twenty-five years . 60 '72
Average amount of rain in June 1*80 inch.
Boston. — June 1, 2. Fine. 3. Fine: rain p.m. 4. Fine. 5 — 7. Cloudy:
rain A.M. and P.M. 8. Cloudy. 9, 10. Cloudy : rain p.m. 11. Fine. 12. Cloudy:
rain A.M. 13. Cloudy : rain p.m. 14. Fine. 15. Fine : rain p.m. 16. Cloudy:
stormy. 17. Fine: stormy. 18 — 20. Cloudy. 21. Fine: thunder and light-
ning, with rain and hail p.m. 22 — 25. Cloudy. 26 — 30. Fine.
Sandwich Manse, Orkney. — June 1 . Bright : showers. 2. Bright ; rain. 3.
Clear. 4. Showers: fine. 5. Fine: showers. 6. Fine: clear. 7. Bright:
fine. 8. Rain : hazy. 9. Showers : clear. 10. Showers : damp. 11. Showers.
12. Clear: fine. 13. Bright: fine. 14. Fine: hazy. 15. Rain. 16. Rain:
drizzle. 17. Showers: clear. 18. Fine: drizzle. 19. Showers: hazy. 20. Fine:
clear. 21. Bright; showers. 22. Cloudy. 23. Bright : drizzle. 24. Cloudy.
25. Bright : damp. 26. Cloudy : clear. 27, 28. Clear : fine. 29. 30. Hot :
fine.
* The observations from the Kev. W. Dunbar of Applegarth Manse have
not reached us.
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THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
SEPTEMBER 1851.
XXVII. On Diamagnetism and Magnecrystallic Action,
Bij John Tyndall, PLD."^
§ 1. On Diamagnetism.
FIVE years ago Faraday established the existence of the force
called diamagnetisnij and from that time to the present some
of the first minds in Germany, France and England have been de-
voted to the investigation of this subject. One of the most import-
ant aspects of the inquiry is the relation which subsists between
magnetism and diamagnetism. Are the laws which govern both
forces identical ? Will the mathematical expression of the attrac-
tion in the one case be converted into the expression of the re-
pulsion in the other by a change of sign from positive to negative ?
The conclusions arrived at by Pliicker in this field of inquiry
are exceedingly remarkable and deserving of attention. His
first paper, " On the relation of Magnetism and Diamagnetism/'
is dated from Bonn, September 8, 1847, and will be found in
Poggendorff^s Annalen and in Taylor's Scientific Memoirs. He
sets out with the question, '' Is it possible, by mixing a mag-
netic substance with a diamagnetic, so to balance the opposing
forces that an indifferent body will be the result ?'' This ques-
tion he answers in the negative. " The experiments,' ' he writes,
^^ which I am about to describe, render it necessary that eveiy
thought of the kind should be abandoned.'^
One of these experiments will serve as a type of the whole,
and will show the foundation on which the negative reply of
M. Pliicker rests. A piece of cherry-tree bark, 15 millims. long
and 7 millims. wide, was suspended freely between the two move-
able poles of an electro-magnet ; on bringing the points of the
* Communicated by the Author, having been read before tlie Physical
Section at the Meeting of the British Association at Ipswich, July 2, 1851,
Phil Mag. S, 4. Vol. 2. No. 10. Sept. 1851. N
166 Dr. Tyndall on Diamagnetism and Magnecrystallic Action*
poles so near each other that the bark had barely room to swing
between them, it set itself, like a diamagnetic substance, with its
length perpendicular to the line which united the two poles. On
removing the poles to a distance, or on raising the bark to a
certain height above them, it turned round and set its length
parallel to the line joining the poles. As is usual, we shall call
the former position the equatorial, and the latter position the
aonal. Thus when the poles were near, diamagnetism was pre-
dominant, and caused the mass to set equatorial ; when the poles
were distant, magnetism, according to the notion of M. Pliicker,
was predominant, and caused the mass to set axial. From this
he concludes, " That in the cherry-tree bark two distinct forces
are perpetually active ; and that one of them, the magnetic, decreases
more slowly with the distance than the other, the diamagnetic.
In a later memoir* this predominance of the diamagnetic force
at a short distance is affirmed by M. Pliicker to be due to the
more general law, that when a magnet operates upon a substance
made up of magnetic and diamagnetic constituents, if the power
of the magnet be increased, the diamagnetism of the substance
increases in a much quicker ratio than the magnetism ; so that
without altering the distance between it and the magnet, the
same substance might at one time be attracted and at another
time repelled by merely vaiying the strength of the exciting
current.
This assertion is supported by a number of experiments, in
which a watch-glass containing mercury was suspended from one
end of a balance. The watch-glass was magnetic, the mercury
was diamagnetic. When the glass was suspended at a height of
3-5 millims. above the pole of the magnet, and the latter was
excited by a battery of four cells, an attraction of one mille-
gramme was obsei*ved ; when the magnet was excited by eight
cells, the attraction passed over into a repulsion of the same
amount.
It is to be regretted that M. Pliicker, instead of giving us the
actual strength of the exciting cun'ent, has thought proper to
mention merely the number of cells employed. From this we
can get no definite notion as to the amount of magnetic force
evolved in the respective cases. It depends of course upon the
nature of the circuit whether the current increases with the
number of cells or not. If the exterior resistance be small, an
advance from four to eight cells will make very little difference ;
if the said resistance be a vanishing quantity, one cell is as good
as a million t.
* Poggendorff' 8 Annalen, vol. Ixxv. p. 413.
t The usual arrangement of the cells is here assumed ; that is, where
the negative component of one cell is connected with the positive compo-
nent of the next.
Dr. Tyndall on Diamagnetism and Magnecrystallic Action, 167
During an investigation on the magneto-optic properties of
crystals*, which I had the pleasure of conducting in connexion
with Professor Knoblauch, I had repeated opportunities of ob-
serving phsenomena exactly similar to those observed by M.
Pliicker with the cherry-tree bark ; but a close study of the sub-
ject convinced me that the explanation of these phsenomena by
no means necessitated the hypothesis of two forces acting in the
manner described. Experiment further convinced me, that a
more delicate apparatus than the balance used by M. Pliicker
would be better suited to the measurement of such feeble mani-
festations of force.
An exact acquaintance with electro-magnetic attractions ap-
peared to be a necessary discipline for the successful investiga-
tion of diamagnetic phsenomena; and pursuing this idea, an
inquiry was commenced last November into the action of an
electro-magnet upon masses of soft iron. I was finally led to
devote my entire attention to the attraction of soft iron spheres,
and the results obtained were so remarkable as to induce me to
devote a special memoir to them alonef.
In this investigation it was proved, that a ball of soft iron>
separated by a small fixed distance from the pole of an electro-
magnet, was attracted with a force exactly proportional to the
square of the exciting current. Now this attraction is in each
case the product of two factors, one of which represents the mag-
netism of the magnet, and the other the magnetism of the ball.
For example, if the magnetism of the magnet of any given mo-
ment be represented by the number 4, and that of the ball by 3,
the attraction, which is a consequence of their reciprocal action,
is represented by the number 12. If we now suppose the mag-
netism of the magnet to be doubled by a current of double
strength, the ball will have its magnetism also doubled, and the
attraction resulting will be expressed by the number 48. Thus
we see that a doubling of the power of the magnet causes four
times the attraction ; and that while the attraction increases as
the square of the current, the magnetism of the ball increases in
the simple ratio of the current itself
Our way to a comparison of magnetism and diamagnetism is
thus cleared. We know the law according to which the magnet-
ism of an iron ball increases, and we have simply to ascertain
whether the diamagnetism of a bismuth ball follows the same
law. For thie investigation of this question I constructed the
following apparatus.
In two opposite sides of a square wooden box two circular
holes were sawed about four inches in diameter. The holes were
* Philosophical Magazine, July 1850.
t Phil. Mag., April 1851. Poggendorff's Annalen, May 1851.
N2
168 Dr. Tyiidall on Diamagnelism and Magnea-ystallic Action,
diagonally opposite to each other, and through each a helix of
copper wire was introduced and wedged fast. Each helix con-
tained a core of soft iron, which was pushed so far forward that
a line parallel to the sides of the box through which the helices
entered, and bisecting the other two sides, was a quai-ter of an
inch distant from the interior end of each core. The distance
between the two interior ends was six inches, and in this space
a little beam of light wood was suspended. At the ends of the
beam two spoon-shaped hollows were worked out, in which a
pair of small balls could be conveniently laid. The beam rested
in a paper loop, which was attached to one end of a fine silver
wire. The wire passed upward through a glass tube nearly
three feet in length, and was connected at the top with a torsion
head. The tube was made fast in a stout j)late of glass, which
was laid upon the box like a lid, and thus protected the beam
from currents of air. A floor of Bristol board was fixed a little
below the level of the axes of the cores, the ' board ' being so cut
as to fit close to the helices : the two comers of the floor adja-
cent to the respective cores and diagonally opposite to each other
bore each a graduated quadrant. When the instrument was to
be used, two balls of the substance to be experimented with were
placed upon the spoon-shaped hollows of the beam and there
exactly balanced. The balance was established by pushing the
beam a little in the required direction through the paper loop in
which it loosely rested ; and to accomplish this with greater ease,
two square pieces were sawed out of the sides of the box, and two
others were exactly fitted into the space thus opened; these
pieces could be taken out at pleasure, and the hand introduced
without raising the lid. The torsion-head was arranged so that
when the beam bearing the balls came to rest, a thin glass fibre
attached to the beam pointed to zero on the graduated quadrant
underneath, while the index of the head pointed also to the zero
of the graduated circle above. A current was sent through the
helices in such a direction, that the poles which operated on the
balls were of opposite names — the balls were repelled. Pre-
serving the current constant, the index above was turned in a
direction opposed to the repulsion until the beam stood again at
zero. The torsion necessary to effect this is evidently the ex-
pression of the repulsive force exeited at this particular distance.
Fig. 1. represents the appearance of the beam and helices
when looked down upon through the glass lid. Fig. 2. repre-
sents the beam and balls attached to the suspending wire.
When the fibre pointed to zero, an interval of about y^th of an
inch usually separated the diamagnetic balls from the core ends.;
The intensity of the current was measured by a galvanometer of
tangents, and was varied by means of a rheostat. Always before
Dr. Tyndall on Diamagnetism and Magnecrystallic Action. 169
commencing a series of experiments,, the little beam was proved.
With very strong currents it was found to be slightly diamag-
Ficf.2.
neticj but so feeble^ that its action, even supposing it not to
follow the same law of increase as the ball (which, however, it
certainly does), could cause no measurable disturbance.
I neglected no precaution to secure the perfect purity of the
substances examined. The entire investigation was conducted
in the private cabinet of Professor Magnus in Berlin ; and at the
same time a gentleman. Dr. Schneider, happened to be engaged
in the Professor^s laboratory in determining the chemical equiva-
lent of bismuth. From him I obtained a portion of this sub-
stance prepared in the following way : — The metal of commerce
was dissolved in nitric acid and precipitated with distilled water ;
whatever iron was present remained in the solution. The preci-
pitate was filtered, washed for six days successively, and after-
wards reduced by means of black flux. The metal thus obtained
w^as again melted in a Hessian crucible, and saltpetre was gra-
dually added, the mass at the same time being briskly stirred.
Every remaining trace of foreign ingredient was thus oxidized
and rose to the surface, from which it was carefully skimmed.
The metal thus purified was cast into a bullet-mould, the interior
surface of which was coated by a thin layer of oil ; the outer sur-
face of each bullet was carefully scraped away with glass, the
ball was then scoured with sea-sand, and finally boiled in hydro-
chloric acid. I have already described the method of experiment.
The bismuth balls were placed upon the hollows of the beam,
and their repulsions by various currents determined in the manner
indicated. The series of repulsions thus obtained are exactly
170 Dr. Tjmdall on Diamagnetis^m and Magnecrystallic Action,
analogous to the series of attractions in the case of the hall of
soft iron. The square roots of thpse attractions give a series of
numbers exactly proportional to the currents employed; the
question therefore is, — *' Will the square roots of the repulsions
give a similar series, or will they not ? **
Calling the angle which the needle of the galvanometer, under
the influence of the current, makes with the magnetic meridian
«, then if the attraction of the iron ball and the repulsion of the
bismuth ball follow one ancl the same law, we shall have the
equation
V'T=wtana,
where T represents thq torsipn necessary \o bring the beam back
to zero, and n is a constant depending on the nature of the ex-
periment. The following tables will show the fulfilment or non-
fulfilment of this equatjpn.
Table I. — Bismuth spheres, 8 millims. diameter.
/i=ll-7.
«.
tana.
T.
VT.
n tan «.
10
0176
5
2-23
206
20
0-364
16-3
4-04
4-25
30
0-577
42-3
6-50
6-74
35
0-700
64
8
8-19
40
0-839
100
10
9-81
45
1-000
136
11-66
11-7
50
1192
195
13-96
13-95
A second series was made with a pair of spheres of the bis-
muth of commerce with the same result.
Sulphur is also a diamagnetic substance, but much weaker in
this respect than bismuth. The next series of experiments were
made with two balls of this substance.
Table II. —Sulphur spheres, 8 millims. diameter.
»=3-3.
«.
tan«.
T.
a/T.
n tan «.
2^ 6
30 45
41 20
54 0
0-364
0-595
0-880
1-376
1-2
3-0
80
210
110
1-73
2-83
4-58
1-20
1-96
2-90
4-54
A pair of sulphur balls were nej^t taken of ^early twice the
diameter of the preceding.
Dr. Tyndall on Diamagnetism and Magnecrystallic Action. 17i
Table III. — Sulphur spheres, 13*4 millims. diameter.
u.
tana.
T.
^/T.
n tan ».
20 d
0-364
6-2
2-45
2-44
30 45
0-595
15-0
3-87
3-98
41 20
0-880
34-5
5-90
5-89
54 0
1-376
89-0
9-43
9-22
The sulphur from which these balls were made was the mate-
rial of commerce. After the experiments one of the balls was
placed in a clean porcelain crucible and brought over the flame
of a spirit-lamp ; the sulphur melted, ignited, and disappeared
in sulphurous acid vapour. A portion of solid substance re-
mained in the crucible unvolatilized. This was dissolved in hy-
drochloric acid, and ferrocyanide of potassium was added; the
solution turned immediately blue ; iron was present. The other
ball was submitted to a similar examination, and with the same
result ; both balls contained a slight admixture of iron.
In this case, therefore, the two opposing forces, magnetism
and diamagnetism, were present, but we find the equation
>v/T=?^ tan a fulfilled notwithstanding. Did one of the forces
increase with the ascending magnetic power more quickly than
the other, this result would be impossible.
Flowers of sulphur were next tried, but found to contain a
considerable quantity of iron. I have to thank Prof. Magnus
for a portion of a native crystal of the substance obtained in Si-
cily, which upon trial was found to be perfectly pure. From
this, two small pellets were formed and laid upon the torsion-
balance ; they gave the following results : —
Table IV. — Spheres of Native Sulphur.
/i=2-65.
K.
tana.
T.
Vt.
ntana.
20
0-364
0-9
095
0-96
30
0-577
2-5
1-58
1-53
40
0-839
5-0
2-24
222
45
1000
70
2-64
2-65
50
1-192
100
3-16
3-16
The next substajice chosen was calcareous spar. The comers
of the crystalline rhomb were first filed away, and the mass thus
rendered tolerably round ; it was then placed between two pieces
of soft sandstone, in each of which a hollow, like the cavity of
a bullet-mould, had been worked out. By turning the stones,
173 Dr. Tyndall on Diamagnetism and MagneoystaUic Action,
one right and the other left, and addinj; a little water, and a
little patience, the crystal was at length reduced to a sj)hcrical
form. The ball was then washed, and its surface carefully
cleansed in dilute hydi-ochloric acid. The first pair of balls were
from the neighbourhood of Clitheroe in Jjancashire.
Table V. — Spheres of Calcareous Spar, 9*2 millims. diameter.
m.
tan«.
T.
Vt.
n tan «.
20
0364
1-8
,34
1-34
25
0466
3-0
1-73
1-72
30
0-577
45
212
213
35
0-700
70
2G4
2-59
40
0-839
97
311
310
45
1-000
140
3-74
3-70
The spar from which these balls were taken was not quite
transparent; to ascertain whether its dullness was due to the
presence of iron, a ciystal which weighed about 3 grammes was
dissolved in hydrochloric acid; the solution was exposed in a
flat basin to the air, and the iron, if present, suffered to oxidize ;
fen'ocyanide of potassium was added, but not the slightest tinge
indicative of iron was perceptible.
A series of experiments were next made with a pair of spheres
of calcareous spar from Andreasberg in the Harz Mountains.
Table VI. — Spheres of Calcareous Spar, 10'8 millims. diameter.
w=5.
«.
tan«.
T.
Vt.
n tan «.
20-0
0-364
2-8
1-68
1-82
250
0-466
50
2 21
2-33
300
0-577
80
283
2-83
350
0-700
112
335
3-50
1 37-30
0-767
14-5
3-81
3-83
57-0
1-540
60-0
775
7-70
The spar from which these balls were taken was perfectly
transparent. After the experiment, the balls were partially dis-
solved in hydrochloric acid, and the solution tested for iron, as
in the former case — no trace of iron was present.
The conclusion to be drawn from all these experiments, and
from many others which I forbear citing, is, that the law of
increase for a diamagnetic body is exactly the same as for a
magnetic — a rcsillt in*econcilable with that arrived at by M.
riucker. I had proceeded further with this investigation than
Dr. Tyndall on Diamagnetism and Magnect^ystallic Action, 1 73
the point which I have ah*eady reached, when I learned that a
memoir on diamagnetism by M. Edmond Becqnerel had ap-
peared in the May number of the Annates de Chimie et de Phy-
sique. In this memoir the views of PlUcker are also contro-
verted, and a number of experiments are adduced to prove the
identity of the laws which regulate magnetic attraction and dia-
niagnetic repulsion. The argument employed by M. Becquerel
is the same in principle as that furnished by the foregoing ex-
periments. He proves that the repulsion of bars of bismuth,
sulphur and wax, increases as the square of the exciting current,
and that the attraction of a little bar of iron follows the same
law. We have both been guided in our inquiries by the same
fundamental thought, though our modes of carrying out the
thought are different.
I have observed many phsenomena, which, without due con-
sideration, would lead us directly to Plucker's conclusions ; a few
of these I will here describe. The bismuth balls were placed
upon the beam, and one core was excited ; on the top of the ball
opposite, a particle of iron, not the twentieth part of a common
pin-head in size, was fixed. A current of 10 circulated in the
helix, and the beam came to rest at the distance of 4° from the
zero of the under graduation. I then permitted the current to
increase gradually. The magnetism of the iron particle and the
diamagnetism of the bismuth rose of course along with it, but
the latter triumphed ; the beam was repelled, and finally came
to rest against a stop which was placed 9° distant.
The particle of iron was removed, and a small crystal of car-
bonate of iron put in its place; a current of 15° circulated in
the helix, and the beam came to rest at about 3° distant from
zero. Tlie current was raised gradually, but before it had reached
30° diamagnetism conquered, and the beam receded to the stop
as before.
Thinking that this apparent triumph of diamagnetism might
be due to the fact, that the crystal of carbonate of iron had be-
come saturated with magnetism, and that it no longer followed
the law of increase true for a larger piece of the substance, I
tested the crystal with currents up to 49° ; the attractions were
exactly proportional to the square of the exciting currents.
Thinking also that a certain reciprocal action between the bis-
muth and the crystal, when both were placed together in the mag-
netic field, might so modify the latter as to produce the observed
result, I removed the crystal, and })laced a cube of the zinc of
commerce upon the opposite end of the beam. The zinc was
slightly magnetic. Bismuth and zinc were thus separated by an
interval of 6 inches; both cores were excited by a current of
10°, and the beam, after some oscillations, came to rest at 4°
174 Dr. Tyndall on Diamagnetism and MagnecrystalUc Action*
distant from zero. Tlie current was now gradually raised, but
when it reached 35° the beam receded and was held firmly
against the stop. When the circuit was broken it left the stop,
and, after some oscillations, came to rest at zero.
These experiments seem fully to bear out the notion of
Pliicker. In each case we waited till both forces were in equi-
librium ; and it might be thought that if the forces followed the
same law, the beam ought not to move. Let us, however, clear
the experiment of all mystery ; when the beam was in equili-
brium with a current of 10°, let us ask what forces were opposed
to the repulsion of the bismuth ? There was first of all the at-
traction of the zinc ; but besides this, there was a torsion of 4°,
for the position of equilibrium for the beam when the magnet
was unexcited was at zero. Let us suppose the magnetism of
the zinc at the distance of 4°, and with the current 10°, to be
equal to 8° of torsion ; this, added to the 4° already present, will
give the force opposed to the bismuth; the repulsion of the
latter is therefore equal to 12. Let us now conceive the current
raised from 10° to 35°, that is quadrupled. Supposing the
magnetism of the zinc to be increased in proportion to the
strength of the current, its attraction will now be 32°; this,
added to 4° of torsion, which remains constant, makes 36, which
is therefore the force brought to bear against the bismuth by a
current of 35° under the present circumstances. But the re-
pulsion of the bismuth is also quadrupled ; it is now 48. This,
opposed to a force of 36, necessarily conquers, and the beam is
repelled.
We thus see, that although the magnetic force on one side,
and the diamagnetic on the other side, follow precisely the same
law, the introduction of the small constant 4° entirely destroys
the balance of action, so that to all appearance diamagnetism
increases in a much greater ratio than magnetism. Such a con-
stant has probably crept into the experiments of Pliicker; an
inadvertency not to be wondered at, when we remember that the
force Vas new ^X the time, and our knowledge of the precau-
tions necessary to its accurate investigation very imperfect.
§ 2. On MagnecrystalUc Action.
Pliicker has discovered, that when a crystal of pure carbonate
of lime is suspended in the magnetic field with its optic axis
horizontal, the said axis always sets itself equatorial. He attri-
buted this action of the spar to a repulsion of the optic axis by
the magnet, wholly independent of the magnetism or diamag-
netism of the mass of the crystal. It was the product of a new
force, which Mr. Faraday has named the optic axis force.
In the memoirs published by Knoblauch and me, this view is
Dr. Tyndall on Diamagnetism and Magnecrystallic Action. 175
dissented from, and it is there proved that the action of the cry-
stal, so far from being independent of the magnetism or dia-
magnetism of its mass, is totally changed by the substitution of
a magnetic constituent for a diamagnetic. Our experiments led
us to the conclusion, that the position of the crystal of carbo-
nate of lime was due to the superior repulsion of the mass of the
crystal in the direction of the optic axis. This view, though
supported by the strongest presumptive facts, has remained up
to the present time without direct proof; if, however, a differ-
ence of repulsion, such as that we have supposed, actually exists,
it may be expected to manifest itself upon the torsion-balance.
But the entire repulsion of calcareous spar is so feeble, that
to discover a differential action of this kind requires great nicety
of experiment. I returned to this subject three different times ;
twice I failed, and despaired of being able to establish a differ-
ence with the apparatus at my command. But the thought
clung to me, and after an interval of some weeks I resolved to
try again.
The spheres of calcareous spar were placed upon the beam,
and the latter was exactly balanced. The index above was so
placed, that when the beam came to rest, the attached glass fibre
exactly coincided with a fine black line drawn upon the Bristol
board underneath. Two dots were placed upon the glass cover,
about the fiftieth of an inch asunder, and the fibre was observed
through the interval between them. The beam was about
4 inches below the cover, and parallax was thus avoided. On
exciting both cores the balls receded, the index above was softly
turned against the recession, till the fibre was brought once more
into exact coincidence with the fine black line, and the torsion
necessary to effect this was read off upon the graduated circle
above.
The repulsion of the spheres was measured in four different
directions : —
1 . The optic axes were parallel to the axes of the iron cores.
2. The spheres were turned through an arc of 90°, so that
the optic axes were at right angles to the cores.
3. The spheres were turned 90° in the same direction, so that
the other ends of the axes faced the cores.
4. The spheres were turned 90° further, so that their axes
were again at right angles to the cores, but with the opposite
surface to that in (2) facing the latter.
The following are the respective repulsions : —
Repulsion.
1st position 28*5
2nd position 26*5
3rd position 27*0
4th position 24*5
176 Dr. Tyndall on Biamagiietisni and Magneanjstallic Action^
Each of the helices which surrounded the cores was composed
of two isolated wires ; the four ends of these could be so com-
bined that the current could pass through both at the same time,
as if they were a single wire, or it could be caused to traverse
one ^vire after the other. The first arrangement was advan-
tageous when a small exterior resistance was an object to be
secured, the second when the force of the battery was such as to
render exterior resistance to a certain extent a matter of indif-
ference. In the above experiments the first arrangement was
adopted. Before commencing, however, I had taken fresh acid
and freshly amalgamated zinc cylinders, so that the battery was
in good condition. Tlie second arrangement was adopted, that
is, the current was allowed to traverse one wire after the other,
and the following repulsions were observed ; the numbers refer
to the positions already indicated : —
1st position 57
2nd position 51
3rd position 53
4th position 48
These experiments furnish the direct proof that calcareous
spar is repelled most strongly in the direction of the optic axis.
That Mr. Faraday has not succeeded in establishing a difierence
here is explained by reference to his mode of experiment. He
observ'ed the distance to which the spar was repelled, and found
this the same for all positions of the crystal. The magnetic
force at this distance is too weak to show a difference. In the
above experiments, on the contrary, the ciystal was forced back
into a portion of the magnetic field where the excitement was
intense, and here for the first time the difi"erence rises to a mea-
sui'able quantity.
Carbonate of iron is a crystal of exactly the same form as cal-
careous spar, the iron filling up, so to speak, the exact space
vacated by the calcium. This crj^stal is strongly magnetic;
suspended in the magnetic field, that line which in calcareous
spar sets equatorial, sets here axial, but with an energy far sur-
passing the spar ; a greater diiFerential action may therefore be
anticipated.
A pair of spheres were fonned from this crj^stal, but their
attraction was so strong, that to separate them from the magnet
would strain the wire beyond its limits of elasticity ; one sphere
only could therefore be used, the other being used as a balance-
weight merely. The core opposite to the latter was removed, and
the current sent round that helix only which surrounded the
former. A piece of Bristol board was placed against the end of
the core, and the torsion-head was so turned that when the index
above pointed to zero the little sphere was ou the verge of con-
Dr. Tyndall on Diamagnetism and Magnecrystallic Action. 177
tact. The magnet was then excited and the sphere attracted.
The index was then turned in a direction opposed to the attrac-
tion until the ball gave way ; the torsion necessary to effect this
expresses the attraction. The crystal was first placed so that its
axis was parallel to the magnet^ and afterwards so that it was
perpendicular to the same. The following tables exhibit the
results in both cases respectively : —
Table VII. — Carbonate of Iron,
axis of Magnet.
Axis of Crystal parallel to
?z = 25*5.
».
tan et.
T.
Vt.
wtana.
15
0-268
43
6-56
6-57
20
0-304
80
8-94
8-91
25
0-466
129
11-36
11-42
30
0-577
200
14-14
14-14
Table VIIL
•Carbonate of Iron. Axis of Crystal perpendicular
to axis of Magnet. /i = 20*7.
u.
tan a.
T.
a/T.
ntana.
15
0-268
30-5
5 52
5-55
20
0-364
56-0
7-48
7-53
25
0-466
92-5
9-62
9-64
30
0-577
142-5
11-44
11-44
We learn from these experiments that the law according to
which the attraction of carbonate of iron increases^ is exactly
the same as that according to which the repulsion of the calca-
reous spar increases, and that the respective forces manifest
themselves in both cases with the greatest energy in the direc-
tion of the optic axis.
Let us observe for an instant the perfect antithesis which
exists between carbonate of lime and carbonate of iron. The
former is a diamagnetic crystal ; suspended before the single
pole of a magnet the entire mass is repelled, but the mass in one
direction is repelled with peculiar force, and this direction, when
the crystal is suspended in the magnetic field, recedes as far as
possible from the poles, and finally sets equatorial. The crystal
of carbonate of iron is, on the contrary, strongly magnetic ; sus-
pended before a single pole the entire mass is attracted, but
in one direction the mass is attracted with peculiar energy, and
this direction, when the crystal is suspended in the magnetic
field, will approach the poles and finally set axial.
. Sulphate of iron in the magnetic field displays a directive
action considerably inferior to that of carbonate of iron. Some
178 Dr. Tyndall on Diamagnetism and Magnecrystallic Action,
large crystals were obtained from a chemical manufactory, and
from these I cut two clean cubes. Each was suspended by a
cocoon fibre in the magnetic field, and the line which stood axial
was marked upon it. The white powder which collects by ef-
floresence around these crystals was washed away, and two
transparent cubes remained. These were laid upon the torsion-
balance, and instead of the Bristol board two plates of glass were
placed against the core ends ; the adhesion of the cubes, which
in delicate experiments of this nature sometimes enters as a dis-
turbing element, was thus reduced to a minimum. As in the
case of carbonate of iron, one core only was excited. The cube
opposite to this core was first so placed that the line which stood
axial in the magnetic field was parallel to the core ; preserving
this line horizontal, the three remaining faces were presented
successively to the core and the attraction measured in each par-
ticular case j these attractions were as follows : —
Cube of sulphate of iron j edges 10 millims.
Attraction.
1st position 43-0
2nd position 36'3
3rd position 40*0
4th position 34*5
Hence the attraction of this crystal in the direction of the
line which sets axial in the magnetic field, is to the attraction in
a direction perpendicular to the same in the ratio of 7 : 6 nearly.
In an article translated from Poggendorf^s Annalen, which
appears in the June Number of the Philosophical Magazine, it will
be seen that Prof. Pliicker has experimented with a cube of sul-
phate of iron, and has arrived at results which he adduces against
the theory of magnecrystallic action advanced by Knoblauch
and myself. He rightly concluded that if the position of the
crystal, suspended between two poles, were due to the superior
attraction exerted in a certain direction, this peculiarity ought
to exhibit itself in the attraction of the entire mass of the crystal
by the single pole of a magnet. He brings this conclusion to
the test of experiment, suspends the ci-ystal from one end of a
balance, weighs the attraction in different directions, but finds
no such difi*erence as that implied by the conclusion. This re-
sult I believe is entirely due to the imperfection of his apparatus j
I have tried a very fine balance with even worse success than
M. Pliicker. Although the torsion-balance furnishes a means
of experiment immeasurably finer, still, with it, great delicacy of
manipulation and a considerable exercise of patience are neces-
sary to ensure invariable success. It is gratifying to find M.
PlUcker's deduction so strictly fulfilled, and I doubt not that he
Dr. Tyndall on Diamagnetism and Magnecrystallic Action, 179
will, with his usual frankness, grant the theory the full benefit
of the corroboration.
Faraday has discovered, that if a bismuth crystal be suspended
in the magnetic field, it will set itself so that a line perpendicular
to the plane of most eminent cleavage will be axial ; this line he
calls the magnecrystallic axis of the crystal. In the memoir
before alluded to, the position of the magnecrystallic axis is
affirmed to be a secondary result, depending on the fact that the
mass in the direction of the planes of cleavage is most strongly
repelled.
Here again the torsion-balance furnishes us with the direct
proof of this affirmation. Two cubes of bismuth were prepared,
in each of which the plane of most eminent cleavage formed two
of the opposite sides. Suspended by a fibre of cocoon-silk in
the magnetic field, the line perpendicular to the cleavage turned
into the axial position, or what amounts to the same as far as
the eye is concerned, the cleavage itself receded from the poles
and stood equatorial. These cubes were placed one on each end
of the torsion-balance ; first, so that the plane of most eminent
cleavage was parallel to the axes of the cores, and afterwards
perpendicular to these axes. ' The respective repulsions are stated
in the following tables.
Table IX. — Cubes of bismuth, crystal edges 6 millims. Plane
of most eminent cleavage parallel to axes of cores.
a,.
T.
20
117
30
34-8
40
78
45
111
50
153
Table X. — The same cubes. Plane of most eminent cleavage
perpendicular to axes of cores.
a.
T.
20
8
30
23
40
53
45
76-5
50
110
A comparison of these two tables shows us that the repulsion
of the cubes, when the plane of most eminent cleavage was parallel
to the magnetic axis, is to the repulsion when the said plane was
180 Dr. Tyndall on Diamagnetism and Magneerystallic Act,ion, ^
perpendicular thereto in the ratio of 15 : 11 nearly. The general
fact of superior repulsion in the direction of tlie cleavages has
been already demonstrated by Mr. Faraday.
What is it, then, which causes this superior manifestation bf^
force in a cei-tain direction ? To this question experiment returns '
the following reply: — "If the arrangement of the component'
particles of any body be such as to present different degrees of
proximity in different directions, then the line of closest proxi-
mity, other circumstances being equal, will be that of strongest ,
attraction in magnetic bodies and of strongest repulsion in dia-
magnetic bodies.''
The torsion-balance enables us to test this theory. A quan-
tity of bismuth was ground to dust in an agate mortar, gum-
w^ater was added, and the mass was kneaded to a stiff paste.
This was placed between two glasses and pressed together ; from
the mass when dried two cubes were taken, the line of compres- '
sion being perpendicular to two of the faces of each cube and
parallel to the other four. Suspended by a silk fibre in the , ,
magnetic field, upon closing the circuit the line of compression
turned strongly into the equatorial position, exactly as the plane
of most eminent cleavage in the case of the crystal. The cubes
w^ere placed one upon each end of the torsion-balance ; first with
the line of compression parallel to the cores, and secondly with t
the said line perpendicular to the cores. The following are the
repulsions exhibited in both cases respectively.
Table XL — Cubes of powdered bismuth, edges 7 millims.
of compression parallel to axes of cores.
Line
a.
tan«.
T.
a/T.
8-3 X tana.
30
Oo77
22
4-69
478
40
0-839
46
678
6-96
45
1000
Q7
8-19
8-30
60
1192
98
9-89
9-89
From this table we see that the law of increase for the artificial
cube is the same as that for diamagnetic substances generally.
Table XIL— The same
cubes. Line of compression perpendi-
cular to cores.
«.
T.
30
! 40
45
; ^«
13
31
46
67
Dr. Tyridail on t)iamdgnetism and MagnecrtjstaUic Action. 181
A comparison of both tables shows us that the line which
stands equatorial in the magnetic field is most strongly repelled
upon the torsion-balance^ exactly as in the case of the crystal ;
the repulsion in the direction of this line and in a direction per-
pendicular to the same being nearly in the ratio of 3 : 2. Similar
experiments were made with cubes of powdered carbonate of
iron. The line of compression in the magnetic field stood axial ;
and when laid upon the torsion-balance, the mass in the direc-
tion of this line was attracted most strongly.
At the last meeting of the British Association, an objection,
which will probably suggest itself to all who study the subject
as profoundly as he has done, was urged against this mode of
experiment by Professor William Thomson. " You have,^' he
said, ^^ reduced the mass to powder, but you have not thereby
destroyed the crystalline property ; your powder is a collection
of smaller crystals, and the pressing of the mass together gives
rise to a predominance of axes in a certain direction ; so that
the repulsion and attraction of the line of compression which you
refer to the mere closeness of aggregation is, after all, a product
of crystalhne action. ^^
I know that this objection, which was specially directed against
the experiment made with powdered bismuth and carbonate of
lime, floats in the minds of many both in Germany and England,
and I am therefore anxious to give it a full and fair reply. I might
urge, that in the case of the bismuth powder at least, the ten-
dency of compression would be to place the little component
ciystals in such a position, that a deportment precisely the re-
verse of that actually observed might be anticipated. If we
pound the crystal to the finest dust, the particles of this dust, to
render Mr. Thomson^s hypothesis intelligible, must have a cer-
tain predominant shape, otherwise there is no reason in the
world to suppose that pressure will always cause the axes of the
little crystals to take up the same predominant direction. Now
what shape is most likely here ? The crystal cleaves in one
direction more easily than in any other ; is it not then probable
that the powder will be chiefly composed of minute scales, whose
opposite flat surfaces are the surfaces of principal cleavage?
And what is the most probable effect of compression ? Will it
not be to place these little scales with their flat surfaces perpen-
dicular to the line in which the pressure is exerted ? In the
crystal, the line perpendicular to the principal cleavage sets axial,
and hence it might be expected that the line of compression in
the model would set axial also ; it does not, however, — it sets
equatorial.
This, however, though a strong presumptive argument, is not
yet convincing ; and it is no easy matter to find one that shall
Phil. Mag. S. 4. Vol. 2. No. 10. Sept. 1851. 0
182 Dr. Tyndall on Diamagnetism and Magneerystallic Action,
be so. Bismuth powder will remain crystalline, and carbonate
of lime is never free from suspicion. I thought 1 had found an
unexceptionable substance in chalk, inasmuch as Ehrenberg has
proved it to be a mere collection of microscopic shells ; but Prof.
Ehrenberg himself informs me, that even these shells, which
require a high magnifying power to render them visible, are in
their turn composed of infinitesimal crystals of calcareous spar*
In this dilemma one way remains open to us : we will allow the
objection to stand, and follow it out to its inevitable conse-
quences ; if these are opposed to fact, the objection necessarily
falls.
Let us suppose the bismuth powder to be reaiTanged, so that
the perfect crystal from which it was obtained is restored. In
this case the axes of all the little component ci*ystals are parallel^
they work all together, and hence their action must be greats
than if only a majority of them were parallel. In a bismuth
crystal, therefore, the difference of action in the line of the mag-
necrystallic axis, and in a line perpendicular thereto, must be a
maximum. It must, for example, be greater than any difference
which the model of bismuth powder can exhibit ; for a portion
of the force attributed to the axes must in this case be annulled
by the confused grouping of the little component ciystals. In
the words of Professor Thomson, it is merely a balance of action
brought about by predominance, which can make itself manifest
here. Hence if we measure the repulsion of the crystal in a
direction parallel to the principal cleavage, and in a direction
perpendicular to it, and also measure the repulsion of the model
in the line of compression and in a line perpendicular to it, the
ratio of the two former repulsions, that is, of the first to the
second, must be greater than the ratio of the two latter, that is,
of the third to the fourth.
Turning to Tables IX. and X., we see that the ratio of the
repulsion of the crystal in the direction of principal cleavage to
the repulsion in a direction perpendicular to the same is ex-
15
pressed by the fraction yy =1-36. Turning to Tables XL and
XII., we find that the ratio of the repulsion of the model in the
line of compression to the repulsion in a line perpendicular to it
3
is expressed by the fraction ^ =1*5. In the latter case, there-
fore, we have the greatest differential effect ; which result, were
the repulsion due to the mere predominance of axes, as urged by
Mr. Thomson, would certainly bear a suspicious resemblance to
the conclusion that a part is greater than the whole. This result
has been entirely unsought. The models were constructed with
Dr. Tyndall on Diamagnetism and Magnecrystallic Action. 183
the view of establishing the general fact, that the repulsion in
the line of compression is greatest. That this has fallen out in
the manner described is a pure accident. I have no doubt what-
ever that models might be made in which this difference of action
would be double of that exhibited by the crystal.
The case, however, is not yet free from suspicion ; the gum-
water with which it is necessary to bind the powder may possibly
exert some secret influence. When isinglass or jelly is com-
pressed, we know that it exhibits optical phsenomena similar to
those exhibited by crystals ; and the squeezing of the metallic
dough may induce a kind of crystalline structure on the part of
the gum sufficient to produce the phaenomena observed.
An experiment to which I was conducted by the following
accident will set this doubt, and I believe all other doubts re-
garding the influence of compression, completely at rest. Having
repeated occasion to refer to the deportment of crystals in the
magnetic field, so as to be able to compare this deportment with
the attraction or repulsion of the entire mass upon the torsion
balance, through the kindness of Professor Magnus, the great
electro-magnet of the University of Berlin* was placed in the
room where I experimented. One morning a cube of bismuth
was suspended between the moveable poles, and not knowing
the peculiarities of the instrument, I chanced to bring the poles
too near each other. On closing the circuit, the principal clea-
vage of the ci-ystal receded to the equator. Scarcely however was
this attained, when the poles were observed moving towards each
other, and before I had time to break the circuit, they had
rushed together and caught the crystal between them. The
pressure exerted squeezed the cube to about three-fourths of its
former thickness, and it immediately occurred to me that the
theory of proximity, if it were true, ought to tell here. The
pressure brought the particles of the crystal in the line of com-
pression more closely together, and hence a modification, if not
an entire reversion of the previous action, was to be expected.
Having liberated the crystal, I boiled it in hydrochloric acid, so
as to remove any impurity it might have contracted by contact
with the iron. It was again suspended between the poles, and
completely verified the foregoing anticipation. The line of com-
pression, that is, the magnecrystallic axis of the crystal, which
formerly set from pole to pole, now set strongly equatorial. I
then brought the poles intentionally near each other, and al-
lowed them to close once more upon the already compressed
cube ; its original deportment was thereby completely restored.
* A notion of the power of this instrument may be derived from the
fact, that the copper hehces alone which surrounded the pillars of soft iron
weighed 243 pounds. „ i .,_ . . .
02
184 Br. Tyndail on Diamagnetism and Magnecrystallic Actioti,
This I repeated several times with several difFercnt crystals,, and
with the same unvaiying result ; the line of compression always
stood equatorial, and it was a matter of perfect indifference
whether this line was the map;necrystallic axis or not. The ex-
periment was then repeated with a common vice. I rubbed the
letters from two copper coins with sandstone, and polished the
surfaces ; between the plates thus obtained various pieces of bis-
muth were placed and squeezed forcibly together ; in this way
plates of bismuth were procured about as thick as a shilling,
and from half an inch to an inch in length. Although the dia-
magnetism of the substance tended strongly to cause such a
plate, suspended from its edge between the poles, to take up the
equatorial position, although the force attributed to the magne-
crystallic axis worked in each case in unison with the diamag-
netism of the mass, every plate set nevertheless with its length
from pole to pole, and its magnecrystallic axis equatorial.
This superior repulsion of the line of compression manifests
itself upon the torsion balance also. The cubes of bismuth cry-
stal already made use of were squeezed in a vice to about four-
fifths of their former thickness ; the line of compression in each
case being perpendicular to the principal cleavage, and conse-
quently parallel to the magnecrystallic axis. From the masses
which were thus rendered oblong, two new cubes were formed ;
these, laid upon the torsion-balance in the positions indicated in
the tables, srave the followinff results : — .*'*
° tiij({qu uii buB
Table XIII. — Bismuth crystals, compressed cubes. Plane of
most eminent cleavage parallel to axes of magnets. ,,.
a,.
T.
20 7-8
30 i 21
40 47
45 1 67
50 101
Table XIV.^ — The same cubes. Plane of most eminent cleavage
' ^ perpendicular to axes of magnets.
1
T. 1
20
9
30
25 5
40
57-3
1 ^^
79
50
113
Ih'. Tyndall on Diaina^netism and Ma^necri/stallic Action, 185
f Looking back to Tables IX. and X., we see that the line
which was there most strongly repelled is here repelled most
feebly, and vice versa, the change being due to compression.
I have been careful to make similar experiments with sub-
stances concerning whose amorphism there can be but little
doubt. A very convenient substance for showing the influence
of compression is the white wax used in candles. The substance
is diamagnetic. A little cylinder of the wax suspended in the
magnetic field set with its axis equatorial. It was then placed
between two stout pieces of glass and squeezed as thin as a six-
pence ; suspended from its edge, the plate thus formed set its
length, which coincided with the axis of the previous cylindei^
axial, and its shortest dimension equatorial. *
The plate was then cut into little squares, these were laid one
Toppn the other and then pressed together to a compact cubical
mass. Two such cubes were placed upon the torsion-balance,
and the repulsions in the line of compression, and in a line per
pendicular to the same, were determined— the former was con^
siderably the greater.
The pith was scooped from a fresh roll, placed between the
glass plates, and squeezed closely together ; after remaining in
the vice for half an hour, an oblong was taken from the plate
thus formed, and suspended from its edge in the magnetic field ;
it set like a magnetic body, with its length from pole to pole.
The mass w^as diamagnetic, its line of compression was repelled,
and an apparent attraction of the plate was the consequence.
Fine wheat-flour was mixed with distilled water into a stiff
paste, and the diamagnetic mass was squeezed into thin cakes.
The cakes when suspended from the edges set always with their
longest dimension from pole to pole, the line of compression
being equatorial.
Rye-flour, from which the Germans make their black bread,
was treated in the same* manner and with the same result.
I have an oblong plate of shale from the neighbourhood of
Blackburn in Lancashire, which imitates Pliicker^s first experi-
ment with tourmaline with perfect exactitude. The mass is
magnetic, like the tourmaline. Suspended from the centre of
one of its edges, it sets aa:ial; this corresponds to the position
of the tourmaline when the optic axis is vertical. Suspended
from the centre of the adjacent edge, it sets even more strongly
equatorial', this corresponds with the tourmaline when the optic
axis is horizontal. If the eyes be closed, and the respective po-
sitions of the plate of shale ascertained by means of touch, and
if the same be done with Pliicker's plate of tourmahne, it will
be impossible to distinguish the one deportment from the other.
Whoever denies the influence of proximity must be prepared
186 Dr. Tyndall on Diamagnetism and Magnecrystallic Action.
to answer the following questions : — How is it possible that a
greater differential action can be exhibited by a cube of pow-
dered bismuth than by the crystal itself? What is it that
causes the magnecrystallic axis of the crystal to forsake its usual
position and to set equatorial when the mass is compressed in
the direction of the said axis ? He must further assume a cry-
stalline structure on the part of wax, flour, shale, and the pith
of fresh rolls.
With regard to the experiment with the cherry-tree bark, '\
have a bar of chemically pure bismuth which does not contain a
trace of magnetism, and which exhibits the precise phsenomena
observed ^vith the bark. These phsenomena do not therefore
necessitate the hypothesis of two conflicting forces, the one or
the other of which predominates according as the poles of the
magnet are more or less distant. I have already commenced an
investigation in which the deportment of the bark and other
phsenomena of an analogous nature will be more fully discussed.
Eveiy physicist who has occupied himself experimentally with
electro-magnetic attractions must have been struck with the
great and speedy diminution of the force by which soft iron i»
attracted in the immediate neighbourhood of the poles. In ex-
periments with spheres of soft iron, I have usually found that
a distance of j^Qih. of an inch between the sphere and the mag-
net is sufficient to reduce the force with which the former is
attracted to -ij^th. of the attraction exerted when the sphere is
in contact. To any one acquainted with this fact, and aware,
at the same time, of the comparative sluggishness with which a
bismuth ball moves in obedience to the repulsive force even
when close to the poles, a law the exact reverse of that affirmed
by PlUcker must appear exceedingly probable.
The bismuth balls were placed upon the torsion-balance ; on
the top of one of them a particle of an iron filing was fixed, and
with this compound mass the space opposite to a core excited
by a current of 50^ was sounded. The beam was bi-ought by
gentle pushing into various positions, sometimes close to the
magnet, sometimes distant. The position of equilibrium for the
beam when the core was unexcited was always zero. When the
beam was pushed to a distance of 4° (about /^jths of an inch)
from the core end, on exciting the magnet it receded still fur-
ther and rested against a stop at 9° distant. When the current
was interrupted the beam left the stop and approached the
magnet ; but if, before it had attained the third or fourth degree,
the circuit was closed, the beam was driven back and rested
against the stop as before.
Dr. Tyndall on Diamagnetism and Magnecrystallic Action, 187
Preserving the current constant at 50°, the index of the tor-
sion-head was turned gently against the repulsion, and in this
way the ball was caused slowly to approach the magnet. The
repulsion continued until the glass fibre of the beam pointed to
2° ; here an attractive force suddenly manifested itself, the ball
passed speedily on to contact with the core end, to separate it
from which a torsion of 50° was requisite.
The circuit was broken and the beam allowed to come to rest
at zero, a space of about yV^^ ^^ ^^ mch. intervening between
the ball and the end of the magnet ; on closing the circuit the
beam was attracted. The current was once more interrupted,
and the torsion-head so arranged, that the beam came to rest at
3° distant ; on establishing the current again the beam was re-
pelled. Between 0° and 3° there was a position of unstable
equilibrium for the beam; from this place to the end of the
magnet the attraction was triumphant, beyond this place repul-
sion prevailed.
Here we see, that on approaching the pole, the attraction of
the magnetic particle mounts much more speedily than the re-
pulsion of the diamagnetic ball ; a result the reverse of that ar-
rived at by M. Pliicker, but most certainly coincident with that
which everybody who has studied electro-magnetic attractions
would expect. Shall we therefore conclude that ^ magnetism^
increases more quickly than ^ diamagnetism V The experiment
by no means justifies so wide a generalization. If magnetism be
limited to the attraction of soft iron, then the above conclusion
would be correct ; but it is not so limited. Pliicker calls the
attraction of his watch-glass magnetism, the attraction of a salt
of iron bears the same name, and it so happens that the attrac-
tion of a salt of iron on approaching the poles increases incom-
parably more slowly than the attraction of iron itself. The proof
of this remarkable fact I will now proceed to furnish.
From one end of a very fine balance a sphere of soft iron, ^th
of an inch in diameter, was suspended. Underneath, and about
^th of an inch distant from the ball when the balance stood
horizontal, was the flat end of a straight electro-magnet. On
sending a current of 30° through the surrounding helix, the
ball was attracted, and the force necessary to efi*ect a separation
was measured : it amounted to 90 grammes. A plate of thin
window-glass was then placed upon the end of the magnet, and
the ball allowed to rest upon it. The weight necessary to eiFect
a separation, when the magnet was excited by the same current,
amounted to 1 gramme. Here an interval of about yV^t of an
inch was sufficient to reduce the attractive force to g^g*^ ^^ ^^^
exerted in the case of contact.
A sphere of sulphate of iron, of somewhat greater diameter than
188 Dr. Tyndall on Diamagneitsm and Magneo^ystalUc Action,
the iron ball, was laid U])on one end of the torsion -balance ; the op-
posite core was excited by a current of 30°, and the force neeessaiy
to effect a sepai-ation of the core and the sphere was determined :
it amounted to 20° of torsion. The same plate of glass used in
the last experiment was j)laccd against the core end, apd.^ie
force necessary to effect a separation from it with a current jpi
30^ was also determined. The difference, whicli in the case, of
the soft iron amounted to f§ths of the primitive attraction, was
here scarcely appreciable. At a distance of j^th of an inch the
sphere of sulphate of iron was almost as strongly attract6(}' AS
when in immediate contact. \'
Similar experiments were made with a pellet of carbonate of
iron, and with the same result. At a distance of |th of an inch
the attraction was two-thirds of that exerted in the case of con-
tact. An interval of y^jVu*^^ °^ ^^^ ^^^^^ ^^ more than sufficient
to effect a proportionate diminution in the case of soft iron.
A salt of iron in the immediate neighbourhood of the poles
behaves like iron itself at a considerable distance, and the de-
portment of bismuth is exactly similar. A slight change of po-
sition will make no great difference of attraction in the one case
or of repulsion in the other. To make the antithesis between
magnetism and diamagnetism perfect, we require a yet undisco-
vered metal, which shall bear the same relation to bismuth, an-
timony, sulphur, &c., which iron does to a salt of iron. Whe-
ther nature has such a metal in store for the enterprizinff phyr
sicist, is a problem on which I will hazard no conjecture., ' ^^ ^^
Principal Results of the foregoing Investigation!^^ "^^f^-i^^
1 . The repulsion of a diamagnetic substance placed at a fixed
distance from the pole of a magnet is governed hy the same daw fiS
the attraction of a magnetic substance. ,hHu< oifi
2. The entire mass of a magnetic substance is most strongly at^
traded when the attracting force acts parallel to that line which sets-
axial when the substance is suspended in the magnetic field ; and the,
entire mass of a diamagnetic substance is most strongly repelled
when the repulsion acts parallel to the line which sets equatorial in
the magnetic field.
3. The superior attraction and repulsion of the mass in a par-
ticular direction is due to the fact, that in this direction the mate-
rial particles are ranged more closely together than in other direcr
tions ; tlie force exerted being attractive or repulsive according as
the particles are magnetic or diamagnetic. This is a law appli-
cable to matte?' in genei'al, the phanomena exhibited by crystals in
the magnetic field being particular manifestations of the same.
Berlin, June 1851.
^XVIIL O/i M« Anticlinal Line of the London and Hampshire
mii\mvivmBmmiy By P. J. Martin, Esq^^ ^iG\.&. x irui:j i,,
m b^^rr f'.f.ah Ho ^^<>*< [Continued from p. 134.] *^- <'^ ^^-itrfJ/oniB :tr
THE concluding words of the foregoing Memoir* on the, ^^^h
ern part of this line might serve for an introduction to what
follows. But as many of my readers may not have seen Dr.
Buckland^s dissertation, before mentioned, and many more not
know anything of my former publications on this subject, I
will quote, in addition, the following passage from the latter, as
t^e key to further discussip^^ aj][^^j|s.the,gj:j9j]^p^i1jipft jiQ>^
WM' elucidation. _ ,,,,;^^ ^ \^:'''''^^,,ll,..^,,,^,/.^^u fhr^r [)nK ^u^'i,
'^The strata which compose these basins, then, previously in
?^^_ horizontal position, suffered disruption; and in the act of
basining (whether by the elevation of the sides, or the subsi-
dence of the central parts, is not now material) all their parts
were deeply and extensively fissured, in an order correspondent
with that act, producing, with the help of diluvian action, a
system of longitudinal and transverse valleys answering to the
double inclination (the dip and lateral bearings, or strike) of
their fractured masses, and a consequent removal of the broken
materials, brought within the range of the denuding force. The
effect of raising from the horizontal position, or in any other
way stretching a ponderous and frangible body, is to produce a
division of its parts, in such order and direction as its varying
strength and tenacity dictate ; the fractured parts taking their
places according to their magnitude or gravity, or the disposition
of those which support them. This irregular fracture, alternate
elevation and subsidence, and settling of parts thus disturbed,
are well cxemphfied in the familiar operation of the heaving of
the spade in digging. If the earth be tenacious and the action
steady, it tears with such a divergence of the principal rents as
will be here described, and tlie more friable parts are seen drop-
ping in, in such a way, and in such proportion as the moving power
dictates and their structure allows. If another illustration were
necessary, it might be found in what we observe in the elevation
and cracking of the flour which covers the fermenting nucleus in
a baker's trought/' '' ''/■ "^ f
The evidence in support of this proposition, — the eleVatidii 'df
the great anticlinal of the London and Hampshire basins, arid
concomitant abrasion, on and around that line of disturbance^ *
— may be classed under four heads. '^^
..^ >.uv '^^^'^
* It is to be remembered that that paper was read to the Geologicd\
Society in 1840; what follows is of present date. ^ i a\
t Geol. Mem. of Western Sussex, p. 59. '""^ .arlid^l
190 Mr. P. J. Martin on tfie Anticlinal Line of
1. The general arrangement or geographical aspect of the
country.
2. Its valleys, and lines of di-ainage.
3. The lacerated state of some of its escarpments, still to be
discerned behind the detrital materials of age, and atmospheric
agencies.
4. The nature and disposition of the diluvium on every part
of its surface.
The first of these is so familiar, in a general sense, and has
been so often described, that it would seem superfluous to take
it into consideration ; — and yet it will be well to cast a geological
eye over it. If we take our stand on the lowest beds of the up-
heaval, say at the well-known point of Crowborough, on the
Ashburnham limestone (supposed by Dr. Mantell to be the
lowest in the series), or on the sand rocks of Hastings, we find
all around us a quaquaversal dip ; a succession of escarpments
or basset edges, confluent at either end; — westward in Sussex
and Hampshire, eastward in the Boulonnais. The successional
courses of clays, sands and limestones of the Hastings sands,
after skirting the " Forest ridge,^' form saddles in the west of
Sussex. To these succeed the lower greensands, the gait, the
malm-rock or upper green, and the chalk; afterwards the
tertiary beds, still confluent above the Hampshire chalk, in
the shape of patches of plastic clay and sand ; and the gray-
weathers of the Hampshire and Wiltshire downs ^'. Turn-
ing to the east, we find that this confluence is maintained in like
manner in all the beds of the Bas Boulonnais ; substituting the
more ancient formations, which take the place of the Wealden
(there reduced to a very small compass). And this confluence
is maintained there also in the tertiary beds, as in Hampshire, in
the shape of relics spread over the chalk hills of the surrounding
Haut Boulonnais. These facts are pretty well known; but for
the satisfaction of those who have not turned their attention
especially to this subject, we may cite the authority of the French
geologist, M. Rozet, who in 1828 followed Dr. Fitton in a de-
scription of this part of France. " On rencontre des lambeaux
de terrain tertiaire sur les montagnes qui limitent le Bas Bou-
lonnais. Au dessus de Tingry, de Niembourg, pres d'Huber-
sent, de Courset, &c., on exploite des lambeaux d'un gres sili-
ceux, tres-semblable a celui de Fontainebleauf/' &c. M. Rozet
also speaks of the same sort of remains found dispersed in the
diluvium of the Boulogne denudation ; to which we may refer
* Vide Dr. Buckland's paper (Geological Transactions) and my foregoing
Memoir.
t Description G^ognostique du Bas Boulonnais. Par M. Rozet. Paris,
1828, p. 31-36.
the London and Hampshire Basins. 191
when speaking of the drift on this side of the Channel. This
gentleman ventures also to use the word " debacle/' and speaks
constantly of the denudation as a '^ great catastrophe/' With
all this evidence before us, it seems then to be no great stretch
of the imagination to suppose that all the tertiaries follow the
secondary in the same order of denudation. From the nature of
their materials^ we do not wonder that they do not present the
bold and prominent escarpments of the chalk and greensands ;
they lie beveled off in succession, as they crop out within the
borders of the so-called chalk-basins. At the back of the Surrey
Hills and South Downs we find the plastic clay and sands thinned
out on the chalk. More remotely from the chalk hills, succeed
the beds of London clay and tertiary limestones ; — at Brackles-
ham and Bognor on one side, and in the bed of the Thames and
at Sheppy on the other. Where the materials of these tertiaries
are of firmer texture and have afforded more resistance, and
where their synclinal position has given them protection, we still
find some signs of escarpment in them, as, east of Croydon, in
the Addington and Keston Hills, and north of Farnham, at Farn-
ham Beacon, and in the line of country north of the Hogsback.
The only escarpment exhibited by the tertiaries south of the South
Downs, and that is synclinal, is the cliff at Castle Hill, described
by Dr. Mantell*. From this point westward great ravages have
been made; but I can say with confidence that considerable
relics of these beds exist in the synclinal of what I have called the
chalk "Outlier-by-protusion'' at Highdown Hill near Worthing f;
again in the eminences between Arundel and Angmering. Shingle
beds of this sera show strongly also at Box-grove. And all the
tract of country called the " Manwood,'' between Chichester and
Bracklesham, is plastic clay, with an occasional sprinkling of
diluvium. West of Chichester, and north of Emsworth again,
the plastic clay emerges from beneath the thick beds of drift
that abound in this line of country. And the forest of Bere,
which is the synclinal of Portsdown, is wholly tertiary. With this
comprehensive view before us of the general denudation of all
the beds on and about the great line of elevation, and looking on it
as the last great change that has come over the S.E. of England^
we discard all notions of marine deposit of a more recent date,
or in other words, as asserted in my memoir of 1828 before
alluded to, '^the chalk basins so often spoken of, never could
have been areas of deposit for beds not to be found also on the
denuded surfaces, at the same level."
2. We pass now to the consideration of the second order of
phsenomena, — the valleys and lines of drainage. Although it is
* Mantell's Geology of S.E. of England, p. 55.
t Geol. Mem. of Western Sussex, pp. 95, 96.
l^'^ Mr. P^ J^ sMarti^ Qn\i/te 4n^iffii:^af Ime of
abimdaiitly apparent that the same causea have produced thp
same effects in the whole course of our line, as regards these
aurface-phsenomena, two circumstances have conspired to giye a
broader aspect and a more decided character to them in that,p^rt
of it which is generally called the " denudation of the \Veal4forf
-.First, the greater violence of disi'uptive force in that, part of
it ; and secondly, the greater variety in the strata there exposed,
and their greater tenacity and durability, as compare4;Wi^h.,<J|^
more ductile and friable chalk. ,;|j
A description of the cross-fractures and drainage of the Weald
w^as begun by myself in 1828, continued in the foregoing memoir
ia 1840, and pi-olonged by Mr. Hopkins, in illustration of his
'fTheoiy of Elevation" (Geol. Trans, vol. vii.). I accept Mr.
Hopkins^s description of the structure of the Weald, as a faith-
ful representation of some of its most prominent features; and
if I am able to add anything to that gentleman^s exposition
of these surface-changes, it is because my long residence on
the spot has made me familiar with many minor details, of
which a cursory observer would not be cognizant. If I differ
from him in my interpretation of the phsenomena in question^
it may be because of my imperfect knowledge of the data on
which he proceeds. It is probable that his " Theory of Ele-
vation" may be fomided in nature, and every one will rejoice
that the exact sciences can be brought to bear in this branch of
geological research ; and that a theory should be propounded as
convincing as a " theory of glacier motion," or of " wave of
transport," or of any other object of geological dynamics. With-
out calling in question the general propositions advanced with
so much mathematical precision by Mr. Hopkins, but as he
allows only with approximate results, we may be allowed to
doubt if they meet all the requirements of the case, or explain,
fully all the appearances exhibited in the structure of the Weald.
I have said that if we could obtain a section of that district, it
would exhibit all the contortions of the older schists*. Subor-
dinate anticlinal lines assist in making up the great anticlinal,
and valleys of elevation exist all over its surface, subordinate to
the great valley of which they form jiarts. I consider these minor
anticlinals us so many foldings of the strata, produced not by
lateral pressure, but by lateral resistance in their struggle up-
wards ; and all the lesser flexm-cs and faults, as so many pucker-
ings and rents to be included in the same categoiy. Mr. Hopkins
considers the principal anticlinals in the light of fissures. I am not
prepared altogether to dispute the proposition ; lines of disturb-
ance may perhaps be changed in their character as they are pro-
pagated through masses of various densities, and various degrees
* Phil. Mag., p. 133 of the present volume.
V; ^tlie London and Hampshire Basing. ^^^ 193
6f^l;efe(*it^. 'Fissures and faults abound in limestblles'kttd'dttflrf^
stones, flexures in clays. Both Dr. Mantell and Mr. Hopkins
have observed perpendicular faults of great magnitude in the
Hastings sands. There are many minor ones in my own neigh-
bourhood,— in the lower greensand ; and there are some remark-
able downcasts along the Surrey Hills. T will here describe one
of them. Where the traces of the Peasemarsh anticlinal are lost
near Albury, a line of disturbance takes off in a north-easterly
direction, through the chalk between Shere and Horseley. The
farms in the Ordnance Map of Pobley, Green-dean and Pots-
dean, between these two villages, mark its direction, till it runs
into the transverse fissure of the Mole near Mickleham. Here-
about are the " swallow-holes " of the Mole, in which that river
is lost in the summer season; and they are probably caused by
the joint operation of these two lines of disturbance. Taking the
direct footpath from Horseley to Shere, after crossing the chalk
downs of the former place, you find yourself on a distinct though
low escarpment of chalk descending on Netley Heath, which
consists of sand of the plastic clay formation. Crossing Netley
Heath, you come again on the chalk, and the descent of the
deep escai-pment to Shere, makes you sensible of having traversed
the whole thickness of the latter formation. East of the Vale of
Mickleham there are patches of tertiary, as at Headley, with
signs of much disturbance thereabout, as at Pebble Hill, — one
of those deep fissures filled with loam and shingle so often met
with in the chalk. jiwiiuj
To return to the structure of the Weald. Mr. Hopkinsr hiSi^
distinguished flexures from anticlinals : why should they differ,
except as in degree or shape ? The flexure, which by its sudden
dip north gives rise to the Hogsback, is an anticlinal, twisted to
one side, that is, of unequal dip*. As it recedes from the chalk,
it becomes a perfect anticlinal at Peasemarsh ; and the Vale of
Peasemarsh is a true ^^ Valley of Elevation -/' as distinctly so as
that of Kingsclere, first described by Dr. Buckland. Again,
Mr. Hopkins has noted a flexure at Pulborough north of the
line of the Greenhurst anticlinal. This flexure is no more than
the commencement or northern edge of the sjmclinal of the last-
mentioned line, and the trough of gait at Hardham ; the river
Arun taking its course along the same depression. These
flexures, when not seeming to have any relation to distinct anti-
clinals, very much modify the surface arrangements; and are
instrumental also in the production of springs and water-coursfes j
and, moreover, like faults and anticlinals, they prolong the out-
crop of the strata in which they are found. There is a remark-
able one of this sort crossed by the lane leading from West
* Phil. Mag. p. 48. ^' * "
194 Mr. P. J. Martin on^he Anticlinal Line of
Chiltington to Wood's Hill. In the Bonghton quarries, near
Maidstone, there is a flexure of this kind ; and the springs which
run on the south side of these quarries, and come down from
Langley, are most probably thi*own out by this flexure. And to
all appearance (although I have not been able to find a section to
enable me to speak positively) the course of the Medway after it
enters the greensand country is for some miles determined east
and west (by Wateringbury) by a flexure or minor contortion.
This flexure also assists in prolonging the extent of the lower
greensand country in the Maidstone district*. In short, the
contortions and flexures, and smaller anticlinals superadded to
the larger ones, over all the Weald denudation, are almost innu-
merable. I will undertake in the drives of two mornings to
show any person, competent to judge of these things, beside the
great line of Greenhurst, at least six well-marked smaller ones,
and as many flexures and faults giving shape more or less to the
neighbouring lands.
We have hitherto confined ourselves to the consideration of
the longitudinal anticlinal folds and contortions. But before we
take a general view of the manner in which these folds on coming
to the surface yielded to the tensive power, and opened to form
fissures, and give admission to the denuding floods, and so
eventually became the valleys and water-courses we now see;
we must advert to another modification of the disruptive action,
not so potent for the production of surface-changes, because not
so extensive, but still of much influence, and inseparable from
the consideration of the one grand and total act of upheaval. I
mean the frequent occurrence of transverse anticlinals, opening
up transverse valleys distinct from those which appear to be th6
result of the cross fracture of the longitudinal ones, at their points
of greatest tension. I can best convey the idea of these trans-
verse flexures by reference to a case or two in point, and eminent
examples, on both sides of the denudation. On looking at the
* Of the manner in which anticlinals, or flexures of any kind, prolong
the extent of ex})osure of a particular stratum, we may cite the following.
The transverse fissure of the Mole changes the dip in the line of the Leith
Hill country, and the escarpment of the lower greensand falls back north-
ward to Brockham, Betchworth and Ileigate ; and between the latter place
and Crawley there is a very broad exi)anse of Weald clay. One flexui-e, at
least, was wanted to account for this broad expanse ; and one was pointed
out to rae by an intelligent observer, who caught sight of it in a road cut-
ting at Norwood Place, between Leigh and Horley. It is there a small valley
of elevation, and conveys an affluent of the Mole, and is probably a con-
tinuation of Mr. Hopkins's Bidborough line. I am told also by Dr. Fitton
that there is another notable flexure in the Maidstone district, which brings
lip the Weald clay through the greensand south of Pennenden Heath,
a circumstance which might be predicated of the broad expanse of the
greensand country east of the Medway.
the London and Hampshire Basins. 195
Ordnance Map^ it is to be observed that there is a very remark-
able valley separating the broad expanse of lower greensand
country in the neighbourhoods of Maidstone and of Sevenoaks,
into two groups : I shall call it the valley of Plaxtole, from the
village of that name. Here all the thick and tenacious beds of
the Kentish-rag, as well as the upper beds of the greensand, have
been swept clean away, so that the drainage from the country
up to the foot of the chalk hills, above Ightham and Rotham
(through which this fissure does not appear to extend), is brought
down by a rivulet running in the bottom of the valley, due south
toward the Medway, near Tunbridge. The escarpments of this
valley are anticlinal; and there is, unless it has been lately
quarried away, a remarkable group of rocks on the road from
Plaxtole to Crouch, tilted westward, and giving undeniable
testimony of the extraordinary swell of the Weald clay below.
Another remarkable instance of this sort of anticlinal may be
seen in a ridge running north and south between Wotton and
Portnail, and crossed by the road from the former place to Dor-
king. This anticlinal ridge throws the watershed of the country
westward into the Wey by Albury and Shalford, and eastward
into the Mole by Dorking. And there can be no doubt that
the copious springs which arise in that part of the Leith Hill
country, each side of this anticlinal, are thrown out by the same
disturbance. If we turn to the south side of the Weald again,
we find examples of the same sort of transverse anticlinal dispo-
sition. The affluent of the western Rother, which in my early
publication I have called " the Lod," cuts the high grounds of
lower greensand at Lodsworth transversely ; and the anticlinal
disposition is to be seen at Halfway-bridge on the Petworth
and Midhurst road. Again, the same disruption is to be observed
where another affluent of the river before-mentioned runs by
Petworth. The tilting of the beds east and west is visible in the
hollow ways near the bridge, on each side of the stream at
Haslingbourne*.
Of the transverse valleys, and the fissures in which they ori-
ginated, which properly belong to the more prominent longitu-
dinal flexures, and which Mr. Hopkins has made use of in illus-
tration of his theory of elevation, I will cite two remarkable ex-
amples. They have already been cursorily mentioned in my former
memoir (pp. 48 and 134), but it will be well to pay more particular
* I quote from memory, but I think that there appeared in the " Pro-
ceedings of the Geological Society " some time since, a description of a
transverse upheaval like these here spoken of, which could be traced all
across the Weald from th6 neighbourhood of Bletchingley to the South
Downs, controlling and directing the watershed east and west. I have not
examined the ground, but I have no doubt of the fact, as there described.
196 Mr. P. J. Martin on the Anticlinal Line of
attention to them now, as offering in themselves an epitome of the
very extensive disruptive operation, to which, in my earhest dis-
sertation on this subject, I gave the name of " the cross-fractures
of the Weakl denudation." The anticlinal of Peasemarsh or
great flexure of the Hogsback shows its greatest intensity at the
first-mentioned place, that is, the greatest elevation of the
subjacents of the greensand are there ; and there the transverse
fracture shoots off northward to transmit the Wey through the
chalk at Guildford, and southward, to bring down a tributary to
the same river from the Weald. If we turn to the great anti-
clinal of Greenhurst, under the South Downs, we find a still
more remarkable example of the same arrangement. This flexure
acts most forcibly between Warminghurst and Henfield ; there,
the Weald clay rises highest, the greensand is entirely swept
away, and a saddle of Weald clay left, with a small outlier of the
sand at Ashurst. In this part of the " Valley of Elevation "
thus formed, two transverse valley fissures present themselves ;
one to convey the Adur through the South Downs in a straight
line to Shoreham. The other, a little further west, is the Vale of
Findon, through which runs the Worthing road.
Over and above these various larger lines of contortion and
fracture, it may be observed, as before adverted to, that change
of dip has had some influence in fissuring and breaking up these
masses. Eveiy such change, if sudden, would produce fracture ;
if more gradual, it would produce contortion and crumbling.
And many of the minor valleys and slopes and lines of drainage
are evidently the result of the crackings and twistings of the
minor disturbances before spoken of. So that, on a general
review of these phaenomena, one is led to the conclusion, that,
although some order is to be observed, answering to the tensive
influence, — greatest in the shorter axis of the upheaval, and less
in the longer axis, — yet the result answers to my earliest pro-
position,— " the effect of raising from the horizontal position, or
in any other way stretching ponderous and frangible bodies, is
to produce a division of their parts in such order and in such
direction as their varying strength and tenacity dictate," — and
that all the surface-changes of the Weald answer to this predi-
cament.
There is yet one remarkable feature to be noticed before we
quit this important branch of our subject. It is the broad and
expanded surface and unvarying course of the central anticlinal
line, from which we see all the principal subordinate ones rolled
back, as it were, on either side.
If we take our stand on that part of it called the '^ Forest
Ridge," — the ground made familiar to all who take interest in the
vestiges of extinct organisms, by the labours of one in whom
the London and Hampshire Basins.
197
palaeontology is a passion, and whose indomitable energy
triumplis over the difficulties of position and infirmities of health,
and makes himself the object of our own "especial wonder ^^ —
from the commanding points of this elevation, we look north and
south over the long ranges of longitudinal flexures, and observe
that the most strongly marked and most influential of these are
the most distant ; they lift the chalk downs on either side and
regulate their position. The strong flexure of the Hogsback is
propagated from Farnham eastwards in a strong line of elevation,
at least as far as Sevenoaks* ; and it is more than matched by
the Greenhurst line, which, with little intermission, regulates the
escarpment of the South Downs from Beachy Head to the borders
of Hampshire. If we advance further west and take our stand
at Itchingfield or Five Oaks, we find that we are still within the
range of the same disruptive courses ; and looking west from
thence, we see in the profile of the country before us, and at
twelve miles distance, the passage of the central line of elevation
through the lower greensand, in the shape of a valley of eleva-
tion at Haslemere, flanked by the bold eminences of Black Down
on the south and Hindhead on the north.
Profile of the Haslemere country, seen from high grounds at
Itchingfield.
Blackdown.
Haslemere.
Hindhead,
Let us advance again to Yar Down in the Alton Hills, and
thence along the chalk dome of Hampshire, and we find our po-
sition again flanked by similar disruptions; the Winchester,
Warminster and Wardour lines of flexure on the south, and the
Eurghclere Hills, and the anticlinal vales of Pewsey and Kings-
clere on the north. In all this long range of country the same
arrangement of hill and valley, the joint operation of fracture and
aqueous erosion, and the same transverse river-courses obtain;
a structural arrangement that cannot but compel the belief of a
unity of cause.
The superior breadth and volume of this central line of eleva-
tion within the Weald denudation, its uniform and almost un-
broken course, make it the body of which the lesser anticlinals
are the wings. And from the greater prominence, and more
notable character of the distant flexures under the chalk downs
* Hopkins, Geol. Trans, loc. cit. ; and Dr. Fitton, vide supra.
Phil. Mag. S. 4. Vol. 2. No. 10. Sept. 1851. P
198 C. L. Dresser on the Conducting Powers of Wires
on each side, we infer that it is there the antagonistic resistance
more effectually overpowers the momentum of the central mass*.
Ideal of upheaval.
Entertaining the idea that all these contortions are super-
ficial and contemporaneous, and the result of a leverage from
below more uniform and of much wider extent, we hasten to the
conclusion, that the protrusion of the Wealden beds through the
chalk, and of the chalk through the tertiaries in this line of ele-
vation, extensive as it is, is only a part of a much greater whole.
We shall revert again to this consideration in the sequel.
[To be continued.]
XXIX. Eocperiments on the Conducting Powers of Wires for Vol-
taic Electricity. By C. L. Dresser, Esq.-\
THE instrument used in these experiments was the glass
thread galvanometer of Ritchie, described in the Philo-
sophical Transactions J. This instrument, though one of the
most perfect kind, easy of construction, well adapted for the
measurement of electro-magnetic forces, and extremely accurate,
has not received that attention from scientific men to which the
facility of its use entitles it. Requiring no calculation, a vast
number of experiments may be read ofi" in rapid succession.
A few alterations were made in its construction.
1. The graduated card placed under the needles was discarded
as being no measure of the forces exerted, and a plain card with
a black mark under the centre of influence of the conducting
wires substituted. To this mark the needles were carefully ad-
justed at every experiment.
* It is not to be supposed that we mean by this, that the Downs quoad
Downs had any share in this resistance, but only that the central impulse
gradually fading in the distance is there more successfully resisted. Tiie
long synclinal that extends with but little interruption northward from
Hindhead, terminating in the sudden flexure of Peasemarsh and the Hogs-
back, is strongly illustrative of the antagonism here spoken of.
t Communicated by the Author.
X Philosophical Transactions, 1830, p. 218.
for Voltaic Electricity.
199
2. The graduated card at the top was enlarged to five inches
diameter, and carefully graduated to degrees ; and by an index
traversing this card_, the degrees of torsion necessary to bring the
deflected needle vertical to the black mark on the lower card was
read off easily to a fraction of a degree.
3. The graduated plate turned on its own axis independently
of the axis of the glass thread, rendering the adjustment of the
needles easy and perfect.
4. The needles were considerably increased in size and highly
magnetized
With these alterations the action of the galvanometer was cer-
tain and delicate, returning after even a deflection of a thousand
degrees, or three times round the card, with certainty to the
index mark on the lower card ; and the same experiment repeated
corresponding to the fraction of a degree.
The battery used was my gas-carbon battery, and the follow-
ing means were adopted to keep it constant.
1. The nitric acid cell was filled with the acid of commerce,
but the zinc cell only half-filled with dilute sulphuric acid.
2. The prism of carbon was suspended at its top to a rack-
work, by which its immersion to a greater or less depth was
regulated ; consequently any required amount of electricity ob-
tained.
With these precautions a constant current of electricity was
maintained for hours ; rarely varying, after efi'ecting a torsion of
three or four hundred degrees, one degree for hours. By this
means also, at all times the same amount of current could be
obtained, rendering it easy to recommence the experiments.
Table I. — Battery power 400. Each wire was No. 20.
Feet.
Copper wire.
Differences.
Feet.
Iron wire.
Differences.
1
398
1
330
2
380
18
2
280
50
3
365
15
3
240
40
4
352
13
4
210
30
5
340
12
5
190
20
6
330
10
6
172
18
7
320
10
7
158
14
9
296
24
9
135
22
10
286
10
10
128
7
12
269
17
12
112
12
14
254
15
14
100
12
16
240
14
16
92
8
18
230
10
18
85
7
20
220
10
20
78
7
22
73
5
24
68
5
26
64
4
28
60
4
P2
200 C. L. Dresser on the Conducting Powers of Wires
From the above table of experiments, it is evident that the
often quoted law of the conducting power of wire being inversely
as the length does not obtain in short lengths. But there is an
evident intimation of some other law, and probably different for
different metals.
Broke glass thread. New thread gives 300 without altering
battery power.
Table II.— One cell. No. 16 wire.
Feet.
Copper.
Differences.
Iron.
Dififerences.
I
282
256
2
275
7
235
21
3
268
7
217
18
4
262
6
200
17
5
256
6
187
13
6
148
5
175
12
7
138
5
164
9
8
133
5
157
7
From this table, compared with Table 1., it does not appear
that with a thicker wii'e there is any nearer approach to the old
law, but also that some other law obtains.
Table III.— No. 16 wire.
Battery power 400.
cells.
Intensity two
Feet.
Copper.
Dififerences.
Iron.
Differences.
1
400
355
2
391
9
320
33
3
382
9
294
26
4
476
6
270
24
5
370
6
252
18
Increase of intensity does not appear to approach near to the
supposed law.
Table IV. — Wire measured with a micrometer in hundredths of
an inch. Battery power 207. One foot of wire. Diameter
of galvanometer wire 740 of an inch.
Measure.
Copper.
Current con-
ducted.
Measure.
Iron.
Current con-
ducted.
370
480
700
740
190
195
206J
207
360
510
640
720
129
165
182
188
for Voltaic Electricity,
201
The wires of iron and copper on parallel lines were said to be
of the same gauge, but the micrometer showed them to be of very-
different diameters. This table does not coincide with the law
of the conduction of wires of different diameters being as the
squares of their diameters.
Power of hydrogen to abstract the heat produced by the passage
of electricity.
Battery power 410. Current through steel wire 175 hundredths
of an inch.
Quantity conducted.
220 . wire red-hot in air.
310 , in hydrogen,, and invisible in the dark.
In this experiment battery power not observed.
Same wire as above.
In air red-hot .... 220
In current of air, quite cold 270
It would appear that the heating power of a current of electricity
diminishes the power of conduction; also that hydrogen, by
absorbing the heat, has the same effect as a current of cold air.
Table V. — No. 20 wire placed in the air-bulb of sulphuric acid
thermometer.
Battery
power.
Differences.
Current
conducted.
Differences,
Degrees of
heat.
Differences,
Q7
58
26
92
25
73
15
44
18
107
15
84
11
75
31
124
17
91
7
90
15
145
21
100
9
124
34
170
25
102
2
143
19
202
32
108
6
160
17
These experiments, very tedious and difficult to conduct, do
not appear to indicate any particular law.
Much in this department of electricity appears yet to be done
before we are able to define the laws of conduction, and there
are many difficulties to be encountered. It is almost impossible
to get wire of any length of equal thickness and texture. It is
also not easy always to obtain the same connexions, and the least
variation in this respect vitiates the experiments. Some of the
anomalies in the tables are to be traced to these causes.
A difference of temperature also, it appears, will affect con-
duction. Even bending the wire with so delicate an instrument
as the torsion galvanometer will affect the experiment; and
twisting will alter its powers permanently.
[ 202 ]
XXX. Suggestions for the Preparation of Phosphorus.
By M. Donovan, Esq,, M.R.I.A*
PHOSPHORUS, a substance abundantly diffused throughout
the animal, vegetable, and mineral kingdom, is obtained
by processes which, although they have undergone many altera-
tions and improvements during nearly two centuries, are still
troublesome, expensive and difficult. According to M. Hellot's
method, the description of which occupies many pages in the
Memoirs of the Academy of Sciences, 1737, in order to obtain
one ounce of phosphorus we must submit to the tedious and dis-
gusting process of evaporating nearly three hogsheads of putrid
urine. Dolfuss, who was more successful, obtained but 54 grains
from 100 pints. Henckel first and Marggraff afterwards, by
adding plumbum corneum to urine evaporated to thickness after
being allowed to putrify for two months, procured two ounces
and a half of phosphorus from nine or ten pounds of the inspis-
sated matter: by this improvement the product was doubled,
provided that the persons from whom the urine was obtained in-
dulged in drinking malt-liquors in preference to vinous. But
still its price was enormous. Mr. Boyle induced a chemist
named Bilgar to extract it from very old night-soil. By some
unknown addition Bilgar produced it so abundantly from this
source, that he lowered the price of it to six guineas per ounce,
yet made a large fortune. It could now be purchased for about
half as many shillings. Giobert, by precipitating fresh urine
with acetate or nitrate of lead, obtained a powder, from 100 parts
of which he distilled from 14 to 18 of phosphorus.
But when Gahn discovered that the earthy part of bone con-
sists of phosphate of lime, a more abundant and available source
of phosphorus was made known to chemists. Crell accordingly
decomposed bone-ashes by caustic alkali, dissolved the mass in
water, precipitated it by nitrate of mercury, and distilled the
phosphate of mercury with charcoal in the usual manner. But
the phosphorus so obtained contains mercury ; just as it contains
zinc when sulphate of zinc is used for the separation of phos-
phoric acid from bone-ashes.
At length the present processes were contrived : bone-ashes
were mixed with dilute sulphuric acid ; a solution was thus ob-
tained consisting of phosphoric acid holding some lime dissolved.
This was either evaporated to dryness and distilled with char-
coal, or it was precipitated with a salt of lead, and the precipitate
distilled with charcoal ; or it was neutralized with ammonia,
filtered, and evaporated to dryness ; the ammonia was expelled
by heat, and the glassy residue finally distilled with charcoal.
* Communicated by the Author.
M. Donovan on the Freparation of Phosphorus. 203
By the distillation of the phosphoric acid with charcoal, Wiegleb
obtained ten drachms and a half of phosphorus from two pounds
of bone-ashes. In the hands of Dolfuss, the same quantity of
bone-ashes furnished rather less than five drachms. Pelletier
sometimes obtained so much as 3^ ounces, and sometimes but
half that quantity from two pounds of bone-ashes.
Although these methods may be thus epitomized, the prac-
tical details are very troublesome. It is not always easy to obtain
an adequate supply of bone-ashes. So truly did Lagrange ap-
pTCciate this difficulty, that in his instructions for burning bones,
he dii'eots. as the^^t step that a brickwork one yard in diameter
and nine inches high shall be erected. Others order a furnace
for the purpose, the chimney of which must necessarily be high,
in order to carry off the truly abominable fumes. When the
burnt bones are procured, the task of pulverizing and sifting
them, so that their substance shall be permeated and acted upon
by the sulphuric acid, is of no small labour, as the middle por-
tions of the cylindrical bones are exceedingly hard. The wash-
ing out of the phosphoric acid from the voluminous, pasty, and
somewhat tenacious sulphate of lime, is troublesome ; for much
of the acid obstinately adheres. If the sequel of the process be
to obtain the acid in the solid state, the evaporation of the various
washings to dryness is exceedingly tedious. But when lead is
employed to engage the phosphoric a(dd from the washings, the
resulting phosphate of lead is so bulky, so retentive of water,
and by the ordinary means so difficult to dry, that the increased
quantity of phosphorus procurable in this way scarcely compen-
sates the trouble and loss of time. Beside all this there is an-
other defect ; the precipitate, whether obtained from acetate or
nitrate of lead, contains lead in some state different from the
phosphate, more in the case of the former salt than of the latter,
and thus, during the distillation, the retort is partly occupied
with an unproductive material. The acid liquor, beside phos-
phate of lime, always contains a little sulphate of lime, great in
proportion to the quantity of water used in the washing; and
this gives origin to sulphate of lead, which not only uselessly
occupies the retort, but by suffering decomposition, during the
distillation with charcoal, evolves sulphur ; and this inquinates
the phosphorus produced to a certain extent.
The precipitation of acetate or nitrate of lead by fresh urine,
and the distillation of the precipitate with charcoal, might to
some persons appear a convenient and simple process when large
supplies of urine can be procured at once, as in barracks, hos-
pitals, or prisons. But the advantage is far from being so great
as it appears ; for there are other substances present besides
phosphates, which will afford precipitates with salts of lead. In
204 M. Douovan on the Preparation of Phosphorus.
an imperial pint measure of ordinary urine, according to the
analysis of Berzelius, there are but 41 grains of phosphates,
while there are nearly three times as much of other salts, all
capable of precipitating acetate or nitrate of lead. Thus but a
small part of the precipitate is available for the purpose, and the
retort is uselessly occupied with substances which contribute
nothing.
From bones, it is true, we procure phosphorus more easily,
and in greater quantity ; but so long as we follow the process
given in chemical works, the details, as already shown, are ex-
tremely troublesome. On this account I have sought for a
more simple method.
Bones are procurable in various commercial states ; we have
them solid ; ground to a coarse powder between crushing rollers,
for manure ; distilled in close vessels for carbonate of ammonia,
and the residual charred bone afterwards ground to a powder,
well known under the name of bone-black ; or in small particles
obtainable from the lathe of the bone-turner. In all these states,
bones afford phosphate of lime ; but there are other sources, one
of the most abundant of which is the horn of certain animals.
The horns of the Stag {Cervus elaphus) and of the Fallow-deer
(Cervus dama), and perhaps those of the whole class of Cervidae,
furnish phosphate of lime abundantly; but those of the Ox, Ram,
Goat and Chamois, scarcely contain any. The commercial repre-
sentative of the horn of the Stag or Fallow-deer is known under
the name of shavings of hartshorn, and may be procured in great
abundance.
Many analyses of bone have been published by chemists ; but
their results are so utterly discordant, owing to the different
states in which the bones were examined, that I could not collect
from them the ratio of salts which constitute the earthy basis.
To arrive at the required information, I made many trials of
recent bones, containing theirnatural quantity of fat and moisture,
and obtained the following average results. Recent ox-ribs, from
which the flesh had been carefully scraped, when calcined to
whiteness, afforded 37*14 per cent, of earthy matter. Recent
sheeps^ bones (from the leg), when similarly treated, returned
38*71 per cent. It may be concluded then that a mixture of
dense, recent bones, with which no pains have been taken to
remove fat or moisture, will afford about 38 per cent, of earthy
salts by incineration. A very porous ox-bone gave but 21 per
cent. Neumann obtained 40*6 per cent. Fourcroy and Vau-
quelin give 49 as their result. Berzelius states his product to be
61 per cent. Von Bibra quotes 66*78 per cent. These great
differences arise from the variable ratio of fat and moisture in
the bones^ which however I took no pains to remove.
M. Donovan on the Preparation of Phosphorus. 205
With regard to the quantity of earthy salts contained in harts-
horn, few analyses have been made. Dr. Pearson calcined his
hartshorn-shavings to a brown colour, and obtained 54| per cent.
Neumann, who only tried the tops of the horns, recoveredGOpounds
of black caput mortuum from 100 pounds. Many trials gave
me an average of 62 per cent, when the shavings were burnt to
whiteness. These white ashes consist almost entirely of phos-
phate of lime; and it appears that hartshorn by calcination
returns at least twice as much phosphate of lime as fresh bones.
The horns of a fallow-deer will weigh about \^ pound.
These different fornas of bones and horns present us with
phosphate of lime ip^tates which possess different advantages :
some^old,_out4h6 inducement of cheapness ; some of facility in
employing them : all of them answer the purpose. Ground
bones may be procured in Dublin at so low a price as 35. per
bushel, weighing about 42 pounds. Bone-black, the caput mor-
tuum remaining after the distillation of carbonate of ammonia
from bones, may be had in quantity at 85. per cwt. This black,
by exposure to a red heat in the open air, becomes white bone-
ashes; but the process is not necessary. Hartshorn-shavings
are expensive, being so high, even in quantity, as Sd. per pound ;
but as the ratio of phosphate of lime contained in them is nearly
double, we may estimate them at 4|^^. ; and if their cleanliness
and facility of employment be taken into account, they become
still more eligible. But what renders their claims to preference
paramount, is that even after having been kept a very long time,
they contain an ingredient in perfectly good condition, which,
when dissolved in w^ater and properly seasoned, constitutes a
light, highly nutritious, and most agreeable jelly, which has
found its way to the kitchen, the nursery, and the sick room. A
legally-authorized process for preparing it is given in many of
the Pharmacopoeias of Europe. Bone also possesses an analogous
substance, which, although it cannot be extracted with the same
facility, and after a lapse of time is not in good condition, has
been recommended in its recent state as an article of food. Every-
one is aware of the employment of the Digester for the purpose
of its extraction.
In order to remove the animal matter from the earthy portion
of bones, the process of calcination is resorted to ; but it is un-
ceconomical, and very troublesome. Instead of this, it will be
better and much easier to withdraw the earthy portion from the
animal matter, and thus preserve both for use. The separation
is easily effected by digesting the bones either in muriatic or
very dilute nitric acid : the earthy salts will thus be dissolved
away, and the cartilage, retaining the shape of the bone, will
remain unaltered. It will presently be shown that diluted com-
mercial nitrous acid is better adapted for the purpose.
206 M. Donovan on the Preparation of Phosphorus,
After the nitrous solution of the earthy salts has been obtained,
the next step is to detach from it the phosphoric acid. This can
be done in the usual manner by a salt of lead. Chloride of lead,
although successful in the process of Henckcl and Marggraff,
does not answer here ; for a boiling solution of it added to the
nitrous solution does not produce any precipitation ; and chloride
of lead crystallizes as the mixture cools. Nor will nitrate of
lead occasion a precipitate ; for the phosphate of lead, if it be
formed at all in this case, remains in solution in the free nitric
acid. Acetate of lead answers the purpose perfectly : if a solu-
tion of it be poured into the nitrous solution of phosphate of
lime, phosphate of lead precipitates instantly.
It has been stated by Giobert that when acetate of lead is^
poured into a solution obtained by acting on bone-ashes with di-
lute sulphuric acid, the acetate is decomposed, not only by the
phosphoric acid, but, as he believes, by the water ; and he adds,
that the precipitate not only contains phosphate of lead, but calx
of lead, which adds materially to its quantity. He'further states
that nitrate of lead comports itself in the same manner but in a
less degree ; and hence he recommends the employment of ni-
trate of lead for detaching the phosphoric acid. In the pro-
cess recommended by me, as the precipitation takes place in a
liquid which contains a considerable quantity of uncombined
nitric acid, the objection of Giobert to acetate of lead cannot
apply.
As to the choice of one amongst these different sources of
phosphate of lime, circumstances must decide. If the process
be conducted in the large way, bones ground between crushing
rollers, or even broken into moderately small bits, will be found
to answer, and to be the cheapest form : the cartilage that re-
mains may be converted to many oeconomical uses, for instance,
the making of glue, or of an excellent size. If bone-black be em-
ployed, according to the process already described, the residuum
is animal charcoal, which, after being washed and heated, is va-
luable as a decolorizing and antiseptic agent. If powder of
burnt bones must be used, there is no incidental advantage, but
the difficulty and trouble of minute division are to be encoun-
tered. The bones in burning ought not to be exposed to a very
violent heat ; for they lose a little phosphorus, as appears by the
white light which issues from them ; and besides this, they suffer
a certain degree of vitrification, which renders them refractory
under the pestle and to the action of acids. When the quantity
of phosphorus to be made is small, and a little additional cost is
no object, the unbumt shavings of hartshorn will perhaps be
preferred. The phosphate of lime may be dissolved out of them
by means of dilute commercial nitrous acid with facility, and in
a very short time ; the process is cleanly ; does not require large
M, Donovan on the Preparation of Phosphorus. 207
vessels ; and the jelly which may be obtained from the residuum
is delicate and nutritious.
When unburnt, crushed or unburnt broken bones^ whether of
beef or mutton, are to be used, provided they be of the dense
kind, I found that the quantity of '^ commercial nitrous acid "
requisite to dissolve the earthy matter is nine ounces and two-
fifths avoirdupois to one pound avoirdupois of bone. When the
same kind of bones have been burnt to whiteness, the ratio must
be 26^ ounces of acid to yone pound of bone-ashes. The acid
must in all cases be dilute^d with ten times its weight of water.
If unburnt shaving^^of hartshorn be employed, each pound
.avoirdupois will require about 17 ounces of commercial nitrous
acTdr — This^^aeid^ is procurable at the price of about Qui. per
pound wholesale.
With regard to the quantity of commercial sugar of lead re-
quired for the precipitation of the phosphoric acid contained in
bones, the following ratio will be found adequate. For unburnt,
crushed or broken bones, if not old, 1 pound avoird. will require
13 ounces. If bone- ash be used, 1 pound will require 41^ ounces.
For 1 pound of unburnt shavings of hartshorn, 1^ pound of
sugar of lead will be necessary.
The cost of sugar of lead, wholesale, is about 5^. per pound :
but much of its expense may be saved in the following manner.
When nitrous solution of bone or hartshorn is precipitated by
means of sugar of lead, the phosphoric acid seizes on the oxide
of lead, and the nitric acid combines with the lime. If the so-
lution be filtered and evaporated, nitrate of lime is obtained.
But the solution contains the acetic acid of the sugar of lead
employed ; and if it be boiled on carbonate of lead, which may
be purchased at M. per pound, a solution of sugar of lead will
be regenerated which will answer for a new precipitation. At
length the liquor becomes so rich in acetic acid, that on a large
scale of manufacture it will be well worth while to distil it for a
product of pure acetic acid.
When the phosphate of lead is first separated, it contains ni-
trate of lime j from this it must be freed by washing, otherwise
some phosphoric acid will be regenerated at the expense of phos-
phorus during the subsequent distillation.
The common process of drying the precipitated phosphate of
lead on the filter is tedious, troublesome, and inconvenient ; so
tenacious is it of water that it will long remain a thin paste. I
find the best mode of drying it is to transfer both filter and preci-
pitate to an iron pot, and to heat it until the matter fall to powder.
Any part of the paper that escapes burning may then be picked
out. The drying is thus easily and quickly accomplished.
The phosphate of lead, when dry, is a voluminous powder : a
208 M. Donovan on ttie Preparation of Phosphorus.
retort of ordinary size would not hold a sufficiency of it to re-
turn a remunerative product of phosphorus. This inconvenience
is not peculiar to the processes here given, but affects all others
equally in which a salt of lead is employed. There is however
an easy remedy. Let the phosphate of lead be transferred to the
kind of crucible called a skittle-pot, and let the crucible covered
be heated red-hot in a common coal fire : it will during the
heating shrink at least to one-half its former bulk; but the
weight will be scarcely diminished. It will be still a loosely
aggregated pulvei-ulent mass ; if the heat be increased, it will
shrink more and melt, but it then becomes rather difficult to
powder.
The last step in the process is the distillation of the phosphate
of lead with charcoal. The phosphate and charcoal, both in fine
powder, and well mixed, are to be introduced into an earthen-
ware retoi-t, the pores of which have been closed with a glaze
consisting of borax and lime as directed by Higgins.
On account of all the foregoing facts, I conclude with recom-
mending the following as the easiest and cheapest processes for
obtaining phosphorus : —
Take of dense bones, crushed or broken into small pieces, as
many pounds as may be deemed sufficient, say ten avoirdupois
pounds. Digest them in a mixture of 6 pounds of commercial
nitrous acid and five gallons of water for a few days. When the
bones feel perfectly soft and flexible, strain oif the liquor, and
add to it 8 pounds of sugar of lead dissolved in a sufficiency of
water. An abundant precipitate will appear ; wash and dry it by
heat in the manner already directed. Its bulk will be reduced to
one-half if it be heated red-hot in a crucible. Mix it well with
one-sixth of its weight of fine charcoal powder or lampblack,
and distil out of large earthen retorts properly prepared.
The phosphate of lead resulting from the above process would,
according to my trial, amount to 91^ ounces avoird. Giobert
states that 100 parts of phosphate of lead precipitated from urine
by acetate of lead affbrded from 14 to 18 parts of phosphorus.
If this be a correct estimate, the 91^ ounces should return from
12 ounces to 1 pound of phosphorus. A large quantity of car-
tilage is also obtained, which is well calculated for making size,
glue, and for many other purposes.
The following is a shorter, neater, and less troublesome,
although a little more expensive process for preparing phos-
phorus, which may be employed when the quantity required is
not very large. Take of unburnt shavings of hartshorn 1 avoir-
dupois pound ; digest it for four hours in a mixture of 17 ounces
weight of commercial nitrous acid and one gallon of water.
Strain the liquor, and add to it 1 j pound of sugar of lead, pre-
On a remarkable Flood at Chipping in Lancashire, 209
viously dissolved in a sufficiency of water : mix, and let the pre-
cipitate subside. Pour off the supernatant liquor; dry and
wash the precipitate as already directed : mix it with one-sixth
of charcoal powder or lampblack, and distil as before.
The charcoal powder or lampblack will in all cases afford a
better product if previously well calcined in a crucible covered
with sand, or in any close vessel. The waste of phosphorus, by
solution in the gas evolved during the subsequent distillation,
will thus be much lessened; and the same end will be further
promoted by a previous exposure of the phosphate of lead to an
obscure red heat, which will also cause a reduction of bulk to
one-half.
These processes appear to ceconomise time, trouble, fuel, and
cost of large vessels. On the whole, they are probably the best
when bones or horns are to be the source. In the Province of
Estremadura, the hills contain considerable quantities of phos-
phate of lime, and houses are built of it in the district of
Truxillo. This stone, when thrown on the fire, emits a beautiful
green light. I know not whether phosphorus can be profitably
extracted from it.
XXXI. An Account of a remarhahle Flood at Chipping in Lanca-
shire, By the Rev. Alfred Weld, B.A., F.R.A.S., M.B.M.S.
- To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
I TAKE the liberty of presenting you with some details of a
very remarkable flood with which this neighbourhood was
visited during the afternoon of July the 1st. The accounts
which reached us of its effects, as well as the subsequent appear-
ance of the river into which the waters were poured, were of so
unusual a character, that I thought it worth while to visit the
site, and satisfy myself as far as possible, from my own observa-
tion and the facts I could collect from eye-witnesses, as to the
nature and extent of a storm that had committed such terrible
ravages, and spread such alarm amongst the unsuspecting in-
habitants of Chipping. ,
It would be useless here to enter into all the particulars of the
devastation j such details would possess no general interest, and
are to be found at length in all the local journals ; but the traces
which I witnessed, relating principally to the origin and extra-
ordinary force of the inundation, and the information I gained
regarding the distribution of the storm in the neighbourhood,
will, I think, afford points of scientific interest ; and it is with
this view I have determined to offer this little account to you,
210 The Rev. A. Weld on a remarkable Flood
hoping that it may be found worthy to be laid before your
readers.
The little village of Chipping lies near the bottom of the val-
ley contained by the parallel ridges of Bowland Hills and Long-
ridge Fell, which bound it on the north-west and south-cast,
leaving it open to the sea in the south-west, while in the east
and north-east the horizon is terminated by Pendle Hill and the
Newton and Waddington Fells. It is watered by a brook to
which it gives its name, whose waters flow in general through a
deep rocky channel lined with wood, but in some parts of their
course emerge among meadows and pasture lands. In ordinary
circumstances it is a shallow stream, barely covering the stones
which form its bed ; but occasionally swollen into a torrent, for
which, however, its natural channel is amply sufficient. This
brook is formed by the junction of two little streams, the extreme
distance between whose sources can scarcely be more than two
miles. It is along the course of these brooks that traces are
exhibited which show the character of the flood, and in my
opinion render the details of all further ravages easily credible.
I was assui'cd that the smaller of these brooks, called Dob-
son's brook, does not di-ain at most above 150 acres of land;
and yet even near its source it bears signs of having been washed
by a furious torrent, such as no ordinary thunder-storm can
account for. Its waters enter the main brook a little more than
a quarter of a mile above Chipping. A little above this place a
weir had been constructed of strong masonry to turn a portion
of the waters to the village mill. This was entirely demolished ;
and one of the stones, which I found to measure 5 feet in length
and 1| in breadth, carried to the distance of about forty yards
and imbedded in the mud of the brook. In places where the
channel widened, the bed was strewn with large stones piled
up in great heaps, every stone bearing evident traces in its chip-
ped and bruised surface of having been rolled and dashed along
by the current. Some blocks of limestone of considerable size
had been freshly broken in two by the force with which they
had been thrown. In order to satisfy myself that these efi^ects
were produced by the rolling of the stones themselves, and not
merely by the passage of smaller stones over them, I caused
some of tne larger of them to be turned over, and found exactly
the same bruised and chipped appearance on every side. A
large stone, which was estimated to weigh about 7 cwt., and
which had been used for a stepping-stone where a path crosses
the brook, was carried about a quarter of a mile down the stream.
Another, which could not have weighed less than 12 cwt., showed
signs of having been borne along by the torrent.
Smaller stones appear to have literally floated, as they may be
at Chipping in Lancashire. 211
found strewn upon the ground several feet above the steep bank
of the stream ; and trees stripped of their bark, four or five feet
above the bed of the brook, by the passage of stones, bear testi-
mony to the force of the current. Where the channel is narrow,
the wreck is still left hanging at the height of seven, and in one
place of nine feet, above the usual surface of the water. In
some places the bed has been lowered to the depth of a yard ;
in others a new channel has been worked out in the clay, and
the old one filled up with stones and gravel.
At intervals throughout its course trees of considerable size
have been rooted up and carried down till some immoveable
obstacle arrested them, or left dry upon the fields on the retiring
of the waters. I learned from a farmer living by the side of the
brook, that the flood reached its height in less than twenty
minutes, and that for the space of about half an hour the rain
fell with extreme violence. At a small farm a little to the west
of this, and situated on an exposed declivity on the southern side
of Saddle Fell, I was told that the rain fell with great violence
for above two hours. It was described to me as having the
appearance of flakes of snow, and it was said that ^^ every drop
seemed of the size of a half-crown. ^^ At this place the water
streamed down the road to the depth of from one to two feet ',
and yet upon examination I found that the whole extent of
ground drained by this road could scarcely be half an acre. This
will aid in conveying an idea of the extraordinary and even tro-
pical violence of the rain which could have produced such a flood
in so short a period. The summit of this road is the extreme
limit of the lands drained by the little brook of which we have
been speaking.
An observer standing at this point and facing west, has before
him a spacious basin, open on the left, bounded by Parlick in
front, and by the main chain of hills on the right. Beneath is
the principal brook which terminates in two gorges among the
hills, from which its waters are supplied. The easternmost of
these, called Greenlough Clough, presented a sight more asto-
nishing than anything I had ever seen. At the point where its
bed opens out from the hills, scarcely a mile from the watershed,
many hundreds of tons of large stones are thrown together in a
great heap, covering an area of about forty yards in extreme
width and at least eighty in length. These stones had been
carried down the steep ravine by the impetuosity of the torrent
and heaped up at this place, where the waters, being spread over
a larger surface, had no longer the force to bear them along.
Still, on ascending the ravine and examining the sides of the
hill above the mark which the waters had reached, I found the
heath and fern growing fresh and unsullied, and presenting no
appearance of having been washed by any great flow of water. "
212 The Rev. A. Weld on a remarkable Flood
It now remains to describe the scene to which my attention
was principally directed, and which alone suffices to distinguish
this flood from all others that I have ever witnessed, or which
have ever been known in this part of the country.
The eastern side of Parlick, which rises to the height of about
1400 feet above the sea, presents an exceedingly steep ascent
richly clothed with fern. On this face of the hill seven huge
scars have been hollowed out by the water, varying from five to
fifteen yards in width, all cut abruptly from the face of the hill ;
and with the exception of two of the most southern, which are
somewhat lower, all commencing nearly in the same horizontal
line. There is in no case any appearance of a water-course open-
ing into them, but in every instance the upper limit is fonned
by a definite line, like the edge of a cliff. The depth to which
the ground has been carried away varies from one or two to
five .or six feet. Between these slips the fern is still green
and flourishing, and I am quite sure that no great body of water
can have passed over it. A little above one of the slips whose
upper limit is lower than the others, the fern is beaten down,
and appears to have been washed by a torrent ; but there is no
channel opening into the hollow produced by the slip, the com-
mencement of which is no less abrupt than the rest. Hence it
appears that several distinct discharges of water must have taken
place, of such tremendous violence as to be able to carry away
hundreds of tons of earth and stones, whilst the land between, in
narrow strips often or twelve yards in width, remained untouched.
The volume of water which flowed down the seven channels
must have been enormous, since the stones and earth are spread
over acres of land below. In some places the stones are thrown
up at the edges of the stream into a sort of mound, one or two
feet in height, by the force of the torrent. Towards the bottom
of the steep declivity the several streams seem to have united
and formed one great river about 150 yards in breadth. This
must have been in some parts at least five feet in depth, as ap-
pears from the remnants of a wall which ran nearly parallel to
the course of the water. The greater part of this wall is thrown
down; but the portions of it that remain, about five feet in
height, are still covered with mud, showing that they were buried
beneath the torrent. Along the foundations of the wall, a chan-
nel four feet deep was hollowed out where previously no water-
course had existed. This great stream had to make its way
across the land, working out for itself a deep and broad bed, till
it mingled with the waters of the main brook coming from Green-
lough and Whitestone Cloughs.
The devastation which the passage of so great a body of water
must have produced will easily be understood. In one or two
places where I measured the channel, I found its area to be
at Chipping in Lancashire. 213
about twelve square yards, and yet the water rose above its banks
and spread over the land on each side. At a place called Wol-
fenhall Mill on the banks of the brook, I was told that when
the flood first came down, it presented a perpendicular breast of
two yards in height. Considering the great body of water which
suddenly descended Parlick, and bearing in mind what I was
everywhere told, that scarcely half an hour elapsed between the
first rise of the flood and its entire subsidence, I am convinced
that this is no great exaggeration. Great numbers of trees
along the banks were washed away ; all the weirs constructed to
turn the water to the various mills situated near the stream de-
stroyed ; walls and fences overthrown ; and all the meadows and
pastures along the banks covered with stones and sand.
The greatest loss was suffered by the owner of a little cotton-
factory, which stands about ten feet above the bed of the stream.
The water rose to the height of four feet six inches on the ground
floor of the factory, ruining part of the machinery, and covering
everything with mud and gravel. The garden, which was on
the same level as the factory, and was laid out with the greatest
taste, and adorned with many varieties of beautiful shrubs and
flowers, is entirely destroyed. It now presents to the view
nothing but great heaps of stones and rubbish, while every shrub
has been either carried away or buried beneath sand and gravel.
A strong wall which had been built to protect the garden from
the brook was entirely carried away, while many tons of large
stones have been raised to the height of ten or twelve feet above
the natural bed, and thrown up on what were formerly flower-
beds and gravel-walks. In Chipping, the water entered the
houses to the depth of nearly six feet, committing great havoc in
the shops and cellars. The large stones which formed the parapet
of the bridge were washed from their places and carried some
distance up the street ; part of the foundation and floor of a house
carried away ; a wooden bridge washed down the stream, and a
little lower down, a stone bridge almost entirely destroyed ; and
many acres of land covered with mud and gravel, and strewn
with wreck of every description.
Leagram Hall is situated about half a mile from the nearest
point of the brook, and on an elevation of about 200 feet above
it. The roar of the torrent created a sudden alarm ; everyone
ran to the windows, which overlook the valley, and beheld the
water spread out like a lake before them; the waves, which
were visible from that distance, gave it the appearance of an arm
of the sea ; while the rapidity with which it spread over field
after field conveyed the impression of the bursting of a great
lake, whose waters were about to inundate the whole valley.
The rain fell here with great fury for about an hour. A rain-
Phil. Mag. S. 4. Vol. 2. No. 10. Sept. 1851. Q
214 On a remarkable Flood at Chipping in Lancashire.
gauge exposed in the garden became choked with sand; not,
however, until it had collected rain to the depth of 2*2 inches
during that single shower. The hour at which the flood passed
through Chipping was, as far as I could ascertain, about 4^ p.m.
From the account which has been given, it appears that the
ovei-flowing of Chipping brook was mainly attributable to the
sudden discharge of a large volume of water on the side of Par-
lick ; that this discharge must have partaken somewhat of the
nature of a water-spout, and must have consisted of several
distinct discharges, all contained within the space of about 150
yards measured in a horizontal line along the side of the hill.
Besides this, rain must have fallen with extraordinary fury along
the whole extent of hills, as appears from the degree to which
the ordinary sources of Chipping brook were swollen, as also the
other brooks which take their rise in the same range of hills*.
Leagram brook, which descends from the same range but more
to the eastward, was also flooded, but not to such a degree as to
be worthy of any very special notice. Graystoneley brook, which
rises among the same hills but still further to the east, rose sud-
denly, as I was assured, to the depth of a yard. Still, a farmer
who saw it about an hour and a half afterwards, told me there
was no flood, and that the water was merely muddied. I do not
look upon these accounts as altogether contradictory, since all
agree that the subsidence of the waters was as rapid as their
rise. Still the Hodder was not even coloured above the con-
fluence of these brooks, showing that at Whitewell there was no
rain of any consequence, but that the watershed of the Gray-
stoneley brook was the extreme eastern limit of the storm;
whereas the Loud, which rises on the western side of Parlick,
was a great flood even before it received the waters of the Chip-
ping and Leagram brooks. So great an efi^ect had the water of
the Loud upon the Hodder, that even at Lower Hodder Bridge,
where the river flows near Stonyhurst, the muddy waters came
* Some persons who were on the top of Parlick at the time describe the
rain as havine fallen in streams or sheets of water, and affirm that they ex-
perienced difficulty in breathing whilst exposed to it. A gentleman who
was exposed to it in Chipping, told me that he experienced the sensation
of warmth as it fell upon his person, although the day was sultry, and he
was heated with walking at the time.
I have been able to discover no traces of marine deposits, which would
probably have been found if the water had been raised up in a body from
the sea, as is the case in a water-spout. I am inclined to look upon the
discharges as produced by the sudden condensation of a cloud loaded with
an enormous amount of vapour, accumulated doubtless during the previous
extremely hot weather, and thus poured down in a volume on the side of
the hill -.the fact of several discharges having taken place so near to each
other is not so easy to explain.
Messrs. Gladstone on the Growth of Plants in various Gases. 215
down in a perpendicular breast of about a yard in height, driving
the fresh water before it. This point is about 9^ miles from
Chipping, following all the windings of the streams, and about
220 feet lower; and as I find that the flood reached it at about
Qh 30m Y.M., it would seem that it took 2^ 30"^ or thereabouts
to travel that distance, which corresponds to the rate of 3*7 miles
an hour. For several days afterwards the water continued
muddy, and a thick deposit is left all along the banks of the
Hodder and Kibble.
It is worth remarking, that on the south-east side of the valley
bounded byLongridge Fell there was no rain; and in several places
at the bottom of the valley, within two miles of Leagram, I found
on inquiry that there had been nothing but a few drops. Every-
where I was told that the lightning was terrific. At Stonyhurst
there was no rain, but the lightning was very brilliant, and the
thunder almost incessant. The storm appeared to be raging in
the direction of Chipping. Still about two miles to the east, at
Higher Hodder Bridge, the rain fell with great violence for
about fifteen minutes. From a point in this neighbourhood, the
whole range of Bowland Hills appeared enveloped in a dense
black cloud, from some points of which the rain seemed to be
descending in torrents. This feature, and the lurid aspect of
the sky, joined to the frequent displays of lightning of the most
vivid description, rendered the whole scene one of the most im-
posing I remember to have witnessed.
XXXII. On the Growth of Plants in various Gases.
By Dr. J. H. Gladstone and G. Gladstone, Esq."^
THAT both plants and animals are very dependent upon the
chemical composition of the atmosphere in which they live,
and that the constituents of it play important functions in their
oeconomy, are matters of every-day observation. These consti-
tuents are oxygen, nitrogen, aqueous vapour, a small amount of
carbonic acid, a still smaller quantity of ammonia, and occasional
traces of other gases.
Since the plant stores up oxygen within its cells at certain
periods, it can scarcely be doubted that this gas fulfils some im-
portant office ; but, excepting in the case of the germination of
seeds, we have little information upon this subject.
It has been doubted whether any of those vegetable principles
which contain nitrogen derive that element by direct assimilation
of the gas existing in the atmosphere. Ammonia is looked upon
* Communicated by the Authors, being the substance of two papers read
before the British Association at the meetings of 1850 and 1861.
Q2
216 Messrs. Gladstone on the Growth of Plants in various Gases,
as the source whence it is obtained ; but when the minuteness
of the quantity is taken into account, the assimilation of nitrogen
by plants, though improbable, may certainly still be held an
open question.
It is to the decomposition of the carbonic acid in the atmo-
sphere that vegetables are mainly indebted for the carbon which
forms the basis of their structure. The proportion of carbonic
acid in the air in which different plants will thrive has engaged
the attention of many experimenters, and is still the subject of
investigation. This at least is clearly ascertained, that, unless
in strong sunshine, plants are destroyed by being placed in an
atmosphere of pure carbonic acid.
The aqueous vapour in the air not only supplies hydrogen and
oxygen to the organized vegetable structure, but serves many
other purposes of a more physiological character.
We proposed examining the growth of plants when exposed to
the action of gases that do not occur in the normal atmosphere,
or of the ordinary gases in very unusual proportions.
Our first experiment was made with hydrogen gas. A pansy
was placed in an atmosphere consisting of 95 per cent, of hy-
drogen and 5 per cent, of carbonic acid. The glass vessel in
which it was confined had a capacity of 53 cubic inches. It
was inverted over water, so that connexion with the outer air
was entirely precluded, and yet there was very little surface of
water exposed to the artificial atmosphere within. A little ad-
ditional carbonic acid was introduced from time to time to re-
place that absorbed by the liquid. The plant when first experi-
mented upon had one blue flower in full bloom and one in the
bud ; for the first ten days the bud was gradually opening ; but
a slight mouldiness then came on, which increased during the
next fortnight, by which time the plant having drooped deci-
dedly, it was thought unnecessary to prolong the experiment.
For the sake of comparison another pansy was placed in a glass
vessel filled with atmospheric air, all other circumstances being
equal ; the plant became mouldy at about the same period as the
other ; but the mould did not advance beyond the lower leaves,
and the plant continued healthy for weeks.
Two flowering grass-plants {Poa annua) were placed in vessels
of the same character and capacity as in the preceding experi-
ment, and protected from the external air in the same manner.
The one vessel was filled with pure hydrogen gas, the other with
common air. The plants grew and appeared healthy for about
a fortnight, when mouldiness supervened in each instance. Thus
the substitution of unmixed hydrogen gas for the normal atmo-
sphere produced no visible alteration.
The next experiment was with a mixture of hydrogen and
Messrs. Gladstone on the Ch^owth of Plants in various Gases, 217
oxygen gases, the vegetable being supplied, as in nature, with
the carbonic acid necessary for its growth through the agency
of animal life. A large glass receiver capable of containing 177
cubic inches was filled with oxygen and hydrogen in the propor-
tion of two measures of the latter to one of the former gas, in
fact, in exactly the proportions requisite to form water. Into
this atmosphere was introduced a pansy in flower, together with
a few common house-flies and some sugar, and it was kept from
communicating with the external atmosphere by being placed
over water. A precisely similar arrangement was made in an^
other receiver of similar capacity, but with the normal atmo-
sphere in place of the mixed gases. It was anticipated that the
plant would derive its nutriment from the aqueous vapour, and
the carbonic acid produced by the respiration of the flies, while
these again would feed upon the sugar ; and we should thus have
the same balance between the vegetable and animal kingdoms as
obtains in nature, except that the animal would not feed upon
the very plant which its breath nourished, a circumstance which
it was obviously necessary for us to avoid. Besides ascertaining
whether the pansy would flourish in mixed hydrogen and oxygen
gases — the direct object of this experiment — it would afford an
opportunity of observing any effects which the unnatural atmo-
sphere might have upon the insects themselves. The pansy con-
tinued in a healthy condition for some time. As to the flies, it
did not appear that the substitution of hydrogen for nitrogen in
the atmosphere had any marked immediate effect upon their
breathing ; and thus the observations of M. Regnault upon ether
living creatures were confirmed by an instance drawn from the
Articulata. But it was curious to observe the effects that resulted
from the low specific gravity of the gaseous mixture. The larger
flies when first introduced found themselves unable to walk up
the glass, nor when they shook their wings did it assist them in
mounting into the air; if they launched themselves from any
prominent object, it was only by a great effort that they were
able to fly an inch or two before falling to the bottom. While
the comparative experiment made with atmospheric air presented
a scene of animation by the rapid evolutions of the winged in-
sects, and their buzzing against the glass which confined them,
the flies walked slowly and in perfect silence about the interior
of the vessel containing mixed hydrogen and oxygen.
Experiments were made in nitrogen gas. A pansy in flower,
a young stock, and a grass-plant (Poa annua) in flower, were
placed in atmospheres of this gas with the same arrangements as
in the preceding instances. Another young stock was placed in
air under similar circumstances for the sake of comparison : it
was thought unnecessary to repeat the comparative experiment
218 Messrs. Gladstone on the Growth of Plants in various Gases,
with the others. The pansy and the stock dried up and died in
the course of a day or two ; but the grass-plant grew and seemed
healthy for several weeks, mouldiness only appearing on partially
decayed portions. We surmised that the deleterious effects of
this gas, which we as well as other experimenters had observed,
might be attributed to the phosphorus vapour which it always
contains when prepared by the usual method. Accordingly, we
have subsequently employed pure nitrogen gas evolved by the
mutual action of nitrite of potash and chloride of ammonium at
a high temperature. A pansy placed in this atmosphere under
a glass vessel of 54 inches capacity inverted over water, remained
flowering and vigorous for between two and three weeks.
It is curious to remark the readiness with which mouldiness
grows in nitrogen gas. A receiver half-full of nitrogen happened
to be left standing over the pneumatic trough, and a bung was
floating 6n the surface of the water inside. In a few days' time
a white growth was observed upon the bung ; and not on it only,
but also in patches over the surface of the water. A bottle also
partially filled with the gas was standing inverted in ordinary
spring- water ; the surface of the liquid inside was soon found
covered with small patches of mould, which continued to increase.
A pansy and grass plant were placed in a receiver containing
180 cubic inches of pure oxygen gas, inverted as usual over
water. Both plants were in flower at the time of their intro-
duction; they grew considerably taller, and the Poa showed
extraordinary luxuriance in fructification. After about twenty-
four days the grass became mouldy, and the pansy drooped a
short time afterwards.
Two similar plants were placed under a receiver of similar
capacity, but filled with nitrous oxide. In order to exclude the
external air, the glass vessel was inverted over water saturated at
the ordinary temperature with the same gas. The water how-
ever gradually absorbed the nitrous oxide within, allowing it to
diffiise into the atmosphere without ; thus the liquid rose in the
receiver, but it allowed of the continuation of the experiment for
two months, during which time no extraordinary effect upon
either plant was observable. Davy records a trifling experiment
upon a sprig of mint, which, so far as it went, indicated the
innocuous character of his laughing gas ; and Drs. Turner and
Christison * found that 72 cubic inches of this, mixed with air
in a vessel of 509 inches capacity, produced no visible effect upon
a mignonette plant in forty-eight hours. They do not appear to
have pursued the investigation further.
The same experimenters concluded that carbonic oxide is pro-
bably of the same class of gaseous poisons, in respect to plants,
* Brewster's Journal, Januans 1828.
Messrs. Gladstone on the Growth of Plants in various Gases. 219
as sulphurous acid or cyanogen, but that " its power is much
inferior/' They found that 23 cubic inches of carbonic oxide,
with five times the volume of air, had no apparent effect upon a
mignonette plant in twenty-four hours, but that it drooped
when removed from the abnormal atmosphere. We imagine that
the death of this plant must be ascribed to some other cause,
since we have kept a pansy in a healthy condition for four weeks
in 53 inches of pure carbonic oxide gas.
It order to ascertain what effect different gases might have in
accelerating or retarding germination, and what compounds of
carbon were capable of affording nourishment to the young plant,
four onions just commencing to sprout were taken, weighed and
placed in vessels containing respectively carbonic acid, carbonic
oxide, coal-gas collected by displacement, and atmospheric air
containing eight per cent, of light carburetted hydrogen pre-
pared by the decomposition by heat of an alkaline acetate. The
four vessels containing these bulbs were each capable of holding
53 to 54 cubic inches of gas, and were inverted over water as in
the previous instances. The water employed to prevent access
of air to the vessel containing the carbonic acid was itself satu-
rated with the same gas ; that employed for the hydrocarbons
was an alkaline solution, so as to absorb any carbonic acid which
might happen to be present in the gas, or which might be gene-
rated by the growing root itself. A comparative experiment was
made with another onion placed under a glass shade under similar
circumstances as to light, heat, &c., but open to the atmosphere.
The onions selected had each a plumule of about half an inch
in length, and the experiments extended through the months of
April, May, and June. The onions in the atmospheres contain-
ing hydrocarbons grew rapidly, and put forth fresh roots. After
thirty days the plants were taken out of the coal-gas and car-
buretted hydrogen, as they had grown to the top of the vessels,
being at the time in a very healthy condition. The onion in air
grew, but not so fast. Those placed in carbonic acid and car-
bonic oxide stopped growing, and eventually became rotten. In
each instance they lost weight.
In the early part of the year a crocus commencing to sprout
was placed in a jar containing 70 cubic inches of carbonic oxide
mixed with 100 cubic inches of atmospheric air, inverted over
alkaline water so as to absorb any carbonic acid that might be
formed. The rootlets of the bulb dipped into clear water. The
crocus grew and put forth abundance of long leaves, but it never
flowered. After remaining in this state for fifteen weeks, the
experiment was discontinued, and the bulb and plant were found
to weigh 285 grains, which was one grain less than at the com-
mencement of the experiment. The gas within the receiver
220 Messrs. Gladstone on the Growth of Plants in various Gases.
decreased very much in volnme, but was beginning to increase
again towards the close, when the plant was becoming unhealthy
in appearance.
A precisely similar experiment was made with light carburetted
hydrogen prepared from the acetates in the place of the carbonic
oxide : the growth of the plant was similarly affected, but it
proved that this gas (at least in the proportion of seven parts of
carburetted hydrogen to ten of air) is not poisonous to the bulbous-
rooted plant in question. We have not performed any experi-
ments with unmixed carburetted hydrogen or olefiant gas ; it is
to be expected, however, that they would be found equally inno-
cuous with carbonic oxide, hydrogen, and others which have been
examined. Drs. Turner and Christison found no deleterious
effect in twenty-four hours from a mixture of 4^^ inches of olefiant
gas, with 100 times as much air. The action of gaseous hydro-
carbons upon plants is a separate branch of inquiry, as it involves
the interesting question as to whether these gases are capable of
being assimilated or decomposed by the living organism of the
vegetable, and thus of contributing to its support.
There is a peculiar circumstance attending the growth of the
plants in most of the experiments above detailed, as also in the
comparative ones made with atmospheric air, — a circumstance
which may be constantly observed in '' Ward's Cases,'' though
perhaps not in so striking a manner. It is this : — they increase
at first somewhat in height, and the leaves or flowers may open
a little further than when first placed in the confined atmosphere,
but after a day or two their growth appears retarded without any
signs of decay. Thus in the experiment with the crocus in mixed
light carburetted hydrogen and air, the bulb was placed in the
inverted vessel on Dec. 27th ; rootlets and leaves of about 5 inches
in length speedily shot forth, but then the functions of the vege-
table seemed suspended, and it remained in the month of July
just as it was in February, a crocus with delicate green leaves
opening for the protrusion of the flower-stalk.
These results indicate that gases may be divided into two great
classes in respect to their action upon vegetable life ; namely,
those which are decidedly poisonous, and those which exert no
deleterious influence. The poisonous gases have been investi-
gated by Drs. Christison and Turner in the memoir already ad-
verted to more than once ; they are sulphurous acid, sulphuretted
hydrogen, hydrochloric acid, chlorhie, and cyanogen ; and a very
minute quantity of any of these is found to destroy plants im-
mersed in them for only a few hours ; indeed some of them,
sulphurous acid for instance, are decidedly more injurious to
vegetable than to animal life. In respect to hydrogen, Davy
came to the conclusion that it was injurious to some plants, but
On Extensions of the Dialytic Method of Elimination. 221
not to others ; Saussure found that a plant of Lythrum Salicaria
flourished for five weeks in an atmosphere of this gas. Is it not
possible that some of the compound gases which frequently con-
taminate hydrogen^ and which are known to be poisonous even
in very small proportion, may have led to the destruction of those
plants which died apparently through the influence of hydrogen
gas ? As far as our own experiments are concerned, we find
hydrogen, nitrogen, oxygen, carbonic oxide, nitrous oxide, and
perhaps gaseous hydrocarbons, to be perfectly innocuous to vege-
table life in any proportion.
The earth^s atmosphere is common to all the tribes of organized
existence which inhabit the land, whether fixed to one locality or
endowed with voluntary motion ; but its component gases per-
form different functions in respect to the two great classes into
which we are in the habit of dividing them. No animal, as far
as we are aware, can exist for any length of time in an atmosphere
devoid of oxygen, whilst on the other hand all those which are
usually included under the appellation of the " vegetable king-
dom '' are dependent for their food upon those gases which con-
tain carbon. We know from Regnault^s experiments that the
amount of oxygen in the air may vary largely, and that the
nitrogen may be replaced by hydrogen gas without any marked
effect upon animal life ; and we now find even more strikingly
in regard to plants, that either of the great constituents of the
atmosphere may prevail to the exclusion of the other, or that
they may be replaced by totally difi*erent gases, without involving
the destruction of the living organism ; of course they cannot
increase in substance without carbonaceous food, yet the depriva-
tion of this appears only to lead to an indefinite suspension of
their functions. Doubtless the actual constitution of the atmo-
sphere is that which is most suited to the permanent well-being
of the whole of the organized creation, and perhaps it is equally
requisite both for plants and animals ; yet it is evident that great
deviations from its normal constitution may take place without
producing serious injury.
XXXIII. On Extensions of the Dialytic Method of Elimination.
By J. J. Sylvester, M.A., F.i?.>Sf.*
THE theory about to be described is a natural extension of
the method of elimination presented by me ten years ago
(in June 1841) in the pages of this Magazine, which I have been
induced to review in consequence of the flattering interest recently
expressed in the subject by my friend M. Terquem, and some
* Communicated by the Author.
222 Mr. J. J. Sylvester on Extensions of
other continental mathematicians, and because of the importance
of the geometrical and other applications of which it admits, and
of the inquiries to which it indirectly gives rise. We shall be
concerned in the following discussion with systems of homoge-
neous rational integral functions of a peculiar form, to which for
present purposes I propose to give the name of aggregative
functions, consisting of ordinary homogeneous functions of the
same variables but of different degrees, brought together into
one sum made homogeneous by means of powers of new variables
entering factorially.
Thus if F, G, H . . . L be any number of functions of any
number of letters a:, y . . .t of the degrees tw, m — t, m—il.,,m — {c)
respectively, F -\- G\* + VL/m^ + . . . L^^'^ will be an aggregative
function of the variables entering into F, G, &c., and of X, fjL,.J.
I shall further call such a function binary, ternary, quaternary,
and so forth, according to the number of variables contained in
the functions (F, G, H, &c.) thus brought into coalition.
It will be convenient to recall the attention of the reader to
the meaning of some of the terms employed by me in the paper
above referred to.
If F be any homogeneous function of x, y, s . . . t, the term
augmentative of F denotes any function obtained from F of the
form
a?«./.a7^.../^xF.
Agaiuj if we have any number of such functions F, G, H . . . K
of as many variables x, y, z . . . t, and we decompose F, G, H ... K
in any manner so as to obtain the equations
F=a?«.P, +y*.P^+^.P3 + &c.... -hf'.i'P)
G=:x\Q, + yKQ^ + z'.Q^ + &c..., +t'.{Q)
H=.z^.Ili + y*.R2 + ^Mt3 + &c +^^.(1^)
K=^.Si -f-y*.S2+^.S3 + &c. . . . +t^,{S),
and then form the determinant
P, l\V,...(P)
Q, Q^Qs-.-CQ)
R] Bg R3 . . . (R)
S, S, S3 . . . (S)
this determinant, expressed as a function oi x, y, 2 . . .t, is what,
in the paper referred to, I called a secondary derivec, but which
for the future I shall cite by the more concise and expressive
name of a connective of the system of functions F, G, H , . . K,
the Vialytic Method of Elimination. 223
from which it is obtained. One prevailing principle regulates
all the cases treated of in this and the antecedent memoir, viz.
that of forming linearly independent systems of augmentatives
or connectives, or both, of the given system whose resultant is
to be found, of the same degree one with the other, and equal in
number (when this admits of being done) to the number of
distinct terms in the functions thus formed. The resultant of
these functions, treated as linear fimctions of the several combi-
nations of powers of the variables in each term, will then be the
resultant of the given system clear of all irrelevant factors. If
the number of terms to be eliminated exceed the number of the
functions, the elimination of course cannot be executed. If the
contrary be the case, but the equality is restored by the rejection
of a certain number of the equations, the resultant so obtained
will vary according to the choice of the equations retained for
the purpose of the elimination. The true resultant will not then
coincide with any of the resultants so obtained, but will enter
as a common factor into them all.
The following simple arithmetical principles will be found
applicable and useful for quotation in the sequel : —
{a.) The number of terms in a homogeneous function of jo
letters of the wth degree is
m.{m-\-\) . . (m+jo— 1)
1.2 ... ^
[h.) The number of augmentatives of the (m + w)th degree
belonging to a function oi p letters of the mth degree is
[n + \){n + 2)...{n+p-l)
1.2 ... p
(c.) The number of solutions in integers (excluding zeros) of
the equation fli + «2+ • • • -{-(ip=^k m
(k-\)(k-2)...{k-p+\)
1.2 ... {p-\)-
To begin with the case of binary aggregatives. Let
^n[x,y) + Gn-i{cc,y)\' + Gn-i'{a^,y)fi''-\-&cc..,. + G«_(t)(a7,y)(9'
(0
Kj,(^,2/) + K^_,(^,2/) V -f K^_,'(^,2/)/.* + &c. ... + K^~ (0 (^,y)<9^'^
be a system of functions (whose Resultant it is proposed to de-
termine) equal in number to the variables x, y, \, fjb . . . 0, and
similarly aggregative, i. e. having only the same powers of \, fM,
224 Mr. J. J. Sylvester on Extensions of
&c. entering into them, but of any degrees equal or unequal
m, n, . .p. Let the number of the functions be r. Raise each
of the given functions by augmentation to the degree s, where
5={m + 7i+ ... +jy}-(t + ^'+ ... +W)~1,
the number of augmentatives of the several functions will be
{s + l)—m
(s-\-l)-n
{s + l)-p,
and the total number will therefore be
r(s + l)-(m + w + &c.+/?),
which
= (r-l)(w + «+ ... ^p)-r(L-^L'+ ... +(0).
Again, the number of terms to be eliminated will be the sum
of the numbers of terms in functions respectively of the 5th,
(5— i)th, (5— t')th . . . (s— (*)th) degrees, which are respectively
s + l—i
s+I-l'
s + l-ii),
and the number of these partial functions is r— 1. Hence the
number of terms to be eliminated is
(r— l)(w + 7i + &c.+jo-fc + t' + &c.4-W}— 0+*' + &c. + (t))
= (r-l)(m + n + &c.+;?)-r(t + t'-f ... -f (t)),
which is exactly equal to the number of the augmentative func-
tions. Hence the Resultant* of the given functions can be found
dialytically by linear elimination, and the exponent of its dimen-
sions in respect to the coefficients of the given functions will be
the number
(r — l)2wi— rX*,
as above found.
The method above given may be replaced by another more
compendious, and analogous to that known by the name of
Bezout's abridged method for ordinary functions of two letters.
As the method is precisely the same whatever the number of the
♦ The Resultant of a system of functions means in general the same thing
as the left-hand side of the final equation (clear of extraneous factors) re-
sulting from the elimination of the variables between the equations formed
by equating the said functions severally to zero.
the Dialytic Method of Elimination, 225
functions employed may be, I shall for the sake of greater sim-
plicity restrict the demonstration to the case of three functions,
U, V, W, whose degrees (if unequal, written in ascending order
of magnitude) are m, n, p respectively. Let
V:=zYm{oo, 2/) +Fm-t(<r, y)z'
Y^Gn{x,y) + On-i[x,y)z'-
W = Yip{x,y) + np-,[x, yy-
Let p, q be taken any two numbers which satisfy in integers
greater than zero the equation 6 -\-(i) = m-\-\, and let
^m{x,y) = <f>m-Q.X^ + (f>m-u).y'^
^n[x, y) = 7n-0 . X^ + yn-oy.y'"
}ip{x,y)=7]p-9.X^-^rjp-a>.y'^,
where the <^'s, 7's, rj's may be always considered rational integer
functions of x and y ; for every term in each of the functions
F, G, H must either contain x^ or y<^, since, if not, its dimen-
sions in X and y would not exceed (0—1) + {(0—1), i. e. m — 1,
whereas each term is of m conjoined dimensions, at least in x
and y. Hence from the equations
U = 0
V=0
W=0,
by eliminating x^, y^ we obtain the connective determinant
yn—e; 7w— w; Gn—i
Vp-O'f Vp-<o; lip-i,
which will be of the degree
(m + 7i4-jo-(^ + tw + 0).
i. e. of the degree [n+p—t — l] in x and y ; and the number of
such connectives by principle (c) is p.
Again, by augmentation we can raise each of the functions
U, V, W to the same degree as the connectives, and by principle
b the number of such will be
n-\-p—m—i
p-i
n — v
from U, V, W respectively, together making up the number
2ri + 2jt?--m— 3t.
Hence in all we have %n + 2p — 3t equations ; and the number
226 Mr. J. J. Sylvester on Extensions of
of terms to be eliminated will be n-fjo— *, arising from Fm,
Gh, H;,; and n-\-p—2t, from Fm-t, Gn-t, Hjo-t; together
making up the proper number 2wH-2j9 — 3*.
Each Connective contains ternary combinations of the coeffi-
cients, viz. one of the coefficients belonging to that part of
U, V, W which contains r*, and two coefficients from the other
part ; the dimensions of the resultant in respect of the coefficients
of the former will hence be readily seen to be equal to the num-
ber of connectives -|- the number of terms in the augmentatives
into which z^ enters, i. e. will equal m-\-n-^p—2c; the total
dimensions of the resultant in respect to all the coefficients of
U, V, Wwill be Sm-'r{2n-\-2p — m—SL),i.e.2m + 2n-{-2pSL;
and consequently, in respect to the coefficients of Fm; G»; H^,
will be of
{2m-\-2n + 2p—SL) — {m + n-\-p — 2t),
«. e. o{ m + n+p — t dimensions. This result, which is of con-
siderable importance, may be generalized as follows.
Returning to the general system (A.), (for which we have
proved that the total dimensions of the resultant are
(r~l)(m + w+ ...p)-r{i + i'+ . . . + (t)),
let the coefficients of the column of partial functions
Fn,
G„
be called the first set ; the coefficients of the column
F»i— I
Gn— I
the second set, and so forth ; then the dimensions in respect of
the 1st, 2nd ... (r — l)th sets respectively are s, s— -t, s— t' . . .
s— (t), where
s = m-\-n-{-Scc. -j-j9 — (tH-t'H-&c. +(0)-
The important observation remains to be made, that all the
above results remain good although any one or more of the
indices of dimension of the partial functions in the system
(A.), as m—i, m^i!, n—i, &c., should become negative, pro-
vided that the terms in which such negative indices occur be
taken zero, as will be apparent on reviewing the processes already
the Dialytic Method of Elimination. 227
indicated upon this supposition. If we take m=:n=p = qj and
t = t' = &c. ={i)=m — e, the exponent of the total dimensions of
the resultant becomes
(r — l)rw— r(r — 2)(m — e)
=srm—r{r—2)ej
when 6=0, this becomes mr, which is made up of 2m units of
dimension belonging to the coefficients of the first column, and
of m belonging to each of the (r — 2) remaining columns. Con-
sequently, if we have
Gm (cc, i/)-\-rjX-\- r)'X = 0
Hm(.r,y) + ?X + 5^X' = 0
or any other number of equations similarly formed, the result of
the elimination is always of m dimensions only in respect of
^) V} ?> ^j» or of f ', 77', f , 6', and of 2m in respect of the coeffi-
cients in F, G, H, K.
I now proceed to state and to explain some seeming paradoxes
connected with the degree of the resultant of such systems of
defective functions as have been previously treated of in this
memoir, as compared with the degree of the general resultant of
a corresponding system of complete functions of the same number
of variables.
In order to fix our ideas, let us take a system of only three
equations of the form
Fm(.r,7/) + F^_,(^,y)/=0^
Gn[a;,y) + Gn-c{a:,y)/ = 0^. . • • (B.)
Up {oc,y) + llp-i (^,?/)/==0^
The resultant of this system found by the preceding method is
in all of 2m-\-2n + 2p — ^(, dimensions. But in general, the
resultant of three equations of the degrees m, w, p is of mn -{- mp
-\-np dimensions.
Now in order to reason firmly and validly upon the doctrine
of elimination, nothing is so necessary as to have a clear and
precise notion (never to be let go from the mind^s grasp) of
the proposition that every system of [n) homogeneous func-
tions of (n) variables has a single and invariable Resultant.
The meaning of this proposition is, that a function of the co-
efficients of the given functions can be found, such that, when-
ever it becomes zero, and never except when it becomes zero,
the given functions may be simultaneously made zero for some
certain system of ratios between the variables. The function so
228 Mr. J. J. Sylvester on Extensioiis of
found, which is suflBcient and necessary to condition the possi-
bility of the coexistence of the equality to zero of each of the
given functions, is their resultant, and by analogy they may be
termed its components. It follows that if R be a resultant of a
given system of functions, any numerical multiple of any power
of R or of any root of R when (upon certain relations being sup-
posed to be instituted between the coefficients of its components)
R breaks up into equal factors, will also be a resultant. This is
just what happens in system (B.) when m — n—p-=L] the re-
sultant found by the method in the text is of the degree 3m ;
the general resultant of the system of three equations to which
it belongs is of the degree 3m* ; the fact being, that the latter
resultant becomes a perfect mth power for the particular values
of the coefficients which cause its components to take the form
of the functions in system (B.).
Suppose, however, that we have still m = 7i=j9,but l less than
(m), 6m — 3t will express the degree of the resultant of system (B.);
but this is no longer in general an aliquot part of 3m*, and conse-
quently the resultant of system (B.) that we have found is no
longer capable in general of being a root of the general resultant.
The tmth is, that on this supposition the general resultant is zero ;
oc u
as it evidently should be, because the values - =0, - = 0 satisfy
the equations in system (B.), except for the case of m=(-; conse-
quently the resultant furnished in the text, although found by the
same process, is something of a different nature from an ordi-
nary resultant ; it expresses, not that the system of equations (B.)
may be capable of coexisting, but that they may be capable of
X 11
coexisting for values of -, - other than 0 and 0. This is what
I have elsewhere termed a sub-resultant. But there is yet a
further case, to which neither of the above considerations will
apply. This is when m, n, p are not equal, butjo — 1=0.
On this supposition the degree of the resultant of B becomes
2m 4- 2/1 —p) which in general will not be a factor of mn-^mp + np;
X
and in this case it will no longer be true that the values — =0,
z
-^=0 will satisfy the system B, inasmuch as the last equation
therein cannot so be satisfied. Now if we call the general resultant
R and the particular resultant R', if R' should break up into fac-
tors so as to become equal to (r'j^x (s')*. • • (0^ i^ might be the
case that R should equal (/)" . {^f . . . (/')^, and there would be
nothing in this fact which would be inconsistent with the theory
of the resultant as above set forth ; but suppose that R' is inde-
the Dialytic Method of Elimination. 229
composable into factors, then it is evident that we must have
R = R' . R", and consequently that the existence of such a parti-
cular resultant as E' will argue the necessity of the existence of
another resultant R" ; in other words, the resultant so found
cannot be in a strict sense the true and complete resultant for
the particular case assumed, and yet the process employed ap-
pears to give the complete resultant, or at least it is difficult to
see how the wanting factor escapes detection. To make this
matter more clear, take a particular and very simple case, where
m=2 n=2 p = 2 = 0, so as to form the system of equations
A'a?2 4-B'^y4-C'/+(D'a? + EV)^=0 I (C.)
Ix + my + nz =0j
By virtue of my theorem, the degree of the resultant R' is
2(2 + 2 + 1) —3 . 1 = 7, but the resultant R of the system
kx^ + Bxy + Qy'^ -A- (D^ + Y^y)z + F^^ ^ q^
Mx^ + B'^y + Cy 4- (D'.2? + EV)^ + r V^ = 0 I (D.)
lx-\-my-\-n2 =0j
which becomes identical with the former when r=0, F' = Ois of
2x2 + 2x1+2x1, 2. e. of 8 dimensions. Hence it is evident
that whenF=0, F = 0, R must become R'xR".
It will be found in fact, that on the supposition of F = 0, F' = 0,
R becomes equal to w x R" ; and accordingly, besides the portion
R' of the resultant of system (C), found by the method in the
text, there is anotRer portion n which has dropped through ; but
it may be asked, is n truly a relevant factor ? were it not so, the
theory of the resultant would be completely invalidated ; but in
truth it is; for n = 0 will make the equations in system (C.), con-
sidered as a particular case of system (D.), capable of coexisting; the
peculiarity, which at first sight prevents this from being obvious,
consisting in the fact that the values of -, -^ which satisfy the
Zi z
three equations when /i = 0 become infinite.
Thus, finally, we have arrived at a clear and complete view of
the relation of the particular to the general resultant.
The general resultant may be zero, in which case the particular
resultant is something altogether diff"erent from an ordinary re-
sultant j or the particular resultant may be a root of the general
resultant, or it may be more generally the product of powers of
the simple factors, which enter into the composition of the general
resultant ; or lastly, it may be an incomplete resultant, the fac-
tors wanting to make it complete being such as when equated to
zero, will enable the components of the resultant to coexist, but
Fhil Mag. S. 4. Vol. 2. No. 10. ^ept. 1851. R
230 Mr. R. Phillips on the Magnetism of Pewtei^ Coils.
not for other than infinite values of certain of the ratios exist-
ing between the variables.
Without for the present further enlarging on the hitherto
unexplored and highly interesting theory of Particular Result-
ants, I will content myself with stating one beautiful and general
theorem relating to them; to wit, "if F = 0, G=0, &c. be a
given system of equations with the coefficients left general, and
R be the resultant of F, G, &c., and if now the coefficients in
F, G be so taken that R comes to contain as a factor or be coin-
cident with R'"*, then will R' = 0 indicate that (when the coeffi-
cients are so taken as above supposed) F = 0, G = 0, &c. will be
capable of being satisfied, not, as in general, by one only, but
by {m) distinct systems of values of the variables in F, G, &c.,
subject of course to the possibility, in special cases, of certain of
the systems becoming multiple coincident systems.'^
I pass on now to the more recondite and interesting theory of
the resultant of Ternary Aggregative Functions, that is to say
functions of the form
which will be seen to admit of some remarkable applications to
the theory of reciprocal polars.
[To be continued.]
XXXIV. On the Magnetism of Pewter Coils.
By Reuben Phillips.
[Continued from vol. xxxvii. p. 2^8.]
149. TT will be in the recollection of the readers of the former
Jl papers, that I thought I had discovered that a jet of
steam escaping into the air is magnetic, which I attributed to
thermo-electric currents passing between the hotter and colder
particles; thence, in endeavouring to discover the equivalent
static effect, I found instead, that mode of electrical development
consisting of the friction of gaseous matter on water, and which
in my opinion completely solves the question of the source of
atmospheric electricity. I have found since then I was wrong
in ascribing magnetic properties to the jet of steam, the magnetic
disturbance being situated in the metallic steam-passages, and
it should seem directly related to terrestrial magnetism.
150. A straight glass tube, about '3 inch diameter and 17
inches long, connected the glass coil with the condenser. All
effect on the magnetic needle now ceased, even when the coil was
kept cool by being partly immersed in water and covered with
wet cloth.
ISd. The brass jet (9.) was united to the end of a glass tube
Mr. R. Phillips on the Magnetism of Pewter Coils. 231
8 inches long, the other end of the tube communicating with
the condenser. The only effect now produced by the steam on
the magnetic needle was a slight tremor, owing to the concus-
sions it produced in the air shaking the apparatus : the mag-
netism of the steam (11.) had completely disappeared. The
boiler was now moved until the condenser stood with regard to
the galvanoscope just as it did before (11.) ; opening the cock
of the boiler gave a strong swing to C, and a strong start to A
when the cock was closed.
152. It is, I think, now quite certain, that in such experi-
ments as (9, 145.) the real place of magnetic excitation is in the
apparatus through which the steam passes before it enters the
atmosphere or the glass tube.
153. The pewter coil (29.) was united to the condenser, and
the other end held the brass jet (9.) ; some of the pewter coil
had been opened out, so that there was a distance of 11 inches
between the nearest part of the condenser and the coil. The
steam was at 6 lbs. on the inch. The coil being cool, when the
steam was turned on the needje moved about f the length of the
scale to C. The coil was removed, and some steam was passed
through the condenser to warm it and to blow the water out of
the steam passages. A piece of cane, of the size before described
(116.), and which had been soaked for some hours in a similar
solution of soda, was now put in the pipe of the condenser, and
then the coil was quickly restored as before. On opening the
cock of the boiler the swing was unaltered in direction, and, as
far as I could judge from many experiments, in force also. The
fluid that escaped from the brass jet felt strongly alkaline. Con-
sidering the ready solubility of the oxides of tin and lead in a
solution of caustic alkali, it appeared to me fair to infer that this
magnetism was not produced by a chemical action. The follow-
ing experiment is, I think, conclusive on this point.
154. A stop-cock was united to the cock of the boiler in the
place of the condenser. From this stop-cock proceeded horizon-
tally a glass tube which continued straight for 14 inches ; it then
descended vertically for 1^ inch, and then again horizontally in
the same direction as before for a distance of 1 inch ; at this place
the glass tube joined a straight platinum tube 5 inches long,
lying in the direction of the glass tube at the place where the
glass and platinum tubes were united ; the other end of the pla-
tinum tube received a glass tube, which, at a short distance
from the platinum tube, ascended nearly perpendicularly, and
then went in the first direction of the glass tube of the stop-cock :
the tube proceeding from the platinum was contracted at the end,
which finally discharged the steam to an orifice J^^ inch diameter.
The steam as it issued from this apparatus was received into a
R2
232 Mr. R. Phillips on the Magnetism of Pewter Coils,
glass catch-tube. A copper pan was brought under the platinum
tube, so that the tube could easily be put under water by filling
i;he copper pan. The pan contained stout wire supports, on
which rested a square piece of iron 4*5 inches in each side and
j\j inch thick, which had been made red-hot and slowly cooled ;
a good bearing for the iron was obtained on three points, and it
lay horizontally at a vertical distance of about -^-^ inch from the
tinder side of the platinum tube : supposing a perpendicular
?plane to have been raised from the iron to the nearest line on
the platinum tube parallel with its axis, it would have been found
that the iron extended | inch in an easterly direction from this
plane towards the galvanoscope, at which distance the iron came
in contact with one of the flat sides of the pan. The platinum
tube was united to the glass tube by India-rubber, oiled silk
and thread only ; and the needle of the galvanoscope lay about
parallel with, and in the same horizontal plane as, the axis of
the platinum tube.
155. With the steam at about 25 lbs. per inch, five puffs
sent the edge of the needle about the whole length of the scale ;
and the swing was to A when the steam was turned on. In this
way I made many experiments, having the platinum tube some-
times partially and sometimes entirely covered with water ; but
I could not obseiTe any decided difference, although I think on
the whole the magnetism was perhaps rather stronger when the
tube was about ^rd immersed ; the tube was always parallel with
the surface of the water. The internal diameter of the platinum
tube was \ inch, and it was about -^^ inch thick.
.. 156. A pewter tube 5 inches long, -^^ inch internal diameter,
and -^-Q inch thick was substituted for the platinum tube. When the
tube was about one-third covered with water, the swing was just
^ias with the platinum tube ; but when the tube lay entirely under
water, the swing was about one-half less; with this exception
everything was as with the platinum tube.
, 157. I could produce no effect on the galvanoscope by sub-
c. ktituting a glass tube, nor with the metal tubes when the iron
was away, nor when the iron was in its place unless the tubes
^were kept cool by water.
_/ 158. The variation in the magnetic intensity of the pewter
^ tube led me to suppose that the direction of the magnetism of a
coil would vary according as cold was applied to it. A pewter
pipe 3 feet 8 inches long, \ inch internal diameter, and -^-q inch
ijhick, was wound up into a helix ; the convolutions lay regularly
rside by side, but without overlapping ; the interior of the coil
! measured 1*3 inch diameter, and there were six convolutions. A
^ piece 7 inches long was left unwound at each end of the pewter
pipe, and the ends were each furnished with a stop-cock having
Mr. R. Phillips on the Magnetism of Pewter Coils. 233
a steam-way 2% inch diameter ; these stop-cocks are denoted re-
spectively by N and 0. There was also a thick wad of loosely
spun cotton, which could either be wrapped about the coil or
stuffed into it. In these experiments it was found necessary to
interpose a sheet of lead-foil between the zinc screen and the
coil ; otherwise the steam produced from the wad, striking on
the shield, considerably interfered with the purity of the result.
159. The wad was placed on the outside of the coil and
thoroughly drenched with water. N was now united by a brass
connecting piece to the cock of the boiler ; 0 was partly and
sometimes fully opened and N shut. On opening N the swing
was to C ; five pufi*s gave a swing about three-quarters the length
of the scale. In these experiments the cock of the boiler is
always to be understood as open.
160. N was partly opened; on alternately opening and shut-
ting 0, the swing was to A when 0 was opened, and to C when
O was shut. When N was fully opened, the swing was much
less.
161. The wad was now removed from the outside and thrust
inside the coil and saturated with water. O being partly open,
on fully opening N the swing was to A, and rather less than the
swing to C when the wad was outside.
162. The stop-cocks N and O were used as described in (160.).
When 0 was shut the needle moved to A, and to C when 0 was
opened. In experiments where either N or O was partly opened,
the area of the steam-way was probably about equal to a circle
y2 inch diameter.
163. Many other experiments were made with this coil, which
it is not considered necessary to mention, as they only showed,
in addition to what I have just narrated, that which is abun-
dantly proved by former experiments ; namely, that the two ends
of the axis of the coil are in opposite magnetic states, and that
the direction of the magnetism is independent of the direction of
the motion of the steam.
164. One end of the pipe of the coil (29.) was united to the
cock of the boiler, and there was a distance of ten inches of
pewter pipe between the coil and the connecting pieces; the
other end of the pipe of the coil held the brass jet (9.). The
axis of the coil was placed perpendicular to the horizon. The
needle of the galvanoscope lay in a horizontal plane about '4
inch lower than a horizontal plane resting upon the upper end
of the axis of the coil. When the steam passed, the swing was
to A, and one puff sent the needle nearly the length of the scale.
The apparatus was now adjusted so that the needle stood '6 inch
lower with regard to the coil ; the swing was still to A, and
nearly as strong as before. The needle was now placed about
equidistant from either end of the coil ; the swing was still to A,
234 Mr. B. Phillips on the Magnetism of Pewter Coils.
but not above half as strong. The galvanoscope was again low-
ered with respect to the coil ; the swing was now to C, and
powerful. Finally, the galvanoscope was again lowered until
the needle stood m the same position with respect to the lower
end of the axis of the coil as it did at the commencement with
regard to the upper end ; the swing was to C, and equally pow-
erful with the corresponding swing to A.
1G5. The coil was now arranged as usual with its axis hori-
zontal, having that end which before pointed to the zenith now
directed to the needle of the galvanoscope. The swing was to
A when the steam passed.
166. The pewter coil (29.) was supported in the same position
as in (165.), and so arranged that the fountain [77.) could easily
be connected with or removed from the coil. The zinc screen
and galvanoscope were used as in the foregoing experiments with
steam ; and the water-way of the cock of the fountain, which
was the passage of the least diameter through which the water
passed, was -f^ inch across. Water was placed in the fountain
and made to boil, the air was then pumped in, and the fountain
was united with the coil. On opening the cock of the fountain,
and so allowing the water to flow through the coil, the needle
started towards A, and the swing produced was about one -third
the length of the scale. The fountain was immediately removed,
rinsed out with cold water, charged again with cold water, and
then reunited with the coil which was still hot. The cock of
the fountain now being opened, the swing was to C, and nearly
as strong as before.
167. The iron core (131.) was placed in the coil. Hot water
now being sent through the coil produced a violent swing to A ;
and then, while the coil was hot, sending cold water through it
produced nearly as strong a swing to C ; in both instances the
needle vibrated across and considerably outside the field of view.
Sending cold water through, the coil also being cool, produced
no magnetic effect.
168. These experiments show that the magnetism of the coils
is an effect of heat independent of condensation.
169. A piece of stout copper wire, 4 feet 2 inches long and
^ inch diameter, was covered by winding tape about it ; some
copper wire, -^-q inch diameter, and covered, was now wound out-
side the tape, and the rounds lay nearly close together without
overlapping. The stout copper wire, having been thus covered
throughout its whole length, was next wound up into a helix of
eleven convolutions, which did not overlap each other, and the
internal diameter of the coil was 1*3 inch. The cuiTcnt from
a galvanic battery being transmitted through the fine copper wire,
caused this compound helix to possess similar magnetic proper-
ties to those of the pewter coils.
Mr. 11. Phillips on the Magnetism of Pewter Coils. 235
170. In the experiment with the pewter coil (159.), there is a
difference of temperature between the exterior and interior sur-
faces of the tube, this difference of temperature being greater at
those parts of the tube forming the exterior of the coil than at
those portions internally situated. Now the difference of tem-
perature will, from a thermo-electric action, throw the surfaces
into opposite electrical states, the intensity of which will vary
with the difference of temperature ; consequently those parts of
the tube which have the greatest difference of temperature will
produce electricity, which will circulate by overcoming the resist-
ance opposed by those pai*ts where the difference of temperature
is less. Suppose a small portion of pipe cut out from the coil
in the shape of a right cylinder. Now looking at one end, which
gives an annulus, and bisecting this annular space, not the metal
itself, by a straight line, and supposing that in one of the halves
so obtained the difference of temperature is greater than in the
other half; then a chain of the metallic particles producing elec-
tricity will cause the current to flow along the curved boundary of
the metal until it comes to a part where the difference of tempera-
ture is less, and at this point it will more or less force its way across ;
thus forming a circuit, the contour of which is some segment of
the annulus, and the tube may be regarded as built up of many
such annuli. Such a system of currents, it can easily be shown
by direct experiments, produces a magnetism parallel in direction
with the axis of this bit of tube ; consequently, the system of
currents existing in the pewter coils in fact resembles that of the
copper helix.
171. But to account for the regular magnetism of the pewter
coils, it is necessary to suppose that the direction of the currents
in each part of the pipe is, on the whole, the same with regard
to the coil ; and this requires the admission of some force or pro-
perty in the coil capable of giving uniform direction to the cur-
rents. This view involves the least assumption, nevertheless its
application to many of the experiments is exceedingly difficult.
If an experiment could be devised in which this magnetism could
be developed under circumstances where thermo-electric cmTents
could not exist, it would perhaps be necessary to look upon the
effect as the direct conversion of heat into magnetism.
172. The magnetism of these pewter coils affords, as far as it
goes, a sufficient explanation of the cause of terrestrial mag-
netism ; for the internal heat of the earth continually passing
outwards produces electric currents ; then, assuming the exist-
ence of a structural force, and which can hardly be unconnected
with stratification, capable, as with the pewter coils, of giving
regularity to the arrangement of these currents, and the product
will be a regular magnetic force, such as is terrestrial magnetism.
That Humboldt^s isothermal bands should coincide with Sabine's
236 Mr. R. Phillips on the Magnetism of Pewter Coils* /
lines of equal magnetic intensity, follows at once from refer-
ring terrestrial magnetism to the internal heat of the earth;
for where the climate is coolest, the difference of temperature
will be the greatest, and there the electric developments will be
more powerful. This explanation of the cause of terrestrial
magnetism is so far independent of the hypothesis used to ac-
count for the magnetism of the coils, that if the magnetism of
the coils proceeds from the direct conversion of heat into mag-
netic force, then terrestrial magnetism results from a similar
transfoimation.
173. On the specific inductive capacity of cloud. — The tin pipe
was arranged before the brass jet of the boiler as in (83.), but
with the longer arm pointing to the zenith ; and in the longer
arm of the tin pipe, and concentric with it, stood a copper tube
having a cork inserted at each end ; the upper one of these corks
received the end of a glass tube, which soon after leaving the
cork turned off at a right angle, and this horizontal portion of
the glass tube was put in a tube-holder and thus supported and
insulated the copper tube ; finally, a copper wire passed through
the whole length of the glass tube to the copper tube ; and con-
sequently, on bringing the knob of a charged Ley den jar into
contact with one end of the wire, the copper tube became elec-
trified inductrically, and the tin pipe inducteously. The copper
tube was externally -^ inch diameter, and it extended a distance
of 7 inches into the tin pipe.
174. A large Ley den jar was now charged positively by a plate
machine, and then the knob of the jar was supported against the
end of the copper wire. The tin pipe was presently connected
with an electrometer, and the electricity was carefully drawn off
from the copper pipe by means of a point which I held in my
hand, until the electricity passed but very slowly between the
copper and the tin pipes ; the tin pipe was now put in commu-
nication with the single-leaf electrometer, and the electric in-
tensity of the Leyden jar still further reduced if the electricity
passed too rapidly. The intensity with which I preferred work-
ing being that at which the positive electricity nearly ceased to
pass to the tin pipe; consequently, the electrometer connected
with the tin pipe, after being discharged, would soon indicate a
feeble positive charge. The cock of the boiler was now opened so
that the issuing steam might leave the boiler positive ; the only
effect of which on the electrometer was a feeble negative action,
produced by the negative steam-cloud acting inductrically on the
tin pipe.
175. It occasionally happened, from circumstances which I
could not succeed in deteimining, that the steam-cloud re-esta-
blished a communication with the copper and tin pipes ; and so
r
Mr. R. Phillips ow /^ie Jfa^ne^zm 0/ Pew^g^ Coils ^ 2^
much positive electricity would at these times pass to the elec-
trometer as was apt to destroy the gold-leaf.
176. The foregoing experiment (174.) is decisive in showing
that the increase of electricity in such experiments as (95.) does
not result from the specific inductive capacity of cloud, which
can differ but little if at all from air. The following experiment
is a proof that this effect of the steam in increasing the electricity
of a jet of water does not depend on the cold water condensing
the steam-cloud.
177. The fountain, tin pipe, &c. were arranged as in (94.),
except that the distance between the lower end of the brass jet
of the fountain and the upper end of the tin pipe was diminished
to 5*5 inches. Water was placed in the fountain and caused to
boil, the air was pumped in, and the glass tube and jet screwed
into its place. The fountain was connected with the ground,
and the tin pipe with the single-leaf electrometer, and then the
cock of the fountain was opened a little to give a stream of suffi-
cient force. The bulb of a thermometer was now held in the
stream of water just inside the upper end of the tin pipe ; the
mercury soon reached 142^ ; the thermometer was removed, and
the electrometer was observed to be scarcely affected ; but on
now opening the cock of the boiler a little, and so filling the tin
pipe with cloud, the quantity of electricity produced by the
stream of water was greatly increased, the gold-leaf rapidly
striking the conducting plate. The thermometer was again
brought into the stream of water as before ; the steam still pass-
ing, it marked 149*^ ; the thermometer was now placed in the
steam-cloud in the tin pipe and soon fell to 125°. ,a
178. Of course these numbers given by the thermometer,
depending as they do upon the extent to which the cocks were
opened, varied in every experiment ; for example, another experi-
ment conducted as the foregoing gave the first temperature of
the water 154°, the second temperature 156°, and the tempera-
ture of the steam-cloud 123°. The increase of electricity pro-
duced by the steam-cloud appeared to be quite as great when
hot water was discharged from the fountain as when the water
was cold.
179. It should seem there can be now only one property of
the steam-cloud to which this increase of electricity can be
ascribed, namely, some species of conduction, which, by lowering
the electrical intensity of the jet of water, would account for the
phsenomenon. Something of this power appears in the experi-
ments (43, 52.) in the connexion existing between the tube and
the boiler. The following experiment is still less ambiguous.
180. A large Ley den jar was charged positively and inverted
on a proper support, so that the distance between the end of the
brass jet of the boiler and the centre of the ball of the jar was
238 Royal Society.
3^ inches. When the cock of the boiler was opened, the steam
struck on the lower side of the ball and passed thence to a wire-
gauze screen, placed at a distance of ten inches from the ball ;
this screen was connected with the two-leaved electrometer.
Positive electricity passed veiy slowly to the screen ; but on now
allowing the steam to escape negatively electrified, the leaves of
the electrometer almost immediately diverged to their full extent ;
on shutting off the steam, ])ositive electricity began to pass about
as slowly as before ; again allowing the steam to play on the ball,
the leaves diverged with positive electricity as previously, and
these actions could be repeated a great many times.
181. The account of the jet of steam (62.), when the rough
noise is being produced, is not sufficiently full and accurate.
The main distinction in the appearance of the jet of steam with
the hiss and the roar is, that with the hiss there is a transparent
space between the orifice and the steam-cloud of about half an
inch ; but with the roar this intei*val is of a dense white ; and
the mass of white can be seen to extend two or three inches into
the steam-cloud, as it does not diverge from the axis of the pro-
jected jet so rapidly as the steam. AVhen there is only a smooth
hiss, one or more transparent lines of water proceed from the
edge of the orifice, and which I think are never longer than the
one-eighth of an inch, and certainly shorter if more than one
fibre appears. If when the roar is set up, the jet of steam be
viewed near to the orifice, the whiteness is seen not to be uni-
form, but to be made up of a number of little white cones, having
their vertices stuck on the margin, and I think also on the inte-
rior of the orifice, which cones coalesce at a short distance from
the orifice. The cones are apt to proceed from the same places
which the fibres of water frequent ; perhaps they are produced
from the fibres by a rotary motion resulting from two rectangular
vibrations.
7 Prospect Place, Ball's Pond Road.
XXXV. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Continued from p. 158.]
May 8, 1851. — The Earl of Rosse, President, in the Chair.
A PAPER was read, entitled " Memoir on the Megatherium.
Part II." By Prof. Owen, F.R.S. Received May 6, 1851.
The author premised a brief sketch of the successive steps which
had led to the knowledge of the Megatherium acquired at tiie date
of his researches, and of the different hypotheses which had been
broached of its affinities, habits and food. He then recounted the
mode of the acquisitionof theeomplete skeleton, and of its articulation,
at the British Museum, and commenced its description by the ver-
tebrae of the trunk. These consist of 7 cervical, 16 dorsal, 3 lumbar.
Royal Society. 239
5 sacral, and 18 caudal vertebrae. The first to the fifth dorsal ver-
tebrae are characterized by having the ordinary number of articular
processes (zygapophyses), two before and two behind ; and by
having three articular surfaces for the ribs on each side, one on the
centrum, one on the neurapophysis, and one on the diapophysis.
The sixth dorsal vertebra has an accessory zygapophysis between
the posterior pair ; the thirteenth dorsal has one between the anterior
pair ; the seventh to the twelfth inclusive have the accessory median
zygapophysis between both the anterior and posterior pairs of the
ordinary zygapophyses. The fourteenth and succeeding dorsals
have no costal surface on the diapophysis or centrum. The fif-
teenth has both metapophysis and anapophysis — the latter with an
articular surface : the sixteenth superadds the parapophysis with an
articular facet.
The lumbar vertebrae lose the costal surface on the centrum, and
retain the metapophyses, anapophyses and parapophyses. The
nature of these accessory processes was explained by reference to
the descriptions and figures of the exogenous processes of vertebrae
in Part I. of the present Memoir.
The characteristics of the cervical vertebrae were next detailed.
Of the five anchylosed sacral vertebrae, three are confluent with
the iliac bones, and two with the ischia.
The fourteen anterior caudals are characterized by articular sur-
faces for haemapophyses. These elements are separate from each
other in the first caudal, and confluent as usual at their distal ends,
forming a ' chevron-bone' in the others. The posterior zygapophy-
ses lose their articular surfaces in the eleventh caudal ; the anterior
ones disappear in the twelfth : the metapophyses have subsided in
the fifteenth. The neural canal is unclosed above in the sixteenth ;
and the vertebra is reduced to its central element in the last two
caudals.
The skull is remarkable for its small proportional size, for its long
and slender cranial portion, its large and complex zygomatic arches,
its broad truncate facial part, with the slender produced premax-
illaries, and for the great depth of the middle of the lower jaw.
The mastoid element developes a large tuberous process and a
deep semicircular articular cavity for the stylohyal. The malar
bone sends down a long process outside the lower jaw. The num-
ber of teeth is ^^=18, the fifth in the upper jaw being the smallest.
They are alike in structure, and differ but little in shape: thegrinding
surface in most is crossed by two transverse ridges ; the summits of
which are formed by hard dentine ; the rest of the tooth being
composed of a central body of vaso-dentine and a peripheral mass
of vascular cement. The microscopic characters of these several
constituents of the teeth were then described. Each tooth is deeply
implanted in the jaw^, where it terminates without dividing into
fangs, by a widely open pulp-cavity for a persistent matrix, ensuring
perpetual growth. The stylohyal bone has the form of a hammer,
with a long, slightly bent handle ; one part of the head being thick-
ened and rounded for articulation with the cavity in the mastoid.
The scapula presents almost the form of a trapezium, with the
t40 Royal Society.
inferior angle bent outwards, increasing the depth of the subspinal
fossa : there is a rudiment of a second spine, below the normal one :
the acromion is expanded, produced and confluent with the coracoid ;
and the supraspinal fossa is perforated by a circular aperture. The
clavicle has a well-marked sigmoid flexure, equally-developed obtuse
extremities, without any articular surface. The humerus is remark-
able for the enormous development of ridges for the attachment of
the muscles, especially at its distal end : the inner condyle is not
perforated as in the Megalonyx\ it is devoid of a medullary cavity.
The ulna and radius are next described. The carpus consists of
seven bones, three of which are proper to the first row, three to the
second, and one is common to both : the latter answers to the *sca-
phoides' and * trapezium' in the human wrist, and articulates with the
radius above, and the rudiment of the metacarpal of the pollex below.
Only four digits are developed, the first or ' pollex ' being obso-
lete. The ' index * or second digit has three phalanges, the last sup-
porting a large claw, and being twice as long as the two preceding
phalanges. The proximal and middle phalanges of the * digitus
raedius' are confluent. The ungual phalanx is shorter than that of
the index, but has twice its vertical breadth. The metacarpals
progressively increase in length from the first to the fifth. The
fourth digit or 'annularis' has three phalanges, the last being un-
guiculate and longer than that of the 'medius.' The fifth digit
has only two very short rounded phalanges, which were doubtless
buried in a thick callous outer border of the foot, on which the
Megatherium rested when applying the foot to the ground.
The pelvis shows the conversion of the ischiadic notch into a
foramen by the anchylosis of the ischia with the posterior sacral
vertebrae, and the union of the ossa pubis at a short anteriorly pro-'
duced symphysis. The ilia are extraordinary for their vast breadth,
and the thickness of the rugged labrum ; indicative of the enormous
muscular forces, of which this conspicuous part of the skeleton was
the centre.
The femur is hardly less remarkable for its breadth and strength.
The head is devoid of an impression for the ligamentum teres: but
from the dimensions of the hemispheroid cavity receiving it, the
author calculates that the muscles are aided in retaining the head
of the femur in its place by an atmospheric pressure, with the baro-
meter at 30 in., of not less than 660 pounds. At the distal end of
the femur there is a great angular projection above the outer con-
dyle. The rotular surface is continuous with that upon the outer
condyle, but not with the inner one. The tibia and fibula are anchy-
losed together at both their extremities. Besides the patella in front
of the knee-joint, there is a sesamoid ' poplitella' behind, wedged
between the outer condyle and the tibia; which was doubtless im-
bedded at its base in the femoro-tibial articular capsule, and gave
insertion to the tendon of the popliteus muscle. This sesamoid is
not to be confounded with the ' fabella,' developed in many quadru-
peds in the origin of the gastrocnemius, behind one or both condyles
of the femur. The most peculiar feature in the tibia of the Mega-
therium is the form of the distal articular surface: especially the
Royal Society. 241
large and deep hemispherical excavation on the inner part of that
surface for an unusually secure interlocking of the foot to the leg.
The bones of the tarsus are six in number in the Megatherium,
and the astragalus offers corresponding peculiarities with those of
the tibia with which it is articulated, and also remarkable modifica-
tions for the articulation of the naviculare and calcaneum. In the
calcaneum,the length and strength of the hinder prominence forming
the great lever for the extension of the foot, are amongst its most
striking characteristics. These, with those of the other bones of
the tarsus, are minutely detailed. There is no digit answering to
the great toe or 'hallux,' nor any trace of the 'os cuneiforme' for
that toe. The innermost of the 'ossa cuneiformia' answers to the
middle one, and if any rudiment of the second toe ever existed in-
dependently, it has coalesced with that cuneiform bone: but this
cannot be supposed to represent both middle and internal cuneiform
bones and their digits blended together, as Cuvier supposed. There
are no little bones missing from the inner side of the middle cunei-
forme, as Pander and D'Alton conjectured. The first or innermost
distinct metatarsal bone is that of the toe answering to the third, or
digitus medius, in the pentadactyle foot : it is a short thick irregular
wedge-shaped bone, with a large triangular concave base for the
* ecto-cuneiforme'; a semicircular flattened surface on the outer side
for the fourth metatarsal, and a small semi-elliptic flat surface on
the inner side for the 'meso-cuneiforme'. The distal end of the
bone presents a strong median vertical obtuse ridge, dividing two
vertically elongated slightly concave surfaces, to which the anchy-
losed proximal and middle phalanges of the strong claw-bearing digit
articulate. The ungual phalanx is shorter in proportion to its depth,
than in the digitus medius of the fore-foot, and differs in the greater
breadth of the upper part of the claw-sheath, and in the straighter
cone, or bony core, which supported the claw. The metatarsals of
the fourth and fifth toes are much larger than that of the third ; but
they support mere rudiments of digits reduced in each to two stunted
phalanges, which were doubtless buried like those of the outer digit
in the fore-foot in a kind of callous hoof.
Having completed the description of the skeleton, which is illus-
trated by an extensive series of accurate and highly finished
drawings, the author proceeds to the comparison of the modifica-
tions of the osseous structure of the gigantic extinct animal with that
in other known existing and extinct species of the class Mammalia.
The teeth agree in number, kind, mode of implantation and
growth, with those of the Sloth, and their structure is a modification
of that peculiar to the Sloth-tribe. All the modifications of the
skull relating to the act of mastication, especially the large and
complex malar bone, repeat the peculiarities presented by the ex-
isting Sloths. There are the same hemispheric depressions for the
hyoid bone in the Megatherium as in the Sloth. In the number of
cervical vertebrae the Megatherium, like the two-toed Sloth, agrees
with the Mammalia generally. In the accessory articular surfaces
afforded by the anapophyses and parapophyses of the hinder dorsal
and lumbar vertebrae, the Megatherium resembles the Ant-eaters
242 Royal Society.
{Mi/rmecophagce): but it does not resemble the Armadillos (/>a5^/?M5)
ia having long metapophyses, the peculiar development of which in
those loricated Bruta has a direct relation to the support of their
bony dermal armour. In tlie mesozygapophyses of the middle
dorsal vertebrae the Megatherium is peculiar. In the small extent
of the produced and pointed symphysis pubis it resembles the Sloths;
and in the junction of both ilium and ischium with the sacrum, it
manifests a character common to the Edentate order ; but in the
expanse and massiveness of the iliac bones, it can only be compared
with other extinct members of its own peculiar family of Phyllo-
phagous Edentata. Its habits necessitating a strong and powerful
tail, we find this resembling in its bony structure that of other
Edentata with a similar appendage, especially in the independency
of the two hoemapophyses of the first caudal, a character which ob-
tains in the Great Ant-eater and in some Armadillos; but this is
no evidence of direct affinity to either of these families ; the habits
of the small arboreal Sloths render their eminently prehensile limbs
sufficient for their required movements, and the tail is wanting.
Had that appendage been proportionally as large as in the Mega-
therium, we cannot suppose that the caudal vertebrae would have
materially differed from those of other Edentata.
In the coalescence of the anterior vertebral ribs with the bony
sternal ribs, the Megatherium resembles the Sloths. This essential
affinity is still more marked in the peculiarities of the scapula and
of the carpus. In the Mi/rmecophagajubata, the scaphoid is distinct:
in the Manis it coalesces with the lunare : in the Dasypus gigas
the trapezoides is anchylosed to the second metacarpal : in the Das,
sexcinctus it has coalesced with the trapezium. Not any of these
characteristics are manifested by the Megatherium : its carpus re-
peats the peculiarities of that in the Sloths, viz. the reduction of the
number of carpal bones to seven by the coalescence of the scaphoid
with the trapezium. The first digit (poUex), which is retained in
the Anteatcrs and Armadillos, is obsolete in the Megatherium as
in the Sloths and Orycteropus : three digits are fully developed and
armed with claws, as in the JBradi/pus tridactylus; and the fifth,
though incomplete in the Megatherium, is better developed, because
it was required in the ponderous terrestrial Sloth for its progression
on level ground. In no existing ground-dwelling Edentate is the
fifth digit deprived of its ungual phalanx, as in the Megatherium.
The bones of the fore-foot of that extinct animal are thus seen to be
modified mainly after the type of the BradypodidcB.
The long bones of all the limbs are devoid of medullary cavities, as
in the Sloths. The femur lacks the ligamentum teres as in the Sloths.
The fibula is anchylosed to the tibia at both ends in Megatherium,
as in Dasypus \ but this is not the case in the closely- allied extinct
Megatherioids called Mylodon^ Megcdonyx and Scelidotherium, a
fact which diminishes the force of the argument which Cuvier de-
duced from the coalesced condition of the bones in the Megatherium
in favour of its affinities to the Armadillos. The semi-inverted but
firm interlocking articulation of the hind-foot to the leg shows the
peculiarities of that joint in the Sloths exaggerated, and departs
Royal Society. 243
further from its characteristics in other Edentata. In all the existing
Edentata, save the Sloths, the hind-foot is pentadactyle, and four of
the toes have a long claw, even in the little arboreal Myrmecophaga
didactyla: the departure by degradation from the pentadactyle type
is a peculiar characteristic of the Sloth-tribe in the order. It is
carried further in the same direction in the great extinct terrestrial
Sloths. In these the mutilation of the foot has commenced on the
outer side by the removal of the ungual phalanx from the fifth and
fourth toes ; but this accompanied by modifications which adapt these
toes to the important office of support and progression of the body on
level ground. Jn the scansorial Sloths, the three middle digits being
equally developed for prehension, one toe on the outer and one on
the inner side of the foot, are reduced to their metatarsal basis. In
the Megatherium the mutilation of the foot on the inner side is
carried to a greater extent; the innermost toe or hallux, with its
entocuneiform bone, is wholly removed : the second toe is repre-
sented, like the first in the Sloths, by its cuneiform bone and a
coalesced rudiment of the metatarse : and it is only the third toe or
medius that repeats the condition of the claw-bearing toes in the
climbing Sloths.
Finally, the author enters upon the question of the habits and food
of the Megatherium. Guided by the general rule that animals
having the same kind of dentition have the same kind of food, he
concludes that the Megatherium must have subsisted, like the
Sloths, on the foliage of trees ; but that the greater size and strength
of the jaws and teeth, and the double-ridged grinding surface of the
molars in the Megatherium, adapted it to bruise the smaller branches
as well as the leaves, and thus to approximate its food to that of the
Elephants and Mastodons. The existing Elephants and the Giraffe
are specially modified to obtain their leafy food ; the one being
provided with a proboscis, and the entire frame of the lofty Giraffe
adapting it to browse on branches above the reach of its largest
ruminant congeners. If the Megatherium possessed, as Cuvier
conjectured, a proboscis, it cannot, judging from the suborbital
foramina, have exceeded in size that of the Tapir, and could only
have operated upon branches brought near its mouth. Of the use of
such a proboscis in obtaining nutritious roots, on the prevalent hypo-
thesis that such formed the sustenance of the Megatherium, it is
not easy to speculate : the hog's snout might be supposed to be more
serviceable in obtaining those parts of vegetables; but no trace of
the preenasal bone exists in the skull. A short proboscis would be very-
useful in rending off the branches of a tree prostrated and within
reach of the low and broad-bodied Megatherium, and it would be
aided in this act by the tongue, of which^ both the hyoid skeleton, by
its strength and articulation, and the foramina for the muscular
nerves by their unusual area, attest the great size and power.
As regards the limbs, the Megatherium differs from the Giraffe and
Elephant in the unguiculate character of certain of its toes, in the
power of rotating the bones of the fore-arm, in the corresponding
development of supinator and entocondyloid ridges in the humerus,
and in the possession of complete clavicles. These bones are requi-
244 Royal Society.
site to give due strength and stability totheslioulder-joint for varied
actions of the fore-arm, as in grasping, climbing and burrowing :
but they are not essential to scansorial or fossorial quadrupeds ; the
Bear and the Badger have not a trace of clavicles, and the mere rudi-
ments of these bones exist in the Rabbit and the Fox. We must seek,
therefore, in the other parts of the organization of the Megatherium,
for a clew to the nature of the actions by which it obtained its food.
In habitual burrowers the claws can be extended in the same plane as
the palm, and they are broader than they are deep. In the Mega-
therium the depth of the claw-phalanx exceeds its breadth, especially
in the large one of the middle finger; and they cannot be extended
into a line with the metacarpus, but are more or less bent. Thus,
although they might be used for occasional acts of scratching up
the soil, they are better adapted for grasping ; and the whole struc-
ture of the fore-foot militates against the hypothesis of Pander and
D' Alton, that the Megatherium was a burrowing animal. The
same structure equally shows that it was not, as Dr. Lund supposes,
a scrnsorial quadruped; for, in the degree in which the foot depart?;
from the structure of that of the existing Sloths, it is unfitted for
climbing ; and the outer digit is modified, after the ungulate type,
for the exclusive office of supporting the body in ordinary terrestrial
progression. It may be inferred from the diminished curvature and
length, and from the increased strength and the inequality of the claws,
especially the disproportionately large size of that weapon of the
middle digit, that the fore-foot of the Megatherium was occasionally
ap])lied by the short and strong fore-limb in the act of digging ; but
\\s analogy to that of the Ant-eaters teaches that the fossorial actions
were limited to the removal of the surface-soil, in order to expose
something there concealed, and not for the purpose of burrowing.
Such an instrument would be equally effective in the disturbance of
roots and ants ; it is, however, still better adapted for grasping than
for delving. But to whatever task the partially unguiculate hand of
the Megatherium might have been applied, the bones of the wrist,
fore-arm, arm and shoulder, attest the prodigious force which would
be brought to bear upon its execution. The general organization of
the anterior extremity of the Megatherium is incompatible with its
being a strictly scansorial or exclusively fossorial animal, and its
teeth and jaws decidedly negative the idea of its having fed upon
insects ; the two extremes in regard to the length of the jaws are
presented by the phyllophagous and myrmecophagous members of
the Edentate order, and the Megatherium in the shortness of its
face agrees with the Sloths.
Proceeding then to other parts of the skeleton for the solution of
the question as to how the Megatherium obtained its leafy food, the
author remarks that the pelvis and hind limbs of the strictly bur-
rowing animals, e.g. the Mole, are remarkably slender and feeble,
and that they offer no notable development in the Rabbit, the Oryc-
terope, or other less powerful excavators. In the climbing animals,
as e.g. the Sloth and Orang, the hind-legs are much shorter than
the fore-legs, and even in those Quadrumana in which the pre-
hensile tail is superadded to the sacrum, the pelvis is not remarkable
Royal Society. 245
for its size or the expansion of the iliac bones. But in the Mega-
therium the extraordinary size and massive proportions of the pelvis
and hind limbs arrest the attention of the least curious beholder, and
become eminently suggestive to the physiologist of the peculiar
powers and actions of the animal. The enormous pelvis was the
centre whence muscular masses of unwonted force diverged to act
upon the trunk, the tail, and the hind legs, and also by the ' latis-
simus dorsi ' on the fore-limbs. The fore-foot being adapted for
scratching as well as for grasping, may have been employed in
removing the earth from the roots of the tree and detaching them
from the soil. The fore-limbs being well adapted for grasping the
trunk of a tree, the forces concentrated upon them from the broad
posterior basis of the body may have co-operated with them in the
labour, to which they are so amply adapted, of uprooting and pro-
strating the tree. To give due resistance and stability to the pelvis,
the bones of the hind-legs are as extraordinarily developed, and the
strong and powerful tail must have concurred with the two hind-legs
in forming a tripod as a firm foundation for the massive pelvis, and
affording adequate resistance to the forces acting from and upon
that great osseous centre. The large processes and capacious spinal
canal indicate the strength of the muscles which surroundedthetail,
and the vast mass of nervous fibre from which those muscles derived
their energy. The natural co-adaptation of the articular surfaces
shows that the ordinary inflection of the end of the tail was back-
wards as in a cauda fulciens^ not forwards as in a cauda prehensilis.
Dr. Lund's hypothesis, therefore, that the Megatherium was a
climber and had a prehensile tail, is destroyed by the now known
structure of that part.
But viewing, as the author conceives, the pelvis of the Mega-
therium as being the fixed centre towards which the fore-legs and
fore-part of the body were drawn in the gigantic leaf-eater's efforts
to uprend the tree that bore its sustenance, the colossal proportions of
its hind extremities and tail lose all their anomaly, and appear in
just harmony with the robust claviculate and unguiculate fore-limbs
with which they combined their forces in the Herculean labour.
The author then referred to the Mylodo7i robustus, a smaller ex-
tinct species of the same natural family of phyllophagous Bruta, and
to the additional arguments derivable from the skeleton of that
animal in favour of the essential affinity of the Megatherium to the
Sloths ; and the light which the remarkable healed fractures of the
skull of a specimen in the Museum of the College of Surgeons
threw upon the habits and mode of life of the species.
Fmally, with reference to the hypothesis of the German authors
and artists of the degeneration of the ancient Megatherioids of South
America into the modern Sloths, the author remarked that the
general results of the labours of the anatomist in the restoration of
extinct species, viewed in relation to their existing representatives
of the different continents and islands, commonly suggested the idea
that the races of animals had deteriorated in point of size. Thus
the palmated Megaceros is contrasted with the Fallow-deer, and the
great Cave-bear with the actual Brown Bear of Europe. The huge
Phil. Mag. S. 4. Vol. 2. No. 10. Sept. 1851. S
246 Intelligence and Miscellaneous Articles.
Diprotodon and Nototherium afford a similar contrast with the
Kangaroos of Australia, and the towering Dinornis and Palapteryx
with the small Apteryx of New Zealand. But the comparatively
diminutive aboriginal animals of South America, Australia and New
Zealand, which are the nearest allies of the gigantic extinct species
respectively characteristic of such tracts of dry land, are specifically
distinct, and usually by characters so well marked as to require a
subgeneric division, and such as no known or conceivable outward
influences could have progressively transmuted. Moreover, as in
England, for example, our Moles, Water-voles, Weasels, Foxes ^nd
Badgers, are of the same species as those that co-existed with the
Mammoth, Tichorrine Rhinoceros, Cave Hyaena, Bear, &c. ; so like-
wise the remains of small Sloths and Armadillos are found associated
with the Megatherium and Glyptodon in South America; the fossil
remains of ordinary Kangaroos and Wombats occur together with
those of gigantic herbivorous marsupials; and there is similar evidence
that the Apteryx existed with the Dinornis: and the author offered
the following suggestions as more applicable to or explanatory of the
ph'enomena than the theory of transmutation and degradation. He
observed, that in proportion to the bulk of an animal is the difficulty
of the contest which, as a living being, it has to maintain against
the surrounding influences which are ever tending to dissolve the
vital bond and subjugate the organised matter to the ordinary che-
mical and physical forces. Any changes, therefore, in the external
circumstances in which a species may have been created to exist,
will militate against that existence in probably a geometrical ratio
to the bulk of such species. If a dry season be gradually prolonged,
the large mammal wi:l suffer from the drought sooner than the
small one ; if such alteration of climate aft'ect the quantity of
vegetable food, the bulky Herbivore will first feel the effects of the
stinted nourishment ; if new enemies are introduced, the large and
conspicuous quadruped or bird will fall a prey, whilst the smaller
species might conceal themselves and escape. Smaller quadrupeds
are usually, also, more prolific than larger ones. The actual presence
therefore of small species of animals in countries where the larger
species of the same natural families formerly existed, is not to be
ascribed to any gradual diminution of the size of such larger animals,
but is the result of circumstances which may be illustrated by the
fable of the * oak and the reed ' ; the small animals have bent and
accommodated themselves to changes under which the larger species
have succumbed.
XXXVI. Intelligence and Miscellaneous Articles.
ON THE ARTIFICIAL PRODUCTION OF CRYSTALLIZED MINERALS.
BY M. EBELMEN*.
nj'^HE author has continued his experiments upon the artificial pro-
■^ duction of minerals. In his recent experiments, instead of the
porcelain furnace he made use of one of Bapterosse's furnaces, the
* An abstract of the author's former experiments was given in the April
Number for 1848.
Intelligence and Miscellaneous Articles. 247
temperature of which is somewhat lower than that of the porcelain
furnace. When large quantities of alumina, magnesia and silica,
were exposed for several days uninterruptedly to the constant tem-
perature of this furnace, he obtained spinelle in octohedra of such
size, that they could be readily distinguished with the naked eye,
and their angles measured. They all consisted of perfectly trans-
parent octohedra, the twelve edges of which were truncated. The
facets of some of the octohedra were between three and four milli-
metres in breadth.
M. Ebelmen has also produced zinc-spinelle or Gahnite. This
mineral, as found in nature, is always coloured brown or green by
peroxide of iron. M. Ebelmen obtained artificial Gahnite in a
perfectly transparent and colourless state. When oxide of chrome
was added to it, beautiful ruby-red octohedra with rhombic dodeca-
hedral facets of from two to three millimetres were obtained.
The specific gravity of pure artificial Gahnite is 4*58, that of the
native mineral 4-23 to 4-70. The hardness of the former is the
same as that of the latter ; both scratch quartz readily. On com-
paring the density and the atomic weight of the aluminates of zinc
and magnesia, their atomic volume is found to be exactly the same ;
thus, that of the magnesian spinelle is 25*2, and that of pure Gahnite
25-1.
M. Ebelmen also obtained chromites of zinc and magnesia,
i. e. compounds of sesquioxide of chromium Cr'^ O^ with bases RO,
which belong to the spinelle series. These, with the protochromite
of iron, which has been already described by the author in his first
memoir, show clearly that the native chromate of iron belongs to
the same family.
The author also procured the ferrite of zinc, Fe^ O', ZnO ; it cry-
stallizes in black strongly sparkling octohedra, which yield a black
powder. They were not attacked by dilute acids, but dissolved in
concentrated hydrochloric acid. Their density is 5' 132. The
author concludes from the existence of this compound, that Frank-
linite is identical with it.
The two following compounds are new, and of very great interest :
1, may neso -borate of chrome; and 2, per-magneso-borate of iron,
which the author regards as compounds of oxide of chrome and per-
oxide of iron, with tribasic borate of magnesia BO^.SMgO. This
borate BO-' + 3MgO is produced by the long-continued action of a
very high temperature upon the borate of magnesia with excess of
acid, and forms to a certain extent the mother-ley, out of which the
two above-described compounds crystallized.
By the aid of boracic acid as a solvent, Ebelmen has also obtained
some silicates which were infusible per se at the furnace heat. In
this way he procured the silicate of magnesia MgO, SiO in perfectly
formed crystals, the angles of which could be measured, and the
measurements of which showed that they were identical with the
transparent Peridote of mineralogists. The bisilicate MgO, 2(SiO)
was obtained in long, beautifully white, pearly prisms, which exhi-
bited the cleavage of pyroxene. The corresponding zinc compounds
were also obtained in crystals.
S2
348 Intelligence and Miscellanecms Articles.
With borax, M. Ebelmen formerly obtained microscopic crystals
of alumina ; the addition of a substance which gives a somewhat more
difficult fusibility to the flux, as carbonate of baryta or silica, caused
the production of beautiful crystals of alumina of the most si)lendid
lustre. These crystals had the form of a six-sided double pyramid,
appearing very considerably truncated on both summits, so tliat they
resembled the strongly flattened plates of iron-glance of the volcanoes.
The measurement of the angle between the lateral facets and the
base showed that it was identical with those of corundum. This
artificial corundum scratched quartz and topaz easily.
By using the phosphates as solvent, tantalic, niobic, and titanic
ncids were obtained in crystals. Titanic acid crystallizes from the
phosphate in long needles, the specific gravity of which is =4*283,
hence identical with rutile.
All the artificial crystals which the author obtained have been
optically examined by him, and found, with the exception of those
belonging to the regular system, to exhibit the action upon polarized
light. — Comptes Rendus, vol. xxxii. p. 330-333.
FURTHER RESEARCHES UPON CRYSTALLIZATION BY THE DRY ME-
THOD. BY M. EBELMEN.
In my former investigations, I employed as solvents for the ele-
ments various fluxes which are volatile at high temperatures, such
as boracic acid, borax, and acid and alkaline phosphates. It struck
me that some new series of compounds might be obtained by using
alkaline instead of acid fluxes, such as the carbonates of potash and
soda, which are so frequently employed in mineral analyses for dis-
solving by the dry method those substances which are not acted
upon by acids. These substances, like boracic acid, possess the
double property of assuming the liquid state at temperatures easily
produced in our furnaces, of dissolving a large number of metallic
oxides, and of becoming completely volatilized in open vessels at a
temperature slightly above that at which they undergo fusion.
When a mixture of silica and magnesia, in such proportions as to
constitute the bisilicate, is exposed to a high temperature with bi-
carbonate of potash, after the lapse of some days we obtain a per-
fectly liquid vitreous mass, at the bottom of which very transparent
colourless crystals are formed. These are easily separated from the
fused mass, by treating it with very weak acids and solution of
potash, whtch dissolves the glass without acting upon the crystals.
They are easily recognized as peridote. I have succeeded in mea-
suring their angles. The facet g' is well-marked ; the other facets
which I have detected are those of e^, e\ g^. A', and a! ; the measured
angles differ scarcely a few minutes from those which have been
obtained with the natural crystals.
It is evident that in this reaction half the silica separates to form
an infusible combination with the magnesia ; the vitreous matter
acted upon by acids also contains magnesia ; a great part of the pot-
ash was volatilized. Titanate of lime, TiO CaO, may be obtained
Intelligence and Miscellaneous Articles. 249
in the same manner crystallized in cubes, the edges of which are
slightly truncated ; the compound is slowly separated, by the action
of weak acids, from the vitreous matter in which it is formed ; its
density is =4*10 ; it is identical with the mineral to which M. G.
Rose has given the name of Perowskite, which was first found in the
Ural, and more recently in the volcanic districts of the Kaiserstuhl.
The silicate of glucina, when fused with excess of alkaline carbo-
nate, yields a semi-vitreous mass, from which microscopic crystals
may be separated by the action of acids ; the crystals consist of per-
fectly pure glucina ; their specific gravity is 3*02 ; they are not acted
upon by acids, excepting hot and concentrated sulphuric acid.
I have also obtained various accessory products in these experi-
ments, as platinum crystallized in very brilliant octohedra and cubo-
octohedra. The results which have just been described, differ very
clearly from the ordinary phsenomena of vitrification. This, it is well
known, occurs in a mass of glass which is slightly softened, but not
fused, and the ill-defined crystals which have been obtained, dififer
but little in chemical composition from the vitreous mass which sur-
rounds them. In the present case, on the other hand, the crystals
are formed in the midst of a perfectly liquid mass of glass, and their
properties and chemical composition are completely diflferent from
those of the vitreous portion.
In conclusion, I must point out another method of crystallization,
which, like the method by evaporation, has its analogue in the ope-
rations of the wet method. We might expect that metallic oxides,
either simply or combined with each other, would separate in the
crystalline state from the fused masses, when these are acted upon
by more powerful bases than those primarily dissolved. In this man-
ner, by causing fragments of lime to act upon borate of magnesia, we
obtain magnesia in diaphanous crystals, the form of some of which
is readily determinable by a lens, and which may be isolated from
the mass in which they are disseminated by the action of weak acids,
which do not attack tliem. These crystals appear identical in form
and composition with the native magnesia discovered in the blocks
of the Somma, and to which M. Sacchi has given the name of Peri-
clase.
I shall soon lay before the Academy a more detailed memoir
upon this subject, and show the consequences deducible from these
experiments in explaining the formation of a large number of mine-
rals belonging to the alkaliferous rocks. — Comptes Rendus, Mav 12,
1851. ,;..,..
NEW STATIC AND DYNAMIC THEORY OF ULTIMATE PARTICLiES.
BY M. ZANTEDESCHI.
As the ancient hypotheses of the constitution of matter and bodies,
and physical and chemical phaenomena, do not completely respond
to the requirements of science in its present state, it appears to me,
that by viewing the formation of bodies and the production of pHae-
250 Intelligence and Miscellaneous Articles.
nomena in the following light, a clear and evident explanation of
them will re8ult.
A body is composed of contiguous but not continuous parts, and
these, instead of being rigid and hard, are eminently compress-
ible and elastic, lliese contiguous parts form molecular groups
and systems, which may be arranged differently in regard to each
other, in virtue of the attractive force acting from molecule to mole-
cule, from system to system. In accordance with this view, liquids
would be formed by strongly compressed and but slightly adherent
molecular groups ; solids, by less strongly compressed but not ad-
herent groups ; and lastly, aeriform fluids would be constituted by
still less compressed molecular groups, and these much less adherent.
If the arrangement of the systems be destroyed, the equilibrium
between the attractive and the elastic force disappears ; the internal
molecular movement increases, the vibrations augment, the elastic
force gains the ascendant, and the matter expands, becomes dissi-
pated and attenuated on assuming the elastic state, which state
precedes every chemical phaenomenon.
I have endeavoured on these principles to explain all the phaeno-
mena of physics and chemistry, in the same manner as the general
laws of mechanics.
In accordance with this hypothesis, the phsenomena of capillarity
are merely a necessary consequence of the expansion of matter at its
edges, of the adhesion of the expanded layer to the adjacent wall,
and of the force of cohesion exerted between the upper parts of the
liquid prism and its base. The limits of this phaenomenon are deter-
mined by the equilibrium of the force of adhesion and cohesion with
the excess of pressure of the internal upon the external level. The
expansive force may be greater or less, according to the nature of
the liquid ; it may give rise to the formation of new prisms, which
cease to remain suspended when the pressure of the external layer
becomes less than the pressure of the liquid outside, which pressure
does not correspond to the weight of the entire column of liquid
raised, considering that a portion of it is supported by the adherence
of the liquid to the adjacent solid walls.
All electrical, magnetic, thermotic and luminous phaenomena, are
finally nothing more than currents, projections of more finely di-
vided, rarer and more elastic matter, which by their encounters
give rise to new solutions or new combinations, which we call
physical, chemical and organoleptic properties. Beyond the animal
sphere, we find merely the motion of matter which becomes disag-
gregated or recomposed. Those bodies, which have hitherto been
called imponderable, dynamides or material forces, are nothing more
than the matter itself in the elastic state, which striking against
the masses, or penetrating between the different molecular systems,
breaks up or alters the primitive arrangement, augments their internal
and vibratory motion, and gives rise to new systems and other ar-
rangements.
In nature there is always motion, which is at the same time both
the cause and the effect of other motions, by causing the relations
Meteorological Observations. 251
between the elastic force and the attraction of the molecules to change
at every moment. When nature is contemplated on these principles,
it appears simple in its manifestations, grand and sublime in its re-
sults, always consistent with itself.
We next have, in the memoir itself, the application of these theo-
retical views to the explanation ; — 1, of combustion ; 2, of the expan-
sions and the contractions of bodies, and the changes in their condi-
tion; 3, of the capacity of bodies for heat, specific heat and latent heat ;
4, of the spheroidal state of liquids ; 5, of irradiation ; and lastly, 6,
of electro-magnetic currents. The more I study, the more I medi-
tate profoundly upon the phsenomena of nature, the more I feel
convinced that nothing is so simple and fertile as this dynamic sy-
stem.— Comptes Rendus, May 19, 1851.
METEOROLOGICAL OBSERVATIONS FOR JULY 1851*.
Chiswick. — July 1. Hazy and mild : rain : cloudy and fine : thunder and light-
ning, with very heavy rain. 2. Fine : very fine : clear. 3. Uniformly overcast:
cloudy and fine : densely clouded. 4. Overcast: very fine : clear, 5 — 7. Very
fine. 8. Cloudy: rain. 9. Cloudy and fine. 10. Rain. 11,12. Very fine.
13. Cloudy and fine : overcast : rain. 14. Cloudy : windy. 15. Fine : windy :
slight rain. 16,17. Very fine. 18, Cloudy. 19. Fine: rain: constant heavy
rain in the evening. 20. Cloudy and fine. 21. Very fine. 22. Dry haze : very
fine. 23. Rain. 24. Heavy rain. 25, 26. Very fine. 27. Cloudy and fine.
28. Cloudy: rain. 29. Very fine. 30. Foggy : very fine. 31. Hazy: overcast.
jMean temperature of the month 60°'71
Mean temperature of July 1850 61 "91
Mean temperature of July for the last twenty-five years . 63 '13
Average amount of rain in July 2*30 inches.
Boston. — July 1,2. Fine. 3, Cloudy. 4, 5. Fine. 6, 7. Cloudy. 8. Cloudy:
rain A.M. and P.M. 9. Rain : rain a.m. 10 — 12. Cloudy. 13. Fine : rain p.m.
14. Cloudy: rain a.m. and p.m. 15, 16. Cloudy. 17. Cloudy: rain with
thunder A.M. 18. Fine. 19. Fine : rain p.m. 20. Cloudy : rain a.m. 21. Fine:
rain P.M. 22. Fine. 23. Cloudy: rain a.m. and p.m. 24. Rain: rain a.m.
and P.M. 25. Cloudy : rain a.m. and p.m. 26. Cloudy : rain p.m. 27. Fine.
28. Rain: rain early A.M. 29. Cloudy: rain p.m. SO. Cloudy. 31. Cloudy:
rain p.m.
Sandwick Manse, Orkney. — July 1. Fog. 2. Cloudy: clear. 3. Clear. 4.
Cloudy : drizzle. 5. Damp : clear. 6. Damp : drizzle. 7. Drizzle : rain.
8. Bright: clear. 9. Bright: clear: fine. 10. Drops. 11. Showers: fog.
12. Rain. 13. Cloudy : rain. 14. Damp. 15. Drizzle : rain. 16. Cloudy.
17. Damp: drizzle. 18. Bright: fine. 19. Fine. 20. Bright: rain. 21. Drizzle:
rain : cloudy. 22. Bright : clear : fine. 23. Fine : clear : fine. 24. Cloudy : fine.
25. Cloudy : drizzle. 26. Cloudy : rain. 27. Drizzle : fine. 28. Rain : cloudy.
29, SO. Cloudy. 31. Rain : drizzle.
* The observations from the Rev. W. Dunbar of Applegarth Manse have
not reached us.
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THE
LONDON, EDINBURGH ano DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
OCTOBER 1851
XXXVII. On a Class of Ammoniacal Compounds of Cobalt.
By Frederic Claudet*.
WHEN ammonia is added in excess to a solution of proto-
chloride of cobalt mixed with four times its weight of
chloride of ammonium^ the solution becomes of a dark brown
colour without any appearance of a precipitate. In this state the
solution rapidly absorbs oxygen from the air ; and on frequently
agitating a bottle half-filled with this solution, removing the stop-
per from time to time to renew the air, the absorption is much
facilitated, and is complete in the space of three or four days,
the colour of the liquid changing at the same time from dark
brown to an intense violet-red. If the air be replaced in this
experiment by pure oxygen gas, the oxidation is still more rapid,
and may be completed (if the quantity of solution be not too
large) without requiring the removal of the stopper. By boiling
this oxidized ammoniacal solution, strongly acidified with hydro-
chloric acid, a heavy crimson powder is deposited. A slight
effervescence takes place at the same time, due to the evolution
of a certain quantity of oxygen, and the liquid becomes nearly
colourless owing to the precipitation of the whole of the cobalt
in the form of the new compound. The liquid when cold is
drawn oif from the red powder, which is washed several times by
decantation with distilled water, thrown on a filter and allowed
to dry in a warm chamber. The precipitated powder thus ob-
tained is nearly pure. Before examination it is, however, neces-
sary that it should be crystallized. The powder for this purpose
is dissolved in boiling water to which a few drops of hydrochloi^c
acid have been added j and on cooling, the salt is deposited in
* Communicated by the Author.
Phil Mag, S, 4. Vol, 2. No. 11. OcU 1851. T
254 Mr. r. Claudet on a Class of
the fomi of regular octohedi'ons, small, sparkling, and of a ruby-
red colour, veiy much resembling small ciystals of chrome-alum.
This salt, which is an intense colouring matter, is sparingly
soluble in cold water, 1 part requiring at 60"^ F. 244 parts of water;
it is soluble to a much larger extent in water at the boiling-point,
to which it imparts a very deep red colour ; it is however slightly
decomposed, and altogether so on boiling the solution ; but this
may be prevented by keeping the solution slightly acid with
hydi-ochloric acid.
Hydrochloric acid, saturated solutions of chloride of ammo-
nium and sodium, completely precipitate the new salt from its
solution ; alcohol acts in the same way. The salt is not decom-
posed by boiling hydrochloric acid. Sulphuric acid evolves hy-
drochloric acid, a corresponding sulphmic salt being formed;
the reaction, however, is not complete, for at the end of the
operation chlorine comes off from some decomposition. Nitric
acid partially transfoims the salt into the nitrate of the base.
Potash and soda decompose the solution of the salt, a hydrated
peroxide of cobalt being thrown down and ammonia evolved in
considerable quantity. Hydrate of baryta decomposes the salt
in the same way with the aid of heat, but not in the cold. Car-
bonate of potash or soda has no effect. Yellow prussiate of
potash gives with a solution of the salt a dirty brown precipitate,
red prussiate none ; but on standing, bright yellow needles cry-
stallize from the solution.
Sulphuretted hydrogen precipitates the whole of the cobalt as
a bisulphide of that metal, ammonia being liberated at the same
time. The analysis of three different preparations of this sul-
phide gave —
ii Found.
Calculated. _.___> .
I.
II.
Hi.
iS'9
49-5
48-2
51-1
50-5
51-8
Cobalt . . 29-5 47-96
Sulphur . . 32__ 52-04
61-5 100-00
On boiling a solution of the new salt, it is decomposed into
ammonia, which escapes, and a superior hydrated oxide of cobalt,
containing a certain amount of a nitride of cobalt which is pre-
cipitated, nothing but chloride of ammonium remaining in solu-
tion. The composition of the precipitated oxide of cobalt appears
tobe CoSO'^-fSHO.
Dried in the air, the salt contains no water of crystallization,
neither does it contain oxygen. When heated to low redness in
a glass tube, a large quantity of ammonia is disengaged, a cer-
tain quantity of chloride of ammonium subhmed, and a residue
of common protochloridc of cobalt remains. In this reaction no
Ammoniacal Compounds of Cobalt. 255
moisture is ppduced, which would necessarily be formed if any
oxygen existed in the compound.
The analysis of this salt was effected in the following manner.
The chlorine was estimated from the chloride of silver, obtained
on boiling the solution with an excess of nitrate of silver and
nitric acid. In the cold the precipitation by nitrate of silver is
not complete. The cobalt was determined by reducing a certain
quantity of the substance introduced into a tube with a bulb, by
pure hydrogen and heat. The nitrogen was estimated as am-
monia, by distilling the salt with caustic soda, receiving the
ammonia into hydrochloric acid, and determining the weight of
the double chloride of platinum and ammonium. The ammonia
was also obtained by heating the salt with soda-lime, according
to the method of Will and Varrentrapp. This last process, how-
ever, gave less accurate results, a deficiency of about 1 per cent.
in the nitrogen being found. The hydrogen was determined by
combustion of the salt with a mixture of oxide of copper and
chromate of lead, and copper turnings.
The following are some of the results obtained : —
Per cent.
20 grains of salt gave 34-14 Ag CI =8-445 CI
12
10
19
8-68
9-48
12-51
14-81
8
13
13-5
11-655
The number of equivalents of chlorine, cobalt, nitrogen and
hydrogen deduced from these results, are 3C1, 2Co, 5N and 16H,
as may be seen from the calculated numbers : —
Found.
34-14 Ag CI
=8-445 CI=42-22
20-56 ...
= 5-086 =42-38
17-08 ...
=4-225 =42-25
4-49 of cobalt
= 23-63
2-04 ...
= 23-50
2-25 ...
=23-73
2-96
=23-66
65-54 PtCP + NH4Cl=4-116N =27-79
34-64
=2175 =27-20
7-38 HO
= -82 H = 6-31
7-70 ...
= -855 = 6-34
6-775 ...
= -753 = 6-46
v^an
:uiutcu.
A
r
3C1= 106-5
42-34
2Co= 59-0
23-46
5N= 70-0
27-83
16H= 18
6-36
^
II.
IIL^
42-22
42-3a
42-25
23-63
23-50
23-66
27-20
'^7-79
6-31
6-34
6-46
,251-5 10000 >
The salt containing a large quantity of chlorine, it might be
expected that the volatilization of minute quantities of chloride
of copper or chloride of lead in the combustion would give an in-
crease in the results for the hydi-ogen, one equivalent of the latter
T2
266 Mr. F. Claudet on a Class of
making a difference only of ()-37 per cent. The results obtained,
liowever, agree pretty well together ; and as they do not differ
much from the calculated numbers, I am much inclined to believe
sixteen the true number of equivalents of hydrogen in the salt ;
and I am further confirmed in this view by the manner in which
the salt is decomposed by heat. A combustion-tube about two
feet long was closed at one end and bent at right angles within
about half an inch of the closed end, so as to form a kind of re-
tort. A certain quantity of the salt was rubbed into a paste
with a little water and rolled up into the size of a pea. When
quite dry, this was dropt into the tube and made to enter the
small retort; mercury was then gently poured into the tube,
which was gradually filled and then inverted in a mercurial
trough. The mercury descended about a quarter of an inch in
the tube, on account of a small quantity of air which remained
in that portion containing the salt. The retort part of the tube
was now slowly heated by means of a spirit-lamp until the salt
was entirely decomposed. The gas produced occupied nearly
the whole of the tube, which was two feet in height. On allow-
ing the tube to cool, and introducing a small quantity of hydro-
chloric acid, the whole of the gas was absorbed with the excep-
tion of a column of about three-quarters of an inch in height,
showing that the space above the mercury was entirely composed
of ammoniacal gas. Now the decomposition of this salt into no
other gas than ammonia, and no other solid products than chlo-
ride of ammonium and protochloride of cobalt, is only compatible
with a certain number of atoms of hydrogen, which is sixteen,
for —
3Cl,2Co,5N,16H=:2CoCl + NH4Cl-F4NH3.
Had there been one or two equivalents less of hydi'ogen, one
equivalent of ammonia would have been broken up, giving hy-
drogen and nitrogen not condensed by the hydrochloric acid.
Assuming, then, the above number of atoms to be correct, and
applying Berzelius's theory of the copulated compounds, the for-
mula of this salt may be written —
3(NH4Cl)+2(NH2Co);
that is, a compound of 3 equivalents of chloride of ammonium
with 2 equivalents of an ammonia, in which 1 atom of hydrogen
is replaced by cobalt. In fact the salt has the characters of
such conjugate compounds. It has the properties of chloride of
ammonium with regard to form and taste ; while on the other
hand the basic property of the 2 equivalents of ammonia have
totally disappeared, the salt being quite neutral to test-paper.
This compound is analogous to the remarkable platinum com-
pounds discovered by Gros and Reiset ; but with this difference.
Ammoniacal Compounds of Cobalt. ^f
that it is a sesqui-conjugated compound, if it may be so called,
being composed of 3 equivalents of the salt united with 2 equi-
valents of the adjunct.
Another way of grouping the atoms of this compound is the
following, proposed by Mr. Graham :-^^ '^ '' -*:;.- jirt; ? inm
fNH^Co^ /d ]>?:!!?oqropoMi> «i il&p. orii
Here NH^ Co^ represents an ammonium in which 2 equivalents
of hydrogen are replaced by 2 equivalents of cobalt; while NIP
NH'* I'epresents an ammonium in which 1 equivalent of hydrogen
is replaced by ammonium itself, as the hydrogen of ammonia is
replaced by ethyle, methyle, &c. in Wurtz's and llofmann's bases.
CINJ i^o + 2ClNJ ^^
N{g
Co2 + '^^^^^\NH4
The compound would then be viewed as a double salt, composed
of 1 equivalent of a chloride of cobalt-ammonium and 2 equiva-
lents of a chloride of ammonium, in which the fourth atom of
hydrogen is replaced by ammonium.
This peculiar compound has the property of forming double
salts with bichloride of platinum and bichloride of mercury.
Double salt with bichloride of platinum. — On adding a warm
solution of the salt to bichloride of platinum in excess, a silky
crystalline buff-coloured precipitate falls down, much less soluble
than the salt itself; it may therefore be well washed with water,
thrown on a filter and dried.
12 grains of this double salt were fused with carbonate of
soda, dissolved in hot water and filtered, to separate the platinum
and oxide of cobalt. The solution neutralized with nitric acid
and precipitated with nitrate of silver gave 20* 11 grs. AgCl =
4"975 CI =41 '6 per cent. The filtrate of platinum and oxide of
cobalt ignited was treated with boiling hydrochloric acid, which
dissolved out the cobalt, and left 4*05 platinum = 33' 75 per cent.
18*59 grains of double salt reduced by hydrogen gave 8*06
mixed metals =43-35 per cent., giving 9'60 per cent, for the
cobalt. The double salt is consequently composed of 1 equiva-
lent of the new compound and 2 equivalents of bichloride of
platinum.
Calculated.
(
Found.
j^jyjffoa shm
5C1:
= 248-5
42-12
41-60
mumomms.
2Pt
=256-2
33-43
33-75
>id offt bfffid
2Co;
= 59
10
Ox.. 9-60
• ylfjstoi
5N :
= 70
.'golmifi '
os'gfdT
iimvsmi mil
a6H:
= 16
■'M. hau eoiO vd b^'i^yougib ebmfoq.
CF{o,x™^;rT.4x+2PtCP.
258 Mr. F. Claudet on a Class of
the formula of which is —
NH^Co*
2(NH8NH'*)
When this salt is decomposed by heat, treated with nitro-
hydrochloric acid, and the excess of acid driven off by heat, the
solution crystallizes in large orange-brown prismatic tables, no
mother-liquor remaining. This salt proves to be a double chlo-
ride of platinum and cobalt, the 2 equivalents of bichloride of
platinum combining with 2 equivalents of protochloridc of cobalt
from the new compound.
Double salt with bichloride of mercury.- — Prepared in the
same way as the preceding double salt, by adding a waim solu-
tion of the cobalt salt to an excess of bichloride of mercury, a
bulky silky precipitate is formed composed of small red needles.
This may be collected on a filter, slightly washed with cold water
and recrystallized from a warm solution, this double salt being
tolerably soluble in hot water.
15 grains fused with carbonate of soda in the same way as the
double platinum salt, gave 18'10 grs. Ag CI = 4*477 CI = 29-84
per cent.
14*16 grs. reduced by hydrogen gave 0*80 cobalt =5*65 per
cent.
Calculated.
Found.
9C1 =319*5 30*00 2984
6Hg=600
2Co = 59 5-54 5*65
5N = 70
16H = 16
This double salt contains, therefore, for 1 equivalent of the co-
balt compound, 6 equivalents of bichloride of mercury.
CH?(NH%H^) + 6"«C'-
Recently prepared oxide of silver throws do^n the chlorine
from the new ammoniacal compound, a highly alkaline red solu-
tion remaining, not having the slightest odom* of ammonia. On
standing a few hours it decomposes, ammonia is evolved, and
hydratcd peroxide of cobalt precipitated. The compound in so-
lution represents before changing, the base of the present class
of salts. It is an oxide, of which the composition is the same as
that of the chloride already described, with the substitution of
3 equivalents of oxygen for 3 equivalents of chlorine : —
fNH^Co^
Formula of new cobalt base .... 0^-^ NH^NH*.
Ammoniacal Compounds of Cobalt. 259
The study of this and other allied compounds of cobalt which
exist will no doubt greatly extend our views respecting the com-
pound ammonias.
The chlorine of the original chloride may also be eliminated
by any silver salt, an analogous cobalt salt containing the acid of
the silver salt being formed and remaining in solution. In this
way I have been enabled to obtain a sulphate, nitrate, oxalate,
acetate, and carbonate of the new base. From the carbonate I
have prepared the bromide and iodide which have the octohedral
form of the chloride, are equally sparingly soluble in water, and
of a still darker ruby colour. The bromide was found to con-
tain 61 '15 per cent, bromine, the calculated amount being 61'8
per cent.
Tlie insolubility of this ammoniacal compound of cobalt in
boiling hydrochloric acid may be advantageously turned to ac-
count in the preparation of chemically pure cobalt, and also in
the qualitative examination of substances containing small quan-
tities of cobalt. The pulverized ore or its oxide to be purified is
dissolved in nitro-hydrochloric acid, diluted with water, and
filtered in order to separate any gangue or insoluble residue.
Chloride of ammonium is now added in large excess, and the
liquid saturated with ammonia ; it is then poured into a glass
bottle, and oxidated in the way I have already described in the
preparation of the new salts. During the oxidation a certain
quantity of the new compound is deposited, especially when the
solutions are rather concentrated, on account of its insolubility
in a strong solution of chloride of ammonium. The solution still
retains a certain quantity of cobalt salt ; it is therefore boiled with
a considerable excess of hydrochloric acid, which causes the total
precipitation of the new compound, dissolving at the same time
any oxide of iron or other oxides thrown down by the ammonia.
When cold the clear liquid is decanted ofi", and the deposit well
washed with acidulated water and then dried. By heating this
compound to low redness it is decomposed, leaving for residue
protochloride of cobalt slightly decomposed, but absolutely free
from any other metal. This may be reduced by hydrogen gas
giving pure metallic cobalt.
By these means I have been able to prepare perfectly pure
cobalt directly from the grey cobalt ore of Tunaberg, which is
an arsenio-sulphuret of cobalt, and also to detect small quantities
of cobalt in different samples of oxide of nickel.
The preceding results embody the most definite conclusions of
an investigation of the ammoniacal salts of cobalt v/hich I have
had in hand for the last two or three years. M. Fremyhas also
lately announced that he is occupied with an extended inquiry
into the same class of compounds, respecting which he has pub*
360 Dr. Beke's Summarfj of recent Nilotic Discoveiy.
lished some important general results*. Dr. A. Genth appeal's
also to have formed several of the salts of the new base deseribed
in this paper, but his analytical results diflfer entirely from minef.
It is in such circumstances that the present contribution is
offered towards the advancement of our knowledge respecting
the salts of cobalt.
University College,
August 29, 1851.
XXXVIII. A Summary of recent Nilotic Discovery,
By Charles T. Beke, Ph.D., F.S.A. ^c.X
^M!^ the Meeting of the British Association at Southampton,
-tV. in September 1846, I had the honour of explaining to the
Section of Geology and Physical Geography my views respecting
the physical configuration of the Table-land of Abessinia§ ; and
at the Meeting at Swansea, in August 1848, 1 enunciated before
the same Section my hypothesis as to the sources of the Nile in
the Mountains of the Moon||. I may be allowed here briefly
to recapitulate the main results of those two communications.
The table-land of Eastern Africa, instead of consisting, as was
generally supposed, of a succession of terraces rising one above
the other, the lowest being towards the Red Sea and the highest
in Enarea, is an elevated region of irregular surface, having its
line of greatest elevation towards the sea-coast, whence the
general level gradually falls westward towards the valley of the
Nile ; the water-parting between the streams tributary to that
gi-eat river and those flowing towards the Red Sea and the
Indian Ocean, being along the extreme eastern limit of the table-
land.
The eastern flank of this table-land is abrupt and precipitous,
the greater portion of the ascent to the height of 8000 or 9000
feet (the average elevation of its eastern edge) being within the
horizontal distance of a veiy few miles ; so that persons ap-
proaching it from the coast can only regard it as a lofty range
* Comptes Rendus, April 7, 1851, and May 26, 1851.
t Chemical Gazette, 1851, p. 286. [The priority of discovery of this
new class of salts belongs, not to M. Fretny, but to Dr. Genth, whose re-
searches were published early in 1850; but unfortunately in a jouinal, the
circulation of which appears to be confined to the German physicians of the
United States.— W. F.J
X Communicated by the Author, having been read before the Section of
Geography and Ethnology of the British Association for the Advancement
of Science, at the Meeting at Ipswich, on the 4th of July 1851.
§ See Report of the British Association for 1846, Report of the Sec-
tions, pp. 70-/2 ; and Journal of the Royal Geographical Society, vol. xvii.
p. 76 et seq.
II See Report of the British Association for 1848, Report of the Sections,
PJ>' 63j64; and Edinb. New PLiv.. Jouin., vol. xlv. p. 221 etseq.
iixfoa
Dr. Beke^s Summary of recent Nilotic Discovery. 261
of mountains running along the eastern side of Africa from north
to soutbj^' '^?m v/:>nyin to bhuk '(a.io ;«io/:t>- iviiivun y;«d o:^ obUj
To the sotitHward' of klyont the Sfnd parallel of sortth* MtiideV
and between the 29th and 34th meridians of east longitude, is
the country of Mono-Moezi or Uniamezi — names which may-
be respectively interpreted ^^ the king of the moon ^^ and ^^ the
possession of the moon ; '' — and in this country, which forms a
portion of the table-land, various considerations induced me to
place the sources of the Bahr-el- Abyad or White River, the direct
stream of the Nile. And I expressed the opinion that the
^' Mountains of the Moon '' of the geographer Ptolemy, in which
he places the sources of the Nile, consist of the mountain range
of Eastern Africa, which flanks the country of Mono-Moezi to
the east, instead of being, as we see them usually marked in the
maps, a range stretching across the continent from east to west.
The direct stream of the Nile, which I thus conceive to have
its sources in the mountains of Mono-Moezi, was in 1840 and
1841 ascended beyond the 5th parallel of north latitude by the
second of the expeditions sent by Mohammed Ali, Pasha of
Egypt, to explore its course, and was found to be joined in about
9° 20' N. lat. by two principal arms, viz. the Ke'ilak or Bahr-el-
Ghazal, and the Sobat, Telfi, or River of Habesh. The former,
which joins the main stream from the west, and of which the
course is yet unexplored, is apparently the Nile of Herodotus
and other writers anterior to Ptolemy. The latter, namely the
Sobat, which falls into the Nile from the east, is the lower course
of the Godjeb, the principal river of KafFa, which in its upper
course is joined by three other streams, bearing in common the
name of Gibbe, and draining the extensive elevated districts
in the south of Abessinia Proper now occupied by numerous and
powerful Galla tribes. Further, the Bahr-el- Abyad or true Nile,
and the Sobat or Godjeb, appear to be the two principal arms of
the Nile described by Ptolemy as having their sources in the
Mountains of the Moon, or the Alpine regions of Eastern Africa;
while the Bahr-el-Azrek, Blue River or Abai, and the Atbara or
Takkazie, which both rise in the more northerly extension of the
same elevated regions, are respectively the Astapus and the As-
taboras of the same geographer.
The foregoing is a brief summary of my views respecting the
orography and hydrography of Eastern Africa, from the 18th
degree of north latitude to probably the 3rd or 4th parallel south
of the Equator, as submitted to the British Association down to
the year 1848. I now propose to take a rapid sm-vey of the
principal additions since made to our knowledge on the subject.
At the date of my last communication, it was not known in
Europe that the members of the Church Mission in Eastern Africa,
stationed at Rabbai ^Mpia, near Mombas, in about 4° south
^C2 Dr, Beke's Summartj of recent Nilotic Discovery.
latitude^ had already begun exploring the interior of the continent.
In the month of October 1847, Mr. Rebmann penetrated west-
wai'ds to Teita, '^ a country whose mountains rise to such a height
out of the vast surrounding plains, that on some eminences near
Rabbai 'Mpia they are to be seen at a distance of 90 miles;''
and in the April following (1848), the same missionary performed
a journey further into the interior, to the still more elevated
country of Djagga, where, at a distance of rather more than 200
geographical miles from the coast, in a direction about W.N.W.
fiHDm Mombas, he made the remarkable discoveiy of a lofty moun-
tain, named Kilimandjaro, of v/hich the summit is covered with
perpetual snow. The existence of snow on Kilimandjaro has
been disputed in Europe, though it is difficult to say on what
reasonable ground. However, on subsequent journeys, both
Mr. Rebmann and his colleague Dr. Krapf have satisfied them-
selves of the fact ; and unless it be intended absolutely to im-
pugn their veracity, their evidence cannot be rejected.
In Djagga Mr. Rebmann obtained information respecting the
country of Uniamezi — or Mono-Moezi, as it is designated by
the early Portuguese, by whom it was first mentioned — situ-
ated considerably further inland ; and tov/ards the end of the
year 1848 the same missionary returned to Djagga, for the
purpose of ascertaining the practicability of reaching Uniamezi.
Having been assured by the king of the former country of his
readiness to assist him on the journey, he returned to the coast,
whence, on the 5th of April 1849, he again set ovit on his way
into the interior ; his intention being to proceed, if possible, as
far as the large lake in Uniamezi, respecting which also he had
obtained information in Djagga, and which, from the name of
Us^mbiro attributed to it, appears to be the Lake Zambre of the
early Portuguese maps ; and when there he purposed making
inquiries as to the road beyond the lake to the west coast of Africa.
On this journey, however, Mr. Rebmann was unable to proceed
beyond Djagga ; the king of that country, Mamkinga, having
"by tomienting beggary taken all his things from him, and
leaving him at last no means whereby to travel any further.''
Dr. Krapf had in the interval been occupied in exploring the
districts to the south-west of Mombas, nearer the coast ; but
after the unsuccessful issue of Mr. Rebmann's last expedition,
he himself determined on undertaking the difficult and perilous
journey to Ukambani, a country situated northwards of Djagga.
This undertaking was successfully accomplished in the months
of November and December 1849. The distance performed by
Dr. Krapf, as measured on the map published in the Church
Missionary Intelligencer for September 1850, is in a direct line
240 geographical miles north-west from Mombas. Towards the
extreme point of his jom'ney Dr. Krapf crossed the river Adi,
Dr. Beke's Nummary of recent Nilotic Discovery, 263
supposed by him to be the upper course of the Sabaki, which
falls into the Indian Ocean close to Melinda. The absolute
height of the bed of the river where thus crossed is not given j
but it must be considerable^ inasmuch as the river thence runs
upwards of 200 geographical miles through a mountainous coun-
try before reaching the ocean. From the valley of the Adi
Dr. Krapf ascended about 1800 feet to ^^the plain of Yata/^ on
reaching which he says, '' We had a majestic view of the whole
region around. We viewed the serpentine course of the Adi
towards the west and north-west ; we saw the hills and plains
of the wild Wakuafi ; we noticed the mountains Noka, Djulu,
Engolia, Theuka, in whose vicinity lay the road we had taken to
Kikiimbuliu. Eastward we saw the mountains of Mudumoni,
which separate the Galla country from Ukambani. To the
north_, Ukambani Proper lay before our view. Had I been a
mere traveller pursuing only geographical objects,, I would, stand-
ing on the plain ofYata,hsive considered myself amply compensated
for the troubles I had sustained on the road ; for a great many
geographical problems were solved in an instant on the height
of Yata*.^' From this it is evident that Dr. Krapf must have
attained an elevation of several thousand feet, even if he had not
already reached the summit level of the table-land of Eastern
Africa.
Of the geographical results of this journey, one of the most
important is the discovery of another snowy mountain, named
Kenia, of larger size, if not of greater elevation than Kilimandjaro.
Kenia is thus described by Dr. Krapf: — ^'^The sky being clear, I
got a full sight of the snow mountain It appeared to be like
a gigantic wall, on whose summit I observed two immense towers,
or horns as you may call them. These horns or tov/ers, which
are at a short distance from each other, give the mountain a
grand and majestic appearance, which raised in my mind over-
whelming feelings. Kilimandjaro in Djagga has a dome-like
summit ; but Kenia has the form of a gigantic roof, over which
its two horns rise like two mighty pillars, which I have no
doubt are seen by the inhabitants of the countries bordering on
the northern latitudes of the Equator. Still less do I doubt
that the volume of water which Kenia issues to the north runs
towards the basin of the White Nilef/^
Though this conclusion of the worthy missionary is only
conjectural, it appears to be founded on substantial reasons;
and it can scarcely be doubted, that, through the discoveries
thus made, we may arrive at a close approximation to the south-
ern limits of the basin of the Nile. In Mr. Rebmann's map,
already adverted to, Kenia is placed in 1° S. lat. and 35°10'E,
* Church Missionary Intelligencer, vol. i. p. 417. t Ibid. p. 470, ^
264 Dr. Bcke's Summanj of recent Nilotic Discovoy.
long., at a distance of 320 geographical miles N. 55^ W. Aim
Mombas ; while the northern limit of the great lake in Unia-
m^zi is, in the same map, laid down conjecturally in about
1° 2(y S. lat. and 29° E. long., at a distance of 650 geographical
miles N. 75° W. from Mombas ; and beyond these two points we
can scarcely look for the continuation of the river, unless indeed
it should actually be found to flow out of the lake itself.
It is proper to remark here, that, according to Dr. Krapf's
explicit declaration*, this lake in Uniamezi is not identical with
Nyassi, — or Niassa, as Dr. Krapf spells the name, — the great lake,
respecting which some years back Mr. Cooley made an elaborate
communication to the Royal Geographical Society of London,
which is printed in the fifteenth volume of the Society^s Journal.
It should be added, that, when in Ukambani, Dr. Krapf heard of
the existence of a volcano in actual activity, at some distance
beyond Kenia to the north-west, but he did not go far enough
to see it. According to my hj^pothesis as to the physical cha-
racter of the '' Mountains of the Moon,^' they may in the most
general manner be likened to the Andes of South America ; and
these particular coincidences of snowy peaks and active volcanoes
serve further to complete the resemblance f.
Turning now to the exploration of the upper stream of the
Nile itself, we may proceed to see how far these conjectural
opinions with respect to the position of its sources are borne out
by facts.
At the period when my opinions on the subject were placed
on record, the course of the river was known only as far as
4° 42' 42'' N. lat., that being the extreme point reached in
January 1841 by the second Egyptian expedition J. In this
expedition M. d'Arnaud and M. Weme took part, and the
particulars famished by those two travellers, from native infor-
mation, respecting the river above the point attained by them,
differed materially; the former stating that it came from the
east, while the latter asserted that it continued a month^s journey
further south.
It is only recently that the question has been decided by
Dr. Ignatius Knoblecher, the Pope's Vicar-General in Central
Africa, who in January 1850, accompanied by two missionaries,
Don Angelo Vinco and Don Emanuel Pedemonte, having sur-
mounted the rapids which had stopped MM. d'Amaud and
* Church Missionary Intelligencer, vol. i. p. 128.
t See Athenaeum of December 1st, 1849, No. 1153, p. 1209.
X It is quite a mistake to suppose that the first expedition penetrated up
the river as far as 3° 30' N. lat. The extreme point reached by it on the
27th of January 1840 was 6° 36' N., which point was passed hy the second
expechtion, as is exj>ressly stated hy M. Weme in his Expedition zur
Entdeckung der Quellen des Weissen Nil, p. 9.
Dr. Beke's Summary of recent Nilotic Discovery. 265
Wemey penetrated up the stream of the Bahr-el-Abyad as far
as 4° 9' N. lat. Here, on ascending a mountain called Logwek,
he saw the Nile trending away in a south-westerly direction
till it vanished between two mountains named Rego and Kidi ;
and he was informed there by the Bari negroes_, the last natives
he met with, that beyond those mountains the river comes
straight from the south. From the summit of Logwek Dr. Knob-
lecher observed, in the extreme distance of the southern horizon,
a lofty mountain-chain, the outlines of which were barely dis-
cernible through the haze of the atmosphere, and which, from
its distance, must be considered as lying nearly in the third
parallel of north latitude.
According to Dr. Knoblecher, the Nile as far as the fourth
parallel of north latitude continues to be a considerable stream,
of the average breadth of 200 metres, with a depth of from 2 to
3 metres ; which proves, beyond all question, that the river must
come from a considerable distance, and most probably from beyond
the Equator, in order to allow of the collection of a volume of water
sufficient to form so large a stream. Dr. Knoblecher was con-
firmed in the opinion that the source of the Nile is to the south
of the Equator, " by the fact that the river was rising on the
16th of January, which he considered as a consequence of the
rainy season having set in in districts much further south *.^^
The longitude of the river at the extreme point reached by
M. d^Arnaud in 18il, is, according to him, 31° 38' east of Green-
wich. If, now. Dr. Knoblecher's "furthest'' in 4° 9' N. lat.
be conjecturally placed in the same longitude of 31° 38' E. —
which cannot be very far from the truth, — we shall have a
distance between that point and Kenia of 370 geographical
miles, on a bearing of S. 33° E. ; while from the same point to
the northern extremity of the lake in Uniamezi the distance is
360 geographical miles, on a bearing of S. 25° VY. Within
these limits therefore we may reasonably look for the southern
boundary of the basin of the Nile \ and it is not at all unlikely
that Kenia itself is the ^' high mountain, the top of which is quite
white,'' of which Baron von Miiller, a recent traveller in Sennar,
heard from the report of a native of the country of Bari, who was
said to have travelled a great way to the south, and to have there
seen the origin of the Bahr-el-Abyad in " the "White Mountain "
in question f.
In the present state of our knowledge on the subject, it would,
of course, be wrong to pretend to establish any absolute identi-
fication. It is most probable that in the Alpine region of which
* See Athenseum of February 22iid and March 29th, 1851, Nos. 1217,
1222, pp. 217, 353.
t See Journal of the Royal Geogi-aphical Society, vol. xx, p. 287^i)^«;i
266 Dr. Beke's Summary of recent Nilotic Discovery.
Kilimandjfiro and Kenia form parts, other snowy peaks of at
least equal altitude will be discovered. And even if it should be
ascertained that one of the head-streams of the Nile has its
origin on the northern flank of Kenia (as Dr. Krapf conjectures),
we may be satisfied that others of those head-streams take their
rise in other mountains further to the west. At all events, having
reached this Alpine region, we have every reason to conclude
that we sliall here find the southern limits of the basin of the
Nile ; and we shall consequently have arrived at the solution, in
general accordance with the statements of Ptolemy as now eluci-
dated and explained, of the greatest problem of geography — the
discoveiy of the mysterious sources of the giant stream of the
African continent, the largest river of the Old World, perhaps
even of the entire globe. One important consideration must
however be constantly borne in mind, namely, that it is not by
arbitrarily fixing on this or that particular head-stream that the
question will be finally set at rest. As I have already observed
in a communication made to the Syro-Egyptian Society of London
on the 9th of January 1849*, ^'^our object must be in the first
place to determine the entire limits of the basin of the river ;
we have next to ascertain what principal arms unite to form
the main stream ; we must then trace to their heads the several
smaller branches which form those arms ; and when we have suc-
ceeded in all these points, we shall then — but not before — be
competent to decide which of these numerous ramifications has
the fairest claim to be regarded as the true Source of the Nile."
London, May 6th, 1851.
Appendix to the foregoing Paper.
The rise of the Nile in 4° 9' N. lat., observed by Dr. Knob-
lecher on Januaiy 16th, 1850, cannot have been caused by the
setting in of the regular rainy season, either north or south of
the Equator.
It is well known that on the Abessinian plateau, north of the
ninth parallel of north latitude, the rains begin about the middle
of June and last till the middle of September : — ^' cominciando
il vcrno gencrale nelP Ethiopia alia metk di Giugno fino a mezzo
Settembre," as was recorded by Alvarez t three centuries ago.
"Within five degrees north of the Line the rains set in nearly
three months earlier than in Abessinia. M. Werne, who was in
the country of Bari, in about 4° 4<y N. lat., at the end of Janu-
* " On the Sources of the Nile, being an attempt to assign the limits of
the Basin of that River," printed in the Philosopliical Magazine for August
1849, vol. XXXV. p. 98 et seq,
t Viaggio, &c. cap. 169.
Dr. Beke^s Summary of recent Nilotic Discovery. 267
ary 1841, was informed there that '' the rainy season would not
commence for two months, that is to say, not till the end of
March or beginning of April*/^
Crossing the Line, we learn from the experience of Dr. Krapf
and Mr. Eebmann, that in the mountainous regions west of
Mombas, within four degrees south of the Equator, the rainy
season sets in towards the end of March or the beginning of
April t, — that is to say, at the same time precisely as it com-
mences within the like distance north of the Line ; and it con-
tinues till the end of June or the beginning of July J. And
seeing that the commencement of the rains is the same within
five degrees north as it is within five degrees south of the Line,
it may reasonably be inferred, in the absence of direct evidence
on the subject, that their duration is likewise in both cases the
same; whence it will result that throughout the equatorial
regions the regular rainy season lasts, as in Abessinia, about
three months, only it takes place there at a period nearly three
months in advance of the time of its occurrence in the latter
country.
But, in addition to the regular rains, there is generally within
the tropics a second rainy season. In Abessinia the two are
distinguished by the names of " the rain of covenant " and " the
rain of bounty -," the former being fixed and constant in its com-
mencement and duration, while the latter is more uncertain and
irregular. The ordinary occurrence of " the rain of bounty '' in
the southern portion of that country is during the entire month
of February, or thereabouts.
We have not any direct evidence as to the period of this
second rainy season within five degrees north of the Equator.
But within the same distance south, according to Dr. Krapf and
Mr. Rebmann §, it commences towards the end of November,—-
*' in the middle of the dry season 1|,^' — and continues through the
month of December; and, by analogy, the same is most pro-
bably the case to the north of the Line likewise.
Taking all these circumstances into consideration, it would
seem to result that the increase of the Nile, observed by Dr.
Knoblecher on the 16th of January 1850 in 4P 9' N. lat., could
only have been caused by " the latter rain '' in the equatorial
regions of Eastern Africa, whether north or south of the Line.
And if, as it is reasonable to suppose, the commencement, amount,
* Expedition zur Entdecliung der Quellen der Weissen Nil, pp. 326, 333.
t Church Missionary Intelhgencer, vol. i. pp. 21, 10/, 329, 377, &c.
X Ibid. pp. 329, 376, 379, &c. j Church Missionary Record, 1847, p. 3.
§ Church Missionaiy Intelhgencer, vol. i. pp. 416, 417, 454, 469-471,
474, &c. -
II Ibid. pp. 151, 273. .viC^i ,,^i>^ ,>..., ^..1,:,^-
268 Dr. Woods on t/te Heat of Chemical Combination.
and duration of this '^ rain of bounty '^ are, like as on tlie Abes-
sinian plateau, iiTegular and uncertain, we may fairly infer that
it has at times no sensible effect on the volume of water in the
Nile. Hence we may understand how it happened that in the
year 1811 the river, so far from rising in the middle of Januaiy,
as it did in 1850, continued falling till the end of that month*.
In Lower Egypt, precisely at the period of the regular equa-
torial rains, namely, " during the months of April, May and
June, the waters of the Nile are at their lowest level. Towards
the end of June the river at Cairo begins to rise, without the
occurrence there of any rainy season, and without the existence
of the slightest apparent cause. The increase of the Nile usu-
ally continues three months, from the summer solstice to the
autumnal equinox, when its waters again begin gradually to
fallf/'
I refrain from discussing here the effect of the flooding of the
various head-streams of the Nile on the inundation of that river
in Egypt ; merely remarking that its occasional abnormal and
momentary increase appears to be solely attributable to the fall
of rain in the eastern mountains of Egypt and Nubia : for in-
stance, the extraordinary rise of the river observed at Cairo in
May 1843 was caused by the rain-waters collected and brought
down by Wady Ollaky in about 23° N. lat-J
August 19tli, 1851.
XXXIX. On the Heat of Chemical Combination,
By Thomas Woods, M.D.
'- ' To the Editors of the Philosophical Magazine and Journal.
Gentlemen, Parsonstown, July 1851.
IN the course of some investigations respecting the cause of
the heat of chemical combination, I found that some facts
hitherto unnoticed, or not sufficiently attended to, required to be
proved. This I have endeavoured to do ; and will, if you allow
me, publish a few papers in the Philosophical Magazine illustra-
tive of these facts, which I intend to employ as data in establish-
ing a theory I have formed on the subject.
;' The first of these propositions is, that the decomposition of a
compound body gives rise to as much cold as the combination of its
elements produces heat.
* Weme, pp. 330, 334.
t Ehrenberg, in Monatsherichte d. Akad. d. Wissensch. in Berlin (May)
1851, p. 334.
X Joum. Roy. Geogr, Soc. vol. xx. p. 292; and see Bui'ckliardt's Travela
in Nubia, p, 10.
Dr. AVoods on tJie Heat of Chemical Combination. 269
-8'>To me this is a new idea, and one with which I have not met
in any work on chemical research. I believe it will be found
important, and in the present paper I will confine myself to a
proof of its tinith.
(2.) That decomposition generally requires a certain amount
of heat is admitted, for as a general rule heat causes decompo-
sition ; that is, to decompose a substance a source for the supply
of heat is necessary, or some body capable of giving up heat to
the compound to be decomposed must be brought into its vicinity
before decomposition takes place.
(3.) That decomposition absorbs as much heat as combination
produces, might be proved by the fact, that in double decompo-
sitions no heat is given off. We know, for instance, that car-
bonic acid and magnesia in combining produce a certain amount
of heat, and that sulphuric acid and potash likewise give rise
to a definite quantity ; and yet when sulphate of magnesia and
carbonate of potash are mixed in solution, although such com-
binations take place, no rise of temperature (except that of soli-
dification) occurs. Does not the decomposition neutralize the
effect of the combination ?
(4.) In cases of simple decompositions the same result does
not obtain. We know from the researches of Andrews and others,
that certain bases produce on combination with acids certain
amounts of heat, and that each base gives rise to a different quan-
tity. Andrews has also proved, that if one base displace another
a definite rise of temperature is the consequence. Now if the
rise of temperature be examined, it will be found that it is the
difference of the amount produced by the combining and separating
body. For instance, an equivalent of potash by combining with
an acid produces 6| units of heat; ammonia, 5^ units. If the
potash displace the ammonia from any of its combinations, one
unit of heat is the result ; the difference between 6^ units of
heat produced by the formation of one salt and 5| units of oold
by the decomposition of the other. ,/ ' r ' ,,''^.
(5.) It occurred to me, however, that the fact might be proved
more satisfactorily by finding what amount of heat is given off
by the combustion of zinc, then ascertaining what quantity ig
evolved by its oxidizement in water ; for, as the water must be
decomposed, we should have the amount of heat in the second
instance less than that in the first, and less by the quantity of
heat produced when hydrogen is burnt. And such I find to
be precisely the case.
Grassi shows that 1 lb. of oxygen uniting with hydrogen raises
the temperature of 43'4 lbs. of water 180°.
The amount of heat produced, according to Despretz^ when
zinc is burnt, is sufficient to raise the temperature of 53 lbs. of
water 180°.
Phil Mag, S. 4 Vol. 2. No. 11. Oct, 1851. U
270 Dr. Woods on the Heat of Chemical Combinations
I find that 1 gi*. of zinc, by dissolving in dilute sulphuric acid,
raises the temperature of GO grs. of water 18*^ F., making the
nccessaiy allowance for specific heats, containing vessel, &c. ; but
1 gr. of zinc is equivalent to 1 j gr. of oxide of zinc, and this
would, by its combination with the acid, raise the temperature
of CO grs. of water 10^° (Graham, Andrews). This amount
must therefore be taken from the 18" in order to find what is
due to the oxidizemcnt of the zinc alone. One grain of zinc, there-
fore, by being oxidized, or \ gr. of oxygen uniting with zinc with
decomposition of water, raises the temperature of 60 grs. of water
7^° F. This is the same as 1 lb. of oxygen uniting with zinc,
with decomposition of water raising the temperature of 10 lbs. of
water 180^, whereas without the decomposition it raises the tem-
perature of 53 lbs. of water 180°; therefore the decomposition
absorbs as much heat as would raise 43 lbs. of water 180° — the
same amount which we saw the combination of oxygen and hy-
drogen was capable of producing.
(6.) If zinc be dissolved in muriatic acidy I find that 1 gr.
causes a rise of temperature equal to 21° F. in 60 grs, of water ;
or 1 lb. of chlorine uniting with zinc, with decomposition of
chloride of hydrogen, raises the temperature of 6 lbs. of water
180°. Abria {Ulnstiiut, vol. xiv. p. 635) found that 1 lb. of
chlorine uniting directly with zinc would raise the temperature
of 36 lbs. of water 180 ; that is, y%ths of what oxygen produces.
If chlorine uniting with zinc produces likewise y^ths of the heat
oxygen does under similar circumstances, 4.2 lbs. of water would
be raised 180° by 1 lb. uniting with the metal. In other words,
zinc uniting with chlorine tvith decomposition of chloride of hy-
drogen produces 6 units of heat, without decomposition 42 units.
The difference, or 3Q units, is what the combination of chlorine
and hydrogen produce, and consequently what is lost by the de-
composition.
(7.) Wlien 1 lb. of zinc is dissolved in nitric acid, it raises
the temperature of 43 lbs. of water 180° F., more than twice as
much heat being produced than when it is dissolved in sulphuric
acid. This combination is accompanied by decomposition of
nitric acid.
The last two instances are brought forward for the present
only to prove, that it is not because zinc is oxidized under dif-
ferent circumstances, as in air and water, that different amounts
of heat are produced, but that an absorption of heat always
accompanies decomposition, and varies with the substances de-
composed. The first instance, the solution of zinc in sulphuric
acid, proves that this absorption is equal to the quantity liberated
when the same elements combine.
(8.) When I had satisfied myself so far, I thought that if a
compound body could be decomposed directly, or without com-
m/WtS^d^Qnthe JFfedtof VkkiicalCmMrMtM 271
Hhiatkln taking place at the same time, a positive logs' bf*ti^iii|)e-
rature ought to result ; and it occurred to me that the decom-
position of water by the galvanic battery might be an expeti-
mentum crucis. I forgot, however, the heat that is produced by
the resistance offered to the current in passing through the
water. Still, on consideration, I saw that the experiment would
prove whether decomposition occasioned loss of heat or not; for
although heat is given out by the resistance, might not the
amount of that heat be greater if no decomposition accompanied
it ? If the idea I adopted were correct, net only should such be
the case, but the difference should be the amount of heat the
liberated gases would give if again chemically combined. And
now the problem w^as to find, whether the heat produced by a
galvanic current passing through water was what was due to the
resistance offered, or whether decomposition made it less, and
how much less ? ^^
(9.) The manner in which I endeavoured to solve this questioil
was as follows : —
Having set a battery, consisting of twelve DanieFs cells, copper
cylinders 5 inches high, 3 inches in diameter, with brown paper
diaphragms and amalgamated zinc, into action as one series, I
noted to what distance the needle of a tangent galvanometer
moved when the current passed through the copper ring, which
was 12^ inches in diameter. I then included in the circuit a
volta-electrometer holding acidulated water, and again noted to
what division of the scale the needle moved, the current having
passed through the fluid in the electrometer with the decompo-
sition of the w^ater. The difference of the tangents of the angles,
when the electrometer was included and when it was not, showed
the resistance the water offered to the current. I now removed
the electrometer, and in its place introduced a fine platina wire
of such a length as offered the same resistance to the current
that the water did, which I knew by the needle of the tangent
instrument being equally deflected by both. I had therefore
two substances offering the same amount of resistance, and con-
sequently developing the same amount of heat ; but in one case
decomposition was present, in the other it was not. What, then,
was the result ? Exactly what I anticipated — the heat liberated by
the passage of the current through the water was less than that pro-
duced by its passage through the wire, and to the same amount that
the gases given off would develope if again chemically combined.
(10.) I tested the truth of this result by many experiments
varied in different ways, both as to the quantity and intensity
of the current, the amount of resistance aijd the duration of the
experiment, and in every case met with a similar result. The
details, therefore, of one or two experiments will suffice.
272 Dr. Woods on the Heat of Chemical Combination.
I filled a glass tube with an ounce of acidulated water (one
part by measure of sulphuric acid spec. grav. 1*84 to six parts
of water) ; I put two platina leaves into the fluid, and sending a
galvanic current through it by means of the twelve-cylinder bat-
tery, I decomposed the water. 1^ cubic inch of gas was given
off in the minute ; and the tangent instrument having been in-
cluded in the circuit, the needle rose to 21 degrees on the scale.
The current passed through the water for two minutes, and the
temperature rose from 75° to 83° F. I now removed the platina
leaves from the fluid, and substituted a platina wire of such a
length as kept the needle, the current having passed through the
wire, at 21 degrees. The same fluid into which the electrometer
leaves had been immersed now surrounded the wire; the current
in the former case passing through the water and consequently
tvith decomposition, in the latter through the wire without it ;
and after traversing the wire for the same length of time, the
temperatm-e of the fluid was raised from 75° to 90°, that is 15
degrees, or 7° more than in the case where decomposition accom-
panied it ; although in both cases the same resistance was ofi^ercd
to the curi'ent, and of course the same amount of heat generated ;
therefore the 7° were absorbed by the decomposition. In the two
minutes that the experiment lasted, 3 cubic inches of gas were
given off : now if these gases were made to combine chemically,
what amount of heat would they produce ? The same that their
separation caused a loss of, viz. about 7° F. to an ounce of water
acidulated as above ; for 3 cubic inches of the mixed gases in
proper proportion to form water weigh '387 gr. ; and as oxygen
is f ths of the mixtui'e, it must weigh '344 gr. Now as 1 lb. of
oxygen combining with hydrogen would cause the temperature
of 43 lbs. of water to rise 180°, 1 grain would raise the tempe-
ratui-e of 43 grs. 180° F. ; then '344 gr. would raise the tempe-
rature of 43 grs. 62° F., or of 1 oz. very nearly 5°-6 F. But the
specific heat of the acidulated water to that of distilled water is
as 8'3 to 10 ; therefore the 5°*6 must be raised inversely in that
proportion, or to 6°*7. In our experiment very nearly the same
amount was lost by their separation. j^ p
(11.) I tried the experiment in another way. Through
the bottom of a glass tube I passed two short pieces of thick
platina wire, and attached to each piece a fine wire which
reached to the top of the vessel, as at AB. * I could join
the wii'es at the bottom so as to make the two thin wires
into one, or separate them by disuniting the thick pieces outside
the bottom of the tube. In the former case the current passed
through the wire, in the latter through the water. Each offered
the same degree of opposition to the passage of the cun-ent.
Here the same wires that acted as the leaves of the electrometer
On the Effect of Fluid Friction in drying Steam. 273
conducted the galvanic current ; the same fluid was used and the
same vessel ; in fact everything was the same, except that in one
case decomposition accompanied the resistance, in the other it
did not ; and in the former the temperature did not rise to the
same degree as it did in the latter, and it was as much less as
the combination of the gases given off would have produced if
combined.
I also placed two glass tubes, each containing the same quan-
tity of acidulated water, in one of which were the leaves of the
electrometer, in the other a platina wire offering the same resist-
ance as the fluid, in the circuit j so that the galvanic current
passed through both at the same time, and with the same result
as in the other experiments.
(12.) I might bring forward many such experiments ; but
although they vary in details they are all the same in principle,
and prove the same fact. Enough I think has been said to esta-
blish the truth of my proposition. If admitted, some interesting
difficulties may be removed by its application ; for instance, it
explains why some compounds, such as alcohol, turpentine, &c.,
do not g:ive out as much heat when burnt as their elements do
when separately ignited. It may also be made the means of
determining the amount of heat produced by the combination of
bodies, as the loss occasioned by their decomposition shows the
gain by theii' combination ; and in many other ways the prin-
ciple may be turned to advantage. For my present purpose, I
only ask that the simple fact I have endeavoured to prove be
allowed, viz. that decomposition of a compound body occasions as
much cold as the combination of its elements originally produced
heat.
XL. Second Note 07i the Effect of Fluid Friction in drying
Steam which issues from a High-pressure Boiler into the open
Air. By Prof. W. Thomson*.
IN the August Number of this Magazine, M. Clausius has
replied to a Note, published in the June Number, in which
I endeavoured to show that the objections he had made to my
reasoning regarding the condition of steam issuing from a high-
pressure boiler, were groundless. I cannot perceive that this
reply at all invalidates any of the statements made in my two
former communications f^ to which I refer the reader who desires
to ascertain what my views are, and to judge as to the correct-
ness of the reasoning by which they are supported. An analy-
tical investigation, according to the principles discovered by
Mr. Joule, of the thermo-dynamical circumstances of the rushing
* Communicated by the Author.
- t Phil. Mag., vol. xxxvii. p. 387 (Nov. 1850), and vol i, 4th Ser.,p.474
(June 1851).
274 On the Effect of Fluid Friction in di-ying Steam.
of any fluid through a small orifice, is given in a paper commu-
nicated last April to the Royal Society of Edinburgh, and since
published in the Ti'ansactions (vol. xx. part II.) under the title
" On a Method of discovering Experimentally the Relation be-
tween the Mechanical Work spent and the Heat produced by
the compression of a gaseous fluid/^
I take the present opportunity of correcting a mistaken ex-
pression in my first communication regarding steam issuing
from a high-pressure boiler, by which I gave a false, or an in-
adequate, representation of the connexion of that application of
Mr. Joule^s general principles which I was bringing forward,
with one which he had himself made in one of his published
papers. The following is the passage of my communication
(addressed as a letter to Mr. Joule), which requires correction : —
'^ The pretended explanation of a corresponding circumstance
connected with the rushing of air from one vessel to another in
Gay-Lussac's experiment, on which you have commented, is cer-
tainly not applicable in this case, since, instead of receiving
heat from without, the steam must lose a little in passing through
the stop-cock or steam-pipe by external radiation and convec-
tion*." I wrote this under the impression that Mr. Joule had,
in his paper '* On the Changes of Temperature produced by the
Condensation and Rai*efaction of Airf/^ pointed out the incor-
rectness of an explanation often given of Gay-Lussac's experi-
ment J, and shown that the phsenomenon could be truly explained
only by taking into account the heat developed in the air by
friction in its passage from one vessel to the other through the
stop -cock. I find, however, on looking to the paper, which I
had not by me when I wrote, that it contains no reference to
Gay-Lussac's experiment, but the following passage, referring
to Mr. Joule's own experiments on the heat developed by the
compression of air, and the heat absorbed by air allowed to
expand from a vessel into which it has been compressed, through
a small orifice, into the atmosphere, from which I obtained the
idea of considering the heat developed by the friction of steam
issuing from a high-pressure boiler.
" It is quite evident that the reason why the cold in the ex-
periments of Table IV. was so much inferior in quantity to the
heat evolved in those of Table I., is, that all the force of the air,
over and above that employed in lifting the atmosphere, was
applied in overcoming the resistance of the stop-cock, and was
there converted back again into its equivalent of heat§." '"^^
Ardmillan, Ayrshire, Sept. 4, 1851.
* Phil. Mag. S. 3. vol5:^!!Cdirp. 388.
t Ibid. vol. xxvi. p. 369 (May 1845).
X See Lara^, Cours de Physique, vol. i. § 352.
§ Phil. Mag., S. 3. vol. xxvi. p. 381.
XLI. On the Motion of a Free Pendulum.
By the Rev. A. Thacker, Fellow of Trinity College, Cambridge,
,,,j To the Editors of the PhilosopMcd Magazine and Journal.
Gentlemen, >ii'oo%.fi:s *: t • .("ir^^-VHimoo -v^iH
THE rotation of the plane of vibration, in M. roucanlt's pen-
dulum experiment, admits of being deduced from the equa-
tions of motion ; and as some of j^our readers may wish to see
the problem solved on dynamical principles, I venture to offer
the following investigation for insertion in your Journal. "'- iM
Let a be the radius of
the earth,
o) its angular velocity,
\ the latitude of the
place,
/ the length of the
pendulum,
R the tension of the
y
the coordi-
nates of the ball mea-
sured along axes fixed in
space, the axis of -s^' coin-
ciding with that of the
earth.
x> Vi
z the coordinates
of theball measured from
the point of suspension
in directions opposite to
those of x^ y y\ z'.
The equations of mo-
tion are
LiiiiOJt 10
nouoiiJ
.i[oo;)-qo>tfr
■S JOfi Inai
Hi/rroqyt! nwo g'aljjol .'iI^l oi
/x,' ■n{ oilt bcfjj ^-np, *lo nof8K3'rqtiiO'>
V. ri rlnhrv otfTf loKa-r/ i\ moii biiBqvs
R
d fi nfd'fl -^iiui^Mi
adt oi v>t/titFMp f flfr "^ ml ;j to ^ituaftrnoq
tiiB.adt'io oo'ioi-ycUjUs tRfll m ^A sideT t.»-rt>(^oiiJ m f)0/,lov'< tod
• ' -0 dqf:0f Jd« 44^ :!^*i^'^iilif\l)a /o[< (-^ — « • y, -^voi I u hiu\ -m fv
where
os'=a cos X cos mI — a?
.y'=a cos X sin (ot—y,.
lA
HrN
,_, .fV=«sin\, 'i^2^iV%-^^^'^ I
276 The Rev. A. Thacker on the Motion of a Free Pendulum: i
Hence
dt^
I
d^u R y
-y^ --((J^co^a) cos X, sin <at-\ y =0
dt^ \./ / ,^ /
d^z
df'
—g sinX
R ^ ^
m I
(1-)
Let the position of the ball be now referred to other coordi-
nates X, Y, Z, the axis of X being taken due east, that of Y due
north, and that of Z towards the centre of the eai-th. We then
,have
X = a; sin ft)^ — y cos ft)/
i Y = .rsin\cos&)/ + ?/sinXsinft)/— ^cosX
Z — x cos X cos (ot + y cos X sin cot + z sin X
a?=X sin «/ + Y sin X cos cot + Z cos Xjcos cot
?/= —X cos ft)/4- Y sin X sin Q)t-\-Z cos X sin cot
z= — YcosX + ZsinX.
EUminating x, j/, and z from equations (1.), we shall find
d^X ^ . ^dY ^ ^dZ 2Y , I^ X ^ "^
•3ft) smX-TT — 2ft) cos X -7- — ft>^AH r =0
at ml
df-
— <^U/ J
5111 /V
dt '
dn
dt^
+ 2ft) sin X
dX
dt
m
Y
=0
d^Z
dt^
+ 2ft) cos X
^x
• dt
m
Z
-i7=0.
ft)^ Y sin^X -f &)^ sin X cos \.[a^z)
co^Y sin X cos X + ft>^ cos^X(a — ;
(2.)
1, Finally, wx will suppose the horizontal motion of the ball re-
ferred to axes which revolve about the vertical with an uniform
angular velocity co sin X. If x^ y be the coordinates of the ball,
we have
0?= X cos (cot sin X) — Y sin {cot sin X)
7/ = X sin {cot sin X) + Y cos {cot sin X)
z=z
X = a? cos {cot sin X) + y sin {cot sin X)
Yi:^ i^'a? sin {cot sin X) + y cos {cot sin X) .
The Rev. A. Thacker on the Motion of a Free Pendulum. 277
Eliminating X^ Y, Z, the equations (2.) become o^oiiaH
d^x U w ^ - , . . ^. dz
-—— -\ • Y — ^wcosXcos (ft)r smX) . -7-
dt^ m I ^ ' dt
— co^ cos^Xcos {cot sinX) {^ cos {cot sin X) +'y sin (cot sin X) }
— 0)^ sin X cos X sin {cot sin X}.{a—z)=0
d^y . R ?/ _, ^ • , . ■ ^sdz
_^ ^ . ^-^2cocosXsin(cotsmX) -rr-
dt^ m I ^ ^ dt , .
^^ -w^cos^Xsin (ft)«f sinX){^cos (w^siiix) +y sinpVsinXJXj,,
— co^ sin X cos X cos {cot sin X) . (« — 5') = 0
J/2 "^ m' 1 "-^ "^ ^^^ I ^^^ \^^ ^^^ ) • ^ "^ ^^^-^ (^^si'^^) • "^ ^
— o>^ sin X cos X{^ sin {cot sin X) —y cos (o)^ sin X) }
+ ft)2cos''^X.(«~-j)=0.
These equations hold for any value of co. In the case we are
considering co is small^ namely — — — — — - ; the terms multi-
X<v P\ \j\J /\ \j\j
plied by cd and co- are small and periodical j and if these be
neglected^ we have ^^ Y\ ^ /ma
(3.)
df^ ^m'l
^^2 '^ m' I
\W ... (4.)
7\j : / sn>
d^z ^ z
which are equations of exactly the same form as mose'wliicli
apply to the motion of a pendulum suspended from a fixed point
in space ; the motion^ therefore^ is the same with regard to the
revolving axes as it would be with regard to fixed axes, if the
earth had no rotation. The angular velocity of the horizontal
axes being co sin X, it follows that the orbit will appear to revolve
at that rate round the vertical.
I am. Gentlemen, *.'..>! s/.
Your obedient Servant^
Trinity College, Cambridge, . A. Thacker.
June 1, 1851. xmV rrr^ /
[It is much to be desired that the approximation should be carried
on one step further, and that at least the general effect should be
made out of such of the neglected terms in the above equations as
contain the first power of w. If the oscillations arenas considerable
278 Mr. V. J. Martin on the Anticlinal Line of
as they have been hitherto usually taken in practice, in comparison
with the length of the string, by those who have busied themselves
in verifying M. Foucault's law, there is no doubt, as is apparent
from the equations, that the accuracy of the law, and probably of the
period of the revolution of the apsides as dependent on the rotation
of the earth, may be appreciably affected. Mr. Thacker's valuable
and interesting contribution is confirmed by precisely identical re-
sults similarly worked out, and shown to us in MS. some consider-
able time back from the able pen of a well-known young English
analyst ; and, since this article has been in type, we have received a
communication, not essentially differing, from our esteemed corre-
spondent the Rev. J. A. Coombe. — Eds.]
XLII. On the Anticlinal Line of the London and Hampshire
Basins. By P. J. Martin, Esq., F.G.S.
[Continued from p. 198.]
BEFORE we quit the subject of the drainage of the Wealden
area, and of its connexion with the phsenomena of up-
heaval, it will be well to take a review of it in its totality. Much
has been said already of the rivers taking their courses north
and south through the transverse fissures, enlarged into valleys
by denudation. But it is of much importance for the mainte-
nance of the opinion we entertain of the unity of the act of up-
heaval, and of its suddenness, to take a comprehensive view of
this great feature.
The first notice we find of it is, I believe, in Conybeare and
Phillips's Outlines of the Geology of England and Wales. The
passage is so remarkable, that I cannot refrain from introducing
it here. " A very interesting geological phsenomenon is presented
by the course of the rivers watering this district, and the arrange-
ment of the valleys which convey them. We have already no-
ticed that the two grand valleys of this district, — that of Holms-
dale and that of the Weald clay, — are parallel to the direction of
the strata ; but these do not form the channels through which any
of the more important streams seek the sea, for these generally
have their source in the central ridge of ironsand (Wealden) ;
and flowing thence both to the north and to the south, in direc-
tions nearly at right angles both to these valleys and the strata,
traverse the ranges of gi'eensand and chalk through gorges
opened across them, in their way to join the Thames on one side,
and the Channel on the other ; instead of being turned by their
escarpments into the great subjacent valleys, as they would be if
the fractures in those escarpments were rcpaii'ed, and forced to
empty themselves into Romney Marsh and Pevensey Level. In
no place perhaps is the important fact of a double system of val-
leys crossing each other transversely (a fact which we shall
V. the London and Hampshire Basins. \t 279
hereafter see to be of the greatest consequence with reference to
theories on the origin of the present inequaUties of the earth's
surface), more strikingly displayed*/'
Since the early publication of my ^^ Theory of the Weald De-
nudation/' and the explanation there given of the nature and
cause of these transverse river-courses_, the subject has become
familiar to a great majority of geologists ; all that remains now
to be insisted on is the collective view of this phsenomenon : —
the watershed diverging by different channels from a common
centre, the curious opposition of the river valleys as they traverse
the North and South Downs (betokening the original stretch of
the deepest rents across the whole breadth of the area), and the
uniform character of the whole arrangement^ from the coast at
Hastings to the Alton Hills, — all bespeaking a general, simul-
taneous, and sudden up burst of the whole.
Westward from the Alton range, the Meon Valley and the
chalk denudation at Winchester maintain the same character of
transverse drainage in the courses of the Itchin and the Test.
But a change takes place as we approach the extremity of our
anticlinal line. The greater part of the Vale of Pewsey, up to
the foot of the Marlborough Downs, sheds its waters across the
whole breadth of the chalk by the Avon ; and the Vales of War-
minster and Wardour send theirs also eastward and southward
into the Avon at Salisbury, and so through the New Forest into
the Channel at Christchurch. This is still transverse drainage;
but it seems to be influenced, if not altogether directed, by the
well-known general rise of the secondary strata in a direction
N.E. and S.W. all across the kingdom, the line of which elevation
passes through that part of Wiltshire. The remarkable trans-
verse valleys of the Avon, and of the stream called the Bourne
in Mr. Greenough's map — like the winter-bournes of the chalk,
very generally dry half the year — seem to answer to this inflec-
taon;; !=This requires, and is worthy of further investigation, ru
" ' In the foregoing sketch I have confined myself chiefly to the
phsenomena of elevation and disruption, the basis of the surface-
changes we are contemplating. I come now to the third and
fourth classes of plia3nomena before spoken of, viz. lacerated
escarpments and drift. And as the first two related to upheaval,
so the latter have reference mainly to the concomitant action of
denuding flood ; — always keeping in mind, that the operations
of elevation and denudation have gone hand in hand.
3. By lacerated escarpments I mean those appearances in the
Ihih QY^ li'Conybeare and Phillips's Outlines, &c., p. 145. ^^^-oi} a^^l
280 Mr. P. J. Martin on the Anticlinal Line of
outcrop of all the strata concerned ; and particularly of those
atony strata in which we should be most likely to find the con-
joint signs of disruptive violence and of aqueous erosion, distin-
guishable from the detrital operations of time and weathering.
Passing by the well-known fact, that where denudation has been
active, the prominence, or the want of it, of any given stratum or
order of strata is in exact proportion to their induration, or their
resisting power, — if soft and destructible, the surface being re-
ceding and low, if hard and stony, hilly and high,— we fix our
attention first on the chalk.
The soft and destructable nature of the material, whilst it pro-
duced the smooth outline of the chalk hills, has so determined
the fonn and constitution of their escarpments, that they exhibit
no signs of laceration beyond their coved and scooped surfaces.
The sharp angles and fracture edges which convulsion had left,
atmospheric agencies have obliterated. The homogeneous struc-
ture of the rock-masses of the chalk has also determined the
straight and even course of the North and South Downs, as well
as the gentle undulations of the saddle or dome-like elevation of
the western part of our anticlinal line, for the most part denuded
of its " tertiary '' covering. But although all the signs of abrupt
fracture have disappeared, we still see how the fissures of this
stratum have had their edges eroded and spread out, — the
deepest into river-valleys, the more superficial into dry trans-
Verse valleys and mountain passes on a small scale. A very cur-
sory view of the river-courses through the North and South
Downs, as they are delineated in the Ordnance Map*, will ex-
plain what is here meant, and show how transverse fissures,
whether of independent formation, or as the necessary accom-
paniments of longitudinal fractures, have been enlarged into
valleys by aqueous abrasion. From the chalk we pass to the
next rocky stratum, the lower greensand. Here we have more
decided evidence of the violence of the denuding operation.
There is nothing in the surface arrangement of the chalk that
might not be accounted for on the principle of a gradual and
gentle removal by sea-currents, or by atmospheric erosion. But
a close inspection of the lower greensand escarpment will soon con-
vince us, that water in a state of violent and tumultuous agita-
tion has been at work immediately consequent on, or in conjunc-
tion with, the act of upheaval and the fracture of the rock-masses.
Of the three groups into which the lower greensand is divided,
and each of which has a distinct country, as faithfully and mir
j * In all matters of local detail the reader is referred to the Ordnance
Map ; and a comprehensive notion of the act of denudation will be mainly
assisted by the study of the arrangements of its high grounds and escarp-
ments.
the London and Hampshire Basins. 281
nutely described by Dr. Fitton*, the lower one only presents an
abrupt and rocky escai'pment. With some interruptions, this
kind of outcrop is continued for many miles together round the
west end, and along the north and part of the south sides of the
Wealden area. It is to these parts of its course I now direct
the observer's attention. Wherever sections in these rocky
escarpments offer themselves, a tumultuous and tortuous disposi-
tion is to be seen penetrating deeply into them, behind their
ordinary coating of alluvial and diluvial rubble. Railway cut-
tings have sometimes brought these into view ; but better exam-
ples may often be found in the stone quarries, and would be still
more frequent, if it were not so often found more convenient and
more profitable to go further back to extract the stone, out of the
way of the ^Mebris'^ above mentioned. There are no better
examples of the tumultuary and contorted appearances of which
I am now speaking than are to be observed in the outskirts and
approaches to the stone pits by the Medway in the Maidstone f
country, where much broken material and unprofitable detritus
(in which large rock-masses lie loose, and are crumpled and
tossed about) have to be removed before the undisturbed rock
can be got at. It is on this account also that the " Fire-stone '*
(the plateau of the upper greensand) is generally quarried by
shafts sunk near or even through the chalk ; as was anciently
the case at the MersthamJ quarries, and as is now done at Rei-
gate Hill. But I remember inspecting a quarry many years ago
opened by Alderman Waithman at Ray Common, near the latter
place, and worked by an open adit, in the entrance to which, to
the extent of twenty or thirty feet or more, the rock -masses lay
in great disorder, broken up and contorted in situ, and not in
the manner of the blocks and broken materials of the talus of a
sea-cliff. Such cases as these might be multiplied from all around
the escarpments of the area under review.
There is another appearance, and one much more conclusive
as to the violence of the diluvial action to which these escarp-
ments owe their existence, which is to be found under favourable
circumstances at the angles of the cross fractures described in
the foregoing pages. In the imperfect description given in my
earliest memoir on this subject, of the course of the river Arun
through the greensand escarpment at Pithingden near Pul-
borough §, I spoke of a remarkable slide of the stony strata on
the east side of the gorge-like valley down toward the river,
which at that place takes its course in the Weald clay beneath.
It is to this extraordinary appearance Mr. Hopkins alludes,
p. 17 of his Memoir on the Structure of the Weald, published,
* Trans, of Geol. Soc, vol. iv. 2nd series. t Kent. % Surrey.
§ Geol. Memoir on Western Sussex, pp. 66, 67.
282 Mr. P. J. Martin on the Anticliniil Line of
as before said, in the Geological Transactions of 1845. Mr.
Hopkins calls it an " anomalous dislocation/' and thought with
me that it was connected with the river fissure. Although I
^escribed and gave a rude figure of this dislocation in the memoir
above mentioned, I did not, up to the time of showing it to
Mr. Hopkins, tlioroughly understand its true nature and the
manner of its production. I will endeavour to make it better
understood. In this part of Sussex the river Arun takes its
course in a direct line from tlie older strata in the centi-al line of
elevation, through the newer strata to the sea; and the gaps in
the escarpments of the lower greensand and of the chalk are
directly opposed to each other, although ten miles apart, and
constitute a remarkable feature in this part of the country. Much
study of this long line of transverse fracture has convinced me
that it is the result of the compound operation of a slight anti-
clinal divergence, and also of a slight change of the general
southerly dip. The first is shown in a sand-bank at Stopham
Bridge ; the second by the immediate advance, west of the river,
of the greensand country two or three miles into the Wealden
area, beyond the greensand country on the east.
It is on the east side or left bank of the river at Pithingden
Farm that the extraordinary slope above spoken of occurs. The
surface line of the country rises very nearly in the line of dip to
about 250 feet above the river, and then drops, generally with
a sharp escarpment, into the Weald clay valley below. But
as it approaches the river-gorge, and at the angle formed by
the intersection of the two lines of longitudinal and transverse
escarpment, the hill slopes gently down over a space of about
twenty or thirty acres of ground ; and by the disclosures of a
hollow way on the side of the hill and of the stone quarry at the
top (seen by Mr. Hopkins, as above mentioned), we learn that
this slope is formed by the breaking down of the great tabular
masses of sandstone, of which all the plateau of the lowest bed
of greensand in this line of country is composed. The rents
which answer to this uncommon deflection from the ordinary
line of dip are to be seen in the stone quarry, in the hollow road
aforesaid, and at the top of the hill where the fall commences.
For a long time I was inclined to think that this phsenomenon
was the result of a sliding down of these stony strata at the
moment of the disruption of the river fissure. But this expla-
nation was not satisfactory, and gave place to a better, and I
doubt not, the true one.
In consequence of some inquiries of Dr. Fitton, when he was
engaged in his exposition of the extension of the Atherfield beds
along the greensand escai-pment of the Weald, I was led to dis-
cover that in all this line of countiy the representatives of the
the London and Hampshire Basins.
283
Atherfield beds consisted of a series of loose porous sands and
clays of no great thickness, interposed between the green sand-
stone and the top of the Weald clay ; and that it was by the
removal of these loose materials, during the act of denudation,
that these large masses of stone had been let down as we now
see them.
To produce this effect to so remarkable a degree at this point,
two circumstances have combined, — the sharpness of the angle
when the denudation was brought down to this part of the river
fissure, and the projection of the greensand country as before-
mentioned into the Bedham Hills ; which rise at least 500 feet
immediately west of the river, and would cause the flood of de-
nudation in the flux and reflux of its wave to impinge violently
on this particular spot. I here repeat with a little variation my
original sketch of the downcast I have endeavoured to describe*.
Possessed with the justness of this interpretation of these ap-
pearances, I have for comparison examined some of the salient
points of the greensand escarpment on the other side of the
Weald, and have not been disappointed. I pass over many
minor indications of the like kind of dislocation and dilaceration
in the hollow ways and small stone pits of the Hartingcombe
and Haslemere country, to mention the highly illustrative stone
quarry now open at Nore Farm, at the eastern extremity of the
Hasscomb Hills f. The Bargate stone beds (as the corresponding
greensand stone of this side of the Weald is called) are not quite
so low in the series as the Pulborough stone, or the Kentish-
rag, and do not lie so close on the Atherfield beds. Never-
theless they have been extensively warped and tossed about by
the removal of the looser and more destructible materials, and
* The dislocation has none of the character of an " under cliff," or of
the "Hawksley slip" described in White's ' Selbome/ Letter 45, but sweeps
round the angle of the eminence, and is CAddently produced by the subsi-
dence of the mass of stone, as the loose mate^als were removed from below.
t Surrey, ujuysoiqin- OiiJ X*i^ilUO» p ;»i! u J^iija'.'Y'>\-
284 Mr. P. J. Martin on the Anticlinal Line of
present, though in a lesser degree, the same dislocation as the
Pithingden Hill.
The transverse fissure-valleys which transmit the affluents of
that branch of the Arun called the Western llother by Pet-
worth and Lodsworth*, present the same downcast of stony beds.
A quarry opened in the Petworth Rectory grounds some years
ago was just the counterpart of the one at Pithingden. In other
less angular parts of the greensand escarpment, wide fissures,
open joints filled with rubble, and other signs of violence, abound
where the intersections of hollow ways or stone quarries expose
their basset edges to observation. On the north side of the
Weald, again, the Kentish-rag country is not without these
signs of violent disruption, — the escarpments of Boughton-
Malerbe, Bougbton-Monchelsea, and Sutton-Vallance, for in-
stance; and I strongly suspect that the dislocation at Tilbur-
stow or Tilvester Hill, described by Dr. Mantellf, is a slide of
this kind.
Much more might be said, and many more localities pointed
out, to show the effects of violent watery abrasion in these escarp-
ments; but I pass on to the equally important subject of dilu-
vium or drift.
4. I should have preferred the use of the foraier word to de-
signate the transported materials of the area under review; because
I abjure for them every idea of other means of transport than a
diluvial action, — be it short and transient, or be it longer, and
frequently repeated till the denudation was complete. But since
the repudiation of the theoretical views on which that term was
founded by its author, and the general adoption of the word
drift, gives latitude to the use of the phrase, I shall use both
words indififerently, with the understanding that if diluvium is
used, I mean (as I believe is everywhere meant now) the drift of
a deluge, and not of the deluge.
To those who are familiar only with the confused masses of
gravel, loam, sand, rounded and angular flints and rolled clays
of the London district, or indeed of the greater part of the south
of England, it will seem rather sui-prising to be told that the
drift of the district under review admits of a division into four
distinct natural zones, which occupy as many lines of country, —
mantling round the nucleus of the Weald. It is not pretended
that the hues of demarcation of these zones are so hard and well-
defined as some other boundary lines in this branch of natural
history. But they are strict enough to be very remarkable ; and
such as I could not myself have predicated, and could hardly
have believed to be in existence, if repeated and extended obser-
vations had not convinced me of the truth.
* Sussex. t Geol. of S.E. of England, p. 177-
'\^> '^f^'the London and Hamijshirc Basins.
285
nriThe first and uppermost we may call the Tertiary Zone. The
beds and sprinklings of this division consist mainly of shingle of
the eocene sera, with some angular flints and sandy or argilla-
ceous loam, abounding everywhere with rounded pebbles.
The next, the Cretaceous Zone, consisting entirely of angular
or unbroken flints, in which we very rarely find a pebble except
when entangled in a more than usual invasion of the clays of
the lowest tertiary formations. . ,i
The Subcretaceous, which consists of angular flints with a large
admixture of the ironstone, sandstone, and chert of the green-
sand beds.
And fourthly, the Wealden Zone, in which the flints, except in
a few points on the margin of this formation, have disappeared
along with the pebbles and other materials characteristic of the
strata higher in the order of geological superposition. It will
be convenient, perhaps, to put this in a tabular form : —
Pebbles and broken shingle
1. Tertiary zone.
2. Cretaceous zone. <
Drift. <
4. Wealden zone.
fxiia{«?( , rr^ .' bcds ; slight admixture of
angular flints; sandandloam,
and some chalk -rubble.
Angular flints. Pebbles very
rare. Very little loam, but
sometimes much chalk-
rubble.
r Angular flint with chert, iron-
3. Subcretaceous zone. < stone and sandstone, much
1^ sand and little loam.
rlron-rag (a conglomerate of the
I debris of the various beds
above and below the Weald
clay) . Beds of diluvial loam^
sometimes of great depth.
Of these, the two first contain the bones of mammals, and the
usual organic remains of what is called the Pleistocene. In the
third, these are very rare ; and in the fourth there are none
at all.
All the mineral substances of these several zones belong to
the strata which are found in and around the great anticlinal
line, if it be determined that the " grey wethers ^' are the pro-
duction of any of the tertiary beds. And no substances foreign
to these strata are to be found in the drifts ; unless it be that
some intrusions from the older beds west of the area in review
may by accident be found in that part of the line ; of which,
whether or no, I am not critically certain.
Moreover, if by pleistocene is meant a marine deposit made in
Phil Mag, S. 4. Vol. 2. No. 11, Oct, 1851. X
286 Mr. P. J. Martin on the Anticlinal Line of
the ordinary way we usually understand the formation of sedi-
mentary beds, from a sea of the range and extent of which we
cannot now have any possible conception, then I unhesitatingly
affirm that no such deposit, or relic of such deposit, is to bo
found in any part of this area.
The first, or Tertiary Zone, ranges all along the edges of the
plastic clay as they basset on the chalk, and contain everywhere
a large admixture of the shingle which abounds so much in that
stratum. As the bare chalk begins to appear, angular flint is
largely added ; and finally angular flint alone is found on the
chalk, and the rounded pebbles disappear, except here and there
a few stragglers.
This change from pebbly drift to broken flint may be conve-
niently studied on the verge of the North Downs, on Walton
Heath*, between the Addington Hills f and the chalk escarpment,
and in all the outcrop of the tertiary beds, to the Darent. Similar
observations may be made along the same outcrop to the Basing-
stoke J and Odiham country. I have not examined this outcrop
to the north of the Pewsey line, but I do not doubt of finding a
similar interchange of rounded pebbles for broken flints there
also.
Crossing the Hampshire and Wiltshire chalk, we find the same
pebbly . drift from Salisbury to Michelmarsh on the Test and
Ilomsey§ ; and we meet it again on the northern borders of the
Forest of Bere, mixed with a very large proportion of flints in
the gravel pits at Horn-dean and Rowland's Castle ||. Eastward
from Bere Forest, where we enter on the line of country south
of the South Downs, so great has been the destruction of the
chalk, that the cretaceous or flint zone falls in and almost excludes
the pebble beds. Nevertheless they appear in force at Box-
grove^, more sparingly along the flat country towards Arundel,
but again strongly at Clapham and Patching, north of Highdown
Hill, and still prevail along the Worthing and Shoreham vicini-
ties, till they are cut ofi" by the Brighton cliffs.
The section of the diluvial beds given by the Brighton cliffs,
from Copperas Gap to Rottingdean, possesses much interest, be-
cause it includes deep masses of drift, composed of chalk-rubble,
angular flints, and sand and shingle of the eocene epoch, so com-
mingled as to have led the historian of the " Geology of the Souths
east of England '' into the belief that they were stratified beds
of the jera of the crag. To these he has given the name of
'^ Elephant beds**," because they yielded the bones of elephants
and other mammals. But Dr, Mantell seems to have had some
* Surrey. f Surrey. J Hants.
§ Hants. II Hants. If Sussex.
♦* Geol. of the S.E. of England, by Gideon Mantell, F.R.S., 1833.
the London and Hampshire Basins. 287
misgivings on this head, for he has allowed the elephant beds
their proper place and prominence in the chapter on diluvium.
Dr. MantelFs description of these cliffs is perfectly faithful ;
and I have only to add, that they form an excellent type of the
passage of the tertiary into the cretaceous zone of drift. In the
composition of that portion of them which lies to the east of
Kemp Town, I imagine the sands to be derived from the plastic
clay ; the angular flints and chalk-rubble from the eroded chalk-
rock in the vicinity ; and the shingle bed or ancient beach at
the bottom belongs to the pre-eocene epoch, and is the beach of a
sea of which we now know nothing more, than that it beat upon
tjie chalk before the deposit of the tertiary formations ; and was
most probably the parent of the great shingle beds of the plastic
clay, of which so much has been said.
The second, or Cretaceous Zone. — As before said, on drawing
nearer to the bare and abraded chalk-hills, the rounded gravel of
the tertiaries ceases to be a feature in the composition of drift ;
and although a few are to be found in the '^ vents '^ (? rents) and
fissures of the chalk, and some stragglers adhering to the rolled
clays and clay loams which still linger amongst the drifts of the
verge of the Downs, they give place to a plentiful coating, and
in some cases large accumulations of entire and broken flints ;
and here and there beds of loam and patches of chalk-rubble.
In the line of country to which these belong also, we find the
^' grey wethers " or Druid sandstones, and the flint conglomerates
of the eocene sera, — witnesses of the demolition of the strata
which lay on the chalk before the catastrophe of elevation.
It is scarcely necessary to say, that all the Down country
affords an ample display of this sort of drift. The largest accu-
mulations of flint are to be found where there appears to have
been the greatest amount of denudation, at the bottom of valleys,
both longitudinal and transverse. On the broad expanse of the
Hampshire chalk, the tops of some of the highest eminences,
which have escaped perfect denudation, afford loams with a few
remaining round pebbles. The Burghclere Hills, for instance,
above the sources of the Test, and the high grounds between
Andover and Micheldever*; and a few round pebbles are also
to be found in the flint gravel beds of the Candover Valley, and
in the loams round the northern borders of the Vale of Meonf.
To this zone also I refer two remarkable accumulations of drift ;
— the one consisting almost entirely of angular flint and strong
loam, at and in the neighbourhood of FarnhamJ; and the
other an equally important one of the same sort of flint, with
chalk- rubble and a very slight sprinkling of rounded pebbles,
near Dorking §, at the entrance of the Vale of Leatherhead, A
* Hants. t Hants. % Surrey. § Surrey.
X2
288 On the Anticlinal Line of the London and Hampshire Basins,
conveniently deep and illustrative section of this bed of creta-
ceous diluvium, long worked for road materials, is to be found
near Burford Bridge. The materials here are firmly impacted
and loosely cemented together, like the Brighton cliffs, by their
own carbonate of lime ; which gives an appearance, as at Brighton,
approaching to regular stratification. But there is nothing here
to remove this accumulation from the category of common cre-
taceous drift. Beds of this kind show themselves on the banks
of the Mole in the hollow way near the bridge on the Reigate
road ; and also on the verge of the gault in digging foundations
of houses at the foot of Reigate Hill. Shifting to the South
Downs country, the same appearances are to be found on the
abraded surface of the chalk near Chichester*. The Port-field
there has long been worked for angular flint mixed with chalk-
rubble ; and between that place and the Union house at West
Hampnet, there was some time since, and perhaps is still, a flint-
gravel pit the exact counterpart of the Dorking one, and com-
posed of the same materials as the diluvial beds there, and as
those on which Brighton is built. I may here observe, that it
was the great denudation of the chalk, and the spread of these
drifts along the flat country south of the Downs from Chichester
to Brighton, and the raised beaches of eocene shingles, which
gave early observers the idea of its being an ancient sea-bed, of
which the chalk downs were the border ; — a position perfectly
untenable.
Before we quit the chalk downs and enter the denudation
below, we may observe that, although the escarpment of these
downs, north and south, seems to have been swept clean of flint,
it presents here and there some beds of rubble. The same may
be said of the ten'aces of the malm or upper greensand. But
the gault has a large sprinkling of flints, which sometimes lie in
considerable hollows, as recorded many years ago by Sir R.
Murchison in his account of Alice Holt under the Alton Hills f.
These belong properly to the cretaceous zone, and are often ag-
glomerated by oxide of iron derived from the stratum in which
they have been imbedded. The gault country forms but a narrow
strip at the foot of the Downs. So narrow is its outcrop in the
western part of Surrey, that it is sometimes intruded on by the
subcretaceous drift. But except in this line of countiy and in that
east of Lewes, where it ceases to be bounded by the high grounds
of the lower greensand, it exhibits very little more than angular
flints.
[To be continued.]
* Sussex. t Geol. Trans., vol. ii. 2nd series, p. 100.
[ 289 ]
XLIII. On the Solution of certain Systems of Equations. By
James Cockle, M,A., Barrister 'at-Law, of the Middle
Temple^, l
(1.) npHE following investigations were suggested to me by
A the perusal of Mr. Sylvester's paper at pp. 370-373
of the last November Number of this Journal ; but they do not
involve the theory of determinants. In no spirit of disparage-
ment of that theory^ nor of the splendid scientific achievements
of Mr. Cayley with reference to it^ I venture to intimate an
opinion that_, as the theory of determinants (in its explicit form
at least) is in no degree indispensable to the progress of the
theory of algebraic equations,, so also that its processes have no
decided superiority over others that enter into the algebraic
theory. This introductory remark must be considered in exclu-
sive reference to the theory of equations, otherwise it would be
indicative of impertinence on my part, as well as of inaccuracy.
(2.) Let there be given for solution m simultaneous equations.
And, further, suppose that, by some of the known artifices of
algebra, those m equations can be put under the respective forms
Mj -f 0 = 0, ^2 + 11 = 0, ..., 1^^+11=0, . . {a.)
then the solution of the system («.) involves that of the given
equations.
(3.) Let u^—Ur+i = v^,
then, if we can satisfy the m relations
we can satisfy the system («.). We might give various forms to
Vr, and consequently to (b.), but I have selected that which ap-
pears to be the most convenient. These forms may however be
departed from as individual examples may render it desirable.
(4.) Let a: be one of the unknowns involved in the given
equations. Then, if we assume that
where A^ either is free from x or capable of being made to vanish
without determining iCj we obtain a very remarkable form of Vr ;
for, in this case, the solution of (b.) reduces itself to that of the
system
Ai=0, A2=0, . . . , A^.,=0, u^ +n=0. . (c.)
* Communicated by the Author, who adds the following note : —
1 [" There are one or two observations which I should have been glad to
have included in the above paper. But, as it has already extended to the
limits within which it is perhaps desirable that I should confine myself, I
shall seek another opportunity of laying them before the readers of this
Journal.— James Cockle."]
290 Mr. J. Cockle on the Solution of
It is immaterial whether X^. contains x, or not, but it is a con-
dition, essential to the solution of (c), that Um+^ should in-
volve X. There are of course other conditions, but I shall not
here examine them in detail.
(5.) Let tt^ -f II be of the nth degree in a: ; we will now pro-
ceed to consider a few instances in which m given equations
admit of what I have (Phil. Mag. S. 3. vol. xxxvii. p. 502, art. 17,
and p. 503, art. 19) denoted by the expression a * determination '
of the wth degree. And, first, let us proceed to the system
U=flP*, V=6P«
already (Ibid. pp. 372, 373) treated of by Mr. Sylvester.
(6.) Let
-P2=fl,
then, in the present case*, we have
and, if we make
we have
where
Ai=A^-, = 6U'-«V',
U=U'^2andV=V'a?^
Now, U and V, being homogeneous quadratic functions of x and
y, U' and V, are quadratic functions of x~hj and involve no other
undetermined quantity. Hence we may satisfy
Ai=0
by means of a relation of the form
y=px,
p being known and x left wholly undetermined. Consequently,
the relation
^-iV-P2=:0 (d.)
being the only one remaining to be satisfied, the problem admits
of an 71^^ determination capable in the present instance of being
reduced still lower.
(7.) For, since Y' is a known quantity of the form
ap^ + ^p-^y,
the equation (d.) is equivalent to
±a: ^/FH^Mn^oTt) =P,
an equation of ^n dimensions; n being, in this particular instance,
even.
* In the present case we might, perhaps advantageously, have made
Q=—abF^. So in art. (9.) we might have employed ABC« in place of «.
certain Systems of Equations. 291
(8.) It is worthy of remark that the same determination may
be effected when U and V are both homogeneous cubicj or both
homogeneous biquadratic functions. The only difference is that
in the former case p is determined by means of a cubic, and in
the latter by means of a biquadratic equation.
(9.) Let us now proceed to the first system given (Ibid. p. 370)
by Mr. Sylvester, viz. \ j ;<i^. i:Orjuai>»>
U=A.a>, V=B.a), W=C.a).
We here have
and, if we make
X,=A-^B"V, X2=B-'C"V, andW=W'^^
we also have
A,=BU'-AV^ and A^rrCV'-BW;
and, if we assume that z=qx, the relations
Ai=0, and A2=0 {e.)
will be ordinary simultaneous quadratics in p and q.
(10.) The solution of these two quadratics would at first sight
seem to entail upon us the necessity of solving a biquadratic.
This however may be avoided by means of the general theory of
linear transformations. Eor, since by linear transformation the
system [e.) may, without the occurrence of any equation higher
than a cubic, be transformed into two pure quadratics in which
the unknowns are linear functions of jo and q, we see that those
quantities may be determined (after the transformation) by re-
duction and quadratic evolution only. But the above is not the
only method of avoiding the occurrence of a biquadratic. The
following algebraic artifice enables us to arrive at the same result
with perhaps greater ease, simplicity and directness. Valuable
and interesting as is the general theory of linear transformation,
it may be questionable whether the sphere of its practical use-
fulness extends over the pure theory of algebraic equations.
(11.) Either of the quadratics [e.) may be put under the form*
a?2/ + «=0, (/.)
* For, adopting the notation of my Method of Vanishing Groups (as to
which see paragraph XV. et seq. of p. 177 of the last [May] number of the
Cambridge and Dublin Mathematical Journal), we have
provided that
a?=^i+j^2'v/~~l a^d2/=Ai— ^2a/— !• • • if')
If, by means of (/'•)> we determine p and q in terms of x and y, we pass to
{g.) by substitution only, and without recourse to any general theory of
linear transformation. When A2 is better adapted for our purpose, we may
form the function y^2(A2) instead of ySi^O'
292 On the Solution of cei^tain Systems of Equations.
and the other may then, after a lineai* substitution, be denoted by
x^-\-bxy + c^y'^+dx + ey-\-fz=:Oi . . . {g,)
let us now examine the relation (g) +X(/.).
(12.) First, let \=2c— 6, and we have
{x^cyY-\-dx + ey-\-2ac—ah-\-f=0, . . (A.)
Next, let Xsr — 2c— i, and we have
(ar-cy)* + (^ + ey-2ac-«6+/=0. . . (f.)
(13.) Now let
a?H-cy4-/'t'=X
and
then we may give {h.) the form
X2 4-M + (^-2/i)^+(e-2c/i)y=0. . . (j.)
So, if we make
x—cy-^-v^Y,
and
-2flc-a64-/-v2=N,
we may represent (i.) by
Y2 + N+(</-2v)^+(e + 2cv)y=0. . . . {k.)
(14.) If we assume that
e— 2c/i< e + 2cv
d-2fi "" ^"" </— 2v'
and, consequently, that
fjL={4ic)~\cd-{-e), v=t{4c)~\cd-e),
and
d-2fi={2c)-\cd^e), d-2v=(2c)-\cd+e)',
and if we also make
W=^M.-(ScT\cd-^eY, N'=N-(8c2)-\c</+^)^
then (j.) and (A:.) may be put under the respective forms
X2+(2c)-'(c(?-c)Y+M'=0 (/.)
Y^+(2c)-'{cd-\-e)X-\-W=0 (m.)
(15.) The equations (/.) and (m.) may be still further simpli-
fied as follows ; assume that
X=etx, Y=^y,
M'=a*m, and N'=/9*»,
and determine a and ^ so as to satisfy the relations
a-^^(2cy\cd''€):=l=^-'ot{2cy\cd'{-e),
Prof. Muspratt and Mr. J. Danson on Carmufellic Acid. 293
then {I.) and (m.) will take the respective forms
x^ + y-\-m-=-0 [n.)
2/^ + ^ + ?is=0 (o.)
(16.) The two last equations may be solved thus : —
Let
2/=— 2r(^--r) + (4r)~^ {p.)
then [n.) and {o) become^ respectively,
(a;-.r)2 + r2+(4r)"' + m = 0 {q)
and
4r2(^— r)2 + r+(4r)""^ + ?i = 0 (r.)
Form the equation 4r^ X (^O "" (^0^ ^^^ *^® result is
4/'4 + r + 4mr2— r-(4r)"^--w = 0,
which last equation^ being multiplied into 2~V^, gives
y.6^^y.4_2-2/ir2-2-^=0 (s.)
a cubic in r^, whence r may be determined. And x may then
be obtained from [q.) and ^^ from (w.).
2 Pump Court, Temple,
August 9, 1851.
XLIV. Ori Carmufellic Acid'^\ By Dr. Sheridan Muspratt,
F.R.S,E., Professor of the College of Chemistry, Liverpool, and
Joseph Danson, F.C.S., late Assistant in the College'^.
ALTHOUGH numerous researches connected with eminent
names in chemistry prove that the importance of a correct
history of the Clove and its derivatives has not escaped conside-
ration, still the meagre and indefinite details upon them which
are to be found in a few scientific manuals indicate that a very
great deal remains yet to be accomplished. The principal results
thus far upon cloves are by Dumas J and Ettling§ ; the former
upon caryophylline, an indifi'erent substance abstracted from
them by alcohol ; the latter upon caryophyllic or eugenic acid,
an oily acid obtained from the undeveloped buds of Caryophyllus
aromaticus, oil of cloves being a mixture of the acid and a
neutral oil. Dumas found the purification of caryophylline ex-
tremely difiicult, owing to a resinous body which tenaciously
adheres to it, and which after months of investigation he could
not remove. It was recently, however, that the following for-
* From the Arabic, Karmufel, the clove-tree.
t Communicated by the Authors, having been read before the Royal
Society of Edinburgh.
% Liebig's Annalen, vol. ix, p. 73. § Ibid. vol. ix. p. 68.
294 Prof. Muspratt and Mr. J. Danson on Carmufellic Acid.
inula for this substance was established : —
CiOHSQ*.
Chemists well know the numerous difficulties presenting them-
selves at every step in organic chemistry ; and as we have now
worked for more than twelve months upon cloves^ we feel convinced
that others who ventured upon this department left it impatiently
on account of the numerous obstacles daily appearing, and the
small quantities of some of the substances derivable from this spice;
e. g. it would be utterly impossible to obtain enough of eugenine
from the aqueous extract of ten or twelve pounds of cloves ; and
the acid we are about to describe, and which is produced by the
action of nitric acid upon the aqueous extract of cloves, could not
be obtained in sufficient quantity for examination from less than
twenty pounds. One pound of cloves yields two grains of im-
pure acid.
Preparation of the Acid.
About twenty pounds of cloves were introduced into a copper
boiler and well-macerated with four gallons of water, and then
boiled briskly for an hour ; the dark brown liquid syphoned off,
and the pulpy mass boiled with successive portions of water untd
the solution withdrawn was nearly colourless. These several
decantations amounted to about thirty gallons of liquor, which
were evaporated to about six gallons. We found upon treating
a small portion of the brownish decoction with nitric acid that
the action was most violent.
The mixture frothed up to about twelve times its volume,
consequently this was a warning for future operations. We
divided the six gallons into twenty or thirty portions, treating
each with nitric acid in the cold. When the intumescence had
subsided, the vessels were ranged on a covered sand-bath and
allowed to digest for several days j the liquid became of a pale
yellow colour, and large quantities of a whitish precipitate
floated through the menstruum. The gas evolved during the
brisk effervescence was most irritating, producing extreme lacry-
mation ; in fact the eyes were quite swollen when subjected for
a short time to its influence. A small quantity of nitric oxide
was evolved collaterally with the suffocating vapours, and a large
quantity of oxalic acid was found in the solution. Carbonic acid
also escapes during the action. If the above extract be concen-
trated to the consistence of syrup, the action is very energetic
even in the cold, and the supernatant liquid cannot be obtained
except of a blood-red coloui*. All the irritating vapours were
completely expelled before separating through bibulous paper
* Dr. Muspratt on Caryophylline, Lancet, Novembers, 1850; Pharma-
ceutical Journal, vol. vii. p. 343,
Prof. Muspratt and Mr. J. Danson on Carmufellic Acid. 295
the deposit from the canary-coloured fluid. • The filtration was ex-
tremely tedious ; it occupied upwards of a month : the precipitate
was edulcorated completely with boiling water, until the liquid
percolating did not redden litmus paper. When cold water was
employed, the filtrates were always milky, which, however, disap-
peared on boiling. The filtrate was evaporated to a small bulk,
when fine yellow micaceous scales deposited. They were col-
lected and redissolved in boiling water, then precipitated by ace-
tate of lead, and the lead salt washed by decantation to separate
the last traces of acetic acid ; an excess of sulphide of hydrogen
was next passed through the lead salt suspended in water, the
whole boiled and then filtered through pure animal charcoal,
which gave a colourless solution that on evaporation yielded to
our satisfaction splendent white crystals of the acid. The crystals
were insoluble in alcohol, sether and cold water, soluble in hot am-
monia, in potassa, and in large quantities of boiling water ; con-
centrated sulphuric acid leaves it intact in the cold, but in the heat
carbonizes it, giving off sulphurous acid. We have not enume-
rated a tithe of the difficulties encountered, as they would only
occupy space, and not prove interesting to the reader ; but those
wishing to prepare the acid will find the preceding directions
sufficiently explicit.
Behaviour of the Acid with Metallic Oxides.
On mixing a moderately strong solution of the acid with any
soluble salt of baryta, strontia or lime, the whole becomes a
perfect transparent jelly of such spissitude as to allow the vessel
containing it to be inverted.
Soluble salts of lead give with the acid a white transparent jelly,
copper ... pea-green flakes,
silver ... white
oxide of iron ... white
sesquioxide of iron pale yellow ...
When the precipitates are dried they occupy a very small
space, and much resemble mica in their feel and crispness. All
these precipitates are soluble to a certain extent in nitric and
hydrochloric acids. The lead salt is perfectly dissolved, the
liquid becoming clear, while with the others it remains opake.
The acid, heated pe7^ se, fuses and gives off fumes resem-
bling those from burnt sugar, together with a yellow oil which
condenses on the sides of the tubes.
Analysis of the Acid and its Salts.
The acid, dried at 100° C, and burned with chromate of lead,
gave the following numerical results i^- 33
Theory.
I.
11. •
144 34-285
34-210
34-285
20 4-761
4-824
4-809
256 60-954
60-966
60-906
296 Prof. Muspratt and Mr. J. Danson on Carmuf elite Acid.
I. 0-456 grm. of substance gave 0-575 grm. of carbonic acid
=0-156 grm. of carbon = 34-210 per cent., and 0-198 grm.
of water = -022 grm. of hydiogen = 4-824 per cent.
II. 0-420 grm. of substance gave 0-528 grm. of carbonic acid
=0-1440 grm. of carbon = 34-285 per cent., and 0-182 grm.
of water =-0202 grm. of hydrogen = 4*809 per cent., which
corresponds with the formula
C24H20O32.
Centesimally represented.
Found.
24 equivs. of Carbon .
20 ... Hydrogen
32 ... Oxygen .
1 ... Acid . . 420 100-000 100-000 100-000
We found the greatest difficulty at first in preparing the salts
of this acid ; e. y. if we added the acid to nitrate of baryta, a
jelly was the result j but this could not be dried on bibulous
paper, as it adhered so persistently that it was impossible to
scrape the salt from it. Our only resource was to prepare the
salt fi*om the acetates, taking atomic proportions.
Carmufellate of Baryta.
Dissolved equivalent proportions of acid and acetate of baryta
in water, mixed the solutions and evaporated to dryness in a
water-bath; washed the residue vrith water, and dried on a
porous tile over sulphuric acid under a bell-jar. It is slightly
soluble in water, but dissolves copiously in nitric and hydro-
chloric acids.
Analysis of the Salt.
0-2950 grm. of salt gave 0-0710 grm. of sulphate of baryta
=0-0466 grm. of baryta =15-796 per cent.
Centesimally represented.
Theory. Found.
1 equiv. of Carmufellic acid . . 420 84592
1 ... Baryta 76-5 15-408 15'796
1 ... Carmufellate of baryta 496*5 100000
Formula BaO,C«4H2o 082.
Carmufellate of Lead,
This salt was similarly prepared to the baryta one. It is
shghtly soluble in water, soluble in nitric acid.
Dr. Beer on the Motion of Light. ^ « / ' V,.. 297
f*< Analysis of the Salt. "' "^ ^
0*1320 grm. of salt gave 0-0375 grm. of sulphate of lead
=0-0272 grm. of oxide of lead =■ 20*606 per cent.
Centesimally represented.
Theory. Found.
1 equiv. Carmufellic acid . 420 78*947
1 ... Oxide of lead . . 112 21-053 2Q-606
1 ... Carmufellate of lead 532 lOO'OOO
Formula PbO,C24H2o 032.
Atomic Weight of the Acid.
Theory. Found. Mean.
Baryta salt . . 420 4071 ..q
Lead salt ... 420 432/^^^^
Having finished the investigation of the acid, we concluded
that it might have been formed from the oxidation of euge-
nine by nitric acid ; but this we found not to be the case. We
obtained eugenine in transparent pearly laminse from the di-
stilled water of cloves, but in very small quantities ; it is only
very slightly affected by strong nitric acid. Dumas assigned it
the subjoined formula, which we deem the correct one : — « ).«..
C20 H12 04.
The following are the formulae of the substances already de-
rived from cloves : — jlot^ a^ti ,/^
Caryophylline . . Q^^H^ O Musprfett. a^
■ Carmufellic acid . C^* H^o O^^ Muspratt and Danson. ^.
Eugenine . . . C^OH^^O^ Dumas.
Eugenic acid . . C^^Hi^O^ Liebig and Ettling.
We are at present engaged upon eugenic acid and the neutral
oil of cloves ; the subject is extremely difficult, but well worthy
of research.
XLV. On the deduction of FresneFs construction from the for-
mulcR of Cauchy for the Motion of Light. By Dr. Beer of
Bonn^.
THE method generally pursued in deducing the optical rela-
tions of crystalline media from the formulae of Cauchy for
the motion of light, leads to the result, that in such a medium
plane waves, whose direction of oscillation is perpendicular to
a principal axis, proceed with one and the same velocity, however
* Communicated by the Author.
298 Dr. Beer on the deduction o/FresnePs construction from
otherwise they may be situated with regard to the axes of the
crystal ; that, on the contrary, the velocity of oscillations which
are parallel to a principal axis are dependent on the position of
the plane of the waves. From this it would follow, that the
vibrations of the extraordinary ray in a crystal of one axis are
perpendicular to the said axis ; that those of the ordinary re-
fracted ray, on the contrary, lie in a principal section. One
might be disposed to believe that the proof is hereby furnished,
that in the case of plane-polarized light the plane of oscillation
and the plane of polarization coincide, and thus to regard the
other view, according to which these planes stand perpendicular
to each other, as refuted. This apparent proof is, however, illu-
sory. Proceeding from the formula? of Cauchy, the last-men-
tioned view, which is known to be that to which Fresnel adhered,
may be established, if other quantities be neglected than those
usually fixed upon, but which we are equally entitled to neglect.
I shall show this in the following ; and by reference to figures
in space, will endeavour to make this subject plainer than would
be possible if we confined ourselves to the geometrical expression
of the final result alone. I am induced to publish the present
paper by the reading of a memoir from W. J. M. Rankin e in
the June Number of this Magazine, in which the question as to
the direction of vibration in plane-polarized light is handled,
and to which the following in some measure attaches itself.
In his Memoire sur la Dispersion de la Lumiere, Cauchy has
shown that in every homogeneous medium, to every plane P
and definite length of wave \ an ellipsoid E belongs, which he
has named the ellipsoid of polarization, with the aid of which it
is easy to give a simple expression to the laws according to which
waves of the length \, whose planes are parallel with P, proceed
through the said medium. In general only three plane-polarized
waves proceed parallel with P ; their directions of vibration run
parallel with the three axes of E ; and if we express the halves
of these axes by A, B and C, then the velocities of these thi'ee
waves respectively are
: iV' ^ 27rA* 27r*B ^"^ 27r*C*
Supposing the centre of the ellipsoid E to be the origin of a
system of orthogonal coordinates, the said origin being conceived
to coincide with any molecule of aether, it will be expressed by
an equation of the following form :
Lx^ + Ml/ + N^2 + 2?ys + 2Q/VZ + 2Ry<j= 1 .
Between the coefficients of this equation on the one side, and
the constitution of the sether, as well as the direction of the
the formuliB o/Cauchy /or the Motion of Light, 29,9
plane P^ the following relations subsist : ■ -■^r-Trwin^'-
{f A^^ (f)l IT
M= analogon mut. mut.^ N= analogon mut. mut.
P = 2mS -?3 . A?/ A^ sin ^ { M A^ + 1? A?/ + ^^ A^ } ^.
Q= anal. mut. mut., R= anal. mut. mut.,
where the symbols denote as follows :
1. m the mass of a particle of sether.
2. Ar the distance of any sether particle whatever from the
origin of coordinates ; the projections of the said distance upon
the three axes, that is to say, the coordinates of the particle,
being denoted by A^, Ay, ^z.
3. / and (\> certain functions of Ar not to be further charac-
terized here.
4. Uj V and w, the cosines of the angles which the normal to
the plane of undulation encloses with the three axes. The
summation expressed by the sign S is, strictly speaking, to be
extended to all the aether particles.
As the motion of the light is due to the play of molecular
forces, by far the greater portion of the accelerating force of any
particle is derived from the action of those particles which lie
near it ; so that in our formulae those members only are to be
retained in which A^, Ay, Az refer to those particles which im-
mediately surround the origin of coordinates. And further,
since the proximity of the particles is very great, in a case where
an approximate result only is required, the members may be
neglected in which any one of the quantities Ao? . . . appears in-
volved higher than the first power. True, the constants which
enter into the resulting laws will be thus rendered independent
of the wave length X, and hence we must give up the expression
of the dispersion ; we obtain only an approximation to the phse-
nomena displayed by homogeneous light. In order, then, to
bring the analysis into harmony with the results of experience,
let us express the constants which enter into the formulae ; that
is to say, the principal indices of refraction for a certain colour,
by the values obtained from measurement. With this procedure
we must rest satisfied ; the results, indeed, almost completely cor-
respond to the exactitude of our observations.
We develope, therefore, in the expressions for the coefficients
of the ellipsoid of polarization, the sinus function in its equiva-
lent series ; and neglecting the members which, in respect to
A^ . . . &c., are of a higher order than the first, we obtaiu^>:i --mi
300 Dr. Beer on the deduction of PresnePs construction from
P=27w^S^.Ay.A2'{MAa?+vAy + w;A2r}2&c.
The most natural way of presenting a symmetrical medium
possessing two axes to the mind, that is, a medium which is
built symmetrically as regards three principal sections which
stand pei-pendicular to each other, is that in it the particles in
three groups of parallel lines, which stand perpendicular to the
three sections respectively, are at equal distances from each other.
If we suflfer the axes of our system of coordinates to run parallel
with the normals to the principal sections, with the so-called
principal axes of the medium, and denote the distance between
two neighbouring particles in the direction of these axes by Sx,
Bi/, Sz, then the coordinates of a particle, according to this me-
thod of representation, will be
Aa7=w.8.r, Ay = n.Bi/, Az=p.Bz,
where wi, n, and jo denote whole numbers.
In a medium characterized as we have supposed, the particles
whose coordinates possess the same absolute value arrange them-
selves by eights which lie in the corners of a parallelopiped, the
centre of which coincides with the origin of coordinates, and the
edges of which run parallel with the axes of coordinates. For
eveiy such eight particles the sum of the members
^.Ax'^.AyKAz^ and ^.Aa?°.A2/*.A^.
is evidently equal to zero when one of the exponents, «, b or c,
is an odd number ; thus in this case we obtain generally
S ^ . Aaf, AyKAz' = 0, S ^ . Aa?«. Ay*. A^ = 0 ;
and according to this, the coefficients for the ellipsoid of polari-
zation passes into the following :
L=2m.^S-r^ + -^.AxA- {u^Ax^+v^Ay'^+w^Az^jkc.
P=2.2m.^2^.Ay«.A^^vw;&c.
For the sake of brevity let us set
im2£:.A.-f^, lm%L.^,^=,^ lm^^.^z^=?
lmZ-^.AfA2^=A lm2^.Aa^.A.'=^, im2^.A*»Ay^=y
imS^.A^-/, lm%^,^/=q^ |mS^3-^='-^
the formulce of Cauchy for the Motion of Light. 301
we tlius obtain for the equation of the ellipsoid of polarization
the following : .„. ^„
+ y\v''{.f + q^) + u\^ + 7^) + w\t,^ + o?) }
■\- ^.yz ,a? .vw -\- ^.xz .^^ Aiw -YA.xy .^'^ .uv— (77— ) .
\27r/
Ifj in the first place^ the normal to the wave coincides with
the X axis^ that is_, if v — ^, iv=.^jU — \, the equation of the ellip-
soid of polarization will he
The velocities of the vibrations which proceed parallel to the y
axis and the z axis respectively will therefore be
\/^2^7^^ and V^^^pK
If, secondly, the plane of the waves stand perpendicular to the
y axis_, we obtain in a perfectly similar manner for the velocity
of the vibrations which are parallel to the x axis and to the z axis
respectively,
V7;^ + 7'^ and V tf" -\- c^^ .
If, finally, the plane of the waves stand perpendicular to the
z axis, the velocities of the oscillations which are parallel to the
axes X and y respectively are
\/?M^ and 'V/^^T^
Experiment teaches, however, that a ray whose plane of pola-
rization coincides with a principal section possesses one and the
same velocity, whatever its direction may be in other respects ;
or, if we assume that the plane of oscillation is peyyendicular to
the plane of polarization, that oscillations which are parallel to a
principal axis are propagated with equal velocities, whatever the
direction of the plane of the waves in other respects may be.
According to this, we are justified in assuming that we have
9;2 + ry2=^ + ^2^ p _^ ^2 ^ ^ _l_ ^2^ f H /32=7;2 + «2 nearly.
These relations, to the assumption of which we are equally
entitled as to the assumptions regarding the connexion between
the planes of polarization and vibration required by the opposite
notion, reduce the equation of the ellipsoid of polarization to the
following :
Phil, Mag, S. 4. Vol. 2. No. 11. Oct, 1851. Y ^
302 Dr. Beer on tJie Motion of Light.
In the place of this ellipsoid of polarization let us substitute
another, concentric, similar, and similarly situated to the former,
but whose dimensions are to those of the first in the ratio of 2" : !•
We thus obtain at once, in the reciprocal values of its semiaxes,
the velocities of the conjugate plane waves. The equation of the
second ellipsoid differs from that of the first only in the circum-
stance, that in the second the place of — is taken by the unit.
For the equation thus modified let us set, for the sake of shortness,
+ 2dvwyz + 2euwxz + 2fuvxy = 1 .
On experimental grounds it is to be assumed, that, of the three
species of oscillations, which, according to the above, belong to
a plane of undulation, there are two always parallel to the said
plane, these two being within the limits of observation ; while
the third, which corresponds to an imperceptible motion of the
sether, coincides with the normal to the wave. According to the
theory, this is exactly the case in isotropic media ; also in homo-
geneous media generally, when the wave falls in a principal sec-
tion ; and for vibrations parallel to an axis, when the plane of
the waves is parallel to the said axis. From this we conclude,
that we incur an imperceptible eiTOr, if, instead of the axes
of the ellipsoid of polarization, which are nearly parallel with the
plane of the waves, and which alone correspond to the motion
which produces light, we make use of the axis of the diametral
section D, which is parallel with the plane of the waves P. From
the equation of the plane of this section, that is, from
icic-\-vy + wz = 0,
and from the equation of the ellipsoid, we obtain for the projec-
tion of the section upon the plane of yz the equation
y^{{X-\-B-2f)u%^-^av'^i-bu^} + z^{A-{-C-2e)uhv^-\-aw'^-^cu^}
2yz{{A-^d'-e—f)u^+a}vw=^l.
The plane of the diametral section D intersects an ellipsoid E',
whose equation is
a/^a + y% 4- z^c^ 1,
in an ellipse D', for the projection of which on the plane yz we
On the Motion of the Apse-Line in the Pendulum Oval, 303
have
y^{av^-\'bu^}+2^{aw^-\-cu^}-\-2i/s.aviv=zl.
Now the ellipses D and D' coincide as often as the normal to
the plane of the waves coincides with a principal axis. When
the plane of the waves runs parallel with a principal axis^ both
these sections in the direction of the said axis possess axes of
equal length. It seems, in fine, that for homogeneous media
these two sections differ from each other only in an inappreciable
degree ; that is to say, for these media the following relations
appear to be very nearly correct :
A + B-2/=0, A4-C-2e=0, A + i-e~/=0.
In order to obtain the directions of vibration and the velocities
for a given plane P, let the diametral section D' of the ellipsoid
E' parallel with P be constructed. The directions of its axes are
the directions of vibration, the planes of which are parallel to P,
and the reciprocal values of its semiaxes furnish the correspond-
ing velocities.
A surface whose rays are equal to the reciprocal values of the
rays of the ellipsoid E' will be represented by the equation
This is the surface of construction of Fresnel, the axes of
which coincide with the principal axes of the medium, and are
equal to double the principal velocities.
and
A diametral section thereof, the plane of which is parallel with
P, furnishes in the directions of its semiaxes and the direct
values of their lengths, the directions and velocities of the vibra-
tions which belong to P ; and this is the principle which forms
the basis of the construction of Fresnel.
XL VI. On the Motion of the Apse-Line in the Pendulum C^val.
By the Rev. J. A. Coombe, M.A.j late Fellow of St. John's
College, Cambridge.
To the Editors of the Philosophical Magazine and Journal,
Gentlemen,
THE following method of investigating the motion qf the
apse-line in the pendulum experiment presents some pe-
culiarities which may be interesting to some of your readers. It
Y2
304 The Rev, J. A. Coombe on the Motion of the Apse-Line
depends upon the principle of the Variations of Elements so beau-
tifully applied by Lagrange to the planetary perturbations.
Let P be the ball of the pen-
dulum ; K the point of suspen-
sion ; PN perpendicular to the
table; PL parallel to AN.
LetKP==/,KL = r,AN=r,
T the tension of the string KP.
Then the force upon P resolved
in the projection AN
.T.J{,|.M!},
and
(vel)«=2^-^ + C and z=: V^/^-r^;
/, force to the centre A
omitting higher powers of r than the third ; or the accelerating
force to centre
The second term may be looked upon as expressing a small
disturbing force upon the first, which alone would cause the pro-
jection of P to move in an elliptic orbit about centre A. Hence
by Lagrange's principle we may consider the motion as taking
place in an ellipse with variable elements ; so that if the disturbing
force were at any moment to cease, the body would go on de-
scribing an ellipse about A as centre with elements corresponding
to their value at that instant.
Let the equation to the instantaneous ellipse be
cos^((9-tg) ,
Then we have, by the theory,
sm-
(l9-'sr)
But
and
1^
7^
0=^
da
COS'
da
dt
+
b^
dr db . dr
+ -,- • -TT
db dt dvr
dm
dt'
(1.)
^-w
a«
dr
db
sin^^-
b^
I dr . -3 . /I 1\
1 ' «fcr \ : r- ^ V V, / . < \b^ a^/
^mvi-a^<\K•?>A^'^ ' in the Pendulum Oval ,, -/^jf 'iiifi W^
"' 'Also to Sn3 -jT and -j-, we have the equations of motibri dbdui
A, ^, y being the cooidinates of N,
■ dt^
\ (vel)^ in disturbed orbit
'.)t(/ 'iO
,M
>??/^
But (vel)^ in undisturbed ellipse
And these by the theory are equal j
Also^ from the equations of motion.
</jf
'^4.
« 9?iii/uiiKd Xi
Hence from (2.) and (3.) we have ' ,^
(/«_ /aW^ dr db ^ /jJbr^ dr ■i^\
'di'^fi{(v'-b^) 'Jt ' Tt^''fM{a^-b^)'Tt'
Hence substituting in (1.), and calling 0—'Cj = (j), we have, re-
membering that
^=-/^sm<Acos0.(^^^^j.^,
^ fJ'' a fcos^rf) sin^<f)"l 5.,
This is at once integrable by making the usual assumptions, r
y:^y>- r cos (J) = a cos yjr; r Bm <l>=zb sin yjr,
306 Mr. J. P. Joule's Account of Expeiiments
and
ACT =
/*2 (cos2 ^ - sin^ ^/r) (fl« cos^ ^/r + Z»« sin* i/r)
or
. u}ah IT
fJL O
Hence in one complete revolution in the oval, or in a double
vibration of the pendulum, the progress of the apse-line
fjJab IT
But it is evident from the equations for the motion of the pen-
dulum, that
yLt = y (approximately) ,
and
Hence we arrive at the final result, that the apse-line will make
S P
a complete revolution in time ^ . — r multiplied by the time of
a double vibration.
This is the same conclusion as that arrived at by the Astro-
nomer Royal in a paper read before the Astronomical Society.
Believe me, Gentlemen,
Yours faithfully,
Alburgh Rectory, Norfolk, J. A. CooMBE.
Sept. 24, 1851.
XLVII. Account of Experiments demonstrating a limit to the
Magnetizability of Iron. By J. P. Joule^ F.R,S.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
SEVERAL years ago I published some experiments on electro-
magnetic attraction, by which I confirmed the law of Lenz
and Jacobi, discovered about the same time, viz. that the mag-
netism induced in a soft ii*on bar is proportional to the electro-
magnetic force of the exciting coils ; but I was led to the con-
clusion that this law fails when very high degrees of magnetiza-
tion are attained, and that, indeed, there is a limit beyond which
it is impossible to increase the intensity of the magnetic virtue
demonstrating a limit to the Magnetiz ability of Iron. 307
in a bar of soft iron. This fact^ which_, although at variance
with the views of Poisson, has been arrived at a priori by Prof.
Thomson from theoretical considerations*,, has been confirmed
by the important researches of Feilitzschf, Gartenhauser, and es-
pecially of Miillert, whose numerous experiments appear to have
been made with very great care^ and to have dispelled all doubt
as to the existence of such a limit. The interest which these
comparatively recent researches have so justly excited has en-
couraged me to hope that you will consent to reprint a few short
papers, in which the discoveries of the above-named philosophers
are confirmed, but which have hitherto only received publication
in a periodical which seems not to have been widely circulated,
I have made a few alterations, but with a view to explain, not in
the smallest degree to alter the meaning of the original.
I have the honour to remain. Gentlemen,
Yours very respectfully,
J. P. Joule.
On the Use of Electro-magnets made of Iron Wire for the Electro-
magnetic Engine, By J. P. Joule, Esq. Communicated in
. a Letter to the late Mr. Sturi^eon§.
Dear Sir, H Salford, March 27, 1839.
In my last letter I gave you an account of some experiments
which were intended to prove that electro-magnets made of iron
wire are the most suitable for the electro -magnetic engine. In
those experiments round wire was used j and it was my opinion
that the wire magnets were put in a disadvantageous position,
in consequence of the interstices between the wires. I have since
confirmed my views on this subject by the following experiment: —
I constructed two magnets. The first consisted of sixteen
pieces of square iron wire, each jyth of an inch square and 7
inches long, bound very tightly together so as to form a solid
mass, whose transverse section was y^ths of an inch square ; it
was enveloped by a ribbon of cotton, and wound with sixteen feet
of covered copper wire, of y^^th inch diameter. The second
was made of solid iron, but was in every other respect precisely
like the first. These magnets were fitted to the apparatus used
in my former experiments, and care was taken to make the fric-
tion of the pivots equal in each. The mean of several experi-
* Phil. Mag., vol. xxxvii. p. 252.
, t " Electromagnetismus in weiches Eisen und iiber den Sattigungspunkt
derselben." — PoggendorfF's Annalen, 1850.
X Ueber den Sattigungspunkt der Electromagnetismus von J. Miiller
in Freiburg.— Fogg. Ann., Feb. 1851, vol. Ixxxii. p. 181.
§ Annals of Electricity, vol. iv. p. 68. '^^^':'*' '*i '
308
Mr. J, P. Joule's Account of Expmiments
ments gave 162 i-evolutions per minute with the firsthand 130
with the second magnet* ,>ff wii-M;frti?^ infU^ib r..? ^nfltd io ^.>. ,;.
In the further prosecution of my inquiries, I took fidx pieces
of round iron of different diameters and lengths, and also a piece
of hollow round iron, half an inch in diameter, and yV^h of an
inch thick in metal ; these were bent into the U-fonn, so that
the shortest distance between the poles of each was half an inch ;
each was then wound (with the usual precautions to ensure insu-
lation) with ten feet of covered copper wire of ^^^th inch dia-
meter. The lengths and diameters are given in the following
table. No. 1 is the hollow magnet. The attraction was ascer-
tained by suspending a straight steel magnet, 1^ inch in length,
horizontally to the beam of a balance, and bringing the several
electro-magnets directly underneath at the distance of half an
inch, which was preserved by the interposition of a piece of wood
half an inch thick. Care was taken that the battery remained
constant during the experiments.
No. 1.
No. 2.
No. 3.
No. 4.
No. 5.
No.
No. 7.
Length in inches
Diameter in inches
Weight lifted in ounces
Attraction for steel 1
magnet in grains... J
6
36
7-5
5i
52
6-3
2#
92
51
5^
a
3^6
50
a
5^2
41
k
20
4-8
3-6
,urA steel magnet of such dimensions as enabled me to compare
it fairly with the electro-magnets, was found to exert an attrac-
tion of 23 grains for the small steel magnet, though its lifting
power was only 60 oz.
These results will not appear surprising if we consider, first,
the resistance which iron presents to the induction of magnetism ;
and secondly, how very much the power of iron to conduct mag-
netism is exalted merely by the completion of the ferruginous
circuit. In order, however, to explain why the long electro-
magnets have a greater attracting power at a distance, though
they lift less weight, than the short magnets of the same dia-
meter, it will be necessary to observe that it was impossible to
wrap the whole ten feet of wire on the smaller magnets, without
disposing it in two or three layers (according to the size of the
magnets). This was a great disadvantage ; and one might have
anticipated in consequence, that the power of the long magnets
would be greater than that of the short ones for lifting, as well
as distant attraction, which is contrary to the results of the
table ; this may however be explained, if we admit that the com-
parative resistance of the iron of the electro-magnet increases to
a very great amount, when its magnetism is so greatly excited
as by the contact of the armature.
demonstrating a limit to the Magnetiz ability of Iron. 309
^^' Nothing can be more striking than the difference between the
ratios of lifting to distant attractive power_, in the different mag-
nets ; whilst the steel magnet attracts with a force of 23 grains
and lifts 60 oz., No. 3 attracts 5-1 grains and lifts 92 oz.
The following are some general directions for making electro-
magnets for lifting : — 1st. The magnet, if of considerable bulk,
should be compound, and the iron used of good quality and well
annealed. 2nd. The bulk of the iron should bear a much
greater ratio to its length than is generally the case. 3rd. The
poles should be ground quite true, and fit flatly and accurately
to the armature. And 4th. The armature should be equal in
thickness to the iron of the magnet.
I shall now proceed to consider with greater care what form
of electro-magnet is best for distant attraction, as that is the
only force of any use in the electro-magnetic engine. Here two
things must be considered ; the length of the iron, and its sec-
tional area.
Now with regard to the length of the iron, I have found that
its increase is always accompanied with disadvantage, unless the
wire is (by using a shorter length) forced to too great a distance
from the iron. In making magnets for an engine, it will be
proper to use a length less than that which gives the maximum
of attraction, on several accounts.
The next thing to be considered is the sectional area. You
have shown* that, on placing a hollow and solid cylinder of iron
successively within the same electro -magnetic coil, the hollow
piece exerted the greatest influence on the needle. I wished to
ascertain whether a hollow magnet could be represented by a
solid one, of which the sectional area and circumference are the
same, and the thickness of which is twice that of the hollow
magnet. The accompanying figures represent
sections of hollow and solid rectangular mag-
nets ; and it will be seen, that if either of them
is divided at the dotted lines, the separate pieces,
when put properly together, will make up the
other. Two electro-magnets were constructed,
each 7 inches long, and wound with twenty-two feet of insulated
copper wire ; the sections were similar to, but twice the size of the
figures. Their attractions at half an inch distance for the con-
trary pole of a straight steel magnet were as follow : —
Hollow magnet. Solid magnet.
Attraction in grains 1-9 1*7,
Do. with a more powerful battery . 4*5 4*0 '
The above results show that the hollow magnet has the greater
* Annals of Electricity, vol. i. p. 470.
310
Mr. J. P. Joule's Account of Experiments
attractive force ; but I do not think that the difference between
the two ia so great as to counterbalance the practical advantages
which solid bars would give if used in the engine. I shall now
therefore attempt to determine the sectional area of solid iron
most proper for various galvanic powers.
I made five straight electro-magnets of square iron wire y^th
of an inch thick ; each was 7 inches long, and wound with
twenty-two feet of insulated copper wire of y^^rth of an inch dia-
meter. No. 1 consisted of nine, No. 2 of sixteen, No. 3 of
twenty-five, No. 4 of thirty-six, and No. 5 of forty-nine square
iron wires, arranged in the form of square prisms. Five other
electro-magnets were made of square iron rod, but in eveiy other
respect were exactly similar to the first. The following are the
attractions (at half an inch distance) for a straight steel magnet,
with three different voltaic forces.
1st experiment.
Attraction of iron bar 1
magnet in grains.../
tttn n( wiro mnomof
iliagltct 111 giaiuo...
Ditto of wire magnet
^ , . . r Iron bar magnet
2ndexpenraent.|^i^g magnet
q~i *^««^«,«„* / '""on liar magnet
3rd experiment. I ^y.^g magne?
1-5
31
20
2-6
27
3-3
No. 2.
1-9
21
2-5
2-8
36
3-8
No. 3.
1-6
17
2-35
21
3-4
30
No. 4.
21
20
245
22
3-2
2-9
No. 5.
2-0
1-9
22
205
31
2-65
The square iron wire of which the wire magnets were con-
istructed, was taken at the same degree of temper that it pos-
sessed when it came from the manufacturer. It was in con-
sequence not so well annealed as the iron bars. On this account
the numbers opposite the wire magnets are less than they would
have been with better annealed wire : still the results of the table
seem anomalous ; for it will be remarked, that whilst the wire
magnets are the most powerful of the smaller electro-magnets,
the bar magnets are most powerful of the larger ones.
* * *
I remain^ &c..
J. P. Joule,
Investigations in Magnetism and Electro-Magnetism.
By James P. Joule. In two Letters to the late Mr. Sturgeon*.
Broom Hill, near Manchester,
Dear Sir, May 28, 1839.
I am now able to send jrou an account of my further investi-
gations on electro-magnetic attraction. It was judged to be a
matter of the first importance, in a research like the following,
♦ Axmula of Electricity, vol, iv. p. 131,
demonstrating a limit to the Magnetis ability of Iron. 311
to use a galvanometer the indications of which might be depended
upon.
The accompanying figure re- oc
presents the form of galvanometer
I have employed. The needle n
is 2 inches long. The wire is 10
feet long, and y^gth of an inch in
diameter : it is disposed in four
circumvolutions, mercury cups
being placed at the parts marked
tti by c, d, e. The coils cross one another at x, x, but in every
other part they are in the same plane. By this contrivance the
forces of the several coils are made equal to one another, or, as
it would seem, not perceptibly different.
The process of graduation was conducted in the following
manner : — The electricity of a constant battery was first passed
through each of the coils in succession, and the deflection of the
needle was observed to be the same in each case. A current of
a certain intensity was then passed from a to b^ a to c, a to d,
and a to ^, taking care to decrease the resistance of the battery
wires in proportion as the length of that part of the galvano-
meter wire through which the current passed was increased, and
I marked the several deflections of the needle on the card of the
. instrument 1, 3, 3, 4. I then increased the power of the battery
until the needle stood at the mark 2, when the current passed
from a to b; the former process was then repeated, and I thus
observed the quantities 2, 4, 6 and 8 ; and going on in the same
manner, I had the card of the galvanometer marked with the
numbers 1, 2, 3, 4, 6, 8, 9, 12, 16, &c. In using the galvano-
meter the current is passed from a to 6, and the above numbers ,
indicate absolute quantities of current electricity.
In order to obtain a definite idea of the quantities indicated
by my galvanometer, I took a diluted acid, consisting of ten
parts water and one of sulphuric acid, spec. grav. 1*8, and passed
through it a current which deflected the needle to the mark 1.
In seven minutes 0*62 of a cubic inch of the mixed gases was
produced. The electrodes employed in the above experiment
were pointed platina wires I'l inch asunder.
The electro-magnets used first were those described in my last
communication. They are straight and square, 7 inches long,
and wound with twenty-two feet of copper wire y^^th of an inch
in diameter. Five of them were constructed of bar iron, and
five corresponding ones of square iron wire. The sections of
those marked No. I. are j^ths of an inch square ; a dimension
which is successively increased in Nos. II. III. and IV. until
No. v., which are jyths of an inch square.
312
Mr. J. P. Joule^s Account of EarperimmU
The bar electro-magnets were suspended in succession, vertically,
from the beam of a balance ; the corresponding wire electro-mag-
nets being brought vertically underneath, so that -j^th of an inch
intervened between the poles of the two magnets. Electrical cur-
rents of the quantities exhibited in the table were passed through
the continuous line of conductors presented by the galvanometer
and electro-magnetic coils. ITie attraction was measured in
grains by ascertaining the weight required to raise the suspended
electro-magnet from a piece of wood ^th of an inch thick, placed
on the upper pole of the lower electro-magnet.
Table I.
Quantities of cur-
rent electricity.
No. I.
No. II.
No. III.
No. IV.
No.V.
6
7Q
65
88
62
42
8
133
100
180
103
98
12
258
296
300
286
206
16
.500
648
530
550
410
24
1080
1280
1190
1210
1050
In order to vary the above experiments, and with a view to
ascertain what effect an increase of length would produce, I con-
structed ten more electro-magnets of the same sectional areas,
but 14 inches long, or double the former length, and wound with
twenty-two yards, or three times the length of similar insulated
wire to that previously used. Nos. VI. and VII. were made of
square ii-on wii'e ; the rest of bar iron.
j.rtoii«L«i. Table 11.
Quantities of cur-
rent electricity.
No. VI.
No. VII.
|No. VIII.
No. IX.
No.X.
8
12
16
24
410
690
1000
1460
667
1170
1920
3500
1150
2150
4575
9625
1205
3025
5687
11812
1175
2625
4675
10500
Eveiy one of the magnets used in the above series of experi-
ments, except Nos. VI. and VII., was wound to two thick-
nesses by the wire ; and in the large ones the iron was left un-
covered at equal intervals. I must mention, however, that
Nos. VI. and VII. had to be wound to three thicknesses in some
parts on account of their small size. On this account the mag-
netic attractions of these two pairs were somewhat deteriorated.
It does not appear from the experiments that any great loss
of power arises from an increase of the length of the mag-
nets. It is plain, that, as the magnets in Table II. are wound
with three times the length of wire, twenty-four of current elec-
demonstrating a limit to the Magnetizahility of Iron. 313
tricity in the first table should have the same effect as eight in
the second table. The difference, if any, should be due to the
increased length of the iron. I do not think myself justified
in assigning any amount to this difference, which, however, seems
to increase in value as the section of the magnets decreases. In
order to determine this and many other circumstances of great
interest, it would be necessary to conduct experiments in a much
more comprehensive manner, and to examine more minutely into
the various powers of hard and soft iron and iron wire.
I think, however, that I have by these experiments discovered
a most important law, namely. The attractive force of the electro-
magnet is directly as the square of the electric force to which its
iron is exposed; or if E denote the quantity of electricity, M the
magnetic attraction, and W the length of wire, M = E^W^*.
It must be confessed that there are many instances in the
above tables which seem to form exceptions to this law. I con-
sider, however, that the effects of magnetic inertia, and sources
of error which I have found it impossible to avoid, are sufficient
to account for these. Perhaps the fairest way of comparing the
law with experiment is, to take the' mean of the magnetic attrac-
tions of all the magnets in the first table, and the mean of
Nos. VIII., IX. and X. in the second table, omitting Nos. VI.
and VII., because it is clear that they are at last becoming satu-
rated with magnetism. The means of the attractions observed^
and the estimated results, are tabulated below. h i
iw
From the 1st table.
From the 2nd table.
3'
Electric cur-
rent.
Experiment.
Calculation.
Experiment.
Calculation.
6
8
66-4
123
66-4
118
265
472
1063
1177
2600
4979
10646
.' to ?.fiirAU.i:
2648
4708
10593
12
16
24
269
508
1163
Anxious to ascertain whether the law obtained in lifting as
well as in distant attraction, I made the following rough experi-
ment with a horse-shoe electro-magnet made of a cylinder of iron,
7 inches long, and f ths of an inch in diameter, and wound with
five yards of thick copper wire. The law seems in this case to
fail principally because the iron is sooner saturated with mag-
netism ; hence the propriety of making electro-magnets for lift-
ing of considerable bulk,
* Jacobi and Lenz communicated their report on magnetic attraction to
the Academy of St. Petersburgh in March 1839, or two months previously
to the date of this paper. In it they announced a law similar to the above.
—Note, May lB5^jioi.-v7i©w;^iettfwM rfJ^oai .3ii^ aoniit ^siri) Mir
814 Mr. J, P. Joule on t/ie Magnetizability of Iron,
Quantities of current
electricity.
Lifting power in lbs.
Calculated power.
4
6
8
12
3-5
6-5
11-6
210
3-5
8'0
140
31-5
I remain, dear Sir^
Yours truly,
J. P. Joule,
Broom Hill, near Manchestel*,
Dear Sir, July 10, 1839.
The following experiments were designed to test still further
the law given in my last letter. Two pairs of electro-magnets
were constructed ; each of the first pair was made of a bar of
iron, 30 inches long and 1 inch square ; each of the second pair
was made of a bar of iron 30 inches long, 2 inches broad, and 1
inch thick. The shai*p edges were ground down to prevent in-
convenience in the v/inding of the wire. Each magnet was pro-
perly insulated, and wound with eighty-eight yards of covered
copper wire y^th of an inch in diameter.
The attractions were measured in precisely the same manner
as before, saving the substitution of copper for wood, to keep the
magnets at the proper distance apart. The attraction of the
suspended magnet for the fixed one was measured in ounces
avoirdupois.
Quantities of current electricity.
6.
8.
12.
16.
24.
2()0
288
32.
s
i
o
Attraction at i inch. {^JP^^j,'"^^"*
18
18
33
32
72
72
124
128
Attraction at ii„oh.{E~»'.
7
7
13
1244
28
28
47
49-7
112
Attraction at J i"ch.{^JP™*
3
3
5-25
5-33
12
12
18
21-3
100
100
38
48
62
85-3
-Attraction .t 4 l„ch.{EjP^^-:'*
14
14
27
25
60
56
240
224
Attraction a. J inch.jfK;,'".'"^
6-25
625
12
111
26
25
40
44-4
100
. , . , f Experiment
Attraction at iiuch.|r,,j^^^^
2-5
2-5
50
4-44
9-5
10
17-5
177
36
40
The experimental results arc quite as near to the theoretical
as could be expected, considering the several sources of eiTor*
Those belonging to the first pair are particularly satisfactory^
.\ %.v Notices respecting New Books, >' 315
especially if, with regard to the numbers under 16^ 24 and 32,
we make some allowance for the approaching saturation of the
iron.
I inferred from the experiments detailed in my last letter, that
little difference of attractive power would result from the mere
alteration of the shape of the sectional area of the iron of an
electro-magnet ; that view is confirmed by the experiments just
related, in which it will be seen that little difference exists be-
tween the magnetic powers of the first and second pairs ; and
even that difference may be partly accounted for by taking into
account the difficulty of winding the covered wire closely to the
surface of broad rectangular iron bars.
The above magnets were wound to two thicknesses by the
covered wire, and in other respects were similar to those I before
used. The effect arising from increase of length may therefore be
estimated. These magnets, which were 30 inches long, wound
with eighty-eight yards of wire, and excited by a current of 6,
sustained a weight of 7000 grains at the mean distance of ^th
of an inch ; whilst the attractive power of the pairs marked VIII.,
IX. and X., in my last, with the same electro-magnetic force, or
twenty-two yards of wire, and a current of 24, was 10646 grains.
*f\ 5fC *^ ^ ^
I remain, dear Sir,
Yours most respectfully,
J. P. Joule.
XL VIII. Notices respecting New Books.
L*Algehre(VOmarAlkhayydmi. Par F. Woepcke. Paris, 1851. 8vo.
THERE is an old tradition that among the Arabic manuscripts
bequeathed by Walter Warner to the University of Leyden,
was one which treated of the algebraical solution of cubic equations*
In 1834 M. Sedillot discovered a manuscript fragment in the Royal
Library at Paris, which, it seemed probable, was part of the same
work ; of this he published some account {N. Jo. Asiat., May 1834 ;
Not. et ext. des MSS. de la Bibl. R., vol. xiii. pp. 130-136). M.
Libri afterwards found a complete manuscript in the Royal Library
{Histoire, &c., vol. i. p. 300), M. Woepcke has now published this
work, with the assistance of the fragment and the complete manu-
script just noted, and also the manuscript of the Leyden library itself.
As noted by M. Libri, the work does not contain the solution of
cubic equations, but only their geometrical construction, by aid of
the conic sections. But though the tradition which we have men-
tioned imposes upon us this depreciatory kind of description, it is
not the less to be noted that what we really have obliges us to form
a much higher idea of the Arabian algebra than could have been
316 Royal Society.
gathered from our own historians. Up to the time (1831) when
Dr. Rosen published his edition and translation of Mohammed Ben
Musa, we knew nothing of the Arab writers except in fragments.
Dr. Rosen's contribution (which is also that of Mr. Warburton)
showed us the manner in which, and the writer by whom, the Indian
science was made Arabian. M. Woepcke lets us into the secret of
the progress made by the Arabs themselves ; and a comparison of
the writings of the introducer and of the improver will show that
the science had made remarkable advances. This comparison, how-
ever, we must leave to the interested reader, on account of the space
it would require.
M. Woepcke gives the Arabic text, a French version, a running
paraphrase in modern language, and various additions and notes.
He has earned a right to the gratitude of all who take hiterest in
watching the progress of science, by the able manner in which he
has performed every part of the task of which we can judge. We
say this that we may not be supposed to give an opinion of the
translation ; this we are compelled to leave to those who know how
to decipher the methodical scratches and scrawls which we fully
believe, upon testimony, to represent Arabic words.
Omar Alkayyami was alive in a.d. 1079 : Mohammed Ben Musa
lived two centuries before him.
Photogenic Manipulation. By Robert J. Bingham. Eighth Edition.
Knight, Foster Lane.
This little work contains a short account of the theory of the
chemical action of light, with simple directions for producing pho-
tographic pictures by different agents, bringing down the descriptions
to the most recent improvements at the time of publication. Among
these the production of images upon glass plates naturally assumes
a very prominent place, forming, as it does, in practice a marked step
in advance, from the extreme beauty and minuteness of detail that
can be attained by the employment of the transparent medium, ren-
dering photography still further available for scientific purposes.
XLIX. Proceedings of Learned Societies,
ROYAL SOCIETY.
[Continued from p. 246.]
May 1, 1851. — The Earl of Rosse, President, in the Chair.
A PAPER was read, entitled " An account of two cases in which
an Ovule, or its remains, was discovered after death in the Fallo-
pian tube of the unimpregnated human female, during the period of
Menstruation." By H. Letheby, M.B., Lecturer on Chemistry and
Medical Jurisprudence in the Medical School of the London
Hospital. Received Feb. 20, 1851.
At the commencement of the paper the author refers to the opi-
nions of Drs. Power, Lee, Paterson, Barry, Girdwood, and Wharton
Royal Society, 317
Jones of this country, and also to those of MM. Valentin, Negrier,
Pouchet, Gendrin, Raciborski, and BischofF on the continent, re-
specting the supposed nature of the physiological phenomena mani-
fested during the period of menstruation ; and he mentions the law
of BischofF, namely, that "the ova formed in the ovaries of the
females of all mammiferous animals, including the human female,
undergo a periodical maturation and exclusion quite independently
of the influence of the male seminal fluid. At these periods, known
as those of * heat' or * the rut' in quadrupeds, and ' menstruation' in
the human female, the ova which have become mature, disengage
themselves from the ovary and are extruded. If the union of the
sexes takes place at this period, the ovum is fecundated by the
direct action of the semen upon it, but if no union of the sexes
occurs, the ovum is nevertheless evolved from the ovary, and enters
the Fallopian tube where it perishes." He states, however, that the
arguments which have been advanced in support of this opinion,
in respect of the human female, are entirely of an analogical cha-
racter; and that although the ovaries of women who have died
during the menstrual period have been frequently examined, and
Graafian follicles found in a recently ruptured state, yet the dis-
covery of the liberated ovule had not, so far as the author was aware,
ever been detected. The importance of his cases rests upon three
grounds, namely, — 1st, the circumstances under which the women
had died ; 2ndly, the finding of recently ruptured Graafian follicles ;
and 3rdly, the discovery of the ovule and its remains in the fluid
matter of the Fallopian tubes.
In the first of the cases recorded, the woman died during a men-
strual period. She had been an inmate of the London Hospital for
twenty-four days before her death, where she was closely watched
day and night by a nurse, in consequence of her having attempted
self-destruction by cutting her throat twenty-nine days before her
death.
An examination of the body showed that the pelvic viscera were
much congested ; that the uterus was considerably enlarged ; that
the vagina contained a sero-sanguineous fluid ; and that the hymen
was unruptured. The ovaries were covered with stellate fissures,
or cicatrices ; and at one part of the left organ there was a purple
spot having a ragged hole in its centre. By means of an incision
into the gland through this spot, it was found that the opening led
into a small cavity which was surrounded at its lower part by a
dense tissue, infiltrated with dark coagulated blood (reference was
here made to the preparation which shows the cavity and its coa-
guluni). After macerating in spirit for a short time, it was noticed
that the clot consisted of four parts, which the author described.
In other parts of the ovary several false corpora lutea, in different
stages of decline, were found. The Fallopian tubes were highly con-
gested, and the cavities of the tubes were filled with a bloody mucus.
The left one contained at about one inch from its fimbriated end, a
small vesicular body, which was, in the author's opinion, an ovule;
for it consisted of nucleated cells and oil-globules. The fluid
mil Mag. S. 4. Vol. 3. No. 11. Oct. 1851. Z
318 Royal Society,
matters of the uterus and Fallopian tubes were made up of blood-
discs, cylindrical epithelium, granular corpuscles, and a few spindle*
shaped bodies.
The second case was that of a girl who had died at St. Luke's
Hospital, where the supervision of the patient was quite as strict as
jthat in the last case. In this instance the anatomical features were
precisely like the preceding. The right Fallopian tube contained a
globular body similar to that found in the left on the former occa-
sion. This globular body, on being crushed between two pieces of
glass and examined under the microscope, was found to consist ex-
ternally of a mass of nucleated cells, the remains of the tunica gra-
nvlosa^ and of a transparent ring, enclosing an opake granular
mass, and a highly pellucid spot. The author considered that this
body was the liberated ovule, and the influence of chemical reagents
served to support his opinion.
An examination of the corpora lutea found in both cases, showed
that they consisted of large granular corpuscles and oil-globules.
The conclusions arrived at by the author were as follows : —
1. That ovules escape from the ovaries of women during the
period of menstruation ; and that their escape is a spontaneous act,
taking place quite independently of sexual intercourse.
2. That immediately before, or else consentaneous with, the
escape of an ovule, the whole substance of the Graafian follicle
becomes charged with effused blood ; and that a sort of fatty dege-
neration of the effused matter soon afterwards takes place.
3. That the mere presence of a yellow body containing a clot in
the ovary, is not by any means a certain sign of recent impregnation.
4'- That a sanguineous fluid is poured out over the whole mucous
tract of the generative system during the catamenial period.
5. That the results of the observation tend to confirm the opinions
entertained by Wagner, Bischoff, Barry, and Wharton Jones, con-
cerning the membranous nature of that portion of the ovule known
as the zona pellucida,
6. That the oil-globules of the yelk are either enclosed in a di-
stinct membrane, or else that a structureless solid material pervades
the entire substance of the vitelline body, and so binds the several
component elements of it together,
7. That the recognition of the germinal vesicle removes some
doubts concerning its appearance and position in the germ-mass.
May 15.— The Earl of Rosse, President, in the Chair.
" Report of further Observations made upon the Tidal Streams
of the English Channel and German Ocean, under the authority
of the Admiralty, in 1849 and 1850." By Captain F. W. Beechey,
R.N. Communicated by G. B. Airy, Esq., F.R.S. &c.. Astronomer
Royal. Received March 27, 1851.
This is the continuation of a report which the author made upon
the tidal phenomena of the Irish Sea and English Channel in 1848.
After detailing the manner in which the investigation had been con-
ducted, and the great care which had been bestowed upon the ob-
* Royal Society. 319
servatlons, which are numerous, the author enters into an explana-
tion of the whole system of tidal streams in the English Channel and
North Sea, as deduced from these observations, and also as to what
he considers to be the cause of the peculiar movement of the streams
in these channels. He supposes, in conformity with Dr. Whewell's
theory, a tide-wave to pass along the western shores of Europe, and
to enter the English Channel and North Sea by opposite routes, and
to arrive off the Texel and Lynn at the same tidal hour as the tide-
wave in the English Channel arrives off the Start and Jersey.
From these points there are thrown off branch or derivative waves,
which differ materially both in dimensions and rate of travelling from
the parent wave. These waves roll on towards the strait of Dover
and there merge into each other and form a combined wave.
The effect of this wave upon the tidal establishments of the Chan-
nel had long been known ; but its influence upon the streams of the
Channel had never before been considered, nor had any observations
upon them been systematically undertaken.
In arranging the plan of observation the author considered that,
as the combined wave was common to both the English Channel
and North Sea, the tidal streams of both these channels would be
found to correspond in every important particular, and that the
movement of the streams throughout the strait would be materially
influenced, if not wholly governed, by the motion of the combined
wave ; that the time of this wave attaining its greatest altitude would
thus afford a standard to which the turn of the streams throughout
the Channel might be advantageously referred ; and that there would
be found in this Channel, as in the Irish Sea, which is equally under
the influence of a combined wave, a stream which would turn nearly
simultaneously throughout the strait with the times of higii and low
water on the shore at the point of combination or virtual head of
the tide.
Accordingly the observations were conducted upon this plan, and
all the movements of the stream were referred to the time of high
water at Dover, which had been determined upon as the standard
from its being situated nearly at the point where the combined wave
is formed. It appeared from the intervals which this mode of com-
parison afforded, that whilst the water was rising at Dover, the
stream of the channels on both sides ran towards that place ; and on
the contrary, in the opposite direction whilst the water wsls falling
there ; and that these streams pursued a steady course throughout the
tide, and extended from a line joining the Texel and Lynn, in the
North Sea, to a line joining the Start and Jersey in the English
Channel. Beyond these limits the streams of the Channel were
found to encounter those of the offing or parent wave, and to occa-
sion the tides in those localities to partake of a rotatory character,
revolving for the most part with the sun, and having scarcely any
interval of slack water.
The line of meeting of these streams was found not to be a sta-
tionary line, neither in those parts where the Channel-stream en-
counters the offing stream, nor where the streams meet in the strait
Z2
320 Royal Society, *
of Dover, but was found to shift from west to cast as the tide rises
and falls at Dover, beginning at Beachy Head and ending at the
North Foreland ; so that the space occupied by the Channel -stream
always preserves the same dimensions, notwithstanding its limits ex-
tend over a distance of 360 miles. The strait of Dover was found
never to have slack water throughout its whole extent at any time,
as was the case in the other ports of the Channel, from which it dif-
fers in this respect ; and the streams in this locality have in conse-
quence been designated as those of the " Intermediate tide."
As the simultaneous turn of the stream throughout the Channel id
a point of considerable interest and entirely new, the author takes
considerable pains to point out the methods by which this important
fact was ascertained, and refers to the observations kept on board
the light vessels along the coast, and to others made at various im-
portant stations; and whenever any contradictory evidence appears,
the cause of the discrepancy is inquired into and explained. It was
found, for instance, that in a port of the North Sea, near the node
referred to by Dr. Whewell, that there was a retardation of an
hour in the turn of the stream ; and, upon an investigation as to the
cause of this delay, it is seen to be owing to the stream running
round the Texel and entering the North Sea at a time when the
Channel-stream had ceased ; but as soon as the Channel-stream ac-
quired sufficient strength, it speedily drove the Texel stream back
and confined it to its proper limits. In the English Channel also a
similar discrepancy is observable near the coast of France ; but this
also the author considers to be fully accounted for by causes inci-
dental to that part of the Channel, and not to be of sufficient con-
sequence to derogate from the character ascribed to the general
motion of the water throughout the strait.
A reference is made to the erroneous opinions which have
hitherto been entertained with respect to the motion of the streams
of our channels ; and the author concludes his paper by explaining
his views as to the manner in which the turn of the stream is ren-
dered simultaneous by the rapid rise of the combined wave in the
centre of the strait, and expresses a hope that he has satisfactorily
shown from the observations, that throughout the English Channel
and North Sea the movement of the stream may safely be referred to
a common standard. This, it is considered, will be of great import-
ance to navigation ; as thus the seaman's progress through these
moving waters will be freed from the numerous and perplexing re-
ferences he was before obliged to make, and which too often — and,
it is to be feand, in many instances too fatally — caused the tides to
be wholly disregarded. All uncertainty as to the effect of the stream
will henceforward, it is expected, be obviated by a simple reference
to a tide table.
The paper, which is accompanied by numerous plans and charts,
forms a practical illustration of the tidal streams of straits, under
the influence of a combined wave. ;^' ' '
-,.-. J- ....
B lo 9eq
Royal Astronomical Society. 321
' a-:? yy ROYAL ASTRONOMICAL SOCIETY, 'n li.ui ^S j70« ! ;,
^ -m^hn^l [Continued from p. 149.] '^'<^^ ^^ ^j^^V^^^
May 9, 1S51. — Some Views respecting the Source of Lights &p.
By James Nasmyth, Esq., F.R.A.S. "' ^'
" Impressed with the conviction that the progress of science has
often been most importantly advanced by the setting forth of hypo-
thetical views as to the nature of those causes which result in great
phsenomena, I am, for these reasons, induced to hazard and venture
forth with some views on the subject of the nature of solar light,
more especially in reference to the well-known but most remarkable
phsenomena, occurring in the case of stars of variable and transitory
brightness, as also in reference to those wonderful results of geolo-
gical research, namely, the unquestionable evidence of the existence
of an arctic or glacial climate in regions where such cannot now
naturally exist ; thus giving evidence of the existence of a condition
of climate, for the explanation of which we look in vain to any, a^
present, known cause. '^
" I must plead the fact of the existence of such wonderful phae-
nomena as these alluded to as my apology for thus attempting to
come forth with what, although they may appear crude, theoretical
notions, yet may, as tending to direct increased attention to im-
portant phsenomena, so lead in due time to the development of
truth, and extend the present bounds of our knowledge of those
mighty laws which are so mysteriously indicated by the existence
of the phsenomena in question, and with the evidences of which we
are yet surrounded. j,
** A course of observations on the solar spots, and on the remark-
able features which from time to time appear on the sun's surface,
which I have examined with considerable assiduity for several years,
had in the first place led me to entertain the following conclusion ;
namely, that whatever be the nature of solar light, its main source
appears to result from an action induced on the exterior surface of
the solar sphere, — a conclusion in which I doubt not all who have
attentively pursued observations on the structure of the sun's surface
will agree. ^ ^ ,
*' Impressed with the correctness of this conclusion, I was ledro
consider whether we might not reasonably consider the true source
of the latent element of light to reside, not in the solar orb, but in
space itself ; and that the grand function and duty of the sun was
to act as an agent for the bringing forth into vivid existence its due
portion of the illuminating or luciferous element, which element I
suppose to be diffused throughout the boundless regions of space,
and which in that case must be perfectly exhaustless.
*' Assuming, therefore, that the sun's light is the result of some
peculiar action by which it brings forth into visible existence the
element of light, which I conceive to be latent in, and diffused
throughout, space, we have but to imagine the existence of a very
probable condition, namely, the unequal diffusion of this light-
yielding element, to catch a glimpse of a reason why our sun may,
in common with his solar brotherhood, in some portions of his vast
322 Royal Astronomical Society,
stellar orbit, have passed, and may yet have to pass, through regions
of space, in which the light-yielding element may either abound or
be deficient, and so cause him to beam forth with increased splen-
dour, or fade in brilliancy, just in proportion to the richness or
poverty of this supposed light-yielding element as may occur in-
those regions of space through which our sun, in common with
every stellar orb, has passed, is now passing, or is destined to pass,
in following up their mighty orbits.
" Once admit that this light-yielding element resides in space,
and that it is not equally diffused, we may then catch a glimpse of
the cause of the variable and transitory brightness of stars, and
more especially of those which have been known to beam forth with
such extraordinary splendour, and have again so mysteriously faded
away; many instances of which abound in historical record.
*' Finally, in reference to such a state of change having come
over our sun, as indicated by the existence of a glacial period, as is
now placed beyond doubt by geological research, it appears to me
no very wild stretch of analogy to suppose that in such former pe-
riods of the earth's history our sun may have passed through portions
of his stellar orbit in which the light-yielding element was deficient,
and in which case his brilliancy would have suffered the while, and
an arctic climate in consequence spread from the poles towards the
equator, and leave the record of such a condition in glacial hand-
writing on the everlasting walls of our mountain ravines, of which
there is such abundant and unquestionable evidence. As before
said, it is the existence of such facts as we have in stars of transi-
tory brightness, and the above-named evidence of an arctic climate
existing in what are now genial climates, that renders some ade-
quate cause to be looked for. I have accordingly hazarded the pre-
ceding remarks as suggestive of a cause, in the hope that the sub-
ject may receive that attention which its deep interest entitles it to
obtain.
" This view of the source of light, as respects the existence of the
luciferous element throughout space, accords with the Mosaic ac-
count of creation, insofar as that light is described as having been
created in the first instance before the sun was called forth."
. Note by the Astronomer Royal.
" In an oral address to the Society, on 1849, December 14, an
abstract of which is printed in the Monthly Notices, vol. x. No. 2,
in describing the method of recording transits by the agency of a
galvanic current, I ascribed certain steps of the invention to Dr.
Locke and Professor Mitchell. I have lately been informed that
the invention was also shared by Mr. Bond, Mr. Walker, and per-
haps by other persons. I am desirous of explaining to the Society
that the history, such as I gave it at that time, was founded upon
the printed papers which had then reached me, and upon my cor-
respondence with American friends ; both necessarily imperfect
sources of information ; and that I had no wish to assert the claims
of Messrs. Locke and Mitchell further than as they seemed to be
implied in those documents, nor to express any opinion on the claims
Royal Astronomical Society. 323
of others, either to the first idea or to the subsequent steps of the
invention." fl.ti3 vsm Jnsmal^ §ftir>i,er{-t«jTi?j. s/ii /loiriY^'m ^sojsqe to
Description ttf tile Appgiratus for observing Transits, b^riiei^ii^ of^
a Galvanic Current, now used at the Observatory of Cambridge,
U.S. By Mr. G. P. Bond*.
The apparatus exhibited to the Society, is the same w^hich has
been for some time past in use at the Harvard Observatory, U.S.,
and is the property of the United States Coast Survey. It consists
of an electric break-circuit clock, a galvanic battery of a single
Grove's cup, and the spring governor, by w^hich a uniform motion
is given to the cylinder carrying the paper.
The electric clock is of the form proposed by Mr. Bond. Though
different in its object and construction, the effect produced is the
same with that of the clock proposed by Professor Wheatstone,
namely, the interruption of the galvanic circuit at intervals of a
second. The pallets and the escapement wheel are insulated, both
from the pendulum and from the other wheels. When the battery
is in connexion, the circuit is broken by the pallet leaving the tooth
of the wheel, and is restored at the instant of the beat of the clock,
which is in fact the sound produced by the completion of the con-
tact restoring the circuit ; the passage of the current being through
the pallet and the escapement wheel alone. With the exception of
the connecting wires, and the insulation of some parts, the clock is
like those in common use for astronomical purposes.
Two wires pass from the clock, one direct to the battery, and
the other, through the break-circuit-key used by the observer, and
through the recording magnet, back to the battery. The length of
wire is of course immaterial.
The magnet, with a slight difference in the form of the armature,
is the same with those used on Morse's telegraph lines in the United
States. The armature carries a glass pen, supplied with ink from a
small reservoir. Under this pen the paper revolves on which the
records are made. The breaking of the circuit by the clock, every
second, is marked by an offset made by the pen, and the breaking
of the circuit by the observer, is similarly recorded between the
second marks of the clock. The paper is wound upon a cylinder, as
suggested by Mr. Saxton of Washington. Unless a motion per-
fectly uniform is given to the cylinder, the second marks at the end
of an hour, instead of being arranged in regular straight lines upon
the paper, will change their relative positions, and the record become
so confused as to make it a most serious undertaking to read off the
observations after they have been taken.
To give a uniform motion to this cylinder has been the chief
obstacle in the way of the application of electro-magnetism to prac-
tical astronomy, so that it should be of general utility ; for although
very rude contrivances will illustrate the process, and even afford
accurate results, the time required to interpret the record may be
greater than that required to make the observations throughout by
* This is the substance of a lecture dehvered by Mr. Bond; in V<r6i<i6 tlfe
whole modw* operawf^* was clearly shown. -ic/ ,. ^ .' ; ti'HiiiiU;
324 Royal Astronomical Society.
the old method > and the liahility to errors in the minutes and secondH
is increased. A saving in the quantity of recording surface was also
requisite.
The apparatus invented at Cambridge for this object is called
the spring governor. The train of wheels which communicates the
motive power to the cylinder connects with a small fly-wheel. This
fly is for supplying momentum, and holds no part in the regulation.
Beyond this fly, reckoning from the cylinder, is a half-seconds
pendulum, with a dead-beat escapement. The connexion between
the escapement- wheel and the fly is through a short spring. The
elasticity of this spring allows the motion of the escapement-wheel
to be completely arrested at each vibration of the pendulum, while
the momentum of the fly, acting for a small fraction of a second
only on the spring, keeps up the motion of the cylinder. The ma-
chinery is thus completely under the control of the pendulum. No
accumulation of irregularity can take place beyond the limits of the
bending and unbending of the connecting spring. After this is
adjusted to its minimum, the continuous rotary motion will be per-
formed with all the accuracy of the beats of the pendulum for any
length of time. It is, in fact, a complete solution of the difliculty
of producing exact uniform motion. An advantageous application
of the same principle might be made to the clock-work for the
equatoreal motion of telescopes.
The cylinder makes a single rotation in a minute. The second
marks and the observations succeed each other in a continuous
spiral. When a sheet is filled, and it is taken from the cylinder,
the second marks and observations appear in parallel columns, as
in a table of double entry, the minutes and seconds being the two
arguments at the head and side of the sheet.
The observer, with the break-circuit-key in his hand or at his
side, at the instant of the transit of a star over the wire of a tele-
scope, touches the key with his finger. The record is made at the
same instant on the paper. The operation may be repeated easily,
at intervals between the successive transits, of one or two seconds
each.
ITie experience we have now had places beyond doubt the fact,
that, for convenience and accuracy of individual results, this new
mode of observing is in advance of the old. The number of com-
parisons for differences of right ascension may be increased to an
extent which distinguishes it, equally with its superior accuracy, as
a real improvement in the science of practical astronomy. The
extension of the method to the registration of difi^erences of decli-
nation, simultaneously with difi^erences of right ascension, promises
great facility in taking zones of small stars.
Owing to the difliculty of obtaining precise information respect-
ing scientific matters in America, considerable inaccuracies have
crept into the historical part of the lecture given by the Astro-
nomer Royal on the American method of observing by the electro-
magnetic circuit (Phil. Mag. S. 3. vol. xxxvi. p. 142). The preceding
note from the Astronomer Royal will prevent misconception on
this point. But, setting aside the claims of individuals in this
Rojjal Asirmbmicat 1^oMet§) ^
matter, so far as this is an American discovery, it is only under
the auspices of the Department of the Coast Survey of the United
States, and with the facilities and means furnished by its present
enlightened superintendent, Dr. A. D. Bache, that the application of
electro-magnetism to the purposes of geodesy and of astronomy has
been successfully accomplished. =9noo-. -^sbxfdfa o.Lt oJ ir>v/oq ^jvijoat
Extract of a Letter from Mr. Lassell. 5]
" I have been very busy, and have brought to a most successfv^q
issue my efforts to support my two-foot speculum free from sensiblat
flexure. All has gone on well and come right at once; and the^
speculum having been once placed in the tube, I have neither,i
reason nor inclination to take it out again. I was pretty sanguine^, j
yet must acknowledge the result has gone beyond my hopes. I aa-itr
nounced the details of the plan to the British Association at Edin^
burgh*, and there is a clear and sufficient description of it in the
Report just about publishing, or perhaps already out. I have scarcely
varied at all in carrying it out. I have found 27 or 28 levers suf-
ficient : and these are about as many as can be conveniently applied
without interfering with the 1 8 discs and levers for zenithal support.
Moreover, I have found cementing fulcral blocks of speculum metal
upon the back with plaster of Paris quite efficient — firm enough to
bear twice the requisite strain. Each lever, in a horizontal position
of the tube, supports 15 lbs. of the speculum's weight; diminishing,
of course, as the telescope approaches the zenith, where they are
inactive. The superiority of action of the telescope since the ap-
plication of this apparatus, I think none but myself who have seen
it in both states can yet appreciate, and the atmosphere now alone
remains my formidable and unconquerable foe, as it is indeed of
all large apertures. So tenderly is the metal sustained in all posi-
tions, that no part of it can ever come into contact, with more than
the pressure of a few pounds, against the tube or box in which it
is placed. The plan seems to me applicable to specula of two or
three times the diameter of mine with equal success. I was scarcely
prepared to believe beforehand that the bending would follow so
regular a law, as that it should be completely eliminated by a re-
gularly devised system of counteracting support. I believe the ap^,
plication of the apparatus does not add more than 40 lbs. toJJ^^^.j
end of the tube which contains the speculum. ^aoaniiq
"Did I mention to you that I had (some time ago now) mad©
an addition and improvement to the polishing machine by com-
municating a regular slow motion to the polisher ? It has given me^
some trouble and looks complex, but it is efficient, and tends, X,,
think, to greater uniformity of curve.v pj^whea I. have leisure, J^t>
must describe it more fully." // <''Vtf/^'>;4^ »— ^
Occultation of a Fixed Star by Jupiter. By the Rev. W. I^^'f
Dawes. ■'^t:?
1851, May 8, 9^ G.M.T. Having turned my 8|-foot refract<?r"
* Reports of the Twentieth Meeting of the British Association, 1850]
Notices and Abstracts, p. 180, &c. On a method of supporting a large ^
speculum, free from sensible flexure, by Mr. Lassell, &c. "^ '
326 Intelligence and Miscellaneous Articles,
upon Jupiter, I instantly perceived a small star near his western
edge, and observed its occultation with power 188. The disap-
pearance occurred at 9*^ 20°^ 48^+G.M.T. ; the angle on the limb,
measured from the planet's northern pole round by the eastern or
following side, being about 250°. Jupiter was obscured by clouds
at the time of the reappearance of the star, which is Hessel (Weisse)
xii. 966. Mean place for 1825, R.A. 12»» 54'" 49*21, a— 4° 12'
33"'2. It is of the 8th magnitude, according to Bessel.
The air was unfavourable, and the time noted is therefore uncer-
tain to a few seconds.
On the evening of March 12, 1851, as the sun was setting in the
midst of a thick haze, Mr. Weld observed a spot on the sun's disc
with the naked eye. On pointing it out to one or two other persons,
they saw it with facility. Next day he observed the sun with the
equatoreal, and found a single large spot nearly round but somewhat
angular. Its greatest measured diameter parallel to the equator was
4'05, that of the nucleus P"60. Its diameter measured along the
meridian circle was 52"*53.
L. Intelligence and Miscellaneozis Articles.
ON THE PRODUCTION OF SUGAR IN THE LIVER OF MAN AND
ANIMALS. BY CLAUDE BERNARD.
ALTHOUGH it has long been known that, under certain condi-
tions, sugar may be found in the blood and other animal fluids,
yet hitherto the presence of saccharine matters has always been con-
sidered as accidental, and dependent exclusively on the nature of
the food. In the present note I shall demonstrate by the result of
my experiments —
1. That the presence of sugar in the animal organism is a con-
stant fact, and is indispensable for the regular accomplishment of
the phsenomena of nutrition.
2. I shall prove that the presence of sugar in the animal body is
not dependent on the kind of food, but that sugar is formed in the
liver by a special function of that organ.
3. I shall finally point out the principal characters of the produc-
tion of sugar in the liver, showing that it is in immediate dependence
on the nervous system.
Ist. Of the presence of sugar in the organism. During the period
of digestion, the blood which issues from the liver by the hepatic veins
(veines sus-hepatiques) invariably contains sugary both in man and
animals, whatever the nature of their food may be.
The liver in most animals, and particularly in mammifera, is
placed intermediately between the abdominal and the general circu-
lation, 60 that the blood of the ventral vena portse, returning from
the spleen and intestines, must pass through the tissue of the liver
before arriving at the heart. Now without attending for the present
to the sourc^.9f the sugar,^l^^^J e^^|)l^h^^^^e;iejral facts :— 1st,
Intelligence and Miscellaneous Articles. 327
that it is by the hepatic veins, and them alone, that the sugar is
conveyed into the general circulation ; and 2nd, that when the he-
patic veins carry sugar, the tissue of the liver is also saturated with
it in a high proportion. No other organ of the body is in the same
condition ; so that the constant presence of the saccharine principle
is distinctive of the tissue of the liver during digestion. These facts
have been proved by a very great number of direct experiments,
and confirmed in a variety of animals belonging to nearly every order
of the zoological series. Without entering on details, I shall enu-
merate the species on which my investigations have been made.
On man, in the state of health, I have three times had the oppor-
tunity of ascertaining the presence of sugar in the liver ; first on the
body of an executed criminal ; next in an individual killed acci-
dentally by a gun-shot ; and lastly, in a case of sudden death.
In the class Mammalia: — Quadrumana — the cynocephalous ape.
Carnivora — dog, cat, hedgehog, mole. Rodentia — squirrel, guinea-
pig, rabbit, hare, black rat, and brown rat. Ruminantia — goat, sheep,
ox. Pachyder^mata — horse, ass, pig.
Birds. Rapaces — hawk, owl, strix and ulula. Passeres — swallow,
sparrow, raven, lark. Gallinacea — pigeon, turkey, cock. Gralla —
snipe. Palmipedes — goose, duck.
Reptiles. Chelonian — land- tortoise. Saurian — green lizard and
gray lizard. Ophidian — anguis fragilis, coluber, and common viper.
Batrachian — common frog, grenouille rousse, red frog, brown toad,
aquatic salamander or triton.
Fishes. — Osseous. Acanthopterygian-^common perch, labrax,
thunny. Abdominal Malacopter^mn —common carp, barbel, leuciscus,
common trout. Suh -branchial Wtdacopterygian — cod, turbot. Apo-
dous Malacopterygian — common eel, conger-eel.
Chondropterygian or Cartilaginous Fishes. Sturiones — sturgeon,
Selacian — sea- dog.
MoUusca. Gasteropodous— pulmonary — the red slug, gray slug,
common snail, fresh- water snail. Pectinibranchiata — paludina vivi-
para. Acephalous MoUusca or Lamellibranchiata — the edible oyster,
pecten, mussel, anodont and unio.
Among the Articulata, I have detected sugar in the liver of some
decapodous Crustacea, as the crawfish and lobster ; but in this branch
of the animal kingdom the organs of nutrition undergo such profound
modifications that the determination of the liver would lead to un-
necessary discussion.
The numerous researches cited above have all been made on ani-
mals in full health, and during digestion, or shortly after it. They
are, I think, sufficient to prove that the presence of sugar in the liver
is a general fact, both in man and in all animals evidently provided
with that organ.
In proportion as the act of digestion draws to a close, the quan-
tity of sugar poured by the hepatic veins into the general circulation
gradually diminishes ; and at the same time the tissue of the liver
eliminates by degrees all the saccharine matter which it contained.
But in warm-blooded animals which are in good health, and in the
usual conditions of supply of food, there is never complete absence
328 Intelligence and Miscellaneous Articles.
of sugar from the liver, because the digestion of another meal com-
mences before the quantity of sacchaiine material already formed iet
exhausted. If, however, we subject animals to forced abstinence,
the sugar after a time completely disappears, and the liver exhibits
no more trace of it than any other organ of the body.
Accordingly, as it is a fact that in all animals during digestion the
hepatic tissue and the blood which issues from it constantly contain
sugar, so it is equally true inversely, that in all animals subjected
to abstinence prolonged sufficiently, the liver and hepatic blood are
entirely deprived of saccharine matter, which, however, immediately
reappears as soon as digestion and nutrition resume their activity.
The duration of abstinence required for the complete elimination
of sugar from the liver presents many variations according to species,
age, health, &c. I shall merely state that in birds the disappearance
is very rapid, occurring at the end of two or three days ; while in
dogs it is complete only at the end of seven or eight days of starva-
tion. In cold-blooded animals a much longer time is required.
We shall afterwards observe, that in cases where the function of
digestion is disturbed or disordered, one of the first results is the
disappearance of sugar from the liver and from the blood of the he-
patic veins. Hence the presence of saccharine matter there must be
regarded in animals in their ordinary condition as the indication of
the normal performance of digestion.
2nd. Sugar is produced in the liver independently of the nature of
the food.
The experiments above cited might serve to show that the sugar
is formed in animals without the intervention of saccharine or amy-
laceous principles in the food, since the presence of sugar was de-
tected in carnivora, as well as in omnivora and herbivora in the
animal series. However, as the fact of the production of sugar in
the liver is still new, and has most important bearings on physiology,
I shall support the above proposition on the evidence of special and
direct experiments.
To demonstrate that the saccharine matter originates in the liver,
and is not introduced with the food, animals such as dogs, cats, or
even rabbits, must be subjected to a diet exclusively animal, and
containing no substance which can by the process of digestion give
rise to saccharine principles in the alimentary canal. Thus I have
fed dogs during three, four,, five, and even eight months exclusively
on flesh ; and on examination at the end of that period, I have con-
stantly found that, while the intestines and blood of the vena portse
at its entrance into the liver contained no sugar, the blood of the
hepatic veins was always abundantly charged with it. But an expe-
riment less prolonged proves the production of sugar in the liver.
In fact, as before stated, the dog's liver may be completely deprived
of sugar by an abstinence of seven or eight days' duration. If at
the end of that period the animal be fed on flesh only, the sugar will
nevertheless reappear in the liver as soon as the process of digestion
determines increased activity in the circulation of the organ. When,
therefore, in animals fed exclusively upon flesh, it is constantly as-
certained that the blood brought to the liver by the vena portse con-
Intelligence and Miscellaneous Articles.^ 329
tains no sugar, and that the blood which leaves the organ by the
hepatic veins is always charged with it, we must admit that the
blood acquires the saccharine principle in passing through the hepatic
texture, or in other words, that the liver is endowed with a peculiar
function in virtue of which sugar is produced.
The liver, therefore, performs two functions at the same time,
namely, the secretion of bile and the production of sugar ; and the
latter function commences even before birth, for I have detected
sugar in the liver of the young of mammalia and birds at different
periods of foetal life. It is remarkable, that while the bile, like other
intestinal secretions, is j)oured out into the alimentary canal, the
sugar, on the contrary, mixed with the portal blood returned from
the intestines and spleen, is carried out into the general circulation,
and disappears in contributing to the phsenomena of nutrition. This
separation of the bile and sugar, however, occurs only in vertebrata,
for in mollusca I have found the biliary fluid highly charged with
saccharine matter.
The sugar produced in the liver presents the chemical characters
of glucose. Along with M. Barreswil, I have ascertained the fol-
lowing properties : —
1. The saccharine principle of the liver ferments when put in con-
tact with yeast, and yields alcohol and carbonic acid.
2. Its solution is rendered brown by the caustic alkalies, and re-
duces the tartrate of copper dissolved in potash*.
I ought to add, that the hepatic sugar undergoes spontaneous
destruction in contact with blood and animal textures much more
rapidly than ordinary glucose ; a circumstance indicating that, to
operate in favourable conditions, the search for sugar in the liver
should be made on animals recently dead.- ^^ b-jJoa:^
3. Influence of the nervous system on the formation- o#-W^¥ ill
the liver. 'ii ^Kis si
The formation of sugar in the liver is a function j^lahed under the
immediate influence of the nervous system.
In vertebrata, the liver receives two kinds of nerves supplied from
the pneumogastric and the solar plexus. In this, as in other func-
tions, it is difficult to determine the kind of participation which the
nervous system has in the chemical acts of nutrition. It is, how-
ever, incontestable that some of the pheenomena of nutrition cannot
be produced external to the living individual, and are connected in
an immediate manner with the integrity of the nervous system ; so
that we can extinguish, exalt, or disturb these chemical phsenomena
simply by modifying the nervous organs which influence them. In
particular, those functions, generally periodical, designated in phy-
siology as secretions, are so placed ; and I shall show that the pro-
duction of sugar in the liver belongs to the same category.
Thus, for example, whatever be the kind of food, \Ve can cause
the complete disappearance, in a few hours, of the saccharine matter
of the liver in dogs or rabbits by the section of the pneumogastric
nerves in the middle region of the neck. The same result occurs
* The latter test is the one commonly used by M. Bernard to detect the
presence of sugar. * _ . ..... -^
380 Intelligence and Miscellaneous Articles.
whenever, by any means, n violent commotion of the nervous system
is produced.
In the whole extent of the nervous system, I have found only one
limited spot of the medulla oblongata where a lesion occasions the
opposite effect. Thus, when in dogs or rabbits we succeed in prick-
ing the medulla oblongata with a sharp-pointed instrument within
the narrow space, limited below by the origin of the pneumogastric,
and above by the emergence of the acoustic nerves, we ascertain after
a short lapse of time that the saccharine principle has been formed
so abundantly as to spread throughout all the organism. The blood
and other liquids of the body are surcharged with it ; the urine eli-
minates the excess ; the animal is diabetic.
Thus we can cause the excess or disappearance of sugar solely by
modifying the phaenomena of innervation.
In conclusion, from the results presented in this paper, I think I
have proved beyond doubt the production of sugar in the liver of
man and animals ; and have established the existence of a function
which, up to the present time, had remained entirely unknown. —
Monthly Journal of Medical Science, September 1851.
ON THE CRYSTALLIZATION OF CYMOPHANE. BY M. EBELMEN.
In 1847, I presented to the Academy the description of the me-
thod by which I was enabled to prepare cymophane, or aluminate of
glucina, in the crystalline state. The crystals were microscopic.
Their specific gravity and their chemical composition agreed with the
form as determinable with the microscope, so as to allow of their
identification with the natural crystals.
Perfect crystals of cymophane are very rare in mineralogical
collections. It struck me that it would be a matter of great inter-
est to mineralogists, to prepare this species in such crystals as
might be easily determined and measured. I easily succeeded in
this, by prolonging the duration of the evaporation and modifying
the composition of the flux, in such a manner as to render it more
liquid. The crystals which I obtained are from 5 to 6 millimetres
, in length. Sometimes they are simple and present the facets m m
of the primitive prism, the facet g' well-developed, the base P and
the modification e' upon the edge of intersection of the facet g' by
the base. The angles which I measured are identical with those ob-
tained by M. Descloiseaux in the crystals of M. De Dree's collection.
The specific gravity of the artificial crystals is 3' 759 ; that of natu-
ral cymophane is comprised between 3-70 and 3*80. A large num-
ber of macled crystals are found among the artificial crystals of cymo-
phane ; the macles are identical either with those of the crystals
from Brazil and Haddam, or those of the crystals from the Ural.
Hence the artificial crystals not only present the same primitive form
and the same angles as the natural crystals, but even their ordinary
facets and the principal accidental crystallizations of the latter. On
the addition to the flux of 1 per cent, of bichromate of potash, cry-
stals of cymophane are obtained, which are green by day light, like
those from the Ural. By candlelight they appear violet. — Cowptes
Rendus, May 12, 1851.
Meteorological Observations, , 331
ON THE PRESENCE OF AMMONIA IN HAIL-STONES. BY M. MENE.
On Monday the 5th of May, there was a somewhat severe hail-
storm at Paris and its environs. Being at the time in my laboratory,
the idea occurred to me of collecting some of this hail and submitting
it to analysis. For this purpose I placed a piece of linen upon some
tressles and collected about 800 grammes. I immediately melted it
in a porcelain capsule with the addition of a little muriatic acid, and
evaporated it to dryness. When this operation was on the point of
completion, I was much astonished at perceiving the occurrence of
crystallization at the bottom of the vessel. I tested some of these
crystals, which in all weighed 2' 78 grammes, and was satisfied that
they consisted of muriate of ammonia.
I must not omit to mention another circumstance, viz. when the
evaporation was almost completed, a black carbonaceous matter was
deposited in rings upon the glaze of the capsule : it resembled the
charcoal of organic matters. These spots were very numerous, and
I believe they were produced by particles suspended in the air, for
I took every precaution to exclude foreign matters. — ComptesRendus,
May 19, 1851.
ON THE APPLICATION OF RECTIFIED OIL OF COAL-TAR TO THE
PRESERVATION OF MEAT AND VEGETABLES. BY M. ROBIN.
When the flesh of animals, entire birds with the feathers, vege-
tables, fruits, &c. are placed in air-tight vessels filled with water, at
the bottom of which there is a little oil of coal-tar, so that the sub-
stances to be preserved are covered by the water, which becomes
charged with the vapour of the oil evaporating at the ordinary tem-
perature, they are perfectly preserved from decomposition. — -Comptes
Rendus, vol. xxxii. p. 650. '.'-"^ ''';; ,^,
METEOROLOGICAL OBSERVATIONS FOR AUG. 1851.
Chiswick. — August!. Cloudy and warm: slight rain. 2 — 5. Very fine. 6. Fine:
densely clouded. 7. Overcast: fine : clear : lightning at night. 8. Very fine.
9. Overcast : cloudy. 10. Cloudy. 13. Sultry. 14. Fine : lightning at night.
15. Cloudy and fine. 16. Very fine. 17. Showery. 18. Cloudy and fine: clear.
19. Very fine: slight haze : clear. 20, 21. Very fine. 22. Very hot. 23. Over-
cast. 24. Heavy showers, with sunny intervals. 25. Very fine. 26. Slight rain.
27. Fine : constant and very heavy rain at night. 28. Fine : densely clouded.
29. Clear and cold : heavy showers, with hail in afternoon: overcast, . 80, 31.
Cloudy.
Mean temperature of the month 62°"84
Mean temperature of Aug. 1850 59 '38
Mean temperature of Aug. for the last twenty-five years . 62 '21
Average amount of rain in Aug 2*41 inches.
Boston — Aug. 1. Cloudy: rain p.m. 2 — 4. Fine. 5 — 7. Cloudy. 8. Fine.
9 — 11. Cloudy. 12. Fine. 13. Cloudy: rain early a.m., and lightning p.m.
14. Fine: rain, thunder and lightning p.m. 15. Fine. 16. Fine: rain p.m.
17. Fine. 18. Cloudy. 19. Fine. 20. Cloudy. 21,22. Fine. 23. Cloudy:
rain a.m. 24. Cloudy : rain p.m. 25. Fine. 26. Cloudy : rain p.m. 27. Cloudy.
28. Fine : rain early A.M. 29. Cloudy : rain a.m. and p.m. 30,31. Cloudy.
Sandwich Manse, Or kiiet/. — Aug. 1. Bright : showers. 2. Cloudy. 3. Bright:
clear. 4. Bright : very clear : fine. 5. Clear : fine: very clear : fine. 6. Clear :
fine : very clear : fine : aurora. 7. Clear : fine ; haze. 8. Cloudy. 9, 10. Cloudy :
bright. 11. Cloudy: drops. 12. Drizzle : damp. 13. Rain : damp. 14. Rain :
drops: fine. 15. Drops: damp. 16. Clear: fine. 17. Cloudy: clear: fine.
18. Clear : cloudy. 19. Rain: cloudy. 20. Hazy : fine. 21. Rain. 22. Damp:
cloudy. 23. Bright : cloudy : thunder. 24. Clear : cloudy. 25. Bright : clear.
26—28. Showers. 29. Showers : drizzle : showers. 30. Bright : clear : aurora.
31. Drizzle : clear : aurora.
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THE
LONDON, EDINBURGH and DUBLIN
¥l[f LOSOPHICAL MAGAZrlfE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
NOVEMBER \m\. — -»
,1 j|
1 1.
LI. On the Polarity of Bismuth, including an Examination of the
Magnetic Field. By John Tyndall, PLD."^ : |.
1. ^T^HE polarity of bismuth is a subject on which philoso-
JL phers have differed and continue to differ. On the one
side we have Weber, Foggendorff, and Pliicker, each affirming
that he has established this polarity ; on the other side w^e have
Faraday, not affirraing the opposite, but appealing to an in- ^-S
vestigation w^hich is certainly calculated to modify whatever con- 'j|.
viction the results of the above-named experimenters might have
created. It will probably have occurred to everybody w^ho has
occupied himself experimentally with diamagnetic action, that
whenever the simple mode of permitting the body experimented : |r J
with to rotate round an axis passing through its own centre of ' ^ i
gravity, can be applied, it is preferable in point of delicacy to all > ^"q
others. A crystal of calcareous spar, for example, when sus- | «. §.
pended from a fine fibre between the poles, readily exhibits its j c ,
directive action, even in a field of weak power ; while to establish \ c X
that peculiar repulsion of the mass which is the cause of the 1 ^^
directive action, even with high power and with the finest torsion
balance, is a matter of considerable difficultyf. These considera- .
=^3
^:^
r
* Communicated by the Author.
t Phil. Mag. 4th series, vol. ii. )). 175. I have much pleasure in re-
ferring here to the following remark of Professor W. Thomson in his paper
" On the Theory of Magnetic Induction," which appears in the Phil. Mag.
for March last. " Thus," he writes, " a ball cut out of a crystal of pure | Z'
calcareous spar which tends to turn -with its optic axis perpendicular to • *^.
the lines of force, and which tends as a whole from places of stronger to I '%
places of weaker force, would experience this latter tendency more strongly \ *i
when the optic axis is perpendicular to the lines of force than when it is I '%
parallel to them ; since, according to § 8 of the text, the crystal must have • | $
the greatest inductive capacity, or (the language in the text being strictly
Phil Mag. S. 4. Vol. 2. No. 12. Nov, 1851. 2 A
V
334 Dr. Tyndall on the Polarity of Bismuth,
tions, together with the fact of having in my possession a piece
of bismuth, whose peculiar structure suggested the possibihty of
submitting the question of diamagnetic polarity to an additional
test, are the inducements in which the present brief inquiry
originated.
2. In December 1847 a paper on 'Diamagnetic Polarity* was
read before the Academy of Sciences in Berlin by Professor Pog-
gendorff, the result arrived at by the writer being, that a bis-
muth bar, suspended horizontally and occupying the equatorial
position between two excited magnetic poles, was transversely
magnetic, — that side of the bar which faced the north pole pos-
sessing north polarity, and that side which faced the south pole
possessing south polarity ; the excitation being thus the oppo-
site of that of iron, and in harmony with the original conjecture
of Faraday.
3. The method adopted by the writer was as follows : — the
bismuth bar was suspended within a helix of copper wire, the
coils of which were perpendicular to the axis of the bar. The
helix was placed between the opposite poles of a magnet, so that
the axis of the hehx was perpendicular to the line joining the
poles. The bismuth took up the usual equatorial position, its
length thus coinciding with the axis of the helix. On sending
algebraic when negative quantities are concerned) least capacity for diamag-
netic induction perpendicular to the optic axis. I am not aware that this
particular conclusion has been verified by any experimenter," &c. Since
the above was written the diflferential action of calcareous spar has been
estabhshed ; and up to a day or two ago, when I subjected Mr. Thomson's
paper to a more cai-eful perusal, my impression was that his theory and my
experiments perfectly harmonized. I now fear that there must be some
misapprehension on my part as regards his meaning, for not only do the
results of my investigation seem to be at variance with his conclusion, but
the conclusion appears to be at variance with the experiment of Professor
Faraday quoted by himself. This is written with some diffidence, as the
manner in which Mr. Thomson has stated Mr. Faraday's experiment proves
that he clearly comprehends the particular result obtained. The repulsion
which a sphere of calcareous spar endures at any particular point may, I
think, be taken as a coiTect measure of its * tendency ' to move from that
point ; but it has been proved that the repulsion of a sphere of calcai*eous
spar when the optic axis is parallel to the lines of force (parallel to the
axis of the soft iron core w hich repels it) being represented bv the number
67, the repulsion experienced when the optic axis is perpendicular to the
lines of force will be represented by the number 61 (see Phil. Mag. for
Sept. p. 176). The * tendency' to pass from stronger to weaker places of
force is therefore stronger when the optic axis is parallel to the lines of force
than when it is perpendicular to them, which is a conclusion precisely the
reverse of that expressed by Mr. Thomson. I would here, however, repeat
my conviction, either that 1 misunderstand Mr. Thomson, or that through
some excusable inadvertence, perhaps through a typographical error, each of
the words 'parallel ' and * perpendicular' occupies the place which should
be occupied by the other. — J. T.
including an Examination of the Magnetic Field. 335
an electric current through the latter the bar was weakly de-
flected in a certain direction, and on reversing the current, a
feeble deflection in the opposite direction was observed. The
deflection was such as must follow from the supposition, that
the north pole of the magnet had excited a north pole in the
bismuth, and the south pole of the magnet a south pole.
4. It will be at once seen that a considerable mechanical dis-
advantage was connected with the fact that the distance from
pole to pole of the transverse magnet was very short, being
merely the diameter of the bar. If a piece of bismuth, instead
of setting equatorial, could be caused to set axial, a mechanical
couple of far greater power would be presented to the action of
the surrounding current. Now it is well known that bismuth
sets in the magnetic field with the plane of most eminent clea-
vage equatorial ; hence the possibility, that if a bar of bismuth
could be obtained with the said plane of cleavage perpendicular
to its length, the directive power of such a bar might be sufii-
cient to overcome the tendency of its ends to proceed from
stronger to weaker places of magnetic action and to set the bar
axial. After repeated trials of melting and cooling in the labo-
ratory of Professor Magnus in Berlin, I succeeded in obtaining a
plate of this metal in which the plane of most eminent cleavage
was perpendicular to the flat surface of the plate, and perfectly
parallel to itself throughout. From this plate a little cylinder,
an inch long and 0'2 of an inch in diameter, was cut, which being
suspended horizontally between the excited poles turned strongly
into the axial position, thus deporting itself to all appearance as
a bar of iron.
5. About 100 feet of copper wire overspun with silk were
wound into a helix of such a dimension that the cylinder was
able to swing freely within it ; through a little gap in the side of
the helix a fine silk fibre descended, to which the bar was attached ;
to prevent the action of the bar from being disturbed by casual
contact with the little fibrous ends protruding from the silk, a
coating of thin paper was gummed to the interior.
6. The helix was placed between the flat poles of an electro-
magnet, so that the direction of its coils was from pole to pole.
It being first ascertained that the bar moved without impedi-
ment, and that it hung perfectly horizontal, the magnet was ex-
cited by two of Bunsen^s cells ; the bar was immediately pulled
into the axial line, being in this position parallel to the sur-
rounding coils. A current from a battery of six cells was sent
through the helix, so that the direction of the current, in the
upper half of the helix , was from the south pole to the north pole
of the magnet. The cylinder, which an instant before was
motionless, was deflected, forming at the limit of its swing an
angle of 70° with its former position ; the final position of equi-
2A2
336 Dr. Tyndall on the Polarity of Bimuth,
librium for the bar was at an angle of 85°, or thereabouts, with
the axial line.
7. Looking from the south pole towards the north pole of the
magnet, or in the direction of the current as it passed over the
bar, that end of the bar which faced the south pole swung to the
left:
8. The current through the helix being interrupted and the
bar brought once more to rest in the axial position (which of
course is greatly facilitated by the proper opening and closing of
the circuit), a current was sent through in the opposite direc-
tion, that is from the north pole to the south ; the end of the
bar, which in the former experiment was deflected to the left,
was now deflected an equal quantity to the right. I have re-
peated this experiment a great number of times and on many
difterent days with the same result.
9. In this case the direction of the current by which the
magnet was excited was constant, that passing through the helix
which surrounded the bismuth cylinder being variable. The
same plijenomena are exhibited if we preserve the latter constant
and reverse the former.
10. A polar action seems undoubtedly to be indicated here ;
but if a polarity be inferred, it must be assumed that the north
pole of the magnet excites a south pole in the bismuth, and the
south pole of the magnet a north pole in the bismuth ; for by
reference to the direction of the current and the concomitant
deflection, it will be seen that the deportment of the bismuth is
exactly the same as that which a magnetized needle freely
suspended between the poles must exhibit under the same
circumstances.
11. The bar of bismuth was then removed, and a little bar of
magnetic shale was suspended in its stead ; it set axial. On
sending a current through the surrounding helix, it was de-
flected in the same manner as the bismuth. The 'piece of shale
was then removed and a little bar of iron was suspended within
the helix ; the residual magnetism which remained in the cores
after the cessation of the exciting current was sufficient to set
the bar axial ; a veiy feeble current was sent through the helix
and the deflection obsenxd, — it was exactly the same as that of
the bismuth and the shale.
12. These results being different from those obtained by
M. Poggendoi'ff', I repeated his experiment with all possible care.
A bar of ordinary bismuth, an inch in length and about 0*2 of
an inch in diameter, was suspended within the helix ; on exciting
the magnet, it receded to the equator and became finally steady
there, llie axis of the bar thus coincided with the axis of the
helix. A current being sent through the latter, the bar wai
distinctly deflected. Supposing an observer to stand before the
including an EMmination of the Magnetic Field. 337
magnet,, with the north pole to his right and the south pole to
his left, then when a current passed through the upper half o£
the coil from the north to the south pole, that end of the bis-
muth which was turned towards the observer was deflected
towards the north pole ; and on reversing the current, the same
end was deflected towards the south pole. This seems entirely
to agree with the former experiment. When the bar hung equa-
torial between the excited poles, on the supposition of polarity
the opposite ends of all its horizontal diameters were oppositely
polarized. Fixing our attention on one of these diameters, and
supposing that end which faced the north pole of the magnet to
be gifted with south polarity^ and the end which faced the south
pole endowed with north polarity, we see that the deportment
to be inferred from this assumption is the same as that actually
exhibited ; for the deflection of a 'polarized diameter in the same
sense as a magnetic needle, is equivalent to the motion of the end
of the bar observed in the experiment.
13. The following test, however, appears to be more refined
than any heretofore applied. Hitherto we have supposed the
helix so placed between the poles that the direction of its coils
was parallel to the line which united them ; let us now suppose
it turned 90° round, so that the axis of the helix and the line
joining the poles may coincide. In this position the planes of
the coils are parallel to the planes in which, according to the
theory of Ampere, the molecular currents of the magnet must
be supposed to move ; and we have it in our power to send a
current through the helix in the same direction as these mole-
cular currents, or in a direction opposed to them. Supposing
the bar first experimented with suspended within the coil and
occupying the axial position between the excited poles, a cur-
rent in the helix opposed to the molecular currents of the magnet
will, according to the views of the German philosophers before
named, be in the same direction as the currents evoked in the
bismuth : hence such a current ought to exert no deflecting in-
fluence upon the bar ; its tendency, on the contrary, must be to
make the bar more rigid in the axial position. A current, on
the contrary, whose direction is the same as that of the molecular
currents in the magnet, will be opposed to those evoked in the
bismuth ; and hence, under the influence of such a current, the
bar ought to be deflected.
14. The bar at first experimented with was suspended freely
within the hehx, and permitted to come to rest in the axial posi-
tion. A current was sent through the helix in the same direc-
tion as the molecular currents of the magnet, but not the slight-
est deflection of the bar was perceptible ; when, however, the
current was sent through in the opposite direction, a very distinct
deflectiou WM the consequence : by interrupting th^ cu^yent
338
Dr. Tyndall on the Polarity of Bismuth,
whenever the bar reached the limit of its swing, and closing it
when the bar crossed the axial line, the action could be increased
to such a degree as to cause the bar to make an entire rotation
round the axis of suspension. This result is diametrically opposed
to the above conclusion — here again the bismuth bar behavea
like a bar of iron.
15. These experiments seem fully to bear out the theory ad-
vanced by M. von Feilitzsch in his letter to Mr. Faraday*. He
endeavours to account for diamagnetic action on the hypothesis
that its polarity is the same as that of iron ; " only with this dif-
ference, that in a bar of magnetic substance the intensity of the
distribution over the molecules ina^eases from the ends to the
middle, while in a bar of diamagnetic substance it decreases from
the ends to the middle.^' So far as I can see, however, the rea-
soning of M. von Feilitzsch necessitates the assumption, that in
the self-same molecule the poles are of unequal values, that the
intensity of the one is greater than that of the other, an assump-
tion which will find some difficulty of access into the speculations
of most physicists. A peculiar directive action might be readily
brought about by the distribution of magnetism assumed by
M. von Feilitzsch ; but up to the present time I see no way of
reconciling the repulsion of the total mass of a piece of bismuth
with the idea of a polarity similar to that of iron.
16. During these inquiries, an observation of Mr. Faraday
perpetually recurred to me. " It appeared to me,^^ he writes f,
" that many of the results which had been supposed to indicate
a polar condition were only consequences of the law that diamag-
netic bodies tend to go from stronger towards weaker places of
action.^' The question here arose, whether the various actions
Fig. 1.
observed might not be
explained by reference
to the change effected
in the magnetic field
when it is intersected by
an electric cun*ent. The
distribution of magnetic
intensity between the
poles will perhaps be
rendered most clear by
means of a diagi*am.
Let AB represent the
distance between the
polar faces ; plotting the
intensity at every point
in AB as an ordinate from that point, the line which unites the
ends of all these ordinates will express the magnetic distribution.
♦ Fhil. Mag., S. 4. vol. i. p. 46. f Ibid., S. 3. vol. xxxvii. p. 89.
including an Ewamination of the Magnetic Field. 339
Suppose this line to be cde. Commencing at A, the intensity of
attraction towards this face decreases as we approach the centre dj
and at this point it is equihbrated by the equal and opposite
attraction towards B. Beyond c? the attraction towards A be-
comes negative^ that is, it is now in the direction c?B. The point
d will be a position of stable equilibrium for a diamagnetic sphere,
and of unstable equilibrium for a magnetic sphere. But if,
through the introduction of some extraneous agency, the line of
distribution be shifted, say to c'c^V, the point d will be no longer
a position of equilibrium ; the diamagnetic sphere will move from
this point to d', and the magnetic sphere will move to the pole A.
17. For the purpose of investigating whether any change of
this nature takes place in the magnetic field when an electric
current passes through it, I attached a small sphere of carbonate
of iron to the end of a slender beam of light wood ; and balan-
cing it by a little copper weight fixed to the other end, the beam
was suspended horizontally from a silk fibre. Attaching the
fibre to a moveable point of suspension, the little sphere could
be caused to dip into the interior of the helix as it stood between
the poles, and to traverse the magnetic field as a kind of feeler.
The law of its action being that it passes from weaker to stronger
places of force, we have in it a ready and simple means of testing
the relative force of various points of action. The point of the
beam to which the fibre was attached being cut by the axis of
the helix produced, and the sphere being also on the same level
with the axis, when the magnet was excited* it passed into the
position occupied by the hard line in fig. 2, thus resting against
the interior of the helix a little within
its edge. On sending a current
through the helix, which in the upper
half thereof had the direction of the
arrow, the sphere loosed from its
position, sailed gently across the field,
and came to rest in the position of
the dotted line. If, while thus sail-
ing, the direction of the current in
the helix, or of the current by which the magnet was excited,
became reversed, the sphere was arrested in its course and brought
back to its original position. In like manner, when the position
of the sphere between the poles was that of the dotted line, a
current sent through the helix in a direction opposed to the
arrow, caused the sphere to pass over into the position of the
hard line.
18. The sphere was next introduced within the opposite edge
* One of Bunsen's cells was found sufficient; when the magnetic power
was high, the change caused by the current was not sufficient to deflect
the beam.
340
Dr. Tyadall on ilie Polarity of Bismuth,
Fig. 3.
ilH
-^ — «^
s
1
1 ^
N
4
|5
of the h^ix (fig. 3). Oil exciting tbc
maguet, the beam came to rest in tlie
position of the hard hne ; on sending a
cun-ent through the hehx in the direc-
tion of the arrow, the sphere loosed,
moved towards the north pole, and
came to rest in tlie dotted position.
If while in this position either the
current of the magnet or the current of the helix was reversed,
the sphere went back; if both were reversed simultaneously, the
sphere stood still.
19. From these facts we learn, that if the magnetic field be
dividedintofourcompartments, asinfig. 4, Y\£c 4
the passage of an electric current through a
helix placed therein, the direction of the cur-
rent in the upper half of the helixbeingthat
indicatedby the arrow, will weaken the force
in the first and third quadrants, but will
strengthen it in the second and fourth. With the aid of this
simple fact we can solve every experiment made with the bismuth
bars. In (12.), for instance, it was found that when an observer
stood before the magnet with a north pole to his right and a
South pole to his left, a current passing through the upper half
of the helix from the north to the south pole deflected a bar of
ordinary bisnmth, which had previously stood equatorial, so that
the end presented to the observer moved towards the north pole.
This deportment might be inferred from the constitution of the
magnetic field; the bar places its ends in quadrants 1 and 3,
that is, in the positions of weakest force.
20. The experiments (7, 8.) with the other bar are capable of
an explanation just as easy. Preserving the arrangement as in
the last figure, the bismuth bar, which previously stood axial,
would be deflected by the surrounding current, so that its two
ends would occupy the quadrants 2 and 4, that is, the positions
of strongest force. Now this is exactly what they did in the
magnetic field before the passage of any current, for the bar set
axial. It was first proved by Mr. Faraday, that the mass of a
bismuth ciystal was most strongly repelled when the repulsive
force acted parallel to the planes of most eminent cleavage ; and
in the magnetic field the superior repulsion of these planes causes
them always to take up that position where the force is a mi-
nimum. It is the equatorial setting of these planes which
causes the bar at present under consideration to set axial. The
planes of cleavage being thus the true indicators, we see that
when these set from the first to the third quadrant, or in the line
of weakest action, the ends of the bar must necessarily occupy
the second and fourth, which is the deportment obseiTcd.
including an Examindtidn of the Magnetic Field, 341
^1. The little test-sphere can also be made available for ex-
amining the change brought about in the magnetic field by the
introduction of a small bar of iron^ as in the experiment of
M. Pliicker quoted by Mr. Faraday*. Removing the helix from
the magnetic field, the little sphere was at liberty to traverse it
from wall to wall. When the magnet was excited, the sphere
passed slowly on to the pole to which it was nearest and came to
rest against it. When forcibly brought into the centre of the
magnetic field, after a moment's apparent hesitation it passed to
one pole or the other with a certain speed ; but when a bar of
iron was brought underneath while it was central, this speed was
considerably increased. Over the centre of the bar there was a
position of unstable equilibrium for the sphere, from which it
passed right or left, as the case might be, with greatly increased
velocity. The distribution of
the force appears in this case «>^f\ '^*'^' i^HM^ -^^^ "'"^j' • ■
to have undergone a change ^s,^^ ; '^"^^ f* '^^^^' 'i"^ l)'^3j>oibiii
represented by the line gef iirii)>H4p imm bxiu jh ill v^ib J^
in the diagram. From the ;.. .X^mu .> \ ^cn.y■2^vii%^
centre towards the poles ^ ''^^
the tension steepens sud-
denly, the quicker reces-
sion of a bismuth bar to- -^ J^ ^'^^
wards the equator, as ob
'Dili ijfo'i:
served by M. Pliicker, being isirar^s*iq.i3i54i ifitMiie/r <il4w iitBiiK
the natural consequence. ' " ■'' '""'"' "^ • <>* fcdto^a&iq
22. Assuming the law i^itn inomi'ioqal) aiflT
of action for a small magnetic sphere to be that' it proceeds from
weaker to stronger places of force, we find that the passage of an
electric current in the manner described so modifies the ' field/
that the positions of its two diagonals are of unequal values as
regards the distribution of the force, the portion of the field in-
tersected by the diagonal which bisects 1 and 3, fig. 4, being
weaker than the portion intersected by the diagonal which bisects
2 and 4. But here the believer in diamagnetic polarity may
enter his protest against the use which we have made of the
assumption. " I grant you,'' he may urge, '' that in a simple
magnetic field, consisting of the space before and around a single
pole, what you assume is correct, that a magnetic sphere will
pass from weaker to stronger places of action ; but for a field
into which several distinct poles throw their forces, the law by
no means sufficiently expresses the state of things. If we place
together two poles of equal strengths but of opposite qualities
close to a mass of iron, it is an experimental fact that there is
almost no attraction ; and if they operate upon a mass of bis-
muth^ there is no repulsion. Why ? Do the magnetic rays^ to
V. .; J :.. * Phil. Mag., S, 3. vol. xxxvii. p. 104.
S42 Dr. Tyndall on the Polanty of Bismuth,
express the thing popularly, annul each other by a species of
interferenee before they reach tJie body ; or does one pole induce
in the body a certain condition upon which the second pole acts
in a sense contrary to the former, both poles thus exactly de-
stroying each other ? If the former, then I grant you that the
magnetic field is rendered weaker, nay deprived of all force if
you will, by the introduction of the second pole ; but if the
latter, then we must regard the field as possessing two systems
of forces ; and it is to the peculiar inductive property of the
body, in virtue of which one system neutralizes the other, that
we must attribute the absence of attraction or repulsion. Once
grant this, however, and the question of diamagnetic polarity, so
far as you are concerned, is settled in the affinnative.''
23. Our hypothetical friend mentions it as ' an experimental
fact/ that if dissimilar poles of equal strengths operate upon a
mass of bismuth there is no repulsion. This was Reich's result —
a result which I have carefully tested and corroborated. I shall
now proceed to show the grounds which the believer in diamag-
netic polarity might urge in support of his last assertion. A
twelve-pound copper helix was removed from the limb of an
electro-magnet and set upright. A magnetized sewing-needle
being suspended from one end, the other end was caused to dip
into the hollow of the spiral, and to rest against its interior
surface. When a cun*ent was sent through the helix in a certain
direction, the needle was repelled towards the axis of the coil ;
the same end of the needle, when suspended at half an inch
distance from the exterior surface of the coil, was drawn strongly
up against it. AVhen the current was reversed, the end of the
needle was attracted to the interior surface of the coil, but re-
pelled from its exterior surface. If we suppose a little mannikin
swimming along in the direction of the current, with his face
towards the axis of the helix, the exterior surface of that end
towards which his left arm would point repels the north pole of
a magnetic needle, while the interior surface of the same end
attracts the north pole of a magnetic needle. The complemen-
tary phsenomcna were exhibited at the other end of the helix.
Thus if we imagine two observers placed, the one within and
the other without the coil, the same end thereof would be a north
pole to the one and a south pole to the other.
24. If we apply these facts to the case of the helix within the
magnetic field, we see that each pole of the magnet had two
contrary poles of the helix in contact with it ; and we moreover
find that the quadrants which we have denominated the strongest
are those in which the poles of magnet and helix were in conjunc-
tion; while the quadrants which we have called weakest are
those in which the poles of magnet and helix were in opposition.
25. ^' Which will you choose ?'' demands our hypothetical
including an Examination of the Magnetic Field. 343
friend ; " either you must refer tlie weakening of a quadrant to
magnetic interference, or you must conclude, that that induced
state, whatever it be, which causes the bismuth to be repelled by the
magnet, causes it to be attracted by the coil, the resultant being
the difference of both forces. In the same manner the strengthen-
ing of a quadrant is accounted for by the fact, that here the in-
duced state which causes the bismuth to be repelled by the
magnet Causes it to be repelled by the coil also, the resultant
being the sum of both forces. The matter may be stated still
more distinctly by reference to Eeich^s experiments*. He
found that when a bundle of magnet-bars was brought to bear
upon a diamagnetic ball suspended to the end of a torsion
balance, when similar poles were presented to the body, there was
a very distinct repulsion ; but if one half of the poles were north
and the other half south, there was no repulsion. Let us imagine
the two halves to be brought to bear upon the ball consecutively;
the first half will cause it to recede to a certain distance ; if the
second unlike half be now brought near, the ball will approach again,
and take up its original position. The question therefore appears
to concentrate itself into the following : — Is this ' approach '
due to the fact that the magnetic forces of the two halves annul
each other before they reach the ball, or is it the result of a
compensation of inductions in the diamagnetic body itself ? If
a sphere of soft iron be suspended from a thread, the north pole
of a magnet will draw it from the plumb-line ; if the south pole
of an exactly equal magnet be brought close to the said north
pole, the sphere will recede to the plumb-line. Is this recession
due to a compensation of inductions in the sphere itself, or is it
not ? If the former, then, by all parity of reasoning, we must
assume a similar compensation on the part of the bismuth.^^
26. That bismuth, and diamagnetic bodies generally, suffer in-
duction, will, I think, appear evident from the following consi-
derations. The power of a magnet is practically ascertained by the
mechanical effect which it is able to produce upon a body pos-
sessing a constant amount of- magnetism, — a hard steel needle,
for instance. The action of a magnet in pulling such a needle
from the magnetic meridian may be expressed by a weight which
acts at the end of a lever of a certain length. By easy practical
rules we can ascertain when the pull of one magnet is twice or
half the pull of another, and in such a case we should say that
the former possesses twice or half the strength of the latter. If^
however, these two magnets, with their powers thus fixed, be
brought to bear upon a sphere of soft iron, the attraction of the
one will be four times or a quarter that of the other. The
strengths of the magnets being, however, in the ratio of 1 : 2, this
attraction of 1 : 4 can only be explained by taking into account
* Phil. Mag., S. 3. vol. xxxiv. p. 127.
344 Dr. Tyndall on the Polarity of Bismuth.
the part played by the sphere itself. We are compelled to regard
the sphere as an induced magnet, whose power is directly pro-
portional to the inducing one. Were the magnetism of the
sphere a constant quantity, a magnet of double power could only
produce a double attraction ; but the fact of the magnetism of
the sphere varying directly as the source of induction leads us
inevitably to the law of squares; and conversely, the law of
squares leads us to the conclusion that the sphere has been
induced.
27. These sound like truisms; but if they be granted, there is no
escape from the conclusion that diamagnetic bodies are induced ;
for it has been proved by M. E. Becquerel and myself*, that the
repulsion of diamagnetic bodies follows precisely the same law as
the attraction of magnetic bodies ; the law of squares being true
for both. Now were the repulsion of bismuth the result of a
force applied to the mass alone, without induction, then, with a
constant mass, the repulsion must be necessarily proportional to
the strength of the magnet. But it is proportional to the square
of the strength, and hence must be the product of induction.
28. In order to present magnetic ph^enomena intelligibly to
the mind, a material imagery has been resorted to by philoso-
phers. Thus we have the ^magnetic fluids ' of Poisson and the
' lines of force ' of Mr. Faraday. For the former of these Pro-
fessor W. Thomson has recently substituted an ' imaginary mag-
netic matter.' The distribution of this ' matter ' in a mass of
soft iron, when operated on by a magnet, has attraction for its
result. We have the same necessity for an image in the case of
bismuth. If we imagine the two magnetic matters which are
distributed by induction on a piece of iron to change places, we
have a distribution which will cause the phsenomena of bismuth.
Hence it is unnecessaiy to assume the existence of any new
matter in the case of diamagnetic bodies, the deportment being
accounted for by reference to a peculiarity of distribution. Fur-
ther, the experiments of lleich, which prove that the matter
evoked by one'pole will not be repelled by an unlike pole, compel
us to assume the existence of two kinds of matter, and this, if I
understand the term aright, is polarity.
29. During this inquiry I changed my mind too often to be
over- confident now in the conclusion at which I have arrived. Part
of the time I was a hearty subscriber to the opinion of Mr. Fara-
day, that there existed no proof of diamagnetic polarity ; and if
I now differ from that great man, it is with the honest wish to be
set right, if through any unconscious bias of my own I have
been led either into errors of reasoning or misstatements of facts.
Queenwood College,
Oct. 1851.
* Phil. Mag., Sept. 1851.
'^^ LII. On the Combination of Arsenious Acid with Albumeni^^^^
-oiq ^ijouiib ^2^ Thornton J. Herapath, Esq,"^ > >K>iiq«^6Ati
jVrOT a little controversy has recently occurred amongst cKe-
i-^ mists with regard to the nature of the combination which
is stated to take place between arsenious acid and albumen.
According to Prof. Liebigf, these two bodies combine in atomic
proportions, and it is owing, he says, to this circumstance that the
vitality of the organs is destroyed in cases of arsenical poisoning.
The same opinion, it seems, is entertained by Dr. Sheridan Mus-
pratt of Liverpool, who has lately published some results J which
certainly appear to establish the truth of the hypothesis. Other
chemists, on the contrary, say that this statement of Liebig^s is
founded on error — that arsenious acid does not, under any cir-
cumstances, form a true chemical combination with albumen,
and is only separated by the latter substance from its solutions
by a species of mechanical action ; that is to say, somewhat in the
same manner, perhaps, as iodine and many vegeto-alkaloids are
well known to be absorbed and extracted from their solutions by
animal charcoal. In evidence, they adduce the results of Mr.
Edv/ards^s experiments, an account of which was published some
few months back in the Transactions of the Chemical Society of
London §. According to this latter experimentalist, the whole
of the arsenious acid may be readily extracted from the compound
by means of boiling water, provided the operator takes care
" thoroughly to break up the mechanical network of the coagu-
late " (I adopt his own expression), by trituration with a pestle
^nd mortar.
'^,, A short time ago, my attention was drawn to the subject by
my father. Prof. W. Herapath, who desired me to repeat the ex-
periments above referred to, with the view, if possible, of deciding
the question, as it was one which he considered of much interest,
in consequence of its bearings on Toxicology. I accordingly did
so. My results may be summed up as follows.
Experiment I. — 499 grains of the glairy albumen of eggs
were taken and intimately mixed, by long-continued trituration,
with 3-0 grs. of arsenious acid ; the latter having been previously
dissolved in a quantity of water sufficient to effect a perfect solu-
tion. The mixture was then coagulated by heat, and afterwards
carefully evaporated to dryness in a water-bath. The yellowish
residue thus obtained was reduced to a very fine powder in a
mortar, and repeatedly digested, for sexei;al, hours to^et)|er,,iu
* Communicated by the Author. - v. ^ > ... , .
t Organic Chemistry, part 2. chap. xiv. p. 358. ,
X Quart. Journ. of the Chem. Soc. of London, No. xiv. p. 178. "^^^
§ Ibid. No. ix. p. 14. .of.T^r«'MMJp
346 Mr. T. J. Herapath on the Combination of
boiling water ; care being taken to reduce the compound to a
still more minute state of division, by patient trituration in a
mortar, after each digestion, &c, The washings, on being treated
by Rcinsch^s process, were found to contain a large propoi-tion
of arsenious acid.
The insoluble residue having been digested in water for about
twelve or fifteen hours, as before described, was dried and weighed.
It amounted to about 29 grs.* It was then boiled in strong
hydrochloric acid, when it dissolved with the characteristic
colour of the proteine compounds. Upon testing this solution in
the usual manner, only exceedingly minute traces of arsenic
could be detected ; a quantity insufficient to yield, on oxidation,
a perceptible sublimate of arsenious acid.
Eocperiment II. — According to the authorities above referred to,
61*07 grms. of albumen will combine with 0'38Ggrm. of arsenious
acid =0*G32 per cent. If this statement be correct, I argued, of
course if I make a mixture of these two substances, so arranging
my experiment that the arsenious acid shall not be present in such
large quantity, or in other words, if I employ an excess of albu-
men, and evaporate the compound to dryness, no trace of ar-
senious acid ought to be extracted from the mass upon subse-
quent digestion in boiling water. 438*5 grs. of glairy albumen
were therefore mixed with an aqueous solution of arsenious acid,
containing 0*25 gr. of AsO"^. The mixture was evaporated to
dryness in a gas-oven, and the brittle residue thus obtained
treated as in the preceding experiment. The washings, when
tested by Reinsch^s process, gave evident tokens of the presence
of a large quantity of arsenic. The insoluble residue, however,
when decomposed in the usual manner by sulphuric acid and
heat, and afterwards introduced into Marshes apparatus, gave
but very faint stains of metallic arsenic.
Escperiments III., IV, and V. — The same experiments repeated,
different proportions of arsenious acid and albumen only being
employed. Similar results were obtained.
Experiment VI, — Experiment II. repeated, the same quan-
tities of arsenious acid and albumen being used. Instead of
evaporating the mixture to diyness, however, as before, it was
merely heated to the boiling-point and then filtered, in order to
separate the coagulum which was formed. This latter was then
divided into two portions ; one of these was treated by Reinsch's
process, and found to contain sensible quantities of arsenic, as
did also the liquid from which the coagulate had been separated,
in cither case bright steel-gray stains being formed upon the
* It must be understood, however, that this quantity does not represent
the whole of the albumen contained in the white of egg employed; a por-
tion was undoubtedly lost during the long-continued washing.
Arsenious Acid with Albumen. 347
copper ; the other half, on the contrary, was triturated for several
minutes in a mortar with about twice its weight of pure quartzose
sand, afterwards boiled in water^ and treated as in the former
experiments. Upon subsequently testing it by Reinsch's process,
only very faint and doubtful traces of arsenic were discovered.
Experiment VII. — 483 grs. of albumen were mixed with
3*0 grs. of dissolved arsenious acid. The mixture was then
coagulated by heat and treated as before. The washings having
been carefully collected and evaporated to dryness left a yellowish
residue, which was redissolved in boiling water. The latter solu-
tion was filtered, in order to remove some few ilocculi of albumen
which had passed through the pores of the muslin strainer ; it
was then acidulated with hydrochloric acid, and treated with
sulphuretted hydrogen, a stream of which was passed through
it for some time, until the liquid smelt strongly of the gas. The
solution was boiled in order to dispel the excess of hydrosul-
phuric acid, and the precipitate of tersulphide of arsenic formed
separated by filtration. When dried at 212° F. it was found
to weigh 3-63 grs. = 2-921 grs. AsO^.
Experiment VIII. — This was undertaken with the view of
ascertaining whether arsenious acid really loses its poisonous
properties on admixture with albumen, as has been asserted.
The whites of three eggs, weighing altogether 1624 grs., were
mixed with water and 6*5 grs. of dissolved arsenious acid. The
mixture, having been evaporated to dryness, was finally commi-
nuted, mixed with food, and administered to a cat. Having eaten
about a fifth or a quarter of the powder, the animal refused to
take the remainder; in a short time it exhibited considerable
uneasiness, vomited repeatedly, and was soon afterwards attacked
with all the symptoms of arsenical poisoning. It lingered on,
however, in a state of extreme torment, for two or three days,
and then died, refusing food to the last, l^o post-mortem exami-
nation of the body was made ; my time being then much occu-
pied with other matters of importance.
As regards the above results, it is in my opinion quite unne-
cessary to offer any observations upon them, as they may be said
to speak for them selves. I shall therefore content myself with
relating the facts I have observed, and leave my readers to draw
their own conclusions.
Mansion House, Okl Park, Bristol,
May 16th, 1851.
IAH. -^n Account of the late Jobs Walsh of Cork. In a letter
from Professor Boole to Professor De Mobgan*.
My dear Sir, Cork, April 12, 1851.
A FTER an interval whicli you will, I fear, think to have been
•^^ needlessly protracted, I am at length able to transmit to
you some of those particulars vi^hich you have desired me to col-
lect respecting the life of the late John Walsh of Cork. What I
have to relate to you will constitute a remarkable, and in some
respects a melancholy story. This I say, not because I think
that there is evidence that the subject of my letter was on the
whole an unhappy individual ; on the contrary, he appears to
have been a man of cheerful habits and hopeful temperament ;
but because upon any serious view of life and of human concerns,
it must ever be a mournful spectacle to see earnestness and per-
severance and many of the nobler elements of character wasted
upon pursuits altogether void of any useful result. That Mr.
Walsh's labours were of this nature you will have already learnt
from the communications which he was in the habit of addressing
to you, and of which I have heard you speak ; but with what
unwearied ardour these labours were pursued, and of how abiding
a passion they were the fruit, you will only learn to estimate
from the facts which I have now to communicate to you. What-
ever may be thought of Mr. Walsh's abilities, you will feel it
impossible not to admire his singular application, and not to
regret that it was not directed to some more profitable if less
ambitious end.
I think it proper to premise that, for the information contained
in this letter, I am mainly indebted to Mr. K., now a scholar of
Queen's College, Cork, who was for some years a pupil of Mr.
Walsh, and to whom his instructor's books and manuscripts
were bequeathed. Mr. K. has been so good as to submit the
latter to my inspection, and has given me full permission to
make such use of them and of his own communications as I
think proper. I have also had the opportunity of conversing
with the physicians who attended Mr. Walsh during his last ill-
ness while a patient in one of the infirmaries, and finally in the
Union workhouse of this city, and from them I have received
much interesting information.
John Walsh was bom at Shandrum, on the border of the
County of Limerick, probably about the year 1786. His parents
were small farmers ; and the only education which he appears to
have received was from itinerant schoolmasters, a class of teach-
ers of humble rank, who resided, while imparting their little
stock of knowledge, with the parents of their pupils, and thus
* Communicated by Professor De Morgan.
Prof. Boole^s Account of the late John Walsh of Cork. 349
may have contributed to foster that respect for learning which
still characterizes the Irish peasant. Of his mother, Mr. Walsh
always spoke with great affection, attributing to her influence
his first love of letters. He also held in kind remembrance one
of his early school-fellows, John Harding, to whom in later life
he dedicated a little tract on '^^The General Principles of the
Theory of Sound. ^'
When about 28 years of age, John Walsh, in company with
Harding, removed to Gork. Necessity, however, compelled the
friends to separate. Walsh, who wrote a fine hand, an accom-
plishment which he stated that he owed to his mother^s instruc-
tion, obtained employment as a teacher of writing in ladies'
schools. He also received private pupils, and at a subsequent
period was engaged as writing-master in two respectable boys'
schools in the city. The teaching of writing and arithmetic
appears to have been his chief source of subsistence ; for although
he sometimes obtained pupils in the higher mathematics, this
was not a frequent occurrence. Mr. "Walsh is said to have been
a careful and diligent writing-master, and to have succeeded in
making his pupils in arithmetic understand and like the subject.
The few testimonies which I have heard of his abilities as a
teacher of the higher mathematics would not lead me to think
that he was equally successful there. He is stated to have been
too intent on enforcing his own peculiar views. Indeed there
can be little doubt, from an examination of his papers, that
upon this subject he laboured under a peculiar mental halluci-
nation. '^-^^^ ■f:Ui>i.>HU^U:
At what time Mr. Walsh began to write ori^'tn^hleiiik'tibal
topics I am not able to determine. By degrees, however, this
class of speculations appears to have absorbed his entire interest.
He became convinced that the differential calculus was a delu-
sion ; that Sir Isaac Newton was a shallow sciolist, if not an
impostor; and that the imiversities and academies of Europe
were engaged in the interested support of a system of error.
Whether this was a sudden conviction, or whether it was the
gradual result of the successive disappointments which he was
destined to endure in his attempts to convince the world how
misplaced its confidence had been, it is not easy to determine ;
but the latter is the more probable view. However this may
have been, Mr. Walsh was for a series of years engaged in a con-
stant endeavour to induce the principal learned societies of
Europe to print his communications. His posthumous papers
show that he was thus in frequent correspondence with the
Prench Academy, the Royal Societies of London and Edinburgh,
the Royal Irish Academy, and other similar bodies.
Pailing in every effort of this nature, he published at his own
PhiL Mac/, S. 4. Vol. 2, No. 12. Nov, 1851. 2 B
350 Prof. Boole's Account of the late Jolin Walsh of Cork,
expense a large number of tracts, in which he endeavoured to
establish his views, and denounced in no measured tenns the
unjust and selfish opposition which he thought that he had met
with. Of a considerable number of these tracts, and also of the
original manuscripts of them, I have found copies among his
papers, and a brief account of them may be interesting.
The printed tracts and papers are for the most part occupied
with the announcement of some discoveiy which was designed
to supersede the differential calculus in its application to pro-
blems respecting curves. The method in question consisted in
transferring the origin of coordinates to a point upon the curve,
developing the ordinate y in terms of the abscissa a?, and making
use of the coefficients of the expansion just in the same way as
the ordinary principles of the differential calculus would dii-ect
us to do. The titles of some of Mr. Walsh's papers will serve
to throw light on the particular objects which he had in view.
The equation of a curve transformed as above Mr. Walsh calls
its '' partial equation .''
" Memoir on the invention of Pai-tial Equations.'^
"The Theory of Partial Functions. Letter to the Right
Honourable Lord Brougham.^'
" Memoir on the Theory of Partial Functions.''
" Irish Manufactures. A new method of Tangents."
" An Introduction to the Geometry of the Sphere, Pyramid
and Solid Angles."
'^ General Principles of the Theory of Sound."
" The Normal Diameter in Curves."
" The Problem of Double Tangency."
" The Geometric Base."
"Letters to S. F. Lacroix, the Editor of the Edinburgh Re*-
view. Rev. F. Sadleir, &c."
" Dublin University. Notes on a Mathematical Controversy
between Dr. Lloyd the Provost, the Rev. Mr. Luby and Dr.
O'Brien, Fellows of the College, and Mr. Walsh, author of the
Geometric Base."
" The Theoretic Solution of Algebraic Equations of the Higher
Orders."
" Metalogia, &c."
The mere list of titles above given, and it is far from being
complete, affords evidence of considerable industry, and Mr.
Walsh's unpublished papers confirm this testimony. The fol-
lowing is an account of the principal ones : —
" llie Elements of Geometry, by John Walsh." (Folio.) This
merely contains a series of definitions and axioms, &c., beginning
with the " doctrine of ratio."
" On the Measurement of Infinite Space, and the Theory of
Prof. Boole^s Account of the late John Walsh of Cork. 351
Parallel Lines/^ (Folio.) A series of definitions, axioms, and
enunciations of propositions without proof annexed.
The definitions are headed by the motto " Space is Space,
Time is Time, Truth is Truth,^^ and the first of the so-called
definitions is '' Space and Time are infinite, coeternal, and can-
not be increased or diminished." For the rest, the propositions
appear to be those of Euchd expressed in another form, the word
'' angular plane " being used for angle.
" Memoir on the Calculus of Variations, showing its total
unreality."
" The Principles of Geometry." This consists of two books ;
the first, on the " Measurement of Infinite Space," apparently
the same as the second manuscript, but with demonstrations ap-
pended; the second on the *' Measurement of Bounded Space."
A manuscript in a brown paper cover, apparently a note-book
containing a series of mathematical speculations on the " mea-
surement of infinite space," the solution of equations of the
higher orders, the trisection of an angle, physical astronomy, &c.
In these, and in nearly all of Mr. Walsh's speculations which
I have taken the trouble to examine, one peculiarity of his mental
procedure is very observable. He takes up some known method
or formula of analysis, makes in it a slight and quite unimport-
ant change (for every theorem admits of some variety in the
mode of its expression), and views the result to which he is led
as an original discovery. Thus, in a page headed '' Cubic Equa-
tions," he writes the name of Cardan opposite to a well-known
algebraic solution, that of Walsh opposite to the same result put
under another and less convenient form, and below these he
gives a formula headed " For a complete Cubic by Walsh only."
It is related of the dramatic poet Wycherley, that in his old
age the functions of memory and of genius were so strangely
mingled and confused, that if verses were read to him in the
evening he would reproduce them the following morning with
all the effort of original composition, quite unconscious of the
source of his borrowed inspiration. Mr. Walsh committed
similar errors without the intervention of a sleep.
What importance Mr. Walsh attached to his supposed disco-
veries will appear from the following extract which I make from
the M S . note-book above referred to. It is not a solitary example.
'' Discovered the general solution of numerical equations of
the fifth degree at 114 Evergreen Street, at the Cross of Ever-
green, Cork, at nine o'clock in the forenoon of July 7th, 1844 ;
exactly twenty-two years after the invention of the Geometry of
Partial Equations, and the expulsion of the diff*erential calculus
from Mathematical Science."
Besides Mr. Walsh's own papers, there remain a large number
2B2
352 Prof. Boole'3 Account of the late John Walsh of Cork.
of letters which had been received by him, in reply to his appli-
cationsj from different learned societies. The most interesting
of these conveys a report by Poisson and Cauchy on one of his
papers submitted to the Academy of Sciences. That report
points out clearly what I have already had occasion to remark in
other instances, that Mr. Walsh's supposed discoveiy, in so far
as it was true, was not original. In a subsequent report by
Poisson upon another communication, that great analyst, refer-
ring to the fonner one, stated explicitly that Mr. Walsh's papers
did not merit the attention of the Academy.
Certainly Mr. Walsh had no right to complain of the treat-
ment which he received from the French Academy. Alluding,
however, to their rejection of his first ])aper, he observes in his
MS. memoir on the Calculus of Variations, —
^'Such was the commencement of a controversy, or rather
persecution, scarcely yet known to exist, but which will hereafter
be recorded as one of the most memorable seras in the history of
human knowledge It [the paper] merited a more profound
consideration of its contents than M. Poisson thought well to
bestow on them; an error of which M. Poisson was not aware
of the consequences, as affecting in the future history of science
not only his own character, and the character of the institution
of which he is a member, but that of the age in which he lives.''
From the scientific societies of his own country and of the
United Kingdom, Mr.Walsh received less attention than from the
French Academy. The latter stated the grounds upon which
his communications were declined; the former simply declined
them. To establish the rule of propriety in such cases is not
easy, but I am disposed to think that it would favour the course
adopted by the French Institute rather than our own. It would
seem in the case of societies, as of individuals, to be the right
course to speak the ti*uth in its simplicity and integrity. To do
this would not entail the further obligation to answer unmeaning
objections, or engage in controversy, nor would occasion often
arise to exercise the right of declining further discussion ; for
it is not to be presimied that all who are mistaken in opinion
are therefore captious and unreasonable. Probably there are
many cases in which a simple and candid statement of the nature
of the error into which an author has fallen would at once pro-
duce conviction. In such cases it would be kind as well as just
to convey the information required. Tliere is indeed too much
reason to fear that Mr. Walsh's case was not one of this nature ;
still it is possible that the sense of neglect and injustice under
which he laboured might by such little attentions have been mi-
tigated, and that a more wholesome feeling might have arisen in
his breast than that which he appears to have indulged.
Prof. Boole^s Account of the late John Walsh of Cork. 353
-iI'Mr. Walsh continued to pursue his avocation as a writing-
master in Cork until the year 1845, when a paralytic seizure
threw him almost helpless upon the charity of those who had
known him in better days. Among his papers is a subscription-
list, testifying that the appeal made for him to the benevolence
of his fellow-citizens was not unheard. I have however been
informed upon credible authority, that the first use which Mr.
Walsh made of the sum put into his hands was to rush into
print. It will not be surprising to learn that about this period
he was for some time confined in the city jail for debt, and that
shortly after he was an inmate of the Union. For the particulars
of this part of Mr. Walshes life I am indebted chiefly to Mr. K.,
who, with a zeal and fidelity of which there are not many exam-
ples, continued to retain his former relation to his old, and one
would think, helpless instructor. In the solitary prison-cell,
or surrounded by paupers in the crowded Union, poor Walsh
might still enjoy the satisfaction of descanting upon his favourite
topics to his one remaining pupil. It is a happy circumstance,
that, never having married, he had no family cares to weigh
upon his spirits. What time poor Walsh spent in the Union
in this his first visit to it I have not ascertained; but before
long he was removed, chiefly through the benevolent interces-
sion of Dr. Finn, one of the physicians of the North In-
firmary, to that Institution, where he remained for some months.
It is not improbable that at this period his disease may have
been accompanied by cerebral excitement, for he is described
as having been a rather intractable patient. Peculiar notions
which he had formed on the subject of religion led him to
attempt to convert some of his fellow-patients to the same
views. I have been informed by one of the physicians who was
then in attendance at the infirmary, that he would rise at night
from his bed, and addressing the other patients, declaim in the
most earnest manner against the belief in the immortality of the
soul. The particular argument upon which he relied is stated
in a paper which a short time before he had printed under the
title of Metalogia. It is, in his own words, as follows : —
" The Deity is coeternal with Time and Space, and has all
his attributes infinite. He cannot confer any of these attributes
on thinking beings ; for if the Divine Being could confer any
one of his attributes, viz. immortality, for example, therefore
inductively he could confer all his attributes on mankind, and
make them coequal to himself in every respect, which would be
contradictory and absurd. Therefore, &c.^^ In the same paper,
which is interesting as being probably his last performance, he
thus defines the science of Metalogia, and describes its claims :
" Metalogia, which signifies beyond reason, is the name I have
354 Prof. Boole's Account of the late John Walsh of Cork,
given to a new branch of knowledge which inquires into the
causes of such phsenomena as ignorance would persuade us had
been beyond the power of human reason to investigate. Already
it has opened the way for three great movements in human
affairs.'^ These movements he describes with a simplicity which
would excite a smile, if the whole history did not too deeply
draw upon the sources of pity, as, First — " The falsehood of the
Greek method of exhausted quantities, so celebrated throughout
all ages, even in our own times, by the mathematicians, astro-
nomers and philosophers of the world, as an admirable and re-
fined invention. And the falsehood of the offspring of that
method, namely, the no less celebrated doctrine of fluxions, dif-
ferentials, limits, &c., the boast and glory of England, France,
and Germany, demonstrated by the great invention of the geo-
metry of partial equations which has superseded them, at least
in my hands, and indefinitely sui'passed the old system in power.''
'' The second great movement in human afi"airs is in physical
science, viz. the falsehood of Newton's law of gravity." "The
third of these great movements " is the above argument against
immoi*tality, which, he says,* " because it is based upon demon-
strated truth will ultimately overspread the earth, and banish
superstition from its surface." Observe the admirable candour
of the admission " at least in my hands " with which poor Walsh
is forced to qualify his harmless boast of the triumphs of his
system. " Whether," he confesses in another part of the same
paper, " it is owing to the prejudices of the philosophers or to
the actual irrational bearing of the human species," his most
important discoveries had been " completely sent to Coventry."
The remainder of poor Walsh's story is soon told. After
remaining without benefit for some time in the North Infirmary,
he was received into the house of a brother, the Rev. M. Walsh,
parish priest of Sneem in the county of Kerry. There, however,
he did not remain long. Restless and unhappy, he returned, at
his own desire, to Cork, and resided on Patrick's Quay, where
he endeavoured again, but vainly, to obtain pupils in his favourite
science. The paralysis from which he sufi'ered had moreover
destroyed the beauty of his hand-writing, which from one speci-
men that I have seen of it appears to have been once remarkable,
and thus cut off all hopes of subsistence from his former employ-
ment. Doubtless it was by the aid of benevolent friends (and
in generous sympathy for misfortune, Cork is not wanting) that
he was able to subsist. I have seen a letter addressed by him
while under these afflicting circumstances to Dr. Finn, who, as
already mentioned, had shown him kindness on a fonner occa-
sion. In that letter he complained that, notwithstanding all his
discoveries, he obtained no pupils, and expressed a desire to be
Prof. Boole^s 'Account of the late John Walsh of Cork, 355
removed into the Union at Kanturk. Shortly after he was again
admitted into the Cork Union. Dr. O^Connor, physician to the
Unionj has thus described to me his appearance on that occasion,
^' I remember Mr. Walsh when brought to me for examination/'
Dr. 0^ Connor says, " as a little neat-looking man, with a very
thoughtful and pleasing expression of countenance, and appa-
rently not at all depressed by the unhappy circumstances in
which he was placed. He had a slate, a black board, and a little
roll of paper under his arm. I said to him, ^ I am sorry, Mr.
Walsh, to see you reduced to your present necessity.^ ' Oh, by
no means,' replied Walsh, ' it is the turn of the wheel of life. I
must bear it like a philosopher.' ' Well, Mr. Walsh,' replied
the good doctor, ' is there anything that I can do to make you
more comfortable here ? ' ^ Oh,' said Walsh, ' if you could
get me a quiet place to put up my board, and allow a pupil of
mine to visit me occasionally, that is all that I shall desire.' "
Thinking to procure for his patient a greater measure of indul-
gence than could otherwise be conceded to him consistently with
the rules of the house. Dr. O'Connor ordered his admission into
the hospital, although medical treatment did not, from the nature
of his malady, appear to be required. There poor Walsh spent
the remainder of his days. After a time, his debility having
greatly increased, he was entirely confined to his bed, but even
then his faithful pupil K. continued to visit him, indulgently
listened to his projects for the reformation of science, and con-
soled him by the tribute of a generous sympathy for the loss of
health, the loss of home and station, and for that which, to the
poor dying enthusiast must have been far harder to bear, the
world's imagined neglect and ingratitude.
Since the period when Mr. Walsh was an inmate of the North
Infirmary some change for the better had passed over his mind.
He was now more docile and tractable, and attended to the
wishes of his physician and of those who were appointed to take
charge of him, nor did he again endeavour to engage his fellow-
patients in religious disputes. In reference to this improvement
of character, the consequence perhaps of a remission of the acti-
vity of disease, or perhaps also of self-reflection under the sobering
influence of adversity. Dr. O'Connor has told me the following
anecdote -.r-^'^ On one of my visits to Walsh's bedside he inquired
of me if he had ever since his admission into the Union endea-
voured to disturb the religious opinions of those around him.
The doctor admitting that he had not, and commending him for
his moderation, Walsh replied, ^ And yet, doctor, I could say a
few words, a very few words, that would make you and the chap-
lain and everybody here abandon your present convictions for
ever.' ^ Well,' said Dr. O'Connor, 'say them, and then see whether
^^ Vvoi. Boole*s Account of the late John Walsh of Cork.
they produce the effect on me.' ' No/ replied Walsh, ' I know
well that they would, hut I forhear to utter them/ '' Some time
after this Walsh consented to see a Roman Catholic clergyman.
To him he revealed the potent spell. It was the argument of
the Mctalogia.
It was at the commencement of an awful period that John
W^alsh sought an asylum in the Cork Union. The autumn of
1846 and the whole of the following winter and summer will
long be remembered in Ireland. The food of a nation had
perished, and a desolation unexampled in modern times came
down upon the land. At the time of Mr. Walshes admission,
the Union house built for the accommodation of 2000 persons was
ah'eady crowded. Ere long the number of its inmates exceeded
7000, and despite of all endeavours to provide accommodation for
the continually increasing throng by the erection of sheds and
temporary hospitals, all the avenues of approach were thronged
Avith the dying and the dead. Amid this scene of national woe
and calamity in the famine year of 1847 poor Walsh breathed
his last. He had been for some time before his death insensible
and unable to recognize his pupil. I have been informed by
Dr. O'Connor that he did not die of the fever which was carrying
off the inmates of the Union house at the rate of two or three
hundred weekly, but of the paralytic affection under which he
had for some time laboured.
Mr. Walsh was a man of agi*eeable address, and, when treated
with the respect which he thought due to himself, of friendly
and courteous manners. In the affairs of the world he was a
child, and was apt to become the dupe of interested persons.
W^ith proper oeconomy he might have saved sufficient to support
himself in old age ; but the easiness of his temper, and, I fear,
dui'ing the latter years of his life, a too great fondness for social
enjoyments kept him poor. The freedom of his opinions upon
religion operated also unfavourably upon his temporal interests.
I have reason to think, from an examination of his papers, that
the looseness of his sentiments upon this subject was not the
result of any desire to release himself from the restraints of
moral obligation, but of an exaggerated self-esteem, and a too
great confidence in his own not very exalted powers of intellect,
the source probably of nearly all his errors and misfortunes. To
this cause we may attribute the intemperate tone of his remarks
whenever he is discussing the merits of those whom the world
has consented to make its guides in science. Upon his favourite
topic of discourse it is said that he was quite unable to bear con-
tradiction.
Mr. Walsh in his day attracted some attention even in high
quarters. The Edinburgh Review, No. 143, p. 192, referring
Prof. Boole's Account of the late John Walsh of Cork. 35 7
apparently to Mr. Walsh's pertinacious obtrusion of his views
upon the public^ says, " Let us hope that the person who in our
day occupies himself with printing his mathematical reveries
against the method of fluxions and the first section of the Prin-
cipia, and who insults the public taste by publishing the foulest,
most vulgar abuse of the ' Saxon Philosopher/ may not succeed
in making his reflecting countrymen believe that the name which
all mankind have consecrated to receive only veneration repre-
sents only a driveller and a knave.'^
I find this passage and another from the same journal copied
in Mr. Walsh's hand-writing among his papers. He there denies
that he made use of the language imputed to him, and addresses
a letter to the editor of the Edinburgh Review upon the subject.
Of this letter, or of a similar one, there is also a printed copy.
It is to be feared that, whether Walsh used the particular terms
in question or not, he had laid himself fully open to the charge
of employing violent and abusive language.
Mr. Walsh is an extreme instance of a class of persons, who,
without having mastered the very elements of received science,
spend their lives in attempting its subversion, and in the vain
endeavour to substitute in its place some visionary creation of
their own fancy. Whether such persons would not in the earlier
stages at least of their career be accessible to the conviction of
their error is worthy of consideration. A^little judicious kind-
ness at that period might in some cases prevent the misspending
of a life. But when that which was originally but a fond and
foolish notion has been fostered into a disease of the mind, the
cure is generally hopeless. Trisectors of an angle, squarers of
the circle, discoverers of perpetual motion, constitute a class of
mankind whose peculiarities deserve the attention of the student
of human nature, and whose personal history is often calculated
to awaken the deepest commiseration. Providence seems to have
in some measure vindicated the equality of its dispensations by
assigning to them a double measure of hope, which serves them
in the stead both of abihty and of success.
But there is a class superior to these whose history is far more
affecting ; men who with both genius and competent knowledge
devote themselves, perhaps in the over hours of labour, to the
improvement of some mechanical invention, and either through
want of means, or through legal impediments, or because they
have miscalculated the requirements of the age, find themselves
doomed to ceaseless disappointment. If they are unburdened
with family ties, the case is not so distressing. Amid the greater
sorrows of the times we may permit ourselves to forget theirs.
But if they have wife and children looking up to them for
support, yet destined to see their comforts depart and their hopes
368 Mr. H. E. Strickland on the Elevatory Forces
grow less ; if, in addition to this, sickness follows in the train
of toil and disappointment, and unstrings the skilful hand and
quenches the lire of the inventive mind, then I confess that,
guilt and its consequences apart, I know of few sadder spectacles
in the varied drama of human life.
A history of some of the cases of this nature which have come
iiuder your knowledge would, I think, be a valuable record —
valuable from its intrinsic interest, valuable as a beacon and a
warning. I presume that you are acquainted with a greater
number of such cases than any other person. That inventors
such as I have spoken of do really constitute a class apart, is, I
think, very evident. Generally it would perhaps be found that
they arc men of innocent and blameless lives, of great simplicity
of character, ignorant of the world, and perhaps for this very
reason imbued with a too great self-esteem, and an unwan*anted
confidence in their own powers. We should probably discover
in them as a class the peculiar effects which a life too special in
its pursuits tends to produce, and which in those who are more
favourably circumstanced are mitigated by intercourse with other
minds, by self-reflection, and by a knowledge of the peculiar
dangers to which they are exposed.
I remain, my dear Sir,
Ever sincerely yours,
Professor De Morgan. George Boole.
LIV. On the Elevatory Forces ivhich raised the Malvern Hills.
By H. E. Strickland, F.G.S.^
[Witli a Plate.]
PEOFESSOR PHILLIPS has already pointed out (Mem.
Geol. SuiTcy, vol. ii. p. 5) that the syenitic ridge of the
Malvern Hills forms a part of a great line of dislocation, extend-
ing for at least 120 miles from Flintshire on the north to So-
mersetshire on the south. He shows that this line of disturb-
ance forms the eastern boundaiy of that vast region of elevation
which includes the whole of Wales and pax*t of Southern Ireland,
and that the principal movement which caused this elevatioij
took place between the Carboniferous andTriassic epochs t, He
* Communicated by the Author.
t We cannot gp^ak more precisely as to the date of a convulsive move-
ment which perhaps extended over a considerable period. According to
the researches of Sir R. Murchison in other regions, an entire geological
epoch, — that of the " Permian System " — intervened between the Carbo-
niferous and the Triassic systems. But deposits of this age are scarcely, if
at all, traceable in the region here described ; and we cannot therefore
AMcrt whether th^ M^vcra ridge wa;^ elevated at the begiiming, the middle.
^n'Nnt?^ which raised the Malvern Hills, 359
further shows that this line of fracture, bounding the elevated
region on the east, partakes throughout the greater part of its
course of the nature of a fault ; that this fault is on an enor-
mous scale in its vertical and horizontal dimensions, and that it
is much concealed by the thick deposits of new red sandstone
which have covered it up on the downcast side, and followed the
sinuosities of its course.
The demonstration of so vast a line of disturbance, evidently-
due to one set of operations acting at a very remote epoch, enor^
mous in dynamic amount, yet comparatively limited in their
duration, is one of the grandest generalizations at which British
geologists have arrived. The nature of the movement which
has produced these results seems consequently to deserve a fuller
investigation than it has yet received.
These disturbing forces appear to have been partially conti-
nued during, and even after, the deposition of the New E-ed
Sandstone. Both that and the incumbent Lias show proofs of
elevation and of dislocation, which may be regarded as the expiring
efforts of those vast forces which raised the mountains of Wales
above the plains of England. Indeed the general south-easterly
inclination of the whole secondary series of Southern England is
a further proof of the continuation of these elevating movements
down to a late geological date. But all these more recent changes
of level were so feeble in amount compared to the vast convul-
sions of the pre-triassic period, that we may eliminate them
altogether from our present inquiry. We shall gain clearer
notions by supposing the New Bed Sandstone and all the supe-
rior formations entirely removed, and by endeavouring to decipher
the state of things which immediately preceded the deposition
of those strata.
Of the whole line of dislocation above mentioned, the ten or
fifteen miles which include the Malvern and Abberley Hills pro-
bably aiFord the best information on this subject. The syenitic
axis of Malvern, eight miles long, about half a mile wide, and
almost perfectly straight, naturally suggests the idea of a vast
dyke of injected trap rock. But Prof. Phillips has successfully
shown, from the absence of lateral ramifications of syenite, from
the rare and slignt indications of metamorphic action, and from
other phsenomena, that this plutonic ridge must have been ele-
vated in a solid state. Indeed the fact that it occurs, not on a
line of simple fissure, but on a line of fault, is conclusive of its
or the end of the Permian epoch. From the conformability, however, of
the " Lower New Red Sandstone " to the Coal-measures in Staifordshire
and Shropshire, and its unconformabiUty to the Triassic or Upper New Red
Sandstone, we may consider the conclusion of the Permian epoch as the
probable date of this event. (See Murchison's Silur. Syst. p. 131.)
360 Mr. H. E. Strickland on the Elevator y Forces
having been elevated as a solid ; for the downcast side being
lower by several thousand feet than the upcast, the syenite, if
fluid, could not have been raised to its present position, but
would have overflowed the downcast side to a great distance.
Admitting this wall-like mass of syenite to have been forced
up from below in a solid state, we at once obtain a clue to the
vertical or highly inclined (sometimes reversed) position of the
sedimentary strata on the west, or upcast side of the Malvern
fidge.' " "^ ''•^ ^ * ' ''* '^^- < •'
' 'It'ap^afirt, thefi/ iiliat the Malvern district, though forming
part of a great line of fault, yet exhibits the phsenomena of a
fault under a very complicated aspect. To explain this I must
refer for a moment to a few elementary principles.
In the simplest form of a fault, when one portion of a hori-
zontal stratum is elevated by an equally diff'used pressure from
below, while the other portion remains at rest, the stratum pre-
serves its horizontality up to the very plane of separation ; or,
more frequently, the friction of the two masses causes the strata
to bend slightly towards each other on the opposite surfaces of
the fault. Again, if the upward pressure be confined to a line
instead of being spread over a surface, the strata are thrown in
opposite directions, and an anticlinal is the result.
But the Malvern region presents us with a combination of
both these kinds of forces, and of both their resulting phsenomena.
There has been an elevatory force diff'used more or less equally
under a vast area, which has heaved up in a mass the entire
region for hundreds of miles to the westward of the Malvern
axis. And there has also been a local force applied immediately
beneath this axis, which has given an extra amount of elevation
to the marginal portion of the upcast area.
It is this excessive development of motive force at the very
margin of an elevated region, and in immediate contact with a
non-elevated tract, that renders the phsenomena of the Malvern
Hills peculiarly anomalous. Under ordinary circumstances, when
an upward force is applied locally along a line, it acts equally on
both sides of that line, elevating the strata, as already shown,
into an anticlinal position. If, however, the resistance be greater
on one side of the axis than the other, a certain amount of dis-
placement ensues, and the anticlinal an'angement is combined
with that of a fault. The Malvern elevation is probably an ex-
treme and unusually exaggerated instance of the last class of
phaenomena. If we could strip off the thick mantle of New Red
Sandstone which conceals the eastern side of this axis, we should
probably find the strata from the Caradoc sandstone up to the
Coal-measures more or less upturned at their edges. (See Plate I.)
So vast a force as was required to elevate the syenitic axis could
which raised the Malvern Hills. 361
hardly have failed to shatter and twist up the margin of the de-
posits on its eastern or downcast side_, although their amount of
statical resistance was such as to forbid any general elevation of
them en masse.
Assuming that such was the condition of things in this region
before the deposition of the New Red Sandstone,, let us endeavour
to trace the mode of action of the forces which produced it.
There is evidence that elevatory movements have taken place
along the axis of the Malvern chain before^ as well as since, that
great and transient outburst which dates between the Carboni-
ferous and Triassic epochs. A mass of syenitic rock had been
elaborated by igneous agency beneath this tract in very remote
geological times. It had become solidified, and had been elevated
above the oceanic surface before the Upper Silurian formations
were deposited. The sections on the west side of the Malvern
Hills show that the Mollusca and Corals of the Caradoc sand-
stone lived and flourished in immediate contact with the plutonic
rock, and that pebbles of the latter were rolled into the sea of
that period, and were there imbedded in company with the animal
remains. (See Mem. Geol. Surv. vol. ii. p. 33.) We may there-
fore suppose that at this period a state of things prevailed such
as is here represented.
Sxirface of /^ "^ llie Sea ^
Cdra^^y^^m^^ ^ yem le
i('i' i iSdndston e
In other portions of the Welsh region we find similar proofs
of elevations having taken place in remote palaeozoic times.
Thus at Bishop^s Castle, and in the country to the north-west of
it, the Caradoc sandstone is found to lie unconformably to the
subjacent rocks ; and the Wenlock shale in the same way over-
laps the Caradoc sandstone near Bishop^s Castle and Builth.
(See Ramsay in Journ. Geol. Soc, vol. iv. p. 296.) Some of these
ancient disturbances were probably connected with those referred
to in the Malvern district. But this most ancient elevation of
the syenite seems to have been comparatively small in amount,
and was wholly covered up by the formations which succeeded
the Caradoc sandstone, and which contain no fragments of sye-
nitic rocks. In order to explain the changes which now took
place, it may be legitimately assumed that the floor of soHdified
syenite on which the sedimentary deposits rested was itself un-
derlaid by igneous rock in a fluid and active state. Let it be
further granted, that the present breadth of the Malvern syenite
362 Mr. H. E. Strickland on the Elevatory Forces
(averaging half a mile) approximately represents the thickness of
the upper or solid portion of the plutonic rock. Such I assume
to have been the condition of things when that great elevatoiy
movement commenced which upheaved the westernmost side of
our island. It is irrelevant here to inquire whether this general
upheaval was effected by the mere expansion caused by increased
temperature, or by the introduction from other quarters of vast
masses of fluid matter beneath the elevated area. It will be suf-
ficient to admit that a special volcanic focus existed beneath the
syenitic axis of Malvern, and that its energies were called into
action simultaneously with the more general movement which
elevated the area of Herefordshire and Wales.
We may now suppose that the elevatoi-y forces beneath the
Cambrian region had accumulated so as to overcome the super-
incumbent weight ; while the region to the eastward, either from
its greater rigidity, or from the less amount of subjacent force,
remained in a quiescent state. A separation would now take
place between these two areas ; a long and sinuous line of frac-
tm-e would divide them ; and the region where Force had over-
come Resistance would begin to rise higher and higher above the
area which remained unmoved.
The previous elevatory movement which has been shown to
have existed along the Malvern axis probably rendered this a
weak point in the earth^s cnist, and caused the line of fracture
to coincide with that axis. As soon as one side of this line
began to rise and a fault to be produced, the volcanic forces
which had been pent up beneath the syenitic axis would now
find, or endeavour to find, a vent. Struggling to escape along
the line of fault, they would thrust up the solid syenite above
them, raising it into a lofty cliff above the downcast area, and
elevating, overturning, or crumpling up the edges of the Silu-
rian, Devonian, and Carboniferous strata which rested upon it.
(See Plate I.)
In the above diagram I have taken as a basis the section across
the Worcestershire Beacon published by the Geological SuiTcy,
and have endeavoured to supply conjccturally those portions of
the strata which have been removed by denudation, or which lie
too deep to be visible. I have supposed that a vast mass of
Devonian and Carboniferous rocks has been upheaved bodily,
while the lower strata nearer the syenite are more or less frac-
tured, crushed and contorted. The thickness of the strata which
have been since denuded may appear enormous ; but it is founded
on the careful measurements of the Geological Survey, which
give about 5500 feet for the Old Red Sandstone of Hereford-
shii'e, and 3500 for the incumbent Carboniferous series at the
nearest point (Dean Forest), where the undulations of the beda
which raised the Malvern Hills. '^ ^^ 363
have saved them from denudation. As_, however, the coal-fields
of Wyre Forest and the Clee Hills on the north present a less
development of the series than is seen in Dean Forest, I have
reduced the thickness of the Coal-measures and Carboniferous
limestone which once existed on the west of the Malvern Hills
to about 2300 feet. Adding these amounts to the thickness of
the Upper Silurian, Caradoc sandstone, and syenite, we obtain
a total of at least 13,000 or 14,000 feet for the amount of dislo-
cation between the two sides of the Great Fault j an amount
greater, perhaps, than can be paralleled in any other instance of
a single fault which the world can produce. Nearly one-half of
this amount may, however, be assigned to the more local forces
which elevated the Malvern syenite ; so that about 7000 or 8000
feet would represent the difference of level between the strata in
the less distm-bed parts of Herefordshire west of Malvern, and
their equivalents now buried beneath the New Red Sandstone of
Worcestershire, allowing about 1000 feet for the thickness of
the latter down to the subjacent Coal-measures.
The fluid matter which I suppose to have thus forced up the
solid syenite may itself have never reached the surface. The
plutonic axis of Malvern seems only to exhibit its upheaving
effects, and shows no signs of fluid ejections contemporaneous
with the elevation. It is possible, however, that volcanic matter
may have poured out over the downcast area, where it is now
concealed by the New Red Sandstone. And the laterally in-
jected dyke of Brockhill, as well as the trappean masses in the
black shales on the west of Ragged Stone and Midsummer Hills,
are not improbably connected with the volcanic forces which
thrust up the syenite. This supposition appears to me at least
equally probable with that of Professor Phillips (Mem. Geol.
Surv., vol. ii. p. 56), that these greenstone eruptions were con-
temporaneous with, and overlaid the black Caradoc shales with
which they are in contact. In the arrangement of the strata
around Eastnor Park, we seem to have indications of a crater of
elevation, caused by an incipient volcanic eruption whose focus
never reached the surface. The great expansion and crumpled
condition of the Silurian rocks at Ledbury, and their general
semicircular arrangement round a central point, indicate a local
and special development of volcanic energy beneath. But the
syenitic axis itself affords no more signs of eruptive force at this
point than at any other. The efficient force seems to have acted
not in, but at the west side of this axis. A mass of basaltic
matter ejected beneath the Caradoc sandstone will explain these
phsenomena. Its ramifications would be likely to select the
black shales as being less resisting than the sandstones above
and below them, and would produce that series of trappean
864 Mr. H. E. Strickland on the Elevatory Forces
dykes which Professor Phillips was the first to describe. By
penetrating the shales (as trap-dykes often do) in the planes of
stratification, they would produce an apj)earancc of contempora-
neity, though their real dates might be long subsequent.
The district here referred to seems to be exactly analogous to
the well-known elevatioii crater of Woolhope, distant only seven
or eight miles to the westward, in which we also see the ineffec-
tual struggles of a focus of volcanic energy to burst through the
incumbent strata. Here also the concealed volcano has left a
collateral proof of its existence in the single basaltic dyke of
Bartestree Chapel.
These detached indications seem to show that the volcanic
matter which underlies, and which has elevated this region, is
different in mineral character from the more ancient syenite of
Malvern, and is probably more allied to greenstone or basalt.
The trap-rocks of Wyre Forest, north of Abberley, further corro-
borate this view.
In tracing to the north or south that long line of dislocation
of which the IMalvern Hills form a part, we find a continuation
of analogous phsenomena more or less modified by local circum-
stances. The Abberley range of hills is, as is ably shown by
Professor Phillips (Mem. Geol. Surv., vol. ii. p. 145), completely
analogous to the Malvern district ; the chief difference being,
that the syenitic axis which upheaved the Silurian rocks is here
almost wholly concealed from view, and (with one small excep-
tion) is only known by its effects. The Silurian and Old Red
formations are here, as on the west of Malvern, overturned for a
distance of several miles. This remarkable phsenomenon may,
I think, be explained in a simpler mode than either of those pro-
posed by Professor Phillips. All that is requisite is to resolve
a certain portion of the vertical uplifting force into a lateral
direction. Now it is certain that an enormous fault-line runs
along the eastern side of all the disturbed and elevated district,
and that the downcast region on the east has remained relatively
rigid and unmoved. In accordance with the well-known law
that the plane of a fault (almost invariably) dips towards the
downcast side, it is evident that this oblique surface would act
mechanically as an inclined plane or wedge, in reference to a
vertical uplifting of the strata on the west, and would force them
over to a certain distance in a lateral direction. (See Plate I.)*
The same lateral force would explain the sharp anticlinal
* A very analogous case occurs at Hohnstein in Saxony, where a mass
of granite, upheaved in a sohd state, has not only elevated but overturned
the contiguous strata, causing beds of the Jurassic series to repose upon
Cretaceous ones. (SeeCotta, Geognostische Wanderungen, Dresden, 1838.)
?.^'>^o'>l y which raked the Malvern HillsM *jM S65
ctirves iiito \thich some parts of the Bidge Hill'nekr Abberley
are compressed. (Mem. Geol. Surv., vol. ii. p. 151.)
At numerous other points, as we proceed northwards along the
eastern limit of the elevated district, or southwards by May Hill
to Tort worth, we find indications of the same great line of fault.
Sometimes, as at Oswestry and Higley, these faults have affected
the Lower New Red Sandstone as well as the Carboniferous
rocks, proving that here at least the elevatory movement was
subsequent to the commencement of the Permian epoch. Gene-
rally the great marginal fault seems to have formed a nearly' ver-
tical cliff, against which the Upper or Triassic portion of the New
Red Sandstone was deposited, as in the Shropshire coal-field, at
Bewdley, Abberley, Malvern, May Hill and Pyrton Passage.
The Cambrian and Herefordshire area having now become
elevated many thousand feet above the eastern region, and the
volcanic forces having spent their energy in thrusting up and
overturning the syenite and incumbent strata of Malvern, a
period of comparative tranquillity ensued. The elevated region
had become dry land, while the downcast area remained beneath
the sea. The sands and marls of the Triassic series filled up the
bed of this sea, while its littoral waves, beating against the sye-
nitic cliffs of Malvern, formed accumulations of conglomerate
such as those of Rosemary Rock and the Berrow and Woodbury
Hills. The oolitic, cretaceous, and tertiary formations were suc-
cessively piled upon the triassic rocks, and may possibly have
raised this downcast area to the same level as the upcast portion,
though there is no evidence that they ever ov;erlaid the latter in
the region west of the Severn. ^^-^^d .y^fj ^nr*
The elevated area meanwhile was undergoing a vast amount
of denudation. During the long ages of the Triassic and Oolitic
systems, it was doubtless exposed to atmospheric degradation,
and supplied the adjacent ocean with much of its sedimentary
matter, as has been ably shown by Prof. Ramsay (Mem. Geol.
Surv., vol. i. p. 297). The denuding forces which were so active
in the Pliocene period terminated these vast operations, and gave
to this rugged and dislocated area those smooth undulating out-
lines which it now generally presents.
I trust that I have now in some degree confirmed and extended
the proofs adduced by the geological suiTcyors of the elevation
and subsequent denudation of the Cambrian region, and that I
have shown how the peculiar phsenomena of the Malvern district
may be explained by the supposition of a local development of
plutonic energy superadded to a more general upheaving force.
Phil, Mag, S. 4, Vol. 2, No. 12. Nov, 1851, 2 C
[ 366 ]
LV. On the Anticlinal Line of tlie London and Hampshire Basins.
By P. J. Martin, Esq., F,G,S.
[Continued from p. 288.]
I HASTEN now to a review of the next in order, namely, the
Subcretaceoits Zone. Immediately that the lower greensand
emerges from helow the gault, we are presented with a great
variety of the subcretaceous diluvium. Here it still consists of
a large share of angular flint, mixed up with fragmentary iron-
stone (carr-stone ?) and sandstone derived from its own rocks,
and bearing slight marks of being drifted or rolled. Amongst
these debris, in two places only I have detected the presence of
a very few rounded pebbles ; at Hurston WaiTcn near Storring-
ton* on the south side of the Weald, with small chalk pebbles,
and near Sevenoaks in Kent ; — in both cases, I presume, strays
from the lost tertiaries.
The most notable fact in regard to these gravel beds is, that
they lie, when in most force, in hollows scooped out of the soft
sand rock. Elsewhere they are widely sprinkled over the surface
of the country, where the grosser materials seem to have been
retained by entanglement in the loose sand. Indeed the only
important accumulations of the angular gravels are to be found on
the soft or shanklin sands, or upper ferruginous beds of the
lower greensand ; where, as I have just said, they seem to have
been retained mainly by their involvement in the broken sand,
and their lodgement in the hollows of the soft rock, which, when
cleared out, have all the appearance of being originally scooped
out by water moving with great violence. One of the most re-
markable beds of this kind is being worked for road material in
and about Peasemarsh near Guildford. In its composition it is
an exact countei'part to the beds on the hill tops at Fittleworth,
Lavington Common, and the ferruginous sand country south of
Midhurstf. The prevailing materials are broken flint, chert
and sandstone, derived from the lower beds of greensand, and
perhaps here and there a stray pebble.
These drifts prevail all round the subcretaceous zone ; on the
south side as far east as the country north of Lewes J, and on
the north from Peasemarsh to Ashford§ ; and I doubt not are
continued on to Hythe, although I have not followed them so
far. But it is a notable fact, that, except in a few instances,
these gravels do not lie on the high bold platforms of the lower
beds of the formation in question, although they may be found
in small quantities on the Weald clay below. In the same manner
* Sussex. t Sussex.
X Mantell's Geol. of S.E. of England, p. 29. § Kent.
On the Anticlinal Line of the London and Hampshire Basins, 367
as the flints have been swept from the outcrop of the malm, but
lie on the gault, so they seem not to have taken any hold on the
rocky beds of the lower greensand, but are sparingly scattered
along the verge of the Weald clay country. I have found a thin
coat of broken flints and ironstone in Hartingcombe*, and have
traced this into the iron conglomerate of the Weald surface, up to
thebanks of theArun. Again, after passing over the high grounds
that range from Wolmar Forest t to Warminghurst {, which are
destitute of flints, we find a thin sprinkling, sometimes associated
with the hard " clinker ^^ ironstones or ^^ carr-stone '' (which
are plentifully distributed in the ferruginous shanklin sands),
along the Weald clay valley below. On the south side of the
Wealden area I find these drifts intruding to the very verge of
the Hastings sand country near Shipley § and West Grinstead
Churches; and into the valley of the Adur, from thence toward
Ashurst. And drift of this sort has been found by Dr. Mantell
at Barcombe in the same line of country ||. On the north side
of the Weald, again, the Godalming Hills, Ewhurst Hills and
Leith Hills 1^, show no flint drift, but it is found in the loose sands
of Betch worth and Reigate ; and in that line of country obtru-
ding, as it does at Shipley, into the Weald clay at Flanchford,
and along the course of the Mole, where it is crossed by the
Brighton road. The plateaux of the Sevenoaks and Maidstone
districts very rarely exhibit angular flint gravel ; but the country
of the upper beds between these high grounds and the outcrop
of the gault abounds, as usual, in the debris of all the surrounding
strata.
Leaving the subcretaceous line of drift, a few observations will
sufiice for the consideration of the —
4th, or Wealden Zone. — There is nothing in the history of
that part of the anticlinal line of the " chalk basins " called the
^^ Weald Denudation'^ more conclusive as to the agency of
strong water currents and the flux and reflux of waves of im-
measurable force (immeasurable, I believe, but by our ideas of the
removal and transport which we suppose they have efiected) than
the bare state of the central parts of the Weald.
The country of the Hastings sands rises geographically higher
than the sandstone hills and chalk downs that surround it; and
it is filled and fortified by strong and tough stone-courses, which
gave it that prominence and stability, whilst the Weald clay was
yielding to erosion. But that the Weald generally is destitute
of diluvium is an opinion which has been too hastily embraced.
Both members of the "Wealden^' have their appropriate drift;
and it is just of that kind which might be expected to be left
* W. Sussex. t Hants. % Sussex. § Sussex.
][ Geol. of S.E. of England, loc. eit.. IT Surrey.
2C2
868 Mr. P. J. Martin on the Anticlinal Lin^ df
behind by the retiring waves of the denuding flood, after the
previous removal of the thousands of feet of upper coatings.
Soon after I began to turn my attention to these surface-
changes, I was attracted to large masses of a ferruginous breccia
which were frequently ploughed up and brought '' to bank " by
the labourers, who gave it the name of '^ Iron-rag." I found
afterwards that it was anciently extensively sought for and taken
out of the hollows in which it lay, and smelted like bog iron -ore
(which it sometimes resembles), when the fields of Sussex were
filled with " iron furnaces." On closer inspection too, I found
that many hill slopes were enriched with a thin coating of dilu-
vial loam, and especially on the borders of the river-courses,
high above the reach of modem alluvium. For the truth of thia
I may cite the border slopes of the river Arun from Stopham to
Rudgwick*, and onward over half the parish of Slinfold towards
Horsham, — ofthe Adurfrom Henfield into the "forest-ridge" —
and of the Medway in the greater part of its course through the
"Weald clay. Dr. Mantell has observed a modification of the
ironrag at Barcombe, Wellingham and Horstedf. And chance
some time since threw in my way one of the best opportunities
that could occur of observing an instructive exposure of the fer-
ruginous drift. In digging the ditches and fencing an enclosure
at Lowfield Heath near Crawley {, large quantities of the rag were
collected and may now be seen mouldering in a heap near the
White Lion public-house ; and if the sides of the ditches are
inspected, numerous sections of the hollows in which this iron
conglomerate lay may be seen ; corresponding very much with
the water-worn depressions filled with gravel on the sand-hills,
in the subretaceous zone as before described. Indeed this brec-
ciated drift is to be found all over the Weald. On the Weald-
clay country of the west of Sussex it is filled with fragments of
chert, with now and then a stray flint. At West Grinstead and
near Knepp Castle it is full of flint, mixed with fragments of
the Wealden sandy-courses ; and on the borders of the forest-
ridge it is composed of fragmentary Hastings sandstone with the
septaria of the upper parts of the Weald clay, or of the super-
incumbent Atherfield beds.
But the most important evidences of drift are to be found
where they might be best expected, — on the beautiful and fertile
slopes of the eastern part of Sussex and the south-east of Kent,
where the Rother and its affluents take their courses through the
longitudinal fissure valleys of the central fine of upheaval. On
these slopes, and in these valleys, beds of diluvial loam exist,
made up of the washings of the surrounding ridges, and give
fertility to localities which would be otherwise of comparatively
* Sussex, , t Geol, of S.E, of England, loc, cit, X Sussex,
the London and Hampshire Basins. 369
little value. The cuttings of the railway now traversing this
line of country from Tunbridge Wells toward Hastings, come
conveniently to our aid in identifying the existence of these
loams ; and I particularly recommend the inspection of a section
near Etchingham Church*, where a luxuriant hop-garden is seen
standing on a bed of loam at least twenty feet in thickness ; and
from thence for several miles across the valley of the Rother by
E/Otherbridge, loam-beds of various thickness are traversed. To
any one having leisure and patience for the task, I think it not
unlikely that amongst these loams minute fragments of many if
not all of the upper beds might be discovered. On a cursory
view, their principal materials seem to be derived from theWealden
beds, — the sweepings, as I before observed, of the I'etiring waters
of denudation.
I have said that diluvial bones have not been discovered in any
of the drifts below the cretaceous zone. Of this I have a word
or two more to say, and an exception to make. That the remains
of the animals that perished in the catastrophe we contemplate,
should be found most numerous in the ruins of the uppermost
strata, was a thing to be expected. But there is another reason
why they should be rare in the arenaceous drifts of the subcre-
taceous group, and that is, the bad preservative quality of these
soils. I am in possession of mammal bones from the chalk-
rubble of West Burton and Bury ; and I have one bone, which
I am told is elephant^ s, from a gravel bed of the ferruginous
sand-drift at Cold Walthamf. I am moreover informed by the
gravel-digger, who has had much experience in the pits at Pease-
marsh X) that he has taken out bones ; but they were invariably
found in the clay at the bottom of the bed.
In taking a general view of the arrangement of these drifts,
and the constancy of their character throughout so wide an
area, we cannot but be struck by a unity of design, and a totality
so much in consonance with the other phsenomena of the anti-
clinal line generally, and of the Weald denudation in particular.
Before we finish with the subject of drifts, it will be well to
give a little consideration to the question, — Do they exhibit any
certain signs of the prevailing direction of the currents which
excavated the valleys and carried off the broken materials ? If
I have succeeded in enabling my readers to realize in their minds
the picture of the conjoint action of earthquake and flood which
I have in my own, they will be able to understand the confused
flux and reflux, and the clash of opposing torrents which must
necessarily follow in the train of so extensive a displacement of
solid matter ; whether the convulsion took place at the bottom
of a sea or in the open air ; and whether or no it was prolonged
* Sussex. t Sussex. J Surrey.
370 Mr. P. J. Martin on the Anticlinal Line of
by a continued heaving and falling (terrene undulations of
incalculable violence) of some continuance*. We have not the
means of following the great bulk of the displaced materials.
Much of it was doubtless cast off over the great synclinals on each
side. We have sufficient evidence of this in the loams and the
extensive gravel beds in the mixed diluvium of the London
basin f. And we have a striking proof of it in the enormous
accumulations of the less destructible parts of them in the Brigh-
ton " elephant beds ; '' in the inexhaustible sources of flint-
gravel, sometimes of unknown depth, from thence to Chichester,
under Portsdown Hill, and further west on the northern slope of
the Hampshire basin. But leaving this out of consideration,
and supposing these accumulations to be only the tithe part of
the lost beds, and the great bulk of them to be lying at the
bottom of the German Ocean, and rising out of it in the Cromer
Cliffs, or spread over the plains of Westphalia, we are soon con-
vinced that the drift I have attempted to describe, is only the
remnants of those materials, and the last leavings of the reti-
ring waters.
The motions of these retiring waters, then, would now, after
the great business of excavation was effected, be determined by
the an*angement of the surface so left. Whether the centre of
the upheaval be in the high grounds of the Weald or in the En-
glish Channel nearer the Boulonnais, it is not material to inquire ;
nor whether the Channel as we now see it had previously to this
convulsion any existence or not : most probably it had not. In
whatever direction the central movement lay, every wave would
have its recoil, and the flood would have so wide a range as to
take whatever courses the great boundary lines would dictate.
As these boundary lines run for the most part east and west, in
the long axis of the upheaval, we expect to see signs of the move-
ment of drift in those directions. Nevertheless there is suffi-
cient proof of cross and contrary movements, and of the frequent
deflection of currents in opposite courses. The large accumula-
tion of flints in the transverse vale of Findon f, is matched by a
similar deposit in the long longitudinal one of Bramdene§. The
long transverse valleys of Leatherhead and Smitham Bottom ||
have at their lower extremities, the one a great accumulation of
♦ I have not been able to detect any appearance of friction like " slick-
ensides.** But such appearances were obsened by Buckland and De la
Beche in Dorsetshire (Geol. Trans, vol. iv. new series). I attril^ute the
absence of such appearances in the Wealden aiea to the friable and loose
nature of the rocks and the flexibility of the clays.
f This does not militate against the opinion that all the beds to be found
there have also suffered denudation, crag and all.
X Sussex. § Hants. || Surrey.
the London and Hampshire Basins, 371
flint and rubble near Dorking (spoken of in a former part of this
paper), and the other an immense deposit of stiff loam traversed
in part by the Merstham-tunnel. Again_, much debris from all
the surrounding beds is lodged in the Peasemarsh valley, appa-
rently favoured by the position of that valley after its earlier exca-
vation; so the great accumulation of strong and fertile loams which
make the hop-gardens of Farnham*, might have been brought
from all directions, — out of the gullies at Alton f, along the
valley of the gault at Bentley, or down from the rear of the Hogs-
back ; perhaps from all of these sources. Cross-currents have
mixed the sandstones of the lower greensand beds with the
upper at EittleworthJ and at Peasemarsh; and much rubble
from the former of these has rushed out on the latter through
the transverse gullies (north and south) between Petworth and
Thakcham§. These instances might be multiplied, and much
more might be said about the range and the other phsenomena
of drift ; but it all comes to the conclusion which I drew- from
these appearances in my earliest essay on this subject, that '^^to
the eye of the practised observer the Weald valley presents the
appearance of a great water-channel after a flood : — some parts of
it clean and clear of all incumbrance, others loaded with drift ;
the banks in some parts torn clean away, in others heaped up
with rubbish || ;" and, to make the parallel more complete, in the
drift of both are to be found the bones or the bodies of animals
that have perished in their several catastrophes.
It is proper for the completion of this sketch to say a few
words about the " Bassin du Bas Bouionnais,^^ as the French
call the eastern extremity of the Weald denudation. Mr. Hop-
kins has described the signs of upheaval it exhibits correspond-
ingly with the phsenomena of like kind on this side of the chan-
nel^!. I have enjoyed two opportunities of a cursory inspection
of the country, but cannot speak of it critically. M. Bozet has
described its diluvium**, which only differs from that of the
Weald in having a larger admixture of materials derived from
the wreck of the tertiaries, and particularly the fragments of the
millstones or '' burrstones " of those beds, which we may suppose
correspond in position with our Druid stones or grey-wethers.
And M. Bozet considers the denudation of the Boulogne country
as the work of the same '^ debacle '' that excavated the Weald.
* Surrey. f Hants. % Sussex. § Sussex.
II Geol. Memoir of Western Sussex, p. 84. London, 1828.
If Vide Geol. Trans, vol. vii.
** Description Geognostique du Bas Boulonnais. Paris, 1828,
372 Mr. P. J. Martin on the Anticlinal Line of
Unfortunately for the progress of theoretical geology, it is
constantly being given up to the domination of a prevailing opi-
nion. I think I speak the sentiments of many faithful observers,
and men whose ambition it is to be thought good practical geo-
logists, when I say, that the persevering attempts that have been
made (doubtless actuated by the firmest convictions) for the last
twenty years, to reduce all theoretical notions of surface-changes
to one standard, and that the lowest of constantly existing agen-
cies, have been carried too far ; and that however necessaiy it
might have been in the infancy of the science to clip the wings
and curb the fancy of its votaries, extreme caution has overdone
its work ; and that it is become necessary, if we are to make any
great advances toward a more perfect knowledge of the nature
of these and some other phienomena that pertain to geological
dynamics, to return, in part at least, to the doctrines that held
sway some quarter of a centmy ago ; to reinvoke the assistance
of some long-neglected agencies, and familiarize ourselves with
scenes of greater activity than the uniform causation of the pre-
sent times will afford. The transporting power of icebergs, the
glacial abrasion of rock surfaces, the accumulation of moraines,
and the " oser " banks of the Scandinavian peninsula have had
their share of attention. But the subject of denudation, in its
larger sense, has long been held in abeyance. Whether it is
that the magnitude of the fields it embraces, or its inexplicable
confusion, deters men from entering into the investigation of its
causes, the fact is unquestionable, that whilst everybody is
speaking of it, or recording instances of its operation on the
scenes they describe, nobody makes any attempt to trace these
effects to their causes. Or if any such attempt is made, they
are carelessly referred to the feeble agencies with which we are
surrounded, without due consideration of their adequacy, or the
propriety of their application. For in many cases, as for instance
in such phaenomena as have been lately descanted on by Sir
Roderick Murchison in his lectures on the alpine regions of
Savoy, agencies have been invoked, which, as he shows, could
not have effected the purposes assigned them, in all time ; agen-
cies, in fact, which are no agents at all, inapplicable, and to appeal
to which is to fall into the " vulgar error '' of non causa pro
causa. Put the case, as of the gradual elevation of the Wealden,
and the quiet removal of the materials into the adjoining basins ;
— then, where are the beaches that should attest such gradual
elevations and gentle retirement of the sea, from the newly-
elevated lands ? Again, could we imagine the extensive excava-
tions under review effected by the slow operation of sea-currents
at the bottom of an ocean, be it shallow or profound ; — then,
whence the smashings and poundings of such mountains of an-
the London and Hampshire Basins, 373
gTilar flints, without a solitary pebble amongst them to bespeak
the scene of a patient attrition ? But it is not so much my wish
to set aside the hypotheses of others as to establish my own
theory. I argue the unity of design and the totality of the
phsenomena of upheaval in all the long line (a line of 200 miles
extent) of the great anticlinal of which the denudation of the
Weald is a part, as proof of a sudden and uniform upward
movement, to which the water-shed, a systematic arrangement
of valleys, begun in fracture and enlarged by aqueous erosion,
lacerated escarpments and drift faithfully respond. I have else-
where said that " an act like the elevation of the anticlinal line
which formed the basins of London and Hampshire, or the sub-
sidence of these basins, would be alone sufficient to raise a wave
that would drown the habitable parts of half a hemisphere. A
few such actions coming into play contemporaneously, or in
quick succession, are cause sufficient for a deluge*.^'' And this I
venture to reassert ; and that the flux and- reflux of the waters
of such an inundation would be sufficient to remove all the mate-
rials here supposed to be excavated, — all the calculations of the
power of '^ waves of transport,^' or of denuding water-currents,
to the contrary notwithstanding.
To those who are startled at the magnitude of such operations,
and who are unwilling to admit such a Deus ex machina into the
great scheme of nature, I recommend an inspection of Plate XL.
of De la Beche^s " Sections and Views,^^ — representing the insig-
nificance of mountain elevations, and of a depth of a hundred
miles, compared with the diameter of the earth,— and his obser-
vation, ^' How insignificant do our tremendous dislocations, stu-
pendous mountains, and the like, become, when we contemplate
such a figure as that before usf! ^' At the same time, it is not
unlikely that the very persons who advance such objections,
grounded on their observation of what is now passing under their
eyes, will indulge freely in a speculation on the bursting of a
planet, and the distribution of the asteroids so created ! There
is another class of objectors, who have more show of reason, who
would split the difference between the extremes of uniformity, or
the slow w^orking-hand of time and catastrophic action, who
think that nature has no need, and does not afford evidence of
operations of such magnitude, and so would have done that
which we see has been done, by a succession of minor convulsions,
piecemeal. Then what becomes, in a case like this of the Weald,
of a widely-extended and uniform class of phsenomena, combined
operations bespeaking unity of cause, acting toward and for a per-
fect and consistent whole ? No advance in our knowledge of the
* Phil. Mag. vol. y. p. 119 (1829).
t Sections and Views illustrative of Geological Phsenomena, by Henry
DelaBeche. London, 1830. \ :y. .. .. :
874 Mr. P. J. Martin on the Anticlinal Line of
denudations of the south of England or investigations into their
causes, have been made since the publication of the description of
the Weymouth countiy, and of its phsenomena of disturbance, the
joint production of Dr. Buckland and Sir H. De la Bcche, in the
Geological Transactions of 1830*. This country lies at the
western extremity of the other great parallel line of upheaval on
the south side of the Hampshire basin, which, as Conybeare and
Phillips sayt, extends at least sixty miles, from the eastern extre-
mity of the Isle of Wight to Abbotsbury in Dorsetshire. This
line there is good reason to believe takes its course also in the
opposite direction across the Channel, like the foregoing, toward
and probably into thej^rench coast.
It would be a task of no great difficulty to bring the phaeno-
mena there described into harmonious relation with those of the
Weald, and to show their great family likeness and their syn-
chronism. There, great perpendicular faults and fissures seem to
have been the subordinate agencies and to have done the part of
the numerous anticlinals of the Weald. There, mutatis mutandis,
the same kind of valleys, the joint operation of fracture and
aqueous erosion, are to be found, and the same sort of dilu-
vium. But the same orderly aiTangement of the drift that we
find in the Wealden area is hardly to be expected, from the
greater irregularity of the denuded surface ; and perhaps also
the greater variety of the strata, or formations, concerned in the
stnicture of the country.
After speaking of the inadequacy of existing causes for the
production of these surface-changes, the authors of the above-
mentioned description say, " The only satisfactory solution we
can find is in the waters of a violent inundation j and in these
we think we see a cause that bears a due ratio to the efiects that
have been produced. How far the causes of this inundation
may be connected with the elevation of the strata in the imme-
diate neighbourhood or in distant regions, is a subject which at
present we conceive it premature to enter into, further than to
suggest that the relation of the one to the other may possibly be
nearer than has been hitherto apprehended J. '^ This was written
a year after the publication of my " Theory of the Denudation
of the Weald,^' in which I had shown the relation of these phse-
nomena to each other, the arrangement of the fissures of the up-
heaval, and their enlargement into a system of longitudinal and
transverse valleys by aqueous abrasion, and the drainage of the
country by their means. If Dr. Buckland had followed out his
original exposition of the phsenomena of " Valleys of Elevation "
* Geol. Trans, vol. iv. new scries.
t Conybeare and Phill?ps*8 Outlines of the Geol. of England and Wales,
1822.
X Buckland and De la Beche, loc, cit.
the London and Hampshire Basins. 375
to its legitimate conclusion^ as I think he might have done, with
the felicity that usually attended his speculations and researches,
it is not saying too much to suppose that we might have been
spared all the unprofitable labour that has been bestowed on the
supposed operations of the pleistocene sea ; which covered a great
part of the continent of Europe, and all the south of England : —
9, sea teeming with icebergs, depositing here and there the mate-
rials they held in suspension, with the remains of animals of the
higher orders that floated in from the adjoining countries ! A
fallacy that has produced more fruitless speculation, and the ex-
position of more false facts and false observations than are other-
wise to be found in the recent records of geology. To conclude :
the obvious inferences to be drawn from what we have seen, are
these: —
Since the deposition of the tertiary beds a great and sudden
upheaval of some parts, and perhaps contemporaneous subsidence
of others, took place over a widely extended area ; perhaps over
the greater part of the south of England.
That the phsenomena of the arrangement of valleys, and of
watershed, over all the length and breadth of the anticlinal
line of the London and Hampshire basins, respond to this con-
vulsion.
That this convulsion was attended or immediately followed by
a devastating flood, which excavated and carried off the broken
materials, and only left a small quantity of drift to attest its
agency ; and that this inundation subsiding, the waters withdrew
at once, a period of tranquillity succeeding^ which has continued
up to the present time. Or, in other words, that this is the most
modern change of any magnitude that has come over this part
of the world : it would be hardly proper to say our island, for in
all probability this country did not previously exist in that form.
That although these convulsions may have been synchronous
with, or in part the effect of changes " in distant regions,^'' as
hinted at by Dr. Buckland and Sir Henry De la Beche, yet to
overlook these evidences of local disturbance, and not to con-
sider them the proximate cause of inundation and denudation,
appears to be a gratuitous dereliction of the proof before us. A
part of the truth at least, and that of the greatest importance, is
at hand; the rest remains as yet at a distance*.
* Since the pubheation of the greater part of this memoir, the writer's
attention has been directed to Mr. Prestwich's " Geological Inquiry on the
Water-bearing Strata of the country around London." He agrees most
cordially with all that Mr. Prestwich has advanced respecting that part of
the country which enters into the area under review. On this and some
other explanatory matters he proposes to make a few observations, which
will be the subject of a postscript to appear in the next Number of the Phi-
losophical Magazine.
[ 376 ]
LVI. On the Motion of a Pendulum affected by the Earth* s Ro-
tation. By Septimus Tebay, Mathematical Master, Bruce^s
Academy, Newcastle-upon-Tyne.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
SHOULD you deem the following brief solution of this in-
teresting problem worthy of notice, its insertion in an
early Number of your valuable periodical will much oblige
Your obedient Servant,
Septimus Tebay.
Let the centre of the earth be the origin, and its axis the
axis of X, and at the commencement of the motion let the plane
scz coincide with the meridian. Let r be the radius of the earth,
I the length of the pendulum, /? the angular velocity of the earth,
6 the inclination of the plane of the pendulum to the plane of
the meridian, e, e\ e" the directing angles of the vertical line,
xyz the coordinates of the centre of oscillation, p the line from
this point to the origin, 77, 77', 77" the directing angles of p, and
^ the inclination of p to the vertical.
The dynamical conditions of the problem are represented by
the equation
(J^ + Gcos6)8^+(J + Gcos6')ay + (J+Gcos8'')s^=0(l.)
(Poisson, Traite de Mecanique, No. 531), G being the whole
attraction of the earth, supposed at rest, on a particle at its
surface.
By the geometry we have
a!=p COST), y=p COST)', z=zp cos rf".
And € being equal to the colatitude of the place,
cos e' = sin € sin fit, cos ^' = sin e cos ^t.
Let €+</) be the polar distance of the ball of the pendulum, and
yjr its longitude measured from the meridian of the place, ^ and
•^ being necessarily small. We have
cos 7) = COS (e + <t>),
cos 7)' = sin (e -f (j)) sin {0t -\- ylr),
COS 7]l'=siD. (e + c/)) COS {j^t + '^).
Also^ putting r + /= R, we have
R2+p2_2Rpcosx=/^.
Hence, as far as small quantities of the second order.
On the Motion ofaFendulum affected by the Earth* s Rotation, 377
But
^=^cos^, 'v/r sine =s;)^ sin ^,
retaining only infinitesimals of the first order. Whence
p^2 = <^2 + i|r2 sin^ Sj
■^ sine=tan^.
Consequently
and therefore,
ij?=r cos (€ + </))+ -^(^^4- ^/r^sin^e) cose,
2/ = r sin (e + </>) sin (y5^ + '^) + -^ (0^ + 'v/^^ sin^ e) sin e sin ^t^
^-ssr sin (e + <^) cos [fit + '^) + o; (^^ + "^^ sin^ e) sin e cos fit.
Substituting therefore in (1.), observing that the virtual velo-^
cities S(f>j S\jr are geometrically independent, and neglecting
small quantities of orders higher than the first, we obtain
^+Af+B^ + C=0, (3.]
^^A'f +B'^ =0, (3.)
in which
A=-/8sin2e, B = |— /32cos2e, C=~|-sin3e,
A'=;Scose, B'=|^.
Q
Write H— ^ for <^, and equations (2.), (3.) become
^+Af ^B'^=0. ...... (5.)
These equations are linear and of the second order. We shall
obtain a particular solution of them by assuming
n=-Re''\ yfr^nke"^'.
Substituting in (4.) and (5.), we have for determining k, m,
m2+A^m+B=0,.
km^+Mm-i'B'k^O,
378 On the Motion of a Pendulum affected by the Earth's Rotation.
Eliminating k,
7wH(B+B'-AA'K+BB'=0.
Denote the roots of this equation by
mV-1, -mV-l,m'V-l, -mV-1;
and let the corresponding values of ^ be
ZJ JJ Lit ^Vf
lij "-"/l J A, f —A. *
The complete solution is
The constants R-i, R-g* B-s, B4 may be determined from the initial
circumstances of the motion, namely when /s=0, in which case
we shall also have
dD. ^ d^!r ^
Let Hp a|rj be the initial values of fl, i/r. We shall have
Oi=Bi + R2+B3 + B4,
, . 0=RX-R2m' + R3m''-R4m",
* ' 0=:RiA/m' + Ra/tW + RgFm" + R4^"m".
Whence
___ m"f n,k" ti \
p m^T a,F ^^ y
^3- 2 \k'm''-k"m"'^kV-k'm" ]'
m' f a,k! jr, \
*^'»"" "2 LA/m'-AV k"m'^k'm"J'
And therefore,
n^
2{k!m'-k"m")
^k^^{^rn"(e^n^^^^^
The Rev. E. R. Anstice on the Motion of a Free Pendulum, 379
These equations may be also written as follows : —
, ,^p „{ -kV cos m't+Jdm! cos m"t} . . . (6.)
-vfr=^,. /\, ■■{ — A;W' cos m't + k!'m! cos m'V} +
^^^i^^{-m"sinm'^ + m'sinm"^} (7.)
The principal object of the problem appears to be the determina-
tion of 6 when % is a maximum for a given number of vibrations.
For maximum values of % we shall have
*S + -^^f =«• ...•■••• (80
The preceding equations give all the circumstances of the motion
for small oscillations^ but I have not yet attempted their solution
in any particular case.
Newcastle-upon-Tyne,
September 5, 1851.
LVII. On the Motion of a Free Pendulum.
% Me Rev. R. R. Anstice/ ilf.^.*
I. \ PLANE is rigidly connected with an axis, which axis
■^^ rotates with an uniform angular velocity = b, carrying
the plane along with it. A material particle is constrained to
move in the said plane^ and also acted upon by a central attract-
ive force varying directly as the distance^ and situated in the
intersection of the axis and plane. To determine the motion, v
This I shall afterwards prove will be the same as the small
oscillations of a simple pendulum at the earth's surface, free to
move in any azimuth : b will then be the angular velocity of the
earth's rotation. The axis will correspond in direction with that
of the earth, and the plane with the horizontal plane at the place
of observation.
Refer the motion to three axes mutually at right angles.
Take origin at intersection of axis of motion and plane ; make
axis of motion axis of z. Then the plane of o^y will correspond
in direction with the earth's equator.
Let If m, n be the cosines of inclination to the axes of oc, y
and z of the normal to the rotating plane at any time t. Then
n will be constant and = sine latitude. / and m will be func-
* Communicated by the Author,
380 The Rev. R. R. Anstice on the Motion of a Free Pendulum.
tions of / ; and their values, as I shall show hereafter, must be
such as to verify the equations
Let a^ be the central force at the unit of distance, N the
normal (accelerative) force of reaction of the rotating plane. We
have then the following equations :
d?l_dlm_.o /I X
I m
n= constant = sine latitude"! .^ \
/2 4.^2^^2 = 1 J • • ^ -^
he+my + nz^O (3.)
£/^2y=~a2y-}-Nm I (4.)
d^z=-a^z-^-^n \
Multiply the first of equations (4.) by /, the second by m, the
tbii'd by n, and add ; and we find (attending to equations (2.)
and (3.)),
-^^Id^x^mdfy^nd^z (5.)
Again, multiply the first by d}, the second by dp,, and add ;
and we have, attending to equation (2.),
dJi.d^x-\-dfi.d^y + a^{oedjt-{-ydfi)=.0. . . : (6.)
Now u and v being any functions of t, we have
d^iuv) = ud^v + '^dp . dp + vd^u
= ud^v — vd^u + 2d^{vd^u) ;
r,ud^^v=d^^{uv)-2d^{vd^u)+vd,''u. , . . (7.)
In this formula write in succession,
in place of u, /, and in place of v,a?"^
m, ... y >j and add;
n, •«. ' z.
Id^x^ f Ix-
-i-md'
+ nd-
That is, by help of equations (1.), (^.) and (5.),
N = — 2d^(xdji + ydpi) — h\lx + my) ;
and agam by (3.),
'!^=z^2d^(xd^l+ydp)'^bhlz (8.)
"' "^ — —
d^x^ r lx-\ r xd}
dfy K^d^X -^-my^ — ^dA + yd pi
IfzJ L + w^J V-^zdp
The Rev. R. R. Anstice on the Motion of a Free Pendulum, 381
Again, in formula (7.) write in succession,
in place of Uj dj,, and in place of Vyx\ , , , ^
••• dfi, ... y-i *
/ dfd,^a^\^J ^^t^\^2d( ''^"^\ + ( ^^"^\-
V + dtmd^yJ * V + yd^mJ ' V + yd^^m/ \ + ydfm) '
or, by help of (1.),
\ + ydffi/ \ + my/ \ + ydffi/
and again by (3.),
= d^( ^^t^\-'2bHd^-'b^( ^^t^\.
\-{-ydfi' \+ydfi'
Therefore, substituting this value in equation (6.),
d^ixdjt+ydfi) + {d^-b^)[xdj, + ydfi) '-2b^nd^z=z0. . (9.)
Also, substituting in the last of equations (4.) the value of N
given by (8.),
d^^z + {a^'~bH^)z + 2nd^{xdJ[-\- ydp) = 0. . . (10.)
Now if, retaining the same origin, we refer the particle to
rectangular coordinates X and Y in the rotating plane itself, and
make the line of nodes t^e axis of X, I shall presently show that
we must have
z^sf\-n^X
xdjt-\-ydfff=h */\
s;i} '"■
Substituting these values, equations (9.) and (10.) become
J/X+(fl2-62)X-257ii,Y=0 \^ .
d^Y-\-{a^-bV)Y-^%bnd^lL=0-^'
which are the equations of motion in their simplest form. It
remains to establish equations (1.) and (11.).
Let, then, i be the inclination of the rotating plane to the plane
of xy, 6 the inclination of line of nodes of said plane to axis of x.
Then of course i = colatitude, cosi=?i, and also
dfi^h (13.)
Then
a?=X cos ^— Y sin ^ cos ?
?/=Xsin^+Ycos^cosn ^ ^ ^ n4.)
^=Ysini= \/r=^Y y
which also is the first of equations (11.) Multiply the first by
sin 6 sin t, the second by ■— cos 6 sin 2, the third by cos i, and add j
.'. a? sin ^ sin i—y cos 6 sin i +5r cos 2=0.
Phil Mag. S. 4. Vol. 2. No. 13. Nov. 1851. 3 D
382 The Rev. R. R. Anstice on the Motion of a Free Pendulum,
Comparing this with (3.), wc get
/= sin ^ sin J m = — cos 6 sin i n = cos t.
From these we find, by help of (13.),
dflz= b sin i cos 6 -\ dp. = h sin i sin Q
d^l-=. — 6 sin « sin 6 J d^m = Jy^ sin i cos 6 .
Therefore
dH d^m
'< " — ^t
-b\
I m
which are equations (1.) And also
xdfl + ydp = 6 sin f (a? cos ^ + y sin 6) ;
that is, by help of (14.),
which is the second of equations (11.).
II. Solution of the equations of motion.
We have then
d;X-\-(a^^b'^)X^2bnd;Y=zO 1
d;'Y-^(a^--b^n^)Y + 2bnd^X=0j''
Let
X=Asin(A:/ + a)"l ,^ v
Y=A'cos(A^H-a)/ ^ *^
be a particular integral ; A, A', k, and a being constants. There-
fore substituting in the equations of motion, we have
A\a^''bV-k^)+2bnkA=0J' ' ' ^ '>
... {a^^b^-k^){a^''bV-k^)-4b^nU^ = 0. . (4.)
Therefore if A', k" are the two positive values of k which verify
equation (4.), the general solution of (1.) will be
X=Asin(A7 + a)4-Bsin(A'7 + ^) 1 .^.
Y=A'co8(A/^ + «)+B'co3(F^ + /3)J * ' ' ^ '^
Here A' and k" are definite constants, determinable by equa-
tion (4.) ; A, B, a, y8 indefinite, being the arbitraries of the
problem.
Also A' and B' are given in terms of A and B by the equations
A' k^^-a^ + b^ 2bnk!
■*■- V kf-a^-^n^^
5! « V-fl^ + 5^ _ 2bnk,^ _ /Jl^^
B "" 2bnk„ -k,^-a^-\-n b^ " -V k^^^a^^n
A "" 2bnkf "■ kf-a'-\-n%''
+ ^2^2
(6.)
The Rer. E-. R. Anstice on the Motion of a Free Pendulum, 383
The problem will be much simplified if we suppose the period
of oscillation of the body very small compared with the period
of rotation of the plane. Then b will be very small compared
with a, so that its square^ &c. may be neglected^ and our equa-
tions become
,\k^=:a-\-hn k! =^a—bn.
Also ^'«.i S'_ _
.*. X=Asin («^ + a + 5w^) + B sin {at+^—bnt) \ . .
Y=sAcos {at + u-{-bnt)-'Bcos{at + 13— but) J '
Now were the term bnt involved in these equations constant
instead of a function of the time^ the orbit we know would be
an ellipse round the centre, or a straight line. That term, how-
ever, contains tj and will in process of time become sensible ;
but as it alters with extreme slowness, we may consider it as
sensibly constant during one oscillation of the body, and deter-
mine the elements of the ellipse on that hypothesis. To do this,
consider for a moment the equations
a; = CBm{at-\-6)\
y='D cos{at + €)J
C, D, a, and e being constants ;
and the orbit is in this case an ellipse, whose axes coincide with
those of the coordinates, and = 2C, 2D respectively.
But if these axes, instead of coinciding with, were inclined at
an angle cj) to the coordinate axes, and X and Y are the coordi-
nates in that case, we have
X=a7 cos </>—?/ sin ^ = Csin {at + e) cos<^— Dcos(«^ + €)sin<^
Y=^sin <^ + 2/cos ^ = Csin (fl^ + 6)sin (^ + Dcos(«^ + €)cos(j5>.
That is,
n
X= — (sin (a^ 4- € + </)) 4" sin (a^ + e — 0))
+ K-(— sin(«/ + e + ^) + sin(fl!^ + €— <^))^
Y=— (— cos(«if + e + 0)+cos(«^-f €— ^))
+ g- (cos {at + € + (!>)+ cos {at+€— <^)) J
2P2
384 The Rev. R. R. Anstice on the Motion of a Free Pendulum,
Or
C4-D C— D
X= — 2 — sin (fl/-f €—</)) H ^ — siii(a/+e + <^)
Y= — ^ — cos(fl/ + e— <^) ^ — cos(a/ + € + </))
By comparing equations (7.) and (8.), we get at once
C+D
(8.)
.CssA+B D = A~B
}
^-« .„. \ (^•)
Therefore equations (7.) refer to an ellipse, whose axes are con-
stant, and =2(A + B), 2(A— B) respectively; but the direction
of which axes have an uniform angular motion of regression
(/. e. contrary to that of the earth), and which —hn— eartVs
angular velocity x sine latitude. If one of the two, A-f-B,
A— B=0. The motion in that case will be rectilinear.
III. It now only remains to prove (what is in fact self-evident)
that the problem already discussed is that of the pendulum at
the earth^s sm-face free to move in any azimuth, provided the
oscillations thereof are small.
Consider, then, the motion of a material particle acted on by
gravity, and constrained to move in a spherical surface attached
to the earth and rotating with it.
Make the earth's axis the axis of z, and take origin at the
point where the vertical of the place of observation cuts the same.
Let /, m, n be the cosines of inclination of the vertical to the
axes of Xy y and z ; .*. w is constant, and = sine latitude.
Let R = distance of particle when at lowest point from origin ;
.*. R/, Rm, Rn will be coordinates of lowest point.
Let R/ + X, Rwi -f- y, Rw + r be coordinates of particle at time t ;
r= radius of spherical surface;
.-. (r/-a7)2 + (m-y)2+(r7i-2')2=r2 . . (1.)
will be the equation to the surface ;
, a? y z
I , m— -, n
r r r
will be the cosines of inclination of the normal of said surface.
Let g be the force of gravity at the given place ; /', m', w' the
cosines of inclination of the direction in which it acts.
The normal accelerative force of reaction may be divided into
two ; one constant, the same as is exercised when there is no
osciUationj and the particle remains in (apparent) rest at its
The Rev. R. R. Anstice on the Motion of a Free Pendulum. 385
lowest point ; this we will call K : another variable, produced by
the motion, which call N. The whole force therefore = K + N.
Our equations of motion therefore are
^/(R/4- ^) = ~^/' + (K + N) (/- ^)
<?/(Rm+7/) = -^m' + (K + N)(m-^) )>. . (2.)
<//(Rw+^) = -y+(K + N)(?i- ~)
Also, as before.
/ m
w= constant
}
(3.)
b being the angular velocity of the earth ; and our equations
become
(4.
Now these equations must be satisfied when there is no oscil-
lation, and the particle remains in (apparent) rest at its lowest
point. In which case
Consequently we must have
0=-^Z'+(K + R62)/ -
0=-^m'+(K + R6V > (^0
0=—ffn' + Kn
If in these equations we bring the term involving g to the
other side, square and add, attending to the relations
/2^wi2-f-w2=Z'2 + m'H?i'2=l,
we find
^2=:.(K + R62)2(l-n2)^KV, . , . (6.)
from which quadratic K may be determined in terms of known
constants.
From the same equations we may also find /', m' and n', in
terms of /, m and constants. But this is not necessary for what
follows.
Now if we subtract each of equations (5.) from the correspond-'
> (7.)
886 Capt. E. M. Boxer on the Effect of the Rotation of the Earth
ing one of equations (4.), our equations of motion become
</>=-(KH-N)^-f-N/"
r?,«;?=-(K + N)-+N»^
Now suppose the oscillations very small. Then a:, y, z, and N
will be small quantities whose squares and products may be
neglected. Therefore equation (1.) becomes
/a7 + 7wy + 7i2r=0 (8.)
Equations (7.) become (calling — ^a^)
^/2^=-fl2y + Nm > (9.)
But equations (3.), (8.), and (9.) are precisely the equations
of motion of the former problem ; and the two problems are
therefore identical.
LVIII. On the Effect of the Rotation of the Earth upon the Flight
of a Projectile. By Captain E. M. Boxer, R.A."^
To the Editors of the Philosophical Magazine and Journal,
Mill Hill, Woolwich,
Gentlemen, June 10, 1851.
HAVING lately been investigating a curious question with
regard to the rotation of the earth, viz. the amount of its
effect upon a projectile in causing it, during its flight, to deflect
from the object to which it was directed, or more correctly speak-
ing, the object to alter its position with regard to the path of
the shot, the data, so far as the range and time of flight are
concerned, not being assumed, but taken from actual practice,
I have been surprised at the result. Although I do not con-
sider it to be of any practical importance in the present state of
gunneiy, yet perhaps at some future time such perfection may
be obtained in the machine from which the shot is propelled, as
well as in the projectile itself, as to make it worth while taking
* It is due to the author to state, that this paper was received by us on
the 17th of June last; its pubUcation has been delayed owing to great presi
of matter.— Edits.
M-xsiii upon the Flight of a Projectile, 387
into account the rotation of the earth : but independently of this
consideration, it becomes a very interesting question on account
of the amount of eiFect that is produced.
When I first heard of M. Foucault^s pendulum experiment, I
felt perfectly satisfied in my own mind that the principle was
correct, by imagining the case of a projectile discharged at an
object at some distance in the line of the meridian ; and I com-
municated to Professor Barlow a solution of the question, as to
the apparent deviation of the plane of the pendulum in different
latitudes, by determining the angular velocity of the tangent to
the meridian, previously to any similar demonstration appearing
in print. Although this may not be the most elegant solution,
I think it is more easily comprehended by the majority of per-
sons. The investigation of the following problem is according
to this method.
In the experimental practice of 1839, a 56-pounder of 97 cwt.
with a charge of 17 lbs. of powder and an elevation of 35°, pro-
jected a ball 5600 yards, the time of flight was 34". What effect
would the rotation of the earth have in causing the shot to fall
to the right or left of the object fired at, assuming the latitude
of the place as 52° ?
Suppose the earth to be a perfect sphere, and a geographical
mile equal to 2000 yards, and for the sake of simplicity the gun
fired due south.
Let AEQA' represent
aportion of the terrestrial
surface between the pa-
rallel of latitude AA' and
the equator EQ, and let
BB' represent another
parallel of latitude, di-
stant from the former
5600 yards, or 2*8 geo-
graphical miles the range
of the shot. Let a gun
be supposed to be placed
at A, and fired at an ob-
ject at B in the meridian.
The time of flight of the shot being 34", which is equal to 0^-566,
therefore during the time of flight of the shot, the earth will have
passed through 8''513 of space. Now suppose at the end of that
time the position of the gun to be A', AA' being equal to 8'*513 ;
and the object fired at to be at B^, BB' being also equal to
8^*513. But the ball participating in the motion of the point A
will have arrived only at C, BC being equal to AA'. Consider-
ing this small portion of the terrestrial surface as a plane, the posi-
888 Capt. E. M. Boxer on the Effect of the Rotation of the Earth
tion of the shot may be found by drawing A'C parallel to AB, and
B'C will be the difference of length of the two arcs AA' and BB',
which will be the deflection of the shot. It will be observed
that the two tangents AB, A'C are assumed to be parallel ; but
this is not strictly correct ; for the same reason as in the pen-
dulum experiment, the apparent revolution of the plane of the
pendulum at any place upon the surface of the earth will not be
OQ.QQA
. , ^ hours. And the reason of it is this : the path of the
sm lat ^
point A when projected upon a horizontal plane will be a curve ;
therefore in the case of the projectile, the shot only receiving an
impulse due to the earth's rotation at the point A from which
position it is fired, the two tangents manifestly will not be per-
fectly parallel ; but the correction from this cause would be so
small as not to be of any moment in an approximation of this
sort. In the case of the pendulum, the path of the point of sus-
pension when projected upon a horizontal plane being a curve,
unless the arc of vibration be infinitely small, the law of inertia
will cause the ball to take an elliptical motion, and an apsidal
motion will be the result. We will therefore take the two tan-
gents to be parallel, or rather AA' to be equal to BC,
2-8 mUes =2' 48".
The latitude of the place being 52®,
51° 57' 12" will be that of B.
The circumference of the earth being 21,600 geographical
miles, the arc
AA'= 8-513 cos EAl . i,- i -i
arc BB'=8-513cosEB j"^ geographical miles;
.-. BC = 8-513(cosEB- cosEA) = 10-914 yards,
which is the deflection of the shot when fired due south.
The motion of the earth being from west to east, or from A
to A', the ball will fall 10*914 yards to the west, or to the
right of its direction. If fired due north from the point A, it is
obvious that the shot would fall nearly the same distance to the
east of the object, but still to the right of its direction.
The next point to be considered is, whether if the ball be
projected due east or west, or in any other direction, the same
amount of effect will be produced. I think there is no doubt
that there would be, and perhaps the most intelligible manner
of showing this is as follows : —
The Hue joining the north and south points of any place upon
the earth's surface is a tangent to a great circle at that point
passing through the two poles ; and the line joining the east
4\^'^»a ^Y\()mi'%^dk the Flight of a Projectile, ^ ' 389
Adiythdt pointi^ is the tangent to another great circle passing
through the place at right angles to the former, and may be re-
presented by the two lines NS, WE ; these lines always of course
remaining at right angles to each other. We will suppose that
K
B'
^sr
^.
E
two guns are placed at P, which is 52° lat., the one pointing due
south and the other due west, at two objects 5600 yards distant
from P in these directions, and that they are both fired at the
same moment. Now the directions in which the balls are fired
are at right angles to each other, and there is nothing in the
rotation of the earth to alter the relative positions of the two lines
drawn from the guns to the shot during any moment of their flight.
It has been shown that the shot fired due south will be
deflected 10-914 yards to the right of the object in 34'^ Let the
above figure represent the north and south, and east and west
lines, at the end of 34". Now the position of the ball fired due
south will be B, SB being equal to 10*914 yards ; join PB, and
draw B'P at right angles to PB ; then if PB and PB' be equal,
WB' will be 10*914 yards. This perhaps may not be rigorously
correct, as the correction necessary to be made on account of
the horizontal curved motion of the point where the gun stands
would not be so great in the one case as in the other.
By the same reasoning, it can be shown that the deviation of
the shot will be the same in amount in the same latitude, or
nearly so, whatever may be the direction of the range, and that
the deviation will in all cases be to the right of the object.
In difierent latitudes, it appears, from what has been stated,
that the amount of deflection depends upon the length of range,
the time of flight, and the cosine of the latitude of the gun ; it
390 Dr. A. Krantz on a new Mineral named Orangite.
will therefore be obviously greatest at the pole^ aud may be said
to vanish at the equator.
It may be interesting here to ascertain what the deflection
ought to bej solving the question by the apparent deviation of
the plane of the pendulum in 34". The tangent of the arc of
vibration maybe looked at in the same light as the line drawn from
the gun to the shot at any moment of its flight ; for there is
nothing in the rotation of the earth to cause this tangent to have
an angular motion in a horizontal direction.
8'-513 = rotation of the earth in 34"nat. sin 52°= -7880108.
8-513 X •7880108=6-708=6' 42" 28"' deviation in 52 lat.
in 34".
Length of cu*. arc of 6' 42" 28"' = -0019512 of radius rad.
= 5600 yards.
5600 X -0019512 = 10-926 yards, which is the deflection.
Taking into account that the amount of deflection of the pro-
jectile has been determined, in the one case, by assuming the
length of a geographical mile to be 2000 yards, and that in the
other, viz. in the pendulum experiment, the amount is indepen-
dent of the size of the earth, the results are as nearly alike as
can be possibly expected.
I am. Gentlemen,
Your obedient Servant,
E. M. Boxer.
LIX. On a new Mineral named Orangite.
By Dr. A. Krantz of Bonn^^,
THIS mineral has been found only at Langesundfjord near
Brewig in Noi-way, and is of veiy rare occurrence.
It has been analysed by Dr. Bergemann, and is stated by him
to contain a new metal which he has named Donarium. [Hia
analysis, together with an account of the properties of the new
metal, were given in the Philosophical Magazine for June 1850,
p. 583.]
No indications of crystalline form have been observed. The
fracture is conchoidal ; structure imperfectly foliated ; transpa-
rent to translucent ; colour deep orange-yellow ; streak yellow-
ish-white ; hardness between fluor and apatite ; specific gravity
5*34 to 5'39. It occurs usually imbedded in felspar, associated
with mosandrite, black mica, hornblende, thorite, zircon and
erdmannite.
♦ Communicated by W. G. Lettsom, Esq.
-^ . ^ .- [ 391 ] ' ■ '* 'm
LX. On a remarkable Discovery in the Theory of Canonical Forms
and of Hyper determinants. By J. J. Sylvester, M.^.,F.i2.>S.*
IN a recently printed continuation of a paper which appeared
in the Cambridge and Dubhn Mathematical Journal f^ I
published a complete solution of the following problem. A
homogeneous function of Xj y of the degree 2n-\-l being given,
required to represent it as the sum of n-\-l powers of linear
functions of x, y. I shall prepare the way for the more remark-
able investigations which form the proper object of this paper,
by giving a new and more simple solution of this linear trans-
formation.
Let the given function be . ... ^l^^ ,, ..
fli.«2«+i ^ ^2n + l)ai,se^y+{2ni-l)^^^~aci.x^''-'^ y, &c.
+«2«+2.y^'*"^S
and suppose that this is identical with
The problem is evidently possible and definite, there being
271 + 2 equations to be satisfied, and (2w + 2) quantities pi, q^,
&c. for satisfying the same.
In order to effect the solution, let
qi=Pi'\ .^. .^^..
q2-P2'\
&c.= &c.
we have then
:'(*Mltra
Pi
+P2-^
+Pn+l
= «1
Pi\
+M2+
+Pn+l
.X„+i
= «2
PiK
+P,\'+
+Pn+l
x\+l
= «3
p,\-
+i?2V +
+Pn^l
'K^^
= ««
p^^r'+p^'^""^'
+ ..
. +Pn+l
'\^i
= «n+l
&C.
= &C.
Eliminate p^, pc^...pn+i between the 1st, 2nd, 3rd...(n + l)th
equations, and it is easily seen that we obtain
««+ 1 •— «„SXi + an-iZ\'K2 &c. + ajXjXg . . . \n+ 1 = 0.
* Communicated by the Author.
t Published under the title of *An Essay on Canonical Forms/ by Bell,
Fleet Street. .
392 Mr. J. J. Sylvester on a remarkable Discovery in the
Again, eliminating in like manner j» 1X1,^92X5, .. .j9„+i\„+i be-
tween the 2nd, Srd, ...(» + 2) th equations, we obtain
fln+2— fln+i2\i + &c . . . 4:^2X1X5 . . .X„+i;
and proceeding in the same way until we come to the combina-
tion of the (n + l)th . . . (2n + l)th equations, and writing
SX, =*i
&c.
2X,.X2 . . . X„+l = *n+I,
we find
On^X^a^S^ + an^X'S,^. » » ±ai,8n^\ =0
«»i+2 — fln+l.«l + «^.*2 • • • +^2'*«+l — ^
flfi+S — «n+a«*l4-«n+l.S2 . . . ±«3.«n+l =0
&C. &C.
Hence it is obvious that
{x-^X^y){x-\-\^) . . . (a:+X«+,.y)
is equal to the determinant
On+i; ««; dn-l', •.. «i
flfn+2j fl5n-ij fln-2^ ••• ^fg ^*
• • • • •
Hence X,, Xg, . . . X„+i are known, and consequently
are known by the solution of an equation of the (n + l)th degree.
Thus suppose the given function to be
IxAiii ==(Pi^-^9iy)^-^{P^+Qi!/?+(P^ + 93'y^)>
we shall have, by an easy inference from what has preceded,
{Pi^ + QiV) {P^ + 9^) [P^ + W)
— a niunerical multiple of the determinant
a^'r
-<^y)
cofy
'f
d\
C'y
b'y
a
e;
d;
c;
b
f:
^>
d;
c.
* These equations in their simplified form arise from the ordinary result
of eUmination in this ease contaming as a factor the product of the dif-
ferences of the quantities Ai, As* . i » An+ 1.
Theory of Canonical Forms and of Hyperdetervnmanfs'. 393
The solution of the problem given by me in the paper before
alluded to presents itself under an apparently different and rather
less simple form. Thus^ in the case in question, we shall find
according to that solution,
{Pv« + W) {P^ + M) {P^ + W) It
s= a numerical multiple of the determinant
ax + hy; hx+cy, cx+dy
bx + cy; cx + dy; dx + ey
cx + dy; dx+ey; ex-\-fy.
The two determinants, however, are in fact identical, as is
easily verified, for the coefiicients of c^ and j/^ are manifestly
alike; and the coefiicient of x^y in the second form will be
made up of the three determinants,
a h d
h d d
h c e
c d f
h b c
c c d
d d e
of which the latter two vanish, and the first is identical with the
coefiicient of x'^y in the first solution. The same thing is obvi-
ously true in regard of the coefficients of xy"^ in the two forms,
and a like method may be applied to show that in all cases the
determinant above given is identical with the determinant of my
former paper, viz.
a^x-\-a^\ ac^+a^; ... aj^+an+iy
a^x + a^; a^x + a^; ... an+iX + an+2y
....... i^ri:i\ \
a^x-^-an+iy, «n+i^ + ««+2y; • • • «2»i^+«2«+iy.
Thus, then, we see that for odd-degreed functions, the reduc-
tion to their canonical form of the sum of (/i+ 1) powers depends
upon the solution of one single equation of the (?i 4- l)th degree,
and can never be effected in more than one way.
This new form of the resolving determinant affords a beautiful
criterion for a function of x, y of the degree 2/i + 1 being com-
posed of w instead of, as in general, {n + 1) powers. In order
that this may be the case, it is obvious that two conditions must
be satisfied; but I pointed out in my supplemental paper on
canonical forms, that all the coefficients of the resolving deter-
minant must vanish, which appears to give far too many con-
ditions. Thus, suppose we have
ffa?7 + 7hx^y + ^Ica^y^ + 35^<2?y +35ea^^4+21/a?V+ 7gxy^+hx\
The conditions of catalecticism, i. e. of its being expressible
under the form of the sum of three (instead of, as in general, four) ^^
894 Mr. J. J. Sylvester on a remarkable Discovenj in t^^
seventh powers, requires that all the coefficients of the different
powers of ar and p must vanish in the determinant
a
b
c
d
c
d
f
d e
e f
f 9
9 h\
in other words, we must have five determinants,
d
6
f
9
d
e
f
9
c
d
d
e
c
d
e
f
f
9
d
e
f
9
e
f
9
h
e
f
9
h.
all separately zero. But by my homoloidal law, all these five
equations amount only (5— 4) (5— 3), i. e. to 2. I may notice
here, that a theorem substantially identical with this law, and
another absolutely identical with the theorem of compound de-
terminants given by me in this Magazine, and afterwards gene-
ralized in a paper also published in this Magazine, entitled '' On
the Relations between the Minor Determinants of Linearly
Equivalent Quadi-atic Forms," have been subsequently published
as original in a recent number of M. Liouville's journal.
The general condition of mere singularity, as distinguished
from catalecticism, i. e. of the function of the degree 2n + 1, being
incapable of being expressed as the sum of 2n + 1 powers, is that
the resolving resultant shall have two equal roots ; in other
words, that its determinant shall be zero, which will be expressed
b^ an equation of 2n(n+l) dimensions in respect of the coeffi-
cients. Mr. Cayley has pointed out to me a very elegant mode
of identifying the two forms of the resolving resultant, which I
have much pleasure in subjoining. 1?ake as the example a func-
tion of the fifth degree, we have by the multiplication of deter-
minants,
^ — ^2y ^2 ^^
1
0
0
0
a b c d
bed €
X
a?
0
X
0
y
0
0
ode f
0
0
X
y
Theory of Canonical Forms and of Hyper determinants, 395
:a3io!LiJ 'ui!
h
»WOf|
0 ax-\-by hx + cy cx + dy
0 bx + cy cx + dy dx-\-ey
0 €X + dy dx-\-ey ex+fy
which dividing out each side of the equation by y^, immediately i
gives the identity required^ and the method is obviously general.
Turn we now to consider the mode of reducing a biquadratic
function of two letters to its canonical form^ videlicet
(A +ffy)^ + (^^ + hY + ^^{fa +ffyY{hx + ky) .
Let the given function be written ,^ ^^
ax"^ + 4ibaPy + Qcx^y^ 4- 4idxy^ + ey\
Let
then we have
k=h\2 mfh=fi A,j + X2=^j Xj.Xg=j
f+h + 6fju=:a
4/Xi + 4<h\ + 6//,(35i) - 4<b
6/\,2 + eh\i + Qfi{si^ + 2*2) = 6c
4f\^ + U\i -I- 6yLt(25iS2) = 4c?
/Xi3 + ^X/ + 6/.522=e.
Eliminating / and h between the firsts second and third, the
second, third and fourth, and the third, fourth and fifth equa-
tions successively, we obtain
(«- ^fi)Sc,- {b-Sfis^)s^ + (c-fiis^^ + 2s^)') =0
(b—Sfjbs^)s^— (c—fi{s^^+2s^)^Si + (d—Sfj,SiS^) =0.
(c— /a(5i« + 252)X+ {<^-'^H'SiSc^)si + {e-6fMSyS^=^,ij^
Let iiow
and we shall have
«52 ■- o^i + c — /A (8^2 — 4^1^) = 0
bS2—' CS^ -f d—fJb{4SiS2 — 25i^) = 0
€S^—ds^ + e—fjb{Ss^^--4!Si\) =0.
Ui J
re ^s
moil
as^—bsi + (c + v) =0
Z>^2—(<J— 0^1 + ^=0
{C -f v)52 — efej + 5 = 0.
Hence v will be found from the cubic equation,
a; h; c + v
c+v, d) e
Tin
396 Mr. J. J. Sylvester on a remarkable Discovery in the
a b c
i.e. i^-j/(ae— 4Z>(/4-3c*)+ bed =0,
c d e
in which equation it will not fail to be noticed that the coeffi-
^cientofv^is zero, and the remaining coefficients are the two
well-known hyperdetenninants, or, as I propose henceforth to
call them^ the two Invariants of the form
aa?*H- 4i^y + 6ca!^y^-\-4dan^ + ^ ;
be it also farther remarked that
'=8(59 -2^» 7^^
in which equation the coefficient of Sfi is the Determinant or
Invariant of
x^ + Siscy + S2.y^
y being thus found, s^y s^ and fi being given by the equations in
terms of v are known, and by the solution of a quadratic X^, \
become known in terms of s^, s^ and/, h in terms of Xp \^
fjL, and the problem is completely determined. The most symme-
trical mode of stating this method of solution is to suppose the
given function thrown under the form
4- 6e(/a? -f ^^y) (/^^ +5'V)-
Then writing
—V, the quantity to be found by the solution of the cubic last
given becomes
8€
(^»-f)
I shall now proceed to apply the same method to the reduction
of the function
a^a^ + SdoF . y + 2Sa^y^ + 56agX^y^ + 70a^a^t/* 4- ^6a^a^y^
-\-2Sae . xY + Sayxy'^ -\-as.f,
tinder the form of
-f 70€(piX + q^yY{p^ + q9y)\Ps^ + q^?{p^x -f q^)\
It will be convenient to begin, as in the last case, by taking
S'i=i'i^i q%—P'P^ %=P'?^ 94=Pi\
€PiPiPaP4=^>
Theory of Canonical Forms and of Hyper determinants, 397
and
(x + \y){x-\-\^){x-\-\^)[x^X^y)
we shall then have nine equations for determining the nine
unknown quantities of the general forni
p{K[ +p^'^ +;?3\* +p^\ + M,m = a,y
where l has all values from 0 to 8 inclusive/ and where
^ (1.2...)(l.2...(8-0)
1.2. ..8
multiplied into the coefficient of y'^ , x^~^ in U^.
Taking these nine equations in consecutive fives,, beginning
with the first, second, third, fourth, fifth, and ending with the
fifth, sixth, seventh, eighth, ninth, we obtain the five equations
following : —
«o • s^--a^s^ + ttc^Sc^^a^ .s^ + a^, ^q— mNi=:0
«i . 54— a^s^ + a^s^—a^^ . 5, + a^ . 5q— mN2=0
«2 . s^—(IqSq + a^s^—a^ .s^ + aQ. Sq— mN3=0
% . 54— ^453 + CgSg— ffg . 5^ -f «7 . ^Q— mN4=0
«4 . s^—a^s^+af^s^—aj .s^+aQ. SQ—mlSi^=0,
where
Ni=MoS4-Mi . 53 + M2S2-M3 . Si + M4
N2 = Mi54-M2.53 + M3S2-M4.5i + M5
N3 = M2S4-M3 . S3 + M452-M5 .Si+Mq
N4=M3S4— M4 . ^g + Mg^g—^e • ^1 + M7
/ .' N5 = M454-M5.53 + M652-M7.5l + M8.
Developing now XJ^, we obtain
Mo=70 Mi=^., M2=5.2+|.,^ M3=|.3+|v.
M4= 2^4 + 2^1^ + 522 M5=^5i54+-^2-% M6= 5^2-^4 +1^3'
Hence Nj = 72^4-185153 + G^g^
N2=185i54-^V%+-522
N3 = 1 252^4 — 351^2 • h + ^2^
9 3
N4= I85354- ^ 51532+ g . ^2^ 53
N5= 72542 - 185^53 . 54 + 652^ . 54.
P/«7. ilf«^. S. 4. Vol. 2. No. 12. Nov. 1851. 2 E
898 Mr. J. J. Sylvester on a remarkable Discovery in the
Hence we havej.^raoi Mtii u^ikv^n-, ui won ikde f
.Ni=:72i v^^mfy''^ '^.^nr% N.r=72i* 'i^itmaA
where it will be observed that I is the quadratic invariant of U.
Making now > -
^i^iitJ-i/'> 5ini>n 72mltiiV^ >^wl t»:w 'lailJuiiw tjljj«9'i &
iy^^liiiirtia^i the five following equatil&sV-l*'7't"'i« •..M .4 na
.':i!oii.;;iii u)V.:iinJ Ij/»f.ij10'-.i|i»\; lo VlOOfii .tB3'i2
4/ ,: - J i 4 ^i^aibnoqadi
(«4-»')^4 + «6*3-<'6-«2~fl^»«^^*^8«*»^^ ^f I "pdcT
so that the problem reduces itself to finding v, which is found
from the equation of the fifth degree : —
'0^
'li
*2^
'2f
'3>
*3 f
^4-¥.
a^-^v
3
&
'3^
«4 +
'5>
4'"^^
■-v^^
^4-n %ji^^ %; 'T *f5 -'^<^
V, it will be observed, being 72 x the quadratic invariant of
(p^x + qy) {pcfc + q^y) {p^ + q^) (p^x + ?42/).
when the function is supposed to be thrown under the form of
^iPi^-^qiyf+70€{p,x-hq,yfx(pc^+q^)^p^x+q.^)^X{p^x+q^)^
It is obvious that in the equation for finding v, all the coefii-
cients being functions of the invariable quantities p^, q^y &c.,
and € must be themselves invariants of the given function ; so
that the determinant last given will present under one point of
view four out of the six invariants belonging to a function of
the eighth degree, and these four will be of the degrees 2, 3, 4, 5
respectively*.
* The reasoning in this paragraph seems of doubtful conclusiveness. It
may be accepted, however, as a fact of observation confirmed and gene-
ralized by the subsequent theorem, that the coefficients are invariants.
Theory of Canonical Porms and of J^ijperddehmmm^,
I shall now proceed to generalize this remarkable law^ arid'Tp
demonstrate the existence and mode of finding 2n consecutively*
degreed independent invariants of any homogeneous function of
the degree 4w, and oin-\-\ consecutively-even-degreed indepen-
dent invariants of any homogeneous function of the degree 4?2 -f- 2;
a result, whether we look to the fact of such invariants existing,
or to the simplicity of the formula for obtaining them, equally
unexpected and important, and tending to clear up some of
the most obscure, and at the same time interesting points in this
great theory of algebraical transformations.
In the first place, let me recall to my readers in the simplest
form what is meant by an invariant* of a homogeneous function,
say of two variables x and y. If the coefficients of the function
f{x, y) be called a^b, c , . ,1, and if when for x we put ax + by,
and for y, cx-i-dy, where ad—bc=\, the coefficients of the cor-
responding terms become a', V, ,»J; andif I (at, Z>, .../)= I («', 6', ».J),
then I is defined to be an invariant of/.
Let now f{x, y) be a homogeneous function in x, y of the 2tth
degree, and write
where f and 97 are independent of a;, y, and lp^mn = 0.
Let ^ x'=lx + my
j .^^ 'i^z=nx-\-py,j'^,ys «
then d>^ d_ __£_^ do^ yd dy^
^dx'^'^dy'^^dxf'dx '^^d^'d^
io inmmLiiohmbnn . ^ ^/ d di/ >=^do 3<^ ^^i'^ Ji r^
'^^'d^'df'^'^dP"^'
wefind,j^5,^Jt:^i - d^ ^ _h ^ i <? '«'^ ^¥i>d ,K:^«9b
Again, from the equations hetwem/x/, y'^x^y we B^f^Jj^^^i^f^
II ,i' n.i' -,OT-h r^^ px'-rm/ _^-f_^^ ,5»3i^9b d)ii-b f>i«
^ pl-mn "^^ ^^ *vf9Vri03q8^
.eJflijn^v.. tmm: Hyperdeterminant constaiit'derivatiVe; ^*^ "^^ ^^^'^^^
3E3
400 Mr. J. J. Sylvester on a remarkable Discovery in the
Hence
di/.
Again,
^ - (f'i +^'iJ«^(^' 2^) +^(V^-ry')*.
d ^^ d d
Hence
(4)'"-;5-''-''"'"(;r)'^+<'""+"-"''")
&c. = &c.
©■•""•-•Gt) ■''•^--'■'(|r)'-.|r.P+ <^~
But P' being of c dimensions in o^' and y', and also in a? and y,
each of the equations above written will be of l dimensions in on
and y, and of no dimensions in a', y' ; in fact, the successive
terms of the right-hand members of the above t + 1 equations
will be multiples of the (i + 1) quantities
Consequently a linear resultant may be taken of
\d^)'^' W ^ ^t; ^^•" V^t;/-^^
treating a^^, a^'" ^ .y', . . . y'* as independent, and as the quantities
to be eliminated ; and this, according to a well-known principle
of elimination, will prove the linear resultant o^ the forj^^oing
equations to be equal to the linear resultant of , ' . ':' ' ,
■~ (J^-^.&-'&-(£)-^. '
Theory of Canonical Forms and of Hyperdeterminants, 401
multiplied by the determinant .^ ,^^ ^^ . _,^,i ^^.^ ^,^
&c. &c. -^
This last above written determinant may be shown from the
t(t+i)
method of its formation to be equal to {Ip — mn) 2 ^ ?. e. to \ipj.ty,
because ^—m7i=l. Again, since »- V\
a^''=zM-\-d'-^m.cv'-'\y + kc. . . . -hm' .y' "^ VfJ. /
+m''~'^ .py''
&c. = &c. \
y'^z^n' .a;' + m'~Kpx"-^ . y + . . . -i-p'-y',
the resultant of (^)'^' • • • (j-)*- ^"^ obtained by treating
x'j x'~^.y, . . .y' as the eliminables, will be equal to the result-
ant of the same functions when w", x'^'^.y,... y" are taken as
the eliminables* multiplied by a power of the determinant. , ,
l~^,n; ...; m!'~^.p
^bifiQ%in ()r\^hikii ^\bi\^ ,4- .t-if/tl' •*■
a J » . , f p y
which determinant, like the last, is unity. Thus, then, we have
succeeded in showing that the resultant obtained by eliminating
x^, x*-"^ .y, . . .y^ between
\d^) ' \d^/ dv '"' \dv/ 'ff^m^Qaa&J
is equal to the resultant obtained by eliminating (a/y, x^''"
* y . . . ?/'^ between
'^ (£rr. (I)- (i)n...(|)'p', •"-
Or, which is evidently the same thing, the resultant obtained by
eliminating x'', x''~^ .y . , ,y^ between
* For the statement of the general principle of the change of the vari-
ables of elimination, see my paper in the March Number, 1851, of the
Cambridge and Dublin Mathematical Journal.
^Xt Mffi^^ liF. Sylvester on a remarkable Discovery in the
that is to say, this last resultant remains absolutely unaltered in
value when for x, y we write respectively
h:-\-my
nx-^-pyy
provided that lp^mn=\*
Hence by definition this resultant is an invariant /(a:, y), and
X being arbitrary, all the separate coefficients of the powers of \
in this resultant must also be invariants. I proceed to express
this resultant in terms of \ and the coefficients of [Xj y). Let
Ki)'-' i ■ -(i)"' i/«(-"-- -
E.
;^-(i)-(l)''-(i)-"-(i)V^M-„-.^=S
2
(4)* • Hi)'-f--^' =^'#
Let now
-lOT'^b brtP/i4 •'TtrMf* ar/ot -k, "^ -.r-h
Theory of Canonical Forms and of Hyperdeterminanis, 403
Accordingly, by eliminating >/ v> >
'^ mif^3-i 3kiA ,^iH? ,YRS o) «t ^m\i.
we obtain as the required resultant,^- '- -^ \t . « ir.'! ajfi/^ snla/
A tc sij^/ofi i)dt io ai^sioSii'JO'j'ofB'im^eoii^ '1_^ . 7'; ^ fuuexf /
.liii
.11 r
taJ .(^^ ^;f,) Io ^itnoiorflooi odi'bxm v/Clb mn'i'2 in JiiiiJlijaai Biiii
-v(i)-'
Inasmucb as all the coefficients of \ in this expression are in-
variants of f{x, 7J), and these are the invariants of the first
order, it is clear that the coefficient of X* must be always zero,
which is easily verified.
Again, if l is odd, the determinant remains unaltered if we
write —X for \; hence when/(^, y) is of the degree 46 + 2, all
the coefficients of the odd powers of \ disappear. Thus, then,
our theorem at once demonstrates that a function of x, y of the
degree 46 has 26 invariants of all degrees from 2 up to 26 + 1
inclusive, and that a function of ocj y of the degree 46 + 2 has
6 + 1 invariants whose degrees correspond to all the even num-
bers in the series from 2 to 26 + 2.
But in order that the proposition, as above stated, may be
understood in its full import and value, it is necessary to show
that these invariants are independent of one another, which is
usually a most troublesome and difficult task in inquiries of this
description, but which the peculiar form of our grand deter-
minant enables us to accomplish with extraordinary facility. In
order to make the spirit of the demonstration more apparent,
take the case of a function of the twelfth degree, whose coeffi-
cients, divided by the successive binomial numbers 1, 12,
— ^ — -, &c, may be called ^
fl, 6, c, d, e,f, g, h, l,j, k, /, m. S>.
* Mr. Cayley has made the valuable observation, that X (given by equa-
ting to zero the above determinant) may be defined by means of the equation
(^ being itself a certain rational integral form of a function of the ith degree,
the ratio of whose coefficients would be given by virtue of the above equa-
tions as functions of X and the coefficients off{x,j/). , v ^
S ."jXJl-i' .aid T '&,^ l" ~' — ~o — r — -*-|-^»''^
404 Mr. J. J. Sylvester on a remarkable Discovery in the
Oui' grand determinant then takes the form
9-^^} ,f) ^> d> f^'y *; «
'*5 >-*g; /; ^y d] c'y b
*; ^y ^+15' /' ^' ^' ^
j'y'^hf^', 9-^'y f> ^y d
\
I', k\ j; i; h; ^-gj / l
m; /; k ; j ; i; A; <7+\.
H^pe it will be observed that
.« a and m appear only 1 time.
b and / ... 2 times.
c and A: ... 3 ...
^andy ... 4 ...
€ and ^ ... 5 ...
/and A ... 6 ...
ff ••• 7^ •••
J^t now the coefficients be called
: Hg H3 H4 H5 Hg H7,
Hg and Hg manifestly are independent.
Again, if possible, let H4 =^pYi^y then a and m would appear
twice in H4, contraiy to the rule.
Hence H4 is independent of Hg, Hg.
For a similar reason H5 cannot depend on Hg, Hg.
Agaiuj if possible, let
H6=i>Hg3 + ^Hg.H4 + rH3^
H/ will contain h^ . /^', which by the rule cannot appear in
Hg . H4, or in Hg . Hg.
Hence />=0.
Also H4 will contain ^^/^ x the coefficient of \^ in
(^+ b) (^- ft) {s+ Y^,
which is not zero. And Hg also contains bl) hence HgH4 will
contain 1^. P. But Hg will evidently not contain b^ or P, or bH
or bP, nor can Hg contain bH^; hence ^=0. Finally, Hg^ will
Theory of Canonical Forms and of HyperdetermmanUi 40^
contain c^ and k^j but Hg can only contain as to these letters the
combination c^. 1^ ] hence r = 0.
Consequently Hg does not depend on Hg, H4, Hg. As regards
Hgj H3, H4, H5, Hg not vanishing, this may be made at once
apparent by making all the letters but g vanish ; the H's then
become identical with the coefficients of
none of which are zero except that of X^. The same or a similar
demonstration may be extended to H7 and easily generalized ;
hence, then, this most unexpected and surprising law is fully
made out*.
To return to the subject of canonical forms, I have not found
the method so signally successful in its application to the 4th
and 8th degree, conduct to the solution of other degrees, such
as the 6th, 12th, or 16th, of all of which I have made trial ; pos-
sibly another canonical form must be substituted to meet the
exigency of these cases f ; and it may be remarked in general, that
if we have a function of the (2?i)th degree, the canonical form
assumed may be taken,
where V, in lieu of being the squared product of
{Pix + qiy){p^a?+q^) . . . {pn+i.^ + Qn+i-y)
* This demonstration, however, does not extend to show that the coeffi-
cients of the powers of X may not possibly be dependents, i. e. exphcit
functions of one another combined with other invariants not included among
their number, or of these latter alone. For example, in the case of the
12th degree, we know by Mr. Cayley's law that there must be two inva-
riants of the 4th order. Our determinant gives only one of these. Call
the other one K4 ; by the above reasoning it is not disproved but that we
may have
H6=i?.H/+gH2.H4+rH32-h5H2.K4.
I believe, however, that the H's may be demonstrated without much
difficulty to be primitive or fundamental invariants. The law of Mr. Cayley
here adverted to admits of being stated in the following terms : — The num-
ber of independent invariants of the 4th order belonging to a function of
X, y of the nth. degr-ce is equal to the number of solutions in integers (not
less than zero) of the equation 2x-{-3y=zn—S. Vide his memorable papei*
(in which several numerical errors occur against which the reader should
be cautioned) On Linear Transformations, vol. i. Camb. and Dub. Math.
Journ., new series. There is no great difficulty in showing, by aid of the
doctrine of symmetrical functions, that there can never be more than one
quadratic or one cubic invariant, and in what cases there is one or the
other, or each, to any given function of two variables. The general law,
however, for the number of invariants of any order other than 2, 3, 4,
remains to be made out, and is a great desideratum in the theory.of iiifitr
transformations. _ ^r» ;,
t See the Postscript for a verification of this conjecture. *' ''^ ' '^^-
406 Mr. J. J. Sylvester on a remarkable Discovery in tlie
may be any hyperdeterminant, or (as I shall in future call such
functions) co- variant of this product, understanding P(a7, y) to
be a CO- variant of («r, y) when V{lx-\-my,nx-\-pij) stands in pre-
cisely the same relation to f{lx -f my, rue -^py) as P(a?, y) iof{x, y),
provided only that Ip—mn^l. For the relation and distinction
between co-variants and contra-variants, see a short article of
mine in the forthcoming Number of the Cambridge and DubUn
Mathematical Journal for this month. In endeavouring to apply
the method of the text to the Sextic Function
aa^ + Gbx^y -f- I6ca/^y^ -f 2da;^y^ -f 1 5exY + Qccy^ + qf,
thrown under the form
S(^a7 + ^y)H20eU^
where
U = (p^x + q^y) [p^ + q^) {p^ + q^y) ^s^-\-s^ochj-^Sc^,xy'^-\-s^,
I obtain the following equations :
asg—bs^ -f csi — <;feo= ^(1^625q%— 54^Q.9i52 + 12^1^)
bs^—cs^ + ifej —^^0= €(54^0^1 •% + Qs^^.Sq—SGsqSq^)
CSg— dSQ + eS^ —fio = € ( — 5450^2 • ■^3 ~" ^^l • *2^ + 3^% • "^1^)
^3 — ^^2 +/*l — ^^0 = ^( "~ 1 6250%^ + 54^05^ + 1 2^3^25) .
In these equations, if we call the quantities multiplied bv e, L,
M, N, P, we shall find
53L- ^s^M- ^s^N-\-Sq.?=0,
and
where I denotes the determinant, or, as I shall in future call
such function (in order to avoid the obscurity and confusion
arising from employing the same word in two difibrent senses),
the Discriminant*, which is the biquadratic (and of course sole)
invariant of the cubic function
SoX^ + SiX^y + Scixy'^ + s^.
* " Discriminant," because it affords the discrimen or test for ascertain-
ing whether or not equal factors enter into a function of two variables, or
more generally of the existence or othenvise of multiple points in the locus
represented or characterized by any algebraical function, the most obvious
and first observed species of singularity in such function or locus. Progress
in these researches is impossible without the aid of clear expression ; and
the first condition of a good nomenclature is that different things shall be
called by different names. The innovations in mathematical language here
and elsewhere (not without high sanction) introduced by the author, have
been never adopted except under actual experience of the embarrassment
arising from the want of them, and will require no vindication to those who
have reached that point where the necessity of some such additions becomes
felt.
Theory of Canonical Forms and of HyperdeterminanU, 407
The reduction of the function of the fourth degree to its ca-
nonical form may be effected very easily by means of the proper-
ties of the invariants of the canonical form, as I have shown in
the paper in the Cambridge and -Dublin Mathematical Journal
before alluded to. Accordingly I have endeavoured to ascertain
whether the reduction of the .sixth degree might not be ejBfected
by a similar method. ' oil j lo
If we start with the ibvm' aa^ + bif -^ c^ ■\-^Omx^y'^z^, where
x-\-y-\-z^=0, and which is only another mode of representing
the canonical form previously given, we shall find that there are
four independent invariants of the second, fourth, sixth, and
tenth degrees. Calling these Hg, H4, Hg, H^q, and writing
^}y ^2> ^3 fo^' a + b + c,ab + ac + bc,abc, it will be found, after
performing some extremely elaborate computations, that ^'^^'i^
, ... Ec,=s^-270m^ .-i.^-..\:r >ivi)^Tl
H4 = 6ms3 + 4^6m\ + 2l6m\ + SOlm^ '^olI(a »4:f ni^jdo I
H6=4^3Hl20v3^-{68452^ + 4325i53}m^ ^^-^^^^.^S^
+ (13 . 27 . 6453-64 . SlsiSc,)m^ -{-S . 81 . 1695^
+ 7 . 128 . 729^1 . m^ + 16 . 729 . 239m«.
Hjo is too enormously long to attempt to compute ; but we
can easily prove its independent existence by making m = 0, in
which case the (determinant, or, to use the new term proposed,
the) discriminant of aw^ + by^ + cs^ becomes the product of the
twenty-five forms of the expression
{abf-\-{acf.r+{bcf.r^.
Now in general the value of such a product for a^+yS^l -f 7 . 1
is obviously of the form
(« + /3 + 7)^ + a^7(/a + /e + 72+^ ajS + ay -{- fiy) ; ihny
for when a=0 or ;S=0 or 7=0, the product must become re-
spectively (/3-{-7)^, (7 + a)^, and (a + /3)^. Moreover, without
* Such a product in the language of the most modern continental ana-
lysis is, I believe, termed a Norrae. If we suppose the general function
of w, y of the 4th degree thrown under the form A%^4-Bz>^+Cw^ where
u+v-\-w=0, and the general function of x, y, z of the 3rd degree thrown
under the form Aw^+Bzj^+Ciy^+D^^, where u-\-v-\-w-\-6=zQ,ihQ theory
of noraies will afford an instantaneous and, so to speak, intuitive demon-
stration of the respective related theorems, that the discriminant {aliter
determinant) of each such function is decomposable into the sum of a
square and a cube. Each of these forms is indeterminate, in either case
there being but two relations fixed between the coefficients A, B, C ; A,
B, C, D ; and we may easily establish the following singular sgecies of alge-
braical porism. In the first case .^3 b^qoL i^™ iisstf
(ABC)2 : (AB+AC+BC)3, Ja«w fjtli rao-d -gukm
and in the second case ? isdi b9iJ[D«9i Trad
(ABCD)3 : (2A2B2C2-2ABCD2AB)2 ,*M
are invariable ratios.
iW Mr»Ji^i Sylvester on et remarkable Discovery m the
caring to calculate /,^*, it is enough for our present purpose to
satisfy ourselves that ^ cannot be zeix)^ as then the product
would have a factor (a-f/3 + 7)*. Hence^ then, on putting
a=bc, ff=^ac, y=ab, we see that the discriminant, when m is 0>
will be of the form
But when »^ is (X H^ vanishes, and there is no term Si or ^3 in
Hg. Hence evidently the discriminant Hjq just found cannot
be dependent on Hg, H4, or Hgj nor is it possible to make
H,o+;jIV + (7H/.H6, i.e. (p + l)s^^+A^ .s^^-hffSs^ .s^ a per-
feet square on account of (/ not vanishing ; so there is no Hg
upon which Hjo can depend. Hence, admitting, as there seems
every reason to do, that the number of invariants of a function
oix, y of the degree m is m— 2, we find that the four invariants
in the case of the first degree are respectively of the second,
fourth, sixth, and tenth dimensions, a determination in itself as
a step to the completion of the theory of invariants of no minor
importance.
But it seems hopeless by means of these forms to arrive at the
desired canonical reduction. The forms, however, of ^i ^g s^ are
very remarkable as not rising above the 1st, 1st and 2ud de-
grees respectively in s^^ s^, %. Also H4 vanishes when m=0 and.
H4 has been obtained by putting
a .x^ + b7/'i-c:^-\- mouhjH^
under the form of
H5^ + 6B^y + 15Ca?y + SODci^^/^ ^ i5E^y 4. 6F^ + G?/«,
and taking the determinant
A
B
C
D
B
C
D
E
C
D
E
F
D
E
F
G
Consequently in general the vanishing of the above-written de-
terminant will express the condition that a function of the sixth
degree may be decomposable into three sixth powers. This also
is true more generally. If F(^, y) be a function of 2i dimen-
sions, the vanishing of the resultant in respect to ^•*, a?*~^ .y,
;': .y', (taken dialytically) of^^' '" '^^
\dx) ' ' \da;J 'dy'^' " ' \dy) '^
will mdicate that F admits of being decomposed into i powers of
linear functions of x^ y\.
*/=-625 ^=3125.
t Such a function so decomposable may be termed meio-catalectic. Meio-
catalecticism for even-degreed fuuctions is the analogue of singularity for
odd-degreed functions.
Theory of Canonical Forms and of Hyperdeterminants. 409
In consequence of the greater interest, at least to the author,
of the preceding investigations, I have delayed the insertion of
the promised continuation of my paper on extensions of the dia-
lytic method, which will appear in a subsequent Number. I
take this opportunity of correcting a trifling slip of the pen
which occurs towards the end of the paper alluded to. The
so u
values of - and - become zero, and not infinite, when 7i=:=0;
z z
and the antepenultimate paragraph should end with the words
'^ an incomplete resultant." The theorem also, in the last para-
graph but one, should be stated more distinctly as subject to, an.
important exception as follows. ,,- noqjj
Whenever the resultant of a system of equations F = 0, G=0,
&c. contains a factor E"", this will indicate that, on making
R'=0, the given system of equations will admit of being satisfied
by m algebraically distinct systems of values of the variables,
except in those cases where there is a singularity in the forms of
F, G, &c., taken either separately, or in partial combination with
one another. An example will serve to make the meaning of the
exception apparent. Let F, G, H denote three quadratic equa-
tions in X and y, so that F = 0, G=0, H = 0 may be conceived
as representing three conic sections. Let R be the resultant of
F, G, H, and suppose the relations of the coefficients in F, G, H
to be such that E, = E'2 ; then ll' = 0 will imply the existence of
one or the other of the three following conditions : viz. either
that the three conies have a chord in common, which is the most
general inference ; or, which is less general, that two of the
conies touch one another; or, which is the most special case of
all, that one of the conies is a pair of right lines.
So, again, if we have two equations in x^ and their resultant
contains F^, this may arise either from one of the functions con-
taining a square factor, or from their being susceptible, on insti-
tuting one further condition, namely of F=0, of having a qua-
dratic factor in common between them. lil^mliiv^._
Lincoln's-Inn-Fields, (p^ '^^^^
October 14, 1861. : ^ hri»iii;i^ ^'lour an'fi if
P.S. Tlie conjecture made in the preceding pages has been
since confirmed by the discovery of a modification in the ca-
nonical form applicable to functions of the sixth degree, which
simplifies the theory in a remarkable manner. Assume /(^,y)
a function of the 6th degree as equal to
ai^ + hv^ 4- cw^ + muvw . (z« — ?;) (v — w) {w — w)^^^,^ ^ __v *^ ^
where u, v, w, linear functions of x and y, satisfy the equatiott ./
410 Messrs. Lamprey and Schaw on Pendulum
then will the product of uvw be capable of being determined by
means of the solution of a quadratic equation, of the square root^
of whose roots the coefficients of uvw will be known linear func-
tions. Thus by an affected quadratic, a pure quadratic, and a
cubic equation, the values of u, v, w may be completely ascertained.
The discussion of this theoiy, and of a general inverse method for
assigning the true (in the sense of the most manageable) Ca-
nonical Form for functions of any even degree, will form the
subject of a subsequent communication.
=*=«=
LXI. An Account of Pendulum Experiments made at Ceylon,
By Jones Lamprey, A.B.y M.B., Assistant Surgeon, 16th
Refft., and Lieut. H. Schaw, R.E.
' ' ih ike Editors of the Philosophical Magazine and Journal.
Colombo, Ceylon,
Gentlemen, September 15, 1851.
AS the following pendulum experiment made in this latitude
(6^ 56' 6" N.) may prove of value to those interested in
similar experiments in Europe, we beg leave to communicate it;
to you, together mth the results of our observations thereon.
The recent publications on this subject which have appeared ia,
your valuable Magazine afforded us much interest, and induced^
us to repeat the experiment here ; thinking that if the law holds,;
good at a place so near the equator, its truth will be confirmed
beyond doubts.
The building in which the experiment was conducted was a
large church belonging to the Dutch Presbyterians of Colombo,
and from its height was the only one at all applicable for such a
purpose. The principal timbers of the roof are sixty-eight feet
above the floor ; between two of these was secured a small beam^,
from which our pendulum was suspended. ,^j ..j.j,^ fjuvi^^iln^. ■';
The ball of the pendulum was of lead, cast in a mbma, ancl
afterwards turned true in a lathe, and was nearly a sphere ; it
weighed 30^ lbs. The wire by which it was suspended was gj-th
of an inch in diameter, and 66 feet 6 inches long ; to its upper
extremity were attached a number of fibres of raw silk, which
were evenly drawn through a small hole in an iron plate and
carefully secured on its other side ; this plate was screwed to the
under side of the small beam before mentioned.
The circle over which the pendulum was made to oscillate, was
in the experiments here recorded only 6 feet in diameter, there
being evidently less inclination to ellipticity when small arcs
were used, and the ellipticity, when it does occur, having less
tendency to cause apsidal motion.
J
- Eocperiments made at Ceylon.
411
The marginal dia-
gram will explain our
method of putting the
pendulum in motion,
which our observations
proved to us must be .^^^
aoiJOifui 'tot irrio'i fBomon
B'
J^ .
,i'Ki{*lUlJ 83 viol
III
iiibnijp jV'io rrojjolo8 •^ririo gnfiocq
> 'io.a:J/iOf;.?rft')oo'Drff ^loot o?foxlw 16
:\s^«,\$1o?:iiii :tiifjpf>oidf/o
tiVbflH ^YlOadi ^ lil J lu < KJ f ^<i.UOKib odT
done with great pre-^ .j^iy \o\^Am ^di m) an-d ydi smas.i8^*5
cision. At the cir4, jjyv«:, /n* lo °" " " 't r .T. „
cumference of the circle :
over which the pen-
dulum was to oscillate,
a box A was made sta- j^«'<tsfral\
tionary by means of K\L
weights. On its upper «apfp¥
surface, at the extremity nearest the circle, was placed a small
block of hard wood, C, which served for adjusting the proper
amount of elevation, and for supporting the thread which held
the ball B by means of a noose, and was stretched over the block
C and secured to the other end of the box A. The ball of the
pendulum being brought to a state of perfect rest in a point of
suspension vertically over the selected line of oscillation, the
thread was severed on the block by the vertical pressure of a
sharp knife : this mode of releasing the ball was attended with
less chance of extraneous motion than by burning the thread, or
by any other means we could devise.
Observations were recorded every hour. When the motion of
the pendulum was renewed, or if ellipticity was not observed, it
was allowed to continue for another hour. i
Previous to the experiment here recorded, many attempts
were made with balls of less weight, thicker wires, different
modes of suspension and starting, &c. ; but the ellipticity of the
pendulum's motion was in all of them so considerable, that the^
results were very unsatisfactory and are not here introduced.
^limMqy
I
«8di Miiii^i.
Direction of the initial motion
witli reference to the mag-
netic meridian.
N. and S.
N.E. and S.W.
. ■cMUiSlishi].
E. ana^^iio
N.W.andS.E.
Angular variation observed
after the lapse of intervals
of one hour each.
Jl
70
h \ih-\
Mean variation per hour 1*87
Calculated do 1-8111
>iyN.
)hm '^ >4Xixad
/Jji fsibi
412 Formula connected with the Motion of a Free Pendulum.
It will be obseiTcd, that, rejecting the two results obtained
from the oscillation in the direction N.W. and S.E., the mean of
the remaining results would be 1'812, — a very close approxima-
tion to that calculated from the sine of the angle of latitude.
The above, however, are all the experiments that have been mado
with this apparatus ; and as the result comes so near to the
mathematical solution, and the means of perfecting our experi-
ments further are not obtainable without great difficulty in this
colony, we consider it would serve no end to multiply our obser-
vations further.
We are, Gentlemen,
Your obedient Servants,
Jones Lamprey, ^.J5.,ili.J3.,
Assistant Surg eon ^ \^th Regt,
H. ScHAW, Lieut, R.E.
LXII. Formula connected with the Motion of a Free Pendulum*
By the Rev. A. Thacker.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
IN your Number for August last, you did me the favour of
inserting a short letter on the apsidal motion of a pendulum.
I observe, in the formulae there given, two errors of the presSj
which I trust you will allow me to correct. The expression for
the apsidal angle should be
lJ\ 4. § ^ M ^ ab(a^'hb^)\
2 l_ 8 * /2 "^ 256 ' Z'* J'
and for the progression of the apse in one revolution,
-.o^ro «^/i 9 a^ + b^\
185°x-^(H-g5.-^).
If the dimensions of the orbit be small compared with the
length of the pendulum, the last tenu may be neglected ; and
we then have the formula given by the Astronomer Royal, by
Messrs. Galbraith and Haughton, and more recently by Mr.
Coombe.
I may add, that by the method I have employed, the approxi-
mation may be continued without difficulty ; for instance, the
next step gives
i'^KO^abr.,9 a^ + b^ , 151(^ + &4) + 58fl^^>n
for the progression of the apse. The complete formula, as might
Notices respecting New Books. ' ^^^^^w^*^*^ |
be expected, is an infinite series, symmetrical wixk respect to a
and b, and convergent for all possible values of those quantities.
The time of revolution (that is, the interval between two suc-
cessive arrivals of the pendulum-ball at the same apse) in terms
of a, b and /, is equal to
V ^1/^ 16/2 ^ 1024/4 +^c.j-.
The demonstration of these expressions, although not long,
might occupy more space than I can venture to claim.
I am. Gentlemen,
Yours, &c..
Trinity College, Cambridge, A. Thacker.
Oct. 9, 1851.
LXIII. Notices respecting New Books.
The Ethnology of the British Colonies and Dependencies. By R. G.
Latham, M.D., F.R.S. 8fC. John Van Voorst, Paternoster Row.
1851.
Man and his Migrations. By R. G. Latham, M.D., F.R.S. 8^c. John
Van Voorst. 1851.
ETHNOLOGY, or the science of races, has for its objects the con-
sideration of the physical, mental, and moral characteristics of the
different races of men, their physiological and philological affinity,
and the question of their descent from one or more sources of origin.
The mere statement of these objects sufficiently indicates the com-
prehensive nature of the science, and the difficulties opposed to a
satisfactory solution of the problems which it involves. Not only
must the living characters of races be faithfully observed and com-
pared, and the influence of intermixture taken into consideration,
but the footsteps of each must be tracked along * the sands of time ;'
and where history ceases, and the mist of ages obscures their course
and movements, the aid of philology and archaeology must be in-
voked, and through these, if possible, their probable affinities and
origin be determined. Man must be considered also in relation to
the earth which he inhabits, and the question entertained, whether
the influences in operation on its surface afford a clue to the different
phases under which he exhibits himself in various regions. Hence
a moderate acquaintance with physical geography is indispensable.
Notwithstanding the varied nature of the qualifying studies, and the
faint hope of attaining by scientific research only to any definite
conclusion as to the specific unity or diversity of human races, the
science has of late years been prosecuted with considerable energy
in this country, as well as on the continent and in America. The
characteristic features of existing races have been accurately deli-
Phil Mag. S. 4, Vol. 2. No. 12. Nov. 1851. 2 F
414 Notices respecting New Books,
neated, their affinities in many instances established, and philologists
have done something towards a solution of the subtle question of
their unity of origin. The general intellectual movement of the age,
the buoyant delight with which the philosopher ever explores the
more unbeaten tracks, and the interest with which the imagination
lingers about those regions of inquiry where facts merge in specula-
tion, may in some degree account for the rapid advancement of the
science. Man, too, is at length beginning to feel that the natural
history of his species constitutes an object of research, which, whilst
it more immediately concerns him, involves questions of equal in-
terest with any that can be agitated in other departments of science.
Unwearied energy, a cautious critical spirit of investigation, and
extensive philological research, entitle Dr. Latham to the highest
rank among modern ethnologists. None have done so much to fill
the void created by the death of Dr. Prichard. Within the short
period of a year no less than three works have emanated from his
pen. Of these, the first constitutes a tolerably comprehensive text-
book of the science, and will prove of infinite service to the ethno-
logical student. Of the other two, whose titles head the present
notice, the one is rather practical in purpose and character, the other
deals with some of the more abstruse and intricate questions which
everywhere beset the inquirer in this department of science. Each
work is arranged in the form of lectures, delivered, one series at
Manchester, the other at Liverpool ; additions having been made by
the author prior to publication.
' Man and his Migrations,' though published the last, is anterior
in point of subject matter, and first merits consideration. The first
three lectures are devoted to a general review of the progress of
ethnology, the several branches of the subject, their relative value,
and the proper mode and order of investigation. Its history is
traced up from the imperfect notices of ancient writers, to the period,
scarce half a century back, when principally through the labours of
Blumenbach, it first assumed the aspect and fair proportions of a
science. A just tribute is paid to the researches of Dr. Prichard,
who first associated the philological and zoological series of inquiries,
and whose work will ever be invaluable as an encyclopaedia of facts
for the student. In reference to the influence of climate upon race,
our author notices an hypothesis of Dr. Knox, that no race can
maintain a permanent footing in any country for which it was not
originally destined. In support of the hypothesis. Dr. Knox ad-
duces the American Anglo-Saxons, whose existence in the NewWorld
he considers to depend on the continual infusion of fresh blood from
the father-land. Notwithstanding this constant renovation, he be-
lieves that they are gradually degenerating ; a notion, we fancy,
which our relatives on the other side of the water will be scarcely
inclined to adopt. Dr. Latham hazards no opinion on the matter,
and merely observes that " it is forcibly and confidently expressed."
We however doubt altogether the truth of the assertion. The fre-
quent migrations from this country are chiefly to settlements in the
interior ; and there is no reason for supposing that the families in-
Notices respecting New Books. 415
habiting the larger towns have for years in any way depended on
such periodical reinfusion for life and vigour. That climate has pro ^
duced some effect, as diminished muscular and adipose development,
a somewhat lower average longevity, we readily admit. Change of
condition, too, has engendered different habits, a peculiar tone of
thought, &c. ; but for the present let us not talk of degradation.
The following suggestions of Dr. Latham throw some light on the
subject of acclimatization.
"A European regiment is decimated by being placed on the
Gambia, or in Sierra Leone. The American Anglo-Saxon is said to
have lost the freshness of the European — to have become brown in
colour, and wiry in muscle. Perhaps he has. Yet what does this
prove ? Merely the effect of sudden changes ; the results of distant
transplantation ; the imperfect character of those forms of acclima-
tization which are not gradual' It was not in this way that the
world was originally peopled. New climates were approached by
degrees, step by step, by enlargement and extension of the circum-
ference of a previously acclimated family. Hence the experience of
the kind in question, valuable as it is in the way of Medical Police,
is comparatively worthless in a theory as to the Migrations of Man-
kind. Take a man from Caucasus to the Gold Coast, and he either
dies or takes a fever. But would he do so if his previous sojourn had
been on the Gambia, his grandfather's on the Senegal, his ancestor's
in the tenth degree on the Nile, and that ancestor's ancestor's on
the Jordan — thus going back till we reached the first remote patriarch
of the migration on the Phasis ? This is an experiment which no
single generation can either make or observe ; yet less than this is
no experiment at all, no imitation of that particular operation of
Nature which we are so curious to investigate." — Pp. 69, 70.
In respect to the phsenomena of the present distribution of races,
and the probable order of migrations, several circumstances must be
considered. Where contiguous races differ materially in character,
as in the case of the Majyars and surrounding European tribes, the
Hottentots and Kafirs, either encroachment or displacement of the
isolated family is implied. Where contiguous islands are peopled
by different tribes, the same conclusion is not necessarily forced
upon us. " The populations of two islands may agree, whilst that
of a whole archipelago lying between them may differ. Yet this is
no discontinuity ; since the sea is an unbroken chain, and the inter-
vening obstacle can be sailed round instead of crossed. The nearest
way from the continent of Asia to the Tahitian archipelago — the
nearest part of Polynesia — is via, New Guinea, New Ireland, and
the New Hebrides. All these islands, however, are inhahited by a
different division of the oceanic population. Does this indicate dis-
placement ? No. It merely suggests the Philippines, the Pelews,
the Carolines, the Ralik and Radak groups, and the Navigator's Isles
as the route ; and such it almost certainly was."
We perfectly agree with Dr. Latham in making so light of the
migration from Asia to America. To account for the peopling of the
Kew World, there is no occasion to call up from the deep any fabu-
2F2
416 Notices respecting New Books.
lous Atlantis, as a resting-place on the high ocean-road for adven-
turers from Europe and Africa. Neither need we fall hack on the
theory of a Scandinavian or Welsh colonization, although the North-
men are known to have visited Labrador, and probably the coast
more southward ; and Madoc, for aught we know, may with his
followers have taken the same direction. Everything favours the
probability that the migration took place from north-eastern Asia,
by Behring's Straits— which were narrower formerly than now — or
by the Aleutian chain of islands. Such is the geographical continuity
here, that Dr. Pickering asks, ' Where shall Asia end, and America
begin .'' ' If we look to the })hysical characters of the tribes inhabiting
these parts, we fmd the American variety passing by insensible gra-
dations through the Xoluschians and Esquimaux into the Mon-
golian. This view is further favoured by certain traits of resem-
blance in customs and religions observances, and by such comparison
of languages as has hitherto been instituted.
Where physical and other characteristics fail in establishing affi-
nity, philology frequently comes to our aid, and vice versd. The
difference between the Hottentots, Kafirs, Negroes, Copts, and other
African races is very striking, but the labours of the philologist have
succeeded in establishing a complete chain of affinity. On the other
hand, if we regard the Chinese in reference to their peculiar mono-
syllabic language, they appear completely isolated from surrounding
races ; but then physical character allies them beyond a doubt to
other Mongolian families. We cannot accompany our author through
the various stages of the argument. It would appear, however, that
while the probable course of migration may be readily traced in re-
ference to America, Africa, Polynesia and Australia, when we come
to Europe difficulties multiply. The more we know of the ethnology
of this quarter, the more are we mystified. The eflfects of conquest,
displacement, intermixture, must be considered ; and the value of
names, ancient or recent, be determined. Isolated languages, too,
the Basque and Albanian, stare us in the face, and archtcological
research presents us with traces of a race anterior to the Celtic dis-
tribution. Our difficulties again would seem to increase tenfold
when we reach south-western Asia, — the suj)posed locality of the
cradle of the human race. But if Dr. Latham has brought us no
nearer to a satisfactory conclusion, he has at least stated fairly the
complicated questions involved in the inquiry, and cleared the road
for future progress. His researches, as far as they have gone, lead
him to believe that the human family originated somewhere in in-
tratropical Asia from a single pair, although he does not pretend to
have arrived at any proof of this.
A knowledge of what we would term practical ethnology, of the
living characters of the races composing various nations, is indispen-
sable alike to the historian and the statesman. Through such know-
ledge only is the former in a position to reason philosophically onj
and trace to their true cause the movements that are ever convulsing
society ; and the government of a dependency will be enlightened
and liberal in proportion as it is based on an intimate acquaintance
Noti'&es respecting New BaoU. 417
A^'ith the genius of the people whom such dependency may embrace.
To Dr. Knox belongs the credit of having advocated with force and
eloquence this application of the science ; and to its ethnological
character M. Thierry's History of the Norman Conquest owes not a
little of its truthfulness and fascination. ' The Ethnology of the
British Colonies ' is a pleasing index of the component elements of
our ' possessions/ and should be in the hands of every British states-
man. The philological affinities of races, as far as they are esta-
blished, are clearly indicated. In these, indeed, lies the author's
strength ; and we cannot but think that the usefulness of the work
would have been enhanced by a more extended notice of the ethical
character, habits, and institutions of the several races. Not that
these are altogether overlooked, but that in a practical treatise they
should occupy the more prominent place. While the * Migrations
of Man ' will probably prove more interesting to the general reader,
both works will be indispensable to the student, who will lind therein
a clear statement of difficulties, and many additions to the accumu-
latingstore of ethnological science. ^i u u j^i;l f-^t.-i-au .(jui
De Morgan's Elements of Arithmetic and of Algebra translated into
the Marathi language by Colonel George R. Jervis, Chief Engi-
neer, Bombay Presidency, assisted by Vishnoo Soonder Chutry,
: Gungadhur Shastri Phudkay, and Govind Gungadhur Phudkay.
Bombay. American Mission Press, 1850 and 1851. ^ ^^vi ^ii^vviii
If there be two questions of interest in their connexion with each
other, upon which the balance of indifference among men of science
in this country is most impartially held, they are the questions how
arithmetic and algebra w-ere imported into Europe from India, and
how they are to be carried back again, with the accessions which
they have received. From this kind of indifference it arises that wx
know nothing of the efforts which a few earnest men, with the help
of the local governments, are making for the improvement of more
than a hundred million of our fellow subjects.
For some time it has been matter of controversy in India as to
whether the higher education should be given to the natives in
English or in their own languages. The plan of teaching English
to selected natives, and thus bringing them into contact with litera-
ture and science by aid of all the facilities for instruction which our
language affords, tempted many friends of education, and obtained
for some time the sanction of the government. But experience
showed that the creation, as it were, of an English mind in the
Hindu was not the way to make him an effective interpreter to
his fellow-countrymen; and experience did no more than confirm
the previous belief of almost all the names of celebrity connected
with India. Persons who had formed their opinions upon associa-,
tions and other modes of arrival as different as, for instance, those
of Mountstuart Elphinstone and James Mill, or Sir John Malcolm
and Professor Wilson, agreed in thinking that the vernacular lan-
guages were the proper medium of the higher instruction for the
418 Notices respecting New Books.
natives of India. And to this conclusion it would now seem that
the government has nearly, if not quite, arrived. We need hardly
say that no one ever doubted that the rudiments were to be taught
in native languages.
Among those who have fought the battle of vernacular instruction,
Colonel George Jervis holds the prominent station due to one whose
way of proving that a thing can be done is to do it. For five-and-
twenty years he has pursued the subject, in the leisure which a labo-
rious profession affords. To use the words of a Bombay newspapef
of three years since, " it is to Colonel Jervis entirely we are indebted
for the earliest successful efforts made to introduce a correct system
of education among the natives. When we were satisfied with schools
and schoolmasters, and before the dream of colleges and professors
had entered our heads, Captain (now Colonel) Jervis laboured with-
out intermission to obtain translations, and have rnen taught to read
and write, and reason and reflect." The principal languages of the
Bombay presidency are the Marathi (or Mahratta) and the Gujerati.
In these two languages Colonel Jervis published translations of Hut*
ton's course of mathematics, of a course of practical geometry, and
of the preliminary treatise to the library of useful knowledge. He
established a lithographic press in the chief engineer's office, and
determined to attempt some works which contain more development
of the principles of mathematical science. In 1848 he published in
lithograph a translation of De Morgan's Algebra. Having prepared
a translation of the Arithmetic also, and ascertained that the works
could be effectively j^rm^ec?, he offered both to the government on
condition of their immediate publication in type. The offer was
accepted, and the publication completed as proposed.
By various testimonies we learn that it is perfectly practicable to
translate works which dwell upon principles into languages, which,
like the Marathi, are derivations from the Sanscrit. Whether those
which, like the Tamul, are not so derived, present the same capabi-
lities, we have no means of knowing. The only criticism which it
is in our power to attempt relates to the translation of the language
of algebra. In the Nagri type, which is that adopted by Colonel
Jervis, the letters of simple formation do not answer to those of the
Italic alphabet. The x, for instance, in Nagri has a form which we
think a child might hit upon to represent a man in abroad-brimmed
hat holding out a snake of ample curl by his single arm. If the
native writer, by habit, has managed to forget the difference between
this letter and others, in point of complexity, we have no more to
say ; but if not, it is worth consideration whether it would not be
advisable to substitute a more simple letter, of which there are many.
In this way the letters of easiest formation might be made those of
most frequent occurrence. This, however, is a small matter, and
has probably been duly considered.
October 17.-^Since the above was printed, we have seen tvith great
regret the announcement of the death of Colonel Jervis, as having
taken place at Boulogne on the 14th*
LXIV. Proceedings of Learned Societies,
CAMBRIDGE PHILOSOPHICAL SOCIETY.
' [Continued from vol. i. p. 568.]
May 19,|r^N the Colours of Thick Plates. By G. G. Stokes, M.A.,
1 85 1 . ^-^ Fellow of Pembroke College, and Lucasian Professor
of Mathematics in the University of Cambridge.
By the expression " colours of thick plates " is usually understood
the system of coloured rings, discovered by Newton, which are formed
on a screen when the sun's light is transmitted through a small hole
in the screen, and received perpendicularly upon a concave mirror of
quicksilvered glass, placed at such a distance from the screen that
the image of the hole is at the same distance from the mirror as the
hole itself. The brilliancy of the rings, as was afterwards discovered,
is greatly increased by tarnishing the surface of the mirror ; and it
is also advantageous to use a lens to collect the sun's rays, and to
place the screen so that the small hole may be situated at the focus
of the lens. These rings were first explained on the undulatory
theory by Dr. Young, who attributed them to the interference of
two streams of light ; of which the first is scattered at the tarnished
surface of the mirror, and then regularly reflected and refracted, while
the second is regularly refracted and reflected, and then scattered in
coming out of the glass. The theory has been worked out in detail
by Sir John Herschel, who has investigated the case in which the
two surfaces of the glass belong to a pair of concentric spheres, and
the hole in the screen is situated in the common centre of curvature.
A set of coloured bands has since been observed by Dr. Whewell
in a common plane mirror. These bands are seen when a candle is
held near the eye, at the distance of several feet from the mirror,
and is viewed by reflexion. It is necessary that the first surface of
the glass should be a little tarnished. The theory of these bands
had not been worked out, and it had even been doubted by some
philosophers whether they were of the nature of the coloured rings
of thick plates.
In this paper the author gave a general investigation, which in-
cludes as particular cases the theory of the rings formed on a screen
in Newton's experiment, and that of the bands which Dr. Whewell
had observed in a plane mirror, and which are not thrown on a
screen, but viewed directly by the eye. He also exhibited to the
meeting a variation of Newton's experiment, in which an extremely
beautiful system of rings is very easily produced without sunlight.
The face of a concave mirror of quicksilvered glass was prepared by
pouring on it a mixture consisting of one part of milk to three or
four of water, and then holding the mirror vertically in front of a
fire to dry. When the flame of a taper, or of an oil-lamp with a
small wick, is placed in front of a mirror thus prepared, in such a
position as to coincide with its inverted image, a beautful system of
rings is seen encompassing the flame. These rings appear to have
a definite position in space, like a bodily object. The rings thus
420 Cambridge Philosophical Society.
formed, which are evidently of the nature of Newton's coloured
rings of thick plates, may be made to pass in a perfectly continuous
manner into the coloured bands observed by Dr. Whewell.
The author has compared theory and experiment in various par-
ticulars, and has found the agreement perfect. It will be sufficient
to mention here one result of theory, which is of great generality
and of considerable elegance. It applies to the system of rings seen
by reflexion in a mirror, either plane or curved, when a luminous
point is placed anywhere near the axis, and the eye occupies any
other position likewise near the axis. The result is as follows :—
Join the eye with the luminous point, and likewise with its image,
whether it be real or virtual, and find the points in which the join-
ing lines, produced if necessary, cut the mirror. Describe a circle
having for diameter the line joining these two points. This circle
will be the middle line of the bright colourless fringe of the order
zero, and on each side of it the colours will be arranged in descend-
ing order.
June 2. — On a new Elliptic Analyser. By Professor Stokes.
After mentioning some of the inconveniences and inaccuracies
attending the use of a Fresnel's rhomb in the analysis of elliptically-
polarized light, and alluding to some other methods which had been
employed for the purpose, the author proceeded to describe a new
instrument which he had invented, and which he exhibited to the
meeting. In the construction of this instrument he had aimed at
being independent of the instrument- maker in all important points
except the graduation. The construction is as follows : —
A brass rim or annulus is mounted so as to stand with its plane
vertical when ])laced on a table. Within this rim turns a brass gra-
duated disc ; and the angle through which it turns is read off by
means of verniers engraved on the face of the rim, and reading to
tenths of a degree. This disc is pierced at the centre, and carries
on the side turned towards the incident light a retarding plate of
selenite, of such a thickness as to give a difterence of retardation in
the oppositely polarized pencils amounting to about a quarter of an
undulation. In front it carries a liollow cylinder, turned on the
lathe along with the disc itself. Round this cylinder there turns a
collar containing a Nicol's prism, and carrying a pair of level-edged
verniers, by which the angle may be read oiF through which the
prism has been turned. Thus the retarding plate moves in azimuth
carrying the prism along with it, and the prism has likewise an in-
dependent motion in azimuth.
In observing, the light is extinguished by a combination of the
two movements, in which case the elliptically-polarized light is con-
verted by the retarding plate into plane polarized, which is then ex-
tinguished by the Nicol's prism. On account of chromatic varia-
tions, the light is not, strictly speaking, extinguished, unless homo-
geneous light be employed, but only reduced to a minimum. There
are two principal positions of the retarding plate and Nicol's prism
in which the light is extinguished, or at least would be extinguished
if the incident light were homogeneous ; and for each principal
Cambridge Philosophical Society. 421
position there are four subordinate positions, since either the retard-
ing plate or the Nicol's prism may be reversed by turning it through
lJiO°. The mean of the four subordinate positions may be taken
for greater accuracy.
Let R, II' be the readings of the fixed, r, r' those of the moveable
verniers in the two principal positions ; I the index error of the fixed
verniers, that is, the azimuth of the major axis of the ellipse de-
scribed, measured from a plane fixed in the disc ; i the index error
of the moveable verniers, that is, the azimuth of the principal plane
of the prism, measured from a" fixed plane in the disc; m the angle
whose tangent is equal to the ratio of the axes of the ellipse de-
scribed ; p the difference of retardation of the oppositely polarized
pencils transmitted through the plate, measured as an angle, at the
rate of 360° to one undulation. Then the unknown quantities I, i,
'HT, and p are given in terms of the known quantities R, R', r, and r'
by the following formulse, which happen to be extremely convenient
for numerical calculation ; —
I=1(R' + R)j '^^:^' 2=i(r' + r)P;^':" -
2^ '' ''croon i •; 2 rlmirln >o;
n sin(r'—- r) tan (r'—r)
cos 2z«r== -^ :— : coso= ^^ —.
sin(R'-R)' ^ tan(R'-R)
The author stated that he liad already observed with this instru-
ment, and after a little practice had found that it worked in a very
satisfactory manner. When the light of the clouds was reflected
horizontally by a mirror, and modified so as to produce ellipti-
cally-polarized light in which the ratio of the axes was about 3 to 1,
it was found that the mean error of single observations amounted
to about a quarter of a degree in the determination of the azimuth of
the major axis, about three or four thousandths in the determination
of the ratio of the minor to the major axis, and little more than
the thousandth part of an undulation in the determination of p.
Since the magnitude of p depends upon the length of wave, or,
what comes to the same, the refrangibihty of the light, it follows
that a knowledge of the former leads to a knowledge of the latter.
It may thus be said that the instrument determines the azimuth and
excentricity of the ellipse described, and the refrangibility of the
light. An error of the thousandth part of an undulation in the de-
termination of p would correspond to an error in the place in the
spectrum assigned to the light operated on amounting to less than
the twentieth part of the interval between the fixed lines D and E.
Now by the use of observing media it is possible, without too much
reducing the intensity of the light employed, to alter greatly its mean
refrangibility ; and yet for each medium the refrangibility may be
determined very accurately by means of the value of p. Accord-
ingly, the instrument is specially adapted for investigations relating
to the dispersion of metals, and for other similar researches, f'' 'f^f^S
^, , .. . J 07/;? 3-iB
ijc* bli/o/r tgooi U to .bsiigfj.fgnriiro ei irJgii ori^r rloirfvv nl
[ 422 ]
LXV. Intelligence and Miscellaneous Articles.
foucault's pendulum experiment.
To the Editors of the Philosophical Magazine and Journal.
Gordon's Hospital, Aberdeen^
Gentlemen, July 1851.
AS M. Foucault's experiment is now an engrossing topic in scien-
tific circles, I beg leave to forward a verification of it for this
place, lat. 57° 9' N., and to offer a few remarks tending to explain
some of the pha^nomena connected with it in a manner somewhat dif-
ferent from that usually adopted.
Every experimenter is struck by a tendency of the pendulum to
get into an elliptical orbit, and is disposed to ascribe the ellipticity
to the imj)erfection of the apparatus, the resistance of the air, or some
Cause accidental and not essential to the exjieriment. But as a
greater or less amount of ellipticity sooner or later makes its appear-
ance in every instance, it would appear reasonable to infer that it
must proceed from some cause inseparable from the conditions of
the motion ; and on consideration, it is obvious that the path of the
pendulum from the very first will not be in a straight line across the
table, but in a curve approaching to an ellipse ; for the body, when
steadied at the circumference of the table and let go, is acted upon
by t\vo forces. Viz. gravity, which would carry it in a straight line
over the centre, and a lateral impulse derived from the rotatory mo-
tion of the circutnference of the table with respect to its own centre.
T^e Joint effect of these two forces will be to produce a motion in
ati elliptical or ellipsoidal orbit passing a little to the right of the
centre, and returning a little to the left of it. The point of the cir-
cumference, to which the body will return, will depend upon \yhether
the major axis of the ellipse is fixed or moveable.
1. If the axis of the ellipse be fixed, the pendulum will return
to a point a little to the left of that from which it set out, and will
have ari apparent motion contrary and equal to the real motion of
thfe table. This is M. Foucault's experiment when successfully
performed.
2. If the axis of the oi-bit move directly, i. e. from west to east at
the same rate as the circumference of the table, the body will return
to the point from which it was let go, and no deviation will be ob-
served. If the motion of the axis is direct and quicker than that of
the table, the body \Vill deviate from west to east with respect to
the cifcutoference. Both these effects are observed in conducting
the experiment, if the pendulum either by accident or design receive
a slight impulse to the right.
3. If the axis or line of apsides of the orbit have a retrograde mo-
tion, the pendulum will deviate from east to west, and at a higher
rate than that of the real motion of the table. This result is ob-
served in most of tlie eiperimcnts, even those conducted with the
greatest care. From the paper contributed by Mr. Bunt of Bristol
to a recent Number of your Magazine, it appears that the observed
Intelligence and Miscellaneous Articles. 425
rate of deviation exceeds the computed rate. This effect seems
paradoxical, and has led many to doubt the soundness of the theory,
as it seems to exceed the cause to which it is ascribed, or to exhibit
a motion in an opposite direction to that of the impulse. A little
attention to the circumstances will however remove this difficulty,
and show that the contradiction to theory is only apparent.
If a pendulum is swung in a tub of water, drawn to the circum-
ference and let go with a considerable lateral impulse from west to
east, the resistance of the dense fluid causes it at each successive
vibration to fall visibly short of the height or distance from the centre
attained by it at the previous one, and the line of apsides sensibly
recedes, i. e. moves from east to west, and this retrogression con-
tinues until the whole fluid has acquired a rotatory motion).
Now the resistance of the air must produce an effect similar in
kind, though not equal in degree, on a body moving in it, and this
retrograde motion of the apsides of the orbit arising from the gra-
dual loss of momentum, explains the excess of the actual deviation
over that expected from computation. The error arising from this
source will obviously be less the slower the loss of momentum, that
is, ccBteris paribus, the smaller the arc of vibration.
A small arc is recommended by another consideration independent
of the resistance of the air or of friction, viz. that with a small arc
the motion of the line of apsides is slower, and the path of the pen-^
dulum approaches nearer to a fixed orbit. I do not know whether
the motion of a body in the circumstances of Foucault's pendulum,
i. e. of a body performing a gyration approaching to a simple oscil-
lation, has been investigated ; and the investigation might prove diffi-
cult, as the path does not lie in one plane. But that the motion of
the line of apsides will be slower the smaller the arc, will appear from
considering generally that the periodic time of such a body must lie
between the time of two oscillations of the simple j)endulum, and the
time of one revolution of the conical pendulum moving at the same
height or distance from the centre from which the simple pendulum
is let go, and must therefore be always less than the time of two
oscillations of the simple pendulum. But the body will require the
full time of two simple oscillations to visit the opposite circumference
and return to its greatest height on the same side from which it set
dut, and will therefore have completed a revolution in its orbit be-
fore this height on the same side is attained, that is, the apsis of the
curve will be in advance of the point of starting, but the less so the
less the difference between the time of a gyration and that of two
simple oscillations, or ceteris paribus, the smaller the arc.
To obviate as far as possible errors arising from the retrograde
motion of the apsides produced by the loss of momentum, and from
the direct motion produced by lateral impulse, a pendulum was em-
ployed, not of a spherical form, but of the shape of the pendulum of
a clock, and hung with its sharp edge horizontal. The height was
about 25 feet, the wire simply passing through a hole in a board, and
the weight 201bs. of lead. The arc of vibration was about four
inches on each side of the centre. For a period of 12 hours, v»^itbout
424 Intelligence and Miscellaneous Articles.
renewing the im])ulse, the average rate of deviation per hour was
12°-8. Having been permitted through the kindness of J. D. Milne
Esq, and the Rev. J. Longmuir to attach the same bob to a vi^ire
of 30 feet in the Mechanics' Institution here, with the same extent
of arc I found the hourly rate on a motion continued for seven hours
to be 12°'6, which is exactly the rate computed from the sine of the
latitude 57° 9'. A nearer coincidence of experiment with theory
cannot in any case be expected.
From the above-mentioned and other experiments similarly con-
ducted, it appears that the deviation is the same in every point of the
compass.
By giving this paper a place in your journal you will honour
Your most obedient humble Servant,
Alexander Gerard.
Oct. 25. — To the above I would now add, that with the small arc
the condition of the body approaches nearer to that referred to in
Newton's Principia, Prop. 47, Book I. ; and that the apparent acce-
leration produced by the resistance of the air may account for the
discrepancy between the observed phsenomena and some of the for-
mulae given in your Number for August or September. — A. G.
BRISTOL. BY THOMAS G. BUNT.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
A short time before I had concluded my pendulum experiments
in St. Nicholas Spire, I was requested by the Curator of the
Bristol Philosophical Institution to try what results I might be able
to obtain from a pendulum which had been erected there. The
suspending apparatus of this pendulum is precisely the same as
that which I last employed at St. Nicholas, and described in your
Number for July. The ball is an accurately turned sphere of lead,
weighing 35lbs ; the suspending wire is of bright iron ; and the length
of the pendulum, carefully computed from the number of its oscilla-
tions in a given time, is 22-73 feet. A pointed wire projects from
the bottom of the ball, and reaches to within about |th of an inch
of the azimuth circle, which is of 12 inches diameter, beautifully
engraved and printed on a card. Across the circle, fastened down
by a pin through its centre, is a moveable index of card, 1 inch wide,
divided lengthwise into inches, and laterally by parallel lines, yVth
of an inch asunder. By watching the motions of the wire over these
divisions the semi-axes major and minor (a and b) may be read off,
the former to tenths, and the latter to hundredths, of an inch.
The Curator informed me, that the earlier trials of this pendulum
were very unsatisfactory. At that time it was suspended from the
floor of the room over the theatre, so as to be liable to disturbance
by persons walking upon it ; but on removing the suspending screw
from the floor, and attaching it to a strong bracket projecting from
Intelligence and Miscellaneous Articles.
425
the wall, the tendency to elliptic motion was greatly diminished, and
other sources of error entirely got rid of.
• In experimenting with this pendulum, I have again confined my-
self to very small arcs of vibration. One of the many advantages of
this method is, that the ball and lower portion of the pendulum can
be easily enclosed, and thus protected against currents of air. This
was at first done by placing round it a rude enclosure of boards ; but
afterwards a square pyramidal frame was constructed, and glazed on
the four sides, one of them opening as a door ; so that the ball vi-
brated, during the experiments, within the glass case, the top only
being left open to admit the wire.
My experiments with this pendulum are divided into two classes,
according to their different duration. Those of the first class have
an average duration of about an hour each ; and the values of a and b
(or semi-axes major and minor), at the beginning and end of each,
have been observed and recorded. These are afterwards subdivided
into six groups, according to the value and sign of b.
The second class contains experiments of much longer duration ;
two of them extending through more than 37 hours each, with only
a single impulse of the pendulum. The ellipticity of these has not
been observed ; but as the mean arcs are small and the direction of
the elliptic motion is twice reversed while the plane of vibration is
passing through 180°, the apsidal motions of the whole mass must
almost entirely destroy one another. It is somewhat remarkable that
the changes from direct to retrograde (or + to — ) motion, fall nearly
on the same parts of the azimuth circle here, as they did on that at
St. Nicholas ; the change from — to + being at about 60° or 70°,
and that from — to + at about 140° or 150°, in both instances.
Experiments of short duration, arranged according to values of b.
i4^j^i\^'*-^!^y^Ti!,, Elliptic Motion Retrograde.
Mean values of
Mean values of
Mean values of
*.
a.
b.
a.
b.
a.
in.
in.
min.
arc.
in.
in.
min.
arc.
in.
in.
min..
arc.
—05
5^9
33-6
iS'2o
-•19
4-7
104-5
18-10
--23
3-6
8;-o
1675
-05
4-5
95-3
V'70
-•19
1-1
73-5
13-85
-•23
2-8
69-5
10-70
-09
2-7
108-0
20-00
-•20
43
118-1
20-55
--20
24
410
8-20
-00
1-9
1920
37-25
-16
4-5
560
1000
--24
44
270
4-95
-•00
45
44-5
9-77
-•15
4-3
45-8
8-90
--21
4-2
130
2-00
-•08
45
80-6
15-11
-16
3-7
690
11-95
-•25
4-9
60-7
10-10
-•00
5-3
87-0
16-95
-•13
3-2
33-3
6-10
-•23
4-1
46-5
8-00
-•03
4-2
89-0
1550
-•19
4-2
41-8
7 20
-•22
3-4
950
1600
-•10
3-5
230
440
-13
4-1
650
11-90
-•21
2-8
31-5
5-70
—00
20
200
385
-19
30
35-5
6-65
-•28
2-5
77^3
1300
• 1 T
2-7
41-6
7-50
-•28
•24
4-0
3-4
490
59-2
8-30
-04
S flO T
7730
146^78
•39 per hr.
9-75
Mean vals. j
or 11°
•17fi
Q.QA -»
684-1
or 10°
122 70
77 per hr.
Mean vals.
-•235
3-51
656-7
113-45
Mean vals. /
or 10"
-36 per hr.
N.B. In finding the mean values of b and a for each group, re-
gard has been had to the different durations of the experiments.
426 Intelligence and Miscellaneous Articles.
Elliptic Motion Direct,
Mean values of
Mean values of
Mean values of
'
b.
a.
A.
a.
b.
a.
in.
+•04
•04
•06
•05
•09
•09
•06
in.
66
18
42
37
3-9
30
36
nun.
440
760
86-4
44-3
17i-4
arc.
°8-85
1365
17-55
8-90
in.
+ •17
•17
•17
•15
52
4-9
37
33
min.
697
215
69-2
45-
arc.
1500
455
15^40
930
in.
+•23
•21
•23
•24
in.
39
36
3^8
3-4
min.
422
657
58-8
153^8
arc.
8-87
1110
1205
34-40
44-3 925
90^8 18-37
+ 167 4-2 1 205 4
Mean vals. J or 12^-
44 25
68 per hr.
+•232 350 (310-5 66^42
Mean vals. J or 12*'^83 perhr.
+•07
Mean
3-6 \ 560-2 11 2-1 7
vals. J or 12°-01 per hr.
Com
we ha\
iparin
^e —
g the me
an values of b and
a in the 3rd and 6th group,
b.
a.
Motion per
hour.
in.
-•235
+ •232
in.
35
3-56
10-36
12-83
•467
Diff.
353
Mean.
247
Diff.
whence, if a=3*53 in., the apsidal motion due to ^=0^467 in. will
be 2°-47 per hour, or 0°*53 per hour for y\jth inch, h.
The 2nd and 5th groups compared give (when a is reduced
= 3-6 in.) 0°^50 per hour for ^^th inch, h.
The 1st and 4th groups give {a being=3*6 in.) 0°'56 per hour for
jJjyth inch, b.
The mean result of all is, that a being=3'6 inches, the .ipsidal
motion per hour for every tenth of an inch of ellipticity (b) will be
0°-52 nearly. Messrs. Galbraith and Haughton's formula gives 0°-445.
By applying the empirical correction 0"^52 per hour for -j^jth of an
inch,^, so as to ehrainate the effects of ellipticity, the mean motion per
hour for each of the six groups of experiments is as follows, viz.-
1st group
2nd
3rd
4th
5th
6th
Mean of all
o
11*60 per hour.
11-73 ..
11-54
11-65
11-67
11-63
11-637
The experiments of longer duratioo,
are the following :—
and unobserved ellipticity.
Meteorological Observations.
427
Arc.
Rate per hour.
h m
0
0
13 30-2
155-30
11-50
13 30
15875
11-76
37 2
446-00
1204
12 40-5
140-50
1111
3 347
43-40
1213
13 44-5
167-50
12-18
2 54-4
2 59-5
35-701
35-30/
1200
15 1
169-20
11-27
5 42-3
69-35
1214
13 4
154-45
11-82
38 4-5
449-50
11-80
4 39
5273
11-33
16 52
197-30
11-70
5 41
64-80
11-40
11 26-3
137-10
1200
210 25-9
2476-88
= 11-770 per hour.
Mean value of a n=l-7 inch.
The latitude of the Philosophical Institution is 5 1° 27' 1 6", the sine
of which X 15° 2' 28" (=the angle through which the earth rotates
in 1 hour oi mean time) gives 11°*7638.
The set of long experiments performed at St. Nicholas gave a
mean motion of 1 1°-750 per hour, instead of 1 1°-763I as per theory,
the latitude being 51° 27' 0".
The close agreement thus obtained between theory land experi-
ment, by two very different pendulums, and at two different stations,
not only confirms the truth of Foucault's hypothesis, but seems to
show that the latitude of a place may be found, by means of this
experiment;, with a considerable degree of accuracy.
I am. Gentlemen, Youj-s respectfully,
7 Nugent Place, Bristol, Thomas G. Bunt.
17th October, 1851.
METEOROLOGICAL OBSERVATIONS FOR SEPT. 1851.
Chiswick. — September 1. Cloudy and fine : overcast. 2. Drizzly : cloudy and
fine. 3. Hazy: very fine : clear. 4. Foggy: cloudy: fine. 5. Very fine:
clear. 6. Fine: cloudy. 7. Clear: very fine. S. Overcast: cloudy and fine.
9 — 13. Mornings foggy : days very fine: nights clear. 14. Slight fog : very
fine. IS. Slight fog : cloudy and fine. 16. Light clouds and fine : over-
cast. 17. Overcast: fine: cloudy. 18,19. Fine: clear. 20 — 22. Very fine*
23. Slight fog: very fine: rain. 24. Foggy: overcast: foggy at night. 25.
Slightly overcast : rain. 26. Partially overcast : cloudy : clear. 27, Cloudy :
drizzly. 28. Clear and fine. 29. Foggy : fine. SO. Rain : overcast,
Mean temperature of the month 55°'l5
Mean temperature of Sept. 1850 54 -23
Mean temperature of Sept. for the last twenty-five years . 57 '18
Average amount of rain in Sept 261 inches.
Boston. — Sept. 1, Fine. 2. Cloudy : rain early a.m. and p.m. 3 — 5. Cloudy.
6. Fine. 7. Cloudy. 8— 11. Fine. 12, 13. Foggy. 14. Fine. 15— 17. Cloudy.
18, 19. Fine. 20. Cloudy. 21 — 23. Fine. 24. Cloudy. 25. Cloudy: rain p.m.
26. Cloudy : rain a.m. and p.m. 27. Cloudy. 28, 29. Fine. 30. Cloudy.
Sandwick Manse, Orkney. — Sept.]. Drizzle : -^ damp. 2. Cloudy: rain. 3.
Drizzle : cloudy. 4. Clear : aurora. 5. Clear. 6. Bright : cloudy. 7. Cloudy :
clear: aurora. S.Clear. 9. Bright : hazy. 10. Cloudy : drops. 11. Cloudy:
fine. 12, 13. Bright : fine : clear. 14. Bright: cloudy. 15. Cloudy : clear :
aurora. 16. Bright : clear : aurora. 17. Bright: clear. 18, 19. Fog: cloudy.
20. Showers: clear. 21. Cloudy. 22. Drops: drizzle. 23. Bright: clear:
aurora. 24, Clear : cloudy. 25. Showers : sleet- showers. 26. Bright : showers,
27. Clear : showers : aurora, 28. Bright ; showers : aurora. 29, Cloudy, 30,
Cloudy; showers.
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THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOUKTH SERIES.]
DECEMBER 1851.
LXVI. On the Mechanical Theory of Electrolysis.
J5y Prof. William Thomson*.
1. I^ERTAIN principles discovered by Mr. Joule^ and pub-
^^ lished for the first time in his various papers in this
Magazine, must ultimately become an important part of the
foundation of a mechanical theory of chemistry. The object of
the present communication is to investigate, according to those
principles, the relation in any case of electrolysis between the
electro-motive intensity, the electro -chemical equivalents of the
substances operated on, and the mechanical equivalent of the
chemical effect produced in the consumption of a given amount
of the materials ; and by means of it to determine in absolute
measure the electro-motive intensity of a single cell of DanielFs
battery, and the electro-motive intensity required for the electro-
lysis of water, from experimental data which Mr. Joule has
kindly communicated to me.
2. If a galvanic current, produced by means of a magneto-
electric machine, be employed in electrolysis, it will generate, in
any time, less heat throughout its entire circuit than the equiva-
lent of the work spent, by an amount which may be called the
thermal equivalent of the chemical action which has been effected,
being the quantity of heat which would be obtained by recom-
bining the elements of the decomposed substance, and reducing
the compound to its primitive condition in every respect; or
generally, by undoing all the action which has been done in the
electro-chemical apparatus. Now the quantity of heat which is
equivalent to the work done is obtained by dividing the number
which measures the work by the number which measures by the
* Communicated by the Author.
Phil Mag, S. 4. Vol. 2. No. 13. Dec. 1851. 2 G
430 Prof. Thomson on the Mechanical Theory of Electrolysis,
same unit the mechanical equivalent of the unit of heat. Hence
if the mechanical equivalent of the thermal unit be denoted by
J, the work done in any time by W, the total quantity of heat
evolved in the same time throughout the circuit by H, and the
thermal equivalent of the chemical effect produced by 0, we have
W
H=y-e; (1)
an equation which may also be written in the form
W=JH + M, (2)
if M be used to denote the value of J@, or, as it may be called,
the mechanical equivalent of the chemical effect produced in the
stated period of time.
3. To avoid the necessity of considering variable or disconti-
nuous currents, let us suppose the " machine " to consist of a
metallic disc, touched at its centre and at its circumference by
fixed wires, and made to revolve in its own plane about an axis
through its centre, held in any position not at right angles to
the direction of the earth's magnetic force*. If these wires be
connected by contact between their ends, there will, as is known,
be a current produced in them of a strength proportional directly
to the angular velocity of the disc, and inversely to the resistance
through the whole circuit. Hence there will be between the
ends of the wires, if separated by an insulating medium, an elec-
tro-motive force the intensity of which will be constant and pro-
portional to the angular velocity of the disc.
4. Let us now suppose the wires to be connected with the
electrodes of an electro-chemical apparatus, for instance a gal-
vanic battery of any kind, or an apparatus for the decomposition
of water ; and let us conceive the electro-motive intensity between
them to be sufficient to produce a current in its own direction.
The preceding equations, when applied to this case, will have
each of their terms proportional to the time, since the action is
continuous and uniform, and therefore it will be convenient to
consider the unit of time as the period during which the amounts
of work and heat denoted by W and H, and the amount of che-
mical action of which the thermal and the mechanical equivalents
are denoted respectively by 0 and M, are produced. If r denote
the radius of the disc, co the angular velocity with which it is
moved, F the component of the earth's magnetic force per-
pendicular to its plane, and 7 the strength of the current
which is induced ; the work done in a unit of time in moving
the disc against the resistance which it experiences in virtue
* This is in fact the " new electrical machine " suggested by Faraday in
the Bakerian Lecture of 1832. (Experimental Researches, § 154.)
Prof. Thomson on the Mechanical Theory of Electrolysis, 431
of the earth's magnetic action on the current through it, will
be expressed by the integral / coz.Y.r^dz; as is easily proved,
whether the current be supposed to pass directly between the
centre of the disc and the point of its circumference touched by
the fixed wire, or to be, as it in reality must be, more or less
difiused from the direct line, on account of the lateral^extension
of the revolving conductor. Hence we have
W=|r2F7a). ...... (3)
5. Let E denote the quantity (in units of matter, as grains
for instance) of one of the elements concerned in the chemical
action, which is electrolysed or combined in the unit of time, and
let 0 denote the quantity of heat absorbed in the chemical action
during the electrolysis or combination of a unit quantity of that
element. Then we have
e = ^.E (4)
M=J.6>E (5)
Now it has been shown by Faraday, that in electro-chemical
action of any known kind, produced by means of a continuous
current, the amount of the action in a given time is approxi-
mately if not rigorously proportional to the strength of the cur-
rent ; and all subsequent researches on the subject have tended
to confirm this conclusion. The only exception to it which, so
far as I am aware, has yet been discovered, is the fact established
by Faraday, that various electrolytes can conduct a continuous
current, when the electro-motive intensity is below certain limits,
without experiencing any continued decomposition*; but from
it we may infer as probable, that in general the quantity decom-
posed with high or low electro-motive intensities is not quite
rigorously proportional to the strength of the cm-rent.
This non-electrolytic conducting power is, however, at least
in the case of water, found to be excessively feeble ; and it is
not probable that when electrolysis is actually going on in any
ordinary case, the quantity of electricity conducted by means of
* It is probable that when an electromotor of an intensity below a cer-
tain limit is put in connexion with two platinum electrodes immersed in
water, there is at the first instant no electrolytic resistance ; and a decora-
posing current passes which gradually falls off in strength, until the elec-
trodes are, by the separated oxygen and hydrogen, put into a certain state,
such that with the water between them, they exert a resisting electric force
very nearly equal to that of the electromotor; after which a uniform cur-
rent of excessively reduced strength passes without producing further de-
composition. I hope before long to be able to communicate to the Maga-
zine an account of some experiments I have made to illustrate these cir^
cumstances.
2G3
432 Pi*of. Thomson on the Mechanical Tfieory of Electrolysis.
it is ever considerable compared with that which is electrically-
conducted ; and the normal law of true electrolytic conduction
will therefore be assumed as applicable to the conduction through
the electro-chemical apparatus, subject to modification in any
case in which the deviations from it can be determined. If,
then, we denote by e the electro-chemical equivalent of the
particular element referred to for measuring the chemical action,
that is, the quantity of it which is electrolysed or combined in a
unit of time by the operation of a current of unit strength, since
the actual strength of the current is y, we have
E = 67 (6)
The deviations from the normal law which may exist in any
particular case may be represented by giving e a variable value.
I^or instance, if it were true that when the electro-motive inten-
sity in an apparatus for the decomposition of water exceeds a
certain limit, there is decomposition at a rate precisely propor-
tional to the strength of the current; and when the intensity is
below that limit, a slight current passes without any decompo-
sition * 6 would be a discontinuous function of the intensity,
having a constant value when the intensity is above, and being
zero when the intensity is below, the limit for decomposition.
6. According to Joule^s law of the generation of heat in the
galvanic cu'cuit, the quantity of heat developed in a unit of time
would be rigorously proportional to the square of the strength
of the current, if the total resistance were constant in all the
circumstances considered ; and therefore we may conveniently
assume
H=K7^; (7)
but as we are not sure that the whole resistance is independent
of the strength of the current when an electrolysed fluid forms
part of the circuit, we must not assume that R is constant. In
what follows, all that is assumed regarding the value of R is,
that it is neither infinitely great nor infinitely small in any of
the circumstances considered *.
* Since the present article was put into the Editor's hands, I have be-
come acquainted mth a paper by Mr. Joule " On the Heat evolved during
the Electrolysis of Water," published by the Literary and Philosophical
Society of Manchester in 1843 (vol. vii. part 3, second series), in which it
is shown, that in some cases of electro-chemical action (for instance, when
hydrogen is evolved at an electrode or battery-plate of a metal possessing
a considerable affinity for oxygen) there is a "resistance to electrolysis
without chemical change," producing " a reaction on the intensity of the
battery," and causing the evolution of heat to an amount exactly equivalent
to the loss of heating power, or of external electro-motive force, which the
battery thus suffers. In any electro-chemical apparatus in which this kind
of resistance occurs, the quantity of heat developed by a current of strength
y will be expressible in the form Ay+By^ where A and B are finite when
Prof. Thomson on the Mechanical Theory of Electrolysis. 433
7. If we substitute the expressions (3), (4) and (6), (7) for
the three terms of the original equation (].), we have
v^-^^if^-ee,, .... (8
from which we deduce
.= t^2^fi^ (.)
8. It appears from this result that the value of 7 will be posi-
tive or negative according as the angular velocity of the disc
exceeds or falls short of a certain value D., given by the equation
"=p|; (10)
and therefore we conclude that^ when the angular velocity has
exactly this value, the electro-motive intensity of the disc is just
equal to the intensity of the reverse electro-motive force exerted
on the fixed wires, by the electro-chemical apparatus with which
they are connected.
9. If we adopt as the unit of electro-motive intensity that
which is produced by a conductor of unit length, carried, in a
magnetic field of unit force, with a velocity unity, in a direction
which is both perpendicular to its own length and to the lines of
force in the magnetic field, it is easily shown that the electro-
motive force of the disc, in the circumstances specified above, is
given by the equation
i=*|r2Fa> , *H.(11)
Hence if I denote the electro-motive force of the disc when it
just balances that of the chemical apparatus, we have by (10)
IzrJ^'e. (12-)
This equation comprehends a general expression of the conclu-
sion long since arrived at by Mr. Joule, that the quantities of heat
developed by difierent chemical combinations are, for quantities
of the chemical action electrically equivalent, proportional to the
intensities of galvanic arrangements adapted to allow the combi-
y is infinitely small. Consequently what is denoted in the text by R will
be equal to — +B, and will therefore be infinitely great when y is infi-
y
nitely small. The modification required for such cases will be simply to
use B in place of R, and to diminish the value of I found in the text (12)
by JA ; but the assumption that R does not become infinite in any of the
circumstances considered is, I believe, quite justifiable in the two special
cases which form the subject of the present communication. — W. T. Nov. 1,
1851.
434 Prof. Thomson on the Mechanical Theory of Electrolysis.
nations to take place without any evolution of heat in their own
localities ; and it may be stated in general terms thus : —
The intensity of an electro-chemical apparatus is, in absolute
measure, equal to the mecfianical equivalent of as much of the che-
mical action as goes on with a current of unit strength during a
unit of time.
10. When o) is less than XI, 7 is (§ 8) negative ; and hence
equations (3), (5) and (6), show W and Al to be negative also.
In this case the direction of the current is contrary to the electro-
motive force of the disc ; the chemical action is the source of
the current instead of being an effect of it ; and the disc by its
rotation produces mechanical effect as an electro-magnetic engine,
instead of requiring work to be spent upon it to keep it moving
as a magneto-electric machine. If we assume
7=-y, M=-M', W=-W',
so that when 7, M, and W are negative their absolute values
may be represented by y, M' and W, we find by (9), (10), (5),
(6), (2), (3) the following expressions for these quantities :
JR
y=-^^(Xl-a,) (13)
M'=j(9€y=:i-^^^:^(a-a,) . . . (14)
W = M'-JH = ^r2Fa).y=g]Vf. . (15)
The first of the three expressions (15) for W merely shows
that the mechanical effect produced by the disc in any period of
time is less than M', the full mechanical equivalent of the con-
sumption of materials in the electro-chemical apparatus, by the
mechanical equivalent of the heat generated in the whole cii'cuit
during that period. From the third we infer, that the fraction
of the entire duty of the consumption which is actually performed
by the engine is equal to jr. If (o were precisely equal to XI,
the electro-motive force of the battery would be precisely ba-
lanced, and there could be no current, and hence the performance
of the engine cannot be perfect ; but if (o be less than X2 by an
infinitely small amount, the battery will be allowed to act very
slowly j a veiy slight current, with a very small consumption of
materials, will be generated; and the mechanical effect produced
from it will be infinitely nearly equal to the whole duty, and in-
finitely greater than the portion of the effect wasted in the crea-
tion of heat throughout the circuit.
11. A condition precisely analogous to that of reversibility,
Prof. Thomson on the Mechanical Theory of Electrolysis* 435
established by Camot and Clausius as the criterion of perfection
for a thermo-dynamic engine*, is applicable to this electro-mag-
netic engine ; and is satisfied by it when the disc revolves with
an angular velocity infinitely nearly equal to 12, since then y,
M', and W are each of them proportional to 12— to, whether this
quantity be positive or negative ; and consequently if the motion
of the disc relatively to a state of rotation with the angular ve-
locity O be reversed, all the physical and mechanical agencies
are reversed.
12. From experiments made at Manchester in the year 1845
by Mr. Joule, on the quantity of zinc electrolysed from a solu-
tion of sulphate of zinc by means of a galvanic current measured
by his tangent galvanometer, I have found the electro-chemical
equivalent of zinc to be •07.284 f ; and I am informed by him, that
from other experiments which he has made, he finds that the
entire heat developed by the consumption of a grain of zinc in a
DanielPs battery is as much as would raise the temperature of
769 grains of water from 0^ to 1° Cent. J Hence, if we wish
to apply the preceding investigations to the case in which the
electro-chemical apparatus (§ 4) is a single cell of DanielPs bat-
tery, we may consider the consumption of a grain of zinc as the
unit of the chemical action which takes place, and therefore we
have
€=•07284, (9=769.
Again, according to Mr. Joule^s last researches on the me-
chanical equivalent of heat, the work done by a grain of matter
in descending through 1390 feet is capable of raising the tem-
* " If an engine be sucli that, when it is worked backwards, the physical
and mechanical agencies in every part of its motions are all reversed, it
produces as much mechanical effect as can be produced by any thermo-
d.3Tiamic engine, with the same temperatures of source and refrigerator,
from a given quantity of heat." (From § 9 of " Dynamical Theory of Heat."
Transactions of the Royal Society of Edinburgh, March 17, 1851, vol. xx.
part 2.)
t See Note on Electro-chemical Equivalents published at the end of this
paper.
X By experiments on the friction of fluids, Mr. Joule has found that the
quantity of work necessary to raise the temperature of a pound, or 7000
grains, of water from 0° to 1° Cent, is 1390 foot-pounds. Hence the me-
chanical equivalent of the consumption of a grain of zinc in Daniell's bat-
tery is 152*7, or nearly 153 foot-pounds. Messrs. Scoresby and Joule, in
their paper " On the Powers of Electro-magnetism, Steam and Horses,"
(Phil. Mag., vol. xxvi. 1846, p. 451) use 158 as the number expressing this
equivalent according to earlier experiments made by Mr. Joule. The ex-
periments from which he deduced the thermal equivalents of chemical
action, communicated to me for this paper, are described in a paper com-
municated to the French Institute, and acknowledged in the Comptes
Rendus for Feb. 9, 1846, but not yet published.
486 Prof. Thomson on the Mechanical Theory of Electrolysis,
perature of a grain of water from 0° to 1°. Hence, since the
unit of force adopted in the measurement of galvanic strength
on which the preceding value of € is founded, is that force which,
operating during one second of time upon one grain of matter,
would generate a velocity of one foot per second, and is conse-
quently ^^^ of the weight of a grain at Manchester, we have
J = 1890x 32-2=44758.
Substituting these values for e, 6, and J in (12), we have
1 = 2507100
for the '^intensity ^' or "electro-motive force^^ of a cell of DanielPs
battery in absolute measure. To compare this with the electro-
motive intensity of a revolving disc such as we have considered
(§ 3), let the axis of rotation of the disc be vertical or nearly
vertical, and, the vertical component of the terrestrial magnetic
force at Manchester being about 9'94, let us suppose that we have
F = 10 exactly, which would be the case with a disc exactly hori-
zontal in localities a little north of Manchester, and might be
made the case in any part of Great Britain by a suitable adjustment
of the axis of the disc. Then we have by (11),
f=5o)r^;
or if w be the number of turns per second,
i=5 X 27rwr2=31-416 x nr^.
Hence
i __ 31*416 xwr^ __ nr'^
T "" 2507100 " 79803'
It appears, therefore, that if the radius of the disc be one foot,
it would, when revolving at the rate of one tura per second, pro-
duce an intensity ^^^ of that of a single cell of DanielFs,
and it would consequently have to make more than 79803
turns per second to reverse the action of such a cell in the
arrangement described in § 4*. We conclude also, that a disc of
one foot radius, touched at its centre and circumference by the
electrodes of a single cell of DanielPs, and allowed to turn about
a vertical axis by the action of the earth upon the current passing
through it, would revolve with a continually accelerated motion
approaching to the limiting rate of 79803 turns per second, if it
* Hence in the multiple form of " the new electrical machine " suggested
by Faraday, about 800 discs, each one foot in radius, would be required,
so that with a rotation at the rate of 100 turns per second about a vertical
axis in any part of Great Britain, it might give an intensity equal to that o
a single cell of DanicU's.
Prof. Thomson on the Mechanical Theory of Electrolysis, 437
were subject to no frictional or other resistance ; and that if, by re-
sisting forces, it were kept steadily revolving at the rate of w turns
per second, it would, in overcoming those forces, be performing
-— — - of the whole work due to the consumption of zinc and
79803
deposition of copper in the battery.
13. If the electro -chemical apparatus mentioned in § 4 be a
vessel of pure water with two plates of platinum immersed in it,
we may consider a grain of hydrogen electrolysed as the unit for
measuring the chemical action which takes place. Now Mr,
Joule finds that, in the electrolysis of one grain of hydrogen
from water acidulated with sulphuric acid, as much heat is ab-
sorbed as would raise the temperature of 33553 grains of water
from 0° to 1°. Hence 6 must be less than 33553 by the quan-
tity of heat evolved when as much pure water as contains one
grain of hydrogen is mixed with acidulated water, such as that
used by Mr. Joule ; but, without appreciable error on this ac-
count, we may take
6'=33553.
I have found also, from results of experiments on the electro-
lysis of water made by Mr. Joule at Manchester in 1845, that
the electro-chemical equivalent of hydrogen is "002201. IJsing
this value for e, and the values indicated above for 6 and J, we
have by (12),
1=3305400
for the electro-motive force, in absolute measure, required for the
decomposition of water. This exceeds the electro-motive force
of a single cell of DanielFs battery, found above, in the ratio
of 1*318 to 1. Hence at least two cells of DanielPs battery are
required for the electrolysis of water; but fourteen cells of
DanielFs battery connected in one circuit with ten electrolytic
vessels of water with platinum electrodes would be sufficient to
efi^ect gaseous decomposition in each vessel.
14. In the Bakerian Lecture of 1832, *^*^0n Terrestrial Mag-
neto-electric Induction," Faraday, after describing some experi-
ments he had made at Waterloo Bridge, without however arriving
at any positive results, to test the existence of an inductive efiect
of the terrestrial magnetic force upon the flowing water of the
Thames, brought forward some very remarkable speculations
regarding the possible efibcts of magneto-electric induction upon
large masses in motion relatively to the earth, or upon the earth
itself in motion with reference to surrounding space. The pre-
ceding investigations enable us to compare the electro-motive
forces in such cases with electro-motive forces the effects of
which are familiarly known to us, and so to form some estimate.
488 Prof. Thomson on the Mechanical Themy of Electrolysis,
it may be very vague, of the anticipated effects. Thus let us
conceive a mass of air or water, or any other substance moving
relatively to the earth with a velocity V, and let A and B be
two fixed points in it or at its two sides, at a distance a apart,
in a line perpendicular to the direction of motion. Then if F
be the component of the terrestiial magnetic force perpendicular
to the plane of AB and the lines of motion across it, there will
be between A and B, or between any fixed conductors connected
with them, and insulated in all other places from the moving
mass, an electro-motive force, the intensity of which is given by
the equation
2 = F.V.a.
15. If, for instance, the velocity be one mile per hour, we
should have V= 1*4667; and if we take F = 10, which will be
nearly the case for a mass moving horizontally in any part of
Great Britain*, we have
«= 14-667 x«.
If we take fl! = 960, we find 2 = 14080 for the electro-motive
force between two platinum plates immersed, as in Faraday's
experiment, below the surface of the Thames, at a distance of
960 feet apart across the stream, when the tide is in such a state
that the current is at the rate of a mile an hour. The electro-
motive force, varying directly as the rate of the current, must
therefore, when there is a current of two miles and a half an hour,
be 35200, which is very little more than y^ of that which
was found in § 13 for the intensity required to decompose water ;
and as there is probably in no state of the tide a current of more
than three or four miles an hour, it is not to be wondered at
that no galvanic current was discovered in a wire connecting the
platinum plates.
16. An experiment on a much larger scale might be performed
by means of the telegraph wires which have recently been laid
between England and France, across the straits of Dover, by
simply connecting the ends of one of these wires with platinum
plates immersed in the sea on the two sides of the channel. If
the distance between the plates be twenty miles, in a direction
on the whole at right angles to the direction of the motion of the
water through the channel, and if, in a particular state of the
tide, there be an average velocity of a mile an hour, there would, as
* In June 1846 the horizontal magnetic force was found to be 37284,
and the dip 68° 58', at Woolwich (Philosophical Transactions, 1846, p. 246).
Hence the vertical force was 37284 X tan 68° 68', or 9-696. At the same
Eeriod it was 994 at Manchester, and it must have been 10 exactly at loca-
ties in England or Scotland not far north of Manchester.
Prof. Thomson on the Mechanical Theory of Electrolysis, 439
we find from the preceding expression, by substituting 20 X 5280
for «, be an electro-motive force of 1,549,000, or very nearly half
of that which is required for the decomposition of water. It
is not probable that the current produced by the action of this
force alone through the wire connecting the platinum plates
would be found to be sensible ; since a sensible continuous cur-
rent with water and platinum electrodes in the circuit can
scarcely be obtained by any electro-motive force less than that
which is required for the continued gaseous decomposition of
water. The existence of the inductive action might, however, I
think, be tested by using a galvanic battery of very low intensity,
to assist the electro-motive force arising from induction, and by
adding a little nitric acid to the liquid till it is found that a sen-
sible current is produced. It might then be observed whether or
not, when the tide turns and the water flows in the other direc-
tion through the channel, the electrical current becomes insensible,
or becomes less than it was ; and whether it goes on again as
before when the tide turns again, and the water flows as it did at
first. There would probably be some difficulty experienced in
keeping the electro-motive force of the battery sufficiently con-
. stant during twelve hours to make the experiment perfectly satis-
factory, and many difficulties that could not be foreseen might
occur. If, however, in any state of the tide the mean rate per
hour of the stream in the Channel exceeds two miles or two miles
and a half, it is probable that the inductive action might produce
a sensible electric current in the telegraph wire without such
assistance. It is very much to be desired that the experiment
should be tried, as it would afford probably the best test that could
at present be apphed, to find whether electrolysable liquids pos-
sess the property of magneto-electric induction discovered by
Faraday in metalHc conductors.
17. The possible magneto-electric efiects of the eartVs rotation
were also considered by Faraday, and it was conjectured that
electricity may, in virtue of them, rise to considerable intensity.
The general nature of the effect was shown to be a tendency for
electricity to flow through the earth from the equator towards
the poles, from whence it would endeavour to return externally
to the equatorial regions. If the distribution of terrestrial mag-
netism were perfectly symmetrical about the axis of rotation,
there could be no other kind of effect than this produced by the
rotatory motion ; and, neglecting at present the currents in com-
plete external circuits, which may exist in virtue of the v/ant of
this symmetry, we may endeavour to form a rough estimate of
the electro-motive force that would exist between the equatorial
regions of the revolving mass and a quadrantal conductor fixed
relatively to the earth^s centre, with one end near the surface at
440 Prof. Thomson on the Mechanical Theoiy of Electrolysis,
the equator and the other touching the surface at one pole. The
electrical circumstances would be the same if the earth were at
rest, and the conductor were made to revolve once round in
23^ 56°* 4*, with one end always touching at the pole, and the
other close to the surface at the equator. In such circumstances
there would be an electro-motive force equal to f.v . ds on any
infinitely small element ds of the moving conductor, if v denote
the velocity of its motion, and / the vertical magnetic force at
the part of the earth over which it is passing. Now if 6 be the
latitude of the element dsj and V the velocity of the surface at
the equator, we have
vsrVcos^;
if the distribution of magnetic force at the surface be, as in
making this rough estimate we may assume it to be, of the sim-
plest type, we have
/=Fsin^,
where E denotes the vertical magnetic force at the pole ; and if
r denote the eai-th's radius, we have
ds=zrdd.
The intensity of the total electro-motive force between the equa-
torial end of the moving conductor and the earth, being the sum
of the electro-motive forces on all its elements, will consequently
be equal to
/^''FVrsin^cos^f^^;
and hence, denoting it by i, we have
Now the eartVs diameter being about 7912 miles, we have
r=3956x 5280; and, by dividing the number of feet in the
earth's circumference by 86164, the number of seconds in the
sidereal day, we find V=1523. If we take r=14, we find, by
substituting these values for the factors of the preceding ex-
pression,
1=222,700,000,000.
This is about 88800 times the intensity of a single cellof DanielPa
battery (§ 12), and may therefore be about 50 times that of the
battery oi two thousand pairs of copper and zinc plates, charged
with nitro-sulphuric acid, by which Sir Humphry Davy only ob-
tained sparks half an inch long in the exhausted receiver of an
air-pump. Now the electro-motive force we have been considering
could in reality only produce galvanic currents by forcing a pas-
sage through the whole thickness of the atmosphere, upwards
Prof. Thomson on the Mechanical Theory of Electrolysis. 441
from the sm'face about the poles, and downwards to the earth
in the equatorial region s, and we may conclude that it does not
produce galvanic currents.
18. From the smallness of the electro-motive intensity in this
extreme case, we may infer that no part of the phsenomena of
atmospheric electricity can be attributed to the inductive action
of the terrestrial magnetism on masses of air or water in motion
near the surface of the earth.
19. If the space surrounding the earth, beyond the limits of the
atmosphere, were capable of conducting electricity, and were
affected as a fixed conductor by the motion of a magnet in the
neighbourhood of it, there would be electrical currents in com-
plete external circuits, induced both by the earth's rotatory mo-
tion, on account of the distribution of magnetism not being sym-
metrical about the axis of rotation, and by its motion through
space ; and it is I think far from improbable that the phsenomena
of aurora borealis and australis are so produced. It is quite im-
possible, in the present state of science regarding the relative
motion of the earth or of the solar system, and the medium fill-
ing all space, which by its undulations transmits light and radiant
heat, to form any estimate on satisfactory principles of the induc-
tive electro-motive forces which may arise from the motion of
translation of the terrestrial magnet through this medium ; but
we may form some idea of those which its rotatory motion may
produce by calculating the total electro-motive force on a closed
conductor held externally in a fixed position with reference to the
earth's centre. Thus let us conceive a circular conductor, of ra-
dius R, to be held with a diameter coincident vdth the earth's
axis of rotation ; and let i be the intensity of the total electro-
motive force which it would experience if it were made to revolve
round the earth once in 23^ 56°^ 4^, and the earth held at rest.
Denoting by P the radial component of the terrestrial magnetic
force at any element of this conductor, and in other respects
using the same notation as before, we have
i^r"" V .^^r co^e .^dd^\^ n V co^OdO.
J r if^ ^ -
If we assume the distribution of magnetic force at the earth^s
surface to be of the simplest type, the force at either magnetic
pole to be 15, and the magnetic axis to be inclined at an angle
of 20° to the axis of rotation, we have, at the time when the
moving conductor is passing over the earth's magnetic poles,
P = 15^,sin ie^%(fm^' ^^''' '^'^^\Y^^'
and in these circumstances we have consequently S^oid^ o-gm
442 Prof. Thomson on the Mechanical Theory of Electrolysis.
i=15Vg-y*'' sin (^+20°) cos ^</^=15 x 1523 .^tt sin 20°.
— IT
If we take r=R, we find, from this,
1=512,700,000,000,
which is about 204000 times the intensity of a single cell of
Daniell's. One-half or one-thii'd of this amount would be the
electro-motive force experienced by a fixed circular conductor of
twice or three times the earth's diameter, at the time when the
earth's magnetic poles are passing under it.
Greypoint, County Down,
October 6, 1851.
Note on Electro-chemical Equivalents,
The electro-chemical equivalents of zinc and hydrogen used in
the preceding paper were deduced from experiments made by
Mr. Joule on the electrolysis of sulphate of zinc and of water aci-
dulated with sulphuric acid, in which the galvanic currents used
were measured by means of a tangent galvanometer consisting
of a needle half an inch in length, suspended in the centre of a
cii'cular conductor one foot in diameter, fixed in the plane of
the magnetic meridian. The electro-chemical equivalent of a
substance, being defined as the mass (in grains) electrolysed
from any combination in a second of time by the action of
a current of unit strength, will be found by dividing the mass
of the substance electrolysed per second in any experiment
by the strength of the current. One way of combining several
experiments so as to obtain a mean result, will be to take
the arithmetical mean of the quantities of the substance found
to be electrolysed per second in the diiFerent experiments, and
divide it by the mean of the observed strengths of the cur-
rents. In the tangent galvanometer, the tangents of the angles
of deflection are proportional to the strengths of the currents,
and consequently the arithmetical mean of the tangents of the
angles of deflection in difi^erent experiments will be the tangent
of the angle of deflection corresponding to a current of mean
strength. The mean results, taken in this way, of four experi-
ments on the electrolysis of sulphate of zinc, and of four experi-
ments on the electrolysis of acidulated water, made at Manchester
on the 8th, 9th, 15th and IGth of September 1845, are as
follows : —
Electrolysis of Sulphate of Zinc,
Mean corrected tangent Zinc deposited
of deflection. per second.
•7345 -01508 grain.
Prof. Thomson on the Mechanical Theory of Electrolysis, 443
Electrolysis of Acidulated Water,
Mean corrected tangent Hydrogen liberated '
of deflection. per second.
1-7600 -001092 grain.
To determine the strength of the current (7) in absolute
measure, which produces a deflection (S) of the needle in thg
tangent galvanometer, we have the equation
7=oz:tan8,
ATT
where r denotes the radius of the circular conductor, and H the
horizontal component of the earth^s magnetic force, in absolute
measure ; since the magnetic axis of the needle will be drawn
from the magnetic meridian into a vertical plane containing the
resultant of the horizontal force H in the magnetic meridian,
and the force — ^ perpendicular to the plane of the conductor,
and consequently to the magnetic meridian. It is impossible
at present to assign with accuracy the values of the horizontal
magnetic force at Manchester at the times when the experi-
ments were made ; but according to data which Colonel Sabine
has kindly communicated to me, it must have been nearly
3*542 in 1846, and cannot probably at any time of observation
during that or the preceding year have differed by as much as
^j-prpr of its value from that amount. Taking, therefore, 3*542 for
lUu 1
H, and taking — for r (the diameter of the conductor being one
rH
foot), we have ^='28186; and consequently, for observa-
tions made with Mr. Joule^s tangent galvanometer at Manchester
in 1846,
7= -28183 X tanS.
Hence from the preceding experimental results, we find for the
electro-chemical equivalent of zinc,
*01508 ^_Q.
*28183x*7345-^^'Q^^^^-
and for the electro-chemical equivalent of hydrogen,
•^^1^^^ or *002201.
•28183x1*7600'
From the mean results of a series of four experiments on the
electrolysis of sulphate of copper, communicated to me by Mr.
Joule, I have found for the electro-chemical equivalent of copper,
•07052.
444 Mr. T. S. Davies on Geometry and Geometers,
IfL Bove's Repertorium (vol. viii. p. 273), values of the electro-
chemical equivalents of water and zinc, determined by Weber,
who was the first to give an electro-chemical equivalent in abso-
lute electro-magnetic measure, and by other experimenters,
are given in absolute measure according to the French units.
To reduce these to British measure, we must multiply by
(2*1692), the square mot of the fraction obtained by dividing
the number (15*438) of grains in a gramme, by the number
(3*2809) of feet in a metre. The electro-chemical equivalent
of water is obtained by multiplying that of hydrogen by 9 ; and
according to the theory of equivalence in electro-chemistry,
it might also be obtained by multiplying the electro-chemical
9 9
equivalent of zinc by ooTo > and that of copper by oTT^- The fol-
lowing table shows the values of the electro-chemical equivalent
of water in British absolute measure obtained in these different
ways.
Observers.
Galvanometer tised.
Electro-chemical action
observed.
Deduced electro-
chemical equiva-
lent of water.
Weber
Bunsen ...
Biinsen ...
Casselmann
Casselmann
Jo e
Joule
Joule
The ** electro-dynamometer"
Tangent galvanometer
Ditto.
Ditto. <
Ditto. I
Ditto.
Ditto.
Ditto.
Decomposition of water
Decomposition of water
Dissolution of zinc
Decomposition of water
in acid and saline so-
lutions
Zinc [deposited or dis-
solved.-']
Decomposition of water
Deposition of zinc from
solution of sulphate of
zinc
Deposition of copper
from solution of sul-
phate of copper ...
•02034
•02011
•01993
•02033
•02021
•01981
•02030
•02002
LXVII. Geometry and Geometers. Collected by the late Thomas
Stephens Davies, F,R,S,L,^E.^c^^
No. VIII.
[Contmued from vol. i. p. 544.]
ONE or two remarks upon points suggested by Professor
Rigaud's letter, apart from all considerations about Pappus,
Halley, and Porisms, will not be out of place here; viz. upon the
♦ Communicated by James Cockle, Esq., M.A., Barrister-at-Law, who
adds the fallowing note : —
[" The above manuscript and its accompanying foot-note, both of which
Mr. T. S. Davies on Geometry and Geometers. 445
references to Professor Leybourn^s speculations as a pub-
lisher*, ih
Mr. Leybourn came to London^ as most young men do/ to
make his way in the world. He had served an apprenticeship
to a business in Shields ; but during that period had contracted
a strong propensity to the study of mathematics,, and had deter-
mined somehow or other (as he should find an opening) to render
his inclinations coincident with his ^^ bread-and-cheese ^^ toils.
The companion of his pilgrimage was the late Mr. Glendinning,
the printer of Hatton Garden.
jT Mr. Leybourn was fortunate enough to obtain the partiality
and friendship of Dr. Hutton; and being a handsome young
(with the exception of the heading, for which I am responsible) are auto-
graphs of my deceased friend Professor T. S. Davies, have been confided to
me by Mrs. Davies. From the strong internal evidence oflPered by the
opening paragraph of the above paper, I infer that the present are the
* remarks ' alluded to by Professor Davies at p. 394 of vol. xxxvi. S. 3, and
reserved by him for another occasion. They were apparently not intended
by their author to stand alone ; but in the difficulty, perhaps impractica-
bility, of realizing the views of one so many of whose scientific aspirations
were frustrated by death, I hope to find a sufficient apology for so placing
them. They form at all events an interesting fragment of mathematical
biography and historj'^, and I considered it better to forward them for pub-
lication now, than to delay them until I could communicate with Mrs. Davies,
and request her to search among Professor Davies' papers for those intended
to accompany them. The result of such a search would moreover be
doubtful, and I have delayed these papers too long already.
" The following references may be found useful, my deceased friend having
omitted to give back -references at the commencement of his papers : —
No. I. of * Geometiy and Geometers ' will be found in the Phil. Mag. S. 3.
vol. xxxii. p. 419 ; No. II., Ibid. vol. xxxiii. p. 201 ; No. III., Ibid. p. 513 ;
No. IV., Ibid. vol. XXXV. p. 497 ; No. V., Ibid. vol. xxxvi. p. 382. In No.V.
will be found Professor Rigaud's letter alluded to in the text.
" James Cockle.
"2 Pump Court, Temple,
Sept. 8, 1851."]
* Mr. Leybourn speculated extensively in the way of publishing mathe-
matical works ; and I am convinced with the purest motives for the ad-
vance of science, and with very little eye to whether he should lose or
gain. All his business operations were conducted through his printer
Glendinning, of Hatton Garden (to whom he w^as greatly attached, and
whose press was alternately at the service of mathematics for Leybourn,
posting bills, bills for the auctioneer, and programmes of the entertain-
ments at Sadler's Wells); but the indifference of the workmanship and
paper, together with the extreme irregularity with which his Repository
appeared (varying from a few months to eight or ten years) prevented the
possibility of pecuniary success attending that undertaking. The book
referred to by Professor Rigaud was one of his " ventures," viz. Strachey's
translation of the Beja Ganita. The editorship of the Gentleman's Diary
for the Stationers' Company, was probably the only undertaking which ever
Phil Mag, S. 4. Vol. 2. No. 13. Dec. 1851. 2 H
446 Mr. T. S. Davies on Geometry and Geometers.
man, was a welcome visitor to the family. This was during the
feverish feeling created in England by the first French revolution.
Whether the Mathematical Repository or the Gentleman's
Mathematical Companion was first projected I do not know with
perfect certainty, but several trivial circumstances incline me to
the belief that the latter was. It is pretty clear, however, that
Mr. Leyboum was fii-st in the open field. I cannot give the
exact date of its first issue ; but from the cover of No. 3 bearing
the date March 1, 1797, and the woi-k being published half-
yearly (at first only and with tolerable regularity) we may put
down its origin as March 1, 1796. The first number of the
Mathematical Companion bears date /or 1798, and was therefore
printed in the preceding year, probably about the same time
(November) as the almanacs. This will explain the ground of
the otherwise unaccountable opposition of the " Diary Editor,'*
Dr. Hutton, to the Mathematical Companion ; the consequent
assumption of a dififerent foi-m of title ; and making it an indepen-
dent work, trusting to its own merits rather than one of homage
to the Stationers' Hall editors of the period.
cleared him a sixpence, and this he held from Dr. Hutton*s death as long
as he himself lived.
If, however, Mr. Leybom*n lost money, he at the same time gained a
high reputation from editing his Mathematical Repository. lie thus ob-
tained one great object of his early ambition, which he could have gained
in no other way ; for the most devoted of his friends and admirers (amongst
whom I place myself) will not contend for a moment, that either his range
of power or his mathematical acquirements could have gained for him that
reputation, in whatever other way exerted. Tlie Repository (as well as the
Diar}') was edited practically by his friends from its origin to its termina-
tion. Dr. Hutton aided him in the outset of the first series, and subse-
quently Dr. Gregory and IVIr. Lowry. In the earlier part of the new series
he was dependent on the judgement of Messrs. Dalby, howry, Wallace and
Ivory, with one or two others occasionally. In closing the fifth volume,
and throughout the sixth, this office devolved partly on Mr. Woolhouse,
but mainly on myself. During this latter period, too, the same may be
said of the Gentleman's Diary. Dr. Gregory, however, suppHedthe almanac
part of the Diary.
I have felt this distinct statement to be necessary to prevent some mis-
conceptions that might hereafter arise, if they have not (as I am led to think
they have) already been fonned, as to my connexion with the Repository
and Diary. My labours were neither few nor small, but they were wholly
gratuitous ; for besides what I wrote in those works, I had immense masses
of papers (often very jejune and absurd) to read ; and from these to select
what should be printed — a kind of labour, the disagreeableness and tedious-
ness of which can alone be understood by those who have exercised similar
editorial functions in respect of mathematical papers and solutions.
I bear my testimony, however, to Professor Ley bourn's honourable in-
tentions, and (as long as he was a free agent — which latterly he ceased to
be) bis high sense ofhouourable friendship. lie was a good if he was not
a great man.— T. S. D.
[ 447 ] '•'' '■ ^
LXVIII. Account of Experiments demonstrating a limit to the
Magnetizability of Iron. By J. P. Joule, F.R.S.
[Concluded from p. 315.] fjt*t\/^^'
On Electro-Magnetic Forces^,
I HAVE shown in a previous paper, that when a current of
voltaic electricity is transmitted through the coils of two
electro-magnets, their mutual attraction is proportional to the
square of the quantity of electrical force, and also that the lifting
power of the horseshoe electro-magnet is governed by the same
law.
I have recently made experiments which prove that the attrac-
tion of an electro-magnet, for a magnet of constant force, varies
in the simple direct ratio of the quantity of electricity passing
through the coil of the electro-magnet. In order to succeed it
was necessary to guard against the eifects of induction by a
proper arrangement of the apparatus.
Magnetism appears therefore to be excited in soft iron in pro-
portion to the intensity of the magnetizing electrical force ; and
electro-magnetic attraction, as well as the attraction of steel
magnets, may be considered as proportional to the product of the
intensities of magnetic force in the bodies attracting one another.
I have recently learned that the Russian philosophers, Jacobi
and Lenz, have arrived at some of the same conclusions with
regard to the laws of electro-magnetic attraction.
The accompanying figure will perhaps illustrate, with
some degree of accuracy, the complex action of the
forces which constitute the aggregate attraction which
exists between two magnets. The magnetic particles, of
which six only, viz. a b cdef, are represented, may be
conceived to be of an indefinitely large number spread
throughout the region of the poles : the straight lines
drawn between the particles represent the directions of
the several attractive forces.
If this view be correct, it is obvious that the closer
the approximation of the magnetic particles in each
magnet, the greater will be the aggregate attraction ;
for in that case the particle «, for instance, will be nearer the
particle/, and tlie force exerted between them will be in a less
oblique direction.
It was in consequence of the entertainment of a different
hypothesis that I was led, by the experiments recorded in the
previous paper, to imagine that I had detected a decrease of
power due to an increase of the length of the electro-magnets.
I gave a comparison of the attractions of electro-magnets 14
inches long and of the several sections yyths, yyths, and y^jths of
* Annals of Electricity, vol, iv. p. 474,
448 Mr. J. P. Joule's Account of Experiments
an incli square, with tlie attractions of electro-magnets 30 indies
long and of the sections 1 inch square and 2 inches hy 1. In
these experiments the poles of the attractive magnets were |fth
of an inch distant from one another, and it is probable that the
deterioration of the attractive energy of the long electro-magnets
was principally owing to the greater extent of their polar surfaces.
, Hence also corrections ought to he applied to the attractions
of the larger electro-magnets in Tables I. and II. of my previous
paper, in order fairly to compare their respective powers with
those of the smaller magnets.
These corrections would not, however, be of sufficient amount
to affect the general conclusion at which I have arrived, with
regard to the laws under which magnetic attraction (as applicable
to the production of motive force) is developed by electricity,
viz. that the attraction of two electro-mo gnets towards each other
is in every case rqiresented by the formula M = W'2E^, where M
denotes the magnetic attraction, W the length of wire, and E
the quantity of electricity conveyed hy the wire in a given period
of time ; a formula modified merely by the effects of approaching
saturation, of the conducting power of the iron, and of the di-
stance of the coils from the surface of the iron.
I have observed that magnetic and electro-magnetic attractions
decrease in certain cases in the simple ratio of the distances.
This was found to be the case, particularly when the magnets
were long and the distance between them small. Mr. Harris
has noticed the same phcenomenon in his " Experimental Inquiries
concerning the laws of Magnetic Forces.^' It may be almost en-
tirely accounted for by the complex action previously illustrated.
It is impossible to doubt, that the law of magnetic attraction is
that of the inverse square of the distances.
?!< ^ ^ Jji >(» 'P
Broom Ilill, near Manchester,
March 10, 1840.
On Electro-Magnetic Forces*.
In resuming the relation of my researches, I shall consider
the laws which govern that peculiar condition which is assumed
on the completion of the ferruginous circuit, viz. the lifting or
sustaining power of the electro-magnet.
Although this wonderful property is known to all, and a
variety of forms have been given to the electro-magnet both as
regards the bulk and shape of its iron and the length and num-
ber of its spirals, I am not aware that any general rules have
been laid down for its manufacture. I shall therefore attempt
to supply this want, and in so doing shall describe a construction
attended by far gi'cater results than have hitherto been produced.
* Annalsof Electricity, vol. V. p. 187.
demonstrating a limit to the Magnetizability of Iron. 449
It was my desire to make my experiments as exact as possible ;
and as I wish the relation of them to be clear and definite/ 1
shall begin with some observations on the measure of current
electricity indicated by my galvanometer. I iuiii^rb do/rr riii 'io-
* * ^ *««''*. • '
The galvanometer of which I made use in the last series of
researches was connected with an electrolytic apparatus furnished
with very fine platina wires. Voltaic currents of varied intensity
were then conducted through the circuit which included the two
instruments^ the circuit being broken at the end of two or three
minutes in each case_, and the hydrogen measured in a graduated
glass tube. The mean of ten trials gave 0*76 of a grain as the
quantity of water decomposed during each hour by the electrical
current indicated by the unit of my former quantity num-
bers. Hence the current indicated by 11-8 of these last would
decompose nine grains, or one equivalent of water per hour.
This current I propose to call a degree in the present paper.
The dimensions of the single coil of the above galvanometer are
12 inches by Q, and the deviation of its needle for one degree,
34° of the graduated card. From these data we may easily
calculate the value of the indications of any similar instrument,
bearing in mind that the electro-dynamic force produced by a
constant current of electricity is directly as the number of coils
and inversely as their linear dimensions.
The quantities of current electricity which were brought into
play in the subsequent experiments were frequently so great, that
the needle of the above galvanometer would have been brought
almost to a right angle with the plane of the coil, if subjected to
their influence. 1 therefore devised a new mea-
sure, which I flatter myself will prove of greater
service in some cases than the instrument pro-
posed for the same purpose by Mr. Iremonger*. .
The plan of my instrument is represented by the
accompanying figure, in which cc is a rod of cop-
per bent double, and fastened firmly to a strong
wooden frame ; m is a magnetized cylindrical bar
of steel, one foot long and half an inch in dia-
meter, supported slightly above the centre of
gravity (like an ordinary balance-beam) by knife-
edges resting on hard concave surfaces of steel.
A scale 5 is attached to one end of the magnet for
the purpose of receiving the weights by which the
electrical currents are measured. Lastly, rr is a
rest which the magnet just touches when at zero.'
In using this instrument, it is merely neces-'
sary to adjust the magnet to zero, either by
n
VI
J
^ *
)l) bii;i iif-j(i
rd LabfliMj
Annals of Electricity, vol. iii. p. 413, 414.
450 Mr. J. P. Joule's Account of Escperiments
means of screws, weights, or by the attraction or repulsion of a
steel magnet kept for the purpose. Then on making the ne-
cessaiy battery communications at cc, the scale s will rise with a
force estimated by the weight, in grains, which is required to
bring the magnet again to zero. In my particular instrument,
I have found that one degree of current is indicated by 0*69 of
a grain.
The value of this new galvanometer (the sensibility of which
may be increased at pleasure by multiplying the number of coils),
besides its usefulness in measuring copious currents, consists
chiefly in its perfect independence of the terrestrial magnetism,
as well as of any magnetic influence of surrounding bodies. In
every possible situation, provided that the intensity of the ba-
lance bar is constant, and that no interference is induced after
the adjustment to zero, the transmitted current will be exactly
proportional to the weight lifted by the scale ; and I should have
as much confidence in working with it on an iron steam-boat as
if eveiy particle of iron were entirely removed from it.
I now proceed to describe my electro-magnets, which I had
occasion to construct of very different sizes, in order to develope
any curious circumstance v/hich might present itself. A piece
of cylindrical wrought iron, 8 inches long, had a hole 1 inch
in diameter bored through the entire length of its axis; one
side of it was then planed away, until the hole was laid open
through its entire length. Another piece of iron, also 8 inches
long, was then planed ; and having been secured with its face in
contact with the other planed surface, the whole was turned into
a cylinder 8 inches long, 3f inches in exterior diameter, and \\
inch in the diameter of the bore. The larger piece (which was
intended for the electro-magnet) was then wound with four
copper wires, each of which was 23 feet long and yV^h of an inch
in diameter, and co-
vered with silk. This Q
electro-magnet*, which
I shall designate No. 1,
is along with its arma-
ture represented by
the accompanying fi-
gures.
I constructed an-
other electro-magnet
(No. 2) of a piece of round iron bar, half an inch in diameter
and 2*7 inches long. It was bent into an almost semicircular
shape, and covered with 7 feet of well-insulated copper wire J^th
of an inch thick. The poles were half an inch asunder.
* This electro-magnet is at present on view in the Exhibition of Industry
of all Nations.— May 1861, J. P. J.
demonstrating a limit to the Magnetizahility of Iron, 451
A third electro-magnet, No. 3, was made of a piece of iron
0*7 of an inch long, 0*37 of an inch broad, and 0*15 of an inch
thick, of which the lateral edges were well-rounded. It was bent
into the semicircular shape, and covered with 19 inches of insu-
lated copper wire ^\jth of an inch in diameter.
Anxious to procure a still greater variety, I made what might,
from its extreme minuteness, be almost termed an elementary
electro-magnet. It was the smallest, I believe, hitherto made;
and was constructed of a piece of iron wire \ of an inch long
and ^jih. of an inch in diameter. It was bent into a semicircle,
and wound with three turns of uninsulated copper wire ^^^th of
an inch in diameter.
In the following tables, in which the experiments with the above
electro-magnets are recorded, the first column gives the quantity
of electrical current in degrees ; the second contains the same
multiplied by the length of the coils in feet ; and the last con-
tains the lifting power in pounds avoirdupois.
Table I. — Electro-magnet No. 1. Weight of its iron 15 lbs.
Length of coils 23 feet.
Quantity of cur-
Electro-mag-
Electro-magnetic
Weight lifted.
rent in degrees.
netic force.
force corrected.
0-8
18-4
6-5
275
1-8
41-4
14-4
10
2-6
59-8
21-0
23
3-8
87-4
31-0
45
81
I860
65-0
238
10-9
2500
88-0
540
4-3
99-3
99-3
670
57
132-5
1325
890
8-6
1987
198-7
1060
14-4
331-0
331-0
1400
2lb'
497-0
497-0
1800
360
828-0
828-0
2030
Subsequently, with a more powerful battery, the weight ne-
cessary to remove the keeper was 2090 lbs., which is, I believe,
a greater weight than any magnet has hitherto carried, and is
certainly vastly superior to the performance of any other of the
same weight ; but I can show that this power, great as it is, is
not so much as is due to the form I have employed.
The latter part of the above table was obtained experimentally
before the first part, and in the mean time the proper insulation
of the coils from the iron was destroyed by accident ; and not
having had the opportunity of refitting the electro -magnet, I
have been obliged to supply the column of corrected electric
forces, calculated from the power obtained when the insulation
was good.
462
Mri Ji P. a oxikt'fi Account of Esoperiments
^K'^^
MBlfe itt^l^^trolniignet^T^. '«: "Weight 1057 M '^t^bW^
of coils 7 feet.
5^wv ^j o\ \0W)$
i
Quantitv of cms-
rent in degrees.
Elcctro-mag-
netic force.
Weight lifted.
-U-51
1-53
iiL-.,i..
3-57
107
427
20
38-5
49
'able III.— Electro-magnet No. 3. Weight 65-3 grs.
of coil 1*58 feet.
Length
Quantity of cur-
rent in degrees.
0-42
10
20
Electro-mag-
netic force.
0-6G
1-58
316
Weight lifted.
5-5
9
11
With great care No. 3 in one instance supported 12 lbs., or
1286 times its own weight.
Electro-magnet No. 4, which weighed only half a grain^ carried
in one instance a weight of 1417 grains, or 2834 times its own
weight*. There was, however, a good deal of difficulty in expe-
rimenting ^vith this minute arrangement, and it is on this account
that its greatest lifting power was not observed ; the relative
power obtained was nevertheless far greater than any that I had
heard of before, and is in fact more tlian eleven times that of the
celebrated steel magnet which belonged to Sir Isaac Newton.
It is well known that the length of a steel magnet ought to
bear a great proportion relatively to its breadth and thickness,
and that a contrary shape occasions the confusion of the poles,
and a general diminution of virtue ; and Dr. Scoresby has found
that if a large number of straight steel magnets are bundled
together, the power of each is thereby greatly deteriorated. All
this is easily understood, and finds its cause in the attempt of
each part of the system to induce upon the other part a contrary
magnetic polarity to its own. Still there is no reason why the
principle of consti-uction should be extended to the electro-mag-
net, especially as in its case a great and commanding inductive
power is brought into play to sustain what the steel magnet has
to support by its own unassisted retentive property. All the
preceding experiments confirm this principle ; and I give the
following table in proof of its obvious and necessary consequence,
* I subsequently had the pleasure of presenting Dr. Roget with a still
more minute electro-magnet, which had sustained about 3500 times its oyija.
weight of iron. — May 1851, J. P. J.
demonstrating a limit to the Magnetizahility of Iron. 453
— that the maximum power of the electro-magnet^ j^directlpmo*^
portional to its least transverse sectional area*^ ": ';' . >. ^f.r'?f
Table IV.
Least sec-
tional area in
square inches.
Bfaximum
lifting power.
Maximum
power divided
by area.
[•No.l
My own electro-magnets. < ^^ g
1No!4! '.''''.
Electro-magnet made by Mr. Nesbit. Length
round the curve 3 feet ; diameter of iron
2| inches ; sectional area 5*7 inches ; do.
of armature 4*5 inches ; weight of iron
about 50 lbs
Professor Henry's : of iron 2 inches square,
the sharp edges being rounded ; length
round the curve 20 inches ; weight 21 lbs.
Mr. Sturgeon's : length about I foot ; dia-
meter half an inch
10
0-196
0-0436
00012
4-5
3-94
0196
2090
49
12
0-202
1423
750
50
209
250
275
162
317
190
255
The results of the table are, I think, sufficient to prove the
rule, if we allow for various sources of error. No. 1 is unfortu-
nately made of a piece of unsound iron, and was in all probabi-
lity not fully saturated, otherwise I have no doubt that its power,
per square inch section of the ferruginous circuit, would have ap-
proached 300 lbs. Again, the specific power of No. 4 is less than
the mean, simply on account of the extreme difficulty of making
a good experiment with it. With regard to Mr. Nesbit^s electro-
magnet, the battery used was so powerful (nineteen of DanielFs
two-feet cells) and the quantity of conducting wire so very large
(fourteen lengths of wire, each 70 feet long and about xV^^ ^^
an inch thick), that its magnetism must have been brought to
the utmost possible pitch of intensity, which therefore exceeded
the mean specific power of the table. On the other hand. Pro-
fessor Henry^s, which was excited only by a single pair, could
not have been nearly saturated.
The mean of the specific powers of No. 2, No. 3, and Mr.
Nesbit^s electro-magnet, may, I think, be fairly taken for the
expression of the maximum magnetic force of iron under ordi-
nary circumstances, which may therefore be taken as equal to
the least sectional area of the magnetic circuit in square inches,
multiplied by 280 lbs*.
With regard to the magnetizing coils, I may observe that each
* According to this, the maximum magnetic attraction of two iron sur-
faces, each 1 inch square, for one another will be 140 lbs. — May 1861,
J. P. J.
Mr. J. P. Joule's Account of Experiments
particle of space through whicli a certain quantity of electricity
is propagated, appears to operate in moving the magnetism of
the bar with a force proportionate to the inverse square of its
distance from the iron j and that when the tension or specific
magnetism is the same, the thickness of the iron upon which
that particle of conducting space acts, has nothing (apart from
resistance and other foreign circumstances) to do with the whole
effect. Now it may be mathematically demonstrated, that, such
being the law, if each pai'ticle induce upon a larffe surface, the
resulting magnetic force will not vary mucli with the distance,
but be a very constant quantity for any distance which bears a
small ratio to the dimensions of that surface. Hence it is that
a coil within a hollow piece of iron has no power to magnetize
it*. And hence also in the case of my large electro-magnet, of
which the surfaces are large, eveiy particle of conducting wire
would perform its full extent of duty, even if it were not quite
close to the iron.
"\ATien the interferences arising from tension are reduced to a
minimum by completing the magnetic circuit and making use
of a very small electrical force, the resistance from length becomes
a veiy sensible quantity, varying probably in the direct ratio of
that element. Some idea of its character may be fonned from
the following table, in which I have compared half the maximum
powers of each electro-magnet with the electro-magnetic forces
which produced them ; and by dividing the former by the latter
I have obtained the third column, which, under the title of spe-
cific power, contains the quantity of lifting power (of that degree
of tension) due to an unit of electro-magnetic force.
Table V.
Electro-mag-
netic force.
Half the maxi-
mum lifting
power.
Specific power.
No. 1
200
4-5
0-66
1060
25
5-5
5-3
5-5
9-2
No. 2
No. 3
The electro-magnetic force against No. 2 is rather greater
than the truth, on account of the greater relative distance of its
coils from the iron; allowing for this, we may observe that the
variation of the specific powers is due to the resistance of length.
It is well knoAvn, that, after the current is cut off from an
electro-magnet, the ai'mature is retained in its place with very
considerable force. I was anxious to try the capability of my
electro-magnet No. 1 in this respect, and have arranged the
* Scientific Memoirs, part 5. p. 14.
demonstrating a limit to the Magnetizahility of Iron. 455
results of some experiments in the following table, the first
column of which contains the forces to which the electro-magnet
had been exposed ; the second, the lifting powers due to those
forces; and the third, the lifting power left after the circuit
was broken. ^
Table VI. ,U
Electro-mag-
netic force.
Lifting power.
Lifting power
retained.
88
29
14-5
540
40
10
33
16
10
There was considerable difficulty in observing the smaller lift-
ing powers. Nevertheless it is certainly the case, that the power
retained after the circuit was broken was very nearly equal to the
lifting power, with small electric forces.
When the whole current is not entirely cut ofi", but merely
reduced in intensity by the interposition of a bad conductor, a
surprising quantity of magnetism may be supported by a very
small electric force. I subjected No. 1 to an electro-magnetic
force of 90, a quantity adequate to bring its power up to 560 lbs.,
and then reduced the current to different degrees of intensity. In
the following table, the first column contains the electro-mag-
netic force to which the force of 90 was reduced ; the second
expresses the lifting power which is simply due to those quan-
tities ; and the third gives the lifting power which the same
quantities could support.
Table YII.
Electro-mag-
netic force.
31
21
14-5
6-2
41
Lifting power.
45
23
10
2-6
l-l
Supported lifting
power.
294
210
112
63
56
A battery of the size of a common thimble was quite sufficient
to produce an electro -magnetic force of 31 in the coil of No. 1,
and consequently to sustain a magnetic attraction of about 300
lbs. j and it is easy to perceive, that by increasing the size of the
electro-magnet and the quantity of its coils, the same minute
source could support a magnetic virtue of indefinite amount.
^ ^ ^ jj{ ^ ^
Broom Hill, near Manchester,
August 21, 1840.
466 Mr. J. P. Joule on the Magnetizabikty of Iron,
^i'.Cl.i/i ./ On Electro-Magnetic Forces^.
•^'h ^' ••+■*-• *****
• Suspecting that the extreme power of the large electro-magnet,
No. 1, had not been attained in my last experiments, on account
of the imperfect insulation of its coils, I detennined to try it
again, using every precaution which was calculated to develope
its magnetism to the full extent.
The old \Tire was removed, and a bundle consisting of twenty-
one copper wires, each 23 feet long and jj'jth of an inch in dia-
meter, was formed by binding the wires together with cotton
tape. This bundle of wires was coiled on the iron of the electro-
magnet, which had been previously insulated by a fold of calico.
Sixteen cast-iron cells, of the same size as those described in
my last, were arranged in a series of four elements, and con-
nected by good conductors with the electro -magnet. The attrac-
tive force developed was then found to be so great, that a weight
of 2775 lbs. had to be applied to the armature in order to sepa-
rate it from the electro-magnet.
Now by the formula ,r=280« given in my last paper, we ob-
tain 2800 lbs. for the greatest lifting power of this electro-
magnet, or only 25 lbs. more than that actually found, which
coincidence cannot but be considered as a striking proof of the
accuracy of the general principles I have before advanced. That
the saturation of the iron must have been veiy nearly effected in
the above experiment appears from the fact, that the quantity of
electrical cun-ent employed was four times as great as that which
was competent to make the same electro-magnet sustain 2128 lbs.
Although the battery used above for obtaining maximum effects
was very powerful, each cell exposing an active surface of two
square feet of cast iron, I have found that a very good lifting
power may be obtained mth this electro- magnet by means of a
very small voltaic arrangement. For instance, it can lift 8 cwt.
when the current generated by a single pair of 4-inch plates of
iron and amalgamated zinc is passed through its coils; and with
a single pair of platinized silver and amalgamated zinc plates
exposing only two inches of surface, the attraction is such as to
require the utmost force I can exert, even to slide the armature
upon its poles.
Broom Hill, near Manchester,
November 23, 1840.
♦ Annals of Electricity, vol. v. p. 470.
[ 457 ] .^J' T T Af r^rl- ~
LXIX. On the Products of the Destructive Distillation of Animal
Substances. — Part II. By Thomas Anderson, M.D."^
I PROPOSE in the followmg pages to communicate to tlie
Society tlie progress of my investigation of the products of
the destructive distillation of animal substances, the first part of
which was published in the 16th volume of the Transactions.
Since that period, partly owing to my numerous avocations, and
partly to the inherent difficulties of the subject, less progress has
been made than I had hoped or expected, but still I have accu-
mulated some facts of considerable interest, which I think de*
serving of the attention of the Society.
It may be remembered that, in the paper just referred to, I
announced the discovery, among those products, of picoline,
which I formerly obtained from coal-tar, and of a new base, to
which I gave the name of Petinine ; and I entered pretty fully
into the method adopted for the preparation of these substances,
and of certain other bases, the existence of which I merely indi-
cated, without at the time attempting to characterize them. On
proceeding to the more minute investigation of these bases, I
soon found that the quantity of material at my disposal was
much too small to admit of satisfactory or complete results, al-
though I had employed for their preparation above 300 pounds
of bone-oil. I found it necessary, therefore, to begin ab initio
with the preparation of the bases from another equally large
quantity of the oil ; and after going through the whole of the
tedious processes described in my previous paper, with the ex-
penditure of the labour of some months, I found my object again
defeated by deficiency of material. After various experiments,
which, though they led to no definite or conclusive results, served
to familiarize me with the nature and relations of the products
obtained, I made up my mind once more to begin again ; and
being resolved on this occasion not to be foiled in the same way
as before, I used for my new preparation no less than 250 gal-
lons of crude bone-oil, the weight of which was somewhat above
a ton. The result of this process, though involving an immense
amount of labour, has been satisfactory, not only in supplying
me with a large amount of material, but has also enabled me to
obtain many substances, some of them possessed of very remark-
able properties, which had escaped my observation when ope-
rating on a smaller scale.
' The employment of so large a quantity of material has, as might
be expected, led to some modification of the process described in
the first part of this paper, which, though convenient enough on
* From the Transactions of the Royal Society of Edinburgh, vol. xx.
part 2; read 21st April 1851. Part I. appeared in the September Number
of this Journal for 1848.
458 Dr. Anderson on the Products of the
the small scale, was too tedious for the large quantities on which
I now operated. The preliminary process of rectifying the oil,
which was quite beyond the resources of a laboratory, was effected
at a manufactory. The whole oil was introduced at once into a
cast-iron retort, furnished with a good condenser, kept cool by
an abundant current of ice-cold water. A very gentle heat was
applied, and the first twenty gallons which passed over were
collected apart ; they consisted of about equal bulks of a highly
volatile oil, and of water charged with sulphide of ammonium,
hydrocyanate and carbonate of ammonia, and a small quantity of
very volatile bases. The oil which distilled over after this frac-
tion had been separated was collected in a succession of casks,
which were numbered as they were filled.
In the after treatment of the oil, a process was employed
similar to that which I had formerly made use of, with this ex-
ception, that the watery fluid, which had formerly been rejected,
was employed for obtaining any bases which might have been
dissolved in it along with the ammonia. For this purpose it was
separated from the oil, and dilute sulphuric acid gradually added,
when carbonic, hydrocyanic, and hydrosulphuric acids escaped
with violent effervescence. When acid enough had been added
to communicate a powerfully acid reaction to the fluid, it was
put into a large copper boiler and boiled for some time, water
being added at intervals, so as to keep up the bulk. After the
ebullition had been sufficiently prolonged, the fluid was allowed
to cool, and slaked lime added in excess. A copper head was
then fitted to the boiler and luted down with clay, a condenser
attached, and heat applied. The distillate was collected in a
large glass receiver, which, in order to prevent the escape of
ammonia and any very volatile products which might be carried
along with it, was connected by a doubly-bent tube with a second
receiver containing water, through which the gaseous products
were allowed to stream. The fluid which distilled was coloured
blue by the solution of small quantities of copper from the con-
denser; it had a powerfully ammoniacal and putrid odour, and
when treated with sticks of caustic potass, in the manner de-
scribed in the first part of this paper, ammonia was rapidly
evolved with effervescence, and a small quantity of very volatile
and pungent bases collected on the surface of the potash. These
bases were separated from the potash fluid, which was preserved
along with the ammoniacal solution obtained by the absorption
of the gaseous products in the second receiver.
The treatment of the oil was conducted in a manner very
similar to that already described, and as I desired to have only
the more volatile products, I employed the first half of the oil
only. It was agitated with dilute sulphuric acid in casks about
Destructive Distillation of Animal Substances, 459
half-full, and after two or three days, during which the agitation
was frequently repeated, more water was added, and the solution
of the bases separated from the oil. To this fluid acid was
added, so as to have a distinct excess ; and it was then boiled for
the separation of Runge^s pyrrol, to which reference has been
made in the first part of this paper. As, however, I observed
that a very powerful and pungent odour was evolved when the
fluid began to boil, and tho vapours presented the characteristic
reaction of pyrrol in a very high degree, the head of the boiler
was luted on, and the condenser attached, for the purpose of
endeavouring to obtain that substance, which in my previous
experiments I had not done. The fluid which distilled over
carried with it a small quantity of oil, which, at the moment of
distillation, was perfectly colourless, but soon acquired a reddish
shade, and in the course of a few days became almost black.
The greater part of this oil passed over with the first portion of
water ; but the last traces adhered with great obstinacy to the
acid fluid, and could only be separated by very protracted di-
stillation. The substance thus obtained proved to be a mixture
of an oil insoluble in acids, and which appeared to be merely a
small quantity of the crude oil, mechanically mixed with the
fluid, and of a series of bases of very remarkable properties, and
obviously related to one another, to which I shall afterwards
refer under the provisional name oipyirol bases.
When these substances had entirely distilled, the fluid was
allowed to cool, excess of slaked lime added, and the distillation
again commenced, in order to obtain the bases which had been
retained by the sulphuric acid. The separation of these was
conducted in a manner in all respects similar to that employed
in the former preparations, solid caustic potash being added in
sufficient quantity to cause the separation of the bases held in
solution in the water. The potash fluid, however, retained a
certain proportion of ammonia, another gaseous base, and of the
most volatile bases, which could be separated only by a very
large excess of potash. The fluid was therefore distilled in glass
vessels, and the product collected in a succession of three re-
ceivers, the first of which was kept cold by water, the second by
a freezing mixture, and the third contained hydrochloric acid,
for the purpose of condensing the gaseous products. The first
receiver now contained the bases dissolved in a small quantity of
water, from which they were readily separated by potash ; the
second receiver contained only a drop or two of liquid ; but in
the third the hydrochloric acid was rapidly saturated, and re-
quired repeated renewal during the progress of the distillation.
The hydrochloric solution thus obtained contained a very large
quantity of chloride of ammonium, along with a small proportion
460 '»' Dr. Anderson on the Products of the' > a
of another base, in order to obtain which the fluid was slowly
evaporated, allowed to cool at intervals, and the sal-ammoniac
which deposited was separated by straining through cloth and
expression. After the separation of several crops of crystals, a
dark- brown mother-liquor was left, which refused to crystallize
by evaporation on the water-bath, but on cooling solidified into
a mass of long foliated crystals, which soon deliquesced in moist
air. These crystals still contained traces of sal-ammoniac, for
the separation of which they were evaporated to complete dry-
ness on the water-bath, and dissolved in the smallest possible
quantity of absolute alcohol, with the aid of heat. The filtered
fluid, on cooling, deposited a few tabular crystals mixed with a
little sal-ammoniac, which was got rid of by a second filtration ;
and the filtrate, when treated with animal charcoal and further
concentrated, solidified, on cooling, into a mass of large foliated
ciystals. ,
These ciystals are long, transparent, and colourless plates,
entirely without odour, and with a pungent and bitter taste.
In moist air they deliquesce rapidly. Solid potash added to
their concentrated solution causes the immediate escape of a
gaseous base resembling ammonia, but distinguished by its
peculiar putrid odour. This gas dissolves readily in water, and
gives a powerfully alkaline solution. It gives with corrosive
sublimate a fine white precipitate, soluble in hot water or spirit,
and deposited on cooling in fine silvery plates ; and its hydro-
chlorate gives, with bichloride of platinum, a soluble salt, depo-
siting from its hot saturated solutions in beautiful golden-yellow
scales. I selected this salt as a means of determining the con-
stitution of its base.
I. 6-885 grs. of the platinochloride, dried at 212°, gave 1-243
carbonic acid and 1'648 water.
II. 6*189 grs. of the salt gave 2*565 platinum.
III. 11 '531 grs. of another preparation gave 4*764 platinum.
Experiment.
Carbon . 4*92 ! .Ji
Hydrogen . 2*67
Nitrogen .
Chlorine .
Platinum . '4J'81 41-44
'''*'" 100^00 237-2
These analyses, then, correspond exactly with the formula
C^ H^ N, IICl, Pt CP ; and the base is consequently methylamine,
with which it and its salts agree in all respects.
The oily bases which had been separated from their solution
Calculation.
A
5-06
C2 12'
2-52
W 6
5-92
N 14
44-89
CF 106-5
41-61
Pt 98-7
Destructive Distillation of Animal Substances. 461
in watei* by means of potash, were dried by the addition of suc-
cessive portions of that substance, as long as it continued to be-
come moist. The dry oil, which was very dark-coloured, was
then introduced into a large retort, furnished v^^ith a thermome-
ter and a tubulated receiver kept cold by ice, and connected first
with a U-tube immersed in a freezing mixture, and then with a
large vessel of water, in order to collect the gaseous bases which
began to escape with effervescence almost as soon as heat had
been applied. At a temperature under 150° Falir. drops began
to condense in the neck of the retort, and the fluid entered into
rapid ebullition. At 213"^' the receiver was changed, and the oil
distilling above that temperature was collected in receivers, which
were changed at every ten degrees.
The quantity of bases which distilled under 212° was much
less than I had anticipated, and proportionably much smaller
than that obtained when operating on a much smaller scale
before ; and I consequently found myself compelled to proceed
very carefully, so as to avoid loss in the purification. By
distilling the product which boiled under 212°, I collected
fractions nearly equal in bulk at every five degrees, all very
similar in their general properties. They w^ere all limpid and
colourless fluids, with high refractive power, and pimgent odour,
remarkably similar to that of ammonia in the lower fractions.
They fumed strongly when a rod moistened with hydrochloric
acid was brought near them, and presented all the properties of
powerful bases. Exposed in the anhydrous state to a mixture
of snow and salt, they remain perfectly fluid, but if a small
quantity of water be added, beautiful white crystals of a hydrate
are deposited. I attempted, by several successive distillations,
to obtain fixed boiling-points ; but the quantity I had to work
with was too small for an operation involving so much loss of
material, and I therefore converted portions of the fractions
which I had reason to suspect corresponded with particular
bases into platinum salts. I selected, in the first place, the
lowest fraction of all, that, namely, which boiled under 150°.
It was dissolved in w^ater, saturated with hydrochloric acid, and
evaporated to dryness on the water-bath. The highly crystalline
residue obtained was dissolved in water, and mixed with a
solution of bichloride of platinum, when a yellow crystalline salt
was slowly deposited, which dissolved readily in water even in
the cold, and still more abundantly on boiling ; and the solution
on cooling deposited fine golden scales, scarcely to be distin-
guished in their appearance from those of methylamine or
of petinine. These crystals were separated, and as the salt
was highly soluble, and much remained in the mother-liquor, a
mixture of alcohol and setlier was added, when the fluid rapidly
Phil Mag. S. 4. Vol. 2. No. 13. Dec. 1851. 2 I
463 Dr. Anderson on the Products of the
filled with small shining scales. The analysis of this salt,
dried at 212°, gave the following results : —
6*970 grs. of plantinochloride gave 3'392 carbonic acid and
2*434 water.
6*475 grain's of the salt gave 2*422 grs. platinum.
8*257 ... ... 3*047
Experiment.
. 13*27
Calculation.
Carbon
13*57
C^ 36
Hydrogen .
. 3*88
3*77
H^o 10
Nitrogen .
• •••
5*27
N 14
Chlorine .
. • • •
40*18
CP 106*5
Platinum .
. 37*56
37*21
Pt 98*7
10000 265*2
From these results we arrive at the formula C^H^.N, HCl,Pt CI*,
which is that of the platinum salt of a base C^ H^ N. The
base is therefore the substance I have before described* as a
product of the action of alkalies upon codeine, under the name
of Metacetamine, but which I now prefer calling Propylamine,
in accordance with the name now usually applied to the acid
with which it corresponds. Unfortunately the quantity of
propylamine obtained was too small to admit of my examining
either its compounds or itself with accuracy. It is, however, a
perfectly limpid and colourless fluid, with a strong pungent
odour resembling that of petinine, but more ammoniacal. It
gives an abundant white cloud when a rod dipped in hy-
drochloric acid is brought near it, and unites with the con-
centrated acids, with the evolution of much heat. Its hydro-
chlorate crystallizes in large plates closely similar to those of
methylamine and petinine.
The discovery of methylamine and propylamine among these
products naturally directed my attention to the probable pre-
sence of ethylamine, the intermediate term of the same series;
but as I had not employed any very particular precautions in
condensing the more volatile products during the successive
rectifications to which I had subjected the crude oil, almost the
whole of it appears to have escaped. By collecting, however, the
first few drops passing over in the rectification of the portion
boiling under 150° in hydrochloric acid, and forming a platinum
salt, I obtained the following result : —
6930 gi-s. of platinochloride gave 2*649 grs. platinum.
This corresponds to 38*22 per cent. Now the per-eentage
of platinum in the ethylamine salt is 39*60, and the result
* Edinburgh Philosophical Transactions, vol. xx. p, 82.
Destructive Distillation of Animal Substances. 463
obtained, which is much too high for the propylamine salt,
shows that I must have had a mixture of the two, which might
have been separated had I possessed a sufficient quantity of the
salt. It will readily be understood that a result of this kind
could not in general be produced as evidence of the existence of
ethylamine, but under the particular circumstances of the case,
the next term of the same series on either side of it having
been detected, it may be considered as sufficiently conclusive of
its presence.
The occurrence of these bases enables us to establish, on
satisfactory grounds, the constitution of petinine. In the first
part of this paper, an analysis of that base is given, which agrees
in the most perfect manner with the formula C^ H^^ N, which
was also confirmed by that of its platinum salt. It cannot,
however, for a moment be doubted that it is homologous with
the bases with which I have now shown it to be associated, that
its true formula is C^ H^^ N, and that it is really butylamine,
the corresponding base of the butyric group. The analysis of
the platinum salt given in my former paper agrees equally well
with this formula, and though that of the base difiers from it
to some extent, much less reliance is to be placed upon it, as it
is scarcely possible, when operating upon so small a scale as that
upon which I was compelled to work, to subject the bases
to a sufficient number of distillations to efiect their complete
separation.
I have thus then established the existence, among the products
of destructive distillation, of ammonia, and the first four members
of the series of bases homologous with it. I have every reason,
however, to believe that the series does not end with petinine,
for the fraction boiling about 200° yields a platinum salt in fine
scales, and having all the characters of the salts of the same
series of bases, and in all probability contains valeramine. I
am not without hope also of obtaining caprylamine ; but this I
expect will be the last of the series, for when we reach the
temperature of about 240°, the character of the bases changes,
and we enter upon an entirely difi'erent series. ■■•■ , ^, ■ ^
■■ >* giiotlBoftM;)')'!
In the separation of the bases boiling above 240^, I have
encountered very great difficulties. After the trial of many
different processes, such as converting them into salts, exposing
them to cold, partial saturation, and every other plan which
appeared likely to answer, I have been compelled to return to
fractionated distillation, as the method most likely to answer
the end I had in view. But even with this process the difficulties
are great, and I have been by no means so successful in obtaining
fixed boiling-points as I was when operating on a smaller scale
212
464 Dr. Anderson on tlie Products of the
in my former preparations. I subjected the whole of the oils
boiling above 212 to a systematic course of fractionation, each
fraction being distilled alone, and the product collected in a fresh
series of bottles, and the receivers changed at every ten degrees.
In the earlier rectifications each fraction spread itself over a
very large number of degrees, and showed little tendency towards
concentration to fixed points. The distillations were repeated
no less than fourteen times, but even after all this the indications
of boiling-points were extremely indistinct. Sometimes in one
distillation certain fractions appeared larger than others, but
their pre-eminence disappeared again in succeeding rectifications.
Still a certain improvement was manifest, some of the fractions
being confined more nearly to the range of degrees within which
they had boiled at the previous rectification. It was obvious,
from the whole phsenomena of the distillation, that the separation
of the difierent bases was going on, although with extreme
slowness ; and at this point I endeavoured, by the examination
of the platinum salts obtained at different temperatures, to
determine the constitution of the bases which these fractions
contained ; and as I knew from previous experiment that the
quantity boiling between 270° and 280° consisted of picoline, I
had from this fact indications of the temperatures at which bases
were likely to be found, and I have thus been enabled to deter-
mine the existence of two substances belonging to the same
homologous series with that substance.
Pyridine. ^)W ^([.1 gnutiei
The first of these bases, to which I give the name of pyridine,
occurs in the fraction boiling about 240°. This fraction has an
odour precisely similar to that of picoline, but more powerful
and pungent. It is perfectly transparent and colourless, and
does not become coloured by exposure to the air. It dissolves in
water in all proportions, and is also readily soluble both in the
fixed and volatile oils. It dissolves in the concentrated acids,
with the evolution of much heat, and the formation of highly
soluble salts. When bichloride of platinum is added to a solution
of its hydrochlorate, a double salt is slowly deposited in flattened
prisms, which are tolerably soluble in boiling water, less so in
alcohol, and entirely insoluble in ether. \\Tien these crystals
are boiled for a considerable time in water, they appear to
undergo decomposition, with the formation of a platinum salt,
crystallizing in golden scales. Two analyses of this salt were
made, one upon the substance simply precipitated from the
hydrochlorate ; the other was the same salt redissolved in hot
water, so as to leave a considerable proportion undissolved. In the
last analysis the salt was mixed with the chromate of lead when
Calculation. ,^.,;,
ui-t
^
21 -03
CIO
60
2-10
H^
6
4-93
N
14
37-34
CP
106-5
34-60
Pt
98-7
'b'
Destructive Distillation of Amftiat SUyfdnces. 465
^ill rather hot, and it immediately evolved a strong smell of the
base, which accounts for the loss of carbon obtained in the
experiment.
I. 8-234 grs. of the platinochloride gave 6*486 carbonic acid
and 1*705 water.
II. 5*396 grs. of the platinochloride gave 4*015 carbonic acid
and 1-091 water. iifniffooiroo
8*138 grs. platinochloride gave 2*792 grs. platinunii^^l^ '^^'^l 00 •
'^^■4*956 ... ... 1*703 ... NjiiiiM Vj
,??ffoiifiOitLtoe)'f :orfibo.i.Expermient.
>fu>a-jini afit V- ■ ( ^ ^
,^,.Car)3^:^,..3, 21*48 20*29
^,^;Hy(irogen,| ^^f^,,^^*^4,,
,,„^Nitrogen^„^.|. .,,,
'wi^hlorme^ ^1 ,
hi .!?t)Tf/tR'oqrn[o:t tfT^T6^f[) IP- b'mriiK' 100*00 285*2 ^^
!^!' The formula C^o H^ N, HCl, Pt CP agrees very closely with
these analyses ; and the salt is consequently that of a base
having the formula C^^ H^ N, which forms a term of the picoline
series. I have not as yet directed further attention to this base,
as the phsenomena observed in the examination of the next base
served to show that, notwithstanding the correspondence of the
salt with theory, much difficulty would be experienced in ob-
taining the base itself in a state of purity.
tafixbi'i?{q to om&ff aiii mi r^f:^:^^ ^^^'^d m^di io ig-iii odT I
IfJ In the fraction boiling about 310°, a base occurs which
possesses precisely the constitution of toluidine, and to which I
give the name of Lutidine. When in the distillation of the
mixed bases the temperature rises to about 305° to 310°, more
distinct indications of a fixed boiling-point are obtained than at
any other temperature, and the base which distils presents
sufficiently distinct characters from those obtained at lower
points. The product is now much less soluble in water;
when dropped into a small quantity of that fluid it floats on the
surface, and is only slowly dissolved on agitation. It possesses
the remarkable property of immediately separating from its
solution on the application of a gentle heat, and collecting on
the surface in the form of an oily layer which dissolves again as
the temperature falls. Its smell is less pungent and more
aromatic than that of picoline, and it is also more oily in its
characters. It unites with the acids and forms salts, all of which
are highly soluble.
466 Dr. Anderson on the Products of the
Analyses were made of the different portions of oil boiling
about the temperature of 310°, with the following results : —
I. 3-840 grs. of the base, boiling between 310° and 815°, gave
11*007 carbonic acid and 3*060 water.
II. 4*012 grs. of the base, boiling between 315° and 320°, gave
11*516 carbonic acid and 3*160 water.
III. 4*319 grs. of the base, boiling between 316°and 320°, gave
12*430 carbonic acid and 3*576 water.
IV. 4*430 grs. of the base, boiling between 320° and 324°, gave
12*812 cai*bonic acid and 3*405 water.
I.
IL
III.
IV.
Carbon .
. 78*17
78*28
78*48
78*87
Hydrogen
. 8*85
8*75
9*10
8*54
Nitrogen .
. 12*98
12*97
12*42
12*59
100*00 100*00 10000 100*00
These results agree very closely with the formula C^"^ H^ N,
as is shown by the following comparison of the mean experimental
and calculated numbers.
Mean. Calculation.
^
Carbon . . . 78*45 78*50 C^^ 84
Hydi'ogen . . 8*81 8*41 H^ 9
Nitrogen . . 12*54 13*09 N 14
10000 100*00 107
Notwithstanding the close correspondence of these results,
however, further experiment showed that some of the fractions,
especially those of lower boiling-points, contained appreciable
quantities of picoline, the presence of which was established by
the analysis of the platinum salts. When, for instance, a portion
of any of these fractions was saturated with dilute hydrochloric
acid and bichloride of platinum added, fine prismatic crystals
were slowly deposited, which, as the result of numerous experi-
ments, were found to contain about 32*8 per cent, of platinum,
which is exactly the quantity present in the picoline salt, of which
the theoretical per-centage is 32*92. On evaporation of the
mother -liquor, crystals were deposited which gave quantities
of platinum vaiying from 32*5 to 32*0 per cent., and which were
obviously mixtures of the picoline and lutidine salts. When the
last mother-liquor, however, was evaporated to a small bulk, and
alcohol and aether added, another salt altogether distinct from
that of picoline, and crystallizing in flattened tables, was de-
posited, which analysis proved to have the constitution of the
lutidine salt.
This platinum salt crystallizes from its solutions in square
Destructive Distillation of Animal Substances^ 467
tables, sometimes very distinct, at other times confused and ir-
regular. It dissolves very readily in cold water, and still more
abundantly in boiling, and appears also to be very easily soluble
in excess of hydrochloric acid. Numerous analyses of this salt
were made, of which the following are the results : —
No. 1. This was the analysis of the salt prepared from the
oil distilling between 315° and 325*^ in the seventh rectification.
6*377 grs. of platinochloride gave 6*187 of carbonic acid, and
1*915 of water.
6*810 grs. platinochloride gave 2*146 grs. platinum.
64*76 ... ... 2*051
No. 2. Portion of the oil distilling between 295° and 300° in
the fourteenth rectification ; the platinum salt of picoline was
separated by crystallization, and the salt analysed precipitated
by alcohol and aether.
7*906 grs. gave 2*491 grs. platinum.
7*835 grs. of the salt recrystallized gave 2*470 grs. platinum.
No. 3. Another preparation from the same portion of oil.
7*330 grs. of platinochloride gave 7*070 carbonic acid and
2*090 water.
6*830 grs. gave 2*155 grs. platinum.
No. 4. Portion of the oil boiling between 300° and 305° in the
thirteenth rectification.
7*40 1 grs. gave 2*328 grs. platinum.
No. 5. Portion boiling between 325° and 335° in the seventh
rectification.
7*194 grs. gave 2*256 grs. platinum.
>[i3f
I. II. III. IV.
.A . _^ -A ^
Carbon . 2641 ... " 26*30
Hydrogen . 3-33 ... ... ... 3*16
Platinum . 31-51 31-67 31*50 31*52 31-55 31-45 31-35
These results correspond very closely with the formula C^^
W N, HCl, Pt CP, of which the following is the calculated result
compared with the mean of experiment.
Mean.
26-35
Calculation.
A
Carbon . .
26-81 C14
84
Hydrogen .
3*23
3*19 Hio
10
Nitrogen .
•••
4*49 N
14
Chlorine .
•••
34-00 CP
106*5
Platinum .
31*50
31*51 Pt
98*7
100*00 313*2
^^ Dr. Axxdtvson on the Products of the
It is clear, from these analyses, that the salt obtained is that
of the base of which the analysis is given above ; but it is equally
evident, fi*om the presence of small quantities of picoline, that
the base itself was not obtained in a state of absolute purity,
notwithstanding the close approximation of the experimental
results with those required by theory. I have been struck
throughout the whole course of the investigation by the fact,
that when the fraction corresponding to the boiling-point of any
particular base has been analysed, results very nearly correct
were obtained, even when the substance was very far from being
pure. I found, for instance, in the earlier part of the investiga-
tion, that the fraction boiling between 270 and 280°, after one
or two rectifications, gives precisely the results obtained from
pure picoline, although on further rectification the fluid will
begin to boil about 250°, and a small portion will still remain in
the retort when the thermometer has risen to 300°. It is, how-
ever, readily intelligible, that this should be the case when we
have to deal with a series of homologous bases, in which the
per-centage of carbon goes on increasing as the boiling-point
rises, so that, as in this particular case, we have the excess of
carbon in the less volatile base exactly counterbalancing the de-
ficiency in the more volatile. Thus lutidine, containing 78*5
per cent, of carbon, and pyridine only 75*9, and each successive
rectification removing equal quantities of the more and less vola-
tile substances of which the boiling-points are equidistant from
that of the intermediate member of the series, must always leave
a substance in which the quantities of the two impurities must
be exactly sufficient to counterbalance the error which each will
occasion.
Hydrargo-chlonde of Lutidine. — I directed my attention to
this compound, which is sparingly soluble and crystallizable, in
hopes that it might be adapted to the purification of the base
itself. I soon, however, abandoned it, as it turned out that it
was not possible, in repeating its preparation, to obtain inva-
riably the same substance, each base appearing, like aniline, to
form different compounds with corrosive sublimate. When a
solution of corrosive sublimate in alcohol is added to an alcoholic
solution of lutidine, a curdy white precipitate falls immediately,
unless the solutions be highly dilute, in which case it is slowly
deposited in gi-oups of radiated crystals. This salt dissolves in
boiling water, with partial decomposition ; it is still more soluble
in spirit, and is deposited unchanged as the solution cools. The
following analysis ^i^^onds exactly with the formula 2Hg
Cl + C^^H^N. ,,ri -nlTt.
7-850 grs. dried in vacuo gave 6*373 of carbonic acid, and
1*905 water.
Destructive Distillation of Animal Buhsimces. 4)59
3*113 grs. gave 2'32 grs. of chloride of silver. ., . , . .
7-684 ... gave 4-090 grs. mercury. *'^7 ^^ '*^f ^ ^7?^'
^ySfi-r KU'l'j?5(k to 5?^eriment. bgriiBtdolO' Calculation;! OBicd 9fii
Carbon. J£/?t S2-14 22*05 C^^ 84
Hydrogen^' . ' 2*6^^^ l,, .miiu^'Mui// ;M? j^ioij^oini
Nitrogen ...-r. .,,.„..-, 3*69!-'.....'!N,f ^ •,^-,,i^.».,-fi
' Chlorine . . 18-43 ' 18-64 CP 71 ^
%^^i>vm\ 4dt to >fpq •rftfl'fr;?> '^rli ni lOO'OO 380 ^
On another occasion results were obtained more nearly cor-r
responding with the formula 3Hg Cl + C^"* H^ N; and inter-
mediate results were also obtained, but as the existence of these
different compounds appeared to me to be fatal to their employ-
ment as a means of purifying the base, I did not attempt to
pursue the subject further. The separation of lutidine from the
other bases was also attempted by forming other salts, but none
were found to answer, all being highly soluble except the carba-
zotate, which crystallizes in beautiful, long, yellow needles, a
property which, however, is unfortunately possessed by the car-
bazotates of all the otlier bases.
Erom all these experiments, it appears that I have been able
to substantiate the existence of two bases, pyridine and lutidine,
although it has been as yet impossible to obtain the bases them-
selves in a state of satisfactory purity. I am inclined, however,
to think that the platinum salts, from their greater stability, and
the ease and regularity with which they crystallize, will aiford
means of purification, but I have been hitherto deterred from
trying this method on the large scale by the enormous, q^^ai^tity
of platinum which would be requisite for the purpose. i/.,|t p,'^(u>i\
It appears, then, that DippeVs oil contains two series of bases,
one that is homologous with ammonia, the other a series peculiar
to that oil, homologous with one another, and remarkable for
their isomerism with the series of which aniline is the type.
Thus we have— ^^ luiioaltJ in o^JsmildiJg ^/igcnoo to aoltuloi
Pyridine. . . . C^^H^N ' .o b ^onibiiiff to ffoilj/Io-i
Picoline . . . . C^Ml^N . oJ a^oUfri:.Ain^^.«^'irur
Lutidine. . . . C^^ H^ N .^lo'^gi; Toluidine. l^
And it is probable that the series existirig'iA jDippeFs oil does
not cease here, as I have found that the bases, with higher boil-
ing-points, give a steadily decreasing per-centage of platinum.
It is impossible, in the present state of the investigation, to give
any opinion as to the intimate constitution and relations of these
two groups of what I may call isohomologous bases. The most
470 On the Destructive Distillation of Animal Substances,
obvious explanatioD, however, would be to suppose the new bases
to be imidogen or nitrile bases, which would enable us to under-
stand why they differ from the aniline series, which we know to
be amidogen bases. If, however, they belong to either of these
classes, they must differ remarkably from any of those hitherto
examined, all already formed being extremely unstable, and de-
composed even by very feeble affinities, while picoline and its
congeners are extremely stable, and resist even the action of
nitric acid. Into these points, however, I shall not now enter,
but reserve their discussion for a future part of this paper.
Pyrrol Bases,
I have already referred, at the commencement of this paper,
to another series of bases, to which I have given the provisional
name of pyrrol bases, and which distil away from the acid fluid
by which the others are retained. They are obtained in the
form of an oil, which is transparent and colourless at the moment
of distillation, but rapidly acquires first a rose, then a reddish-
brown, and finally an almost black colour, and the mixture gives,
with hydrochloric acid and a piece of fir-wood, the purple-red
colour which Runge describes as characteristic of pyrrol. In
fact, I imagined that 1 had at length obtained this substance,
which had escaped me in my previous experiments, but I soon
found that the product was really a mixture of several different
bases. When distilled with the thermometer it began to boil
at about 212°, and the temperature gradually rose to above 370°,
and during the whole of the distillation pretty large fractions
were obtained at every ten degrees, but those between 280° and
310° were decidedly larger than the others. These oils were all
bases, with a peculiar and disgusting odoui', quite different from,
and much more disagreeable than, that of the picoline series of
bases. They all acquire colour on standing, although more
slowly than the crude oil. These substances dissolve easily in
a small quantity of hydrochloric acid, and give, with bichloride
of platinum, a precipitate which is at first yellow, but is rapidly
converted into a black substance. When dissolved in an excess
of acid, and heated along with it, they present a vciy remarkable
character ; the solution at a certain temperature becomes filled
with red flocks, so abundant and bulky, that, if not too dilute,
the fluid becomes perfectly solid, and the vessel can be inverted
without anything escaping. The same change takes place,
though more slowly, in the cold, and the substance deposited is
then of a pale orange-colour, but becomes darker by boiling or
exposure to the air. When this substance is collected on a filter,
washed, and dried, it forms a reddish-brown and very light and
porous mass. It is insoluble in water, acids, and alkalies, but
On the Anticlinal Line of the London and Hampshire Basins. 471
soluble in alcohol, and tlie solution on evaporation leaves a dark
resinous mass. When subjected to dry distillation, it leaves a
bulky charcoal, while an exceedingly disgusting oil distils.
The acid fluid which has been separated from this substance
by filtration, when supersaturated by an alkali, evolves the odour
of the bases of the picoline series. These pyrrol bases I conceive,
therefore, to be substances formed by the coupling of the picoline
series with some substance which yields the red matter to which
I have alluded. I have not as yet, however, pursued the inves-
tigation of these bases, but shall communicate the result of their
examination in a future paper.
The Non-hasic Constituents of Bone-Oil.
, I have as yet directed very little attention to this branch of
the subject. I have found, however, that when the most volatile
part of the oil, after separation of the bases, is repeatedly rec-
tified, it improves in odour, and at length there is obtained a
substance which, when acted upon by nitric acid, and then by
sulphide of ammonium, gives the reaction of aniline, — indicative
of the presence of benzine in the oil. It is probable, therefore,
that this series of homologous carbohydrogens forms a part of
the oil, but not the whole of it, for I have found that when the
oil is boiled for some time with potash, ammonia is evolved, and
on supersaturating the potash solution with sulphuric acid, the
odour of butyric acid, or at all events of one of the fatty acids,
becomes apparent ; from which pha^nomena I draw the conclusion
that it also contains the nitriles of these acids.
LXX. Postscript to Mr. P. J. Martin's Paper On the Anti-
clinal Line of the London and Hampshire Basins.
SINCE the publication of the greater part of this memoir, I
have read Mr. Prestwich's exposition of the range of the arena-
ceous and other water-bearing strata round London j and of their
probable capacity for the reception and transmission of a supply
of water to the metropolis, and especially of their aptitude for
giving that supply by means of Artesian wells*.
A small part only of the area comprised in Mr. PrestwicVs
review belongs to that which I have made the subject of my
particular research ; although every part of it, of course, is com-
prehended in the range of the surface-changes brought about by
the convulsion which produced the great synclinal called the
London basin.
After the chalk, the most important member in this order of
* A Geologic^^l Inquiry, &c, London, 1851.
471^ Ml*. P. JF. Martin on the Anticlinal Line of
strata & tt^tvtiter-bearing one, as Mr. Prestwich has obseiTed, is
the gi'eensand. The upper greensand of the Vale of Pewscy and
the suboixiinate valleys of that line of elevation, is satisfactorily
disposed of by Mr. Prestwich. Its rainfall, like that of the chalk
of that line of countiy, is stopped by the gault, and much of it
carried off southward by the Wiltshire Avon. But the inflection
which brings down the Kcnnet eastward, and the synclinal which
throws out the waters of the Basingstoke Canal, would assist in
filling the beds under London, and feeding any Artesian wells
carried deep enough there.
Of the greater and more important exposure of the Lower
Greensand in the great plateaux of Wolmar Forest, Hind Head,
the HambledoD^ Uasscomb and E^whurst Hills^ there is more to
be said. ' iu;> fiiilr '^tiini\ Una ^.nji/alt -ion ski oiij. io /au -joh tmiidi
A cursory inspection dnly of thfe map \vill show thdt tte' stlt'-
face-drainage of all this country, including also a part of Leith.
Hill, is taken off by the Wey. This river draws some water out
of the Malm country near Alton, and in its course by Farnham
takes in the Bourne and other springs thrown out by the sharp
flexure of the Hogsback. It then receives the sui-plus of the
Frensham Ponds, which are maintained on the middle argillaceous
beds of the lower greensand of Dr. Fittou, of which there is a
considerable exposure from that line of country by Pepper Har-
row to Godalming. It then takes in the stream that works the
paper-mills at Haslemere, and passing by Elsted drains Hind
Head, takes in other subordinate streams from the Godalming
and Hasscomb countries, and finally receives the large supply
out of the Albury and Shiere Valley at Shalford*. All these
watei*s are thrown out by the Weald clay ; and looking at the
collective stream as it is constantly flowing under Guildford
Bridge, one cannot but suppose that it insufficient to account for
all the rain that falls on the above-mentioned superficies, not lost
by evaporation, iniin-miin iRtns oiii to ij;i J
The sharp flexure at the bolder 'of ^hie chalk escarpment fronf
Farnham eastward, and the rise of the Weald clay in all the an-
ticlinal of which the Peasemarsh exposure is a part, extending
eastward toward Albury and then resumed in the flexure at Buiy
Hill, must preclude the thought of much infiltration toward and
under the chalk of the London basin. I therefore incline to the
opinion, that if the rain which falls on the greensand countiy
north of a line drawn from Leith Hill by Hambledon to Hasle-
mere, and from thence to the gault under the Alton Hills, is to
benefit London, it must be collected from the sources of the Weijj
and led there by artificial means.
H Massing eastward toward the next largest greensand exposures,
'' * None comes down from the Weald except in flood-times.
the London and Hampshire Basins, 473
the Sevenoaks and Maidstone countries, we find that the flexures
which rule the Hne of the escarpment of the North Downs run
longitudinally south of the greensand escarpment ; so that the
infiltration of the Reigate, Nutfield and Westerham Hills, is
turned toward London. But further east in the Sevenoaks
district, the flexure at Montreal, first noticed by Dr. Fitton and
afterwards spoken of by Mr. Hopkins as the " Sevenoaks anti-
clinal,'' and then another in the Maidstone district, which, as
Dr. Fitton informs me, brings the Weald clay up at Tenterden
Heath, must produce a strong diversion, and throw much of the
rainfall of these districts severally into the Medway and the
Darent.
But if I may venture an opinion on such a subject, neither
these nor any of the minor flexures and faults that can be traced
through the districts, the subject of Mr. Prestwich's research^
should militate against a trial of the efficacy of Artesian wells
carried through the superincumbent strata into the greensand
under London. The faults and flexures that run east and west
within the great synclinal cannot be of much moment as ob-
structive agencies. In my earliest publication I have spoken of
Windsor as a chalk " outlier-by-protrusion,'' and of the Isle of
Thanet as another, and it is probable that the Deptford chalk is
intermediate in the same parallel of elevation ; but these, and
such as these, would not be likely to off'er any serious obstruc-
tion to the constant infiltration from higher levels. Borings
through the chalk to the level of the gault would probably absorb
the supply of the springs which now issue from that stratum round
London, and especially those which take their rise only during
great engorgements of it. Such are the ^^ winter-bournes " of
Hampshire and Wiltshire, and such intermitting streams as the
Lavant and the Bourne, which do not fill till the ordinary issues
are insufficient for the transmission of the superabundant supply.
I reside in the synclinal of the great anticlinal flexure of Green-
hurst, and I have an Artesian well in my garden, which soon
after it began to operate, dried up a perennial spring about two
hundred yards off and about twenty feet above me. And so it
continues to do, except in long- continued rainy seasons, when the
natural spring discharges again for a short time. What I have
said of the waters of the chalk, as they are stopped by the gault,
may apply to those of the greensand, which is constrained to throw
them out because they do not find issue at a lower level ;. and
such issue the Artesian wells would afibrd them. ^ (iii>] ^-r; »iir
Nomenclature. — I share in Mr. Prestwich's objection' t6 the
name of " plastic clay," and I only use it in submission to the
tyranny of prescription. Mr. Prestwich's ^^ lower tertiary " is a
better phrase. The imposition of names is seldom well-consi-
474 Mr. P. J. Martin on the Anticlinal Line of
dered. At the time I suggested the use of the word " Wealden*/'
which was adopted by Br. Fitton and Sir H. De la Bechcf, I
also advocated the use of the word " Glauconite '' for greensand,
upper and lower, and to include everything from the chalk to the
Wealden. If this also had been adopted, it would have been
taken up by the French geologists, who would have found their
subdivisions of Glauconie crayeuse and Glauconie sabloneuse con-
veniently included, and we should not have been incommoded
by the introduction of the synonym of " Neocomien.^^ Or if
Dr. Fitton (who of all men has the greatest right to be name-
father in such a case) had given earlier enunciation to his happy
thought of " Vectine,^' the propriety and convenience of such a
collective appellation for all the members of the lower part of
the cretaceous system, must have assured its general approval
and adoption.
Evidence of upheaval. — As the evidence of the continuation of
the same upheaving forces, from the great denudation of the
Weald westward into what I have called the great chalk dome of
Hampshire, is a matter of so much importance, I have again
visited the line of country pointed out by Dr. Fitton as likely to
contain signs of disturbance, bringing the eastern and western
denudations into direct relation with each other.
I am induced to dwell on this point more particularly, be-
cause in his map of the Weald, and adjoining country, Mr. Hop-
kins has drawn an imaginary line round the ^^ disturbed district J,^'
which conveys to the cursory observer, more strictly perhaps
than the author intended, the notion, that the signs of disturb-
ance are confined within those limits. We are to imderstand
only, I believe, that within the area so described, the best evi-
dence is to be found in exemplification of Mr. Hopkins^s
''Theory of Elevation.^'
The last examination, the third I have especially made of this
line of country, confirms my opinion of the projection of the
Winchester anticlinal westward, as far at least as the banks of
the Test, and eastward into the great valley of the Weald by the
Vale of Meon ; the high grounds between these two points being
the true continuation of the elevation of the South Downs. The
valley which carries the Itchin from Alresford to Winchester ia
the synclinal of this elevation, and is, as I suspected, occupied
by " lower tertiary."
In the above-mentioned visit, I discovered a flexure and fault
in the Malm rock north of the new church at South- Harting,
which I suspect to be the expiring point of this line of disturb-
* Geol. Mem. of West Sussex, 1828.
t See " Table of Superposition."
X See map in Geol, Trans, vol. vii.
the London and Hampshire Basins. 475
ance. This arrangement in relation to tlie long and important
flexure of Greenhurst on one side^ and of the anticlinals of the
Vale of Wardour and Portsdown on the other, appears to corre-
spond with that intercurrency, or digitation of fissures, which
Mr. Hopkins seems to consider an essential part of his system*.
J have previously spoken of the same arrangement on the
north side of the great anticlinal, in the decline respectively of
the Peasemarsh line, or more properly of the Froyle and Pop-
ham-beacon line, and that of Pewsey, in the Basingstoke country.
Lacerated Escarpments. — Although minor indications of this
phsenomenon, familiar to the practised eye, occasionally peep
out, it is not often that we can get behind the mass of debris
with which the basset edges of stony strata are encumbered. I
have spoken of the entrance to a quarry of the upper green sand-
stone at Ray Common near Reigate, exhibiting unequivocal
marks of the original violence. That quarry is now in disuse,
but an open one is being worked a little to the east of the same
place, on the outskirts of which obscure indications of contor-
tion and displacement are visible ; such as to show, that if a
clean section could be obtained, transversely to *the plane of
stratification, from the chalk above to the gault beneath, a good
specimen of lacerated escarpment would be brought into view.
There is at this point a very remarkably prominent terrace of
the stratum in question, illustrative of the projection given to
such indurated layers at the angles of cross fracture, the trans-
verse valley of Smitham-bottom running out southward here by
Merstham and Redhillf.
Denudation and Diluvium. — It has been suggested to me that
so remarkable a feature as the bare sand-rocks about Tunbridge
Wells ought to be noticed in any disquisition on the Weald-
area, however summary. No one can look at these rocks, or
walk over those of Bridge Park, without being struck with their
singular position and prominence, not in any way accountable
but on the supposition of the violent abrasion of diluvial flood.
It is well known that similar appearances are to be found all the
world over, where layers of durable and destructible materials
alternate with each other. And no one can view the wilds of
Henley Heath and Bexley Hill, and the head of HartingcombeJ
(covered as they are with boulder stones, and other signs of the
* ^- , -i-- If, Greenhurst
1 ■ yf'-. ,-i-
Winclipstfr
Wardour
Porfsflnwn
■u
t This upper greensand platform is also noticed by Mr. Prestwich,—
"Water-b.earing Strata," &c., p. 80.
X West Sussex.
476 On the Anticlinal Line of the London and Hampshire Basins,
catastrophe we contemplate, only skimmed over by a scanty
herbage), or walk round the slopes of Hind Head, and look down
into the combs and gullies below, without having his mind filled
with images of the mighty flux and reflux, that not very long
ago (speaking in geological epoch) scooped out these valleys and
modeled the picturesque and remarkable scene before him.
I have not time to do more than notice the account of Mr.
Mackie's bone-bed at Folkstone, in the last Number of the
Journal of the Geological Society. It is a specimen, and within
the range, of my subcretaceous zone of drift, into which a few
pebbles of the lowest tertiary have strayed. Much loam and brick
earth seem to enter into the composition of this bed, and make
it, as in the bottom of the Peasemarsh gravel, more than usually
preservative of diluvial bones.
The same Number of the Journal contains Mr. PrestwicVs
description of, and speculation on, the cliff's and diluvial beds of
Sangatte. That deposits of this sort on the chalk confines of
the Boulogne denudation should correspond with those we find
at Dover, Foljcstone and Brighton, on the flanks of the Weald,
on this side of the Channel, is only just what might be expected.
It is probable that an examination of the French coast, south
and west of the Somme, where the chalk sinks again under the
tertiary beds, would aff'ord the same intermixture of drift and
the same transition from the angular and fractured flint of the
'' cretaceous " into the pebbly, sandy and loamy debris of the
'^ tertiary drift zone '' of the foregoing memoir. It cannot have
escaped Mr. Prestwich's notice, that his ancient chalk cliff* of the
pre-eocene, or earliest tertiaiy shingle-bed at Sangatte, exactly
corresponds with the sectional view given by Dr. Mantell in his
Geology of the S.E. of England, of the ancient cliff" and beach,
with the superincumbent mingled drift materials in the cliff's
between Kemp-town and Rottingdean; — all of which appearances
are there still visible.
I have spoken cursorily of the diluvial deposits of the London
basin and the eastern counties, the rolled clays and the heteroge-
neous admixtures of the Cromer Cliff's, and other phajnomena
indicative of the marginal relations of the massif of trans-
ported materials at the bottom of the German Ocean. It is not
necessary to be reminded of the mammalian bones which are
occasionally fished up at Harwich, and along all that line of
coast, to be assured of the identity of the several bone-beds of
Brighton, Folkstone, Cromer, the chesil-bed of Portland*, the
elephant-bed at Peppering near Arundel f, the gravel-pits near
* Vide Dr. Buckland and Sir H. de la Beche, loc. cit.
t ManteU's Geol. of S.E. of England.
-,,.,., sOn th^ Integration of Linear Differential JE^quations. 4i77
Guildford, with all ^t other diluvial heds of this age in the
South of England. ! . /
The nomenclature of transported maiiQviaX?, [terrain de' trans-
port) is not yet well determined. Diluvial drift will probably
serve for the materials under review, in contradistinction to the
loose materials of undoubted " moraines/' " erratic boulders/'
"^glacial accumulations,^' &c.
• In my prefatory letter (p. 41), I have alluded to a paper by Sir
Roderick Murchison, on the flint-drift of part of the area I have
here had under review, read before the Geological Society on the
1,4th of May last, and of which an abstract was given in the Athe-
naeum of the week following. I had the pleasure of affording
some assistance locally to Sir Roderick in his researches pre-
paratory to the production of that paper, and it was agreed that
I should be present at the reading; and it was my intention
then and there to have advocated the opinions here advanced, and
to have adduced in brief, the facts and geological phsenomena in
their support, as imperfectly detailed in the foregoing pages ; but
from some misunderstanding I did not receive the intimation I
expected of the day on which the reading and discussion were to
take place.
The publication of Sir R. Murchison's paper is promised in
the next forthcoming number of the Society's Journal ; and
" although I am a stranger to that gentleman's precise opinions
on the subject of the Weald denudation, 1 do not doubt of meet-
ing with his support and full concurrence in relatipn to, facts,
however we may differ as to inferences. '"*''^- rr^.'^'^pf^^'^^^^ '
, i .Pulborough, Nov. 7, 1851. ' ' ' ^ ' ' ''""■'^^''
>itfa ■' =?nf
V ILXXI. On the Integration of Linear Differential Equations}^
Mtii; :Mii iv jgy fj^^ ^^^ Brice Bronwin*. ^ -^^U liilW
TN this paper D is used for -7-, and the coefficients are sup-
posed to be integer functions of oc. The following formula is
supposed to be well known : — m- ;> --in.u.M.i;. -.:' m«
If p^{7r + k)u-'np^u, ''^^^"' ^^^ '^^ ayivWithiti
where p and tt denote operative symbols. Any forms of p and
TT therefore which satisfy the first of these will satisfy the second.
From this we have the theorem
* Communicated by the Author, j ,v\,^\( ^^^
Phil Mag, S. 4. Vol. 2. No. 13. Dec, 1851. »inijM 1 2 K
478 The Rev. B. Bronwin on the Inte^ation of
which is equivalent to ^
sv^JlxJ) + A:)M=/(a:D) A,
into which it is changed by changing e* into a. But this last is
only a particular case of the more jrencral theorem,
a*J['jr+k)u:=Jl',r)x'u, (A)
where
w=afD + X(a7).
Here \{x) denotes any arbitrary function of a?, and may be a
constant or nothing. This theorem is a modification of one
which I have given in a memoir printed in the second part of
the Philosophical Transactions for 1851.
A more general form is
^{x)''f{'7r + k)u=flwmxYu, . . . (B)
where
The first of (a) is easily verified in both these cases, as also in
the two that follow ; therefore the theorems (A), (B), &c. are true^
'D^f{'GT-k)u=f{7r)J)'u (C)
if
v='Dx+\{J)), or ^^zxD + XCD);
where, of course, the arbitrary function X(D) may be a constant
or nothing.
A more general form than this is
^{ji)>'f{^-k)u=j{^mu)''u, . . . (D)
where
-(J-^)>+MI>).or.=.(^)+MD).
These might be derived from (A) and (B) by the commutation
of symbols; that is, by changing x into D, and D into —x, or
by changing x into —I) and D into x, and by suitably changing
the functions /, X and </>, when necessary.
In order to apply these theorems to the integration of linear
difi'erential equations with integer functions of x for their coeffi-
cients, suppose
\{x) = a + fl,.r + flfgX^ + . . . . ,
and X(I)) a function of the same form ; we can put any equation
under the form
X=/{7r)u+f,{7r)xu^M7r)x^u+ (1)
For
ITU = xDu -h\(x)u,
Linear Differential Equations. 479
and therefore : "
Du=.x~''^wa-'X~'^\[x)u.
Change u into a?D + \{x) in the first member, and into ttu in the
second, and we have
'DxJ)u-\-J)\{x)u=^x~'^Tr^u—x~^\[x)'Tru,
or
xTi% + (\+\{x)^l)u—x-^'Tr%--x-'^\[x)'iru—^{x)u.
Whence by eliminating J)u and dividing by Xj there results
D^^x-Vw-x-^Q. + %\{x)')'jru-x-^(\[xY+\[x) H-a^X^)).
In like manner, we should find D%, D^u, &c. We can thus
eliminate D, and find a resulting equation containing only ir
and Xy which by (A) can be put under the form required.
Also if
vsu—Dxu-\-\(J))u,
then
Change u into J)ocu + X(D)w in the first member, and into 'ou in
the second, and we have
a?D^ + ^X(D)w=D"Vw-D'~'X(D)tsrw,
or
and
A=D-Vm+D-'(1-X(D))^m+D-'(x(D)2-X(D)+DX'(D)),
Similarly, we should find A, x^u, &c. ; and thus eliminating
X, we should have a resulting equation in -dt and D, which by (C)
may be put under the form
^=f{'^)u+f,{'^)J)u+M'u^Wu+ (2)
But if
'mu=-xJ)u-\-\{J))Uf
change u into D~ V ; then
'^'Y)~^u-xu + \{'D)'D-\
and
a?w='crD"^M~X(D)D"^M.
By continuing to change u into xu^ and eliminating x from
the second member, we should have the values of x'^u, a^u, &c.
in terms of ct and D. Thus by eliminating x, we should have^
as in the last case, a resulting equation in the form of (2).
We might have proceeded in the second case with
a7M = D"'ii7w-D"^X(D)w
2K2
480 The Rev. B. Bronwin on the Integration of
in the same manner ; and similarly in the first case, or
by changing u into Dm and eliminating Du from the second
member.
The equations (1) and (2) may be put under the forms
X,=M + <^(7r)^rM4-^i(7r)A+ ....
Then it will sometimes happen that by (A) and (C) they may
further be put under the forms
'X,iiBU-\-a<f){7r)xu-\-b<l){'7r)a:(f){7r)xU'^ ....
Xi=w + «<^(«')DM4-ft</>WI></>(w)DM+ ....
Make <j^('7r)a?=^, and also </)('bt)D = ^, and both take the form
Xi=M-fa^M + 6^M+
or
Xi = (l--Jfc^)(l-^i^....M;
which may be treated in the manner explained by Mr. Boole.
We can, however, rarely integrate when the second member
contains more than two terms. Let then
X=f{7r)u+f,{7r)w^u.
We may consider /(tt) and/j(7r) as integral functions of ir, and
therefore as factorial functions.
Assume
«={7r + A)(7r + Ai) ('7r + A«)Mi,
or
u-(7r + h)-'(7r + h^)-' .... (7r + A„)- V
as the case may require. Then by (A) we have
x^u={7r + h—r) .... (7r-f ^„~r)a?'*Mi,
er
a?^M = (9r + A— r)-^ . . . (tt + A^— r)~^a7*'Mi.
The constants h, h^, &c. being suitably chosen, after substi-
tuting the assumed value of u in the given equation, we must
operate on both members with the inverse of all those factors
which are common to the two terms of the second member. When
the method succeeds, the result will be an equation of an order
lower than the given one.
But if the given equation be
X=/Ww+/,(tir)D%
make
tt=(«r + /0 {nr + h„)ut,
or
Linear Differential Equations: 481
Then by (C),
D''M=(t!r-f A + r) .... (w + A„ + r)D^w„
or
D''w=(«r + A + r)-> (tT + ^„ + r)-^D''wi,
and the remainder of the process as before.
We will now illustrate this by two examples in each case. Let
X = 7r(7r + a)w + A;(7r + 2V)(7r + ^>)a?'M. ... (3)
Assume
Ms=(7r-f r)(7r-|-2r) .... (7r + 2V)wj,
then
af^u^x^inr + r) (7r + «V)wi = 7r(7r + ?') (7r+(i— l)r)a7''Wi
by (A), It will be obvious that i is supposed to be an integer
number. Substituting these values, and operating with the in-
verse of the factors common to the second member, we have
Xi = (tt + a)u^ + k{ir + ^x'^Uy^,
Xj='7r-i(7r + r)-»....(7r+2V)-^X.
This being only of the first order is immediately integrable.
The next example is chosen because it cannot be reduced in
the same manner, and because it leads to a result of a very dif-
iferent form.
Let X= 7r(7r— r)M + k{ir-\-a)(jr-\-a— (2i -f ly^x^^'u, (4)
Make
w=(7r+a)(7r + a— 2r) (-Tr + a— (2i— 2)r)wi.
Then by (A),
^2r^--(^^^__2r) (TT + fl — 22V)a?2''Mi.
By substitution and reduction as before, we have
Xi = 7r(7r — r)wi + A;(7r + a— 2«V) (tt H- « — (22 + l)r)a?2''wi,
and
Xi = (7r + «)-' .... (7r + a-(22-2)r)-'X.
If we put the last equation under the form
X,= u, + ^(7rH-^~2fr)(7r-f^-(2i+l)r) ^^.^^^
7r(7r — r)
it will reduce by (A) to
^ \ IT / \ TT /
Therefore, making
(TT + a — 2i>\
-^7— ;* =?'
482 On the Integration of Linear Differential Equations.
it becomes
which may be treated in Mr. Boole's way.
These examples may serve to indicate the mode of procedure
in other cases ; they belong each to a distinct class, but the
mode of reduction is the same. We have employed only one of
the forms assumed for u ; in other cases it may be necessary to
employ the other, and cases may perhaps arise in which it will
be necessary to use a combination of both forma.
Now let
X = «r('sr + a)w-f A(CT—ir)('ar-ti)D*'w. , . (5)
Assume
w=;('cr— r)('cr— 2r) .... (w— zV)wi.
Then
D'M=D''(txr-r)...(w-zV)Mi = txr(«r-r)...(w-(i-l)r)D^Wiby(C),
Substituting these values in the given equation, and operating
with the inverse of the factors common to the terms of the second
member, we have
Xi = {'aT-\-a)uj-\-k{'ST + b)'D\. .
The solution of the given equation is therefore made to depend
upon that of one an order lower.
In the last place, let
X=^(«r-f r)w + X;(^ +a)('cr + a + (2i + l)r)D2'-M, . (6)
Make
w = (tsr + fl)(«r+a-l-2r) (w + «+ (2i—2)r)t«i.
Then by (C),
D^M=(OT + a + 2r) .... {m + a-{-2ir)D^\,
And proceeding as before, we find
X, = 'ar(txr + r)Mi-f ^(txr + fl + 2fr)(CT + a+(2? + l)r)D^\.
Xi=('«r + a)-i .... (w + a + (2z-2)r)-'X.
This by (C), in the same manner as in the second example, may
be put under the form
Mate
then
Xj=«i+^^'m,.
On the Tension and the Latent Heat of different Vapours. 483
Thus the solution of the proposed is made to depend upon those
of equations of a lower order.
Examples might be given to illustrate the use of the theorems
(B) and (D), which are a generalization of (A) and (C) ; but the
method must be plain from what has been done, the only dif-
ference being that we should have <f){x) in the room of Xj and
^(D) in the room of D, and the symbols tt and m would be more
general.
In reducing equations to the forms {!), (2), &c., we shall
obtain from the same equation results of different forms by giving
different forms to the arbitrary functions \[x), X(D) ; which is
one advantage which these functions give us, and we must give
them that form which will render our transformed equation the
most convenient for solution. But in some cases, instead of sup-
posing X(^), X(D) integer, or even rational functions, of x and
D, we may so determine their form as to take away from the
equation functions of them which are neither integer nor rational.
The examples (5) and (6), with their solutions, might be de-
duced from those of (3) and (4) by the commutation of symbols
mentioned further back, and by a suitable change in the func-
tions concerned ; and it may be presumed universally, that by
making this interchange of symbols in any linear equation and
its solution, we shall obtain as the result another equation and
its solution. But when the coefficients of a differential equation
are integer functions of x, those of the commuted one will like-
wise be integer functions of Xj and in this respect they will be
alike. Therefore either of the formulae (A) and (C) may be em-
ployed to effect its solution, but not perhaps with equal facility
or equal success. A variety of means, however, is better than
one only, as it augments our chances.
When the second member of an equation contains three or
more terms, its solution may sometimes be made to depend on
the solution of several other equations having only two terms in
their second members; but I cannot enter upon that subject
here.
October 30, 1851.
LXXII. On the Theoretic Connexion of two Empirical Laws re-
lating to the Tension and the Latent Heat of different Vapours.
By 6. Clausius*.
A SUPERFICIAL contemplation of the tension series, expe-
^•^ rimentally developed for the vapours of different fluids,
suffices to show that a certain uniformity exists therein ; and
* From PoggendorfF's Annalen, vol. Ixxxii. p. 2/4.
484 M. R. Clausius on the Tension and the Latent Heat
hence the various efforts which have heen made to ascertain a
definite law by means of which the series which holds good for*
one fluid, water for instance, might be applied to other fluids.
A veiy simple law of this nature was expressed by Dalton.
Calling those temperatures which belong to equal tensions cor-
respoiiding temperatures, the law ran thus : — In the case of any
two fluids the differences between the corresponding temperatures
are all equal,
Tliis law agrees pretty well with experience in the case of
those fluids whose boiling-points are not far apart; for those,
however, which possess very different degrees of volatility it is
inexact. This is shown by a comparison of the vapour of mercury
with that of water, according to the observations of Avogi-ado*.
Still more decidedly does the divergence exhibit itself in the in-
vestigations of Faradayt on the condensation of gases.
In the '^ Additional Remarks '' to his memoir, Mr. Faraday,
after having disproved the applicabihty of the law of Dalton to
gases, expresses himself as follows : — ^' As far as observations
upon the following substances, namely, water, sulphurous acid,
cyanogen, ammonia, arseniuretted hydrogen, sulphuretted hy-
drogen, muriatic acid, carbonic acid, olefiant gas, &c., justify any
conclusion respecting a general law, it would appear that the
more volatile a body is, the more rapidly does its vapour increase
by further addition of heat, commencing at a given point of
pressure for all;" and further on, "there seems every reason
therefore to expect that the increasing elasticity is directly as
the volatility of the substance, and that by further and more
correct observation of the forces a general law may be deduced,
by the aid of which and only a single observation of the force of
any vapour in contact with its fluid, its elasticity at any other
temperature may be obtained."
What Faraday here expresses with evident reserve and caution,
we find again in the form of an equation in a later memoir by
M, GroshansJ, The equation (3.) of the said memoir contains
implicitly the following law ; — If all temperatures from --273'' C.
downwards (that is, downwards from that temperature which is
expressed by the inverse value of the coefficient of expansion for
atmospheric air) be reckoned^ then for any two fluids the corre^
sponding temperatures are proportional,
Although this carries with it a great degree of probability, at
least as an approximate law, and is undoubtedly proved by the
* Ann. de Chim. et de Phys. xlix. p. 369. Pogg. 4nn. vol. jcxvii. p. 60.
Complete in M^. de VAcad. de Turin, vol. xxxvi.
t Phil. Trans, of the Roy. Soc. of London for 1845, p. 165.
j Pogg. Ann. vol. Uxviii. p. 112.
of different Vapours. 485
experimental researches of Avogrado and Faraday to be preferable
to the law of Dalton, still the manner in which M. Groshans
deduces his equations leaves much to be desired. He premises
the deduction by two equations which can only be regarded as
approximately correct, inasmuch as they contain the expression
of the law of Mariotte and Gay-Lussac for vapours at their
maximum density. For the further development, however, he
makes use of the following proposition : — If in the case of any
two vapours the temperatures are so chosen that the tensions
of both are equal, then, if the density of each vapour at the
temperature in question be measured by its density at the boiling-
point, these densities are equal. This proposition is introduced
by the author in the memoir alluded to without any proof what-
ever. In a later memoir*, however, he says that he was led to
the above conclusion by observing that in the case of seven dif-
ferent bodies composed oipQ + qR + rO the density of the va-
pour at the boiling-point compared with the density of steam at
100° could be expressed by the formula
^~" 3 '
and immediately afterwards he states, that "there are several
bodies to which the formula
3
is inapplicable.^' From this it appears that the foundation on
which the proposition rests cannot be regarded as established.
It seems to me, that although the law mentioned above has ob-
tained from M. Groshans a more definite form than in Faraday's
expression, its probable validity is in no way augmented thereby.
In this state of uncertainty every new point of view from
which a more extended insight as to the deportment of fluids
during evaporation may be obtained is deserving of attention ;
and hence it will not perhaps be without interest, to establish
such a connexion between the above la^ as regards the tension
and another law regarding the latent heat, — the latter being also
empirically established in a manner totally independent of the
former — that the one shall appear to be a necessary consequence
of the other.
I refer to the law, that the latent heat of a unit of volume of
vapour developed at the boiling-point is for all fluids the same.
Although this has not been completely corroborated by the ex-
periments hitherto made, and even if it were perfectly true could
not be so corroborated, our knowledge of the volumes of vapours
at their maximum density being too scanty, still, an approxima-
* Pogg, Ann. vol. Ixxviii. p. 292.
486 On the Tension and the Latent Heat of different Vapours,
tion is observed which it is impossible to regard as accidental.
We will therefore for the present assume the law to be correct,
and thus make use of it for further deductions.
In the first place, it is clear that if tlie law be true for the
boiling-points of all fluids, it must also be true for every other
system of corresponding temperatures; for the boiling-points
depend merely upon the accidental pressure of the atmosphere,
and hence the law can be immediately expanded thus : the latent
heat calculated for the volume is for all fluids the same function of
the tension. Let r be the latent heat of a unit of weight of va-
pour at the temperature /, the volume of the unit of weight for
the same temperature being =5, the latent heat of a unit of vo-
lume will then be expressed by the fraction - j let jo be the cor-
s
responding tension ; the law will then be. expressed by the
equation
^-=fip)> (I)
in which / is the symbol of a function which is the same for all
fluids.
7*
Let this function be substituted for - in the equation (Va.) of
s
my memoir '^On the Moving Force of Heat*,^' by neglecting
therein the volume cr of a unit of weight of water as compared
with that of vapour, we thus obtain
/(p)=A(a + <)|,
where A and a are two constants, the latter denoting the number
273, so that a -H / is the temperature of the vapour reckoned from
—273° downwards. If, for the sake of brevity, we call this
quantity T, we have
d^_kdp
' T -fipY
and from this we obtain by integration
c.T=F(p),
in which F is the symbol of another function, which is likewise
the same for all fluids, and c an arbitrary constant which must
be determined for each fluid. Let us suppose this equation
solved for ^, it will assume the form
P=<i>{c.T), (II)
♦ Pogg. Ann. vol. Ixxix. p. 508; and Phil. Mag. p. 10/ of the present
volume.
Dr. Andrew Fyfe on the Detection of Arsenic. 487
where <^ is the symbol of a third function, which is the same for
all fluids.
This equation is evidently the mathematical expression of the
law of tension mentioned above ; for to apply the function which
in the case of any one fluid determines the tension from the tem-
perature, to any other fluid, it is only necessary to multiply the
temperature by a different constant, which constant is easily
found when the tension for a single temperature is known.
It is thus shown, that, in so far as the validity of equation
(V«.) is granted, the two laws expressed by the equations (I) and
(II) are so connected with each other that when one of them is
true, the other must necessarily be true also.
But in case both laws are only approximations to the truth,
as to me appears most probable, the equation (Va.), which by
introducing T instead of t becomes
enables us at least to conclude as to the manner and degree in
which two vapours diverge from each other with regard to their
latent heat, likewise as to their divergence from the tension
series, and the reverse. Thus, for instance, in comparing water
with other fluids, it is observed that the tension of the vapour of
the former increases more quickly with the temperature than the
tension of other vapours. There is a complete coincidence be-
tween this fact and that observed by Andrews*, that the vapour
of water possesses a greater latent heat than an equal volume of
the vapour of any other fluid which Andrews examined, alcohol
excepted. From this we perceive that it is by no means advan-
tageous for the application of the above two laws to choose, as
is generally done, water as the fluid of comparison ; but that, on
the contrary, the comparison of water with fluids of lower boiling-
points is peculiarly calculated to support the law of Dalton.
LXXIII. On the Detection of Arsenic. By Andrew Fyfe, M.D.,
F.R.S.E,, Professor of Chemistry, University and King's Cot-
lege J Aberdeen-].
IT is well known that some metals unite with chlorine, not
only synthetically, but also by decomposition of their com-
pounds, and form volatile chlorides. Arsenic is one of the
metals that comes under this class, and hence it can be volatilized
as a chloride, and, under certain conditions, can be separated^
* Quarterly Journal of the Chem Soc. of London, No. 1 . p. 27. ;
t Communicated by the Author,
488 Dr. Andrew Fyfe on the Detection of Arsenic.
not only from non-volatile chlorides, but also from those metala
the chlorides of which are easily volatilized. That arsenic might
be volatilized in this way, and be thus detected, occurred to Dr.
Clarke, Professor of Chemistry in Marischal College, Aberdeen,
some years ago, but, so far as I know, he has not prosecuted the
subject. My attention was lately drawn to it more particularly,
by the perusal of a paper, in which processes are described
for the separation of metals from one another, in analysing
their ores and alloys*. The perusal of that paper induced me
to take up the consideration of the subject, and the results of
the experiments which I have made have confirmed the opinion
I had entertained, that the volatilization of arsenic, by the action
of chlorine, as suggested by Professor Clarke, would add another
to the many tests which we have of the presence of arsenic.
The question at first occurred. How is arsenic, in the state of
arsenious acid, to be made to unite with chlorine ? This was sug-
gested by the results of the trials recorded in the paper referred to,
viz. causing the decomposition of a chloride in solution in the fluid
containing the arsenic. For this purpose the fluid is heated with
oil of vitriol in a flask, to which a bent tube is adapted, and by
which the product of distillation is conveyed into a cool receiver.
When the mixture is brought to the boiling-point, a little dried
sea salt is thrown in, and the distillation is continued for some
time. By this process the hydrochloric acid evolved yields its
hydrogen to the oxygen of the arsenious acid, while the liberated
arsenic and chlorine unite, and come over as chloride, which
is condensed in the receiver.
(As 0^ + 3S0'^ HO -h 3C1 Na=3S03 NaO + 3H0 + As CF).
We thus obtain a transparent colourless liquid, in which arsenic
is easily detected by the transmission of sulphuretted hydrogen,
which gives the yellow sulphuret. By the addition of nitrate
of silver in excess to the product of distillation, a copious white
deposit of chloride of silver is formed. On filtering this fluid,
and then adding ammonia solution, continuously ^ or, which I pre-
fer, by holding over it a rod dipt in the ammoniacal solution, so
as to avoid excess, the yellow arsenite of silver is either precipi-
tated or appears on the surface as a yellow film, according to its
quantity.
Though this method of detecting arsenic acts easily with pure
fluids in which arsenious acid only is dissolved, it was necessary to
ascertain whether it would act with mixed fluids, particularly
those containing organic matter. A number of these was ac-
* So far as I remember, the paper alluded to appeared in one of the
Foreign Journals — I think the Comptes Rendus — two or three years ^o,
but, though I have again and again searched for it, I have not succeeded
in discovering it.
Dr. Andrew Fyfe on the Detection of Arsenic. 48
cordingly tried, and with all the rest was found to be equally
delicate. The following are a few of the results : —
1st. AsO^-j-SO^ HO + Water were boiled together for some
time, and ClNa was then thrown in and distillation carried on.
SH passed through the product of distillation, gave a copious
yellow deposit, and NO^ AgO + filtration + rod dipt in NH^, gave
a yellow precipitate.
2nd. Strong solution of starch was treated in the same way ;
SH and the addition of NO^ AgO + NH^ gave the same results.
3rd. AsO^ was boiled in a solution of starch and gelatine,
and the product of distillation was collected in the usual way ;
when treated with SH and NO^AgO + NH^, it gave no indica-
tions of the presence of arsenic.
4th. Trials similar to 1 and 2 were made with barley broth
and hare soup, with the same results.
5th. To try the delicacy of the test, 0*5 -0-1 -0*05 gr. of
AsO^ were boiled, each in an ounce of hare soup, with SO^ HO,
to which was afterwards added CI Na. In the product of distil-
lation arsenic was detected by SH. In the last trial the AsO^
was dissolved in nearly 10000 of fluid.
6th. A quarter of an ounce of flesh was soaked for 24 hours
in a solution consisting of 0'5 gr. of AsO^ in one ounce of
water. The flesh was then boiled for some time in SO^, slightly
diluted and distilled with ClNa. In the distilled liquor arsenic
was easily detected by SH.
The only metal likely to cause a source of fallacy in this
method of detecting the presence of arsenic is antimony, which,
with chlorine, forms a volatile chloride. But the antimonial
compound which may be supposed to exist in a suspected fluid,
I mean tartar-emetic, does not yield a volatile compound when
treated with oil of vitriol and sea-salt, or, if it does, does so with
great difficulty. Allowing that it does afl'ord a volatile chloride,
as the product of distillation is in general colourless, there is
usually no difficulty in distinguishing the sulphuret of arsenic
from that of antimony. If we cannot distinguish them, or sup-
posing both metals to be present, the addition of nitrate of silver
in excess, filtration and consequent application of ammonia to
the filtered liquor, will show the presence or absence of arsenic.
I consider the method which I have now described as a valu-
able addition in toxicological researches. It is very easily per-
formed j it separates the arsenic from substances which interfere,
and render, in other methods, the results fallacious ; indeed, in
some cases, prevent the arsenic, though in considerable quantity,
from being detected; such as the presence of organic matter,
which, as in Marshes process, occasionally causes annoyance
by the frothing up of the materials, and consequent rise of the
mixture into the tube.
490 Dr. Andrew Fyfe on the Detection of Arsenic,
The method which I now follow in conducting the process is
to pour the suspected fluid into a flask with a wide mouth, to
which is adapted a cork having two apertures in it. To one of
them is fitted a bent tube, one end of which terminates in the
flask immediately below the cork ; the other end terminates in
a tube containing distilled water, and placed in a cold fluid.
Into the other aperture is placed a cork. Oil of vitriol is now
poured in, and the mixture is boiled for some time ; after which
cb-ied sea-salt is thrown in rapidly, and the cork is quickly re-
placed. The distillation is then continued for some time, taking
care to keep the fluid, in which the tube is placed, as cool as
possible. Instead of one, I sometimes employ two or even three
tubes, with distilled water, in each of which the product of
distillation is condensed, and all of which, if necessary, are
tested for arsenic. When any of the tissues is to be examined,
it is introduced into the flask with oil of vitriol, and boiled for
some time, or till it entirely disappears. Sea-salt is then thrown
in, and the process is conducted as described.
As the trfinsmission of SH through the product of distillation
in general gives satisfactory evidence of the presence or absence
of arsenic, it is scarcely necessary to have recourse to any other
test. It may however be more satisfactory to have recourse to
others, and of these by far the best is nitrate of silver. It is to
be added as long as it causes precipitation. The fluid is then
to be shaken and filtered, by which the whole of the chlorine
and hydrochloric acid is removed. After this a rod dipt in solu-
tion of ammonia is held over the filtered liquor. If arsenic is
present the yellow film appears.
In using SH the operator requires to be on his guard, be-
cause the presence of uncombined acid causes the decomposition
of the gas, and consequent deposit of sulphur, which may, by
one not accustomed to observe precipitates, be mistaken for yel-
low arsenic.
It may be objected to this method of detecting arsenic, that
it will not succeed when the arsenical compound is in the state
of sulphuret ; with King's yellow, for instance, which is some-
times taken as a poison. This must be admitted, when the sul-
phuret is pure. In one trial, in which sulphuret, prepared from
an arsenical solution by precipitation, after being well washed,
was treated with oil of vitriol and sea-salt, as described, the
distilled fluid did not show indications of arsenic by the usual
tests.
This, however, is not the case with the commercial sulphuret,
which, in all the trials that I have made with it, has afibrded a
fluid by distillation with oil of vitriol and sea- salt, in which
arsenic was easily detected. This is owing to its containing
arsenious acid. Accordingly, when King's yellow was washed
Royal Society* 491
till it was pure, and was then treated with oil of vitriol and sea-
salt, it did not yield arsenic by distillation. In conducting this
process, the King^s yellow requires to be washed for a long time
before the whole of the arsenious acid is removed. In the trial
above referred to, boiling water was used repeatedly for one day,
and cold water was allowed to flow on it, in a constant stream,
for another day, before the water came off pure. The first wash-
ings were alkaline, and gave a yellow precipitate on the addition
of muriatic acid, and also by the transmission of sulphuretted
hydrogen, showing that it contained not only arsenious acid, but
also sulphuret of arsenic, held in solution by an alkali.
King's College, Aberdeen, July 1851.
LXXI V. Proceedings of Learned Societies,
ROYAL SOCIETY.
[Continued from p. 320.]
May 22, *'/^N the Annual Variation of the Magnetic Declination,
1851. ^^ at different periods of the Day." By Lieut.-Col.
Sabine, R.A., V.P. and Treas. R.S. &c.
In this communication the author has arranged and presented
together the Annual variations which the magnetic declination
undergoes at every hour of the day at the four Colonial Observatories
established by the British government, at Toronto, Hobarton, the
Cape of Good Hope and St. Helena. This has been done by
means of a graphical representation, in which the annual variations
at every hour are shown by vertical lines varying in length accord-
ing to the amount of the range of the annual variation at each
hour; each line having also small cross lines marking the mean
positions of the several months in the annual range. The mean de-
clination in the year at the respective hours is marked by a hori-
zontal line which crosse.4 all the verticals at each station. The
hours are those of mean solar time at each station, the day com-
mencing at noon. The annual variations represented in the plate
were obtained at Toronto from three years of observation, viz. 1845,
46, 47 ; at Hobarton from five years, viz. July 2nd, 1843 to July 1,
1848; at the Cape of Good Hope from five years, viz. July 2nd,
1841 to July ist, 1846 ; and at St. Helena from three years, viz.
July 2nd, 1844 to July 1st, 1847.
The author observes that it is perceived at the first glance at the
plate, that the range of variation at all the four stations is consider-
ably greater during the hours of the day than during those of the
night ; and that there is a great similarity, though not a perfect
identity, at all the stations in the relative amount of the range at
different hours. Further, that the amount does not progressively
enlarge to a maximum at or about noon, when the sun's altitude is
greatest ; or at the early hours of the afternoon, when the tempera-
492 Royal Society,
ture is greatest; but that at all the stations the increase of the range
is most rapid in the first or second hour alter sunrise ; and that its
extent at the hours from 7 to 9 a.m. is not exceeded at any subse-
quent hour at Hobarton, the Cape and St. Helena, whilst at Toronto
the great enlargement takes place even earlier, the hours of 6,
7 and 8 a.m. being exceeded by none, though they are equalled by a
second increase at noon and the two following hours. This second
enlargement is perceptible at the same hours at Hobarton and St.
Helena.
With reference to the relative positions of the several months in
each of the vertical lines, or at the different hours, it is observed that
certain months, which are found congregated at the one extremity
of the range during the early hours of the morning, undergo a
transfer towards the opposite extremity at a subsequent period of the
day; thus the months June, July, August usually occupy one
extremity of the range, and November, December, January the
other extremity, in the morning hours, and until from ^^ to 10**
A.M., when each of the two groups is respectively transferred
towards the opposite extremity to that which it previously oc-
cupied. The period at which this transfer takes place is somewhat
earlier at Toronto and St. Helena than at the Cape of Good Hope
and Hobarton. The comportment of the two equinoctial months,
March and September, at the Cape of Good Hope and St. Helena is
pointed out as presenting a remarkable contrast to that of the two
solstitial groups which have been described, and at the same time a
still more remarkable contrast to each other, March being at almost
all the hours on the West, and September on the East, of the mean
line.
In conclusion the author points out one or two practical conside-
rations suggested by the facts under notice : —
1. That as, in the Annual Variation represented in the plate, the
same months occupy positions on opposite sides of the mean line at
different parts of the twenty-four hours, the mean annual variation,
or that which is shown by the mean values in each month taken from
all the observation hours, must be merely a residual and not an abso-
lute quantity ; and that consequently natural features must be more
or less masked in deductions in which only mean values are brought
into view. In fact, as has been shown in the published volumes of
the observations at St. Helena and Hobarton, the mean annual va-
riation at those stations is so small as to be scarcely sensible. But
when we resolve these mean results into their respective constituents,
viz. the annual variation at each of the observation hours, there is
then at once disclosed to us an order of natural phenomena, very
far from inconsiderable in amount, systematic in general aspect, and
apparently well deserving the attention of those who are occupied
in the delightful and highly intellectual pursuit of tracing the agen-
cies of nature.
2. We perceive in the variations of the position of the several
months in the annual range, the necessity of paying regard to the
period of the year, as well as to the period of the day at which ob-
Royal Society. 493
servations have been made which do not include long intervals, and
from which, nevertheless, inferences are drawn in respect to secular
change. Such observations, when not those of a fixed observatory,
are usually made at some hour in the day-time, when it needs only
a glance at the plate to perceive that annual as well as diurnal
variation-corrections are required, unless the month as well as the
hour are the same in the earlier and later observations. A table of
corrections for every hour of the day to the mean value in each
month — corrections derived, as in the instances now before the So-
ciety, from a series of strictly comparable observations continued for
several years — should be considered, not merely as a desirable, but
as an almost indispensable provision, in countries where magnetic
surveys are conducted with the degree of perfection of which they
are now susceptible.
" On Induced and other Magnetic Forces." By Sir W. Snow
Harris, F.R.S. &c.
The question as to identity in the source of those several and
mysterious powers of nature by which'masses or particles are moved
either toward, or from each other, being a question of deep physical
interest, the author of this paper has been led to some further in-
vestigation of the nature and laws of magnetic force, in the course
of which several new facts have presented themselves which he
thinks not altogether unworthy of attention.
Magnetic attraction as commonly observed being found to depend
on certain impressions made on the attracting bodies usually de-
signated by the general term induction, it appears essential to the
progress of any inquiry into the laws of those forces operating ex-
ternally to a magnet through space, to commence with a rigid exa-
mination of the nature and mode of action of those inductive forces
upon which the reciprocal force of attraction between the bodies
immediately depends. These forces of induction may be considered
as a series of successive or reverberating influences, operating be-
tween the near and opposed surfaces of the magnetic bodies. When,
for example, a magnet is opposed to a mass of soft iron, a direct
impression is first made on the iron by which the iron is rendered
temporarily magnetic ; this induced force operates in its turn by a
species of reverberation or reflexion upon the near pole of the mag-
net, and calls into play a portion of the magnetic force in the direc-
tion of the iron, which was previously operating toward the centre
of the magnet; this action being once set. up, may continue for a
series of waves reverberating between the opposed surfaces, until
the action sinks away as it were into rest. The author examines
experimentally, by means of instruments, the principles of which he
has already detailed in the Transactions of the Royal Society, this
peculiar kind of action, and arrives at the following deductions re-
lative to the laws of magnetic induction.
A limit exists in respect of induced magnetic force, different for
different magnets, and varying with the magnetic conditions of the
Phil Mag. S. 4. Vol. 2. No. 13. Dec. 1851. 2 L
494 Royal Society,
experiment, toward which the increments in the force continually
approach, as if the opposed bodies were only susceptible of a given
amount of induction under the existing circumstances.
Taking the force toward the limit of action, the amount of induc-
tion is in some inverse ratio greater than that of the simple distance ;
it was not however in any case found to exceed the inverse sesqui-
plicate ratio or f power of the distance ; as the distance is diminished
the induction is as the distance inversely, but may in the mean time
be as the f or |^ powers of the distances inversely, or near those
powers. On further diminishing the distance, the induction was
found in certain cases to be as the f and \ powers of the distances,
thus causing a series of changes in the law of magnetic attraction as
commonly observed, which have hitherto greatly embarrassed the
views of philosophers in their inquiries into this species of force.
"When the convergence is slow the induced force may not for a long
series of terms appear to change, but when from any circumstance
the convergence is accelerated, then the changes become more
marked and successive. As a general result, however, the author is
led to conclude, that magnetic induction is as the magnetic intensity
directly, and from the \ to the f power of the distance inversely.
In the course of these inquiries, it was found that the induc-
tive action depended, not on the mass, but on the surface of the
magnetic substance, and that magnetism, like electricity, exhibits a
decrease of intensity when the surface of the iron upon which it is
disposed is extended. A hollow cylinder of soft iron was carefully
prepared in a lathe, and fitted with a solid interior core capable of
being drawn out from within the cylinder ; this compound body was
exposed to the inductive action of a poM'erful magnetic bar, and the
induced force estimated by the reciprocal force of attraction ex-
erted between the mass and a cylinder of soft iron suspended from
the author's magnetic balance, or from one arm of a light beam, set
up in the way of a common balance. The degree of force being
observed, the solid core was drawn out so as to extend the surface
of the mass under induction. The intensity immediately declined,
and again increased on replacing the solid within the hollow cylin-
der, being a result of exactly the same character as that produced
by the extension of an electrified surface. When the interior solid
core was removed altogether, then the induced force remained un-
changed, it being precisely the same whether the body were taken
hollow or solid. In accordance with this result, hollow cylindri-
cal magnets were found as susceptible of magnetic power as solid
masses of the same temperament and dimensions; an unmagnetized
solid and tempered steel cylinder, placed within a hollow tempered
steel cylinder, does not become magnetic on touching the external
cylinder in the usual way. The magnetism, however, of a hollow
cylindrical magnet is partially destroyed by placing within it a cy-
linder of soft iron, or the reverse poles of another magnet ; nor can a
hollow cylinder of tempered steel having a solid core of soft iron
be rendered magnetic by the usual methods of touch. These re-
sults, it is considered, supply the experiments thought by Mr. Barlow
Royal Society, 495
80 desirable to confirm his deductions relative to the action of iron
shells and balls on the compass needle, which he found to be as the
f power of the surface, whatever the weight and thickness of the
iron.
The author now proceeds to notice the investigations of Hawks-
bee, Brook Taylor, Muschenbroek and others, and thinks the inqui-
ries of these philosophers have not been sufficiently considered or
appreciated ; that instead of the results exhibiting anomalies and
discrepancies, they are really necessary consequences of the more
elementary laws of induction, and perfectly explicable upon the fun-
damental principles of magnetism. He endeavours to show, that by
the changes in the law of the induction, as already stated, laws of
force will arise perfectly coincident with the results arrived at by
Hawksbee, Brook Taylor and others ; that is to say, the law of force
may appear to be as the f power of the distance inversely, as found
by Brook Taylor; or as the f power inversely, as found by Martin ;
or in the inverse duplicate ratio of the distance, as observed by
Lambert ; or as the simple distance inversely, as determined by Mus-
chenbroek in several cases; or it may be as the cubes of the di-
stances inversely, as stated by Newton. Examples are given in
which these several laws were found to obtain.
In examining the laws of magnetic repulsion, similar results are
arrived at. The inductive forces here, however, are subversive of
the existing polar arrangements ; hence the apparent repulsion : so
long as the existing magnetic polarities remain unchanged, the law
of force will be generally as the second power of the distance in-
versely ; when the distances are small, it will be inversely as the
simple distance ; when the inductive actions subvert the existing
polarities, then the law of force appears irregular and subject to no
regular variation, as observed in all the early experiments wiih re-
pellent poles.
The author is led to conclude, that the apparent law of attractive
force will be found to depend in certain cases on the distances at
which the force operates, as referred to the total distance or limit of
action. Taken between f ths and fths of the limit of action, the
force may be inversely as the third powers or cubes of the distances ;
taken between f ths and f ths of the limit of action, it may be in the
inverse sesquiduplicate ratio, or f power of the distances ; between
-i-rd and fths as the squares of the distances inversely. From the
ith to -i- of the limit of action it may be as the f power of the
distance inversely ; within less than itli, it will be generally as the
simple distance inversely.
On a further review of these laws of magnetism, it is evident that
the immediate effect of an increase or decrease of distance, is an in-
crease or decrease of the effective magnetism on which the total or
reciprocal force depends. Thus taking the cases just quoted, it will
be seen that the total force is always as the square of the induction,
whatever be the resulting law of the attraction. Hence the force
may as well be taken as the square of the quantity of effective
magnetism directly, as some power of the distance inversely.
2L2
496 Royal Society.
The author admits the difficulty in the way of the employment of
such terms as quantity of magnetism, magnetic charge, and the lii^e,
and therefore only employs them according to the common accepta-
tion of such terms, and not as referring to any particular hypothesis :
he thinks there must necessarily be in such inquiries an element fairly
enough expressed by the general term quantity as expressive of the re-
lative or absolute magnitude of the cause, whatever it be, upon which
the observed effects depend, and thinks it so far essential to obtain
exact quantitative measures. In electricity we may estimate the
charge conveyed into a battery by means of the unit measure, and we
can at pleasure operate with one-half, one-third, &c. the quantity of
electricity numerically expressed; but we have as yet no such mea-
sure in magnetism, and we are quite uncertain as to the quantity of
effective magnetism in operation. The author hence endeavours to
verify the law of magnetic charge just mentioned by a direct quan-
titative experimental process. A cylindrical rod of soft iron being
surrounded by three successive coils of covered copper wire, was
placed under the trial cylinder of the magnetometer and exposed to
the operation of one or more precisely equal and similar batteries ;
one coil being appropriated to each battery. It is inferred that if
one battery and one coil produced one measure of magnetism, two
batteries and two coils would develope two measures, and so on ; so
that we should have only to determine the attractive force under
this condition ; now the attractive forces were found to be as the
square of the number of batteries in action upon this cylinder, that
is to say, as the square of the magnetism induced in the iroa; hence
the quantity of magnetism is as the square roots of the reciprocal
forces. If therefore the reciprocal force between a magnet A and
a cylinder of soft iron taken at a constant distance were represented
by an equivalent of 4 grains, whilst the similar force with a magnet
B at the same distance were represented by 9 grains, then the effect-
ive quantities of magnetism and operation in each case would be as
A^i : V'g, that is as 2 : 3.
Availing himself of this law, the author endeavours to deduce ex-
perimentally the magnetic development in different points of a regu-
larly tempered and magnetized bar, taken between the magnetic
centre and extremities ; and he finds by a very careful manipulation,
that the magnetism in these points is directly as the distance from
the magnetic centre; the reciprocal force on a small trial cylinder
being as the squares of the distances from the centre.
Some striking analogies in the state of a magnetized steel bar and
the common Leyden jar are noticed in this communication, from
which it would appear that the conditions of electrical and magnetic
force are precisely the same, and from which the author concludes
that magnetic attraction is reducible, as in electricity, to an action
between oppossed surfaces ; he thinks that a predisposition to identify
these forces with that of gravity and other central forces has led
many profound mathematicians and philosophers to question unduly
the accuracy of every result not in accordance with such a deduction.
He observes that Sir Isaac Newton considered "that the virtue of the
Hoyal Societtj. "497
magnet is contracted to the interposition of an iron plate, and is almost
terminated by it, for bodies further ofFare not attracted by the magnet
so much as by the iron plate*;" as also that this power is essentially
different from gravity, " and in receding from the magnet decreases
not in the duplicate, but almost in the triplicate proportion of the
distance*," a result which has been shown to be perfectly consistent
with experiments. Newton however has been supposed to have had
" very inaccurate ideas of magnetic phenomena f ;" it would be very
difficult however to show from the little which this great author has
advanced upon this subject in his grand work, the Principia, in
what his views of magnetic action were defective ; they appear on
the contrary to be in most perfect accordance with experimental
facts. In associating magnetic action with a law of the " centri-
fugal forces of particles terminating in particles next them," Newton
never pretended to offer any theory of magnetism, but says with
his usual diffidence, " whether elastic fluids do really consist of par-
ticles so repelling each other is a physical question," and " which he
leaves philosophers to determine." On the other hand, a large
amount of experimental research by Hawksbee, Brook Taylor,
Whiston, Muschenbroek, and other eminent men, has been sup-
posed by Dr. Robison as unworthy of confidence, and ill-adapted to
the object for which it was designed |:. The same learned writer
thinks that magnetic attractions and repulsions are not the '* proper
phenomena for declaring the precise law of variation." Yet was it
by these same attractions and repulsions that Lambert, and more
especially Coulomb, deduced what this accomplished author con-
siders as being the true law of force. The author of this commu-
nication is led to believe, that all the results of these inquiries, in-
cluding the deduction of Newton, are not only consistent with, but
necessary consequences of, the laws of induced magnetic forces, as
he has endeavoured to prove, and that the action of magnetism as
commonly observed is something different from what has been
usually imagined. That future inquiries may lead to the identity
in origin of magnetic and gravitating force he thinks not impro-
bable ; there may be some diffuse emanation through space, the
source of gravity, and other central forces ; and it is not impossible
but that the relations of this medium to the particles of common
matter may admit of considerable modification or change, and which
may be the source of that peculiar power we find displayed in those
bodies we consider as being magnetic and call magnets. It has been
occasionally supposed that in the reciprocal force between magnets
and iron there is a peculiar agency in operation, the law of which is
disturbed by the new forces of induction liable to ensue in changing
the distances. The author however is of opinion that such a notion
is inconsistent with the course of nature ; it is induction which con-
stitutes magnetic action, there is no other form of action ; when in-
duction is not present there is in fact no action ; we must hence look
to these very changes for an explanation of variable magnetic force.
* Principia, Books 2 and 3. f Edinb. Ency. vol. xiii. p. 270., .
% Mechanical Philosophy, vol. iv. p. 217. 'ir>; jjqiJ} fe!AVT[<>gdo ^H
498 Royal Society,
" Researches into the Identity of the Existences or Forces, Light,
Heat, Electricity and Magnetism." By John Goodman, M.D.
Communicated by Thomas Bell, Esq., Sec. R.S. &c.
In this communication the author describes the effects that were
produced on a moderately sensitive galvanometer by exposure to
the sun's rays, and which were observed by him during a period of
four months, commencing on the Hth of November, 1850. The
instrument is described as consisting of forty-six turns of covered
copper wire, j^ih of an inch in diameter. The helix is blackened with
ink at its southern extremity, and has a single magnetized sewing-
needle suspended by about sixteen inches of silken fibre in its centre.
The dial, which is of card-board, and divided into the usual number
of degrees, rests upon the upper surface of the helix, and shades it
from the ordinary light or sun's rays, except at its extremities, and
occasionally some portions of the lower bundle of wires ; and when
the sun is very low the rays may be seen also to illumine to some
extent the surface of the upper bundle. The indicator is formed of
a slender filament of light wood in the usual manner, and the whole
is enclosed in a glass shade. This instrument was placed for ex-
periment in a window having a southern aspect; and whilst the sun
was strongly shining upon it, it was frequently observed that there
could not be obtained, either on account of vibrations or the erro-
neous condition of the instrument, any true indications. On shading
the instrument from the sun's rays by a screen, the vibrations ceased,
and the needle again adjusted itself north and south.
On removing the screen the needle began again to vibrate, and
was soon discovered to become stationary at some distance from
zero, indicating the transmission of a current in the helix. This de-
flection of the needle was soon found to be always, under the same
circumstances, in the same direction, and to give indications of a
current corresponding to the brightness of the sun.
This action appeared to depend upon the incidence of the sun's
rays upon the south extremity, and some of the lower or upper
bundle of wires only of the helix ; for when they began to illumine
the opposite extremity, either very slight indications, or a neutral
result, constant vibrations, or the movement of the needle some de-
grees in the opposite direction, were always observed. The maxi-
mum deflection, at any time attainable by the galvanometer, when
the sun was quite unclouded, was about 12°, generally only 10°. It
may be observed that in all these experiments the power of the rays
was probably somewhat diminished, by passing though the glass
pane of the window, and through the glass shade of the instrument
itself.
In order to show that the effect was not thermo-electric action,
the extremities of the helix were removed from their mercury cups
and wrapped in paper, so as to exclude the mercurialized portion of
the copper from the action of the sun's rays ; but no alteration oc-
curred in the ordinary results of the experiments. There is, more-
over, the author considers, no evidence on record of any thermo-
electric action ensuing from the application of heat to copper wire
Royal Society, 499
alone, nor without the formation of a complete electrical circuit.
But in these experiments hitherto the completion of the circuit
had not been attempted. During the course of the experiments
the circuit was established by means of a connecting wire between
the mercury cups, and the circuit was again and again completed,
and as frequently broken, without any deviation occurring in any
of the results, either during the progression, stationary condition, or
decline of the needle.
That these phenomena were the result of the action of the sun's
rays upon the helix itself,was further shown, from the circumstance
that when the sun remained clouded for days together, there was no
deflection of the needle ; that when the helix was partly shaded by a
pillar, or the window-frame, the instrument indicated an amountof cur-
rent corresponding to the number of coils of wire illumined; and that
the illumination of the whole bundle of wires at the southern extremity
of the helix was necessary to produce the usual results, for when a
burning lens of high power was employed to condense the rays and
throw them in a focus upon one or two wires only, no deflection of
the needle was observed. It was also further shown that the action
of the rays upon the helix was attributable to that portion situate
chiefly at the southern extremity, for the whole instrument was in a
variety of ways and at different periods shaded from the solar rays ;
but its results were unaffected, unless the south end was obscured,
when the needle immediately declined; or the north end was illu-
mined when the deflections were lessened, .or the motion of the
needle took place in the opposite direction.
A pile of red-hot burning embers held in the vicinity of one ex-
tremity of the helix caused a slight deflection of J°, and when held
at the opposite extremity, caused a deflection in the opposite di-
rection.
The author states a remarkable circumstance, viz. that vibrations
and neutral action were observed during bright sunshine about the
11th of December, and again on the 23rd of January ; that previous
to the former period the deflections of the needle were to the left'
hand; between these two periods they were to the right-hand; and
after the latter period always to the left, after a given hour of the day.
During the early sun, however, they were to the right-hand, and as
the sun approached a given altitude, they were invariably to the
left-hand. Deflections observed during the summer season were
also to the left-hand \ but those of the early sun were not submitted
to the test.
On testing the instrument with a voltaic pair, it was shown that
the current passed from south to north above the needle with the early
sun, or when the indicator deflected to the right-hand, and beneath
the needle with the rays which proceeded from a considerable eleva-
tion, or when the needle deflected to the left-hand.
In conclusion, the author states that the results of these experi-
ments evince to his mind more than ever the unity of force-, and
that experimental evidence appears to justify the conclusion at
which he has long since arrived, that there is one, only, universal force
500 Intelligence and Miscellaneoics Articles.
in nature^ which is modijied by the accidental and varied conditions
to which it is subjected^ hut that its essential nature and characteristics
are at all times unchangeably tha same.
CAMBRIDGE PHILOSOPHICAL SOCIETY.
[Continued from p. 421.]
May 6, 1851. — Of the Transformation of Hypotheses in the
History of Science. By W. Whewell, D.D.
The author remarks that new theories supersede old ones, not
only by the succession of generations of men, but also by transfor-
mations which the previous theories undergo. Thus the Cartesian
hypothesis of vortices was modified so that it explained, or was sup-
posed to explain, a central force : and then, the Cartesian philoso-
phers tried to accommodate this explanation of a central force to the
phaenomena which the Newtonian principles explained ; so that in
the end, their theory professed to do all that the Newtonian one did.
The machinery of vortices was, however, a bad contrivance to pro-
duce a central force ; and when it was ai)plied to a globe, its defect
became glaring. Still however, the doctrine of vortices has in it
nothing which is absurd anterior to observation. The " nebular
hypothesis" is a hypothesis of vortices with regard to the origin of
the system of the universe, and is now held by eminent philosophers.
Nor is the doctrine of the universal gravitation of matter at all in-
consistent with some mechanical explanation of such a property ;
for instance, Le Sage's. We cannot say therefore that if the planets
are moved by gravitation, they are not moved by vortices. The Carte-
sians held that they were moved by both : by the one, because by
the other.
Like remarks may be made with respect to the theories of mag-
netism and of light.
LXXV. Injtelligence and Miscellaneous Articles.
ON THE CONSTITUTION OF THE ATMOSPHERE. BY M. LEWY.
npHE memoir which I have the honour to submit to the Academy
-■- contains the results of a series of researches on the constitu-
tion of the atmosphere, executed between France and New Granada,
and from the coast up to 3193 metres above the level of the sea.
The analyses were performed by the new process of MM. Reg-
nault and Reiset, which consists, as is w^U known, in analysing the
air by volumes. To measure the elastic forces of the gas, I em-
ployed an excellent cathetometer constructed by M. Perraux ; the
process thus combined enables us to obtain much greater precision
than has hitherto been reached in this class of experiments. To
judge of the degree of accuracy attainable, it suffices to examine
the numerical details of two analyses ; and it will be seen that the
greatest difference between two analyses made with the same sample
Intelligence and Miscellaneous Articles. 501
of air never exceeded io^th, and most frequently was not more J^Ii^n
loo.ooo''"' i'ti J'vj
The various samples of air which I analysed were collected in
bulb-tubes with the two ends drawn out and open ; the capacity of
these tubes was about 100 cub. centims. The air was collected in
the following manner: — One of the extremities of the tube was
connected, by means of caoutchouc tubing, with a little pair of
bellows, which was moved sufficiently long to be certain that the
whole of the air contained in the tube was replaced by the atmo-
spheric air of the locality, taking the necessary precautions to avoid
any mixture of the air of respiration ; as soon as the air was col-
lected, the tubes were sealed b(^fore the lamp.
1 have divided the analyses into three series : — 1st, analysis of the
atmospheric air of France ; 2nd, analysis of the atmospheric air of
the Atlantic Ocean and Carribean Sea; 3rd, analysis of the air of
New Granada.
The comparison of the results obtained in this investigation with
previous ones shows that the constitution of the atmosphere is nearly
the same in the New and the Old World. Taking the mean of the
analyses, executed in eleven different localities of New Granada, we
find that 10,000 vols, of normal atmospheric air contain 4-'008 carbonic
acid, 2101*425 oxygen, and 7894<*557 nitrogen, which are nearly
the same proportions as those which have been found for normal
atmospheric air in various parts of Europe. However, on examining
carefully all the experiments hitherto made on the constitution of
the atmosphere, it is readily seen that the composition of the air is
not absolutely constant. Perceptible differences exist, which vary
with the meteorological conditions ; thus after a long rain the car-
bonic acid and oxygen are always in smaller proportion than after
a long drought; however, these differences are only appreciable
when the analysis has been carried out with very great accuracy.
In the New World, where the seasons are more defined than in
Europe, these variations are more easily detected. During the fine
season the normal air always contains a little more oxygen and a
little more carbonic acid than in the season of the rains. Thus,
taking the mean of a large number of analyses, I found that 10,000
vols, of normal atmospheric air of Bogota contain —
With a With a ,\
cloudy sky, and bright sky, and
nO)j
during the rains. during^the fine season. '^^'"^
Carbonic acid 3*822 4*573
Oxygen 2099*542 2102-195
Nitrogen 7896*636 7893*232 ^ ;
The difference which exists between the atmospheric air of the
two seasons is therefore on an average 0*751 for the carbonic acid
and 2*653 for the oxygen in 10,000 vols, of air.
Taking the maximum and minimum of the results obtained in the
analyses performed during the two seasons, we have —
502 Intelligence and Miscellaneous Articles.
During the rainy season. During the fine season.
Carbonic acid 3*609 5-043
Oxygen 2099*032 2103*199
Nitrogen 7897*359 7891*758
The greatest difference amounts consequently to r4«34 for the
carbonic acid and to 4*167 for the oxygen. These differences are
nearly the same as those which I found between the atmospheric air
of Paris and that of Havre, analysed under meteorological condi-
tions corresponding to the two seasons of South America.
It follows that the composition of the air which we respire is the
same in Europe and in the New World as far as regards the oxygen
and the nitrogen, whether it be taken at the level of the sea or at an
elevation of 3000 metres ; the only difference is the amount of car-
bonic acid, which appears, especially on the high mountains, to be
somewhat greater than in the valleys and on the sea-shore.
With respect to the analyses of the air collected on the ocean, they
have yielded a very interesting result. In the day-time this air con-
stantly contains a little more oxygen and a little more carbonic acid
than during the night. This difference becomes more perceptible
as we leave the coasts ; and it is probably owing to the solar rays,
which, heating the surface of the sea during the day, disengage a
portion of the gases which the sea-water holds in solution, and which,
as is well known, contains more oxygen and carbonic acid than
atmospheric air.
Taking for term of comparison the samples of atmospheric air
collected on the Atlantic, on the same day, with the same wind, and
at more than 400 leagues distant from land, we find —
At 3 A.M. At 3 P.M.
Carbonic acid 3*346 5*420
Oxygen 2096*139 2106*099
Nitrogen 7900*515 7888*481
The difference is therefore 2*074 for the carbonic acid and 9*960
for the oxygen in 10,000 vols, of air.
The analyses of the abnormal air of New Granada present us
with results not less interesting. From time to time, once or twice
in the year, the atmosphere of New Granada contains an extraordi-
nary proportion of carbonic acid, which coincides with an appre-
ciable decrease of oxygen, and consequently alters the constitution
of the atmosphere in a very marked manner.
The great number of volcanoes which exist in the New World,
and the clearing of forests which are effected every year in this
country, may cause these alterations. It is, in fact, during these
clearances that the constitution of the atmosphere experiences the
extraordinary changes which I have just mentioned.
These clearings, which are effected by vast conflagrations, called
in the country las quernas^ produce considerable quantities of car-
bonic acid, which, mixing with the atmosphere, alter its composition.
The amount of carbonic acid which I found in this air rose in some
Intelligence and Miscellaneous Articles. 503
analyses to ^^ in 10,000 volumes of air. It is consequently from
10 to 11 times greater than in the air in its normal condition. The
diminution of oxygen amounted sometimes to 68*350 in 10,000 vols,
of air; instead of 2101-425 oxygen, I found only 2033-075. This
decrease is therefore readily detected even by less sensitive methods
than the one which 1 employed.
On the other hand, the air of the plain of Bogota sometimes pre-
sents an amount of carbonic acid far greater than the atmosphere
of the tierra caliente. This difference may be explained either by
the existence of volcanoes, which are situated not far from Bogota,
or by the more or less active influence of the solar light. It will be
conceived, in fact, that in the tierra caliente, where the temperature
is very elevated, the decomposition of the carbonic acid by the
green parts of the vegetables must be effected in a far more rapid
manner than on the high plain of Bogota, where the temperature is
not higher than from 57° to 64° F.
It is perhaps allowable to suppose, on observing this enormous
quantity of carbonic acid appear from time to time in the atmosphere
of the New World, and considering the large number of volcanoes
which exist in the country, that a portion of the carbonic acid of
the air is due to them, and that they thus contribute in part to
nourish the vast and beautiful vegetation of the tropics. — Comptes
Rendus, Sept. 29, 1851.
ON THE MAGNETISM OF GASES. BY M. PLUCKER^.
I introduce the gases to be examined into a thin glass bulb, 45
millimetres in diameter, and which can be closed by a cock, also
composed of glass. I attach the bulb to one of the arms of a delicate
balance capable of indicating -^th of a millegramme with perfect
distinctness. The glass of the bulb is slightly magnetic ; its mag-
netism is exactly compensated by the magnetic action of the sur-
rounding air, so that the action of the magnet upon the bulb, pre-
viously exhausted, is absolutely null, whilst the attraction of the
bulb when filled with a gas, either compressed or expanded, is exactly
that of the same gas. At the ordinary pressure, the weight of the
oxygen contained in the bulb is about equal to 57 millegrammes,
and the attraction exerted upon this gas by the electro-magnet,
when 6 of Grove's elements are used, is equal to 20 millegrammes.
1. On comparing the specific magnetism of oxygen with that of
iron, taken as unity, I found the number 0"003500, which differs
considerably from that given by M. E. Becquerel, but agrees tole-
rably well with the valuation made by Prof. Faraday.
2. Oxygen loses its sensible magnetism in almost all those gases
with which it enters into chemical combination. Nitric oxide (NO^)
forms an exception, which is unique at present ; its magnetism in
round numbers is f th of that of oxygen. The protoxide of nitrogen
(NO) did not exhibit the least trace of action, i.e. if this action
* Extract from a letter to M. Arago.
6CNI Intelligence and Miscellaneous Articles.
MfStsi'^t' is not equivalent to xJiyth of that exerted in the case of
oxygen.
3. If oxygen gas is introduced in small quantities at a time into
the bulb filled with nitric oxide, the magnetism diminishes until the
proportion of the two gases becomes sufficient to form hyponitric
acid (NO^). The action is then apparently null. On adding still
more oxygen, the magnetism reappears and continues to increase.
4. Hyponitric acid (NO4), when condensed, is a diamagnetic
liquid ; nothing is at present opposed to the view that the gas, in pro-
portion to its volume, is but very feebly magnetic. All my attempts
to decide this important question have failed : does nitrous acid gas
(NO3), which is pretty strongly magnetic, retain its specific magne-
tism when it becomes liquid ?
5. The magnetism of oxygen and of nitric oxide, as also that of
the magnetic mixtures, is in proportion to the density of the gases.
6. A magnetic gas, when mechanically mixed with any other in-
different gas, retains its magnetism, whatever the density of the
mixture may be ; but in the vicinity of the j^oles, separation of the
gases appears to take place to a certain extent, which must slightly
increase the attraction of the entire mass. In certain cases this
separation does not appear to take place instantaneously ; it is found,
at least in the case of a mixture of oxygen and chlorine, that the
magnetic attraction augments uniformly if the bulb remains for some
minutes exposed to the magnetic induction of the electro-magnet.
The primitive attraction is found to be exactly that which corresponds
to the quantity of oxygen contained in the mixture.
7. A magnetic gas which has been attracted by the electro-magnet
for some minutes, is very distinctly repelled by it, if thepolarity of the
latter be changed by means of a commutator. I therefore conclude
that gases possess what has been called the coercive force to a
well-marked degree. — Comptes Rendus, Sept. 15, 1851.
ON THE FORMATION OF DOLOMITE BY THE ACTION OF MAGNE-
TO smiilov «.U jSIUM VAPOURS. BY M. DUROCHER.
Pieces of a porous limestone and anhydrous chloride of magnesium
were introduced into a gun-barrel, so that neither substances were
in contact. The closed tube was then exposed for three hours to a
dull red heat, in order to maintain an atmosphere of chloride of mag-
nesium vapour round the limestone. At the end of that time the
pieces of limestone were found to be covered with a crust of fused
chloride of calcium and chloride of magnesium, mixed with a little
peroxide of iron and the oxides of the two earths. The chlorides
were separated by washing with water, and the nuclei were thus
found to be partially converted into dolomite. On the addition of
hydrochloric acid, the limestone which had not been altered dissolved
first with strong eflFervescence, which subsequently became less ener-
getic, as is the case with dolomite. Transparent groups of crystals
were visible under the microscope : the mass had a white colour
passing into yellow and grayish -yellow, and was, like dolomite, full
Intelligence and Miscellaneous Articles, 505
of cavities. Durocher is of opinion, that the assumption of some
geologists, that dolomite has been formed naturally by aqueous
agency, is proved by this experiment not to be absolutely correct, as
it may also have been formed by magnesian vapours issuing from the
interior of the earth, and gradually converting limestone into dolo-
mite.— Comptes Rendus, vol. xxxiii. p. 64. . ^^j,-^ ,^ U/li bJO'jS'
NEW PHOTOGRAPHIC PROCESS UPON GLASS.
BY M. J. R. LE MOYNE.
The process in question is completely practical, and does not
merely refer to a few accidental occurrences. Nearly a year ago, I
found that the impressions upon glass sometimes presented a posi-
tive aspect, and after a short period, my researches in this direction
furnished me with tolerably good specimens ; but I did not succeed
in arriving at a sure and constant method until after making a long
series of continuous attempts ; these have extended to the present
time.
The object of most of my experiments was to overcome the well-
known inconveniences of the albuminous plates, and, independently
of the positive process, I have made considerable progress in the
production of the impressions by the following modifications, which
in fact constitute a new method of preparation : —
1. Purification of the albumen of the whites of eggs by keeping
them for a long time, and even adding sugar to produce slight fer-
mentation, which clarifies them much better than the beating process
which is generally adopted. This first addition of sugar (8 grs. to
each white of egg) does not prevent the necessity of subsequently
adding the quantity already recommended (38 to 46 grs.) to obtain
greater sensibility to light; and with the processes I afterwards
employ, the presence of this substance increases the adhesion of the
coating, instead of diminishing it, which has been urged as an ob-
jection to it.
2. Iodizing the albuminous part, after it has dried, by immersing
it in a bath of tincture of iodine to which yo^h part of its volume of
nitric acid of specific gravity I'SSO has been added.
This method is very simple, and is not attended with any of the
defects inherent to the use of albumen containing iodide of potassium
in solution. There is but one of the processes known which could
be brought into competition with this ; it is the employment of the
vapour of iodine ; but the moist method has the advantage, both in
the rapidity of execution and in the simplicity of the apparatus.
3. Omission of the use of acetic acid, and employing a simple
solution of nitrate of silver (1 part to 10), for rendering the plates
sensible.
I do not know whether acetic acid is really necessary, upon albu-
minated glass, when gallic acid is used to bring out the image ; but,
with the sulphate of iron, it is undoubtedly an expensive superfluity;
moreover, the volatility of this acid is a cause of spontaneous
changes in the solutions, and this is also a serious inconvenience.
506 Intelligence and Miscellaneous Articles.
4. The use of a second bath of nitrate of silver (1-20) after
washing the plates with fluoride of potassium used as an accelera-
ting agent. The object of this operation is not only to increase still
more the sensibility, but especially to transform the excess of fluoride
of potassium into fluoride of silver, and thus to prevent its acting
upon the glass and causing the separation of the albumen ; it is also
useful, but in regard to the first point only, whatever the accelera-
ting agent used may be.
5. Substitution of a strong bath of sulphate of iron at the tempera-
ture of 194° F. for the gaUic acid generally used for bringing out the
image. This modification produces an enormous increase of sensi-
bility ; moreover, the high temperature furnishes images of a very
light shade, and this is the essential point upon which the production
of proofs upon glass depends ; lastly, the opacity is less than by the
other processes ; hence, in regard to the productions upon paper, there
results a softness which does not exclude delicacy, and the absence
of which has hitherto frequently been urged as an objection to the
employment of albuminous films.
6. Fixing the proofs in four or five minutes by the perfect solution
of the iodide of silver, by means of a bath of cyanide of potassium
and hyposulphite of soda of proper strength.
This method of fixing is superior in every respect, both to the
bromide of potassium, and the hyposulphite generally employed un-
mixed. It gives in a very short time, and without injuring the
proofs, not only unexceptionable fixation, but also complete trans-
parence in the parts which have not taken the impression, and lastly,
considerable increase in the adhesion of the entire coating. It may,
moreover, be easily applied to all the known processes of photography
upon glass, and even without any doubt to the operations upon
paper.
The proofs obtained by this process consist of opake, yellowish
white images, lying in a diaphanous medium, and presenting, there-
fore, the positive or negative aspect, according as to whether they
are placed upon a darker or lighter ground.
As negative proofs, they resist changes of temperature better, are
more transparent (which allows of their being produced by a feeble
light), and lastly, as I have stated, they furnish softer drawings
upon paper than those prepared by other processes.
As positive proofs, and to allow of their being included under this
head, the side of the albumen has only to be coated with black
paint ; they present a clearness and delicacy comparable to metallic
plates, infinitely more beauty of outline, and lastly, a variety of
shades, of which many are very artistic.
In regard to the time requisite for exposure to the light, I may
add that I have obtained landscapes by the sun in a second (with
a plano-convex objective consisting of a combination of glasses, fur-
nished with a diaphragm the aperture in which was 0™03), and por-
traits in the shade out-of-doors in 4 or 5 seconds, and in a room in
from 8 to 15 seconds (with the same object-glass without the dia-
phragm). Moreover, the proofs are naturally erect; and hence, even
Meteorological Observations. 507
if the metallic plate sometimes offers a slight advantage in regard to
rapidity, it loses it completely when inversion of the images would
be inadmissible, and apparatus for reversing it is required. — Comptes
Rendus, Sept. 15, 1851.
REFLEXION OF LIGHT FROM THE SURFACE OF LIQUIDS.
The following are the conclusions' of M. Jamin, from a series of
experiments recorded in the Annates de Chimie et de Physique for
February 1851 : —
1st. Liquid surfaces polarize light incompletely and elliptically.
2nd. Liquids having a high index of refraction have a positive
anomaly, or difference of phase, between the principal components
of the reflected motion.
3rd. This anomaly becomes negative when the index is very small.
4th. There are substances, whose indices are about 1*4, whose
polarization is rectilineal.
5th. The laws of the intensities and anomalies are represented by
the formulae of M. Cauchy.
6th. If substances are superposed, the reflexion from their surface
of separation follows the same laws.
7th. In this case it is impossible to predict the value and the sign
of the coefficient of ellipticity.
The memoir moreover includes a table of the constants of reflexion
for a number of liquids. — Journal of the Franklin Institute, July 1851 .
METEOROLOGICAL OBSERVATIONS FOR OCT. 1851.
Chiswick. — October 1. Densely clouded : rain. 2. Overcast: showery. 3. Fine:
showery. 4. Rain : very fine : clear. 5. Fine. 6. Rain early : very fine. 7.
Rain. 8. Very fine. 9. Foggy: drizzly: rain. 10. Cloudy. 11. Foggy:
very fine. 12. Cloudy. 13. Very fine: rain. 14. Very fine. 15. Constant
rain. 16,17. Clear : very fine. 18. Fine: rain: cloudy. 19. Fine : overcast.
20. Slight drizzle : uniformly overcast. 21. Foggy : fine. 22. Slight fog : hazy.
23, 24, 25. Overcast. 26. Fine. 27. Overcast : exceedingly fine. 28. Over-
cast: rain. 29. Fine : clear. 30. Clear : fine. 31. Very fine.
Mean temperature of the month i 51°*25
Mean temperature of Oct. 1850 44 -32
Mean temperature of Oct. for the last twenty-five years . 50 '50
Average amount of rain in Oct 2*66 inches.
Boston. — Oct. 1. Fine: rain p.m. 2. Fine. 3. Rain: rain a.m. and p.m.
4. Cloudy: rain a.m. 5. Fine: rain a.m. and p.m. 6. Fine: rain early a.m.
7,8. Fine. 9. Cloudy : rain a.m. and p.m. 10,11. Fine. 12. Cloudy. 13.
Cloudy: rain p.m. 14. Fine. 15. Cloudy: rain early a.m. and p.m. 16 —
19. Fine. 20. Cloudy. 21. Rain. 22. Fine. 23— 25. Cloudy. 26, 27. Fine.
28. Cloudy: rain p.m. 29. Fine: rain p.m. 30. Cloudy : rain a.m. and p.m.
31. Fine: rain p.m.
Sandwick Manse^ Orkney. — Oct. 1. Bright: clear: aurora. 2. Rain : clear :
aurora. 3. Bright: clear. 4. Rain: clear: large lunar halo. 5. Bright:
showers. 6. Cloudy : showers. 7. Cloudy : rain. 8. Bright : lunar rainbow.
9. Bright: showers. 10. Showers : cloudy. 1 1 . Clear : showers. 12. Cloudy:
damp. 13. Cloudy: showers. 14. Bright: showers. 15. Rain: bright:
showers. 16. Bright : clear. 17. Showers : drops. 18. Showers : rain: aurora.
19. Clear : showers : aurora. 20. Bright: cloudy: rain. 21. Bright: cloudy.
22. Bright : clear : aurora, 23. Damp ; drops : aurora. 24. Fog : fine. 25.
Fog : rain. 26. Drizzle: rain. 27. Fine : cloudy : rain. 28. Rain : showers :
aurora. 29. Sleet-showers: aurora. 30. Cloudy. 31. Rain : showers : aurora.
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THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
SUPPLEMENT to VOL. II. FOURTH SERIES.
LXXVI. On the Centrifugal Theory of Elasticity, as applied to
Gases and Vapours. By William John Macquorn Ran-
KiNE, C.E., F.R.S.E., F.R.S.S.A. ^c*
(1.) npHE following paper is an attempt to show how the
-»- laws of the pressure and expansion of gaseous sub-
stances may be deduced from that which may be called the
hypothesis of molecular vortices, being a peculiar mode of con-
ceiving that theory which ascribes the elasticity connected with
heat to the centrifugal force of small revolutions of the particles
of bodies.
The fundamental equations of this theory were obtained in the
year 1842. After having been laid aside for nearly seven years,
from the want of experimental data, its investigation was resumed
in consequence of the publication of the experiments of M. Reg-
nault on gases and vapours. Its results having been explained
to the Royal Society of Edinburgh in February 1850, a sum-
mary of them was printed as an introduction to a paper on the
Mechanical Action of Heat in the twentieth volume of the
Transactions of that body. I now publish the investigation in
detail in its original form, with the exception of some interme-
diate steps of the analysis in the second and third sections,
which have been modiiied in order to meet the objections of
Professor William Thomson of Glasgow, to whom the paper was
submitted after it had been read, and to whom I feel much in-
debted for his friendly criticism.
This paper treats exclusively of the relations between the den-
sity, heat, temperature, and pressure of gaseous bodies in a sta-
tical condition, or when those quantities are constant. The
laws of their variation belong to the theory of the mechanical
action of heat, and are investigated in the other paper already
referred to.
The present paper consists of six sections.
The first section explains the hypothesis.
* Communicated by the Author, having been read to the Royal Society
of Edinburgh, February 4, 1 850.
Phil. Mag. S. 4. No. 14. Suppl. Vol. 2. 2 M
510 Mr. Rankine on ike Centrifugal Theory of Elasticity,
The second contains the algebraical investigation of the statical
relations between the heat and the elasticity of a gas.
The third relates to temperature and real specific heat.
The fourth treats of the coefficients of elasticity and dilatation
of gases, and compares the results of the theory with those of
M. Regnault's experiments.
The fifth treats of the laws of the pressure of vapours at satu-
ration.
The sixth relates to the properties of mixtures of gases of dif-
ferent kinds.
I have endeavoured throughout this paper to proceed as directly
as possible to results capable of being compared with experiment,
and to carry theoretical researches no further than is necessary
in order to obtain such results with a degree of approximation
sufficient for the purpose of that comparison.
Section I. On the Hypothesis of Molecular Vortices.
(2.) Tlie hypothesis of molecular vortices may be defined to
be that which assumes — that each atom of matter consists of a
nucleus or central point enveloped by an elastic atmosphere, which
is retained in its position by attractive forces, and that the elasticity
due to heat arises from the centrifugal force of those atmospheres,
revolving or oscillating about their nuclei or central points.
According to this hypothesis, quantity of heat is the vis viva
of the molecular revolutions or oscillations.
Ideas resembling this have been entertained by many natural
philosophers from a very remote period ; but so far as I know.
Sir Humphry Davy was the first to state the hypothesis I have
described in an intelligible form. It appears since then to have
attracted little attention, until Mr. Joule, in one of his valuable
papers on the production of heat by friction, published in the
London and Edinburgh Philosophical Magazine for May 1845,
stated it in more distinct terms than Sir Humphry Davy had
done. I am not aware, however, that any one has hitherto ap-
pHed mathematical analysis to its development.
(3.) In the present stage of my researches, there are certain
questions connected with the hypothesis as to which I have not
found it necessary to make any definite supposition, and which
I have therefore left indeterminate. Those questions are the
following.
First. Whether the elastic molecular atmospheres are conti-
nuous, or consist of discrete particles. This may be considered
as including the question, whether elasticity is to a certain ex-
tent a primary quality of matter, or is wholly the result of the
repulsions of discrete particles.
Secondly. Whether at the centre of each molecule there is
as applied to Gases and Vapours. '-'^^ jI/ 511
a real nucleus having a nature distinct from that of the atmo-
sphere, or a portion of the atmosphere in a highly condensed
state, or merely a centre of condensation of the atmosphere, and
of resultant attractive and repulsive forces. Therefore, although
the word nucleus properly signifies a small central body, I shall
use it in this paper for want of a better term to signify an atomic
centre, whether a real nucleus or a centre of condensation and
force. I assume, however, that the volume of the nucleus, if any,
is inappreciably small as compared with that of the atmosphere.
(4.) I have now to state a supposition, which, so far as I aift
aware, is peculiar to my own researches. It is this : — that the
vibration, which, according to the undulatory hypothesis, constitutes
radiant light and heat, is a motion of the atomic nuclei or centres,
and is propagated by means of their mutual attractions and repul-
sions.
It will be perceived at once, that from the combination of this
supposition with the hypothesis of molecular vortices, it follows
that the absorption of light and of radiant heat consists in the
transference of motion from the nuclei to their atmospheres, and
conversely, that the emission of light and of radiant heat is the
transference of motion from the atmospheres to the nuclei.
It appears to me that the supposition I have stated possesses
great advantages over the ordinary hypothesis of a luminiferous
aether pervading the spaces between ponderable particles, espe-
cially in the following respects.
First. The propagation of transverse vibrations requires the
operation of forces, which, if not altogether attractive, are of a
very different nature from those capable of producing gaseous
elasticity, and which it is difficult to ascribe to such a substance an
the aether is supposed to be ; while attractive forces between the
atomic centres are perfectly consistent with their being kept
asunder by the elasticity of their atmospheres.
Second. The immense velocity of light and radiant heat is a
natural consequence of this supposition, according to which the
vibrating masses must be extremely small as compared with the
forces exerted by them.
Third. According to the most probable view of the theory of
dispersion, the unequal refrangibility of undulations of different
lengths is a consequence of the distances between the particles
of the vibrating medium having an appreciable magnitude as
compared with the lengths of the undulations. This is scarcely
conceivable of the sether, but easily conceivable of the atomic
nuclei.
Fourth. The manner in which the propagation of hght and of
radiant heat is affected by the molecular arrangement of crystal-
line bodies is rendered much more intelligible if the vibrations
2M2
512 Mr. Rankine on the Centrifugal TJieory of Elasticity,
are supposed to be those of the atomic nuclei, on whose mutual
forces and positions the form of crystallization must depend.
[Note. — The consequences of this supposition, in the theory
of double refraction and polarization, are pointed out and shown
to be corroborated by Professor Stokes's experiments on diffrac-
tion, in a paper read to the Royal Society of Edinburgh on the
2nd of December 1850, and published in the Philosophical Ma-
gazine for June 1851.]
Section II. Investigation of the General Equations between the
Heat and the Elasticity of a Gas.
(5.) I now proceed to investigate the statical relations between
the heat and the elasticity of a gaseous body ; that is to say,
their relations when both are invariable. The dynamical rela-
tions between those phaenomena which involve the principles of
the mutual conversion of heat and mechanical power by means
of elastic fluids, and of the latent heat of expansion and evapo-
ration, form the subject of another paper.
(6.) It is obvious that, in the condition of perfect fluidity, the
forces resulting from attractions and repulsions of the atomic
centres or nuclei upon their atmospheres and upon each other,
must be considered as being sensibly functions merely of the
general density of the body, and as being either wholly inde-
pendent of the relative positions of the particles, or equal for so
many different positions as to be sensibly independent of them ;
for othei-wise a certain degree of viscosity would arise,, and con-
stitute an approach to the solid state. For the same reason, in
the state of perfect fluidity, each atomic atmosphere must be
considered as being sensibly of uniform density in each spherical
layer described round the nucleus with a given radius, and the
total attractive or repulsive -force on each indefinitely small por-
tion of an atmosphere must be considered as acting in a line
passing through its nucleus ;• that force, as well as the density,
being either independent of the direction of that line, or equal
for so many different and symmetrical directions as to be sen-
sibly independent of the direction.
(7.) An indefinite number of equal and similar atoms, under
such conditions, will arrange themselves so that the form of their
bounding surfaces will be the rhombic dodecahedron, that being
the nearest to a sphere of all figures which can be built together
in indefinite numbers.
(8.) I may here explain, that by the term bounding surfaces of
the atoms, I understand a series of imaginary surfaces lying be-
tween and enveloping the atomic centres, and so placed that at
every point in these sui-faces the resultant of the joint actions of
all the atomic centres is mUl. To secure the permanent existence
as applied to Gases and Vapours, 513
of each atom, it must be supposed that the force acthig on each
particle of atomic atmosphere is centripetal towards the nearest
nucleus or centre.
The variation of that force in the state of perfect fluidity must
be so extremely small in the neighbourhood of those surfaces, that
no appreciable error can arise, if, for the purpose of facilitating
the calculation of the elasticity of the atmosphere of an atom at
its bounding surface, the form of that surface is treated as if it
were a sphere, of a capacity equal to that of the rhombic dode-
cahedron.
(9.) If the several atoms exercised no mutual attractions nor
repulsions, the total elasticity of a body would be equal to the
elasticity of the atomic atmospheres at their bounding surfaces.
Supposing such attractions and repulsions to exist, they will
produce an effect, which, in the state of perfect fluidity, will be
a function of the mean density of the body ; and which, for the
gaseous state, will be very small as compared with the total
elasticity. Therefore \i p be taken to represent the superficial
elasticity of the atomic atmospheres, P the actual or total elasti-
city of the fluid, and D its general density,
P=;,+/(D), (1)
w^here/(D) is a function of the density, which may be positive
or negative according to the nature of the forces operating be-
tween distinct atoms.
(10.) The following relations must subsist between the masses
of the atmosphere and nucleus, and the density and volume of
each atom.
Let R represent the radius of the sphere already mentioned,
whose capacity is equal to the volume of an atom, that volume
being equal to — - R^.
o
Let jju denote the mass of the atmosphere of an atom, m that
of the nucleus, and M = //- + m the whole mass of the atom (so
that if there is no real nucleus, but merely a centre of conden-
sation, m=0, and M=/t).
Then D being the general density of the body, =^ I^ is the
mean density of the atomic atmosphere, and M = -^ WJ).
If wR be taken to denote the distance of any spherical layer
of the atmosphere from the nucleus, the density of the layer may
be represented by
and the function -^u will be subject to this equation of condition,
614 Mr. Eankine on the Centrifugal Theory of Elasticity,
which is equivalent to
lz=sJ^du{u^^|ru) (2)
(11.) So far as our experimental knowledge goes, the more
substances are rarefied, that is to say, the more the forces which
interfere with the operation of the elasticity of the atomic atmo-
spheres are weakened, the more nearly do they approach to a
condition called that of perfect gas, in which the elasticity is
simply proportional to the density. I therefore assume the elas-
ticity of the atomic atmosphere at any given point to he repre-
sented by multiplying its density at that point by a constant
coefficient b, which may vary for different substances, but, as I
have already stated, without deciding whether that elasticity is a
primary quality or the result of the repulsion of particles. Con-
sequently the superficial atomic elasticity
p = b ^J)f{l), (3)
1/^(1) being the value of yjru which corresponds to the bounding
surface of the atom, where u=l,
(12.) Let an oscillatory movement have been propagated from
the nuclei to every part of their atmospheres, the size of the
orbits of oscillation being everywhere very small as compared
with the radii of the atoms, and let this movement have attained
a pei-manent state, which will be the case when every part of
each atmosphere, as well as each nucleus, moves with the same
mean velocity v ; mean velocity signifying that part of the velocity
which is independent of periodic changes. It is necessaiy to
suppose that the propagation of this movement to all parts of a
molecular atmosphere is so rapid as to be practically instan-
taneous.
We shall conceive all the masses and densities referred to, to
be measured by weight. Then taking g to represent the velocity
generated by the force of gravity at the earth's surface in unit of
time, the whole mechanical power to which the oscillatory move-
ment in question is equivalent in one atom will be represented
in terms of gravity by
^=^' (^^
that is to say, the weight of the atom, M, falling through the
v^
height ^r- due to the velocity v ; and this is the mechanical
measure of the quantity of heat in one atom in terms of gravity.
as applied to Gases and Vapours, v't; .■ 515
(13.) Any sucli motion of the particles of a portion of matter
confined in a limited space will in general give rise to a centri-
fugal tendency with respect to that space. In order to obtain
definite results with respect to that centrifugal tendency in the
case now under consideration^ it is necessary to define, to a cer-
tain extent, the general character of the supposed movement.
In the first place, it is periodical ; secondly, it is similar with
respect to so large a number of radii drawn in symmetrical direc-
tions from the atomic centre, as to be sensibly similar in its
effects with respect to all directions round that centre. This
symmetry exists in the densities of the different particles of the
atomic atmosphere in a gas, and in the forces which act upon
them ; and we are therefore justified in assuming it to exist in
their motions.
Two kinds of motion possess these characteristics.
First. Radial oscillation, by which a portion of a spherical
stratum of atmosphere surrounding an atomic centre, being in
equilibrio at a certain distance from that centre, oscillates pe-
riodically to a greater and a less distance. This forms part of
the vis viva of the molecular movements ; but it can only affect
the superficial atomic elasticity by periodic small variations,
having no perceptible effect on the external elasticity.
Second. Small rotations and revolutions of particles of the
atomic atmosphere round axes in the direction of radii from the
atomic centre, by which each spherical layer is made to contain
a great number of equal and similar vortices, or equal and similar
groups of vortices having their axes at right angles to the layer,
and similarly situated with respect to a great many symmetrical
directions round the atomic centre.
Let us now consider the condition, as to elasticity, of a small
vortex of an atmosphere whose elasticity is proportional to its
density, inclosed within a cylindrical space of finite length, and
not affected by any force at right angles to the axis except its
own elasticity. Let Z denote the external radius of the cylinder,
/Dj its external density, p its mean density, p' the density at any
distance z from the axis (all the densities being measured by
weight), w the uniform velocity of motion of its parts. The con-
dition of equilibrium of any cylindrical layer is, that the differ-
ence of the pressures on its two sides shall balance the centri-
fugal force ; consequently [h being the coefficient of elasticity)
gz dz
The integral of this equation is jfl-«r3fl
p'^=^ciz^g. ym^ih'^m
516 Mr. Rankiue on the Centrifugal Theory of Elasticity,
The coefficient a is determined by the following relation, ana-
logous to that of equation (2), between the densities
whence
Mm-'>-^-
.Zbff
And the general value of the density is
Mi-^'Kif (^)
Making <2r=Z, and multiplying by the coefficient of elasticity
b, we obtain for the elasticity of the atmosphere, at the cylin-
drical surface of the vortex,
bp, = bp+'0; (5<.)
which exceeds the mean elasticity bp by a quantity equivalent
to the weight of a column of the mean density p, and of the
height due to the velocity w, and independent of the radius of
the vortex.
Supposing a sphericallayer, therefore, to contain any number
of vortices of any diameter, in which the mean density is equal,
it is necessary to a permanent condition of that layer that the
velocities in all these vortices should be equal, in order that their
lateral elasticities may be equal.
Although the mean elasticity at the plane end, or any plane
section at right angles to the axis of a vortex, is simply =bpj
being the same as if there were no motion, yet the elasticity is
variable from point to point, and the law of variation depends on
the velocity. Therefore if two vortices are placed end to end, it
is necessary to a stable condition of the fluid, not only that their
terminal planes should coincide, and that their mean elasticities
should be in equilibria, but also that their velocities should be
equal, or subject only to periodical deviations from a state of
equality.
Therefore the mean velocity of vortical motion, independent
of small peiiodic variations, is the same throughout the whole
atomic atmosphere ; and the mean total velocity, independent of
small periodic variations, being uniformly distributed also, the
7ns viva of the fonner may be expressed as a constant fraction of
that of the latter, so that
'o'=j, (5*)
as applied to Gases and Vapours. 517
r being the mean value of a coefficient which is subject to small
periodical variations only*.
This coefficient, being the ratio of the vis viva of motion of a
peculiar kind to the whole vis viva impressed on the atomic atmo-
spheres by the action of their nuclei, maybe conjectured to have
a specific value for each substance, depending in a manner as yet
unknown on some circumstance in the constitution of its atoms.
It will afterwards be seen that this circumstance is the chemical
constitution.
Let the entire atmosphere of an atom be conceived to be di-
vided into a great number of very acute pyramids meeting at the
centre, and having even numbers of faces, equal and opposite in
pairs; and let one of these pyramids, intersecting a spherical
layer whose distance from the nucleus is Rw and thickness
"Rdic, cut out a frustum, containing and surrounded by vortices.
Consider one pair of the faces of that frustum ; their length being
Udu, let their breadth be h and their distance asunder /. Then
they make with each other the angle at the apex of the pyramid
their common area is hRdu j and the sum of the volumes of the
two triangular frusta of the spherical layer, included by diagonal
planes drawn between their radial edges, is
fhRdu
the sum of all such triangular frusta being the whole volume of
the spherical layer.
The additional pressure due to the centrifugal force of vor-
tices, viz.
v^p
* As it has been represented to me, that I have, without stating sufficient
grounds, assumed the velocity of revolution w to be constant throughout
each individual vortex, I add this note to assign reasons for that supposition.
First. Unless w, the velocity of revolution of a particle, is independent
of z, its radius vector, the atomic atmosphere cannot be in a permanent
condition.
For if wis a function of 2, the external elasticity of a vortex will be a func-
tion of its diameter. If the whole atmosphere is in motion, vortices of dif-
ferent diameters must exist in the same spherical layer ; and if their ex-
ternal elasticities are different, their condition cannot be permanent.
Second. Whatsoever may be the nature of the forces by which velocity
is communicated throughout the atmosphere, the tendency of those forces
must be to equalize that velocity, and thus to bring about a permanent
condition.
518 Mr. Rankine on the Centrifugal Theory of Elasticity y
acts on the two lateral faccs^ its total amount for each being
t^KKdu,
2gk
The transverse components of this pair of forces balance each
other. Their radial components, amounting to
nu ^ ^gr^"^""- 2gku '
constitute a centrifugal force relatively to the atomic centre,
acting on the pair of triangular frusta whose mass is
pfli^du
2 •
The condition of permanent, or periodical equilibrium of this
pair of frusta, requires that this centrifugal force shall be ba-
lanced by the variation of the mean elasticity of the atmosphere
at the two surfaces of the spherical layer, combined with the
attraction of the nucleus. The action of the former of these
forces is represented by
—b^dux'^T-.
du 2
Let the accelerating force of attraction towards the nucleus be
represented by
__ (t>rRu)
R '
(j) being a function, which, by the definition of an atomic bound-
ing surface in article 8, is null at that surface, or when m=1.
Then the attraction on the pair of frusta is
_ pfhdu<l)(Ru)
2 *
Add these three forces together ; let the sum be divided by
2 pfhdu,
and let the density p be denoted, as in article 10, by
then the following differential equation is obtained, as the con-
dition of a permanent state of the atomic atmosphere :
gku "^{u) du T* *
This equation will be realized for each layer at its mean posi-
tion, on each side of which its radial oscillations are performed.
as applied to Gases and Vapours, ^ '^' 519
The variation of this expression being of opposite sign to the
variation of ^ ', shows that any small disturbance of the den-
sity produces a force tending to restore that distribution to the
- state corresponding to the position of equilibrium of the layers,
and therefore that the state indicated by equation (5c) is stable.
(14.) The integral of equation (5c) is
'ylru^u^^^e^'bj^ d^'1> (6)
The arbitrary constant a is determined from the ' equation of
condition (2) in the following manner.
Substituting for yjru in equation (2) its value as given above,
we obtain
,gkb e
or
(7)
which integration having been effected, we shall obtain for the
value of the superficial elasticity of the atomic atmospheres,
p=b^3f{l)=b^J)e'
M
M
(8)
To obtain an infinite series for approximating to the value of
the integral in equation (7), let the following substitutions be
made :
and let the values of the successive differential
coefficients of &) with respect to X, when X=0,
^ = 0, and a) = l, be denoted by
(o-O, K), K'), &c.
Then
(9)
-/".
</\.e30Xft).
The value of which (when the function ^ is such as to admit of
its having a finite value) is
whence
620 Mr. Rankine on the Centrifugal Theory of Elasticity,
t(i)=««=<i+g+(^5^) h (10)
(a>')''-2(o,')K) + (a>"') \
^ 27^ + ^"-J
Now because [a') = — t ^(u=i)=0,
which may be represented by ^; . . (10 A)
F(D, 6) being a quantity which becomes continually less as the
density becomes less and the heat greater. The complete ex-
pression for the elasticity of a gas is therefore, according to
equations (1), (8) and (lOA),
P=;,+/(D)=^d(^+6)(1-F(D,^))+/(D); . (11)
when each atom contains a quantity of heat measured by the
mechanical power coiTesponding to the velocity v in the weight
M, or
according to equation (4) .
Section III. Of Temperature, and of real Specific Heat,
(15.) The definition of temperature consists of two parts : —
first, the definition of that condition of two portions of matter
when they are said to be at the same temperature ; and second,
the definition of the measure of differences of temperature.
Two bodies are said to be at the same temperature, when there
is no tendency for one to become hotter by abstracting heat from
the other; that is to say (calling the two bodies A andB), when
there is either no tendency to transmission of heat between them,
or when A transmits as much heat to B as B does to A. Now
it is known by experiment, that any surface or other thing which
aflfects the transmission of heat being placed between B and A,
has exactly the same influence upon the same quantity of heat
passing in either direction ; therefore to produce equilibrium of
temperature between A and B, the powers of their atoms to com-
municate heat must be equal.
as applied to Gases and Vapours. • 521
(15«.) If we apply to vortices at the surface of contact of the
atmospheres of two atoms of the same or different kinds, the
conditions of permanency laid down in article 13 for vortices in
the same atmosphere, these conditions take the following form : —
First. The superficial atomic mean elasticities must be the
same; in other words, the superficial atomic mean densities
must be inversely as the coefficients of elasticity of the atmo-
spheres. This is the condition of equilibrium of pressure.
Second. The law of variation of the elasticity from the centre
to the circumference of a vortex, as expressed in equation (5),
must be the same for both atoms ; and this law depends on the
quantity -j- = y-, ; therefore the condition of equilibrium of heat
is, that the square of the velocity of vortical motion, divided by
the coefficient of atmospheric elasticity, shall be the same for
each atom. Of this quantity, therefore, and of constants com-
mon to all substances, temperature must be a function.
Taking the characteristics (A) and (B) to distinguish the
quantities proper to the two atoms, we have the following equation :
J^Df{l)(A) = 4^Dt(l)(B)
S(-^)=S(«)
!>• (12)
temperature =<P{tI) universal constants)
(16.) In 2i perfect gaSy equation (11) is reduced to
the pressure being simply proportional to the mean elasticity of
the atmospheric part of the gas, multiplied by a function of the
heat, which as equation (12) shows, is a function of the tempera-
ture, from its involving only 77 and universal constants.
Therefore in two perfect gases at the same pressure and tem-
perature, the mean elasticities of the atmospheric parts are the
same, and consequently — •
The mean specific gravities of the atmospheric parts of all perfect
gases are inversely proportional to the coefficients of atmospheric
elasticity.
Let n therefore represent the number of atoms of a perfect
gas, which fill unity of volume under unity of pressure at the
temperature of melting ice, so that nM is the total specific gra-
vity of the gas, and n^ji, that of its atmospheric part ; then
Z>w/i = constant for all gases, . . . (126)
522 Mr. Rankine on the Centrifugal Theory of Elasticity,
and consequently
¥«-T (12o)
Therefore
Temperature is a function of universal constants, and of the vor-
tical vis viva of the atomic atmospheres of so much of the substance
as would, in the condition of perfect gas, fill unity of volume under
unity of pressure at some standard temperature.
The equation (12a) further shows, that in any two perfect gases,
the respective values of the quotient of the pressure by the density
corresponding to the same temperature, bear to each other a con-
stant ratio for all temperatures, being that of the values of the
coefficient b ~.
M
Therefore the pressure of a perfect gas at a given density, or
its volume under a given pressure, is the most convenient mea-
sure of temperature.
Let Vq represent the elasticity of a perfect gas of the density
D at the temperature of melting ice, P that of the same gas at
the same density, at a temperature distant T degrees of the ther-
mometric sca'e from that of melting ice, and C a constant coeffi-
cient depending on the scale employed ; then the value of T is
given by the equation
P— P
T=C^-p^^
or "^ y (13)
T+C=C^
The value of the constant C is found experimentally as follows :
— Let Pj represent the elasticity of the gas at the temperature of
water boiling under the mean atmospheric pressure, Tj the num-
ber of degrees, on the scale adopted, between the freezing- and
boiling-points of water; then
and
^0
(14)
C is in fact the reciprocal of the coefficient of increase of elas-
ticity with temperature, or the reciprocal of the coefficient of
dilatation, of a perfect gas at the temperature of melting ice.
(17.) As it is impossible in practice to obtain gases in the
theoretical condition referred to, the value of C can only be
obtained by approximation. From a comparison of all M. Reg-
nault's best experiments, I have arrived at the following values,
which apply to all gaseous bodies.
as applied to Ga^es and Vapours. 523
For the Centigrade scale, C = 274°'6, being the reciprocal of
0-00364166.
For Fahrenheit's scale, if adjusted so that 180° are equal to
100° Centigrade,—
C for temperatures measured from the freezing-point of water
= 494°-28.
C for temperatures measured from the ordinary zero
= 494°-28 - 32° = 462°-28.
The point C degrees below the ordinary zero of thermometric
scales may be called the absolute zero of temperature ; for tempe-
ratures measured from that point are proportional to the elasti-
cities of a theoretically perfect gas of constant density.
Temperatures so measured may be called absolute temperatures.
Throughout this paper I shall represent them by the Greek letter
T, so that
T=T + C (15)
It is to be observed, that the absolute zero of temperature is
not the absolute zero of heat.
(18.) If we now substitute for P in equation (13) its value
according to equation (I2fl), we obtain the following result : —
Let n represent, as before, the theoretical number of atoms in
unity of volume, under unity of pressure, at the temperature of
melting ice, of the gas in question, supposing the disturbing
forces represented by — F(D, ^) and/(D) to be inappreciable;
then nM is the weight of unity of volume under those circum-
stances, and it is evident that
I> TIT
p-=/iM.
Consequently
r=T+C=C.;.(^+6), .... (16)
being the complete expression for that function of heat called
temperature.
It follows that the function 6, which enters into the expres-
sions for the elasticity of gases, is given in terms of temperature
by the equation
^=^+1=0^ (i«^)
If, according to the expression 4, for the quantity of heat in
one atom, we substitute -^ for v^ in equation (16), we obtain
624 Mr. Rankine on the Centrifugal Theory of Elasticity,
the following equations :
=c»'*(^-^0
>
(17)
Me' Zm( T ,\
and if Q represent the quantity of heat in unity
of weight f
^"M""2^ " 2\CnfjL ) J
(19.) The real)specific heat of a given substance is found by-
taking the differential coefficient of the quantity of heat with
respect to the temperature. Hence it is expressed in various
forms by the following equations, in which the coefficient r is
supposed not to vaiy sensibly with the temperature.
Real specific heat of one atom,
dr ~~ 2Cnfju '
real specific heat of unity of weight,
£?Q __ Sk
dr " 2Cnfju ' ^. . . . (18)
real specific heat of so much of a perfect gas
as occupies unity of volume under unity of
pressure at the temperature of melting ice,
dq_ SAM
The coefficient , representing the ratio of the total vis viva
of the motions of the molecular atmospheres to the portion of
vis viva which produces elasticity, multiplied by the ratio of the
total mass of the atom to that of its atmospheric part, is the
specific factor in the capacity of an atom for heat. The view
which I have stated as probable in article 13, — that the first
factor of this coefficient is, like the second, a function of some
permanent peculiarity in the nature of the atom, — is confirmed
by the laws discovered by Dulong : that the specific heats of all
simple atoms bear to each other veiy simple ratios, and generally
that of equality; that the same property is possessed by the
specific heats of certain groups of similarly constituted compound
atoms ; and that the specific heats of equal volumes of all simple
gases, at the same temperature and pressure, are equal.
as applied to Gases and Vapours. 525
The coefficient — varies in many instances to a great extent
for the same substance in the solid, liquid, and gaseous states.
So far as experiment has as yet shown, it appears not to vary,
or not sensibly to vary, with the temperature ; and this I con-
sider probable a priori, except at or near the points of fusion of
solid substances.
Apparent specific heat differs from real in consequence of the
consumption and production of certain quantities of heat by
change of volume and of molecular arrangement, which accom-
pany changes of temperature.
This subject belongs to the theory of the mechanical action of
heat.
Section IV. Of the Coefficients of Elasticity and Dilatation of
Gases.
(20.) If in equation (ll)we substitute for ^-7 H-i its value 7^ — ,
we obtain the following value for the elasticity of a gas,
in which -^ denotes the ratio of the actual weight of unity of
volume to the weight of unity of volume under unity of pressure,
at the absolute temperature C, in the theoretical state of perfect
gas;
T is the absolute temperature ;
--r(D, 6) is a function of the temperature and density, repre-
senting the effect of the attraction of the atomic nucleus or centre
in diminishing the superficial elasticity of its atmosphere ;
and /(D) is a function of the density only, representing the
effect of the mutual attractions and repulsions of the atoms upon
the whole elasticity of the body.
From this equation are now to be determined, so far as the
experiments of M. Regnault furnish the requisite data, the laws
of the deviation of gases from that theoretical state in which the
elasticity is proportional to the density multiplied by the abso-
lute temperature.
(21.) The value of — F(D, 6) is given by the infinite series of
equations (10), (lOA), substituting in which for 0 its value
T
p — T, we obtain the following result :
Aj, Ag, A3, &c. being a series of functions, the value of which is
given by the following equation :
Phil. Mag. S. 4. No. 14. Suppl. Vol. 2. 2 N
526 Mr. Rankine on the Centrifugal Theory of Elasticity,
-A^ = ^£ Ci-.„»; . . . (20)
Ci+m^eingthe coefficient of 0?^+"* in the development of the
reciprocal of the series
1 - {co')x + (co")x^ - (o)" V + &c.,
when (ft)') &c. have the values given in equation (9).
Equation (19) is thus transformed into
^=^,Cc-^-^'-^-ym. . (21)
The series in tenns of the negative powers of the absolute
temperature converges so rapidly, that I have found it sufficient,
in all the calculations I have hitherto made respecting the elas-
A
ticity of gaseous bodies, to use the first term only, .
(22.) Instead of making any assumption respecting the laws
of the attractions and repulsions which determine the functions
A and /(D), I have endeavoured to represent those functions by
empirical formulae, deduced respectively from the experiments of
M. Regnault on what he terms the coefficient of dilatation of
pases at constant volume, which ought rather to be called the co-
efficient of increase of elasticity with temperature, and from his
experiments on the compressibility of elastic fluids at constant
temperature.
From the data thus obtained I have calculated, by means of
the theory, the coefficients of dilatation of pases under constant
pressure, which, as a test of the accuracy of the theory, I have
compared with those deduced by M. Regnault from experiment.
(23.) The mean coefficient of increase of elasticity with tem-
perature at constant volume between 0° and 100° of the Cen-
tigrade thermometer is found by dividing the difference of the
elasticities at those two temperatures by the elasticity at 0°, and
by 100°, the difierence of temperature. It is therefore repre-
sented by V —V
==I^' (22)
where E represents the coefficient in question, and Pq and P,
the elasticities at 0° and 100° Centigrade respectively.
Now by equation (21), neglecting powers of - higher than the
'^^*'^^'^^V^o=„4(l-^)+/(B)
p _ D /'100°+C A \ „^.
^'- m\ — 0 100*+ c J ■'■•^"''
whence -^(L + ^ „) (zv^
as applied to Gases and Vapours. 527
Supposing the value of ^p to be known, this equation
affords the means of calculating the values of the function A cor-
responding to various densities, from those of the coefficient E as
given by experiment.
As a gas is rarefied, -yrn- approximates to unity, A dimi-
nishes without limit, and the value of E consequently approxi-
mates to YT) the reciprocal of the absolute temperature at 0^ Cen-
tigrade. This conclusion is verified by experiment; and by
means of it I have determined the values already given, viz.
C = 274F'6 Centigrade, and -i =-00364166 for the Centigrade
scale. -p.
(24.) In order to calculate the values of ^p , I have made
use of empirical formulae, deduced from those given by M. Reg-
nault in his memoir on the Compressibility of Elastic Fluids.
In M. Eegnault's formulae, the unit of pressure is one metre of
mercury, and the unit of density the actual density correspond-
ing to that pressure. In the formulae which I am about to state,
the unit of pressure is an atmosphere of 760 millimetres of mer-
cury, or 29*922 inches ; and the unity of density, the theoretical
density in the perfectly gaseous state at 0° Centigrade, under a
pressure of one atmosphere, which has been found from M. Reg-
nault's formulae by making the pressure =0 in the value of
M/iP
— YY"^. M. Eegnault^s experiments were made at temperatures
slightly above the freezing-point, but not sufficiently so to render
the formulae inaccurate for the purpose of calculating the ratio
in question, ^^.
The formulae are as follows : —
Supposing jjj^ given,
C»MP . D ^jDy
which, when T is small, or t nearly = C, gives an
approximate value of — tT"^-
Supposing Py given,
which, when T is small, gives an approximate
value of
> ' . (24)
»MPo
2N2
628 Mr. Rankine on the Centrifugal Theory of Elasticity ,
The values of the constants u, y9, 7, e, and of their logarithms,
are given, together with the mean temperatures above the free-
zing-point at which M. Regnault's experiments were made, for
atmospheric air, carbonic acid gas and hydrogen.
Atmospheric Air. T=4°*75.
Constants. Logarithms.
« = - 7 = - -000860978 49349920
/9= + -000011182 5-048514Q
6= --000009700 6-9867717
Carbonic Acid Gas. T = 3°-27.
«= -7= --00641836 3-8074242
y9=: --0000041727 6-6204126
€= + -0000865535 5-9372846
Hydrogen. T=4°-75.
«= -7= + -000403324 4-6056546
^=: + -0000048634 6-6869401
€= - -0000044981 6-6530291
The three substances above-mentioned are the only gases on
which experiments have yet been made, under circumstances
sufficiently varied to enable me to put the theory to the test I
have described in article 22.
(25.) M. Regnault has determined the values of the coeffi-
cient of elasticity E for carbonic acid at four different densities,
and for atmospheric air at ten. By applying equations (23) and
(24) to those data, I have ascertained that the function A for
these two gases may be represented empirically, for densities not
exceeding that corresponding to five atmospheres, by the formulse
given below, which lead to formulae for the coefficient E,
For Carbonic Acid,
where log a =0-3344538, and consequently
nMPo C V''"C + 100' nM/
log ^^j:^ =3-7608860.
(25)
as applied to Gases and Vapours.
For Atmospheric Air,
where log a=0"3176168, and consequently
629
E
TiMPo Cl C-}-100° \nM/ J
>.
log
C + 100°
= 3-7440490
(26)
The value of log p is
3-5612995.
The following table shows that those empirical formulse accu-
rately represent the experiments, the greatest differences being
less than one-half of -0000136, which M. Regnault, in the
seventy-first page of his memoir, assigns as the limit of the errors
of observation due to barometric measurements alone.
As the coefficient E for hydrogen has been determined for one
density only, it is impossible to obtain an empirical formula for
that gas. The single ascertained value of E is nevertheless in-
serted in the table.
Table of Coefficients of Increase of Elasticity with Temperature
at Constant Volume.
Pressure at
Density
D
Coefficient
Coefficient
DiflFerence be-
0° Cent, in
E
E
tween the for-
atmospheres
according to
according to
mulae and
=Po.
niVl
the formulae.
experiment.
experiment.
Carbonic Acid.
I.
0-9980
1-00448
-0036865
-0036856
+ 0000009
II.
11857
1-19487
-0036951
•0036943
+ -0000008
III.
2-2931
2-32788
-0037465
•0037523
- -0000058
IV.
47225
4-87475
-0038647
•0038598
+ 0000049
Atmc
ispheric Air
I.
01444
0-1444
-0036484
•0036482
+ -0000002
II.
0-2294
0-2294
-0036507
•0036513
- -0000006
III.
0-3501
0-3502
-0036535
•0036542
-•0000007
IV.
0-4930
0-4932
-0036564
•0036587
-•0000023
V.
0-4937
0-4939
-0036564
•0036572
--0000008
VI.
10000
1-00085
-0036652
•0036650
+ -0000002
VII.
2-2084
2-2125
-0036810
•0036760
+ -0000050
VIII.
2-2270
2-2312
•0036812
-0036800
+-0000012
IX.
2-8213
2-8279
-0036880
-0036894
-0000014
X.
4-8100
4-8289
-0037081
-0037091
- -0000010
Hydrogen.
1-0000
09996
No formula.
•0036678
1
530 Mr. Rankine on the Centrifugal Theory of Elasticity,
(26.) The empirical formiilai (24), representing the experi-
ments of M. Regnanlt on the compressibility of carbonic acid
gas, atmospheric air, and hydrogen at certain temperatures, give
for these temperatures the values of a function which is theo-
retically expressed by
CnMP_ CA CnMf(D)
tD "^""■^ "^ tD ^"^^f
It is evident, that supposing the value of — =r— for any given
density to be known by experiment, and that of A to be calcu-
lated from the value of the coefficient E, or from the empirical
formulae (25) and (26), the corresponding value of the function
— i^ — - may be determined by means of equation (27).
By this method I have obtained the following empirical for-
mulae for calculating the values of that function : —
For Carbonic Acid,
D ~ nW
where log h = 3- 1083932.
For Atmospheric Air,
^M/(D) _ / D^y
D ~ ^ \nM/ '
where log ^ = 3-8181545.
As only one value of — -^ — - for hydrogen can at present be
ascertained, it is impossible to determine a formula for that gas.
The single value in question is —
For Po=l atmosphere, ^^^^^^ ='01059. . . (29)
(27.) I now proceed to determine theoretically, from the data
which have already been obtained, the mean coefficients of dilata-
tion at constant pressure, between 0° and 100° of the Centigrade
scale, for the three gases under consideration, at various pressures.
Let E' represent the coefficient required ; Sq and Si the re-
nM.
spective values of ^jir- for 0° and 100° under the pressure P, that
is to say, the volumes occupied by the weight wM at those tem-
peratures ; Aq and Aj, /q and /j, the corresponding values of A
(38)
as applied to Gases and Vapours. 531
and /(D). Then from equation (21) we deduce the following
results : —
So=J(l-^»+So/o)
„ 1 /, , 100° A. „ ^\
^'- p V+ "c~ ~ cTioo^ +^^f')'
and consequently
E'= ^"~ 0
100° s.
SoPVc
+
Ai
So/o^Sj/i
C^IOOC 100(C + 100) 100
). . (30)
In applying the empirical formulae (25), (26), and (28) to de-
termine the values of Aj and Sj/j in the above equation, it will
produce no appreciable error to use ^ Dq as an approxi-
mate value of D^, for that purpose only. By making the neces-
sary substitutions, the following formulae are obtained : —
For Carbonic Acid,
where log a =5*51 89349.
For Atmospheric Air,
E'
~ nMV I C "^ \nM/ ^ ' \nM.J J'
(31)
where log «= 5-4717265
log ^=6-9759738
(28.) The following table exhibits a comparison between the
results of the formulae and those of M. Regnault^s experiments.
It is not, like the preceding table (article 25), the verification of
empirical formulae, but is a test of the soundness of the theo-
retical reasoning from which equations (30) and (31) have been
deduced.
It is impossible, from the want of a sufficient number of ex-
perimental data, to give a formula similar to (31) for hydrogen.
I have calculated, however, the value of the coefficient E' for that
gas, corresponding to the pressure of one atmosphere, on the
assumption that at that pressure a formula similar to that for
carbonic acid gas is applicable without sensible error.
532 Mr. Raukine on the Centrifugal Theory of Elasticity,
The table shows only one instance in which the difference be-
tween the result of the theory and that of experiment exceeds
•0000136; the limit, according to M. Regnault, of the errors of
observation capable of arising from one cause alone, — the uncer-
tainty of barometric measurements. That discrepancy takes
place in one of the determinations of the coefficient E' for car-
bonic acid gas under the pressure of one atmosphere. In the
other determination, the discrepancy is less than the limit.
The agi'eement between theory and experiment is most close
for the highest pressures ; and M. Regnault has shown (p. 100)
that the higher the pressure the less is the effect of a given eiTor
of observation in producing an error in the value of the co-
efficient.
The theory is therefore successful in calculating the coefficients
of dilatation of gases, so far as the means at present exist of put-
ting it to the test.
Table of Coefficients of Dilatation under Constant Pressure,
showing a Comparison between Theory and Experiment,
Pressure in
atmospheres.
Coefficient E'
according
to the
theory.
Coefficient E'
according to
M. Regnault's
experiments.
Difference
between
theory and
experiment.
Carbonic Acid Gas.
1^000
3-316
•0036988
•0038430
First Memoir.
•0037099
Second Memoir.
•003719
First Memoir.
•0038450
-•0000111
-•0000202
- -0000020
Atmospheric Air.
10000
3-3224
3-4474
•0036650
•0036955
•0036969
First Memoir.
•0036706
Second Memoir.
•003663
•003667
First Memoir.
•0036944
•0036965
-•0000056
+ 0000020
-•0000020
+ 0000011
+ 0000004
Hydrogen.
10000
•0036598
•0036613
-0000015
as applied to Gases and Vapours. 533
Section V. Of the Elasticity of Vapour in contact with the same
Substance in the Liquid or Solid State.
(29.) As the most important phsenomena of evaporation take
place from the liquid state, I shall generally use the word liquid
alone throughout this section in speaking of the condition op-
posed to the gaseous state; but all the reasonings are equally-
applicable to those cases in which a substance evaporates from
the solid state.
(30.) In considering the state of a limited space, entirely oc-
cupied by a portion of a substance in the liquid form, and by
another portion of the same substance in the form of vapour,
both being at rest, the most obvious condition of equilibrium is,
that the total elasticity of the substance in each of the two states
must be the same, that is to say,
P=i'o+/(I>o)=;'.+/(D,), .... (33)
where Pq represents the superficial atomic elasticity in the liquid
state, p^ that in the gaseous state, and/(DQ), /(l)j) the corre-
sponding values of the pressures, positive or negative, due to
mutual actions of distinct atoms.
(31.) A second condition of equilibrium is, that the super-
ficial elasticities of two contiguous atoms must be equal at their
surface of contact. Hence, although there may be an abrupt
change of density at the bounding surface between the liquid
and the vapour, there must be no change of superficial atomic
elasticity except by inappreciable degrees ; and at that bounding
surface, if there is an abrupt change of density (as the reflexion
of light renders probable), there must be two densities corre-
sponding to the same superficial atomic elasticity.
(32.) A third condition of equilibrium is to be deduced from
the mutual attractions and repulsions of the atoms of liquid and
of vapour. In a gas of uniform density, those forces, acting on
each individual particle at an appreciable distance from the
bounding surface, balance each other, and have accordingly been
treated as merely afiecting the total elasticity of the body by an
amount denoted by /(D) ; but near the bounding surface of a
liquid and its vapour, it is obvious that the action of the liquid
upon any atom must be greater than that of the vapour. A force
is thus produced which acts on each particle in a line perpendi-
cular to that bounding surface, and which is probably attractive
towards the liquid, very intense close to the bounding surface,
but inappreciable at all distances from it perceptible to our
senses. Such a force can be balanced only by a gradual increase
of superficial atomic elasticity in a direction towards the liquid.
Hence, although at perceptible distances from the surface of the
534 Mr. Rankine on the Centrifugal Theory of Elasticity,
liquid, the density of vapour is sensibly uniform, the layers close
to that surface are probably in a state of condensation by attrac-
tion, analogous to that of the earth's atmosphere under the in-
fluence of gravity.
Professor Faraday has expressed an opinion, founded on his
own experiments and those of MM. Dulong and Thenard, that
a state of condensation exactly resembling that which I have
described is produced in gases by the superficial attraction of
various substances, especially platinum, and gives rise to chemi-
cal actions which have been called catalytic.
To express this third condition algebraically, let the boundary
between the liquid and the vapour be conceived to be a plane of
indefinite extent, perpendicular to the axis of a? ; and let positive
distances be measured in a direction from the liquid towards the
vapour.
Let X, x + dx represent the positions of two planes, perpen-
dicular to the axis of x, bounding a layer whose thickness dx is
very great as compared with the distance between two atomic
centres, but very small as compared with any perceptible distance,
and let a portion of the layer be considered whose transverse
area is unity.
Let p represent the mean density of the layer. Then it is
acted upon by a force
—pXdx,
the resultant of the actions of all the neighbouring atoms, which
has the negative sign, because it is attractive towards the liquid,
X being a function of the position of the layer in question, and
of the densities and positions of all the neighbouring layers.
The superficial atomic elasticity behind the layer being p, and
in front of it j9 + ~ dx, it is also acted on by the force
-^dx-
dx"^^'
hence its condition of equilibrium is
S+''X=0 (33)
In order to integrate this equation, so as to give a relation
applicable at perceptible distances from the surface, let Xq, Xy
represent the positions of two planes perpendicular to the axis
of X, the former situated in the liquid, the latter in the vapour,
and so far asunder that the densities beyond them are sensibly
uniform, and equal respectively to Dq for the liquid and D, for
the vapour, the corresponding superficial atomic elasticities being
Pq and;?|. TJien dividing equation (33) by /?, and integrating
as applied to Gases and Vapours. 535
between tlie limits Xq and a?^ the result obtained is
r^-E = -nd..X (34)
'^PO P ^^0
Had we a complete knowledge of the laws of molecular forces
in the solid, liquid and gaseous states,, this equation, taken in
conjunction with the two conditions previously stated, would be
sufficient to determine formulae^ for calculating the total elasti-
city, and the respective densities of a liquid and its vapour when
in contact in a limited space, at all temperatures.
(33.) In the absence of that knowledge, I have used equation
(34), so as to indicate the form of an approximate equation suit-
able for calculating the elasticity of vapour in contact with its
liquid, at all ordinary temperatures, the coefficients of which I
have determined empirically, for water and mercury, from the
experiments of M. Regnault, and for alcohol, sether, turpentine,
and petroleum from those of Dr. Ure.
It has been shown (equation 19) that the superficial atomic
elasticity is expressible approximately in terms of the density
and temperature for gases by
P
=p'i^y^^{p^c^b)y
where the function F is a very rapidly convergmg series, m
terms of the negative powers of the absolute temperature, the
coefficients being functions of the density. It is probable that
a similar formula is applicable to liquids, the series being less
convergent.
It follows that the density is expressible approximately in
terms of the superficial atomic elasticity by
the function <l> being also a converging series in terms of the
negative powers of the absolute temperature, and the coefficients
being functions of p.
Making this substitution in the first side of equation (34), and
abbreviating <I> Ip, p—i) into <I>, we obtain the following
result : —
/*Pi , 1 T /*Pl J
Po '^Xl+*)
(log,;,.-log.;,„-^'" dp . ^(i:p^)
■'<fe.X;. . (35)
536 Mr. Rankine on the Centrifugal Theory of Elasticity,
from which, making \o^ePo + T ^ dp . ='^ and
^ Pa pyi-t^)
CnM/ dir . X=n, the following value results for the hyper-
bolic logarithm of the superficial atomic elasticity of the vapour
at sensible distances from the surface of the liquid :— -
Iog.p,=^P-" (36)
In the cases which occur in practice, the density of the vapour
is very small as compared with that of the liquid. Hence it fol-
lows, that in such cases the value of ^ depends chiefly on the
superficial atomic elasticity of the liquid, and that of 11 on its
density. The density is known to diminish with the tempera-
ture, but slowly. The superficial atomic elasticity, according to
equation (32), is expressed by
i"o=;'i+yi;i>,)-/(i>o),
where jt?i and/(Di) are obviously small as compared with/(Do),
a function of the density of the liquid, so that the variations of
Pq and of "^ with the temperature are comparatively slow also.
Therefore when the density of the vapour is small as compared
with that of the liquid, the principal variable part of the loga-
rithm of its supei-ficial atomic elasticity, and consequently of its
whole pressure, is negative, and inversely proportional to the
absolute temperature ; and
a —
T
(a and /3 being constants) may be regarded as the first two terms
of an approximate formula for the logarithm of the pressure.
A formula of two terms, similar to this, was proposed about
1828 by Professor Roche. I have not been able to find his
memoir, and do not know the nature of the reasoning from
which he deduced his formula. It has since been shown, by
M. Regnault and others, to be accurate for a limited range of
temperature only. The quantity corresponding in it to t is
reckoned from a point determined empirically, and very different
from the absolute zero.
Thus far the investigation has been theoretical. The next
step is to determine empirically what other terms are requisite
in order to approximate to the effect of the function /(D), and
of the variation of the functions "^ and fl.
The analogy of the formulae for the dilatation of gases, the
obvious convenience in calculation, and the fact that the devia-
tions of the results of the first two terms from those of experi-
as applied to Gases and Vapours. 537
ment are greatest at low temperatures, naturally induced me to
try in the first place the effect of a third term inversely propor-
tional to the square of the absolute temperature, making the en-
tire formula for the logarithm of the pressure of vapour in con-
tact with its liquid
and the inverse formula, for calculating the
absolute temperature from the pressure.
1- (37)
^'^/^
7 "^ 4^rf 2r/
the values of the constants a, /S, 7 being determined by the or-
dinary methods from three experimental data for each substance.
(34.) The agreement of those formulse with the results of ex-
periment proved so remarkable, that, as they are calculated to
De practically useful, I thought it my duty not to delay their
publication until I should have an opportunity of submitting my
theoretical researches to the Royal Society of Edinburgh. I
therefore communicated the formula3 to the Edinburgh New
Philosophical Journal for July 1849, together with the full de-
tails of their comparison, graphic and tabular, with the experi-
ments of M. Regnault upon water and mercury, and with those
of Dr. Ure upon alcohol, sether, turpentine and petroleum,
but without giving any account of the reasoning by which I had
been led to them.
Without repeating those details here, I may state, that the
agreement between the results of the formulse and those of ob-
servation is in every case as close as the precision of the experi-
ments renders possible. This is remarkable, especially with
respect to the experiments of M. Regnault on the elasticity of
steam, which extend throughout a range of temperatures from
30° below zero of the Centigrade scale to 230° above it, and of
pressures from ggVo^^ ^^ ^^ atmosphere to 28 atmospheres,
and which, from the methods of observation adopted, especially
those of measuring temperature, necessarily surpass by far in
precision all other experiments of the same kind. From 20° to
230° Cent, the greatest discrepancy between calculation and ex-
periment corresponds to a difference of yg^ of a Centigrade
degree, and very few of the other dift'erences amount to so much
as ^\jth of a degree. Below 20°, where the pressure varies so
slowly with the temperature that its actual value is the proper
test of the formula, the greatest discrepancy is yo%*^^ ^^ ^ milli-
metre of mercury, or g^^th of an inch. If the curves repre-
senting the formulse were laid down on M. Regnault's diagram.
588 Mr. Rankine on the Centrifugal Theory of Elasticity ,
they would be scarcely distinguishable from those which he has
himself drawn to exhibit the mean results of his experiments.
Annexed is- a table of the values of the constants a, log fi,
^^S yy Q~y ~A73.i ^or *^® fluids for which they have been calculated.
As the existing experiments on mercury, turpentine and petro-
leum are not sufficiently extensive to indicate any precise value
for the coefficient 7 (which requires a great range of tempera-
tures to evince its effect), I have used for these fluids, as an ap-
proximation, the first two terms of the formula only, a— — .
For different measures of pressure, the contact a evidently
varies equally with the complement of the logarithm of the unit
of pressure.
For different thermometric scales, ^ varies inversely as the
length of a degree, 7 inversely as the square of that length,
— directly as the length of a degree, and 7-2 directly as the
square of that length.
For all the fluids except water, it will probably be found neces-
sary to correct more or less the values of the constants, when
more precise and extensive experiments have been made, espe-
cially those for the more volatile sether, and for turpentine, pe-
troleum and mercury, which have all been determined from data
embracing but a small range of pressures.
In reducing the constants for the Centigrade scale to those
for Fahrenheit's scale, 180° of the latter have been assumed to
be equal to 100° of the former. In order that this may be the
case, the boiling-point of Fahrenheit's scale must be adjusted
under a barometric pressure of 760 millimetres, or 29*922 inches,
of mercuiy, whose temperature is 0° Centigrade.
In the ninth and tenth columns of the table are given the
limits on the scales of temperature and pressure between which
the formulae have been compared with experiment. It is almost
certain that the formula for the pressure of steam may be em-
ployed without material error for a considerable range beyond,
and probably also that for the pressure of vapour of alcohol ; but
none of the formulae are to be regarded as more than approxima-
tions to the exact physical law of the elasticity of vapours, for
the determination of which many data are still wanting, that can
only be supplied by extensive series of experiments.
as applied to Gases and Vapours.
539
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640 Mr. Rankine on the Centrifugal Theory of Elasticity,
The following are some additional values of the constant a for
steam, corresponding to various units of pressui*e used in prac-
tice : —
Units of pressure. Values of a.
Atmospheres of 760 millimetres of mercury —
= 29*922 inches of mercury
= 14*7 lbs. on the square inch
= 1-0333 kilog. on the square centim. 4-950433
Atmospheres of 30 inches of mercury —
= 761-99 millimetres
= 14-74 lbs. on the square inch
= 1-036 kilog. on the square cent
Kilogrammes on the square centimetre
Kilogrammes on the circular centimetre .
Pounds avoirdupois on the square inch
Pounds avoirdupois on the circular inch ,
Pounds avoirdupois on the square foot
All the numerical values of the constants are for common
logarithms.
(35.) According to the principles which form the basis of cal-
culation in this section, every substance, in the solid or liquid
state, is surrounded by an atmosphere of vapour, adhering to its
surface by molecular attraction ; and even when the presence of
vapour is imperceptible at all visible distances from the body^s
surface, the elasticity of the strata close to that surface may be
considerable, and sufficient to oppose that resistance to being
brought into absolute contact, which is well known to be very
great in solid bodies, and perceptible even in drops of liquid. It
is possible that this may be the only cause which prevents all
solid bodies from cohering when brought together.
The action of an atmosphere of vapour, so highly dense and
elastic as to operate at visible distances, may assist in producing
the spheroidal state of liquids.
If the particles of clouds are small vesicles or bubbles (which
is doubtful), the vapour within them may, according to these
principles, be considerably more dense than that which pervades
the external air, and may thus enable them to preserve their
shape.
Section VI. Of Mixtures of Gases and Vapours of different
kinds.
(36.) The principle stated in Section II. article 11, that the
elasticity of the atomic atmosphere is proportional to its density,
might be otherwise expressed by saying, that the elasticity of any
number of portions of atomic atmosphere, compressed into a given
space, is equal to the sum of the elasticities which such portions
would respectively have, if they occupied the same space separately.
as applied to Gases and Vapours. 541
If the same principle here laid down for portions of atomic
atmosphere of any one kind of substance be considered as true
also of portions of atomic atmosphere of substances of diiferent
kinds mixed, and if it be supposed that when two or more gases
are mixed, there is no mutual force exerted between atoms of
different kinds, except the elastic pressure of the atomic atmo-
spheres, it will then evidently follow, —
First, that the mixed gases will only be in equilibrio when
the particles of each of them are diffused throughout the whole
space which contains them.
^econdlij, that the particles of each gas taken separately will be
in the same condition as to density, elasticity, arrangement and
mutual action, and also as to gravitation, or any other action of
an external body, as if that gas occupied the space alone.
Thirdhj, thsit the joint elasticity of the mixed atomic atmospheres
at any given point will be the sum of the elasticities which they
would respectively have had at that point, if each gas had occu-
pied the space alone.
Fourthly, that the value of the elasticity, positive or negative,
resulting from the attractions and repulsions of separate atoms,
will be the sum of the values it would have had if each gas had
occupied the space alone. And,
Fifthly, that the total elasticity of the mixed gases will be the
sum of the elasticities which each would have had separately in
the same space.
If there are any mutual actions between the particles of dif-
ferent gases except the elasticity of the molecular atmospheres,
these conclusions will no longer be rigidly true ; but they wdll
still be approximately true, if the forces so operating are very
small. This is probably the actual condition of mixed gases.
(37.) On applying the same principle to the case of a gas
mixed with a vapour in contact with its liquid, it is obvious, that
if the attractions and repulsions of the particles of the gas upon
those of the vapour are null, or inappreciable, the direct effect of
the presence of the gas upon the elasticity assumed by the va-
pour at a given temperature will also be null, or inappreciable.
The gas, however, may have a slight indirect influence, by
compressing the liquid, and consequently increasing its superfi-
cial atomic elasticity and its attractive power, on which the func-
tions ^ and 12 in equation (36) depend. The probable effect of
this will be, to make the elasticity of the vapour somewhat less
than if no gas were present. There appear to be some indica-
tions of such an effect ; but they are not sufficient to form a
basis for calculation.
Supposing the gas, on the contrary, to exercise an appreciable
attraction on the particles of vapour, the elasticity of the latter
Phil, Mag. S. 4. No. 14. Suppl. Vol. 2. 2 0
542 M. W. HankePs Account of some Experiments
will be increased. Traces of an effect of this kind are perceptible
in M. Regnault's experiments on the vapour of mercury, in
which air was present.
(38.) I have already referred to the property ascribed by Pro-
fessor Faraday to various substances, of attracting, and retaining
at their surfaces, layers of gas and vapour in a high state of
condensation. Supposing a solid body to acquire, in this man-
ner, a mixed atmosphere, consisting partly of its own vapour and
partly of foreign substances, the total elasticity of that atmo-
sphere at any point will be equal, or nearly equal, to the sum
of the elasticities which each ingredient would have had sepa-
rately ; and thus solid metals, glass, charcoal, earthy matters,
and other substances, may acquire a great power of resisting co-
hesion, although producing no perceptible vapours of their own.
at ordinary temperatures.
LXXVII. An Account of some Experiments upon the Electricity
of Flame f and the Electric Currents thereby originated. By W.
Hankel*.
IT is known that by the combustion of bodies free electricity
is generated ; all investigations on the electric deportment
of flame have hitherto been limited exclusively to the examina-
tion of the free electricity which the flame contains. A deeper
consideration of the entire electric deportment in such cases con-
ducted me to the idea, that the electric opposition which different
portions of the flame exhibit, not unlike the relation which sub-
sists between a copper and a zinc plate, ought, like the latter, to
be capable of developing an electric current. This proves to be
the case. I have succeeded in establishing, in a manner which
excludes all doubt, that a flame when properly closed in a con-
ducting circuit is the origin of an electric current.
During the experiments three lamps were made use of. The
parts of the lamps No. 1 and No. 2, which immediately sur-
rounded the flame, were of the same dimensions ; in other re-
spects, however, the lamps were very different. The diameter of
the outer brass cylinder which encompassed the wick was 32*5
millims., and the diameter of the inner cylinder was 22*7 mil-
lims. Between these two cylinders No. 1 carried a new double
wick, while No. 2 held a single wick which had been for some
time in use. The chimney of No. 1 was of sheet-brass, that of
No. 2 was of sheet-iron ; both chimneys were 52 millims. high,
and reached about 10 or 11 millims. below the rims of the cylin-
ders from between which the wick protruded. The lamp No. 2
* Abridged from Poggendorif' s Annalen, vol. Ixxxi. p. 213, and com-
municated by Dr. J. Tyndall.
upon the Electricity of Flame. 543
was provided with a bellows, by means of which air could be
forced through five small openings into the space between the
outer cylinder which inclosed the wick and the surrounding
chimney. The lamp No. 3 was an old one, not capable of giving
out any great amount of heat.
For the detection of the current a galvanometer was used,
which consisted of a pair of astatic needles, around which were
wound 16,454 feet of wire.
The first electric current which I obtained from the flame, was
by uniting one end of the wire of the galvanometer with the
lamp No. 1 j while the other end, to which was attached a piece
of platinum foil, was held in an inclined position in the flame
above the chimney. The time of oscillation of the needles was 16",
and in the present case the action of the stream excited caused
a divergence of 1°. The direction of the current could be
altered by a commutator which was introduced into the circuit ;
and by properly managing this, the swing of the needle could
be so increased, that after a few reversions it reached an am-
plitude of 15° or 16°. In this way the action of weaker cur-
rents, such as those of small flames, or of the flames of alcohol
and sether, was rendered evident. It was, however, desirable to
obtain a greater angle than the above ; and for this purpose a
pair of needles was chosen, whose magnetism was so nearly ba-
lanced that the time of oscillation amounted to 45". Placing a
new wick in the lamp, and raising it so as to obtain the greatest
flame possible, a deflection of 20° was obtained. The current passed
■moreover from the top to the bottom of the flame. Most of the
experiments have been made with the last-mentioned pair of
needles.
The strength of the electric current depends upon the magni-
tude of the flame. When a piece of platinumfoil 0-23 millim. thick
was brought over the lamp so that a space of 8 millims. separated
it from the upper rim of the chimney, the flame being made so
great that the entire platinum was encompassed by it, an angle
of 20° was obtained. The platinum being allowed to remain in
the same position, and the lamp being lowered, the needle fell to
16° ; and as the flame was made still smaller, the needle descended
correspondingly. Although an increase of flame in the present
case caused an increase of the deflection from 16° to 20°, it by no
means follows that this was due to an increased electric tension
between the portion of the flame in contact with the platinum and
that in contact with the lamp. The same might be the result of
a diminution of the resistance within the flame. If even a decrease
of electric tension accompanied the enlargement of the flame,
still a more powerful stream would be exhibited if at the same
time the diminution of the resistance to conduction were suffi-
202
544 M. W. HankePs Account of some Eocperiments
ciently great. It will be afterwards shown by experiment that
the result last nientiomed actually occui-s.
But it is not the size of the flame alone which detennines the
character of the current, it also depends upon the intensity of
the combustion. The portions of the lamp No. 2 which surround
the wick are exactly of the same dimensions as the corresponding
parts of No. 1 . In the experiment, however, the wick of No. 2
was a simple one, and had been used for some time. On raising
it until a flame of equal magnitude with the former was attained,
the needle still showed a weaker current. Even the lamp No. 1
itself, after having burnt for some time, was no longer able to
cause a divergence of 20°.
The inclined position, which, as before stated, was given to
the platinum foil, is more favourable than the horizontal, for
the latter causes a weaker combustion. When the platinum was
held at some height above the chimney, and was changed from
a horizontal to an inclined position, the angle was increased by
the change from 9° to 10°; this is a natural result of the fact,
that a greater draft is pei*mitted by the latter position, and thus
the power of the flame is increased. The platinum being held
high above the chimney in a horizontal position, an angle of 5°
was observed; and on inclining it, the angle increased to 6°-8.
As might be expected, the artificial introduction of a current
of air also increases the action. This was effected by means of
the bellows attached to lamp No. 2. The platinum foil was first
held over the chimney, and before the bellows were applied, an
angle of 1° was obtained; when the bellows were set in action-
the needle mounted to 10^*6, and on continuing to blow, rose to
116°(11°-6?T.)'^
The different specimens of alcohol and sether which I applied
gave currents of different power. In order to obtain results
which might be compared with each other, I poured the fluid
into a small platinum crucible and ignited it. With the crucible
one end of the wire of the galvanometer was connected, and to
the other end a piece of platinum foil was attached which was
dipped into the flame in an inclined position, so that the distance
of itg upper edge from the rim of the crucible was i2'l millims.,
while its lower edge was 21*5 millims. distant. The crucible as
well as the platinum remained unmoved during the entire series
of experiments. The fluid in this case burnt without a wick.
On pouring alcohol of the specific gravity 0-850 into the vessel
and igniting it, an angle of 0° 8 was observed ; this was increased
to 1°-1 when alcohol of the specific gravity 0'835 was used, and
amounted to 2°*6 with absolute alcohol. The latter angle, how«
ever, remained constant only so long as the alcohol remained
without boiling; when it boiled, an angle of 5°-5 was obtained;
upon the Electricity of Flame. 545
and this was also the case when aether was added^ which boiled
during its combustion.
When instead of the platinum crucible an iron vessel of some-
what similar shape was used^ on igniting the aether therein con-
tained an angle only half the size of that with the platinum cru-
cible was observed.
When sheet-iron or a plate of zinc was substituted for the
platinum foil which was held in the flame, the current was
weaker. With iron it was about four-fifths, with zinc about two-
thirds of its amount with the platinum. This was equally true,
whether the aether burnt in the platinum crucible or in the iron
vessel ; in the latter case the diminution was proportionate.
To exhibit the current, it is not necessary to introduce metal
into the flame ; the same can be effected by bringing the moist
hand into it, or what is more convenient, a strip of paper satu-
rated with moisture. When, for instance, one end of the wire
was connected with the lamp, the other end being held in one
of my hands or in my mouth, the current could be developed in
die manner described. As was natural to expect, a less angle
was observed in the present case.
The magnitude of the resistance offered by the flame, in com-
parison with the not inconsiderable resistance of the 16,454 feet
of exterior wire, is exhibited in the following experiments. The
lamp No. 1 alone with the piece of platinum held in the flame
above it, gave an angle of 8°'3. The lamp No. 2 with its plate
of platinum gave an angle of 3°'8 -, and the lamp No. 3 with
its platinum gave a considerably less angle. When the lamps
No. 1 and No. 2 were placed one after the other like a galvanic
battery, the angle was 8°-4 ; and when all three were used in
this manner, the angle was only 2°*7. When, however, the
lamps 1 and 2 were both connected with one end of the wire of
the galvanometer, while the two pieces of platinum foil placed
over their flames were connected with the other end, an angle of
10°*3 was obtained; and when all three lamps were used, the
angle amounted to 11°* 7*.
* It is perhaps worth remarking, that the two arrangements of the lamps
liere spoken of correspond to two distinct arrangements of the galvanic
battery ; the first being used when an exterior resistance is to be overcome,
the second w^hen the resistance within the cells is to be diminished. Let^
be the strength of the current exhibited, e the electro-motive force, n the
number of cells, R the resistance within them, r the resistance without them;
in the former arrangement p would be expressed by the formula p^= ,
while in the latter ai-rangement we should have the formula »=—
The above experiments therefore show that the resistance of the flame itself
is great in comparison to the resistance of the exterior wire- — T.
646 M. W. HankePs Account of some Experiments
The investigation of these currents by means of the galvano-
meter carries along with it the doubt, as to whether the increase
of the angle is due to an increase of the electric tension between
the diflferent parts of the flame from which the electric fluid is
conducted, or to a diminution of the resistance within the flame.
It is therefore necessary to separate these quantities. This sepa-
ration is generally effected by the introduction of other known
resistances. To obtain a general notion of the electric tension
of the different portions of the flame, I have resorted to a some-
what shorter method, which consists in introducing the current
caused by the flame into a circuit in which another current of
known value circulates. Heretofore the circuit was composed
of the flame, the connecting wires and the galvanometer ; into
this I now introduced a bit of zinc and copper which dipped into
a vessel of water. Let this aiTangement of zinc and copper be
called an element. By means of the commutator, the current
developed by this element might be transmitted in the same
direction as the current due to the flame, or in an opposite direc-
tion. I will name the side to which the flame-current causes
the needle to move the positive side, and the opposite side the
negative.
When the lamp No. 1 was so regulated that its flame did not
quite reach the top of the chimney, and the platinum foil held at
a small distance above the latter in the inclined position already
mentioned, before the zinc and copper element was introduced
the angle due to the flame-current was not quite 10°. By intro-
ducing the element so that its current moved in the same direc-
tion as that proceeding from the flame, the angle increased some
degrees ; when the direction was reversed, the needle went back
to 5°. A similar result was observed when the chimney was
taken away and the flame increased at pleasure. In the case of
lamp No. 2, when the chimney was removed and the bellows set
in action, the position of the needle indicated that the direction
of the current was the same as before ; thus compelling the in-
ference that the electro-motive force of the flame (the electric
difference between its top and bottom) is greater than the electro-
motive force of the zinc and copper element. When, however,
two such elements were introduced, and the current which they
originated was directed against that proceeding from the flame,
the latter was overcome and the needle moved to the negative
side.
The deviations of the needle were different when the chimneys
were set upon the lamps. When the lamp No. 1 had its chim-
ney set on, the current of a single element was unable to com-
pete with the flame-current as long as the luminous portion of
the flame did not reach the full height of the chimney. When,
upon the Electricity of Flame. 547
however, the wick was raised by degrees, and the flame by this
means increased, the needle receded more and more towards Oj
and by continually increasing the flame, was caused to cross to
the negative side. In this case, therefore, the current of the
single copper and zinc element overcame that of the flame,
although both had to contend with the same amount of resist-
ance. This change in the direction of the needle must therefore
be referred to a change in the electro-motive force which origi-
nates the current. As the zinc and copper have remained un-
changed, the cause of the phsenomenon must be sought in a di-
minution of the electro-motive force of the flame. This diminu-
tion is without doubt due to the fact, that the flame when thus
increased acts against the inner surface of the chimney so as to
originate a number of conducting threads of flame between the
chimney and the platinum, which, owing to their shortness and
position in the flame, possess a greater power of conduction, but
a less tension at their extremities, than that existing between
the top and bottom of the flame. That the resistance to con-
duction in this state of the flame is very much decreased, may
be inferred from the magnitude of the negative angle. Even
this reversion of the angle could be brought about with a single
element when the chimney was removed, and a piece of platinum
was pushed sideways into the flame at a greater or less distance
above the wick, and then connected with the lamp ; for in this
case also the electric difference between the respective portions
of the flame which encompassed both pieces of platinum was less
than the difi'erence between the top and bottom of the flame.
When a platinum wire, which was smelted into a thin glass tube,
was introduced into the flame, and when the plate of platinum was
held a little above it, both being connected with the wires of the
galvanometer (the lamp was not in the circuit), an angle of 15°
was observed. By directing the current of the zinc and copper
element against this, the needle was brought down and set on
the negative side. When the flame was diminished until its
luminous point reached merely to the summit of the chimney,
the flame-current gave an angle of 20° ; which increase was cer-
tainly due, not to an increase of conductibility, but to a higher
tension. The opposition of the zinc and copper element reduced
this angle only to 14°.
These experiments furnish a convincing proof that the flame
itself is the birth-place of an electric current ; for if it merely
played the part of a conductor, then an increase in the conducti-
bility of a certain portion of the circuit could not cause the needle
to pass from the positive to the negative position.
The experiments prove further, that between the different
portions of the flame the powers of conduction, as also the elec-
548 M. R. Clausius on the Influence of Pressure
trie tensions, are very different. By plunging two platinum wires
into certain portions of the flame, we might even obtain a cur-
rent which passes, not from top to bottom, as in the cases here-
tofore described, but from bottom to top. On this point I will
remain for the present silent, as my intention at the commence-
ment was to limit myself to the simplest cases of the phse-
nomena.
LXXVIII. On the Influence of Pressure upon the Freezing of
Fluids. By R. Clausius*.
ly/I R. WILLIAM THOMSON has described an experimental
•i-'J- investigation, conducted by himselff, and originating
in a theoretic view entertained by his brother, James Thomson.
The latter had concluded, from the known principle of Camot,
that by an increase of pressure the freezing-point of water must
be lowered, which view was completely verified by experiment.
Some time ago I published a theoretic memoir J, in which
the principal part of Camot's law is retained, but altered in
one minor particular. This alteration rendered certain of the
conclusions heretofore deduced from the principle impossible,
while others remained valid ; the latter being those whose cor-
rectness or higli probability had been demonstrated by expe-
riment. Now as the above conclusion regarding the freezing-
point of fluids has also been substantiated experimentally, and
thus in a scientific point of view has obtained a greater signifi-
cance than one would be inclined at first sight to attribute to so
small a difi*erence, I feel myself called upon, in behalf of my
theory, to show that my alteration of Carnot^s principle is in no
way opposed to this result §. And applying at the same time
the original maxim which I have assumed, a new conclusion is
arrived at, which, although practically unimportant, on account
of the smallness of the numbers wliicli it embraces, deserves
nevertheless theoretic expression.
A lengthened analysis of the subject is not here necessary.
The considerations dwelt upon in my former paper regarding
the evaporation of a fluid, may be a})plicd almost vei'batim to the
freezing of the same. We have only to conceive the vessel im-
pervious to heat to be filled partly with a solid body and partly
with a fluid one, instead of, as in the former case, partly with a
* From PoggendorfF's Annalen, vol. Ixxxi. p. 168.
t Proceedings of the Royal Society of Edinburgh, February 1850; and
Phil. Mag., S. '6. vol. xxxvii. p. 123.
X Phil. Mag. S. 4. vol. ii. pp. 1, 102.
§ I need hardly mention that I have here no thought of disputing with
Mr. Thomson the priority of his ingenious application of the princijde of
Camot.
upon the Freezing of Fluids. 549
fluid and partly with a vaporiform body ; and then, instead of per-
mitting a fresh portion of the fluid to evaporate, to allow a por-
tion of it to freeze, &c.
One of the two principal equations deduced therefrom was— •
r=A(« + 0(s-<^)|; (Va)
and this holds good for the freezing also, p and t again denoting
the pressure and temperature, and or the volume of a unit of
weight of the fluid, whereas s denotes the volume of a unit of
weight of a solid body (instead of vapour, as in the former case),
and r the latent heat of the freezing (instead of the evaporation).
The latter, however, must be here taken as negative, because by
freezing, heat will be liber'ated, and not rendered latent. We
have therefore —
dt _ K{a + t)[s-a)
dp~ r ^ ^
Let the value of -r-, given by Joule in his last investigation* as
the most probable result of all his experiments, that is 423'55
(772 English), be here substituted, as also for a the number
273; further, with regard to the water, ^=0, r=79, o-«: 0*001,
and 5=0'001087 ; and, finally, let jo be expressed in atmospheres
pressing upon, a square metre, instead of in kilogrammes, we
then obtain —
^ = -0-00733,
dp
which may be regarded as equal to the value calculated by
James Thomson, and corroborated by William Thomson, namely
-00075.
The other principal equation deduced from the maxim on the
equivalence of heat and work was —
| + c-A=A(.-.)|. . . . . (III.)
To apply this to the case of freezing, besides their former
meaning, w^e must regard c and h as two quantities which diffbr
from the specific heat of the fluid and solid body only so far as
they express, not the heat which must be imparted to a body
when it is simply warmed, but that which is necessary when
the pressure varies with the temperature in the manner indi-
cated by equation (I.). This difi'erence cannot be considerable,
as Regnaultf has found that water, by an additional pressure
* Phil. Trans, of the Royal Society of London for the year 1850, Part L
p.61.
t Mem. de VAcad. de VInst. de France, vol. xxi. Mem. VII.
550 On the Influence of Pressure upon the Freezing of Fluids.
of 10 atmospheres, does not increase Ath of a degree Cent, in
temperature; besides this, as the differences of c and h take
place both in the same sense, and hence in the difference
c— A are subtracted, we can set with a near approach to accu-
racy for c—h the difference of both specific heats simply. If
the value of -j- estimated from (I.) be substituted in (III.)>
dr
and if the sign of -j- be changed like that of r in the former case,
we have — dr , . f /nx
— =c-A-f— — . ...... (2)
dt a-\-t ^ '
From this we must conclude, that when the freezing-point
changes, the latent heat must also change; for water is c=l,
and, according to Person*, /i=0'48. Hence we have —
dr
^=0-52 + 0-29 =0-81;
at
that is to say, when the freezing-point of water is lowered by
pressure, the latent heat decreases 0"81 for every degree.
We must not confound this result with that already expressed
by Personf. From the circumstance that the specific heat of
ice is kss than that of water, the latter concluded with great
probability, that when the freezing-point, without increasing the
pressure, is simply lowered by preserving the fluid perfectly mo-
tionless, the latent heat must then be less than at 0°. This
decrease may be expressed by the equation —
dr ,
the above equation (2) therefore shows, that when the freezing-
point is lowered by pressure, the latent heat, besides the change
due to the last-mentioned cause, suffers a still further diminution
expressed by the quantity ; this in the case of water is =0*29,
and it is this which corresponds as equivalent to the exterior
work accomplished.
The late obsei-vation of Person J, that ice does not melt com-
pletely at a definite temperature, but becomes softer immediately
before it reaches the melting-point, I have left unnoticed, as its
introduction would merely render the development more difficult,
without serving any important end ; for the decrease of latent
heat which corresponds, as equivalent, to the produced work,
must be independent of the little irregularities which may take
place dui-ing the melting.
♦ Comptes Rendus, vol. xxx. p. 526. t Ibid vol. xxiii. p. 336.
X Ibid. vol. xxx. p. 526.
[ 551 ]
LXXIX. Applications of the Principle of Mechanical Effect to the
Measurement of Electro-motive Forces, and of Galvanic Resist-
ances, in absolute Units. By Prof. W. Thomson*.
1. TN a short paper "On the Theoiy of Electro -magnetic In-
A duction," communicated to the British Association in
1848t^ I demonstrated that "the amount of mechanical effect
continually lost or spent in some physical agency (according to
Joule, the generation of heat) during the existence of a galvanic
current in a given closed wire_, is, for a given time, proportional
to the square of the strength of the current f^ and I showed that
Neumann's beautiful analytical expression for the electro-motive
force experienced by a linear conductor moving relatively to a
magnet of any kind, is, in virtue of this proposition, an imme-
diate consequence of the general principle of mechanical effect.
At that time I did not see clearly how the reasoning could be
extended to inductive effects produced by a magnet (either of
magnetized matter or an electro-magnet) of varying power upon
a fixed conductor in its neighbourhood, or to " the induction of
a varying current on itself ;'' but I have recently succeeded in
making this extension, and found that the same general principle
of mechanical effect is sufficient to enable us to found on a few
elementaiy facts, a complete theory of electro-magnetic or electro-
dynamic induction. The present communication, which is ne-
cessarily very brief, contains some propositions belonging to that
part of the theory which was communicated to the British Asso-
ciation ; but it is principally devoted to practical applications
with reference to the measurement of electro-motive forces arising
from chemical action, and to the system of measurement of
'^ galvanic resistance in absolute units,'' recently introduced by
Weber {.
2. Prop. I. — If a current of uniform strength be sustained in a
linear conductor, and if an electro-motive force act in this con-
ductor in the same direction as the current, it will produce work
at a rate equal to the number measuring the force multiplied by the
number measuring the strength of the current.
3. Let the electro-motive force considered be produced by the
motion of a straight conductor of unit-length, held at right
angles to the lines of force of a magnetic field of unit-intensity,
and carried in a direction perpendicular to its own length and to
those lines of force. The velocity of the motion will be numeri-
* Communicated by the Author.
t Report, 1848; Transactions of Sections, p. 9.
X " Messungen galvanischer Leitungswiderstande nach einem absoluten
Maasse ; " von Wilhelni Weber. — Poggendorff's Annalen, March 1851,
No. 3.
552 Prof. Thomson on the Applications of Mechanical Effect
cally equal to the clcctro-motivc force, wliich will be denoted by
F, thus inductively produced, since the unit of electro-motive
force adopted by those who have introduced or used absolute
units in electro-dynamics is that which would be produced in the
same circumstances if the velocity of the motion were unity. If
the ends of the moveable conductor be pressed on two fixed con-
ductors, connected with one another either simply by a wire, or
through any circuit excited by electro-motive forces, so that a
cuiTcnt of strength 7 is sustained through it, it will experience
an electro-magnetic force in a direction perpendicular to its own
length and to the lines of magnetic force in the field across
which it is moving, of which the amount will be the product of
7 into the intensity of the magnetic force, or, since this is unity,
simply to 7*. The motion of the conductor being in that line,
the force will be directly opposed to it when the current is in the
direction in which it would be if it were produced solely by the
electro-motive force we are considering; and therefore, if we
regard 7 as positive when this is the case, the work done in
moving the conductor during any time will be equal to the pro-
duct of 7 into the space through which it is moved, and will
therefore in the unit of time be F7, since F is numerically equal
to the velocity of the motion. But this work produces no other
efiect than making the electro-motive force act, and therefore
the electro-motive force must produce some kind of efiect me-
chanically equivalent to it. Now if an equal electro-motive force
were produced in any other way (whether chemically, thermally,
or by a common frictional electrical machine) between the same
two conductors, connected in the same way, it would produce
the same efi'ects. Hence, universally, the mechanical value of
the work done in a unit of time by an electro-motive force F, on
a circuit through which a current of strength 7 is passing, is F7.
4. If the algebraic signs of F and 7 be different, that is if the
electro-motive force act against the direction of the current, the
amount of work done by it is negative, or effect is gained by
allowing it to act. This is the case with the inductive re-
action, by which an electro-magnetic engine at work resists the
current by which it is excited, or with the electrolytic resistance
experienced in the decomposition of water.
5. The application of the proposition which has just been
proved, to chemical and thermal electro-motive forces is of much
imoortance. I hope to make a communication to the Royal
Society of Edinburgh before the end of this year, in which, by
the application to thermal electro-motive forces, the principles
* This statement virtually expresses the definition of the " strength " of
a current, according to the electro-magnetic unit now generally adopted.
to the Measurement of Electro-motive Forces. 553
explained in a previous communication* '^On the Dynamical
Theory of Heat/^ will be extended so as to include a mechanical
theory of thermo-electric currents. The application to chemical
electro-motive forces leads immediately to the expression for the
electro-motive force of a galvanic battery, which was obtained by
virtually the same reasoning, in another paper published in this
Volume of the Magazine f (p. 429) : for if e be the electro-chemi-
cal equivalent of one of the substances concerned in the chemical
action ; if ^ be the quantity of heat evolved by as much of the
chemical action concerned in producing the current as takes place
during the consumption of a unit of mass of this substance ; and
if J be the mechanical equivalent of the thermal unit, the me-
chanical value of the chemical action which goes on in a unit of
time will be iOey, and this must therefore be equal to Yy, the
work done by the electro-motive force which results. Hence
we have
which is the expression given in the paper referred to above, for
the electro-motive force of a galvanic battery in absolute measure.
6. In applying this formula to the case of DanielPs battery, I
used a value for 6 derived from experiments made by Mr. Joule,
the details of which have not yet been published, but which I
believe to have consisted of observations of phsenomena depend-
ing on the actual working electro-motive forces of the battery.
I am now enabled to compare that value of the thermal equiva-
lent, with the results of observations made directly on the heat
of combination, by Dr. Andrews J, who has kindly communicated
to me the following data : —
(1.) The heat evolved by the (3.) The heat evolved by the
combination of one grain of zinc combination of the equivalent quan-
with gaseous oxygen amounts to tity, '9/27 of a grain of copper, with
1301 units. oxygen, amounts to
588-6 units.
(2.) The heat evolved by the (4.) The heat evolved by the
combination of the 1246 grains of combination of the 1'221 grains of
oxide thus formed with dilute sul- oxide thus formed, with dilute sul-
phuric acid'amounts to phuric acid, amounts to
369 units. 293 units.
Hence the thermal equivalent of the whole chemical action which
goes on in a Daniell's battery during the consumption of a grain
* March 1851. Published in the Transactions, vol. xx. Part II.
t "On the Mechanical Theory of Electrolysis."
X Published in his papers "On the Heat disengaged during the Com-
bination of Bodies with Oxygen and Chlorine" (Phil, Mag. vol. xxxii.),
" On the Heat disengaged during MetaUic Substitutions" (Phil. Transac-
tions, Part I. for 1848), "On the Heat developed during the Combination
of Acids and Bases" (Trans. Royal Irish Academy, vol. xix. Part II.), &c.
554 Prof. Thomson on the Applications of Mechanical Effect
of zinc is
1301 + 369-(588-6-|-293), or 788-4 . . . (I.):
the thermal equivalent of the part of it which consists of oxida-
tion and deoxidation alone is
1301-588-6, or 712*4 . . . (II.)
The thermal equivalent which I used formerly is
769 ... (III.)
If the opinion expressed by Faraday, in April 1834 (Exper.
Researches, 919), with reference to the galvanic batteries then
known, that the oxidation alone is concerned in producing the
current, and the dissolution of the oxide in acid is electrically
inoperative, be true for DanielPs battery, the number (II.) is the
thermal equivalent of the electrically effective chemical action.
Joule's number (III.) is considerably greater than this, and falls
but little short of (I.), the thermal equivalent of the whole che-
mical action that goes on during the consumption of a grain of
zinc. If we take successively (I.), (II.), (HI.) as the value of 6,
and take for e and J the values -07284 and 44758, which were
used in my former paper, we find the following values for the
product J^e : —
(I.) 2570300, which would be the electro-motive force (in Bri-
tish absolute units) of a single cell of DanielPs
battery if the whole chemical action were elec-
trically efficient.
(II.) 2322550, which would be the electro-motive force of a
single cell of DanielFs battery if only the oxida-
tion and deoxidation of the metals were elec-
trically efficient.
(III.) 2507100, which is the electro-motive force of a single cell
of DanielPs battery, according to Joule's experi-
ments.
7. The thermal equivalent of the whole chemical action in a
cell of Smee's battery (zinc and platinized silver in dilute sul-
phuric acid), or of any battery consisting of zinc and a less
oxidizable metal immersed in dilute sulphuric acid, is found by
subtracting the quantity of heat that might be obtained by burn-
ing in gaseous oxygen the hydrogen that escapes, from the quan-
tity of heat that would be obtained in the formation of the sul-
phate if the zinc were oxidized in gaseous oxygen instead of by
combination with oxygen derived from the decomposition of
water. Now the quantity of hydrogen that escapes during the
consumption of a grain of zinc is g^^ of a grain (if 32-53, which
corresponds to the equivalents used by Dr. Andrews, be taken
to the Measurement of Electro-motive Forces, 555
as the equivalent of zinc, instead of 32*3 which I used in my
former paper). According to Dr. Andrews^ experiments, the
combination of this with gaseous oxygen would evolve
3^!^ X 33808, or 1039-3 units of heat.
Hence the thermal equivalent of the whole chemical action cor-
responding to the consumption of a grain of zinc in Smee^s
battery is
1301 +369~1039-3, or 630-7 (I.)
The equivalent of that part which consists of the oxidation of
zinc and the deoxidation of hydrogen is
1301-1039-3, or 261*7 (XL)
Hence (I.) if the whole chemical action be efficient in producing
the current, the electro-motive force is 2056200.
(II.) If only the oxidation and deoxidation be efficient, the
electro-motive force is 853190.
The external electro-motive force (or the electro-motive force
with which the battery operates on a very long thin wire connect-
ing its plates), according to either hypothesis, would be found by
subtracting the "chemical resistance *^^ due to the evolution of
hydrogen at the platinized silver, from the whole electro-motive
force : but, on account of the feeble affinity of the platinized sur-
face for oxygen, it is probable that this opposing electro-motive
force, if it exist at all, is but very slight.
(III.) The external electro-motive force of a single cell of
Smee's battery is, according to Joule^s experimentsf, -65 of that
of a single cell of DanielPs ; and therefore if we take the prece-
ding number (III.), derived from his own experiments, as the
true external electro-motive force of a single cell of DanielPs,
that of a single cell of Smee^s is
1,629,600.
This number is nearly double that which was found for the elec-
tro-motive force on the supposition that the oxidation and de-
oxidation alone are electrically efficient ; but it falls considerably
short of what was found on the suppositions that the whole che-
mical action is efficient, and that there is no " chemical resist-
ance.^^
8. It is to be remarked that the external electro -motive force
determined for a single cell of Smee's, according to the pre-
ceding principles, by subtracting the " chemical resistance '' from
the value of J^e, is the permanent working extevuBl electro- motive
force. The electro-statical tension, which will determine the
* See foot-note on § 6 of my paper on the Mechanical Theory of Elec-
trolysis.
t Phil. Mag. 1844, xxiv. p. 115, and Dove's Rep. vol. viii. p. 341.
556 Prof. Thomson on the Applications of Mechanical Effect
initial working cxtcraal electro-motive force, depends on the pri-
mitive state of the platinized silver plate. It could never be
greater than to make the initial working force be
J X 1670 X e, or 5441500,
corresponding to the combination of zinc with gaseous oxygen,
and of the oxide with sulphuric acid. It might possibly reach
this limit if the platinized surface had been carefully cleaned,
and kept in oxygen gas until the instant of immersion, or if it
had been used as the positive electrode of an apparatus for de-
composing water, immediately before being connected with the
zinc plate ; and then it could only reach it if the whole chemical
action were electrically efficient, and if there were no " chemical
resistance'' due to the affinity of the platinized surface for
oxygen.
9. It is also to be remarked, that the permanent working elec-
tro-motive force of a galvanic element, consisting of zinc and a
less oxidizable metal immersed in sulphuric acid, can never exceed
the number 2056200, derived above from the full thermal equi-
valent for the single cell of Smee's, since the chemical action is
identical in all such cases, and the mechanical value of the ex-
ternal effijct can never exceed that of the chemical action. In a
pair consisting of zinc and tin, the electro-motive force has been
found by Poggendorff * to be only about half that of a pair con-
sisting of zinc and copper, and consequently less than half that
of a single cell of Smee's. There is therefore an immense loss
of mechanical effect in the external working of a galvanic battery
composed of such elements ; which must be compensated by heat
produced within the cells. I believe with Joule, that this com-
pensating heat is produced at the surface of the tin in con-
sequence of hydrogen being forced to bubble up from it, instead
of the metal itself being allowed to combine with the oxygen of
the water in contact with it. A most curious result of this
theory of "chemical resistance" is, that in experiments (such
as those of Faraday, Exp. Researches, 1027, 1028) in which an
electrical current passing through a trough containing dilute
sulphuric acid, is made to traverse a diaphragm of an oxidizable
metal (zinc or tin), dissolving it on one side and evolving bub-
bles of hydrogen on the other; part (if not all) of the heat of com-
bination will be evolved, not on the side on which the metal is
eaten away, but on the side at which the bubbles of hydrogen
appear. It will be very interesting to verify this conclusion, by
comparing the quantities of heat evolved in two equal and similar
electrolytic cells, in the same circuit, each with zinc for the posi-
♦ " Berl. Acb. 46, 242," Pogg. Ann., Ixx. 60. Dove's Repertorium,
vol. viii. p. 341.
to the Measurement of Electro-motive Forces. 557
tive electrode,, and one with zinc, the other with platinum or
platinized silver for the positive electrode. The electro-motive
force of the latter cell would be sufficient to excite a current
through the circuit, but it might be found convenient to add
electro-motive force from some other source*.
10. Prop. II. The resistance of a metallic conductor, in terms
of Weber' s absolute unit, is equal to the product of the quantity of
heat developed in it in a unit of time by a current of unit strength,
into the mechanical equivalent of a thermal unit.
11. If H denote the quantity of heat developed in the con-
ductor in a unit of time, by a current of strength 7, the me-
chanical value of the whole effect produced in it will, according
to the principles established by Joule, be JH. But this effect
is produced by the electro-motive force, F, and therefore, by
Prop. I., we have
JH = F7.
Now, according to Ohm^s original definition of galvanic resist-
ance, if k denote the resistance of the given conductor, we have
F
If the electro-motive force and the strength of the current be
measured in absolute units of the kind explained above, the
number k, expressing the resistance in this formula, will ex-
press it in terms of the absolute unit introduced by Weber.
Using the value ky derived from this, for F, in the preceding
equation, we have
This equation expresses the law of the excitation of heat in the
galvanic circuit discovered by Joule; and if we take 73=!, it ex-
presses the proposition to be proved.
12. In Mr. Joule^s original paper on the, heat evolved by
metallic conductors of electricity f, experiment! are described, in
* An examination of the thermal eflPects of a current through four equal
and similar vessels containing dilute sulphuric acid, and connected by means
of electrodes of zinc and platinum, varied according to the four permuta-
tions of double zinc, double platinum, zinc-platinum, platinum-zinc, in one
circuit, excited by an independent galvanic battery or other electromotor,
would throw great light on the theory of chemical electro-motive forces and
resistances. Vessels containing electrodes of other metals, such as tin,
variously combined, and direct and reverse cells of Darnell's battery, might
all be introduced into the same circuit. If the exteriors of all the cells
were equal and similar, the excesses of their permanent temperatures above
that of an equal and similar cell in the neighbourhood, containing no source
of heat within it, would be very nearly proportional to the rates at which
heat is developed in them.
t Proceedings of the Royal Society, Dec, 17, 1840; Philosophical Ma-
gazine, vol. xix. (Oct. 1841), p. 260.
Phil. Mag. S. 4. No. 14. Buppl. Vol. 2, 2 P .
658 Prof- Thdmaon on the Applications of Meclmmcal Effect
which the strengths of the currents used arc detennined in ab-
•olute measure, the unit employed being the strength which a
current must have to decompose 9 grains of water in an hour of
time. But the electro-chemical equivalent of water, according
to the system of absolute measurement introduced by Weber, is,
in British units, very nearly -03, and therefore a current of unit
strength would decompose 72 grains of water in an hour. Hence
Joule's original unit is very exactly ^th of the British electro-
magnetic unit for measuring current electricity. By using the
formuUblmng nuot fii hfis / jjj -^ sib no eln^mn >
.. .^..lii R vd b3-iJj?.B9nT iaoTj^?=,-^*. 1 VfrfOTom ^Ai no x
d^Bs nr ^haB. ^-loionhno*) orlj jliiToult [)!?^ixf >(:// -lOj^^firon/r/to
and taking for 7 ©ne^eighth the number of Mr j Joule's "de-
grees of current/' for H the quantity of heat (measured by
grains of water raised 1° Cent.) evolved by the current through
the conductor experimented on; and for J the value 44758; I
have foundi loJonbiioi) i»jt^^ 13240000"^ M^^ '^^^ ^^^ ^^ tluj^ui
-MM.Mii>j iJt 'i, .. .;..'i -i'li-nw, -idi')i\ ^i\Vi'i\ i\l
as the absolute resistance of a certain wire used by Mr. Joule
for an absolute standard of resistance in the experiments on the
heat evolved in electrolysis, described in the second part of the
same paper*. ^ ; ■ i
13. The '' specific resistance" of a metal referred to unity of
volume, may be defined as the absolute resistance of a unit
length of a conductor of unit section ; and the specific resistance
of a metal referred to unity of mass, or simply '' the specific re-
sistance of a metal" (since the term, which was introduced by
Weber, is, when unqualified, so used by him), is defined as the
absolute resistance of a conductor of uniform section, and of
unit length and unit weight. Hence, since the resistance of
conductors of similar substance are inversely proportional to
their sections, and directly proportional to their lengths, we have
' km
oil ^ = -j2>
ifi; 'to dl/^. hill, i^i:. • )ii u1 li'itnV yi'u/ t. ito S- ? '■'■
'' * The 'iJir»i experiments £00111 ivvliioh the Aifmbwiil the text was de-
duced as a mean result (described in §§ 25, 26, 27 of the paper, Phil. Mag.
S. 3* vol. xix. p. 266), lead separately to the following values for the resist-
^■IIOBp»**tJii on tjwiJ ,i97'jv^o:i 13260000 '^' Ji .iioirfi il'jiij n
.(MR-c/Don dlirr H^t'rn zhl "io 13360000 'f'"''J'>f'' ^^ .^^^■(^^ aV
none of w1i\'ci['S¥*^'b'f ils'fatflcli as ^Vth from the mean givfeiiln'^Hetdit.
t By means of this I have found 4*1 for the specific resistance of cop-
per, according to the statement made in § 21 of Mr. Joule's paper, that
V:><il\'3: fQ f]^Q Measurement of Electro-motive Fc^ceh'^^ 559
if / be the length, co the area of the section, and m the mass (or
weight) of a conductor, k its absolute resistance, and €r„ and a
the specific resistances of its substance referred respectively to
unity of volume and to unity of mass. ojiojI) ;»ii) iufl .-)nri
14. The absolute resistance of a certain silver wire, and of
a column of mercury contained in a spiral glass tube, may be
determined from experimental data extracted from a paper of
Mr. Joule^s laid before the French Institute [Comptes Rendus,
Feb. 9, 1846), and communicated to me by the author. In
four experiments on the silver wire, and in four similar expe-
riments on the mercury tube, a current measured by a tangent
galvanometer was passed through the conductor, and, in each
experiment, the quantity of heat evolved during ten minutes was
determined by the elevation of temperature produced in a mea-
sured mass of water, the temperature of the conductors during
all the experiments having been nearly 50° Fahr. The mean
result of the four experiments on each conductor is expressed
in terms of the square root of the sum of the squares of the tan-
gents of the galvanometer-deflections, and the mean quantity of
heat evolved in ten minutes. The weight of the silver wire in
air and in water, the weight of the mercury contained in the
glass tube, and the exact length of each conductor, were deter-
mined a short time ago, at my request, by Mr. Joule, and the
areas of the sections of the conductors have been deduced. The
same galvanometer having been used as was employed in the expe-
riments on electrolysis, referred to in the " Note on Electro-che-
mical Equivalents," contained in this Volume of the Magazine
(p. 429), and the experiments at present referred to having also
been made at Manchester in 1845, the strength of the current
in absolute measure is found by multiplying the tangent of de-
flection by -28186. The various experimental data thus obtained
are as follows : —
-«0A
his standard conductor was "10 feet long and '024 of an inch thick;'* but
there must be some mistake here, as it will be seen below that this is about
double what we might expect it to be. I have found 2*17 for the specific
resistance of copper referred to unity of volume, according to the experi-
ment described in § 9, on a wire stated to be 2 yards long and -i^i^n of an
inch thick; and 178 and 1*98, according to the experiments described in
§§9 and 11, on a wire stated to be 2 yards long and -gLth of an inch thick;
also 77 for that of iron, in a wire stated (§ 11) to be two yards long and
:jVth of an inch thick. It is to be remarked, however, that no attempt was
made by Mr. Joule to determine the sections of his wires with acciuracy,
and that the " thicknesses" are merely mentioned in round numbers, as
descriptive of the kinds of wire used in his different experinieii^.^ .^^ ^^^^
iiidi ^lyqitq g'aiwot /iM 'to iS: <J ai •^hnln JnoniaiBte? 3ifJ o* ^nibTOooB ^lyq
2 P 2
560 Prof. Thomson on the Applications of Mechanical Effect
Conductor.
Length
in feet.
Mouin
grains.
Sectional area in
•quare feet.
Mean correct-
ed tangent of
deflection.
Mean strength
of current in
absolute units.
Mean quantity of
heat produced in
10 minutes.
SUver \dre..
Mercury in
glass tube
271
} ^*
434-51
1511-5
•0000054462
•000048119
1-4526
•40943
19375 grs. of water
raised 1°-7718 C.
in temperature.
The resistance of the mercury conductor
was found to be -74964 of that of the sUver
wire.
Taking as the thermal unit the quantity of heat required to
raise the temperature of a grain of water by 1° Cent., we find
5 7*2 13 as the heat generated in the silver wire in one second,
of which the mechanical equivalent is 44758 x 57*213. Divi-
dmg this bjj the SQ^ of the strength of the cupent^weftad
^Mo!>..!m,' "h '■:' 15276000 '\'---lj-''i''.l
for the absolute resistance of the silver wire ; and by multiplying
by '74964, we deduce
11451000
for the absolute resistance of the mercury conductor. Multi-
plying each absolute resistance by the sectional area of the con-
ductor to which it coiTcsponds, and dividing by the length ; and
again, multiplying each resistance by the mass, and dividing by
the square of the length, we obtain the following results with
reference to the specific resistances of silver and mercury at about
10° Cent, of temperature.
Metal.
Specific resistance
referred to units of
volume.
" Specific resistance."
Silver
1-9028
11913
8671500
648410000
Mercury
A .m
16* The ^'conducting powers ^^ of metals, as ordinarily de-
fined, are inversely proportional to their specific resistances re-
fen-ed to unity of volume. Hence, according to the preceding
results, the conducting powers of silver and mercury at about
10° Cent, of temperature are in the proportion of 1 to •01744.
According to the experiments of M. E. Bccquercl (Dove's Reper-
torium, vol. viii. p. 193), the conducting powers of silver and
mercury at 0^ Cent, are in the proportion of 1 to •017387; and
at 100^ Cent., of 1 to -022083 : at 10° Cent, they must there-
fore be nearly in the proportion of 1 to '01786, which agrees
veiy closely with the preceding comparative result. Again, accord-
ing to M. BccquerePs experiments, the conducting powers of
silver and copper are, —
■^^sV^
ib the MeasurenMfdfilledW'mtive Forces. 561
at 0° in the proportion of 1 to '91617,
at 100° ... 1 to -91030,
and therefore
at 10'
1 to '915.
mm
Hence the specific resistance of copper at about 10° Cent. refeBv
red to unity of volume, may be found by dividing that of silver
by '915 ; and from the preceding result, it is thus found to be
2*080. Multiplying this by 3810500, the weight in grains of a
cubic foot of copper, (found by taking 8*72 as the specific gra-
vity of copper,) we obtain for the *' specific resistance ^^ of copper
the value 7925800.
16. Weber, in first introducing the measurement of resistances
in absolute units, gave two experimental methods, both founded
virtually on a comparison of the electromotive forces with the
strengths of the currents produced by them, in the conductors
examined ; and he actually applied them to various conductors^,
and obtained results which, reduced to British units, are shown
in the following table. The first four numbers in the second
column are deduced from M. Weber^s results, on the hypothesis
that the specific gravity of each specimen of copper is 8*72.
The only numbers given on the authority of M. Weber are the
first four of the column headed "Specific resistance.^^ The
specific resistances derived above from Mr. Joule^s experiments
are shown in the same table for the sake of comparison.
Quality of metal, &c. —■
Specific resistance
referred to unity of
volume.
" Specific
resistance."
No. 1. Jacobi's copper wire
2-851
10870000
No. 2. Kirchhoff' s copper wire
No. 3. Weber's copper wire
2-365
2-303
2-079
9225000
8778000
7924000
7926000
8671000
648400000
No. 4. Wire of electrolytically precipi- 1
tated copper J
No. 5. Copper at about 10° Cent., accord- 1
ing to Joule and Eecquerel J
No. 6. Joule's silver wire at about 10° C...
No. 7. Mercury at about 10° Cent
2-080
1-903
1191
The great discrepancies among the first four numbers of the
third column, each of which is probably correct in three of its
significant figures, show how very much the specific resistances
of the substance of different specimens of copper wire may differ
from one another. The specific resistance of copper (No. 5),
deduced indirectly from Joule's absolute by means of BecquerePs
relative determinations, agrees very closely with that of the elec-
trolytically precipitated copper (No. 4) expei^imented on by
^gjjgj.^ Hi IJlpjUJ IjLtH Vjdi/
ifiite Royal Society.
17*. It is very much to be desii-ed that Weber's direct process,
and the indirect method founded on estimating, according to
Joule's principles, the mechanical value of the thermal effects of
a galvanic current, should be both put in practice to determine the
absolute resistance of the same conductor, or that the resistance
of two conductors to which the two methods have been separately
applied, should be accurately compared. Such an investigation
could scarcely be expected to give a more approximate value of
the mechanical equivalent of a thei^nal unit than has been already
found by means of experiments on the friction of fluids ; but it
would afford a most interesting illustration of those principles
by which ]\Ir. Joule has shown how to trace an equivalence be-
tween work spent and mechanical effect produced, in all physical
agencies in which heat is concerned.
f I J / J 1 1 1
Nov. 19, 1851. t. ,. . .. ^. .-r r.
fli 3TU.1 LXXX. Proceedings of Learned Societies,
: e-'^Lf ^Ir ^niiqH m .n^'uiS^OYAL SOCIETY. ' i^
[Continued from p. 600.]
*'/^N the Mean Temperature of the Observatory at Highfield
^^ House, near Nottingham, from the year 1810 to 1850."
By Edward Joseph Lowe, Esq., F.R.A.S. Communicated by Mar-
shall Hall, M.D., F.R.S.
The object of the author in this communication is to connect the
series of thermometrical observations made by the late Matthew Need-
ham, Esq., at Lenton House, at the distance of only 200 yards from
the observatory of Highfield House, with those made by himself from
184'2 to the present time at the latter place. He procured Mr. Need-
ham's observations from the Committee of the Bromley House Li«
brary, Nottingham, and also the instrument with which they were
made, and which, upon comparison with his own standard, was found
by Mr. Glaisher to be correct.
Mr. Needhara's observations were registered at 8 a.m. and 1 1 p.m.,
and to the monthly means of these records corrections have been
applied to convert them into mean monthly values. Those made by
the author were registered at 9 a.m. and 9 p.m., and these, together
with the highest and lowest readings of self- registering thermometers,
have been subjected to the same process.
The folloM ing tables deduced from the observations are given in
the paper: —
1. The meatt t^Aiperatiireo^ tid^li month at Highfield House from
tSlOto 1850. ' <f ^^•>«H'nr — .,[^ U. ^'Muu-vnruv^^ ^^1^ i.^ -;:ra ,-■'
('From this table iW^ded^ddd tli'^ rt^feft't^rtipf^kure bf'each moiith
ffom all the observations, viz.
• '^January 36°-2; February 3 8°-9 ; March 42^4; April 47^*6; May
Royal Society,^ 5j$^
Sa^-G; June 58°-7 ; July 61°-i ; August ^05^2 ; September^ 5S'':6i
October 50°-0 ; November 42°-9 ; December 39°-l. lir bn;
2. The highest and lowest monthly mean temperature in^^everv
ar, from 1810 to 1850, wM the Mount <^ $#6^600^ Vfifiin-
year
perature. ' ,
"^,From this table it appears that the coldest month in the year has
occurred in January 22 times ; in February 10 times; in March once ;
and in December 8 times. -'->."ii^qiHoa vloiu-ju'^:)); x.i iiljioiis .boiiqcp
The hottest month in the j'^ar has'ddcni'red in J«nfe'5<tiraefe^ii»
July 26 times; in August 12 times; and in September once. ; ; odi
The coldest month in the whole pefiiod fOCQ^rred i«:Ja»u^iryii8Wb'i
the mean temperature being 26°-8. ..-n^y'iotiii teofii r iri>>fti^ hhuri^
The hottest month during the whol^g^i(^^C5:|i^/jffd.j^J}^Ijyff^
the mean temperature being 68°-8. ,\. ,j,^,^,^, f,,,,. k,.,.,.^ -f.,^^,,,' j.,,,,.,yi
The means of all the differences between the hottest ^and'cdlaest
month in every year is 27°'2 : the least difference occurred in 1828,
viz. 21°*3; the greatest difference in 1814, viz. S5°*0.
3. The excess of the monthly mean temperature in every year,
above the temperature of the month from all the years.
The means of the numbers in each column of this table, taken
without regard to sign, gives the variability of the temperature in
spring 2°*1 ; in summer l°-7; in autumn 2°'0 ; in winter 3°*0.
The greatest difference in the monthly means in spring is 11°'9 ;
in summer 12°*5 ; in autumn 13°*9; in winter 18°'3.
Ijj.The coldest year in this series was 1814, when the mean annual
temperature was only45°*0; the hottest ye^r.yy^as, l§i6^.^e m§an
annual temperature being 51°-4. ;^^j Ha'«ot [rl/s^/ha vd
4. The mean temperature in every month iii|83|C'c^ai^ei^^j||^I
10 years, and for the whole year. , 'tiit to ioyjdo .'>dr '
5. The mean temperature, |fiiq\ia^|€^^^pf,^i(^4^^q^^yf^^^^
of 10 years. uH.-ih r»(i .tn .-muM aoiiv-)J in ..fwf rrn .^
.jjFrom this it is stated that the mean temperature of the 1st quarter
jg 39°-5 ; of the 2nd, 53°*3 ; of the 3rd, 59°-3 ; of the 4th, 44°-0.
..V 6. The mean temperature in spring, ^^mm^Yi ^^f^TO i^9A)^^ft('f F?
in. successive groups of 10 years. ,» .,;,), Iwin .fnnd>;(Tftto/ .vrrrrrf
From this it is concluded that the mean temperature of spring is
47°-8 ; of summer 60°-0 ; of autumn 49°*9 ; of winter 38°1.
Cold springs occurred in 1810, 12, 14, 16, 17, 37, 38, 39, 42, 45,
49 and 50; and the mean of the temperatures of these springs is
45°'5. The coldest spring was that of 1837^ the meft^. temperature
being only 43°-3.
Hot springs occurred in 181 1, 15, 19, 22, 23, 27, 28, 30, 31 and
41 ; and the mean of the temperatures of these springs is 50°'4 : the
hottest spring was that of 1841, the mean temperature being as high
as51°-4.
^y.Cold summers occurred in 1816, 17, 21, 23, 41, 43 and 49; and
the mean of the temperatures of these summers is 58°*0. The cold-
est summer was that of 1816, the mean temperature being only
57°'3.
v^lHot summers occurred in the years 1818, 24, 26, 31, 46 and 47;
564 Royal Society,
and the mean of the temperatures of these summers is 64«°'0. The
hottest summer was that of 1846, the mean temperature being as high
as 65°-0.
Cold autumns occurred in the years 1814, 16, 20, 29, 36, 37, 38,
42, 44, 45, 49 and 50 ; and the mean of the temperatures of these
autumns is 47°*8. The coldest autumn was that of 1849, the mean
temperature being only 47°'0.
Hot autumns occurred in the years 1810, 11, 18, 21, 27, 28, 40
and 46 ; and the mean of the temperatures of these autumns is 52°*3.
The hottest autumn was that of 1818, the mean temperature being
as high as 54°*5.
Cold winters occurred in 1814, 16, 20, 23, 30, 38, 41, 45 and 47 ;
and the mean of the temperatures of these winters is iJ4°'4. The
coldest winter was that of 1814, the mean temperature being only
S2°-7.
Hot winters occurred in 1822, 24, 28, 34, 35, 46, 48 and 49 ; and
the mean of the temperatures of these winters is 41°'5. The hottest
winter was that of 1834, the mean temperature being 43°*3.
" On Depressions of the Wet-bulb Thermometer during the Hot
Season at Ahmednuggur, in the Deccan." By Colonel Sykes, F.R.S.
&c.
The author states that he is indebted to Major William Coghlan
for the tables of hourly depressions of the wet-bulb thermometer
during the months of March and April of the present year, which
form the subject of this communication, and which are a necessary
supplement to his paper recently published in the Philosophical
Transactions. The observations at Ahmednuggur, lat. 19° 05'
49" N., long. 74° 48' 10", elevation above the sea 1911 feet, which
were undertaken by Dr. Forbes Watson, commenced on the 18ih
of March, and were continued to the 14th [of April inclusive.
They were made hourly from 6 a.m. to 9 p.m., giving 16 hourly re-
cords daily ; but on the 24th and 29th of March, and on the 4th,
8th and 10th of April, they were continued throughout the twenty-
four hour?. The instruments employed were a dry- and a wet-bulb
thermometer, by Adie, perfectly alike and giving precisely the same
indications when both were dry, and a self-registering thermometer.
They were suspended on a platform attached to a window under the
verandah of the house, with a N.W. exposure, and were protected
from radiation and reflexion of heat from the ground. As, from
some preliminary observations, it appeared that the depression of the
wet-bulb varied in every case with the intensity and duration of the
draught of air upon it, in each observation a slight current of air
was produced by a fan near the mouth of a funnel, the small end of
which abutted on the wet-bulb, and the operation was continued
until no further depression of the thermometer could thus be pro-
duced ; a stronger current of air was then forced on the bulb by
means of a large double bellows ; and the result of each operation
was recorded.
To obviate the anomalies which might arise from single observa-
tions, and to fix a mean state, for each hour, of the temperature of
Royal Society, 565
the air, the temperature of evaporation, and the mean depression of
the wet- bulb, the means of these elements have been taken and are
presented in a table. In this table are also given the dew-points as
determined by means of Mr. Glaisher s factors and by Dr. Apjohn's
formula, with the differences by the two methods. The author re-
marks that the first feature which presents itself, in running the eye
over this table, is the enormous amount of the depression of the wet-
bulb compared with our European experience. In March, the mean
depression at no hour was less than 14?°*8 at 7 a.m., increasing to
29°*6 at 3 P.M. ; in April, the mean depression was never less than
17°'3 at 7 A.M., increasing to 29°*9 at 3 p.m. ; and many observations
necessarily much exceeded the maxima means. The next feature is
the increase of the mean depression with that of the mean tempera-
ture, from 6 a.m. until 3 p.m., and then a decline with the decline of
temperature until 9 p.m. ; but not in the same ratio as the increase
in the morning. With reference to the practical application of these
observations with a view to determine the amount of moisture in the
atmosphere, or to fix the dew-point, the author remarks that it will
be seen from this table that Mr. Glaisher's factors give a higher dew-
point than Dr. Apjohn's formula, varying in March from 6°'l at 8 a.m.
to 1 1°-9 at 6 p.m., and in April from 5°'6 at 7 a.m. to 10°*4 at 9 p.m. ;
and these varying discrepancies do not appear to have gradations of
increment or decrement dependent upon increase or diminution of
mean temperature, or increase or decrease of the depression of the
wet-bulb. These remarks apply to the means of the observations ;
but with reference to isolated observations, the discrepancies by the
two methods become much greater. On the 9th of April, at 8 p.m.,
the temperature of the air being 97°, the wet-bulb with a moderate
draught 60°*5, and with a strong draught 60°, the depressions were
respectively 36°*5 and 37°, and the dew-point for the latter depres-
sion determined by Mr. Glaisher's factors would be 41*5, and 12*6
by Dr. Apjohn's formula. In illustration of this part of the subject
the author gives an extract of a letter from General CuUen, from
which it appears that at Cochin on the Malabar coast, the tempera-
ture of the air being 96°, the wet- bulb 61°, the dew-point by Jones's
hygrometer 38°, the dew-point by Mr. Glaisher's factors would be
43°-5, and by Dr. Apjohn's formula 22°-l.
" On a General Law of Density in saturated Vapours." By
J. J. Waterston, Esq. Communicated by Lieut.-Colonel Sabine, R.A.,
V.P.andTreas.R.S.&c.
The author of this paper commences by stating that the relation
between the pre ssure and temperature of vapours in contact with
their generating liquids has been expressed by a variety of empirical
formula?, which, although convenient for practical purposes, do not
claim to represent any general law ; and that some years ago, while
examining a mathematical theory of gases, he endeavoured to find
out, from the experiments of the French Academy, whether the den-
sity of steam in contact with water followed any distinct law with
reference to the temperature measured from the zero of gaseous ten-
sion (situated at — 4<61°Fahr. by Rudberg's experiments, confirmed
566 Royal Society,
by Magnus and RegnauU). To avoid circumlocution, he calls tem-
peratures measured from this zero G temperatures, and observes
that if t represents the G temperature, A the density of a gas or
vapour, and p its elastic force, the equation
t^=p
represents the well-known laws of Marriotte and of Dalton and Gay-
Lussac. He then states that, as the function which expresses a
general relation between p and f, in vapours, must include a more
pimple function expressing a general relation between A and #, the
proper course seemed to be to tabulate the quotients y" fromitW
experiments of the Academy, and to project them in a curve. For
reasons connected with the vis viva theory of gases, which repre-
sents the G temperature as a square quantity, he projected these
quotients or densities as ordinates, to the square root of the G tem-
peratures as abscissae ; and found that the curve traced out was of
the parabolic kind, but of a high order. Considering the density
as a cubic quantity, the cube roots of the densities were set off as
ordinates to the same abscissae, and the author was gratified to find
that the resulting curve was the Conic Parabola. To ascertain
whether this was accurately the case, the square roots of these ordi-
nates, corresponding to the sixth roots of the densities, \vere set off
to the same abscissae, that is the square roots of the G temperatures.
The result is shown in a chart, in which, as the author observes, the
points determined from the observations range with great precision
in a straight line, any slight divergence being sometimes to the right
and sometimes to the left; precisely as might be expected from
small errors of observation. Other series of experiments on steam
were projected in a similar manner, and it was found that, although
no two exactly agreed with each other, each set ranged in a straight
line nearly. The vapours of ether, alcohol and sulphuret of carbon,
were found to conform to the same law, as were likewise M. Avo-
gadro's observations on the vapour of mercury, and Faraday's ex-
periments on liquified gases (Phil. Trans. 1845). Of these last
defiant gas is remarkably in accordance with the law, as are nitrous
oxide, ammonia, cyanogen, sulphurous acid, and carbonic acid at
the upper part of its range; but muriatic acid, sulphuretted and
arseniuretted hydrogen, do not show the same regularity.
The co-ordinates of the points being the square root of the G
temperatures and the sixth root of the densities, the equation to the
straight line which passes through the points expresses the sixth root
of the density in terms of the G temperature. The constants to be
determined in this equation are the inclination of the straight line
to the axis of x or that on which Vt is measured, and the distance
from the origin at which it cuts this axis, calling the cotangent of
this angle A, and this distance ff, Aj^ A,3 densities at G temperatures
^l> ^2> 111
n A= //a'— A^A ®°^ ^^ V^j—A/^Ai. .iroianai aavrg
Royal Society, 567
The constants ^ and h being thus determined from two observations,
the equation for the density at any other G temperature i^o'futmoq
and for the pressure
»\ axleijifi hi ^ ba£ <'iwoqfiv
;t--'J?--rr -,;ft -■"^n'iT'.'nrYT.
The several equations, with the numerical values of the constants
g and h, for the series of observations previously referred to and
represented on the chart, are then given, the G temperatures being
in degrees of Fahrenheit's scale, and the values of h being calculated
so as to give the pressure in inches of mercury.
The author remarks that the observations on the vapour of water
below 80° show a small excess of density above what is required by
the line corresponding to those at higher temperatures ; and that it
is a curious circumstance that the law of expansibility of water also
becomes disturbed at about the same temperature. In proof of this,
the observations of M. Despretz (Ann. de Chim. vol.lxx.) being pro-
jected, by making the volume the ordinate to the square root of the
G temperature as abscissa, these observations above 25° C. or
77° F. give in the most exact manner a conic parabola ; but below
77° they no longer give that curve.
The equation to the parabola for temperatures above 77° F. is
a(v— 0) = ( V^— <^)S in which v is the volume at the G temperature
t, in terms of its volume unity at 39°*2 F. or 4° C. (its point of
maximum density^ a=352-38, 0=-99872, and 9=21*977 or
02=483°.
The law of the increase of density and temperature in saturated
vapours having a certain analogy with the law of increase of density
and temperature in air while suddenly compressed or dilated, the
author next discusses the latter subject in a manner similar to that
in which he had discussed the former. From this discussion he
draws the following conclusions : —
1. When air is compressed or dilated, the G temperature varies
as the cube root of the density ; and the tension as the 4th power
of the G temperature, or the cube root of the 4th power of the
density.
2. The mechanical force exerted by a given quantity of air while
expanding from one density to another, is proportional to the differ-
ence of the cube roots of these densities, or to the difference of their
G temperatures : hence the fall of temperature is proportional to the
force expended,
3. The mechanical force exerted upon a given quantity of air,
while compressing it from one density to another, is proportional to
the difference of the cube roots of these densities, or to the differ-
ence of their G temperatures : hence the rise of temperature is pro-
portional to the force exerted.
4. The total mechanical force exerted by a volume of air of a
given tension, while expanding indefinitely, is equal to that tension
acting through three times the volume.
568 Intelligence and Miscellaneous Articles,
5. The total mechanical force exerted by a volume of air while
expanding indefinitely is proportional to its G temperature.
6. A given quantity of air while expanding, under a constant
pressure, from one temperature to another, exerts a mechanical force
equivalent to one-third the diiference of temperature ; and the quan-
tity of heat required to change the temperature of air under a con-
stant pressure, is four- thirds of that required to effect the same change
of temperature with a constant volume.
The author concludes by observing that it is singular that these
simple and, he considers, important deductions from MM.Gay-Lussac
and Welter's experiments, have been overlooked by the eminent ma-
thematicians who have elaborately discussed this subject. The arti-
ficial position of the zero-point on the ordinary scales of temperature
may perhaps account for this by its tendency to confine our ideas.
Dalton's and Gay-Lussac*s law of expansion seems imperatively to
have required that, in all computations having reference to gases and
vapours, the temperature should have been reckoned from the zero
of gaseous tension ; yet it has not been so ; and it is impossible to
avoid the conclusion, that if it had been otherwise, if no other tem-
perature but what we have had so often to refer to as the G tempe-
rature had been indicated in their analyses, we should have profited
more by their labours, and been further advanced in the science of
heat and elastic fluids.
^ LXXXI. Intelligence and Miscellaneous Articles.
^N THE HYPOTHESES RELATING TO THE LUMINOUS iETHER, AND
V AN EXPERIMENT WHICH APPEARS TO DEMONSTRATE THAT
THE MOTION OF BODIES ALTERS THE VELOCITY WITH WHICH
LIGHT PROPAGATES ITSELF IN THEIR INTERIOR. BY M. H.
FIZEAU.
MANY hypotheses have been proposed to account for the phseno-
mena of aberration in accordance with the doctrine of undula-
tions. Fresnel in the first instance, and more recently Doppler, Stokes,
Challis, and many others, have published memoirs on this important
subject ; but it does not seem that any of the theories proposed have
received the entire assent of physicists. In fact, the want of any defi-
nite ideas as to the properties of the luminous aether and its relations
to ponderable matter, has rendered it necessary to form hypotheses,
and among those which have been proposed there are some which are
more or less probable, but none which can be considered as proved.
These hypotheses may be reduced to three principal ones. They
refer to the state in which the aether existing in the interior of trans-
parent bodies may be considered to be.
This Kther is either adherent, and as it were attached to the
molecules of bodies, and consequently participates in the motions to
•which the bodies may be subjected;
, Or the ajther is free and independent, and is not influenced by the
motion of the bodies ;
Intelligence and Miscellaneous Articles. 569
Or, lastly, according to a third hypothesis, which includes both
the former ones, only a portion of the aether is free, the other por-
tion being attached to the molecules of bodies and participating in
their motion.
This latter hypothesis was proposed by Fresnel, and con-
structed for the purpose of equally satisfying the phsenomena of
aberration, and a celebrated experiment of M. Arago, by which it
has been proved that the motion of the earth has no influence
upon the refraction which the light of the stars suffers in a prism,
"We may determine the value which in each of these hypotheses
IV is necessary to attribute to the velocity of light in bodies )yljen
the bodies are supposed to be in motion. u ^*i
If the aether is supposed to be wholly carried along with the't)0^
in motion, the velocity of light ought to be increased by the whole
velocity of the body, the ray being supposed to have the same direc^
tion as the motion. ' j
If the aether is supposed to be free and independent, the veloci^
of light ought not to be changed at all. v-
Lastly, if only one part of the aether is carrie^ along, the velocity
of light would be increased, but only by a fraction of the velocity of
the body, and not, as in the first hypothesis, by the whole velocity.
This consequence is not so obvious as the former, but Fresnel has
shown that it may be supported by mechanical arguments of great
probability.
Although the velocity of light is enormous comparatively to such
as we are able to impart to bodies, we are at the present time in
possession of means of observation of such extreme delicacy, that it
seems to me to be possible to determine by a direct experiment what
is the real influence of the motion of bodies upon the velocity of
light.
We are indebted to M. Arago for a method based upon the phae-
nomena of interference, which is capable of indicating the most
minute variations in the indexes of refraction of bodies. The expe-
riments of MM. Arago and Fresnel upon the difference between the
refractions of dry and moist air, have proved the extraordinary
sensibility of that means of observation.
It is by adopting the same principle, and joining the double tube
of M. Arago to the conjugate telescopes which I employed for deter-
mining the absolute velocity of light, that I have been able to study
directly in two mediums the effects of the motion of a body upon
the light which traverses it.
I will now attempt to describe, without the aid of a diagram, what
was the course of the light in the experiment. From the focus of
a cylindrical lens the solar rays penetrated almost immediately into
the first telescope by a lateral opening very near to its focus. A
transparent mirror, the plane of which made an angle of 45° with
the axis of the telescope, reflected the rays in the direction of the
object-glass.
On leaving the object-glass, the rays having become parallel among
themselves, encountered a double chink, each opening of which cor-
responded to the mouth of one of the tubes. A very narrow bundle
670 Intelligence and Misd^llaTieom Articles,
of rays thus penetrated into each tube, and traversed its entire
length, l"»-487. .\ ■vyyuu ^i^-iV- o
The two bundles, always parallel to each other, reachfed the ob-
ject-glass of the second telescope, were then refracted, and by the
eiFect of the refraction reunited at its focus. There they encoun-
tered the reflecting plane of a mirror perpendicular to the axis of the
telescope, and underwent a reflexion back again towards the object-
glass ; but by the effect of this reflexion the rays had changed their
route in such a way that that which was to the right before, was to
the left after the reflexion, and vice versa. After having again passed
the object-glass, and been thus rendered parallel to each other,
they penetrated a second time into the tubes ; but as they were
inverted, those which had passed through one tube in going passed
through the other on returning. After their second transit through
the tubes, the two bundles again passed the double chinks, re-entered
the first telescope, and lastly intersected at its focus in passing
across the transparent mirror. There they formed the fringes of
interference, which were observed by a glass carrying a graduated
scale at its focus.
It was necessary that the fringes should be very large in order to
be able to measure the small fractions of the width of a fringe. I
have found that that result is obtained, and a great intensity of
light maintained, by placing before one of the chinks a thick mirror
which is inclined in such a way as to see the two chinks by the
effect of refraction, as if they were nearer to each other than they
really are. It is in this way possible to give various dimensions to
the fringes, and to choose that which is the most convenient for ob-
servation. The double transit of the light was for the purpose of
augmenting the distance traversed in the medium in motion, and
further to compensate entirely any accidental difference of tempera-
ture or pressure between the two tubes, from which might result a
displacement of the fringes, which would be mingled with the dis-
placement which the motion alone would have produced ; and thus
have rendered the observation of it uncertain.
It is, in fact, easy to see that in this arrangement all the points
situated in the path of one ray are equally in the path of the other ;
60 that any alteration of the density in any point whatever of the
transit acts in the same manner upon the two rays, and cannot con-
sequently have any influence upon the position of the fringes. The
compensation may be satisfactorily shown to be complete by placing
a thick mirror before one of the two chinks, or as well by filling only
one of the tubes with water, the other being full of air. Neither of
these two experiments gives rise to the least alteration in the posi-
tion of the fringes.
With regard to the motion, it is seen, on the contrary, that the two
rays are subject to opposite influences.
If it is supposed that in the tube situated to the right the
water runs towards the observer, that of the two rays which
comes from the right will have traversed the tube in the direction
of the motion, while the ray coming from the left will have passed
in a direction contrary to that of the motion.
Intelligence arid Miscellaneous Articles, 571
3?;By making water move in the two tubes at the same time and in
contrary directions in each, it will be seen that the effects should be
added. This double current having been produced, the direction
maybe again reversed simultaneously in the two tubes,' and the
eflfect would again be double. IS '•
All the movements of the water were produced in a very simple
manner, each tube being connected by two conduits situated near
their extremities, with two reservoirs of glass, in which a pressure
is alternately exercised by means of compressed air. By means of
this pressure the water passes from one reservoir to the other by
traversing the tube, the two extremities of which are closed by the
mirrors. The interior diameter of the tubes was 5™™* 3, their length
i*l'-487. They were of glass.
jrf'.The pressure under which the flowing of the water took plac^
ftiight have exceeded two atmospheres. The velocity was calculated
by dividing the volume of water running in one second by the area
of the section of the tube. I ought to mention, in order to prevent an
objection which might be made, that great care was taken to obviate
the effects of the accidental motions which the pressure or the shock
of the water might produce. Therefore the two tubes, and the
reservoirs in which the motion of the water was made, were sus-
tained by supports independent of the other parts of the apparatus,
and especially of the two lunettes ; it was therefore only the two
tubes which could suffer any accidental movement ; but both theory
and practice have proved that the motion or flexions of the tubes
alone were without influence upon the position of the fringes. The
following are the results obtained.
When the water is set in motion the fringes are displaced, and
according as the water moves in the one direction or the other, the
displacement takes place towards the right or the left.
The fringes are displaced towards the right when the water is run-
ning from the observer in the tube situated to his right, and towards
the observer in the tube situated to his left.
The fringes are displaced towards the left when the direction of
the current in each tube takes place in a direction opposed to that
which has just been described.
With a velocity of the water equal to 2"^* a second, the displace-
ment is already very sensible ; with a velocity of 4 to 7 metres it is
perfectly measurable.
After having demonstrated the existence of the phsenomenon, I
endeavoured to determine its numerical value with all the exactitude
which it was possible to attain.
By calling that the simple displacement which was produced when
the water at rest in the commencement was set in motion, and that
the double displacement which was produced when the motion was
changed to a contrary one, it was found that the average deduced
from nineteen observations sufficiently concurring, was 0"23 for the
simple displacement, which gives 0*46 for the double displacement,
the width of a fringe being taken asounity. The velocity oi the
water was 7*069 metres a second. > oj) vb-j; yri.t -jiifivr ^noiJom ■pnii lo
■ 'u,jum .:'u; io inAi OJ V'V/v'IJnOO floila'j-iil) .^ fli
572 Intelligence and Miscellaneous Articles.
This result was afterwards compared with those which have been
deduced by calculation from the different hypotheses relative to the
ather.
According to the supposition that the sether is entirely free and
independent of the motion of bodies, the displacement ought to be
null.
According to the hypothesis which considers the aether united to
the molecules of matter in such a way as to participate in its mo-
tions, calculation gives for the double displacement the value 0*92.
Experiment gave a number only half as great, or 0*46.
According to the hypothesis by which the sether is partially carried
along, the hypothesis of Fresnel, calculation gives 0*40, that is to
say, a number very near to that which was found by experiment ; and
the difference between the two values would very probably be still
less if it had been possible to introduce into the calculation of the
velocity of the water a correction which had to be neglected from
the want of sufficiently precise data, and which refers to the un-
equal velocity of the different threads of fluid ; by estimating the
value of that correction in the most probable manner, it is seen that
it tends to augment a little the theoretical value and to approach
the value of the observed result.
An experiment similar to that which I have just described had
been made previously with air in motion, and I have demonstrated
that the motion of the air does not produce any sensible displace-
ment in the fringes. In the circumstances in which that experiment
was made, and with a velocity of 25 metres a second, which was
that of the motion of the air, it is found that according to the hy-
pothesis by which the aether is considered to be carried along with
the bodies, the double displacement ought to be 0*82.
According to the hypothesis of Fresnel, the same displacement
ought to be only 0*000465, that is to say, entirely imperceptible.
Thus the apparent immobility of the fringe in the experiment made
with air in motion is completely in accordance with the theory of
Fresnel. It was after having demonstrated this negative fact, and
while seeking for an explanation by the different hypotheses relating
to the aether in such a way as to satisfy at the same time the phae-
nomena of aberration and the experiment of M. Arago, that it aji-
peared to me to be necessary to admit with Fresnel that the motion
of a body occasions an alteration in the velocity of light, and that
this alteration of velocity is greater or less for different mediums,
according to the energy with which those mediums refract light, so
that it is considerable in bodies which are strongly refractive and
very feeble in those which refract but little, as the air. It follows
from this, that if the fringes are not displaced when light traverses
air in motion, there should, on the contrary, be a sensible displace-
ment when the experiment is made with water, the index of refrac-
tion of which is very much greater than that of air.
An experiment of M. Babinet, mentioned in the ninth volume of
the Comptes Rendus, seems to be opposed to the hypothesis of an
alteration of velocity in conformity with the law of Fresnel, But
Intelligence and Miscellaneous Articles. 573
on considering the circumstances of that experiment, I have remarked
a cause of compensation which must render the effect of the motion
imperceptible. This cause consists in the reflexion which the light
undergoes in that experiment ; in fact it may be demonstrated, that
when two rays have a certain difference of course, that difference
is changed by the effect of the reflexion upon a mirror in motion.
On calculating separately the two effects in the experiment of M.
Babinet, it is found that they have values sensibly equal with con-
trary signs.
This explanation renders still more probable the hypothesis of an
alteration of velocity, and an experiment made with water in motion
appears to me completely appropriate to decide the question with
certainty.
The success of the experiment seems to me to render the adop-
tion of Fresnel's hypothesis necessary, or at least the law which he
found for the expression of the alteration of the velocity of light by
the effect of motion of a body ; for although that law being found
true may be a very strong proof in favour of the hypothesis of
which it is only a consequence, perhaps the conception of Fresnel
may appear so extraordinary, and in some respects so difficult, to
admit, that other proofs and a profound examination on the part of
geometricians will still be necessary before adopting it as an ex-
pression of the real facts of the case. — Comptes Rendus, Sept. 29,
1851.
ON THE FORMATION OF ANHYDROUS CRYSTALLIZED ALUM.
BY THE PRINCE OF SALM-HORSTMAR.
Alumina, obtained by precipitating ammonia-alum by ammonia
and heating the precipitate to redness, was fused with four times i;s
weight of bisulphate of potash ; on treatment of the fused mass with
water, six-sided tables which did not doubly refract light were left,
and on analysis were found to consist of anhydrous alum. — Journ.
fiir Prakt. Chem. vol. Hi. p. 319. .*c
ON THE COMPOSITION OF THE GASES EVOLVED ON THE PRODUC-
TION OF COKE FROM COAL. BY M. EBELMEN.
The question might arise, whether in the formation of coke from
coal in a furnace, the air which enters the furnace gives up its
oxygen to the matters which are evolved in the gaseous state, or to
the solid carbon ; and again, whether the oxygen forms carbonic
oxide or carbonic acid. Ebelmen examined the composition of the
gases of the coke-ovens at Seraing, and found that more than two-
thirds of the hydrogen of the coal is burned, the remainder existing
in the evolved gaseous mixture. The quantity of carbonic acid is
three times that of the carbonic oxide. — Comptes Rendus, vol. xxxii,
p. 92.
Phil Mag, S. 4. No. 14. Suppl Vol. 2. 2 Q
574 Intelligence and Miscellaneous Articles.
MAGNECRYSTALLIC PROPERTY OP CALCAREOUS SPAR.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen, Glasgow College, Nov. 7, 1851.
A mistake (I cannot call it a misprint) which occurred in the
footnote to § 12 of my paper on Magnetic Induction, published in
your Number for last March, has, although corrected in the " Errata"
of the volume containing it, caused considerable perplexity regarding
my meaning, as I perceive by some remarks of Dr.Tyndall's, contained
in a foot-note on his paper on the Polarity of Bismuth, published
in your Number for this month. Vou will oblige me by publishing
the following, which is the correct form of the passage referred to.
" Thus, a ball cut out of a crystal of pure calcareous s})ar, which
tends to turn with its optic axis perpendicular to the lines offeree, and
which tends as a whole from places of stronger towards places of
weaker force, would experience this latter tendency Isss strongly
when the optic axis is perpendicular to the lines of force than when it
is parallel to them ; since, according to § 8 of the text, the crystal
must have the greatest inductive capacity, or (the language in the
text being strictly algebraic when negative quantities are concerned)
least capacity for diamagnetic induction, perpendicular to the optic
axis."
In the passage, as originally published, the word ** more" occurred
in the place of ** less." The mistake was pointed out to me last
April by Professor Stokes, and I immediately requested you to cor-
rect it, which you accordingly did by an intimation in the " Errata."
When the perplexity occasioned by the mistake is removed, it is ob-
vious to any one reading the passage carefully, that the mistake itself
was only a slip of the pen, as at the conclusion of the sentence it is
asserted that a crystal of pure calcareous spar must have the " least
capacity for diamagnetic induction, perpendicular to the optic axis."
This conclusion is verified by Dr. Tyndall, who describes experi-
ments, in a paper published in your September Number, by which it
appears that the diamagnetic inductive capacity of calcareous spar in
a direction parallel to the optic axis is to its diamagnetic inductive
capacity perpendicular to the optic axis as 57 to 51.
I remain. Gentlemen,
Your obedient Servant,
William Thomson.
[We have also received a communication on this subject from
Mr. Tyndall, who in reference to a note received by him from Prof.
Thomson writes as follows : — "I have only to say that the facts are
precisely what they are here stated to be. Previous to writing the
remarks in question, I looked to the Errata, but not it seems with
sufficient attention, for Professor Thomson's correction escaped me.
Not only do our results agree in principle, but the same substance
and form of substance which Professor Thomson had referred to in
Intelligence and Miscellaneous Articles. 575
illustration of his theory was unwittingly examined by me in Berlin,
and the exact result which he had theoretically predicted arrived at
by way of experiment." — Edit.]
OBSERVATIONS UPON THE RADIATION OF LUMINOUS BODIES.
BY M. BAUDRIMONT.
On looking at a very brilliant light, it sometimes appears to be
surrounded by brilliant luminous rays, clear, free from cloudiness,
and which must not be confounded with those caused by the eye-
lashes when the eyes are partially closed. These rays may be ob-
served most distinctly by looking at an image of the sun reflected
upon the surface of a convex glass, or still better upon a lens having
a considerable curvature. They may be most easily observed by
looking at an image of the sun formed in the focus of a lens placed
at the extremity of a tube blackened in the interior. If the observer
place himself in a room into which the light penetrates only through
a narrow opening, the phaenomenon appears with great splendour,
and it may even be said with extraordinary magnificence. The rays
are either white, or present all the colours of the spectrum. In that
case a motion appears to take place in their interior, which cannot be
compared with anything better than that of a liquid circulating with
difficulty in narrow channels in which it meets with obstacles.
There are also seen irregular concentric rings, which appear to move
from their common centre. Whatever may be the circumstances in
which the observer places himself, and whatever may be the precau-
tions which are taken to obviate the complication of the phsenome-
non, the rays do not appear disposed as those in a circle ; they have
not all a common centre, but form entangled bundles in a very pe-
culiar manner.
At first sight I was struck with the resemblance which appeared
to me to exist between the arrangement of these rays and that of
the fibres of the crystalline lens ; and I attempted immediately some
experiments directed from that point of view. From among those
which I have made I will quote the two following, which, if they
do not prove that this apparent radiation is to be attributed to the
crystalline lens, at least show completely that the phsenomenon takes
place in the eye, and depends upon the structure of that organ.
1. On looking at an image of the sun produced in the circum-
stances above described through a black screen with a circular
opening of 5 or 6 millims. diameter, the image is seen upon the sur-
face which reflects it ; while the rays are separated from it, and ap-
pear to be superimposed upon the screen, and this even when it is
brought very near the eye.
2. If the head is inclined to the right or the left, the want of sym-
metry which is observed in the arrangement of the rays follows the
movement of the eye, which under those circumstances turns upon
its axis in the direction in which the head is inclined. — Comptes
Renclus, Nov. 3, 1851.
2Q2
576
INDEX TO VOL. IL
AlR-ENGINE, description of an,
150.
Airy (G. B.) on the vibration of a free
pendulum in an oval diflfering little
from a straight line, 147.
Albumen, on the combination of, with
arsenious acid, 345.
Alum, on the formation of anhydrous
crystalUzed, 6/3.
Ammonia, on the presence of, in hail-
stones, 331.
Anderson (Dr. T.) on the products of
the destructive distillation of ani-
mal substances, 457.
Anstice (Rev. R. R.) on the motion of
a free pendulum, 379.
Arsenic, on the detection of, 487-
Arsenious acid, on the combination
of, with albumen, 345.
Ascaris mystaxy on the reproduction
of the, 157.
Astronomy, on the application of
electro-magnetism to purposes of,
61 ; Airy's Lectures on, reviewed, 68.
Atmosphere, on the constitution of
the, 500.
Atmospheric shadows, observations
on, 160.
Azimuths, on the measurements of,
on a spheroid, 145.
Baudrimont (M.) on the radiation of
luminous bodies, 675.
Beechey (Capt. F. W.') on the tidal
streams of the English Channel and
German Ocean, 318.
Beer (Dr.) on the motion of light, 297.
Beke (Dr. C. T.) on recent Nilotic
discovery, 260.
Bernard (C.) on the production of
sugar in the hver of man and ani-
mals, 326.
Beudantite of Levy, on the, 21.
Bingham's (R. J.) Photogenic Mani-
pulation, noticed, 316.
Bismuth, on the polarity of, 333.
Bond (G. P.) on the apphcation of
electro-magnetism to geodetical
and astronomical purposes, 61 j on
an apparatus for observing transits,
323.
Books, new: — Airy's Lectures on
Astronomy, 68; Woepcke's Al-
gebre d'Omar Alkhayytlmi, 315;
Bingham's Photogenic Manipula-
tion, 317 ; Latham's Ethnology of
the British Colonies and Depend-
encies, 413; Latham's Man and
his Migrations, 414 ; De Morgan's
Elements of Arithmetic and of Al-
gebra, translated into the Marathi
language, by Colonel G. R. Jervis,
417.
Boole (G.) on the theory of probabi-
lities, 96 ; on the late John Walsh
of Cork, 348.
Boxer (Capt. E. M.) on the effect of
the rotation of the earth upon the
flight of a projectile, 386.
Brodhurst (B. E.) on the human iris,
155.
Bronwin (Rev. B.) on the integration
of linear differential equations, 477.
Brooke (H. J.) on the Beudantite of
Levy, 21.
Brooke (C.) on the automatic tempe-
rature-compensation of the force
magnetometers, 156.
Bunt (T. G.) on pendulum experi-
ments, 37, 81, 158, 424.
Calcareous spar, on the magnecrj'stal-
lic property of, 574.
Calendar, Gregorian, observations on
the, 146.
Cambridge Philosophical Society,
proceedings of the, 419, 600.
Canonical forms and hyperdetermi-
nants, on the theory of, 391.
Carmufelhc acid, researches on, 293.
Chemical affinity, on the measurement
of, 85.
combination, on the heat of, 268.
Clarke (Lieut. A. R.) on the measure-
INDEX.
577
ments of azimuths on a spheroid,
145.
Claudet (F.) on a new class of ammo-
niacal compounds of cobalt, 253.
Clausius (R.) on the moving force of
heat, and the laws regarding the na-
ture of heat, 1, 102 ; on the effect of
fluid friction, 139 ; on the theoretic
connexion of two empirical laws re-
lating to the tension and the latent
heat of different vapours, 483 ; on
the influence of pressure upon the
freezing of fluids, 548.
Cloud, on the specific inductive capa-
city of, 236.
Coal, on the composition of the gases
evolved in the production of coke
from, 573.
Coal-tar, on the application of recti-
fied oil of, to the preservation of
meat and vegetables, 331.
Cobalt, on a new class of ammoniacal
compounds of, 253.
Cockle (J.) on the solution of certain
S5^stems of equations, 289.
Colours of thick plates, on the, 419.
Cooke (J. B.) on the measurement of
chemical affinity, 85.
Coombe (Rev. J. A.) on the motion
of the apse-line in the pendulum
oval, 303.
Corundum, on the artificial formation
of, 161.
Crystalline bodies, on the deportment
of, between the electric poles, 33.
Crystallization by the dry method,
researches on, 248.
Cymophane, on the artificial produc-
tion of, 330.
Danson (J.) on carmufellic acid, 293.
Davies (T. S.) on geometry and geo-
meters, 444.
Dawes (Rev. W. R.) on the occulta-
tion of a fixed star by Jupiter, 325.
De Morgan (A.) on the Gregorian
Calendar, 146. "^
Determinants, on a fundamental
theory of, 142.
Diamagnetisra, researches on, 165.
Diaspore, on the artificial formation
of, 161.
Dolomite, on the formation of, by the
action of magnesium vapours, 504.
Donkin (W. F.) on certain questions
relating to the theory of probabili-
ties, 55.
Donovan (M.) on the preparation of
phosphorus, 202.
Dove (Prof.) on the reversion-prism,
27 ; on several prism-stereoscopes,
and on a simple mirror-stereoscope,
29.
Dresser (C. L.) on the conducting
powers of wires for voltaic electri-
city, 198.
Durocher (M.) on the formation of
dolomite by the action of magne-
sium vapours, 504.
Earth, effect of the rotation of the,
upon the motion of a pendulum,
376 ; upon the flight of a projectile,
386.
Ebelmen (M.) on the artificial pro-
duction of crystallized minerals,
246 ; on the crystalhzation of cy-
mophane, 330 ; on the composition
of the gases evolved in the produc-
tion of coke from coal, 573.
Eclipse of the sun on the 28th July,
on the total, 81.
Electricity, on the identity of, with
light, heat, and magnetism, 498 ;
of flame, account of experiments on
the, 542.
, voltaic, on the conducting
powers of wires for, 198.
Electric poles, on the deportment of
crystalline bodies between the, 33.
Electrolysis, on the mechanical theory
of, 429.
Electro-magnetic engine, use of
electro-magnets made of iron-wire
for the, 307.
Electro-magnetic forces, observations
on, 447.
Electro-magnetism, on the application
of, to geodetical and astronomical
purposes, 51 ; investigations in, 310.
Electro-motive forces, on the mea-
surement of, 551.
Elimination, on extensions of the dia-
lytic method of, 221.
Elliptic analyser, on a new, 420.
Equations, on the solution of certain
systems of, 289 ; on the integration
of linear differential, 477.
Ethnology of the British Colonies
and Dependencies, Latham's, re-
viewed, 413.
Faye (M.) on the total eclipse of the
28th July, 81.
Fizeau (H.) on the hypotheses rela-
578
INDEX.
ting to tbe lunnnous rctber, and on
the propagation of light in the in-
terior of bodies, 568.
Flame, on the electricity of, 642.
Flood, account of a remarkable, 209.
Fluid friction, on the effect of, 139.
Fluids, on the influence of pressure
upon the freezing of, 648.
Franklinite, observations on, 247-
Fyfe (Dr. A.) on the detection of
arsenic, 487-
Gahnite, on the artificial production
of, 247.
Galbraith (Rev. J. A.) on the apsidal
motion of a freely suspended pen-
dulum, 134.
Gases, on the growth of plants in
vai'ious, 215 ; on the magnetism
of, 503 ; on the centrifugal theory
of elasticity as applied to, 509 j on
the composition of the, evolved in
the production of coke from coal,
673.
Geology, — on the anticlinal line of the
London and Hampshire Basins, 41,
126, 189, 278, 366, 471 ; on the
elevatory forces v^hich raised the
Malvern Hills, 358.
Geometry and geometers, observations
on, 444.
Gerard (A.), observations on Foucault's
pendulum experiments, 422.
Gladstone (Messrs. Dr. J. H. and G.)
on the growth of plants in various
gases, 215.
Goodman (Dr. J.) on the identity of
light, heat, electricity, and mag-
netism, 498.
Greg (R. P., jun.), description of Mat-
lockitc, 120.
Hankel (W.) on the electricity of
flame, 642.
Harris (Sir W.S.) on induced and other
magnetic forces, 493.
Haughton (Rev. S.) on the apsidal
motion of a freely suspended pen-
dulum, 134.
Heat, on the moving force of, and the
laws regarding the nature of heat, 1 ,
102 ; on the mechanical theory of,
61 ; on the identity of, with light,
electricity, and magnetism, 498.
of chemical combination, on the,
268.
Herapath (T. J.) on the combination
of arsenious acid witli albumen, 345.
Hunt (T. S.), description and analysis
of Loganite, 65.
Hydrodynamics, on the principles of,
*60.
Hvperdeterminants, on the theory of,
'391.
Iris, on the structure and physiology
of the human, 155.
Iron, account of experiments demon-
strating a limit to the magnetizabi-
lity of, 306, 447.
Jamin (M.) on the reflexion of light
from the surface of Hquids, 507.
Joule (J. P.) on an air-engine, 150;
on some experiments demonstrating
a limit to the magnetizability of
iron, 307, 447.
Kamtz (Prof.) on corrections of the
constants in tlie general theory of
terrestrial magnetism, 7 1 •
Knoblauch (Prof.) on the deportment
of crystalline Ijodies between the
electric poles, 33.
Kr.intz (Dr. A.) on the new mineral
orangite, 390.
Lamprey (J.) on some pendulum ex-
periments, 410.
Lassell (W.) on a method of support-
ing a large speculum, 325.
Latham's (R. G.) Ethnology of the
British Colonies and Dependencies,
review^cd, 413; Man and his Mi-
grations, 414.
Le Moyne (J. R.) on a new photo-
graphic process upon glass, 505.
Letheby (II.) on two cases in which an
ovule, or its remains, were disco-
vered after death in the Fallopian
tube of the unimpregnated human
female, during the period of men-
struation, 316.
Lewy (M.) on the constitution of the
atmosphere, 500.
Light, on the influence exerted by,
upon oxygen, 22; on the motion
of, 297 ; on the source of, 321 ; on
the identity of, with heat, electri-
city, and magnetism, 498 ; on the
reflexion of, from the surface of
liquids, 50/ ; on the propagation
of, in the interior of bodies,
568.
Liver, on the formation of sugar in
the, 326.
Loganite, description and analysis of,
6.5.
INDEX.
579
Lowe (E. J.) on the mean tempera-
ture of the Observatory of High-
field House, near Nottingham, from
1810 to 1840, 562.
Lutidine, on the preparation and pro-
perties of, 465.
Magnecrystallic action, researches on,
174,574.
Magnetic declination, on the annual
variation of the, at different periods
oftheday, 491.
Magnetic forces, on induced, 493.
Magnetism, of pewter coils, on the,
230 ; investigations in, 310 ; on the
identity of, with electricity, light,
and heat, 498.
, terrestrial, corrections of the
constants in the general theory of,
71 ; on the cause of, 235.
Martin (P. J.) on the anticlinal line
of the London and Hampshire ba-
sins, 41, 126, 189, 278, 366, 471.
Matlockite, description and analysis
of, 120.
Mechanics, on symbolical, 121.
Megatherium, memoir on the, 238.
Mene (M.) on the presence of am-
monia in hail-stones, 331.
Meteorological observations, 82, 163,
251, 331, 427, 562.
Methylamine, 460.
Mineralogical Notices : — Beudantite,
21 ; Loganite, 65 5 Matlockite, 120;
orangite, 390.
Minerals, on the artificial production
of crystallized, 161, 246, 248, 330.
Mirror-stereoscope, description of a
simple, 29.
Muspratt (Dr. S.) on carmufellic acid,
293.
Nasmyth (J.) on the source of light,
321.
Nelson (Dr. H.) on the reproduction
of the Ascaris Mystax, 157-
Nilotic discovery, summary of recent,
260.
O'Brien (Rev. M.) on symbolical me-
chanics, 121 ; on symbolical physics,
149.
Orangite, description of the new mi-
neral, 390.
Owen (Prof.) on the Megatherium,
238.
Oxygen, on the joint influence exerted
by light and the oxidability of cer-
tain substances upon common, 22.
Pendulum experiments, account of,
37, 81, 158, 410, 422, 424.
Pendulum, on the apsidal motion of
a freely suspended, 134; formula
for calculating the apsidal motion of
a, 159 ; on the motion of a, afifected
by the earth's rotation, 275, 303,
376, 379, 412; on the vibration of
a free, in an oval differing little
from a straight line, 147 ; on the
deviation of the plane of vibration
of a, from the meridional and other
vertical planes, 150.
Periclase, on the artificial production
of, 249.
Peridote, on the artificial production
of, 247.
Perowskite, on the artifical production
of, 249.
Pewter coils, on the magnetism of,
230.
Phillips (J.) on the deviation of the
plane of vibration of a pendulum
from the meridional and other ver-
tical planes, 150.
Phillips (R.) on the magnetism of
pewter coils, 230.
Phosphorus, suggestions for the pre-
paration of, 202.
Photographic images, note on in-
stantaneous, 154.
Photographic process, on a new, upon
glass, 505.
Physics, symbolical, researches in,
149.
Plants, on the growth of, in various
gases, 215.
Pliicker (M.) on the magnetism of
gases, 503.
Potter (Prof.) on the theory of sound,
162.
Prism- stereoscopes, description of
several, 29.
Probabilities, on certain questions re-
lating to the theory of, 55, 96.
Propylamine, 462.
Pyridine, on the preparation and pro-
perties of, 464.
Pyrrol bases, observations on the, 470.
Rankine (W. J. M.) on the theory of
sound, 36 ; on the mechanical
theory of heat, 61 ; on the centri-
fugal theory of elasticity, as applied
to gases and vapours, 509.
Reversion-prism, remarks on the, 27.
Robin (M.) on the application of rec-
580
INDEX.
tified oil of coal-tar to the preser-
vation of meat and vegetables,
331.
Royal Astronomical Society, proceed-
ings of the, 145,321.
Roval Society, proceedings of the, 71,
149, 239, 316, 491, 662.
Sabine (Lieut.-Col.) on the annual
variation of the magnetic declina-
tion at different periods of the day,
491.
Salm-Horstraar (Prince) on the forma-
tion of anhydrous crystallized alum,
573.
Schaw (Lieut. H.) on pendulum ex-
periments, 410.
Schoenbein (C. F.) on the joint influ-
ence exerted by light, and the ox-
idability of certain substances upon
common oxygen, 22.
Senarmont (H. de) on the artificial
formation of corundum and diaspore
by the wet method, 161.
Sound, on the theory of, 36, 162.
Spheroid, on the measurements of
azimuths on a, 145.
Steam, on the effect of fluid friction in
drying, 273.
Stokes (Prof.) on the principles of
hydrodynamics, 60 ; on the colours
of thick plates, 419 ; on a new ellip-
tic analyser, 420.
Strickland (H. E.) on the elevatory
forces which raised the Malvern
Hills, 359.
Sugar, on the production of, in the
liver of man and animals, 326.
Sun, total echpse of the, on the 28th
July, on the, 81 ; notice of a spot
on the disc of the, 326.
Sykes (Col.) on depressions of the
wet-bulb thermometer at Ahmed-
nuggur, 564.
Sylvester (J. J.) on a certain funda-
mental theory of determinants, 142;
on the dialytic method of elimina-
tion, 221 ; on a remarkable disco-
very in the theory of canonical
forms and of hyperdeterrainants,
391.
Talbot (H. F.) on instantaneous pho-
tographic images, 154.
Tebay (S.) on the motion of a pendu-
lum affected by the earth's rota-
tion, 376.
Thacker (Rev. A.) on a formula for
calculating the apsidal motion in
pendulum experiments, 159 ; on the
motion of a free pendulum, 275,
412.
Thomson (Prof. W.) on the etlect of
fluid friction in drying steam which
issues from a high-pressure boiler
into the open air, 273 ; on the me-
chanical theory of electrolysis, 429;
on the application of mechanical
effect to the measurement of electro-
motive forces, and of galvanic re-
sistances, in absolute units, 551 ;
on the magnecrystallic property of
calcareous spar, 574.
Tidal streams of the English Channel
and German Ocean, observations on
the, 318.
Transits, description of an apparatus
for observing, 323.
Tyndall (Dr. J.) on the progress of
the physical sciences. 26 ; on dia-
magnetism and magnecrystallic ac-
tion, 165, 574; on the polarity of
bismuth, including an examination
of the magnetic field, 333.
Vapours, on the tension and latent
heat of different, 483 ; on the cen-
trifugal theoiy of elasticity as ap-
plied to, 509 ; on a general law of
density in saturated, 565.
Walsh (J.), memoir of the late, 348.
Wartraann (Prof. E.) on atmospheric
shadows, 160.
Waterston (J. J.) on a general law of
density in saturated vapours, 565.
Weld (Rev. A.) on a remarkable flood
at Chipping, in Lancashire, 209.
Weld (W. R.), notice of a spot on the
sun's disc, 326.
Wet-bulb thermometer, on depres-
sions of the, at Ahmednuggur, 564.
Whewell (Rev. W.) on the transfor-
mation of hypotheses in the history
of science, 500.
Woods (Dr. T.) on the heat of che-
mical combination, 268.
Zantedeschi (M.) on a new static and
dynamic theory of ultimate par-
ticles, 249.
END OF THE SECOND VOLUME.
Fhil.Mag. Ser.^ Vol.^PII.
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