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RICHARD TAYLOR, F.L.S. G.S. Astr.S. Nat.H.Mosc.&c. 

" 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. 




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** 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, 





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 



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 


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 


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 


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 


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 


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 


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 



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 


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 


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 


Page 144, line 17 from top, /or 


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. 


Illustrative of Mr. H. E. Strickland's Paper on the Elevatory Forces 
which raised the Malvern Hills. 






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 


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 

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 


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. 


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 



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. 


M. R. Clausius o?i the Moving Force of Heat, 



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 : 



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 


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)]"- _. 




^/^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 


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. 



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 


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 


and hence the content of the rectangle, or 

The work produced 

(s— o") -jidm dt. 


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 



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 


of latent heat which has been extracted from the body A ; and 
in the second case, the quantity 



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 

rBm—fi . cdt—m . hdt = ; 

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 : 




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 ; 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 


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.) 


* 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= , 


. :■< , 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, 

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. 

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.) 


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.) 


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 

[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- 


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 

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 

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 

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 

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 

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 

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 


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 

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 

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 

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 

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, 

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 


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- 

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, 


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 ] 


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 














368-4 = 11-945 per hour. 



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 

Mr. T. G. Bunt on Pendulum Experiments, 



Table I. — Thirty-seven hours^ motion in Azimuth of Plane of 
Vibration, "showing the rate of motion for each hour. 



Part of circle 

Rate per 











20 to 33 


May 27. 




57... 69 






/ 69... 761 

1 120... 126/ 

128... 139 











/ 140 ...1451 
1 122 ...126/ 
/ 127 ...1351 
1 50... 54/ 
/ 54... 621 
' 145 ...148/ 
148... 161 















161... 171 






171 ... 180 






180... 9 






9... 20 





20... 32 


June 2. 

' .58-0 



33... 45 



' >^ 601 



/45... 511 

174... 81/ 



^^ ;' 633 



81... 94 



^ifi 59-9 



95 ... 107 



,y, 59-3 



107... 119 



. 71-6 
^^' 53-3 



119 ...133 




132 ...142 



fejr 60-3 



142... 152 



i;j- 69-1 



152... 165 






165... 177 






177... 6 






6... 19 






19... 28 





30... 42 






41... 52 






51... 64 





65... 75 






75... 88 






88... 101 






101 ... 114 




+ 015 

114 ...126 






126... 139 






139 ...148 





148 ... 156 






432-41 = 

ll°-677 n 

lean rate per hou 


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. 




June 2. 







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. 


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 


56 ...67 
57. ..60 
80 ...85 


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 

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. 


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 

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 

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 

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 

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- 

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 

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:. ,\ 


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 

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 

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 

[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, 

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 

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 

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 

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 . . . 


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 


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 

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^)$% 


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. 


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. 


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 


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 


5rU= 89-8 
^2,1 _ __ J40'6 

^.1= ii2'3 
^.1=. — I03'2 

^.ic= —115-1 



A2.1=_ 14-1 


A3.i= 48-5 


A4.i=- 1 8-2 


h^^= 72-8 




A^.2= 43-4 

ff*^= i8-8 A4.3= 1 8-6 

^,3= 2*3 ^8.3= _ i'6 

5^'^ = 3*9 

flf5,5= -o 


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 — ■ 


-69 54 
-69 52 

Means —69 53 


179 55 

180 04 




-84 30 1999 

-83 34 1994 

-84 02 


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 ^ 


"^ '^^"'f' 

















40 ] 






Fairliaven, Spitzbergen 


Tukansk, Isl 

Grundsat ..,>:..,'.;.£./.'.. 
Sundsvall M«frA.'i..<wK«. 










Nowaja River 








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 


Dubuque's Town 

St. Mary's 


Alleghany Summit ... 



St. Louis 




Loch Slapin 











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 






















-f- 20-8 

+ 31-9 






351 44 

357 25 




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. '''' 









Liitke, Erman, Belcher. 

Lefroy^,^:^j^^-qxnoa A 

Lefroy. . . 

Lefroy.*"^'"^'^'^^^ eriJ 03 

Lefroy. '' :>bjiiiJBf 












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. ^^^^ ^^^^'^ 


All Observers. 


Lloyd, Ross. 


Royal Society. 


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 


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 «. 


971. At sea 

981. At sea ».... 

991. At sea 

Lat. N. 

51 31 
51 4 

48 24 

43 SO 
36 44 

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 

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 




I I'D 









- 35-i 













All Observers. 

Lloyd, Ross. 



Fox, Humboldt. 

Norwegian Officers. 

Keilhau, Kreil. 



Humboldt, d'Abadie,Quetelet. 

Norwegian Officers. 




r Humboldt, Freycinet, Du. 

■< perrey, Sabine, Bethune, 
L Wick'ham, 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. 



Humboldt and Bousingault. 















All Observers. 

Moore and Clerk. 

Moore and Clerk. 

Duperrey, Fitzroy, Moore and 

Dayman. [Clerk. 



Royal Society. 




1 02 
























. At sea.. 
. At sea.. 
. At sea.. 
. At sea. . 
. At sea.. 
. At sea.. 
. At sea.. 
. At sea.. 
. At sea.. 
. At sea. . 
. At sea 

At sea 

Bay of Islands .. 


At sea 

At sea 

At sea 

At sea..... 

At sea 

Kerguelen Island 

At sea 

At sea 


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. 




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 







- 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 


- 4*1 

- 53'8 
+ 40*4 

- 18.3 

- 67 











3 '4 




Moore and Clerk. 




Erebus and Terror. 





Moore and Clerk. 


All Observers. 

(British only). 


Duperrey, FitzRoy, Erebus. 





Erebus. -Maximum of proba 

Erebus. ble error. There 

Erebus, are great anoma- 

Erebus. lies in this meri- 

Erebus.-' dian. 

All Observers. 




Moore and Clerk. 







King and FitzRoy. 


All Observers. 

Moore and Clerk. 

Moore and Clerk. 

Moore and Clerk. 

Moore and Clerk. 













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 


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. 


Dorpat* .. 
Kardis ..... 


Nawast ... 
Werderf ... 


Pernaw . . . 
Tammiss ... 







Kyrkstad .... 



Abborfors .... 



Turkbauta .... 

Tavastebus .... 

Wilman strand . 

Imatra Fall .... 

Huutjarwi .... 

Pumala \6i 


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 




Warkauss-Sluss . 












21 21 






70 9-8 

70 507 







70 38-0 

71 19-9 

3 . 


70 48-3 












Vertical Force. 



1421-9 1347-1 













27*3 73 









4547!i374*5 ^o^** 
484-6I 1385-4 1302-2 

458-411380-1 1305-9 
476*2 1378-711298-0 




323*4 ^;l' 


+ 29-1 

446-0 i394-3'i325-o 
441*4 1391-41^323-2 
442-6 1385-1I1316-2 

44o-8| 1401-8, 1334-3 
450'o|i4o6-2| 1335*9 
446-2 1360-9 1289-4 
425-5 i395-iii332-2 

439'o 1410-2 1344-0 

433-51 1405-8! 1340-9 
431-711406-9 ^^--'f' 


419*4:141 1*7 
420-1 1 1400- 1 
399-4! 1402-6 



* 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. 



Sundby . . 




22;27 13 

36122 40 

2 26 27 

Wirda 63 3727 

47 ^7 



Tuomala .. 


Wuornos ., 
Rautiola .. 




Kexiswaarat ... 
Muonioniscai ... 



Kaaressuando ... 



Hamraerfest II ... 


Kielwig Mageroe 
Kitai-Insel** ... 
Archangel ft ... 




Krassnowskaja. . . 





Petersburg t J ... 

65 52 

66 20 

66 36 

66 42 

67 o 

67 15 

68 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 


22 45 

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 







" 'inclination. 


duced to 

o / 

72 53*1 

73 18-9 


73 50'5 

74 6-0 

74 4*8 
74 49*9 
74 52-3 

74 50-3 






74 i8-2 
74 31*9 

74 47*7 

75 4*4 
75 45*2 
75 32*0 











19*5 381*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 













13*0 344*3 












143 5 "2 









Vertical Foi*ce. 






















— 22*0 

— 26*0 

— 6*1 


+ 6*8 
— 26*0 

- 8*1 

— 12*2 

- 8*4 

— 10*9 


• 16*6 


• 1*0 


• 6*9 

■ 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 ; 

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, 

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 ] 


XV. Intelligence and Miscellaneous Articles. 


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. 


muth per hour. 


in. in. 


o o 


12 to 9 

+ 0-18 

49 ... 62 


13 ... 9 

-1- 0-19 

62 ... 74 


f4... 9 

f 11-90 


74 ...113 

\ 11-90 


14 ... 11 

+ 0-22 

113 ...127 


14 ... 9 

+ 0-27 

141 ...156 


14 ... 11 


50 ... 63 


14 ... 9 

- 0-0/ 

65 ,.. 89 

j 11-50 

1 11-50 


15 ... 11 


90 ...102 

16 ... 11 

- 013 

102 ...113 


14 ... 10 

- 0-02 

113 ...133 

r 11-35 
1 11-35 

14 ... 10 

- 0-13 

134 ...144 


15 ... 11 


127 ...140 


• ■\ 





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 

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. 

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. 




— Si 


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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 . 

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 

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 

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 

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. 


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 


2 1 


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 

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, 
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- 

All Ys are Xs 

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 

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 


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, 




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 



The quantity of work produced at the same time was 

V ' 

and from this we can construct the equation 
^dv .dt 




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 


The quantity of work thereby produced was 

and hence we obtain the equation ,. 

{s—o)~~' dm.dt 1 

rdm C 


'•=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, 




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^- € 




t in Cent, degrees. 

C according to Clapeyron. 

C according to Thomson. 













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 

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- 

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 7=A.R«. 


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 

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«.) 


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 

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- 

/in r^i^Tlf t^atYvAaa 

p in millimetres. 

I m i./eut. ue^ees 
of the air-ther- 

according to the 
curve of the 

according to the 
curve of the 



































































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. 



\p dt), 



10. M 


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. 


* in Cent, degrees 
of the air-ther- 







According to the values 

According to 


equation (27.). 





- 5 













































29-47 29-50 


-0-14 -0-17 


29-16 29-02 


-fO-01 +0-15 


28-89 28-93 


+0-10 +0-06 


28-88 29-01 


-0-08 -0-21 


28-65 28-40 


-0-05 +0-20 


28-16 28-25 


+0-22 +0-13 


28-02 2819 


+012 -0-05 


27-84 27-90 


+005 -0-01 


27-76 27-67 


-0-14 -0-05 


27-45 27-20 


-0-12 +0-13 


26-89 26-94 


+0-13 +008 


26-56 26-79 


+0-12 -Oil 


26-64 26-50 


-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 , 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* 


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 



and from this follows 

d rps \ 1 in—nll-\-k(a + t)]^^ 

dt\ pSn J 



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. 


dt Kpsq)' 1 


dt \psoJ 

1 .. ! 
1 1 

dt \psj 





1 1 

1 140 



0-00.338 1 



1 150 



000334 i 



j 160 



000329 ! 



j 170 






i 180 






i 190 






I 200 


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 

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 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 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 
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 




^rf rijso \8v 


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. 













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. 


-1-9161 -1-465 



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 

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 


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, 


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' 


[ 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 

The proportions by theory would be — 

Chloride of lead 55-46 

Oxide of lead 44*53 


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. 


mfim' — Oil 

tiooIjiiM cr 
-iCfSiiTroaq^ re 


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 


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. 

(^,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 


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 = . (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 


^'*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 

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 ^ ■ ■ ■ ■ — I t - rrfnv tu-o't vrnrmlff'). '-^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. 


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. 



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)) 



\,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 


i-, 2^06 

tan r 


cosa)= — —J lis 06 

tan r 

and therefore 


cos ft)' = ^, ^fff 


smft)'= -, 


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)^ 


Let N be the number of degrees described in one hour, then 

N = 

135 X 1800 




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, ^= ; 
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. 

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. 



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 

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. 

r«l «2 • • • «« I /«1 «2 • • • «n 1 

\b, b, 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) 

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, 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 

Now leaving <^i, <A2 • • • </*p^ ^^^ '^p '^2' - ^'^p ^^^^^^^^^^t,!^^ 
may take a system of values ^/, ^2 • - - ^»^ ^^^ch that '^''*' > ^'^ 


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 


XXV. Proceedings of Learned Societies. 


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 

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 

•' 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." 


[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 

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 

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 



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 

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 

Direction at origin. 

of time. 


Chord at 





Minor axis. 

1. E. andW.... 

2. N. andS. ... 





None ob 
None ob 


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 



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 


Left. Right. 

Chord at 




Direction. Minor 

None ob served. 
None ob served. 


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. 

at origin. 




Time to 


ting effect 
of ellipse. 




Minor axis. 


times of 3°. 


m 8 

7 3 
14 28 
16 56 
19 58 
24 16 
27 38 
;34 18 
42 8 
50 36 




















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 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' 


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. 


/3. Corrected for Ellipse* ''\^^ ■ 
Exp. 5. On E. and W. line ..... 12-50. 

i;v>kfm>(J ^ 


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. 








Minor axifl. 

(6). N.E. and S.W. . \ 







None ob 
None ob 




(7). N.W. and S.E. | 



None ob 



(8.). N.E. and S.W. • 



None ob 





(9). N.W. and S.E. ■ 




None ob 




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 

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. 


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. 


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. 




Number of 

Motion per 

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 











1 1-804 -<* 



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. 



To the Editors of the Philosophical Magazine and Journal. 
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. 


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 

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. 


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 

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. 


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 

p =gmh( l+s + ff) 

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." 

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 : 

* The observations from the Kev. W. Dunbar of Applegarth Manse have 
not reached us. 












SI I •»•. 





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^^§9 = ?^??^? i !^^^ jr |?;?S?S8 

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S 9 2" ; o : S CO 9 c« 9 9 <o 


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^ o « • 







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 

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 

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. 


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- 


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 


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. 





n tan «. 




































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. 





n tan «. 

2^ 6 
30 45 
41 20 








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. 





n tan ». 

20 d 





30 45 





41 20 










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. 































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. 





n tan «. 































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. 






n tan «. 









2 21 












1 37-30 










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 

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 

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 : — 


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 

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. 
























Table VIIL 

•Carbonate of Iron. Axis of Crystal perpendicular 
to axis of Magnet. /i = 20*7. 


tan a. 







5 52 

















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. 


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 

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. 













Table X. — The same cubes. Plane of most eminent cleavage 
perpendicular to axes of cores. 













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. 






8-3 X tana. 





















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. 




! 40 


; ^« 


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 

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. 

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 

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- 


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 


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 .,_ . . . 


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. ,,. 



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. 


T. 1 




25 5 



1 ^^ 




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 

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 

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 

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 

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- 

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. 


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 




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. 


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 

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- 

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. 


Copper wire. 



Iron wire. 

































































































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. 












































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. 

Intensity two 





























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. 


Current con- 


Current con- 





for Voltaic Electricity, 


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 





Degrees of 









































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 

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 

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 

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 

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 

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. 


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 

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. 


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 


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 


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' 


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)-p, 
and the total number will therefore be 

r(s + l)-(m + w + &c.+/?), 

= (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 + 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'" 

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 = 
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 — 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 


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) 

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 = 
Hm(.r,y) + ?X + 5^X' = 

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, - = 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 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; 


and in this case it will no longer be true that the values — =0, 


-^=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^ = 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 = 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 = 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' = 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 


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 ; 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 was opened, and to C when 
O was shut. When N was fully opened, the swing was much 

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 was shut the needle moved to A, and to C when 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 

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 


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 

7 Prospect Place, Ball's Pond Road. 

XXXV. Proceedings of Learned Societies. 


[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 

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. 


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 

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. 


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. 


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- 

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. ,;..,.. 


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- 

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. 


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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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. _.___> . 










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 





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 : — 


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 ... 




65-54 PtCP + NH4Cl=4-116N =27-79 


=2175 =27-20 

7-38 HO 

= -82 H = 6-31 

7-70 ... 

= -855 = 6-34 

6-775 ... 

= -753 = 6-46 





3C1= 106-5 


2Co= 59-0 


5N= 70-0 


16H= 18 
















,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 


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 — 


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 ^^ 


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 




j^jyjffoa shm 


= 248-5 








>id offt bfffid 


= 59 


Ox.. 9-60 

• ylfjstoi 

5N : 

= 70 

.'golmifi ' 


iimvsmi mil 


= 16 

■'M. hau eoiO vd b^'i^yougib ebmfoq. 


258 Mr. F. Claudet on a Class of 

the formula of which is — 



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 




9C1 =319*5 30*00 2984 

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 : — 

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- 

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. 


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 '( ;«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 

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 

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 

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- 

(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 

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 

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' *: 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 

/ the length of the 

R the tension of the 


the coordi- 

nates of the ball mea- 
sured along axes fixed in 
space, the axis of -s^' coin- 
ciding with that of the 

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 



■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 


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 


os'=a cos X cos mI — a? 
.y'=a cos X sin (ot—y,. 



,_, .fV=«sin\, 'i^2^iV%-^^^'^ I 

276 The Rev. A. Thacker on the Motion of a Free Pendulum: i 



d^u R y 

-y^ --((J^co^a) cos X, sin <at-\ y =0 

dt^ \./ / ,^ / 


—g sinX 

R ^ ^ 

m I 


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 

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 


— <^U/ J 

5111 /V 

dt ' 


+ 2ft) sin X 








+ 2ft) cos X 

• dt 




ft)^ Y sin^X -f &)^ sin X cos \.[a^z) 

co^Y sin X cos X + ft>^ cos^X(a — ; 


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) 


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') = 

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 


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- 

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. 


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. 


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- 

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 

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. 


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 

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 

[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, ^2 + 11 = 0, ..., 1^^+11=0, . . {a.) 

then the solution of the system («.) involves that of the given 

(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 

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 


then, in the present case*, we have 

and, if we make 
we have 

Ai=A^-, = 6U'-«V', 


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 

by means of a relation of the form 


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, 


* 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 


then we may give {h.) the form 

X2 4-M + (^-2/i)^+(e-2c/i)y=0. . . (j.) 
So, if we make 



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), 

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 


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 : — 

2/=— 2r(^--r) + (4r)~^ {p.) 

then [n.) and {o) become^ respectively, 

(a;-.r)2 + r2+(4r)"' + m = {q) 


4r2(^— r)2 + r+(4r)""^ + ?i = (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 : — 


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 



11. • 

144 34-285 



20 4-761 



256 60-954 



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 


Centesimally represented. 

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 

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^ = ; 

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. 


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— ) . 


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 

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^} 


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 



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. 


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, 

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 


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 



(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, 












dr db . dr 

+ -,- • -TT 

db dt dvr 








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 



But (vel)^ in undisturbed ellipse 
And these by the theory are equal j 

Also^ from the equations of motion. 



« 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 


^ 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 


ACT = 

/*2 (cos2 ^ - sin^ ^/r) (fl« cos^ ^/r + Z»« sin* i/r) 

. 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) , 


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. 

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 ' 


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. 7. 

Length in inches 

Diameter in inches 

Weight lifted in ounces 
Attraction for steel 1 
magnet in grains... J 
















,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. 


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? 



No. 2. 




No. 3. 







No. 4. 







No. 5. 







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 

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. 


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. 
































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. 

















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 


From the 1st table. 

From the 2nd table. 


Electric cur- 
















.' to ?.fiirAU.i: 







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 

Lifting power in lbs. 

Calculated power. 













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 

Quantities of current electricity. 











Attraction at i inch. {^JP^^j,'"^^"* 








Attraction at ii„oh.{E~»'. 







Attraction at J i"ch.{^JP™* 









-Attraction .t 4 l„ch.{EjP^^-:'* 






Attraction a. J inch.jfK;,'".'"^ 






. , . , f Experiment 
Attraction at iiuch.|r,,j^^^^ 






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 

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, 


[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 

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 


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 

" 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 

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 

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. 


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. 


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 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. 


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. '.'-"^ ''';; ,^, 


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. 

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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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- . 




* 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 


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 

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- 


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 

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 

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 


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. 


Dr. Tyadall on ilie Polarity of Bismuth, 

Fig. 3. 


-^ — «^ 



1 ^ 




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 

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 

" 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 

" 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 


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- 

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 

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. 


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