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^' Nee araneuum sane iextas ideo mdior quia ex se flia gignunt, nee notter 
Yilior qnia ex alienis libamiu at apes." Just. Lips. P6^t» lib. i. cap. 1 . Not. 



Prffif«r« and Publishers to the Universiiy of London ; 






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Meditationit est perscmtari occulu; contempUtionii est adminuri 

penpicua Admiratio generat qutestionem, quettio iiiTestigationem, 

invesdgatio inventioiiem." — Hugo de S, Vietore, 

— " Cur Spirent venti, cur terra dehiscat. 
Cur mare turgescat, pelago cur tantus amaror. 
Cur caput obscura Phoebus femigine coudat. 
Quid toties diros cogat flagrare cometas; 
Quid pariat nubes, veniant cur fulmina coelo, 
Quo micet igne Iris, superos quis conciat orbes 
Tam vario motu." 

J. B. PinelU ad Masonimm, 

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Prof. R. Oausius on different Forms of the Virial 1 

Mr. F. P. Purvis on Amsler's Planimeter 11 

Prof. A. W. Wright on the Polarization of the Zodiacal Light, 13 
Baron N. Schilling on the Constant Currents in the Air and 

in the Sea : an Attempt to refer them to a common Cause . . 21 
Mr. R. Mallet on the Tidal Retardation of the Earth's Rotation. 88 
Mr. E. W. Hilgard on some points in Mallet's Theory of Vul- 

canidtir 41 

Mr. J. W . L. Glaisher on a New Formula in Definite Litegrals. 53 
Dr. J. Rae on some Physical Properties of Ice ; on the Trans- 
position of Boulders from below to above the Ice; and on 

Mammoth-remains ... '. 56 

Mr. P. Clowes on a Glass Cell with Parallel Sides 61 

Notices respecting New Books : — 

Mr. T. M. Goodeve's Prindples of Mechanics 62 

The Rev. S. J. Johnson on Eclipses Past and Future, with 

General Hints for Observing the Heavens 64 

Proceedings of the Royal Society : — 

Mr. W. Crookes on the Action of Heat on Gravitating 

Masses 65 

Mr. G. Gore on Electrotorsion 70 

Proceedings of the Geological Society : — 

His Grace the Duke of Argyll on* Six Lake-basins in 

ArgyUshire 72 

Prof. R. Owen on the Skull of a dentigerous Bird 73 

Mr. J. W. Hulke on the Anatomy of Hypsilophodon Foxii. 74 
Mr. J. Geikie on the Glacial Phenomena of the '* Long 

Isknd" 74 

Mr. J. F. Campbell on the Glacial Phenomena of the 

Hebrides 75 

Prof. P. M. Duncan on Fossil Corals from the Eocene 

Formation of the West Indies 76 

Mr. R. Etheridge on the Lignite-deposit of Lal-Lal, Vic- 
toria, Australia 76 

On the Flow of Saline Solutions through Capillary Tubes, by 

Theodore Hiibener 77 

On Melde's Experiment, by W. Lowery 78 

On Constant Electric Currents, by M. Heine, of Halle ..... 79 
On the Nature of the Action of Light upon Silver Bromide, 
by M. Carey Lea, Philadelphia 80 

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Mr. W. Crookes on Attraction and Eepulsion accompanying 

Eadiation. (With a Plate.) 81 

Mr. J. O'Kinealy on Fourier's Theorem 96 

Baron N. Schilling on the Constant Currents in the Air and 

in the Sea : an Attempt to refer them to a common Cause 97 
Prof. M'Leod on an Apparatus for the Measurement of Low 

Pressures of Ghw 110 

Dr. W. H. Stone on Wind-pressure in the Human Lungs du- 
ring Performance on Wind Listruments 113 

Dr. W. H. Stone on the Fall in Pitch of Strained Wires 

through which a Ghdvanic Current is passing 115 

Mr. H. G. Madan on an Improvement in the Construction 

of the Spectroscope 116 

Mr. L. Schwendler on the General Theory of Duplex Tele- 
graphy 117 

Dr. W . H. Stone on a simple Arrangement by which the Co- 
loured Eings of Uniaxial and BiaxuJ Crystals may be shown 

in a common Microscope 138 

Prof. W. F. Barrett on the Modification of the usual Trombone 
Apparatus for showing the Literference of Sound-bearing 

Waves 139 

Notices respecting New Books : — 

M. J. Plateau's Statique Exp^rimeutale et Theorique des 

Liquides sounus aux seuleis Forces Mol^culaires 140 

Mr. W. B. Birt's Contributions to Selenography 141 

Proceedings of the Boyal Society : — 

Dr. A. C. Bamsay on the Comparative Value of certain 
Geological Ages (or groups of formations) considered 

as items of Geological Time 143 

Prof. O. Eeynolds on the Forces caused by Evaporation 

from, and Condensation at, a Sur&ce 146 

Proceedings of the Geological Society : — 

Prof. W. H. Flower on the Skull of a Species of Halithn' 

rium from the Bed Crag of Suffolk 163 

Mr. H. Woodward on Forms intermediate between Birds 

and Eeptiles .,*.,.»... 154 

Mr. J. W. Hulke on the Astragalus of IguanodonManUUi; 
and on a very 1r^ Saurian Limb-bone from the Kim- 

meridge Clay of Weymouth, Dorset 155 

On a Simple Ocular-Spectroscope for Stars, by F. Zollner . . 156 
Note on the Cause of Tides, by E. J. Chapman, Ph.D., Professor 
of Mineralogy and Geology in University College, Toronto. 157 

On the Temperature of the Sun, by J. Violle 158 

On a Peculiar Phenomenon in the Path of the Electric Spark, 
by Prof. Toepler, of Graz 160 

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Captain Abney on the Opacity of the Developed Photographic 

Image 161 

Mr. C. Homer on the Behaviour of certain Fluorescent Bodies 

in Castor-oil 165 

Baron N. Schilling on the Constant Currents in the Air and 

in the Sea : an Attempt to refer them to a common Cause. 166 
Prof. Challis on the Hydrodynamical Theory of the Action 

of a Ghilvanic Coil on an external small Magnet. — Part I. . . 180 
Prof. A. Stoletow on the Magnetization-Eunctions of various 

Iron Bodies 200 

Mr. A, Tylor on Tides and Waves.— Deflection Theory. (With 

Three Plates.) 204 

Proceedings of the Boyal Society : — 

Mr. H. E. Boscoe on a Self-recording Method of Measu- 
ring the Intensity of the Chemical Action of Total Day- 
light 220 

Mr. J. Cottrell on the Division of a Sound- Wave by a 
Layer of Flame or heated Gas into a reflected and a trans- 
mitted Wave 222 

Mr. A. E. Donkin on an Instrument for the Composition 

of two Harmonic Curves ' 223 

Proceedings of the Geological Society : — 

Mr. J. W. Hulke on the Anatomy of Hypsilophodon 

Foxii 227 

Mr. T. Mellard Eeade on the Drift-beds of the North- 
west of England 227 

Mr. E. D. Darbishire on a deposit of Middle Pleistocene 

Gravel near Leyland, Lancashire 228 

Mr. H. G. Fordham on the Structure sometimes deve- 
loped in Chalk 228 

Mr. £. Pinchin on the Geology of the Eastern Province 

of the Colony of the Cape of Good Hope 229 

Lieut. A. W. Stiffe on the Mud-craters and geological 

structure of the Mekran Coast 230 

On the light reflected by Permanganate of Potassium, by 

Dr. Eilhard Wiedemann 231 

On the Temperature of the Sun, by M. J. Violle 233 

Physics of the Internal Earth, by D. Vaughan, Esq. 237 

On the Conversion of Ordinary into Amorphous Phosphorus 
by the Action of Electricity 239 


Dr. E. J. Mills on Gladstone's Experiments relating to Che- 
mical Mass 241 

Dr. E. W. Davy on a very singubr Sulphuretted Nitrogenous 

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Compound, obtained by the Action of Sulphide of Ammo- 
nium on the Hydrate of Chloral 247 

Dr. A. Schuster on Unilateral Conductivity 251 

Lord Bayleigh on the Vibrations of Approximately Simple 

Systems 258 

The late W. S. Davis on a simple Method of Illustrating the 
chief Phenomena of Wave-motion by means of Flexible 

Cords. (With a Plate.) . . , 262 

Prof. A. M. Mayer's Eesearches in Acoustics. — Xo. V 266 

Prof. J. J. Miiller on a Mechanical Principle resulting from 

Hamilton's Theory of Motion 274 

Mr. J. O'Kinealy on a New Formula in Definite Integrals . . 295 

Mr. F. Guthrie on an Absolute Galvanometer 296 

Notices respecting New Books : — 

The Eev. J. F. Twisden's First Lessons in Theoretical 

Mechanics 298 

Mr. E. Butler s Supplement to the First Book of Euclid's 

Elements 300 

Mr. F. Cuthbertson's Euclidian Geometry 300 

Proceedings of the Boyal Society : — 

Mr. J. H. N. Hennessey on Displacement of the Solar Spec- 
trum 303 

Mr. J. H. N. Hennessey on White liines in the Sdair 

Spectrum 305 

Messrs. Negretti and Zambra on a New Deep-sea Ther- 
mometer 306 

Proceedings of the Geological Society : — 

Mr. A. B. Wynne on the Physical Geology of the Outer 

Himalayan region of the Upper Punj&b, India 310 

Mr. E. J. Dunn on the mode of occurrence of Diamonds 

in South Africa 311 

Mr. J. C. Ward on the Origin of some of the Lake-basins 

of Cumberland 311 

Mr. D. Mackintosh on the Traces of a Great Ice-sheet in 
the Southern part of the Lake-district and in North 

Wales 313 

Mr. A. W. Edgell on some Lamellibranchs from the Bud- 

leigh-Salterton Pebbles 313 

On the Action of two Elements of a Current, by J* Bertrand. 314 

On Earth-currents, by L. Schwendler, Esq 315 

Experiments on the Dissipation of Electricity by Flames, bv 

J. W. Fewkes \ 319 

On the Stratification of the Electric Light, by M. Neyreneuf . 320 


Mr. H. A . Rowland on the Magnetic Permeability and Maxi- 
mum of Magnetism of Nickel and Cobalt 321 

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Dr. A. Schuster's Experiments on Electrical Vibrations .... 340 
Prof. ChaUis on the Hydrodynamical Theory of the Action of 

a Gkdvanic Coil on an External Small Magnet. — Part U. . . 350 
Sir W. Thomson on the Perturbations of the Compass pro- 
duced bj the rolling of the Ship 363 

Br. W. M. Watts on the Spectrum of Carbon 369 

Prof. A. M. Mayer's Besearches in Acoustics. — No. V 371 

Mr. C. Tomlinson on the Action of Solids and of Friction in 

liberating G^ &om Solution 385 

Prof. O. Eeynolds on the Surfiice-Forces caused by the Com- 
munication of Heat 389 

Proceedings of the Boyal Society : — 

Mr. W. N. Hartley on the Chemical Constitution of Saline 

Solutions 391 

Mr. G. Gore <hi the Attraction of Magnets and Electric 

Conductors 393 

On the Temperature of the Sun, by J. Violle 395 

Preliminary Notice on a new Method for Measunng the Specific 

Heat of Gases, by Eilhard Wiedemann 398 

On a new Formula in Definite Integrals, by J. W. L. Glaisher. 400 


Dr. C. B. A. Wright on the Relations between Affinity and 
the Condensed Sjrmbolic Expressions of Chemical Facts and 

Changes known as Dissected (Structural) FormulaB 401 

Prof. Challis on the Hydrodynamical Theory of the Action of 
a Gblyanic Coil on an external small Magnet. — Part III. . . 430 

Prof. A. M. Mayer's Besearches in Acoustics. — No. V 445 

Lord Bayleigh on a Statical Theorem 452 

Dr. W. M. Watts on Carbon-Spectra 456 

Mr. J. W. L. Glaisher on the Problem of the Eight Queens . . 457 
Notices respecting New Books : — 

The Hon. Sir W. E. Grove's Correlation of Physical 

Forces 467 

Mr. W. G. WiUson's Elementary Dynamics 471 

Proceeduigs of the Eoyal Society : — 

Dr. W. Huggins on the Motions of some of the Nebul© 

towards or from the Earth 471 

On the Intensity of the Light reflected from Glass, by Dr. P. 

Glan 475 

Pohurization of the Plates of Condensers, by A. S. Thayer . . 478 
On Electrical Currents accompanying the non-simultaneous 
Immersion of two Mercury Electrodes in various Liquids, 
by G. Quincke 479 

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M. H. Herwig : the Heat-conducting Power of Mercury in- 
dependent of the Temperature 481 

Prof. J. Lovering on the Mathematical and Philosophical 

State of the Physical Sciences 493 

Mr. B. H. M. Bosanquet on Temperament, or the Division 

of the Octave 507 

Mr. S, Sharpe on Comets and their Tails 512 

Prof. A. M. Mayer s Researches in Acoustics. — No. V 513 

Mr. F. Guthrie on an Absolute Galvanometer 526 

Notices respecting New Books : — 

Mr. D. D. Heath's Elementary Exposition of the Doc- 
trine of Energy 527 

Mr. B. A. Proctor's Transits of Venus 529 

Dr. W. Huggins's Approaching Transit of Venus 529 

Proceedings of the Boyal Society : — 

Prof. O. Beynolds on the Befraction of Sound by the 

Atmosphere 530 

Mr. T. Grubb on the Improvement of the Spectroscope. 532 
Drs. Stewart and Schuster's Preliminary Experiments on 

a Magnetized Copper Wire 535 

Proceedings of the G^ologicil Society : — ' 

Mr. J. W. Judd on the Secondary Bocks of Scotland . . 541 
Mr. A. W. Waters on Possils from Oberburg, Styria . . 545 
On the Cosmic Dust which falls on the Surface of the Earth 

with the Atmospheric Precipitation, by A. E. Nordenskiold. 546 
On the Passage of Gases through Liquid Films, by Dr. F. 
Exner 547 

Index 548 

Page 203, note f", line ^A^for liniiteil r*ff<iiClo»ed. 


L lUuatratiTe of Mr. W. Crookes's Paper on Attraction and Repulsion 
accompanving Radiation. 

II.. III., and iV. Illustrative of Mr. A. Tylor's Paper on Tides and Waves. 

V. Illustrative of Mr. W. S. Davis's Paper on a simple Method of Illus- 
trating the chief Phenomena of Wave-motion by means of 
Flexible Cords. 

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JULY 1874. 

I. On different Forms of the Virial. By R. Clausius*. 

MY theorem of the virial has already given rise to some 
discussions on the forms which the virial can assume. 
I myself, in my first memoir relative to itfi indicated that when 
the movable points partly exert forces upon one another, and 
partly are acted on by forces from without, the virial can be 
analyzed into an internal and an external, and gave their forms 
for certain frequently occurring cases. Yvon Villarceau subse- 
quently [Comptes Rendus, vol. Ixxv.) effected other transforma- 
tions of the equation relating to it, especially by resolving the 
total motion of the system of material points into the motion of 
the centre of gravity and the relative motions of the individual 
points about the centre of gravity, and referring the equation to 
each of these two constituents singly. Prompted by this, in a 
note published in the same volume of the Comptes Rendus I 
added a series of further transformations. As, however, in that 
brief note results only, without demonstrations, could be com- 
municated, and those but imperfectly, a more connected treat- 
ment of a subject so important in itself will not be void of 

1. The simplest form of the equation in question is the fol- 
lowing. If m denotes the mass of a material point which is in 
stationary motion together with other material points, of, y, z 
its rectangular coordinates at the time /, and X, Y, Z the com- 

* Tianslated from a separate impression, communicated by the Author, 
from PoggendorflTs Annalen, Jubelband, p. 41 1. 

t Bertchie der Niederrhein. Gesellsch. fur Natur- u. Heilkunde, June 
1870; Phil Mag. S. 4. vol. xl. p. 122 ; Pogg. Ann. vol. cxli. p. 124. 

PhiL Mag. S. 4. Vol. 48. No. 315. July 1874. B 

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2 Prof, R. Clau8iu8 on different Forms of the ViriaL 

ponents of the force acting upon it^ then 

or, if (as will always be done in the following) the first differen- 
tial coeflScient according to time be indicated by affixing an 

-;r«=:-^X^+5-^ (1«) 

From this results, indicating mean values by drawing a hori- 
zontal stroke above : — 

'^¥'=-\y^x (2) 

If we name the quantity ^ a^^ the vis viva with respect to the 

^-direction, and the quantity "" 5 ^ ^^^ virial relative to the 

a?-direction, since the x- is any direction we please, the meaning 
of the equation can be expressed thus : — For each freely movable 
point f the mean vis viva relative to any direction is eqital the virial 
relative to the same direction. 

If we form for a point the equations relative to the three di- 
rections of its coordinates and add them up, we get (r denotin<^ 
the velocity of the point, and / its distance from tlie origin of 
the coordinates): — 

J.--|(Xx + yy + Z.) + ^^P. ... (3) 

If, further, we denote by L the component, in the direction 
of /, of the force acting on the point, and i*eckon it positive fi-om 
the origin of the coordinates onward, the equation (as is readily 
seen) becomes: — 

2*'=2^'+4-rfl* (*) 

It is obvious that these equations, which are valid for each 
individual point, can be extended by simple summation to the 
entire system of points. We thus obtain : — 

-. m « 1 -., , 1 d^XmP 

2.jr»=22L/+^-^^-5- (7) 

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Prof. R. Clausius on different Forms of the ViriaL 3 

In the formation of the mean values, in all these equations 
just as in (1), the last term on the right-hand side falls away ; 
and the expression then remaining on that side represents the 

2. The first method of transformation of these equations is 
based on the fact that when the points are acted on by forces of 
different sorts which we wish to consider singly, the force-com- 
ponents can be separated into as many summanda as the kinds 
of force that are to be distinguished, whereby the virial is divided 
into just as many parts. 

If, for instance, the above-mentioned distinction be made be- 
tween the forces which the points of the system exert on each 
other, and those which act upon the system from without, and 
this be denoted by the indices i and e, we can put X = X, -f X^; 
and the same holds for the components Y, Z, and L. It is 
readily seen how the above equations are changed by the inser- 
tion of these sums. Equation (6), for example, thereby changes 

^is?- ^^) 

When more special assumptions are made concerning the 
nature of the forces, the expressions also take more special forms, 
of which I will briefly cite two which are exhibited in my first 
memoir. When, namely, the internal forces consist of reciprocal 
attractions or repulsions^ which, according to any law, depend 
on the distance, so that for two points whose distance is r the 
force (which as an attraction is reckoned positive, and as a repul- 
sion negative) can be represented by a function ^(r), we can put 

-\l.{7.f + Y,y^Z,z) = \lr<i>{r), ... (9) 

in which the sum on the right-hand side refers to all combina- 
tions of two mass-points each. When the system of points is 
further considered as a body on which the only external force 
acting is a symmetrical pressure/? normal to the surface, we can put 

-|2(X,^+Y,y + Z,r)=|pV. .... (10) 

in which V denotes the volume of the body. 

3. Another mode of transformation depends on the separation 
of the coordinates of the points into summanda. 

To this belongs the transformation effected by Yvon Villar- 
ceau. If, namely, besides the fixed systems of coordinates, we 


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4 Prof. R. Clausius on different Forms of the Virial. 

introduce a movable system having for its origin the centre of 
gravity of all the material points^ and parallel to the fixed sy stem, 
and if we name the coordinates of the centre of gravity in rela- 
tion to the fixed system Xc, y^ ^o ^^^ the coordinates of any one 
of the material points in relation to the movable system ^, 77, ^, 
then is 

^=^c+f, y-Vc^Vy ^='8'r+(; 
If we now form the equation 

and consider that we may put 

we gct^ if M denotes the total mass of all the material points^ 
consequently the sum Sm, the equation 

2wa^=Ma:J + 2wf« (11) 

In precisely the same manner we obtain 

2W*=M;r'J + 27n^« (12) 

Finally, the mere substitution in SXj? of a?^ + f for the coor- 
dinate X, Xp denoting the sum 2X, gives 

2Xa- = X,^e + 2Xf (13) 

If now we form for the centre of gravity the identical equation 
which for a single material point has served for the derivation 
of (1), viz. 

2 <//« ~\dt) '^''' dt*' 

which, after multiplication by ^,canbe writtcD thu.4. 

and suppose herein 

we then obtain 

** rf?^^'"5?''^^^^" 

2^'- 2^*'+ 4^r« (^*) 

With the aid of this equation in conjunction with (11), (12), 
and (13), the following equation can be immediately derivtd from 


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Prof. R. Clausios on different Forms of the VirtaL 5 

2^r»=-^2Xf+l^. . . . (15) 

All the equations above derived for the j?-direction, of course 
bold good in a corresponding manner for the other two direc* 
tions of coordinates ; and when each three equations thereby 
arising are added together^ a new system of equations is ob- 
tained. In order to write these conveniently^ let us introduce 
the following symbols. We will nanie the distance of the centre 
of gravity from the origin of the fixed coordinates /<.; and the 
distance of a mass-point from the centre of gravity, \. Let the 
velocity of the centre of gravity be called Vc, and the relative 
velocity of a mass-point about the centre of gravity, consequently 
the quantity \/f 4-»/*+|^*, be called w. Further, of the force 
whose components in the coordinate-directions are X^, Yc, Z<., 
the component in the direction of /« may be denoted by 17^ ; and 
of the force acting on a mass-point, let the component in the 
direction of X be denoted by A. Then the equations will be 
written as follows : — 

2w/«=M/J-f-2mX«, (16) 

ltnv^=Mvl +^, (17) 

2L/=LA-h2xV\, (18) 

*^.« Iri^^^i^) 119) 

^t.,= ^LA+4 ^^. .... (19) 

2fu;'=l2AX+^^'|p^'. •. . . (20) 

4. We will now turn to the kind of transformation which I 
communicated in the Comptes Rendus, and which depends on the 
introduction into the formulee of the mutual distances and rela- 
tive velocities of each two material points. 

Firsts if V and fi represent any two of the indices 1, 2, 3, &c., 
and accordingly m^ and m^ are any two of the given mass-points 
with the coordinates Xy, yy, Zy and ^^ y^, z^^y we can form, corre- 
sponding to the above, the following identical equation, 

or, differently arranged and written. 

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6 Prof. R. Clausius on different Forms of the ViriaL 

which by introducing the force-components is changed into 

Just such equations hold for the other two coordinate-directions ; 
and we will add up these three equations. Therein the distance 
between the two points shall be denoted by r ; and their relative 
velocities, consequently the quantity 

we will call u. Lastly, of the forces acting on the mass-points 
m^ and m^, let the components which fall in the direction of r 
be denoted by B^ and R^, and at the same time let the direction 
of force from each point to the other point be reckoned positive. 
We can then put : — 

Xy{x^—Xy) +Y^(y^— y^) +Z^(j2r^-5r^) = R^, 

X^(^,,-4?^) + Y^yr-y^) + Z^(j8r,--r^)=R^r. 

Accordingly the equation resulting from the above-mentioned 
addition takes the following form : — 

Into this we will introduce another simpUfying symbol, putting 

the equation will then read : — 

„.=a,+^) (24) 

Multiplying this equation by ^—^ and extending it to the 
entire system of points, wc get 

A2«^^„«=_l-2m^^»,+ _l.^^', . (2J) 

wherein the three sums refer to all the combinations of two each 
of the given mass-points. 

5. Between the sums which occur in this equation and the 
sums previously considered, there are simple relations, which 
can be discovered by means of a general formula of transforma- 
tion. For, besides the masses tw,, 7n^ . . . m„, given two other 
groups of quantities belonging to them, which shall provisionally 

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Prof. R. Clausios on different Farms of the ViiioL 7 

be denoted hj p^,p^ .../>« and jj, y^, . . . j«, then the following 
identical equation holds : — 

2m^^(/?^--/?^)(gf^— gr^)=2m2inpj— SmpSmj; . . (26) 

in which the sum on the left-hand side refers to all combinations 
of two masses each^ while the sums on the right-hand simply refer 
to all the masses. A conviction of the correctness of the equation 
can be obtained by carrying out the multiplication on the left- 
hand side^ and suitably arranging and collecting the terms then 
contained in the sum. We will now apply this equation to our 
case by attributing successively different significations to the 
quantities p and q. 

First let ua prxtp^q^x; the result is: — 

Xm^f^{x^^x^^='ZmS,ma^'- (2i?wr)*=M2mar'— M*a?J. 
We then fxitp=q=a^, and obtain in a corresponding manner 
2f7i^^(a/, -a^^)«=M2ma/«-.M«a?';. 

Lastly, we put /;= — and q^x; then comes 

2m,»i^(~ - ^-^)(a?,-ar^)=2m2Xa?-2X2in^ 


Just such equations are valid for the other two directions of 
coordinates ; and if we form the sum of each three belonging to 
one another and divide it by M, we obtain the equations ex- 
pressing the relations sought, namely : — 

j^2m,7n^r«=2m/«-M/2, .... (27) 
^2m,7n^u«=2mt^-MrJ, .... (28) 

^2^^»r=2L/-Le/e (29) 

Combining these with equations (16), (17), and (18), we get 
the following very simple equations : — 

^2m,m^r« = 2»«\«, (80) 

jg-2m^^tt'=2mi(;*, (31) 

^2m,m^»r=2A\ (82) 

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8 Prof. R. Clausius on different Farms of the Firiat. 

It scarcely needs to be meotioDed that in equations (8), (14), 
(15), (19), (20)^ and (25)^ as well as in the earlier corresponding 
equations, with the formation of mean values the last term 
(which is a differential coefficient according to time) drops out, 
and the terms then remaining on the right-hand side are forms 
for virials, the special signification of which is readily seen in the 
individual cases. 

6. Having thus far been occupied in introducing special quan- 
tities of various kinds for the determination of the virial^ we will 
finally derive some equations which, in relation to the variables 
to be employed, are perfectly general. 

Given any variables serving to determine the positions of the 
points, and denoted by q^, q^ q^ &c., then the coordinates of 
the points, and all the quantities determined by them, are to be 
regarded as functions of these general variables. The velocities, 
and the quantities determined by them, can accordingly be re- 
presented as functions of these variables and of their coefficients 
of differentials according to time. Let us now assume that the 
forces acting in our system have a force-function or ergal U, we 
can treat this as a function oi q^, q^^ q^ &c., and at the same 
time the vis viva T of the system as a function of ^„ q^ q^ &<;. 
and ^,, 9',, q'of &c. Between these two functions there subsists, 
according to Lagrange, the following equation, 

in which the sum refers to the variations of all the variables 

9v 99> 9s9 &c* If* fo** abbreviation, we introduce the symbols 

Pv P2f P9> ^'» ^^^ f^^ 


^ P'-W.' ^''^* 

V signifying any one of the indices ^, v s> ^^^ preceding equa- 
tion becomes : — 


=X[^-j/)Sq. .... (85) 

Besides, according to Lagrange, the following easily derived 
equation holds for the vis viva T : — 

T=|2;»?' (86) 

If wc now differentiate according to time the product p^, q^, 
we have 

rf(M.) =p^,^,^qj,, 

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Prof. R. Clausius on different Forms of the ViriaL 9 

whence results 

;'y.= -?y,+ ^ (37) 

Herein^ (orp^,, we can put an expression to be obtained from 
(85). For this purpose we will write (35) in the following 
form: — 

2f «?=2(^-p'>. . . . (88) 

If now the variables q^, q^ q^ &c. are each independent of the 
others^ their variations are also independent of each other, and 
the equation which holds for the sum of all the terms must also 
hold for each term singly ; we consequently obtain 

dq, dq^ ^ -^ 

If we insert this expression for j&^ in equation (37), after mul- 
tiplying it by \, we get 

2^'^" 2 dq^ ^'^ 2 dt' ' ' • • ^^^> 

and when we form the sum of all the equations of this kind, we 
obtain, in accordance with (36), 

1 rf(U-T) \dtpq 
^"2^ dq ^^% dt ' • • • ^^^^ 

These equations (40) and (41) are two new equations represent- 
ing generalizations of equations (1) and (6). 

By forming the mean values, new forms of virial-cxpressions 
can be deduced from them. In the first place, the expression 
for the total virial resulting from the last equation is : — 

2^ dq *+2'^r" 

In regard to the last term in this expression a special remark 
must be made. ITie variables q.^ q^, S's > • • • s^^^ve for the deter- 
mination of the positions of the movable points; and, con- 
versely, the values of the variables can be determined from the 
positions of the points. This latter determination, however, 
may take place in two ways. It may have but one meaning — 
which is the case for right-line coordinates, the distances of the 
movable points from one another or from fixed points or the 
centre of gravity, and for the trigonometrical functions of the 

Digitized by VjOOQ IC 

10 Prof. R. Clausius on different Farm of the Virial. 

angles made by such right lines; or it may be ambiguaui — 
which is the case with the angles themselves^ since to one direc- 
tion an infinite number of angles belongs which differ from one 
another by 27r. In the former case l,pq is a quantity the value 
of which, with a stationary motion, varies only within certain 
limits , and accordingly the mean value of the differential coe£S- 
cieut, taken according to time, of this quantity may at once be 
regarded as vanishing and be omitted from the above expres- 
sion. In the latter case, on the contrary, the mean value of that 
differential coe£Bcient does not necessarily vanish, and hence it 
must remain in the expression for further consideration. 

Should the variables q^, g^, g^, &c. not be all independent, 
but connected with one another by certain condition-equations, 
then we can, notwithstanding, obtain equations similar in form 
to (40) by employing Lagrange's indeterminate coefficients. 
Let, namely, 


be the given condition-equations, we form instead of (38) the 
following equation, 

where p, o-, &c. are indeterminate coefficients ; and this equation 
is to be resolved, in the usual way, into as many partial equa- 
tions as there are variations. The partial equation correspond- 
ing to the variable q^ is then 

dV rfT I ^ d4>^ dit . 
dq^ dq, "^"^ "^dq^ dq^ 

whence results 

rf(T--U) d^ rff 


By the insertion of this value of j/^ equation (87) is changed 

^"^^ L dq^ ^dq^ dq^ ^^^ dt ^ ^ 

As many equations of this form are obtained as the given vari- 
ables 9„ ^9, ^3, &c.; and the work can be supplemented by eli- 
minating from them the indeterminate coefficients. 

It is thus shown in a general way how the equations which 

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Mr. Y. P. Parvis on Amsler's Plardmeter. 11 

serve for the determination of the virial can be formed with the 
employment of any variables; and with this I think I may on 
the present occasion be satisfied^ without entering upon special 
applications of the equations — which may be of very various 
kinds, and^ hence, would lead to extended discussions. 

II. On Amskr^s Plmimeter. By F. P. Purvis, Esq.* 

THE following is a simple and thoroughly general explana- 
tion of the action of this perplexing little instrument. 
Suppose, for simplicity and greater generality, that the instru- 
ment consisted simply of the straight bar A B, of length /, car- 

rying a pencil at each end, A and B ; and suppose any lines A a, 
B b were traced out by these pencils : we will consider how the 
area A a ^ B may be expressed in terms of / and the motion of 
some point in the line AB. 

Let the motion from AB to ayS represent an elementary 
motion of the bar, the centre of it C moving from C to 7, and 
the bar turning about y through the angle dO ; let rfnaa the 
normal distance from y to A B ; this motion may be considered 
to take place in two parts : — Ist, the motion of A B parallel 
to itself into the position xy ; 2nd, the motion of AB about its 
centre into the position a/S; the required area A a ^ B is, in 
this elementary motion, equal to the area AxyB {^Idn), since 
the area 7 a x = the area 7 jS y, and the areas A aw and B^y 
are negligible with respect to Idn, being the product of two in- 
finitesimal quantities, while Idn is the product of one infinitesi- 
mal quantity (comparable with each of the two just mentioned) 
and the finite quantity /. 

Integrating for the whole area A a & B, we see that it is ex- 
pressed by In, where n is the travel of the point C normally to 
the bar A B. 

Now we may obtain that normal motion n by centring a 
wheel on the bar at C, free to revolve in the plane at right angles 

* Communicated bv the Author. 

Digitized by VjOOQ IC 


Mr. r. P. Purvis on Amsler's Planimeter. 

to A B^ and resting at its circumference on the paper. That it is 
given by the circumferential motion of this wheel may be seen 
by considering again the elementary motion of the bar from A B 
to « ^ : while the bar moves from AB to ar j^, the wheel turns 
through the normal distance from 7 to AB; while the bar 
turns about the point y, the wheel remains stationary. 

If instead of centring the wheel at C we centre it at any 
other point J), distant m from C, its circumferential travel for 
the elementary motion will be the normal from z to A B( = dn) 
--mdO, and for the whole motion from A B to a ^ will be n-^mO, 
where ^= the inclination of a & to A B. 

If a retrograde motion be now given to the instrument, bring- 
ing it into the position c/b', the product nl will still equal the 

area included between AaJ^Bb b\ and the two straight lines 
A B and Jlf, part of that area being, in the case shown, negative ; 
nl=iAaa! IB-^lbb^ If instead of allowing B to take any path 
bV ift constrain it to move only along the line already traced, 
while A traces out a new line a a, the negative area will be nil, 

and the product nl will equal the area Aaalb^B, If this motion 
be continued, B being always kept in the path A^B until AB 
occupies its initial position, the product nl will equal the area 
A a a' A, whatever be the nature of the line Bbf b. Also for the 
whole motion ^=0; so that the circumferential travel of the 
wheel at D = n, entirely independently of the value of m. 

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On the Polarization of the Zodiacal Light. 1 3 

Now in Amsler'a planimeter the point B is constrained to 
move in the arc of a circle, while the pencil A is traced ronnd 
the contour of the required area ; this is simply a limitation of 
the more general case taken above. Also the wheel whose 
travel is measured is placed away from the centre of the bar C, 
and indeed on the opposite side of B ; but, as we have seen, its 
position, so long as its centre is oa the line AB, is quite imma* 
terial, its motion in the aggregate being the same as if it were 
placed at G. 

In the planimeter the length / is capable of variation ; so that, 
by setting it differently, the same graduation on the wheel will 
give areas in different units, the unit of area being always Ix 
the circumferential travel of the wheel required to alter its read- 
ing by unity. 

III. On the Polarization of the Zodiacal Lif/ht. 
By Professor Arthur W. Wright*. 

FROM the published accounts of observations upon the zo- 
diacal light, it would seem that few attempts have as yet 
been made to determine whether or not any portion of the light 
is polarized, and the results thus far obtained leave the question 
still undecided. The few notices that can be found in the scien- 
tific journals, though uncertain and contradictory, tend to the 
view that it is either not polarized at all, or that the proportion 
of polarized light is so small as to render its detection a matter 
of excessive difficulty. It may be observed that most of the 
observations giving negative results appear to have been made 
with Savart's polariscope ; but with an instrument which ab- 
sorbs so large a proportion of the light as a Savart, the amount 
of polarization necessary to render the bands visible increases 
very greatly as the light becomes fainter, and especially so as it 
approaches the limit of visibility. Numerous attempts have 
been made by the writer to detect traces of polarization with a 
Savart, but never with the slightest result, excepting that on one 
especially clear evenings when the zodiacal light was unusually 
distinct^ the bands seemed to be visible by glimpses, on the 
utmost exertion of visual effort. The observation was so un- 
certain, however, that it was considered worthless. 

Nearly a year ago a series of observations was begun, in the 
course of which a variety of apparatus were employed, by the use 
of which it was hoped polarization might be detected, either, as 
in the Savart, by bands or other variations in the brightness of 
parts of the field, or as with the double-image prism, the NicoPs 

* From Silliman's American Journal, May 1874. 

Digitized by VjOOQ IC 

14 Prof. A. W. Wright en. the Polarization 

prism^ or a bundle of glass plates set at the polarizing angle> by 
a diminution of the brightness of the object itself. None of 
them, however, gave results of any value. In resuming the 
study of the subject some months later^ the attempt was made 
to find a combination which should give a large field of view, 
and which, while absorbing as little light as possible, should in- 
dicate the pre^nce of even small proportions of polarized light, 
by sufficient variations of intensity to render it available with 
the faintest visible illumination. 

A Savart in which the tourmaline was replaced by a Nicol, 
though possessing almost perfect transparency, was found to 
give too small a field of view, and bands too faint to render it 
of any service. Amother instrument was constructed on a plan 
similar to that adopted by Mr. Uuggins in observations upon 
Encke*s comet*, by placing a large double-image prism in the 
end of a tube 18 inches long, the other end of which had a 
square aperture a little more than an inch in diameter. The 
distance was so adjusted that the two images just touched with- 
out overlapping. This seemed to promise well ; and on using 
it diflferences of intensity were perceived which indicated polari* 
zation in a plane passing through the sun. Two defects, how- 
ever, are inherent to this mode of investigation : — one, that if 
the field is not of uniform brightness thi-oughout, the brighter 
side of one image may be juxtaposed to the fainter side of the 
other, thus giving rise to false conclusions ; another is the un- 
equal sensibility of diflFerent parts of the i*etina. In consequence 
of this, the one of the images directly viewed seems always the 
more obscure, and the true relation of their intensities can only 
be found by indirect vision, the eye being turned to some point 
in the median line of the images. Although when used with 
the observance of the necessary conditions this instrument is 
capable of ginng trustworthy indications, it was soon abandoned 
for a better. 

Among the polariscopic apparatus belonging to the physical 
cabinet of Yale College, a quartz plate was found, cut perpendi- 
cularly to the axis, and exhibiting by polarized light an unusual 
intensity of colour. It is a made, the body of the plate consist- 
ing of left-handed quartz, through which passes somewhat ex- 
centrically a band of right-handed quartz, 6*5 millimetres in 
breadth. This band is not bounded by sharp lines of division 
on the sides, but by intermediate strips {b, o in the figures), 
about 2 millimetres in breadth, which are of different structure, 
and are apparently formed by the interleaving of the strata of 
the two portions at their edges. In the polarizing apparatus 
these strips simply vary from bright to dark, without marked 
♦ Phil. Mag. S. 4. vol. xliii. p. 382. 

Digitized by VjOOQ IC 

of the Zodiacal Light, 1 5 

appearance of colour. Placed between two Nicols, the plate has 
the appearance represented in the accompanying figures^ which 
are drawn of full size. When the corresponding diagonals of 

Fig. 1. Fig. 2. 

the Nicols are parallel, or nearly so, the bands are white upon 
a deep reddish- puq)le ground, as shown in fig. 1 ; with the 
Nicols crossed, the bands are dark upon a light greenish-yellow 
background, as represented in fig. 2. Turning one of the 
Nicols 45° in one direction, the observer sees the central band 
a intensely blue upon a yellow ground ; turning in the other 
direction, a bright yellow upon a dark blue; and intermediate 
positions give the usual varying tints. Examined with one Nicol 
and unpolarized light the plate is perfectly colourless, and shows 
no trace of its heterogeneous structure. 

The quartz plate was placed in one end of a tube, large enough 
to admit its full size very nearly, and 11 inches in length. 
This was found better than a shorter one, as the bands are most 
easily seen when not nearer the eye than the limit of distinct 
vision. In the other end was placed a good-sized Nicol ; and 
the tube was provided with a joint, so that the latter could be 
easily turned. Thus mounted the plate and Nicol form a po- 
lariscope of extraordinary sensibility, with faint light far excel- 
ling the best Savart, and even with strong light somewhat 
superior to it. The instrument is especially suited for the detec- 
tion of small degrees of polarization, and the examination of 
very faint lights. The occurrence of the narrow strips is pecu- 
liarly advantageous, as with very feeble illumination they appear 
bright upon a dark ground, or the reverse, and are thus more 
easily seen. The efficiency of the instrument is further increased 
by the comparatively large field of view and the perfect trans- 
parency of the whole combination. 

As a test of its delicacy may be mentioned that when a glass 
plate is laid upon the window-sill, and the light of the sky in a 
clear moonless night, after reflection from it, is viewed through 
the instrument, both bright and dark bands are easily seen, the 
former appearing surprisingly luminous in contrast with the 

Digitized by VjOOQ IC 

16 Prof. A. W. Wright on the Polmisalion 

darkened field. The plane of polarization is easily determined 
with it^ since when the bright bands appear, as iu fig. 1, the 
longer diagonal of the Nicol is in that plane ; when the bands 
are dark, the plane of polarization is parallel to the shorter 

On the completion of the instrument the first favourable op- 
portunity was iinproved to test its efficiency upon the zodiacal 
light it was almost immediately found to indicate the exist- 
ence of light polarized in a plane passing through the sun. 
The bands were fainter than had been expected, and at first were 
overlooked. More careful attention, however, and the obser- 
vance of suitable precautions established their presence beyond 
a doubt. The observations were made in a room in the upper 
floor of one of the college buildings, the windows of which look 
toward the south-west, and command a clear view nearly to the 
horizon. The room during the observations received light only 
from the sky, which sufficed to render objects dimly visible. After 
being exposed only to this dim light for ^ih^exi or twenty minutes, 
the eye became sufficiently sensitive for observation. This was 
a very necessary precaution, as a moment's exposure to a bright 
light rendered the eye unfit for delicate discrimination of lumi- 
nous intensities for a long time. The Nicol of the instrument 
was now turned round and round, so that no previous know- 
ledge of its position relatively to the bands of the quartz plate 
might intiuence the judgment as to their character and position. 
On looking through the tube at the zodiacal light, and turning 
the whole instrument slowly round, it was possible to find a 
position where the bands could be seen, and their nature and 
direction determined. They could rarely be seen steadily by 
direct vision, and then only for a few moments, as the excite- 
ment and fatigue of the eye consequent upon the straining 
effort of vision soon rendered the field a confused blur. Allow- 
ing the eye to rest a few minutes, also on turning it obliquely 
and rapidly directing it to different parts of the field, and espe- 
cially by suddenly bringing it to focus upon* the quartz plate, 
the bands could be distinctly seen, and their direction fixed with 
a good degree of certainty. On the clearest nights the brightest 
bands (6, b, fig. 1) were seen without much difficulty, the broad 
dark band (a), corresponding to an inclination of 45^ in the 
Nicol, less easily, and the dark bands (6, A, fig. 2) by glimpses. 
After determining, by repeated observations, the angle made by 
each of the bands with some fixed line, as the axis of the zodiacal 
light, or a line nearly parallel to it drawn between two known 
stars, the position of the plane of polarization was found, by 
means of light from a gas- flame reflected from a sheet of white 
paper placed in a suitable position, or by observing the position 

Digitized by VjOOQ IC 

of the Zodiacal Light. 17 

of the Nicol. The resalts of the numeroad observations of dif- 
ferent evenings were entirely concordant^ and showed that the 
plane of polarization pasaes through the sun^ as nearly as it was 
possible to fix its direction. In no instance when the sky was 
clear enough to render the bands visible did their position^ as 
determined by the observations, fail to agree with what would 
be required by polarization in a plane through the sun. Not 
the slightest trace of bands was ever seen wl^n the instrument 
was directed to other portions of the sky. 

These observations, for the most part, were made in the ten 
days preceding new moon in January and February of the pre- 
sent year. During this time there was an unusual number of 
clear nights, with the atmosphere cold and still. A few good 
evenings in March and April also were improved in verifying 
the results previously obtained. The absence of the moon, and 
the distance of any of the brighter planets and stars from the 
field of observation, removed all uncertainties from these sources. 
As the instrument was directed to points from 30 to 40 or even 
more degrees from the sun, the polarization could not have pro- 
ceeded from faint vestiges of twilight. That it did not arise by 
reflection of the zodiacal light itself in the atmosphere, or from 
atmospheric impurities, is shown both by its amount and the fact 
that it was always most easily discernible on the clearest nights. 

The next step was to determine what percentage of the light 
is polarized. The failure of the common apparatus to detect it 
shows that the proportiou is not large ; but it must be recollected 
that for a light so very faint much greater differences of inten- 
sity are imperceptible than in cases where the luminous intensity 
is greater. The determinations were made as follows. A bundle 
of four pieces of excellent plate glass was placed vertically at the 
centre of the horizontal divided circle of a DeleuiPs goniometer, 
the telescope of which was replaced by the polariscope used in 
the preceding observations. The latter was so placed that iu 
axis was perpendicular to the surface of the bundle when the 
index of the goniometer was at zero. With the instrument thus 
adjusted no bands are seen when unpolarized light is passed 
through it ; but on turning the glass plates bands become visible 
corresponding to polarization in a vertical plane. The amount 
of the light polarized by refraction through four glass plates at 
different incidences has been calculated by Professor W. G. 
Adams* for intervals of 6^ from 10° to 70°, and at 72°. Taking 
the values given in his Table for crown glass ()b(=sl*5), those for 
intermediate angles are readily determined by interpolation, or 
graphically. The latter method was employed, a curve being 

* Monthly Notices of the Royal Astronomical Society* March 10, 1871, 
p. 162. 

Phil. Mag. S. 4. Vol 48. No. 815. July 1874. C 

Digitized by VjOOQ IC 

18 Prof. A. W. Wright on the Polarization 

drawn representing all the values in the Table. The results 
given in the Table correspond very well with those obtained by 
Professor Pickering*, who verified his values experimentally, 
and showed that the deviation from theory in the case of four 
plates only becomes perceptible above 65^. As Professor Pick- 
ering used the value /a =1 '55, the numbers in his Table are 
slightly greater than those used in constructing the curve from 
Professor Adams's Table. 

The determinations were made by observation of the percent- 
age necessary to render the bands visible with the same distinct- 
ness as in the zodiacal light. A set of experiments were made 
with light from the clear sky in a moonless night, the instrument 
being directed to one of the brightest points of the galaxy, 
where the light, though less bright than that of the zodiacal 
light, did not very greatly diflFer from it in intensity. The glass 
plates being turned until the bands had the same degree of di- 
stinctness as in the previous observations, the mean of several 
observations gave as the polarizing angle 41^, corresponding to 
a percentage of 20*5. This value, on account of the inferior 
brightness of the light compared, is somewhat too large, and 
may be taken as an upper limit. 

To find a lower limit and, at the same time, an approximate 
value, light reflected from a nearly white wall with a dead sur- 
face was employed. The point observed with the instrument 
was so chosen as to be equally distant from two gas-flames so 

f>laced that the planes through them and the axis of the po- 
ariscope were at right angles, thus giving light entirely free 
from polarization. The flames were now turned down equally, 
so that the field had, as nearly as could be estimated, the same 
brightness as it had with the zodiacal light. A small scratch 
upon the quartz plate, which could just be seen by the light of 
the latter, served as a means of control in adjusting the inten- 
sity. The experiments being conducted as before, gave, as the 
mean of numerous determinations, the angle 86^*6, correspond- 
ing to a proportion of 16 per cent.^ which is probably not far 
from the true value of the amount sought. Another, in which 
the light was made perceptibly brighter than that of the zodiacal 
tract, gave for the angle 28^*5, and a percentage of 9*4, which 
is certainly too small. We may safely take 15 per cent, as near 
the true value. 

The fact of polarization implies that the light is reflected, 
either wholly or in part, and is thus derived originally from 
the sun. The latter supposition is fully confirmed by various 
spectroscopic observations, of M. Liais f. Professor C. Piazzi- 

* Silliman's American Journal, S. 3. vol. vii. p. 102. 
t Comptes Rendus, 1872, vol. Ixxiv. p. 262. 

Digitized by VjOOQ IC 

of the Zodiacal Light. 19 

Smyth 'i'^ and others^ which show that the spectram is continuous, 
and not perceptibly di£ferent from that of faint sunlight. The 
writer has also made numerous observations with a spectroscope 
specially arranged for faint light, of which an account will be 
published hereafter, and which lead to the same conclusion. It 
may be mentioned further that a particular object in these ob- 
servations was to determine whether any bright lines or bands 
were present in the spectrum, or whether there is any connexion 
between the zodiacal light and the polar aurora ; and the results 
give, as an answer to the question, a decided negative. This is 
important here, as excluding from the possible causes of the 
light the luminosity of gaseous matter, either spontaneous or 
due to electrical discharge. The supposition that the light is 
reflected from masses of gas, or from globules of precipitated 
vapour, is not to be entertained, since, as Zollnerf has shown, 
such globules in otherwise empty space must evaporate com- 
pletely, and a gaseous matter would expand until its density 
became far too small to exert any visible effect upon the rays of 

We must conclude, then, that the light is reflected from mat- 
ter in the solid state — that is, from innumerable small bodies 
revolving about the sun in orbits, of which more lie in the 
neighbourhood of the ecliptic than near any other plane passing 
through the sun. Although such a cause for the zodiacal light 
has often been assumed as probable, no satisfactory proof of it 
has hitherto been found ; and the establishment of the fact of 
polarization was necessary to its confirmation, since spectroscopic 
appearances alone leave it uncertain whether the matter is not 

If these meteoroids, as there is no good reason to doubt, are 
similar in their character to those which have fallen upon the 
earth, they must be either metallic bodies, chiefly of iron, or 
stony masses with more or less crystalline structure and irre- 
gular surfaces. If we accept Zollner's conclusion that the 
gases of the atmosphere must extend throughout the solar sys- 
tem, though in an extremely tenuous condition in space, the 
oxidation of the metallic meteoroids would be merely a question 
of time. They would thus become capable of rendering the 
light reflected from them plane-polarized ; and the same effect 
would in any case be produced by those of the stony character. 

In order to ascertain whether the proportion of polarized light 
actually observed approached in any degree what might be ex- 
pected from stony or earthy masses of a semicrystalline cha- 
racter with a granular structure and surfaces more or less 

* Monthly Notices of the Royal Astronomical Society, June 1872, p. 277* 
t l/«6er die Natur der Cometen, p. 79 ^t seq. 


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20 On the Polarization of the Zodiacal Light* 

rough, a large number of substances possessing these charac- 
teristics were subjected to examination with a polarimeter. For 
this purpose the apparatus already described was employed, 
there being added to it a support for the object, with a hori- 
2ontal circle for determining the azimuths in placing the object 
and the light. The substances examined had approximately 
plane surfaces, which were placed vertically and so that the 
normal, at the point observed, bisected the angle between the 
lines from it to the eye and the illuminating flame. The light 
being thus polarized in a horizontal plane, was depolarized (that 
is, compensated) by turning the glass plates through the neces- 
sarv angle, the percentage corresponding to which was immedi- 
ately found by means of the curve. 

If we suppose a line drawn from the place of observation to a 
point in the zodiacal light, and another drawn from the sun to 
this at its nearest point, the two lines would meet at right 
angles ; and a surface at the point of intersection must be so 
placed as to have an incidence of 45^ in order to send the re- 
flected light to the eye of the observer. We may in general 
assume that there would be as many meteoroids on the nearer 
side of the line from the sun as on the other. Those on the 
more remote side, while presenting a larger illuminated surface, 
would reflect the light at a smaller angle, and therefore polarize 
a smaller amount of it. Those on the earthward side would 
send less light to the earth, but polarize a larger proportion of 
it. The differences would so nearly complement one another 
that we may take their united effect as equivalent to that of a 
body placed at the point of intersection mentioned above. For 
this reason the objects tested were so placed that the angles of 
incidence and reflection were 45°. . 

Some of the substances, and the percentages obtained, were 
as follows : — ^Porphyry, ground smooth but not polished, 35 per 
cent. ; another surface thickly covered with accumulated dust, 
16*5 ; dark blue shale, 25*7 ; syenite, coarsely crystalline and 
rough, 16'4; gneiss, rather fine-grained, 8*8; granite, fine- 
grained, 11*8; red jasper, rough broken surface, 23*5; sand- 
stone 12*1 ; brick, rough fragment, 8*1 ; the same, smooth sur- 
face, 11*3; red Wedgewood ware, unglazed, 14*2; indurated 
clay, light brown, 11; mortar, whitewashed surface, 12*1; the 
same, rough side^ 6 ; white chalk, cut plane, 2. A fragment of 
the great meteorite of Pultusk, which the writer owes to the 
kindness of Professor 0. C. Marsh, gave from a broken surface 
11*7, from the blackened surface, 36 percent, of polarized light. 
It is of the stony class, and of a light bluish grey colour. 

The results show that from surfaces of this nature the light 
reflected has in general but a low degree of polarization, not 

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On the Constant Currents in the Air and in the Sea. 21 

greatly different, on an average, from that found in the zodiacal 
light. Although no certain conclusions can be drawn from ex- 
periments like these^ their results are not inconsistent with the 
supposition in reference to which they were made, but, so far as 
they go, tend to confirm it. The results of the investigation 
may be summarized as follows : — 

1. The zodiacal light is polarized in a plane passing through 
the sun. 

2. The amount of polarization is, with a high degree of pro- 
bability, as much as 15 per cent, but can hardly be as much as 
20 per cent. 

8. The spectrum of the light is not perceptibly different from 
that of sunlight, except in intensity. 

4. The light is derived from the sun, and is reflected from 
solid matter. 

5. This solid matter consists of small bodies (meteoroids) 
revolving about the sun in orbits crowded together toward the 

Yale CoUege, April 6, 1874. 

IV. 7%^ Constant Currents in the Air and in the Sea : an At- 
tempt to refer them to a common Cause. By Baron N. Schil- 
ling, Captain in the Imperial Russian Navy*. 


THE currents of the sea and of the atmosphere have been 
observed from times immemorial ; much has been written 
on both ; but, unfortunately, science has hitherto made but very 
unsatisfactory progress in this department. The laws which 
govern them are still very little understood ; and their origina- 
ting causes, in particular those of the great ocean -currents and, 
indeed, of the trade-winds, are as good as totally unexplored, 
since, on closer examination, every explanation yet given must 
be regarded as not at all sufficient. A complete knowledge and 
u comprehensive theory of all currents will long remain impos- 
sible, because the currents are subject to the action of very 
various influences, and these, accompanied by very manifold cir- 
cumstances, exhibit themselves in such different fashions and 
are so complicated that it has not hitherto been possible to sub- 
mit them to exact mathematical analysis. Apart from the theo- 
retical difficulties, practice often opposes insuperable obstacles 
when we wish to trace a current through the whole extent of its 

* Tranilated from a separate publication commuiiicated by the author, 
entitled Die bestandigen Strdmungen, &c., Berlin, 1874. 

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22 Baron N. Schilling on the Constant Currents 

course* The air-currents escape our observations in the upper 
strata of the atmosphere^ and those of the sea in the depths of the 
ocean* Notwithstanding all the improvements of nautical instru- 
meuts, we still possess no means of accurately determining the 
currents at sea. Usually the ship's reckoning (f . e. the distance 
run in a certain direction) is proved from time to time by astro- 
nomical determinations of latitude and longitude ; and the dif- 
ference thus brought to light is without hesitation attributed to 
currents, although it may often result from quite different causes. 
Although the unsatisfactoriness of this method has long been 
acknowledged^ it is still universally retained for want of a 

The currents of the sea and those of the atmosphere have 
hitherto been considered apart — ^probably because water and air 
are^ in many respects, so very different ; but, in spite of this 
great difference, there can be no doubt that the movements of 
the sea and of the atmosphere, as fluids, are subject to the same 
general laws. For, in air as well as in water, gravity is the 
force which generates currents, because it tends to restore equi- 
librium wherever it has been disturbed. But equilibrium is 
disturbed only by the following three principal causes, which, 
again, are the same for sea and air : — 

A. Alteration of the specific gravity of the water or air ; 

B. The rotation of the earth on its axis ; 

C. The attraction of the sun and moon. 

We see, then, that the currents of the sea and the air depend 
on the same principal causes, and hence cannot well be separated 
in the consideration of their theory ; only the following circum- 
stances must be kept in view. 

1. The air is a highly elastic, readily expanding, gaseous 
body, while water is almost entirely destitute of elasticity. 

2. The atmosphere is heated by the sun principally in the 
lower strata, causing them to expand, become lighter, and, as- 
cending, communicate their heat to the higher. The sea, on 
the contrary, is heated by the sun's rays on its surface only to 
a very slight depth, and, in consequence of evaporation, gives up 
the greater part of its heat, as latent heat, to the air. 

3. In the atmosphere we mostly observe only the currents of 
the lower strata, and pay little attention to the upper currents, 
though the latter are often very different, both in direction and 
velocity, from the lower. In the water, on the other hand, we 
direct our attention mostly to the upper currents; and only 
quite recently have temperature-determinations at greater depths 
begun to throw a scanty light on the deeper currents of the 

4. The seas are bounded by continents, which set impassable 

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in the Air and in the Sea. 28 

lifluts to the currents^ and thereby exert great influence on their 
direction, extension, and velocity. It is quite otherwise with 
the atmosphere, which encompasses the globe, and is undisturbed 
in its free motion, save, perhaps, in some degree by lofty moun- 
tain-ranges. But, on the other hand, currents may arise in the 
atmosphere through the influence of the interior parts of the 
continents, to which the sea has nothing to correspond. 

Lastly, mention should be made of a certainly only conventional 
difference between air- and ocean-currents. This is, that the 
winds are universally named after the point from which they 
come, while ocean-currents always bear the name of the point 
toward which thev flow. This difference of nomenclature ap* 
pears at first sight inconvenient; but use has so naturaliied 
these designations in all languages that, as Laughton^ quite cor- 
reetly remarks, any attempt to alter this custom would ouly give 
rise to misunderstandings. To impress this upon young sailors, 
the following phrase is used in the Russian navy : — *^ The wind 
blows to the card ; currents flow from the card.'' 

The differences just mentioned between the air and water ex- 
plain why the currents in the atmosphere often appear to us 
quite different from those of the ocean, since the two classes of 
currents are exposed to the action of so manv and various colla- 
teral circumstances that the community of their fundamental 
laws can almost be no longer discovered. And yet we must be 
clear about these fundamental laws before we can enter upon the 
consideration of the collateral actions. 

The constancy with which the great ocean-currents and the 
trade-winds move, and the analogy which prevails between them, 
justify us in believing that they are less exposed to the opera- 
tion of secondary causes and, therefore, are especially adapted 
for the study of the general laws of currents. Hence we will 
examine singly the above-named three causes, which, to our 
knowledge, are alone capable of disturbing the equilibrium of 
the sea and the atmosphere. We will ascertain how far each of 
them is to be regarded as a generator of the constant sea-cur- 
rents and the trade-winds, and in what measure it answers to 
the existing explanations of these currents. The shifting winds 
and smaller coast-currents we will in general leave unnoticed, 
because (as already said) our information is still much too 
limited for us to be able to form even the remotest idea of a 
theory embracing all currents. 

However, before we come to the examination of the forces 
which call forth the constant currents, we will briefly describe 
the great oceanic currents and the trade- winds, and indicate how 

* Physical Geography (London, 1870), p. 176. 

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24 Baron N. Schilliug an the Constant Currents 

the origination of these natural phenomena is at present ac- 
counted for. 

Constant Currents and Trade-winds, Views hitherto held on 
their origin. 

The analogy which subsists between the constant currents of 
the different oceans, as well as between the trade-winds and the 
equatorial currents, is most striking. 

Both in the Atlantic and in the Pacific and Indian Oceans 
there flows from east to west, on each side of the equator, a cur- 
rent extending over about 20 degrees of latitude* and many 
thousand feet deep. This is named the equatorial current^ 
while for more particular designations the names of the ocean 
and hemisphere in question are added. Between these two 
equatorial currents, there is found in all three oceans, nearly on 
the equator, a relatively narrow zone, in which either no current 
or one flowing in the opposite direction is observed. The equa- 
torial streams continue their westward course till they encounter 
coasts, which turn aside their direction, according to the posi- 
tion of the coasts, and give them a more or less meridional direc- 
tion, until, in both hemispheres, in the vicinity of 40^ lat. they 
turn eastward to intersect the ocean again in this direction* 
This latter stream, flowing from west to east, pretty well takes 
in a zone of 10 degrees of latitude, and in all the oceans and 
both hemispheres is met with between the 40th and 50th 
parallels. This stream has different denominations in different 
oceans ; but Miihry gives it the general name of the equatorial- 
compensation stream ; for, arrived at the eastern boundary of 
the ocean in question, the stream turns back again into the 
equatorial region, to begin afresh its westward course. In this 
way, in each hemisphere, regular circulations are formed, which 
are comprehended under the denomination of rotation-currents. 
In the centre of these circulations, about in the region of the 
80th degree of latitude, there is in all the oceans a broad strip 
in which no current is observed, and which is known by the 
name of the Sargasso-sea. To these currents parallel to the 
equator, with their included streamless zones, the trade-winds 
with their zones of calms exactly correspond. On each side of 
the equator there is a zone from 16 to 20 degrees broad in which 
a constant trade- wind blows in the principal direction of east to 
west. In the vicinity of the polar boundary of this zone the di- 
rection of the wind is indeed mostly, in the northern hemisphere, 
from the north-east — and in the southern, from the south-east. 
In the middle latitudes, chiefly between the 40th and 50th 

* In the Indian Ocean the northern equatorial current, interrupted by 
the south coast of Asia, has less breadth. 

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in the Air and in the Sea. 25 

parallels^ therefore entirely as with the compensation-currents, 
constant west winds prevail, under the name of anti-trades. 
Between these constant air-currents there are, just as with the 
' sea-currents, both in the vicinity of the equator and not far from 
the 80th degree of latitude in both hemispheres, zones of no 
wind, which are known by the name of the equatorial and the 
tropical calms. The trade-winds, with the calm-zones belonging 
to them, shift a little with the seasons — ^in the summer of the 
northern hemisphere moving somewhat northward, and in the 
winter toward the south. In the currents of the ocean this 
shifting of the zones is less marked; hence the currents of 
water and air do not exactly correspond ; yet, excepting slight 
deviations, the trade-winds with their calms present the same 
picture as the equatorial currents with their streamless zones. 
In spite, however, of this striking similarity, the trade- winds 
have till now been ascribed to quite different causes from those 
of the gre-at rotation-currents of the ocean. 

We shall presently return to this subject; we will now only 
mention further that the rest of the great currents in the dif- 
ferent oceans likewise correspond so completely that the exist- 
ence of very determinate laws must thence be inferred. Thus 
the Gulf-stream and the Japanese Kurosiwo exhibit precisely 
the same phenomena : both are currents of warm water, flow in 
a north-easterly direction, and are separated from the coast to 
the west of their course by a cold current flowing in the oppo- 
site direction. The cold current of Peru corresponds to that of 
South Guinea, just as does the warm Brazilian current to that 
of Mozambique. Lastly, a feeble current from south-west to 
north-east prevails in the entire south polar sea. 

The trade- winds have from the 17th century been represented 
as polar winds which are deflected from the direction of the meri- 
dian by the earth^s rotation : this theory was, as far as we know, 
first set up (very imperfectly, it is true) by Varenius, in 1660; 
it was subsequently improved by Halley in 1686, and Hadley 
in 1785, and is for the most part named after the latter, as it 
has since made no advance. That this theory has been so gene- 
rally accepted is so much the more surprising, as many pheno- 
mena of the trade-winds are scarcely in accordance witn it. 

According to this theory, the masses of air in the equatorial 
regions, rendered lighter by heating, are continually ascending, 
through which the cooler and heavier air of higher latitudes is 
impelled to flow toward the equator. As the velocity of rota- 
tion is greater at the equator than at any other latitude, and 
gradually diminishes to the poles, while the air-particles (by the 
law of inertia) do not at once take up this greater velocity as 
soon as they arrive at parallel circles where the motion is more 

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26 Baron N. Schilling im the Constant Currents 

rapid, the polar wind is turned westward, and expresses itself in 
the northern hemisphere by a north-east, in the southern by a 
south-east wind. In the higher strata the ascending air returns 
to the poles to serve as a compensation for the air which has 
flowed thence to warmer latitudes. As this upper anti-trade 
streams polewards, it receives from the rotation of the earth a 
deflection eastward in both hemispheres. Compressed by cool- 
ing and the polar convergence of the meridians, it sinks at about 
the latitude of 80^ to the surface of the earth and so forms the 
constant west wind of the middle latitudes. The ascent of the 
air at the equator and its descent in 30° lat. will produce in the 
first case the equatorial calms, and in the second the calms of 
the tropical zones. 

This is, as briefly as possible, the generally recognised theory 
of the trade-winds, which, however, is not at all adapted for ex- 
plaining the perfectly analogous rotation-currents of the ocean. 

The equatorial current is still regarded by manv as a drift- 
stream produced by the trade-winds. This already long-per- 
sistent opinion received such a confirmation by the authority of 
Franklin and Rennell, that, notwithstanding its forcible refuta- 
tion by Maury and MUhry, it is still maintained, although only 
in England. For instance, Herschel, Carpenter, and Laugh- 
ton have recently pronounced in favour of this explanation. 
Far more prevalent, however, is now the view that the cause 
of the equatorial current is to be sought immediately in the 
axial rotation of the globe. Columbus, the discoverer of this 
current (in 1492), accounted for it by the universal motion of 
the heavens {con los ciehs) from east to west*. This notion of 
the ^'primum mobile ^' was followed by all, till Kepler at the 
commencement of the 17th century pointed out, and Yarenius 
(1650) proved in detail, that the current was occasioned not by 
the "primum mobile/' but by the rotating motion of the earth, 
the water not being able to keep up with the earth^s rapid mo- 
tion. Miihry, the chief authority on ocean-currents, substanti- 
ally shares this view, only giving to it a different and not quite 
intelligible expression. He saysf* as Fourier j: before him, that 
the staying behind of the water is effected by the centrifugal 
force of the earth. By this expression we are accustomed to 
understand the force that throws off from the centre, which 
always acts in the direction of the radius of each parallel circle ; 
and hence we cannot see how this force could cause the swift- 
ness of rotation of the water to be less than the rotation-velocity 
of the entire globe. 

♦ Kohl, Geschichte des OolfstromSt p. 30. 

t Ueber die Lehre von den MeereS'Stromungeny p. 5. 

J Ann. de Chim, et de Fky$. 1824, p. 140. 

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m the Air and in the Sea. 27 

On the other hand^ Miihry accounts for the compensation- 
corrent, flowing in the middle latitudes from west to east, by 
the aspirating or attracting force of the equatorial current — that 
is, by the tendency of water to find its levels which impels it to 
fill up the void caused by the primary current. He therefore 
makes the aspirating force operate in a vast arc across the 
entire ocean^ and chiefly between the 40th and 50th parallels of 
latitude — a decided circubu vitiogus. 

The meridional currents* are mostly accounted for by the 
constant difference of temperature of the equatorial and polar 
re^ons ; and Miihry attributes to the cold and heavy polar flow 
the primary, and to the warmer and lighter compensating anti- 
polar flow the secondary action. At the same time, in conse- 
quence of the velocity of the earth^s rotation progressively dimi- 
nishing in the direction of the poles, all the cold or polar streams 
receive a deflection of their direction to the west, and the warm 
autipolar currents a deflection eastward. Franklin and Bennell 
explained also the meridional currents by the action of the 
trade-winds ; for they believed that by the driving force of these 
winds the waters are accumulated in the Gulf of Mexico and 
are discharged in the Gulf-stream, — a view that probably now 
possesses scarcely any adherents. 

Having briefly indicated the existing explanations of the 
origin of the great ocean-currents and the trade-winds, we will 
now endeavour to ascertain in what manner each of the three 
forces before mentioned is capable of acting upon the currents, 
how their influence must express itself, and, finally, how far the 
explanations hitherto given correspond with the facts. 

A. Alteration of the Specific Gravity of the Water 
AND Air. 

a. Difference of Temperature. 
Every material substance possesses the property of occupying 
a greater space when its temperature is raised, while still re- 
taining the given number of its molecules and its weight. From 
this it follows that, after a rise of temperature of a body^ fewer 
of its particles can find room in a given space; so that the 
specific gravity must diminish with rise of temperature. Sub- 
stances of different kinds differ widely in their degrees of ex- 
pansion, and hence also in the alteration of their specific gravity. 
According to determinations by Ermanf, sea- water expands 
0*00027 of its volume with every degree between 0** and 12° R. 
On this ground it has been calculated ;[ that the entire mass of 

^ These, which flow in the direction of the meridian, Miihry calls lati- 
tudinal. T Pogg. Ann, vol. xz. p. 114. 
I Biflchof, Lehrbuch der chem, u, phys. Oeologie, p. 7- 

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28 Baron N. Schilling on the Constant Currents 

equatorial water would stand 14 feet higher than the water of 
the polar seas^ if it could not flow off. It has been thought 
that this tendency of the equatorial water- surface to rise would 
serve to account for the Gulf-stream^ which accordingly would 
flow down hill. But this inconsiderable elevation of the surface 
of the equatorial sea would not give a fall of even ^ inch in a 
German mile, which, in relation to the velocity, is much too 
little. Even the assumed elevation of the surface, however, can 
never actually be produced; for as soon as any particles of 
water become a little lighter, they must, in obedience to the law 
of gravitation, immediately spread uniformly over the entire 
surface. Thereby is necessarily produced a flow of the warmer 
and therefore lighter superficial water to the colder regions, and 
of the heavier cold water at the bottom to the warmer regions. 
Such an exchange of the waters of the warmer and colder seas 
exists in reality. A proof of this is furnished by the tempe- 
ratures of the ocean diminishing with increasing depth — the 
temperatures of the greater depths being very low, even in the 
equatorial regions. An exception to this rule is formed by 
those seas which are divided from the ocean by a ridge over 
which the water is considerably less deep. In such seas the 
temperature sinks merely to a depth corresponding to the height 
of the water above the ridge, and below that remains nearly 
unaltered, because the colder water, cut off by the ridge, can 
have no influx. We have an example in the Mediterranean, 
united with the ocean by the Straits of Gibraltar, the depth of 
which is onlv a little over 100 fathoms, — and in the Skagerrack 
and some Norwegian fjords, for which the bottom of the pro- 
portionally much shallower North Sea forms a ridge. It is 
therefore unquestionable that water flows at the surface of the 
sea out of warmer into colder, and in its depths out of colder 
into warmer regions ; so that there only remains to get an idea 
of the velocity of these currents. 

Water, as a bad conductor of heat, is warmed only very 
slowly, and expands just as slowly. Now, as this expansion is 
moreover very trifling, the streaming produced by difference of 
temperature must likewise be only an extremely slow, creeping 

In order to give an idea of the origination of the meridional 
currents from difference of temperature. Dr. Carpenter showed, 
on the 9th January 1871, at the Royal Geographical Society in 
London, the following experiment. He filled a glass tank, 
several feet long, with water, which at one end of the tank he 
cooled with ice, and at the other end, bymeans of a special 
arrangement, he heated at the surface. The cooled water was 
coloured red ; the heated, blue. At the close of the lecture. 

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in the Air and in the Sea. 29 

which may have lasted an hour^ the blue water had moved along 
the surface^ and the red along the bottom ; but^ notwithstanding 
the pretty considerable difference of temperature and the length 
of time, the coloured water particles had travelled only a few 
feet. This experiment proves, therefore, only what we have 
already said — ^that through difference of temperature an ex- 
change of the water particles must take place, but that this 
exchange proceeds verv slowly, even with considerable difference 
of temperature and with little distance between the differently 
heated waters. 

In nature, however, the difference of temperature of sea- 
water is proportionally inconsiderable, never amounting in the 
whole to more than about 80^ C, while this difference is dis- 
tributed over the vast distance of the polar from the equatorial 
seas. It thus appears, then, impossible that this cause can have 
power to set in motion such a current as the Oulf-stream. Even 
the mass of the heated water, which is so readily invoked, cannot 
here exert any accelerating action, because only an incon- 
siderable superficial layer is warmed by the sun, and nothing 
hinders the direct, gradual, and immediately complete inter- 
change of the water particles. Only when large basins of 
water of different temperatures are united by a channel can the 
mass of the warmer water play a part, and the difference of 
temperature generate a considerable current in the channel. 
Thus, for example, we may regard the northern part of the 
Atlantic between Norway and Greenland as a broad channel 
connecting the north-polar basin with the ocean. 

The air, however, expands 15 times as much by heating as 
water^ and the influence of temperature-difference on air- 
currents is undeniable ; yet even here that influence is generally 
very much overrated. For air, as well as water, is a bad conductor 
of heat, and therefore only slowly changes its temperature and 
therewith its specific gravity. Hence we are decidedly of 
opinion that the expansion of air by heating in the open can at 
most occasion only a gradual inflow of air^ never a sudden gust 
or a rapid fall of the barometer. The gradually heated air 
rises only gradually and slowly, and is just as slowly replaced 
by cooler air. A burning light, or a cbimney-fire gives us the 
best proof of the correctness of this assertion. Although the 
temperature produced in the fireplace is incomparably higher 
than ever occurs in nature through the heat of the sun, and the 
draught is artificially increased by the height and narrowness 
of the flue, yet this draught is so inconsiderable that it can 
seldom carry up a piece of paper thrown into the chimney, and 
even the ashes of burnt paper are hardly lifted. This shows us 
that even a strong heating occasions only a slow ascent of the 

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80 Baron N. Schilling on the Constant Currents 

air ; so that by it^ at all events in ordinary circumstances, a 
breath of air, but no wind, can be produced. In a forest-con- 
flagration, the enormous heat appears to cause a considerable 
ascending current of air; but even then the inflow of air 
thereby e£fected is perceptible only in the immediate vicinity of 
the burning. 

Hence we believe that wind can mostly arise only from con- 
densation of the aqueous vapours in the atmosphere, which 
possess the property of very suddenly changing considerably 
their degree of elasticity and the pressure resulting from it ; 
this must, of course, exert a great influence on all atmospheric 
phenomena. Certainly the elasticity of the aqueous vapour 
stands in the closest relation with the temperature, which so 
far, therefore, operates indirectly in the origination of wind. 
Whether change of temperature is the only cause of the con- 
densation of vapour, we know not : as, when the aqueous vapours 
are condensed, electricity is always set free, perhaps conversely 
the condensation may be caused by electricity. 

At any rate it is changes in the tension of the aqueous vapour 
that produce strong winds ; and only in very peculiar cases can 
the, by itself, slow expansion of the air develop stronger winds. 
Thus, for instance, when the greater portion of a continent is 
powerfully heated by the sun, the mass of air rising, though 
only slowly, from the whole of the vast surface, would require 
for its replacement (that is, for the restoration of equilibrium) 
such a mass of air that the inflow must be much accelerated, 
because it forms a stratum of little height in comparison with 
the magnitude of the heated surface. An example of winds 
thus produced is afforded by the monsoons. Over the ocean the 
atmosphere can never be so much heated as over the land ; and, 
besides, evaporation of the water of the sea and the elasticity of 
the aqueous vapour are augmented as the temperature of the air 
rises. If, therefore, the expansion of the air diminishes the 
atmospheric pressure, on the other hand the augmented elasticity 
and quantity of aqueous vapour will again increase it ; and it is 
difScult to decide which of these two may exert the greater in- 
fluence. Admitting that the diminution of the atmospheric 
pressure by expansion of the air is greater than the rise of the 
pressure by aqueous vapour^ it yet appears to us self-evident 
that the wind resulting from the heating of a continent must be 
much stronger than that produced by the heating of the air 
over the ocean, supposing both to take place over very consider- 
able spaces. 

If, then, the recognized theory of the trade-winds were cor- 
rect and they were produced by the ascent of the heated air, the 
trade- winds would blow in summer towards the Sahara, since 

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in the Air and in the Sea. 81 

there the thermometer not seldom shows 50^ C. in the shade^ 
while in the equatorial regions of the ocean the temperature of 
the air never rises above 30** C. The trade-wind, however, at 
the north-west coast of Africa blows constantly from the desert, 
carrying the fine sand far out to sea. 

Farther, in summer the temperature of the 20th and 30th 
degrees of latitude is not lower, indeed it is higher than that of 
the equator, and yet the shifting of the trade-zones is inconsi- 
derable, and the wind keeps its usual direction. 

Likewise, according to Hadley's theory an ascending or a de- 
scending current should prevail in the calm-zones. Now this 
current must be very considerable, if it brings forth the fresh- 
blowing trades and anti-trades ; and the ascent of the air in the 
equatorial calms, and its descent in the tropical calms, would 
make themselves perceptible, even if the motion were very slow. 
This, however, is not the case : a particle of dust loosened from 
the sails falls, both in the equatorial and the tropical calm-zone, 
quietly to the deck, without exhibiting the slightest tendency to 
be impelled upward or downward. From this we conclude that 
the upward and downward currents of air in the zones of calms, 
if they really exist, must be so slight that the generation of the 
trade-winds and anti-trades cannot possibly be ascribed to 

Let it further be remembered that in the middle latitudes of 
the northern hemisphere the anti-trade often blows from the 
north-west instead of south-west, and in the southern hemisphere 
from south-west instead of north-west — which could not be, if, 
as required by Hadley^s theory, it formed a current directed 
toward the poles. 

Lastly, in Central Europe these constant west winds blow in 
summer very moderately, while in winter their force is much in- 
creased — which again does not correspond with the theory ; for 
in summer the eastern steppes are strongly heated and should 
attract the west wind, while the cold which prevails in Eastern 
Europe in winter would, on the contrary, contribute to the 
weakening of the west wind. 

All this and many other reasons'^ show that the existing 
theory of the trade-winds is not sufficient to account for the 
phenomenon, and that another must be sought. 

We do not on this account dispute that heated air must 
ascend ; we only believe that, since the heating and expansion 
proceed very gradually, the ascent must also be very slow and 
hence cannot constitute the principal cause of the trade-winds. 
Their main motive cause appears therefore to lie in other forces, 
of which we will speak subsequently. 

* Laughton, 'Phyrical Geography,' pp. 120-127. 

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82 Baron N. Schilling on the Constant Currents 

If, then^ difference of temperature can only call forth incon- 
siderable winds by the expansion of the air, it is clear that in 
water, so much less expansible, heated to only a proportionally 
slight depth, no great current can be generated by this cause. 
If this force were sufficient to occasion a considerable current, it 
would extend over the entire surface of the ocean, and not merely 
show itself in a narrow strip at its margin. 

We nevertheless allow that the heating of the water may, in 
certain cases, have an important influence on the maintenance 
and extension of an already existing current. If, e. g., a cur- 
rent arising from other causes strikes upon a coast, it usually 
takes the direction of this coast, along which it continues until 
it gets beyond the sphere of the action to which it owes its de- 
velopment. But if it accumulates at the coast the heated sur- 
face-water of the sea, the mass of warmer and lighter water, 
continually replaced, will perpetually exhibit the endeavour to 
spread over the heavier water of colder regions. Difference of 
temperature will therefore in this case have an essential influence 
on the continuance and the direction of the currents toward 
higher latitudes, but cannot independently generate the currents. 
This, then, explains to us also how it is that warm and cold cur- 
rents are found preeminently at sea-coasts. The first impulse, 
however, to the flowing which collects the heated water does not 
arise from difference of temperature, but always from other 
causes. The ascertaining of these initiating causes is of very 
great importance for the foundation of a theory ; for without 
accurate knowledge of the fundamental laws, we can get no 
account of the action of the accessory causes. 

Let us now consider the possible influence of evaporation. As 
already said, the evaporation of water is in close connexion with 
heat ; for with a rise of temperature the capability of the air to 
take up aqueous vapour is also increased. Hence much more 
water is evaporated in the equatorial regions than in higher 
latitudes; and the vapours are driven by air-currents into other, 
cooler regions, where, on the cooling of the air, they are given 
back to the sea as an atmospheric precipitate. Evidently from 
this cause must arise a sea-current toward the equator, though 
only a very inconsiderable one. Miihry calculates that in the 
tropics about 15 feet of water evaporate yearly, therefore 
about half an inch daily. Perhaps half of this evaporation is 
returned to the tropical seas as rain and river-water, and only 
the other half (J inch daily) returns by sea-currents from higher 
latitudes. But a current which in the course of 24 hours re- 
places only a layer of water a quarter of an inch in thickness, 
must be imperceptible. This slight current flows at the surface, 
and is directed to the equator ; it thus counteracts the current 

Digitized by VjOOQ IC 

m tlie Air and in the Sea, ' . 83 

arising from difference of temperature, which, as above remarked, 
must flow at the surface from warmer into colder zones. 

Evaporation, then, also cannot occasion any perceptible cur- 
rent in the open sea ; but in channels connecting an inland sea 
with the ocean a diflerence of level between the two seas, arising 
from greater evaporation of the inland sea, may occasion a strong 
current. We have instances of this in the Straits of Gibraltar 
and Babelmandeb. 

Let us now turn to the consideration of the influence which 
heat may have indirectly on the origination of sea-currents 
when, through its action upon the aqueous vapour in the atmo- 
sphere^ it generates wind. The action of wind upon the surface 
of water is familiar not only to the inhabitants of coasts, but to 
almost every one. Indeed we see in every pond how the water 
is driven by a strong wind ; and if the basin is flat and not very 
deep, not seldom does the water recede from the windward 
side, and accumulate on the lee side. Such heapingsup of the 
water in shallow bays, and at the mouths of great rivers, by 
strong winds occasion inundations. At a straight coast-line, 
too, the water may rise considerably by the force of the wind, 
if the depth inci*eaBe8 very gradually and thereby the outflow 
beneath is checked. 

Indeed, on the open sea the wind often drives the water 
before it, and thereby forms what ai« called drift or superficial 
currents ; but these, as irregular phenomena, do not here come 
into consideration; we can only occupy ourselves with those 
currents which are called forth by constant winds, t. e, the 
trade-winds. Even the constant action of the trade-winds, 
however, is hardly able to occasion any very deep-going current, 
as has already been sufficiently shown by Maury and Muhry. 

According to FitzRoy^s data, the highest waves rise to the 
height of 60 feet*, measured from the trough to the crest of the 
wave, therefore 30 feet above the smooth surface of the sea. If 
we might assume that the entire wave could be driven forward 
by the wind (which is decidedly assuming too much), thus 
would be produced a current of 30 feet depth. Through the 
friction of the water-particles, the efiect of the wind upon the 
current may become sensible somewhat deeper still ; but the 

* This number appears to us very high ; for we have often, in a severe 
storm, ascending the shrouds, tried to bring our eye into such a position 
that, at the moment when the ship was exactly in the trough, we could 
see several wave-crests in a hori2ontal Hne. The height of the eye above 
the ship's water-line then determines the greatest height of the wave. In 
this way J have only once at Cape Horn (where the waves rise uncommonly 
high) measured a height of 46 feet, and at the coast of Japan, in a typhoon, 
one of 38-40 feet ; at other times the height was mostly less than this. 

P/uL Mag, S. 4. Vol. 48. No. 315. July 1874. D 

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34 Baron N. Schilling; on the Constant Currents 


flowing must rapidly diminish downward^ and soon entirely 
cease. A. Findlay* thinks that the wind can never call forth 
a current of greater depth than 5 fathoms. James Croll's re- 
mark t> that the duration of the wind, as well as its force, must 
have great influence on the depth to which it acts, may to a 
certain extent be quite correct ; but, nevertheless, action of the 
wind upon currents at a depth of thousands of feet (as, for in- 
stance, in the equatorial current) is not possible; hence we 
must see that Franklin and Rennell's view, that the equatorial 
current results from the action of the trade-winds, cannot be 

Nature herself gives us decisive proofs against that view. 
With the shifting of the zone of calms it happens that the 
equatorial current flows just as well in that zone as in the trade- 
wind. In the Indian Ocean the change of the monsoons has 
scarcely any influence on the equatorial stream. The Gulf- 
stream often flows in opposition to very violent storms, which 
would be impossible if its motive force lay in the trade-wind. 

Even the opinion that the trade-wind raises the level of the 
Gulf of Mexico, and so produces the Gulf-stream, is untenable. 
In the flrst place, it is proved by the levelling of the isthmus of 
Panama and the peninsula of Florida that this is not the case, 
as the level of the Mexican Gulf pretty closely accords with 
both that of the great ocean and that of the Atlantic. Secondly, 
in the open sea an enduring higher level can never be product 
by the action of the wind ; for as soon as any particles of water, 
driven by the wind, change their place, they compel by their 
pressure just as many others immediately to take the place lef^ 
free by them. Only where the formation of the coast hinders, 
or at least impedes, this back-flowing motion, can an alteration 
of level take place. 

Certainly the mechanical pressure of the wind upon the sur- 
face of the water can, in the open sea, somewhat alter the level ; 
but as the wind mostly acts horizontally, or at a very acute 
angle, upon the surface, the mechanical pressure is so little 
that the oscillations of the sea-level brought about by it must 
likewise be inconsiderable. 

Just so must the variations of the atmospheric pressure exert 
an influence on the height of the water of the seas, and con- 
sequently also on their currents. When, for example, the 
barometer falls an inch, the surface of the sea at the place must 
rise 13'6 inches, and vice versd, and thus a current be formed 
from where the pressure is high to the region where lower pres- 

♦ A Dictionary for Navigation of the Pacific Ocean (London, 1851), 
vol. ii. p. 1222. Also Miibry, Geograph. Mittheilungen, 1872, p. 136. 
t Phil. Mag. October 1871, p. 2G8. 

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in the Air and in the Sea. B5 

sure prevails. It is self-evident that a current thus produced 
in the ocean can only be very inconsiderable and inconstant, 
since it changes with every change of the atmospheric pressure. 
This foi-ce, again, can only make itself perceptible in channels. 

Suppose that on an inland sea connected with the ocean 
only by a strait the barometer suddenly fell 1 inch, the level of 
this sea would stand 13*6 inches lower than equilibrium with 
the ocean at the moment would require. The mass of water 
wanting must therefore pass from the ocean through the strait. 

We must ascribe it to this circumstance that, in the Sound, a 
change in the direction of the current mostly occurs 24 hours 
before a change in the direction of the wind. Just so the water 
usually rises in the Gulf of Finland before the south-west wind 
comm^ices; and this rise is noticed also in winter, when the 
entire surface of the sea is covered with ice, and thereby the 
direct action of the wind is withdrawn. 

b. Saltness of Sea-water. 

Alterations in the saltness of seas greatly aflfect the specific 
gravity of the water. The observations, however, which have 
been made in different parts of the world have proved that the 
difference in saltness of the various oceans is extremely slight 'i^. 
This compels as to the conclusion that currents immediately 
tend to equalize the slightest difference in the saltness of the 

The causes of change in the saltness may be accidental and 
temporary, or constantly repeating themselves in certain regions. 
In the first case they produce variable currents, which do not 
belong to the subject we are considering; but in the second 
they must confer upon the water a constant tendency to inter- 
change, and call forth constant currents. 

In the equatorial regions^ for example, the half inch of water 
evaporated daily leaves constantly its salt behind, which, with 
the vast depth of the ocean, can hardly add perceptibly to the 
specific gravity of the rest of the water. 

Nevertheless this water, very gradually becoming slightly 
Salter and heavier, and sinking, must occasion in the depths a 
current, although a very feeble one, the direction of which must 
be into the regions where there is little evaporation and consider- 
able atmospheric precipitation, therefore into higher latitudes. 
Consequently, as we have already seen, the current called forth 
by the evaporation of the water counteracts that which is pro- 
duced by the expansion of the water from difference of tem- 

* ** On the Composition of Sea-water in different parts of the Ocean," 
Pbil. Trans. Roy. Sck?. London, 1865. ]). 203. 


Digitized by VjOOQ IC 

86 Baron N. Schilling on the Constant Currents 

In the polar sea much water is, in winter, turned into ice, 
and its salt separated. This salt adds, though only inconsider- 
ably, to the specific gravity of the cold, and hence already heavy, 
polar water, and^ebntributes a little to the undercurrent in the 
dii*ection of the equator ; so that it acts, contrary to the pre- 
ceding case, just the same as the difference of temperature. 
Perhaps it is partly owing to this, that the flow of the Gulf- 
stream is somewhat stronger in winter than in summer. 

In an extremely interesting article on the currents at the 
southern extremity of America, Miihry*, on the ground of the 
winter temperature of Patagonia, conjectures that the Brazilian 
current also is stronger in the winter of the southern hemi- 
sphere than in summer. 

In summer, when the polar ice melts, a superficial polar 
current results; for the water from the melting of the ice, 
having but little saltness, remains at the surface in spite of its 
coldness. Scoresby remarked that near Spitzbergen the water 
of the surface was warmer than at some feet depth ; and this 
observation has been recently confirmed by the Swedish Expe- 
dition and by the Norwegian Captain Ulvef* 

Unfortunately, we do not yet possess any accurate determina- 
tions of the greatest density of sea-water at different tempera- 
tures and under various pressures. At all events, however, 
Miihry^s view, that sea-water, as well as fresh water, attains its 
greatest density at -h4^C., appears destitute of proof; for it 
has recently been found that the temperature at very great 
depths is often below 0^ C. It is probable that the great pres- 
sure to which the water is there exposed has an influence in 
preventing it from freezing, even below 0^ C. If earlier obser- 
vations seem to contradict this, the reason may well be that the 
thermometers were not sufficiently protected against the pres- 
sure of the depths, and hence always gave the temperature of 
the bottom too high. On this defect rests also Uoss's well- 
known theory of a constant temperature of -h39^ F. at the 
bottom of the sea. 

At the mouths of rivers, the fresh water must spread upon 
the surface, and therefore give rise to a current running out- 
wards from the mouth, until it is mixed sufficiently with the 
salt water. To this end, however, the heavy salt water will 
flow in the opposite direction, toward the mouth — which, even 
with a slight current, must greatly favour the formation of 
sandbanks there. 

In the case of inland seas where the inflow is greater than the 
evaporation, as ^.^. in the Black Sea and the Baltic, just as 

* Petermann's Geographische Miltheilungen, 1872^ vol. xviii. p. 12G. 

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in the Air and in the Sea. 87 

"With rirer-mouths, the upper current in the channel of discharge 
will flow outwards, while an undercurrent of constantly salt 
water must flow inwards. But in seas where the evaporation 
exceeds the influx (for example, in the Mediterranean and the 
Red Sea), the upper current must flow in through the channel, 
and the undercurrent carry out the superfluous salt. An 
extremely interesting example of this sort is presented by the 
Gulf of Karabughaz, which is connected with the Caspian b^ a 
very flat channel of only a few feet depth. As the evaporation 
from the very spacious surface of the gulf, into which no streams 
flow, is very great, especially in summer, water is perpetually 
flowing in from the Caspian with a velocity that sometimes rises 
to 6 knots an hour. Of course this current brings much salt 
into the gulf, from which it cannot get out again, because the 
channel is too shallow to permit an outflow beneath. The salt 
thus accumulating is deposited in crystals on the bottom; and 
thus the Gulf of Karabughaz plays the part of a saltpan conti- 
nually withdrawing salt from the Caspian Sea. If in the course 
of time the sand washed in by the waves should completely 
block up the shallow strait which joins the gulf to the sea (which 
would long since have happened if the current were not so 
strong), Karabughaz as a lake would soon evaporate completely 
and leave behind a basin of solid salt, such as we see in the 
Elton-See and in lletzkaja Saschtschita as formations of pri- 
meval times. 

If in any part of the ocean animal life be developed in greater 
abundance than in others, the excessive abstraction of salt or 
lime from the water by the animals will also give rise to slight 
movements of the water. Although such movements could 
scarcely be called a current, it cannot be doubted that such must 
take place in the deepest seas even at the bottom, because other- 
wise no life would be possible there ; for among the animals 
living in the depths there are creatures that cannot change their 
place ; nourishment must consequently be brought to them by 

The theory of perfect stillness in the bottom waters of the 
sea * is therefore, like the theories of Boss and Forbes, to be 
regarded as incorrect. 

We have thus examined all the causes which afiect the specific 
gravity of sea-water and the air, and come to the conclusion thit 
differences of temperature and in the saltness of the water of the 
sea assist only in a slight degree in maintaining the great ocean- 
currents and the trade-winds, but cannot possibly produce them ; 

* Miifiry says, " At the bottom of the ocean we must assume that there 
is almost complete stillness."— L^Are uber die Metres- Stromungen, p. 6. 

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38 Mr. R, Mallet on the Tidal Retardation 

to explain the origiDation of these currents we must search for 
other forces. 

In certain cases, if an already existing current accumulates 
the heated water in greater quautity, the diflFerence of tempera- 
ture may indeed accelerate this current ; and in the air, if it 
operates over very considerable spaces, it can generate wind ; 
but in general it is the quickly condensing aqueous vapour 
which, by the diminution of its tension, plays the chief part in 
the production of wind. 

[To be continued.] 

V. Tidal Retardation of the Earth's Rotation. 
By Robert Mallet, F,R,S.* 

THE general idea of the retardation of the earth's rotation by 
the great tide-wave acting as a friction-brake as it pro- 
gresses under the coercion of the moon, commonly ascribed 
to Mayer, was, I have good reason to believe, anticipated by 
Emanuel Kant, though I have not been able myself to verify the 
passage in his writings. Of the real existence of such a re- 
tarding force, however small may be its effect, there can be little 
doubt since the masterly researches of Adams upon the moon's 
acceleration. The subject, probably from its inherent complexity, 
has attracted but little attention, except from astronomical 
mathematicians ; and some points respecting it which have been 
referred to in more popular work8, appear involved in some ob- 
scurity. Professor Tyndall, who, in his 'Heat a Mode of Motion,' 
gives a very lucid popular account of the phenomena (almost, 
as he states, in the words of Mayer), has in paragraph 697> 
p. 483 (4th edit.), the following passage : — " Supposing, then, 
that we turn a mill by the action of the tide, and produce heat 
by the friction of the millstones ; that heat has an origin totally 
different from the heat produced by another pair of millstones 
which are turned by a mountain-stream. The former is pro- 
duced at the expense of the earth's rotation, the latter at the 
expense of the sun's heat which lifted the mill-stream to its 
source." This distinction, it seems to me, cannot be main- 
tained. The power of a tide-mill is not derived from the 
rotation of the earth, nor from the retardation of that rotation 
by the great tide-wave. The sea, no matter from what cause, 
rises above its normal level, to which it after a time sinks again. 
If during the interval we can impound a portion of the mass of 
water so elevated and let it descend through some machine 
recipient of water-power, we have the tide-mill, the power of 
* Communicated by the Author. 

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of the Earth's Rotation. 89 

which is as directly derived from gravitation as is that of a 
water-mill upon a mountaia-streara. The water is raised in the 
former case by gravitation towai*ds the moon and by gravitation 
falls back towards the earth ; iu the latter it is raised by evapo- 
ration^ and falls back to the sea by gravitation. It is true that 
the earth^s and the moon's rotation are '^ inseparable accidents '' 
to the rise and then the fall of the surface of the sea at any 
particular point; but the source of the power is derived, not 
from the mechanism nor at the expense "of the earth's rotation/' 
but as directly from gravitation as is the case in any ordinary 
mill-stream. If I am wrong in this I shall gladly accept cor- 
rection. My chief object here, however, is to ask whether 
(assuming the actuality of retardation of rotation by the tidal 
wave acting as a brake, and be its amount more or less) there 
may not be other forces in action upon our globe tending to 
countervail this to a greater or less extent. It seems to me that 
there arc — though, so far as my reading goes, I have not seen 
-any notice of such on the part of physical writers. Every particle 
of matter (rotating as part of our earth) which descends from a 
higher to a lower elevation, must in doing so part with kinetic 
energy proportionate to its decrease in velocity of rotation between 
its higher and its lower positions, and the energy so lost is trans- 
ferred at the lower point to the earth itself. Every drop of water, 
therefore, every flake of snow that precipitates upon the higher 
parts of our globe, if assumed to reach these points without 
relative velocity, must in descending to the sea-level tend to 
accelerate the earth's rotation. So also every block of ice or of 
stone that descends from the mountain-tops, every particle of 
detritus carried along from higher levels towards the sea, must 
have the same effect. With regard to the first it may be said, 
every particle of water raised by evaporation from the surface of 
the ocean ascends into the atmosphere with only a velocity of 
eastward rotation due to the earth's radius at the sea-level, and 
at the latitude at which it is taken up, and that therefore when 
precipitated upon some much higher level it takes away from 
the earth as much kinetic energy as it returns to it in descending 
in streams again to the sea-level. But is this so? What 
actually passes when a particle of sea-water at the surface of 
the ocean, parting with its salt, rises therefrom under the in- 
fluence of the sun's heat, and becomes an invisible vapour 
held in suspension by the air, is to a great extent still un- 
known. The particle of water, whatever be its physical con- 
dition on leaving the liquid surface, undoubtedly only possesses 
the velocity due to its low position upon the earth's surface ; 
before it has risen even a fraction of an inch, however, it is taken 
possession of by the air (that is to say, by the winds) ; and all its 

Digitized by VjOOQ IC 

40 On the Tidal Retardation of the Earth's Rotation. 

subsequent movemeDts are coerced by them. Except througa 
the winds it has no point d^appui upon the solid earth. Now 
the movements of the winds, however largely modified by the 
form and rotation of our earth, mainly depend upon differences 
of temperature produced by the sun's heat ; it would seem there- 
fore that, so far as the kinetic energy of the ascending particle 
of vapour is concerned, it may or may not affect, and, if at 
all, very slightly, the horizontal motions of the winds, but can 
have no effect upon the rotation of the earth. 

The case is different, however, as soon as the particle of vapour 
raised by molecular forces to the level of a mountain-top is pre- 
cipitated thereon as rain or snow, and begins to desceod again 
towards the ocean whence it came : at every foot of its descent 
it parts with kinetic energy, which it transfers directly to the 
earth as a whole. On the other hand, such particles of vapour 
as assumed the form of rain or snow at greater or less elevations, 
and fall directly as rain^drops to the sea-level, can produce no 
effect in accelerating the earth's rotation, each drop being co- 
erced in its movements until within a short distance of the earth 
by the winds — that is, by the same molecular forces which raised 
them up. 

If this speculation be admissible, then we have a source of 
sensible acceleration to the earth's rotation in the vast volume of 
water which is precipitated upon the dry land and runs off into 
the ocean. Adopting Gardner's estimate of the surface of the 
land, exclusive of the antarctic continent, and assuming a mean 
annual rainfall for the whole earth of 60 inches per annum, and 
that two thirds of the entire rainfall returns to the ocean by 
streams and rivers, we have 23,891 cubic miles of water annually 
precipitated and fiEJling back into the ocean ; and assuming the 
mean height of the land to be about 1000 feet, this immense mass, 
on reaching the ocean, has lost kinetic energy due to the difference 
in velocity of rotation between the earth's mean radius at the 
sea-level and the same plus 1000 feet, the portion of this which 
is effective in producing acceleration depending upon the cosine 
of the latitude. 

As respects the descent of solids from higher to lower levels^ 
there seems no room for doubt as to their tendency to produce 
acceleration in the earth's rotation. It is true that at remote 
epochs, when continents and mountains were originally ele- 
vated, their uplifting tended to retard the earth's rotation, and 
that their complete ablation could do no more than restore the 
energy of rotation the earth had before their upheaval. But 
the ocean- bed was depressed ; and its area is four times that of 
the land, and its mean depth probably greater than the mean 
height of the continents ; if, therefore, we assume the present 

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On some points in Mallet's Theory of Vulcanicity. 41 

ocean-level as a datum plane^ the changes of level originating 
land and sea may have tended rather to accelerate than retard 
the earth's rotation. Taking the mean of the sediment stated 
to be carried by six great rivers, namely the Mississippi, Po, 
Vistula, Rhine, Ganges, and Rhone, it amounts to about y^Vir 
in volume of the water discharged ; and if we apply this to the 
water discharged from the whole surface of the land, as above 
stated, we have -8j^^^= 19*90 cubic miles of sediment annually 
discharged at the sea-level. These rough estimates are pro- 
bably far from correct, and we do not know with any pre- 
cision what is the mean specific gravity of this sediment, nor 
from what mean height it may be considered to have descended ; 
but we can easily see that the loss of rotative energy during the 
descent of this vast mass, if transferred to the globe as a whole, 
is scarcely negligible. Nor does this represent all that we have 
to deal with. The sediment finally carried into the sea repre- 
sents the real annual degradation of the land by rain and rivers ; 
and the huge block that falls to-day from a Sierra summit and 
wedges itself a few miles off immovably in the cleft of a canon, 
though it may not reach the sea for thousands of years, daring 
which it is slowly transformed into sediment, is nevertheless 
effective, as is the ice which thaws or falls in avsJanche, in trans- 
ferring to our earth the energy of rotation they lose in descent. 
Whether or not it be true that, viewed on its largest scale and 
at some indefinitely remote period yet to come, the movements 
of all the bodies of the universe tend to ultimate rest, and an 
end of the present order of things, it seems a fact that all the 
smaller perturbations of planetary movement at least, as for 
example those of precession and nutation, are involved in con- 
ditions which prevent their passing a certain limit, and which in 
other cases equilibrate the disturbing cause. It would seem, 
therefore, contrary to analogy to suppose the case of the retar- 
dation of our globe by tidal friction, whatever niay be its actual 
amount, to be an exception and to go on unchecked, until the 
astronomical consequences pointed out by Thomson and others 
shall have occurred in the motions of our satellite, our earth, 
and the sun. 

VI. On some points in Mallet's Theory of Vulcanicity, 
By EuG. W. HiLGAKO, University of Michigan** 

THE main points of Mallet's Theory of Vulcanicity have 
been before the world of science for some time, and have 
excited some lively discussions on both sides of the question, 

* From Silliman's American Journal^ June 18/4. 

Digitized by VjOOQ IC 

42 Mr. E. W. Hilgard on some points in 

mainly in the English press. I think it is to be greatly regretted 
that the original memoir, very tardily published in the Transac- 
tions of the Royal Society, should be so difficult of access, that 
few of those interested are enabled to appreciate the caution and 
laborious conscientiousness which Mallet has brought to bear on 
his investigation and discussion of this most complex problem^ 
and to what extent he has himself anticipated most of the ob- 
jections raised. In calling attention to some apparent omissions 
in this respect, it may be useful to recall the state of the ques- 
tion as regards some of the more prominent points at issue. 

The first and most sweeping attack upon the very basts of 
Mallet^s theory comes from Sir William Thomson, in a letter to 
Mr. Poulett Scrope (Nature, Feb. 1, 1872), in which he calls 
attention to, and reaffirms the results of his investigation (supple- 
mentary to that of Hopkins) on the effect which a fluid nucleus 
and imperfect rigidity of the earth must exert upon precession 
and nutation, and which led him to the conclusion that, unless 
the rigidity of the globe as a whole were greater than that of 
steel, there must ensue a tidal deformation of the solid mass, 
which would sensibly change the amount of precession. He 
denies that Delaunay has shaken, in any important point, the 
conclusions of Hopkins or himself. 

The subject has since been taken up by General Bumard 
(Smithes Contr. No. 240), who, while confirming the results of 
Thomson upon the premises assumed by that physicist, also 
shows that there are assumable and admissible conoitions upon 
which a fluid nucleus with a moderately thick crust may exhibit 
the same constant, or periodically recurrent, amounts of preces- 
sion and nutation as a solid globe. 

Mallet refers to Thomson's argument in favour of great rigi- 
dity as corroborative of the necessity for assuming a crust of 
great thickness^ such as would render it inadmissible to assume 
a direct connexion between volcanoes and the liquid nucleus. 
But it is difficult to see how the '' preternatural rigidity,'^ made 
a postulate by Thomson, could in any manner be compatible 
with the requirements of Mallet's theory. For the latter repre- 
sents the earth's crust as a congeries of fragments^ sustained 
partly by the contracting liquid nucleus, partly by each other 
on the principle of the arch — therefore necessarily often locally 
in a state of unstable equilibrium, and liable to be disturbed 
by slight outside forces. That the tendency to tidal deforma- 
tion contributes toward producing such disturbances has been 
rendered probable by Perrey's discussions, and by the repeated 
coincidence of violent earthquakes with tiual extremes, lately 

Thomson's assumption, that the postulated rigidity might 

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Mallet's Tl^eory of Vulcanieity. 43 

result from compression, would scarcely seem admissible, save in 
a case of absolute homogeneity and equilibrium — if then. It is 
certainly incompatible with the demonstration made by Professor 
Belli of Favia (as quoted by Mallet), to the effect that rigid 
bodies are weakened by the simultaneous application of ortho- 
gonal pressures — that no known materials could sustain, under 
any circumstances, a strain several hundred times greater than 
that which would crush it if laterally free to yield — ^that such 
strains exist in the contracting crust, and that upward deforma- 
tion must result, if such contraction takes place at all, as the 
annual loss of heat by the earth compels us to assume is the case. 

Whether we view the question of rigidity by the light of our 
direct knowledge of the first twenty- five miles of crust, and of 
the profound commotions it experiences from time to time, or 
by that of the demonstrated increase of temperature as we de- 
scend, rendering it extremely probable that at a comparatively 
slight depth the rigidity of all materials must be seriously im- 
paired by a high temperature despite of pressure — or whether 
we even consider alone the secular loss of heat by radiation, 
which must result in a contraction affecting unequally the hete- 
rogeneous couches of which, on any hypothesis, the solid portion 
of the earth must be composed — it will be difficult to persuade 
geologists of the actual existence of the '^ preternatural rigidity '' 
until every reasonable hypothesis that can dispense with this 
assumption shall have been exhausted. 

Among the objections raised by geologists, the first, and ap- 
parently gravest, was that of Forbes (Nature, Feb. 6, 1872), 
who argues the untenableness of Mallet's theory on the ground 
of the asserted general identity of composition of volcanic 
ejecta. In fact, from Mallet's point of view, it would seem that 
lavas might have the composition of any fusible rock whatso- 
ever in whose strata the crushing might happen to occur, and 
hence that, if taking place within the sedimentary strata, there 
ought to be a very great diversity between the ejecta of different 

In his rejoinder Mallet calls attention to the very serious dif- 
ferences of composition between the extremes of trachytic and 
basaltic lavas, and to the generally admitted fact that volcanoes 
are located along axes of upheaval, where the hypogene rocks, 
and therefore those of the crust proper, approach the sur- 
face — hence that crushing along these lines of weakness would 
be by no means likely to produce a greater diversity of lavas 
than we actually observe. Furthermore, that the ^' local lake " 
theory is liable to the same objection, unless the lakes are sup- 
posed to be located within the (uniform) crust itself. 

He might, it seems to me, have added that the maximum of 

Digitized by VjOOQ IC 

44 Mr. E. W. Hilgard on some points in 

twenty-five miles of sedimentary rocks is not anywhere (on the 
continental areas at least) actually superimposed vertically upon 
the crusty and hence that it is not unreasonable to assume 
that a pressure sufficiently great to produce fusion may never 
occur within the limits of the sedimentary strata^ albeit other 
manifestations of subterraneous thermal action may not be 
wanting. It is true that^ on the whole, Mallet's memoir leaves 
upon the reader's mind the impression that he seeks the source 
of volcanic action at depths sufficiently shallow to justify in a 
measure the objection raised by Forbes, although he ex- 
pressly declares that, with our present data, the determination 
of the points at which the maximum of crushing-effects occurs 
is impossible. 

Similar considerations apply to the objection raised by P. W. 
Button (Nature, Nov. 27, 1873), that *Maults show no heating- 
effects, even where considerable crushing has taken place.'' 
The pressure under which the faulting occurred may have been 
inadequate, in the cases coming under our observation; but 
above all, time is a most essential element in this connexion. 
No matter how great the dislocation or crushing, no great in- 
crease of temperature can occur if it takes place slowly , however 
great may be the quantity of work performed, or of heat pro- 
duced. And very many, if not the majority of extensive faults 
actually occurring, show evidence of having been formed without 
cataclysmal disturbance. 

Among the other points raised by Hutton {loc. cit.) there are 
several which are at once disposed of by a perusal of the original 
memoir. There are others of some weight. That ^' lines of 
least resistance once chosen must remain," is doubtless true in 
a very wide sense ; and in that sense this is scarcely at variance 
with observed facts, since the lines of weakness along the bor- 
ders of continents are still those which exhibit volcanic activity 
(and earthquake phenomena) most frequently. But in the fold- 
ing and upheaving of strata by tangential thrust the question 
of equilibrium must often*of necessity be very delicately balanced, 
depending as it does upon the vertical pressure of the masses^ 
their nature, dislocation, subsequent consolidation, igneous 
effusions from iissures, &c. Lines of weakness as to rigidity 
may thus easily acquire sufficient static resistance to cause a 
subsequent yielding to take place at some distance from the 
original axis, as is exemplified in the formation of successive 
parallel ranges. What is true with regard to the formation of 
folds is equally so as concerns the settling down of the crust- 
fragments in consequence of interior contraction. Each frag- 
ment as a whole may remain as such, being only, as it were, 
abraded at its circumference. But it is only necessary to have 

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Mallet^s Theory of Vulcanicity. 46 

observed the gradual yielding of detrital rock-masses under pres- 
sure^ to understand why the cataelysmal yielding which mani- 
fests itself in earthquakes should so frequently change its locality 
of occurrence — why for long periods a region may be completely 
exempt from these movements^ in consequence either of an un- 
resisted and therefore gradual descent of the crust-fragments 
underlying it, or of an arch-like arrangement, whose sudden 
breaking down will result in a catastrophe, succeeded perhaps 
by a long period of quiescence. 

Thus Mallet^s theory accounts equally well for the sporadic 
and apparently lawless occurrence of seismic phenomena, and 
for the probable correlation between the frequency and violence 
of earthquakes and tidal extremes. Unlike the theory of a thin 
crust, which would lead us to expect almost diurnal earthquakes 
corresponding to oceanic tides, according to Mallet's view there 
should be a near coincidence in time and space of two indepen* 
dent factors (viz. of a condition of very unstable equilibrium of 
some crust-fragment, with a tidal extreme) in order to produce 
a maximum of disturbance. It cannot be expected that such 
coincidence should be of frequent occurrence, or that the casual 
connexion should manifest itself in a greater predominance than 
that claimed by Perrey for the times of spring and neap tides. 
Mallet does not, however, allude to this point — whether from a 
distrust of Perrey's data and method, or theoretical scruples on 
the score of " rigidity .'' 

The objection, that according to Mallet's theory earthquake;?} 
ought always to be followed by eruptions, could obviously 
apply only during the period of fissure eruptions from the 
liquid interior — it being conceded that the volcanic eruptions 
of to-day are due to contact of water with the molten rock, and 
that steam, not static pressure, is the vis a tergo. It is, of 
course, very probable that the access of water to the volcanic 
focus* is generally caused or facilitated by such crust-move- 
ments as would at the same time result in the production of 
more heat and perhaps of fused rock, such movements being 
indicated by the (mostly slight) earthquakes that so frequently 
precede a period of volcanic activity. Hutton's objection, that 
according to Mallet's view each eruption ought to be preceded 
by a sensible subsidence, is therefore groundless. 

One point, however, must strike every reader of the original 
memoir, viz. the preeminence given by Mallet to the crushing of 
solid rock as the means of producing heat and fusion. Que 
would naturally look to the results of his experiments on this 

♦ Hut ton {loc. cit,) avers that " to cause a volcano the heat must go to 
the water ; the water cannot go to the heat>" but omits any explanation of 
this singular axiom. 

Digitized by VjOOQ IC 

46 Mr. E. W. Hilgard on some points in 

subject for the proof of the efficiency of this agency. But we 
find that the maximum of temperature resulting from the crush- 
ing to powder* of the hardest rock is something over 217^ 
Fahr. This, then, represents the maximum increment of tem- 
perature that can be rendered efficient toward the fusing of 
rocks by the crushing process under the most favourable cir- 
cumstances, viz. upon the supposition that it takes place in- 
stantaneously, or under such circumstances that the heat can- 
uot be conducted away, and, further, that the resistance of the 
rock has not been materially diminished by the downward in- 
crease of hypogeal temperature. At the most moderate depths 
at which volcanic phenomena can be supposed to originate, the 
last-mentioned factor must exert a very considerable influence, 
reducing mateiially the available heat-increment. Hence the 
numerical results of Mallet's laborious experiments on rock- 
crushing, however interesting and useful as affording a definite 
measure of the thermal effects producible by this means, yet 
fail to carry conviction as to the efficacy of this particular modus 
operandi in reducing large masses of solid rock to fusion, unless 
essentially supplemented by friction, not so much of rock walls 
against each other, but more probably by the heat produced 
within more or less comminuted detrital or igneoplastic masses 
by violent pi'essure and deformation. 

It may be doubtful what would be the physical and thermal 
effect of enormously great pressures upon rock powder such as 
was produced in Mallet's experiments ; but it would seem that 
if made to yield, the frictional effect must produce very high 
temperatures. A fortiori, solid detrital masses of variously 
sized fragments intermingled (such as, rather than powder, 
would be likely to result from steady pressure), yielding rapidly 
under great pressures, might, under the combined influence of 
friction and rock-crushing, well be supposed to reach the tempe- 
rature of fusion, which a simple crushing of a solid mass by 
pressure would have failed to produce. Mallet mentions the 
probable influence of friction, and of the squeezing of igneo- 
plastic masses, but does not attach to these agencies such im- 
portance as they seem to me to deserve. 

Of the complex thermal effects of the movements of detrital 
masses under great pressure. Mallet's figures of course offer no 
measure whatsoever ; nor is this, or even the thermal coefficients 
resulting from his rock- crushing experiments, at all necessary 
to the establishment of the postulates of his theory. 

* Mallet does not go into the consideration of the physical nature of this 
" powder," and of the thermal and other differences likely to result from 
its production under pressures enormously greater than those employed 
by him. 

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Mallet's Theory of Vtdcamcity. 47 

Taking for granted the correctness of Hirn's theorem, '^ that 
the heat evolved in the crushing of rigid bodies is the equiva- 
lent of the work performed/' Mallet's experiments on the con- 
traction of fused rock in cooling, and his estimates of the amount 
of volcanic energy manifested on the globe, coupled with that of 
the earth's annual loss of heat, completed the proof of the qimu' 
titative adequacy of the cause invoked by him. And when it is 
understood that the earth's present loss of heat during sixteen 
and a half years is the mechanical equivalent of all the volcanic 
work performed since the period of fissure eruptions, the burthen 
of proof of the qualitative inefficiency of the several modes of 
action that may come into play would seem to be effectually 
thrown upon the opponents of the theory. 

Among these modes of action, the fusion of masses already 
existing in a pasty, or generally more or less igneoplastic con- 
dition, by squeezing or forcible displacement, seems to me to 
deserve especial attention. At the depth at which volcanic 
phenomena must be supposed to originate, this condition must 
be closely approached, especially in the early times of the vol- 
eanic period — that of the '^ Maare " of the Eifel and other simi- 
lar cases representing the transition phase between the regime 
of fissure-eruptions and that of volcanoes proper. In this 
period of a ^ greatly stiffened and thickened crust,'' even slight 
flexures, whether synclinal or anticlinal, would occasion great 
displacements and movements in the half-stiffened upper layers 
of the "viscous couchc/' and if these experienced local re- 
fusion, the fused matter may well be presumed to have often 
been disposed of by eruption through fissures or volcanic vents, 
rather than by overcoming downward the inertia of the viscous 
couches* This mode of action seems to me likely not only to 
afford a more copious, but also a more constant or lasting source 
of supply than the supposed crushing of solid rock, and appears 
especially applicable to the case of large fissure-eruptions. 

Among the greatest services rendered by Mallet's (or, in this 
connexion, Wurtz's) theory is the unstrained explanation of 
many of the phenomena of mctamorphism that were quite un- 
intelligible so long as the heat required for the observed 
changes was supposed to be derived from below, and perhaps 
by transmission through strata which themselves bad experi- 
enced little or no change of condition. The principle that the 
heat evolved in the flexure or forcible compression of strata is, 
cateris paribus, proportional to the resistance offered by them 
to the external force, throws a flood of light upon numerous 
apparently contradictory phenomena, which have long been 
quoted as incompatible with the doctriue of metamorphism as 
held in this country, and have stood in the way of its general 

Digitized by VjOOQ IC 

48 Mr. £• W. Hilgard on some points in 

acceptance by geologists, particularly on the continent of 
Europe. In its application to the formation of synclinoria 
especially, the principle works most instructively and satisfac- 
torily. It can scarcely be doubted that in the first folding of 
the vertex of a geosynclinal^ weakened below by fusing away 
and heating of the crust and lowest strata, the movements 
were comparatively localized and rapid, and therefore capable 
of producing high temperatures, and their results such as we 
now usually find them along the main axes of elevation of syn- 
clinoria. But as the resistance along this axis increased by 
emergence and solidification, the points of yielding (t. e, the 
folds) would be muli^lied, while the absolute amount of motion 
transformable into heat would be diminished in each. Hence 
the decrease in general of metamorphic effects as we recede 
from the main axis. And yet it is perfectly easy to conceive 
of large local exceptions to the general rule (such as we actu- 
ally observe), on the basis of greater resistance in perhaps a 
localized stratum of a lateral fold, yet so situated that it could 
not successfully resist the influence of an advantage of leverage 
causing a rapid deformation. It is even predicable that under 
such circumstances sudden breaks and crushings must occa- 
sionally have occurred, giving rise to fusion of rocks and limited 
fissure-eruptions, or at least to pasty rock intrusions — as sug- 
gested by Dana for granitic and analogous veins^ that show no 
evidences of the cooperation of very high temperature in the 
act of formation. 

LeConte's view, that the first mashing of a geosynclinal 
would produce less heat than later plications*, in which (pre- 
sumably) a greater resistance would have to be overcome, seems 
hardly to be compatible with facts as generally observed away 
from the Pacific-coast eruptions ; and his argument is the less 
cogent, as the temperature produced is a function, not only of 
the resistance of the rocks, but also of the degree and rapidity 
of the motions, both of which have been on the decrease in late 
geological periods^ in accordance with the diminishing rate of 
contraction of the earth and the increased resistance of the crust 
to flexure. 

While Mallet's theory accounts satisfactorily for earthquake 
phenomena and volcanic activity as manifested since the cessa- 
tion of fissure-eruptions, and also for the gradual or sudden 
depression of both large and small areas even subsequent to 
that time, it makes no provision for their elevation, and there- 
fore leaves unexplained the numerous oscillations of level of 
which we find the record down to our own time. In assuming 

* " On the great Lava-flood of the West«'* Silliman's American Journal, 
March 1874, p. 179. 

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Mallet's Theory ofVukanieity. 49 

the movements as taking place exclusively within the solid 
shell, he (unnecessarily as it seems to me) leaves a point open 
to obiection. 

While admitting that slow secular oscillations, or those minor 
changes of level constantly occurring in volcanic areas, may 
even now in many cases be reasonably attributed to changes of 
temperature occurring within the solid rocks themselves, and 
within their limits of elasticity, it is impossible to assign this 
as an adequate cause of those extensive oscillations which 
have characterised the Quaternary period, and are recorded, 
€. g.y by the raised beaches of the North-Atlantic coasts and 
inlets, and by the drift-pebbles even now found four hundred 
and fifty feet below the level of the Gulf of Mexico, while the 
emerged formations record a complementary elevation to at 
least a similar extent during the Terrace epoch. This record 
of an oscillation of near a thousand feet on the Gulf-shore 
since the glacial-drift epoch, implies at least a corresponding one 
over the greater portion of the area drained by the Mississippi, 
unless that river flowed backward at one time*. Doubtless 
these oscillations, like the glaciation of which they probably 
were cooperative causes, were of continental extent, as was the 
(more or less contemporary) emergence of the Siberian plain ; 
and as such they must be presumed to have been true move- 
ments of the earth's crust, although lying quite within the vol- 
canic period proper. It is but reasonable to suppose that the 
sinking of the great Pacific area was then, and may still be, 
of a similar nature. 

If Mallet's theory, as well as the geological facts with which 
it deals, is incompatible with Hopkins's and Thomson's postu- 
late of extreme rigidity ; if, as it appears to me, the events of 
very recent geological epochs in connexion with the very slow 
rate of cooling since that time render it unlikely that the crust 
can even now be considered rigid in a geological sense; if^ 
finally, as General Barnard affirms, the astronomical objection to 
a comparatively pliant crust and liquid nucleus is not absolute, 

* It is a cunous fact that in the vaiious hv pothenes regarding the oscil- 
lations of the continental interior during tlie Drift epoch, the facts ob- 
served on the Gulf-shore have over and again been quietly ignored, 
although the Gulf is unequivocally the natural reference-level most directly 
related to that interior, not only at the present time, but; as the direction 
of the Drift currents and the trend of the formations show, ever since the 
time of the Cretaceous emergence. Nevertheless the reference- level has 
been sought bevond the Alleghany upheavals, or beyond the fixed Azoic 
area upon which the movement appears, in a measure, to have pivoted, 
and wnere, as Dana has shown, it was materially diminished in extent. 
Assuredly no hypothesis which disregards the changes of level registered 
at the continental outlet has any raison (Petre ! 

PhU. Mag. S. 4. Vol. 48. No. 315. July 1874. E 

Digitized by VjOOQ IC 

50 Mr. B. W. Hilgard on some points in 

but may be obviated by admissible assumptions regarding the 
mode of distribution of the solid and liquid matter constituting 
the globe^ — ^we are led to the reasonable assumption that while 
the thickness and rigidity of the crust is evidently too great to 
admit of further folding or fissure-eruptions^ and (probably) to 
admit of connecting ordinary volcanic phenomena directly with 
the (virtually or actually) liquid interior^ yet we need not as- 
sume it to be so great as to render the crust incapable of yield- 
ing somewhat^ on a large scale, to static upward pressure. Such 
pressure may be either the resultant of tangential stress^ such 
as might slightly deform an arch without fracture or folding, 
or even the direct result of a corresponding subsidence else- 

The latter effect would of course be incompatible with a 
shrinking away of the fluid interior &om the crusty as required 
by Mallet's theory^ if it were necessary to assume that the in- 
terior crust-surface is substantially '^ smooth/' t. e. free from 
important downward projections or upward sinuosities. But so 
far from this, the cooling influence that has so long acted on 
the oceanic areas, contrasted with those enormous outwellings 
of igneous rock that have occurred even in late Tertiary or 
Posttertiary times, together with other considerations, necessi- 
tate the assumption that such inequalities do exist to a notable 
extent. Hence the overlapping alluded to by Mallet of the 
period of fissure-eruptions and of that of volcanic activity 
proper, which appear to have coexisted, in different portions of 
the globe, from early Tertiary to early Quaternary times. For 
even Mallet himself considers the outpourings of igneous rocks 
on the Pacific coast "wholly inconsistent with existing vol- 
canic forces/' and few geologists will agree with LeConte* in 
ascribing precisely these most extensive fissure-eruptions in the 
world to the " ineffectual fires '' of the volcanic period, arising 
alone from transformed motion. 

Indeed it is not easy to understand the precise mechanism 
of the great fissure-eruptions as a consequence of nucleal con- 
traction, without the aid of some static head of pressure that may 
exist more or less locally, in consequence of inequalities in the 
crust (whether of form, thicknessi or density), and thus act as 
Si vis a tergo. 

At first blush the '' squeezing out of sub-mountain liquid 
matter," assumed by LeConte as the consequence of the fold- 
ing and fissuring of strata by tangential thrust, appears natural 
enough. Yet it seems hardly possible that the same force 
which makes and elevates mountain folds (being the result of 
interior shrinkage) should at the same time serve to compress the 
* SiUiman's American Journal, March 1874, p. 1/9. 

Digitized by VjOOQ IC 

Malleus Theory of Vuiamkiiy. 51 

wUerior Uqwii, xuaikm either sueh folding oeeon benealh tke 
g^Mral k^ of the liquid, or the latter is locally confined, 
or the morement is so (comparatively) brusque or cataclysmal, 
that viscosity would prevent the lateral or downward escape of 
the liquid rock. In the case of the Pacific eruptions the evi- 
dence of steady static outflow and regular upbuilding is espe- 
cially eogent; and, as LeConte remarks, it has been ^ow work, 
as indeed is usually or universally the case with mountain* 

The assumption of locally limited fire seas with a solid globe 
as made by Danaf in conformity with Hopkins's views, would 
remove the difficulty if the ^rust ocrald be assumed as contract- 
ing on the whole independently of the portions over fire seas. 
But when we come to discuss the appUcation in detail of this 
intrinsically improbable hypothesis, we find the required ex- 
tent and localities of these fire seas to be such that we can 
hardly imagine them to be eflfectually separated from eaeh 
other; in other words, we approach very near to a condition of 
general undercrust fluidity up to late geological periods j:. It 
then becomes a question of minor importance whether there is 
a central nucleus solidified by pressure, or whether all within 
the crust is actually liquid. 

The inherent improbability of the depression of a ^eosyn- 
dinal trough to a level so low as to allow the liqmd rock 
to rise into t/, as it were, is too great to render its discussion 

Indeed it seems almost impossible to imagine a mechanism 
explaining satisfactorily fissure-eruptions such as those of the 
Pacific coast, on the basis of a slowly contracting 9oHd crust 
with a rapidly contracting liquid layer or nucleus beneath. A 
more satisfactory explanation seems possible if, in accordance 
with Mallet's suggestion and the intrinsic probabilities of the 

* When LeConte savs {loe, cit, p. 179) that the outoqueezing of the 
liquid hai been caused by " enormous horizontal pressure, determined by 
the interior contraction of the whole earth," and then (p. 180) that, 
^ whether by uplifting or upbuilding the actual increase of height would 
be precisely the same, being detennmed by the amount of kteral crush- 
ing,'' he seems to think of crust-oontrac^on upon a nucleus too large for 
it, rather than of Mallet's " freely descending " crust. Or, if he considers 
the fused rock the result of motion transformed, it is difficult to see on 
what ground a simple ** uplifting " could be considered the precise mecha- 
nical equivalent of an upbuilding by eruption of Uquid rock. In either 
ease the UfHng done would be the same ; but what of the enormous heat 

t " On some of the Results of the Earth's Contraction," Silliman's 
American Journal, August 1873, p. 105. 

t Ibid. July IB73, p. 7 et seqq. 


Digitized by VjOOQ IC 

63 On game pdiaU in Maliet's Theory of VulcanieUy. 

case, we as^ame the existence of a thickly viscid/ igneoplastic 
uodercrnst layer. Such a byer, while barely or very slowly 
obeyine the laws of li(^uid equilibrium, would be capable of 
being liquefied by a slight increase of tCDiperature, such as 
might be produced by squeesing or kneading. Portions of 
such plastic matter would occasionally become involved in the 
anticlinal folds of syndinoria, and thus supply the material for 
limited fissure-eruptions, in that case literally '* squeezed out." 
But the inverse ratio pointed out by Dana as existing between 
folding and fissure-eruptions points to the rarity of such 

At any rate they could not explain the outwellings of the 
Pacific border^ which continued long after close plications had 
ceased to be made — in fact, as it would seem, up to the end of 
the period of elevation of the main Sierra Nevada. 

It is but fair to assume that near lines of weakness indicated 
by plications or fissure-eruptions, the isogeotherms have been 
during the elevation of mountain-chains (and probably still are 
where such lines are marked by volcanic vents) considerably 
above their general leveL In an anticlinal upheaval they 
would probably conform to the progress of the sublevatory 
movement, in a ratio more or less directly proportional to the 
rapidity of the upward movement, and would gradually descend 
during periods of repose. This would happen independently of 
any heat generated by transformation of motion. 

In a polygenetic chain Uke the Sierra Nevada, after the coU 
lapse and folding of the geosynclind and the subsequent stif- 
fening of the backbone (so to speak), any further elevation of 
the main ridge becomes a ^tioM-anticlinal movement, accom- 
panied necessarily by the compression and " squeesing " of the 
heated rocks embraced within the arch. The heating being 
greatest, aeteris paribus, where the resistance and motion is a 
maximum, more heat would be generated by the compression 
of the upper, half-stifiened portion of the viscous or igneoplastic 
layer, than in the lower ones ; and the liquid matter so formed 
would constitute a head of pressure, from which fissure-erup- 
tions might derive their material ; whether directly, or by pres- 
sure communicated to more distant points of rupture and fusion 
by lateral stress. 

If, then, as LeConte^s data seem to show, the final and most 
considerable anticlinal elevation of the great interior range took 
place during the same period that witnessed the great fissure- 
eruptions of the Coast and Cascade ranges, it may not be un- 
reasonable to suppose these events to have not only been con- 
temporaneous, but to have borne to each other something of 
the relation of cause and effect, and that each of the numerous 

Digitized by VjOOQ IC 

On a New Formula inDefinite Integrals* 53 

saperimposed strata of igaeoas rock in the latter region may 
represent not only the direct effect m loco of more or less par- 
oxysmal thrusts^ but also the reflex action of the simultaneously 
progressing anticlinals in the high Sierras. 

VII. A New Formula in Definite Integrals. 
By J. W. L. Glaishbr, M.A*. 

1. 1 NT£6BATE the identity 

^-«i^+^----=i+^-^^(I^« + ^'^0(^ (1) 

(where Aa«=:a»4.|~a») between the limits zero and infinity^ and 
the right-hand side becomes 


= 1 (flocos*^— Aflotan«tfcos*tf+.,.)»«c*ft» 


= r'(flro- Atfo Bin* tf + A«flo sin* tf- . . .)d0 
'tA 1 a . 8 1 .o 5 8 1.- \ 

so that 


The definition of the symbol E is contained in Ea«=:a»4.i ; and 
of course, a^ being only defined for n a positive integer, a.| is 
without meaning. But in cases where On involves factorials,, 
there is a strong presumption, derived from experience in similar 
questi9us, that the formula will give correct results if the conti- 
nuity of the terms is preserved by the substitution of gamma 
functions for the factorials. This I have found to be true in 
every case to which I have applied (2). 

* Commmiicated by the Author. 

Digitized by VjOOQ IC 

64 Mr. J. W. L. Olaisher an a New Formula 

E.ff.{\) Let 

1.2...(2n+l)"r(2n+2) ' 
then a-.^=l^ and 


which is true, 
(u) Let 



the true result. 

"'" 1.2...» ~ r(n+l)' 

a-i 1 

^ '* *^* «•- n^n = rWTT)' '• ^•^ 



TU. sin oossOj the value we should expect to find by any process 
that gave a result at all. 

2. Divide (1) by 1+^ and integrate as before: the right- 
hand side 


= j (aoCOs«^-Afli>sin«^cos«^+A*aown*^cos«d— ...)iW 

TT/l 1 1 A . 8 1 1 .o 5 8 1 1 ..^ \ 
= 2(2"4-2^+6-4-2^-5-r4-2^+---;^ 

•wv/ITA— 1^ _*»r 1 

2 A ''^"2l+-v/E^' 

so that 


«*• ^ 

1.2...2n r(2n+l)' 

Digitized by VjOOQ IC 

in Definite Integrak. 55 


J. i+i«'^=2(i-''+r:2---r2''- • • (*> 

Similarly, by taking a»=s ^ , we obtain the correct value of 

® X sin ax , 


The peculiarity of (2) and (3) consists in the appearance on 
the right-hand side of terms with fractional arguments. In such 
an equation as (4), where one side is a function of a^, while the 
other involves uneven powers of a, it seems as though it would 
be impossible to evaluate the integral by any direct procedure; 
for d priori it would appear that no method of expansion and 
integration term by term could transform a function of (f 
into one of a, and thus, as it were, extract the square root 
of a constant involved. The way in which the symbolic pro- 
cess introduces i/£, and so actually does effect this conver- 
sion, is interesting: when I first applied the identity (1) to 
the integral in (4), I scarcely expected to obtain any result 
capable of interpretation. 

Whenever (2) and (3) admit of interpretation, it is highly pro- 
bable that the result so given will be the true one ; e. g., taking 

1 +««'**- 2 lr(i) r{|) ^ r(2) r(5) +• * •/ 

_ir r 2a* . 2at «« \ 

~2L v^A 1.3 1.8-6 // 

the known vslae. Bat (2) and (3), as general formule, are re- 
markable ; and diey would give results in very many cases where 
it might not be easy to evaluate the integrals otherwise. | 

Trinity College, Cambridge, 
June 19, 1874. 

Digitized by VjOOQIC 

[ 56 ] 

VIII. On some Physical Properties of Ice; on the TVansposition 
of Boulders from below to above the Ice ; and on Mammoth" 
remains. By John Rae, M,D,, LL.D., ifc*. 

IS the ice formed on salt water fresh f or, in other words, if 
ice formed on the sea is thavred, will the water obtained 
thereby be fresh ? 

For a number of years past I have spoken with many persons 
on the above subject; and seldom » if ever, have I found a single 
individual who did not say that the ice of the sea was fresh. 

Some of these gentlemen are known in the scientific world ; 
and many of them supported their opinions by quoting the 
highest written authorities on the subject, chiefly Tyndall's 
'Forms of Water,' p. 132, par. 339, which tells us that "even 
when water is saturated with salt, the crystallizing force studi- 
ously rejects the salt, and devotes itself to the congelation of 
the water alone. Hence the ice of sea-water, when melted, pro^ 
duces fresh water," 

It IS the sentence in italics to which I wish to draw particular 

It would be the extreme of folly and presumption on my 
part to question the correctness of results obtained b^ scientific 
men in their experiments in freezing small quantities of sea- 
water by artificial means, more especially those of the distin* 
guished gentleman whose name I have mentioned, who, in 
addition to holding the high position of being one of our 
greatest authorities in all that relates to physical science, pos- 
sesses the rare gift of being able to communicate his knowledge 
in such plain, clear, and forcible language, illustrated by admi- 
rable experiments, as to make his meaning fully understood, 
even by those who had previously been perfectly ignorant of 
the subject. 

It is only where I have had opportunities of witnessing the 
action of cold carried on in a manner which may have been 
denied to the scientific man, that I venture to differ from him ; 
and it is in this way that the conviction has been forced upon 
me, that the ice of sea-water if melted does not produce finesh 

Before entering upon this subject, however, let me say a word 
or two on the first part of the quotation I have given. 

If a saturated solution of salt is frozen, and the ice so formed 
is fresh, it is evident that the salt that has been ''rejected'^ 
must be deposited or precipitated in a crystalline or some other 
solid form, because the water, if any, that remains unfrozen, 

* Read before the Physical Society, May 9, 1874. Gommunicated by 
the Society. 

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Dr. J. Rae an same Physical Properties qflce. 57 

h&ng already saturated^ can hold in solution no more salt than 
it already contains. 

Could not salt be obtained readily and cheaply by this means 
from sea- water in cold climates ? 

During several long journeys on the Arctic coast^ in the early 
spring before any thaw had taken place^ the only water to be 
obtained was by melting snow or ice. By experience I found 
that a kettleful of water could be obtained by thawing ice with 
a much less expenditure of fuel^ and in a shorter time, than 
was required to obtain a similar quantity of water by thawing 
snow. Now, as we had to carry our fuel with us, this saving of 
fuel and of time was an important consideration, and we always 
endeavoured to get ice for this purpose. We had another in- 
ducement to test the sea-ice frequently as to its freshness or 
the reverse. 

I presume that almost every one knows that to eat snow 
when it is very cold, tends to increase thirst, whereas a piece of 
ice in the mouth is refreshing and beneficial, however cold it 
may be ; we were consequently always glad to get a bit of fresh 
ice whilst at the laborious work of hauling our heavy sledges ; 
yet with these strong inducements we were never able to find 
sea-ice, in situ*, either eatable when solid or drinkable when 
thawed, it being invariably much too salt. The only exception 
(if it may be cidled one) to this rule, was when we found rough 
ice, which, from its wasted appearance and irregular form, had 
evidently been the formation of a previous winter. This old 
ice, if projecting a foot or two above the water-level, was almost 
invariably fresh, and, when thawed, gave excellent drinking- 
water. It may be said that these pieces of fresh ice were frag- 
ments of glaciers or icebergs ; but this could not be so, as they 
were found where neither glaciers nor icebergs are ever seen. 

How is this'to be accounted for? Unfortunately I have only 
a theory to o£fer in explanation. 

When the sea freezes by the abstraction of heat from its 
surface, I do not think that the saline matter, although retained 
in and incorporated with the ice, assumes the soUd state, unless 
the cold is very intense, but that it remains fluid in the form of 
a very strong brine enclosed in very minute cells. So long as 
the ice continues to float at the same level, or nearly the same 
level, as the sea, this brine remains ; but when the ice is raised 
a little above the water-level, tbe brine, by its greater specific 
gravity, and probably by some solvent quality acting on the ice, 
gradually drains off from the ice so raised; and the small cells, 

*■ What I mean by ice mi situ is ice lyin^ flat and unbroken on the 
sea, as formed during the winter it is formed m. 

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58 Dr. J. Bae on the IVaMpoiitum ofBoulden 

by eonnecting one with another downwards^ become channek of 

There may be seTeral other requisiteB for this change of salt 
ice into fresh^ sach as temperature raised to the freezing-point, 
so as to enable the brine to work out the cell-walls into channels 
or tubes — that is^ ifmy theory has any foundation in fact, which 
may be easily tested by any expedition passing one or more 
winters on the Arctic, or by any one living where ice of con* 
siderable thickness is formea on the sea, such as some parts of 

All that is required, as soon as the winter has advanced £sr 
enough for the purpose, is to cut out a block of sea-ice (taking 
care not to be near the outflow of any fresh-water stream) about 
8 feet square, remove it from the sea to some convenient posi- 
tion, test its saltness at the time, and at intervals repeat the 
testing both on its upper and lower surfiEU^es, and observe the 
drainage if any. 

The result of the above experiment, even if continued for a 
long while, may not be satisfactory, because the fresh ice that I 
have described must have been formed at least twelve months^ 
perhaps eighteen months, before. 

The JVanapoeition of Boulders from below to above the lee. 

When boulders, small stones, sand, gravel, 8cc. are found 
lying on sea-ice, it is very generally supposed that they must 
have rolled down a steep place or fallen from a clifi*, or been 
deposited by a flow of water firom a river or other source. 
There is, however, another way in which boulders &c. get upon 
floe-ice, which I have not seen mentioned in any book on this 

During the spring of 1847, at Bepulse Bay. on the Arctic 
shores of America, I was surprised to observe, after the thaw 
commenced, that large boulders (some of them 3 or 4 feet in 
diameter^ began to appear on the surface of the ice; and after a 
while, about the month of July, th^ were wholly exposed, 
whilst the ice below them was sttong, nrm, and something like 
4 feet thick. 

There were no clifls or steep banks near from which these 
boulders could have come ; and the only way in which I could 
account for their appearance, was that which by subsequent 
observation I found to be correct. 

On the shores of Bqpulse Bay the rise and frdl of the tide 
are 6 or 8 feet, sometimes more. When the ice is forming in 
early winter, it rests, when the tide is out, on any boulders &c. 
that may be at or near low-water mark. At first, whilst the 

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fmm behw to above the Ice. 59 

ice 18 weak, the boalden break through it ; but whea the ice 
becomes (say 2 or 3 fe^) thick, it freezes firmly to the boulder, 
and when the tide rises, is strong enough to lift the boulder 
with it. Thus, once fastened to the ice, the stone continues 
to riae and fall with the rise and fall of ^ush tide, until, as the 
winter advances, it becomes completely enclosed in the ice, 
which by measurement I found to attain a thickness of more 
than 8 feet 

SmaU stones, gravel, sand, and shells may be fixed in the 
iee in the same way. 

In the spring, by the double efiisct of thaw and evaporation, 
the upper surface of the ice, to the extent of S feet or more, is 
removeidy and thus the boulders, which in autumn were lying 
at the bottom <tf the sea, are now on the ice, while it is stiU 
strong and thick enough to travel with its load, before favour- 
able winds and currents to a great distance. 

The finding small stones and gravel on ice out to sea does not 
always prove that such ice has been near the shore at some time 
at other. 

I have noticed that wherever the Walrus in any numbers 
have been for some time lying either on ice or rocks, a not 
inconsiderable quantity of gravd has been deposited, apparently 
a portion of the excreta of that animal, having probably been 
taken up from the bottom of the sea and swallowed along with 
their food. 

Mammoth'remaiM. The position in which their Skeletons are 
found, Sfc, 

In LyelFs ' Principles of (Geology,* vol. i. p. 186, we read ^— 
''In the flat country near the mouth of the Yenesei river, 
Siberia, between latitudes 7(f and 75*^ north, many skeletons of 
mammoths, retaining the hair and skin, have been found. The 
heads of most of these are said to have been turned to the south/' 

As fsur as I -can find, the distinguished geologist gives no 
reason why the heads of the mammoths were turned to the 
south ; nor does he say all that I think might be said of the 
reasons why, and the means by which the skins have been pre- 
served for such a long period of time. 

Having lived some years on the banks of two of the great 
rivers of America, near to where they enter Hudson's Bay, and 
also on the M'Kenzie, which flows into the Arctic Sea, 1 have 
had opportunities of observing what takes place on these streams^ 
all of which have large alluvud deposits, forming flats and shal« 
lows at iheir mouths. 

What I know to be of common occurrence in these rivers 
may, if we reason by analogy, have taken place in ancient timea 

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60 Dr; J. Rae on Mammoth-remains. 

on the great rivers of Siberia, making due allowance for the 
Dincb higher northern latitude to which these streams run before 
reaching the sea, and for the difference in size of the fauna that 
used to frequent their banks. 

When animals, more especially those having horns, tusks, or 
otherwise heavily weighted heads, are drifting down a riv^, 
the position of the bodies may lie in any dir^ion as regards 
the course of the stream, as long as they are in water deep 
enough to float them ; but the moment they get into a shallow 
place, the head, which sinks deepest (or, as sailors say, ^^ draws 
most water *'), takes the ground, whilst the body, still remaining 
afloat, swings to the current, just as a boat or ship does when 
brought to anchor in a tideway. 

It is probable that the mammoths, having been drowned by 
breaking through the ice or in swimming across the river in 
spring when the banks were lined with high precipitous drifts 
of snow, which prevented them from getting out of the water, 
or killed in some other way, floated down stream, perhaps for 
hundreds of miles, until they reached the shallows at the mouth, 
where the heads, loaded with a great weight of bone and tusks, 
would get aground in 8 or 4 feet of water, whilst the bodies 
still afloat would swing round with the current as ahready 

The Yenesei flows from south to north, so the heads, being 
pointed up stream, would be to the south*. 

Supposing, then, these bodies anchored as above in 8 or 4 feet 
water ,* as soon as the winter set in, they would be frosen up in 
this position. The ice in so high a latitude as 70^ or 75^ north 
would acquire a thickness of 5 or 6 feet at least, so that it would 
freeze to the bottom on the shallows where the mammoths were 
anchored. la the spring, on the breaking np of the ice, this 
ice being solidly frozen to the muddy bottom, would not rise to 
the surface, but remain fixed, with its contained animal remains, 
and the flooded stream would rush over both, leaving a covering 
of mud as the water subsided. 

Part of this fixed ice, but not the whole, might be thawed 
away during summer ; and (possibly, but not nec^sarily) next 
winter a fresh layer of ice with a fresh supply of aninial re- 
mains might be formed over the former stratum ; and so the 
peculiar position and perfect state of preservation of this ini« 

* Not many yean ago, when buiblo were very abundant on the Saskat* 
chewan, hundreds of them were aometimea drowned in one seaaon whilat 
awimming acroaa the river; and many reindeer, mooae, and other animala 
are annually destroyed in Uiia way in other large American rivers. 

Sir Charlea Lyell mentiona a number of yaka being aeen frozen up in 
one of the Siberian rivers, which, on the broking up of the ice in apnog, 
would be liberated and float down the alream. 

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Mr. F. Clowes on a Glass Cell with Parallel Sides. 61 

menae collection of extinct animals may be accounted for without 
having recourse to the somewhat improbable theory that a very 
great and sudden change had taken place in the climate of that 

I have seen at the mouth of Hayes River in America animals 
frozen up as above described ; but as the latitude of this place is 
only 57^ norths the fixed ice usually wholly di8apf>ear8 before 
the next winter sets in, and liberates the animals shut up in it ; 
but when the rivers reach the sea, as some of those of Siberia 
do, 1000 or 1200 miles further to the north, it may be fairly 
assumed that a large part of this fixed ice, protected as i would 
be by a layer of mud, might continue unthawed. 

IX. Glass Cell with Parallel Sides. 
By F. Clowes, Esq., B.Sc, F.C.S.* 

THE following method has proved very convenient for making 
a glass cell, which may be readily fitted up from ordinary 
laboratory apparatus, and may also be rapidly taken to pieces 
for the purpose of being cleansed. 

A piece of india-rubber tubing with stout walls, or, better, a 
length of solid rubber, is placed pig. | . 

in the form of a letter iJ be- 
tween two plates of glass, the 
ends of these plates being then 
firmly held together by slipping 
over them stout in<ua-rubber 
rings. A glass cell is thus obtained, the parallel faces of which 
are formed by the glass plates, whilst its thickness, depth, and 
length can be suitably varied by the stoutness and length of the 
rubber tube and the shape which this tube is made to assume. 

With a glass cell of the size of an ordinary magic-lantern 
slide (fig. 1), thedifierence in specific gravity between hot and 
cold water t may be well shown upon the screen by a magic 
lantern, the liquid admitted by a pipette being preferably tinged 
by dissolving in it a crystal of potassium permanganate ; and 
the convective currents occurring in the mass of a liquid may be 
thrown upon the screen by passing a galvanic current through 
a fine platinum wire stretched between two thick copper wires 
beneath the surface of the liquid in the cell : these currents are 
rendered much more evident by allowing the platinum wire to 
be immersed in a stratum of potassium -permanganate solution 
which has been cautiously introduced beneath the water by 
means of a pipette dipping to the bottom of the cell. 

* Read before the Physical Society, May 23, 1874. Communicated by 
tile Socdetv* 
t See iVndairs 'Heat, a Mode of Motion,' pp. 173 and 174. 

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d3 Noticet r$tj9eeHng New Books. 

A smaller cell made to fit into the wooden firame o( a kntern- 
riide (fig. 2), which has attached Fig. 2. 

to it platinum wires connected 
by copper wires and binding- 
screws with a galvanic battery, 
serves to project electrolytic de- 
compositions npon the screen. 
Perhaps the most beautifdl ap- 
pearance is that presented oy th^ crystallucation (^ the metd 
from a solution of lead-acetate which is undei^ing electrolysis*. 

In order that the cell mav be water-tight, it is necessary that 
the india-rubber rings should exert a somewhat powerful com- 

f)ression; but even under favourable circumstances slight 
eakage is liable to occur in about half an hour after the cell 
has been filled ; this, however, would allow ample time for the 
display of any of the phenomena above alluded to. Rings cut 
from large-sized india-rubber tubing have been found wdl 
adapted for the construction of small cells. 

X. Notices respecting New Books. 

Text'Books of Science. — Principles cf Mechanics. By T. M. GkK)D- 
EYE, M.A,j Lecturer on Applied Mechanics at the Bcyal School of 
Mines, London : Longmans, Green, and Co. 1874 (small 8vo, 
pp. 313). 
npHIS book contains an exposition of the principles of mechanics, 
•^ such as is commonly given in elementary treatises on that sdenoe. 
The exposition is illustrated in two wa,ya— first by means of exam- 
ples of the ordinary type, secondly by reference to actual mecha- 
nical contrivances mainly of a modem character. There are about 
a hundred and eighty illustrations of the former kind ; and of these 
about one in every four is taken from the Science Examination 
papers drawn up for the annual examinations of the Department 
of Science and Art. The second class of illustrations constitutes 
the chief peculiarity of the book, and unquestionably its most valu- 
able part. The mere names of some of these illustrations will be 
enough to show this — e. g, the carrying of com on bands, the feed- 
ing of running trains with water, the disintegrating flour-mill, the 
ventilation of coal-mines, the lifting of coals, the stone-crushing 
machine, Weston's friction coupling, the break-dnun, the crown 
valve, the blowing-engine, the hydraulic accumulator, the hydnmlic 
crane, &c. These form an assemblage of contrivances which have 
never before, to our knowledge at least, been described in any ele- 
mentary book ; they render the work before us worthy of the study 
of all who are interested in mechanical science ; and we do not 

• Mr. W. Crookes, F.R.S., Miggests the electrolysis of solution of thal- 
lium sulphate as furnishing a still more beautiful example of crystallization. 

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Notices reipecting New BocJm. 68 

Axibt tbiit these iUnslrations alone will csii«e the book to have, as 
it undoabtedlj desenres to hare, an extensive oircolatkm. 

It wDl be evident from i^e large nnmber of contrivances men- 
tioned in ^e above list, that the description of each must be brief, 
and that the attention of the reader is mainlj directed to the dj- 
namical principles involved in their use. It could scarcely fail to 
happen, undw these drcumstanoes, tiiat in some cases p<nnts in 
the contrivances are not quite so fully described as the reader 
might wish. In others the contrivance is regarded from a p<Hnt of 
view which does not bring quite the whc^ subject under notice ; 
and tiiis is sometimes a little misleading. For instance, the ooor 
trivanee for feeding a running train wi^ water is e<Misidered 
simply as an illustration of inertia ; and this probably accounts icft 
^ke statement that the water which runs up the tube *' is at rest 
ezc^t so far as the movement in a vertical direction is concerned " 
(p. 49). As one end of the tube is vertically over the other end, it 
is plain that the water before it leaves i^ tube must have acquired 
Ihe forward velocity of the train as well as ^ v^tacal velocity 
with which it ascends the tube ; and in fact the illustration of thd 
inclined plane^ushed beneath the water (p. 49), if properly worked 
out, shows this very point : e, g, conceive a particle (P) at rest 
* acted on by no forces, and an inclined plane (with an angle c) 
moving forward wit^ a velocity Y to come into contact with it ; an 
instantaneous action takes place between the plane and the point 
alcHig the perpendicular to the plane ; and after Ihe action, P will 
move with a uniform velocity aJong a line in space coinciding with 
the position of the perpendicular at the instiuit of the action. If 
we further suppose that there is no force of restitution, P, while 
moving in space along the above-mentioned line, will continue to 
touch the plane and appear to run up it. Supposing the mass of 
the plane large in comparison with that of P, the horizontal and 
vertical components of Ps velocity will be V sin' « and Y sin » cos «. 
It is evident from the former expression that, if the plane were 
steep, the forward horieontal velocity of P would be nearly equal 
to V, and would be quite equal to it if the plane were vertical. 
The velocities would be incr^tsed if there were restitution, and the 
point would be thrown forward from the plane, of course along the 
aforesaid perpendicular. This is true supposing P to be not acted on 
by any other force than the momentary action of the plane ; if we 
suppose P to be under the action of gravity, the above vdodties 
are its horizontal and vertical initial velocities, and the subsequent 
motion can be easUy determined on the usual suppositions. Now 
the contrivance for feeding running trains with water differs from 
the case we have been considering in this — that instead of a mere 
inclined plane, a tube with a gradually increasing slope is em- 
ployed ; the effect of this is threefold : in th!^ first places the increas- 
ing sl<^ makes the action gradual instead of instantaneous, thereby 
diminishing the tendency of the instrument to dash the water out 
of the trough ; in the neifft place^ if the water, when once in the 
tube, have any tendency to fly forward owing to restitution or any 

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64 Notices respecting New Books. 

otiier cause, the tendency has no effect so far as the presort qaes«- 
tion is concerned ; and, finally, as the tube for a lai^ part of its 
.length is nearly or quite rertical, the horizontal velocity of the as- 
cending stream cannot fail to acquire the forward velocity of the 

The Statement of General Principles and the proofs of particular 
theorems contained in the text are (it is almost needless to say so) 
correct as far as we have noticed ; and the student who works at 
the book conscientiously will doubtless not fail to make it out, 
though the style does not generally show in any marked degree tiie 
power of clear exposition. There is one point which ought not to 
be left unnoticed, as the author lays considerable stress upon it : 
he states that he has endeavoured '* above all to show tiiat the re- 
lation of the theory of heat to mechanics should be approached by 
the student in his earliest inquiries with the same careful thought 
with which he will surely regard it when his knowledge and his 
powers have become extended and strengthened." And accordingly 
the book contains articles in which are explained what is meant by 
the mechanical equivalent of heat, by the kinetic theory of gases, 
and one or two otner matters. What parts of a subject an author 
puts into his book is a matter depending so much on his own judg- 
ment as to be rarely the proper subject of criticism ; but we may 
perhaps be allowed to record a difference of opinion. It seems to 
us, then, that the subject of energy of motion presents difficulties 
to the beginner so great that it is best to give him a isxr chance of 
becoming familiar with it before introducing him to the far more 
difficult subject of Potential Energy, and accordingly that it is better 
not to deal with the latter subject in a purely elementary treatise 
on mechanics. 

EeUpses Past and Future, with Oeneral Hints fcr Observing the Heavens, 
By the £ev. S. J. JomrsoH, Parker & Co.: Oxford andLondcm. 

Mr. Johnson, in the work before us, has added considerably to 
our prospective knowledge of eclipses, transits, and allied pheno- 
mena, and has also given us some interesting information relative 
to ancient eclipses, mentioning that the first of which we have a 
clear record happened at Nineveh in the year 763 b.c. Noticing in 
the order of their sequence the most celebrated eclipses of antiquity, 
and bringing up the catalogue of observed eclipses to the present 
date, the aumor gives us two interesting chapters (Y. and YI.) : — ^tiie 
first on the prospects of the amateur, showing the paucity of large 
eclipses in England during the next thirty years ; and the second, 
" Curiosities in Lunar Echpses," as bright and black total eclipses, 
and those in which both luminaries were above the horizon at the 
time of the moon being eclipsed, an obvious effect of refraction. 
The first part of the work, m which we have notices of eclipses 
from the celebrated one of Ho and Hi 2127 b.c. October 13, to 
A j>. 2381 July 21, contains a large amount of information on an in- 
teresting branch of astronomy. 

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Royal Society^ G5 

From edipsee of the Sun and Moon, the author passes in the 
second part of his work to describe prospectirely tiie most interes- 
ting planetary phenomena, the periods at which thej may be^ most 
adyantageoosly looked for, with the peculiar features they are likely 
to present. Allusions are made to the Aurora, Zodiacal light, 
Meteors, &c. ; and we notice a remarkable suggestion embodied in a 
communication to the ' Spectator ' by the Bey. E. L. Gkui)ett, that 
the cities of Sodom and Gk>morrah were destroyed by a group of 
tiie meteors following TempeFs telescopic comet of 1866. Mr. 
Oarbett giyes six reasons for his suggestion as follows : — 

1. From the deduced period of node passage of the comet a 
yifiit must haye occurred in the autumn between b.o. 1898 and b.c. 
1897, which is fl;enerally assumed as the date of the catastrophe. 

2. The earth^ passage of node was on July 31. 

3. A yertical tiul of meteors as rain was only possible at sunrise, 
the hour of the destruction of the cities. 

4. The latitude of the yertical fall agrees with that of the cities. 

5. Sodium, the chief element in the deposits formed in the loca- 
lity, is the chief element in these meteors as observed by Secchi. 

6. Magnesium, which also occurs in the locality, is the only other 
ingredient in the meteors conspicuous to Secchi by means of the 

" Suppose," says the writer, " any eyent not due to this comet to 
be recorded. The diances against the account presenting these six 
agreements with its elements and no disagreements, are three mil* 
Hons to one that the history of Sodom is true, and this the phy- 
sical cause.** 

The work closes with a list of 152 double stars and nebul», ar- 
ra ng ed much in the same way as the portion on the Starry Heayens 
of Webb's ' Celestial Objects for Common Telescopes,' the angles 
ci position of the double stars, as seen near the meridian, being in- 
dicated by dots, an addition which we haye no doubt will be duly 
i^predated by those readers who are just commencing their obser- 
vational career. 

XI. Proceedings qf Learned Soeieties. 

[Continued from toI. zini. p. 457.] 

December 11, 1873. — Joseph Dalton Hooker, C.B., President, 
in the Chair. 

THE following communication was read : — 
" On the Action of Heat on Grayitating Masses." By Wil- 
liam Orookes, FJEt.S. &c. 

The experiments recorded in this paper haye arisen from ob- 
senrations made when using the yacuum-balance, described by the 
author in his paper "On ttie Atomic Weight of Thallium"*, for 

» PbiL Tranf . 1873, toL olriii. p. 277. , " 

Phil. Maj. S. 4. V(d. 48. No. 815. Jvly 1874, F 

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66 Royal Society .—Mr. W. Crookes on the 

weigfainff Bubetanoes which were of a higher temperature than the 
Burroanding air and the weights. There appeared to be a dimimi- 
tion of the force of grayitation ; and experiments were instituted 
to render the action more sensible, and to eliminate sources of error. 

In an historical resume of the state of our knowledge on the sub- 
ject oi attraction or repulsion by heat, it is shown that in 1702 
the Bev. A. Bennet recorded the fiict that a light substance de- 
licately suspended in air was attracted by warm bodies : this he 
ascribed to air-currents. When light was focused, by means of a 
lens, on one end of a delicately suspended arm, eitiier in air (Mr in 
an exhausted receiver, no motion could be perceiyed distinguish- 
able from the efEects of heat. 

Laplace spoke of the repulsive force of heat. Libri attributed 
the movement of a drop of liquid along a wire heated at one end, 
to the repulsive force of heat ; but Baden Powell did not succeed 
in obtaining evidence of repulsion by heat from this experiment. 

Fresnel described an experiment by which concentrated solar 
light and heat caused repulsion between one delicately suspended 
and one fixed disk. The experiment was tried in air of different 
densities ; but contradictory results were obtained under apparently 
similar circumstances at different times, and the experiments weto 
not proceeded with. 

Saigey described experiments which appeared to prove that a 
mark^ attraction existed between bodies of different temperaturea. 

Forbes, in a discussion and repetition of Trevelyan s experi- 
ment, came to the conclusion that there was a repulsive action ex<- 
erdsed in the transmission of heat from one body into another 
which had a less power of conducting it. 

Baden Powell, r^eating Fresners experiment, explained l^a 
results otherwise than as due to repulsion by heat. By observing 
the descent of the tints of Newton's Bings between glass pliU«s when 
heat was applied, Baden Powell showed that the interval between 
theplatea increased, and attributed this to a repulsive action of heat^ 

Faye introduced the hypothesis of a repulsive force of heat to 
account for certain astronomical phenomena. He described an 
experiment to show that heat produced repulsion in the luminoua 
arcjriven by an induction-coil ii^ rarefied air« 

l£e author describes numerous forms of apparatus successivelj 
more and more delicate, which enabled him to detect and then to 
render very sensible an action exerted by heat on gravitating bodies, 
which is not due to air-currents or to any other known form of 

The following experiment with a balance made of a straw beam 
with pith-ball masses at the ends enclosed in a glass tube and con- 
nectea with a Sprengel pump, may be quoted from the paper : — 

<* The whole being fitted up as here shown, and the i^paratus 
being full of air to begin with, I passed a spirit-fiame across the 
lower part of the tube at 6, observing the movement by a low-power 
micrometer; the pith ball (a, h) descended slightly, and then im- 
mediately rose to considerably above its originaJ position. It 

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Action of Heat on Gravitating Masses, 67 

seemed as if the trae action of the heat was one of attraction, in- 
Btantiy oyercome bj ascending currents of air 

" 31. In order to apply the heat in a more reguUr manner, a 
tii^mometer was inserted in a glass tube, having at its extremity 
a glass bulb about 1| inch in diameter ; it was filled with water and 
then sealed up. . . The water was kept heated to ,70^ C, the tem- 
peratnre of the laboratory being about 15° 0. 

^* 32. The barometer being at 767 milUms. and the gauge at zero, 
tiie hot bulb was placed beneath the pith ball at h. The ball rose 
n^dly ; as soon as equilibrium was restored, I placed the hot- 
water bulb above the pith ball at a, when it rose again, more slowly, 
however, than when the heat was applied beneath it. 

•* 33. The pump was set to work ; and when the gauge was 147 
miUims. below the barometer, the experiment was tried again ; the 
same result, only more feeble, was obtained. The exhaustion was 
continued, stopping the pump from time to time, to observe the 
effect of heat, when it was seen that the effect of the hot body 
regularly diminished as the rarefaction increased, until when the 
gauge was about 12 miUims. below the barometer the action of 
the hot body was scarcely noticeable. At 10 millims. below it was 
still less ; whilst when there was only a difference of 7 millims. be- 
tween the barometer and the gauge, neither the hot-water bulb, 
the hot rod, nor the spirit-flame caused the ball to move in an ap- 
preciable degree. The inference was almost irresistible that the 
rising of the pith was only due to currents of air, and i^at at this 
near approach to a vacuum the residual air was too highly rarefied 
to have power in its rising to overcome the inertia c^ the straw 
beam ana the pith balls. A more delicate instrument would doubt- 
less show traces of movement at a still nearer approach to a vacuum ; 
but it seemed evident that when the last trace of air had been re- 
moved from the tube surrounding the balance — when the balance 
WES suspended in empty space only — the pith ball would remain 
motionless, wherever the hot body vrere applied to it. 

^ 34. I continued exhausting. On next applying heat, the result 
showed that I veas hr from having discoveied the law governing 
tiliese phenomena; the pith ball rose steadily, and without that 
hesitation which had been observed at lower rarefactions. With the 
gaoge 3 millims. below the barometer, the ascension of the pith 
when a hot body was placed beneath it was equal to what it 
had been in air of ordinary density ; whilst with the gauge and 
barometer level its upward movements were not only sharper than 
they had been in air, but they took place under the influence ci 
£nr less heat ; tbe fii^^er, for example, instantly sending the ball up 
to its fullest extent.** 

A piece of ice produced exactlythe opposite effect to ahotbody. 

Numerous experiments are next given to prone that the action 
is not dae to efeetridty. 

The presence of air having so marked an influence on the action 
ol heat, an apparatus was fitted up in whidi the source of heat (a 
platinum spiral rendered incandescent by electricity) was inside the 


Digitized by VjOOQ IC 

68 Royal SocUty .—Mr. W. Crooket on the 

Yftouum-tube inatead of outoide it as bef(»e ; and the pith balls ol 
the former apparatus were replaced by brass balls. By careful mar 
nagement and turning the tube round, the author could place the 
equipoised brass pole either over, under, or at the side of the source 
of heat. With this apparatus it was intended to ascertain mcHre 
about the behaviour of the balance during the progress of the ex- 
haustion, both below and above the point of no action, and also to 
ascertain the pressure corresponding with this critical point. 

After describing many experiments with the ball in various po- 
sitions with respect to the incandescent spiral, and at different 
pressures, the general result is expressed by the statement that 
the tendency in each case was to bring the centre of gravity of the 
brass ball as near as possible to the sourbe of h^^t, when air of or- 
dinary density, or even highly rarefied air, surrounded the balance. 
The author continues : — 

*' 44. The pump was then worked until the gauge had risen to 
within 5 millims. of the barometric height. On arranging the ball 
above the spiral (and making contact with the battery), the attrac- 
tion was still 8tr<»ig. drawing the baU downwards a distance of 2 
millims. The pump continuing to work, the gauge rosauntil it was 
within 1 milHm. of the barometer. The attraction of the hot spiral 
for the ball was still evident, drawing it down when placed below 
it, and up when placed above it. The movement, however, was 
much less decided than before ; and in spite of previous experience 
(33, 34) the inference was very strong that i£e attraction would 
gradually diminish until the vacuum was absolute, and that then, 
and not till then, the neutral point would be reached. Within one 
millimetre of a vacuum there appeared to be no room for a change 
of sign. 

*' 45. The gauge rose until there was only half a millimetre be- 
tween it and the barometer. The metallic hammering heard when 
the rare&ctioQ is dose upon a vacuum commenced, and the fillip- 
ing mercury only occasionally took down a bubble of air. Oa 
turning on the battery current, there was the faintest possible 
movement of the brass ball (towards the spiral) in the direction ol 

. " 46. The working of the pump was continued. On next ma- 
king contact with the battery, no movement could be detected. 
The red-4ot spinJ nmther attracted nor repelled I had arrived at 
the critical point. On looking at the gauge I saw it was level with 
the barometer. 

** 47. The pump was now kept at full work for an hour. The 
gauge did not rise perceptibly ; but the metiJlic hammering sound 
increased in sharpness, and I could see that a bubble or two ol air had 
been carried down. On igniting the spiral, I saw that the critical 
point had been passed. The sign had changed, and the action was 
mnt but unmistakable repuUum. The pump was still kept going, 
and an observation was taken from time to time during several 
hours. The repulsion continued to increase. The tubes of the 

Digitized by VjOOQ IC 

Action of Htat ok QravUating Ma$i€$. 69 

pump were now washed oat witii oil of Titriol*, and the working 
was ocmtinued for an hoar. 

'^ 48. The aeti(m of the incandescent sniral was now |oand to ba 
exiesr^UcaIljrq>dlefU, whether it was placed aboTe or below the 
brass ball. The finsers exerted a repeUent action, as did also a warm 
glass rod, a spirit-lame, and a niece of hot oopper.** 

In order to decide once for all whetiier these actions really were 
dueto-aar-carrents, a form of apparatas was fitted op which, whilst 
it woold settle the qoestion indispatablj, woald at the same time 
be likel J to afford information <^ mach interest. 

Bj chemical means the author obtained in an apparatus a Tacuam 
so neariy perfect that it would not carry a current inm ^ Buhm-^ 
ko^s coil when connected with platinum wires sealed into the 
tube. In such a vacuum the repulsion by heat was still found to 
be decided and energetic. 

An experiment is next described, in whidi the rays of the sun, 
and then ihe di&rent portions of the solar spedrum, are projected 
on to the delicately suspended pit^ball balance. In vacuo the 
repulsion is so strong as to cause danger to the apparatus, and 
resembles that which would be produced by the physical impact of a 
material body. 

Experiments are next described in which various substances were 
used as the gravitating masses. Amongst these are ivory, brass, 
pith, platinum, gilt pith, silver, bismuth, selenium, copper, mica 
(horisontal and vertioJ), charcoal, Ac. 

The behaviour of a glass beam with glass ends in a diemical va- 
cuum, and at lower exhaustion, is next accurately examined when 
heat is applied in different ways. 

On suspending the light index by means of a cocoon fibre in a 
kmg glass tube furnished with a bulb at the end, and exhausting 
in various ways, the author finds that the attraction to a hot bodv 
in air, and the repulsion from a hot body in vacuo are rendered stiu 
more apparent. 

Speaking of Cavendish's celebrated experiment, the author says 
^bat he has experimented for some months on an apparatus of this 
kind, and gives the following outline of one of the results he has 
obtained : — 

<' A heavy metaUic mass, when brought near a delicately sus- 
pended light ball, attracts or repels it under the following circum- 
stances: — 

'' I, WJten ike ball ia in air of ordinary density. 

a. If the mass is colder than the ball, it repels the ball. 
6. If the mass is hotter than the ball, it aUraets the ball. 
** II. When the baU is in a vacuum. 

a. If the mass is colder than the ball, it attracts the ball. 
h. If the mass is hotter than the ball, it repels the ball." 

The author continues: — *' The density of the medium surround- 

* This can be effected without interfering with the eihmusiion. 

Digitized by VjOOQ IC 

70 Royal Sbdeiy : — 

ii^ tii0 bttB, the mfttonal of \diich the ball is nuMle, and a Tsty 
«l]£ht difference between the temperatures of the mass and tbi 
baU, exert so strong an ii^umiee over the attraotiTe and ropulsiYe 
force, and it has be^ so difficult for Bie to eliminate all interfeiiDg 
actioDs of temperature, eleotrioity, Ac, that I have not yet been 
aUe to get distinct evidence of an independent force (not being of 
the nature of heat) urging the ball and the mass tqgeUiw. 

«* Experiment has, however, showed me that, whilst the action is 
in one dhrection in dense air, and in the <^posite direction in a 
vacuum, there is an intermediate pressure at whidi differences of 
tampeiwture appear to exert little or no interfering action. By 
experimenting at this critical pressure, it would seem that such an 
action as Was obtained by Cavendish, Beidi, and Baily should be 
rendered evideaxt.'' 

After discussing the explanations which may be given iA these 
actions, and i^owing that they cannot be due to auMnirrents, the 
author refers to evidences of this repulsive action of heat, and at- 
kactive action of cold, in nature. In that portion of Uie sun's 
radiation which is called heat, we have the radial repulsive f oroe^ 
possessing successive propagation, required to explain the phenc^- 
mena of comets and the shape and changes of the nebnl». To 
compare small things with great-— to argue from pieces of straw up 
to heav^ily bodies— it is not improbable that the attraction, now 
shown to exist between a cold ana a warm body, vdll equally prevail 
when, for the temperature of meltine ice is substituted the cold of 
space, f <»r a pith oall a celestial sphere, and for an artificial van 
cuum a stellar vmd. In the radiant molecular energy ci. cosmical 
masses may at last be found that " agent acting constantlv accord- 
ing to certain laws," which Newt<m held to be the cause of gravity. 

January 8, 1874, — Joseph Dalton Hooker, G.B., President, in 
the Qiair. 

The following communication was read : — 

" On Electrotorsion.** By G^eo^ge Gore, P.E.S. 

This communication contains an account of a new phenomenon 
(of rods and wires of iron becoming twisted while under the in- 
fluence of electric currents), and a full description of the con- 
ditions under which it occurs, the necessary apparatus, and the 
methods of using it. 

The phenomenon of torsion thus produced is not a microscopic 
one, but may be made to exceed in some cases a twist of a quarter 
of a circle, the end of a suitable index moving through a space of 
80 centimetres (be31 inches). It is always attended by emission 
of sound. 

The torsipns are produced by the combinea influence of helical 
and axial dectric currents, one current passing through a long 
copper-wire cml surrounding the bar or wire, and the other, in 
an axial direction, through the iron itself. The cause of them is the 
combined influence of magnetism in the oidinary longitudinal direc- 

Digitized by VjOOQ IC 

Mr. 6. Gore on Bk^rot€Tium. 91 

tion inAaoed in: liie bar by the ooil-cnrrent, and transterse mag- 
netism indueed in it by the axial one. 

The torsions are remsibbl j symmetrical, and are as definitely 
lebted in dbreclaon to dectric currents as magnetism itself. The 
chief law of them is — A current Jhwing from a norih to a 90%Uh 
pole produces left-handed toreion, cmd a reveree one rtg7u4uxnded tor^ 
non (L e. in the direction of an ordinary screw). Although eadbi 
eorrmt ahme will produce its own magnetic effect, sound, and in- 
ternal molecular morement, neither al<me will twist the bar, unless 
the bar has been preyiously maenetised by the other. Suceessiye 
coil-eurrents alone in opposite oirections will not produce torsion, 
neither will suceessiye and opposite axial ones. 

Hie torsions are influenced by previous mechanical twist in the 
iron, by mechanical tension, and by terrestrial magnetic induction. 
The direction of them depends both upon that of the axial and of the 
oofl-currents, but appears to be determined most by the former. A 
few cases occur in which the currents, instead of developing torsion, 
produce detorsion ; but only two instances, out of many hundreds, 
have been met with in which torsion was produced in a direction 
opposite to that required by the law. 

Bingle torsions vary in magnitude from 0*5 mUlim. to nearly 30 
millims. of movement of the end of an index 47 centimetres long ; 
the smaller ones occur when the two currents are transmitted 
alternately, and the large ones when they are passed simultane- 
ously ; the former generally leave the bar in a twisted state, the 
latter do not. Those produced by axial currents succeeding coil 
ones are nearly always much larger than those yielded by ooU-cur- 
rents succeeding axiiu ones, because the residual magnetism left by 
ttie coil-current is the strongest. The order of succession of ihe 
currents affects the torsions in all cases, altering their magnitudes, 
and in some few instances even their directions. In steel all the 
torsional effects are modified by the mechanical and magnetic 
properties of that substance. 

Each current leaves a residuary magnetic effect in the bar, 
amounting in iron to about one tenth of its original influence. The 
residuary magnetism of coil-currents is affected and sometimes re- 
versed by axial ones ; and that of axial currents is also removed by 
coil ones, and by a red heat. The condition left by an axial current 
is smaller in degree and less stable, in a vertical iron wire or one in 
the terrestrial magnetic meridian, than that left by a coil one, partly 
because of the influence of terrestrial magnetism ; but in a position 
at right angles to that the effect is different. 

The torsion produced by a coil-current may be used as a test, 
imd partly as a measure, of the residuary effect of an axial one ; 
and that produced by an axial currrait may be employed to detect, 
and to some extent measure, ordinary magnetism in the bar. As 
an opposite coil-current at once reverses the ordinary longitudinal 
magnetism of a bar of iron, so also an opposite axial one at once 
reverses its transverse magnetism. 

Many instances have been met with in which the transverse and 

Digitized by VjOOQ IC 

78 Oeoloffical Society : — 

kmfltudiBal magnetic stateB produced bj the two currraits coen- 
istea in the same substance. The tinrsional influence of the ex- 
cited heHz is distributed equally throughout its l^agth ; so also is 
that of the current in the bar. AU the torsions are doselj reUted 
to the well-known electric sounds, and to particular positions and 
internal moyements of the particles of the iron. 

Signs of electrotorsion were obtained with a bar of nickel, bat 
not with wires of pUitinum, silver, copper, lead, tin, cadmium, 
sine, magnesium, aluminium, brass, or German-silTer, nor with 
a tldak rod of sine, or a cord of gutta percha. 


[Continiied from toI. zlvii. p. 462.] 

June 25, 1873.— Joseph Frestwich, Esq., F.B.S., Yice-Preeident, 

in the Chair. 
' The following communications were read : — 

1. '* On six Lake-basins in Argyllshire." By His Grace the Duke 
of Argyll, K.T., F.R.S., President 

The author referred to the part ascribed to glacial action in the 
formation of lake-basins, and described the basins of six lakes in Ar- 
gyllshire, the characters presented by which seemed to him incon- 
sistent with their having been excayated by ice. Among these lakes 
were Loch Fyne, Loch Awe, Loch Leokan, and the Dhu Loch. The 
upper part of Loch Fyne was said to be out off fh>m the rest by a bar 
of islands, with only one or two deeper passages. The country about 
Loch Fyne was described as consistiog of Upper and Lower l^urian 
mica-slates, which have been violently contorted, their normal strike 
being indicated by the direction of the valleys. Loch Fyne occupies 
a niche in the slope of the rocks, having an escarpment on one side 
and the shelving strata on the other, ^e existence of a fault along 
the line of the loch was probable, but could not easily be ascertained. 
Its greatest depth in this part was said to be 84 fathoms. Its 
banks show marks of glaciation, whereon the sur&oe is well adapted 
for their preservation ; the strongest marks are on those rock-faces 
which look up the loch. Between Loch Fyne and Loch Awe the 
mica-slates are interstratified with granite, which the author be- 
lieved to have been forced up between the plains of stratification by 
the pressure caused by the falling in of the mica-slates, as frag- 
ments of the latter rock are imbedded in the granite. The author 
described the different structure of the two banks of Loch Awe, the 
upper part of which seemed to him to lie in a synclinal trough ; and 
its waters were only prevented by a low col from finding their way 
to the Atlantic in this direction, instead of from the lower end. 
The formation of the basin of Loch Awe seemed to the author to be 
due solely to geological structure, as vras also the case with another 
lake beyond the head of Loch Awe. The surrounding country was 
said to be full of smaller lake-basins, the formation of which might 
be due to the denudation of the softer mica- schists lying below the 

Digitized by VjOOQ IC 

Prof. R. Owtn on the SkuU of a dentigerous Bird. 78 

gnmite ridges. But in some cases the basins were excavated in the 
latter; Loch Leckan was mentioned as an example. It is about a mile 
long, from 100 to 200 yards broad, and no less than 18 Ifiathoms deep. 
At the top of its southern bank, which consists of granite, there is 
another lake (Loch-nar-Craig), about 200 yards broad and 9 fathoms 
deep. The surrounding hUls are low, and there appeared to be no 
source which could furnish ice to'excavate a lake of such depth as Loch 
Leckan ; and further, the author contended that if one of these two 
basins had been excavated by ice, the other could hardly have been 
preserved intact. Two other lakes, excavated on the summits of 
granite ridges, were mentioned; and the author could not conceive 
how either a glacier or an ice-cap could have produced such basins. 
The Dhu Loch, separated from Loch Fyne by a bank of gravel about 
a mile broad, is entirely in detrital matter, which the auUior thought 
might have been accumulated in its present form by the sea beating 
against the end of a glacier. From its position and level, the Dhu 
Loch rises and falls with the tide; and it would appear that it 
formerly extended some miles furUier up the valley, where the 
author had found days containing a mixture of marine and fresh- 
water DiatomacesB. In five of these cases the author thought it was 
impossible that the basins are due to glacial action. 

2. <' Description of the Skull of a dentigerous Bird {Odantopteryx 
uHiapiais, Owen), from the London Clay of Sheppey." By Prof. 
Kichard Owen, F.R.S., F.G.S. 

The specimen described by the author consisted of the brain-case, 
with the basal portion of both jaws. The author described in detail 
the structure and relations of tiie various bones composing this skull, 
which is rendered especially remarkable by the denticulation of the 
alveolar margins of the jaws, to which its generic appellation refers. 
The denticulations, which are intrinsic parts of the bone bearing 
them, are of two sizes, — ^the smaller ones about half a line in length, 
the larger ones from two to three lines. The latter are separated 
by intervals of about half an inch, each of which is occupied by 
several of the smaller denticles. All the denticles are of a triangular 
or compressed conical form, the larger ones resembling lania- 
riee. Sections of the denticles show under the microscope the un- 
mistakable characters of avian bone. The length of the skull be- 
hind the fronto-nasal suture is 2 inches 5 lines ; and from the pro- 
portions of the frtigment of the upper mandible preserved, the author 
concluded that the total length of the perfect skull could not be less 
than between 5 and 6 inches. The author proceeded to compare 
the fossil, which he declared to present strictly avian characters, 
with those groups of birds in whidi the beak is longer than the true 
cranium, a character which occurs as a rule in the Aves aquaiiecB, 
He stated that none of the Waders have the nostrils so remote from 
the orbits as in Odoniopteryx ; and this character, with the absence 
of the superorbital gland-pit, limits the comparison to the Totipal- 
mates and Lamellirostrals. The former are excluded by their not 
having the orbit bounded by a hind wall as in OdontopUryx ; and in 
this and other peculiarities the fossil seems to approach most nearly 

Digitized by VjOOQ IC 

74 Geotogical Sociefy: — 

to the Attatid», in the aear alUeB of which, the Gkweanden and Mer- 
gansers, the beak is fonushed with strong pointed denticnlations. 
In these, however, the tooth-like processes bdong to the homy bill 
only ; and the author stated that the production of die alveolar margin 
into bony teeth is peculiar, so fiur as he knows, to Odnntopteryx, 
He condiuded, finom the consideration of all its characters, '' that 
Odontopteryx was a warm-blooded, feathered bqied, with wings ; 
and further, that it was web-footed and a fish-eater, and that in the 
catching of its slii^>ery prey it was assisted by this pterosanroid 
armature of its jaws." In oondusion, the author indicated the dia- 
factors separating Odawtopteryx from the Cretaceous fossil sknll 
lately described by Prof. 0. G. Manh, and which he affirms to have 
small, similar teeth implanted in distinct sockets. 

3. " Contribution to the Anatomy of Hypsihphodon fbxii, an 
Account of some recently acquired Remains of this Dinosaur." By 
J. W. Hulke, Esq., F.R.8., F.G.8. 

After referring to Professors Owen and Huxley's descriptions of 
the Mantell-Bowerbank skeleton in the British Museum, and to tiie 
paper by the last-named gentleman on the skull of this Dinosaur 
read at a meeting of this Society in 1 870, the author communicated 
details of its dentition, the form of its mandible, and that of the 
cones of the shoulder and fore limb, and of the haunch and hind 
limb, hitherto imperfectly or quite unknown. The resemblance to 
Igwmodon is greater than had been supposed ; but the generic di- 
stinctness of HypsUcjphodon holds good. 

4. << On the Glacial Phenomena of the ' Long Mand,' or Outer He- 
brides." By James Geikie, Esq., F.R.S.E., F.GJ3., of H.M. Geolo- 
gical Survey of Scotland. — First piqper. 

The author commenced by describing the physical features of 
Lewis, which he stated to be broken and mountainous in the south, 
whilst the north might be described as a great peat moss rising 
gradually to a height of about 400 feet, but with the rock breaking 
through here and there, and sometimes reaching a higher elevation. 
The north-east and north-west coasts are comparatively unbroken ; 
but south of Aird Laimisheadar in the west and Stomoway in the 
east, many inlets run far into the country. The island contains a 
great number of lakes of various sizes, which are most abundant in 
the southern mountain tract and in the undulating ground at its 
base. The greater part of Lewis consists of gneiss, the only other 
rocks met with being granite and red sandstone, and conglomerate 
of Cambrian age. The stratification of the gneissic rocks is generally 
well-marked ; the prevalent strike is N.E. and 8.W., with S.E. dip, 
generally at a high angle. The author described in considerable 
detail the traces of glaciation observed in the lower northern part of 
Lewis, and inferred from his observations that the ice passed from 
sea to sea across the whole breadth of this district, and that it not 
only did not come from the mountainous tract to the south, but must 
have been of sufficient thickness to keep on its course towards the 
north-west undisturbed by the pressure of the glacier masses which 
must at the same time have filled the glens and valleys of that 

Digitized by VjOOQ IC 

Mr» Campbell on the Okdal Phenomena of the Hebrides. 76 

nMmQteb^egion. After deeoribing the ohareoten prsBented by the 
bottom-till in the northern part ^ Lewis, the antiior proceeded to 
notice those of the lakes, wane of whieh toend nortii-weet and south- 
east, others north-east and sonth-west, irfailsl those <^ the mountain 
district follow no particolar direction. The lake-basins of the first 
seiies he regarded as fonned at the same time and by the same 
agency as the roehee mouionnies and other marks of glacial action ; 
jthey are tme rock-basins or hollows between paiallel banks formed 
whoJly of till, or of till and rock. The N JB. and S.W. lakes coin- 
cide in direetion precisely with the strike of the gneiss ; and the 
anyior explained their origin by the deposition of till by the land-ice 
in passing over the escaipments of tiie gneiss facing the nortii-west. 
Hie lakes of the mountain district are regarded by the author as all 
prodneed by glacial erosion. The auth^ considered ^t the ice 
which passed over the northern part of Lewis could only have come 
from tiie mainland. Beferring to the glaciation of Eaasay, he 
showed that the ice-sheet which effected it must have had in the 
Jnner Sound a deftth of at least 2700 feet ; and taking this as ap- 
proximately Uie thickness of the mer de glace which flowed into the 
Minch, which is only between 50 and 60 fathoms in depth, no part 
of this ice could have floated, and the mass must have pressed on 
over the sea-bottom just as if it had been a land suiiiace. Lse 
coming from Butherland must have {urevented the flow of the Boss- 
shire ice through the Minch into the North Atlantic, and forced it 
over the low northern part of Lewis ; and the height to which Lewis 
has been glaciated seems to show that the great ioe^heet continued 
its progress until it reached the edge of the 100-fathom plateau, 40 
or 50 miles beyond the Outer Hebrides, and then gave off its ice- 
bergs in the deep waters of the Atlantic. 

5. *' Notes on the Glacial Phenomena of the Hebrides." By J. 
F. Campbell, Esq., F.G.S. 

This communication consisted of notes extracted from the author's 
journal, giviog his observations of indications of glacial action in 
various idands of the group of the Hebrides. Heynish in Tiree is 
500 feet high, and has many large perched blocks on its top. These 
blocks are <^ gneiss ; and the author thought they came from the 
north-west The Barra islands are described as rocky, and resem- 
bling the hill-tops of a submerged land. All ice-marks found by the 
author seemed to him to come from t^e north and west. He thought 
that the final grinding was given by floating ice when the land was 
more submerged than at present. At Castle Bay, in Barra, the au- 
thor observed well-preserved glacial strise at the sea-level in a direc- 
tion from N.N.W. The whole island is glaciated and strewn with 
perched blocks. Glacial indications were also observed in South Uist, 
B^ibecula, and Skye ; and the aitthor stated that, on the whole, he 
was inclined to think that the last glacial period was marine, and 
that heavy ice came in from the ocean, the local conditions being 
like those of Labrador. The author regarded most of the l^e- 
basins of the Hebrides as formed by ice-action, and considered that 
the ice by which those islands were glaciated came from Greenland. 

Digitized by VjOOQ IC 

76 Geological SocUly. 

6. *' On Fossil Corals from the Eocene Formation of the West 
Indies." By Prof. P. Martin Duncan, M.B., F.R.S., V.P.G.8. 

The author had considered his lahours amongst the fossil corals of 
the West-Indian Islands finished ; hut lately a yery fine collection has 
heen sent to him from the Unirersity of Upsala, and Mr. P. T. Clere 
of Stockholm. The specimens were collected from limestone and coral 
conglomerates, which are covered by and rest upon ydoanic d^ris 
and ejectamenta in the Island of St. Bartholomew. The species re- 
presented there are numerous, and may he divided into :— ^roup 1, 
species not hitherto known ; 2, species with a Cretaceous fades ; 
3, species characteristic of the horizons of the Upper Eocene and 
Oligocene deposits of Europe ; 4, species found also in the Nummu- 
Utic deposits of Europe and Sinde; 5, species belonging to the 
recent coral fauna ; 6, species belonging to genera which belong to 
the Jurassic fauna, and to the Caribbean. 

The determination of the forms of the associated MoUusca and 
Echinodermata permit the following deposits being placed on a 
general geologic^ horizon — the limestone and conglomerate of St 
Bartholomew, the dark shales beneath the Miocene of Jamaica, 
the beds of San Fernando, Trinidad. These were probably contem- 
poraneous with the Java deposits, the Eocene of the Hala chain, 
the great reefs of the Castel Gomberto district, the reefs of Ober* 
berg in Steiermark, and the Oligocene of Western Europe. 

The author has already described reef corals from the Lower Cre* 
taceous (Upper Greensand) of Jamaica ; and the size of the sped* 
mens proves that the reef was exposed to the surf of an open sea. 
To these reefis succeeded on the same area others in the Eocene 
time, in the Miocene and Pliocene ; and there are modem reefis in 
the neighbourhood. 

The affinities and identities of the fossil forms with those of con- 
temporaneous reefs in Asia and Europe, and the limitation of the 
spedes of the existing Caribbean coral fauna, point out the correct- 
ness of the views put forth by 8. P. Woodward, Carrick Moore, and 
the author, concerning the upheaval of the Isthmus of Panama after 
the termination of the Miocene period. 

7. " Note on the Lignite-deposit of Lal-Lal, Victoria, Australia.'' 
By R. Etheridge, Esq., Jun., F.G.S. 

The author described this depodt, which is worked at the village 
of Lal-Lal, south of Mount Bunniyong. A boring towards the centre 
of the deposit showed about 73 feet of sand, day, and gravel, 3 feet 
of fireday, and 1 15 feet of lignite. The lignite is an earthy bitu- 
minous coal, composed of branches, roots, &c. of coniferous trees. 
In the mass there are a few thin seams of jet and day-beds, accom- 
panied by two kinds of resin. The lignite is very poor in carbon. 
It is almost entirely composed of remains of coniferous plants not 
now existing in Victoria ; and the author conddered that it is nearly 
of the same age as the Lignite depodt of Morrison's Diggings, whidi 
has been regarded as Miocene. 

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C 77 ] 
XII. IntelUgenee and Migcellaneau$ Articles. 


rPHE velocity of the flow of solutions in capillary tubes appears 
^ not to depend solely on their weight and capillary adhesion. 
Poiseuille has demonstrated that the velocity of flow of a mixture of 
water and alcohol decreases in proportion as the specific gravity 
increases by the addition of larger and larger quantities of water, 
to a Tninimiim which corresponcis exactly to the maTiTnum of con- 
traction of the mixture. GKrard found that the velocity of flow of 
chloride of sodium is less than than that of a solution of chloride 
of potassium of the same density. 

M. Hiibener thought that, beside the adhesion and the weight of 
the liquid, an important factor for the velocity of flow of a solution 
must be the intermolecular friction resulting from its greater or 
less cohesion ; and to test this he has compared the velocities of a 
nomber of solutions of very different chemical compositions brought 
to the same density. 

The liquid was introduced into a vertical rectilinear glass tube of 
50 centims. length and 1*78 centim. diameter, having a capillary 
continuation of about 40 centims. length. The large tube presented 
two marks; and with a seconds-watch the time was accurately 
measured which was required for the level of the liquid to tall from 
one of these marks to the other. 

Operating in this way upon solutions of chloride, bromide, and 
iodiae of potassium, of chloride of sodium and of ammonium, with 
a density of 1*059 and at a fixed temperature, the author ascertained 
tiiat the velocity of flow of saline solutions is as much lower as the 
atomic weight of the salt dissolved is less. For the different binary 
bodies abovein£cated, it is the metal which has the greatest influence 
opon the velocity of flow, much more than the metalloid. The va- 
riations presented by the velocity from one body to another are as 
much more marked as the tube is more capiUary and as the con- 
centration of the solution is greater. 

On comparing two solutions, of chloride of sodium and potassium, 
at 1*1058 density, the author arrived at the remarkable result that 
the times of flow of these two salts are found to be very sensibly 
proportional to their equivalents. From this experiment, and from 
others fuialogous, extended also to the chlorides of the alkaline-eiarthy 
metals barium, strontium, magnesium, M. Hiibener thinks it may be 
concluded generally with a high degree of probability, that the velo- 
cities of flow of these bodies in solution in. water, to a certain degree of 
concentration, are in the same ratio as their equivalents. 

The explanation of these facts is, according to M. Hiibener, 
to be found in the circumstance that the molecules of substances 
which have a higher equivalent are larger, but, on the other hand, 
in less number, and consequently must give rise to less friction 
with the solvent in which they ai*e held, thus communicating greater 

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78 IrUeUigenee and Miseellaneoui Articki. 

mobility to the solution. — BihUaiheque UniverBsUe, AreMvu dtt 
Sciences Phys. et Nat. No. 197, pp. 76, 76. 


In performing Melde'e experiment upon the vibrations of 
strings, it is desirable to change the tension of the vibrating cord 
in a continuous manner. The ordinary method of attaching 
weights to the cord does not admit of this with precision ; and with 
small weights the movement of the weight itself, on account of the 
rapid vibration of the string, prevents the formation of the ventral 
segments with regularity. I have adopted the following method : — 
A glass tube graduated into millimetres is weighted so as to float 
in a vertical position: this is attached to the silk cord whidi 
hangs from the prong of the tuning-fork, and is placed in a glass 
vessel filled with water. This latter vessel is provided with a 
siphon, by means of which the water can be drawn ofF at pleasure. 
It will be readily seen that, by drawing off the water from the 
larger vessel, the displacement produced by the graduated glass 
tube is diminished, ana the tension of the string thereby is increased. 
By diminishing or increasing the amount of water in the larger 
vessel the tension can be diminished or increased to the desirod 

In order to make quantitative experiments, the tube is in the first 
place connected with the arm of a delicate hydrostatic balance. 
The balance is adjusted when the level of the water in which the 
tube floats is at the zero of the millimetre scale. In order to 
avoid errors in reading, it is best to use a cathetometer. The 
weights which are necessary to keep the index of the balance at 
aero, when the level of the water in the outer vessel falls through 
the millimetre divisions on the graduated tube, are noted, llie 
upward pressure of the water, and consequently the tension upon 
the suspending cord, are then given in grams. 

In order to show the regiuarity of the method, the following 
results of one experiment are given. In the experiments, a glass 
tube which, immersed at 110 millims. on the scale, weighed two 
grams gave, when the level of the water in the outer vessel was 
lowered, the following : — 

Immersed at 110 millims. Weight « 2 grams. 

102 „ „ 2-5 „ 

tf 93'5 „ „ 3 „ 

„ S5 ^ „ „ 3*6 „ 

»> 76-5 „ „ 4 „ 

„ 67*6 „ „ 4*5 „ 

»» ®0 „ „ 6 „ 

ff 43 „ „ 6-6 „ 

In these experiments a fidl *of 8*1 millims. corresponded to a 
difference of *5 of a gram. It is evident by increasing the sise of 
the outer vessel that a large amount of water would measure a 
slight displacement. When the cord was set in vibration, the fol- 
lowing results were obtained : — 

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TntelUgenee and Miscettaneaus Articles. 79 

Paint Wmgfate 

of immenion. in grams. yibrations. 

110 2 6 

84 3-5 6 

76 4 4 

30 6-7 3 

The ratio of the numbers in the second and third columns will be 
found to follow Melde's law. 

For qualitative or quantitative experiments upon beats or Lissa- 
jous curves this method of loading the prong of a tuning-fork can 
advantageously replace the bit of wax or the sliding weight, since 
we have at our command a quick and precise method of adjustment. 
— Silliman's American Joumaly May 1874. 


Kirchhoff* has developed a simple expression for the elebtric 

Potential, with a constant current, in every point P of a circular 
omogeneous plate into which the current enters at given points 

Aj, A^, If each letter E represents a constant depending on 

the strength of the current entering at the point A„ and if B^ is 
the conjugate point to A^, the electric potential of the circle in the 
point P becomes 

V=2E,log(PA,.PBJ, (a) 

when the summation is extended to all the points of inflow. Two 
points A, B of the circle are called conjugate which lie on the same 
right line M AB starting from the centre M, if the radius forms the 
mean proportional between MA and MB. 

I have found the expression of the potential also for plates of 
other shapes, and will here give it for the ellipse and the rectangle. 
Let the excentridty of the ellipse be 1 ; let the fourth power of 
ihe difference of the semiaxes (oi which the greater represents the 
axis of the real, the smaller that of the imaginary) be put =sq. 
Let each point z of the ellipse be described by the elliptic function 

/2K . \ 
$nl — arc sin z j, 

therefore the entire ellipse upon a circle with the radius -j^ (as M. 

Sdiwarz has shown). If now a, p are the images of the inflow- 
points A and an arbitrary point P of the ellipse, and if h denotes 

the point in the circle of radius —t=. conjugate to a, the electric po- 

tential of the ellipse in the point P will be 

V«SE'log(pa..i>5j (/3) 

If, lastly, we have a rectangle OXNY, whose base OX has the 
leneth w and is the axis of the real, and its height OY equals 
— log ^ and is the axis of the imaffinary, we construct for each 
point ot inflow A the three reflected images B, G, D which arise 
when A is assumed to be luminous, OX and OY reflecting (^-l:y», 
«— y», — ^— y», — ^-fy*)* I^ ^^^ ®*<5h point z be represented by 
♦ Pogg. Aim. vol. Ixiv. p. 497, v<^. Ixvit. p. 344. 

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80 Intelligence and Miicellaneoui Art%ele$. 

«n* — , and thereby A, B, C, D, and the arbitrary point P of the 


rectangle fall upon points a, 5, c^ d, p, the electric potential of the 
rectangle in the point P is 

V=5 E, log (pa, .pb, .pc, .pd,). (y) 

Quincke* bases his experiments, on the potential in very large 
square plates when the points of inflow are in the diagonal, upon 
a formiila of approximation which in our notation would be 

V=? E, log (PA, . PB, . PC, . PDJ. 
It is now apparent, if this be compared with the exact formula (y\ 
that it results from the latter, if $nz may be supposed propor- 
tional to z, therefore with very large rectangular plates — or, betttf , 
under the supposition that P and the A's lie near an angular 
point of the rectangle. The approximation-formula therefore holds 
also when the rectangle is not a square and when the inflow-points 
do not lie on the diagonal. 

The derivation of these expressions I intend to communicate, in 
a connected form, to Borchardt's Journal fur Mathematik. For 
this reason I omit here the exhibition in a purely analytical form, 
without the aid of geometry, of the relations expressed by (/3) and 
(y). — Monatsherieht der honiglich preussischen Akademie der Wia- 
senseh, zu Berlin, March 6, 1874. 


When silver bromide is exposed for a moment to light, it under- 
goes no visible change, but has acquired the property of passing to 
an intense black when treated with p3rrogallic add and an alkaU. 

As to the nature of this black substance, there has existed con- 
siderable diversity of opinion. In a paper published on the subject 
about a year since by Captain Abney, F.C.S., he expressed the 
opinion that it was an oxide of silver. 

Some years since, while investigating the action of light upon 
silver iodide, I succeeded in provins; that the black substuice 
which is produced when silver iodide is exposed to light in presence 
of silver nitrate contains iodine, and is therefore either a sub- 
iodide or an oxy-iodide. The quantity obtained was too small to 
enable me to ascertain which. When this black substance was 
treated with nitric acid, normal yellow silver iodide was left behind, 
and silver was found on solution. 

I have recently applied the same treatment to the bromine com- 
poimd with similar results. I And that when silver bromide is 
treated with pyrogallic acid and alkali after exposure to light, the 
black substance which remains contains bromine, and is resolved by 
nitric add into normal silver bromide (left behind as a pale yellow 
film) and silver, which passes into solution. It is therefore either 
a subbromide or an oxy-oromide, not an oxide, probably the former. 

The existence of these compounds is evidently an argument for 
doubling the atomic weight of lUver, as has recently been proposed 
on other grounds. — SilHman's Am&riean Journal^ May 1874. 
* Pogg. Ann, vol. xcvii. p. 382. 

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AUGUST 1874. 

XIII. On Attraction and Repulsion accompanyirw Radiation^ 

By William Crookes, F.U.S. ^c.*^ 

[With a Plate.] 

BEFORE describing the apparatus and experiments which 
illustrate the attraction and repulsion accompanying ra- 
diation^ it will perhaps be best to draw attention to the modifi- 
cation of the Sprengel pump which has so materially assisted 
me in this investigation. 

Fig. 1 (Plate I.) shows the pump as now in use. Working 
so much with this instrument^ I have endeavoured to avoid the 
inconveniences attending the usual mode of raising mercury 
from the lower to the upper reservoir. The mercuiy is con- 
tained in a closed glass reservoir A^ perforated with a fine hole 
at the top. This reservoir is attached to a block capable of free 
movement in a vertical line and running in grooves, and con^ 
nected with the lower resei*voir by a flexible tube g. This tubing 
is specially made to stand a considerable pressure of mercury. 
It consists of a double thickness of india-rubber tubing enclosing 
a canvas tube in the centre, the whole being vulcanized together. 

When the whole of the mercury has run through the pump, 
the reservoir and slide can be lowered by liberating a detent, T, 
and letting it descend to the block L. H is a glass reservoir 
which receives the mercury after flowing through the pump. 
When the reservoir A is emptied and has been lowered to the 
block L, the mercury from H is admitted into A by opening 
ihe tap I. At/ is another tap, of platinum, to regulate the flow 
of mercury through the pump, c, c, d are mercury joints, it 

* A Lecture delivered before the Physical Society, June 20, 1874. Com- 
municated by the Societv. 

Phil. Mag. S. 4. Vol. 48. No. Z\Q. Aug. 1874. G 

Digitized by VjOOQ IC 

82 Mr, W. Crooke« on Attraclion and 

being inconvenient to have the apparatus in one piece of tubing, 
and not always possible to seal the different portions together 
by fusion. « « is a barometer dipping into the same vessel as 
the gauge-barometer P> the two thus forming a differential 
system by which the rarity of the atmosphere in the apparatus 
undergoing exhaustion can be easily estimated, dd is a milli- 
metre-scale with pointed end, attached to the gauge and capable 
of being raised or lowered so as to make the point just touch 
the surface of the mercury, i is a reservoir of strong sulphuric 
acid, exposing as much surface as possible, but allowing the air 
to pass across it without resistance. The mercury joint (f may 
either be closed with a piece of glass rod ground in, or it may have 
either of the two pieces of apparatus t and k fitted to it. A is a 
mercurial siphon gauge, which is useful for measuring very high 
rarefactions in experiments where difference of pressure equal 
to a tenth of a millimetre of mercury is impoitant. t is for still 
higher rarefactions ; it is simply a small tube having platinum 
wires sealed in, and intended to be attached to an induction- 
coil. At exhaustions beyond the capabilities of the mercurial 
gauge I can still get valuable indications of the nearness to a 
perfect vacuum by the resistance of this tube. I have frequentlv 
carried exhaustion to such a point that an induction-spark will 
not strike across the small distance {\ inch) separating the wires 
of the vacuum-tube, h is the mercury-tap usually employed for 
letting air into the apparatus, and also for moistening the inte- 
rior of the pump with oil of vitriol. / is a spiral of glass for 
attaching the various pieces of apparatus requiring exhaustion. 
As blown or fused joints are indispensable, this form of con- 
necting piece is adopted to ensure the necessary flexibility, 
m is a trap to catch any air which might leak in through the 
platinum tap/, or the various joints in the lower part of the 
tubing g. 

The reservoir A being filled with mercury, the tap I is turned 
off and the reservoir is raised to the top of the slide where it is 
supported by the detent T. On opening the tap /the mercury 
rises in the tube /A, and, falling through the chamber N, carries 
with it the air contained in the tube R, and in the apparatus 
attached to the tube /, as in the ordinarv Sprengel pump. At N 
the tubing is enlarged in order that the mercury may not be 
forced up the tube R, as otherwise frequently happens if the 
tubes or the mercurv gets soiled. 

J, J are iron brackets supporting tie apparatus. S is a large 
inverted glass receiver, to collect the small portions of mercury 
which are unavoidably and constantly being spilled; it should 
contain a little weak alkaline solution. 

The part of the tubing g,f, A, N forms a barometric siphon 

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Repulsion accompanying Radiation. 88 

arrBBgement, which effectually prevenU air getting into the 
pump from the reservoir A when the mercury has comphjtely 
run out. In this case no harm whatever is done to the opera- 
tion : the vacuum is not injured ; and the exhaustion proceeds 
immediately on retransferring the mercury from the reservoir H 
to the reservoir A^ and raising A again into its place. The ap- 
paratus, as thus aiTsnged^ is readily manageable with certainty 
of obtaining a barometric vacuum. 

The mercury fall-tube of a pump in constant use frequently 
wants cleaning. I find the most effectual means of doing this 
is to put oil of vitriol into the funnel h, and then^ by slightly 
loosening the glass stopper^ allow a little of the strong acid to 
be carried down the tube with the mercaiy. With care this 
can be effected without interfering with the progress of eihaus«> 
tion. The residual acid adhering to the walls of the chamber 
N does good rather than harm. When sufficient sulpbnrio acid 
has run into the fall-tube, the funnel-stopper can be. perfectly 
closed by pressing it in with a slight twist and then filling up 
with mercury. 

Many physicists have worked on the subject of attraction and 
repulsion by heat. In 1792 the Bev. A. Bennet recorded the fact 
that a light substance delicately suspended in air was attracted 
by warm bodies; this he ascribed to air-currents. When^ by 
means of a lens, light was focused on one end of a delicately sus- 
pended arm, either in air or in an exhausted receiver, no motion 
could be perceived distinguishable from the effects of heat. 
After Mr. Bennet the subject has been more or less noticed 
by Laplace, libri, Fresnel, Saigey, Forbes, Baden Powell, and 
Faye ; but the results have been unsatisfactory and contradictory. 

My first experiments were performed with apparatus made on 
the principle of the balance. An exceedingly fine and light arm 
is delicately suspended in a glass tube by a double-pointed 
needle ; and at the ends are affixed balls of various materials. 
Amongst the substances thus experimented on I may mention 
pith, glass, charcoal, wood, ivory, cork, selenium, platinum, 
silver, aluminium, magnesium, and various other metals. The 
beam is usually either of glass or straw. 

The apparatus, consisting of a straw beam and pith-ball endS| 
being fitted up as here shown attached to the pump, and the 
whole being full of air to begin with, I pass a spirit-lamp across 
the upper part of the tube just over one of the pith-balls. The 
ball rises. The same effect is produced when a bulb of hot water, 
or even the warm finger is placed over the pith-ball. 

On working the pump and repeating the experiment, the 
attraction to the hot body gets less and less, until it becomes nily 
and after a certain barometric pressure is passed, the attractiou 


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81 Mr. W. Crookea on Attraction and 

gives place to repulsion^ which gets stronger and stronger as the 
vacuam approaches perfection. 

In order to illustrate more strikingly the influence exerted by 
a trace of residual air, an apparatus (fig. 2) is here shown in 
which the source of heat (a platinum spiral, a, rendered incan- 
descent by electricity) is inside the glass tube instead of out- 
side it as before. A mass of magnesium, i, turned conical, is 
suspended in a glass tube, c J«, by a fine platinum wire of such 
a length as to vibrate seconds. The upper end of the platinum 
wire is sealed into the glass at «, and passes through to the out^de 
for the purpose of electrical experiments. The platinum spiral 
is arranged so that when the pendulum hangs free the magne- 
sium mass is about \ inch from it. In air the red-hot spiral 
produces decided attraction on the magnesium ; and by properly 
timing the contacts with the battery, a considerable swing can 
be acci^mulated. On perfectly exhausting the apparatus, how- 
ever, tha^ incandescent spiral is found to energetically repel, 
and a very few contacts and breaks properly timed are suffi- 
cient to get up the full swing the pendulum is capable of. 

A siiMpler form of the apparatus for exhibiting the phenomena 
of attraction in air and repulsion in a vacuum consists of a long 
glass tube a b (fig. 8) with a globe c at one end. A light index 
of glass with pith-balls at the ends d^ e is suspended in this globe 
by means of a cocoon fibre. When the apparatus is full of air 
at ordinary pressure, a ray of heat or light falling on one of the 
pith-balls gives a movement indicating attraction. 

When the apparatus is exhausted until the barometric gauge 
shows a depression of 12 millims. below the barometer, neither 
attraction nor repukion results when radiant light or heat falls 
on the pith. When the vacuum is as good as the pump will 
produce, strong repulsion is shown when radiation is allowed to 
fall on one end of the index. The heat of the hand, or even of 
the body several feet ofl^, is quite sufficient. The action is in 
proportion to the surface acted on rather than to the mass. 

The barometric position of the neutral point dividing attrac* 
tion from repulsion varies with the density of the mass on which 
radiation falls, on the ratio of its mass to its surface, and in a 
less degree on the intensity of radiation. In the case of pith it 
is seen to lie at about 12 millims. below a barometric vacuum, 
whilst with a heavy metal it is within a tenth of a millim. of a 
vacuum. Experiments to try to determine the law governing 
the position of the neutral point are now in progress. 

Ice, or a cold substance, produces the opposite effects to heat. 
Thus a bar of pith suspended in a vacuum is energetically re- 
pelled by the warm hand, whilst it is as strongly attracted by a 
piece of ice. Cold being simply negative heat^ it is not easy at 

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Repulsion accompanying Radiation. 85 

first sigbt to understand how it can produce attraction. The 
law of exchanges, however, explains this perfectly. The pith 
index and the whole of the surrounding bodies are incessantly 
exchanging heat-ra^s ; and under ordinary circumstances the 
income and expenditure of heat are in equilibrium. A piece of 
ice brought near one end of the index cuts offthe influx of heat 
to it from that side, and therefore allows an excess of heat to 
fall upon it from the opposite side. Attraction by a cold body 
is thus seen to be only repulsion by the radiation from the op- 
posite side of the i*oom. 

Instruments of the kind just described are perhaps the best 
for exhibiting large and striking movements of attraction or 
repulsion. Two glass globes 4 inches in diameter, fitted up with 
bars of pith 3^ x ^ inch, are now before you. One is full of air 
at ordinary pressure, whilst the other is completely exhausted. 
A touch with a finger on a part of the globe near one extremity 
of the pith will drive the bar round over 90^, in the vacuum. 
In air the attraction is not quite so strong. 

If I place a lighted candle an inch or two from the vacuous 
globe, the pith bar commences to oscillate. The swing gradu- 
ally increases in amplitude until one or two complete revolu- 
tions ar» made. The toraion of the suspending fibre here inter- 
feres, and the vibrations pi*oceed in the opposite direction. The 
movement continues as long as the candle burns* This con- 
tinued movement ceases if the source of radiation is removed 
some distance off; the pith index then sets equatorially. The 
cause of the continued vibration when the radiant body is 
at a particular distance from the pith is easy to understand on 
the supposition that the movement is due to the direct impact 
of waves on the suspended body. 

For more accurate experiments I prefer making the apparatus 
differently. Fig. 4 represents the best form, ab is a, glass 
tube, to which is fused at right angles another, narrower tube, c d; 
the vertical tube is slightly contracted at e so as to prevent the 
solid stoper d, which just fits the bore of the tube, from falling 
down. The lower end of the stopper de'iB drawn out to a point ; 
and to this is cemented a fine glass thread about O'OOl inch 
diameter, or less, according to the torsion required. 

At the lower end of the glass thread an aluminium stirrup 
and a concave glass mirror are cemented, the stirrup being so 
arranged that it will hold a beam fg having masses of any de- 
sired material at the extremities. At c in the horizontal tube 
is a plate-glass window cemented on to the tube. At & is also 
a piece of plate glass cemented on. Exhaustion is effected 
through a branch tube h projecting from the side of the upright 
tube. This is sealed by fusion to the spiral tube of the pump, 

Digitized by VjOOQ IC 

86 Mr, W. Crookes on Attraction and 

The stopper de^ aad the glass plates c and b^ are well fastened 
with a cement of resin 8 parts and bee's- wax 3 parts** 

The advantage of a glass-thread suspension is that the beam 
always comes back to its original position. Before jou is an 
instrument of this description^ perfectly exhausted and fitted up 
with pith plates at each extremity. A ray of light from the 
electric lamp is thrown on to the mirror c, and thence reflected 
on to the opposite wall. The approach of a finger to either extre- 
mity of the beam causes the luminous index to travel several 
feet^ showing repulsion. A piece of ice brought near causes the 
spot of light to travel as much in the opposite direction. 

Here is another form of the apparatus (fig. 5). The letters 
and description are the same as in fig. 4^ the apparatus, 
however^ being double. The pieces /, g on the end of one 
beam consist of platinum-foil exposing a square centimetre of 
surface, whilst the extremities /',y on the other beam consist of 
pith plates of the same siec. It Las already been explained that 
the neutral point of rarefaction for platinum is much higher than 
for pith ; conaequently at a pressure intermediate between these 
two neutral points, radiation ought to eause the platinum to 
be attracted and the pith to be repelled. This is seen to be 
the case. A wide beam of radiant heat thrown in the centre of 
the tube on to the plates gyf causes g to be attracted andy to 
be repelled^ as shown by the light reflected from the mirrors 
Cy c\ The atmospheric pressure in the apparatus is equal to 
about 40 millinos, of -mercuiy. 

The position of the neutral point not only depends on the 
density of the body acted on by radiation^ as in the above case, 
but also on the relation of surface to mass. Thus a square cen- 
timetre of thin platinum-foil on the extremity of the beam 
requires a lower exhaustion for neutrality than a thicker piece 
exposing the same surface. Also a flat disk of platinum has a 
lower neutral point than the same weight of platinum in the 
form of a sphere. 

Intensity of radiation likewise affects the neutral point. With 

* This is the best cement I have used for standing a Tncuura : for a 
few hours it is perfect. But at the highest exhaustions it seems to leak in 
the course of a day or two. India-rubber joints arc of no use in these ex- 
periments, as, when the vacuum is near upon perfect, they allow oxygenized 
air to pass through as readily as the pump will remove it. Whenever 
possible the glass tubes should be unitca by fusion ; and where this is im- 
practicable mercury joints should be used. The best way to make these is 
to have a well-made perforated eonical stopper, cut from plain india-rubber, 
^tting into the wide funnel-tube of the jomt and carrying the narrow tube. 
Before fitting the tubes in the india rubber this is heated in a spirit-lamp 
until its surface is decomposed and vciy stickv ; it is then fitted into its 
place ; mcrcurj- is poured over, and oil of vitriol on the top of that. When 
well made, this joint seems p^fect. 

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RepuUion accompanying Radiation. 87 

pith extremities a point of rarefaction can be obtained at which 
the warm fingers repel and incandescent platinum attracts. 

Baring the coarse of this lecture I have spoken frequently of 
repalsion by heMt^ and have used a spirit-lamp as a source of 
h4»t to illustrate the facts described. I now wish to show that 
these results are not confined to the heating rays of the spec- 
trum, but that any ray, from the ultra-red to the ultra-violet, will 
produce repulsion in a vacuum. 

In ray own laboratory I have used sunlight, and have experi- 
mented with a very pure spectrum, taking precautions to avoid 
any overlapping or difi'usion of one part of the spectrum with 
another. Here I can only use the electric light, and, in order 
to get results visible at a distance, the spectrum cannot be very 

The spectrum is formed with one disulphide-of-carbon prism, 
and is projected on to the screen by a lens. Immediately be* 
hind the screen is an exhausted bulb, having a movable index 
with pith terminals suspended with a cocoon fibre (fig. 3). This 
is delicate enough to swing over 90^ with a touch of the finger, 
and it will even move under the influence of a ray of moonlight. 
I first of all arrange the spectrum so that the extreme red would 
fall on one pith disk were it not for the screen* On removing 
the screen the index immediately retreats, making nearly half a 

I now replace the screen, and arrange the spectrum so that 
the invisible ultra-violet rays are in a position to fall on the pith 
disk. On removing the screen the index at once behaves as it 
did under the influence of the red rays, and is driven away 
twenty or thirty degrees. The action is not so powerful as when 
the other end of the spectrum is used ; but this may partly, if 
not wholly, be accounted for by the much greater concentration 
of energy at the red end of the spectrum, and expansion at the 
violet end, when using glass or disulphide-of-earbon prisms. 

I now, without disturbing the position of the spectrum, inters 
pose in the path of the rays a cell containing a solution of iodine 
in disulphide of carbon, which is opaque to the luminous and 
ultra-violet rays, but transparent to the invisible heat-rays. Not 
a trace of repulsion is produced. The iodine solution is now re- 
moved and the ultra-violet rays again fall on the pith, producing 
strong repulsion. A thick screen of clear alum cut from one of 
Mr. Spencers gigantic crystals is now interposed ; but no efiect 
whatever is produced by it, the ultra-violet rays acting with un- 
abated energy. As alum cuts off all the dark heat-rays, this 
experiment and the one before it prove the suflBcient purity 
ef my spectrum. 

The spectrum is again turned iditil the dark ultra-red heating 

Digitized by VjOOQ IC 

88 Mr. W. Crookes on Attraction and 

rays fall on the pith. The movement of repulsion is energetic. 
The iodine solution, interposed, cuts off apparently none of the 
Action. The alum plate cuts off a considerable amount, but by 
no means all. On uniting the alum and the iodine solution the 
whole of the spectrum is obliterated, and no action is produced, 
whatever be the ray which would, were it not for this double 
sifting, fall on the pith. 

Throughout the course of these investigations, which have 
occupied much of my spare time for some years, I have endea- 
voured to keep in my mind the possible explanations which may 
be given of the actions observed ; and I have always tried, by 
selecting some circumstances and excluding others, to put each 
hypothesis to the test of experiment. 

' The most obvious explanation is, that the movements are due 
to the currents formed in the residual gas which theoretically 
must be present to some extent even in those vacua which are 
most nearly absolute. 

Another explanation is, that the movements are due to elec- 
tricity developed on the moving body or on the glass apparatus 
by the incident radiation. 

A third explanation has been put forward by Professor 
Osborne Reynolds, in a paper which was read before the Royal 
Society on June 18th last. He considers the results to be due 
to evaporation and condensation. 

I will discuss these explanations in order. 

First, the air-current theory. However strong may be the 
reasons in favour of this explanation, they are, I think, answered 
irrefragably by the phenomena themselves. It is most difficult 
to believe that the residual air in a Sprengel vacuum, when the 
gauge and barometer are level, can exert, when gently warmed 
by the finger, an upward force capable of instantly overcoming 
the inertia of a mass of matter weighing 20 or 30 grains. It 
must be remembered that the upward current supposed to do 
this is simply due to the diminished weight of a portion of the 
gas caused by its increase in volume by the heat applied. 

An air-current produced by heat may possibly cause the 
beam of a balance to rise, may drive a suspended index side- 
ways, and by a liberal assumption of eddies and reflections, 
may perhaps be imagined to cause these movements to take 
place sometimes in the opposite directions ; but as rarefaction 
proceeds these actions must certainly get less, and they will 
cease to be appreciable some time before a vacuum is attained : 
a point of no action or neutrality will be reached. But this 
neutral point should certainly be nearer to a vacuum when a 
light body like pith, exposing much surface, is under experiment| 

Digitized by VjOOQ IC 

Repulsion accompanying Radiation. 89. 

than when the mass acted on is heavy like brass ; whereas in 
practice the contrary obtains. Pith ceases to move under the 
influence of radiation at a rarefaction of about 7 to 12 millims., 
whilst brass only ceases to be affected when the gauge and ba- 
rometer are appreciably level. 

But even could the phenomena up to the neutral point be 
explained by air-currents^ these are manifestly powerless to act 
after this critical point is passed. If a current of air within 7 
millims. of a vacuum cannot move a piece of pith^ certainly the 
residual air in a Sprengel vacuum should not have more power; 
and a fortiori the residual gas in a perfect chemical vacuum 
cannot possibly move a mass of platinum. 

It is^ however^ abundantly demonstrated that, in all cases after 
this critical point is reached^ the repulsion by radiation is most 
apparent ; it increases in energy as the vacuum approaches per- 
fection, and attains its maximum when there is no air whatever 
present, or at all events not sufficient to permit the passage of 
an induction-spark. 

I will now refer to the electrical explanation. Very early in 
my investigation, phenomena were noticed which caused me to 
think that electricity played a chief part in causing the move* 
ments. When a hot glass rod is held motionless against the 
side of an exhausted tube containing a pith index, repulsion 
takes place in a perfectly regular manner; but if the glass rod 
has been passed once or twice through the fingers, or is rubbed 
a few times sideways against the exhausted bulb, the index im- 
mediately moves about in a very irregular manner, sometimes 
being repelled from, and at others attracted to, the side of the 
glass, where it adheres until the electncal excitement subsides. 
Friction with the finger produces the same results; and a small 
spirit-flame causes similar, but much fainter, electrical effects. I 
soon ascertained, however, that, although electricity is capable 
of producing many movements similar to those caused by radia- 
tion, they are never so alike as to be mistaken. Electricity fre- 
quently interferes with, disturbs, or neutralizes the true action of 
radiation ; but it acts in such a manner as to show that it is not 
the primary cause of the movement. At the highest rarefactions, 
and when special precautions have been taken to avoid the pre- 
sence of aqueous vapour, slight friction with the finger against 
the bulb, or a touch with the flame of a spirit-lamp, excites so 
much electrical disturbance in the pith and other indexes that 
accurate observations become impossible with them for several 
hours. I have tried many means of neutralizing the electrical 
disturbance ; but they are only partially successful, and at the 
highest rarefactions interference through electrification is very 

Digitized by VjOOQ IC 

90 Mr. W. Crookes on Attraction and 

I miiy draw attention to the following experiments^ which are 
devised with the objeet of showing that the attractions and re* 
pulsions are not due to electricity. 

In describing the pendulum apparatus (fig. 2) which I set in 
motion at the early part of this lecture^ I explained that the 
mass of magnesium forming the weight was in metallic con- 
tact with the platinum wire which supported it^ and that the 
Upper end of this platinum wire was fused into the glass tube 
and passed through to the outside. With this apparatus I have 
tried a great number of experiments. I hsTc connected the pro- 
jecting end of the platinum wire with " earth/' with either pole 
of an induction-coil the other being insulated more or less^ with 
either pole of a voltaic battery^ with a delicate electroscope ; I have 
charged it with an electrophorus^ and have submitted it to the 
most varied electrical conditions ; and stilly on allowing radiation 
to fall upon the suspended mass^ I invariably obtain attraction 
when air is present^ and repulsion in a vacuum. The heat has 
been applied both from the outside^ so as to pass through the 
glass^ and also inside by means of the ignited platinum wire ; 
and the results have shown no diflFerence in kind, but only in 
degree, under electrical excitement. I have obtained interference 
with the usual phenomena, but never of such a character as would 
lead me to imagine that the normal results were due to electricity. 

It occurred to me that the repulsion might be due to a deve- 
lopment of electricity on the inner surface of the glass bulb or 
tube under the influence of the radiation as it passed from the 
glass into the vacuum. This appears to be disproved by the 
fkct that the results are exactly the same whether the radiation 
passes through the glass, or whether it is developed inside the 
apparatus as in the above instance. 

I have produced exactly the same phenomena whether the 
exhausted apparatus has been standing insulated in the air, or 
whether it was completely immersed in water connected electri- 
cally with " earth,'' or surrounded with wet blotting-paper. 

Here are two experiments which bear on this subject. A 
straw beam furnished with brass balls at each end is suspended 
on a double-pointed needle, and the brass balls and needle 
are placed in metallic connexion b^ means of fine platinum wire. 
The needle does not rest on the sides of the glass tube, but in 
steel cups, to which is soldered a platinum wire passing through 
the glass tube and connected with ''earth." The tube is then 
exhausted, and the usual experiments are tried with hot and 
cold bodies^ both with and without a wet blotting-paper cover. 
In all cases the moving beam behaves normally, being repelled 
by heat and attracted l^ cold. 

An apparatus is prepared similf^r to that shown in fig. 4. 

Digitized by VjOOQ IC 

Repubiott accompanying Radiation* 91 

The inside of the tube ab \% lined with a cylinder of copper 
ganse, having holes cut in the centre for the passage of the snp^ 
porting thread dc and the index ray of light felling on th« 
mirror c, and holes at each end to admit of the plates / and g 
being experimented with. A wire attached to the copper gause 
passes through a hole in the plate b, so as to give me electrical 
access to the copper gauae lining. Under the most diverse elec-* 
trical conditions^ whether insulated or connected with '' earth/' 
this apparatus behaves normally when exhausted* 

A further reason why electricity is not the cause of the move- 
ments I have described is^ that they are not only produced by 
heat^ but also by ice and cold bodies. Moreover 1 shall pi^- 
sently show that any ray of the spectrum^ besides those red and 
ultra-red rays which produce dilatation of mercury in a thermo- 
meter, excite an electric current between antimony and bismuth 
couples, and cause a sensation of warmth when falling on the 
skin, will produce the effect of repulsion in a vacuum. It is 
therefore to my mind abundantly proved that electricity, such 
as we at present kuow this force^ is not a chief agent in these 
attractions and repulsions, however much it may sometimes in- 
terfere with and complicate the phenomena. 

I will now discuss Professor Osborne Beynolds's theory, that 
the effects are the results of evaporation and condensation. 
In my exhausted tubes he assumes the presence of aqueous 
vapour, and then argues as follows : — " When the radiated heat 
from the lamp falls on the pith, its temperature will rise, and 
any moisture on it will begin to evaporate and to drive the pith 
from the lamp. The evaporation will be greatest on that ball 
which is nearest to the lamp ; therefore this ball will be driven 
away until the force on the other becomes equal, after which 
the balls will come to rest, unless momentum carries them 
further. On the other hand, when a piece of ice is brought 
near, the temperature of the pith will be reduced, and it vtill 
condense the vapour and be drawn towards the ice." 

Professor Reynolds has tried an experiment with pith-balls at- 
tached to a light stem of glass and suspended by a silk thread in a 
glass flask. The exhaustion was obtained by boiling water in the 
flask and then corking it up and allowing it to cool. The gauge 
showed an exhaustion of from ^ to | of an inch. The pith-balls 
behaved exactly as I have already shown they do at that degree of 
exhaustion, heat repelling and iee attracting. He found that the 
neutral point varied according to whether air was present with 
the aqueous vapour, or whether the vapour was pure water-gas« 
Professor Reynolds states v^^" From these last two facts it ap- 
pears as though a certain amount of moisture on the balls was 
necessary to render them sensitive to the heat. • • • * These ex- 

Digitized by VjOOQ IC 

92 Mr. W, Crookes on Attraction and 

periments appear to show tbat evaporation from a surface is 
attended with a force tending to drive the surface back, and 
eondensation with a force tending to draw the surface forward/' 

It does not appear that Professor Reynolds has tried more 
than a few experiments ; and he admits that they were in reality 
undertaken to verify the explanation above quoted. I have 
worked experimentally on this subject for some years ; and the 
last experiment recorded in my notebook is numbered 584. 
From the abundant data at my disposal, I can find many facts 
which will, I think, convince you that this hypothesis has been 
arrived at on insufficient evidence. 

In the first place, I will show that the presence of moisture or 
of a condensable vapour is not necessary. Besides pith, which from 
its texture and lightness might be supposed to absorb and con- 
dense considerable quantities of vapour, I have used glass, mica, 
and various metals ; and with a proper amount of exhaustion 
they all act in the same manner. The fact that the neutral 
point for platinum is close upon a vacuum, whilst that for pith 
is so much lower, tends to d&ow that the repulsion is not due to 
any recoil caused by condensable vapour leaving the surface 
under the influence of heat. Were it so, it would certainly 
require more vapour to be present when platinum had to be 
driven backwards than when pith had to be moved ; but the 
contrary obtains in all cases. The rule seems to be, the greater 
the density the higher the neutral point. 

I have worked with all kinds of vacua ; that is to say, I have 
started with the apparatus filled with various vapours and gases 
(air, carbonic acid, water, iodine, hydrogen, &c.) ; and at the 

E roper rarefaction I find no difference in the results which can 
e traced to the residual vapour. A hydrogen vacuum seems 
neither more nor less favourable to the phenomena than does a 
water vacuum, or an iodine vacuum. 

If moisture be present to begin with, I find it necessary to 
allow the vapour to be absorbed by the sulphuric acid of the 
pump, and to continue the exhaustion, with repeated heating of 
the apparatus, until the aqueous vapour is removed. Then and 
then only do I get the best results. 

When pith is employed as the index, it is necessary to have it 
thoroughly dried over sulphuric acid before using it, and during 
the exhaustion to keep it constantly heated to a little below its 
charring-point, in order to get the greatest sensitiveness. 

Professor Reynolds says, '' In order that these results might 
be obtained, it was necessary that the vapour should be free from 
air.'' On the contrary, I find the results take place with the 
greatest sharpness and rapidity if the residual gas consists of 
nothing but air or hydrogen. 

Digitized by VjOOQ IC 

Rqmkion accompanying Radiation. 93 

Professor Ueynolds further says^ '' Mr. Crookes only obtained 
his results when his vacuum was nearly as perfect as the 
Sprengel pomp would make it. Up to this point he had nothing 
but the inverse effects, viz. attraction with heat and repul- 
sion with cold.'' In the abstract of my paper published in the 
Proceedings of the Boval Society, I describe an experiment with 
a pith-ball apparatus in which the neutral point is 7 millims. 
(about I inch) below the vacuum, repulsion by heat taking place 
at higher exhaustions. At the Royal Society SoirSe, April 22, 
1874, 1 showed, and fully described in print, the apparatus now 
before you, consisting of a pith bar suspended by a cocoon fibre 
in a glass bulb, from which the air is exhausted until the baro* 
metric gauge shows a depression of 12 millims. below the ba« 
rometer. Neither attraction nor repulsion results when radiant 
light or heat falls on the pith. Exhaustions of 7 and 12 mil- 
lims. are certainly very inferior vacua for a Sprengel pump. 

As a matter of fact, however, I have obtained repulsion by 
radiation at far higher pressures than these. The true effect of 
radiation appeal's to be one of repulsion at any pressure, over« 
balanced when a gas is present by some cause — possibly air- 
currents, but probably not. I have already explained that the 
barometric height of this neutral point dividing attraction from 
repulsion varies with the density of the substance on which ra- 
diation falls, on the relation which the mass bears to the surface, 
and on the intensity of radiation. By modifying the conditions 
it is not difficult to get repulsion by radiation when the appa- 
ratus is full of air at nearly the normal pressure of the atmo- 

Professor Reynolds again says, '' The reason why Mr. Crookes 
did not obtain the same results with a less perfect vacuum was 
because he had then too large a proportion of air, or non- con- 
densing gas, mixed with the vapour.'' On this I may remark 
that the writer, before he explained how it was I could not get 
certain results, should have made sure that what he assumed to 
be the case was reallv so. I have not the least difficulty in 
showing repulsion by heat in imperfect vacua when mixed va- 
pours and gases are present. 

In ray arguments against the air- current theory, I have shown 
that the best results are obtained when the vacuum is so nearly 
perfect that an induction-spark will not pass through it. This 
IS an equally good argument against the presence of a conden- 
sable vapour as it is against that of air. 

From the construction of my Sprengel pump I am satisfied 
that the vapour of mercury is absent from the apparatus. 

The following experiments have been specially tried with the 
object of testing this theory. A tolerably thick and strong bulb 

Digitized by VjOOQ IC 

94 On Attraction and Repulsion accompanying Radiation. 

it blown at the end of a piece of eombnttion-tabing ; and in it 
ii supported a bar of aluminium at the end of a long platinum 
wire. The whole ii attached to the Sprengel purop, and ex- 
haottion it kept going on for about two dayt^ until a tpark will 
not past through the raeuuro. During thit time the bulb and 
itt oontentt are frequently raised to an incipient red heat. At 
the end of that time the tube is sealed off, and the bar of alumi- 
nium is found to behave exactly as it would in a lest perfectly 
exhausted apparatut; vis. it it repelled by heat. A timilar 
experiment, attended with timilar retultt, has been tried with a 
glass index. It is impossible to conceive that in these experi- 
ments sufficient condensable gat was present to produce the 
effects Professor Reynolds ascribes to it After the repeated 
heatings to redness at the highest attainable exhaustion (the 
gauge and the barometer being level for nearly the whole of the 
48 hours), it is impossible that sufficient vapour or gas should 
condense on the movable index to be instantly driven off, by the 
warmth of the finger, with recoil enough to drive backwards a 
heavy piece of metal. 

M ^ own impi*ession is that the repulsion accompanying radia- 
tion IS directly due to the impact of the waves upon the surface 
of the moving mast, and not aecondarily through the interven- 
tion of air-currentt, electricity, or evaporation and condentation. 
Whether the setherial waves actually strike the substance moved, 
or whether at that mysterious boundary-surface separating solid 
from gaseous matter there are intermediary layers of condensed 
gas which, taking up the blow, pass it on to the layer beneath, 
are problems the solution of which must be left to further 

In giving what I conceive to be reasonable arguments against 
the three theories which have been supposed to explain these re- 
pulsions, I do not wish to insist upon any theory of my own to 
take their place. The one I advance is to my mind the most 
reasonable, and as such is useful as a working hypothesis, if the 
mind must have a theory to rest upon. Any theory will account 
for some fticts ; but only the true explanation will satisfy all the 
conditions of the problem, and this cannot be said of either of 
the theories I have already discussed. 

My object at present is to ascertain facts, varying the condi- 
tions of each experiment so as to find out what are ^e necessary 
and what the accidental accompaniments of the phenomena. 
By working steadily in this manner, letting each group of expe-* 
rinients point out the direction for the next group, and follow- 
ing up as closely as possible, not only the main line of research, 
but ako the little bylanes which often lead to the most valuable 
results, after a tin e the facts will group themselves together 

Digitized by VjOOQ IC 

Mr. J. O'Kiuealy on Fourier's Theorem. 96 

and tell their own tale. The eonditiona under which the phe- 
nomena invariably occur will give the laws ; and the theory will 
follow without much difficulty! To use the eloquent language 
of Sir Humphry Davy, ''When I consider the variety of theories 
which may be formed on the slender foundation oi one or two 
facts, I am convinced that it is the business of the true philo- 
sopher to avoid them all together. It is more laborious to accu- 
mulate facts than to reason concerning them ; but one good ex- 
periment is of more value than the ingenuity of a brain like 

XIV. Fourier's Theorem. 
By James (yKiNEiLY, Bengal Civil Service*. 

THE proof given of Fourier's theorem in all the text-books I 
know of, is a modified form of that first given by Poisson. 
What is at present proposed is to prove it by an analytical pro- 
cess for periodic functions, and to show that it is simply the 
solution of an exponential differential equation. 

l{f{x) =/[x+\), where X is the wave-length, we have, putting 
it into the symbolical form, 



It is a well-known theorem in differential equations^ that if we 
get an equation of the form F(Djr)/(a') =0, and can find the 
roots of F (D,)=0, the equation can be put in the form 

(D,-«)(D.-«,) (D.-«.).../(*)=0, 

where a, a^ a^ &c. are the roots of F(D;r)»0, and that the 
solution will be 

yt^) = Ae*" + A ,€«»'+ AgC-** .... , 

A, A„ Ag, &c. being constants depending on the nature o{/{x). 
In the present case F(Da.) is 6^^*— 1. Assume D^asjsr, and 
the equation to solve is 



* Communicated by tbe Author. 

Digitized by VjOOQ IC 

96 Mr. J. O'Kinealy on Fouiier^s Theorem^ 

(where t is cipher or a positive integer), or 

The original differential equation becomes thus 

D,.(D.+ ?^X"'- K=^)-/(*)=0, 

^i \ k . k 27ra? , . Afirx , 

/(a?) :=A + A, COS-r— + AgCOS -r— + . • . . 

+ D,8in-:r h B^ Sm -rr- .... 

At At 

1=1 X 

+ 2B,8in^^. 

*=l A, 

This is Fourier's theorem ; and, determining the constants in 
the usual way by integrating between and \, and by multi- 

plying by cos — .r— . sin — — and then integrating, we get the 

A. At 

usual form, 

/W = s: 1 yi^)-^«+r2co8-^-— I f{x) coH-.r— dn 
A- Jo ^'=» ^ ^'o ^ 

2'=« . 2'irix 
+ - S sin -^ 

A| — I A» 

j /(^)8in-^-< 

In the same way we can obtain other forms of Fourier's theo- 
rem. K f{^)=Jlx + h), we have generally f{x)=f{x-{-nh), 
where n is an integer; or (c"*^— l)yi[a:)=0, which gives the 
same solution as above if we put nX in place of X. 

Hence we find 

iv \ 1 r% \j . 2 r*^-, ,, 2to V Zirix ^ 

^^^^X ^^""^ '^^Jo /(^)^«-^^^-nX--^^^^-7iX-^^- 

= ^J^ /Wrfn+^^Scos--.J^ /(^).cos— rfn 

, 2 %« . 27r?> T"^^ , . 27r/ar , 

The above method of solution may be applied to other some- 
Digitized by VjOOQ IC 

Oa the Comtant Currents in the Air and in the Sea. 97 
what similar forms. Suppose 



The roots of the equation e^^* +• 1 =0 are 

where t is any odd integer. Hence 

f{x) = 2 A|C08-r- 

+ S B| sin-r— J 

where t is an odd integer. 

Several other theorems of a similar nature will readily sug- 
gest themselves as capable of similar treatment. 

11 Elysium Row, Calcutta. 

XV. T/ie Constant Currents in the Air and in the Sea : an At- 
tempt to refer them to a common Cause. JBy Baron N. Scbil* 
LING,. Captain in the Imperial Russian Navy. 

[Continued from p. 38.] 


IN the daily motion of the earth on its axis^ every point of the 
surface describes a circle. These parallel circles become 
smaller and smaller from the equator to the pole. Now, as all 
points of the surface describe their circles in one and the same 
time of nearly 24 hours, it is evident that as the poles are ap* 
proached the velocity of motion of the points diminishes, and 
this in the ratio of the cosines of the latitudes. As already men- 
tioned in discussing Hadley^s theory of the trade-winds, a body 
approaching the equator, continually coming into circles of 
greater velocity, will, in consequence of the law of inertia, have 
the tendency to perform its revolution more slowly than these ; 
and hence the direction of motion of that body will undergo a 
westerly deflection. Conversely, a body moving from the equator 
will b^ continually meeting with parallel circles of less and less 
velocity, and hence will take a direction swerving eastwards. 
Since the commencement of the 18th century the correctness of 
this law has been admitted, and it has been made use of to ex- 
plain the direction of the trade-winds and many other pheno- 
mena. The Academician von Baer, for example, ascribes it to 
Phil. Mag. S. 4. Vol. 4S. No. 316. Aug. 1874. H 

Digitized by VjOOQ IC 

98 Baron N. SclulliDg an the ComtatU Ctarenit 

this deviation arising from the eartVs rotation thatj in the 
northern hemisphere, all the rivers which run in a meridional 
direction undermine their right banks — ^through which these 
banks are the high; but the left the low ones. The whirling 
motion of cyclones, or Buys-Ballot's law, and the deviation of 
the meridional currents of the ocean, are all explained by the 
axial rotation of the earth. 

It is indubitable that the direction of every independent mo- 
tion on the surface of the earth receives, through its rotation, a 
certain tendency to deviation; yet it seems to us that the 
amount of this deviation is only too often greatly overrated. It 
is usually assumed that, in consequence of inertia, air and water 
particles can retain for hours the velocity of the paralleb which 
they have long left behind. In reality, however, the friction 
and resistance of other particles will more speedily overcome the 
inertia and comnel the particles in motion soon to take up the 
new rotation-velocity of the parallel circles which they enter. 
It must also be remembered that the velocity of adjacent paral- 
lels only very gradually changes; and therefore, with a slow 
motion of the particles, the least friction will be sufficient to 
overpower the difference existing between neighbouring parallels. 
The true proportion between the friction and the tendency to 
conserve the earlier rotation-velocity is very difficult to determine 
; iccurately ; nevertheless it seems clear to us that the deviation 
thereby occasioned in the direction of motion in a short time 
laust always be very inconsiderable. The defenders of Hadley's 
theory will admit this, although they generally believe that, by 
itself slight, the deviation can, by continual repetition of the 
action, accumulate and so become gradually considerable. They 
think, namely, that a current of air or sea, originated by differ- 
ence of temperature, flowing along the meridian, would, when a 
little deflected by the earth's rotation, continue to flow in this 
new direction, and so on. In other words, it is generally be- 
lieved that the angle which a current makes with the meridian 
must continually increase with *the duration of the current ; and 
some go so far as to see, not only in the south-west wind of the 
middle latitudes of our hemisphere, but even in the north-west 
wind of the same, an antipolar current diverted from its direc- 
tion by the rotation of the earth. But this evidently false con* 
elusion results from the false assumption that a current onoe 
deflected would continue to flow in the new direction. It ia 
forgotten that the rotation of the earth cannot effect a deviation 
of the direction unless a motion is present. If the motive force 
ceased to act, the current would soon cease also, being over- 
powered by friction and other resistance. It cannot, therefore, 
flow further in the deflected direction, but will always again 

Digitized by VjOOQ IC 

in Uie Air and in the Sea. 99 

teek to proceed in the direction in which the force acts that pro- 
duces the motion^ therefore in that of the meridian* Now^ ao« 
cording to the eiiating theory, two forces are constantly acting 
both upon trade-winds and the meridional currents of the ocean t 
—-of which the one, the impelling force, springs from the differ- 
ence of temperature of the equatorial and polar regions^ and 
hence operates only in the meridian-direction ; while the otheri 
the rotating force of the earth, acts in coDsequence of the inertia 
of the particles, and always in the direction of the parallel circle, 
therefore at right angles to the motive force. If, then, both 
forces remained constantly unaltered, the direction of the current 
would also remain invariably the same; that is, the angle which 
the current forms with the meridian would neither increase nor 
diminish. In our case the action of the force in the meridional 
direction must be assumed to be constantly uniform ; while the 
lagging behind, or the advance, called forth by the transition 
into other latitudes is more considerable in the higher than in the 
lower latitudes, because the parallel circles diminish only very 
gradually in the latter, but rapidly in the former. From this 
it follows that the deviation from the meridional direction would 
necessarily be greatest in the high latitudes, and vice versd. 
Every current, of air or sea, springing from difference of tem- 
perature would therefore, when flowing toward the equator, come 
constantly nearer to the direction of the meridian ; while a cur* 
rent flowing away from the equator must be continually adding « 
a little to the angle which it forms with the meridian. Accord- 
ing to Hadley's theory, the trade-winds, flowing to the equator, 
should therefore be continually approximating nearer to the 
direction of the meridian; instead of which we see just the op- 
posite^ — that at thehr polar limit they blow from the north-east or 
south-east, according to the hemisphere, and as they near the 
equator they come ever nearer to comcidence with the direction 
of the parallel drcles. 

The sea-currents of the southern hemisphere also demonstrate 
that the earth's rotation has but little, if any, influence on the 
direction of currents. The warm currents (those of Brazil and 
Mozambique^ lean to the east coasts of the continents, and are 
directed to tne south-west, instead of deviating eastwards ; while 
the cold currents (those of Peru and South Guinea, and the 
general current of the entire Antarctic Ocean) agree in directing 
their course to the north-east, instead of flowing south-west as 
required by the theory of the deviation of direction arising from 
the rotation of the earth. We see in this circumstance a proof 
that the influence of the rotation is in the whole very little, 
although the direction taken by the currents of the northern 
hemisphere appears to correspond entirely with that theory: 


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100 BaroQ N. Schilling on the Constant Currents 

namely^ the Oulf-stream and the Kurosiwo flow north-east ; and 
the cold currents of the seas of Japan and Greenland go aonth- 
west, just as the earth's rotation demands. But since the cur- 
rents of the southern hemisphere^ notwithstanding the ample 
space open to them, are quite unaffected by the rotation of the 
earth, we cannot but see that the direction of the currents in the 
northern hemisphere must be referred to other causes. The 
bend which the Gulf-stream makes again to the north by Cape 
Hatteras, after a considerable inclination to the east, seems also 
to speak in favour of our view. 

If the rotation of the earth deflects the direction of the sea- 
currents only inconsiderably, then its influence on the direction 
of the rivers can also only be very slight ; but even the slightest 
friction of the water flowing along the bank, if constantly re- 
peated on one side during thousands of years, must at length 
perceptibly undermine the bank ; and hence Von Baer's view 
may in this respect be right, notwithstanding the extreme 
slightness of the deflection of the current. 

On the rotation of cyclones we will speak subsequently. 

Besides the action, above considered, upon already existing 
currents, many ascribe to the earth's rotation the power to be 
independently the motive cause of a current. MUhry, for in- 
stance, seeks the force which impels the equatorial stream in the 
centrifugal force of the earth. But this, as we know, acts 
always in the direction of the radius of the different parallel 
circles, and hence cannot possibly either accelerate or retard the 
rotation-velocity of the water and the air. Miihry evidently 
adheres to Kepler's explanation of the origination of the equa- 
torial current, by the water staying behind the general motion 
of the earth. This, however, contradicts all the laws of mecha- 
nics, and is therefore quite inadmissible. The water and the 
air adhere to the globe by the pressure of their weight, and 
must, in the course of the thousands of vears during which the 
earth has turned on its axis, have very long since attained the 
same velocity, through friction, since velocity once acquired is 
not again lost so long as there is no resistance. The perma- 
nence of the earth's rotation, however, sufficiently proves that 
in the universe no such resistance is present. The phenomena, 
too, of both air- and ocean-currents absolutely contradict the 
assumption that the water and air are subject to a slower rota- 
tion than the earth itself. 

If this assumption were correct, the atmosphere, being less 
dense, must be far more exposed to the action of the retardation 
than the water, and over the entire surface of the earth wc 
should constantly have strong east winds. Besides, although 
decreasing from the equator to the poles; the retardation wo^d 

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in the Air and in the Sea. 101 

yet be perceptible everywhere. But this is by no means the 
case. At the equator itself^ or in its vicinity^ no such current 
is to be observed either in the air or in the water; nay^ in the 
equatorial zone we find that the sea has a slight current flowing 
east ; so that here, not only is no retardation to be traced, but 
the water moves faster than the earth turns. In the zones of 
the Sargasso-seas, again, and in the calms of the tropics, in both 
hemispheres, neither in air nor sea can any diminution of the 
rotation-velocity be perceived. Farther polewards, especially 
between the 40th and 50th parallels of latitude, the constant 
west winds and currents flowing east testify that water and air 
move eastwards more rapidly than the earth rotates. This cur« 
rent in the atmosphere in the middle latitudes is explained by 
the anti-trades, of which we have already spoken. It expresses 
itself in the sea just as it does in the atmosphere ; but as the 
anti-trade explanation is absolutely inapplicable to the water> 
Miihry accounts for the sea-current by the aspirating force of 
the equatorial stream. Why, however, this force has no action 
at all upon the zones of the Sargasso-seas, but goes round them 
in a wide arc, remains unexplained. Thus, for example, in the 
South Atlantic the action of this aspirating force stretches along 
the coast as far as the Cape of Good Hope, and thence across 
the ocean to the American shore. If the aspirating force of the 
Atlantic equatorial current were actually so great that its influ- 
ence could make itself perceptible not only to the Cape of Good 
Hope, but also from there to the American coast, then it could 
not fail to lay bold of the Mozambique current at the Cape and 
lead it into the Atlantic to supply the equatorial stream. Yet, 
as is well known, at the Cape of Good Hope the Mozambique 
cunrent makes a strikingly sharp bend to the east, and returns 
on a wide circuit to compensate the equatorial stream which 
flows in the southern part of the Indian Ocean, after first wash* 
ing the west coast of Australia. The insufficiency of the expla- 
nation of currents by aspiration presents itself so distinctly that 
it is scarcely necessary to dwell longer on the subject. 

The earth's rotation cannot, then, generate any currents in air 
or sea; it can only effect a slight tendency of the freely moving 
air- and water-parcicles to shift their direction towards that of 
the equator. This tendency, however, is so feeble that from it 
no perceptible current can arise; hence we have not touched 
this point in the Russian edition of this work. We will never- 
theless more closely consider here the action of the centrifugal 

Every rotating motion, and therefore also that of the earth 
about its axis, generates a centrifugal force. The quantity of 
this force for every single point of the earth's surface is readily 

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102 Baron N. Schilling on the Comiani Currents 

jl^termined by dividing the tqnare of its rotational velocity by 
the radius of its uarallel circle. It thence follows that the oen* 
trifugal force of the earth is greatest at the equator (0*11124 foot 
in a second)^ and from that to the poles it diminishes in the 
ratio of the cosines of the latitudes. By its action every thing 
on the surface of the earth would be thrown off, if the earth's 
gravitation were not greater than its centrifugal force. Now 
kt us suppose the gravitation of the earth to cease to act during 
one second. Every particle not firmly adherent to the earth 
would instantly leave the surface and continue its motion in the 
direction of the tangent of the corresponding parallel circle with 
its previous rotational velocity; and the relative distance of the 
particle at the end of the second, from its point of separation, 
which the rotation has meanwhile carried forward on the earth's 
surface, would serve as an expression of the quantity of the cen<- 
trifugal force of the corresponding parallel circle. 

Thus, if a particle at A (fig. 1) were no longer subject to the 

Fig. I. 

earth'sg^vitation,it would 
oontinuo its motion in the 
direction of the tangent 
AM, and after the lapse 
of a second would arrive 
at M instead of at B. A, 
the point at which it was 
discharged, would mean- 
while have reached B; and 
B M would denote for us 
the centrifugal force cor- 
responding to the parallel 
circle ABD. Now in 
reality the action of gravi* 
tation never ceases, but is 
constantly directed to the centre of the earth, therefore at a 
certain angle to the direction of the centrifugal force B M. A 
freely displaceable particle of the surface would thus, under the 
action of the two forees, after the lapse of a second not be at M, 
but would slide on the surface of the earth to F, if there were 
no friction or other resistance. Eveiy particle of water or air, 
being free to move, must thus have a tendency to recede from a 
particle (B) firmly adherent to the earth, and to approach the 
equator in the direction of the meridian. This tendency is ex- 
pressed by the quantity BF, which is equal to BM. sin BMP, 
or the centrifugal foree of the parallel cirele multiplied by the 
sine of the latitude. The centrifugal force 


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m the Air and in the Sea. 108 

where C denotes the eentrifagal force of the equator, and ^ the 
latitade of the parallel circle. Consequently BF n= C . cos ^ . sin (f>, 
and therefore reaches its maximum quantity when ^=45^, 
•monnting then to sin*45^x 0*11124 foot 3:0*05668 foot in a 
second^ or 4806*4 feet in 24 hours (which makes 1^ verst, 
nearly y of a Oerman^ or almost exactly ^ of a British statute 
mile). This inconsiderable tendency toward the equator is 
farther diminished by friction, and therefore cnnnot possibly be 
thought of as the inotive force of a current. Yet it may per- 
haps contribute something to this — that in each of the oceans 
the current flowing^ in the middle latitudes^ from west to east 
gradually inclines in its direction a little to the equator. . 

The earth's centrifugal force, acting in an opposite direction 
to that of gravity, occasions over the entire earth, with the 
single exception of the two poles, a more or less perceptible di- 
minution of weight. This is greatest at the equator, amounting 
to nearly the 290th part. Thence to the poles the quantity to 
be deducted from gravity diminishes in the ratio of the squares 
of the cosines of the latitudes. Now, as all bodies (air and water 
not excepted) are somewhat lighter in the vicinity of the equator 
than in higher latitudes, one would think that this must pixnluce 
currents in the ocean and atmosphere equal to those arising from 
the lightening of the water and air by heating. These currents 
must flow beneath to the equator, and as upper currents from 
the equator to the poles. But in reality this does not appear to 
be the case; for degree-measurings and pendulum-observations 
have shown thai the surface of the sea has the form of an ellip* 
toid slightly compressed at the poles, the long diameter of which 
(measured in the plane of the equator) is ^^^ of its length 
greater than the shorter diameter (measured in the line of the 
earth's axis). From this we see that the level of the ocean at 
the equator is nearly as much raised as the weight loses there 
through the action of the centrifugal force; hence probably 
none, or a scarcely perceptible portion of the lighter water at 
the equator can flow off. 

It is, perhaps, just the same with the atmosphere; yet it is 
probable that, with diminished pressure, the strong elasticity of 
the air will produce by expansion a greater raising of its level 
(if such an expression can be used) than the centrifugal force 
requires. If it is so, certainly the upper, much rarefied air 
liiust flow off from the equator, and be replaced by an under- 
current. Now, since the mass of the inflowing and of the out- 
flowing air must be the same, the dense undercurrent will be 
considerably less perceptible than the upper strongly rarefied 
one. The centiifugal force may thus, combined with the differ- 
ence of temperature^ generate the currents in the upper strata 

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104 Baron N. Schilling on the Constant Currents 

of the tropical atmosphere^ and bo also exert a certain influence 
on the trade-winds^ bnt cannot possibly develop sufficient force 
to give rise to those winds. 

We conclude the consideration of the influence of the eartVs 
rotation on air- and sea-currents with the conviction that the 
existing explanations are altogether insufficient for the currents 
which flow parallel to the equator, because the rotation of the 
earth can only inconsiderably alter the dii*ection of an already 
existing current, whether in air or sea, but can never indepen- 
dently produce a current of any importance. 

C. Attraction op the Sun and Moon. 

As is known, all the heavenly bodies attract each other, the 
force therein developed being, according to the law of the im- 
mortal Newton, directly as the mass and inversely as the square 
of the distance between the two bodies. If, therefore, we take 
as the unit of mass that of the earth, and as unit of distance the 
semidiameter of the earth, then, according to Newton's law, the 
force with which the sun attracts the earth's centre will be ex- 

pressed by ■ g . The moon attracts the centre of the earth 

with the force kph^f^q*' The ratio of the attractive force of 


the 'other heavenly bodies will be readily found in the same 

manner. For example, the force with which Jupiter attracts the 
earth when nearest to it is one 25th part of that of the moon. 
The action of all the rest of the heavenly bodies, so vastly dis« 
tant, is again considerably less. 

Now, as the force with which a given heavenly body (the sun 
for instance) attracts the earth depends entirely upon the dis- 
tance between the two, it is self-evident that the parts of the 
earth's surface which are nearer to the sun must be exposed to a 
greater attraction than those more distant. This can have no 
effect on the solid surface of the earth ; but the easily displace- 
able particles of the sea and the atmosphere must nave their 
equilibrium destroyed by its influence; and to restore the equi- 
librium currents must arise. In order to form true ideas of 
these currents, it is absolutely necessary to investigate more mi- 
nutely the forces which call them forth, and the action of these 
forces. Before all things we must realize that we wish to con- 

* We have assumed, after Klein (Das Sonnensystem), that the mass of 
the sun is 319500 times, and that of the moon one 80th part of that of the 
earth. For the mean distance, wc have assumed that tlie distance of the 
sun is 390 times that of the moon, whot^mean distance we estimate at 60 
•emidiameters of the earth. 

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in the Air and in the Sea. 


gidcr^ not tlie absolute motion of each particle^ but only the re- 
lative motion of the particles with respeet to the earth's centre. 
Hence we have not to do with the whole of the attraction whibh 
any heavenly body exerts on the earth ; the difference between 
the forces with which the earth's centre and the point of its sur- 
face to be considered are attracted gives the limits for our consi- 
deration. Thus^ e.ff., the point which has the sun or the moon in 
the zenith is nearer to this heavenly body than the centre of the 
earth ; and the difference of the attraction upon these two points 

. , , , , , 819500 819500 - ,, , , 

might be expressed by -^g^^i - J234mj^ *""' ^ 

80(59)* "^ 80(60)* ^^^ ^^^ ""^°' The second quantity is equal 
to about 2^ times the first ; and from this we infer that although 
the attraction of the sun is 168 times that of the moon^ yet the 
difference between the attraction of a point at the surface and 
the centre of the earth by the moon is greater than the same by 
the sun; and therefore the effect produced by her attraction 
upon the currents of air and sea must also be greater. 

For all other heavenly bodies this difference is so slight that 
we need not take it into consideration. 

Supposing that the circle ACED (fig. 2) represents the 

Fig. 2. 








jw ^ 1 




earthy L the place of the centre of the moon or sun^ and that k 
denotes the difference between the attraction of a point at the 
surface and the centre of the earth. The point A is attracted 
more strongly than the centre by the quantity k^, Now^ as this 
attraction in the half of the earth turned towards the sun or 
moon acts in the opposite direction to the earth's attraction, 
^— it, will express the weight of any particle in the point A, the 
earth's gravitation being denoted byy. At the point B the dif- 
ference between the attraction of it and the centre will be some- 
what less. Let us call this, difference k^; then the weight at 
the point B may be expressed by ^— Ar^.cosLBA; for here the 

Digitized by VjOOQ IC 

106 Baron N. Sohilling on the Constant Currents 

attraction of the moon acts at the an^le LBA with the earth's 
gravitation. We thus see that the weight of the water and air 
becomes greater the further we remove from the point where 
the moon or the sun is in the senith. In the points C and D, 
which are as distant as the centre of the earthy A=0; therefore 
the full attraction of the earth corresponds to the weight of the 
water and air in these points. In the other hemisphere, turned 
away from the moon, A is a negative quantity, because the centre 
of the earth is more powerfully attracted than any point of the 
surface of this hemisphere. But k acts in the same direction 
with gravitation, and must therefore be added to it in order to 
determine the weight of a particle in this hemisphere. The 
point E, most remote Arom the moon, is the most feebly attracted ; 
hence in £ also the quantity to be added to gravitation is the 
least, and the weight of a particle in E lighter than in any of the 
other points of the hemisphere which is turned away from the 
moon. In the point F, tor example, the weight of a particle 
might be expressed by^— A:3 • cos OFL ; and it would constantly 
diminish the more we approached the point E, which has the 
SUB or the moon in the nadir, where its expression would be 
ff-^k^' When the sun is in question, k^ is only slightly less 
than k^ ; but the difference is not insignificant when the attrac- 
tion of the moon is taken into consideration ; the difference be- 
tween the attraction of the point which has the moon in the 
zenith and that of the centre of the earth is 1^ the difference 
between the attractions of the centre and the point which has 
the moon in the nadir. Briefly, in each of the two hemispheres 
(one turned to the sun or moon, and the other turned from it) 
the minimum of the weight is found in the point of the surface 
which has the sun or moon in the zenith or nadir, but the maxi- 
mum on the line D M G N, which divides the two hemispheres. 
The pressure of the greater weight must cause a portion of the 
water and air to flow into the region where water and air arc 
lighter ; and hence a raising of the level will take place there, 
corresponding to the less weight, while in the region of the 
greatest weight the level will sink. Consequently both the sea 
and the atmosphere must endeavour to take the form of an ellip* 
■oid the summits of which are on the line which passes through 
the centre of the earth and the moon. By the action of the suu, 
as by the moon's attraction, an ellipsoid somewhat less elongated 
will be formed in the sea and the atmosphere, its major axis 
being on the line which passes through the centre of the earth 
and the sun. In reality the actions of these two attractions 
will be combined and form only one tidal ellipsoid, which is most 
ekmgmted when the actions of the sun and moon coincide--that 
is, at the timet 9f full and new mp^Dr On the contrary, the 

Digitized by VjOOQ IC 

in th Air and in the Sea. 107 

ytising of the level will be less when* the major axes of the two 
dlipaolda are perpendicular to each other — that ii^ at the timet 
of the first and last quarters of the moon. 

All this we see confirmed in nature by the phenomena of ebb 
and flow of the tides. Many renowned mathematicians (among 
whom Newton^ Euler^ Laplace^ and Airy occupy the first place) 
have endeavoured to determine by very ingenious mathematical 
calculations the laws of the tides ; their theories^ however^ do not 
in all respects perfectly agree with the phenomena. We find, 
for instance, that on the coasts of the islands in mid*ocean the 
tide often rises only a few inches^ and seldom amounts to more 
than from 2 to 8 feet, while one would think that it was just in 
the open ocean that the tide could be fully developed. Accord-* 
ing to the theory, the tide should assume the greatest dimen* 
sions in the tropical regions—instead of which, we find that, 
with very trifling exceptions, it is very moderate in the tropics, 
and does not reach, by a long way, the height it attains in the 
English Channel or on the coasts of the Bay of Fundy in Nova 
Scotia. Airy based his tide-theory on the theory of waves, and 
hence ascribes to the water-particles only a vertical oscillating 
motion. But, self*evidently, there cannot be anywhere an ele« 
vation of the sea*face, unless the necessary water flows to the 

Ci% of elevation, water being incapable of elastic expansion ; 
ce, among tidal phenomena, the existence of a horisontal 
motion of the water is undeniable. Nay, the horizontal motion 
must be very considerable, since it is dble, in the course of a 
few hours, to call forth a not unimportant elevation of the 
water-surface over many thousands of square miles. 

If the earth stood still and the same points had the sun or 
the moon in the senith constantly, the surface of the sea would 
probably take the position of the tidal ellipsoid given by the 
theory, and always retain the same form. But now the relative 
position of the sun and moon to the earth is perpetually chang- 
ing through the rotation of the latter ; and therefore a very 
large volume of water and air must continually flow out of one 
part of the ocean into the other, in order to compensate thefar^ 
extended disturbance of equilibrium. 

Now, as the relative change of place of the sun and the moon 
i s very rapid, while for the complete formation of the tidal ellip* 
aoid a certain time is necessary, it may be that the ellipsoid has 
not sufficient time to take its perfect form ; the tendency, how- 
ever, to form it must call forth currents in air and water, which 
will constantly follow the motions of the moon and the sun. If 
this be admitted, it explains to us why, in the open ocean, where 
these currents proceed undisturbed, no tide, or a very slight on^ 
is observed j for only whe]:e insufficient depth ox the shi^ of 

Digitized by VjOOQ IC 

108 Baron N. SchilliDg on the Constant Currents 

the coast detains the current which follows the sun and the 
moon must the water more or less swell, and thereupon, in aa 
undulatory motion, push the swelling further, in accordance with 
the law of the wave-theory, and in this manner carry the tide 
into high latitudes, whither, according to the theory of the 
moon's attraction, it should not come. 

We are confirmed in this view of the tides by the circumstance 
that the tide* wave in the atmosphere has not yet been observed, 
although according to the theory it must show itself there more 
considerable than in the sea. The question of the atmospheric 
tide-wave has occupied many scientific men. Laplace, after a 
long series of observations, expressed a decided opinion that 
there is no atmospheric tide. More recently Bouvard, Eisenlohr, 
and Sabine have thought they could perceive a very small tide, 
expressing itself only m hundredth parts of a line on the baro- 

By the way we must remark that the mercury of the barome- 
ter, just like all other bodies on the earth's surface, loses a por- 
tion of its weight by the attraction of the moon and sun ; so 
that it cannot show the variation of the atmospheric pressure 
produced by the attraction of the moon, so long as the mass of 
air above it remains the same ; every current, however, must 
alter the height of the mercury column. It is just the same 
with respect to the diminution of weight effected by the centri- 
fugal force. An aneroid, as such, is not exposed to these influ- 
ences, and therefore always gives the absolute pressure of the 
atmosphere ; so that in principle it is preferable to the barome- 
ter. In practice, however, it still needs considerable improve- 
ments, because errors arise from the metal not possessing per- 
fect elasticity. It is to be wished that observations of the two 
instruments were more frequently compared. 

It was not until the present memoir had already appeared in 
Russian that I got a sight of the extremely interesting and in- 
structive treatise on Tidal Phenomena by Dr. Schmick. This 
writing (which, while throwing much light on the phenomena 
of the tides, contends for many views to which we cannot assent) 
well deserves a closer consideration than would be in place here. 
Yet we cannot omit to say a few words on his notion of the dis- 
placement of the earth's centre of gravity. Since the height of 
the tide-wave is greater in the hemisphere turned towards the 
moon or sun than in the opposite one, Ur. Schmick thinks that 
the centre of gravity of the earth is displaced somewhat towards 
the side of the greater gathering of waters, and that the earth 
cannot by its own force recover its original centre of gravity 
after it has suffered displacement from without. A constantly 
repeated displacement^ in this way, of the centre of gravity 

Digitized by VjOOQ IC 

in the Air and in tie Sea. 109 

in the direction of the southern hemisphere occasions there^ 
according to Schmick^ an accumulation of the waters. That 
the centre of gravity, displaced by external force, cannot of 
its own accord resume its former position is perfectly true; 
only Dr. Schmick seems to have forgotten that if the water 
rises higher on the hemisphere turned towards the moon than 
on the opposite, it is because it is lighter there on account of the 
greater attraction of the moon, and a greater gathering of the 
lighter water is necessary in order to restore equilibrium, with* 
out displacing the centre of gravity. If, therefore, the entire 
globe consisted of a liquid and had no rotation, the moon's at- 
traction would cause it to take the form of an ellipsoid, of which 
the cusp directed to the moon would be somewhat higher than 
the cusp turned away from it; but the centre of gravity of the 
entire mass would remain undisturbed in its old place, because, 
as already said, the rise of the water on each point must be 
exactly equivalent to its loss of weight. As, however, the earth 
consists, for the most part, of a solid mass, which cannot alter 
its shape, and the hemisphere turned to the sun and moon loses 
more of its weight than the opposite one, the centre of gravity 
must be displaced in the opposite direction to that supposed by 
Dr. Schmick ; namely, it must remove to a somewhat greater 
distance from those bodies. Of course the displacement is only 
very inconsiderable, even when the moon is at its least distance 
from the earth ; yet it may to some extent favour temporary 
variations of the atmospheric pressure. In the moon, which 
constantly shows one side to the earth, the earth's attraction 
must thus cause the centre of gravity to lie permanently on the 
side which is turned away from us. 

When the tidal wave does not attain its greatest height at the 
time required by the moon, or in consequence of collateral cir- 
cumstances attains a far greater height than the moon's at- 
traction demands (as in the Bay of Fundy, the English Channel, 
and many other places), the earth's centre of gravity will cer- 
tainly remove temporarily in the direction of the elevation of the 
waters; but Schmick's view*, that the water must spread over 
the surface in accordance with the new centre of gravity as soon ' 
as the accumulating force ceases, cannot be regarded as correct, 
because any excessive accumulation of the water is. followed by 
an equal sinking of the level. The earth's centre of gravity 
must follow these oscillations of the water, and hence, when this 
gradually comes to rest, will probably have returned to its old 

[To be oontinued.} 

• Fluth^Phanmene, p. 128. 

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[ 110 ] 

XVI. Apparatus for Measurement ^L(nvPrei9ur^qfOai. Bv 
TrofeuorWLzoD, Indian CivU'Engmeermg CoUei,e, Coopefs 

THIS apparatus was devised for estimating the pressure of a 
gas when its tension is so low that the -^r--^^ 

indications of the barometer cannot safely 
be relied on, unless indeed a very wide 
barometer and an accurate cathetometer 
be employed. The method consists in con- 
densing a known volume of the gas into 
a smaller space and measuring its tension 
under the new conditions. 

The form of the apparatus is the follow- 
ing J — The tube a communicates with the 
Sprcngel, and with the apparatus to be ex- 
hausted ; J is a siphon-barometer with a 
tube about 5 millimetres in diameter ; and 
the principal parts of the measuring-appa- 
ratus consist of c, a globe of about 48 cubic 
centims. capacity with the volume-tube at 
the top, and d the pressure-tube; these 
two are exactly of the same diameter, to 
avoid error from capillarity. The tube at 
the bottom of the globe is ground into a 
funnel-shaped portion at the top of the 
wide tube e ; and to the side of the latter 
the pressure-tube d is joined. The volume- 
tube at the top of the globe is graduated 
in millimetres from above downwards, the 
lowest division in this particular apparatus 
being 45 ; the pressure-tube d is also gra- 
duated in millimetres, the being placed 
at the level of the 45th division on the vo- 
lume-tube. A ball-and-socket joint con- 
nects the bottom of e with a vertical tube 
/ about 800 millims. long, which is con- 
nected at its lower extremity by means of 
a flexible tube with the mercury-reservoir g ; 
a stopcock at h permits the regulation of 
the flow of mercury into the apparatus: 
this may be conveniently turned by a rod, 
so that the operator may watch the rise of 

♦ Read before the Physical Society, June 13, 1874. 
the Society, 

Ccirirvnicated by 

Digitized by VjOOQ IC 

On an Apparatus far Meaiurement of Low Presiurei of Gas. Ill 

tlu^ mereury through a telescope and have the stopoook at the 
same time at command, 

Ti'.e volume-tube was calibrated in the usual way^ by intro« 
ducing weighed quantities of mercury into it^ and making the 
necessary corrections for the meniscus. The capacity of the 
volums-tube, the globe^ and upper part of the tube e was 
determined by inverting the apparatus and introducing mercury 
through e until the mercury flowed down the pressure-tube | 
the weight of this quantity of mercury, divided by the weight of 
that contained in tne volume-tube^ gives the ratio between the 
volumes; in tlie present case it is 1 to 54*495. While the appa^ 
ratus is being exhausted^ the reservoir ff is lowered so as to 
prevent the mercury rising out of the tube /; but when it is 
desired to make a measurement of the pressure^ the reservoir is 
raised and the mercury allowed to pass through the stopcock h. 
On the mercury rising into the tube e it cuts off the communi- 
cation between the gas in the globe and that in the rest of the 
apparatus. Ultimately the whole of the gas in the globe is con- 
densed into the volume-tube ; and its tension is then found by 
measuring the difference of level between the columns of mercury 
in the volume- and pressure-tubes. On dividing this difference 
by the ratio between the capacities of the globe and volume-tube, 
a number is obtained which is approximately the original pres- 
sure of the gas; this number must now be added to the differ- 
ence between the columns, since it is obvious that the column 
in the pressure-tube is depressed by the tension of the gas in 
the remaining part of the apparatus ; on dividing this new num- 
ber once more by the ratio between the volumes the exact 
original tension is found. 

An example will best illustrate this. A quantity of gas was 
compressed into the volume-tube, and the flow of mercury was 
arrested when its surface reached the lowermost division on the 
tube. The volume was then ^.\ ^-= of its original volume, and 

54*49 5 " . 

the difference between the levels of the mercury m the volume- 
and pressure-tubes was 66*9 millims. ; this number, divided by 
54*495, gives 1'228 as the approximate pressure. 1*2 must 
therefore be added to the observed column, which thus becomes 
68*1 ; and on dividing by 54*495, the number 1*2497 is ob- 
tained as the actual pressure. 

The relations existing between the contents of the other divi- 
sions of the volume-tube and the total contents of the gk)be 
were determined by measuring the tensions of the same quantity 
of gas when compressed into the different volumes. By this 
means the values of the divisions 40, 85, 30, 25, 20, 15, 10, 9, 
8, 7, 6, 5, 4, 3, and 2 have been found ; the experimenter is 
thus enabled to employ a division suitable to the quantity of gas 

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112 On an Apparatus for Measurement of Low Pressures of Gas. 

with which he has to deal. The Bmallest division contains oq)/ 
149^2-35 ^^ ^^^ globe ; consequently when a quantity of gas 
hf^ been condensed into this space^ its original tension wil! be 
multiplied 1492*35 times. In one case an amount of gas, w'aich 
originally filled the globe^ exhibited a pressure of onl^ *5 m' llim. 
when it had been compressed into the smallest dinsion c f the 
volume-tube ; this indicates an original pressure of only *00033 

When measuring a tension^ it is advisable to make two read- 
ings under different condensations, and to take the mean of the 
results. The foUowbg will give some notion of the precision 
attainable :— 

I. At division 5 -0225^ -kr^^ .noQn 
„ 2 -0235/ Mean -0280. 

Mean -0232. 

At division 5 -02281 
2 -0236/ 

II. Barometer millim. : — 

At division 10 -igSSl fuf ^^ .moo 

5 -1980/ Mean -1982. 


At division 10 •1953\ t., ,^^^ 

6 -1967/ Mean -1960. 

III. Barometer 0*6 millim. :— 

At division 15 •5488*] 

„ 10 -5488 y Mean -5492. 
„ 6 •550lJ 

At division 15 •54641 

„ 10 -5464 y Mcau 5469. 
„ 6 •5480j 

IV. Barometer 1 millim. : — 

At division 20 1-20421 ^ .^^.^ 
„ 15 1-2069/ ^^" ^ '*"^^- 

At division 20 1-20821 ^i- , ^^^ 
„ 15 1-2099/ *'^^ 1-2090. 

V. Barometer 1*5 millim. : — 

At division 30 1-91391 t^ i.mAn 
„ 25 1-9080/ Mean 1-9109. 

At division 30 190411 t.^ , ^^.^ 
„ 25 1-9039/ M^^ ^'^^' 

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Dr. W. H. Stone on Wind-pressure in the Human Lungs* 113 
VI. Barometer 2*1 millims.: — 

AtdivisioaSS 2-60171 Mean 2-6045 
80 2-6078/ ^^^*^ ^ ^"^• 

At division 35 261601 ^ o.., ^ 
30 2-6220 J ^^" ^ ^^^• 

It may be mentioned incidentally that connexions for appa<» 
ratus may be conveniently made by means of balKand-socket 
joints of glass. The ball is made by thickening a piece of tube 
in the bWpipe-flame^ and the socket by cutting in half a thick 
bulb blown on a glass tube. The ball is then ground into the 
socket by means of emery and solution of soda^ and afterwards 
polished with rouge and soda solution. When slightly greased 
and with a small quantity of mercury in the cup, a joint is ob<« 
tained which is perfectly air-tight and flexible*. 

XVII. On Wind-pressure in the Human Lungs during Perform^ 
once on Wind Instruments. By Dr. W, H. Stone f. 

THE object of these experiments was originally physiological. 
It had been stated by many writers that the forced expi« 
ration employed in playing tended to produce emphysema of 
the lungs ; but the real amount of such pressure had never 
been measured. 

The facts elicited had also an interest of a purely physical 
character, which was the principal cause of their being brought 
before this Society, although, the writer of the paper remarked, 
it was on the border-ground between two great subjects of study 
that new phenomena were often to be looked for. 

The experiments were two in number. The first aimed simply 
at measuring, by means of a water-gauge, the extreme pressure 
which could be supported by the muscles of the lips, both in 
trained musicians and in persons unaccustomed to the con- 
tinuous exercise of these organs. The difference between dif- 
ferent individuals was very great, some untmined persons 
having naturally considerable muscular power. About 6 feet 
of water was the ordinary maximum when a small tube was 

* Since the above was written Dr. Sprengel has pointed out that Mr. 
Hartley (Proc. Roy. See. vol. xx. p. 141) has descnbed as a ''Sprengel 
joint " a connexion between two glass tubes made by grinding a conical 
tube into a conical cup and placing mercury or water in the cup. The 
difference between this and the one above mentioned is obvious: the 
former is quite rigid, the latter perfectly flexible. 

t Read before the Physical Society, April 18, 18/4. Coiumunicated 
by the Society. 

PhU. Mag. S. 4. Vol. 48. No. 316. Aug. 1874. I 

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1 14 Dr. W. H. Stone on Wind-pressure in the Human Lungs. 

inserted between the lips. When the lips were sapported by a 
cupped mouthpiece, such as is used for brass instruments, a 
greater height of the column could be obtained. The great 
majority of untrained persons could not support more than 
three or four feet of water. It was to be noticed that the lip- 
muscles invariably gave way long before the expiratory power 
of the thoracic muscles was exhausted. By pinching the lips 
round the orifice of the tube with the hand, and thus prevent- 
ing their yielding, a far higher column of water could be 

The second experiment consisted in introducing a small bent 
glass tube into the angle of the mouth, connected with a flexible 
tube passing over the shoulder. It was found that most instru- 
ments could be played as well with this addition as without it. 
It obviously established a communication between the cavity of 
the performer's mouth, and therefore of his thorax, and the 
pressure-gauge. The following Table was compiled from many 
observations on some of our principal English musicians. The 
person experimented on was placed with his back to the gauge, 
the small tube was inserted in his mouth, and he was directed 
to sound in succession the chief notes of his instrument. As 
soon as the tone became full and steady, the position of the 
water-gauge was noted. A fair " mezzo-forte " note was em- 
ployed. Of course, by forcing the wind and overblowing the 
instrument, much greater pressure could be obtained; but those 
given here were sufficient to produce an average orchestral 

Oboe . . 

• lower notes 

9 inches ; 

highest 17 i 


Clarinet . 

• 99 







• 9f 






Horn . . 







Comet . . 







Trumpet . 

• }f 







• it 







• 9} 






It is to be noticed that the clarinet, in this as in some other 
respects, differs from its kindred instruments — and also that 
most of the pressures are small, not exceeding or, indeed, attain- 
ing the pressure of a fit of sneezing or of coughing. They are 
therefore very unlikely to injure the lungs, or to produce the 
emphysema erroneously attributed to them. 

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C 115 ] 

XVIII. On the Fall in PUch of Strained Wires through which a 
Galvanic' Current is pasting^ By Dr. W. H. Stone*. 

THE object of this paper was to apply tbe vibrations of sound 
to the measurement of electrical currents^.and to distin- 
guish what was due to heating-effects from those caused by 
alteration of elasticity. 

Strings of brass and steely such as are used for pianofortes 
(No. 16 gauge)^ were stret^hed^ by means of wrest-pins^ across 
a resonant box^ over bridges surmounted by brass bearings^ and 
tuned to unison. On passing a current fi*om two or more 
Grovels batteries through them, a very marked fall in pitch wa? 
obtained. The vibrating string being 24 inches long, and tuned 
to two-foot C, the tone sank above a fourth in steel and a major 
third in brass. 

This result being a compound of actual lengthening by heat 
and of other causes, it was, in a second experiment, endeavoured 
to eliminate the former element by straining similar strings 
between the same bridged by means of a weight. This was 
attached to the arm of a bent lever, to the short end of which 
the string was made fast. By shifting the position of a four^ 
pound weight along the arm, very accurate unison, or definite 
periodicity of beats could be obtained. When the curi*ent from 
the battery was passed through this string, free to expand by 
the falling of the weight, and therefore at a constant tension, a 
fall of pitch was still noticed. There was also a very marked 
loss of tone, which,* on approaching a red heat, amounted to 
total extinction of sound. 

A third experiment exhibited the changes of electrical resis- 
tance in a wire subjected to variations of strain. The wire wlas 
accurately balanced against another resistance in a Wbeatstone's 
bridge, and the spot of light from a mirror-galvanometer join- 
ing the two circuits thrown on the screen. On suddenly in- 
creasing the tension and raising the musical pitch of the string, 
the galvanometer was visibly deflected. This was not an effect 
of heat (since the balance nad been brought about during the 
passage of the current), and must be due to altered molecular 
state caused by the strain. 

It was incidentally noticed that, when beats were produced 
by two strings on the same sonometer, they continued to be 
sensible to the touch by laying the hand on the instrument long 
after, from diminution of amplitude in the vibration, or from 
slowness in the beats themselves, they had ceased to be audible,. 
This afforded a good demonstration of the continuity of sensa- 
tion in touch and hearing. 

* Read before tbe Physical Society, May 9, 18/4. Communicated by 
tbe Society. 


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[ 116 ] 

X[£, On an Improvement in the Construction of the Spectroscope. 
By H. G. Madak. 

To the Editors of the Philosophical Magazine and Journal. 

IN the ' Proceedings of the Royal Society/ No. 152, p. 808, 
there it an account by Mr. Grabb of a very satisfactory 
method of correcting the curvature of the spectrum-lines, a de« 
feet inherent in all spectroscopes as at present made. This dis-» 
tortion is due, of course, to the fact that the rays from different 
parts of the slit fall on the prism under different vertical angles ; 
and Mr. Grubb proposes to correct it by making the slit itself 
curved instead of straight, the distorting effect of the prism 
being then simply employed in rendering straight the slit-images 
which form the spectrum. 

I think it just worth while to mention, in corroboration of 
Mr. Gkubb's paper, that the same sufficiently obvious remedy 
oceurred to me some time ago, and that since November last I 
have had curved slits in use for a lantern-spectroscope with per- 
fectly satisfactory results. These are screwed on (in front of) 
the ordinary slit-plates, which latter are opened wide ; and the 
curved plates are thus readily replaced by others by loosening a 
couple of milled-head screws. Any spectroscope may in this 
way have the additional slit-plates fitted to it with very little 
difficulty or expense. 

I have two pairs of slit-plates with curved edges thus fitted to 
my original slit : — one with edges curved to a radius of 21 cen- 
tims., which sensibly corrects the distortion of a single carbon- 
disulphide prism, the refracting angle of which is 60^ ; the other 
slit has a radius of curvature of 10 ccntims., and is used with a 
train of two similar prisms. In using such slits with a conden- 
^ug-lens between them and the prism, they should be so placed 
that the centre of curvature is on the side towards which the 
rays are refracted by the prism. The above curvatures were de- 
termined empirically by trials with tinfoil slits, which were easily 
made by attaching a piece of tinfoil to a plate of glass with gum, 
and (before the gum was dry) cutting out very narrow strips by 
a knife fixed to one leg of a pair of beam-compasses. In this 
way a number of trial slits may be made and tested ; and when 
the curvature of that one which performs best is noted, any 
good optician will make a pair of brass plates with edges of the 
proper form. 

I remain, 

Yours faithfully, 

H. G, Madan. 

Eton College. July 18, 18/4. 

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[ 117 ] 

XX. On the General Theory of Duplex Telegraphy. 
By Louis Schwendler* 

rpHE name of "duplex telegraphy '^ has been given to that 
-»- node of electric telegraphy which admits of the simulta- 
neous transmission in opposite directions of signals between two 
stations through a single wire. That this name is far from 
happily chosen is evident ; but as it is current and has aJready 
gained a recognized footing, it is not considered advisable to en- 
deavour to replace it now by a more rational one, and it will 
therefore be adhered to throughout this paperf. 

In the following investigation I shall endeavour to develop 
the mathematical theory of *' duplex telegraphy *' in its most 
general form, with the object of determining not only the best 
arrangement for any particular method, but also the relative 
values of different methods. 

It is manifest that, having from general considerations decided 
on the best method, and further determined the best arrange* 
roent for this method, the remaining diflSculties, due to the 
nature of the problem itself, will be exhibited in a clearer light, 
and the means of overcoming them may then be more easily 

It is believed, however, that the sequel will show that, if the 
best method be adopted, and for this method the best arrange- 
ment be selected to suit the particular line on which the method 
is to be employed, the difficulties that stand in the way of duplex 
telegraphy will hardly be greater than those which are encoun- 
tered every day in ordinary single telegraphy. 

Imperfect Historical Sketch. 

Having access to but scanty records in this country, I am 
not in a position to give an exhaustive' history of this most im- 
portant invention ; and consequently the following sketch is ne- 
cessarily incomplete, and must be taken as merely introductory, 
it being relegated to those better situated in this respect than 
myself to clear up the doubtful points of priority, and produce, 
what is much required, a complete history. 

The idea of sending signals in opposite directions simulta* 
neously through a single wire is by no means a new one. As 

* From the ' Jounial of the Asiatic Society of Beagm]/ vol. xliii. pt. 2, 
1874> having been read before the Society on the 4th of February, 1874. 
Communicated by the Author. 

t The German language potsesses a peculiarly suitable word in "Oegert' 
sprecheH;'* and the idea is fully rendered by ** glekhzeitige$ Gegen-» 

Digitized by VjOOQ IC 

118 Mr. L. Schwendler on the General Theory 

early as 1849 Messrs. Siemens and Halskej of Berlin^ took out a 
patent in England^ for the simultaneous transmission of a plu- 
rality of messages' by a suitable combination of wires; and 
although this patent does not refer directly to duplex telegraphy 
as it was subsequently understood, it must^ notwithstanding^ 
be regarded as a forerunner of it. In point of fact. Dr. W. 
Siemens'! idea represents the general problem of which duplex 
telegraphy is only a particular case. 

In 1854 Dr. Gintl^ of Vienna, tried his ''compensation'^ 
method of " duplex" working between that capital and Prague fj 
and on the 30th November of the same year read a paper before 
the Kaiserlich-konigliche Academic of Sciences of Vienna ^ on 
the practical solution of the same problem by employing a Bain's 
electrochemical telegraph-apparatus instead of a Morse's receiv* 
ing instrument. 

In the summer of 1854, after Dr. Gintl's experiments be- 
tween Vienna and Prague had brought the subject prominently 
to notice, Messrs. Siemens and Halske, of Berlin, and Herr 
Frischen independently^ invented the " differential " method. 

In January 1855 Edlund§ made experiments oh the line be* 
tween Stockholm and Gothenburg. He employed a ''differen* 
iial " method, which he had invented in 1848, for the purpose 
of measuring accurately Faraday's *' extra currents." 

In papers read at Paris on the I6th July and 6th Aug^t, 
1855 II, before the Academy of Sciences by M. Zantedeschi, he 
claims the honour of having first suggested the idea of duplex 
telegraphy ; for as early as 1829 he had proved the possibility 
of the simultaneous transmission of currents in opposite direc- 
tions through a single conductor. Having never seen his ori- 
ginal communication of 1829, it is impossible for me to say how 
far these early ideas of Zantedeschi bear on the problem ; but it 
is certain that both he and Dr. Gintl took a great deal of trouble 
to prove an erroneous theory, viz. that two distinct electrical 
currents can pass simultaneously in opposite directions through 
the same conductor without in any way interfering with each 
other. Such a supposition is in direct opposition to the elec- 
trical laws which were already known in 18291, and besides 
is in no way required in order to explain the simple pheno- 
nienon of duplex telegraphy**. 

* 23rd October, 1849. The actual wording of the English patent is 
unknown to me. 

t Polyt. Centralbl 1863, p. 1476. 

X Wien, Akad, Sittungsber, zir. 

§ Pogg. Ann. 1856, vol. xcviii. p. 634. H Ibid. p. 123. 

' 'If Ohm published hisclatticfll work Die siakanische Kette mathemati$ck 
bearbeitet in the year 1828. 

•♦ I>r. W. Siemens, Pogg. Ann, vol. xcviii. p. 123, 

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qf Duplex TeUgrc^hy. 119 

* None of the above methodd^ however, came to have ex- 
tended, or indeed any, practical application. They appear to 
have been attempted doabUngly and without confidence; and 
although the trials are generally reported to have been bug- 
eeasful, yet the methods were rejected aa impracticable, and 
came to be regarded aa merely of scientific interest 'i'. 

Only recently, after a torpid existence of almost twenty 
Tears, has duplex telegraphy been revived, and come to be the 
leading topic in telegraphy, securing after such a lapse of 
time the amount of public interest it rightly deserves. 

To Mr. Stearns, an American telegraph-engineer, is due 
the honour of having appreciated the real value of duplex tele« 
graphy, and of having (by giving the system, modifiecl by im** 
provements of his own, an extended application on the lines of 
the United States) proved its thorough practicability. 

Inquiry into the Caiues which have delayed the introduction of 
the System. 

When Steinheil in 1837 announced his discovery of the feasi- 
bility of employing the earth to complete the electric circuit in- 
stead of a return-wire, telegraph-engineers immediately recog- 
nised its immense mercantile value, and did not delay to verify 
his results. 

Now, in the career of telegraphy, the invention of duplex work- 
ing ranks second only in importance to SteinheiPs discovery. 
The utilization of the earth reduced by one half the number of 
wires required to carry a given traflSc : duplex telegraphy again 
almost halves this number. In the face of this fact it is not easy 
to understand why the one idea received immediate and universal 
application, while the other, of only about ten years more recent 
date, has met, until now, with universal neglect ; but on closer 
examination it will be found that there have been perfectly com- 
prehensible, although not all rational, infiuences at work. 

An inquiry into the circumstances, therefore, that have caused 
ihe discovery of a system, the introduction of which must mark 
the second great era in telegraphy, to lie fallow for nearly twenty 
years is of the utmost interest, and cannot fail to be instructive 
with regard to the prospects of future progress. 

From an examination of the methods originally proposed for 
duplex working, it will be found that they do not in any way 
essentially dififer from those which may now come into actual 
use. The causes, therefore, which have prevented the intro- 
duction of the system must be sought for external to the 

. * For the light in which daplex tdegraphv was regarded till quite lately, 
see SchellcD, Dab, Sabine, Blarier, Kuho, &c. 

Digitized by VjOOQ IC 

120 Mr. L. Schwendler on the General Theory 

The fir&t of these^ we find> is that the invention was in ad- 
vance of the requirements of the age. Telegraph-lines had 
already been constmcted which were quite capable of carrying 
the given traffic and even more. Further^ any increase in traffic 
could be easily met by an increase in the number of wires on the 
existing telegraph-posts^ instead of by resorting to a system which 
had a complex appearance^ and after all might not answer. 

However^ although the above considerations explain the course 
of events in certain limited instances^ and up to a certain time^ 
they do nothing towards justifying the costly expedients that 
have been generally adopted until recently in preference to in- 
troducing duplex telegraphy — for instance, the reconstruction 
and multiplying of long overland lines^ and especially the laying 
of a second submarine cable when the traffic became too great 
for one. 

• It is time that the successful application of any duplex me^^ 
thod requires lines of a more constant electrical condition, re- 
ceiving-instruments of a larger range*, and telegraph-operators 
of a somewhat better professional education ; but surely these 
three conditions have not all at once become fulfilled (since 1872)| 
so as to make duplex telegraphy possible only just now f No; 
the causes which have delayed its introduction so long have 
been of a much less technical and more irrational nature* 

The mere fact of the duplex methods appearing complex pre- 
vented telegraph-administrations from thinking seriously of in- 
troducing them. The ingenious methods were never tried with 
that zeal and perseverance which is necessary to carry a new 
invention successfully through. They were indiscriminately 
Injected after a few trials made without method or considera- 
tion ; and the real conditions of success or failure were never 
examined or pointed out. Thus naturally a prejudice was 
created against duplex telegraphy, and it was fostered by a 
host of school literature up to the latest time, as pointed out 
before. Further, not a single physicist or electrician investi- 
gated the question with a view to ascertaining what quanti- 
tative effect the variable condition of lines has on duplex work- 
ing as compared with single working. 

If such an investigation had been made, it would have been 
found that the technical obstructions in the way were by no 
means so formidable as had been represented, and that the 

• By the " reuge " of a telegraph-instniment I undcrstnnd the ratio of 
the largest to the smallest force by which the instrument in question can 
be worked without requiring a fresh mechanical adjustment, ror instance, 
Siemens's beautiful relays can be easily adjusted to a range of 20 ; i. e. 
they can be made to work with one cell through an external resistance 
equal to their own resistance, and w ith ten cells tlirough no external resist- 
ance, without giving the tongue a fresh adjustment. 

Digitized by VjOOQ IC 

ofDt^lex Telegraphy. 121 

electrical condition of the lines^ as well as the perfection of the 
instraments and the professional education of the staffs would 
have fully admitted of the successful introduction of duplex 
telegraphy at least ten^ if not twenty, years ago. 

It is true indeed that the suggestion of using condensers for 
balancing the charge and discharge of a line has only been made 
very lately, being one of Stearns's happy ideas ; but this should 
have been no reason against introducing the system on short 
and overworked lines, where the charge and discharge is imper* 
ceptible. If only one telegraph -administration had shown the 
perfect practicability of the system on a short line, the cloud 
of prejudice would have been dissipated, and suggestions for 
overcoming the charge and discharge on long overland lines 
and submarine cables would have been readily enough given, 
and thereby large capitals saved. 

To sum up, therefore, we have the following causes which 
acted persistently against the introduction of duplex telegraphy^ 

First, the invention was in advance of the age. 
. Secondly, the telegraph profession, young as it is, is far more 
conservative than is good for the advance of telegraphy ; and, 
on the whole, telegraph-administrations and staffs have by no 
means that professional education which is required to conduct 
practical experiments with a clear understanding, and thence 
deduce rational conclusions. Thus prejudice was created, which 
was increased from year to year by authors of school literature 
writing most discouragingly on the subject. 

Thirdlv, unfortunately during all that time no physicist found 
it worth his while to investigate the duplex methods with a view 
to ascertain quantitatively what can be expected of them, and 
how they actually compare, with respect to safety, with single 

Fourthly, duplex working itself could not progress, because 
it was neither tried nor investigated, and hence no sugges--! 
tions for overcoming the difficulty of charge and discharge 
were called for. 

Great honour must therefore be given to Mr. Stearns, who 
brought up the subject again so prominently, and who by his 
zeal succeeded in introducing it on a large scale, and so elevated 
the ingenious methods from the questionable position of '^ inter- 
esting scientific exi>eriments.'' 

I think far less of his idea of introducing condensers or 
Ruhmkorff's coils to balance the charge and discharge of lines> 
than of his having taken the neglected child up again against 
the prejudice of his own profession, and shown that it could 
have a healthy existence even in the backwoods of Ameriea* 
I trust that these remarks will not be considered irrelevant in 

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I2i Mr. L. Schwandler on the General Theoty 

the present iDvestigition, siDce they tend to show how real 

Erogress in one of the youngest branches of applied seienoe may 
e retarded for a considerable period by nothing bat prejudice 
of the profession themselres^ for whom the progress should be 
the first essential ; and administrations will see how much the 
advance of telegraphy will always depend on their recognising 
and encouraging by experiment inventions that are theoretically 
sound and tend in the right direction. 

General Consideratiane. 

Before entering on the solution of the problem for any par- 
ticular duplex method, it would be advisable once for all to 
state definitely the nature of the general question before us. 
This will not only save time, but the subsequent special 8olu« 
tions can then also be made under a general guide ; and thus, 
being well linked together, the whole investigation will become 
£ir more lucid and concise than it otherwise would be. 

While in ordinary (single) telegraphy the signals are always 
produced in the same way, t. e. by the signalling current arri- 
ving through the line from the distant station, the signals in 
duplex telegraphy may be produced in either of two ways essen- 
tially different from each other. Namely, if the times of slid- 
ing from the two stations fall together, t. e, no current, or 
double current, or any difference of currents is in the line, the 
signals, so long as this state of the line exists, are produced 
wholly or partly by the battery of the receiving-station. Sig- 
nals produced m this way we shall call ^* duplex signals ;" and 
these signals alone indicate the essential difference between 
duplex and ordinary telegraphy. 

If, however, the moments of sending from the two stations 
do not fall together, the signals are then produced as in ordi- 
nary telegraphy, and may be appropriately designated ^* single 

It will be clear, then, that when the two stations are at work 
at the same time, " duplex signals '* and " single signals ^' must 
necessarilv follow each other in accidental succession. Nay, 
one and the same signal produced in either station may be partly 
a ^'duplex '^ and partly a '' single^' signal. 

To secure, therefore, regularity of working, the signals pro- 
duced in either way should be invariably of equal strength. 

Further, as in duplex telegraphy the receiving-instruments 
must be always permanently connected up with the line, it is 
one of the first reauirements that the out-going or sent current 
from any station snould in itself have no effect whatever on the 
reeeiving-instrument of that station, in order that the instru- 
ment may be entirely fr^ \g r^y^ ^gnals from the disunt 

Digitized by VjOOQIC 

of Duplex Telegraph}f. 123 

sUtioii, Thus we invariably have two conditions to fnlfil in 
duplex workings independent of the particular method adopted, 
namely :i — . 

1. The reeewmg-ingtrument of each station ihouldnot be affected 
by its own sending. 

2. Tlie duplex signak and single signals must be of equal 

If these two conditions, which are necessary and sufficient, 
eould be always fulfilled, duplex telegraphy would be entirely 
on a par with single telegraphy ; for the sending would not only 
not interfere with the receiving (the more important condition of 
the two), but the received signals would also be constant in 
strength, and therefore frequent adjustment of the receiving- 
instrument would be no more required than in single telegraphy. 

Theoreticallv, of course, every duplex method hitherto sue* 
gested fulfils these two conditions; otherwise the method would 
have to be rejected a priori, and could not find any place in this 

Practically, however, the different methods may behave very 
differently with respect to the fulfilment of these two conditions ; 
nay, even one and the same method is sure to give quite different 
results in this respect by only altering the magnitude of the 
resistances of which the arrangement consists. For in practice 
variations, especially in virtue of the line having by no means a 
constant electrical condition, are necessarily going on. These 
unavoidable variations, it is clear, may cause very diffei*ent quan- 
titative disturbances of the two conditions (1) and (2), either if 
we compare different methods, or the same method under differ- 
ent resistance arrangements. 

To make the foregoing clear, we will designate : — 

by p the force which acts on the receiving-instrument on 
account of not being able to fulfil the first condition absolutclv ; 

by P the force which acts on the same instrument when the 
distant station is sending alone, i. e. ^' single sisals;'' 

and by Q the force which acts on the same instrument when 
both stations are sending simuUaneouslg, i. e. ** duplex signals.'^ 
. Then the first condition (1) is expre^ed by 

p-o, (I.) 

and the second (2) by 

P-Q«0. (II.) 

Further, if p cannot be always kept rigidly equal to zero (on 
account of unavoidable variations in the system), we should at 
leadt have 

£-&sD as small as possible; • . • • (III.) 

Digitized by VjOOQ IC 

124 Mr. L. Schweudler on the General Theory 

and if P cannot be always kept rigidly equal to Q, we should at 
least have 

P^QsbS as small ^ possible^ • . . (IV.) 

p, V, and Q being functions of the resistances and electromo- 
tive forces of the system^ which are known so soon as the parti- 
cular duplex method has been selected. 

The general problem which is to be solved for duplex tele- 
graphy may now be clearly stated as follows : — 

I) and S are two known Junctions which must be rigidly equal 
to zero when no variation in the system occurs, and which for any 
given variation in the system must be as small as possible, and ap^ 
proximate rapidly towards zero as the variation in the system 
becomes smaller and smaller. 

Thus the solution of the problem for any civen duplex method 
will always be a question of the minima and maxima calculus. 

Having then ascertained the best arrangement for each duplex 
method^ the methods can be compared inter se; and that method 
will be best^ and should be selected for use^ which for any given 
variation in the system gives the least absolute magnitude to the 
functions D and S. 

If we suppose, however, that the particular duplex method is 
not given, the problem to be solved becomes more general, but 
would still be entirely within the limits of the variation cal« 
cuius, furnishing, no doubt, a very interesting and important 
application of that most powerful mathematical instrument. 
The general solution would at once determine the best method 
possible, after which special solutions would give the best ar- 
i^ngemcnt for that best method. 

It is, however, not my intention to endeavour to solve here 
the duplex problem in this most general form. To be able to 
indicate so general and desirable a solution is by no means 
identical with being able to effect it. The task before me is ht 
more simple, since, as already pointed out, I shall investigate 
each duplex method separately to determine its best quantitative 
arrangement, and ultimately compare the different methods to 
ascertain their relative values. 

To do this, the question may be attacked in two different 
ways, . depending on . the purpose for which the solution is 

Namely, either the solution is to be made when considering 
the line as a variable conductor only, but not acting perceptibly 
as a Leyden jar ; or the line is to be considered as constant in 
conduction and insulation, but acting as a Leyden jar of large 
capacity. In the first case the solution would be directly appli- 
tMt to short overland lines (not over 200 miles in length), and 
in the second case to submarine cables, which, if good, may 

Digitized by VjOOQ IC 

of Duplex Telegraphy, 125 

always be considered sensibly constant in conduction and in- 

Further^ as a long overland line acts both as a variable con- 
ductor and as a Leyden jar of sufficiently large capacitv^ it would 
then be necessary to give a solution with respect to both these 
effects. To obtain^ however^ the same result without rendering 
the problem too intricate, it will be best to separate the two 
questions from the beginning, and afterwards combine their 
solutions judiciously for application to the case of overland 

1st Problem. What is the best arrangement of any given duplex 
method when the line is regarded as a variable conductor^ but not 
as acting perceptibly as a Leyden jar? 

2nd Paoblem. What is the best arrangement of any given duplex 
method when the line is regarded as a Leyden Jar of large capacity, 
but not as a variable conductor. 

The second problem may be expressed more clearly as fol- 
lows: — 

2nd Problem. What must be the distribution of condensers 
along a given resistance, in order that the two essential conditions 
(I. and II.) may be least disturbed for a speed of signalling variable 
between two fixed limits ? * 

* A tele|^raph-liDe always acts as a condenser with capacity and con- 
duction-resistance in each point of its entire length, while an artificial 
condenser (such as a Leyden jar) which we are ahle to produce sufficiently 
cheaply has only capacity but no perceptible conduction-resistance in each 
point. This is in fact the essentud difference between a line and a con- 
denser; and therefore, in order to render their charges and discharges 
under the same circumstances as nearly as possible equal, as is required 
for duplex working, it will be necessary to find the law according to which 
to distribute a certain given system of condensers along a given re- 

This law will clearly be a function of the signalling speed within its 
limits of variation. For instance, say the signalling sp^d is constant, or 
its range zero, then clearly one condenser connected to any point of the 
given resistance would suffice ; only the magnitude of the capacity of this 
one condenser would be determined bv its position with respect to the re- 
sistance, and, in addition to this, would of course be fixed by the signalling 
speed and the known capacity of the line. 

Further, say the speed of signalling is variable betwen and oo , or its 
range is infinite, then clearly only an infinite number of small condensers 
distributed alon^ the given resistance in the very same manner as the 
capacity is distributed dong the line would strictly answer the purpose ; 
in £ACt, the condenser required in this imaginary case would be nothing 
more or less than a second telegraph-line, identical with the one used for 
signalling. In practice, however, the speed of signalling varies only be- 
tween narrow limits ; and therefore the number of condensers required to 
reproduce as nearly as possible the action of the line with respect to charge 
and discharge, will become few, especially if the best system of distribu- 
tion has been determined. Until this law is known, we can do nothing 

Digitized by VjOOQ IC 

126 Mr. L. Schwendler on the General Theory 

It U clear that the natare of these two problemg ia very 
different, because in the first we have to deal with forces con- 
stant with respect to time, while in the second the forces acting 
are functions of time, i. e. of the signalling speed. (The fwces 
in this case are proportioned to the true currents.) The latter 
problem being far the more intricate, and for my special purpose 
only of secondary importance, I shall begin with the solution of 
the first. 

Solution of the first Problem for my given Duplex Method, 

What is the best arrangement of any given duplex method when 
the line is regarded as a variable conductor ^ but not as acting per'- 
ceptibly as a Leydenjarf 

I. The bridge method*. 

This arrangement for duplex working is based on the well* 
known method of comparing electrical resistances, 'MVheat-* 
stone^s bridge ;'' and the figure (p. 127) gives the general dia- 
gram when this method is applied for duplex working. 

/9 is the internal resistance of the signalling. battery. 

1/ the ^'measured conductor ^^f resistance of the line when 
measured from station I. ; 

but find it spproximately by experiment, however tedious it may be t« 

It has also been proposed to use Ruhmkorff's coils for balancing the 
effect of charge ana discharge. This method, however, I l>elieve must be 
always much inferior to the one of using condensers, inasmuch as the 
strength of a voltaic induction-current scarcely depends on the speed of 
signalling, while the charge and discharge of a line, it is well known, is 
not at all an inconsiderable function of the signalling speed. 

Therefore if the strength of the induction-current had been a4insted to 
balance the charge and discharge of the line for a certain signalling speed* 
the balance would be considerably and at once disturbed if tbs speed 
varied even slightly; and since so long as hand signalling is used a certain 
variation in the speed of signalling wiU always exist, this method will prove 
a fisilure, or at afi events will render fresh adjustments more frequently 
necessary than when condensers are used. 

* Dr. W. Siemens mentions this in Pogg. Ann, vol. xcviii. p. 122 (1866). 

Mr. O. Heaviside (Phil. Mag. 1873, voL xlv.) sUtes that Mr. Eden, of 
Edinburgh, claims to have suggested this method at about the same time 
as Mr. Steams, of Boston, U.b.A., took out a patent for it. 

t Genendly these measured values U and L" will be different from each 
other, especially for lon^ overland lines. They can become equal only 
under two conditions— either if the resistance of the resultant fault (t) is so 
great that the total conductor resistance of the line (/'-|-r'as/} can be nej^* 
lected against it, or for any magnitude of t if the latter has a position m 

the middle of the conductor, t. e. when Ts/^a^* 

Digitized by VjOOQ IC 

of Duplex Telegraphy. 127 

JP the '' measured conductor '' resistance of the line when 
measured from station II i 

•••"=''+ i^- 

(f the complex resistance of the duplet arrangement in station 
I.^ t. e. the resistance between point 1 and earth. 

fff the complex resistance of the duplex arrangement in sta- 
tion 11.4 1. e. the resistance between point 2 and earth. 

£^ electromotive force of the signalling-battery. 

ffy the resistance of the receiving-instrument. 

K, telegraph-ke]^ of peculiar constniction^ to be described hereafter. 

g, the receiving-instrument eonnccted up in that branch of the bridge 
which, when measuring resistances, would contain the galvanometer*. 

a, b, and d are the branches of the bridge. 

/, the resistance between the rest-contact of the key and earth. 

w, an additional resistance to be inserted in the battery-branch, for rea- 
sons to be ^ven further on. 

t, the resistance of the resultant fault {" real absolute insulation " of the 
line) acting at a distance /' from station I. and at a distance f from sta- 
tion II. (both /' and T expressed in resistances so that f+r=sl equal the 
" real conductor resistance " of the hue). 

To be quite general^ we must suppose that the telegraph-line 
which connects the two stations I. and II. has a different resist- 
ance when measured from station I. than when measured from 
station 11.^ and that therefore the best resistance-arrangement 
of station I. must be also different from that of station II. with 
respect to magnitude of resistances. 

* Siemens's polarized relays are well adapted for this purpose, on account 
of their great sensitiveness and wide range ; D* Arlincourt's relays would 
also answer well. . 

Digitized by VjOOQ IC 

128 Mr. L. Schwcndler on the General Theory 

The resistances which are similarly sitoated in both the sta- 
tions will be designated by the same letters ; and to indicate the 
station to which they belongs each letter will have one accent in 
station I. and two accents in station II. 

Further^ if a relatioa between the resistances of one station 
has to hold good between those of the other station also^ the let- 
ters will be used without any accents. 

The great practical advantage of the bridge method, it will be 
clear at once^ is that any kind of receiving-instrument which has 
been used for single working may also be employed for duplex 
telegraphy. This fact must always be of great consideration for 
any administration that contemplates the general introduction 
of duplex telegraphy. 

General esfpressions for the two functiom D and S. 

To obtain the functions D and S^ we have first to develop the 
general expressions for the forces /»^ P, and.Q> say for station I. 

By j/ we understand the force which acts on the receiving* 
instrument g^ of station I. when that station is sending alone 
(station II. at rest). 

y, in our particular case, is therefore proportional to the cur- 
rent which passes through the galvanometer in a Wheatstone^s 
bridge when balance is not rigidly established ; thus 



N'=y(i' + dO(«' + c') +/{y(a' f i' + c' + rf') + (^+rf')(«' + iO } 

Further, by P' is understood the force which acts on the re- 
ceiving-instrument in station I. when station II. is SLnding 
alone : single signals. 

This force in our particular case is proportional to the current 
which passes through the receiving-instrument of station I. when 
station II. is sending alone ; and we have consequently 

where C" is the current which enters the line at point 2 when 
station II. alone is sending, C"/jJ the part of this current C" 
which arrives actually at point 1 (on account of leakage between 
points 2 and 1, a part of C is lost), and CV'V^ ^hat part of the 
current C"/J which ultimatelv produces the signal {sirigle signal) 
in station I. The current CV' arriving at point 1 branches off 

Digitized by VjOOQ IC 

of Duplex Telei/raphtf. 129 

ia two ; one part goes through a* and the other through ^ to 
Farther, n»_w »»" 







and N" an expression identical in form with N'. 

Farther^ by Ql we understand the force which acts on the 
receiying-instrument of station I. when both stations are send* 
ing simoItaneoQsIy : duplex signals. 

This force is again proportional to the current which, under 
these circumstances, passes through the receiving- instrument ^ 
of station I. 

This current can be expressed by 

and therefore 

a* being the current actually in the line at point I when both 
stations are sending simultaneously ; and this current, being the 
algebraical sum of two currents, may be either +, 0, or — . 
We will suppose that <r' contains the sign itself. 
Further, we have 

, EW E'W , 

and ^ is a function which becomes identical with '^' if we put 

Therefore the two functions D and S are for the bridge me- 
thod (station I.) most generally expressed as follows : — 

E'N" 1 A' ,„„. 

Phil. May. S. 4. Vol. 48. No. 316. Aug. 1874. K 

Digitized by VjOOQIC 

ISO Mr. L. Schwendler on the General Theory 


s'^E'^/.y-^+o'^'j . . (IV.) 

and similar expressioDs will be obtained for station II., namely 


S''-F^M''^-^f+^^. . . (IV".) 

Bigid fulfilment of the first condition, L e. D=0« 
For statton I. we have 

which equation can only be satisfied by 

since the other factor of D' cannot become sero for quantities 
larger than or smaller than oo. Then, substituting for A' its 
value^ we have 

a'd'-4'(L'+/)=0; (V.) 

or balance in station I.^ when that station is sending and sta- 
tion II. is at rest, must be rigidly established. 

Therefore if balance in station I. is disturbed, say by 1/ vary- 
ing or by any other cause* external to U, we most have means 
of conveniently reestablishing balance without delay. This, of 
course, could always be done by altering either all the branches 
of, V, and d!, or any two of them, or only one of them ; but it 
is clear that so long as the variation of V which disturbs the 
balance does not exceed certain limits, balance may be regained 
by altering only one of the three branches available ; and as this 
will also be more convenient in practice than altering two of the 
branches, or all three simultaneously, we shall make the suppo* 
sition that 

" Balance is reestablished by an appropriate readjustment of one 
of the three available branches" f. 

* Causes of disturbance to balance external to L' are inappreciable in 
practice and therefore may be neglected from the beginning. 

t Finally, when the hest resistance-arrangement has been found, the 
resistance of the different branches will be expressed in terms of L ; and 
therefore to keep the best arrangement when L varies between any two 
given limits will involve necessarily a simultaneous alteration of the resist- 
ance of all the branches. 

If, however, the variation of L is small in eorapnrison with L itself, an 
alteration of one branch for the purpose of reestablishing balance is justified, 
and would be absolutely correct if the variation of L \\erc iufinitesimal. 

Digitized by VjOOQ IC 

of Duplex Telegrophy^ 131 

The question therefore is^ which of the three branches^ a, b, 
or d, is the best adapted for the purpose? 

To decide this we must remember that for station 11.^ in ac- 
cordance with the first condition (DsO)| a similar equation has 
to be fulfiHed, namely^ 

fl"J"-J"(LW+p')«0. .... (V.) 

Now o'^ the complex resistance of the arrangement in station 
I., is a function of all the resistances in station I. ; and similarly 
pf, the complex resistance of the arrangement in station 11.^ is 
a function of all the resistances in station II. Therefore^ gene- 
rally, if in order to obtain balance, say in station I., any of the 
three branches of, V, tP were adjustecC ff would alter in conse- 
quence of this readjustment, and thereby the balance in station 
II. (equation Y".) would be disturbed, and vice ver$d. In other 
words, the readjusting in one station would interfipre with the 
balance in the other station, and therefore rigid balance could 
be only attained after a series of successive adjustments in both 
the stations — and then only, from a theoretical point of view, 
approximately, introducing practical difficulties almost insur- 

However, examining the positions of the three branches, it 
will be seen at once that b acts as the galvanometer-branch of a 
bridge for any current arriving through the line. Thus, if we 
were to fulfil the condition 

ad^fff^O (VI.) 

for both stations, the value of p would become at once indepen- 
dent of b^, and consequently any adjustment of V to reestablish 
balance in station I. would not affect in the slightest degree the 
balance in station II., and vice versd. 

Thus, presupposing the fulfilment of this condition (equa- 
tion VI.) for both the stations, the branch b would evidently be 
the best suited for adiustmentf. Under these circumstances it 
would then be clear that balance in either station can be obtained 
by a smgk adjustment of b ; and therefore we mav call equation 
VI. ** the immediate-balance condition ;^' and the fulfilment of this 
condition being of the greatest practical importance to ensure 
the success of duplex working, we are justified, nay even com- 

* ^, (y+^)(«+/) _ (arf~/y)« 

Therefore if ad—fg is very near sero» p becomes most rapidly indepen- 
dent Of b. 

t Farther, it mutt be remarked that, even if the condition ad—fg^O be 
not rif^dly fulfilled, still 1^ adjusting in the branch b we have '* aecele* 
rated" balance, whereas by adjusting in a or d we should, on the contrary, 
We "retarded'* balance. 


Digitized by VjOOQ IC 

132 Mr. L. Schwendler on the General Theory 

pelled, to use this relation (equation VI.) as the basis for all 
subsequent investigations. 

We will therefore suppose henceforth that 

ad^fg^O (VI.) 

is rigidly fulfilled for both the stations. 

But as the value of / depends on the position of the key, 
which during signalling moves from contact 3 to contact 4 and 
back, the rigid fulfilment of equation (VI.) necessitates at once 

u;+i9=/, (VU.) 

not only for both the contacts 3 and 4, but also for all the in- 
termediate positions of the key. Thus, supposing that u^ + ^ »/> 
t. e. the resistance from contact 4 through battery to earth equal 
to the resistance from contact 3 to earth, a key constructed in 
such a way that contact 4 is not broken before contact 8 is made, 
and that contact 8 is not broken before contact 4 is made, would 
fulfil the required condition entirely. Keys of this kind can be 
easily enough constructed. It is true that in any such key there 
will be alwavs a moment when the contacts 3 and 4 are simul- 
taneous, and when therefore the resistance to earth is not /, as 

it ought to be, but only ^. Considering, however, that the time 

during which this error lasts is very small compared with the 
time it takes to make a signal, its disturbing effect will never 
be appreciable in practice ; t. e. p will remain sensibly constant 
during the time the key is moved to produce a signal. 

There will be no practical difficulties connected with the ful- 
filment of equation (VII.), and therefore also none with the ful- 
filment of equation (VI.) ; for 0, the internal resistance of the 
signalling-battery is the only Quantity which of itself can alter 
in time. However, this variation of fi for any efficient form of 
signalling-battery being invariably steady and small, it will be 
always possible to neutralize its action in time by a simple read- 
justment of w. 

If Leclanch^'s cells are used, or well prepared Minotti's, a 
weekly adjustment of w should be sufficient. The measuring 
of ^8 will always be an easy matter*. 

* My friend Mr. R. S. Brough suggested the following very simple me- 
thod for keeping 

«^+/3=/. (VII.) 

Insert a small galvanoscope in the branch b, for which balance is estab- 
lished with res|)ect to the received current, t. e. 

ad^fff^O (VI.) 

Now note the deflection on the galvanoscope when both stations are 

Digitized by VjOOQ IC 

of Duplex Telegraphy. ) 38 

Rigid fulfilment of the second condition^ i, e. SsCX 
The general expression for S' was 

S'=-j^Kr — ;f+^i>'^ • • • (IV.) 
Bememberingthat by equation (VII,) 

we know that V^=<^; and substituting further for a' its value, 
the general expression for S' becomes 

S'--jprA*y— ^+ |-^--j^-^/|v^; (m) 

and this form of S' shows at once that it is perfectly immaterial 
for duplex working by the bridge method whether the same or 
opposite poles of the two signalling-batteries be put to line^; for 
in both cases equation (IV.) becomes 

S'=^V^-B'^ (IV.) 

Further, it will be seen that the right-hand member of eqna- 

tion (I v.) can be transformed f into E'm, which is equal to//, 

or we have generally 


i. e. the difference offerees by which duplex and single signals in 

sending timultaneonslv, snd agsin when the station for which /3 is to be 
measured is sendinr alone. Then dearlv, if these two deflections are equal, 
ID+/S must be equal to/. If the two deflections are not eoualy then alter 
w until they hecome equal. After the determination is maae the galvano- 
scope is short-circuited. 

* In practice, however, I prefer to put the same (namely the positive) 
poles to the line, as then defective insulation will not be felt so much. 

t We have 

j^^mifc— All 


b ' 


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184 Mr. L. Schwendler on the General Theory 

the same station are produced is equal m magnitude and sign to 
the force by which balance in that station is disturbed. 

Consequently the rigid fulfilment of the fint condition (DbO) 
will entail the rigid fulfilment of the second condition (S=0) ; 
and this, it will be clear, is only due to the fact that the complex 
resistance p is independent of b, and that the key during signal- 
ling does not alter p ; whence it follows that the perfection of 
the key in this respect is of the greatest importance. There are, 
however, no practical difficulties connected with the construction 
of a key which fulfils condition (VII.) perfectly. 

By the aid of the relations giren in equations (VI.) and (VII.) 
we have therefore gained the*great practical advantage that du- 
plex telegraphy will be entirely on a par with single telegraphy, 
if the means of attaining rigid balance are sufficiently accurate, 
eoavenient, and rapid. 

But, even sunposing that we are unable to keep that balance 
rigidly for any length of time (on account of L varying), we can 
nevertheless bring the regularity of duplex working as near as 
possible to that of single working by making D and S as small 
as possible. foe any given variation of L« 

Rapid approsimatian of the twofunetions D and S towards i$ro. 
For station I. we had 

s'=y«^^-^, . . . . OV.) 

which we may also write 


Further, if we call V the value of b which in station L esta- 
blishes rigid balance for any given values a', d', and 1/, we have 


where SV is the variation of L' which throws the balance out, 
and which variation may be either positive, eero, or negative 
(SL' shall contain the sign in itself). 

Digitized by VjOOQ IC 

of Duplex Telegrt^ky. 135 

Further, substituting 



rt ' 

the expression for S' may be written as foUovs : — 


1 , 



which is the best form of S' for our purpose. 

The function S' consists of two factors — namelyi of C, which 
at or near balance is proportional to the current by which duplex 
and single signals in station I. are produced, and of V, which 
at balance ssO. 

Therefore to make S' as small as possible when balance is 
disturbed, we can only do so by making F as small as possible, 

which is evidently the case for y's: -^ a maximum. Further, 

and since at or near balance 

it follows that j)/^ p . 

t. e. the first eondition is also fulfilled by 

y'ss -^ a maximum. 

Our problem for station I. would therefore be most generally 
solved if we make the function ^ a maximum, remembering that 
the variables contained in y' have to fulfil two condition equa- 
tions, namely the immediate balance (equation YI.) and the ba* 
lance (equation Y.). 

Substituting for m' its value, and remembering that 

on account of the immeiiaie-balance condition (equation IV.), we 

Digitized by VjOOQ IC 

136 Mr. L. Scbwendler on the General Theory 


the complex resistance of station I. (the expression for p has be« 
come thus simple on account of the immediate-balance condition 

(on account of balance in station I. being established^ equationV.). 
Thus we have 

y' = p' + p"+I/ 

for station L ; and similarly 

for station II. 

Therefore the rapid approximation of both the functions D and 
S towards zero in both stations is obtained \f we make the complex 
resistances p! and p" maxima. 

Now the form of p shows at once that it has a maximum for 

• (fl+/)=(y+rf), 
which, in consequence of equation (VI.)> gives at last 

«=^=rf=/. (VIII.) 

From the development of this result it will be clear that the 
relation expressed by equation (VIII.) must hold for either. 
station independent of L. 

All that now remains is to determine b, and further to fix the 
absolute magnitude of any one of the branches. Before doing 
this, however, it is necessary to inquire what the other factor of 
8, namely G, becomes in consequence of fulfilling the regularity 
condition as expressed by equation (VIII.). 

The current which passes through the receiving-instrument 
to produce ''single'* as well as "duplex'' signals is at balance 
expressed by 

^=^ • 7 — . MT / — . N . o / — rifv; X const., 
(a+y){L(a+y)+2%+rf)} ' 

which expression has a maximum for either a or g. 

The maximum of G with respect to a, it will be seen, contra- 
dicts the regularity condition, since a=^g^d could only satisfy 

if d were negative, a physical impossibility. 

Digitized by VjOOQ IC 

of Duplex Telegraphy. 187 

However^ the maximum of G with respect to g gives 

which is satisfied by a^g^d. 

This is a fortunate coincidence, and speaks well for the bridge 

Now substituting for a and d their value g in the expression 
for the current G, we get 

n E 1 

and this expression multiplied by ^g gives the magnetic effect 
of the receiving-instrument, namely 

which has an absolute maximam with respect to g for 


Ftrrtfaer, substituting in the balance-equation (V.) 
a = d=g=r^, 

^'-'' ft=| (IX.) 

Wc have therefore the following two equations by which the 
problem is generally solved : — 

a^g=d^f=\, (VIII.) 

*=i = B m 

by L being understood the measured conductor resistance of the 
line from that station for which the best resistance -arrange- 
ment is to be calculated. 

General Results. 

1. The branches of the bridge y with the exception of the one 
lying opposite the line, must be equal to each other, and severally 
equal to half the measured conductor resistance of the line. 

2. The branch lying opposite the line should be equal to the 
sixth part of the measured conductor resistance of the line; and 
only in this, the smallest of all the branches, should readjustment of 
balance be made. 

Nos. 1 and 2 necessitate the alteration of all the branches if 
\i, the measured conductor resistance, alters within wide limits. 
A determination of L will therefore be required from time to time. 

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188 On the Coloured Wnge of Uniaccial and Biaxial Crystals. 

From the development of these general retulti it frill be evi* 
dent that they fulfil the following conditions :— i» 

I. 7%6 irregtdarity of signals in the one station is entirely inde^ 
pendent of the irregularity of signals in the other station, 

U. The irregul^irity of signals in each statitm is due only to 
balance not being rigidly established. 

III. If balance in either station is disturbed, a single adjustment 
in the branch b will reestablish that balance. 

IV. Any disturbance of balance will have the least possibh 
effect on the received signals. 

V. Maximum current at balance. 

VI. Maximum magnetic effect of the maximum current on the 

[To he continued.] 

XXI. On a simple Arratwement by which the Coloured Rings of 
Uniaxial and Biaxial Crystals may be shown in a common Mi* 
croscope. By Dr. W. H. Stonb*. 

THE author was not aware that any arrangement had been 
hitherto supplied to the ordinary microscope other than an 
extra top to the eyepiece containing a supplementary stage and 
an analyzer. This could only be considered a clumsy expedient. 

The objects to be obtaineci were clearly two : — ^first, to transmit 
the ravs at considerable obliquity through the' plate of crystal ; 
secondlvj to gather these up and form a real image within the 
tube of the microscope. Amici had accomplished this by a 
special combination of lenses which bears his name ; it might, 
however, be done simply by placing a screwed diaphragm 
on the end of the upper araw-tuoe within the body of the mi- 
croscope. The screw should be that ordinarily used for object- 
glasses. To this an object-glass of long focus was fitted, and 
another of higher magnifying-power in the usual place. The 
whole body was then drawn out and adjusted to a telescopic 
focus on a distant object. The lower objective formed the 
object-glass of the telescope, and the inner objective with the 
Huygenian eyepiece a compound ocular. On reinserting the 
body thus arranged, and illuminating the crystal on the stage 
with convergent light by means of a condenser, the rings and 
brushes could be perfectly seen. The whole double series of 
rings in a biaxial crystal of carbonate of lead was thus shown. 

The condenser used was a '' kettle-drum " of two plano-convex 

lenses. The objective on the nozzle of the microscope was a f 

of Ross; that within the draw-tube a 3-inch objective of the 

same maker. 

* Read before the Ph^-«ici4 Spn^t^i June 13, 1874. Comoniiucated by 
the Society. 

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[ 189 ] 

XXII. Modijhation of the utual Trombone Apparaiuif^ 

the Interference of 8o9mi4>earmg Wavet. By W. r. BabbbtTj 
F.I18.E. hie., Profeeeor of Phyeia in the Royal College of 
Science, Dublin*. 

A SIMPLE apparatus for showing the interference of sound, 
bearing waves may be made by employing a circular 
arrangement of tubes, one sliding within the other. One tube, 
A, to which the mouthpiece M is fixed, is three fourths of • 
circle ; the other tube, B, to which the n<»ile N is attached, is 
half a circle, and of such diameter that it slides freely over the 
tube A. 

When the nossle is diame- 
trically opposite the mouth- 
piece, the path of the sound- 
waves is of equal length, and 
hence the sound from any 
convenient source placed near 
to or within the mouthpiece 
is distinctly heard. By tum- 
direction shown by the dotted 
lines, one limb of the tube 
is lengthened whilst the other 
is correspondingly shortened; 
the path of the waves being 
now unequal, a point is soon 
reached where tne sound is nearly obliterated. 

Employing a suitable source of sound, and a sensitive flame 
or a resonant jar as a phonoscope, an audience can perceive at 
once the gradual destruction of the sonorous pulses ; and more- 
over the relative lengths of the two branches of the tube clearly 
indicate the principle of interference thus illustrated. 

One instrument I made was 2 feet in diameter, of 1-inch- 
square zinc tubing; another and better instrument (skilfully 
made by Mr. B. H. Bidout) was of brass tubing, 1 foot in 
diameter, the one limb being ^inch, the other |^inch tube. 
About 18 inches in diameter would probably be the best and 
most convenient size. In making the experiment, care should be 
taken to avoid {a) the conduction of sound to the ear by the 
metal substance of the instrument; (13) the direct transmis- 
sion of sound through the surrounding air. The latter can be 
overcome by attaching a sufficiently long gutta-percha tube to M, 

* Read before the Physical Society, June 20, 1874. Commuiiicated 
by the Sodety. 

Digitized by VjOOQ IC 

140 Notices rejecting New Books. 

thus removing the mouthpiece to a diBtance from the ear. The 
former can be obviated to some extent by having an inelastic 
mouthpiece or similar covering to the end of the tube. But 
Mr. Woodward's device of putting a source of sound, such as a 
reed, entirely within the tube, and a trumpet mouthpiece at N, 
is undoubtedly the best and most suitable class method of making 
the experiment. 

. F.S. — ^With an ordinary pitch-pipe inserted at N, I have to-day 
(July 26) repeated the experiment to the class of science teachers 
now at South Kensington. A continuous blast of air was driven 
through the pipe from an acoustic bellows ; and the loud note 
heard at first was utterly extinguished by altering the relative 
lengths of the tubes. By pushing the tube still further round 
the note again came out; thus the sound of the pitch-pipe could 
be turned on and off at pleasure. Extinction is not confined to a 
mere line in adjusting the pipe, but spreads over a short and 
definite range. In this case it is probaoly, as Professor Ooodevc 
suggests, the interference of two resonant columns of air, rather 
than the coalescence of two progressive waves in opposite phases. 

XXIII. Notices respecting New Books. 

Statique ExperimentaU et Theorique des Liquides soumis aux seuUs 
Forces MoUculaires, Par J, Plateau. 2 vols. 8vo, pp. 450 & 
495. Ghent and Leipzig : F. Clemm. London : Trubner & Ca 
T^HIS work consists essentially of the collected series of papers 
-■- "On the Figures of Equilibrium of a liquid Mass without 
Weight," which the distinguished physicist of Gthent has published 
in the * Memoirs of the Bel^n Academy of Sciences ' during the 
years 1843 to 1868. The substance of these papers having appeared 
Irom time to time in the pages of the * Philosophical Magazme,' in 
the form of comparatively full abstracts of the original memoirs, it 
is not needful to say much here by way of introducing or recom- 
mending the work to our readers. It should be observed, however, 
that this book is not merely a republication, offering simply the 
convenience of presenting in a collected form results whicn were 
previously accessible only in a number of separate papers published 
at intervals during a period of twenty-five years ; thanks to the 
careful revision which the whole has received, and to numerous ad- 
ditions (some of them of considerable extent, relating chiefly to the 
work* of other investigators in the same field of research), the work 
before us possesses much of the continuity and completeness of a 
systematic treatise. 

The chief scientific interest of the phenomena which Professor 
Plateau has investigated lies in the simplicity of the physical prin- 
ciple to which they are all of them referrible, and in the compre- 

Digitized by VjOOQ IC 

Notices respecting New Books* 141 

hensiveness of the geometrical relation which forms the mathematical 
expression of this principle. But, independently of these characters, 
which are inherent in the nature of the phenomena, and not liable 
to modification in consequence of the greater or less power brought 
to the study of them, the present book derives a special value and 
beauty from the sagacity with which the author has followed out 
the physical and mathematical consequences involved in the prin- 
ciple of the equality in all directions of the tension of a liquid sur- 
face, and in the resulting geometrical relation of the constancy of 
the sum of the principal curvatures of such a surface, comlnned 
with the completeness and accuracy of the experimental verification 
of theoretical deductions which he has obtained. In fact, the judg- 
ment and ingenuity shown in devising the methods of experiment, 
and the skill with which they have beien applied, have enabled the 
author to trace out, with a minuteness that has not often been 
equalled in other branches of Physics, the characteristics of the phe- 
nomena under investigation. These phenomena also being compa- 
ratively simple, in the sense of its being possible to isolate almost 
completely by the methods adopted the effects of the particular 
causes it was the author s object to study, these researches form a 
remarkable example of the close correspondence between theory 
and experiment, worthy to be compared with Schwerd's memo- 
rable work on the Phenomena of Diffraction, a work with which 
Professor Plateau's presents another point of analogy in the familiar, 
every-day character of many of the phenomena with which it deals. 

ContrihiUioTis to Selenography, By William Eadclifp Bibt, 
FJl^AJS,, F.M.S. London : Taylor and Francis. 1 874. 
We are glad to see, by a copy of the above work which we have 
received for review, that Mr. Birt has put together in one volume 
his more recent labours connected with Selenography ; for not only 
are there to be found among them able discussions of matters con- 
n3cted very closely with interesting questions of present interest in 
t*ie science, but we are convinced, from a careful examination of 
Mr. Birt's production, that it will prove of great value to every 
shident of the lunar surface who may possess a copy — and that 
not only because in future years it will be a work to which the ama- 
teur may turn to compare his own observations with those there 
recorded of some of the most minute of all lunar objects, in the full 
confidence that they were carefully drawn and correctly described 
for the epochs of observation, but because it is a volume likely to 
be of essential service to every real student in connexion with his 
own method and mode. Headers of the Eeports of the British As- 
sociation for the Advancement of Science will remember that in 
1864 the Association voted a grant for the purpose of mapping the 
surface of the moon, which was continued for three years — the re- 
sult being that three areas of the contemplated map, on a scale of 
230 inches to the moon's diameter, by Mr. Birt, with catalogues <rf 
the objects, were published in the volumes for 1866 and 1868. The 
first of Mr. Birt's contributions to Selenography, published inde- 

Digitized by VjOOQ IC 

142 Notkes respecting New Booh, 

pendentlj of the Assodatioii in 1870, is a fourth area of tiie map* 
in continuation of the original jphm, and which occupies the first 
pkce in the present Yolume. Facing page 1 we have an excellent 
map of the area, carefully drawn in outline, accompanied hy a full 
descriptive Catalogue oi 99 craters and other objects situated upon 
the area. The description is completed by a comparison of four pno- 
tograms* The numerous notes and woodcuts of interesting objects 
must be highly suggestive to every earnest stud^it. 

The very complete monograph of the Mare Serenitatis is of itself 
a work capable of sustaining the reputation of the author of the 
four areas, comprising as it does so large a descriptive catalogue of 
objects within tnu) la^e and perhaps b^t*known of all lunar plains, 
supplemented by copious notes, and illustrated by a map completely 
crowded with objects, some of them very small indeed. As f^ as 
we are able to judge, it is quite a model production. It also con- 
tains a very- interesting examination of Schroter's drawings of the 
region, and a comparison of them with recent photograms and ^e 
present appearance of the plain. 

Uipparchus is the subject of another masterly monograph, illus- 
trated by a well-eugraved map, accompanied by a full catalogue of 
objects and numerous descriptive notes, together with a comparison 
of the region on different photograms. The scale of the map is 
100 inches to the moon's diiuneter. We notice that the paging of 
the letterpress of Bipparchtu runs on from that of ihe Mare Sere-- 
nitatis, from which we suppose other monographs are to follow. 
Certainly every lunar observer must hope that may be the case ; 
indeed the continuance of the areas of the map is a very desirable 
thing while we have nothing at all of the kina which depicts one 
hundredth of the lunar features revealed by the average telescope 
now in the hands of amateurs. Beer and Madler's map was a 
worthy work in 1837 ; but nearly forty years have brought about 
great improvements in instruments tor the purpose of observa- 
tion, and, as it seems to us, a map which would bring sel^io- 
Rraphy more nearly level with the times is really an important 

Following the three maps to which we have referred, we have 
specimens of the Catalogue of Lunar Objects according to ihe plan 
originally devised by lkj&. Birt. This catalogue certiunly has the 
merit of clearness and conciseness ; and, by means of a most useful 
accompanying table of references and synonyms, the student is able 
easily to compare the notes of difEerent observers and authors on 
each particular locality which may be under discussion. This is a 
valuable adjunct to the descriptive notes and illustrations. What 
oiur star-catalogues are to stdlar observers, that would Mr. Birt's 
projected work be to students of the moon, if it were only carried 
out to completion. The method of arrangement adopted through- 
out all Mr. Birt's productions seems to be a specialite of his own. 
Other works on the moon mo could name, written in what is called 
the popular style, and illustrated by excellent pictorial representa- 
tions of the general character of the lunar surface ; but from all 

Digitized by VjOOQ IC 

Royal SoeUiy. 143 

tiieae, which Are more suited to the general reader, the Ydame be- 
fore us differs in kind ; and those who desire to be reaUy acquainted 
wit^ ihs pumUer detail* of the yarious regions treated of will find 
that Mr. Birf s work treats of these especaally • Herein it is unique, 
and contains a mass of yaluable information to be met with, so far 
as we know, in no other work extant. Indeed all Mr. Birt's maps 
and notes are distinguished bj a painstaking accuracj that will con- 
fer upon them great value shoula another case arise similar to that 
of LiiiiU in any of the areas already completed ; for there will be 
found every known spot, streak, craterlet, or other feature de- 
scribed, and often distinctly illustrated; so that, so far as this 
work is concerned, no future selenographer will be likely to be 

Anotiier portion of the volume is occupied by two series of 
papers, entiued '* Selections from the Portfolios of the Editor ot 
the Lunar Mf^ and Catalogue/' in the preparation of which Mr. 
Birt has been assisted by gentlemen who have given scnne attention 
to selenography, and in which will be found many very interesting 
papers. EspeciaUy noticeable is one by the Bev. T. W. Webb, 
•« On the Study of Change in the Lunar Surface," and another by 
Messrs. Webb and Birt on the formation named Cleomede$. The 
latter contains formula for computing the length of a measured 
line on the moon's surface in English feet, in itself a really impox^ 
tant acquisition to every selenographer. Many other papers, treat- 
ing of various topics, mil be found suggestive. 

From a notice on the wrapper of the second issue of the '* Selec- 
tions," we learn that increased subscriptions are required to con- 
tinue them. But we cannot suppose that the want of subscriptions 
is dependent upon any inferiority in the work itself, but rather on 
its being not generally known amongst astronomers, and also on 
the absence of an interest in the study of the moon's surface, which 
contrasts so remarkably with the assiduity with which amateurs 
prosecute their studies in other branches of astronomy. We there- 
fore hope that before long we shall be called upon to notice a f ur^ 
ther contribution to selenography by Mr. Birt. 

XXIV.. Proceedings qf Learned Socieiiei. 

[Continued from p. 720 

January 29, 1874. — Joseph Dalton Hooker, O.B., President, in 
the Chair. 
'^PHE following communication was read: — 
-•- " On the Comparative Value of certain Geological Ages (or 
groups of formations) considered as items of Geological Time." 
Bj A. C. Eamsay, LL.D., V.P.E.S. 

The author first renews briefly several methods by which 
attempts have been made to estimate the value of minor portions 

Digitized by VjOOQ IC 

' 144 Royal Society : — ^Prof. A. C. Ramsay on the 

of geological time, such as: — calculations intended to estimate 
the age of deltas, founded on the annual rate of accumulation 
of semments ; the astronomical method foUowed by Mr. Croll, in 
connexion with the recurrence of glacial epochs; the relative 
thicknesses of different formations; and the relation of strong 
unconformity between two sets of formations in connexion with 
marked disappearance of old genera and species, and the appear- 
ance of newer forms. Having shown that none of these metliods 
give any clear help in the absolute measurement of time in years 
or cycles of years, even when founded on well-established facts, he 
proceeds to attempt to estimate the comparative value of long por- 
tions of geological time, all of which are represented by im- 
portant series of formations. 

The author then alludes to the subject of two papers by himself, 

S'ven^ to the Geological Society in 1871, on the Red Rocks of 
ngland, in which he attempted to show that the Old Red Sand- 
stone, Permian, and New Red series were all deposited in great 
inland lakes, fresh or salt ; and this, taken in connexion with the 
wide-spreading terrestrial character of much of the Carboniferous 
series, showed that a great continental age prevailed over much 
of Europe and in some other regions, from the close of the Silu- 
rian epoch to the close of the Trias. He then endeavours to show 
the value of the time occupied in the deposition of the above- 
named formations, when compared \iith the time occupied in the 
deposition of the Cambrian and Silurian strata, and of the marine 
and freshwater strata which were deposited between the close of 
the Triassic epoch and the present day. 

After alluding to the probable mixed estuarine and marine cha- 
racter of the purple and grey Cambrian rocks of St. David's, it is 
shown that the Cambrian and Silurian series may be massed into 
three great groups : — first, from the bottom of the purple Cambrian 
rocks to the top of the Tremadoc slates ; these being succeeded 
iinconformably by the second group, the Llandeilo and Bala or 
Garadoc beds ; on which rest unconformably the members of the 
third series, ranging from the base of the Upper Llandovery to 
the top of the Upper Ludlow beds, — each imconformable break 
in stratigraphical succession being accompanied by a correspcnding 
break in paiseontological succession. 

These three great divisions are next shown to be comparable, 
in the time occupied for their deposition, to the three divisions 
of Lower, Middle, and Upper Devonian rocks, which are consi- 
dered to be the marine representatives of the Old Red Sand- 
stone ; and therefore it follo\*'s that t?ie time oc^mpied in the depo- 
aition of the latter may have been as long as that taken in the deposition 
of the Cambrian and Silurian series. This position is strengthened 
by the great palfiBontological differences in the fossils of the Upper 
Ludlow and those of the marine Carboniferous series, which seem 
to indicate a long lapse of time during which, in Old Red Sandstone 
areas, no direct sequence of marine deposits took place. 

The next question considered is, what relation in point of time 

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Comparaiive Value of certain Geological Affei. 145 

the depositioii of the Old Bed Sandstone may have taken, when 
compiled with the time occupied in the deposition of certain 
members of the Mesozoic formations. Through a series of argu- 
ments, lithological, stratigraphical, and pal»ontoiogical, the oondu* 
sion is arrived at, that the whole of the Liassic and Oolitic series 
present the various phases of one fades of miurine life, and, in tiiis 
respect, are comparable to the changes in the fossil contents of the 
various subformations of the Cambrian and Lingula-flag series, 
of which the Tremadoc Slates form an upper meml^r. In 
like manner the Lias and Oolites may be compared with the 
Lower Devonian strata ; and therefore a lower portion of the Old 
Red Sandstone may have taken as long for its deposition as the whole 
of the time occupied in the deposition of the Jurassic series. 

Following out this train of argument through the Neoccnnian 
and Cretaceous strata, the result is arrived at tlMt the whole of 
the time occupied in the deposition of the Old Red Sandstone may 
have been equal to the whole of the time occupied in the deposition 
of aUthe Jurassic, WeaMen, and Cretaceous strata collectively. 

In the same manner the next term of the Continental era, tha 
Carboniferous epoch, is compared with the Eocene period, both 
being locally of marine, estuarine, freshwater, and terrestrial 
origin, and both connected with special continental epochs. Next 
comes the Permian series, comparable in its lacustrine origin to 
the Miocene strata of so much of Eur(^, though in the case of 
the Permian watery the lakes were salt. After this the Triassic 
series of Europe alone remains of the old continent, the maiine 
and salt-4ake strata of which are not likely to have taken a shorter 
time in their deposition than the older Pliocene strata. 

If the foregoing method be of value, we arrive at the general con- 
clusion that the great local continental era, which began voith the Old 
Red Sandstone ami closed with the New Red Marl, is comparable, in 
point of Geological Time, to that occupied in the deposiUon of the whole 
of the Mesozoic series later than the New Red Marl, and of all the Cai- 
nozoic formations, and, nufre probably, of all tlie tims that has elapsed 
since ^ beginning of the deposition of the Lias down to tJie present 
day; and consequently the more modem continental era, which 
locally began with the Eocene period and lasts to the present day, 
has been of much shorter duration. 

The author then pointed out that during the older continental 
era there flourished two typical floras — one extending from the 
time of the Old Bed Sandstone to the close of the Permian strata ; 
while the second, which is largely of Jurassic type, characterized 
the Triassic formations. From the time of the Lias onward in 
time, we have also two distinct typical floras — ^the first of Jurassic, 
and the second of much more modern type, beginning with the 
Upper Cretaceous strata of Aix-la-Chapelle and lasting to the pre- 
sent day. 

In like manner the faunas connected with the land resolve them- 
selves into two types : — ^the first chiefly Labyrinthodontian, as shown 
in the Carboniferous and Permian strata ; and the second charac- 

Phil. Mag. S. 4. Vol. 48. No. 316. Aug. 1874. L 

Digitized by VjOOQ IC 

146 Royal Sociehj : — ^Piof, 0. Eeyiu)lda on Surface-forces 

twiBiic of ihe Tzias, vith [Crocodilift, many land-lkards, Aiiomo- 
doDtia, Deinosauria, and Marsupial MaHunalia. This buna, as 
regards genera, with the exception of Labynnthodontia and the 
appearanoe of Fterosauiia, is represented through the remaining 
members of the Mesosoic formations, from Jurassic to Creta- 
ceous indusive. After this comes the Pachydermatous Mammalian 
Eocene fauna, and after ihaJb the Miocene land-fauna, which, 
in its main diaracters, is of modem type. From Jurassic to Cre- 
taceous times, indusively, there was therefore, as far as we know, 
in this area a land-&una chiafly^Be^tilian, iSaurian, and Marsupia], 
and in Tertiary times diiefly Beptilian and PlaoenUl. (Illusianted 
b^ a Table.) 

In conclusion, the recent character c^ the early nuucine faunas 
of the Cunbrian and lingula-fleg series was pcMnted out, such 
as Spongida, Annelida, Ediinodermata, Crustacea, Polyioa, Bra* 
dnopoda, Lsmellibram^iata, Pteropoda, Nudeobranobiata, and Ce- 
phalopoda. This was kmg ago insisted on by Professor Huxley ; 
and we find no evidence of its having lived near the beginning 
ci the zoological series; for below the Cambrian series we fure 
at once involved in a sort of duios of metamorphic strata. Of 
tbe geological history, in the words oi Darwin, '* we possess the 
last volume alone, rdating only to two or three countries.^ The 
connexion of this question with that of the comparative value oi 
different geological eras is obvious, especially in rdation to the 
palieontological part of the question. 

June 18. — Joseph Daltim Hooker, C.B., President, in the Chair. 

The following communication was read : — 

*\0a the Forces caused by Ev^)oration from, and Cond^isation 
at, a Surface." By Prof. Osborne Beyndds, of Owais College, 

It has been noticed by several philosophers, and particularly by 
Mr. Crookes, that, under certain cuxnimstances, hot bodies appear to 
repel uid cold ones to attract other bodies. It is my object m this 
paper to pdnt out, and to describe experiments to prove, that 
liiese effects are the results of evaporation and condensation, and 
that they are valuable evidence of the truth of the kinetic theory 
of gas, viz. that gas consists of separate molecules moving at great 

The experiments of whidi the explanation will be given vrere as 
f dlows : — 

A light stem of glass, with pith-balls on its ends, was suspended 
by a silk thread in a glass flask, so that the balls were nearly at 
the same level. Some water was then put in the flask and boiled 
until all the air was driven out of the flask, which was then corked 
and allowed to cod. When cold there was a partial vacuum in 
it, the gauge showing from | to | of an inch pressure. 

It was now found that when the flame of a lamp was brought 
near to the flask, the pith-ball which was nearest the flame was 
driven away, and ihat with a piece of ice the pith was i^tracted« 

Digitized by VjOOQ IC 

caused by Evaporation and Con4en$aiion. 147 

This expenment wm rroeated under a rmety of drcomstances, 
in dilEeient Badk» and with different balaxioes, the stem bmngiome- 
times of glass and sometimes of platamun ; the results, howeyer, 
were the same in all cases, except such variations as I am about to 

The pith-balls were more sensitive to the heat and oM when the 
flask was cold and the tension within it low ; but the effect was 
perceptible until the gauge showed about an inch, and even after 
that the ice would attract the ball. 

The reason why ^e repulsion from heat was not apparent at 
greater tensions, was deaiiy due to ihe convection-currentB which 
the heat generated within the flask. When there was ^lough 
vapour, these currents carried the pith witli them ; they were, in 
&ct, then sufficient to overcome the forces which otiierwise moved 
the pith. This was shown by the fact that when the bar was 
not quite level, so that one ball was higher than the other, th6 
curr^its affected them in different degrees ; also that a different 
eSeet could be produced by raising or lowering the position of the 

The condition of the pith also perceptibly affected the sensitive- 
ness of the balls. When a piece of ice was placed against the side 
of the glass, the nearest of the pith-balls would be £awn towards 
the ice, and would eventually stop opposite to it. If allowed to 
remain in this condition for some time, the vapour would con- 
dense on the ball near the ice, while the other \M would become 
dry (this would be seen to be the case, and was also shown by the 
tipping of the balance, that ball against the ice gradually getting 
lower). It was then found, when the ice was removed, that the 
dry ball was insensible to the heat, or nearly so, while that ball 
which had been opposite to the ice was more than ordbarily sen- 

I£ the flask were dry and the tension of the vapour reduced 
with the pump until the gauge showed | of an inch, then, although 
purely steiun, the vapour was not in a saturated condition, and 
the pith-balls which were dry were no longer sensitive to the lamp, 
although they would still approach the ice. 

From these last two &cts it appears as though a certain amount 
of moisture on the balls were necessary to render them sensitive to 
the heat. 

In order that these results might be obtained, it was necessary 
that the vapour should be free from air. If a small quantity 
of air was present, although not enough to appear in t^e gaue^e, 
^e ^ects rapidly diminish^, partictdarly that dE the ice, until nie 
C(mvecti(m-currents had it all their own way. This agrees with the 
&ct that the presence of a small quantity of air in steam greatly 
retards condensation and even evaporation. 

With a dry flask and an air-vacuum, neither the lamp nor the 
ice produced their effects ; the eonvection-currrats reigned supreme 
^n v(^hen the gauge was as low as | inch. Under these circum- 
sUno^s the lamp generally attracted the balls and the ice repelled 


Digitized by VjOOQ IC 

148 Roifal Society :-*VroL 0. Reynolds on Sw/ace-forces 

them ; i. e» the curreoits carried them towards the lamp and from 
the ice ; but, by placing the lamp or ice very low, the reverse effects 
could be obtained, wfajjch goes to prove that they were the effects 
of the currents of air. 

These experiments appear to show that evaporation from a sur- 
face is attended with a force tending to drive the surface back, and 
condensation with a force tending to draw the surface forward. 
These effects admit of explanation, although not quite as simply 
as may at first sight appear. 

It seems easy to omc^ve that when vapour is driven off from a 
body there must be a certain reaction or recoil on the part of the 
body ; Hero's engine acts on this principle. If a sheet of damp 
paper be held before the fire, from that side which is opposite to 
the fire a stream of vapour wHl be drawn off towards the fire wil^ 
a perceptible velocity ; and therefore we can readily conceive that 
there must be a correspcmding reaction, and that the paper will be 
forced back with a force equal to that which urges the vapour f or^ 
wards. And, in a similar way, whenever condensation goes on at 
a surface it must diminish the pressure at the surface, and thus 
draw the surface forwards. 

It is not, however, wholly, or even chiefly, such visible motions as 
these that afford an explanation of the phenomena just described. 
If the only forces were those which result from the perceptible 
motion, they would be insensible, except when the heat on the 
sur&use was sufficiently intense to drive the vapour off with con- 
siderable velocity. This, indeed, might be the case if vapour had 
no particles and was, what it appears to be, a homogeneous elastic 
medium, and if, in changing from liquid into gas, the expansion 
took place gradually, so that the only velocity acquired by the vapour 
was that necessary to aUow its replacing that which it forces 
before it and giving place to that which follows. 

But, although it appears to have escaped notice so far, it follows, 
as a direct consequence of the kinetic tbeory of gases, that, when- 
ever evaporation takes place from the surface of a solid body or a 
liquid, it must be attended with a reactionary force equivalent to 
an increase of pressure on the surface, which force is quite in- 
dependent of the perceptible motion of the vapour. Also, conden- 
sation must be attended with a force equivalent to a diminution of 
the gaseous pressure over the condensing surface, and likewise 
independent of the visible motion of the vapour. This may be 
shown to be the case as follows : — 

According to the kinetic theory, the molecules which constitute 
the gas are in rapid motion, and the pressure which the gas exerts 
against the bounding surfaces is due to the successive impulses of 
these molecules, whose course directs them against the surface, from 
which they rebound with unimpaired velocity. According to this 
theory, therefore, whenever a molecule of liquid leaves the sur&ce 
henceforth to become a molecule of gas, it must leave it with a 
velocity equal to that with which the other particles of gas re- 
bound ; that is to. say, instead of bebg just detached and quietly 

Digitized by VjOOQ IC 

earned by Evaporation and Condeniation. 140 

passing off into the gas, it must be shot off with a Telocity greater 
than that of a cannon-ball. Whateyer may be the nature of the 
forces which give it the velocity, and which consume the latent 
heat in doing so, it is certain, from the principle of conservation 
of momentum, that they must react on the surface with a force 
equal to j^hat exerted on the molecule, just as in a gun the pressure 
of the powder on the breech is the same as on the shot. 

The impulse on the surface from each molecule which is driven 
off by evaporation must therefore be equal to that caused by the 
rebound of one of the reflected molecules, supposing all the mo- 
lecules to be of the same size ; that is to say, since the force of 
rebound will be equal to that of stopping, the impulse from a par- 
ticle driven off by evaporation will be half the impulse received 
from the stopping and reflection of a particle of the gas. Thus 
the effect of evaporation will be to increase the number of impulses 
on the surface ; and although each of the new impulses will only be 
half as effective as the ordinary ones, they will add to the pressure. 

In the same way, whenever a molecide of gas comes up to a 
Bur&ice and, instead of rebounding, is caught and retained by the 
surface, and is thus condensed into a molecule of liquid, the impulse 
which it will thus impart to the sur&ce will only be (me half as 
great as if it had rebounded. Hence condensation will reduce the 
magnitude of some of the impulses, and therefore will reduce the 
pressure on the condensing surface. 

For instance, if there were two surfaces in the same vapour, 
one of which was dry and the other evaporating, then the pres- 
sure would be greater on the moist surface than on that which 
was dry. And, again, if one of the surfaces were dry and the 
other condensing, then the pressure would be greater on the dry 
surface than on that which was condensing. Hence, if the opposite 
sides of a pith-ball in vapour were in such different conditions, the 
ball would be forced towards the colder side. 

These effects may be expressed more definitely as f oUows : — 

Let V be the velocity with which the molecides of the vapour 

p the pressure on a unit of sur&u^, 
d the weight of a unit of volume of the vapour, 
w the weight of liquid evaporated or condensed in a second ; 
then the weight of vapour which actually strikes the unit of dry 
surface in a second will be 


and the pressure p will be given by 

and/ (the force arising frcnn evaporation) will be given by 

- wv 

* See Maxwell, 'Theory of Heat»' p. 294. 

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ISO Royal Sodtty ;— Prof. O. Reynoldi on Sttrfaet-forca 

Thus we hare an expresBioii for the force in terms of the qnaiH 
titj of watw evaporated and the ratio of the pressure to^the imf 
Bit J of the yapour; and if the heat neoessary to evaporate the 
liquid (thd ktent heat) is known, we can find the force which 
would result from a given expenditure of heat. 

Applying these results to steam, we find that, at a tmnperatore 
of 60 , the evaporation of 1 lb. of water from a surfaoe would be 
sufficient to maintain a force of 65 lbs. for one second. 

It is also important to notice that this force will be proportioaial 
to the square root of the absolute temperature, and, oonseqnenily, 
will be approximately constant between temperatures of 32° and 

If we take mercury instead of water, we find that the force is 
only 6 lbs. instead of 65 lbs. ; but the latent heat of mercury is only 
^ that of water, so that the same expenditure of heat would main- 
Uin nearly thi-ee times as great a force. 

It seems, therefore, that in this way we can g^ve a satisfactory 
explanation of the experiments previously described. When tiiie 
radiated heat from the lamp falls on the pith, its temperature will 
rise, and any moisture on it ^vill begin to evaporate and to drive 
the pith fro«n the lamp. The evaporation will be greatest on that 
ball which is nearest to the lamp ; therefore this ball will be driven 
away until the force on the other becomes equal, aftei^ which tiia 
balls will come to rest, unless momentum carries them further. 
On the other hand, when a piece of ice is brought near, the tem^ 
perature of the pith will be reduced, and it will condense the va* 
pour and be drawn towards the ice. 

It seems to me that the same explanation may be given of Mr. 
Crookes's experiments ; for, although my experiments were made on 
water and at comparatively high pressures, they were in realify 
undertaken to vemy the explanation as I have given it. I used 
water in the hope oi finding (as I have found) that, in a conden- 
sable vapour, tne results could be obtained with a greater density 
of vapour (that is to say, with a much less perfect vacuum), the 
elEect being a consequence of the saturated condition of the vapour 
rather than of the perfection of the vacuum. 

Mr. Oookes only obtained his results when his vacuum was 
nearly as perfect as the Sprengel pump would make it. Up to this 
point he had nothing but the inverse effects, viz. attraction with 
neat and repulsion with cold. About the cause of these he seems 
to be doubtful; but I venture to think that they may be entirely 
explained by the expansion of the surrounding gas or vapour, and 
the consequent oonveotion-cun^ents. It must be remembered that 
whenever the air about a ball is expanded, and thus rendered 
lighter by heat, it will exercise less supporthig or floating power 
on the ball, which will therefore tend to sink. This tendency will 

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caused by Evaporution and Condensaiion. ISl 

be in opposition to the lifting of the Mcendinc current, and it will 
depend on the slwpe and thickness of the hsS whether it will rise 
or fall when in an ascending enrrent of heated gas. 

The reascn why Mr. Crookes did not obtain the same results 
with a less iperte(A> Taoanm was because he had then too large a 
proportion of air, or non-condensing gas, mixed with the Tapour, 
whM^h i^so was not in a state of satimition. In bis experiments 
the condensable raponr was that of mercurj, or something whidi 
required a siill higher temperature, and it was necessary thi^ the 
Tacnam should he ybtj perfect for such Tapour tp be any thing 
like pure and in a satmrated condition. As soon, howerer, as this 
state of perfection was reached, then the effects were more appa* 
rent than in the corresponding ease of water. This agrees well 
with the explanation ; for, as preriously shown, the effect oi mercury 
would, for the same quantity of heat, be three times as great as 
that of water ; and, besides this, the perfect state of the vacuum 
would oUow the pith (or whateyer the ball might be) to move much 
more freely than when in the vapour of water at a considerable 

Of course this reasoning is not confined to mercuiy and water ; 
any gas which is conden»Bd or absorbed by the balls when cold 
in greater quantities than when worm would give the same re- 
sults ; and, as this property appears to belong to all gases, it is 
only a question of bringing the vacumn to the right degree of 

There was one fact connected with Mr. Crookes's experiments 
which, independently of the previous considerations, led me to the 
conclusion that the result was due to the heating of the pith, and 
was not a direct result of the radiated heat. 

In one of the experiments exhibited at the Soir^ of the Boyal 
Society, a candle was placed close to a flask containing a bar of 
pith suspended from the middle : at first, the only thing to notice 
was that the pith vras oscillating considerably under the action of 
the candle ; each end of the bar alternately approached and receded, 
showing that the candle exercised aninfiuenoe similar to that which 
might have been exercised by the torsion of the thread had this been 
stiff. After a few minutes' observation, however, it became evi- 
dent that the oscillations, instead of gradually diminishing, as one 
naturally expected them to do, continued ; and, more than this, they 
actually increased, until one end of the bar passed the light, after 
which it seemed quieter for a little, though the osciUaticms again 
increased until it again passed the light. As a great many people 
and lights were moving about, it seemed possible that this might 
be due to external disturbance, and so its full importance did 
not strike me. Aft e r ward s, howe\ er, I saw that it was only to bo 
explained on the ground of the force being connected with the 
temperature of the pith. During part of its swing one end of the 
pith must be increasing in temperature, and during the other part 
it must be cooling. JiJid it is easily seen that the ends will not be 
hottest when nearest the light^ (xr coldest when furthest away ; they 

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152. Royal Society. 

will acquire heat for some time after they have begun to reeede, and 
lose it aft^r they have begun to approach. There will, in fact, be 
a certain lagging in the effect of the heat on the pith, like that 
which is apparent in the action of the sun on a comet, which causes 
the comet to be grandest after it has passed its perihelion. From 
this cause it is easy to see that the mean temperature of the ends 
will be greater during the time they are retiring than while i^- 
preaching, and hence the driving force on that end which is leaving 
will, on the whole, more than balance the retarding force on that 
which is approaching ; and the result will be an acceleration, so that 
the bar will swing further each time until it passes the candle, after 
which the hot side of the bar will be opposite to the light, and will 
for a time tend to counteract its effect, so that the bar will for a. 
lame be quieter. This fact is independent evidence as to the nature 
of the force ; and although it does not show it to be evi^ration, 
it shows that it is a force depending on the t^operature of the pith, 
and t^at it is not a direct result of radiation from the candle. 

Since writing the above paper, it has occurred to me that, accord- 
ing to the kinetic theory, a somewhat similar effect to that of eva- 
poration must result whenever heat is communicated from a hot 
surface to gas. 

The particles which impinge on the surface will rebound with a 
greater velocity than that with which Ithey approached ; and con- 
sequently the effect of the blow must be greater than it would have 
been had the surface been of the same temperature as the gas. 

And, in the same way, whenever heat is communicated from a 
gas to a surface, the force on the surface will be less than it other- 
wise would be, for the particles will reboimd with a less velocity 
than that at which they approach. 

Mathematically the result may be expressed as follows — the 
symbols having the same meaning as before, e representing the 
energy communicated in the form of heat, and Sv the alteration 
which the velocity of the molecule undergoes on impact. As before, 

p=_ort;=V -d' 

Therefore, in the case of steam at a temperature of 60^, 

•^ 2000 
and in the case of air 

/as— L. 



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Geological Society. l53 

It must be remembered that c depends on the rate at which 
cold particles will come up to the hot surface, which is very slow 
when it d^nds only on the diffusion of the particles of the gas 
infer se and the diffusion of the heat amongst them. 

It will be much increased by convection-currents; but these 
wiU (as has been already explained), to a certain extent, produce 
an opposite effect. It would also seem that this action cannot have 
had much to do with Mr. Crookes's experiments, as one can hardly 
conceive that much heat could be communicated to the gas or va- 
pour in such a perfect vacuum as that he obtained, unless, indeed, 
the rate of diffusion varies inversely as the density of a gas*. It 
wiD be interesting, however, to see what light experiments will 
throw on the question. 


[Continued from p. 76.] 

November 5, 1873.— Prof. Eamsay, F.R.8., Vice-President, 

in the Chair. 

The following communications were read : — 

1. "On the Skull of a Species of IlalitTierium from the lied Crag 
of Suffolk." By Prof. W. H. Flower, F.R.S., F.G.S. 

The specimen described, which is in the collection of the Rev. H. 
Canham, ofWaldringfield, is from the so-called coprolito- or bone-bed 
at the bnse of the Red Crag, and presents the usual aspect of the 
mammalian remains from that bod. It is of especial interest as 
furnisliina: Iho first recorded cvideuce of llie existence in Britain of 
animals belonging to the order Sircnia. The fmgracnt consists of 
the facial part of the cranium, separated, probably before fossiliza- 
tioc, from the posterior part at the fron to-parietal suture, and in a 
line descending vertically therefrom. It was afterwards subjected 
to severe attrition, by which many of the projecting parts have been 
removed ; but sufficient remains to enable its general relationship to 
known forms to be determined. The whole of that portion of the 
maxillsc in which the molar teeth were implanted is preserved. 

The author compared the fossil skull with those of the existing and 
extinct spedes of the order, and stated that, while it presents many 
characters common to the Manati and the Dugong, there are others 
by which it differs from both, the most striking being the more 
normal development of the nasal bones and the outer wall of the 
nasal fossie, and especially the dentition, in all of which it shows a 
more generalized condition. The existence in it of maxillary teeth 
removes it still further from Bhytina, In general character the 

* June 10. — ProfesKor Maxwell has shown that the diffusion both of heat 
and of the gas varies inversely as the density; therefore, excepting for con- 
vection-currents, the amount of heat communicated from a surface to a gas 
would be independent of the density of the gas, and hence the force /would be 
independent of the density; that is to say, this force woidd remain constant 
as the vacuum improyed, while the convection-currents and counteracting 
forces would gradually diminish. It seems probable, therefore, that Mr. 
Crookes's results are, at least in part, due to this force. 

Digitized by VjOOQ IC 

164 0$ohgkal SoeUiy ;— 

molars eorrespond with those of the genus HdUAsrkam^ in which 
the anthor oonsiclered that this fossil found its nearest ally in if. 
Schitm, Kaup, from the Miooene of the Bhine YaUeyi a fbnnaticm 
inwhidi several of the animals of the Bed-Crag bone*hed are known 
to oocur. The difPerenoes, however, espeoiallj the larger sue of the 
eranium, in the Crag specimen^ and the larger size of its teetb> 
induce the author to regard it as a diitinot species, which he pro- 
poses to name HalUhsrium Canhamu 

2, " New Facts hearing on the Inquiry concerning Forms inter- 
mediate between Birds and Beptiles." By Henry Woodward, Esq., 

The author, after giving a brief sketch of the Sauropsida, and 
referring especially to those points in which the Pterosaurians 
approach and differ from birds, spoke of the fossil birds and land 
reptiles which he considered to link together more closely the 
Sauropsida as a dass. 

The most remarkable reoent discoreries of fossil birds are :-* 

I. ArchceopUryx macrura (Owen), a Kesozoic type, which has a 
peculiar reptilian-like tail, composed of twenty free and apparently 
unanohylosed cylindrical vertebr«D, each supporting a pair of quill- 
feathers, the last fifteen vertebne having no transverse processes, 
and tapering gradually to the end. 

II. Ichthyomis dispar (Marsh), discovered by Prof, 0. C. Marsh 
in 1872 in the Upper Cretaceous beds of Kansas, XT. S. It possessed 
well-developed teeth in both jaws. The teeth are set in distinct 
sockets, and are all more or less inclined backwards. 

m. Odontopteryx iolmpica (Owen), an Eocene bird from the 
London Clay of Sheppev, the skull of which alone has been dis- 
covered, has very prominent denticulations of the alveolar margins 
of the jaws. 

The author then referred to the Dinosauria, some of whidi he 
considered to present points of structure tending towards the so- 
called wingless birds. 

I. CompiOQWiikM hiigipes (A. Wagner), from the Oolite of Solon- 
hofen, is about two feet in length, having a small head with toothed 
jaws, suDDorted on a long and slender neck. 

The iliac bones are prolonged in front of and behind the aceta- 
bulum ; the pubes are long and slender. The bones of the fore 
limbs are small, and were probably furnished with two clawed 
digits. The hind limb is very large, and disposed as in birds, tlie 
femur being shorter than the tibia. The proximal division of the 
tarsus is anchylosed with the tibia as in birds. 

II. The huge carnivorous Megcdosaurus, ranging from the Lias to 
the Wealden, had strong but not masslTe hind limbs, and short 
reduced fore Hmbs ; it moved with free steps, chiefly if not solely 
on its hind Umbs, which is trua also rf the vegetable-eating lisarcb 
of the Mesoaoio rooks. 

The author next drew attOBtiott to the Frilled Lizard oi Australia, 
Cfhlamydifsaurus Kingxi (Gray), which has its fore Hmbs very much 
smaller than the hind limbs, and has been observed not only to sit 

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Mr. J. W. Haike on a very large Saurian Limb-bane. 156 

up oceasionaQy, Imt to nm habitoally upon tiie gvovmA <m its bind 
1^;b, its fore paws not touching the earth, which upright eaiiiage 
neceesitatM qMcial mo^ftcations of ibe sacrum and palTio bones. 

The Solenhofen limestone, in which Pterosauiia are frequent, 
and which baa yielded the remains of ArehcBopUryx and of Cem-' 
]^$ognaihus^ has also furnished a slab bearing a bipedal track, re- 
sembling what might be produced by Chlamydosauru$ or Comp$o^ 
ffnathue. It shows a median track formed by the tail in being drawn 
along the ground ; on each side of this the hind feet with outspread 
toes leave their mark, while the fore feet just touch the ground, 
leaving dot-like impressions nearer the median line. Hence the 
author thought that, while some of the bipedal tracks which are met 
with from the Trias upwards may be the " spoor " of struthious 
birds, most of them are due to the bipedal progression of the 
Secondary Beptiles. 

3. <*Nota on the Astragalus otigwtnodon MawtdU."^ By JT. W. 
Holke, Esq., P.B.fl., F.G.S. 

The author exhibited and described an astragalus of Iguanod&n 
from the collection of E. P. Wilkins, Esq., F.6J9. The bone was 
bdieved to be previously unknown. It is a bone of iregular form, 
having on its lower surface the characteristio pulley-shape of a 
movable hinge-joint The upper surface presents a form exactly 
adapted to that of the distal end of the tibia ; so that the applied 
surfaces of the astragalus and tibia must have interlocked in such a 
manner as to have precluded all motion between them. The author 
remarked upon the interest attaching to this fact in connexion with 
the question of the relationship between the Dinosauria and Birds. 

4. " Note on a very large Saurian limb-bone, adapted fbr progres- 
sion upon land, from the Kimmeridge Clay of Weymouth, Dorset.*' 
By J. W. Hulke, Esq., F.R.S., F.G.S. 

The bone described by the author presents a closet resemblance 
to the Crocodilian type of humerus than to any other bone ; and he 
regarded it as the left humerus of the animal to which it belonged. 
Its present length is 64 inches'; but when perfect it eould hardly 
have been less than 68 inches in length. The middle of the shaft 
is cylindroid. Its transverse section is of a subtrigonal figure, and 
presents a large coarsely cancellated core, enclosM in a compact 
cortical ring. The bone is considerably expanded towards the two 
extremities ; the distal articular surf&ce is oblong, and divided into 
a pair of condyles by a very 'shallow vertical groove; below, the 
anterior border, in its proximal half, is much wider than the cor- 
responding portion of the posterior border, and is flattened and pro- 
duced downwards into a ventrally projecting crest ; and tiio distal half 
of this border forms a thin, rough crest, projecting forwards. The 
presence of these crests distinguishes the present humerus fh>m 
those of Pelorosaufus and of Ceteoeaurus &a<mien$i8 ; but the general 
correspondence of th6 bone with the humerus of the latter species 
leads the author to refer it provisionally to a species of Ceteommrue, 
whicb he proposes to name C hwm^o-irietafus^ 

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[ 156 ] 
XXV. Intelligence and Miscellaneous Articles. 


^rilE annexed figure shows, of the natural size, the section of a 
A compendious form of staivspectroscope in combination with 
the ocular of a telescope. 

It consists of a small direct-vision prism fixed in a tube CD, the 
dispersion of which is about 
equivalent to that of the sys- 
tem of prisms of a Browning 
miniature spectroscope. The 
tube C D is movable in a se- 
cond tube, A B, which can be 
screwed upon the head of the 
eyepiece and contains a cylin- 
drical lens L of about 100 
millims. focal distance. As 
the length of the line of light 

produced by this lens depends both on its focal distance and also 
on the dimensions and proportions of the optical parts of the tele- 
scope, it is advisable to have in readiness several cylindrical lenses 
of different lengths of focus, so as to be able to employ them ac- 
cording to the length of the line of light (and consequently the 
breadth of the spectrum) desired. 

0^ and O^ are the two lenses of the eyepiece, and hence do not 
belong to the spectroscope. 

If with this instrument the spectrum of a star is to be observed, 
the tube C D vdth the prism is first removed, and the ocular bo ar- 
ranged that when the eve is at O a sharp line of light is seen. It 
is essential, in doins this, that the eye should be at about the same 
distance from the lens L as when the prism is employed. The 
tube C D is now inserted, in such a manner that the refracting 
edge of the prism lies, as usual, parallel to the luminous line, and 
consequently the spectrum attains its greatest breadth. Self-evi- 
dently, for a given telescope, the suitable arrangement need only 
be once ascertained ; so that then by a small screw S the prism can 
be fixed in an invai;^ble position >\ith respect to the cylindrical 
lens L. The prism is manufactured by M. Mens, of Munich ; and 
he prefers to use it in this compendious form for microscopes. 

The intensity of the light of this ocular-spectroscope is so consi- 
derable, that, in combination with a small portable telescope, the 
objective of which has only 35 millimetres aperture and about 400 
millims. focal distance, it shows distinctly the lines of stars of the 
first magnitude, such as Wega, a Ononis, and even a Herculis wJieti 
the state of tJie atinosphere corresponds^ as Professor Winnecke and 
Dr. Yogel convinced themselves and others on the occasion of their 
visit to Leipsdg in the course of the past year. When Venus ap- 
pears as a slender crescent, its spectrum is singularly beautiful. 

Although, according to the well-known methods employed by 

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Intelligence and Miscellaneous Articles. 157 

Browuiug, Yogel, and others, a scale could be very easily connected 
with this instrument, it can be recommended even without one for 
systematic mass-observations o£ fixed-star spectra, in which the 
prime object is to ascertain the typical constitution o£ the spectra. 
As the essential differences between these types probably depends 
only on the temperature and mass of those incandescent bodies, and 
according to the observations of Secchi and others those types stand 
in a certain relation to the distribution of the stars in space, such 
systematically conducted mass-observations may in future become 
of high importance for the progress of astrophysics. 

I permit myself, in conclusion, the remark that the combination 
above described was explained and exhibited by me at the last meet- 
ing of the Astronomical Society at Hamburg, in September 1873. — 
Berichte der Icon, sdchs. Oesellschctft der Wissenschaften math.-phys. 
Classe, April 23, 1874. 


The phenomenon of the tides, stated broadly, consists of a pass- 
ing elevation, real or apparent, of oceanic waters at two opposite 
points on the surface of the globe. These elevations, which follow 
the moon in its course, may become greatly intensified under local 
conditions, as where opposing coast-lines impede the progress of 
the tidal wave ; but in the open ocean, it is well known, they are 
of but slight significance. According to the received theory, they 
are occasioned essentially by the unequal degree of attraction ex- 
erted by the moon on different parts of the earth — this attraction 
being, of course, modified by that of the sun. It is thus assumed 
that the waters, owing to their comparative mobility, are drawn 
towards the moon on one side of the globe, whilst the solid earth 
is drawn away from the waters on the other side — or, to use the 
common phraseology, is drawn towards the moon faster than the 
waters can follow. 

This view, although not without opponents, has been almost uni- 
versally adopted in default of a more satisfactory explanation. 

The explBoiation of the cause of tides now suggested has at least 
this merit : it applies the same principle in elucidation of both tides 
— that nearest the moon, and that on the opposite side of the globe. 
It is briefly this : — When two bodies pull against each other, there 
must necessarily be a contraction of particles towards the centre of 
each body along the line of pull or resistance. In the pull, there- 
fore, of the earth upon the moon, the earth (and of course the moon 
also) must suffer a passing contraction, the part along the line of 
pull, so to say, contracting more than the other parts. But this 
contraction is mechanical only, and is therefore a compression ; and 

* Commiinicated by the Author. Condensed from a commuDioation 
made to the Canadian Institute, February 7, IS74, 

Digitized by VjOOQ IC 

158 fnietligence and Miscellaneoui Articles* 

M water is practically incompressible, tiie sea remains essentially 
unoffectod, whilst the earth shrinks beneath it, and l^us causes the 
tide. The shrinkage of course becomes greater, and the tide higher, 
when both sun and moon take part in the counter-pull, whether 
acting on the same side of the eaiih or on opposite sides. It may 
be assumed, however, from the known heignt of the tidal wave 
where the march of this wave is unopposed, that the maximum 
amount of contraction does not exceed a foot for each thousand 
miles of the earth's radius — being thus, in round numbers, less than 
one part in five millions. In the tremendous pull of the earth upon 
the moon, by which the moon is kept upon its course, a passing 
contraction of this comparatively slight amount may be easfly con- 
ceived to follow. According to the commonlv adopted theory, one 
tide is assumed to result from the withdrawal of the earth, locally, 
from the waters above it ; in the view now proposed, both tides are 
assumed (although on a different principle) to be thus caused. 


Several months since, I undertook some experiments to deter- 
mine, by various methods, the temperature of the sun. I beg the 
Academy to kindly permit me to submit to it the first results St my 

Measurements of solar heat can be made in two ways. In the 
first, a thermometer is placed successively during equal times in the 
shade and then in i^e sun, and the course of the instrument is folr 
lowed in each case : this is the dynamic methody that of the pyrohe- 
liometer of Pouillet. In the second the thermometer remains sub- 
mitted to solar radiation until the temperature indicated by the 
instrument becomes stationary ; and at tne same time the tempe- 
rature of the thermometer and that of the enclosure are noted: this 
is the static method, that which appears to be adhered to by most 
ot the physicists who occupy themselves with the measurement of 
solar heat. I shall for the moment speak only of the latter me- 
thod, and in the first place copsider its principle. 

Let a spherical envelope be maintained at a constant temperature 
i, and let the bulb of a thermometer be in i^e centre of the sphere, 
which bulb I will for an instant suppose infinitely small. The en- 
closure is coated with lampblack, as well as the bulb of the thermo- 
meter. Let us suppose equilibrium of temperature established. 
The enclosure then sends to the thermometer a quantity of heat Sa<, 
a being Dulong's constant or 1*0077 ; and the thermometer sends 
back to the enclosure the same quantity of heat Sa^ Let us now 
pierce in the spherical enclosure a circular aperture w of such di- 
mensions that it will be seen from the centre under the angle which 
measures the apparent diameter of the sun, and let us direct this 
aperture toward the sun. It is manifest, according to the law of 
the variation of calorific intensity inversely as the square of the 
distance, that the real action of the sun on the bulb of the thermo- 

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Intelligence and Miscellaneoue AriicUi. 160 

meter is identical with ihnt which would be exerted by a disk of 
8ur&ce M placed at the i^perture (rf our sphere, tius disk haying Uie 
same tempeniture and emissive power as iAie sun. We can there- 
fore define the temperature of the sun by that whidi would have to 
be attributed to this imaginary disk, possessing the emissive power 
of lamp]i>Uok, to produce upon the thermometer the same effect 
which IS actually produced by the sun. Let a; be t^e temperature^ 
thus defined, of the sun, the stationary temperature of we ther- 
mometer nceinng the solar radiation throu^ the aperture ta ; the 
quantity oi heat emitted by the t^rmometer (which was Ba^ at the 
temperature t) has become So' ; and putting that quantity ot heat 
equal to the sum of the quantities enutted by enclosure and by the 
sun, we have at once 

This is precisely the equation as written by H. Yicaire ; but it was 
established under reserves from which we must now free ourselves. 
The dimensions of the thermometer are necessarily finite ; and cof^- 
sequently the aperture thrpugh which the solar ravs penetarate must 
be widened to permit them to reach the whole of the bulb : hence 
comes a double complication. 

Let us now consider an admission-aperture Q large enough for 
an entire hemisphere of the bulb to receive the rays of the sun. I( 
^e diameter of the bulb is sufiiciently small in proportion to that of 
the enclosure, every point of it will be sensibly in the same condi- 
tions ; so that in order to account for the actual state of the appa- 
ratus, it is sufficient to consider any one point whatever ox the 
bulb. This point is submitted: — (1) to the radiation of all the 
preserved portion of the enclosure ; (2) to the radiation of the sun, 
which is equivalent to that of a surface w placed at a distance equal 
to the radius of the enclosure and kept at the temperature of the 
sun ; (3) to the radiation of the whole of a portion of the sky bor- 
dering the sun, which acts as ^ surface Q— im at an unknown tem- 
perature y. The precise equation is, therefore, 
Sa*« Sa<-f iMa*-f Oay. 

I will indicate in a forthcomine note how, making Q to vary by 
means of diaphragms pierced with apertures of known dimensions, 
the correction-term fl«y can be determined mth sufficient exact- 
ness. An idea of its quantity will be given by the following result, 
the only one I shall cite at present : — 

On March 14, 1874, the sky being very clear, although the ground 
was covered with snow, at 1 p.m. the quantity of heat arriving from 
the sun at the surface of the ground was the same as that which 
would have been given by a disk of the same apparent diameter as 
the sun, of maximum emissive power, and at the temperature of 
1238*^ C. The temperature of the air was + 1°, and the barometric 
pressure 758 millims. In these conditions, the diameter of the 
admission-aperture being about 25 times the sun's apparent dia- 
meter, the portion of the sky bordering the sun, and seen from the 

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160 Intelligence and Miscellaneous Articles. 

bulb of the thermometer, acted as a surface Q heated to near 100^, 
the enclosure being at 9^-2. The total intensities of the three 
radiations sent to the thermometer by the surfaces S, m, and O were 
then sensibly proportional to the numbers 15, 1, and 0*1. 

It will not be uninteresting, and I have. already some measure- 
ments on this point, to compare at different periods, and especially 
at different altitudes, the radiation of this portion of the sky bor- 
dering the sun, the illumination of which exhibits at times remark- 
able intensity. Perhaps we shall find there a portion of the heat 
lost by the direct rays in their passage through our atmosphere. — 
Oomptes lUndus de VAcad, des Scietices, May 18, 1874. 


It is well known that the sparks from the discharge of a Leyden 
jar leave upon the surfaces of insulators a trace, conditioned by cer- 
tain mechanical processes. The phenomenon is especially charac- 
teristic upon very delicately smoked glass surfaces to which sparks 
spring between pointed conductors. I have therein observed a re- 
gular microscopic structure. 

With a length of spark of 4 to 6 centims. the trace is generally 
a bright streak 3 mlUims. wide, with a dark axis, produced by the 
soot-particles being partly throwTi to the sides, partly going to 
the axis and there accumulating. On this trace there is further 
found a mostly very striking knot-like thickening just where the 
lateral motion of the air has taken place with peculiar violence — a 
place in the spark which had already struck me in my optical 
observations (Pogg. Ann, vol. cxxxiv.). Before this spot the 
trace is altogether different from what it is beyond. Towards 
the positive conductor the spark-path is mostly branched off like 
a tuft, towards the negative not so. When the trace is ex- 
amined with a mcOgnifying-power of 15-20, there appears fre- 
quently on the positive side, never on the negative, in the dark 
axis of the spark-path a very fine dark zigzag line resembliug a mi- 
croscopic sine-curve, of 0- 12-0' 13 millim. wave-length. From the 
internal angles of this lino issue laterally equidistant bright streaks 
inclined to the axis of the spark in the direction of motion of the 
positive electricity. This microscopic structure (the regularity of 
which is sometimes surprising) is often found also just as distinct 
on the fine side branches which break forth from the positive part 
of the spark-path. I remark, further, that the soot-particles wnich 
exhibit the structure are in some measure fixed to the glass surface ; 
for when the layer of soot is removed, say, with a fine hair pencil, 
the dark streak in the axis of the spark remains adhering, though 
of course the microscopic delicacy of the figure is destroyed. — 
Sitzung der math.-naturiv, Classe dtr haiserl, Akad. d. Wissensch, in 
TTtVn, May 15, 1874. 

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XXVI. On the Opacity of the Developed Photographic Image, 
By Captain Abnby, KE.y F.R.A.8., F.C.S.* 

IN a series of pictures of the sun which have lately been taken 
by photography^ I found the opacity of the image by no 
means varied directly as the time of exposure. This caused me 
to institute an inquiry into the relation of time of exposure and 
intensity of light on the one hand, and the resulting opacity of 
the image on the other. 

Primarily it was necessary to obtain some known gradation 
of intensity of light, and then to measure the resulting opacities 
caused by it on a photographic plate. The gradation was ob- 
tained by causing a " star ** to revolve rapidly round its centre. 
The " star " was cut out with great exactness from white card- 
board and made with eight '' points.^' The curve of each point was 
made to take the form of a portion of an equiangular spiral. 
By this means an arithmetical progression of white was obtained 
when the star was made to rotate. When revolving in front 
of a black background, at two inches from the centre of the card 
(and within that distance) pure white was obtained ; whilst at 
fourteen from the centre pure black was obtained. The black 
background employed was of such a dead nature that sunlight 
gave no appreciable shadow on it when an opaque body was 
placed before it. 

The star was made to revolve at the rate of fifty revolutions a 
second. In some cases a dead-black star was made to rotate 
before a clear sky, the only access of light being through the 
openings of the points. • 

* Communicated by the Author. 
Phil. Mag. S. 4. Vol. 48. No. 317. Sept. 1874. M 

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Captain Abney on the Opacity of the 

Plated were exposed on this object^ the negatives being ob- 
tained by the ordinary wet process, with simply iodised collo* 
dion, an 8-per-cent. nitrate-of-silver bath, and 4-per-cent. iron 
developer. The strength of the developer was afterwards varied ; 
but for the purposes of these experiments any variation was ex- 
cluded. Other negatives were obtained on dry {Elates made with 
bromised collodion, a 16-per-cent. nitrate-of-silver bath, albu- 
men preservative (washed off, after application, as far as possible), 
and alkaline development of one particular strength. By alka- 
line development, as is well known, the bromide of silver is re- 
duced to metallic (or oxide of) silver in situ, no free nitrate of 
silver being applied to the image during development. The 
opacity of the image obtained by this method is particularly 
adapted for giving the necessary means of measuring the action 
of any relative intensities of light acting on the silver for any time. 

In order to determine the relstive opacities of the image, it 
was necessary to obtain some standard scale with which to mea- 
sure. The ordinary methods were tried without success, the 
image being '' matt,'' or only translucent. Failure with them 
was inevitable. After various experiments with coloured gela- 
tine wedges, I determined to use coloured glass wedges, and, 
owing to the kindness of Mr. Browning, obtained three smoke- 
coloured ones, corrected for refraction by crown glass. These 
in varying combinations have given me every thing that could be 
desired. The mounting I adopted for them is as follows. 



A is the wedge in position, B a space in the frame E, in which 
any glass whose opacity is to be measured is placed, C a slit, 
and D a fixed scale dividing the wedge into arbitrary divisions. 
In actual use the whole of the frame was glased with finely 
ground glass, the slit being next to it, and the wedge against 
that again. When measurements of opacity were taken, the 
glass to be tested was nlaced in B and a light placed at a known 
distance behind the slit. Great care was taken to ensure the 
equal illumination of C. The length of the wedges are severally 
6*5 inches. They do not give a sero of absorption at their thin 

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Developed Photogrtqkhic Image. 163 

ends^ it being found necessary in grinding to have an appreciable 
thickness. I was enabled to calculate the relative absorptive 
values of each wedge ; and the following Table will give an idea 
of the degree of accuracy with which they were scaled. The 
values are given in lengths of a half-inch s(»de, starting from the 
calculated sero of the wedge which I have called A. Each of 
the wedges were reduced to the same scale. The numbers refer to 
different opacities which were measured. A mean of six read- 
ings was taken in each case ; and in no instance did any reading 
vary more than '15 from the mean. 




No. I. . 

. 715 



No. II. . 

. 10-21 



No. III. . 

. 12-44 



No. IV. . 

. 17-60 



No. V. . 

. 18-60 



From careful measurements it was found that the coefficient 
of absorption for each unit of scale of wedge A for the light with 
which the measurements were taken was *192. 

The photographs of the rotating star were taken of the full 
size of the original, only half of the disk being in some cases on 
one plate. Strips were cut from these negatives, one edge 
always passing through the centre of the image of the star. The 
relative transparencies of every \" or ^" were obtained by •com- 
parison with the wedges. From these values the accompanying 
curves (fig. 2) have been formed, the ordinate being the translu- 
cenc^, whilst the abscissa is a measure of the intensity of the 
original reflected light. Only four results are shown — ^two ob- 
tained by wet, and two by dry plates. About thirty were 
measured with almost identical results. 

Each strip was compared with the wedge by daylight^ and 
also by an artificial monochromatic light. The results obtained 
by the one were nearly proportional to those obtained by the 
other ; hence only one curve for each strip is given ; and this 
was obtained by the latter light. To guard against a false ratio 
of intensity of light due to the lens, negatives of the star were 
takmi at different parts of the plate, and a mean taken. As the 
lens used was non-distorting and of long focus, the edge and 
centre of the plate, when directed towards the sky or on a uni- 
formly white surface, had sensibly the same illumination. Each 
portion of the strip cut from the negative whose opacity was 
to be compared was placed above the wedge, at B, and opposite 
the slit C. These were clamped together and moved till Ught 
from behind, shining through the slit and through the image 
and the wedge respectively, appeared of the same brightness on 

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164 On the Opacity of the Developed Photographic Image. 

the ground glass. The position of the slit in regard to the scale 
was noted, and the intensity of light transmitted calculated by 
the ordinary formula. Each strip was compared six times — 
three times by myself^ and three times by an assistant. A mean 
of the six readings was taken as correct. 

Fig. 2. 

F C 

A and B tre the curves given by the images on the dry plates. 

C and D are the curves given by the image on wet plates. 

The dotted lines indicate the line whose ordinates give an arithmetic 
progression of transparency, £ F being unity or transparency. 

FG represents the length of the strips examined, and therefore the 
varying intensity of Ught, F being zero and G the maximum. 

Regarding the curves given by the dry plates^ if we sup- 
pose 'that varying intensities of light cause a corresponding re- 
duction of the bromide of silver after development^ it can be 
easily demonstrated that the intensity of light passing through 
the image after clearing away the unaltered bromide would be 

l'=:n.e-", (a) 

where n and k are constants depending on the thickness and 
opacity of the bromide film^ and I the intensity of the light pro- 
ducing any one part of the image — ^that is, on the supposition 
that the image is formed of matter continuous but of varying 
density. This is not the case^ but there is an approximation to it. 
Under the same supposition we can assume that there is a function 
of time into a function of intensity of light acting on an infi- 
nitely thin layer of the bromide of silver which will cause an 
entire reduction of the bromide on development : this we might 
call a state of saturation. In the image of the star there may 
be some point where the upper layer of bromide (of infinite 
thinness) is saturated. From that point along the image to be 
produced bv the higher intensities the whole surface is satu- 
rated^ and the saturation must gradually approach the bottom 
surface. From the point where the whole depth of the layer is 
saturated^ along the image to be produced by still higher inten- 

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On the Behaviour of certain Fluorescent Bodies in Castor^oil. 165 

sities, there can be no further change. Here it can be demon- 
strated that, between the two points above alluded to, the curve 
should have the form 

V^pl-U-r\ {0) 

where p, q,r vre constants, and I is the original variable inten- 
sity producing the image. From the last point parallelism 
would result, and y would become a constant. Theoretically, 
then, the measure of the varying translucency would be com- 
pounded of (a), (fi)f and a straight line. 

The curves shown above lead us to suspect that this is the 
practical result of increase of intensity and time. From other 
experiments, however, I am inclined to think that even where 
there is no saturation the relation between time and inten- 
sity is not so simple as has hitherto been imagined. When 
light actually reduces bromide without the aid of a developer, 
a compound curve somewhat similar to (a) and 09) will result. 
In collodio-chloride printing on glass a like result would oc- 
cur. Presumably the same also occurs when printing on albu- 
menized paper. The curves deduced by experiment, and also 
from calculation, show the reason why iu a negative the detail in 
the shadows and highest lights is more difficult to render 
faithfully than in the half-tones. They may also show why in 
a print the details in the first-named portions is liable to be 
obliterated, even should they be well defined in the negative. 

The curves measured from the dry plates show that bromide 
of silver is less sensitive to low intensities of light than is the 

The action of different strengths of developers I propose to 
treat of in a separate communication, as also the relation between 
time of exposure and intensity of light. 

XX VII. A Note on the Behaviour of certain Fluorescent Bodies 
in Castor-oil. By Charles Horner'^. 

SOME colouring-matters derived from woods, not showing 
any fluorescence when dissolved in water, alkaline solu- 
tions, alum, or alcohol, are found to exhibit this phenomenon on 
treatment with castor-oil ; whilst other substances, which fluo- 
resce in alcohol &c., are observed to show this property with 
augmented intensity. 

To obtain clear solutions, the materials are first boiled in 
alcohol, filtered, evaporated to dryness, and then heated with 
the oil. On transferring some of the prepared solution to a 
test-tube and reheating, the fluorescence disappears as the tem- 

* Communicated bv the Author. 

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166 Baron N. Schilling on the Constant Currents 

Grature approaches the boiling-pointy bat retoms on cooling, 
oreover this operation may be repeated without the substances 
suffering decomposition. Cudbear, camwood, logwood, and tur- 
meric are selected as illustrations of the properties citdl. 

Cudbear yields a brilliant orange fluorescent light, and is 
idsible in diffused daylight without the agency of a condensing 
lens, which is necessary to show it in an alcoholic solution. 

Camwood exhibits a powerful apple-green fluorescence, 
although wholly destitute of this propeorty in aqueous or alco- 
holic media. The spectrum of the fluorescent light is continuous 
from E downwards, interrupted by two narrow faint shadings 
situated at 8| and 5 of Sorby's soede. 

With regard to logwood, unless the castor-oil solution be sa- 
turated, sunlight and a lens are requisite to bring out its fluo- 
rescent character. The colour very much resembles that of 
camwood, but is distinguished by its spectrum, which is conti- 
nuous from b, but interrupted by two shadings at 4^ and 5}. 

Turmeric is well known to fluoresce powerfully in alcohol a 
yellow-green, and in benxole a blue-green. In castor-oil, how- 
ever, the fluorescent light is at least three times as bright as 
in other fluids, and may be described as a vivid emerald-^reen, 
evident in the dullest daylight ; but if a flat bottle of the solution 
be placed on black velvet behind rather deep cobalt-glass when 
the sun is shining, the phenomenon is of a most brilliant descrip- 
tion, and without exaggeration may be compared to that pro- 
duced by the beautiful uranium-glass. The spectrum furnished 
by the fluorescent light is characterised by transmission of red 
and green rays, and blue to F, with a faintly perceptible shading 
at the yellow end of the green. 

These facts therefore show that, in studying the phenomena 
of fluorescence, advantage should be taken, whenever possible, 
of this valuable solvent property of castor-oil. 

XXVIII. The Constant Currents in the Air and in the Sea : an 
Attempt to r^er them to a common Cause, By Baron N. Schil- 
ling, Captain in the Imperial Russian Navy. 
[Concluded ftrom p. 109.] 

AS we are speaking of wave-motion, it will not be out of 
place to mention here a circumstance which will subse- 
quently be of importance for our argument. 

It is that the theory of waves, which is commonly laid as a 
foundation for all tidal phenomena, has called forth two views 
which cannot possibly be both together correct. In the first 
place, it is generally assumed that the flood tide rises just as far 

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in the Air and in the Sea. 


above the ordinary aea-level aB the ebb sinks below it. Secondly, 
it is assumed that the middle time between high and low water 
corresponds to the normal level. The highest water is formed 
by the two cusps A and E (fig. 8) of the tidal ellipsoid APES, 

Fig. 3. 

and the lowest bv the circle P S, which halves the surface of the 
ellipsoid at its mmor axis. The normal level will therefore, ae- 
cording to the common assumption, be found on the circles D C 
and i^^ 6, which run parallel with the circle P S and are distant 
45^ of arc both from the points A and E and from the circle 
PS; so that PF=FE and PC=AC; that is, about three 
hours after flood the normal level, and three hours later the ebb 
comes in. On this assumption, however, the superficial space 
of the surfaces A C D and E F 6 together, occupied by the flood 
tide, is 2^ times as small as the superficies of the middle zone 
C F O D, in which the water stands at the ordinary level. But 
since the water which forms the accumulation of the flood can 
only be derived from the ebb-zone, it is clear that, on this assump^ 
tion, the same mass of water must rise considerably more on the 
smaller space than the water-surface sinks in the ebb-zone. If, 
on the other hand, we adhere to the assumption that the water 
rises as high above the normal level as it sinks below it, the sur^ 
face occupied by the two floods must be just as great as that 
occupied oy the middle ebb-zone, and the two circles at which 
the normal level is found must be only 30^ distant from the 
central circle, but 60° from the cusps A and E of the ellipsoid. 
Flood tide would thus last eight hours, but ebb only four. Or 
the water must fall as much in the last two hours of its going 
down as in the first four after high water, and likewise rise as 
much in the first two hours after its lowest as in the remaining 
four. Probably the reality lies between the two assumptions ; 
that is^ the rise of the water during flood is probably more con- 
siderable than its fall during ebb, and, on the other hand, the 

Digitized by VjOOQ IC 

168 Baron N. Schilling on the Constant Currents 

circles of normal level are more than 45^ and leas than SOP of 
arc distant from the cusps of the tidal ellipsoid 'I'. 

As at coasts the currents produced by the flow and ebb are 
always observed to flow alternately in precisely opposite direc^ 
tions, it is generally believed that the attraction of the moon and 
sun cannot exert any influence on the constant currents. Miihry 
says, *' It is scarcely necessary to mention that the tidal motion, 
which daily carries its two meridian waves round the globe, is 
something altogether different from the rotation-current: the 
former extends over all latitudes, and generally occasions no 
forward motion of the mass of water, but only waves, t. e. oscil- 
lations .... Such an assumption is contradicted also in a pe- 
culiarly decided manner by the return* currents flowing on both 
sides of the equatorial current in a wide semicircle from west to 
east (therefore against the tide-wave) — the compensation-arms 
of the rotation-current, which at the same time enclose each a 
wide central space filled with still water and floating seaweed, 
the Sargasso-seas. How can the tide-wave call forth such phe- 
nomena ? We are of opinion, moreover, that, if there were no 
moon, the equatorial current would still exist while the earth 
revolved on its axis ; but it would not exist if the globe did not 
turn on its axis, even though the moon should daily travel round 
the earth^t. 

We cannot possibly share this opinion of Miihry^s. We will 
besides let the thing speak for itself, subjecting the action of the 
attraction of the sun and moon to a closer consideration. 

Suppose the circle AGED (fig. 4) to be the equator, and 
L the centre of the moon, which we will imagine in the plane of 
the equator. If, then, the earth had no rotation, the surface of 
the sea must take the form of the dotted line aced. To form 
this ellipsoid, currents must proceed from all sides towards the 
cusps a and e, lasting until the ellipsoid had attained its due 
elongation. But since the earth is constantly turning, the moon 
relatively to the earth will have already arrived at another point 
before the water and the atmosphere have had time to properly 
form the ellipsoid aced. Of course the currents will immedi- 
diately direct their course to the new point of attraction ; and 
since this again alters its position, a current must be produced 
in the air and water which must endeavour to follow the motion 
of the moon and shift the cusps of the ellipsoid perpetually from 
east to west. On the other hand, by the shifting of the moon 

* It appears, therefore, that the zero-point of the tide-gauffes has not 
et received its true position. This must lead to erroneous resulti in lerel- 
Jng-surveys Tvhen the heights of two neighbouring seas are to he compared 
in which the heiehts of the tides differ (as, for instance, Panama). 

t Miihry, Veber die Lehre von den MeereS'Strommnffen, p. 9. 


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in the Air and m the Sea. 


from L to I/, all the points in the titeecaf are moved somewhat 
nearer to the moon, and therefore the attraction of the moon on 

Fig. 4. 














all these points is increased; while every point in the fitc e^da 
has removed a little further from the moon, and is consequently 
less attracted. We will represent the attraction of the moon by 
two threads L c and L d fastened to the circle. We will gradu- 
ally more and more draw the thread L c, to represent the con- 
stantly augmenting attraction of the point c. We will constantly 
let the thread L d give way, to imitate the diminution of the 
attraction of the point d. Of course, through greater tension of 
the thread Lc and continual yielding of the thread LJ, the 
points c and d receive a motion in the direction of the arrows C 
and D. This motion will be the quicker the greater the circle 
to which the points belong, because in greater circles the change 
of distance from the moon, and consequently the alteration of 
her attraction, is more considerable for every point than in 
smaller circles. 

All that we have just said of the moon holds good also for the 
sun, with onl^ this difference — that the motions of air and water 
produced by its attraction will be somewhat less than those pro- 
duced by the moon. 

We see therefore that the attractions of the sun and moon 
must each present two reciprocally counteracting developments 
of force. The one, which cidls forth an east-to-west current and 
corresponds to high water, we will henceforth name the flood- 
current force ; the other, corresponding to the ebb and impelling 
air and water from west to east, we will call the ebb-current 

If these two forces are of equal intensity, they will balance 
each other and produce no current ; but as soon as one of the 
two is greater, the water and air will be subject to the action of 
the greater force and move onward with the velocity correspond- 
ing to the difference between the two forces. 

Digitized by VjOOQ IC 

170 Baron N. Schilling on the Constant Currents 

Before we compare^ howeverj with one another the quantities 
of these two forces, it will be necessary to illustrate further what 
has been said, representing the earth in the plane of the meridian. 

Let the circle P A S £ (fig. 5) be a terrestrial meridian, and 

Fig. 6. 

L the centre of the moon (or of the sun), which, as before, is on 
the equator. The dotted Wnepase marks the form of the tidal 
ellipsoid. Through the rotation of the earth the moon appa- 
rently moves from east to west ; with it the ellipsoid /? a s e turns 
about the axis P S, and develops, as we have seen, at the equator 
two forces opposed one to the other. The one, the force effect- 
ing the flood-current, directs its course from east to west, and 
in the case here given is strongest at the equator, on which the 
cusps of the ellipsoid move forward as long as the moon is on 
the equator. This force will act in nearly the same direction on 
both sides of the equator; only it must rapidly diminish as the 
latitude increases; and in the latitude of the points nt, where 
there is no rise of the water, the force acting from east to west 
must be =0. Further polewards the tendency to form the 
tidal ellipsoid may probably develop an inconsiaerable current 
from the pole towards the equator, as shown by the lines p L 
and s L. 

The ebb-current force acts from west to east, as if the circle 
pCsD revolved in this direction on the axis PS. As alreadv 
said, it arises from the circumstance that all points in one half 
of the earth are brought nearer to the moon by the rotation, 
while all those in the other half are carried further from it. The 
ebb-current force has its greatest intensity at the equator, and 
diminishes very gradually on both sides of it, since the parallel 
circles in low latitudes become only gradually smaller. Only in 
high latitudes, where the circles diminish rapidly, does the force 
of the ebb-current quickly diminish ; and only at the poles does 
it entirely cease. 

Since, as we have shown, the flood rises more above the nor- 

Digitized by VjOOQIC 

m the Air and in the Sea. 171 

Dial level of the sea than the ebb sinks below it, we think we 
can assume, as an hypothesis, that the force of the flood-current 
will also be greater than that of the ebb-current. 

In our case, if the cusps of the ellipsoid are on the equator, 
and therefoie both forces develop their maximum on that circle, 
the greater force must overpower the smaller, and both in air 
and sea a current from east to west must prevail all along the 
equator. On both sides of the equator the force of the flood- 
current, acting from east to west, diminishes rapidly polewards; 
the counteracting force of the ebb-current diminishes more 
slowly. Therefore, at a certain distance from the equator, the 
greater but rapidly diminishing force directed from east to west 
will be only just as great as the smaller only slowly decreasing 
force directed from west to east. In these parallels the forces, ba- 
lancing each other, will generate no current. Still further pole- 
wards the force of the flood*current, still continually more de- 
creasing, will be less than that of the ebb-current, and, both in 
the sea and in the atmosphere, currents from west to east will 
make their appearance. In the latitude of the points m the 
east-to-west force ceases entirelv ; while the opposite force has 
in this latitude lost onlv a small portion (less than half) of its 
action, and hence mav here produce a considerable current. In 
higher latitudes the force of the ebb-current will also quickly 
diminish, and the currents from the west become considerably 
less, and their direction probably turn more towards the equator. 
Accordingly, in the northern hemisphere, in high latitudes, cur- 
rents will arise from the north-west, and in the southern from 
the south-west. 

TVlien, therefore, the moon and sun are at the same time in 
the vicinity of the equator, a current in air and sea must flow 
there from east to west. On both sides of the equator this cur- 
rent will diminish polewards until it entirely ceases ; and there 
must thus be produced a streamless zone parallel to the equator. 
Further polewards a west-to-east current will prevail, which 
must at first increase gradually until it attains its maximum ; 
then will this current dso again diminish gradually, and in high 
latitudes flow from the north-west in the northern hemisphere, 
and from the south-west in the southern. 

In reality we find this to be the constitution of the currents. 
In middle latitudes constant west winds and sea-currents directed 
eastwards prevail. In the latitude of about 80° there is in each 
hemisphere a zone of no current, and in the tropical regions we 
find currents flowing perpetually from east to west, both in air 
and sea. An apparent exception is, that on the eouator we 
meet with a zone m which no current is perceptible eitner in the 
atmosphere or in the ocean. 

Digitized by VjOOQ IC 

172 BaroD N. Schilling on the Constant Currents 

This circamstance seems at the first glance to contradict the 
theory of the moon's attraction; yet the origination of this 
equatorial streamless zone is easily explained when we reflect 
that the moon and san are simultaneously in the vicinity of the 
equator only for a very brief time twice yearly. They usually 
describe parallel circles which lie between the equator and the 
tropics ; the moon only goes sometimes slightly beyond the last- 
mentioned circles. The ellipsoid arising from the united attrac- 
tions of the moon and sun must always have its cusps between 
the sun and moon ; and hence these cusps must mostly describe 
parallels between the equator and the tropics. 

Supposing the tidal ellipsoid in the position asep (fig. 6), 

Fig. 6. 

its major axis a e making a certain angle with the equator 
A C E i)^ by the earth's rotation on its axis P S the cusps a 
and e of the ellipsoid will describe the parallel circles a a! ^nd 
eef } and therefore the maximum of the flood- current will also 
be observed on these parallel circles. The current will also not 
preserve its exact east- to- west direction^ but^ as shown by the 
arrows B and F^ come from E.S.E. in the southern hemisphere, 
and from E.N.E. in the northern. 

On both sides of the parallel circles a d and e ff the force of 
the flood-current will, as already said, diminish rapidly ; while 
the ebb-current keeps, as before, the maximum of its force at 
the greatest circle, therefore at the equator, and, also with this 
position of the ellipsoid, diminishes only slowly polewards, con- 

Digitized by VjOOQ IC 

m the Air and in the Sea. 1 73 

sequently will have already become slightly less at the parallel 
circles al a and ef e, on which the maximum of the flood-carrent 
is found. The direction of this current will also not be purely 
from west to east, but, as the arrows C and D show, alternate 
between W.N.W. and W.S.W. The opposite forces of the ebb- 
and flood-current mast therefore on both sides of the parallel 
circles a a' and e ef balance one another and form a zone of no 

This appears to occur in the vicinity of the equator and of the 
parallels of 30^ latitude, the zones of calms and of the Sargasso- 
seas being found there. In the latitudes of the parallel circles 
a a' and ee! must be the maximum of the east-to-west flood- 
current ; this perfectly corresponds with the phenomena of the 
trade-winds and the equatorial currents. Polewards from the 
streamless zone in the 30th parallel of latitude the rapidly dimi- 
nishing force of the flood-current must be overpowered by that 
of the ebb-current, and a constant current from west to east be 
produced — which also actuaUy happens ; for between the 40th 
and 50th parallels of latitude, or thereabouts, both in the air 
and in the water, in all oceans and in both hemispheres, a cur- 
rent directed eastwards is constantly observed. 

Hence, it seems to us, the action of the attraction of the sun 
and moon explains the origination of the trade- winds and anti- 
trades with their zones of calms, and the rotation-currents run- 
ning parallel with the equator, with the Sargasso-seas and the 
streamless equatorial zone, considerably better than all hitherto 
existing hypotheses. 

If our explanation of the trade- winds and equatorial currents 
is correct, also the position and the breadth of the current-zones 
and the strength of the currents must themselves depend entirely 
on the position of the tidal ellipsoid or on the position of the 
moon and sun with respect to one another and relative to the 
earth. When, for instance, moon and sun are both very near 
the equator, the equatorial calm-zone must be non-existent, the 
calms of the tropics must approach towards the equator, and the 
constant west winds blow with greater force in lower latitudes. 
Whether all this happens is unknown to us ; yet strong west 
winds usually rage in Europe at the times of the equinox. 
Just so, perhaps, it sometimes happens that ships cross the line 
without calms ; but whether this chiefly coincides with the time 
when the moon crosses the equator we know not. 

When moon and sun are at the same time in the vicinity of 
the tropics, the current-zones must be displaced polewards, and 
the equatorial calm-zone be especially broad. It is possible that 
then the ebb-current may predominate in the middle of the zone, 
and that this circumstance accounts for the west-to-east current 

Digitized by VjOOQ IC 

174 Baron N. Schilling on the Comtani Currents 

which flows in a narrow band along the equator and is named^ 
in Berghaus's 'Chart of the World/ the '' equatorial counter- 
current/' In the air this current does not exist. It would 
therefore have to be ascertained if this equatorial counter-current 
is a constant one or is only to be observed when the moon ap- 
proaches the tropics^ and whether it is not wanting when the mm 
and moon are simultaneously in the vicinity of the equator. 

The shifting of the trade-wind zones appears to be on the 
whole more considerable than that of the sea-currents, and seems 
in many cases to coincide with the change of the seasons of the 
year — which, then, proves that the sun by its heat also exercises 
an influence on the trade-winds. This probably takes place 
chiefly through the sun's action on the aqueous vapour in the 
atmosphere and through other collateral circumstances. The 
main cause, however, of the production of the trade-winds must 
certainly be ascribed to the attraction of the moon and sun ; 
and hence their position relatively to each other must have a 
sensible influence upon various atmospheric phenomena. It 
appears, therefore, possible that the well-known old popular tra- 
dition of the phases of the moon affecting the change of the 
weather may have some foundation ; only it might be more cor- 
rect to ascribe this influence not to the phases, but to the dis- 
tance and declination of the moon, which latter, it is true, stands 
in a certain connexion with the moon's phases and the sun's 
declination. At the times, namely, of new and full moon the 
difference between the declination of the moon and that of the 
sun is always inconsiderable, although at the time of fuU moon 
the sun and moon are in different hemispheres but at nearly 
equal distance from the equator. 

Only at the time of the quadratures can the difference of de- 
clination of the sun and moon be considerable ; at the periods of 
the equinoxes and the solstices the difference rises at the utmost 
to near 28^ 

From the production of currents by the moon's attraction not 
only can the sea-currents parallel to the equator, but also the 
meridional currents be naturally derived. 

If the whole earth were covered with water, the equatorial 
current would flow round it unhindered ; but now the continents 
stand as insuperable obstacles in the way of this motion. As, 
however, the cause of the flow is not hereby removed, the cur- 
rent in the ocean must continue and cannot suddenly cease on 
impinging against the coast, but must change its dire^lion ac- 
cording to the position of the shore. Thus we aae. in Ae 
Atlantic Ocean, that the southern equatorial stream itvides at 
Cape St. Boque (which opposes it Uke a wedge), and, following 
the direction of the coast, is turned aside, part to the north-west 

Digitized by VjOOQ IC 

m the Air and in the Sea. 175 

and part to the sonth-west. The north-west branch of this car- 
rent unites in the Caribbean Sea with the northern equatorial^ 
and in this way impels almost the whole of the warmed water of 
the surface of the Atlantic equatorial zone into the Gulf of 
Mexico. The great mass of this warmer and therefore lighter 
water driven together by the equatorial current must, of course, 
have the tendency to spread over the colder and heavier water, 
and to flow off northward. Thus arises, then, a current of warm 
water flowing out of the Gulf of Mexico, commonly known by 
the name of the Gulf-stream. 

The motive force of the Gulf-stream musttherefoiebe derived 
partly from the pressure of the equatorial current, partly from 
the tendency of the warm water to spread over the cold of the 
higher latitudes, but partly also from the attraction of the cur- 
rent, directed eastward, of the middle latitudes ; but all these 
causes spring directly from the attraction of the sun and moon, 
which thus must be regarded as the prime motive force of the 

The eastward current of the middle latitudes and the north- 
east movement of the entire northern portion of the Atlantic 
Ocean form the continuation of the Gulf-stream, and hence are 
often designated by the same name — to which we have no ob- 
jection, if it be kept in view that the prime cause of motion of 
the two last-mentioned currents lies in the force of the ebb-cur- 
rent. As already said, in about 30° latitude this force com- 
mences to overpower the force of the flood-current, and develops 
the maximum of its effect somewhere between the 40th and 50th 
degrees of latitude ; farther polewards it diminishes considerably, 
and becomes so feeble that it is no longer perceived as a current. 
Nevertheless a slight movement eastwards appears to extend 
considerably further towards the pole, and gradually to collect 
the warmer water on the coasts of England and Norway. This 
warmer water is derived partly from the Gulf of Mexico; but 
part of it may have been heated on the surface of the ocean in 
higher latitudes. The ebb-current, therefore, collects the su- 
perficial warmer water in the eastern part of the ocean ; and the 
tendency of the warm water to spread over the colder impels it 
north-eastward, and thus accounts for the motion of the north- 
ernportion of the Atlantic. 

The principal force of the -ebb-current, flowing eastward, is 
deflected south by the coasts of Europe, and, following the coast 
of Africa, returns again into the equatorial stream. The attrac- 
tion of the latter perhaps forms the principal cause of the south- 

* Self-evidently it is not meant that the tan and moon's attraction heats 
the water of the Gnlf of Mexico ; bat it is that which generates the equa- 
torial current and thus odlects the warm water in the gnlf. 

Digitized by VjOOQ IC 

176 Baron N. SchilliDg cm the Constant Currents 

ward bead, but may be assisted in some degree by the tendency 
of the particles to move towards the equator^ produced by the 
rotation of the earth. Only a small portion of the east-directed 
current passes Cape Finisterre unhindered, and continues its 
course in the natural direction along the north coast of Spain 
till the coast of France compels it to curve sharply to the north- 
west and follow exactly the course of the shore of the Bay of 
Biscay, under the name of the Rennell current, to be lost at the 
English coast in the general north-east current of the Atlantic. 
The Rennell current shows distinctly how much power the 
direction of coasts has to determine that of currents, even to 
reverse their direction. 

A portion of the South-Atlantic equatorial current turns to 
the south-west from Cape St. Roque, along the coast of South 
America. The impelling force of this Brazilian current is the 
same as that of the Oulf-stream — partly the pressure of the 
equatorial^ partly the high temperature of the water heated in 
the Atlantic Ocean and collected at the coast by the equatorial 
current, and partly the attraction of the eastward-directed ebb- 
current fuiibtioning in the middle latitudes, into which the 
greater portion of the Brazilian current passes to form the South- 
Atlantic rotation-current. This latter, after crossing the ocean 
from west to east, and having curved a little to the north, strikes 
upon the African coast, and (for the same reasons as those above 
discussed for the northern hemisphere) returns along it again 
to the equatorial current, forming the South-Atlantic Guinea 
current. The entire rotation-current, then, is originated by the 
attraction of the moon and the sun, as this by its direct action 
carries the water in the equatorial regions from east to west, and 
in the middle latitudes from west to east, and hence also gene- 
rates indirectly the currents flowing in the direction of the meri- 
dian (the Gulf-stream and the North-African current, the Bra- 
zilian and the South-Ouinea currents). 

In the entire southern hemisphere all the cold polar currents 
are directed north-east, which coincides perfectly with the action 
of the moon's attraction in higher latituaes. Only in the north- 
em hemisphere the directions of the cold polar currents contra- 
dict the laws of the moon's attraction ; for the Greenland cur- 
rent and the cold current of the Japanese sea have a south-west 
direction, and not a south-east one, which they should have ac- 
cording to our considerations. This, however, may well have 
its cause in the action of the ebb-current, directed from west to 
east, which gradually withdraws the warm northward-flowing 
current from the coast ; and this is replaced partly by the cold 
water of the bottom, but principally bv the less-salt and there- 
fore lighter water derived from the melting of the ice. A similar 

Digitized by VjOOQ IC 

in the Air and in the Sea. 177 

phenomeuoQ is often produced at coasts by the action of the 
wind; and those who have sought a sea-bath will remember 
that with a land-breeze the water is always colder than with a 
sea-breeze. The former removes the warmed superficial water 
from the coast^ by which the colder water beneath is brought to 
light. The sea-breeze^ on the contrary^ drives to the shore the 
water which has been warmed on the surface of the sea. WI at 
the wind does in this case may well be brought about in a 
higher degree by a permanent sea-current. In the depths, 
even in the northern hemisphere, the polar currents appear to 
be directed to the south-east. This is demonstrated by the 
many icebergs which, near Newfoundland, cut through the 
Gulf-stream in that direction. Dana^s chart of the isothermal 
lines of the sea-surface in the coldest month^, on which the dis- 
tribution of the corals is given, permits us also to draw a similar 
conclusion. The polar limit of the coral zone, both in the 
Atlantic and in the Pacific, is (probably on account of the water 
being too cold) about lOP nearer the equator on the east side 
than on the west side of the same ocean. It is interesting that, 
according to this chart, the northern boundary of the corals is 
10 degrees more to the north in the Pacific than in the Atlantic 
Ocean. The reason is probably to be sought in the fact that the 
Atlantic forms almost the only discharge^ and the main supply, 
of the north polai' basin. 

The alternating warm and colder strips of water in the Gulf- 
stream, as well as in the Kurosiwo, seem to us to favour the 
idea that the force which carries away from the coa^t the entire 
current eastwards is not constantly of equal strength, but, so to 
speak, has a reflex action — which perfectly corresponds with our 
hypothesis, according to which, in the middle latitudes, the force 
of the ebb-current must on the whole take the upper hand, but, 
through the westward-directed force of the flood-current, may 
be subject Co periodical interruptions. 

L. von Schrenk, Member of the Academy of Sciences of St. 
Petersburg, has recently, in a very interesting work [StrdmungS' 
Verhalinisse im Ochotskischen und Japanischen Meere), pointed 
out that in the Yellow, as well as in the Japanese and partially 
in the Ochotsk Sea^ the temperature of the water is constantly 
lower at the east coasts of the continent and the islands than at 
the west coasts. We see in this a proof that in these inland seas 
there is the same tendency of the water to move eastwards, and 
that thereby the upper warmer water is accumulated at the east 
side of the sea or at the west coast of the land. In the 
White Sea also, and the Varanger Fjord in North Lapland^ 
the temperature of the water is higher in the eastern parts than 
* Stieler'B Hand-Atlas, 1867, No. 9, Cartoo. 

Phil. Mag. S. 4. Vol. 48. No. 317. Sept. 1874. N 

Digitized by VjOOQ IC 

178 Baron N. Schilling on the Constant Currents 

in the western. As we have already remarked, the warmer 
water accumulated on a coast must flow away polewards, while 
the cold water of the west side of the sea seeks to occupy the 
space left free, and so flows towards the equator. It is also in- 
teresting that Schrenk^ has pointed out the existence of strips 
of cold water in the warm current of the Japanese Sea. The 
colder but very slightly less salt water may, under some circum- 
stances, have exactly the same specific gravity as the warm, 
somewhat salter water; and hence they may flow a long time 
side by side without mingling. These strips of colder water 
have not yet been demonstrated in the Brazilian and Mozam- 
bique currents ; but it is probable that they are present there 
also, especially in the Brazilian current, which extends further 
south. Indeed it is likely that these warm currents are sepa- 
rated from the coast by colder water. 

The Mozambique current, it seems to us, strikingly corre- 
sponds with the theory of the moon's attraction. It has its 
origin in the equatorial stream of the Indian Ocean, then foU 
lows the east coast of Africa in a south-westerly direction, 
and, still foUowiug the coast, at the southern extremity of the 
continent takes a westward direction, but thereby comes into 
the region of the ebb-current and at once, with a remarkably 
sharp bend, returns eastward. We can only account for this 
sudden flexion by the action of the moon^s attraction ; for it 
is impossible to admit that the aspirating force of the Indian 
equatorial stream can occasion this sudden bend in order to 
carry the Mozambique current to the shores of Australia and 
New Zealand. Moreover the depth to which the constant 
ocean-currents extend appears to us to be explicable only by 
the attraction of the moon and the sun ; for it acts on all 
the water-particles as far as the bottom of the ocean, if its 
action below is slightly less than its action above. The cur- 
rents of the remaining oceans are so perfectly similar to those 
above discussed, that in describing them we should have to 
repeat nearly the same things. They are all originated prin- 
cipally, either directly or indirectly, by the action of the flood- 
and ebb-currents, and hence can only be satisfactorily explained 
by that action. 

The currents of the atmosphere rest at all events upon pre- 
cisely the same laws ; but air-currents are far more susceptible 
to all possible collateral causes than ocean-currents, and are 
therefore subject to many other influences, amongst which dif- 
ference of temperature plays a certain part. Unfortunately this 
influence has hitherto been considerably overrated; for polar 
and antipolar currents generated by difference of temperature 
* Op. cit. p. 66. 

Digitized by VjOOQ IC 

in the Air and in the Sea. 179 

have been regarded as the basis of meteorology, or as currents 
on which all the movements of the air depend. To this opinion 
we cannot assent ; on the contrary, we believe that in the atmo- 
sphere, just as in the sea, the principal motions take place in 
directions nearly parallel to the equator. 

Perhaps, in the future, with more accurate knowledge of the 
action called forth by the attractions of the sun and moon, we 
shall succeed in explaining the causes of rotatory storms by the 
two opposite directions of the flood- and ebb-current. May 
not in certain cases, at the time of the quadratures, the ebb-cur* 
rent caused by the moon meet at a certain angle the flood-cur- 
rent called forth by the sun and thereby produce the rotating 
motion f Up to the present time the important natural pheno- 
menon of cyclones has by no means been explained; for all 
hitherto-given explanations have been quite inadequate. 

As is known, these storms always have two motions — one 
rotating, and one progressive. The progressive motion corre- 
sponds well with the theory of the moon's attraction ; for these 
storms almost always commence in low latitudes, and, in both 
hemidpheres, the centre of the storm moves westward in the 
region of the flood-current, at the same time slightly increasing 
its distance from the equator and thereby arriving m the calm- 
zone of the tropic. Here the velocity of the progressive motion 
becomes cqnsiderably less, and its course makes a sharp curve 
eastward, the hurricane passing into the region of the ebb-cur- 
rent; and now, in both hemispheres, it moves with great velo- 
city to the east and somewhat polewards. Therewith its dia- 
meter gradually increases and the circular motion diminishes 
until the hurricane is lost in higher latitudes. The usual dura- 
tion, from beginning to end, of the hurricane is about 14 days. 

The rotating motion of these storms is subject to quite deter- 
minate but not yet discovered laws. In the northern hemisphere 
they rotate in the opposite direction to that of the hands of a 
cluck ; but in the southern hemisphere they go round in the 
same direction as the latter. In other words, in both hemi- 
spheres the storm always blows from the west on the side to- 
wards the equator, and from the east on the polar side. West- 
wards of the centre of the hurricane, the direction of the storm 
is always to the equator ; eastward of the centre, away from the 
equator; so that hurricanes rotate in an opposite direction to 
the cuiTcnts of the seas. Ordinary storms appear to stand in 
the closest connexion with cyclones ; at least this conjecture is 
corroborated by Buys-Ballot's law, according to which the winds 
revolve about the minimum of atmospheric pressure in the same 
direction as the cyclones. 

The explanation that the rotating motion of cyclones arises 


Digitized by VjOOQ IC 

180 Prof. Challis on the Hydrodynamical Theory of the 

from the rotation of the earth is altogether inadmissible ; for 
the hurricane always commences in very low latitudes^ with a 
diameter which seldom occupies more than 2 or 3 degrees of 
the meridian. The difference in magnitude of the parallel 
circles^ however^ i^ so inconsiderable that the air streaming to 
the centre can only be deflected by the earth's rotation to an 
angle of 2 or 3 degrees from the meridional direction. As- 
suming that the centre of the cyclone is^ at the beginning of the 
hurricane, in 10^ latitude, that its radius occupies 2 degrees of 
the meridian, and that the air requires two hours in order to 
traverse this distance, and retains during the whole time the 
rotation-velocity of the parallel circle which it has left behind, 
in this case the air- particles from the 12th degree of latitude, 
streaming to the centre of the hurricane, would deviate a little 
to the west from the meridian, forming with it an angle of 2^45'. 
Those from the 8th degree of latitude, streaming to the centre, 
would deviate eastwards, their direction forming with the meri- 
dian an angle of 2^ 21'. But this much too small deviation 
from the meridian cannot possibly occasion the rapid whirling 
motion of the storm. 

Not doubting that such a theory of the ocean-currents and 
the trade-winds, founded on the attraction of the moon, may be 
the correct one, we nevertheless acknowledge how much our view 
needs to be subjected to further elucidation. Time must bring 
a multitude of fresh observations before the special authorities 
can have spoken their last word on this subject. To us, how- 
ever, it will afford the fullest satisfaction if we have had the 
good fortune, by the foregoing analysis of our views, to contri- 
bute, at least indirectly, to the advancement of this department 
of physical geography, which has hitherto wanted a uniting fun- 
damental idea. 

XXIX. The Hydrodynamical Theory of the Action of a Galvanic 
Coil on an external small Magnet, — Part I. By Professor 
Challis, M.A., F.R.S.* 

1. rr HE mathematical theories of the physical forces which I 
-L have published from time to time in this Journal have 
been made to rest exclusively on the following hypotheses : — All 
visible and tangible substances consist of inert spherical atoms 
of constant magnitude, and all physical force is either mode of 
pressure of the aether on the surfaces of the atoms, or reaction 
of the atoms at their surfaces due to the constancy of their form 
and magnitude. The sether is supposed to be a continuous 
elastic substance, filling all space not occupied by atoms, of 
• Communicated by the Author 

Digitized by VjOOQ IC 

Action of a Galvanic Coil on an external small Moffnet. 181 

perfect fluidity, and of the same density every where when at 
rest, and when in motion varying in density always and at ali 
points in exact proportion to variations of its pressure. Also 
the size of the atoms is supposed to be so small that even in 
dense bodies they fill a very small portion of a given space. 

2. These hypotheses, which I have enunciated on several pre- 
vious occasions, are repeated here for the purpose of directing 
attention to what especially characterizes them. They involve 
no assertiun that is not comprehensible by the indications of com-- 
mon sensation and eaiperience. It is because they possess this 
character that the physical theories I have founded on them 
differ from those generally maintained by contemporary physi- 
cists, which rest for the most part on experimental data con- 

ioined with arbitrary hypotheses not in the same manner intel- 
igible. It does not, however, follow from the dissimilarity of 
the hypotheses that the two modes of philosophizing are con- 
tradictory to each other. This I think I shall be able to show 
by pointing out the distinction between their fundamental prin- 
ciples, and the consequent relation in which they stand to each 

3. For this purpose reference will be more particularly made to 
the physical theories of magnetism and galvanism, as proposed 
by Gauss and Ampere, or illustrated and extended by other 
physicists who have adopted their views. The object of all in- 
vestigations of this class is to deduce from the results of certain 
fundamental experiments, by the inter\'ention of arbitrary or 
provisional hypotheses, mathematical expressions of the laws of 
the phenomena. Accordingly natural philosophy is not thereby 
advanced beyond a stage analogous to that to which physical 
astronomy was brought by the results of Kepler^s observations. 
Newton*8 hypothesis of a gravitating /orc^ varying inversely as 
the square of the distance, and his discovery of the mode of cal- 
culating its effects by mathematics, were steps necessary for 
completing that science, inasmuch as they gave reasons for 
Kepler^s laws. In the empirical theories I am referring to, the 
consideration of physical force is included, and from certain 
hypothetical modes of action of the forces mathematical expres- 
sions of the laws of the phenomena are deduced. But con- 
fessedly the intrinsic nature of the forces, and the reasons for 
the facts and hypotheses on which the investigations rest, ai*e 
left undetermined. 

4. The final stage of physical investigation is reached when 
explanations of phenomena and of their laws have been given by 
means of mathematical deductions from hypotheses satisfying 
the condition of being intelligible from sensation and experience. 
Till this is done, we can hardly be said to have arrived at theory 

Digitized by VjOOQ IC 

182 Prof. Challis on the Hydrodynamical Theory of tlie 

properly so called. The antecedent steps of theory ought, for 
distinction, to be called empirical or provisional^ as resting on 
arbitrary hypotheses, and as subsidiary to true and complete 
theory. True theory rests on hypotheses that are not only com- 
prehensible^ but also ultimate and necessary — that is, such as do 
not admit of being accounted for by any ulterior hypotheses. 
This will be proved to be the specific quality of the hypotheses 
stated above (art. 1), if they should be shown to be adequate to 
the explanation of the nature, laws, and consequences of the 
operation of all the different kinds of physical force. To de- 
monstrate their adequacy for this purpose has been the express 
object of the many theoretical researches I have been occupied 
with relative to the modus operandi of physical force generally. 
This course of philosophy I propose to call Newtonian, its 
*' foundation ^' having been indicated by Newton in the Third 
Book of the Principia. (See the discussion of this view in the 
Philosophical Magazine for October 1863, p. 280.) 

5. Having thus pointed out that a distinction is to be made 
between empirical theory resting on arbitrary hypotheses and 
ultimate theory resting on strictly a priori hypotheses, I have 
further to state in what respect the two kinds of theory may be 
considered to be related to each other. Let it be supposed that by 
means of a theory depending on certain ascertained facts, and on 
hypotheses thereby suggested, a true mathematical expression 
of the laws of the phenomena proposed to be accounted for has 
been obtained. According to views entertained by some theo- 
rists of the present day, natural philosophy consists in thus 
arriving at phenomenal laws, and there is no occasion for any 
further investigation. But the principles of the philosophy I 
call "Newtonian^' demand that the explanations of all phe- 
nomena and their laws should be inferred by mathematical rea- 
soning from the before-mentioned fundamental hypotheses. 
Now this may be done in two ways — either directly, by in- 
dependent deductions from the a priori hypotheses, or inter- 
mediately, by deducing from the same hypotheses explana- 
tions of the facts and hypotheses which form the basis of a 
true empirical theory. It is evident that in either way the phe- 
nomena are shown to be consequences of the operation of intel- 
ligible causes, and are completely explained. It appears thus 
that the empirical method is subsidiary to the h prioii method 
whenever the explanation of phenomena is effected by the aid 
and intervention of the former, and that in this respect the two 
methods may be mutually related. These remarks will receive 
elucidation in the course of the subsequent discussions. 

6. I propose, in the first instance, to give an h priori expla- 
nation of the facts relating to the action of a large magnet on a 

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Action of a Galvanic Coil on an external small Magnet, 183 

small needle from whicb^ by the intervention of certain arbitraiy 
hypotheses, Gauss inferred the law of the inverse square in mag- 
netic action. For this purpose it will be convenient to refer to 
the detailed exhibition of Gauss's argument given in the Astro- 
nomer Royal's ' Treatise on Magnetism ' (Macmillan and Co., 
1870). I have already discussed this question on hydrodyna- 
mical principles in a " Note on the Hydrodynamical Theory of 
Magnetism '' contained in the Philosophical Magazine for July 
1869, to which I beg to refer for details of the mathematical 
reasoning relating to the physical conditions of magnetic force. 
I propose to reproduce here only so much of that discussion as 
may be required for understanding the subsequent theory of the 
action of the galvanic coil on a small magnet, which is the ulti- 
mate object of the present communication. 

7. In the article just referred to it is assumed that in a mag- 
netized bar there is a small and regular increment of atomic 
density from end to end, like that which must be produced by 
the action of gravity from the top to the bottom of a solid or 
fluid mass resting ou a horizontal plane. In a '' New Discus- 
sion of the Hydrodynamical Theory of Magnetism,'' contained 
in the Philosophical Magazine for June 1872, 1 have proved (in 
arts. 4-9) that if any body in which such gradation of density 
exists be traversed either by a steady setherial stream, or by a 
uniform series of undulations of the sether, a secondary steady 
stream will be produced by impulses continually given to the 
fluid in the direction from the rarer to the denser parts of the 
body, this being the direction of the contraction of channel 
by the occupation of space by the atoms. The application of 
this result forms an essential part of the hydrodynamical the- 
ories of electric and magnetic attractions and repulsions which 
I have proposed and discussed in several previous communica- 
tions. In the case of a magnet^ the gradation of atomic density^ 
when once induced, subsists independently of the action of an 
external body, and is consequently maintained by the intrinsic 
molecular forces of the magnet itself. Accordingly I have as- 
sumed that whereas in general the molecular attractions acting 
on a given atom in equilibrium counteract each other, as do 
also the molecular repulsions, in the case of a magnetized steel 
bar the equilibrium of the atom results from an equality between 
the molecular attraction towards the denser end and the mole- 
cular repulsion towards the rarer end. This, in short, is con- 
sidered to be the distinctive property of a substance suscep- 
tible of being magnetized. Steel possesses this property in an 
eminent degree, and can be permanently magnetized. Soft 
iron admits only of temporary magnetization. 

8. The magnetic state of a substance being thus defined^ 

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18i Prof. Challis on the Hydrodipiamical Theory of the 

and its magnetic action being supposed to be attributable to 
the setherial streams which^ as indicated above^ this state ge- 
nerates when the substance is traversed either by steady streams 
or a uniform series of vibrations^ we have next to inquire re- 
specting the origination of these primary movements of the 
ffither. I thought^ at firsts they might be due to the sethe- 
rial streams which relatively pass through atpmically constituted 
substances in consequence of the earth's revolution about its 
axis and motion in its orbit^ and of the motion of the solar 
system in space. But since in that case the primary^ and by 
consequence the secondary^ motions would be subject to large 
fluctuations of intensity to which there is nothing corresponding 
in the phenomena of a magnet^ it follows that the streams which 
are the exponents of magnetism cannot be to any sensible 
amount due to the above-mentioneil primaries^ and must have 
a different origin. 

9. Having proved^ as stated in art. 7, that the secondary 
streams might be generated by a uniform series of setherial un- 
dulations^ and having repeatedly maintained (in articles in the 
Philosophical Magazine and in my work on the Principles of 
Physics) that attractions and repulsions may be attributed to 
the dynamical action of such undulations on the individual 
atoms of bodies, it occurred to me that those vibratory motions 
of the sether which by their attractive effect maintain the regular 
gradation of density might be the primaries sought for; and 
this supposition is in accordance with the fact already adverted 
to, that magnetism pertains to the magnetized body apart from 
any extraneous action. [See^ respecting '^ Attraction by Vibra- 
tions of the Alt" an article in the Philosophical Magazine for 
April 1871. I cannot but regard the results of Mr. Guthrie's 
experiments as singularly confirmatory of my theoretical anti- 
cipations.] According to the views I have advocated relative to 
molecular forces, the maximum velocity of the attractive vibra- 
tions would be so much larger than that of the repulsive vibra- 
tions, that in the present inquiry the latter may be left out of 
account. Also it may be presumed that it is because that 
maximum velocity very much exceeds the rotatory^ orbital, and 
translatory motions of the earth, that these motions have com- 
paratively no magnetic effect. 

10. Consequently, if, for simplicity, the magnet be supposed 
to be of a cylindrical form, in its interior an impulsive action 
upon the sether is continually operating in the directions parallel 
to its axis. Now as the attractive action of a series of undula- 
tions is in the direction contrary to that of propagation, and the 
attraction is towards the denser end of the magnet, it follows 
that the direction of the propagation, which is that of the maxi- 

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Action of a Galvanic Coil on an external small Magnet. 185 

mum velocity in the condensed half of the wave, is towards the 
rarer end. At the same time, according to the mathematical 
result obtained in art. 8 of the article in the Philosophical Ma- 
gazine for June 1872, the impulsive action on the sether, whether 
the primary vibratory motions be backwards or forwards, is 
towards the denser end, out of which consequently the generated 
streams flow. 

11. The next point is to determine the forms of the courses 
of the magnetic streams generated under the above-described 
circumstances. To do this it is necessary to begin with admit- 
ting the truth of the following general hydrodynamical theorem, 
of which great use will be made in the subsequent investiga- 
tions. [For proof of the theorem see art. 10 of the communi- 
cation just cited.] It is not possible that the motion of an un- 
limited fluid mass can be such as to transfer any portion of the 
fluid on one side of an unlimited fixed plane to the other side 
without the transfer of an equal portion from the latter to the 
former. Thus the motion must be circulating or reentering \ 
and accordingly a general characteristic of magnetic and gal- 
vanic currents is accounted for on the principles of hydrody- 

12. This being understood, the forms of the magnetic linen 
of motion are determinable, at least approximately, by the fol- 
lowing argument. We have seen that in consequence of the 
regular gradation of the atomic density of a cylindrical magnet, 
and the velocities due to the outstanding undulations which by 
their attractive action maintain this state of density, the fluid is 
impelled in each transverse section at every instant towards the 
denser end of the magnet. These impulses operating against 
the inertia of the surrounding mass of fluid, have the effect of 
generating streams which, as being due to a steady action, are 
steady, and^ as fulfilling the condition stated in art. 11^ are ne- 
cessarily circulating. To give a first idea of the courses of these 
streams, at least in the immediate neighbourhood of the mag- 
net, I cannot do better than refer to the figure in p. 17 of the 
Astronomer RoyaFs ' Treatise on Magnetism,' the directions of 
the axes of the small magnets indicating (as will be shown sub- 
sequently) the directions of the lines of motion at the positions 
where they are situated. An approximate analytical expression 
for the forms of these magnetic curves is derivable from the pre- 
sent theory by the following investigation. 

13. From what is argued above, the impulses are produced 
by variations of pressure due to variations of the square of the 
mean of the velocities within the cylinder estimated in directions 
parallel to its axis, these variations being caused exclusively by 
the mean contraction of channel resulting from the increasing 

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186 Prof. Challis on the Hydrodynamical Theory of the 

occupation of space by tbe atoms towards the deuser end. Now 
we may conceive this mean eflFect to result from the separate 
effects of a vast number of atoms contained within a thin trans- 
verse slice of tbe cylinder, inasmuch as the individual motions 
due to the occupation of space by the atoms may coexist^ and 
the parts of the motions resolved transversely to the axis will in 
that case destroy each other. Also it is to be considered tliat 
the motions of the aether resulting from the mean of the impulses 
must satify the condition of circulating. 

14. This being understood, it will be seen to be allowable 
to substitute for the impulsive effect of contraction of channel 
that of a motion forward in the same direction of the aggre- 
gation of atoms contained in the above-mentioned slice, the 
fluid being relatively at rest. For on this supposition there 
will be a mean impulse parallel to the axis of the cylinder^ 
which will be the sum of the impulses of the individual atoms 
resolved in that direction, and moreover will give rise to a 
drwlating motion. The last assertion rests on Poisson^s so- 
lution of the problem of the simultaneous motions of a ball-pen- 
dulum and the surrounding fluid, according to which the lines 
of motion of the fluid are reentering ; and this being the case 
with respect to each atom, the result of the composition of all 
the motions will be circulating motion. Now, assuming the 
transverse section of the cylinder to be small, it is evident 
that the stream resulting from the action of all the atoms in 
the slice will have quum proxime the same form as that pro- 
duced by a single atom situated at the middle point of the slice. 
But by Poisson's solution we obtain the analytical expression 
of the motion of the fluid in this case. Hence a formula for 
expressing the motion due to all the atoms in a given small 
slice may be at once inferred. 

15. Let A and B be the extreme points of the axis of the 
cylinder, its middle point, P any extraneous point the coor- 
dinates of which reckoned from along and perpendicular to 
the axis are p and g, and Q being a point of the axis distant by 
X from O ; let the straight line joining P and Q make an angle 6 
with the positive direction of the axis. Then if PQar, /a be 
the velocity of the atom, and a its radius, by the above-men- 
tioned solution the velocity at P in the direction from Q to P is 

^ cos 0, and that perpendicular to P Q tending in the negative 

direction is —-g sin 6. Hence, denoting by X and Y the total 

velocities resolved along and transversely to the axis, we have 

^= ^ cos« tf- ^sin« tf, Y= ^%08 sin 0+ ^sintfcos^: 

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Action of a Galvanic Coil on an external small Magnet. 187 
or, since cos 0=^ , sin ^= -, and r^= [p—xY + q^, 

x^aefi jLPz:?)*±i?!_ Y=: ^f^'^^Jp-^) 

Hence^ to calculate the total velocity at P in the longitudinal 
and transverse directions, we have to add the velocities due to 
all the slices of given thickness dx from end to end of the mag- 
net, or to obtain the integrals k^Xdx and k^Ydx from a?= — / 
to a?= + /, the length of the magnet being 21, and * a constant 
factor. The results will be found to be 

Longitudinal^ _ k^ut^ f p-^l P±i__\ 

velocity J 2 L((j»-/)« + ^«)J ((;? + /)* + ^«)? J ' 

Transverse \ _ J^f g q \ 

velocity / 2 L(g«+(p-/)«)f (g« + (;, + /)«)* /• 

16. It will now be shown that these velocities are propor- 
tional to the directive actions of the magnet in the longitudinal 
and transverse directions on a small needle having its centre at 
P, and movable about an axis perpendicular to the plane con- 
taining P and the axis of the cylinder. The small magnet will 
be supposed to be surrounded by magnetic streams exactly like 
those which, according to the foregoing theory, belong to the 
large magnet, and to be of such small dimensions that the 
streams from the large magnet may be considered to have the 
same direction and velocity at all the positions of the atoms of the 
other. To find the action of the large magnet on the small one, 
it is now required to determine for any point the accelerative 
action of the pressure of the fluid resulting from the coexistence 
of the two sets of motion. 

1 7. It is clearly not necessary to take account of any force 
acting* perpendicularly to the plane passing through P and the 
axis of the cylinder, because all such forces are equal and oppo- 
site on the two sides of the plane. Let, therefore, that plane 
contain the axes of a? and y, and let u„ t7. be velocities, parallel 
to the axes, due to the large magnet, ana t^ v^ be those due to 
the small one. Then by hydrodynamics, the motion being 
steady, and, as vanishing at an infinite distance, such as makes 
udx+vdy+wdz an exact differential, we have 

Let V, be the velocity of the incident stream of the large mag- 
net, and let its direction make an angle ^^ with the axis of x. 
Then Wj=Vi cos ^, and t?j=Vj sin ^,. Again^ let the velocity 

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188 Prof. Challis on the Hydrodynamical Theory of the 

of the small magnetos stream at the position of any one of its 
atoms be V,, and be in a direction making the angle a with the 
axis of the magnet, and let this axis make the angle 6^ with the 
axis of X, Then we have 

UgSsV^cos (^g—a), Va=V2 sin (^g— «). 

Hence, by substituting in the above expression for p, 

;,=C«i(VJ + 2V,V4C0S (^^-^, + a)-hVj). 

The pressure /?, so far as it depends on the term VJ, can have 
no effect in producing either rotation or motion of translation of 
the small magnet, because the velocities Vj are symmetrical 
both with respect to its axis, and to the transverse plane passing 
through its centre. Hence, omitting this term, we have, since 
y^ and 9, have been supposed constant, and 0^ is a constant 

^P -tr /zi /ivrf.VaCOSa „ . .^ /j.rf.VflSina 

- £ = V, cos {0,-0^) —^ V, sin {0,-0^ j—- i 


^P -ir //J /jvrf.VoCOsa ,, . .^ yjvrf.Vasina 

- fy = V. COS {0,-0^) —1^ V, 8.n {0,-0,) —^- 

18. We may now simplify the reasoning, without loss of ge- 
nerality, by supposing that the axis of x coincides with the axis 

of the small magnet, or that d^=^0. In that case S .— ^p =0, 


because by reason of the symmetry of the motion the positive 
values of J are just counteracted by the negative, and 

the same is the case with respect to the values of — ^ V — • 

Hence the forces parallel to the axis of the magnet have no ten- 
dency to produce motion of translation. Neither do they tend 
to produce rotation, because corresponding to a force at any 
point on one side of the axis there is an equal force at an equal 
distance on the other side, and equally distant from the axis of 
motion. We have thus only to consider the effects of the forces 

- ^. Now the sum of these forces is zero, because by reason 

of the symmetry of the motion, the sums of the positive values 

.^.V^cosa jd.V-sina . , i ^ ^i. 

oi ^ and ^ are respectively equal to the sums 

of their negative values. Hence there is no tendency to motion 
of translation transversely to the axis. Also the forces expressed 

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Action of a Galvanic Coil on an external small Magnet, 189 

by the different values of the first term of the formula for r- 

produce no motion of rotation^ because they are equal and in the 
same direction at equal distances from the axis of rotation on 
the same side^ whether positive or negative^ of the axis of the 

19. But the forces expressed by the second term of the same 
formula are at a given distance from the axis of motion equal 
and in the same direction at points equally distant from the axis 
of the magnet on opposite sides, and at the same time the direc- 
tions are opposite on the opposite sides of the axis of motion. 
Accordingly these forces produce motion of rotation, and are 
the only forces that have this effect. Hence if x^ be the distance 
of any atom from the axis of rotation, the whole momentum of 
rotation is propoitional to 

TT • zi ftx? rf.VflSina 

— V, sin ^1 X 22 . X. 5 > 


the summation embracing all the atoms on one side of the axis 
of rotation. It is now to be considered that the accelerative 
action of the fluid in steady motion on any atom in any direction 
has a constant ratio to the accelerative force in the same direc- 
tion of the fluid itself at the position of the atom. [This pro- 
position is proved in pp. 313-315 of * The Principles of Mathe- 
matics and Physics.'] Hence, if H be a constant factor having 
a certain ratio to the result of the above summation, the directive 
force of the incident current will be 


tending always to place the axis of the small magnet in such a 
position that its proper current along the axis and the incident 
current flow in the same direction, in which case d|=0. 

20. *It follows from the foregoing argument that the longitu- 
dinal and transversal components of a stream from a large mag- 
net incident upon a small one are proportional to the directive 
forces of the stream in th#two directions, and that consequently 
the forces may be supposed to be expressed by the formula for 
the velocities obtained in art. 15. 

I take occasion here to remark that the Astronomer Royal 
has deduced in the Philosophical Transactions (vol. clxii. p. 492) 
expressions for the same forces wholly different from those in 
art. 15, by assuming the intensity of the magnetism along the 
axis of a magnet to vary proportionally to the distance from its 
centre, and finds that they give numerical results which do not 
sufficiently agree with experiment. According to the theory I 
am advocating that assumption is not allowable. 

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190 Prof. Chailis on the Hydrodynamical Theory of the 

21. I proceed now to account by the hydrodynamical theory 
for the experimental facts on which the Gaussian argument for 
the law of the inverse square in magnetism rests. In one set 
of experiments the small magnet was placed so that the prolon- 
gation of the axis of the large magnet passed through its centre 
and cut its axis at right angles. Under these circumstances the 
ordinate ^=0^ so that the transverse velocity vanishes^ and the 
expression for the longitudinal velocity becomes 

kfic^f 1 1 \ 

2 \{p-l)^ {p^l)V' 
which, if the ratio of I top be small, is very nearly 

In another set of experiments the small magnet was placed 
with its axis pointing to the centre of the large one transversely 
to the axis; in which case^ since /?=0^ the transverse velocity 
again vanishes^ and^ supposing the ratio of / to g to be small^ 
the approximate expression for the longitudinal velocity becomes 

Hence in both cases the directive force varies inversely as the 
cube of the distance from the centre of the large magnet, and at 
equal distances is double in the former case to what it is in the 
other. The two principal results of the experiments having 
been thus accounted for, the hydrodynamical theory has effected, 
at least to a first approximation, all that may strictly be de- 
manded from it. In order, however, to exhibit its applicability 
more fully, I shall now employ it to show why Gauss's empirical 
theory succeeds in representing the same facts. 

22. It has been inferred from the hydrodynamical theory that 
the action of the large magnet on the small one is simply directive* 
Hence, assuming that each magnet has near its ends a positive 
pole and a negative pole, and that like poles repel each other 
and unlike poles mutually attract, it will readily be seen that, 
according to the arrangements of the two experiments described 
in art. 21, the actions on the poles of the small magnet are nearly 
equal, and nearly in the same direction, and that the action on 
one is attractive and that on the other repulsive. These forces 
are, therefore, proper for acting as a kind of cotgple, and giving 
direction to the axis of the needle. Also in this mode of viewing 
magnetic action, if, as is empirically assumed, the force varies 
inversely as some power of the distance from the pole, the law 
of the inverse square is alone applicable, because experiment and 
the hydrodynamical theory concur in indicating that the direc- 

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Action of a Galvanic Coil on an external small Magnet. 191 

tive force varies nearly as the inverse cube of the distance from 
the centre of the magnet^ which law results from the joint action 
of an attractive and a repulsive force expressed thus. 


9 ^ 

the differential force being nearly -^— , which for a given value 

of Br varies inversely as the cube of the distance. 

23. The whole preceding argument points to the conclusion 
that the assumed attractive and repulsive magnetic forces have 
only a hypothetical existence, and that what really exists is hy- 
drodynamical pressure. 

24. Proceeding now to discuss in a similar manner the pro- 
blem of the action of a galvanic coil on a small magnet, I propose, 
first, to solve it according to the principles of the hydrodyna- 
mical theory of galvanism, and then to inquire how far the same 
theory will account for the facts and hypotheses on which Am- 
pere's empirical solution of the problem rests. The hydrodyna- 
mical considerations will differ in some essential respects from 
those applicable to magnetism. 

25. First it will be necessary to ascertain what motions of the 
fiether correspond to the transmission of a galvanic current along 
a fine wire. For this purpose certain hydrodynamical theorems 
will be employed, the principles and the proofs of which I have 
discussed in various antecedent researches. I consider it to be 
an axiom that^ whatever be the motion of a fluid mass, the lines 
of direction of the motion may at all times be cut by a surface 
made up of portions, either finite or indefinitely small, of differ- 
ent surfaces of continuous curvature, so joined together that the 
tangent planes at the points of junction of two contiguous por- 
tions do not make a finite angle with each other. The reason 
for the latter condition is a dyrmmical one, whereby infinite forces 
are excluded. The other is an abstract geometrical condition of 
continuity, to which the directions of the motion of a fluid 
assumed to be continuous are necessarily subject, and in virtue of 
which the motion admits of being calculated. If any one thinks 
that there are motions of a fluid which this condition does not 
embrace, let him calculate them if he can ; I do not concern 
myself with them. 

26. It follows from the foregoing theorem that the general 
differential equation of the above-defined surfaces of displacement 
is (according to the usual notation) udX'\-vdy-\-wdz^O, and 
that consequently the left-hand side of this equality is either in- 
tegrable of itself or by a factor. Reasoning on the principle 
that this must be the case always and at ail points of the fluid. 

Digitized by VjOOQ IC 

192 Prof. Challis on the Hydrodynamical Theory of the 

I have obtained a general hydiodyuamical equation in which the 
factor enters as an unknown quantity. The present investiga- 
tion does not require reference to that equation further than to 
state that it serves to demonstrate the reality of the factor^ and 
consequently to establish the truth of the equation 

/dv dw\ , fdw du\ . rdu dv\ ^ , . 

which^ as is known^ is the general expression of the condition that 
udx 4- vdy + wdz is integrable by a factor. 

27. I have recently learnt with some surprise from more than 
one quarter that the equation (a), and^ by consequence^ the an- 
tecedent views on which it is founded, are considered to be untrue 
for reasons drawn from a discussion on certain hydrodynamical 
questions which I had with Professor Stokes in the Philoso-* 
phical Magazine so long ago as 1842. Claiming to adopt views 
expressed by Professor Stokes on that occasion, a correspondent 
sends me the following argument relative to the equation [a). 
Conceive to be impressed on all parts of the fluid the arbitrary 
constant velocities a, ^, 7 in the directions of the axes of coor- 
dinates. Then the equation becomes 

, . .fio dw\ . , as fdw du\ . . .fdu dv\ ^ 

which, since a, ff, 7 are perfectly arbitrary, cannot be true unless 

dv ^^_n ^^ ^" ~n ^" ^^ —A. 
dz dy^"' dx dz '^ ^ dy dx~ ^ 

that is; unless in every instance of the motion of a fluid 
udx^vdy-\-wdz is an exact differential. As this is certainly not 
the case, it is concluded that the equation (a) is untrue. 

28. The answer to this argument is that the equation (a) was 
deduced on the principle of its being exclusively applicable to mo- 
tions which are peculiar to a fluid, and which, consequently, a 
solid is not capable of, the motions, namely, by which the parts 
of a fluid mass in motion can change their relative positions. 
This is the sole raison d'etre of the equation. Hence the intro- 
duction of the velocities a, jS, y common to all the parts of the 
fluid is a violation of the principle on which it is founded ; or 
rather the above argument is a proof h posteriori that the equa- 
tion excludes such common velocities. If, therefore, that equation 
be satisfied, there is no need to '^ define ^' the velocity that may 
be common to all the parts of the fluid ; for either such motion 
takes place under given conditions, and is consequently known, 
or, if not known and not knowable (whether it be due to the 
earth^s rotatory and orbital motions^ or to the motion of the 

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Action of a Galvanic Coil on an external small Magnet, 193 

solar system in space) ^ the determination of the motions whereby 
the individual parts of the fluid alter their relative positions 
remains the same. 

29. If while such change of relative position is taking place 
each rectangular fluid element is also changing form^ the lines 
of motion are necessarily not parallel ; an(i since^ by hypothesis^ 
they are in the directions of normals to continuous curved sur- 
faces, it follows that for such motions v>dx-\-vdy + wdz is an exact 
difierential. But if each rectangular element retains the same 
form^ the lines of motion must be parallel^ the surfaces of dis- 
placement are planes, and udx+vdy-k-wdz is integrable by a 

In the course of my many hydrodynamical researches I have 
had from time to time the benefit of criticisms^ and arguments 
ex adverso, from my mathematical contemporaries ; and I wil- 
lingly admit that I have thereby been induced in several instances 
to modify my original views. But hitherto I have not perceived 
that there is any ground for questioning the truth of the prin- 
ciples and the reasoning which have conducted me to the equation 
which I call the third general equation of hydrodynamics, and I 
have consequently not hesitated to employ the equation (a), 
which is a logical consequence of that general equation, in lay- 
ing a foundation for the subjoined hydrodynamical theory of the 
action of a galvanic coil. 

30. A current of the sether being supposed to flow uniformly 
along a straight cylindrical conductor, the motion of the fluid 
at any point may be determined by the following reasoning 
(given in more detail in the ' Principles of Physics,' pp. 563-565) . 
The motion is plainly a function of the distance from the axis of 
the cylinder, but cannot be wholly parallel to it ; for if that were 
the case, since the motion is, by hypothesis, steady, and in such 
motion the pressure is everywhere less as the velocity is greater, 
and sinc« in this instance the velocity will evidently be less the 
greater the distance from the axis, it would follow that on all 
sides there would be tendency to motion towards the axis, which, 
if not counteracted, would put a stop to the current. To coun-. 
teract this tendency there must be centrifugal force due to cir- 
cular motion about the axis ; and according to the hydrodyna- 
mics of steady motion the rectilinear and circular motions may 
coexist. Hence, if r be the distance from the axis, and the rec- 
tilinear and circular motions at that distance be respectively 
F(r) and/(r), we shall have 

u=^f[r), t.= -^y(r), w=¥{r). 

These equations satisfy the condition of constancy of mass ex- 
Phil. Mag. S. 4. Vol. 48. No. 317. Sept. 1874. O 

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194 Prof. Challis on the Hydrodynamical Theory of the 
pressed by the equation 

dx dy dz^ * 

which is true for a compressible fluid inclusively of small terms 
of the second order ; so that the subsequent reasoning, although 
strictly applicable to an incompressible fluid, may be taken to 
apply to the sether. Now, from the known expressions for 

^« -J-} -^ for steady motions of an incompressible fluid, it 
will readily be found that 

W ^ {My ^ the centrifugal force. 

8L These results are independent of the forms of the func- 
tions f(r) and F(r) and of any relation between them. But 
since the assumed values of u, v, w do not make udx + vdy + wdz 
an exact differential, according to the principles maintained above, 
they must be such as to satisfy the equation (a). By substitu- 
ting them in that equation, and integrating, the result is 

F(r) - r' 

c being the arbitrary constant introduced by the integration. 
We have thus demonstrated that the current must be such as to 
satisfy the relation between the velocities/(r) and F(r) indicated 
by this equation. 

32. By taking account of this relation the equation 

udx + vdy '^ wdz =0 

^^ " rW) ^^^^^y^ ^ ^ (xdy-ydx). 
Hence, by integration, 

xrssctan"*- +J, 


which is the general equation of the surfaces of displacement, 
the orthogonfd trajectories of which determine the directions of 

the motion. If tan~'-a^, and r, be a given distance from the 

axis, we have 

which shows that the motion in the cylindrical surface of radius 
r, consists of spiral motions the directions of which make with 

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Action of a Oalvcmic Coil on an external email Magnet. 196 

parallels to the axis the angle whose tangent is -^. The motion 

is thus completely determined if only the forms of the functions 
f(r) and F(r) can be found. In my work already cited I have 
expressed (in p. 566) a doubt as to the practicability of doing 
this in the existing state of hydrodynamics. I have/ however, 
since discovered the following argument, which I consider to be 
adequate to this purpose. 

33. Suppose the straight galvanic current to be cut by a plane 
transversely, and on the plane three concentric circles to be de- 
scribed having the common centre on the axis, and let their 
rady be r+«, r, and r— «, « being verj' small. Also let there be 
drawn in the plane from that centre two straight lines separated 
by the small angle 80. Then the space bounded by these lines 

and the first and second circles is ((r+«)*— ^))-o-# ^^^ ^^^^ 

bounded by the same lines and the second and third circles is 

(r*— (r— «)*) -^. Now, according to the foregoing investigation, 

these spaces may be considered to be transverse sections of ele- 
mentary channels in which the galvanic current is constrained to 
move. Let V be the mean velocity of the current through the 
space furthest from the axis, and V that of the current through 
the other. Then, inclusively of small terms of the second order, 

V'=F fr+ ^Yand V=F(r- ^Y Hence the excess of fluid 

which in a second of time passes through the larger space above 
that which in the same time passes through the other is 

which, omitting terms containing efi &c., becomes 

34. We have now to take into account the principle adverted 
to in art. 11, according to which the inertia of an unlimited mass 
of incompressible fluid opposes an insuperable obstacle to any 
alteration of the quantities of the mass on the two sides of any 
unlimited fixed plane. Since in the case of the galvanic current 
fluid is being transferred every instant across the above-men- 
tioned transverse plane, not only roust the rheophore furnish a 
channel for the circulation of the fluid, but there must also be a 
general stress, like hydrostatic pressure, which, taking effect 
always in the directions of any channels of circulation, maintains 


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196 Prof. Challis on the Hydrodynamical Theory of the 

the current in opposition to the tendency of the inertia of the 
fluid to put a stop to it. In the present theory this stress is due 
to the action of the battery ; the wire supplies a channel for the 
current; and^ as is shown in art. 11^ it is dynamically necessary 
that the current should flow in a complete circuit. 

35. It is clearly possible that the form of the function F(r) 
might be determined by arbitrary conditions. For instance^ if 
the above-mentioned stress were arbitrarily caused to be the same 
at all points of the transverse plane^ the velocity parallel to the 
axis would be the same at all points^ and F(r) would be a constant. 
But it is evident that this is not true of a galvanic current. The 
principle of the present inquiry demands that as a definite rela- 
tion between the functions y][r) and F(r) was obtained in a unique 
manner by integration^ the form of the function F(r) should be 
similarly determined. Now the only way in which that form can 
be obtained exclusively by integration is to equate to zero the 

above factor — ^ H — "> > ^^ which case integration gives 

Thus the velocity parallel to the axis varies inversely as the dis- 
tance from the axis ; and the stress which maintains that velocity, 
and is therefore proportional to it^ varies according to the same 
law. Since the transverse sections of the elementary channels 
above defined vary directly as the distances^ it follows that 
through each elementary channel outside the wire the same 
quantity of fluid flows in a given interval. Also^ since it has 

been shown (art. 31) that/(r)= - F(r), we obtain 

or the transverse circular motion varies inversely as the square 
of the distance. These results are essential to the hydrodyna- 
mical theory of galvanism. 

36. But for the theory of the action of a galvanic coil we re- 
quire to know the motion of an setherial current along a fine 
wire the axis of which has the form of a circle^ and the trans- 
verse section of which is circular and uniform. For this case it 
will be assumed that^ by reason of symmetry^ the motion at any 
given point is compounded of motion parallel to the axis^ and of 
motion in the plane passing through the point and the centre of 
the axis^ and cutting the axis at right angles. Let the plane of 
this axis be parallel to that of xy, and its centre be on the axis 
of z 'i and let h be the height above the plane xy of the point of 
intersection of the circular axis by the above-mentioned trans- 

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Action of a Galvanic Coil on an external small Magnet. 197 

verse plane^ and a the distance of the same point from the axis 
of z. Also in the same plane let r and be the polar coordi- 
nates of the given point P referred to the point of intersection 
as pole^ and to the straight line through the pole parallel to the 
plane xy. Then, the rectangular coordinates of P being x, y, z^ 
if we put R for (a?'-f y')^, and suppose the velocity parallel to 
the plane ocy to be F(R, z), and that in the transverse plane to 
be f{r, 0), we have 

together with the equalities r* = (z — A)* -f (R — a)*, and 

tan tf = p . By analytical operations, the details of which, as 

being somewhat long but presenting no difficulties, are not in- 
serted here, it may be shown (1) that 7" + T" + ;/~=0# 

(2) that udx+vdy-hwdz is not an exact differential; (8) that by 
substitution in the equation {a) there results the following equa- 
tion of condition connecting the functions / and F : 

37. Respecting this equation we may, first, remark that since 

it does not contain ^ it shows that the assumed motion requires 

that /should be a function of r only, and consequently the mo- 
tion in planes transverse to the axis of the wire is proved to be 
circular. This result is in accordance with the original assump- 
tion, that the transverse section of the wire is circular, as should 
plainly be the case, since the surface of the wire bounds the cir- 
cular motion. 

38. The proof that /is a function of r only having taken no 
account of the magnitude of a, and being clearly independent of 
that of h, we may infer that the function has the same form 
whatever be the radius of the axis of the wire, and therefore the 
same as if the radius were infinite, in which case a finite portion 
of the wire might be considered to be a straight cylinder. But 

we have shown (art. 35) that for the straight cylinder/(^r) = 4. 

Consequently, substituting this value of /(r) in the equation (i), 

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198 Prof. Challis on the Hydrodynamicd Theory of the 
there results for determining the form of the function F the 



This partial differential equation integrated in the usual way 


Now it is certain that the expression for the velocity F(R, z) 
must involve the distance r of the point P from the axis of the 
wire. This condition is satisfied by the above value of F by 
assuming that 


and can be satisfied in no other way. We have therefore the 
unique solution 

p_ C, C^ 

R((^»A)«+ (R-fl)«)i ^ 

C, being an arbitrary constant. Thus exact expressions for the 
velocity in any plane transverse to the axis and for that parallel 
to the axis having been found, the total motion, which is com- 
posed of these two, is completdy determined. 

89. From the above expression for F, that which applies to a 
straight cylindrical wire mav readily be deduced. For putting 
a + « for R, ft being a variable quantity restricted within compa- 
ratively small limits, and giving to C, the form {/a, </ being an 
arbitrary factor, we have 

F= '^'^ ""' 



which for a straight wire, for which a is infinite, becomes 


agreeing with the result obtained in art. 35. 

40. It would seem that the foregoing investigation might be 
-generalized so as to apply to a wire conductor of any form, when 
it is considered that the determinations in arts. 30-35 of the 
forms of F(r) and/(r) for a straight cylinder did not involve the 
length of the axis, and would remain the same for a cylinder of 
infiinitesimal length if the condition of circular motion about the 
axis were satisfied. We have shown that this condition is in fact 
satisfied by a uniform conductor of circular form, which may be 
regarded as made up of a series of right cylinders of infinitesimal 

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Action of a Galvanic Coil on an external small Magnet. 199 

lengths ; and as any portion of a uniform conductor of any form 
may be supposed to be similarly composed^ the expressions for 
/(r) and F(r) for a circular wire would appear to apply generally^ 
if the radius a be taken to represent the varying radius of curva- 
ture of the axis of the wire. This question^ however^ requires 
more consideration than I can now give to it. 

41. Returning now to the circular conductor^ if in the expres- 
sions for u, V, w in art. 36 the values found for /(r, 6) and 
F(R, z) be substituted, we shall have 

cjp{z-h) c^ 

c^yjz'-h) _ c^ 
^^ R/^ RV 


Hence, since R*=^+y* and r*= (ar— A)«+ (R_fl)«, it will be 
found that 

^ r (z— A)*4-(R— «)* r x^ + y^ 

Consequently the right-hand side of this equation becomes an 
exact differential when multiplied by the factor r. Before pro- 
ceeding to the next step, it is necessary to take into account that 
in the foregoing investigation the arbitrary constants e, and c^ 
have been introduced in such manner as to show that they 
are wholly independent of each other. Hence, on equating 
r{udx+vdy+wdz) to zero, we must have separately 

(z— A)dR — (R--g)ig _^ ydx—x dy __^ 

which means that both the motion transverse to the axis of the 
wire and that parallel to the same are such as require a factor 
for making udx + vdy + wdz integrable. Both are steady motions 
and therefore coexist. Instead of the above two equations we 
may, by introducing an arbitrary constant factor X, employ the 
single equation 

(z— A)rfR- (R,—a)dz ydx—xdy __^ 

Hence, by integration, 


supposing that ^=tan^, and, as before, that =-— = tantf. 

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200 Prof. A. Stoletow on the Magnetization- Functions 
DiffereDtiating this last equation^ we get 0=c d0+\c^<f>, or 

dif}'^ c, 

42. Assuming that c^ and c, are positive quantities in the 
expressions for u, v, w in art. 41, it will be seen that those values 
were formed so that 6 and <b each decrease with the motion. 

Hence ^will be positive, and X must be a negative quan- 
tity. According to the supposed directions of the decrements, 
the spiral motion will be dextrorsum. If the motion were 
assumed to be such that d0 and d<f> had different signs, the 
spiral motion would be sinistrorsum, and we might by the same 
reasoning as before obtain C=c^6'\'\^c^<f>, c^ and c^ being still 

positive. In that case tt = ^= a negative quantity, and V 

is consequently positive. As the factors X and X' are wholly 
arbitrary, we have thus shown that, as far as hydrodynamics is 
concerned, the galvanic current might be either dexirorsum or 

Having in the preliminary part of this communication dis- 
cussed the action of a large magnet on a small one, and having 
now ascertained the exact form of a galvanic current along a cir- 
cular wire, I propose in a second Part to investigate the action 
of a galvanic coil on a small magnet, and to show why it agrees 
approximately with that of a magnet, and in what respect espe- 
cially the two actions differ. In the course of the investigation 
the facts on which Ampere's theory rests will be accounted for 
by the hydrodynamical theory, for the purpose of fully establish- 
ing the claim of the latter to be considered a strictly h priori 

Cambridge, August 10, 1874. 

XXX. On the Magnetization-Functions of various Iron Bodies, 
By Professor A. Stoletow*. 

IN my work on the magnetization of ironf I have taken 
Neumann's coefiScient « as a measure of the magnetizability. 
This, as is well known, expresses the ratio in which the magnetic 
moment, referred to the unit of volume, stands to the quantity 
of the magnetizing force, presupposing that the iron forms an 

* Translated, from a separate impression communicated by the Author, 
from the Bulletin de la SocUt4 Imp, des Naturalistes de Moscou, 1873, 
No. 4. 

t Pogg. Ann. vol. cxliv. p. 439; Phil. Mag. S. 4. vol. xlv. p. 40 ; more 
fully at a separate brochure in Russian, Moscow, 1872. 

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of various Iron Bodies. 20 1 

nfiaitely long cylinder and is uniformly magnetized longitadi- 
nally. I have named this coefficient (in that essay denoted by 
k) the magnetizing -function of the given iron, since it depends 
on the quantity of the magnetizing force. A.n analysis, namely^ 
of the experiments of Quintus Icilius (with ellipsoids) and of 
my own (with a ring) showed that the function k at first in- 
creases rapidly as the decomposing force rises^ and then again 
diminishes. This behavour seems to take place with all sorts of 
iron ; yet the absolute numerical values of ky with the same val ue 
of the argument, are very different, according to the quality of 
the iron. These results have been corroborated by a thoroug h 
investigation by Mr. H. A. Rowland*. He shows that the 
course of the function k is precisely similar for steel and nic kel 
as well as iron, and can be represented by the same empiric 
formula, but that the constants of the formula, even for two 
varieties of one and the same metal, come out very different f* 

Professor Biecke, in his '' Contributions to the Knowledge of 
the Magnetization of Soft Iron '' (Pogg. Ann, vol. cxlix. p. 433), 
proposes, instead of the magnetizing-function of the infinite 
cylinder, to consider another function p, which has the same 
signification in reference to the sphere. 

The two quantities, referred to the same decomposing force, 

* '* On Magnetic Permeability, and the Maximum of Magnetism of Iron, 
Steel, and Nickel," Phil. Mag. August 1873, p. 140. The term "mag- 
netic permeability " is used, alter Sir W. Thomson, to denote the quantity 
/t=l4-4iriir, which, as ib is here generally much greater than unity, varies 
nearly proportionally with k, 

t Professor Wiedemann, when discussing my work (in Galvanismus^ 
2nd ed. vol. ii. p. 518), regards the function which is calculated from ex- 
periments with the ring as another magnetization-function, not to be con- 
founded with that obtained from experiments with *' unclosed systems." 
There does not seem to me sufficient reason for this distinction. Residual 
magnetism, which is here in question, is present in burs also. If we con- 
sider a veiy thin and lon^ bar and a ring, both magnetized uniformly, the 
difference between them m relation to the residual magnetism is hardly to 
be reckoned considerable. The demagnetizing force proceeding from the 
mass of its iron wiU in the ring be equal to nil; in the bar it is a small 


quantity, of the order of ~p, where a> is the cross section, and / the length 

of the bar. (Maxwell, ' Treatise on Electricity and Magnetism,' vol. ii. 
p. 67.) In both cases an external force is requisite in order to expel the 
residual magnetism. If we always observe the reversal of the magnetism 
of the iron, the calculation of k is only to this extent vitiated by the residual 
magnetism, that a certain portion of the reversed decomposing force is ex- 

E ended in discharging it. But M. Wiedemann's own experiments with 
ars, and those of Poggendorff with closed systems (Wiedemann, /. c.p.519), 
show that that portion is only very little. 

A survey of the numbers obtained by Mr. Rowland, partly with bars, 
partly with rings, establishes that the most essential cause of^^ their differ- 
ence is not the form, but the quality of the material. 

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202 Prof. A. Stoletow on the Magnetxzation^Fimctumi 
are connected by the relation 


49r 1 
3 ■*■* 

The function py he says, deserves the preference because^ 
" within a very large sphere of magnetizing forces^ it possesses 
a nearly constant value for all sorts of iron '^ (/. c. p. 435). The 
values of j9 calculated by M. Riecke from his own and others' 
experiments do in fact accord very well; they give (p. 470) as 
mean value for moderate decomposing forces the number 0*2372^ 
and as maximum value 


The purpose of the present note is to bring out that these 
results are self-evident, and the above numbers have a very 
simple meaning ; they are, namely, pretty close approximations 
to the number 

^ =0-2387, 


which is obtained as the upper limit of p when we put A:= oo, 
and consequently represents the ideal maximum of p. With 

moderate decomposing forces t is always small compMfed with — 

(since A here lies somewhere between 20 and 200*), and may, in 
the first approximation, be neglected. On this account p remains 
always nearly constant and independent of the quality of the iron\. 
Indeed, for every other strongly magnetic material, about the 
same value of j9 would result ;(. 

From this we see, on the one hand, that the numbers calcu- 
lated by M. Riecke furnish a fair confirmation of the theoretical 
consideration ; but, at the same time, we see that the quantity p 
is very little suitable for characterizing the magnetizability of a 
material, since for the sphere the influence of the quality of the 
substance nearly vanishes before the influence of the form. It 
can be proved that this holds good generally for every body the 

* For my iron ringthe maximum of k wat => 174 ; with the kinds of iron 
investigated by Mr. Rowland it was in nearly every case higher, and in one 
case reached the value Ar=4d9 {fk^bSXb). 

t A brief note in reference to this I find in Wiedemann's Gahamtmrns^ 
2nd ed. vol. ii. p. 403. 

X For a ring of annealed nickel Mr. Rowland found the maximum of 
its 24 (/iss305). According to this, even for nickel (at its maximum of 
inagnetizability) p may reach the value 0*2364. For sted the approxima- 
tion to the absolute maximum 0*2387 becomes still closer, and holds be- 
tween wider Umits of the decomposing force. 

Digitized by VjOOQ IC 

of various Iron Bodies. 203 

dimensions of which in all directions are of the same order*. In 
order to calculate it priori, with satisfactory accuracy, the mag- 
netization of bodies so formed, a rough estimation of the coeffi- 
cient k is sufficient. The magnetization- functions of such bodies, 
ascertained by experiments, will always exhibit much less varia- 
bility than that of a thin bar or ring, of a thin plate or scale, 
and may almost be regarded as constant. But if, starting from 
such mean value, we try to calculate the magnetization of any 
body of the category last mentioned, we may arrive at very in- 
accurate results ; for, with bodies one or two dimensions 0/ which 
are very small in comparison with the third, the tangential compo- 
nent of the magnetic moment will, with the same decomposing 
force, increase proportionally with kf. The influence of the 
specific qualities of the substance appears here, therefore, in full 
intensity. If we wish to bring such bodies also within the range 
of our considerations, we must take into account the specific 
quality of the substance, and the knowledge of the magnetiza- 
tion-functions of bodies of this sort will be indispensable. The 
function k perfectly suffices for this purpose, and has the advan- 
tage that in it abstraction is made of the transverse dimensions 
of the thin body. 

Those bodies the dimensions of which are of different orders 
of magnitude play a peculiar part in several branches of physics. 
In hydrostatics their theory is most essentially conditioned by 
the capillary forces. In the science of elasticity they require a 
special method of treatment ; in that of paramagnetic magneti- 
zation they make a very precise knowledge of the magnetization- 
functions absolutely indispensable. 

Christmai (O. S.) 1873. 

* Compare pp. 66-67, vol. ii. of Maxwell's Treatise — for example, 
" When ic 18 a large positive quantity, the magnetization depends princi- 
pally on the form of the body, and is almost mdependent of the precise 
value of «c, except in the case of a longitudinal force acting on an ovoid so 
donated," &c. (p. 66), We always presuppose here that the magnetiza- 
tion IS uniform. 


t More strictly, proportionally with TTTZt where c is a number vanish- 
ing with the transverse dimensions, and the value of ^ is not referred to the 

whole tangential force of decomposition T, but to TXT'* For a limited 

bar €=0. These considerations explain, for example, the experiments of 
Von Waltenhofen on the magnetization of bundles of thin wires, thin- 
walled tubes, &c. (Wiedemann's Galvanismus, 2nd ed. vol. ii. p. 430). The 
great power of the magnets composed of thin bands of steel (rubans d'acier) 
of M. Jamin ( Comptes Rendus, vol. Ixxvi. p. 789) appears also to stand in 
relation therewith (compare especially art. X. p. 794). 

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[ 204 ] 

XXXI. On Tides and Waves,— Deflection Theory. 

By Alfred Tyloe, F,G.S. 

[With Three Plates.] 

To the Editors of the Philosophical Magazine and Journal. 

Gentlemen^ London, August 15th, 1874. 

I SHOULD be glad if any of your readers will send me a re- 
ference to any work of authority in which there is any direct 
statement of the height of the level of the ocean (say the central 
Atlantic) compared with high-water mark on the east and west 
coasts of Ireland and England. This is an important point in 
the general theory of the tides^ a subject I am about to dis- 
cuss. The view I shall advocate is that the level of the ocean is 
nearly represented by high -water mark on coasts and bays where 
there is free access of the tide and a channel without a sudden 
taper. Mr. E. Roberts^ of the Nautical Almanac OfiSce, editor 
of the Reports of the Tidal Committee of the British Associa- 
tion^ informed me last month he was not aware of any statement 
in print on good authority on this point. The only opinion I 
have on this subject is from Professor 6. G. Stokes^ F.R.S. (and 
that is an unprinted one*), who wrote, " Nobody maintains that 
the general level of the ocean is that of low water ; it is the 
mean between high and low, except in shallow channels &;c., 
where it is not the exact mean/^ In the absence of further 
authorities I shall give my deflection theory of tides. 

In Plates II. and III. I give a drawing of what I suppose is the 
relation of high and low water on the coast and in estuaries and 
channels to that of the sea. I show that the level of the central 
ocean approximates to mean high-water mark on the coast of 
Ireland, and is about 4 feet above the English Ordnance Datum, 
which datum may be treated as an arbitrary line, being only the 
mean level of the sea at Liverpool, Penzance, and Falmouth, all 
places in which the tide is affected by the converging contour 
of the coast. 

The velocity of the central ocean- stream, if reduced by the 
inequalities of the sea-bottom at a different ratio to the depth, 
would cause the water to heap, and vice versd. I do not think 
it does heap perceptibly until near the coast, and then in very 
different degrees (see Plates II. and III.). When the increase 
of velocity exactly balances the decrease of depth ; that is, using 
Y and v for the old and new velocity, and I and t for the re- 
spective distances from the centre of the earth, 

V n 
when I = t, then — = ^ (1) 

* In some remarks about the views expressed in Plates IL and IIL sent 
to him for examination, March 7; 1874. 

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f 1 





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Mr. A. Tylor on Tides and Waves. 205 

This is the equatioo to equilibrium of the ocean-surface in the 
case where no interfering currents, caused by difference of tern- 
perature in the ocean, are present*. A complete oceanic tide 
stretches from coast to coast, and is always divided into three 
regions (central, anterior flowing, and posterior ebbing), re- 
versing direction each six hours ; that is, in the part where there 
was propulsion, aspiration succeeds, and vice versd. A perfect 
tide would stretch over a space on parallel of latitude repre- 
sented by the rotation of the earth in six hours. 

The mass of tbe central ocean is represented, in PI. 11. figs. 
1 and 2, and PI. III. fig. 1, as moving 180 feet per hour on 
the average of each tide of six hours, but in alternate and oppo- 
site directions. A movement of 3 feet per minute in the cen- 
tral ocean 20,000 feet deep would communicate a velocity of 
three miles an hour where the water was 238 feet deep, by the 
composition of forces. 1 suppose that this slow motion in a 
vast mass of water of great and equal depth would be horizontal 
alone, as it is not possible to suppose vertical motion without 
creating a gap below or behind the tidal current. The hori- 
zontal motion would be also limited ; for the sum of the motion 
of all the particles of water in the Atlantic tidal stream could 
not exceed the area of the gap emptied and filled on the oppo- 
site coasts of the Atlantic each alternate tide. In this respect 
the tide is like a wave, the relation of whose movements to 
the size of the gap made when generated is clearly shown in 
fig. 1 (p. 216). The force of the moon will be estimated; and 
the relation of its attraction to a particle on the ocean is shown 
in fig. 4, PL IV. The direction in which the moon can affect 

* From the equation Q=AV, using Q and g for discharge per second, 
and A for cross section, and from observation, I have 

i - vTi • ■ <^>- "- '^'^¥1 " V -^/iA ■ • • <^> 

from which I obtain a new equation to the flow of water in uniform motion 
— that is, only when V=r. This is 

i=KM) <^' 

which applies to water in canals in uniform motion, as in fi^. 3, Plate III. 
The tendency of every river is to approximate in all parts of its course to a 
uniform mean velocity. The river carries sand and mud from the mountuios 
to the sea along its channel at a nearly uniform rate. Increase of quantity 
of water flowing at any point balances decrease of slope throughout all 
livers. A steamer ascending the Rhine meets a current descending at one 
velocity at different slopes. This is proved by the consumption of fuel 
being equal per mile from the sea to Mayence, except where back-water 
on one side increases velocity on the other, or where shallows retard the 
ship. I do not find (R the mean hydrauUc depth) of value in calculations. 

Digitized by VjOOQ IC 

206 Mr. A. Tylor on Tides and Wavu. 

particles of water and move them is represented in a new manner. 
The sun's effect can be calculated similarly to the moon^s. 

The attraction of the moon when in a vertical line would not 
produce any horizontal or vertical movement in a particle of 
water below it ; and the attraction could not produce a heap of 
water below it without the water being propelled from some 
point of the ocean on which the rays of attraction fell at an angle 
less than 90° ; and then I do not think the heap could exceed 
2 inches in height*, for reasons which will be given hereafter. 

The mass of the moon is equal to a spherci^of 118*75 miles 
diameter of the same density as the earthy and situated at 3956 
miles from the point to be attracted — that is^ at the distance 
of the radius of the earth. The circle F near C (fig. 4, PI. IV.) 
should be only one sixth of an inch if drawn to scale. It' 
is shown in the position in which it would i«present the action 
of the moon on the ocean if it revolved round C in a lunar 
month. Thus any point on the circumference of the earth must 
be attracted to the centre of the earth by an attraction greater 
than that of the moon to the same point in the ratio of 295520 
to ]. For 60*263«=8681, and 60263 is the mean distance 
of the moon from the earth ; then the density of the earth is to 
that of the moon as 1*647 to 1^ and the mass of the earth to 
that of the moon as 49*5 to 1. Then 

3631 X 49-5 X 1647=295520; 

that is, the effect of the attraction of the moon in a particle on 
the surface of the earth (at the moon^s mean distance) is only 
^—^ of that arising from the attraction of the earth itself f. 

The weight of any body on the earth would therefore be 
lightened in that ratio, or in the proportion of 1 grain to 4^ 
gallons of water (70^000 grains to the gallon), the moon being 

* This is a different case altogether from that of tbe estimate of coUec- 
tion of water at the equator; and the practical test given above is better 

t This IS calculated differently in a note to page 628, Herschers * Out- 
lines of Astronomy/ 1873 : the cube of the sun's distance is erroneously in- 
troduced into the calculation for finding the moon's maximum power to 
disturb the water in the surface of the earth ; this brings the relative effect 
of the moon's attraction to-jyr^VTinr of K^s^vity, according to Herschel. 
This, however, is only -^^ ot the real quantity. My calculation is ac- 
cording to the following law:— "Two such globes would (by the same 
proposition) attract one another with a force decreasing in the duplicate 
proportion of the distance between their centres " (Newton, page 24, edit. 
819). If Herschel's figures were correct, we should have tides of 3 inches 
on our coast instead of 12 feet in height. Also the fictitious moon F placed 
near C (fig. 4, PI. IV.^, to represent the effect of the real moon, would 
have only a diameter of 34*03 miles, and contain 2^,629 cubic miles instead 
of the larger quantity mentioned by me in tbe text. , 


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MMIIs ~ 

tsgirw oyer ^tetBar-withMV Iflsavpttydj^^ 
ter mde^,runmjy at^wMmey^^fetd^oiin. 

u , „ • supposed^ tahe ^tatUmary . 

NOTE For oalcuJUUxnf rAoeuty c^Wbitr w 

Thus, v^ fO ^.i mr y " 36 J^.v . or/uf& 

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Mr. A. Tylor on Tides and Waves. 207 

at its mean distance. The attraction of the moon I calculate to 
be one fifteenth greater at a point on the near side of the earth 
than at a point vertically below it on the offside at the antipodes. 
Every day the change of position of the moon with regard to 
the earth would affect all weights on the surface of the earth 
temporarily^ but only to the extent of 1 grain in 61 gallons^ a 
quantity which is not susceptible of measurement by a balance. 
The effect of the moon^s direct attraction is really very small 
on each cubic foot; but as it affects water at the bottom of 
the sea nearly as much as on the surface^ it amounts to an 
enormous moving force when a stream 20^000 feet deep is set 
in motion. It is only perceptible to observation when motion 
is accumulated by composition at certain points^ such as where 
there is a great composition of forces^ as in soundings. Navi- 
gators do not observe the motion of the tide except near the 
coast. I calculate the amount in the following manner. If 
the effective force of 'the moon has to be multiplied eighty-four 
times to raise a 12-foot tide at a point of the coast where the 
sea is 238 feet deep^ then the direct effect of the moon's attrac- 
tion on water 238 feet deep would only be \ foot^ or something 
under 2 inches. Thus T consider 2 inches is the greatest height 
that the moon could possibly raise the level of the sea under it 
with 238 feet depth of water^ |~J- of the elevation of 12 feet 
being the effect produced in deeper water by the moon and 
sun, transferred by the composition of forces to shallow water. 
The drawings (figs. 1, 2, and 3, PI. IV.) from standard works 
on tides are therefore great exaggerations by their authors ; and 
the descriptions accompanying them would lead any one to 
suppose a great heap of water could be rapidly accumulated in 
the central ocean by vertical attraction on deep water. The 
authors do not specify how the water is obtained, or whence it is 
comes, or the data by which they prove such a heaping up 
possible as is proposed by the equilibrium theory. 

Time is the essence of such an operation, which, if done at 
all, must be completed in six hours, or a contrary current would 
set in. The heaping-up movement, to keep up with the rota- 
tion of the earth, would have, in the latitude of Brest, to make 
water flow at 11*3 miles per minute, which is clearly impossible. 
It is not, therefore, surprising that the effect of the tidal wave is 
hardly perceptible at oceanic islands, whereas, if figs. 1, 2, and 3, 
PI. IV., were correct, it ought to be as large there as on the 
mainland coast. 

Fig. 1, PI. IV. is an explanation of the tides copied from the 
' Penny Cyclopsedia ; ' figs. 2 and 3, PI. IV., are from Dr. Lard- 
ner's ' Astronomy,' pp. 324-5 ; and my own view is given in 
fig. 4; so that the reader may compare the different theories. 

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208 Mr. A. Tylor on Tides and Waves. 

If fig. 4, PI. IV., is correct, there can be no great heaping up 
of water or any tidal wave generated in one direction, as has 
been sometimes assumed ; for I show that the action of the tide 
is a reciprocating action, and has as much motion from west to 
east as from east to west. 

The assumption of a great heap of water travelling in one 
direction, or producing a certain amount of retardation of 
the rotary movement of the earth, quite unbalanced by ac- 
celeration, has been taken as a serious fact; many writers 
of reputation have supposed that the rotation of the earth 
must be affected by this hypothetical wave-action in one di- 

My view of the general theory of the tides (fig. 4, PI. IV.) 
differs materially from those generally accepted ; and I cannot 
understand the existence of an intumescence (shown in figs. 1, 
2, and 3, PI. IV.) under the moon at all if the subject is treated 
in the ordinary manner of reasoning. 

I entirely disbelieve in tidal action having the smallest effect 
on the rotation of the earth. It is a balanced action. The sun 
might produce currents by unequally heating water, which 
might affect the surface-level of the sea and cause inequalities ; 
but of this there is no positive evidence. I show by fig. 3, PI. III. 
that, under certain circumstances observed, a curi'ent may travel 
against the slope of the surface. This I noticed in your Journal 
in 1853. The existence of a current is of itself, therefore, no 
proof of what is the direction of the slope of the surface. I find 
that an elevation of level of 2 inches on the east maintained over 
the west side of the Atlantic, or ince versd, where water is very 
deep, would generate a current of 3 feet per minute in the ocean 
in the direction of the slope, supposing the Gulf-stream did 
not intervene and there was no tidal action. The western water 
would take 5 years to cross the Atlantic at a speed of 3 feet 
per minute, to reestablish equilibrium. If the difference of level 
were produced by luni-solar action, it would cause no current 
until the force creating it was withdrawn. 

If 58 miles per hour is the greatest velocity a surface- wave 
could travel at in the deepest part of the Atlantic, such an in- 
tumescence, even if maintained, would have only proceeded 348 
miles before the moon's influence would be exerted against its 
motion. The great earthquake-impulse of Lisbon in 1755, pro- 
ceeding through deep water, did not travel to Barbadoes faster 
than 6 niiles per minute; and an intumescence of equal force or 
impulse created on the W. coast of America, in the latitude of 
Brest, would meet contrary luni-solar attractions when half- 
way across the Atlantic. No intumescence could be raised in 
deep water without forming a gap below. 

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Qiope, is fapponed to i«r?oWe in the circle A.E.B. W in 24 > 
fhe sMne niean yeloeity each 24 hoan,)»is retarded and 
at the exact lunar hours marked, but within them 

>od tide. 

loean below the speed of the earth-baain holding it, 
_iiP9Fy:Aot the rotation) at ebb tide shown in B. B. and W. A,, 
Jl/. J/, isesca flowing ti de as in A. B. and B. W. Fig. 4 plate IV. 


ition in alternate directions, the real mean velocity 

the one direction, and only difference of speed is 

>oking from one to the other only can estimate the 

it of America, for there the ebb tide is in tbe direction 

oceanic water and a flowing tide before it (propulsion ) . 


I present, Jointly attracted by Mi.Mii, attraction 
'/?tnC/^e time. The resultant motion of the particle P n. is 
Jf,JlT, article P. IV is in a contrary direction, because th« 

^through the Earth, deflected by meeting the curved 
Lhich accelerates the ocean in the direction of B to W. 

Aon of £ to B, and the force M. iv being deflected 
on to P. vm and retards water in tbe quadrant W A. 


kuses alack tide at low and high water. 

>f the Barth deflecting attraction rays at vari(>us 

near C, Pig. 4, plate iv supposed when revolving 

M^ do. 

»een accelerated above US per minute back to that 
)w water for convenience. 1 omit the action of 

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Mr. A. Tylor on Tides and Waves. 209 

In fig. 4, PI. IV.^ I take a particle of water at certain points on 
opposite hemispheres^ and show the direction of the resultants 
of the two forces (the moon and earth's attraction) and the pro- 
bable deflection of the moon's attractive rays in passing through 
the earth. Sir J. Herschel (p. 528) only gives one position on 
his Plate (p. 464), and leaves it to the reader to try the position 
of particles on other parts of the circle and find their direction. 
I have tried to do so according to his rule, and find that his 
diagram would only apply to the moon's attraction by the earth 
at such an immense distance that gravity could be considered as 
acting to and from single points, viz. the centres of the two 
attracting bodies, and surface attractions need not be considered. 
Now the case of the tides is clearly that of a point or particle 
at the surface of the earth being attracted by the two centres of 
the earth and moon. IlerschePs figure (p. 464) is not appropri- 
ate to the conditions of the tides ; iot it has no special relation 
to surface attraction at all. If it proved any thing about tides, 
it would prove there would only be a tide every twenty-four 
hours. On the contrary, in fig. 4, PI. IV., I take into account 
the deflection of the rays of attraction on entering the earth, 
and find that, if they pass through the earth with the rapidity 
of light, when they reach the other hemisphere they cause a 
twelve-hours tide, simultaneously produced to that on the oppo- 
site side of the globe. 

I have proved by analyzing the experin^euts on waves 
by J. S. Russell and by Darcy, that the velocity measured in 
feet per second of any wave when generated does not exceed 
three times the cube root oi' the depth of the water it was gene- 
rated in, measured in feet; that is, v=B\/p, a new formula, 
which answers both for small and great depths, the usual for- 
mulae giving results much too high for waves generated in deep 

. Mr. W. Parkes (Phil. Trans. 1868) suggests that the al- 
4emate tides are produced in different hemispheres, and that 
the evening tide which reaches Kurrachee twelve hours after 
the morning has travelled a greater distance. This does not 
seem probable; nor does he give any evidence on the point. 
Then, with regard to the diurnal variations of the two tides, 
Mr. W. Parkes (p. 686y says the diurnal inequalities disappear 
when the attracting bodies are in the plane of the equator. It 
appears to me, from the observations at Kurrachee, that when 
the diurnal irregularity of the high-water points is at its 
maximum, the diurnal irregularity of the low-water points is 
at its minimum, and vice versd. Curiously enough, at Kurra- 
chee the mean diurnal low-water irregularity is about 2 feet, 
against about 1 foot (the mean diurnal irregularity of the high 

P/iiL Mag. S. 4. Vol. 48. No. 317. Sept. 1874. P 

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310 Mr. A. Tylor en Tides and Waves. 

water). Tbat is, instead of tV of the height of this lunar portion 
of the tide representing the diurnal irregularity (which I con- 
sider is the mean of the world), at Kurrachee the tides are so 
exceptional that the diurnal irregularity amounts at low water to 
if and at high water to | of the total height on the average of 
the tides for a month, lliis opposite action cannot be owing 
to the position of the attracting bodies in the respective tides 
being in the plane of the equator. 

I would observe that the deep central ocean without any 
vertical tidal movement or tide-wave observed is certainly forty 
times as large as the shallow coast^sea, where a rise of tide is 
observable. The composers of figs. 1, 2, and 3, PI. 1V.| seem 
to r^ard the coast alone, which I consider the exception. 
They do not seem to think of the tidal conditions in the great 
mass of the ocean at all in forming their theory* 

It appears from figs. 1 and 2, PI. II., and fig. 1, PL III., 
from observation, that the level of the sea at high water, even 
in the tidal estuary of the lliames, is only raised 5 feet, and in 
that of the Clyde 1 foot, above the central ocean. 

The high-water points from Falmouth to Sheemess are nearly 
level; they only deviate 1 foot in 500 miles from a straight line. 

The fact has not been sufficiently considered, that water in 
open channels can be moved under certain conditions against 
gravity, and that the great central mass of the ocean swinging 
backiN^irds and forwards every six hours is one of the forces that 
can easily overeome gravity when producing a slow current. As 
early as 1868 I gave a drawing in your Journal (p. 259) of the 
bottom-water outside the bar of the Mississippi being raised to 
the surface 16 feet against gravity by the current of fresh water 
flowing outwards, partly impelled by gravity (propulsion) and 
partly sucked or drawn by the tidal water in front of it (aspira- 
tion) : see fig. 4, PL III. I still believe that the tidal current 
acts like the piston of a pump, and reduees the pressure in its 
rear, and draws or sucks out the coast-water after it in the ebb- 
tide, and piQshes the water back again to fill up the gap when 
its notion is reversed by the luni-solar force in the flowing tide. 
I first observed evidence of this action on the bars of rivers, and 
represent it in fig. 2, PI. III. As the water in the Mississippi 
is 100 feet deep at a comparatively short distance behind the 
bar BC, and is in motion from^ top to bottom, the lower 
water is evidently drawn over the bar and up an asceut of 84 
feet against gravity, by the pressure of the water at B C on 
the bar being reduced by the tide or mass of oceanic water mo- 
ving steadily before it. Motion, of course, ensues in the direc- 

* Humpbrys and Abbott record rapid motion at the bottom at Carrol- 
iqn, page 149. 

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Mr. A. Tylor on Tides and Waves. 211 

tion of least pressure ; and that happens to be^ as far as the upper 
part of the water is ooneerned, against gravity, and is similar to 
what happens in a mill-raee (fig. 8, PI. III.). This action, 
which takes place at the mouths of all large rivers, is a clue to 
the tidal movements. It is true that in the Severn at Beachley 
the high-water level of spring tides is 25 feet above the 
Ordnance Datum, and 21 feet above the level of the central 
ocean. But this is an exceptional case that can be explained. 
At Beachley at high water the cross section is 400,000 sup. feet, 
and at low water only 25,000 sup. feet (see fig. 1, PI. II.)- 

At Stonebench, 36 miles higher, there is only a cross section 
of 240 feet, and a depth of 8 feet at low water. 

The cross section at Beachley is not a tenth of the sexstion a 
few miles lower down in the Bristol Channel. 

The exceptional height of the tide there is solely due to the 
funnel shape of the c^nnel, caused by the hard recks that pre- 
vent the tideway being excavated to the usual form. This 
exception proves the rule. I compare the ebb-tide to the action 
of a mill-stream, thus i-^ 

Fig 8, PL III., represents, from actual observation, a case 
of water moving against gravity in an open channel, and against 
the direction of the slope of the surface of the water. The 
atream of water passing over the weir at B falls in a thin stream at 
great velocity to C^. Here it changes its direction and the current 
is against the slope of the surface, vis. towards D^ instead of 
towards C^, which would be the direction of gravity. The 
stream D E in uniform motion niduces the pressure at D and 
draws the water from C after it— just as the great central 
oceanic stream represented in figs. 1 and 2,. PI. II., and in 
fig. 1, Plate III., draws the coast-water westwards and forms a 
gap which is filled by the tide, the oceanic stream having reversed 
its direction in six hours, as shown in fi^« % PL IV., by luni- 
solar attraction pushing on to the coast-hne the flowing tide. 

My explanation of Che luni-solar attraction in fig. 4, PL IV., 
is placed, adjoining the drawing. 

It will be observed I omit in the diagram (fig. 4, PL IV.) the eits* 
tomary theoretical intumescences opposite to each other movine 
with the moon, but through eadi of which every part of the earth 
is supposed to pass daily, as in figs. 2 and 8, PL IV«, and I show 
an alternating tide in the ocean itself instead, in fiig. 4. I con- 
fess I cannot follow the supposed changes of form of the ocean- 
surface in figs. 1, 2, and 8, PL IV., nor imagine either that such 
movements could possibly occur, or that they .would at all de- 
ncribe the tidal changes at any point of the globe as known to 
obs^rvera. I remark, the writera give no dimensions of the in- 
tumescences, or calculate the force to convert the circle ab into 


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212 Mr. A. Tylor on Tides and Waves. 

the ellipsoid a, by M. Arago very justlv wrote that '^ details are 
the touchstones of theories ;'' and all details are absent in the 
well-known articles on this subject. In fig. 1 the earth is 
represented as a circle^ and the ocean as an ellipsoid* In figs. 
2 and 3 the water is the circle^ and the earth the ellipsoid. 

According to figs. 1, 2, and 8, PI. IV., the velocity of the 
tide would be equal at high, low, and half tide to any observer 
on the earth. 

The greatest action, on the contrary, is shown to be at the half 
tide, both ebb and flowing, in my diagram, fig. 4, PI. IV. Cap- 
tain Beechey* remarked that the velocity of the current was 
greatest at half tide ; and this disproves any theory in which 
the tide is supposed theoretically equally strong at all parts. 

Dr. Lardnerf explained his diagrams, figs. 2 and 3, PI. IV., 
by stating that the moon forces down the water at the sides at 
right angles^o her direction, and raises it at the two ends of its 
diameter pointing to her. In figs. 2 and 3, PI. IV., the moon 
pulls the water in one hemisphere and pushes it away in the 
other. This is the first time that the property of repulsion or 
forcing has been attributed in this manner to the heavenly bodies. 
He shows an exactly opposite direction of forces on the near and 
far side of the earth prodbced at the same moment by the moon. 

Notwithstanding any language that may be used to make 
figs. 1, 2, and 8, PI. IV., appear to satisfy the actual tidal con- 
ditions, it will, I think, be evident to the reader that the posi^ 
tions of the forces as drawn are not in accordance with the ordi- 
nary laws of mechanics. Herschel refers the reader to his 
drawing (Astronomy, p. 461), in which the retardation and acce^ 
leration of the moon in its elliptic orbit round the earth at a 
mean distance sixty times the radius of the earth is proved to be 
according to the law of equal spaces being described by the moon 
in equal times, and consequent variation of motion. 

The reader is recommended by Herschel to prove the accele- 
ration or retardation of the tides from the diagram (p. 464), 
which is really impossible, as the figure relates to an entirely 
different case, and is in a part of his book relating to the motions 
of the moon. It is admitted that the moon is a free body attracted 
at a great distance by the earth, and made to mo\ e at varying velo- 
cities round the earth in a lunar month at a rate dependent, among 
other causes, upon the relative weights and distances of the moon 
and earth, and the original impetus and angle at which these 
bodies were projected into space. The tidal water, on the con- 
trary, is held as- an inseparable mass of fluid reposing in a basin 
of earth ; and it travels at the same uniform speed of rotation as 

♦ Phil. Trans. 1851, p. 711. 

t Lardner*8 'Astronomy,' p. 336. 

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Mr. A. Tylor on Tides and Waves. 213 

the earthy except when modified in velocity to a very small ex- 
tent by the attraction of the celestial bodies, producing the tides. 
The two cases are not parallel, and the diagram mentioned by 
Herschel is certainly not applicable to the tides at all. The 
oceanic water has no tangential force independent of the earth ; 
for two points in the ocean^ reaching 180°, opposite to each other 
are at the same distance from the centre of the earth, and are in 
exact equilibrium if the difference of tidal action i& left out of 
consideration. I think the authors have not taken into consi- 
deration the fact that the rays of attraction from the moon to 
the water, when the water is screened from the moon by the 
earth, would pass through the earth, in order to reach the oppo- 
site side, not in a straight line. They would not only lose force of 
course as the square of the distance increased, but I think no 
ray or vibration or impulse or line of attractive force could fall 
upon or pass through a curved body such as the earth at an acute 
angle without being in some way defiected or diverted from its 
direct course in passing through the earth to water on the other 
side ; and the reverse is true. I believe a vibration of any kind, or 
attraction-ray, would have to be modified in its direction or bent 
at the point of contact, so as to enter the surface of the earth at a 
right angle to a[tangent of the curve at the point, as shown in fig. 4. 

My own view (PI. IV. fig. 4) shows slack water at the turn 
pf the tide both near high and near low water; but of course these 
events do not always coincide. When the luni- solar attraction-rays 
fall near A and B (fig. 4, PI. IV.), they are evidently deranged and 
deflected so as to produce very little effect ; in fact the state of 
the tide near those points is what might be called bordering on 
motion, which state accords with observation. Although the angle 
M|P^R^ is onljr i"'07y or two thirds of the angle M^^P^^R^,, yet the 
factual effect m producing tidal motion is much less than that 
proportion. For at P the tidal motion is being reversed^ and 
the speed of the flowing tide has to be created from slack water; 
while at P^^ the effect of attraction from M^^ is to accelerate the 
tide then moving freely and in the same direction as it has been 
between P^ and P^^ and also in the line of the earth's rotation. 
The actual effect in velocity theoretically is quite four times as 
much in the half hour near P^, as at that near P^ ; and this accords 
with observation. The angle of the resultant B^ is found thus. 
The angle M^P.C is 88^ 30? 4"=318604 seconds. 

The force M.P, is to C P, as 1 to 295,520 ; .'. the angle 

M|P^Bp the resultant, equals q," q^ =F'07. In the same 

manner the angle M^^P^,B^^=1"*66. The depth of the Atlantic 
(five miles) favours movement very much, as there is room for the 
force in the direction A B^ to be transferred easily into the direc- 

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214 Mr. A. Tylor on Tides and Waves. 

tion P^, E, which is that of the line of rotation. In an inland sea 
like the Mediterranean, where the deep water is 6000 feet, the 
movement of the tide on the coast is often not more than 1 foot. 
There are 7-feet tides in one or two places in the Mediterranean 
where the contour of the coast is like onr Bristol ChanneL 

If the deep water in the Mediterranean Sea were one twelfth 
of the depth of that in the Atlantic, we should expect a 1-foot tide 
there in place of a 12-feet, according to the law of compositimi 
of forces'!'. The peculiar circumstances of the Mediterranean 
make the tides much smaller than I should have calculated from 
the experience of the Atlantic. Taking 6000 feet as the basis of 
the deep water and 9 inches as the tide, diffusion of the tidal force 
from deep central to surrounding shallow coast-basins seems to 
absorb i of the force. The proportion of deep water is very small. 

The Mediterranean standard of rates of depths of ocean to 
height of tide along its coasts, seems to match more with 
Pacific and west*coast-of- America standards than with the obser- 
vations on the eastern Atlantic coast. The European tides seem 
exi^gerated, even when compared with the east coast of America* 
This may be explained by less diffusion c£ tidal force and the 
contour of the sea- bottom on our coast being more favourable 
to receiving impulses giving velocity to the coast-water than 
that on the east coast of America. For want of space I have 
hardly been able to allude to the solar influence of the tides, 
which differs in some respects from the lunar relations. 

Hie diurnal and semidiurnal tides are known to vary about 
4 inches in an 8-feet tide. Then, supposing that 2 feet of the 
8 feet is caused by solar attraction, the variation is one fifteenUi 
of the height due to lunar action. If the tide generated in deep 
water is twelve lunar hours reaching a part of the coast, the greater 
alternate twelve-hours' tide will become the lesser of tl^ two. 
There are many other considerations to take into account which 
materially modify the sise of the alternate tides at different parts 
of the month ; and I do not put forward mv own view with any 
pretensions to improve the prediction of tiaes, which indeed is 
already perfectlv done by the machine invented by Sir W. 
Thomson and Mr. E. Roberts of the Nautical Almanac Office. 
What I wish to do is to give an explanation of a theory of the 
tides which shall accord with the physical facts. Supposing 
the point E is thirty diameters of the earth from the moon on 
any day, then the point W will be 81. Then, the attraction 

* In the Admiralty Tide Tables there are odI^ tides at tea placet in the 
Meditemuiean recorded. The highest spriag tide is 7 feet, and the ave- 
rage 4*3 feet. Admiral Spratt, F.R.S.» has just iafomed me that the 
average of all spring tides in the Mediterranean is firom 9 to 10 inches, 
perceptible within three days of the highest tide. It is evident to me that 
the tide in that tea is generated in hasms^ so that it is diffused in getting 
to the coast, by which ) of the proper height must be lost. 

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Mr. A. Tylor on Tides and Waves. 215 

being inversely as the square of the distance, the force at E will 
be to that at W as 31^ to 30S or as 961 to 900 (that is, one 
fifteenth greater) . This calculation ought to agree with obser- 
vation at ports where the variation in height each alternate tide 
is eliminated from other disturbances, and where there are no 
exceptional circumstances, if this is a correct explanation of the 
difference between the height of the diurnal and semidiurnal 
tides (which 1 term the near-side and far-side tides). 

The luni-solar attraction-rays in passing through the earth 
may encounter changes from fluid to solid substances having 
surfaces not at right angles to the incident ravs ; and the rays 
would not then follow straight lines, although I have for con- 
venience represented them as straight in fig. 4, PI. IV. 

Those rays passing throi^rh the higher parallels of latitude 
far from the centre might aflfect the tides apparently in an irre- 
gular manner. These changes of direction might explain why, 
in order to predict with great accuracy the height and time of 
the tide at some stations, Sir W. Thomson and Mr. £. Roberts 
have been obliged to employ twenty-seven fictitious stars instead 
of only the number to express the effects of the moon and sun's 
various positions. 

The different currents that occur, causing different establish- 
ments at ports near each other, seem to indicate movements of 
masses of water apparently at different angles to each other. 
These motions can be illustrated by an experiment in the injector. 
In the water-pipe, at right angles to the body of the injector 
(where steam is at 101 lbs. pressure), there is a partial vacuum, 
say equal to 2 inches of water. I find that the motion of the 
steam will increase its own pressure 1 lb. by friction against the 
metal instrument. The steam travelling with great velocity de- 
flects the water-current and bends it into its own direction, and 
forces water into the steam-boiler, where the pressure is 100 lbs. 
The water-pipe is all the time open to the atmosphere and to 
the boiler two ways through the injector; but little steam 
escapes through the open water-pipe. The barometer is another 
instance. The column of mercury ought to lengthen if that 
instrument registered the absolute weight of the atmosphere 
alone, when the column of air is loaded with vapour. The mo- 
tion of the vapour in the act of condensing, however, generates 
currents and produces motion of particles in a direction across 
the column. This reduces the pressure of the column on the 
cistern of the barometer; and therefore the column shortens 
for motion instead of lengthening for weight. Motion in 
main water-pipes reduces pressure in branches where there is 
no motion. 

Currents in motion in different directions, owing to different 
temperatures or other causes, affect the tidal currents materially, 

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216 Mr. A. Tylor an Tides and Wooes. 

and prevent the tide-gauge ever r^stering the tidal inflaencea 
alone at any point. This is the cause of different establishments 
at neighbouring ports apparently in similar position as regards 
the luni-sokr influences. 

Fig. 1 shows that the area of the gap formed when the wsfe 


V.M Lines of veat/cal motion of particles without horizontal motion. 


was generated is the limit of horizontal movement of particles 
throughout the run of that wave. Experiments show that if 
waves artificially produced for experiments continue the same 
height their velocity diminishes^ and if their height diminishes 
they may keep up their velocity. It is impossible to keep up 
both the velocity and height of any wave a long distance. If it 
were possible it would involve perpetual motion, as the wave is 
resisted by the air above and by the water in which it vibrates. 
Let t^ represent velocity of the motion of a wave measured in 
feet and the time (a second) in which its crest passes a fixed point, 
and p the depth of the water in feet ; then by means of the for- 
mula v^S^yp the actual velocity found by experiment may be 
{predicted as accurately as by the usual formula t;=\/^A^. The 
atter formula appears extremely incorrect for great depth, as it 
indicates impossible velocities for waves. If the depth of the 
Atlantic was 21,952 feet, the greatest velocity that could by any 
means be given to a wave wouldbe 84 feet per second^ or 58 
miles p er hour ; for if vsa\^Sp, then from this we have 
84=8v^2l952, that is, 84 feet per second is the maximum ve- 

* The gravity formula, v*j=2gh, only applies where there is no resistance 
to motion. It is of no use in cases of uniform motion. My new formula 
(page 205) gives the due effect of weight on velocity. Thus in a river or 
a glacier with sixty-four times the quantity (or weight^ flowing or sliding, 
the velocity would increase four times at the same slope. "jHiis law ex- 
plains why in the glacial period frozen rivers reached such low levels, and 
why denudation was so lar^ in the pluvial period, as destructive effect is 
in a high ratio to the velocity. 

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Mr. A. Tylor an Tide$ and Waves. 217 

loeity of the wave, instead of the impossible velocity of 800 miles 
per hoar suggested by some authors. 

An earthquake might transmit a blow through the deep water 
in the ocean at six miles per minute, as a wave was formed at 
Barbadoes 8000 miles from the supposed origin of the shock in 
585 minutes after it was observed at Lisbon. Michelle in 1755 
wrote '^ when the bar at the mouth of the Tagus was seen dry 
from shore to shore, then suddenly the sea, like a mountain, came 
rolling in/' When this blow struck a distant coast below the level 
of the sea, it would be reflected and cause the sea to ebb from the 
coast first. Then when the force which heaped up the water away 
from the shore diminished by work done upon the water in raising 
up the level of the sea, a great wave would be moved shorewards 
by gravity. The first announcement of the approach of an 
earthquake- wave is the ebb of the water'*', not a surface- wave. 

If a great surface-wave were generated by an earthquake, it 
would not travel veiy far, but would soon diminish in height 
and speed, and would not be preceded by a wave in an opposite 

In some careful experiments in a course of one fifth of a mile t 
a surface-wave lost five sixths of its height. A powerful shock 
or impulse could possibly be communicated through deep water, 
like a blow through a solid body, an immense distance with 
great velocity ; but that is not the case of a surface-wave at all. 

There is, therefore, a great distinction between primitive tidal 
impulses and the secondary waves that accompany or follow 
them, or the movements in coast-water produced at distant places 
and times by means of the composition of forces. The tidal im- 
pulse is communicated rather in the manner motion is conveyed 
from a steam-engine through mechanical gearing, such as drivers 
and followers, and where there is lost time and lost motion be- 
tween the teeth of the driving-wheels, or bands and pulleys, or 
levers, or other parts of the apparatus through which the move- 
ment is communicated from a prime mover to some distant 

Thus the piston may have commenced its down-stroke before 
the effect of the former up-stroke had reached the extremity of 
the shafting. This lost motion is very perceptible in figs. 1 and 
2, Plate II., and fig. 1, Plate III. 

The particles of water may revolve along their axes ; or all the 
vibrations may not be effective, some of them neutralising others, 
and for a short time destroying the impulse of the central tide- 
generating force, soon to be renewed. 

The hours at which high water arrives are written against the 

♦ MicheU, Phil. Trans. 1766. 
t Brit. Assoc. 1838, p. 465. 

Digitized by VjOOQ IC 

218 Mr. A. Tylor on TideM and Waves. 

names of the towns situated on the coast or river-bank in Plates 
II. and III. 

In fig. \, Plate II.j a point is assumed in the Atlantic 800 
miles from the Land's End, where the high- and low-water level 
is assumed to be invariable, and where the mass of the ocean 
water is supposed to move east and west very slowly in alternate 
and opposite directions in each tide. 

When the flowing tide is moving a ship 8 miles an hour, there 
is 360 miles difierence in distance, and 6 hours' time, between 
high water at Plymouth and Dover ; therefore the lost motion 
is 18 miles out <^ 860, or 5 per cent. The impulse received at 
Plymouth from the central slowly moving oceanic water must 
have been transmitted through the deeper water at a much 
higher rate, but only reaches Dover after travelling at 60 miles 
an hour. Then the impulse is transmitted from Dover to Lon- 
don at the rate of 120 miles in three hours, or 40 miles an hour, 
the tide only taking a ship 9 miles in 8 hours ; so that the lost 
motion is 9 miles out of 120, or 7 per cent., the difference of 
time between Plymouth and Dover (21 minutes) not being taken 
into account. 

I have allowed a slope of 1 foot in Plates II. and III. to bring 
the water to the mouth of the Clyde, and 5 feet to bring the water 
to Falmouth from the Atlantic 

If the level of the ocean were kept up above its due level only 
2 inches between the western and eastern boundary of the 
Atlantic deep wator^ that slope would suffice to create a current 
of 8 feet per minute in the whole mass of deep water. This is 
supposing the law of velocity followed the ratio I observe in 
smaller cases. If the two inches were only water heaped up in 
consequence of, or by the hmi-solar attraction, it would create 
no current at all while that attraction continued. 

As the effect of the moon on the oceanic water is only eqoal 
to that of a sphere of 118*75 miles in diameter, equal in mean 
density to the earth, placed near and revolving about C in a lunar 
day, it occurred to me that some geological difficulties, such as 
the evidence in the Crag and Quaternary deposits of the tides in 
the Quaternary period being three or four times as large as at 
present, might be explained by periodic changes of position 
of part of the interior of the earth, rather than by supposing 
great changes in the distance of the moon from the earth. Also 
the quantity of water in the ocean can only be the difference 
between that of the vapour held in the atmosphere or condensed 
into snow or ice on the land, and the quantity of water or vapour 
of water mechanically or chemically combined with the strata of 
the earth. These are Quantities capable of enormous variation in 
geological periods under different conditions. There is also a 

Digitized by VjOOQ IC 

Mr. A. Tylor on Tides and Waves. 219 

periodicity about the alternation of land and water surfaces, 
particularly in the Carboniferous period^ which might be ex- 
plained by slow changes in long intervals of the disposition of 
the solid and fluid internal substance of the earth with regard 
to and about its centre. 

A slow circulation of an eccentric mass of fluid may occur in 
the interior of the earth, and gases may periodically pass from one 
part of the solid portion to another, their place being supplied 
by fluids, attracting the ocean unequally. 

Unequal attraction from variable subterraneous inequalities 
would affect different points of the surface and raise the water- 
level on one part for long periods and depress it on alternate and 
opposite points to an equal extent. The theory of inconstancy 
of rainfall and of fluctuation of the sea-level in ^logical periods 
is gaining ground since I first advanced these views (in 1858) in 
this Journal, in a paper entitled ^' Fluctuations of the Sea4evel 
in stated Periods of Time." 

We must not gauge our interpretation of nature by the pre* 
sent temperature, rfonfall, or tide-gauges^ but from the actual 
evidence presented in the strata themselves. 

In conclusion, if all the lines of Itmar attraction M^ M^ &c. 
(flg. 4, PI. IV.) were continued through the earth without deflec- 
tion from a straight line, then there could be only one lunar tide ill 
the twenty-four hours; for all the water on one side of the axial 
line, E G W or half the globe, moving in the direction of the ro- 
tation of the earth, would be accelerated, and all the water in the 
other half,E B W, of the globe would be retarded, a^ th^ attraction 
of the moon in that half would be contrary to the direction of the 
rotation of the earth. The fact of the tides occurring ^v^ry twelve 
hours is a proof that the view J have put forward of the defleo* 
tion of the attracting rays in their passage through the earth is 
a correct one. The twelve-hour tides on the opposite side of the 
earth to the moon are physical proofs that att»*action-rays are de- 
flected. If not, there could be no such effect of attraction on th^ 
ocean as is shown by the twelve-hour tide. The theoretical 
differences of one fifteenth of the height of alternate tides I 
believe accord with observation, taking the average of the world. 

According to Professor Stokes, any solution of a problem that 
satisfies all the conditions must be the true one. I believe 
the solution suggested in this letter conforms entirely to the* 
facts, and that the deflection-theory, now, I believe, first pro- 
posed, is true. YourB truly, 

A. Tylor. 

P.S. With regard to the new equations to the flow of water 
in page 305, 1 use coefficients for different materials of channels : 
see note to PI. III. fig. 3. 

Digitized by VjOOQ IC 

[ 220 ] 
XXXII. Proceedings qf Learned Societies. 

[Continued from p. 153.] 

February 6, 1874. — Joseph Dalton Hooker, C.B., President, in 

the Chair. 

n^HE following c<Mnmunication was read : — 

^ ** On a Self-recording Method of Measuring the Intensity of 

the Chemical Action of Total Daylight.** By H. E. Eosooe, F JI.S. 

The object of the present communication is to describe an instru- 
ment by which the varying intensity of the chemically active rays, 
as affecting chloride of silver paper of constant sensitiveness, can be 
made self-recording. The method described by the author in the 
Bakerian Lecture for 1865, although it has been the means of 
bringing into notice many impor^mt tscta concerning the distribu- 
tion of the sun^s chemical activity throughout the atmosphere, as 
well as in different situations on the earth's surface, has not as yet 
been introduced as a portion of the regular work of meteorological 
observatories, owing to ihe hxt that, in order to obtain a satis&o- 
tory curve of daily chemical intensity, at least hourly observations 
need to be made, and this involves the expenditure of more time 
and labour than it has been found possible to give. In the pre- 
sent communication a method is described, which, whilst preserving 
untouched the principles and accuracy of the former method, re- 
duces the personal attention needed for carrying out the measure- 
ments to a minimum, and thus renders its adoption in observatories 

According to this plan, a constant sensitive paper is exposed by 
a self-acting arrangement for accurately known times, at given 
intervals throughout the day. The insolation apparatus stocked 
with sensitive paper is placed in position either eany in the morn- 
ing of the day during which the measurenients have to be made, or 
on the previous night, and by means of an electric communication 
with a properly arranged clock, the sensitive paper is exposed every 
hour during; the day, so that, in the evening, the observer has only 
to read off, in the ordinary manner, the hourly intensities which 
have been recorded on the paper during the day. 

This self-recording arrangement, though apparently simple, in- 
volves points which mive rendered its successful completion a some- 
what difficult matter, owing, in the first place, to the great varia- 
tions which occur in the chemical intensity of total daylight in 
different places, at different times of the day, and in different pe- 
riods of the year ; and secondly, owing to the fact that, in oraer 
to be able to estimate the chemical intensity, the coloration ac- 

2uired by the paper must reach, but not much exceed, a given tint, 
t becomes necessary therefore that on each occasion when an ob- 
servation is needed, the sensitive paper should be exposed me- 

Digitized by 


Royal Society. 221 

chanically, not once, but for several known but varying intervals 
of time quickly succeeding each other ; so that whatever may be 
the intensity of the total daylight (supposed during these intervals 
to remtdn constant), some one ajb least of the several expose^ 
papers will possess the requisite shade. This is accomplished by 
a duplicate arrangement of a clock and insolation-apparatus, by 
means of which disks of the constant sensitive paper are exposed 
each hour for successive known intervals of time, varying from two 
to thirty seconds. After an interval of an hour, another set of 
• disks are exposed for the same series of intervals ; and these series 
of insolations are repeated once every hour during the day. The 
mechanical arrangements for effecting this with accuracy are fully 
described in the paper. On unrolling, at the end of the day, the 
strip of sensitive paper which has served for the exposures, black 
disks showing where the paper has been stationary for the hour 
are seen ; and between each of these are found ten ordes variously 
tinted, from that, probably, scarcely visible, which was exposed for 
two seconds, to that, perhaps too dark to read off, which was inso- 
lated for thirty seconds. Amongst these, some one at least, will 
be found of such a shade as to enable it to be read off by the mo- 
nochromatic soda-flame, on a graduated fixed strip, as described in 
former communications. 

A new method of calibrating the fixed strips of standard tints 
necessary for these measurements is next described ; and the ques^ 
tion as to the possibility of preparing constant sensitive paper in 
long strips instead of in large sheets is next experimental^ dis- 
cussed, the result of the examination being that it is possible to 
prepare silvered paper in long narrow strips such as are used in 
Morse's tel^raph-apparatus, so that it shaU throughout its length 
preserve the standard sensitiveness. 

The time during which the disks of constant sensitive paper are 
exposed is next ascertained for each instrument by a chronc^raph. 

During wet weather the insolator is covered by a semicircular 
glass shade ; and the value of the coefficients for refraction and 
absorption due to- this glass shade is determined. 

The latter portion of the communication contains the results of a 
deries of comparisons of the curves of daily chemical intensity ob- 
tained (1) with the hand-insolator, and (2) with the self-recording 
instrument. Comparisons of this nature were made during the 
months of May, June, and July, 1873, by simultaneous hourly de^ 
terminations in the neighbourhood of Manchester according to both 
methods. Of these observations, six full days are selected ; and the 
tables and curves accompanying the communication show the close 
correspondence of both sets of observations. The integrals of total 
chemical intensity for these days are also given, and exhibit as close 
an agreement as, from the nature of the experiments, can be ex- 

Digitized by VjOOQ IC 

222 Rnyal SoeUty :— 

Feb. 12. — Joseph Dalton Hooker, C.B., President, in the Chair. 

The following communication was read : — 

" On the Division of a Sound- Wave by a Layer of Flame or heated 
Gas into a reflected and a transmitted Wave." By John Cottrell, 
Assistant in the Physical Laboratory of the Royal Institution. 

The incompetency of a sound-pulse to pass through non-homo- 
geneous air having been experimentally demonstrated by Dr. Tyn- 
daU, and proved to be due to its successive partial reflections at the 
limiting surfaces of layers of air or vapour of different density, 
further experiments were conducted in order to render visible the ' 
action of the reflected sound-wave. 

The most successful of the various methods contrived for this 
purpose consists of the following arrangement. A vibrating bell 
contained in a padded box was directed so as to send a sound- 
wave through a tin tube, B A (38 inches long, 1 1 inch diameter), 
in the direction BF, its action being rendered manifest by its 
causing a sensitive flame placed at F* to become \iolently agitated. 

The invisible heated layer immediately above the luminous por- 
tion of an ignited coal-gas flame issuing from an ordinair bat's- 
wing burner was allow^ to stream upwards across the end of the 
tin tube B A at A. A portion of the sound-wave issuing from the 
tube was reflected at the limiting surfaces of the heat«d layer ; 
and a part being transmitt-ed through it, was now only competent 
to slightly agitate the sensitive flame at F. 

The heated layer was then placed at such an angle that the re- 
flected portion of the sound-wave was sent through a second tin 
tube, A F (of the same dimensions as B A), its action being ren- 
dered visible by its causing a second sensitive flame plaodd at the 
end of the tube at F to become violraitly i^ected. This action 
continued so long as the heated layer intervened; but upon ite 
withdrawal the sensitive flame placed at F, receiving the whole of 
the direct pulse, became again violently agitated, and at the same 
moment the sensitive flame at F, ceasmg to be affected, resumed 
it« former tranquillity. 

Exactly the same action takes place when the luminous portion 
of a gas-flame is made the reflecting layer ; but in the experimente 
above described, the invisible layer above the flame only was used. 
By proper adjustment of the pressure of the gas, the flame at F 
can. be rendered so moderately sensitive to the direct sound-wave. 

Digitized by VjOOQ IC 

Mr. Donkin on the Contrition of two Harmonie Curves. 223 

that the portion transmitted through the reflecting layer shtAi be 
incompetent to affect the flame. Then by the introduction and 
withdrawal of the batVwing flame the two sensitive flames can be 
rendered alternately quiescent and strongly agitated. 

An illustration is here afforded of the peif ect analogy between 
light and sound ; for if a beam of light be projected from B to F", 
and a plate of glass be introduced at A, in the exact position of the 
reflecting layer of gas, the beam will be divided, and one portion 
will be reflected in the direction A F, and the other portion trans- 
mitted through the glass in the direction F*, exactly as the sound- 
wave is divided into a reflected and a transmitted portion by the layer 
of heated gas or flame. 

Feb. 19. — Joseph Dalton Hooker, C.B., President, in the Chair. 

The following communication was read : — 

'* On an Instrument for the CompoBiticm of two Harmonic 
Curves.'' By A. E. Donkin, MA., F.iLa.S., Fellow of Exeter Col- 
l^;e, Oxford. 

The interest in such compound curves lies in the fact that, as a 
simple harmonic curve may be considered to be the curve of pres^ 
sure on the tympanic membrane when the ear is in the nei^bour*- 
hood of a vibrating body producing a simple tone, so a curve com- 
pounded of two such simple harmonic curves will be the carve of 
pressure for the consonance of the two tones which they severally 
represent, and thus the effect on the ear of different oonsonances 
can be distinctly represented to the eye. 

If the motion of a point be compounded of rectilinear harmonic 
vibrations and of uniform motion m a straight line at right angles 
to the direction of those vibrations, the point will describe a simple 
harmonic curve. 

Thus a pencil-point performing such vibrations upon a sheet of 
paper moving umformly at right angles to Hkeir direction would 
oraw such a curve. 

The same kind of curve would also be drawn by keeping the 
pencil fixed and by giving to the paper, in addition to its continuous 
transverse motion, a vibratonr motion similar and parallel to that 
whidi the pencil had ; and ii ihe motion of the latter be ndw re^ 
stored, a complicated curve will be produced whose f onn will depend 
on the ratio of the numbers of vibrations in a given time or the 
pencil and paper, and which will be the curve m pressure for the 
interval corresponding to this ratio. 

The manner in which these three motions are combined in the 
machine is as follows : — ^Two vertical spindles, A and B, revolving 
in a horizontal plate carry at their lower ends each a crank, and 
D, and at their upper ends each a wheel cut with a certain number 
of teeth ; these two wheels can be connected by means of an inter- 
mediate one, as is seen in the figure ; and since either wheel of the 
pair can be replaced by another with a different number of teeth, the 
relative angular velocities of the spindles can be regulated at plea- 
sure. The paper upon which the curve is to be drawn is carried upon 

Digitized by VjOOQ IC 

224 Roifal Society :— Mr. A. E. Donkin on an Instrument 

a rectangukr frame, E F G H, capable of sUding boriax)ntally up and 
down in a direction parallel to that of the plane passing througli the 

spindles. This frame has a pair of rollers, E F and G H at eax^b end 
connected by tape bands, between which the paper passes as t^^ ^^' 
lers turn. In order to give a motion of reyoiution to the roH^^^' * 
wheel, L, is fixed upon the axis of one of them whose teet>li Sl^ 

Digitized by VjOOQ IC 

for the Composition of two Harmonic Curves. 225 

into those of a pinion, P Q, alongside which the frame slides, and 
which is itself driven by one of the vertical spindles. A connecting- 
rod, D M, is carried to the frwne from the crank of this spindle, so 
that upon turning the latter a vibratory motion is given to the 
former ; and since the transverse motion of the paper aJso d^jends 
upon the same spindle, a fixed pencil-point resting on it would 
draw a simple harmonic curve whose amplitude would depend on 
the radius of the crank, and wave-length on the transverse speed of 
the paper, which can be regulated at pleasure by means conj^ived 
for the purpose*. 

A vibratory motion similar and parallel to that of the frame is 
^ven to a small tubular glass pen, E, so arranged as to move with 
its point lightly resting upon the paper. This motion is commu- 
nicated by a connecting-rod, C N, from the other crank, which is 
carried underneath the sliding frame and jointed to the lower end 
of a small vertical lever, S, to whose upper end the arm carrying 
the pen is attached. 

The weight W serves to regulate the pressure of the pen on the 
paper, as it can be screwed in or out. T is merely a pillar upon 
wluch the change-wheels can be placed for convenience. 

If the pair of wheels on the spindles are now connected by the 
intermediiftte one, it is plain that, upon turning either of the spin- 
dles by a winch provided for the purpose, the two motions of the 
paper will be combined with that of the pen, and the curve drawn 
will be that composed of the two simple harmonic ones which 
would be the result of separately combining the harmonic vibrations 
due to each crank with the transverse motion of the paper. Thus, if 
m and n are the numbers of teeth on the pair of wheels respectively, 
the equation to the resultant curve will be 

y=sin ww7-f sin nx. 

This equation implies not only that the radii of the cranks are the 
stune, but also that they start parallel to each other and at right 
angles to the vertical plane passing through their axes : both these 
conditions can, however, be altered ; and therefore the general form 
of equation to the curves which the machine can draw will be 

y=a sin (ww?-fa)-f6 siu (wa? + /3), 
where a and h are the radii of the cranks, and a and ^ are depen- 
dent on their relative inclinations to the above-mentioned vertical 
plane at starting. 

As an example, suppose that a =6, while the ratio of m to n is as 
2 to 1 ; then the above equation will represent the curve of pressure 
for the octave. Similarly, ifmistonasl6 to 15, the resultant 

* It BhouM be observed here that the vibratory motion thus given to the fVame 
is not truly barmonic. In order to make it so, a more complicated contrivance 
tban the simple crank and connecting-rod would bave to ue adopted ; but this 
would probably introduce, through unavoidable play, an error greater than the 
present one, the length of the connecting-rods and Uie small size of the cranks 
rendering the latter nearly inappreciable. The motion will, however, for the sake 
of convenience, be considered truly harmonic throughout 

Phil Mag. S. 4. Vol. 4«. No. 317. Sept. 1874. Q 

Digitized by VjOOQ IC 

226 Royal Society. 

curve represents the effect on the ear of a diat<Hiic semitone, while 
the ratio 81 to 80 would give that of the comma. In hoth these 
curves, and more especially in the latter, the beats which would 
ensue on actually sounding the two tones together are shown with 
lemarkable distinctness. 

As the machine is provided with a set of change-wheels, many 
different curves can be produced, while ihe form of leach can be 
more or less changed by altering the relative positions of the 
cranks before bringing the idle wheel into gear. It is also possible 
to obtain very large values of m and n in the above equation by 
using two idle wheels on the same axis, which shall come into gear, 
the upper one with the wheel on the one spindle, the lower one with 
that on the other. 

Thus, suppose A and B are the numbers of teeth on the spindle- 
wheels respectively, C and D those on the idle wheels, ana let A 


gear with C and D with B ; then — s -r^ . Now, by properly 

n AD 

choosing the four wheels, large values of m and n may be obtained. 

If, for instance, A=81, B=80, C=55, and D-27, - =^^ ; this 

n 2187 

ratio being nearly = -, the corresponding curve will represent the 

effect of an octave slightly out of tune. The period of such curves 
as these being very long, it is necessary to have a good supply of 
paper ; and this is arranged by carrying a reelf ul on the horizontal 
frame, from which it is slowly unwound between the rollers. The 
rate at which this takes place has a good deal of influence on the 
form of the resultant curve ; the slower it is, the more compressed 
will the latter appear. Instead of using paper, the curves, pro- 
vided the periods are short enough, may be drawn on slips of black- 
ened glass, which can be carried along between the tapes connecting 
the rollers ; they can be at once pUced in a lantern and thrown on 
a screen. 

The width of contour of any curve depends on the radii of the 
cranks : these may have any value between and half an inch ; and 
therefore the limit of possible width at any part will be two inches ; 
so also, by altering the radii, a series of curves may be produced 
corresponding to the consonances of tones not of the same inten- 
sities. Since the maximum width of any curve will be double the 
sum of the radii of the cranks, the paper is cut to a width of two 
and a half inches, within which all curves which can possibly be 
drawn will be comprised. 

The instrument is constructed by Messrs. Tisley and SpiDer, of 
Brompton £oad, to whom some improvement upon the original 
model it due. 

Digitized by VjOOQ IC 

Geological Society. 227 


[Continued from p. 155.] 

November 19, 1873.— Prof. Ramsay, F.R.S., Vice-President, 
in the Chair. 

The following commnnications were read : — 

1. ** Supplemental Note on the Anatomy of HypsHaphodon 
Foxii:' By J. W. Hulke, Esq., P.E.S., P.G.S. 

The material for this note was a slab from Cowleaze Chine, oon- 
taining portions of two indiyidoals of HypsUophodon Foxii—one con* 
sisting of a skull with a great part of the vertebral column, the 
other of a portion of the vertebial column. The author described 
some details of the structure of the skuU, and especially the palatal 
apparatus. The pterygoids, which are not mesially joined, have a 
stout body, the posterior border of which bears a very large basi- 
sphenoidal process ; and the left pterygoid retains the root of a strong 
quadratic process, in front of which the hollow outer b<Nrder runs out 
into an ectopterygoid. In front of the pterygoids the palatines are 
partially visible, also separated by a fissure. Of the eight vertebrae, 
the last three are firmly anchylosed, and the seventh and eighth 
form part of the sacrum. They are constricted in the middle ; 
and their transverse processes, which spring from the junction of 
two vertebrsB, are bent backwards, joiniog the dilated outer end of 
the trausverse processes of the next vertebra, including a laige sub- 
circular loop. The second fragment of a vertebral column, which 
belonged to a smaller individual, includes the sacrum and several 
vertebrcB. Near the skull the slab contains several very thin bony 
plates of irregularly polygonal form, regarded by the author as 
dermal scutes. In connexion with the question of the generic rank 
of Hypsilophodon^ the author stated that in Hyp9ihphod(m the 
centra of the sacral vertebrae are cylindroid and rounded below, 
whilst in Iguanodon they are compressed laterally and angulated 

2. " The Drift-beds of the North-west of England.— Part 1, Shells 
of the Lancashire and Cheshire Low-level Clay and Sands." By T. 
Mellard Eeade, Esq., C.E., F.G.8. 

The author commenced by explaining a section in a cutting at 
Booth-Lane Station, in which most of the beds seen about Liverpool 
are typically represented. This section shows in ascending order : — 
1. Pebble-beds of the Trias ; 2. shattered rock.; 3. compacted 
red-sand rubWe (ground moraine) ; 4. lowest bed of Boulder-clay 
(largely composed of red sand); 5. stratified sand, with shell- 
fragments ; 6. bed of fine unctuous clay ; 7. brick-clay (with many 
shells) ; 8. sand-bed ; 9. stratified yellow sand (" Washed Drift 

The author next gave a list of the loealities in which shells were 
found, and stated that in all forty-six species had been met with 
distributed through the day-beds, those found in the sand-seams 
being rare and generally frtigmentary and rolled. The shells mobt 


Digitized by VjOOQ IC 

228 Geological Socieiy :— 

commonly found entire are usuallj of small tjiize, and of a form cal- 
culated to resist pressure, — such as TurriteUa communis, Trophon 
daihratus, and Mangelia turricula, Pusus antiqutM and Buccinum 
undatum are generally represented only by worn fragments of the 
columella; and Cyprina islandica is always found in fragments. 
The author thought that the association of the various species dis- 
tributed without order through the clays shows that they could not 
have lived together on the same bottom, but that they must have 
been to a great extent transported. He contended that the ad- 
mixture of shells in the Boulder-clay was due to tbe tendency of the 
sea to throw up its contents on the beach, whence changing cur- 
rents and floating ice might again remove them, and to the oscilla- 
tions of the land bringing all the beds at one time or another within 
reach of marine erosive action. He maintained that it is in the 
distribution of land and sea at the period of deposition of the Lan- 
cashire deposits, and not in astronomical causes, that we must seek 
the explanation of the climate of that period, the conditions of which 
he endeavoured to explain by a consideration of the proportions of 
the species and the natural habitats of the shells found in the drifts. 

3. " Note on a deposit of Middle Pleistocene Gravel near Ley- 
land, Lancashire." By R. D. Darbishire, Esq,, F.G.8. 

The bed of gravel, about 40 feet thick, and about 240 feet above 
the level of the sea, is covered by yellow brick clay, and overlies an 
untried bed of fine sea-sand. The shells dhd fragmens occur chiefly 
at the base of the gravel. 

The most noticeable shells in this list of forty-two species, col- 
lected by Miss M. H. Farington, were Panopoea norvegica, Macira 
glauca, Cyiherea chione, Cardium rusticum, Fusus propinquuB, and 
Fusus antiqutts, var. contrarius. One specimen of a Fmus, doubt- 
fully identified as F. Fabricii (craticulatus), had occurred. 

The group was by no means characteristically Arctic or Glacial. 
It represented most nearly the Wexford lists, especially in present- 
ing the reversed Fusus, and might be regarded as connecting those 
beds with the Macclesfield drifts, also containing a Celtic assortment, 
with Cytherea chimie and Cardium rusticum. 

The author considered the Leyland deposit, like those on the west 
of the Derbyshire hills, to be more probably littoral and truly cli- 
matic than that of the Liverpool clays, the subject of Mr. Keade's 
Paper, and hazarded the conjecture that the latter were sea-bottom 
beds, into which, during some process of degradation and redistri- 
bution, the specimens found and enumerated by Mr. Keade had been 
carried down from the former more ancient retreating coast-lines. 

December 3rd, 1873.— Joseph Prestwich, Esq., F.R.8., 
Vice-President, in the Chair. 

The following communications were read : — 
1. '* Notes on the Structure sometimes developed in Chalk.'' By 
H. George Fordham, Esq., F.G.S. 

After referring to Mr. Mortimer's paper on tbe same subject (see 

Digitized by VjOOQ IC 

Mr. R. PiDchin on the Geologg of the Cape of Good Hope. 299 

Q. J. G. 8. vol. xxix. p. 417), the author stated that in a pit near Ash- 
well the ** Lower Chalk without flints *' exhibits a bed of a concre- 
tionary nature, the concretions in which are marked nearly all over 
with lines. The lines are found only on the concretions and in their 
immediate neighbourhood. The fossils in the bed are invariably 
crushed, as if by pressure. The author believes that the strisB are 
due to an incipient crystallization arising from the formation of the 
concretions ; and in support of this view he adduced a specimen of 
iron pyrites from the chalk of Beachy Head, attached to which is a 
small portion of very hard striated chalk, and suggested that the 
crystallization of the pyrites had induced a crystallization in the chalk. 
He considers, however, that in some places an almost identical 
structure may be due to slickensides, but only in very broken and 
faulted beds. 

2. " A short description of the Geology of the Eastern Province 
of the Colony of the Cape of Good Hope." By R. Pinchin, Esq., 
C.E. Communicated by H. W. Bristow, Esq., F.R.S., F.G.S. 

In this paper, which was illustrated by maps and sections, the 
author gave the results of his observations on the geology of the 
above region. The two principal sections described were fiim Cape 
Saint Francis, across the Great Winterhoek and Langeberg ranges, to 
the lacustrine Triassic rocks near Jansenville, and from Port Eliza- 
beth to Somerset. The lowest rock in the first section is the quartzite 
of the Great Winterhoek, which is immediately overlain to the 
northward by day-shales and sandstones containing Devonian fossils. 
Beds with similar fossils occur at the Eromme river, Cape St. 
Francis, and near Uitenhage. A patch of horizontal secondary 
strata stretches west from the Gamtoos river, overlying the Enon 
conglomerate in the same way as the Jurassic strata of Uitenhage. 
They contain no fossils. The Enon conglomerate is seen on the 
flanks of the higher hills. The northern ranges, Langeberg, Elein 
Winterhoek, and Zuurbergen, are regarded by the author as formed 
of rocks belonging to the Carboniferous series, although closely 
resembling those of the Great Winterhoek in lithological character, 
except that among them are bands of the peculiar rock described by 
Bain as " Claystone porphyry," by Wyley as a ** Trap conglomerate,'* 
by Tate as a " Trap-breccia," and by Atherstone as an " intrusive 
Trap." Eubidge regarded it as a metamorphic rock ; and this view 
is adopted by the author, who describes it as underlying and over- 
lying the clay-shales, which always separate it from the quartzite, 
and as passing imperceptibly into the clay-shales. The mottled 
sandstone or Ecca rock is referred by the author to the Carboni- 
ferous series. The author also noticed the occurrence of Tertiary 
or recent rocks containing remains of Mollusca identical with 
species now living in the adjacent seas, lying unconformably upon 
the Devonian, and conformably upon the Secondary rocks at various 
places near the coast. 

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230 Geological Society. 

S. '* On the Mad-craters and geological structore of the Mekran 
Co^." By lient. A. W. Stiffe, F.R.A.S. Communicated by Prof. 
Ramsay, F.R.8., V.P.G.S. 

The coast of Mekran, extending from near the western frontier of 
India to the month of the Persian Gulf, was stated by the author to 
be a nearly rainless district, consbting of clay plains with pre- 
cipitous tabular hills, the former veined here and there with crystal- 
line gypsum, the latter composed of clay capped and sometimes 
interstiutified with coarse, friable, fossiliferous calcareous strata, 
from 5 to 30 feet thick, supposed to be of Miocene age, and all 
horizontal or nearly so, except at the extreme east and west, where 
the strata are inclined at an angle of frt>m 40^ to 60^. Along the 
coast there are no distinct traces of volcanic action; but on the 
north coast of the Persian Gidf a similar formation has been much 
disturbed by the protrusion of recent volcanic material, near J&shak 
to the west there is a hot mineral spring, and near Ear&chi there 
are springs of pure hot water. The author described the mode in 
which denudation is effected in this region by occasional heavy 
rains, and by the constant action of the sea upon the coast, and then 
noticed the occurrence, within a few miles of the shore, of numerous 
peculiar mud-craters, forming hills varying in height fr^m 20 to 
300 or 400 feet above the plain, of a regular conical form, with 
truncated tops, and the sides sloping at an angle of about 40^. The 
summits of these hills present a circular cup with a narrow border, 
filled with semifluid mud, which occasionally flows slowly over the 
margin of the crater. The author considered that the conical hills 
have been formed solely by these overflows. He believed that a 
small shoal occurring off the coast near Jdshak might be produced 
by one of these craters, and was inclined to ascribe their existence 
to hydrostatic pressure rather than to volcanic action, especially as 
by tiie concurrent testimony of several natives the discharge from 
the craters b greater during spring tides. The thickness of the 
clay forming the plain is probably very considerable ; it extends for 
some miles from the shore, sinking gradually to 20 or 30 fathoms, 
when there b a 'sudden and often precipit<>us descent to a depth 
of 300 or 400 fathoms. The author suggested that, since the de- 
position of the Miocene beds, the great submarine cliff may have 
been raised above the sea, that the land was then depressed to near 
its present level, causing the removal of the beds to the present 
coast Hue, and that a farther depression followed by upheaval gave 
origin to the inland cliffs. Evidence of the last depression is frir- 
nbhed by the presence of borings of lithodomous mollusca in the 
clifls considerably above the present sea-leveL 

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[ 231 ] 
XXXIII. Inteliigence and Miscellaneous Articles. 


PROFESSOE STOKES* observed that in the spectrum of the 
light reflected from solid permanganate of potassium dark 
streaks oecur^ and that they are exhibited most distinctlj with a 
certain angle of inetdenee ; further, the minima of brightness in i^e 
speetnim of the reflected light correspond to the rays transmitted 
in the greatest intensity by the permanganate. 

I have pursued this subject further, and examined not only the 
lijght reflected at the boundary of permanganate of potassium and 
air, but also that at ihe boundary of benzine, sulphide of carbon, 
and a mixture of these two substances, and the above salt. More- 
over the polarizotioii of the inddent light wa& kept in view. To 
obtain the reflecting surfaces, triturated crystals of the salt were 
polished upon ground glass plates by means of a jet-burnisher. 
Clean surfaces, free from oxide, were thereby secured for the inves- 
tigation, which is not the case when whole crystals are employed. 
The glass plate thus prepared was inserted in a rectangular hollow 
prism (which could be filled with the different liquids) in such wise 
that its coated face was turned to the rectftngnlar edge. The pridm 
was placed upon a graduated circular table that could be rotated, 
and sunlight so thrown upon one of the two surfaces including the 
right angle that the light refracted there fell upon the coated plate 
and, through reflection, passed out at the other surface. Thence it 
arrived at the sHt of a spectrum-apparatus. The angle of incidence 
on the coated plate was determined thus : the Mght from the first 
surfaee of the prism was reflected back in its own direction ; the 
position of the table was then read oSt ; the rotation of the table 
with the prism ^es immediately the incidence- angle at the first 
surfaee ; from this angle and that between the glass plate and the 
first face of the prism, and the index of refraction of the medium 
i!n contact with ttie permanganate, the incidence-angle at the latter 
can then be found. 

The position of the streaks in the specttuM was determined by 
means of a photographed scale applied to the spectmm-apparatus, 
the cross^threads of the observing-telescope having previously been 
placed on the centre of tho dark streak. 

These positions with pretty large angles of incidence are given 
in Table I. The columns ifi^r A refer to the streaks in the light 
polarized parallel to the plane of incidence, those under B to thos6 
in the light polarized perpendicular to that plane. The first cohnmi 
gives the names of ^e surrounding media. Table II. gives the 
positions of the absorption-streaks in the transmitted light. Eraun- 
hofer's lines correspond as follows to the strokes on the photo- 
graphed scale : — 

D:*=Oj B=il8; b^21', F=«33. 

♦ Phil. Mag. 1863, vo!. vi. p. 393. Pogg". Ann, 1854, vol. xci. p. 300. 

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232 Intelligence and Miscellaneous Articles. 

Tabm I. 









87 ; 

38i 1 45 
894 1 47 


Mixture of benzine tnd sulphide of carbon. 
Snlnhide of eftrhon 

! - 1 1 







82 38| 
82 38 
82 39 



Mixture of benzine and sulphide of carbon. 
Sulohide of carbon 

Tabls II. 

4}, Hi, 18J, 26i, 33^. 

These numbers show : — 

1. That, with large angles of incidence, the streaks in the light 
polarized perpendicular to the incidence-plane, with respect to those 
in the light polarized parallel to the plane of incidence, are displaced 
towards the olue, and that in the former another streak occurs in 
the yicinity of D. 

2. That with the increase of the refraction-index of the surround- 
ing medium the streaks in the parallel-polarized light undergo dis- 
placements towards the blue ; while, on the contrary, in the per- 
pendicularly-polarized light the streaks preserve their position un- 
changed, or lilter it but Httle. Observation of the streaks in the 
blue beyond E is attended with great difficulties, as is the entire 
investigation, through the breadth of the streaks and the impossi- 
bility of obtaining perfectly reflecting sur&bces. 

A comparison oi the streaks obtained in the transmitted and in 
the reflected light shows that never do two of such streaks cover 
one another, and that neither do the former lie each in the middle 
between two of the latter. 

As to change of position of the streaks with the angle of inci- 
dence, it result^ that in the light polarized parallel to the plane of 
incidence, and likewise in natural bght, the position was as good as 
independent of the angle of incidence ; but in the light polarized 
perpendicular to that plane the streaks have, up to a certain angle 
of incidence, which amounted to 


about 62^, 

Sulphide of carbon, 
about 52°, 

the same position as in the paraUel-polarized, and then, with a 
small alteration of the incidence-angle, suddenly suffer a disj^laoe- 
ment characterized by the appearance of the streak ihe details of 

Digitized by VjOOQ IC 

Intelligence and Miscellaneous Articles. 233 

which are given in the first column under B. Accordingly, for 
angles ^eater than those given, the above Tables hold good. 

Precisely the same phenomena as on the ground and polished salt 
may be observed on crystals. Just so are they exhibited on per- 
manganate of ammonia ; but here measurements were impossible, 
on account of the great decomposability of the salt. 

The above observations were verified in every way possible. For 
example, the dependence of the situation of the streaks on the index 
of refraction was again established by putting benzine and sulphide 
of carbon in layers one above another, immersing a glass plate 
coated with polished permanganate of potassium, and comparing 
immediately the spectra of the light reflected at the boundaries of 
the two media by the permanganate. The streaks in the spectrum 
of the fight which had passed through the sulphide of carbon were, 
in relation to those in the spectrum of that which had traversed 
the benzine, displaced towards the blue. — Poggendorff's AnnaleUy 
1874, No. 4, pp. 625^628. 


I have previously indicated and discussed the method I most 
frequently employ in my measurements concerning the temperature 
of the sun. I shall today describe the apparatus I use, and shall 
develop the calculus of the experiments. 

My apparatus is composed of two concentric spherical envelopes 
of brass. The interior one, 15 centims. in diameter, constitutes 
the enclosure, in the centre of which is the bulb of the thermometer 
submitted to experiment. This enclosure, blackened on the inside, 
is kept at a constant temperature by a continuous current of water 
furnished by the conduit-pipes of Uie city and circulating between 
the two balls. The exterior ball has a diameter of 23 centims. ; it 
has been carefully polished on its outer surface, and is, besides, 
protected by screens which leave free only the admission-aperture. 
This aperture is at one of the extremities of a brass tube 17*5 mil- 
lims. in diameter, directed along one of the radii of the sphere, and 
opening at the other end into the inner ball. The free extremity 
of the admission-tube carries a movable diaphragm pierced with 
three circular apertures of different sizes. Three other tubes tra- 
verse, in radial directions, the space comprised between the two 
spheres : two of them, placed one at 45°, the other at 90° from the 
admission-tube, serve, the one or the other according to circum- 
stances, to give passage to the stem of the thermometer ; the third, 
closed by ground and slightly blackened plate glass, is directed 
along the prolongation of the admission-tube, and permits the 
ascertaining that the solar rays fall exactly on the bulb of the ther- 
mometer. The suitable orientation of the apparatus is, besides, 
attained without difficulty, thanks to its spherioil form, which per- 
mits it to be turned gradually in the wished-for direction upon a 
circular ring which serves as its support. 

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Intelligence and MisceUanema Articles. 

The following is the course of an experiment : — All the tubes 
being carefuUy closed, and the thermometer in place, the tempera- 
ture (which is stationary if all has been well regulated for a suffi* 
dent time) is read ; then the admission-tube is opened after bring- 
ing opposite to it such aperture* of the diaphiagpn as is judged 
suitable. Now, the apparatus being kept in accurate orientation, 
we wait until the temperature again becomes stationary, and then 
note the excess shown by the thermometer. 

Experiment shows that this excess depends both on the thermo- 
meter employed and on the diameter of the aperture of admission. 
No precise ccmclusion, therefore, can be drawn from experiments m 
which we have not preoccupied ourselves with the dimensions of 
the thermometer, and with the magnitude of the admission-ap^ture 
pierced in the enceinte, with the temperature constant. On the 
contrary, by employing in succession different thermometers and 
different apertures of the diaphragm, we can evaluate very accu- 
rately : — (1) the cooling due to the contact of the air ; (2) the heat- 
ing which proceeds from the radiation of the portion of the sky 
bordering the sun and seen at the same time from the bulb of the 
thermometer. I shall show this by an example, the data of which 
I take from one of my last series of observations. 

On the 20th of June last, operating successively with two ther- 
mometers, the spherical reservoirs of which had the diameters 12 
millims. and 7 miDims. respectively, and with three different aper- 
tures a, 6, c of the diaphragm, the respective diameters of which 
were 17*5, 14*5, and 12 milluns., I obtained the following results : — 


the enceinte. 

Temperature of the 

Temperature ctf the 
•mall thermometer. 

h m 
3 10 
3 30 

3 45 

4 10 
4 SO 
4 35 


2?03 (diaphragm a) 
26-56 (diaphragm h) 

24-05 (diaphragm h) 
23-63 (diaphragm c) 
23*85 (diaphragm a) 

28-43 ((Saphraga a) 
23-30 (diaphragm «) 

28-05 (diaphragm a) 

Let us take first the observations of 2* 55" and 3^ 10* ; these 
two, made nearly at the same time, should lead to sensibly equal 
excesses of temperature. The considerable difference between the 
two numbers observed arises from the complication introduced into 
the experiment by the presence of air ; to the radiation from the 
bulb of the thermometer is added the cooling produced by the air ; 
and in these two ways the bulb loses a quantity of heat equal to 
that which it receives from the sun. The loss of heat in vacuo, 
making equilibrium with the same quantity of heat received from 
the sun, would therefore be equal to the loss observed plus the loss 
due to the air. But, according to Bulong and Petit, the lowering 

Digitized by VjOOQ IC 

Intelligence and Miacellaneoue Articles. 235 

of temperature resulting from this last cause can be represented by 

g r>**^, m being a constant dependent only on the elasticity of the 

air, and r the observed excess. We should have, then, in vacuo 
with the two thermometers the two equal excesses 

12-6H-^12-51»«»=10+^10>-233, whence w=2-24. 
o 3-5 

Let us take in the same way the observations of 3^ 45"^, 4^, and 
4^ 20™, all three made with the same diaphragm, but different from 
the preceding one; they conduct to the equation 

9.77-1. ;^9-77»««»=12-15+ ^12-15>«», whence m=2-09. 

Let us adopt for the value of the coefficient of cooling m the mean 
of the two values thus obtained, ms=2'15 ; with the aid of this co- 
efficient we can draw up the following Table of the temperatures 
which would have been observed in vacuo : — 


Temperature of 
the enceinte. 

Temperature of the 
large thermometer. 

Temperature of the 
imall thermometer. 

h m 
2 40 

2 55 

3 10 

3 45 

4 20 
4 35 


34-61 (diaphragm h) 

34-54 (diaphragm ») 
33*65 (diaphragm c} 
34-20 (diaphragm a) 

38 50 (diaphragm a) 
33*10 (diaphragm a) 

33^83 (diaphragm a) 

On tracing the curve representing the course of the thermometer 
for one and the same admission-aperture, it is readily recognized 
that the relative temperatures at the different periods all combine 
with perfect regularity, whether they come from the large or the 
small thermometer. 

Let us now consider two experiments made with different dia- 
phragms ; and as the small thermometer is that which approximates 
most nearly to the theoretical conditions (especiaUy for small ad- 
mission-apertures), let us take the three experiments relative to 
3^ 10", 3** 30", and 3** 45". Making use of the curve of the tem- 
peratures for the diaphragm a, and reducing all to one and the 
same temperature, 14°, of the enceinte, we have for the tempera- 
tures at one and the same period: — 

Diaphragm a 34*45 

Diaphragm h 34-08 

Diaphragm c 33*70 

Applying to these data the equation I established in my previous 

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236 IiUelligenee and Miscellaneoui Articles. 


Sa«=Sa+*»a'+Oay or fl^— a'= ^0*+ -^ of, 
we have 

(Dii^h. a) l-0077»***-l-0077>*« igieo ^'^^^'^' 

+ (0.0009493- ^g3^)l.0077.. 

(Diaph. 6.) l-0077»*w-l-0077"» jg^ 1-0077' 

whence x=1355°, and 
(Diaph. a) l-0077"«-l-0077'«= 1^60^'^^'^'^' 

(Diaph. c) l-0077«-'-10077'«= Jg^o ^'^'^'^' 

(0-0009493- ^^)10077», 
'*- 18^60 1-0077' 

whence a? =1363°. 

The agreement of the two values of x shows that the correction 
necessitated by the radiation of the region of the sky in the vicinity 
of the sun is made with sufficient exactness by writing for the total 

radiation of the different portions of this surface ^ of, as if all 

these parts were at one and the same mean temperature y. 

Therefore, in the example selected, it will be concluded from these 
calculations that, on the 20th June, at Grenoble, the temperature 
of the sun, defined as I have indicated above, was, at 3^ 30'°, 


But this number itself, to give the true temperature of the sun, 
ought to be further corrected on account of divers influences, par- 
ticularly the absorption of the terrestrial atmosphere. It is chiefly 
by operating at different altitudes, and (of course) noting the pres- 
sure and the hygrometric state of the air at each station, that I 
hope to solve this problem. For this purpose I have already made 
several ascents of the Alps ; and I shall resume them as soon as 
possible. — Comptes Bendus de TAcad. dt$ Sciences, June 29, 1874. 

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Intelligence and Miscellaneous Articles, 237 


In 1853 I first attempted to trace the consequences of subter- 
ranean heat, bj taking into consideration some facts and principles 
which seemed to l^ave received but little attention. The results of 
my inquiries on the subject were given in a circular in 1854, in a 
pamphlet in 1856, and in a paper which I sent to the British 
Association in 1861, and of which an abstract is published in the 
Eeports of the Sections, page 134. In that paper I endeavoured 
to show that the terrestrial crust, if reposing on lava of a declining 
temperature, would receive accessions of buoyant solid material, 
chiefly on such points as extend deep into the fiery menstruum, and 
that the consequent growth of internal mountains would be inter- 
rupted only by the occasional movements of vast portions of this 
light matter to positions much higher than those at which they were 
first deposited. To the collisions of such rising masses against the 
weaker parts of the earth's crust I ascribe eiurthquakes ; but the 
theory affords a more satisfactory explanation for volcanic phe- 

Avalanches of siliceous rocks, ascending through buoyimcy from 
deep subterranean peaks or depressions, would lead to important 
results by conveying heat from a lower to a higher stratum of the 
internal earth. Owing their solidity to pressure, such stony masses 
would fuse during the ascent ; and, like our mountain-floods, would 
erode channels which must for a long period direct them to the same 
localities. The same spots of the earth's crust, being thus exposed 
for many ages to the repeated inroads of intensely heated matter 
from great depths, would be reduced in thickness by the frequent 
fusion, and would present a weaker barrier to subterranean vio- 
lence. Such an internal convection of heat would end in perforating 
the earth's crust and producing an immense lake of lava on its sur- 
face, were it not for the cooling influence of aqueous action ; and the 
presence of water on our globe, though tending much to increase 
the violence of earthquakes and volcanic eruptions, has the effect of 
confining their ravages within a more limited range. To the 
absence of water from the moon we may ascribe the enormous 
diameters of the craters of lunar volcanoes ; while their height is 
displayed on a far less scale, and there are no long ranges of lunar 
mountains. On our satellite also volcanoes have for the most part 
an insular character, conforming little to the linear arrangement so 
common on the earth ; so that the cooling agency of water appears 
to have been concerned in producing the vast rents or fissures on 
which so many volcanic ormces seem to be located. 

Apart from the evidence which the pendulum and geodetic mea- 
surements give of inequalities on the invisible side of the earth's 
crust, it can be proved theoretically that they are inevitable in the 
course of solidification over the molten mass. One source of solid 
matter light enough to form the external framework of our globe 

Digitized by VjOOQ IC 

238 Intelligence emd Miscellaneous Articles. 

is to be found in the decomposition of many of the heavy silicates 
by enormous pressure when the temperature of the menstruum in 
which they were fused sunk below the melting-point of quartz. 
An equivalent of oxide of lead and of crystallized silicic acid would 
have their common volume increased about 14 per cent, on comlH' 
ning and forming lead glass. Now, at a depth of 1000 kilometres 
below the earth's surface, the pressure is equal to about 300,000 
atmospheres ; and accordingly the formation of a cubic inch of 
glass by the union of quartz and oxide of lead would, in conse- 
quence of the expansion it involves, be resisted by a force the ther- 
mal equivalent of which may be represented by the heat expended 
in melting 14 cubic inches of ice. A force of equal energy would 
be exerted by the same pressure for the decomposition of a cubic 
inch of silicate of lead, in the supposed locality, and for the crys- 
tallization of tiie resulting silicic acid. As far less heat is evolved by 
the union of the strongest adds and bases, and as a crystallization 
or atom-arrangement can make no heavy demands on force, it is 
reasonable to conclude that in the supposed case chemical affinity 
would be overruled and that the silicate ai lead would be decom- 
posed. From similar estimates it would also appear that other 
silicates, especially those of heavy metals, would undergo a similar 
decomposition at great depths, and would part with their silica 
when the temperature became low enough to allow its solidification. 

Another source of buoyant matter is to be found in the transfer 
of silica from the heavy metallic oxides to the alkalies and other 
strong bases. The light compounds thus formed would, according 
to Delesse and Deville, contract more than other igneous rocks in 
passing into a solid state ; and it is evident that in propcnrtion to 
this contraction vnll their production be favoured by pressure on the 
decline of the primitive heat. The growth of a floatmg crust would 
also be promoted by other circumstances. Of many of the metallic 
oxides, the most infusible compounds are those in which the silicic 
acid is very small or in a very large proportion. But the latter 
bodies, which have almost invariably the lowest specific gravity, 
bave also their fusibility reduced most by pressure m consequence 
of the contraction which they undergo in assuming a solid form. 
On this point more satisfactory evidence may be obtained by an 
investigation similar to that of Clausius, but in which the effects of 
pressure upon fusion is determined frcmi the change of volume and 
the modulus of elasticity. 

Of tJie various products which separate from the subterranean 
lava in cooling, the most dense parts would sink to the centre, 
though solidifying in the uppermost stratum ; while the li£;hter 
material, though taking the solid form at great depths, would rise 
towards the surface. But the solidity of the light silicated matter 
could be permanmit only when kept under the influence of immense 
pressure, by settling on prominent points which extend from the 
inner side of the crust deep into the lava. The great centres of ac- 
cumulation of this buoyant matter must be under continents, where 

Digitized by VjOOQ IC 

Intelligence and Miscellaneous Articles. 239 

the eArtb's crust has evidentlj the greatest thickziess and reposes 
on the deepest internal prominences ; and to the ocoasional slides 
and asc^iding movements of matter from these parts ot the subter- 
ranean regicMis, we may ascribe the prevalence oi vulcanicity on so 
many continental coasts. 

If only one per cent, of terrestrial matter passed into a solid form 
in the course of ten miUicms of years, there would be still sufficient 
grounds for assigning to rock-slides a mass so great that the me* 
chanical effects of their collisioos against the thinner parts of the 
crust mayproduce the most violent earthquake shocks. But the most 
obvious efcecta must be ascribed to the sudden elevation of tempera- 
ture which the thin spots of the earth's crust should experience, 
and which may be reasonably estimated at many thousand degrees. 
Exposed to such a fierce heat, the solid structure would be rent by 
the unequal expansion of its parts, or by the elasticity of its volatile 
constituents. 8team would manifest an irresistible power when 
rock containing moisture tumbled into tlie molten liquid or encoun- 
tered it wh^i penetrating through fissures. But a motive power 
of long continuance would arise from the property which silica has 
pf expelling other acids from bases at high temperature. As the si- 
liceous rocks come into coUisicm with the strata containing limestone 
or any other carbonates, the resulting mass should swell with the 
evolution of carbonic acid, and boil over a volcanic crater or even 
open a new (me. In consequence of the pressure, this expulsion of 
carbonic acid will require a higher temperature ; and the cooling, 
chiefly through the agency of water, would soon occasion a state of 
repose until there occurred a new influx of heated matter from 
deep regions. An estimate of the rate of cooling, as invdved in 
the mere production of steam alone, would show that, during their 
numerous eruptions, Etna and Vesuvius must have 1/ost a quantity 
of heat too great to be supplied by any conceivable chemical or 
mechanical action in their immediate vicinity ; and evidence may be 
thus obtained of the necessity of the convection of caloric, and of 
the introduction of incandescent matter from distant localities to 
the theatre of volcanic activity. 

CiDcinoati^ 0., July 16, 1874. 


In the Anzeiger of the Imperial Academy at Vienna, Professor 
V. Schrotter gives the following notice of this transformation, dis- 
covered by Dr. Geissler : — 

Already in 1860 Dr. Qeissler endeavoured to show that electri- 
city by itself effects this change ; and he had the goodness, on the 
occasion of his visit to Vienna at the time of the Universal Expo- 
sition, to give up to me some of the glass apparatus. 

The simplest of these is an exhausted glass tube of about 35 cen- 

Digitized by VjOOQ IC 

240 Intelligence and Miscellaneotu Articles* 

tims. length and 2 centims. diameter, to the ends of which additions 
were attached (by fusion) containing the conducting-wires, so that 
in the experiment the wires were at least 45 centims. distant from 
each other. The tube was filled with phosphorus vapour of very 
little tension ; after the experiment its sides were coated with a 
thin layer of amorphous phosphorus brownish red changing to 
ffolden yellow, and in many places exhibiting the colours of thin 

The second apparatus serving for the same purpose, a master- 
piece of the glassblower's art, has the form and sue of a beaker- 
shaped double-walled champagne-glass. The thin layer of amor- 
phous phosphorus distributed over the inner surfaces of its walls 
exhibits the play of all the colours of thin films, giving to the glass 
a pleasing appearance. 

The third, still more elaborately executed apparatus is designed 
to show that the conversion of the phosphorus is effected even by 
the inducing action of the current. For this purpose the ends of 
the two aluminium conductin^-wires are inserted in exhausted 
spheres in which there is no phosphorus. These spheres are en- 
closed in others, which are united by a tube 40 millims. long and 1 
millim. wide. The interspaces thus formed, likewise exhausted, 
contain the phosphorus, which is therefore completely shut off from 
the conducting-wires by a wall of glass. The distance between the 
conducting-wires amounts to 26, and the diameter of the outer 
spheres to 5 centims. The interval between the walls of the 
spheres amounts to 5 millims. Here also the inner side of the 
outer, and the outer side of the inner sphere, in like manner as 
above stated, were coated with amorphous phosphorus. Only in 
the narrow connexions was no phosphorus deposited. 

The above-mentioned facts furnish, perhaps, the best demonstra- 
tion that the conversion of phosphorus into the amorphous modifi- 
cation is effected neither by the light nor by the heat which accom- 
pany the current, but exclusively by the electricity itself. 

The instructive experiments which Hittorf published in 1865 
(Pogg. Ann. vol. cxxvi. p. 195) were made with another arrange- 
ment of the apparatus, as the platinum wires, fused into glass 
spheres of 6 to 8 centims. diameter, were only a few millims. dis- 
tant from one another ; so that sparks passed, and the course of 
the phenomenon was somewhat different from that above described ; 
but the conclusions deduced therefrom by Bittorf were the same. 

I hope to be able to resume this subject in greater detail ; for 
the present the above account may suffice to recall attention to it. 
— Poggendorff's Annalen^ vol. clii. pp. 171-173. 

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OCTOBER 1874. 

XXXIV • On Gladstone's Experiments relating to Chemical Mass. 
By Edmund J. Mills, D.Sc, F.R.S* 

I. rpHE Philosopbical Transactions for 1855 (vol. cxlv.) con- 
J- tains an important memoir by Gladstone " On Cirenm- 
stances modifying the Action of Chemical Affinity/' In this 
memoir numerous sets of experiments are described, which 
mainly serve to determine, by means of an increase or diminu- 
tion of colour, the progress of certain selected reactions. The 
results are exhibited in curves, several of which show a regular 
course, while all are continuous ; but no mathematical expres- 
sion of the law of action^ is given. About eleven years after- 
wards (Phil. Trans. 1865-6) it was shown by Esson, on the 
basis of Harcourt's experiments, that when a substance under- 
goes chemical change, the residue y of changing substance is 
connected with the unit intervals x of change (time, reagent, or 
other operator) by the equation 

where a represents the amount of substance originally present, 
and « the amount of it disappearing ])er unit o(x. This relation 
is graphically represented as a logarithmic curve ; but, as a rule, 
even in very simple cases, its expression is more complex, and 
corresponds to the form 

which indicates that two bodies are undergoing change, or that 
one body is undergoing dual change. In cither case the amount 

♦ Communicated by the Author. 
Phil. Mag. S. 4. Vol. 48. No. 318. Oct. 1874. R 

Digitized by VjOOQ IC 

242 Dr. E. J. Mills on Gladstone's Experiments 

of change per unit interval is proportional to the amount of sub- 
stance then changing. 

As Gladstone's results were the first in which the continuity 
of the chemical process was experimentally demonstrated (at any 
rate on a sufficient scale)^ I felt much interested in ascertaining 
whether Esson's equation would apply to them^-especially when 
I considered how few have been the contributions to chemical 
dynamics^ the laborious (and consequently unpopular) nature of 
such researcheSi and the inexpediency of allowing good work to 
remain dumb or unexpressed. 

II. The colorimetrical method^ which was used throughout by 
Gladstone, has considerable disadvantages, and is most service- 
able when only small quantities, as in the case of the Nessler 
test, have to be measured and an inaccuracy of about 5 per cent, 
is of no consequence. It is probable that the observer's estimate 
of colour varies during a long course of experiments, and is 
really under training in the earlier ones; so that, as will 
actually be found below, all the more serious errors occur, as a 
rule, at the outset. We must also remember that colour-effects 
in solutions are not unfrequently slow in attaining their maxi- 
mum, thus making a particular observation too low; on the 
other hand, the subsequent arrival of this maximum will make 
a following observation too high : hence also, by virtue of com- 
pensation, the later observations may be expected to be mora 

A further difficulty lies in the computation itself. The amount 
of chemical energy (or substance) originally present is not given 
in terms of the reagent, and has to be arrived at by successive 
and wearisome approximations; and these might perhaps have 
been carried a stage further with advantage. Again, the sue- 
cessive values of a are very seldom given in the experiments, 
which had not been arranged to test any particular hypothesis; 
they had consequently to be obtained by graphic interpolation 
on curves which, for such a purpose, should have been consider* 
ably longer. 

If we bear in mind these and other drawbacks, we shall regard 
the coincidence between theory and experiment as very striking. 

III. Ferric Nitrate and Potassic Sulphoct/anide [loc. cii. p. 187, 
pi. 7. fig. 1). — ^To one *' equivalent '' of ferric nitrate successive 
groups of '^ equivalents '' of potassic sulphocyanide are added, 
in presence of water; the amount of "red salt produced*^ is 
estimated by eye-observations, the liquid being diluted for that 
purpose up to a standard. The total amount a of red salt thus 
producible represents in special measure the original unexhausted 
energy of the nitrate. I have taken each unit of x as represent- 
ing 25 '' equivalents " of potassic sulphocyanide. The equation 

Digitized by VjOOQ IC 

relating to C/iemical Mass. 




bat the results are expressed in percentages of the initial value 

Tablb I. 


y, calculated. 

jff found. 














































Gladstone gives two variations of this experiment. 

IV. Ferric Sulphate and Potassic Sulphocyanide {loc. cU. 
p. 189, pi. 7. fig. 1). — On accouut of the weakness of the colour 
produced when a sulphate is present, the amount of the salts 
employed was doubled. One equivalent of ferric nitrate was 
taken. The equation is 

y=488 {-8208)'+ 182 (-1400)'; 

and the unit of x is 15 equivalents. 

Table II. 


y, calculated. 

y, found. 









































Digitized by VjOOQIC 

244 Dr. E. J. Mills an Gladstone's Experimenti 

V. Ferric Chloride and Potctmc Sulphocyanide (loc. ^ii. p. 189, 
pi. 7. fig. 1). — ^This experiment is described as "precisely ana- 
logous to the preceding.^' The equation is 

y=406 (•8900)'+214 (-2500)'; 

and the unit of x is 20 equiyalents. 

Table IIL 


y, calcnltted. 

y, found. 







41 •« 





















VI. Ferric Nitrate and Hydric Sulphocyanide {loc. cit. p. 190, 
pi. 8. fig. 2). — ^Ferric nitrate, 1 equivalent. Unit of ^ = 4 equi* 
Talents. The equation is 

y=533B (-91093)' +89-5 (-82670)'. 
Table IV. 


y, ctlculaied. 

y» found. 











59 1 


















• 337 



30 7 


The above results seem to have been the sequel of consider- 
able experience with the method, and are in exceptional ac- 
cordance with theory. 

VII. Ferric Citrate and Hydric Gallate {loc. cit. p. 193, pi. 9. 
fig. 1). — One equivalent of ferric citrate was mixed with 6 kc 
equivalents of hydric gallate, and the increasing black coloration 
measured. Unit of or = 3 equivalents. The equation is 

y=660 (•9127)'+90 (•8072)'. 

Digitized by VjOOQ IC 

relating to Chemical Mass. 
Table V. 



y, calcnlated. 

y, found. 


































VIII. Ferric Citrate and Potassic Ferrocyanide {loc. cit. p. 199, 
pi. 9, fig. 5). — One equivalent of ferric citrate was mixed with 3 
&c. equivalents of potassic ferrocyanide in presence of bydric 
oxalate, and the increasing blue coloration determined. Unit 
of ;r s 3 equivalents. The equation is 

y=102 (•2010)'+23 (-7699)'. 
Table VI. 


y, calculated. 

y, found. 











IX. The above equations represent the greater part of Glad- 
stone's results as figured at the end of his memoir. I have not 
worked out the remainder, either (1) because they form mere 
continuations or repetitions of the reduced curves, or (2) because 
the experiments were not numerous enough, nor the theory of 
the reactions sufficiently evident, to enable the calculation to be 
made. The curves representing the formation of ferric meco- 
nate and acetate somewhat resemble, but are not identical with, 
the cubical parabola. Similar ones are drawn by Harcourt and 
Esson (Phil. Trans. 1866, pi. 17), and Guldberg and Waage 
{Etudes sur les Affinit(s chimiques, Christiania, 1867, pis. 14, 15, 
16). It is obvious that they represent duplex reactions ; but 
their complete reduction may perhaps be a matter of consider- 
able difficulty. 

In order to estimate the accuracy of the experimental work, 
and the soundness of the hypothesis involved in its symbolic 
^xpressioi)^ I have drawn up the following en*or Table, showing 

Digitized by VjOOQ IC 

246 On Gladstone's Experiments relating to Chemical Mass. 

a sammary of the differences between calcolation and observation^ 
as compared in percentages. 

Table VII. 

AboTe S-3. 

Above 1-S 

Above 0-5-1-0 

Above 0HM)-5 

Table I 

Table II. ... 
Table III. ... 
Table IV. ... 
Table V. ... 
Table VI. ... 










The entire number of comparisons is sixty-seven. Thus it 
appears that 64 per cent, of the errors are such as would^ on 
their average^ be found in very good analytical work ; 33 per 
cent, of them occur, on their average, in ordinarily good analy- 
tical work ; the remaining 13 per cent, lie, on their average, 
within the usual limits allowable in colorimetry, 

X. The foregoing equations show that any such expression as 

i[Fe«Cl«] + 3KpNS=i[Fe*(CNS)«] + 3KCI 

h wholly erroneous^ if intended to represent the chemical energy 
of a ferric salt, or the amount of potassic sulphocyanide that is 
capable of acting thereon; for the energy of the quantity 
i[Fe«Cl^ is not exhausted until about 400 units (KCNS) have 
been brought to bear upon it ; and other ferric salts are repre- 
sented by similarly high numbers. The ordinary equations of 
chemistry represent the result of distributing weight, and give 
no account of work done ; these, on the other hand, represent » 
dynamical process as well as distribution of weight. Hence it is 
clear that the '^equivalents^' or valencies inferred from the com- 
mon equations rest upon a wholly fallacious basis, and cannot 
be depended upon in scientific reasoning. To assert, for instance, 
that G is equivalent to U^, amounts to stating that hydrogen 
and carbon have been compared as to the work they can do 
under certain circumstances, just as ferric chloride is compared 
with ferric sulphate in Gladstone's experiments. No such re- 
search has, however, been made ; and it would not be likely to 


yield the ratio TTi =1 i^ it were made. What, then, becomes of 

the doctrine that carbon is tetravalent ? 

It is worthy of remark that, while the ordinary equations in- 
variably express that quantity consists of parts (that, for example^ 
potassic chloride contains potassium and chlorine, whereas we 

Digitized by VjOOQ IC 

On a very singular Sulphuretted Nitroffenoue Confound. 247 

only know that it contains the joint weights of potassium and 
chlorine)^ the logarithmic equations make no suggestion upon 
this subject. All the above experiments might have been accu- 
rately performed and symbolically expressed by a person totally 
ignorant of the ''constitution'* of ferric salts or of potassic sul- 
ptioeyanide ; and the reagent might have been extremely impure, 
provided that it produced a red coloration. What we owe to 
Esson and Gladstone we might have inherited from Wenzel or 

12 Pemberton Terrace, 
8t. John's Park. N. 

XXXV. On a very singular Sulphuretted Nitrogenous Compound, 
obtained by the Action of Sulphide of Ammonium on the Hydrate 
of Chloral. By Edmcnd W. Davy, A.M., M.D., M.R.I, A., 
Professor of Forensic Medicine, Royal College of Surgeons, 
Ireland, and late Professor of Agricultural Chemistry, Royal 
Dublin Society^. 

THE substance termed hydrate of chloral, or chloral hydrate, 
from the many valuable therapeutic properties it has re* 
oently been found to possess, has within the last four or five 
years been prepared in considerable quantities, and has become 
an article of some commercial importance; and numerous as 
are the useful applications which have already been made of 
that substance in medicine, there can be but little doubt that 
their number may be greatly increased; so that we may justly 
regard chloral hydrate as one of the most, if not the most, im- 
portant of the recent additions to our materia medica. 

It being thus a substance of such practical importance, any 
information which may tend to extend our knowledge of its che- 
mical properties and relations should not, I conceive, be regarded 
as devoid of interest. I shall therefore briefly state the results 
of some observations which I have recently made as to the action 
of sulphide of ammonium on that substance (a subject that has 
been but little studied), and describe the properties of a very 
singular compound thereby produced, the constitution of which, 
as far as I am aware, has not hitherto been determined. 

When sulphide of ammonium is added to an aqueous solution 
of chbral hydrate, the mixture after a few moments acquires a 
deep yellow colour, and, rapidly becoming orange, passes to 
a reddish brown, which finally assumes so dark an appearance 
that the liquid, when in any quantitv, looks almost black by 
reflected light. It was also observed, after the mixture had 

* Communicated by the Author. 

Digitized by VjOOQ IC 

248 [Dr. E. W, Davy on a very singular 

assumed an orange tint, that almost immediately more or less 
of a solid matter invariably separated from the liquid^ appear- 
ing at first of a bright orange or light red colour, from its being 
suspended in the orange or red liquid, but that, after it was 
separated from it by filtration and washing, it was found to 
possess a light brown appearance. Whilst the changes just de- 
scribed were taking place, it was also noticed that the mixture 
became sensibly warm to the hand, and that the odour of the 
sulphide disappeared, whilst that of ammonia and of chloroform 
was easily detected. 

It was further ascertained that when the dark reddish-brown 
liquid obtained in the way just stated was acidified with an acid, 
it yielded a copious brown precipitate, which, though somewhat 
darker in its colour than that which separates from the liquid 
before the addition of the acid, appears to be essentially the 
same compound, the difference of shade being probably due, at 
least in some measure, to different amounts of free sulphur 
present in each. 

As the principal feature of interest connected with the reac- 
tion referred to, I considered, was attached to the formation 
of the brown solid compound just noticed, a quantity of it 
was made as follows : — Four hundred grains of chloral hydrate 
being dissolved in about ten ounces of distilled water, sulphu- 
retted hydrogen was passed through the solution till it poss^sed, 
after being shaken, the odour of that gas. Sulphide of ammo- 
nium was then added in small portions at a time, continuing 
the passage of the sulphuretted hydrogen through the mixture 
when the effects before described were produced. This treat- 
ment was continued till no further action appeared to take place, 
and the mixture possessed, after being well shaken, a strong 
odour of sulphuretted hydrogen. 

I ma^ here observe that, after the addition of the sulphide of 
ammonium, the evolution of ammonia was from the first percep- 
tible, whilst the odour of the sulphide and of the gas for some 
time continually disappeared, and it was not till the later stages 
of the process that the smell of chloroform could be detected. 

To the mixture so treated, which was distinctly alkaline, pure 
diluted sulphuric acid was added till it acquired an acid reaction, 
and the whole was thrown on a filter, when the brown solid was 
separated from a deep amber-coloUr^d liquid. The former was 
then washed with cold distilled water till no indication of sul- 
phuric acid in the filtrate could be detected by chloride of barium; 
but finding that it exhibited traces of ammonia when treated with 
caustic lime, the washing of the brown solid was continued, first 
using cold distilled water ; and this failing to accomplish the 
object sought, it was washed with a considerable quantity of hot 

Digitized by VjOOQ IC 

Sulphuretted Nitrogenous Compound. 249 

distilled water till the presence of ammonia could no longer be 
discovered in the filtrate. The brown matter was subsequently 
dried, first by exposure to the air on the filter at the ordinaiy 
temperature^ then at a very gentle heat^ and afterwards by ex- 
posing it for some time under a bell-glass to the drying influ- 
ence of sulphuric acid. 

As I thought it more than probable that the substance, from 
the way in which it had been procured, contained some free 
sulphur (which was afterwards shown to be the case), a portion 
of that which had been so dried was placed in a stoppered bottle 
and digested for some days along with bisulphide of carbon ; the 
mixture was then thrown on a filter, and washed with repeated 
fresh portions of pure bisulphide till but a faint trace of residue 
remained after the evaporation of a little of the filtrate; and this 
seemed to be due, not to sulphur as at the first, but to the brown 
compound being soluble to a very slight degree in the bisul- 
phide. After this treatment the bisulphide was allowed to eva- 
porate off from the substance, when it was placed as before under 
a bell-glass along with a vessel containing sulphuric acid, where 
it remained for some days. Thinking, however, that it might 
still not be perfectly dry, it was subsequently heated in a water- 
bath or oven to about 212° F., when I found that a very slight 
amount of moisture was expelled from it, accompanied by a pe- 
culiar sulphurous smell ; and as soon as it appeared to lose no 
further weight by this temperature, it was placed in a well-stop- 
pered bottle and reserved for examination. 

The substance so obtained, and in this dry condition, possesses 
the following properties: it is an amorphous solid of a light 
brown earthy appearance, is easily reducible to a state of impal- 
pable powder, and has a specific gravity of about 1*62. When 
gently heated on platinum-foil it evolves a very peculiar odour, 
then blackens, partially fuses, and, taking fire, burns with a pur- 
plish-coloured flame, emitting a faint odour of sulphurous acid, 
whilst it leaves a large carbonaceous residue, which on the appli- 
cation of a stronger heat ignites and slowly burns away. 

It is very slightly soluble in water, alcohol, bisulphide of car- 
bon, and in ether , whilst it is almost insoluble in chloroform 
and in benzol. It is, however, readily dissolved by solutions of 
the caustic alkalies, and by those of the alkaline cai*bonates and 
sulphides, forming dark brown or reddish-brown solutions, from 
which it is again precipitated, apparently unchanged, by the ad- 
dition of an acid in excess. It dissolves also in solutions of the 
hydrate of lime and of baryta, and is soluble to some extent in 
alkaline chlorides and iodides. 

As to the action of acids, when it was treated with concen- 
trated sulphuric acid it acquired a darker colour, and dissolved. 

Digitized by VjOOQ IC 

260 On a very iingular Sutphweiied Nitrogtnow Compound. 

forming a brown tolution^ which on being heated became almost 
black in appearance ; and this on the addition of water gave a 
flocculent dark brown precipitate resembling the original sab* 
stance^ except in its being of a darker colour. 

Strong nitric acid^ even at the ordinary temperature^ was 
found to act rapidly on the substance^ which it oxidises and disi 
solves; but neither it nor sulphuric acid in a diluted condition 
appears to exercise any effect on it \ for when boiled for some 
time with them no apparent change was observed to take place. 
As to hydrochloric acid^ even when in a tolerably concentrated 
condition it seemed not to produce any effect on the substanee 
either at the ordinary temperature or when boiled with it. 

The compound^ some of the properties of which have just been 
noticed^ on being submitted to analysis gave results which agree 
most closely with the formula C"» H«* S*' N* 0®, showing that 
the substance is an extremely complex one^ the formation of 
which> under the circumstances described^ may be explained by 
supposing the following reaction to take place : — 

9(C«HC1«0,H«0) + 16[(NHVS]+2H«S=C«H«*S«N^0« 

-f"27(NH*Cl)-f"NH»+5S + 12H«0, 

where equivalents of chloral hydrate^ being acted on by the 
conjoint action of 16 of sulphide of ammonium and 2 of hydro- 
sulphuric acid; give rise to the formation of I equivalent of the 
brown compound^ together with 27 of chloride of ammonium^ 
1 of ammonia^ 5 of sulphur, and 12 of water^ 9 of which latter 
exist already as constituents of the chloral hydrate; and the pro- 
bability that such changes do take place appears to be strength- 
ened by the fact that chloride of ammonium^ ammonia, and free 
sulphur were detected amongst the products of the reaction ; and 
the presence of a trace of chloroform may be easily accounted 
for by the action of the free ammonia on a portion of the un- 
changed chloral hydrate. 

I may observe that those results as to the composition of the 
brown compound were obtained as follows : — The carbon and 
hydrogen were determined by combustion with chromate of lead, 
using a long combustion-tube and placing a layer of copper 
turnings in its anterior part ; the nitrogen by burning with 
soda-lime, and estimating the resulting ammonia by means of the 
chloride of platinum; the sulphur by converting it into sul- 
phuric acid, which was effected by treating the substance with 
nitric acid and chlorate of potash (as recommended lately by 
Pearson for the determination of sulphur in organic compounds), 
and then estimating the sulphuric acid so pi*oduced in the usual 
way by chloride of barium ; and lastly the oxygen was deter- 
mined by difference after the estimation of the other constituents. 

Digitized by VjOOQ IC 

Dr. A. SchuBter on Unilateral Conductivity. 361 

But I may remark that the peculiar properties and great com- 
plexity of this compound offer considerable difficulties in the 
way of an exact determination of its different constituents^ and 
of its true nature as a chemical combination. It appears^ how* 
ever^ from the circumstance that it readily dissolves in alkaline 
solutions^ which then yield insoluble or sparingly soluble dark- 
coloured precipitates with different metallic salts, that it partakes 
somewhat of the character of an acid ; but this and several other 
obvious matters of inquiry connected with the compound are 
subjects for further investigation. 

Before concluding, it is right to state that, after I had observed 
many of the facts which I have here described, I found, on look- 
ing over the ' Chemical News/ that there was in volume xxv. 
page 87, a notice of a communication *' On the Reaction of 
Chloral Hydrate and Sulphide of Ammonium,'' which had been 
read by Dr. J. Wala before the Lyceum of Natural History of 
New York, in which he notices some of the changes which I 
have described as taking place in that reaction, as well as the 
formation of a light-yellow substance, the properties of which 
(as observed by him) do not altogether agree with those of the 
sulphuretted compound, which I prepared in a somewhat differ- 
ent manner from that which he adopted. I may also add that 
Dr. Wah did not attempt to analyze the substance he obtained, 
for want, as he says, of material — and that he further states, in 
speaking of it, that 0. Low asserts that in physical appearance 
and chemical properties it resembles exactly the sesquisulphide 
of carbon which he has described in the American Journal of 
Science, vol. xli. p. 251. 

Be this as it may as regards the substance obtained by Dr. 
Walz, my analyses of the brown sulphuretted compound, pre- 
pared in the manner stated, show that it possesses a totally dif- 
ferent chemical composition from the sulphide described by L5w 
in the Journal to which he has referred. 

XXXVI. On Unilateral Conductivity. 
By Arthur Schuster, Ph>D.^ 

I. Introductory, 

WHILE I was engaged in other work I met with an irre- 
gularity which seemed to me to be of such a peculiar 
nature that I subjected it to a separate investigation. The 
residts of this investigat'on have not been entirely satisfactory. 
I have not been able to raise the phenomenon, to which I allude, 

* Commimicated by the Author, having been read in Section A. of the 
British Association at Belfast (1874). 

Digitized by VjOOQ IC 

253 Dr. A. Schuster on Unilateral Conductivity* 

above the rank of an irregularity ; that is to 8ay> I am not able 
to produce it at my own will^ although when it is present I am 
generally able to destroy it. My experiments, however^ leave 
no doubt as to the facts^ and they show clearly that^ in a circuit 
composed entirely of copper wires, joined together by means of 
binding-screws^ the electric conductivity may be different in 
opposite directions. It would be difficult to discover such a 
difference in the resistance by means of the ordinary ways of 
measuring it. The changes in the electromotive force of the 
battery and in the resistance of the wire^ through an alteration 
of temperature or other accidental causes^ would be sufficient to 
mask the effect. If we use, however, the electromotive force of 
a moving magnet, we are sure that it is always constant as long 
as the strength of the magnet does not vary and the magnet 
moves always between certain limits. A magnet rotating rapidly 
within a coil of wires induces currents in alternate directions in 
the coil. We are perfectly sure that the electromotive force 
producing these currents is the same in both directions ; and if 
we can detect any difference in the strength of the currents 
going in opposite directions through the wire, we may be sure 
that only a difference in the resistance can produce such a result. 
I have calculated the effect on the galvanometer-needle of in- 
duction-shocks following each other in alternate directions at 
regular intervals of time. If the galvanometer is provided with 
a damping arrangement, a final condition will be arrived at in 
which the galvanometer-needle swings between certain limits. 
These limits decrease as the interval between the induction- 
shocks decreases. If, therefore, the rotation of the magnet is 
rapid enough, the effect of the induced currents on the gidvano- 
meter ceases to be visible. It should, however, be remembered 
that, although the limits between which the galvanometer-needle 
moves approach zero, the velocity of the needle remains finite. 
This, of course, is only true if the two induction-shocks are of 
equal strength. If the induction-cuiTcnt in one direction is 
stronger than the current in the opposite direction, the galvano- 
meter will show a permanent deflection. As we have two strong 
currents balancing each other, a very small difference in the 
resistance will have a strong effect. 

II. Description of Apparatus. 

The magnet which was used as electromotive force was fixed 
to the plate of a siren, which could be set into motion by means 
of a pair of bellows. The same instrument has been formerly 
used by R. Kohlrausch and W. Weber*, and later by Kohl- 

* " Electrodynamic Measurements, with special reference to the reduc- 
tion of intensitv to absolute measure,*' proc. pf the Royal Saxonian Society 
of Sciences, vol. iii. 

Digitized by VjOOQ IC 

Dr. A. Schuster on Unilateral Conductivity. 233 

rausch and Nippoldt iu a research on the conductivity of sulphuric 
acid*. I take the following data from the latter paper. The 
resistance of the wire wound round the magnet is 30 mercury 
unitsf. The mean electromotive force of the induction-shocks is 

-^-T Grove in each direction if the magnet rotates n times in a 

second. During the following investigation the magnet rotated 
about forty times a second ; so that the resultant electromotive 
force in each direction was about 0*12 Grove. 

The resistance of the galvanometer was found to be about 
2477 mercury units ; so that the resistance of the whole circuit 
was as nearly as possible 2500 units. The galvanometer had a 
plane mirror, and was read off by means of a telescope and scale 
at a distance. In order to have an idea of the delicacy of the 
instrument, I measured the deflection produced by a known 
electromotive force, and I found that the electromotive force of 
TsVir Daniell caused a first deflection of 200*4 divisions of the 
scale. The whole arrangement is therefore extremely simple, 
and is represented by the following diagram :-^ 

© <$ > 

G is the galvanometer, I a coil of wires within which the rota- 
ting magnet is placed. 

III. Description of Experiments. 

When I first joined the galvanometer to the inductor and ro- 
tated the magnet, the effect on the galvanometer-needle was such 
that I was afraid of a bad contact either in the galvanometer or 
in the inductor. The needle started wild to one side, then 
suddenly stopped, turned back to the opposite side, and moved 
from one side to another without any law. The only regularity 
I could perceive was that it started always in the same direction. 
On changing the wires leading to the galvanometer, the needle 
invariably started to the opposite direction. I broke the con- 
nexions and left for about two hours. When I came back every 
thing had changed. On working the siren the needle now went 
slowly to one side, and after a few oscillations came to rest at a 
point about ninety divisions of the scale from the zero-point. 
On changing the wires leading to the galvanometer the needle 

* " On the Validity of Ohm's law for electrolvtes, and a numeric deter- 
mination of the conductivity of sulphuric acid. Poffff. Ann, vol. cxxxviii. 
p. 379 (1869). 

t All resistances in this research are referred to mercury units. 

Digitized by VjOOQ IC 

254 Dr. A. Schuster on Unilateral Conductivity. 

went to the other side, and the permanent deflection was nume- 
rically the same* The same experiment was repeated several 
times, and the same deflection was always observed. While 
thinking over this result, I took the apparatus to pieces, t. «« 
disconnected all wires and joined them again together. The 
effect had now entirely disappeared, the needle coming to rest 
exactly at its sero-point* The next dav a small unilateral con- 
ductivity (as the raect may be properly called) was observed, 
but after a few experiments disappeared again. During several 
days I found that this unilateral conductivity generally appeared 
when the wires had had some rest ; and I therefore joined into 
the circuit different wires which had not been used for some 
time. Some of these wires showed the effect, and some did not ; 
in all cases it disappeared after several experiments. A wire 
which had never been used before showed the effect in a remark- 
able degree. The introduction of this wire, which could not 
have a resistance larger than 0*1 unit, was sufficient to drive 
the needle wild to one side. I must mention here a remarkable 
fact. Suppose we have a circuit in its normal state (that is, 
showing no unilateral conductivity) ; let us introduce a wire, and 
suppose that the unilateral conductivity is now observed. Take 
the wire out again, so that the circuit is exactly the same as it 
was before when no unilateral conductivity existed. The uni- 
lateral conductivity will now appear, generally even in the same 
degree as it did with the new wire. If we now by experimenting 
destroy the unilateral conductivity and join the wire which had 
caused the disturbance into the circuit again, it will generally 
behave quite neutral ; t. e, no unilateral conductivity wUl be ob- 
served. If it do not behave quite neutral, it will only show a 
small unilateral conductivity, which will be destroyed by a second 
or third experiment of the same kind. 

IV. Proposed Theory of the Phenomenon. 

It is chiefly the remarkable fact just described (as well as the 
previous observation, that generally new wires, or such wires as 
have not been used for some time, showed the effect) that has 
led me to a theory which, although proved afterwards to be, if 
not erroneous, at any rate incomplete, explains so well many of 
the most startling observations that I think it welt to give it 
here. Supposing we pass an electric spark from a sphere to a 
point, it is known that the distance the electric spark will pass 
for a given electromotive force is different according as the sphere 
is positively or negatively electrified. A circuit composed of a 
metallic wire, terminated at one end by a sphere, separated by a 
thin layer of air from the other end of the wire would therefore 
show unilateral conductivity, the positive electricity passing more 

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Dr. A. Schuster on Unilateral Conductivity. 255 

easy in one direction through the air than in the other. It is 
also known that metals condense air in great quantity at their 
surface ; and if we screw two wires with their condensed air to* 
gether, it is quite conceivable that particles of air will separate 
the two surfaces of copper^ and that a small voltaic arc will there- 
fore be formed. Unilateral conductivity would be the result. 
If we screw a wire which has air condensed on its surface to a 
binding-screw^ part of the air will pass from the wire to the 
binding-screw ; and it would thus be explained that the tempo* 
rary addition of a new wire may produce a unilateral conductivity 
in a circuit which has not shown it before, 

V. Experiments confirming the Theory. 

Many minor coincidences seemed to confirm this theory* 
Cleaning the ends of the wire with the knife generally destroyed 
the effect. It was, as a rule, observed in those parts of the cir- 
cuit which had been disconnected over night. It is always easy 
to find out in what part of the circuit the effect has its seat. 
We have only to change the connexions in various places, and 
to observe in what direction the needle is deflected. I mention 
one particular case. 

The rotation of the magnet one day caused a permanent de- 
flection of the needle of 295 divisions of the scale. On reversing 
the wires at the ends of the induction-coil, the needle was de- 
flected towards the other side. The effect, therefore, had its 
seat in the induction-coil. The coil was divided into two halves, 
which were connected by means of a stout copper wire about 
half an inch in length. I remembered that this piece of wire 
had been exposed to the air over night, and I therefore reversed 
the wire ; the needle was deflected 295 divisions of the scale to 
the other side, showing that my supposition had been correct, 
and that this small piece of wire, the resistance of which may 
have been about the hundred-thousandth part of the whole 
resistance, had caused the deflection. On reversing the wire 
again, the effect had disappeared. 

Another wire was now taken to join the two halves of the in- 
duction-coil ; a permanent deflection of about 80 divisions of 
the scale was observed. On cleaning the ends of the wire with 
a knife the effect disappeared. 

These experiments seemed alone sufficient to prove the theory. 
In order, however, to subject it to a severer test, I thought of 
condensing air artificially on the surface of the wire. This can 
readily be done by means of powdered charcoal, which, as is 
known, absorbs air in great quantity. A wire which was in its 
normal state was therefore laid with one end into powdered 
charcoal for about five minutes. When reintroduced into the 

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256 Dr. A. Schuster on Unilateral Conductivity. 

circuit, the wire showed a very strong unilateral conductivity. 
Cleaning and scraping the wire had at first apparently no effect ; 
screwing the wire^ however, to another binding-screw attached 
to the induction-coil destroyed the effect entirely, so that the 
wire, even when screwed to the original binding-screw, showed 
no unilateral conductivity. The same experiment was repeated 
a second time, and with the same result. Five minutes' lying 
in powdered charcoal was sufficient to reproduce a strong 
unilateral conductivity; and the same operation as before 
destroyed it. 

VI. Failure of the Theory. 

A third trial to obtain unilateral conductivity by the same 
means failed. The wire was put into the charcoal for several 
hours instead of several minutes ; but even then it remained in 
its neutral state. All the various circumstances which generally 
had produced unilateral conductivity were now tried; but none 
succeeded. New wires were tried; the whole apparatus was 
left untouched and disconnected for several days ; but I could 
not obtain the effect again. I used the same instrument in 
another investigation during three consecutive weeks, during 
which various new wires were tried and new combinations em- 
ployed ; but the effect only came out once more, and this time 
m the galvanometer. The deflection amounted to about 20 
divisions of the scale. It lasted for several days and then dis- 

VII. Relation of unilateral conductivity to previously known 

It is perhaps worth while to ^ay a few words about the rela- 
tion in which the phenomenon described in these pages stands' 
to other phenomena to which a similar name has sometimes been 
given. Before attempting to do this, however, it is necessary 
to allude to one or two objections which might be raised against 
my interpretation of the experiments described above. 

Can the experiments be explained by thermoelectric currents 
set up by the heating of the wire through the electric vibra- 
tions f I think that a careful perusal of the experiments will 
convince everybody that they cannot be explained that way. I 
need only draw attention to the unstableness of the effects and 
to the different facts upon which I thought myself justified in 
founding the theory mentioned above. These facts certainly 
cannot be explained by thermoelectric currents. 

At first sight my experiments seem to have some relation to 
a class of phenomena discovered by Poggendorff*^, and described 

♦ Annalen, vol. xlv. p. 353 (1838), vol. liv. p. 192 (1841). 

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Dr. A. Schuster on Unilateral Conductivity. 257 

by him under the name of bilateral deflection {doppelsinnige 
Ablenkunff), It seems that the currents in alternate direction 
affect to a certain degree the temporary magnetization of the 
needle. This has of course an influence on the time of vibra-* 
tion, which is shorter while the current increasing the mag* 
netism passes through the galvanometer. While the current 
passes in this direction the needle makes a greater way than in 
the same time while the current in the opposite direction is 
passing. The two currents succeeding each other at regular 
mtenrals of time will therefore not counterbalance each other^ 
but the current increasing the magnetism of the needle will have 
the upper hand. 

The result will be that the needle will be driven towards the 
side to which it was originally deflected. This^ of course^ only 
happens if the effect of this magnetization is sufficiently strong 
— that is to say^ if the original deflection is sufficiently large ; 
for the magnetizing effect on a needle^ placed at right angles to 
the axis of the galvanometer-coil^ is zero^ and increases as the 
sine of the angle of deflection. According to Poggendorff, 
a needle which is not deflected more than eight or ten degrees 
from its zero-pointy will return to that point if currents in alter- 
nate directions are sent through the galvanometer. If, how- 
ever^ the original deflection is greater than 10 degrees, the 
needle is driven violently towards the side of this deflection. 

It is evident that this effect of the electric vibrations is a 
function merely of the position of the needle ; altering the con- 
nexions could therefore never produce a reversal of the effect. 
As, however, I could always drive the needle towards the other 
side by suitably changing the connexions, this bilateral deflec- 
tion has evidently had nothing to do with the abpve experi- 

It remains to say a few words about what has been called 
unipolar conductivity. This unipolar conductivity has been ob- 
served in electrolysis and in flames. The unipolar conductivity 
in electrolytes has been explained by secondary influences of 
electrolysis', and, therefore, does not stand in any relation to 
what I have called unilateral conductivity. The unipolar conduc- 
tivity of flames has not yet been satisfactorily explained. If my 
supposition is correct, and if we must look to the air condensed 
on the surface of the wires for the explanation of unilateral con- 
ductivity, it will most likely prove to be closely allied to the 
unipolar conductivity of flames. 

VIIL Conclusion, 

The result of the foregoing investigation may be perhaps best, 
stated as follows *^— * 

Phil. Moff. S. 4. Vol. 48. No. 818. Oct. 1874. S 

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258 Lord Baykigh tm the VHrMHam of 

The current produced by an eledramotive force m a circuit 
compoeed entirely of copper wiree joined together by maosf of 
Unding^ecrewi may, under certain eircumttancet, be different frmn 
the current produced by the eame electromotive force acting in the 
opposite direction. 

I have called this phenomenon " unilateral condnetirity;^ and 
I have tried to bring it into connexion with known facts. Hie 
most plausible explanation seemed to me to be^ that a thin layer 
of air may sometimes intervene between the two wires which 
are screwed together. This explanation has been confirmed by 
some experiments. Other experiments have shown that the ex* 
planation is insufficient. I do not think that the evidence is 
sufficiently strong to abandon altogether an explanation which 
seems to agree so well with the most characteristic features of 
the phenomenon. Secondary causes may intervene which pre* 
vent the phenomenon from being formed. I suggest the dif- 
fusion of the gases into the wires as such a secondary pheno- 
menon. E£Fects which are so unstable, however, are never 
explained by a simple set of experiments. They will only be 
satisfactorily explained by a number of observations from dif- 
ferent experimenters. It is, I hope, a sufficient justification for 
the publication of the above experiments if they draw the atten* 
tion of physicists to a class of pnenomena which sometimes may 
seriously interfere with their measurements. 

XXXYU. On the Vibrations of Approximately Simple Systems. 
By LoKD Batleigh, M.A., F.H.S.'^ 

IN a paper with the above title, published in the Philosophieal 
Magazine for November 1873, 1 drew attention to the fact 
that when the natural vibrations of a system are thoroughly 
known, the effect of a small variation in the system in changing 
the types and periods of vibration may be readily calculated by 
a general method. In particular I proved that the altered pe- 
riods may be found from the new values of the potential and 
kinetic energies on the hypothesis that the types are unchanged, 
subject to an error of the second order only. The present note 
shows how a farther approximation may be made, and how a 
similar method may be applied to a system subject to small dis- 
sipative forces. 

If ^p ^^ &c. be the normal coordinates of the original system, 
the expressions for the kinetic and potential energies are 


* Communicated by the Author. 

• • • >T 

f .... (1) 

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Jfproximaiefy Single Syiiems. 259 

Now let the system be dightly varied, so that T and Y become 

T+CT=i([ll +S[1])^!+ . . . +8[12]^i^,+ • • • . 

V+8V=i({l} + 8{l}>I+...+8{12}^i^,+ ..., 
giving for the equations of vibration of the altered system 

+ ...=0, 

(S[12]D«+8{12}>i + ([2]D«H.8[a]D«+{2} + 8{2}>« 

+ ...=0, 

In the original system one of the natural vibrations is that 
denoted by the sole variation of if>^. In the altered system this 
will be accompanied by simultaneous small variations of the 
other coordinates. If the whole motion vary as cos Pft, we get 
from the sth equation, as was proved in the paper referred to, 

an equation which may be regarded as determining approximately 
the character of the altered types of vibration. 
Now the rth equation of (2) gives 
i/>r(-/>J[r]-pj8[r] + {r}+8{f}) + .-. + ^.(-p;8M 

+ 8{r*}>+...=0. (4^ 

Using in (4) the values of <f>t : ^^ given in (3), we get for the 
value ofjE>Jj^ 

' „«- M + 8{r} (;>;gW-8{r.}X . . (g) 

''' [r].+ S[r] [r]M{/»;-i>;) 

in which the summation extends to all values of $ other than r. 
The first term in (5) gives the value of fl calculated withoujt 
allowance for the change of type, and is sufficient when the square 
of the alteration in the system may be neglected. If pr f^^r to 
the gravest tone.of the system, pi— pi is always positive, and the 
term of the second order in (5) is negative, showing that the 
calculation founded on the unaltered type gives in this case a 
result which is necessarily too high. 

If obly the kiiietic energy undergo variation, 



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260 Lord Rayleigh on the Vibrations of 

As an example we may take a uniform string of length / and 
density p, carrying a small toad m at its middle point. If y be 
the transverse displacement at point x, 

the origin of x being at one end. In this case for the gravest 
tone we have 

so that 


since pjjpj— pj=l :«*— 1. 

Fr here denotes the value of/),, when there is no load. 

«*— 1 *— 1 *+l 
in which the values of s are 3, 5^ 7> 9> &c. Accordingly 

■^zTi^'i* • • .^ • • • • (y) 

and therefore 

pJ=P»{l-^ + ^' + cube«}, . . (10) 

which gives the pitch accurately as far as the square of the ratio 

l^e free vibrations of a svstem subject to dissipation-forces are 
determined in general by the equations 

^#-1-^-' • • • • <") 

where\ T and V are as before^ and F, called the dissipation-func- 
t^n, is of the form 

* See ft paper " On lonie General Tlieorcms relating to Vibrations," 
Mathematical Society's Proceedings^ June 1873. 

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Approximately Simpk Systems^ 261 

3y a suitable transfcHrmation any two of the functions T, P, V 
can be reduced to a sum of squares^ but not in general all three. 
When all three occur^ the types of vibration are more complicated 
than those of a conservative system, or of that of a dissipative 
system with one degree of freedom. When, however, the fric- 
tional forces are small, as in many important applications they 
are, it is advantageous to proceed as if the system were conser- 
vative, and reduce T and V to sums of squares, leaving F to take 
its chance. In this way we obtain equations of the form 

in which the coefficients (11), (22), (12), &c. arc to be treated 
as small. 

Let the type of vibration considered be that which differs little 
from the sole variation of ^,., and let all the coordinates vary as 
c'r', where pr will be complex, as also the ratios of the coor* 
dinates. From the ^ equation^ 

(fM + {*}>.+ (^*)pA+ • • . =0, 

we get, by neglecting the terms of the second order, 

^''^^ w^^wv ' • • * ^ ^ 

which determines the alteration of type. Although p is com- 
plex, the real part is small compared with the imaginary part ; 
and therefore (14) indicates that the coordinates ^, have appi*oxi«> 
mately the same phase, and that phase a quarter period different 
from that of ^y. The rth equation gives, by use of (14), 

i';W+{r}+(rK-2-^|^=0, . . (15) 

from which it appears that^^r may be calculated approximately 
from the equation 

ir-\p\-\-{r)Pr+\r)=0; .... (16) 

that is, as if there were no change in the type of vibration. The 
rate at which the motion subsides will not be altered, even though 
the terms of the second order in (15) be retained. 

The reader mav apply these formulse to the case of a uniform 
string whose middle point is subject to a small retarding force 
proportional to the velocity. 

It is scarcely necessary to point out that these methods apply 
to other physical problems than those relating to the vibrations 

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262 Mr. W. B. Davis an m Mtthdd oflUiairaiing 

of materitl syttemt* For the free motioii of heat in a eondoetor^ 
we obtain equations eorresponding to those of materisl systona 
which are supposed to be devoid of inertia« The funetioiiB F and 
y may thus be reduced to sums of squares ; and the effect of a 
small variation in the system may be investigated by methods 
parsllel to those employdl in the present paper. 

TerKng Pbce» Withsm, 
September 11, 1874. 

XXXVIIL On a simple Method of Illustrating the chief Pheno- 
tnena of Wave-Motion by means of Flexible Otris. By the late 
W. S. Davis, FJt.A.S.^ Derby*. 

[VTith a Plste.J 

THE simple methods about to be described, of exhibiting the 
chief phenomena of wave-motion, were suggested during 
some experiments lately made by the author on the refraction of 
liquid waves t* These experiments consisted in the production 
of waves on the surfaces of two liquids of different densities, 
lying side by side : on agitating the surface of either liquid, 
waves were produced whicn passed from one liquid to the other, 
at the same time undergoing changes in amplitude, lengthy and 
form of front. In preparing diagrams to represent these phe- 
nomena it became necessary to make drawings of vertical sec* 
tions through the two liquids, perpendicular to their line of 

The appearance presented by the sinuous lines on these dia« 
grams immediately suggested that a similar appearance could be 
exhibited by means of waves on flexible ooras. India-rubber 
tubes, variously suspended, and both empty and loaded, were 
tried without satisfactory success ; the waves moved too quickly 
to be well observed, and the reflected waves interfered with the 
direct cfne^. Further experiments led the author to devise the 
simple apparatus now exhibited, which, however, has been made 
to serve for many other illustrations of wave-motion in addition 
to those it was at first intended to show. 

The apparatus consists essentially of: — (1) a piece of stout 
board about 20 feet long and 9 inches wide, which should be 

Cted black; and (2) three or four ropes, which must be both 
y and flexible : the ropes used by builders for securing their 
sctffibldiDg have been found to answer very well^ especially if 
they have been in use some time. To enable the eye to readily 

♦ Read before the Physical Society, May 9, 1874. Commumcated by 
the Society, 
t Bee Brit. Assoc. Report, 1873. 

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Gog gle 

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Phenomena of JFwe^MoHon by memo of Flexible Ccrde^ d63 

distinguish any ptrtieolar rope when two or more are used 
together^ it is well to coyer the ropes with di£ferently coloured 
fabrics^ say red^ bluci and green. A few other accessories are 
necessary^ which will be described as they are required* 

By means of this apparatus wares may be produced which 
more slowly enough to be readily examined by the eye. The 
chief phenomena of wave-motion which can oe shown are as 
follows :— 

1. TroMsmiseion of a Wave. — One end of a rope^ a few feet 
longer than the boards is fixed to a hook at the end of the board. 
The free end of the rope is then taken in the hand^ and^ the 
the rope being quite slacks a sudden up-and-down movement of 
the hand is made. A protuberance is thus formed which moves 
very slowly along the rope, presenting the appearance shown in 
Plate y. fig. 1* 

A single up-and-down movement produces a wave consisting 
of a crest only, the trough being suppressed by the board ; if, 
however, with the rope very slack, the hand be moved up and 
down very quickly and energetically, a series of waves, consisting 
of both crest and trough, are produced (fig. 2). 

2. Amplitude and Wave-length. — Waves having any length, 
from 1 to 6 or 7 feet, and amplitudes of similar dimensions, are 
easily produced by properly controlling the rapidity and energy 
t)f the motion of the hand. 

8. Decrease of Intensity with Dietance. — ^This is illustrated by 
a succession of waves produced by the well-timed motion of the 
hand (fig. 2). The actual decrease of amplitude in this case is, 
of course, due to the loss of energy by friction, and not to lateral 

4. Relation of Velocity to Elasticity, — Two similar ropes, one 
covered with red and the other with blue, are laid side by side 
along the board and fastened to hooks at one end. The free 
ends of the ropes are held in the hand, with the finger between 
them, and, care being taken that they are equally loose, the hand 
is moved up and down as usual. The result is that a wave of 
the same height and length is produced on each rope, and the 
two waves travel side by side to the ends of the ropes. The ex- 
periment is repeated with one rope somewhat tighter than the 
other, when the wave on the tighter rope is observed to travel 
faster than that on the looser one (fig. 3). On continuing to 
tighten the rope the velocity of the wave is more and more in- 
creased, and may be caused to reach the end of the rope a whole 
length or more before its fellow. 

5. Relation of Velocity to Density, — ^To exhibit this relation a 

* The length of the board in the figures \b drawn to a much smaller 
'scale than the other parts. 

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264 , Mr. W. S. Davis an a Method of lUuUrating 

loaded rope is required. That now used has strung upon it m 
number of rings of lead cut from a leaden water-pipe; these 
are placed about 6 inches apart, and are covered with india- 
rubber bands to prevent their making unpleasant noise. IW 
loaded and an unloaded rope are laid on the board side by side, 
and fixed at one end. Then^ taking care the tension is equal 
in the two ropes, waves are simultaneously generated on theroi 
as before described. It is then observed that the wave on the 
loaded rope lags considerably behind the other (fig. 4). By suffi- 
ciently tightening the loaded rope the velocity of its waves may 
be made equal to, or even greater than that of the waves of tl^ 
unloaded rope. This may be used to explain whv the velocity 
of sound in water is greater than in the much less oense medium^ 

6. Transmission of Waves from one Medium to another of dif- 
ferent Density. — The loaded cord is attached end to end to one 
much lighter than itself; the united cords are laid on the board 
with the splice at about the middle of its length. Then, fasten- 
ing the end of the lighter cord, waves are generated on the 
heavier one. These waves pass onwards to the lighter cord, on 
reaching which they acquu*e greater amplitude, velocity,, and 
length (fig. 6). If the heavier cord be fixe4 and waves be gene- 
rated on the lighter one, the reverse changes to those just stated 
occur on the waves reaching the heavier cord. It is an interest- 
ing experiment to transmit waves along a succession of three or 
more cords alternately heavy and light. With three cords joined 
end to end, the middle one being heavier than the others, a good 
illustration is produced of the changes of velocity, length, and 
amplitude which setherial waves unaergo in passing perpendi- 
cularly through a medium with parallel faces. 

7. Separation of a Wave into two or more smaller Waves. — A 
single cord extending half the length of the board is joined to a 
double one extending the other half. Waves are transmitted 
from the single cord to the double one ; on reaching the latter 
each wave divides in two, one wave traversing one part of the 
double cord, and the other wave the other part. By giving each 
part of the double cord a different tension, the velocity of the 
waves will be different in each (fig. 6). The waves on the double 
cord may be made to move in planes at right angles to each 
other by the use of proper guides, thus furnishing an illustration 
of some of the phenomena of double refraction. 

8. Superposition and Interference. ^The same arrangement is 
used as in 7, but the waves are transmitted from the double 
cord to the single one. With equal tension in each part of the 
double cord, the waves simultaneotusly produced on each part run 
side by side until they enter the single cord^ when they are su- 

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Phenomena of Wave-motion by iheans ofFUiXiible Cords. 265 

perposed and produce a wave of doable amplitude. One half of 
the double cord may be tightened until its wave reaches the single 
cord half a wavers length before the wave on the other half ^ 
when interference occurs^ there being little or no lateral motion 
to be observed in the single cord. 

- 9. Plane of Waves, — In the experiments previously described 
the waves were transmitted in a vertical plane ; but by properly 
directing the motion of the hand, the waves may be transmitted 
in planes variously inclined to the board, or in a plane parallel 
with it. Waves in space of three dimensions, corresponding to 
circularly polarized light, are produced by rapidly and regularly 
moving the hand in a circle, the cord then taldng the form 
shown at the right of figs. 7 and 9. 

10. Polarization. — A series of flat boards are used as guides; 
which are clamped on the long board. These are shown in 
figs. 7, 8, 9. The vertical and oblique guides are each in two 
pieces, which are so approximated to each other as to just allow 
the cord to move freely between them. The horizontal guide is 
in one piece only. The vertical and horizontal guides being 
fixed as shown in figs. 7 and 8, waves in a vertical plane are 
transmitted from that end of the rope nearest the vertical guides ; 
the waves then pass freelv through the vertical guides^ but are 
completely stopped by the horizontal one. Waves in a hori« 
zontal plane transmitted from the other end of the apparatus 
pass the horizontal guide, but are stopped by the vertical ones 
(fig. 8). Waves in an oblique plane transmitted from either end 
are resolved by the nearest guide into a component in its own 
plane and a component at right angles which is suppressed; 
the former passes on and is stopped by the next guide. Circularly 
polarized waves on reaching the guides are similarly resolved 
(fig. 7). , 

11. Depolarization, — A pair of oblique guides are required in 
addition to those described in 10. The arrangement of these is 
shown in fig. 9, which needs no further explanation. The waves 
are supposed to proceed from right to left. With a single cord 
as in fig. 9, or with a partly double one as in fig. 6, an endless 
variation of experiments relating to polarization maybe produced. 

12. Radiation and Absorption. — ^A rod of iron about 2 feet 
in length, having an eye at the centre and at each end, is fixed 
by means of a screw or pin through the central eye to an up* 
nght support of wood clamped at about the middle of the board 
(fig. 10). The iron rod must be able to rotate freely about the 
pin in a vertical plane parallel to the board, but in no other 
plane. Attaching a cord to one end of the iron rod and conti-^ 
nuing it to the end of the board, a series of properly timed waves 
are sent fdOPg itj when the rod vibrates in synchronisni with th^ 

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waves. If a second cord be attached to the other end of the 
rod and waves be transmitted as before^ the vibrations of the 
rod set up waves in this cord which correqKmd in period and 
length to those on the first cord^ thus furnishing an illustration 
of the reciprocity of radiation and absorption. 

The autnor has reason to think that, as nearly all the above- 
described illustrations have been devised during the last twdve 
months, the method is capable of much further development and 
greater perfection. 

XXXIX. Researches in Acoustics. — ^No. V.* 
By Alfred M. MATKRf* 

1. An Experimental Confirmation of Fourier's Theorem as ap^ 
plied to the Decomposition of the Vibrations of a Comporiie 
Sonorous Wave into its elementary Pendulum^vtlfrations^ 

A SIMPLE sound is a sound which has only one pitch. Such 
a sound is produced when^ with a bow, we gently vibrate the 
prongs of a tuning-fork and bring them near a cavity which ir- 
sounds to the fork's fundamental tone. An almost pure simple 
sound can be obtained by softly blowing a closed organ-pipe. 
On examining the nature of the vibratory motions of the 
prongs of the fork:^ and of the molecules of air in the resound- 

* This paper it the fifth in the series of those on Aeoustict aliesdy 
published m the Philosophical Magaxine. The preceding papers, however* 
were not numbered. 

t Communicated by the Author, with corrections, from Silliman*s Ame- 
rican Journal for August 1874. 

Sections 1, 2, 3, b, 6, and 7 of this paper were read before the National 
Academy of Sciences during the Session of Norember 1873. Section 4 was 
read before the Academy on April 21, 1874. 

X In my course of lectures on Acoustics, I thus show to my students 
that the prong of a tuning-fork vibrates like a pendulum : — I take two of 
Lissajous's reflecting forks, giving, say, the major third interval, and with 
them I obtain on a screen the curve of this interval in electric light. On 
a glass plate I have photographed the above curve of the major Uiird pas- 
sing through a set of rectangular coordinates formed of the sines of two cir- 
cles whose circumferences are respectively divided into 20 and 25 equal 
parts. I now place this plate over the condensing-lens of a vertical lantern 
and obtain on the screen the curve, the circles, and their net of coordinates. 
Suspended over the lantern is a Blackburn's compound pendulum* which is 
so constructed that its^' bob " cannot rotate around its axis. The bob is 
hollow, and a curved pipe leads from its bottom to one side of the pendulum. 
The pendulum is now defiected into a plane at 45*^ with its two rectangu- 
lar planes of vibration, so that the end of the curved pipe coincides with the 
beginninff of the curve over the lantern. The bob of the pendulum is fas- 
tened witn a fine cord in this position, and fine hour-glass sand is poured 
into it j the cord is now burned, and the sand is delivered from the pipe 
as the swinging pendulum gives the resultant of its motions in the two 
planes of vibratioB, while the photograph^ ^rve o^tbe. lantern is pro- 

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Fh>f. A. M* Mayer's Eeitatehei m Acauftia. 267 

ing eavity* and in the cloeed organ-pipe f, we find that each of 
these vibrations follows the same law of reciprocating motion 
as governs the vibrations of a freely swinging pendulum. But 
other bodies, for instance the free reeds of organ-pipes and of 
melodeonsj^ vibrate like the pendulum ; yet we can decompose 
the vibrations they produce in the air into many separate pen* 
dulum-vibrations^ each of which produces in the air a simple 
sound of a definite pitch* Thus we see that a pendulum-vi- 
brating body^ when placed in certain relations to the air on 
which it acts, may give rise to highly composite sounds. It is 
therefore evident that we cannot always decide as to the simple 
or composite character of a vibration reaching the ear solely 
from the determination of the motion of the body originating 
the sound, but we are obliged to investigate the character of the 
molecular motions of the air near the ear, or of the motion of a 
point on the drum of the ear itself, in order to draw conclusions 
as to the simple or composite character of the sensation which 
may be produced by any given vibratory motion. Although we 
cannot often detect in the ascertained form of an aerial vibration 
all the elementary pendulum-vibrations, and thus predetermine 
the composite sensation connected with it, yet if we find that 
the aerial vibration is that of a simple pendulum, we may 
surely decide that we shall receive from it only the sensation 
of a simple sound. Thus, if we arm the prong of a tuning- 
fork with a point, and draw this point on a btmp-blackened 
surface with a uniform motion and in a direction parallel to 
the axis of the fork, we shall obtain on the surface a sinusoidal 
or harmonic curve §; and this curve can only be produced 
by the prongs of the fork vibrating with the same kind of 

gressively covered with the gand if the times of the two vibrations of the 
pendulam are to each other as 4 to 5. 

* Helmholtz, Tbnen^findmngen, 1857> p. 75. Grelle's J<mm,fUr Math., 
ToL Ivii. 

t See Mach's Optisch-ahutische Versuche, Prag, 1873, p. 91. Dig 
Stroboskopische Darstellung der Luftschvoingvngen. 

X The Rey. S. B. Dod, one of the trustees of the Stevens Institute, has 
recently made an experiment which neatly shows this : — He silvered the 
tips of two melodeon-reeds, and then vibrated them in planes at right angles 
to each other, while a beam of light was reflected from them. The rdbul- 
tant figure of their vibrations is the same as that obtained by two Lissajous's 
forks placed in the same circumstances and having the same musical inter- 
val between them as that existing between the reeds. 

§ The equation of this curve is y = a sin (^r^+ « ) • The length, on the 

axis, of one recurring period of the curve is X ; the constant a is the maxi- 
mum ordinate or amplitude. The form of the curve is not affected by a ; 
but any change in its value slides the whole curve along the axis of x. It 
is interesting to observe that this curve expresses the annual variation of 
temperature in the temperate zones. 

Digitized by VjOOQ IC 

268 Prof. A. M. Meyer^s Researches in Aeouatiesr 

motion as that of a freely swinging pendnlum. If we now brin^ 
this vibrating fork near the mouth of a glass vessel whose mass 
of air responds to the tone of the fork, and, by the method of 
Mach, examine the vibratory motions of the air, we shall see it 
swinging backward and forward; and by combining these vibra* 
tions with the rectangular vibrations of forks placed outside of 
the vessel we shall obtain the curves of Lissajous* If the mem- 
brane of the drum of the ear be placed in connexion with the 
resounding cavity, it must necessarily partake of the motion of 
the air which touches it, and ultimately the auditory nerve fibrilbe 
are shaken in the same manner, and we receive the sensation* 
of a simple sound. Here the mind naturally inquires the reason 
of this connexion existing between the sensation of a simple 
sound and the pendulum-vibration. It has always appeared to 
me that the explanation of this invariable connexion is that the 
pendulum-vibration is the simplest vibratory motion that the 
molecules of elastic matter can partake of, and that the con- 
nexion of the sensation with the mode of vibration is the con- 
nexion between the simplest sensation perceived through the 
intervention of the trembUug nerves, and the simplest vibration 
which they can experience. Indeed the pendulum-vibration is 
the only one which produces the sensation of sound ; for if any 
other recurring vibration enters the ear, it is decomposed by the 
ear into its elementary pendulum- vibrations ; and if it cannot 
be so decomposed, then the given vibration is not recurring and 
does not produce in us the sensation of sound, but causes that 
which we denominate noise. This remarkable connexion be- 
tween a simple sound and the pendulum or harmonic vibra- 
tion, together with the fact of the power of the ear to decompose 
the motions of a composite sonorous wave into its vibratory 
elements, was thus distinctly enunciated by Ohm : — The ear has 
the sensation of a simple sound only when it receives a pendulum- 
vibration ; and it decomposes any other periodic motion of the air 
into a series of penduhtm-vibrations, each of which corresponds to 
the sensation of a simple sound. 

We have seen that the harmonic curve is the curve which 
corresponds to the motion which causes the sensation of a sim- 
ple sound ; but a molecule of vibrating air or a point on the 
tympanic membrane may be actuated by vibratory motions 
which, when projected on a surface moving near them, will 
develop curves which depart greatly from the simplicity of the 
harmonic, or curve of sines f; but nevertheless these curves 

* See Helmholtz on the distinction between a sensation and a perception* 
Tonempfindungeny p. 101. 

t In section 6 of this paper I have constructed several important curves 
corresponding to composite vibrations. 

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Prof. A. M. Mayer's Researches in Acoustics, 269 

will always be periodic if the sensation corresponding to their 
generating motions is that of sound. Now Fourier has shown^ 
and states in his theorenii that any periodic curve can always be 
reproduced by compounding harmonic curves (often infinite in 
number) having the same axis as the given curve and having the 
lengths of their recurring periods as 1^ ^, i, {, ke, of the given 
curve ; and the only limitation to its irregularity is that its ordi- 
nates must be finite^ and that the projection on the axis of a 
point moving in the curve must always progress in the same di- 
rection. Fourier demonstrates that the given curve can only 
be reproduced by one special combination, and shows that, by 
means of definite integrals, one can assign the definite sinusoids 
with their amplitudes and differences of phase. Now Helm- 
hoitz* has shown that di£ferences of phase in the constituent 
elementary sounds do not alter the character of the compo- 
site sound, and, therefore, that although the forms of the curve 
corresponding to one and the same composite sound may be 
infinite in variety (by reason of differences in phase in the com- 
ponent curves), yet the composite sound is always resolved 
into the same elements. This experimental result of Helmholtz 
also conforms to the theorem of Fourier in reference to the 
curves projected hj such motions ; for he has shown that only 
one series of sinusoidal resolution is possible. 

Fourier's theorem can be expressed as follows : — The con- 
stants C, G|, Cqy &c., and ay, a^, &c., can be determined so that 
a period of the curve can be defined by the following equation f : — 

y = C + C,sin(?^+«,) + C,sin(2?^+^,) 

+ ... 

But Fourier's theorem is the statement of a mathematical 
possibility; and it does not necessarily follow that it can be im- 
mediately translated into the language of dynamics without 
experimental confirmation ; for, as Helmholtz remarks, '^ That 
mode of decomposition of vibratory forms, such as the theorem 
of Fourier describes and renders possible, is it only a mathe- 
matical fiction, admirable because it renders computation facile, 
but not corresponding necessarily to any thing in reality ? Why 
consider the pendulum-vibration as the irreducible element of 
all vibratory motion ? We can imagine a whole divided in a 
multitude of different ways; in a calculation we may find it con- 
venient to replace the number 12 by 8 + 4, in order to bring 8 

* Tonenmfindungenj p. 190 f/ seq. 

t For other and more convenient forms of expression of this theorem, 
as well as for a demonstration of it, see pp. 62 and 60 of Donkin's 'Acous- 
tics' — the most admirable work ever written on the mathematical theory of 

Digitized by VjOOQ IC 

270 Prof. A. M. Mayer's Ruemrches m Acauitics. 

into view ; but it doet not neoesMtrily follow that 12 should al- 
ways and necessarily be considered as the sum of 8+^ Ia 
other cases it may be more advantageous to consider the number 
as the sum of 7+5. 

'' The mathematical possibility^ esUblished by Fourier, of de* 
composing any sonorous motion into simple vibrations, cannot 
authorise us to conclude that this is the only admissible mode 
of decomposition, if we cannot prore that it has a signification 
essentially real. The fact that the ear effects that decomposition, 
induces one, nevertheless, to believe that this analysis has a 
signification, independent of all hypothesis, in the exterior 
world. This opinion is also confirmed precisely by the Aict 
stated above, that this mode of decomposition is more advanta- 
geous than any other in mathematical researches ; for the me- 
thods of demonstration which comport with the intimate nature 
of things are naturally those which lead to theoretic results the 
most convenient and the most clear.'^ 

The theorem of Fourier, translated into the language of dy- 
namies, would read as follows : — *' Every periodic tfihraiory motion 
can ahiHtt/s, and always in one mannery be regarded a$ the turn of 
a certain fmnber ofpendulum-vibratione/^ 

Now we have seen that any periodic vibratory motion, which 
has the proper velocity, will cause the sensation of a musical note, 
and that a pendulum-vibration gives the 'sensation of a iimple 
souud'*^; therefore, if Fourier's theorem is applicable to the 
composition and decomposition of a composite sonorous wave, ii 
will be thus related to the phenomena of sound: — ^^ Every w- 
bratory motion in the atutitory canal, corresponding to a musical 
sound, can always, and always in one manner, be considered as 
the sum of a certain number of pendulum-vibrations, corresponSng 
to the elementary sounds of the piven musical note.** 

Heretofore we have called in the aid of the sensations (as* 
sumed to be received through the motions of the covibrating 
parts of the ear) to help us in our determination of the simpk 
or composite character of a given vibratory motion ; but Fou« 
rier^s theorem does not refer to the subjective effects on the 
organ of hearing, the dynamic function of whose parts are yet 

♦ Professor DonkiD; in his 'Acoustics/ Oxford) 1870, p. 11, advises tk« 
use of tone to designate a simple sound, and the word note to distinguish 
a composite sound. His reasons are *^ that tone (Gr. r6poi) really means 
tension, and the efiect of tension is to determine the pitch of the sonad of s 
string;" while a musical note is generally a composite sound. Professor 
Donkin further states, " Helmholtz uses the words Kkmg and Ton to signify 
compound and simple musical sounds. We have followed him in adoptmg 
the latter term ; but such a sound as that of the human voice could haidfy 
in Enslish be called a olanjf, without doing too mudi vi<;4ence to established 

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Prof. A. M. Mayer's Re$earehe$ in Acausties. 271 

very imperfectly understood. Ohm's theorem, on the other 
hand, refers entirely to these sabjective phenomena of the ear's 
analysis of a complex sensation into its simple elements. As 
Fourier's theorem refers only to the decomposition of a com- 
posite recurring vibration intQ its elementary pendulum-vibra- 
tions, it has nothing to do with the physiological fact of the co- 
relation of the pendulum-vibrations and the simplest auditory 
sensation; though this well-ascertained relation gives us the 
privilege of using this sensation as an indicator of the existence 
of an aerial pendulum-vibration. Hence, as Fourier's theorem 
IB entirely independent of our sensations, we must endeavour to 
verify it directly by experiments, which must perform the actual 
decomposition of the composite periodic motion of a point into 
its elementary pendulum-vibrations. But many difficulties pre* 
sent themselves when we would bring to the test of experiment 
the dynamic signification of Fourier's theorem. For example, 
the composite sound-vibration, on which we would experiment, 
emanates from a multitude of vibrating points; parts of the 
resultant wave-surface differ in their amplitudes of vibration; 
while points equally removed from one and the same point of 
the body originating the vibrations, may differ in their phases of 
vibration; so that when such a wave falls upon oovibrating 
bodies which present any surface, the effects produced are the 
result of extremely complex motions. The mind sees at once 
the difference between this complicated coneeption and the sim* 
pie one embodied in the statements of the dynamic application 
of Fourier's theorem. 

As the mathematician decomposes seriatim every point of the 
recurring curve into its harmonic elements, so the physicist, in 
eonfirming the dynamic application of Fourier's theorem, should 
decompose into its simple pendulum-vibrations the composite 
vibratory motion which such a curve represents, and indeed re* 
froduces when it is drawn with a uniform motion under a slit in 
a diaphragm which exposes to view only a point of the curve at 
once. Therefore only one vibrating point of the composite so- 
norous wave should be experimented on; and the composite vi<^ 
bratory motion of this point should be conveyed along lines to 

Joints of elastic bodies which can only partake of simple pen* 
ulum-vibrations. All of these essential conditions I have 
succeeded in securing in the following arrangement of ap- 

A loose inelastic membrane (thin morocco leather does well) 
was moimted in a frame and placed near a reed-pipe ; or, as 
in other experiments, the membrane was placed over an opening 
in the front of the wooden chamber of a (ireni^'s free-reed pipe. 
The ends of sev^ fine fibre* from a silk-worm^s ooooou were 

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272 Prof. A. M. Mayer's Researches in Aeaustics. 

brought neatly together and cemented to one and the same point 
of the membrane, while the other ends of these fibres were at- 
tached to tuning-forks mounted on their resonant boxes, as 
shown in fig. 1. In the experiment which I will now describe 

Fi«- 1. 

eight forks were thus connected with one point of the membrane. 
The fundamental tone of the pipe was Ut,, of 128 vibrations per 
second ; and the pipe was brought into accurate unison with a 
fork giving this sound 'l^. The forks connected with the mem- 
brane were the harmonic series of Ut,, Vt^, Sol,, Ut4, Mi4, Sol4y 
Bi", Utg. In the first stage of the experiment we will suppose 
that the fibres are but slightly stretched ; then, on sounding the 
pipe, all the fibres at once break up into exquisite combinations 
of ventral segments. If the sunshine fall upon a vibrating fibre 
and we look on it obliquely in the direction of its length, we 
shall see ventral segments superimposed on ventral segments in 
beautiful and changing combinations. On gradually tightening 
the fibres, we diminish the number of their nodes ; and on reach- 
ing a certain dgeree of tension with fibres 1 m. long, I have seen 
them all vibrating with single ventral segments. On increasing 
the tension, the amplitudes of these single segments gradually 
diminish and at last disappear entirely, so far as the unaided 
eye caii discern ; and then we have reached the conditions re- 
quired in our experimental confirmation. 

The point of the membrane to which the fibres are attached 
is actuated by a motion which is the resultant of all of the 
elementary pendulum-vibrations existing in the composite 
sonorous wave ; and the composite vibrations of this point are 

* Since the number of beats per second ffiyen by any harmonic (of a 
pipe out of tune with its harmonic series of forks) will be as the order of 
the harmonic, it is better to tune a reed to unison with a fork giving one of 
its higher harmonics* I generally used the Sol, fork, or the 3rd harmonic. 

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Prof. A. M. Maycr*8 Researches in Acoustics. 273 

sent through each of the fibres to its respective fork. Thus 
each fibre transmits to its fork the same composite vibratory 
motion^ while each fork can onl^ vibrate so as to give the 
simple pendulum-vibration of a simple sound ; for each fibre is 
attached to its fork at a point which lies in the upper node of 
the s^ments into which the fork divides when it gives its 
higher harmonic. Now, if Fourier's theorem has '^ an existence 
essentially real/^ any fork will select from the composite vibra- 
tory moticm which is transmitted to it that motion which it 
has when it freely vibrates; but if its proper vibration does not 
exist as a component of the resultant motion of the membrane^ 
it will not be m the least affected. Now this is exactly what 
happens in our experiment ; for when the pipe is in tune with 
the harmonic series of forks, the latter sing out when the mem- 
brane is vibrated ; but if the forks be even slightly thrown out 
of tune with the membrane, either by loading them or by alter- 
ing the length of the reed, they remain silent when the sounding- 
pipe agitates the membrane and the connecting fibres'*^* Thus 
have I shown that the dynamic application of Fourier's theorem 
has " an existence essentially real.'' 

It is indeed very interesting and instructive thus to observe 
in one experiment the analysis and synthesis of a composite 
sound. On sounding the reed it sets in vibration all the forks 
of the harmonic series of its fundamental note ; and after the 
reed has ceased to sound, the forks continue to vibrate, and 
their elementary simple sounds blend into a note which approxi- 
mately reproduces the tiuibre of the reed-pipe. If we could by 
any means obtain all of the elementary vibrations and have them 
with their relative intensities correctly preserved, we should have 
an echo of the sound of the reed after the latter had ceased to 
vibrate ; but the impossibility of thus obtaining the highest com- 
ponents of the reed, and the difficulty of reproducing the relative 
intensities of the harmonics in the covibrating forks, allow us 
but partially to accomplish this effect. 

2. An Experimental Illustration of Helmholtz's Hypothesis of 


The experiment which we have just described beautifully illus- 
trates the hypothesis of audition framed by Helmholtz to account 
for this, among other facts — ^that the ear can decompose a 
composite sound into its sonorous elements. Helmholtz founds 
his hypothesis on the supposition that the rods of Corti, in the 
ductus cochleaiis, are bodies which covibrate to simple sounds-* 

* See section 5 of this paper for an account of the degree of precision 
of this method of sonorous analysis. 
Pm, Mag. S. 4. Vol. 48. No. 318. Oct. 1874. T 

Digitized by VjOOQ IC 

974 Prof. J. J. M&ller on m Uedumatl PrineipU 

■omewhit, I imigine, ai lodkd strings^ of graded kngtlis and 
diameters would aet in itmilar drenmstanoes. The Tibrntiona 
of the eompoeite wave fall upon the membrane plaeed near the 
reed at they fall upon the membrane of the tympanum ; and 
these vibrations are sent through the stretched fibres (or ddicate 
splints of rye-straw, which I have sometimes used) from the 
membrane to the tuned forks, as they are sent firom the mem- 
brana tympani through the ossicles and fluids of the ear to the 
rods of Corti. The composite vibration is decomposed into its 
vibratory elements by the covibration of those forks whose vi* 
bratory periods exist as elements of the composite wave*moti<m j 
so the composite sound is decomposed into its sonorous elements 
by the oovibrations of the rods of Corti, which are tuned to the 
elementary sounds which exist in the composite sonorous vibra* 
tion« The analogy can be carried yet further by placing Uie 
forks in line and in order of ascending pitch, and attaching to 
each fork a sharply*pointed steel filament. If the arm be now 
stretched near the forks, so that the points of the filaments nearly 
toueh it at pmnts along its length, then any fork will indicate 
its covibration by the fact of its pricking the skin of the anoi 
and the localiiation of this pricking will tell us which of the 
series of forks entered into vibration. The rods of Corti shake 
the nerve-filaments attached to them, and thus specialise the po* 
sition in the musical scale <^ the elements of a composite sono- 
rous vibration. Thus a complete analog is brought into view 
between our experiment and Helmholtrs comprehensive hypo* 
thesis of the mode of audition. 

[To be continued.] 

XL. On a Mechanical Principle retuUing from Hamilton's Theory 
qf Motion. By J. J. MCllxb, Profeuor at the Polytechnic 
in ZUrichf. 

WHEN a system of material points moves under the influ* 
ence of forces proceeding from the reciprocal attraction 
and repulsion of the points, all the integral equations of the mo* 
tion can, as Hamilton has shown|, bcrepresented by the par- 
tial differential quotients of a function of the coordinates (the 
primary function), in a manner similar to that in which, accord- 
ing to Lagrange, its differential equations can be represented by 
aid of the partial differential quotients of the force-function. 
Therein the primary function satisfies two partial differential 
equations ; but even one of these equations, as Jacobi demon- 

♦ For ditcnnions of the vibretory phenomena of loaded strings, sec Don- 
kin't ' Acoustics,' p. 139, and Ilelmholtz's Tonempfindungen, p, 267. 
t Tnnslated from PoggendorflTs Annalen, vol. clii. pp. 10^-131. 
J Phil. Trans. 1834, 1835. 

Digitized by VjOOQ IC 

reiuUingjrom Hamilton^B Theory of Motion. 275 

fttrated^ is sufficient for its definition. The primary function is 
a complete solution of this differential equation ; and any com- 
plete solution of the latter^ analogously differentiated according 
to the constants^ gives the system of the integral equations. 
Hence, in the Hamilton-Jacobi method, the entire problem is 
concentrated into the one integration of the partial differential 
equation, in contrast to Lagrange's way of proceeding, in which 
only single integrals are found by aid of the known principles* 
The integration of the partial differential equation was developed 
by Jacobi't^ generally both in the way already pursued by La^ 
grange and Pfaff, and also by a new and grand method, both of 
which methods have been adopted in a series of more recent 

The theory above mentioned has recently undergone expan- 
sbn in two respects. If the investigation by Hamilton and 
Jacobi referred to actual space, for which the element of a line 
proceeding from a point is capable of being represented by the 
iquare root of the sum of the squares of differentials of the ordi* 
nates of the point, Lipschitsf formed a more general conception 
of the problem, inasmuch as he assumed the line-element to be 
equal to the pi\k root of any real positive form, of the /7th degreCi 
of the differentials of any coordinates of the point in question. 
The element of its integral corresponding to the primary func« 
tion becomes the sum of any form of the pih, degree of the dif- 
ferential quotients, taken according to time, of the variables and 
any force-function depending only on the variables— this sum 
multiplied by the time-element ; so that the problem of mecha« 
nics is changed into a perfectly general one of the calculus of 
variations. If, further, Hamilton assumed a force-function 
which depended only on the coordinates of the moved point, and 
if Jacobi extended the investigation to a force-function explicitly 
containing the time, Schering j: conceived the problem in this 
direction more generally, introducing forces dependent not only 
on the position but also on the state of motion of the masses. 
This dependence is so chosen that, tmderstauding by R the re^ 
suiting force, and by dr the virtual displacement of the mass* 
points, SR£&* becomes the difference oetween a total variation 
and a total derived according to time ; and this generalization ii 
at the same time accomplished from Lipschitz's enlarged point 
• of view. In it, therefore, motions can be treated which, for in* 

* ''Vorletongen iibeir Dynamik: Nora methodus" &c., Borcbsrdt's 
Journal, 60. 

t "Untersuchung eines Problems derVariationsrechnung," Borcbardt's 
Journal, 74. 

X Hamilton- Jacobi'sche Tbeorie fiir Krafte, deren Maass von der Bewe- 
gungder Korper abhangt/' Abhiindl.derGdtting.Oes.derJVissenschASlS. 

T2 . 

Digitized by VjOOQ IC 

276 Prof. J. J. Mullet on a Mechanical Principle 

atance, satisry Weber*^ law, or motions in Ghiass'a and Riemaun's 
space of multiple dimensions. 

The slight improvement of the physical side of Hamilton's 
method stauds far from the high degree at which these analytical 
investigations have arrived. An essential peculiarity of it con-^ 
sists in this — that it passes from a given motion of the svstem 
of points to another in a similar manner to that in which La- 
grange's process passes from one configuration of the points to 
another. The primary function, a definite integral which is ex- 
tended over the original motion, undergoes an alteration by the 
Variation of the arbitrarv constants of the motion ; and this va- 
riation, or that of a similar integral representing the expenditure 
of the force, is given by Hamilton's symbolic equations of mo- 
tion. Hence Hamilton's method differs, secondly, from La- 
grange's (in which the force-function changes according to the 
elements of the given motion) in the same way as the variation 
differs from the differentiation of the functions. This second 
aspect of it could not but lead immediately to a new treatment 
of the perturbations, which has by Hamilton, Jacobi, and Sdie- 
ring.been developed into a series of new systems of pertnrbation- 
formule. . Only the above-mentioned application of the variation 
of the motion, which is in principle only a particular way of re- 
presenting the latter, is not the essential of the new view ; that 
must much rather be sought in similar principles to those on 
which the ordinary differential equations of the mechanical pro- 
blem are based. It is true that one signification of these prin- 
ciples, the representation of individual integrals, does not here 
iM>me into consideration in the indicated general process of inte- 
gration ; their physical meaning, however (independent of the 
other), which was proved most evidently in the proposition of 
4he vis viva, especially with the generality given to it by Helm- 
lioltz, remains here also; and this iustifies an examination of it. 

Such an examination of the physical aspect of Hamilton's 
method is attempted in the sequel. It appeared the more re- 
quired, as the endeavours of physicists to deduce the second 
proposition of the mechanical theory of heat in a similar manner 
as the first, from purely mechanical conceptions, clearly per- 
mitted the supposition of a new mechanical principle. Bolts- 
mann'i', Clausiusf, and LedieuJ have succeeded in obtaining 
from Lagrange's differential equations the proposition mentioned: 
it did not, however, like the first proposition, come from a uni- 
versal principle ; but, on the contrarVi those investigations led 
to new mechanical propositions, which certainly did not possess 

♦ Wiener SUiunosberickte, vol. liii.; Po^j. Ann. vol.cxliii. p. 211. 
t Pogg. Ann. vol. cxlii. p. 433. Phil, Mi^. S. 4. vol. xlii. p. 161, 
J Comptes Rendus, 1873, 1874, 

Digitized by VjOOQ IC 

resuliingfrom Hamilton's Theory of Motion. 277 

the amplitude of the principle of the vis viva. An attempt by 
Szilv* to get the proposition out of Hamilton's treatment of thq 
subject comes nearer to the above notion ; only, not to mentiop 
that, on account of a limitation adhering to the form in which it 
has hitherto appeared, it could not lead to the general deduction 
required, it does not approach more closely the physical side of 
this method. 

It resulted from the investigation that the new treatment 
satisfies a general principle similar to that satisfied by Lagrange's; 
for perfectly coordinate with the proposition of the vis viva is 
the following : — In a motion whose equations of condition and 
force-function do not explicitly contain the time, let the primarv 
function and expenditure of force respectively be denoted by V 
and W, so that 

-V=r(T-U)rf/, W=r2Trf/, 
Jo Jo 

understanding by T the vis viva, and by U the force-function ; 
and let it be assumed that V may be represented as a function 
of the initial and final coordinates and the time, W as a function 
of the initial and final coordinates and the energy ; then for 
every change of motion occurring during an element of time dt 
the relation 

dt ^l ht J-"" 

holds, in which the symbol d signifies the whole of the alteration 
which is connected with change of motion, while d denotes all 
alterations of V-hW not produced by variations of the coordi- 
nates. Therefore^ in every motion whose equations of condition 
and force-function do not explicitly depend on /, the change of 
the primary function and force-expenditure produced by the 
variation of the coordinates alone is =0. The two quantities W 
and y are here capable of a physical interpretation similar to that 
of T and U. The former has already been designated by Ha- 
milton as the vis viva accumulated in the motion ; the significa- 
tion of the latter results from a peculiarity of the entire Hamil- 
tonian theory of motion : namely, while la micanique analj/" 
iique prefers to introduce the forces into the equations of motion, 
Hamilton's treatment involves the introduction of the momen- 
tary impulses — ^indeed, so that the place of the forces is taken by 
those impulses which at each instant are capable of producing 
the velocities actually present. Now, in a group of motions, 
these impulses can, analogously to the forces, be represented as 
negative pai*tial differential quotients of a function of the coor- 

* ^ofg' Ann, vol. cxlv. p. 295; vol. cxlix. p. 74. Phil. Mag. S. 4. 
vol. xliu. p. 339 ; vol. xlvi. p. 426. 

Digitized by VjOOQ IC 

278 Prof. J. J. Muller on « Meehankal Prine^U 

dinates j and this function is nothing else but the above-defined 
primary function of the system. This peculiarity gives to the 
primary function a real signification simdar to that obtained by 
the force-function in the potential energy, and makes the coor- 
dination between the principle of energy and the new proposi** 
tion still more evident. 

If this proposition was the general principle at which those 
investigations of the theory of heat aimed, it must have included 
as a special case the second proposition of that doctrine, in the 
same way as the principle of energy included the first In this 
relation it is remarkable that, applied to the mechanical theory 
of heat, it leads direct to the second main proposition as soon as 
we make the apparently indispensable supposition that the tem« 
perature of bodies is proportional to the vis viva of their mole- 
cular motion. Corresponding to this, the principle seems also 
capable of a series of further applications like those of the prin- 
ciple of energy ; those which will be here given, however, are 
limited to the case belonging to the theory of heat. 

The proposition cited resulted from the combination of two 
long-known mechanical equations. Hamilton, namely, had 
given his equations of motion both in reference to the function 
y and in reference to the function W ; and the separate results 
needed only to be combined, in order at once to furnish the new 
one. It would be obtained in the most general form by intro- 
ducing the integral elements generalized in the sense of Lip- 
schits and Schering. As, however, the essential point was its 
application to real physical motions, and it had to be presented 
first in its simplest form, I have preferred to give it in connexion 
with the older method of Hamilton and Jacobi, which moves en* 
tirely on this ground. But then this process must in another 
respect be conceived more generally ; for, in every form in whidi 
it has hitherto been carried out, it presupposes the force-func- 
tion unaltered in form with the variation of the motion, while 
such an alteration of form is sometimes essential in physical 
considerations. This is the case, for instance, with the mole- 
cular motions designated as heat, as soon as the bodies are sub- 
jected to changes of volume and pressure. In regard to the 
quantities accentuated especially by Clausius, which occur toge- 
ther with the coordinates in the force-function, and vary with 
the variation of the motion, while they remain constant within a 
given motion, it was therefore needful that the method should 
be amplified ; and this has led to a somewhat more general form 
of the equations of motion. 


Given a system of n material points reciprocally attracting and 

Digitized by VjOOQ IC 

ruuUingfrom Hamilton's Theory of Motion. 370 

repelling, but subject to no other forces, so that the soliciting 
forces can be represented by the negative partial differential 
quotients of a fnnction of the coordinates of all the points, the 
force*function U. This function contains as variable quantities 
at all events the coordinates g^ of the points in motion, of which 
it is here always presupposed that thev identically satisfy at any 
moment the eouatious of condition, of whatever form> and there- 
fore, if m sucn equations are given, occur to the number of 
8n-*mr;i/i. Moreover the time / may appear explicitly in the 
force-function, as well as other quantities Ck, which change only 
when a transition takes place from one motion to another. For 
motions of this general sort, Hamilton's method for gaining the 
general symbolical equation of motion which refers to the varia- 
tion of the motion is to be extended. If the via viva of the 
point-system be denoted by T, and the primary function Y Re- 
fined by 



the problem is nearer to that of finding the variation of this inte- 
gral on the hypotheses made. 

In forming this variation, the time / is fii'st regarded as an 
independent variable which is not variated. All the quantities 
present in the primaiv function are therefore regarded as func- 
tions of/ and a number of arbitrary constants; and from the 
variation of these constants alone will the variation of those 
quantities, and hence that of the primary function, result. Of 
such arbitrary quantities there will always be 2/jl in the quantities 
mentioned, which can be supposed to arise from the iutegration 
of the /A differential equations of the second order of the motion ; 
but since a variation of the force-function on the transition from 
one motion to another is presupposed, to those 2/i constants any 
number of others may be added ; these latter, which at all events 
are assumed to be independent of one another, are the quantities 
c^ If, then, these 2/i+v constants change, but / be supposed 
unchanged, we obtain 

-8V=Sr(T-U)rf/« rS(T-U)rf/, 
Jo Jo 

and we have only to do with the variation of the quantity (T-*U). 
Since the equations of condition of the system may explicitly 
contain the time t, the vis viva T will in general, as well as the 
force-function U, likewise explicitly contain it; but since the 
time is not variated, in the formation of the total variation 5V 

Digitized by VjOOQIC 

280 Prof. J. J. Muller on a Mechanical Principle 

there occur only the variations 8y,, hq\, hcj^ and we have 

By partial integration in the second part of the right-hand 
side there hence results, if the values of the various quantities 
for the time /=sO be denoted by the index 0, 

and if we put the dtiferential quotients of the via viva, taken ac- 
cording to y'p 

according as they are referred to the time / or to the initial time 
0, we get 

This is an equation of motion of the most general kind, similar 
to one to which prominence is given b^ Jacobi* and to another 
by Scheringt ; but it has the peculiarity that the quantities r^, 
not contained in the latter equations, occur in general in the 
force- function likewise. 

AH the quantities in equation (1) are presumed to be functions 
of / and 2/i+v arbitrary constants, of which the first 2/i have 
arisen from the integration of the differential equations of the 
motion. The quantities y^, q\ can now, by means of the integral 
equations, be expressed by the arbitrary constants and /; but 
by the same integral equations the 2/i arbitrary constants can 
also be represented by the quantities q^^ q^, and t. Let the latter 
be presupposed. Then Y becomes a function of / and 2/jl quan- 
titics q^, q^ ; but it contains in addition the arbitrary constants r^^ 

* Vorhsungen uber Dynamik, pp. 143, 356. 
t HamiUon^Jaeobi'sche Theorie, p. 19. 

Digitized by VjOOQ IC 

resulting from Hamilton's Theory of Motion^ 281 

which, in consequence of the supposition made^ are not connected 
with one another by any relation. Hence all the variations 
iq^, iq\f Bcj^ become mutually independent. 

In consequence of this^ equation (1) can be immediately split 
up into single equations. Puttings that is to say, the expression 
which stands under the integral-symbol 


we get the differential equations of the motion 

dt "" ^g, ' 

and as, conversely, the latter are demonstrated by Lagrange to 
be independent of equation (1), it follows that the expression 
standing on the right-hand side under the integral-symbol va« 
nishes under all circumstances. Therefore neglecting it, we 



and this is Hamilton's symbolic equation expanded. Because, 
namely, the variations are all independent one of another, they 
furnish at once the integral equations 

Equation (2), with only an unimportant difference in the way of 
writing it, has already been given by Clausius*; it is, however, 
to be remarked that his deduction refers only to motions of which 
the force-functions and equations of condition do not explicitly 
contain the time. The form in which it gives the variation SV 
is not su£Sciently general for the following considerations, because 
in general the time t likewise varies, and therewith a partial 
change is produced both in T and in U and consequently also in 
V, which is neglected in equation (2). 

It shall therefore now be assumed that the time t is no longer 
the independent variable, but undergoes the change Bt on the 
variation of the motion. In order to understand the sense of 
this variation, it must be considered that the time is not to be 
variated wherever it occurs, but only where it occurs explicitly ; 
for a variation of the other would amount to a variation of the 
initial and final coordinates ; and this is already done. In this 
case, therefore, the primary function V is taken as dependent on 
the initial and final coordinates, this explicit time /, and the 
* Pogg. Ann, vol. cl. p. 122. 

Digitized by VjOOQ IC 

383 Fiof. J. J* MOUer an m MmAaniMi Prk^ctpk 

qumtitias Cki tnd their Tariatkm it to be ftmnedb^Tiriatingdl 
these qoantities timaltMieously. Hence the total variation formed 
under inclusion of the time becomes 

and the question is^ to determine the last term ^ • 

In order to obtain this^ let it be remembered that, in the dif- 
ferentiation according to i, the quantities e^ contained in the 
force-function U have been supposed not to vary. From this it 
follows that 

and from thU we get immediateljr the partial differential quotient 

If we introduce this value into the above equation for 8V, the 
result is 

-(U-T+2;>,9',)8/. . (3) 

This general equation relative to the variation of motion, which 
corresponds to the equations 7**^ aud 7a given by Lipschitz, 
pp. 122, 138, as well as to Schering's equations [5] and [6], 
p. 19, oontaining also the differential equations, is also valid, as 
soon as a force-function exists, when the force-function and equa- 
tions of condition explicitly contain the time. For the special case 
which alone comes into consideration in the following, where the 
time does not explicitly appear in the force-function and condi- 
tions, it takes a somewhat simpler form. 

That is, in this case the relation holds, 

if E denotes the energy of the system. Hence, if we add and 
subtract, on the right-hand side of the equation for ^, the value 
2T, we get 

|^=E + 2;7,7,-2T. 

But, with the hypotheses laid dowui the vis viva becomes a ho- 

Digitized by VjOOQ IC 

reiulttngjirmn Uamilton't Theory of Motion. 283 

mogemaoos fanction of the second d^;Fee of the variable g'l ; 

consequently we have simply 

and after substitution in the above equation, 

-SV=Sp,Sy,-2pjSffJ-r2|^5c*rf/-E8<. . . (4) 

This form, connecting itself with Hamilton's equation*^ is the 
starting-point for the following. At the same time it is signifi*. 
cant that the ordinary equations of motion of Lagrange are re- 
garded as satisfied only in the motion itself, and not during the 
change of motion. The system must therefore, in the motion, 
always be a closed one, subject to no action from without ; on 
the contrary, during the variation of motion such an action from 
without must take place. Meanwhile the energy of the system 
may remain constant or vary ; whether the one or the other, has 
no influence on the validity of equation (4). This independence 
of Hamilton's equation upon the nature of the variation of the 
motion has the same signification as that of Lagrange's equation 
of motion upon the nature of the variation of the configuration » 
If, therefore, Lagrange's method reaches to systems with and 
without conditions, Hamilton's equation (4) extends to systems 
which with the alteration of their motion retain the energy con- 
stant or even receive energy from without. 

Hamilton's symbolic equation of motion plays in the treat- 
ment of the mechanical problem a part like that of the symbolic 
equation of motion of Lagrange, only with the difference that it 
refers to the variation of the motion, while the latter concerns 
the variation of the configuration in a motion. If, now, in La- 
grange's method from the equation of motion a series of princi- 
ples result which have partly the purely analytical signification 
of integrals of the differential equations, ana partly the essen- 
tially physical meaning of general propositions valid for motion 
generally, the question arises whether similar principles do not 
connect themselves with Hamilton's equation. This shall be 
investigated especially in regard to the proposition concerning 

• Phil. Tnuis. 1884, p. 30/. 

Digitized by VjOOQ IC 

284 Prof. J. J, Muller on a Mechanical Princgfle 

the vii viva, which has acquired by far the greatest importance 
in Lagrange's method. 

For that purpose, the already indicated presupposition is made, 
that in all motions henceforward to be examined time does not 
occur explicitly, either in the force-function or in the equations 
of condition ; so that Hamilton's equation takes the form 

-SV=2;?,Sy,-2pJS}J-f 2|5^M^-E«/, ... (4) 
Jo ^^k 

Making use of the well-known substitution given by Euler^ and 
employed also by Hamilton and Jacobi^, 

from which 

SV=-8W+ES/ + /8B, 

this equation of motion changes into 


SW^:Ep^q,-lp^hq^-C^^Scf^t + tSE (5) 



Jt Jo 

and is therefore nothing else but the quantity known under the 
name of the expenditure of force. It is to be understood as a 
function of the quantities q^, q^, E, c^ ; and the time t, which in 
the integral in equation (5) remained over, is to be replaced by 
the equation 

so that / and E in equations (4) and (5) occupy a perfectly ana- 
logous position, in such sort that the one quantity may always 
replace the other. If now the two relations (4) and (5) be com* 
pared, there comes 

In this equation the variations are still quite undetermined. 
One of the infinitely many systems of virtual variations will now, 
under the suppositions made, be the system of the variations 
which enter with the actual change of motion during the minute 
portion of time dt. Referred, however, to these actual variationsi 

* Compare the general transformations of Lipscbitz and Schering. 

Digitized by VjOOQ IC 

resulting from Hamilton's Theory of Motion. 285 

it makes 

ind the second and third terms in equation (6) can each/ in rela* 
tion to the coordinates, be conceived as an explicit alteration 
according to / which may be expressed by 


Then comes 

ffljm_[B<^]=„, . . . „ 

and this is the proposition sought: The sum of the alterations 
in the primary function and the force^ea^nditure, which are pro* 
duced by the variation of the initial and final coordinates alone, is, 
in the variation of every motion that presupposes a force-function 
and neither contains the time explicitly in this nor in the conditions, 
equal to nil. 

As the variation of the motion is only subject to the condition 
that it does not destroy the limitations of the system, but in the 
rest, as already shown, may very well take place under accession 
of energy, the proposition we have gained is independent of the 
special kind of the accession. In this relation the coordination 
with the proposition of the vis viva, which likewise gives the in- 
crease of the latter independent of the kind of variation of the con« 
figuration, is evident. But this independence forms only one side 
in the latter proposition ; it has received, as is known, another, 
more important, through the remark that the force-function (in 
the above representation) is nothing else but the potential energy 
of the system. In such a new direction the new proposition 
shall now be investigated. 

The sought signification of the primarv function readily ap* 
pears if we give up the forces on which the ordinary theory of 
motion rests, and introduce in their place momentary impiuses 
capable of producing the velocity existing at any instant. That 
such a manner of consideration stands in essential connexion 
with Hamilton's theory of motion has not yet, so far as I know, 
been rendered evident, although Thomson and Tait have recently* 
drawn attention to the importance of this second method of pro- 
cedure, not inferior to the first, and have more nearly completed 
its theory. In it the components of the momentary impulse 
(formed according to the general coordinates), if the components 
of the forces taken according to the rectangular coordinates be 

♦ TreatiBe on Natural Philosophy, pp. 206 et seqq. 

Digitized by VjOOQ IC 

686 Prof. J. J. Miiller on a Mechanical Principle 

XYZ, are 

On the other hand, if tf and v denote the componenta (formed 
aeoording to the coordinate qt) of the velocity before and after 
the impulse Pf, the meohanioal work done by the forces during 
the impulse is 


If now a system of /i impulse-components Pj be presuppoaed^ 
which shall bring forth the whole of the velocities ^t from the 
state of rest of the system, so that the velocities prec^ng them 
are all kO, but the velocities after them those 70 then the me- 
chanical work done by the forces during the impulse becomes 

But the equivalent vi$ viva 



-sl-'.^ <•' 

that iS| the negative partial differential quotients of the primary 
function, formed according to the coordinates, represent the 
components of the momentary impulse which is capable of bring* 
ing about the velocity existing at the time in question. 
If, from («), the vdue of P| be inserted in 

there results further 


-x^dg,=2hdt} m 

that is, the negative partial differential of the primary function, 
formed according to the whole of the coordinates, represents the 

Sroduct of the time- element dt into twice the mechanical work 
one by the impulses which bring forth from the state of rest 
the actual velocities q'i. 
If, finally, the value of this partial differential, from (fi), be 

Digitized by VjOOQ IC 

rmdiing from Hamilton's Tkem) of Motion. £87 

introdaoed into the equation 

we get 

and from this. 

V=J'(E-2L)rf/, (y) 

a relation which is immediately obtained from the earlier defini* 
tion-eqoation of V by making use of the proposition of the 
energy, was used by Hamilton without hesitation as a definition 
of the function Y, and expresses the proper mechanical meaning 
of the primary function. 

As, then, in (7) the primary function appears to be formed 
analogous to the earlier quantity W, it will be convenient to in- 
dicate this by a similar notation ; and the names of potential 
and kinetic action may commend themselves for Y and W. If 
we put, moreover, 


and name this simply the action of the system, equation (7) 
changes into 

#-[|^].o. ...... <e, 

and the proposition reads : — That alteration of the action which 
is conditioned by the variation of the initial' and final coordinata 
alone, vanishes with the change of every motion that presupposes a 
force-function and does not contain the time escplicitly either in this 
or in the limitations. In this form it may be designated as the 
principle of the action. 

Here {^ential and kinetic action are quantities characterizing 
the given motion in like manner as the potential and kinetic 
energy the corresponding configuration* If we imagine the 
whole series of constantly altered motions to be run through, 
they will in general be distinguished by different values of these 

Suantities : in proportion as, by the mere alteration of the coor* 
inates, the one diminishes, the other increases through the 
same alteration; so that in this new view perfect correspondence 
exists with the proposition of the energy. 

In regard to the limitations under which the proposition of 
the action has been obtained, it is to be remarked that the for- 
mation of 1 2Tdt, like that of T, remains possible even without 
a force-function. Now the question, what in these cases becomes 

Digitized by VjOOQ IC 

288 Prof. J. J. MuUer on a Mechanical Prineipk 

of the proposition of the action when there is no force-fanction, 
and consequently no primary function^ gives occasion to bring 
oat its position to another well-known equation in medianicSy 
which relates to the above-mentioned momentary impulses. 

If, namely, the components of the impulses, formed according 
to the axes of the rectangular coordinates, are BHZ, and the ve- 
locity-components induced by them are s^y'sf, the equation of 
motioA i? 

2[{a-iiwp')&r+(H-my08y+ (Z-»»^S^] =0. 

If now as a system of virtual variations the actual alterations of 
the coordinates be introduced, there results 

Integrated over the given motion, there comes 
Und from this results, by variation. 


This is the equation which, in the general case assumed, takes 
the place of the action-equation ; its terms have a similar mecha- 
liicu meaning to that of the terms of the latter. That is to say, 
the sum of the left-hand side is nothing else but twice the me- 
chanical work which the sum of the forces constituting an im- 
pulse perform during the same. The equation, therefore, imme- 
diately passes into 

' 'iTdt; (10) 

Jo Jo 

and the action-proposition also can be easily brought into this 
form; for, according to (7), 

which, inserted in its equation, furnishes immediately the form 
(10) . The difference between the two cases consists only in this, 
that in the case of a force-function the terms of the equation are 
functions of the coordinates, in the other case they are not so — 
relations analogous to which occur likewise with the proposition 
of the energy. 


In order to illustrate the principle found, which represents a 
characteristic property of the variations of motion of all systems 
which satisfy the oft-insisted-on conditions, a simple example, 

Digitized by VjOOQ IC 

resuliinfffrom Hamilton's Theory of. Motion. . 289 

for which the propoution can readily be verified, may first be 
discussed. For tnis I select the motion of a pendulum which 
takes place in the vertical plane of xy about the downward- 
directed axis of the positive y in infinitely small amplitudes; and 
I give the determination of the two functions V and W accord- 
ing to known methods''^. 

The length of the pendulum being denoted by /, and the elon- 
gation each time by 9^ so that 

x^lwOiOy y^lcoH0, 

the energy E expressed by the quantities Pi and q^ becomes 

B = i^-^/C08tf, 

where ps^-». Accordingly the differential equations of the 
motion are^ taking account of the infinitely small amplitude, 


and the two integral equations 

where 0q and|>o denote the values of and/? for /=0. 

Introducing now these values into the expression for the vis 

and substituting for the squares and products of the trigonome- 
trical functions the doubled variables, we get 


* Compare Hamilton's and Jacobi's examples. 
PhiL Mag. S. 4. Vol. 48. No. 818. Oct. 1874. U 

Digitized by VjOOQ IC 

SgO Prof. J. J. Mailer on • Mtiktamtl Pv it uirle 

When theMunevilaesaK alao introdooed into the fiHce-fiiactian 

there remiUe, aftar a eimikr redoetioo, 

and inserting, finally, both these values m the primary fonetion 

we obtain 

or^ if by aid of the first of the integral equations we put 

and, lastly, introdnce again into the trigonometrical fonctions the 
simple variables^ 

-\:r.gU + i{0' + 0tily/7li>OtAyp—^Sllb^. (11) 

Referred to the same variables / and 0, we have on the othor 

If this, together with the value of U, be inserted in the known 
differential equation for A, 


Digitized by VjOOQ IC 

remUmg from Hantilton's Theory of Motion, 291 
die retttU is 

and from tbu the integral 

W-JV2i^/»+2/«E-^/»fl«i^. . . (12) 
If we now form out of (11) and (12) the differential quotients 

Jt nn^i; 


= -V'2^/»+2/«E-^/»^, 

and introduce them into the action-equation, we get 



'• • • 


Indeed it ean be readily shown that the indiyidaal derivata 
are p and p^ respectively. For if the quantity p^ be eliminated 
from the second of the integral equations for example by aid of 
the first, we get immediately 

tanA/^/ sin-v/l^ 


and if we put this value of /> in the expression of the energy, it 
changes into 




and hence 




/ gl'0*coH*^it-2gPB0oCOBAy' 
V tin* A /it 




Digitized by VjOOQIC 

29.2 Prof. J. J. Miiller on a Meehamcal Principle 

Of the applications of the proposition of the action^ those shall 
be introduced here which can be made of it in the mechanical 
theory of heat. If heat be conceived as molecalar motion, the 
application to it of the Ener^ proposition leads immediately to 
the first main proposition of this doctrine. Corresponding to 
this, we are now mvestigating what, on the same hypoth^ia, 
resalts from the Action theorem. These molecular actions are 
stationary motions of a system of points ; and the simplest case 
of such motions is obviously that in which all the points move 
in closed paths, and with a period common to all of them. TUs 
shall first be supposed. 

As, for closed paths, the two limits of the integral which 
forms the action coincide, when the integration is extended over 
an entire revolution we obtain 

m of the Action propi 

and hence the equation of the Action proposition is transformed 

or, written explicitly, 


If now, for one revolution, we name the mean value of the mt 
viva T, and that of the force-function U, we obtain 




and if we insert this value in the above equation, we obtain 

from which 

dU-.2|^&^=i?T+21Wlog/, . . . (14) 

a well-known equation, already advanced by Clausius'*' for audi 

If now we apply this or related equations to the molecular 
♦ Pogg. Ann. vol. cxUi. p. 433. Phil. Mag. S. 4. vol. xlii. p. 161. 

Digitized by VjOOQ IC 

resulting from Uamiltoii^s Theorjf of Motion. 293 

motion designated heat, making use at the same time of the hy- 
pothesis that the temperature is proportional to the vis viva of 
the motion, we arrive (as Boltzmaun, Clausius, and Ledieu have 
shown) easily at the second proposition of the mechanical theory 
of heat. In general, however, the motion of the molecules of a 
body does not take place in closed paths. With respect to fluids, 
for example, we are not even justiiSed in assuming for them a 
fixed mean position ; and in the case of solids, where such an 
assumption is indeed necessary, the actual motion will yet be 
distributed along all the dimensions. Now, for such cases Clau- 
sius has recently called attention to a second, analogous equation, 
which substitutes another hypothesis for that of closed paths. 
A more direct derivation of the second main proposition from 
the theorem of the action shall here be given. 

The suppositions which have been made respecting the system 
of pNoints representing the body are simply that the motion is a 
stationary one, and t^^t it is infinitesimally changed by the com- 
munication of an elementary quantity of heat. The subject of 
investigation is the quantity 

which refers to the variation mentioned. Since infinitesimal 
alterations of the velocities in the time-particle dt produce only 
infinitesimal path-changes of the second order, this makes 

Further, the system of variations -^ can be split into two. 

Let the first be the distances qidt which are traversed in the ori- 
ginal motion during the time-element dt from the points q^, 
Iliis portion furnishes the sum 

Let the second partial system be the distances Cidt which lead 
from the above-mentioned last positions in the original motion 
to the final positions in the changed motion. In it, under the 
suppositions made, to every value o{p there come just as many 
positive as negative e; this portion therefore furnishes the sum 

Accordingly, for the infinitesimal variation which in the sta- 
tionary motion of the point-system is conditioned by an infinitely 
small quantity of heat. 

Digitized by VjOOQ IC 

294 APrimiipkrenMiiffJhmEmaSiUm'tTkimytfMttiom. 
Ilierefore, introdaeiDg th« fanetion "V, 

and the equation of the aeiton ean be written 

But since 

we have 


and from this 

rfE-2 |^ifc*=JWT+2'rrflog/, 

^E-2||^,=2TJlog(/T) (15) 

Now this equation, which has already been given by Siily* 
for the special case in which no Ck are present, the paths arc 
closed, and the periods are the same for all the points, leads im- 
mediately to the second proposition of the mechanical theory of 
•?*Lr • . ^ **^** purpose let us consider, first, that the left-hand 
side of It IS nothing else but the energy which, with the ehange of 
the molecular motion, is communicated to the body as heat from 
without ; and therefore, in the usual noUtion of the theory of heat, 

it is J rfQ. If we then make use of the assumption that f is 

proportional to the absolute temperature 8, we immediatel/ 

■8=^' (16) 

understanding by dS a complete differential. 

Thus the Second Proposition is derived, like the First, from 
a general mechanical principle. But the above representatiofi 
permits us to perceive for the two propositions not merely this 

♦ Pogg. Ann. vol. cxlv. p. 295. Phil. Mag. S. 4. vpl. xliii. p. 339. 

Digitized by VjOOQ IC 

Mr. J. CVKuMtly onMNewFommU in Definite Int^als. 206 

confortnihr of position, bat d80 a eommon origin. Tho derelop- 
ment of the variation of Hamilton's integral bias the peeoliarity 
that it leads simultaneously to the differential and integral equa- 
tions of mechanieal problems. This remarkable &ct gives to 
the principles of Energy and Action a common origin in the 
general equation of motion ; and by this the latter b^mes the 
connecting band foi^ the two propositions of the mechanical 
theory of heat. 
Zurich, April 1874. 

XLI. On « New Formula in Definite Integrals. 

To the Editors of the Philosophical Magazine and Journal. 

11 Elysium Row, Calcutta, 
6BNTLBMBN3 Augurt 2, 1874. 

I SEE in the July Number of your Magazine two new for- 
muln in definite integrals of some importance are given by 
Mr. Glaisher. The integrals admit of a direct general solution 
without using the identity on the right-hand side of the equa- 

^o-«i^+««^&c. = x^, - (r^t^- 

The portion to the left is evidently equal to 


or putting Es=€^*, 
From this 


And taking the limits n and 0^ the value for this particular ease 

E_i IT IT 

2 * ^"* 2 ' ^''*' 
The second theorem is obtainable in the same way. It is 


=(1-E)-'. {tan-'x-E*tan-'E**}<^,. 

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296 Mr. F. Guthrie on an Absolute Gatponometer. 

This is the general solation ; and where the limits are infinity 
and cipher^ there results 


whieh is the same as given by Mr. Glaisher. 

It is evident that there are numerous theorems of the same 
kind, such as 

cos Ej? . flo=flo~ 1^ + *^v 

sinEa?.flro=«i*.- 123**^-' 

which will give definite results between the limits infinity and 

Yours obediently. 

Jams O^Kinealt, B.CS. 

XLII. On an Absolute Galvanometer. 
By Frederick Guthrie *. 

MESSRS. ELLIOTT have constructed for me a galvano- 
meter which willy I believe, be found to possess for some 
purposes certain advantages over those at present in use. Its 

Erinciple depends upon the measurement of the current-strength 
y the measurement of the mechanical force necessary to bring 
toa given distance of one another two electromagnets, which 
are excited by the current in such a fashion that they repel one 

The current'enters at a by the screw-damp ; thence it passes 
beneath the circular wooden stand C along the copper wire mb. 
It rises vertically and coils round a soft iron mass/, which lies 
horizontal and tangential to the axis of the instrument. It 
passes down And across the centre of the board, then rises and 
coils round a soft iron mass /', exactly similar and similarly 
placed to/, but on the opposite side of the instrument. Having 
encircled/', the current- bearing wire again descends, and carries 
a mercury- cup y, through whose bottom it passes, and which is 
exactly in the axis of the instrument. The current then leaves 
the mercury by the wire t, which dips into it. It then traverses 
the wire around the iron, m. Thence it crosses the instrument 
and forms a spiral around m!, after which it passes into the mer- 
cury-cup A, and so to the binding-screw c. The spirals are such 

* Read before the Physical Society, May 23^ 1874. Communicated by 
the Society. 

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Mr. F. Guthrie em mAb$obUe Galvanometer. 297 

that there is repulsion between /and m, and also between m! and 
/'. It is seen that the magnetic pair//' is fixed. The pair 

m m! is movable about a vertical axis. The system mm' is hung 
by a metal or glass thread k from the rod l, which works stif9y 
through the nut o. The latter carries an arm and vernier, p, 
which slides over the graduated head, q. The scale, nut, &c. 

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398 Ai9/jc«t rup$eiins New Booh. 

are tnpported on the glass tabe r^ whieh is fastened by the sap t 
cm to the plate-glass disk t, which rests upon the tap of we 

!;las8 cylinder u clamped upon the wooden base e resting on 
evelling-screws. In the side of v is a plate-glass window, w^ 
through which a vertical line of light may be focused upon x (a 
mirror fastened to the mrrl system), and thence thrown upon a 
scale in the manner which is now so often employed. 

A word or two about the way in which the instrument is used. 
The upper plate / and the system m mf are removed by lifting r. 
The edge of u is rubbed with beeswax to prevent t from slipping 
upon it. The copper wires penetrating the cups are amalgamated 
and a little mercury poured in. Amalgamated thin platinum- 
foil is then pressed into the cups, and mercury is poured upon 
this. By this means a concave meniscus is obtamed. The upper 
partis then replaced, and so adjusted by turning the plate / and 
the cylinder u that the mirror x is parallel to the window v, 
when the axis of m ni makes an angle of about 15^ with that 
oiff. The rod / is adjusted so that the wires of m mf just touch 
the mercury ; and by the leveUing-screws A is so swung that m 
and^ and ako ni and/', are exactly opposite to one another and 
the wires in the centres of the mercury-cups. A slit of light is 
then sent through w, reflected on to a screen, and the head o is 
then turned till the slit is split bv an arbitrary vertical line on 
the screen. The reading of /> is then noted. A current passing 
through the system forces mwl away from//'. Turn the head 
untu the slit of light is again brought to the mark on the screen. 
The angle through which it must be turned is directly propor- 
tional to the magneto-repulsion — that is, to the square of the 
current-strength. Many of the laws of electrodynamics may be 
readily illustrated by this instrument; and not only may differ- 
ent currents be compared with the greatest accuracy, but the 
absolute mechanical magneto-value of the current may be at 
once arrived at. By bringing the repellent magnets alwaj's to 
the same distance from one another, a whole class of sources of 
error is removed. 

XLIII. Notices respecting New Booh. 

First Lessons in Theoretical Mechanics. By (he Eev. Johh F. 
Twisnm, MJL, Professor of Mathematics in the Staff CoUege, 
and formerly Scholar of Trtnity College^ Cambridge, London : 
Longmans, Oreen and Co. 1874: pp. 243. 

npHOSE teachers and students who are already acquamted wi^ 
-L t^e author's large Treatise on Medianics, will naturally ex* 
peot to^find in the work bow before us perfect exuct^ude both ia 

Digitized by VjOOQ IC 

Notices rstpesting New Booh. 309 

and esqpreseion; nor will ther, making due allowanoe 
for the cOflELculty of the undertaking, be m any way diflappointed. 
It is^ not an easy task to teaoh eyen the first principles of me- 
chanics to those of whom only a knowledge of jtnthmetic, a little 
Geometry, a few rules of Mensuration, an aptitude in the use of 
compasses, scale, and protractor, and enough Algebra to solye a 
simple equatioa are demanded. Tet the author has performed 
this task in a manner which shows that with him teaching is an 
art of which he is an accomplished master. It is true tmkt now 
and then he is obliged to omit or postpone the proofs of certain 
important theorems which inyolye a knowledge of GFeometry and 
Trigonometry not possessed by beginners. In the parallelo- 

ri of forces (art. 37), for instance, the student is told to find 
resultant by consianiction. That the resultant is the diagonal 
of a parallelogram of which the two giyen forces are adjacent sides, 
is assumed to be true — ^the reason of the rule being giyen in a sub- 
sequent cluster (137), to which, howeyer, no clue is ^yen. And 
this seems a suitable place, in our notice of Mr. Twisden's book, 
for remarking that a work containing so much matter (&r more 
than at first sight appears) ought cer^inly to be furnished with a 
copious index. 

That the centre of Rrayitjr of a triangle is the intersection of the 
three straight lines which join the yerfcices to the middle points 
of the opposite sides, is a proposition also giyen without proof 
(art. 18), showinff that the litue Geometry which Mr. Twisden 
requires of his readers does not eyen extend to the proof of so simple 
a theorem. In art. 18 (6) we are told that <' any area may be 
conceiyed to be made up of a number of parallel straight lines," 
a conception which mujst be inconsistent with the youmy; geo- 
meter's notion of a straight line. By use of the principle of limits 
in finding the centre of grayity of the surface of a triangle, this 
inconsistency would certamly be ayoided. 

The book consists of eight chapters, the first fiye of which are 
made as simple as possible. Each chapter is followed by a collec- 
tion of excellent questions, not less than foor hundred altbgether 
being giyen in this manner. Besides, nearly two hundred complete 
solutions of useful and interesting problems are scattered through- 
out the book, inyaluable to those who study without a teadier. 

There are also Tables of Specific Grayities, Moduli of Elasticity, 
Tenacities, and Besistances to Compressions. 

We rec(Hnmend the book to the notice of that numerous class 
for whom it is speciaUy intended — ^those who must know mechanics 
and yet possess out little mathematical knowledge — to Students, as 
beinff suitable to the curriculum of the TJniyersity of London, and 
to all Teachers, on account of the always clear, ana often ingeniousi 
deyelopments of the most important parte of the subject. 

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800 Notice* respecting New Booh. 

Supplement to the First Book of Euclid's Elements, eontaininff ihe 
Sixth-Book Propositions proved independently of the Fifth Book^ 
and the Elementary Propositions of Modem Geometry, By "Edward 
Botleb, M.A.T.C.D. Dublin : Alejomder Thorn. 1872 (12mo, 
pp. 60). 

Euclidian Geometry. By Fbakcis Cuthbebtsok, MJL, late Fellow 
of Corpus C?iristi CoUege, Cambridge, Head Mathematical Master 
of the City of London School. LondQa : Mftcmillm and Co* 
1874 (fcap. 8yo, pp. 266). 

The titlepages of these works suffidentlj indicate their pur- 
pose ; they are intended to be substitutes for Euclid's G^eomet^T, 
or for nart of it, and while retaining the form and spirit of the 
original, to improve on it in detail and to supplement its supposed 
deficiencies. Both books are, to all appearance, written hj madie- 
matidans of average competency ; and one, at least, of the authors 
(Mr. Cuthbertson) is in a position which makes it highly probable 
that he is a teacher of considerable experience*. But though this 
is the case, we regret to have to add that, after having looked into 
these books with some care, we do not see why they have been pub- 

With Mr. Butler's book the difficulty is not so great as with 
Mr. Cuthbertson's. We may surmise that it is adapted to s<Mne 
course of instruction sanctioned by the Commissioners of National 
Education in Ireland ; and if so, its somewhat fragmentary form is 
explained. It consists of a number of propositions designed as a 
substitute for Euclid*s sixth book, and a selection of elementary 
propositions on Harmonic and Anharmonic Section and some allied 
subjects. It is hardly necessary to notice this book further ; and 
were we asked for the reason, we should regard it as a sufficient 
answer to state that Mr. Butler's definition of proportion runs 
thus : — " Four straight lines are said to be proportionals, that is, 
the same ratio the first to the second as the third to the fourth, 
when the rectangle contained by the first and fourth is equal to 
the rectangle contained by the second and third." Putting out oi 
the question the typographical error which may be presumed to 
exist in the passage, the sentence betrays a view of the functi<m 
of definition which is above or below criticism. 

Mr. Cuthbertson's book covers just the same ground as Euclid*8 
Books 1-6, and the first twenty-one propositions of Book 11. He 
has manifestly expended a great deal of care and thought on its 
composition, and yet we are constrained to say that his attempt 
to improve on Euclid is a failure. In the first place, his book is 
about as Ions; and quite as abstruse as Euclid's. In the next, he 
has increased the difficulty of his task by adapting his book to a 
certain form of examination which our limits will not allow us to 

* We do not know what position Mr. Butler holds ; he calb himself *' Pro- 
fessor Ao. under the CommissionerB of National Eduoation in IreUnd." We 
are wholly in the dark aa to the meaning of the *' Ac." 

Digitized by VjOOQ IC 

Notices rapecting New Booh. 801 

explain. Then, again, the substance o£ his book seems to us of a 
far inf eri(»r qui^tj to Euclid's : this is no more than might be ex- 
pected; but we will giye an instance of what we mean. Euclid's 
treatment of the Corollaries to the 32nd prop, of Book 1 is not, per- 
haps, wholly proof against minute criticism ; still i£ any thing be 
wanting it could be supplied by a word or two of explanation ; 
and surely nothing can be plainer or more direct than his method. 
Mr. Cuthbertson, however, wishes to improye upon it, and he does 
so as follows: — On p. 39 he gives a Corollary, which is stated 
thus : — " If A B, B C are two straight lines respectiyely parallel to 
DE, EF,then shall the angle ABCbe equal to the angleDEF." 
This is traie or not according to the direction in which E F is drawn : 
e. g, it is true in the case shown in Mr. Cuthbertson's diagram ; 
but the needful qualification is not given in^the Corollary, nor, so 
&r as we have noticed, anywhere else. On p. 48 this Corollary is 
used to prove the theorem *' if the sides of a polygon be produced 
in order, the exterior angles shall together be equal to four right 
angles." The proof consists in taking a point outride the polygon and 
drawing from it rays parallel to sides respectively. This proof, of 
course, may be made perfectly sound ; but in the case before us it 
fails owing to the above-mentioned ambiguity. This is the way in 
which he treats Euclid's second Corollary, and then he goes on to 
prove Euclid's first Corollary. The method is in no respect better 
than Euclid, and the way of stating it inferior to the extent of in- 

There is one question of general interest, suggested by a perusal 
of Mr. Cuthbertson's book, on which we will say a few woi^s, viz. 
"What are axioms?" Td the mathematician they are merely 
truths of geometry assumed without proof, as premises needful for 
proving other truths of geometry. It is usual to answer that 
axioms are self-evident truths. But, not to say that the question at 
oAce arises " Self-evident to whom ? " it is to be observed that the 
question " How do we come by our knowledge of the axioms of 
geometry ? " is one with which the mathematiGian, as such, has 
nothing to do. There are, of course, two distinct ways of answering 
this question, and each doubtless capable of numerous modifications. 
Some hold that the axioms of geometry are what they are in virtue 
of the conformation of the mind antecedently to all experience of 
space. Others hold that the axioms are nothing but the expression 
of our most elementary experiences of space, and that what is 
called their necessary truth is merely a consequence of the uni- 
formity of our experiences, joined to the absence of any experience 
which suggests so much as a type of something inconsistent with 
them. "We believe this to be a sufficiently correct, though brief, 
stl^ment of the two rival answers ; and the observation we have 
to make on them is, that whether either or neither of them be true 
is a question wholly outside of geometry. 

We may not, perhaps, be justified in doing more than suspecting 
(but at all events we do very strongly suspect) that the reason of 
Euclid's 12th axiom being so much objected to is that many mathe- 

Digitized by VjOOQ IC 

302 Noiicei retp^iing New Booh. 

maticiaiiB renrd tha former m ihe correct answer to the abora 
question. There is not much difficulty in bebeving that we are 
bom into the world with minds so constituted that as soon as wo 
know the meaning of words we cannot do otherwise than hold that 
things equal to the same thing are equal to one another; hdt na 
one except a hardened metaphysician could suiq[K)se that a belief of 
the 12th axiom is produced by any thin^ but an acgnaintmoe witii 
the actaal properties ot space. Accordmgly many wish to substir 
tute for it something which is more " self-eyident," «. s. something 
more consonant with their metaphysical views. 

It is not easy to see, on other grounds, what adTantage is ffi*^ 
by substituting; <me axiom tor another. No (me has any dimcoli^ 
inunderstandmg what the 12th axiom means, nor in seeing that it 
is undoubtedly true. If any one will proye the conTerse of pro* 
position 27 without assuming more than the first eleyen axioms 
and the first 27 propositions, he will do something worthy of all 
honour. But when the question is to proye the point by means oi 
a special axiom which oi&rs from Sudid*s our interest in tha 
matter is but small, e. g. U any one prefers Playfair^s azioBi to 
Euclid's we do not know why he should not; only we would remaik 
that it is merely a question of preference, that tiie two asdoms an 
quite coordinate with each other, and that if either is taken £or 
granted the other can be immediately proyed. 

Mr. Cuthbertson, however, takes a oifEerent view from this, and 
he goes to work to imnrove upon Euclid as follows : — On p. 83 ha 
gives ** Deduction G-, vis, " If points be taken along one of iho 
arms of an angle &rther and further &om the vert^ their dia» 
tances [meaning, as explained, perpendicular distances] from the 
other arm will at length be greater than any given straight 
line.'' It is obvious that this statement as it stands is not tme; 
however, the needful correction could be supplied wiihont mneh 
difficul^; #• g. it would be sufficient for present purposes fiir it to 
run, '* If points be taken at equal distances ^^ and this is wpfOr 
rently what is meant. Further, the demonstration of the dedootoi 
assumes that any angle however small can be multiplied until an 
angle is obtained greater than a right angle. We have no objeotioB 
to t^ being assumed, onl^ to its being assumed implicitly. In a 
book which f ormaUy specifies the axioms assumed, it ought to 
have been separately enunciated as an axiom ; and we canned find 
that this has been done. On p. 34 Mr. Cuthbertson g^ves the 
axiom which he proposes to substitute for Eudid's 12th axiom, vis. 
" If one straight Ime be drawn in the same plane as another it 
cannot first recede from and then approach to the other, neither 
can it first approach to and then recede from the other on Hie sama 
side of it.*^ By means of this axiom and deduction G, he succeeds 
in proving Playfair's axiom. In other words (putting accidental 
detects out of the question), he succeeds in proving one axiom by 
assuming two. We willingly accord to this the praise of inpraiuity ; 
but we strongly suspect that few besides the author will thmk it an 
improvement on Euclid's method. 

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Royal Society. 808 

We had marked for notiee our author's way of treating the 
subject of proportion; but our limits will not allow us to fulfil our 
intention. We will only saj that it seems to us a feasible way of 
treating the subject (in the same manner as his treatment of paral- 
lels is feasible^ but as to its being an improyement on Euclid's 
method, that is quite another matter. 

XLIV. Proceedings of Learned Societies. 


[Continiied firom p. 226.] 

Feb. 26, 1874.— Joseph Dalton Hoc^r, C.B., President, in the 


'T^HB following communications were read : — 

-^ "Note on Displacement of the Solar Spectrum." By J. H. 

N. Hennessey, rjt.A.S. 

The following experiments were made with the (new) spectro- 
scope (three prisms) of the Boysd Society, to ascertain for uds in- 
strument the amount of displacement in the solar spectrum from 
chanjB;e of temperature. The spectroscope was set up on a pillar 
withm a small tent at a time ot the year when ike thermal range 
is considerable : the cdlimator was placed horizontal, and directed 
through a window in i^e tent to a heliostat, which was made to 
reflect the sun's image when required. On closing the window 
darkness preyailed in the tent, so that the bright sodium linea 
were easily obtained from a spirit-lamp. Before commencing, the 
slit was adiusted and the spectroscope clamped ; and no moy^nent 
of any kind was permitted in the instrument during the experi- 
ments. The displacement was measured by means of a micrometw 
in the eye-end of the telescope, readings being taken (out of curio- 
sity) successiyely to both dark and bright lines, i. «. to K 1002*8= Dr 
and K 1006*8 sDtr A yerifi^ed thermometer was suspended directly 
oyer and almost touching the prisms. The meteorological obser* 
yatory referred to was some fiffy yards north of the tent. 

Bejecting obseryation 5 (in the following Table) because the 
thermomet^ was eyidently in adyance of the prisms, we deduce 

By Dsrk lines, displacement equal g 

Dr to Dt; is produced by ... . 31*3 change of t^nperature. 
By Bright lines, displacement equal 

Dr to Dt; is produced by. . . . 29*4 „ 

Mean.... 30 

f nnn which it appears that the displacement in question may not 
be neglected in inyestigations made under a considerable thermal 

Digitized by VjOOQ IC 


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Mr. J.H.N. Hennessey on White Lines in Solar Spectrum. 805 

" On White Lines in the Solar Spectrum." By J. H. N. Hen- 
nessey, F.B.A.S. 

Extract from a Letter jrom Mr, Hennessey to Professor Stokes. 

" Mussoorie, Not. 12, 187a 
*' My deab Snt, — Aa I cannot account for what is described and 
drawn in enclosed, I hasten to place the same before you, intending 
to look for the white lines in question so soon as I move down to 
a lower altitude. Amongst others, no doubt KirchhofE closely ex- 
amined the region in question, without notice of the lines ; and this 
only adds to my perplexity, unless what I see here is due (1) to 
altitude, or (2) is instrumental. In the latter case I cannot ac- 
count for the absence of the white lines at Dehra, where I ex- 
amined the spectrum generally several times ; I must, however, add 
that without close examination and some experience, the lines 
might easily be passed over. But if instrument^, to what are they 
due ? I very much regret that the old spectroscope is not avail- 
able at present [it had been temporarily sent elsewhere for a special 

object] to enable me to verify the phenomena " 

[In the drawing sent by Mr. Hennessey, the intervals between 
the dark lines are coloured green, except in the place of the two 
white lines. To transfer this distinction to a woodcut, an additional 
horizontal band has been added below, in which only those parts 
of the drawing which are left white appear as white, while in the 
upper part the white of the woodcut represents the white or green, 
as the case may be, of the original. — G-. G-. S.] -^ 

Part of Solar Spectrum, drawn to Kirchhoff*8 scaler observed at MuS" 
sooric, N. W. Provinces, India, Lat. N. 30° 28', Long. E. 78° 4' ; 
Height 6700 feet above sea (about^, toith the Spectroscope belonging 
to t^ Hoyal Society. 

Note for diagram. — In course of studying the solar spectrum for 
atmospheric lines, with an excellent 3-prism (new) spectroscope 
belonging to the Eoyal Society, I gradually exteiided my searcn, 

PAi7. Mag. S. 4. Vol. 48. No. 818. Oct. 1874. X 

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806 RoifMlSomty;^ 

began at the red end, until on arriyal at theiedonabontt myatten- 
tionL wm atta^acted by ilie faot tliat K 1657*1 Dy no meanB appeared 
as the strong line depicted in Kirchhoffs map, Plate EL Cm ex- 
amining tbis xegian oarefullj, I was surprised to find i^ oolimrless 
lines shown in the diagram ; these lines, from want of a more ap- 
propriate name, I shall call white lines (or spaces); they cannot ab- 
solutely be described as bright lines, jet they doselr resemble 
threads of white floss silk held in the light. The spec&oscope in 
nse, witJi the most oonyenient hi^est-power eyepiece, presents 
images of about two thirds to seyen nintlis of those drawn in the 
diagrami the former are exa^rated by reckoning to agree with 
Kirchhoffs millimetre scale; it will theiefore be readily understood 
that the white lines do not present striking objects in the spectro- 
scope, especially about the time of sunset, when I happened first 
to notice them ; the^ are best seen about noon, when their resem- 
blance to threads of white floss silk is very close ; but once sem, 
the lines in question can always bereadily detected. So fiiras imr 
instrumental means permit, the wider line extends between K 
1657*1 and K 1658*3; more accurately speaking, it fiJls short of 
the latter and rather underlies the former; the narrower white line 
is underneath K 1650*3, sensibly more of the former appearing 
beyond the edge towards yiolet of the latter, which presents the 
quaint look of a blade Une on a white surface enclosed in a green 
band. These are the only white lines in the speotirum from extreme 
red to F; they are not bright (or reyersed Imes), so far as I haye 
had opportumty to judse. Were they bri^t lines, the question 
would arise, why these alone should be reyersed at 6700 feet aboye 
sea. like the black lines the white lines grow dim and disappear 
with the slit opened wide. As seen here, K 1657*1 is senmbly 
weakw than K 1667'4, whereas KiiehhoS assigns 5 5 to the former 
and only 3 a to the latter. 

March 12. — JoBeph Dalton Hooker, C.B., President, in the CSiair. 

The following communication was read s — 

" On a New Deep-sea Thermomet^." By Henry Negretti and 
Joseph Warren ISambra. 

The Fellows of the Boyal Society are perfectly aware of the 
assistance afforded by Her Majestys Ooyemment (at the request 
oi the Bojal Society) for the purpose of deep-sea inyestigations, 
and haye been made acquainted with their results by the Aeports 
of those inyestigations published in the ' Proceedings of the Koyal 
Society ' and by the interesting work of Professor WyyiUe Thom- 
son. Among other subieots, mA of the temperature of the sea at 
yarious depths, and on the bottom itself, ig dtike greatest import- 
ance. The Fellows are also aware that for thb purpose a peculiar 
thermometer was and is used, haying its bulb protected by an 
, outer bolb or casing, in order that its indications may not be yiti- 
ated by the pressure of the water at yarious depths, that piessure 
being atx>ut 1 ton per square inch to every 800 fiithoms. This 

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Messrs. Negretti and Zambra on^^ De$j^$ea Thermometer. 807 

tberounnetery as regards the protection of the bulb and its Hon- 
lial^ty to be affecred hj pressure, is all that can be desired ; but 
unf ortuiuktelj the onlj thermometer available for the purpose of 
registering temperature and bringing those indications to the sur- 
&ce is t^ which is oommonlj Known as the Six's thermometer 
— an instrument acting by means of ^cohol and mercury, and 
having movable indices with delicate springs of human hair tied to 
thekn» This form of instrument registers both maximnm and mi» 
nimnm temperatures ; and as an orfnary out-door thermometer it 
is verj useful; but it is unsatisfactory for scientific purposes^ 
and for tiie object for which it is now used (viss, the determination 
of deep-sea temperatures) it leaves much to be desired. Thus 
the alcohol and mercury are liable to get mixed in travelling, or 
even by merely holding the instrument in a horizontal positiim ; 
. the inmces also are liable either to slip if too &ee, or to stick if 
too tight. A sudden jerk or concussion will also cause the in- 
strument to give erroneous reading bv lowering the indices, if 
the bl«ir be downwards, or by raismg them, if toe blow be uth 
wards. Besides these drawbacks, the Six's thermometer causes the 
observar additional anxiety on the score of inaccuracy; for, although 
we get a fnmimum temperature, we are bv no means sure of the 
poiiS where this minimum lies. Thus nx)fessor Wyville Thomson 
says ('Pepths of the Sea,' p. 139): — ^'^ The de»^rmination of tern-* 
perature has hitherto rested chiefly upon the reg^straoon of mini- 
mum tiiermometers, It is obvious that the temperature registered 
by mmimum thermometers sunk to the bottom of the sea, even if 
their registration were unaffected by the pressure, would only give 
the lowest temperature reached Bcmewher^ between top and bottom, 
not neutiarihf at the bottom itself. The temperatures at various 
depths might indeed (provided they nowhere increased on goinf 
deeper) be determined by a series of minimum thermometers placed 
at mfferent distances luong the line^ though this would involve 
considerable difficulties. Still, tiie^ liability of the index to slip, 
and the probability that the indication of the thermometers would 
be affected by the great pressure to which they were exposed, ren- 
dered it very desirable to control their indications by an indepen- 
dent method." Again, at page 299, we find : — " I ou^ht to men- 
tion that in taking the bottom temperature with the Six's thermo- 
meter the instrument simply indicates the lowest temperature to 
which it has been subjected; so that if the bottom water were 
warmer tlum any other stratum through which the thermometer 
had paased^ the observations would be erroneous." Undoubtedly 
this would be the case in extreme latitudes, or in any spot where 
the temperatiu*e of the air is colder than that of the ocean* 
Ge^rtainly ttie instrument might be warmed previous to lowering ; 
but if tbi c^^t water should bQ on the sur&ce, no reading, to be 
depended oppn, could be obtained. 

It wfl« on reading these passages in the book above referred to 
that it beaame a matter (^ serious consideration with us wheth^ a 


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Royal Sociefy : — 

thermometer could be constructed which could not possibly be put 
out of order in travelling or by incautious handling, and which 
should be above suspicion and perfectly trustworthy in ite indica- 
tions. This was no very easy task. But the 
instrument now submitted to the Fellows of the 
Boyal Society seems to us to fulfil the above 
onerous conditions, being constructed on a plan 
different from that of any other self-register- 
ing thermometers, and containing as it does 
nothing but mercury, neither alcohol, air, nor 
indices. Its construction is most novel, and 
may be said to overthrow our previous ideas of 
handling delicate instruments, inasmuch as its 
indications are only given by upsetting the in- 
strument. Having said this much, it will not 
be very difficult to guess the action of the ther- 
mometer ; for it is by upsetting or throwing out 
the mercury from the indicating column into a 
reservoir at a particular moment and in a par- 
ticular spot that we obtain a correct reading of 
the temperature at that moment and in that 
spot. Ymt of all it must be observed that this 
instrument has a protected bulb, in order to 
resist pressure. This protected bulb is on the 
principle devised by us some sixteen years since, 
when we supplied a considerable number of ther- 
mometers thus protected to the Meteorological 
Department of the Board of Trade ; and they 
are described by the late Admiral EitsBoy in 
the first Number of the * Meteorological Papers,* 
page 55, published July 5th, 1857. Beferriiig 
to the erroneous readings of all thermometers, 
consequent on their delicate bulbs being com- 
pressed by the great pressure of the ocean, he 
says: — "With a view to obviate this failing, 
Messrs. Negretti and Zambra undertook to make 
a case for the weak bulbs, which should trans- 
mit temperature, but resist pressure. Accord- 
ingly a tube of thick glass is sealed outside the 
delicate bulb, between which and the casing is a 
space all round, which is nearly filled with mer- 
cury. The small space not so filled is a vacuum, 
into which the mercury can be expanded, or 
forced by heat or mechanical compression, with- 
out doing injury to or even compressing the 
inner or much more delicate bulb:^ 

The thermometers now in use in the * Chal- 
lenger' Expedition are on this principle, the only 
difference being that the protecting chamber has 

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Messrs. Negretti andZamhrtk on a Deqhsea Thermometer. 809 

been partly filled with alcohol instead of with mercury ; but that 
has nothing to do with the principle of the iavention. 

We have therefore a protected bulb thermometer, like a siphon 
with parallel le^, aU in one piece, and haying a continuous com- 
munication, as in the annexed figure. The s^e of this thermo- 
meter is pivoted on a centre, and, being attached in a perpendi- 
cular position to a simple apparatus (which will be presenfly de- 
scribed), is lowered to any depth that may be desu*ed. In its 
descent the thermometer acts as an ordinary instrument, the mer^ 
cury rising or &lling according to the temperature of the stratum 
through which it passes ; but so soon as the descent ceases, and 
a reverse motion is given to the line, so as to pull the thermometer 
to the B\irface, the instrument turns once on its centre, first bulb 
uppermost, and afterwards bulb downwards. This causes the 
mercury, which was in the left-hand column, first to pass into 
the dilated siphon bend at the top, and thence into the nght-hand 
tube, where it remains, indicating on a graduated scale the exact 
temperature at the time it was tunied over. The woodcut shows the 
position of the mercury after the instrument has been thus turned on ' 
its centre. A is the bulb ; B the outer coating or protecting cy- 
linder ; G is the space of rarefied air, which is reduced if the outer 
casing be compressed ; D is a small glass plug on the principle of 
our Patent Maximum Thermometer, which cuts off, m the mo^ 
ment of turning, the mercury in the column from that of the 
bulb in the tube, thereby ensuring that none but the mercury in 
the tube can be transferred into the indicating column ; E is an 
enlargement made in the bend so as to enable the mercury to pass 
quickly from one tube to another in revolving ; and F is the indi- 
cating tube, or thermometer proper. In its action, as soon as 
the thermometer is put in motion, and immediately the tube has 
acquired a sb'ghtly oolique position, the mercury breaks^off at the 
pomt D, runs into the curved and enlarged portion E, and even- 
tually f aUs into the tube F, when this tube resumes its original 
perpendicular position. 

The contrivance for turning the thermometer over may be de- 
scribed as a short length of wood or metal having attached to it a 
small rudder or fan ; this fan is placed on a pivot in connexion 
with a second, and on this second pivot is fixed the thermometer. 
The fan or rudder points upwards in its descent through the water, 
and necessarily reverses its position in ascending. This simple 
motion or half turn of the rudder gives a whole turn to the ther- 
mometer, and has been found very effective. 

Yarious other methods may be used for turning the thermo- 
meter, such as a simple pulley with a weight which might be released 
on touching the bottom, or a small vertical propeller which would 
revolve in passing through the water. 

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810 a$ohgkal BoeUty :^ 


[Contiaued from p. 230 J 

Dooembmr 17tli, ld73^~Pro£ BotuMiyi F.BA, T^oe-Preildetitj 

The fbllowing commonioatioiui were read : — 

1. ** Observationfl on some features in the Physical QwAojtf of tho 
Outer Himalayan r^on of the Upper Punj&h, India.'' By A. B. 
Wynne, Esq., F.G.8. 

The district of the Upper PunjAb described by the anther con- 
sists of crystalline, granitoid, syenitic, and schistose rocks far in 
among the hills, succeeded by slates and limestones, possibly of 
Silurian age, unconformably overlain by Triassic and perhaps older 
iDcks, which are in their turn unconformably succeeded by a series 
of mutually conformable Jurassic, cretaceous, and nummuutic lime- 
stones and shaly beds. These secondary and Tertiary beds, which are 
. chiefly limestones, are called the ** Hill Limestones." Beyond these 
comes a zone of hiUs and broken plains, composed of sandstones, clays, 
and conglomerates, of great thickness and of Tertiary age (Eocene 
and Miocene), which the author calls the '' Murree beds.*' Thia belt 
passes generally along the whole southern foot of the Himalayas, 
from Assam to AfghanisUin. In the district described by the 
author it is bounded on the south by the Salt Bange, beyond which 
stretch tho deserts of the Punjftb and Sind. 

The outer Tertiary belt presents a gradation towards the hill 
character. Among the rocks of the Murree zone there are harder 
beds than elsewhere; limestones occasionally appear, sometimes 
like those of the hiU-beds, and the Hill Nummulitic limestones may 
have alternated in their upper part with the Murree beds. The 
nummulitic limestones of the Salt Bange, containing large Bitalven 
and Gasteropoda, were probably of shallow*water origin, whilst the 
diminutire organisms of the Hill Nummulitic limestone inhabited 
greater depths. 

Contortion of the strata is a common feature of the country, 
affectmg some of the newest Tertiary beds so as to place them in a 
vertical position, and almost everywhere throwing the rocks into 
folds, producing in many ca^es invendons of the strata. 

The author compares these rocks with those of the Simla area 
described by Mr. Medlicott, who found there two strong imoon- 
formities, namely, between his Siwa^ik and Kalum, and Nalum and 
Subathu groups, and rejarded the whole of the beds of the outer 
Tertiary detrital 2one from the base of the Subathu group upwards 
as discordant to the Himalayan or'Hill-series and to each o^er. 

The junction of the newer Tertiaries with the rocks forming the 
higher hills of the outer Himalaya, both In the Simla area and in the 
outer Punj&b, is marked by disturbance, distortion, and inversion or 
abnormal superposition in the Tertiary strata along the contact. 

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Mode of Ocenmnoi qfDianwndt in South Africa* 811 

In iha Upper Ftmjftb the jutustton Mbws a curred Hm^ raudng^ 
nenrhr east sad wesi to the nort^ of Banml Pindee ; than de« 
•erimiig aa an|^ whidi doeelf fottows the great bend of the Jhilam 
virer near Kocnfferabad, it rana more or less in a sontii-eaaterly 
direetkm through Kashmere towards Simla. Thia Jtmction Ihie is 
inaeparaldy eonneeted with the eauaation of the great mountain-' 
ehama ; it ahowa a panlleliam to the axes of the outer ranges, and 
is Mety due to intensity of disturbance^ the result of bteral 

The author also refers to the difference existing between the 
geology ol the outer Himalayan region and that of &e Salt Bange, 
as bong similar to tiiat wliioh obtains between the Alpine and 
extra- Alpine diaraeters of Eur(n>ean nx^-groups, and suggests that 
the recurrence of such similar features at such distances may indi- 
eate a connexion between the former eonditions of deposition and 
the early history of the great chains themselres. 

2. '' On the mode of occurrence of Diamonds in South Africa.'^ 
By E. J. Dunn^ Esq. Communicated by Prof. Bamsay, FJEU3.« 

In this paper the author stated that the diamonds of South AMca 
occur in peculiar circular areai^ which he regards as <* pipes,'' which 
formerly constituted the connexion between molten matter below 
and surfece Yolcanoes. The surrounding country counts of horizontal 
shales, through which these pipes ascend nearly yertically, bending 
upwards the edges of the shales at the contact. The rock occupying 
uese pipes was regarded by the author as probably Gabbro, al« 
thon^ in a yery altered condition. Intercalated between the 8hale« 
beds there are sheets of dolerite <&o. ; and dykes of the same rocks 
also intersect the shales at firequent intervals. "Within the pipes 
tiiere are unaltered nodules of the same dolerite. With regard to 
the relation of Ihe diamonds to the rock of the ^ipes in which they 
are found, tiie author stated that he thought it probable that the 
latter was only the agent in bringing them to the surface, a large 
proportion of the diamonds found consisting of fragments. At 
the same time he remarked that each pipe furmshed diamonds of a 
different character fh>m those found in other pipes. 

Jannaiy 7th, 1874.— Prof. Bamsay, Y£XJA^ Yioa-Pie«dent, 
in the Chair. 

The following communications were read : — 

1. " The Origin of some of the Lake-basins of Cumberland.'* 
— First Paper. By J. Clifton Ward, Esq., P.G.S., Assoc. E.S.M. 

After rearing to the fkct that the question of the origin of lake- 
basins cannot be satisfactorily discussed unless the depth of the 
lakes and the heights of the mountains are brought before the 
ndnd'is eye in their natural proportions, the author sketched out the 
physical geography of the lakes under discussion (Perwentwatery 

Digitized by VjOOQ IC 

312 GeohffuuU Society: — 

Bassenthwaite^ Buttennere, Gnunmooky and Loweswater), and 
pointed out what must have beeft their original edse and shape 
before they were filled up to the extent they now are. These lakes 
were not moraine-dammed^ but true rock-basins. The belief that 
the present Lake-district scenery ^was the result of the sculpturing 
of atmospheric powers, such as we see now in operation, varied by 
dimatal changes and dianges in the height of the district above the 
sea, was enforced, and the opinion given that the work of elabora^ 
tion of the lake-country scenery has been going on ever since Gar- 
boniferous or pre-Carboniferous times. The lake-hollows repre- 
sented almost the last rock-shavings removed by Nature's tools. 
What were the special tools producing these hollows ? Th^re being 
no evidence of ^eir production by marine action or by running 
water, since they do not lie in syndin^ troughs, nor along lines of 
Assuring and faulting, and cannot be supposed to be speciid areas of 
depression, it remained to see how far Professor Eunsay's. theory 
accounted for their origin. The oourse of the old Borrowdale 
glacier was then fully traced out, and the power the numerous 
tributary glaciers had of helping to urge on the ice over the long 
extent of flat ground from Seathwaite to the lower end of Bsssen- 
thwaite Lake, commented on. . The same was done with regard to 
the Bultermere and Lreton glacier, and the depths of the lakes, 
width and form of the valleys, and thickness of the ice shown by 
numerous transverse and longitudinal sections drawn to scale. 
When all the evidence was considered — the fact of the lake-hoUows 
under examination being but long shallow troughs, the thickness 
of the ice which moved along the valleys in which the lakes now 
lie, the agreement of the deepest parts of the lakes with the points 
at which, from the confluence of several ice-streams and the nar- 
rowing of the valley, the onward pressure of the ice must have been 
greatest — the conclusion was arrived at that Prof. Bamsay's theory 
was fully supported by these cases, and that the immediate cause of 
the present lake-basins was the onward movement of the old 
glaciers, ploughing up their beds to this slight depth. It was 
pointed out dat since the general form of tiie Buttermere and 
Grummock valley was that of a round-bottomed basin, as seen in 
transverse section, the effect of the ice was merely a slight deepen- 
ing of the basin or the formation of a smaller basin of similar 
form at the bottom of the larger ; whereiis in the case of the Der- 
wentwater and Bassenthwaite valley, which in transverse section 
was a wide flat-bottomed pan, the action was to form long shallow 
grooves at the bottom of the pan. This consideration was thought 
to explain the fact of the greater depth of Buttermere and C^m- 
mock than of Derwentwater and Bassenthwaite, although the size and 
thickness of the old glacier in the former case was probably less 
than in the latter. Li conclusion, the author stated that he hoped 
to test the results obtained in these cases by bringing forward in a 
foture paper like details of Wastwater and other lakes and moun- 
tains in the district. 

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On a great Ice-sKeet in this Lake^dktrUt. 818 

2. << On the Traces of a Great loe-sheet in the Sonthem part of 
the Lake-district and in North WaleeJ'' By D. Maddntoeh, Esq.. 

In this pap^r the author brought forward the eyidence which 
seems to him to establish the existence in the sonthem part of the 
Lake*district of a *< valley-ignoring and ridge-concealing ice-sheef 
With regard to ice-marks, he distingnished between primary strias 
and those produced at a subsequent period, and stated that in the 
Lake-district the direction of the primary strife generally coincides 
with that of the action by which nKhes mou^onneM have been pro- 
duced. He gave a table of the direction of ice-marks observed by 
him in the district under notice, and stated that about Windermere 
and Ambleside the general direction is nearly N.N.W., round Gras- 
mere between N.W. and N.N.W., north-west and west of Grasmei^ 
in upland valleys and on high ridges about N. 30^ W., south of Gras- 
mere and in Great Langdala N. 35^ W., and in the Coniston district 
a little W. of N. In many places he recognized an uphill march of 
the ice. He thought that the iceflow producing these marks 
might be anterior to the flow from south to north, of which traces 
are observed in the northern part of the Lake-district, and that 
its source was probably a vast mass of ice covering many square 
miles of country north of Far Easdale. The author also referred to 
the glaciation of North Wales, some of the marks of which, observed 
by him in a district south of Snowdon, seemed to him to indicate the 
southerly movement of a great ice-sheet capable of ignoring or 
crossing deep valleys. He noticed that towards the top of the pass 
of lianberis there is a thin covering of drift on the 8.W. side, 
resembling the gravelly pinnel of the Lake-district. He also men- 
tioned the occurrence near Llyn Ilydan of numerous mounds 
composed of clay, sand, and fine gravel, the stones having generally 
been rolled by water, and ascribed their formation to a combination 
of glacial and marine actions. 

8. '< Notes on some Lamellibrandis from the Budleigh-Saltcrton 
Pebbles.*' By Arthur Wyatt Edgell, Esq., F.G.8. 

In this paper the author commenced by noticing the accordance 
between many of the pebbles of Budleigh Salterton and beds occur- 
ring on the opposite side of the channel in Brittany, and then de- 
scribed several species of Lamellibranchiata found in the Budleigh- 
Salterton pebbles. The species described were : — ModiolopsU ar- 
morioi (Salter), M. Lebeseontiy sp. n., Sangumalites ?, sp. (contartus ?, 
Salter), Avieulopecien Tromelini^ sp. n., Fterinasa retrofleaa (Hi- 
singer) and three other species, Pdlcearca, sp.^ Avicula, sp., Okido^ 
pTwrw?, sp., Lunvloeardvum ventricomtni sp. n., CkfMdonta^ sp., and 

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C 81* ] 
XLY. InielSgenoi and MUeithneoui Artklm. 


««rnwO p«nM owrents ftttnoi one isotiier when tbej ]mm iba 

are oppoeite^" After enunfliatnig this rule, Ampiae beliered hm 
could immediatelj ^^lenJiae it bj extending it to the elemantt of 
the correntfl^ to which he i^plm^ wheterer nuij be thcdr rdaim 
direction, the ide* of a coune in the latne or in opposite directicns^ 
Two currenis ue Mid to be in the aame direction iriien they boUi 
increaBC their distance from the foot of the common perpendiciihr» 
oar when thej both approach it; in the contruy cases thejr hare 
di&rent directions. Adoptang this kngoage, it is not aocozate to 
sav that two elements haying the same diroction attract one the 
other; it is not accurate eren for parallel elements. As theasser* 
tion l»s been reprodnced in all the treatises on^jsics, and senrea 
as a basis for sereral important e^lanations, I haye thought it 
would be important to show tiiat it is inconsistent with Ampere's 
law itself, and to solve the following problem : — 

GKyen an element oi a current, to nnd in a point M of space tte 
diredion whidi must be assigned to another ekmeiit in order that 
thttr mutual action may be attractire, repellent, or nil. 

Suppose the dement d* placed at the origin of the ooordinateB 
and diiected along the axis of the X's, let us seek the condition on 
whidi an element whose coordinates are ^, y', 2^ will be without 
acti<mon<2f. Namina the angles formed by the two elements inth 
the straight line which joins them d and a , and ihe an^ which 
they make with one anouier «, according to the law of Ampere the 
condition is, 

cose=|cosdcos^ (l) 

But, naming the radius yector 1*, and the atbiMsting element ds', we 

^ af ^ dr dad 

COSe«-, COSa^acTj, COSCB^. 

Equation (1) becomes 


^ ""U 

of which the integnd is 

i^^hji^, (3) 

the equation of a sur&ce of reyolution whose axis is the axis of X, 
and of which the meridian curye has for its equation, in polar co- 

r=Acos«e (4) 

Whatever the form and direction of a current enveloping such a 

Digitized by VjOOQ IC 

IrUeUigenei and MkeetUmeoui Articki. 815 

s urfiice, the addon upon m dement situated at the stunmit and 
ilirected along the axis will be nil. The presence of Hie arfattrarjr 
oontftant in equation (4) permits tlie snnaoe to be made to pass 
thi^iuffh any pdnt whatever of space; and conseqnently there exist 
in eacn point an infinity of directions in which an element dt^ may 
be placed so as to amml its action upon the riven element ds. 
Those directions are ail in the tangent plane to the surface found. 
It is readily seen that the action is a maximum when the element 
is normal to the suHace, and that, for an element of riven length 
and intensity,it is proportional to the cosine of the angle made yinth 
the normal. If the element dg, placed along the axis ot the surfiice, 
is directed outward, every element starting from a point of the 
same surface and like it directed outward wiU be repellent, and 
every element directed inward will exert an attractive action.—^ 
Chmpte$ Smdm de VAoadimie dea Seieneeg, vol. Ixxix. pp. 141-1^. 


Mr. Bchwendler said that the phenomenon of earth-currents 
seemed to be intimately connected with the earth*magnetism and 
its variations. 

He would, however, point out from the beginning that though 
the two phenomena, "earth-magnetism" and " efuih-currents,'^ 
were undoubtedly connected with each other, it was by no means 
established as yet that they were cause and effect, or, what certainly 
seems to be fajr more probable in the present state of knowledge on 
the subject, parallel effects of one and the same general but en- 
tirely unknown cause. 

GThe three elements of the earth-magnetism, intensity, inclination, 
and declination, had been quantitatively and most accurately deter^ 
mined in almost all dvilized parts of the world TGalcutta excepted) 
by the introduction of Qbmbb and Weber's well-4mown syst^ rf 
magnetic measurements ; and though the results obtained had been 
very general and satisfactory, establishing the most interesting 
facts OT diurnal and secular periods of variation in the three mag- 
netic elements, and had also been of direct practical benefit to na« 
vigation, still the physical nature of the phenomena had not been 
unveiled by these observations. To solve the problem, it would 
seem that quantitative measurements of other phenomena, directly 
or indirect^ connected with it, were required ; and it was most f ot^ 
tunate that at least one such phenomenon not only existed but was 
even susceptible of accurate measurement ; he meant the " earth- 

The chances of giving a true physical explanation of any pheno- 
menon, he observ^ increased in geometrical progression with the 
number of phenomena directly or mdirectiy connected with the one 

♦ Commimi^ated by the Aiithor, from tho Froceediogs of the Asiatio 
Society of Bengal for Jtuie^ 1874. 

Digitized by VjOOQ IC 

316 IiUeUigmee and MiaeeUaneom ArHeles. 

to be explained, supposiag tiiat they were all susceptible of accunte 

In this particular case he had to deal with two such parallel phe- 
nomena — ^the magnetism of the earth, quantitatively ascertainea for 
more than 40 years past, and " earth-currents," sadly neglected. 

He said he was perfectly aware why " earth-currents had not 
been measured ; and then, after mentioning the special purpose of 
his paper (i. e, not to start a fresh theory of the earth-magnetism 
with the scanty and imperfect material available, but to lay before 
the Society some more b^cts connected with its parallel pheno- 
mencNo, the earth-currents in the telegraph-lines, which haa been 
quantitatively measured during the l^t six years in -widely dif- 
ferent parts of the empire, Ceylon included), he proceeds as fol- 
lows : — 

** That it was well known that from time to time telegraph-lines, 
overhind, underground, and submarine, were affected by what had 
been called * magnetic storms/ 1. e, by very strong currents passing 
through the wires and overpowering entirely those used for signal- 
ling, with which electrical disturbances coexisted magnetic varia- 
tions far exceeding the limits generally observed when no such 
electrical disturbances exist, and very often accompanied in the 
northern (and most likely also the southern) part of the planet by 
vivid auroras. Now these currents observed in the telegraph-lines 
were * earth-currents.' 

" For instance, on the 10th of November, 1871, and on the 4th 
of February, 1872, earth-currents of considerable strend^h had 
been observed in all the lines throughout India, and the submarine 
cables terminating on its shores. These great electrical disturb- 
ances were by no means local, but existed almost simultaneously 
throughout the earth, showing us a most interesting feature of 
our phmet. 

" The fact of the secular changes of the earth-magnetism occu- 
pying such a long period as about 1000 years (the principal mag- 
netic pole moving round the astronomical pole in 1000 years) 
pointed most probibly to a cause external to the planet. If he 
were allowed to follow his own imagination, he would say that 
earth-magnetism, its diurnal and secular variations, auror» boreales 
and austnJes, and electrical disturbances, weak or intense, in the 
planet, were sJl due to the movement of the earth and of the heavenly 
Dodies generally — ^that the great electric convulsions observed from 
time to time were nothing but the telegraph-signals transmitted 
from far distant regions to our planet, indicating great physical 
changes in the universe, long before, if ever, they could be felt by 
the more rough instruments (light, heat, and gravitation) at pre- 
sent the only means by which we recognise our kinship with the 
outer word. 

" It could be, therefore, easily perceived how important it was 
to investigate such a phenomenon (probably of all the most widely 
connected) by direct measurements. 

**Now if such electrical disturbances only existed by fits and 

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InielUgenee and Miscellaneous Articles. 317 

starts, as was the case during magnetic storms, it wonld be almost 
hopeless to attempt a general system of measurement. This was, 
however, fortunately not the case, since these earth-currents, which, 
during magnetic storms became so violent, seemed to exist perma- 
nently, only of very feeble strength ; and it was on this subject that 
he would give some observed facts." 

The general outline of the rest of Mr. Schwendler^s commmuni- 
oatibon will be best given in extracts from his paper, which will be 
printed in full in Fart IL of the Journal. 
Mr. Schwendler says : — 

*' The currents observed at all hours of the day and all seasons of 
the year, in every line throughout India, may be obviously due 
to many different causes actmg separately or conjointly. These 
currents I have designated * natural currents,^ to indicate the fact 
of l^eir being in the lines without any direct, or at least intentional, 
human agency. The causes which may produce natural currents 
in tolegraph-Unes are : — 

" 1. Gkdvanic action between the earth-plates. 
** 2. Polarization of the earth-plates by the signalUng-currents. 
" 8. Polarization of badly insulated' points in the line. 
" 4. Atmospheric electricity. 
"6. Thermo-electricity. 
" 6. Inductive capacity. 
"7. Voltaic induction, 
"8. Earth-currente. 

" The latter must be regarded as produced by an actual difference 
of potentials between the two points of our planet with which the 
ends of a telegraph-line are in contact. 

" Surely if these * earth-currente * do permanently exist, and, fur- 
ther, if they are strong enough to overpower the others, which are 
evidently of a much more accidental and less permanent nature, 
then a large number of quantitative observations, judiciously re- 
duced and conveniently compiled, should at least show the tendency 
of the general law that governs them in strength and direction, 
leading perhaps finally to the true explanation of the earth's mag- 
netism and the causes of its variations. 

" Such were in short my reasonings when, in 1868, 1 was intrusted 
by Colonel Bobinson, the Director-Ghneral of Telegraphs, with the 
introduction of a system of testing the lines in India ; and although 
the practical objects of that system had nothing whateoever to ao 
with the solution of the problem, yet the fact thatin each test measure- 
mente had to be made with positive and negative currents (for the 
very purpose of eliminating the influence of the natural currente) 
secured all the data necessary for the quantitative determination of 
the electromotive force in the line, to which the natural current 
must be considered proportional, involving only a slight additional 
calculation without any extra observations. To this end the neces- 
sary provisions were made and instructions issued ; and in this 
manner more than 10,000 electromotive forces, producing the 
natural currente in the lines of India, have been calculated from the 

Digitized by VjOOQ IC 

818 InUUigenei and Miialbmsous ArticUt. 

tests mads between 1868 and 1872, and are now at our diiponJ ; 
and although the results of these numerous observaticnu have noft 
as yet been all a^yxed, or oTenoompiledt yet in manj sDacial cases, 
ana for limited periods, this has been dona; and from these weara 
justified in statmg the following as facts :-^ 

'' 1. All the lines in India are atbcted bj natural corrents* 

*' 2. From moie than 10,000 observations it has been establiahed 
that the prevailing flow of these currenU between anj pair of sta** 
tions is as of a copper-euirent from the east to the west ; but which 
is the true direction, or that of maTimum intensity, and, further, 
whether there is ozdy one such direction, has not been computed 
as vet. 

^'3. The strength of the natural current in one and the same Una 
is very variable. 

" 4. The direction of the natural current in one and the aaiae 
line, though also variable to a certain extent, is vet far more 
constant than its strength, and out of a number of observations 
there is generally a marked preponderance of current* flowing in 
the same direction. 

'*5. The variation instrenffth and direction of the natural currents 
in parallel lines of the same length is ba more nnijbnn than might 
have been expected, considering the many accidental influences to 
which long overland lines are exposed. 

'* 6. The prevailing direction of the natural current in any line is 
generally also the direction of the maximnm current observed ; but 
this is not the case invariably. 

" These general &cts point to one probable condusion-^namely, 
that < earth-currents * do permanently exist in the lines of India, 
though they are often, ana under certain circumstances even much, 
obscured by many ottier causes, of commensurate magnitude, bat 
more unstwle axid accidental in character. 

''For example, the two railwajr lines between Bombay and Madraa, 
one of which is very perfect in insulation, while the other is quite 
the reverse, both euiibit a copper^current flowing permanently 
from Madras towards Bombay ; and this fact, having been asceiv 
tained from a large number of tests, extending over a considerable 
period, and made from botii Madras and Bombay, proves that tl^ 
cause is a general one with respect to time, and that tjie method 
and place of measurement do not influence the direction of the 
current observed. Further, as one of the wires is used txxt the 
through traffic towards Bombay, while the other is used for the 
through traffic towards Madras, and as both circuits are worked 
witli copper-currents, the natural currents, which flow in the same 
direction in the two wires, certainly cannot be due to the polarizer 
tion of tjie earth^platee or of faulty phuses in the lines. The ave- 
rage electromotive force in these wires is about 4*5 Daniells ; and 
maxima of 15 and 20 Daniells are occasionally rea<^ed. 

''I consider it therefore established that ' earth-currents' do per- 
manently exist in the lines of India, their general drift beinff mon 
east to weat, and that w^ shonld b» mm ]ustifli9d in ^tobliihing ii 

Digitized by VjOOQ IC 

Intdligence and Mi$e$lUmeou» AriuUi. 619 

spedal system for the purpose of observing them acceding, to % 
miif orm plan and wit^ unproved tes<>*metlioas.'' 

Mr. Sohwendler concluded \>j sarjing that, based on the &cts 
above stated* he had proposed to the Council of t^ Adriatic Sooietj 
to urge on Goyemment the introduction of a sjstem cl measorse- 
ment of earth-currents ; that the Council had received the proposal 
most warmbr, and had appointed Colonel Hyde, Mr. B. S. Brough, 
and himseli to wcnrk out apractical system; and that Colonel Sor 
binson, the Director-General of Teleg^phs, had intimated bis Idnd 
cooperation in the matter. 


Bv means of an electrometer made on the pijnemle of Big 
William Thoms<m's quadrant, I have been able to perionn a bfw 
experiments in relanon to the dissipation of small quantities ot 
electricity by different kinds of flames. 

These experiments were conducted with such small quantities of 
electricity as could be obtained by rubbing a vulcwoite plate six 
inches square with a oatskin. The sensitiveness of the electro- 
meter te the electricity thus formed was very great. The experi- 
ments are given below. 

EmerimmU 1. — An alcohol lamp, carefully insulated, was con- 
nected with the electrometer. The sectiona of the quadrant to 
which it was attadied were then charged by means of the vulcanite 
plate, the opposite sections being at the same time in connexion 
with the earth. The lamp was then carefully lighted. The spot 
of light, which had been deflected te the edge of the scale by the 
chai^, quiekly r^;ured to the sero-point, indicating a quick dissipa- 
tion of the electricity by tiie flame. 

Enop. 2.— The same conditions as those in Exp. 1 weveobsenred, 
with the exception that a Bunsen burner was snbstititted im Hem 
alcohol lamp. Tbediasipationof eledridty was t^same as before, 
and took place, as near as could be observedt at the same rate as 

Exp, 3.— *I then substituted for the Bunsen flame a very fine jet 
of lig^t, obtained by passiiu[ the gas throagh a find^ pointed glass 
tube. The resulte obtained from this ex^mment indicate that tiie 
rate of dissipation is in no respect related to the size (rf the flame. 

Exp. 4.— The end of the wire connected with the quadrant was 
then placed so that when the gas was lighted the wire point would 
be in the flame. The quadmit was tb^i oharffed and tbe gae 
turned on without being lighted. The spot of tig^t had no move- 
ment, and save no sign of any loss of electricity by the quadrant* 
An artificial current of air across the wire point likewise had no 
effect in dissipating the charge. 

Exp. 5. — ^The eim of the wire was then placed in the jet of an 
atomizer, the same conditions being observed as in Exp. 1. 3^e 

Digitized by VjOOQ IC 

820 Intelligence and MtseeUaneoui AritcUt. 

fine globules of Bteatn and water issuing from the atomizer had no 
effect in dissipatinK the electricity^ of the quadrant. 

I also performed two very stnkinfl; experiments, which seemed 
to have some bearing upon this subject. The instruments used 
were the same as in uie former experiments ; and the manipulation 
was as follows : — 

Exp^ 1. — Carefully insulate a wire communicating with the 
dectrometer, and place its point within a few inches of the 
flame of an insuli^;ed Bunsen burner. Let the spot of light be at 
the Eero-point. Electrify the vulcanite plate with the catskin, 
and hold it at an equal distance from flame and wire point. It is 
yery difficult under these conditions to sufficiently electrify the 
quadrant so as to produce any deflection of the spot of Hght. 

Exj^, 2. — ^Place the wire point in the flame and l^en hold the 
electrified yulcanite plate up to the flame as before. The spot of 

Sjrht immediately is yiolently deflected, indicating the presence of 
ectridty in the quadrant. This charge, however, is soon dissi- 
pated by the flame, and the spot quickly returns to the zero-point. 

These last experiments seem to inmcate that the flame has a 
much greater attraction for the electricity of the vulcanite plate 
than the copper point of the wire. Hence the difficulty of 
chaiging the quadrant in the first experiment. 

"Wien, however, the wire is in direct communication with the 
flame, as in the second experiment, the flame and the quadrant are 
at the same potential, and the increase of electricity in the flame 
produces a corresponding defloction of the spot of light. — Silliman's 
American Journal, Septmber 1874. 


The stratiflcations of the electric light can be obtained in the 
following circumstances, which permit the production, with static 
electricity, of inversions of the charge as rapid as those given by 
the employment of the Suhmkorff coO. 

Suppose the two condensers of Holts's machine united by a 
G^issier tube instead of communicating by a continuous me- 
tallic plate. Place the exciting stem of the machine so as to obtain 
only small sparks in very rapid succession. Two opposite currents, 
one of charge, the other of discharge, will then pass through the 
GMssler tube ; and very distinct stratifications will be seen. It is 
necessary, in order to succeed even with very long and wide tubes, 
to replace the ordinary small bottles by jars of hrge dimensions. 
Those which I used had a surface of 1873 square centimetres. — 
Camptes Bendue de VAcadimie de$ Sciences, vol. ix^dx. p. 168. 

Digitized by VjOOQ IC 







XLY I* On the Magnetic PenneabiUty and Maximum of Magne^ 
tism of Nickel and Cobalt. By Henry A. Rowland, C.£.* 

SOME time ago a paper of itiine on the magDetie permeabi- 
lity of iroDi steel, and nickel was published in the Philo- 
sophical Magazine (August 1873); and the present paper is to 
be considered as a continuation of that one. But before pro- 
ceeding to the experimental results^ I should like to make a few 
Yemarks on the theory of the subject. The mathematical theory 
of magnetism and electricity is at present developed in two radi- 
cally different manners^ although the results of both methods of 
treatment are in entire agreiement With experiment as far as we 
can at present see. The first is the German method ; and the 
second is Faraday's^ or the English method. When two mag- 
nets are placed near each other, we observe that there is a mu- 
tual force of attraction or repulsion between them. Now, accord- 
ing to the German philosophers, this action takes place at a dis- 
tance without the aid of any intervening medium : they know that 
the action takes place, and they know the laws of that action ; but 
there they rest content^ and seek not to find how the force tra- 
verses the space between the bodies. The English philosopher^, 
however, led by Newton, and preeminently by Faraday, have 
seen the absurdity of the proposition that two bodies can act 
upon each other across a perfectly vacant space, and have 
attempted to explain the action by some medium through which 
the force can De transmitted along what Faraday has called 
*' lines of force.'^ 

These difierences have given rise to two different ways of look- 

* Communicated by Professor J. Clerk Maxwell, M.A., F.R.S. 
Phil. Mag. S. 4. Vol. 48. No. 819. Nov. 1874. Y 

Digitized by VjOOQ IC 

822 Mr. H. A. Rowland on the Magnetic Permeability 

ing upon magnetic induction* Thus if we place an electromag* 
net near a compass-needle^ the Germans would say. that the 
action was due in part to two causes — the attraction of the coil, 
and the magnetism induced in the iron bv the coil. Tbo^ewbo 
hold Faraday's theory, on the other handi would consider the 
substance in the helix as merely *' conducting " the lines of force, 
so that no action would be exerted directly on the compass* 
needle by the coil, but the latter would only afect it in virtue 
of the- lines of foree passing along its interior, and so there 
could be no attraction in a perfectly vacant space. 

According to the first theory, the magnetization of the iron 
is represented by the excess of the action of the electromagnet 
over that of the coil alone; while by the second, when the coil 
is very close around the iron, the whole action is due to the 
magnetization of the iron, The natural ut|it of magnetism to 
be used in the first theory is that quantity which will repel an 
equal quantity at a unit's distance with a unit of force ; on the 
second it is the number of lines of foree which pass through « 
unit of surface when that surface is placed in a unit field per- 
pendicular to the lines of force. The first unit is 4ir times the 
secopd. Now when a magnetic force of intensity ^^ acts upofi 
a magnetic substance, we shall have 9s=i&+w3i in wbiou 9 
is the magnetization of the substance according to Faraday'a 
theory^ and is what I forinerly called the inagnetic fielcl, but 
which I shall hereafter cail^ aft^r Professor Maxwell, the ma(>- 
netic induction. 3 is the mtepsity of magnetization ficeordiog 
to the German theoryi expressed in terms of the magnetic mo- 
ment of the unit of volume. Now, when the substance is in the 
shape of an infinitely long rod placed in a magnetic field parall^ 

to the lines of force, the ratio 7^/^ ia called the magnetic pe^• 


meability of the substance, and tlie ratio -r =ir is Neumann's 

eoeffioiept of magnetisation \y induction. Now cKpariment 
shows that for large values of ^ the values of both $k and « de- 
crease, so that we may expect either 3 or both 8 and ^ to attain 
a ma^dmum value. 

In my former paper I assumed that 8 as well as 3 attain a 
roaiumum ; but on further considering the subjeel I see that we 

a I shall hereafter in all my papers use the notation as given in Pro- 
fessor Maxwell's ' Treatise on Electriottjr and Magnetism; ' for eonparison 
with my former paper I give the foDowmg :--« 

9 in this paper bQ in former one. 
^ „ B4irM „ 

3 , =4i""^ '• 

Digitized by VjOOQ IC 

and Maximum of Magnetism of Nickel and Cobalt, 823 

have no data for determinuig which it is at present. If it were 
posaible for S to attain a maximum vahie bo that fi should ap-* 
proach to 0^ k would be negative^ and the substance would then 
become diamagnetic for very high magnetizing forces*. This is 
not contrary to observation ; for at present we lack the means of 
producing a su£Sciently intense magnetic field to test this expe-r 
rimentally^ at least in the case of iron. To produce this effect 
at ordinary temperatures^ we must have a magnetic field greater 
than the following— for iron 176^000, for nickel 63^500, and 
for cobalt about 100^000 (?). These quantities are entirely be« 
yond our reach at present, at least with any arrangement of 
solenoids. Thus, if we bad a helix 6 inches in diameter and 3 
feet long with an aperture of 1 inch diameter in the centre^ a 
rough calculation shows that, with a battery of 860 large Bun* 
sen cells, the magnetic field in the interior would only be 15,000 
or 20,000 when the coils were arranged for the best effect. We 
might obtain a field of greater intensity by means of electro** 
magnets, and one which might be sufiScieut for nickel ; but wa 
cannot be certain of its amount, as I know of no measurement 
of the field produced in this way. But our principal hope lies 
in heating some body and then subjecting it to a very inieme 
magnetixing«foroe ; for I have recently found, and will show pre» 
sently, that the maximum of magnetiMtUum of nickel and iron de^ 
ereaeee a» the temperature rises, at least for the two temperatures 
QP G. and 22QP C. I am aware that iron and nickel have been 
proved to retain their magnetic properties at high temperatures^ 
but whether they were in a field of sufficirat intensity at the time 
cannot be determined. The experiment is at least worth trying 
by some one who has a magnet of great power, and who will 
take the trouble to measure the magnetic field of the magnet at 
the point where the heated nickel is placed. This could best be 
done by a small coil of wire, as used by Verdet. 

But even if it should be proved that S3 does not attain a maxi^ 
mum, but only % it could still be explained bv Faraday's theory ; 
for we should simply have to suppose that the magnetic indnci- 
tion 93 was composed of two parts— the first part, 4f!r% being 
due to the magnetic atoms alone, and the second, «^, to those 
lines of force which traversed the ether between the atoms. To 
determine whether either of these quantities has a maximum 
valae can probably never be done by experiment; we may be 
able to approach the point very nearly, but can never arrive at 
it, seeing that we should need an infinite magnetinng-foroe to 
do so. Hence its existence and magnitude must always be in- 
ferred from the experiments by some such process as was used 

• Sec Maxwell's 'Treatise on Electricity and Magnetism,' art. 844.^ 
J. 0. M. 

Digitized by VjOOQ IC 

821 Mr. H. A. Rowland on the Magnetic Permeabilitjf 

in my first paper, where the curve of permeability was continued 
beyond the point to which the experiments were carried* 
Neither does experiment up to the present time furnish any due 
as to whether it is S or 3 which attains a maximum. 

As the matter is in this undecided state, I shall hereafter, in 
most cases calculate both 3 and te as well as 93 and /t, as I am 
willing to admit that 3 may have a physical significance as well 
as S, even on Faraday's theory. 

There is a difficulty in obtaining a good series of experiments 
on nickel and cobalt which does not exist in the case of iron. 
It is principally owing to the great change in magnetic permea« 
bilitv of these 'substances hy heat, and also to their small per* 
meability. To obtain sufficient magnetizing-force to trace out 
the curve of permeability to a reasonable distance, we reauire at 
least two layers of wire on the rings, and have to send tnrough 
that wire a very strong current. In this way great heat is de% 
veloped ; and on account of there being two lasers of wire it 
eannot escape ; and the ring being thus heated, its permeability 
is changed. So much is this the case, that when the rings are 
in the air, and the strongest current circulating, the silk is soon 
burned off the wire; and to obviate this I have in these experi* 
xnents always immersed the rings in some non-conducting liquid, 
such as alcohol for low temperatures and melted paiuffin for 
high temperatures, the rings being suspended midway in the 
liquid to allow free circulation. But I have now reason to sus- 
pect the efficacy of this arrangement, especially in the case of the 
paraffin. The experiments described in this paper were made at 
such odd times as I could command, and the first ones were not 
thoroughly discussed until the series was almost completed; 
hence I have not been so careful to guard against this error as 
I shall be in the future. This can be done in the following 
manner — ^namely, by letting the current pass through the ring 
ibr only a short time.'. 'But there is a difficulty in this method, 
because if the current ^s stopped the battery will recruit, and 
the moment it is joined to the ring a large and rapidly decreas- 
ing current will pfss which it is impossible to measure accu- 
rately. 1 have, however, devised the following method, which 
I will apply in future experiments. It is to introduce into the 
circuit between the tangent-galvanometer and the ring a cur- 
rent-changer, by which the current can be switched off from the 
ring into another wire of the same resistance, so that the current 
from the battery shall always be constant. Just before making 
an observation the current is turned back into the ring, a read- 
ing is taken of the tangent-galvanometer by an assistant, and 
immediately afterward the current is reversed and the reading 
taken for the induced cuiTent ; the tangent-galvanometer is then 

Digitized by V:»OOQ IC 

and Maximum of Magnetism of Nickel and Cobali. 825 

again read with the needle on the other side of the zero-point. 
The pressure of outside duties at present precludes me from 
putting this in practice. But the results which I have obtainedi 
though probably influenced in the higher magnetizing-forces by 
this heatings are still so novel that they must possess value not* 
withstanding this defect ; for they contain the only experiments 
yet made on the permeability of cobalt at ordinary temperatures^ 
and of iron^ nickel, and cobalt at high temperatures. 

The rings of nickel and cobalt which I have used in the expe- 
riments of this paper were all turned from buttons of metal ob- 
taiued by fusing under glass in a French crucible^ it having 
been found that a Hessian crucible was very much attacked by 
the metal. The cracibles were in the fire three or four hours, 
and when taken out were very soft from the intense heat. As 
soon as taken out, the outside of the crucible was wet with water, 
so as to cool the metal rapidly and prevent crystallization; but 
even 'then the cooling inside went on very slowly. As the phy- 
sical and chemical properties of these metals exercise great in- 
fluence on their magnetic properties, I will give them briefly. A 
piece of nickel before melting was dissolved in HCl ; it gave no 
precipitate with H' S, and there were no indications of either 
iron or cobalt. A solution of the cobalt gave no precipitate 
with H' S, but contained small traces of iron and nickel. After 
melting the metals no tests have been made up to the present 
time ; but it is to be expected that the metals absorbed some 
impurities from the crucibles. They probably did not contain 
any carbon. One button of each metal was obtained, from each 
of which two rings were turned. The cobalt was quite hard, 
but turned well in the lathe, long shavings of metal coming off 
and leaving the metal beautifully polished. The metal was 
slightly mdleable, but finally broke with a fine granular frac- 
ture. The rings when made were slightly sonorous when struck ; 
and the colour was of a brilliant white slightly inclined to steel- 
colour, but a little more red than steel. The nickel was about 
as hard as wrought iron, and was tough and difficult to turn in 
the lathe, a constant application of oil being necessary, and the 
turned surface was left very rough ; the metal was quite mal- 
leable, but would become hard, and finally fly apart when 
pounded down thin if not annealed. When the rings were 
struck, they gave a dead sound as if made of copper. In both 
cases the specific gravity was considerably higher than that gene- 
rally given for cast metal ; but it may be that the metal to which* 
they refer contained carbon, in which case it would be more 
easuy melted. There is great liability to error in taking the 
specific gravity of these metals, because they contract so much 
on cooling, and imless this is carried on rapidly crystals may 

Digitized by VjOOQ IC 

826 Mr. H* A. Rowland on {h$ Magnetic Permeabilitjf 

(onh, between which^ as the metal contracts, vacant spaces may 
be left. As the specific grarity of my rings approaches to that 
of the pure metals precipitated by hydrogeni I consider it 
erideuce of their purity. The dimensions of the rings and their 
other constants are giren below s*^ 


Weight tf» 
vacKO, in 

water at 


Mean dia- 
meter, in 

Nickel. No. I 






Nickel. No. II 

Cobalt, No. I 

Cobalt, No. II 


in centi- 

Number of 

coils of wire 

on ring. 

Coils per 
metre of 

Area of 
section, in 
square cen- 

Nickel, No. I 

Nickel, No. U. 


Cobalt, No. IL 










Up to the present time only the rings whose dimensions are 
given have b^n used. 

The following Tables from the nickel ring No. I. leave little 
to be desired in point of regularity^ and confirm the fact proved 
in my first paper^ that the laws dedaced for iron hold uko for 
nickel, and also confirm the valne given in mv other paper for 
the maximum value of magnetisation of nickel. But the moat 
important thing that they show is the efiect of heat upon the 
magnetisation of nickel ; and Table III. contains the first nume* 
ricid data yet obtained on the efifect of heat on the magnetic pro- 
perties of any substance. 

As all the rings were wound with two layers of wire, a slight 
correction was made in the value of 99 for the lines of inductive 
force which passed through the air and not through the metal. 
In all the experiments of this paper greater care was used to 
obtain T than in the first paper. Each value of p, S, and T is 
the mean of four readings. In all the Tables I have left the 
order of the observations the same as that in which they were 
made, and have also put down the date, as I now have reason to 
suspect that the leaving of a ring in the magnetised state in 
which it is after an experiment will in time affect its properties 
to a small extent. Let me here remark that the time necessary 
to simply make the observations is only a very small fraction of 
that required to prepare for them and to afterwards discuss 

Digitized by VjOOQ IC 

Mi Mmnmufn ofMagnetkm qfNiekel and Cobalt 897 

them. And this^ with the small amount of time at my disposal, 
will account for Uie late day at which I publish my results. 

The following is the notation used^ the measurements being 
made on that absolute system in which the metre, gramme^ and 
second are the fundamental units* 

tis the magnetising-force noting on the metal, 
is the magnetic induction within the metal (see Maxwell's 
'Treatise on Electricity and Magnetism/ arts. 400, 692, 
imd 604). 

/i is the magnetic permeability of the metal = -^ =49r/c+l» 

T is the portion of S which disappears when the current is 

F is the portion of 9 which remains when the current is 


3 is the intensity of magnetisation ss y * 



K is Neumann's coefficient of induced magnetization ss ^ 

Table L 

Cast Nickel, fiormftl, ftt 15^ C. 

Experiments made November 29, 1878. 


«. (Sb. 




P. 1 3. 











675 62-6 








2169 80-8 


- -2 








7461 166 1 










11140 198-6 










15410 217*8 

217 5 

- -8 








17100 220-6 









20180 222-8 


- -3 








25170 218-2 










28^40 204-7 


- -4 








82460 187*8 








1 07 


84680 177 3 










37340 162-8 








: -15 


40860 1481 










46470 111-9 










62690, 725 









66680 63-4 


- -6 3068026000 


417 417 




^=«Bri„ps3M:I!59). ,=iy6rin(3+»;g+'<">). 

Digitized by VjOOQ IC 

828 Mr. H. A. Rowland on the Magnetic Permeability 

Table II. 

Cast Nickel, magnetic, at 12^ C. 

Experiments piade December 6, 1878. 












































































Table III. 

Cast Nickel, magnetic, at 220^ C. 

Experiments made December 6, 1873. 




























24 96 


























































lents mi 

ide Decei 

tnber 10, 
















, , 

















In Table I. are given the results for nickel at about 16^ C, 
together with the values of fi and k calculated from the formulae 
given below the Table. We see that the coincidence is almost 
perfect in both cases, which thus shows that the formula which 
we have hitherto used for X and fi can also be applied to it, at 
least within the limit of experiments hitherto made, although it 
must at last depart from one or the other of the curves. The 

Digitized by VjOOQ IC 

atul Maximum of Magnetism of Nickel and Cobalt. 329 

greatest relative error is seen to be in the first line^ where S^ is 
small : this does not indicate any departure from the curve^ but 
is only due to the too small deflections of the galvanometer; and 
the error indicates that of only a small fraction of a division at 
the galvanometer, 

In the calculation of ft and k a method was used which may 
be of use to othera in like circumstances^ who have to calculate 
a large number of values of one variable from a function which 
cannot be solved with reference to that variable, but can be 
solved with reference to the other. Thus we have 

^=^8m(^ ^ y (1) 

which can be solved with reference to S3 but not to fii for we 
have / \ 

^ g5=D8in->(gj-J/A-7r (2) 

Suppose we have values of 93, and wish to find the correspond- 
ing values of /t. We first calculate a few values of 93 from (2) 
so that we can plot the curve connecting 93 and fi. We then 
from the plot select a value of fi which we shall call fi\ as near 
the proper value as possible, and calculate the corresponding 
value of 93, which we shall call 93^ Our problem then is, know- 
ing 93' and fJ, to find the value of a corresponding to © when 
this is nearly equal to 93^ Let 93 receive a small increment 
A93', so that 93 = 93' + A93'; then we have, from Taylor's theorem, 
since /t=^(93'+ A93') and /t'=^(93'), 

Remembering that the constants in (1) refer to degrees of arc 
and not to the absolute value of the arc, we have 

/t=/+ Yj 5 -f &c., 

which is in the most convenient form for calculation by means 
of Barlow's Tables of squares, &c., and is very easy to apply, 
being far easier than the method of successive approjumation. 

On comparing the magnetic curve Table II. with the normal 
curve Table I., we see that the magnetic curve of nickel bears 
the same relation to the normal curve as we have already found 
for iron; that is, the magnetic curve falls below the normal 
curve for all points before the vertex, but afterwards the two 

Hence we see that at ordinary temperatures the magnetic pro* 

Digitized by VjOOQ IC 

890 Mn H« A. Bowkmd on the Maffneiic PermMobUUy 

perties of nickel are a complete reproductioa of those of iron on 
a smaller Scale. But wheb we come to study the effect of tempe« 
rature we shall find a remarkable difference^ and shall find nickel 
to be maoh more susceptible than iron to the influence of heat« 

In Table III. we have experiments on the permeability of 
ilickel at a high temperature^ the ring being maintained at 
230° C. by being placed in a bath of melted parafBn i in this 
bath the silk covering of the wire remained quite perfect, but 
after niany hours became somewhat weak. After completing 
the experiments on this and the cobalt rings^ on uuwindbg 
some of them I found the outside layer quite perfect ; but^ espe- 
cially in the smallest ring, the silk on the inside layer was much 
weaker, although the insulation was still perfect when the wire 
was in place, I can only account for this by the electric current 
generating heat in the wire, which was unable to pass outward 
DecauSe of the outside layer and also of the pieces of paper 
which were used to separate the layers of wire ; hence the ring 
at high magnetizing-powers must have been at a somewhat 
higher temperature than the bath, to an amount which it is im- 

Eossible to estimate. It is probable that it was not verv great, 
owever; for at this high temperature continued for nours it 
requires but little increase of heat to finally destroy the silk. 
We can, however, tell the direction of the error. 

We see, on comparing Tables I. and II. with Table III., the 
great effect of heat on the magnetic properties of nickel. We 
see that for low magnetization the permeability is greatly m- 
creased, which is just opposite to what we might expect ; but on 
plotting the curve we also notice the equally remarkable fact^ 

1. Carve at 15^ C. 

9. Curve at M0« C. 

that the maximum of magnetization is decreased (rom 95=63400 

.or 3=4940 to ©=49000 or 3 =8800. This curious result is 

shown ii; the annexed figure, where we see that for low magne« 

Digitized by VjOOQ IC 

andMammum ofMagnetiitn of Nickel and Cobalt 881 

tizing-forcJes /l^ is increased to about three or four times its value 
at 15^ Cy and the maximum value of /t is increased from 222 
to 815. When S has a value of 82,000> /« is not affected by 
this change of temperature^ seeing that the two curves coincide; 
but above that point /a is less at 220^ C. than at IS"" C. In 
other words^ if nkkel is heated from 15° C. to 220P C, the mag" 
netization of nickel mil increase if the magnetizing-force is small, 
but will decrease if it is large. It is impossible to say at present 
whether increase of temperature above 220° will always produce 
effects in the same direction as below it or not. 

These remarkable effects of heat, it seems to me, will, when 
followed out, lead to the discovery of most important connexions 
between heat and magnetism, and will finally result in giving 
us much more light upon the nature of heat and magnetism, 
and that equally important question of what is a molecule. To 
accomplish this we must obtain a series of curves for the same 
ring between as wide limits of temperature as possible. We 
must then plot our results in a suitable manner j and from the 
curves thus formed we can find what would probably happen if 
the temperature were lowered to the absolute xerO| or were in- 
creased to the point at which nickel is said to lose its magnetism. 
In such inquiries as these the graphical method is almost inva« 
luablci and little can be expected without its aid* 

In applying the formula to this curve, we do not find so good 
an agreement as at the lower temperature. I do not consider 
this conclusive that the formula will not agree with observa^ 
tion at this temperature; fot 1 have noticed that the curves of 
different specimens of iron and nickel seem to vary within a 
minute range, not only in their elements but also in their form. 
This might perhaps be accounted for by some small want of ho- 
mogeneltv, as in the case of burning in iron and nickel ; but at 
present tne fact remains without an explanation. But the 
amount of the deviation is' in all cases very small when all the 
precautions are taken to insure good results. The nature of the 
deviation is in this case as follows : when the constants in the 
formula are chosen to agree with the observed curve at the ver- 
tex and at the two ends, then the observed curve falls slightly 
below the curve of the formula at nearly all other points. In a 
curve plotted about 5 inches high and broad, the greatest dis- 
tance between the two curves is only about ^^ of an inch, and 
could be much reduced by changing the constants. For the 
benefit of those who wish to study this deviation, I have calcu- 
lated the following values, which will give the curve touching 
the vertex and the two ends of the observed curve of Table III. 
They are to be used by plotting in connexion with that Table. 

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832 Mr. H. A. Rowland on the Magnetic Permeability 
















X have not as yet obtained a complete curve of iron at a high 
temperature ; but as far as I have tried^ it does not seem to be 
affected much^ at least for high magnetizing-powers. I have, 
however^ found that the maximum of magnetization of iron 
decreases about 2 per cent, by a rise of temperature from 15^ C. 
to 222*^ C, virhile that of nickel decreases 22*7 per cent. 

The experiments which I have made with cobalt do not seem 
to be so satisfactory as those made with nickel and iron. There 
are some things about them which I cannot yet explain ; but as 
they are the only exact experiments yet made on cobalt, they 
must possess at least a transient value. The diflSculties of getting 
a good cobalt-curve are manifold^ and are due to the following 
properties — (1) its small permeability^ (2) its sensitiveness to 
temperature, and (8) its property of having its permeability 
increased by rise of temperature at all magnetizing-powers within 
the limits of experiment. The following are the results with 

Table IV. 

Cast Cobalt, normal, at 5^ C. 

Experiments made November 27, 1878. 













































































26769 '141-6 








30580 1 139-3 









































































Digitized by VjOOQ IC 

and Maxhrnan of Magnetism of Nickel and Cobalt. S33 

Table V. 

Cast Cobalt, magnetic, at — 5°C, 

Experiments made November 28, 1878. 




















































54 84 





Table VI. 

Cast Cobalt, magnetic, at 280^ C. 

Experiments made February 8, 1874. 















25 67 




















































































From Table IV. we see that at ordinary temperatures cobalt 
does not offer any exception to the general law for the other 
magnetic metals — ^that as the magnetization increases, the mag* 
netic permeability first increases and then decreases. We also 
see that the results satisfy to a considerable degree of accuracy 
the equation which I have used for the other magnetic metals. 
The departure from the equation is of exactly the nature that can 
be accounted for in either of two ways — either by the heating 
of the ring by the current for the higher magnetizing-forees, 
or by some want of homogeneity in the ring. According to 
the first explanation, the maximum of magnetization at Cr C. 
will be somewhat lower than the curve indicates; but by the 
second it must be higher. I, however, incline to the first, that 
it is due to heating, for two reasons : first, it is sufficient ; and 
secondly, the smaller cobalt ring gives about the same maximum 

Digitized by VjOOQ IC 

334 Mr. H. A. Rowland on the Magneiie PermeabiUty 

as this. Hence we may take as the provisional value of the 
maximuni of magnetization of cobalt in ronnd numbers 3=8000, 
or 33=100,000. 

We also see from Table IV. tbat^ at least in this case, the per- 
meability 0^ cobalt is less than that of nickel, though we could 
without doubt select specimens of cobalt which should have this 
quality higher than a given specimen of nickel. The formula 
at the foot of the Table also shows, by the increased value of 
the coefficient of k in the right-hand member, that the diameter 
of the curve is much less inclined to the axis of 3> in this case 
than in the case of nickel or iron. In this respect the three 
metals at present stand in the following order^-'-cobalt, nickel, 
iron. This is the inverse order also of their permeability ; but 
at present I have not found any law connecting these two, and 
doubt if any exact relation exists, though as a general rule the 
value of the constant is greater in those curves where the per- 
meability is least. 

In a short abstract in the 'Telegraphic Journal,' April 1, 
1874^ of a memoir by M. Stefan, it is stated " that the resist- 
ance of iron and nickel to magnetisation is at first very great, 
then decreases to a minimum value, which is reached when the 
induced magnetic moment is become a third of its maximum.'^ 
This will do for a very rough approximation, but is not accu- 
rate, as will be seen from the following Table of this ratio from 
my own experiments >^ 

Experimenttpubliihed ia August 187S. 


Tables I. 

and. II. 

Table III. 


Table IV. 

Table V. 

Table VI. 

Table VII. 







Experiments of present paper. 

Tables I. and IT. 

Table III. 

Tables IV. and V. 




The average of these is, if we include Bessemer steel with the 
iron, as it is more iron than steel :^— 

Iron,g^5 = ^5 Nickel, g:jyl Cobalt,^. 

Digitized by VjOOQ IC 

and Maximum of Magnetism qf Nickel and Cobali, 835 

Hence the place of greatest permeability will vary with the kind 
of metal. From these, however, we can approximate to the 
value of b in the formula ; for we have 

. J . 27,000 . TM- 1 1 . 11,000 
for Iron, b =* — ^ — j for Nickel, b = — 75 — ] 
P P 

for Cobalt, 6=^26,000. 

In Table V. we have the results for cobalt in the magnetie 
state. We here find the same effect of magnetisation as we havt 
before found for iron and nickel. 

In Table VI. we have results for cobalt at a high temperatortt, 
and see how greatly the permeability is increased by rise of tem« 
perature, this being for the vertex of the curve about 70 per 
eept But on plotting the curve I was much surprised to find 
an entire departure from that regularity which 1 bad befom 
found in all curves taken from iron and nickel when the metal 
was homogeneous. At present I am notable to aoeount for this; 
and especially for the fact that one of the measurements of 
higher than Uiat which we h%ve taken for the maximum of mag« 
netisatioB, at, however, a lower temperature. The curve is 
exactly of the same nature as that which I have before found 
for a piece of nickel which had been rendered unhomogeneous l^ 
heating red-hot, and thus burning the outside. ^0 smaller 
cobalt ring gives a curve of the same general shape as this, but 
has the top more rounded. I will not attempt without fresh 
experiments to explain these facts, but will simply offer the'foU 
lowing explanations, some one of which may be true* First, it may 
be due to want of homogeneity in the ring ; but it seems as if 
this should have affected the curve of Table IV. more. Secondly, 
it may be at least partly due to the rise in temperature of the 
ring at high magnetizing-powers ; and indeed we know that this 
must be greater in paraffin than in alcohol for several reasons 1 
there is about twice as much heat generated in copper wire at 
080^ G. as at 0^ with the same eurrent ; and this heat will not 
be conducted off so fast in paraffin as in alcohol, on account of 
its circulating with less freedom ; it probably has less specific 
heat also. Thirdly, it may be due to some property of cobalt, 
by which its permeability and maximum of magneti8ati(m are 
increased by heat and the curve changed. 

The experiments made with the small ring confirm those 
made with the large one as far as they go j but as it was so 
small, they do not possess the weight due to those with the 
larger one. But, curious as it may seem, although they were 
turned from the same button side by side, yet the permeability 
of the larger is about 45 per cent, greater than that of the 
smaller. I have satisfied myself that this is due to no error in 

Digitized by VjOOQ IC 

336 Mr. H. A. Rowland on the Magnetic Permeability 

experiment, but illustrates what extremely small changes wiU 
afiect the permeability of any metal. 

We have now completed the discussion of the results as far 
as they refer to the magnetic permeability, leaving the discus- 
sion of the temporary and permanent or residual magnetism to 
the future, although these latter, when discussed, will throw 
great light upon the nature of the coercive force in steel and 
other metals. The whole subject seems to be a most fruitful 
one, and I can hardly understand why it has been so much neg- 
lected. It may have been that a simple method of experiment 
was not known ; but if so, I believe that my method will be 
found both accurate and simple, though it may be modified to 
suit the circumstances. Professor Maxwell has suggested to me 
that it would be better to use rods of great length than rings, 
because that in a ring we can never determine its actual mag* 
tietization, but must always content ourselves with measuring 
the change on reversing or breaking the current. This is an 
important remark, because it has been found by MM. Marianini 
and Jamin, and was noticed independently by myself in some 
unpublished experiments of 1870, that a bar of steel which has 
lain for some time magnetized in one direction will afterwards 
be more easily magnetized in that direction than in the other. 
This fact could not have been discovered from a ring; and in- 
deed if a ring got a one-sided magnetism in any way we might 
never know it, and yet it might affect our results, as indeed we 
have already seen in the case of the magnetic curve. But at the 
tame time 1 think that greater errors would result from using 
long bars. I have tried one of iron 8 feet long and ^ inch dia- 
meter ; and the effect of the length was still apparent, although 
the ratio of length to diameter was 144. To get exact results it 
would probably have to be several times this for the given spe- 
cimen of iron, and would of course have to be greater for a piece 
of iron having greater permeability. This rod must be turned 
and must be homogeneous throughout — conditions which it 
Would be very difficult to fulfil, and which would be impossible 
in the case of nickel and cobalt. We might indeed use ellipsoids 
of very elongated form ; and this would probably be the best of 
all, as the mathematical theory of this case is complete, and it is 
one of the few where the magnetization is uniform, and which 
consequently will still hold, although the permeability may vary 
with the amount of magnetization. This form will, of course, 
satisfy Professor Maxwell's objection. 

The method of the ring introduces a small error which has 
never yet been considered, and which will affect Dr. Stoletow's 
results as well as mine. The number of lines of induction pass- 
ing across the circular section of a ring-magnet we have seen 

Digitized by VjOOQ IC 

and Maximum of Magnetism of Nickel and Cobalt. 837 
to be 


in which a is the mean radius of the ring^ B. the radius of the 
section, v! the number of coils in the helix, and f the intensity 
of the current. Now in integrating this before, I assumed that 
lA was a constant throughout the section of the ring : now we 
have found that /l& is a function of the magnetization, and hence 
a function of the magnetizing-force ; but the latter varies in dif- 
ferent parts of the section, and hence ia must vary. But the 
correction will be small, because the average value will be nearly 
the same as if it were a constant. We may estimate the correction 
in the following manner. Let /^ and <p be the values of those 
quantities at any point in the section of the ring, [J and «^' the 
values at the centre of the section, and ft; and i^^ the observed 
values. Then, by Taylor's theorem^ 

But & = and «fi'= — , and so we have 

But in my Tables I have already calculated • 


'*' 7 — iB? \' 

TR'^'O+i^ + fec) 

and as |l^ is very nearly equal to fif^ and ^^ to «^', we have ap- 

which will give the value of iJ corresponding to Q' and <^'. 
Hence the correct values of the quantities will be fJ, fi/, and 

The quantities -J^ and j^ can be obtained either by mea- 
Phil. Mag. S. 4. Vol.'48. No. 819. Nov. 1874. Z 

Digitized by VjOOQ IC 

388 Mr. H. A. Rowland an the Magneiie PemetAilihf 
suring a plot of the curve^ or from the empirical equation 

when we know the yalues of the constants. In this case 

in which 

C=57'8D + (^ + ft)\/B«-/i,«. 

In all these the upper signs are to be taken for all values of J^, 

less than ^ , and the lower signs for greater valnesi 


On applying these formulae to the observations, I have found 

that the corrections will in no way influence my conclusions, 

being always very small ; but at the same time the calculation 

shows that it would be well to diminish the ratio — as much a^ 


possible. In all my rings this ratio did not depart very much 
from ^^ ; but I would advise future experimenters lo take it at 

least as small as ^ : the amount of corirection will be very 

nearly proportional to the square of -• 


The following laws have been established entirely by my own 
experiments, though in that part of (2) which nrfers to iron I 
have been anticipated in the publication by Dr. Stoletow (Phih 
Mag. Jan. 1873). When any measurements are given^they are 
on the metre, gramme, second system. 

(1) Iron, nickel, and cobalt, in their Inagnetie properties at 
ordinary temperatures^ differ from each other only m the quan- 
tity of those properties and not in the quality. 

(2) As the magnetizing-force is increased from upwards, 
the resistance of iron, nickel, and cobalt to magnetisation de- 
creases until a minimum is reached, and after that increases 
indefinitely. This minimum is reached when the metal has 
attained a magnetisation of from '24 to *38 of the mazimuin of 
magnetisation of the given metal. 

Digitized by VjOOQ IC 

md Maximum of Magnetism ofNiekel and CobaU. 83& 

(3) The curve showing the relation between the magnetiza- 
tion and the magnetic permeability^ or Neumann's coefficient^ is 
of snch a form that a diameter can be drawn bisecting chords 
parallel to the axis of $^ and is of very nearly the form given by 
the equation 

/A=B am ^- f 

where B, h^ and D are constants^ /a is the ratio of the magneti- 
zation to the magnetiun^-force in an infinitely long bari and $ 
is the amount ofmagnetlzation. 

(4) If a metal is permanently magnetized^ its resistance to 
change of magnetism is greater tor low magnetizing-powers than 
when it is in the normal state^ but is the same for high magne- 
tizing-powers. This applies to the permanent state finally 
attained after several reversals of magnetizing-force; but if we 
strongly magnetize a bar in one direction and then afterwards 
apply a weak magnetizing-force in the opposite direction^ the 
change of magnetization will be very great. 

(6) The resistances of nickel and cobalt to magnetization vary 
witA the temperature ; but whether it is increased or not in 
nickel depends upon the amount of magnetization : for a mode- 
rate amount of magnetization it decreases with rise of tempera- 
ture very rapidly ; but if the magnetization is high the resistance 
is increased. In cobalt it apparently always decreased^ whatever 
the magnetization. The resistance of iron to magnetization is 
not much affected by the temperature. 

(6) The resistance of any specimen of metal to magnetization 
depends on the kind of metal^ on the quality of the metal, on the 
amount of permanent magnetization, on the temperature, and on 
the total amount of magnetization, and, in at least iron and 
nickel, decreases very much on careful annealing. The maxi- 
mum of magnetization depends on the kind of metal and on the 

(7) Iron, nickel, and cobalt all probably have a maximum of 
magnetization, though its existence can never be entirely estab- 
lished by experiment, and must always be a matter of inference; 
but if one exists, the values must be nearly as follows at ordinary 
temperatures. Iron when 33=175,000 or when 3=139,000; 
nickel when 95=63,400 or when 3=4940; cobalt when »as 
100,000(?) or when 3=8000 (?). 

(8) The maximum of magnetization of iron and nickel de- 
creases with rise of temperature, at least between 10^ G. and 
220® C, the first very slowly and the second very rapidly. At 
220® C. the maximum for iron is when 33=172,000 and 
3=13,600, and for nickel when 33=49,000 and 3=8800. 


Digitized by VjOOQ IC 

340 Dr. A. Schuster's Experiments on Electrical Vibrations. 

The laws which govern temporary and residual magnetism, 
except so far as they have been hitherto giveui I leave for the 
future, when I shall have time for further experiment on the 
subject to develop some points which are not yet quite clear. 

Troy, New York, U.S.A., 
April 1874. 

Errata m Vol. 46. 

Page 144, equation (2), first term of second member, /of ( VRR'+f') 
rearf (VRR'-j'). 

— 144, second line of note, /or vol. iv. p. 669 read vol. iii. p. 77. 

— 148, line 24 from top,/or 14'61 read 14-16. 

— 156, line 7 from bottom, for ^ read-^ . 

4ir oir 

XL VII. Experiments on Electrical Vibrations. 
By Ahthur Schuster, Ph.D.* 

I. Introductory. 

IN a previous paperf I described a curious effect of elec- 
trical vibrations on the galvanometer-needle. The effect 
could only be explained by assuming a different conductivity in 
opposite directions. This unilateral conductivity, as it was called, 
is never a stable phenomenon, but generally disappears very soon 
by suitable manipulations. The condition of the circuit in which 
no unilateral conductivity appeared was called the normal con- 
dition of the circuit. The experiments which are described in 
this paper were all made when the wire was in its normal con- 
dition, and when, therefore, a magnet rotating in a coil of wires 
connected with the galvanometer produced no effect on the gal- 

It occurred to me to send a permanent current through the 
galvanometer, in addition to the electrical vibrations induced by 
the rotating magnet. From previously known facts it would 
be expected that the electrical vibrations would counterbalance 
each other independently of any permanent current going through, 
the galvanometer, and therefore that the permanent current 
would produce the same deflection whether the magnet is rota- 
ting or not. This, however, is not the case, but the rotation of 
the magnet always increases the deflection of the permanent 

II. Description of Experiments. 

The instruments us«d were the same as those described in my 

* Communicated by the Anther, 
t Phil. Mag. vol. xWiii. p. 251 . 

Digitized by VjOOQ IC 

Dr. A. Schuster's Experiments an Electrical Vibratwiia. 341 

paper ''On Unilateral Conductivity, 
shown by the following diagram : — 


The arrangement is 



6 is a galvanometer^ the resistance of which was 2477 mer* 
cury units; I is the induction-coil within which the rotating 
magnet is placed ; C is a commutator ; E a DanielFs cell. 

It is seen by the diagram that only a small part of the perma- 
nent current passed through the galvanometer^ as the resistance 
of the wire a b was very small compared with the resistance of the 
galvanometer. The experiments were conducted in the following 
way: — 

1. The rotating magnet was first left fixed in a certain posi- 
tion^ and the first deflection produced by E was measured. It 
was found that this deflection was the same in whatever position 
the magnet was fixed ; and we may therefore conclude that the 
reaction on the current of the magnetization produced by the 
current was too small to be observed. The magnet was set in 
rotation now after contact had been broken at c; and when the 
needle in 6 had come to rest again^ which was done in a very 
short time (the galvanometer having a strong logarithmic decre- 
ment)^ the first defiection produced by E was measured. It 
was found that the first deflection was always larger when the 
magnet rotated. The following is a series of observations which 
I take at random out of my laboratory book. 

First deflection, in 

MAMiAt flniftt 1 





»» «VW»«M.g 


» M****** • ' • • 



„ rotttinff 


Mean for mftsnet rotating 


Maah for inaffTiet auiet 



2. By altering the resistance of the wire ab,l could alter the 
strength of the permanent current without sensibly afiecting the 

Digitized by VjOOQ IC 

843 Dr. A, Schuiter's Esfperiments on Bleetrieal VihraHani, 

itreogth of the electrical vibrations. The following Table shows 
that the difference in the first deflection whieh is observed ac« 
cording as the magnet rotates or not^ is sensibly proportional to 
the strength of the permanent current. The first column gives 
the first deflection observed when the magnet was not rotating; 
the second column gives the difference in the deflection when 
the magnet rotated ; and the third column gives the ratio of the 
numbers given in the first two columns. The numbers given in 
the third column are as nearly constant as could be expected. 
The chief error of observation is caused by the difficulty of keeping 
the rotation of the magnet constant for a sufficient lengtn <n 

First deflection 
(magnet quiet). 

first deflection. 










8. By altering the resistance of the wire ft 6 1 a and that of the 
wire a ft at the same time^ we can alter the strength of the elec- 
trical vibrations^ without altering the strength of the permanent 
current produced by the electromotive force E. The following 
Table shows that the effect decreases very rapidly as the strenjgth 
of the electrical vibrations decreases. The first column gives 
the resistance R introduced into the circuit ft 6 la; the second 
column gives the ratio n of the difference in the first deflection 
observed according as the magnet rotated or did not rotate^ to 
the first deflection observed when the magnet was quiet. 







4. Another series of experiments was made with a galvano- 
meter the resistance of which was only a few units. The first 
deflection produced by the electromotive force in E was about 
the same as had been observed with the other galvanometer^ 
because^ although the delicacy of the galvanometer was much 
smaller^ a greater part of the current passed through the galva- 
nometer^ the resistance ft I G a being now a great deal smaUor 

Digitized by VjOOQ IC 

Dr. A, Bcbottar^i B^g^erimef^ on Ekctrical Vibrationif 848 

than it had been before. The electrical vibrations were^ of 
eenrse^ much stronger now ; but each of them taken separately 
woold have prodneed about the same deflection of the galvano« 
meter. The galvanometer had no damping-arrangement. The 
needle^ therefi^e, never was entirely at rest; and^ accordinglyi 
the first deflection could not be measured. Five successive elon- 
gations were taken, and the position of rest calculated from these 
elongations. As the observations necessarily extended over a 
much greater length of time^ they were less accurate. The result 
is given in the following Table. The first column gives the first 
deflection observed when the magnet was not rotating; the 
second column gives the ratio n of the difference in the first de- 
flections to the first deflection observed when the magnet was not 

First deflectloa 

obsenred whea 


nagoet was quiet 











"^Titb the exception of the last observation but one^ therefore| 
tb^ effect decreases more rapidly than the current. 

III. Discussion of Experiments. 

We shall have to discuss now whether these experiments can 
be explained in any simple way or by any known causes. At 
first sight three possible explanations suggest themselves; and 
we have to see whether one of them^ or several of them taken 
together account satisfactorily for the different experimentSi 
before we assume that we have to do with a new set of pheno- 
mena. We might assume : — 

1. That the electrical vibrations affect the electromotive force 
of the battery; 

2. That the electrical vibrations affect the magnetism of the 
galvanometer-needle so as to increase the deflection of the per- 
manent current; 

8* That the permanent current affects the magnetism of the 
rotating magnet in such a way as to increase its momentum 
prbile the current in one direction is passing, and to decrease it 
while the current in the opposite direction is passing. The two 
opposite currents induced by the rpagnei would therefore not 
counterbalance each other^ but one would be stronger than the 

Digitized by VjOOQ IC 

344 Dr. A. Schuster's Eaperiments an Electrical Vibn^umi^. 

We shall discuss these explanations in their order. 

1. The explanation given under 1 does not at first sight seem 
unlikely. We do not know how these electrical vibrations affect 
the polarization of the battery. They might decrease it for all 
we know^ and thereby cause the phenomena which we have 
observed. In order to settle this question experimentally, the 
apparatus was disposed as indicated by the following diagram : -> 




The inductor I was taken out of the galvanometer circuit and 
put into the circuit of the battery. The strength of the elec- 
trical vibrations passing through the battery was therefore now 
about 1700 times as great as before. We should expect the 
effect to be much stronger now if it were caused by any effect 
of the electrical vibrations on the battery. As, however, the 
deflection was exactly the same now whether the magnet rotated 
or not, we may safely conclude that this explanation is not the 
correct one. I do not say it. is proved by these experiments 
that electrical vibrations do not affect the polarisation of 
the battery. On the contrary, I think it would be important to 
make more careful experiments on the subject ; but an inspection 
of the diagram will show that a small alteration in the electromo- 
tive force would not be apparent in these experiments. All we can 
say, therefore, is, that the change in the electromotive force of 
the battery, if it exists, is not sufficiently large to affect the de- 
flection of the permanent current if the apparatus is disposed 
as indicated in the above diagrams. This, of course, is sufficient 
for our purpose. 

2. We have now to see whether the electrical vibrations can affect 
the galvanometer- needle in such a way as to produce the effect 
which was observed. No other cause than the bilateral deflec- 
tion, discovered by Poggendorff, and mentioned in my paper on 
unilateral conductivity, is known which could affect the experi- 
ments. It can be shown that the bilateral deflection is no 
stable phenomenon ; that is to say, either it does not influence 
the position of rest of the needle, or it places the needle parallel 
to the axis of the galvanometer-coil. Experiments were there- 
fore made in which, instead of taking the first deflection as a 
measure of the strength of the current, the permanent deflection 
was measured. It was found that when the needle had come to 
rest while the permanent current was passing, the position of 
rest was altered by the rotation of the magnet. 

Digitized by VjOOQ IC 

Dr. A. Schuster's Experiments on Electrical Vibrations. 845 

Additional experiments to prove the impossibility of accounting 
for the effect by bilateral deflection were made. The needle was 
deflected by permanent magnets placed near the galvanometer. 
The relative position of the galvanometer-needle to the axis of 
the coil was therefore changed ; and this was done in such a way 
that bilateral deflection, instead of increasing the deflection, 
would tend to diminish it. As, however, in this case the deflec* 
tion was just as much increased by the rotation of the magnet 
as before, I consider it proved beyond doubt that no change of 
magnetization of the galvanometer-needle can have caused the 

3. It remains for us to consider in detail what effect the per- 
manent current has on the magnetism of the rotating magnet. 

Let a c be the axis of the coil within which the magnet ro- 
tates. The wires of the coil 
are therefore parallel to bd. 
Suppose the current passes in 
the direction indicated by the 
arrow-head in that part of the 
coil which is above the plane 
of the paper. The permanent 
current would in that case in- 
crease the strength of the ro- 
tating magnet while the north 
pole moves from b to d, the 
rotation being in the direction 
of the movement of the hands 
of a watch. The magnetism, 
on the other hand, is decreased 
while the north pole moves 
from d to b. The induction will be in the direction d b while 
the magnet moves from a to c, and in the direction b d while 
it moves from c to a. The weakening and strengthening of the 
magnet, therefore, take place symmetrically with respect to the 
direction of the induction-shocks. While the induction-shock 
passes from b to d, the magnet is first strengthened and then 
weakened. While the induction-current passes from d to i, the 
magnet is first weakened and then strengthened. Such a differ- 
ence in the magnetism could not, therefore, alter the strength of 
the induction-shocks ; and they would counterbalance each other 
iust as much as before, were it not for a secondary effect which, 
indeed, tends to produce the phenomenon that has to be ex- 
plained. There will be an induction of currents in the coil due 
not to the motion of the magnet, but to its magnetization 
and demagnetization. While the north pole moves from i to c, 
the magnet is strengthened c^nd the current in 5 df weakened 

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840 Dr. A. Schuster's Bxperimenfs on Bkeirical Viira(i(m$t 

\n eonsequenoe. While the north pole moves from cto d,^e 
temporary magnetism dies away again^ and thereby strengthens 
the current in b d. The consequence of this reaction of the 
magnetisation on the eurrent is that the maximum of magneti- 
sation does not take plaoe when the north pole is at o, but only 
^fter it has passed e. Similarly the minimum does not take 

5 lace when the north pole is at a, but only after it has pitssed a. 
'he induction-shock is therefore stronger while the north pole 
of the rotating magnet moves from c to a than while it moves 
from aXoe. The two induction-shocks are not of equal strengtbj 
but the direction will have the upper hand in which the perma- 
nent current goes. A phenomenon similar to the one observed 
would therefore take place. We have therefore to settle the 

Suestion whether this effect would be sufficiently strong to pro- 
uce any visible effect. This could best be done experimentally. 
While I was engaged with these experiments I did not think 
of this retardation of the maximum of magnetism, to which 
my attention has since been drawn by Professor Kirchhoff. \ 
can therefore, unfortunatelv, offer no direct evidence on the 
subiect ; but I hope to be able to show that it is extremely un^^ 
likely, and even next to impossible, that the phenomenon is due 
to the cause just described. The strongest argument which I 
can offer regarding this point is this : — The magnetism induced 
by the permanent current must have been much weaker than 
the magnetism induced by the earth. The temporary magnetism 
induced by the earth did not, however, affect the experiments j 
and I conclude therefore that magnetism induced by the current 
did not affect the experiments. 

That the magnetic force of the current was weaker than the 
magnetic force of the earth is shown as follows : — ^The tangent 
of the deflection of the galvanometer-needle never exce^ed 
0*3. This is therefore the ratio of the magnetic force of the 
current on the galvanometer-needle to the retaining force, which, 
as the needle was astatic^ was much weaker than the earth^s 
horisontal force. The magnetic force of the current on the gal- 
vanometer-needle must have been much stronger than that on 
the rotating magnet, as the resistance of the galvanometer was 
2477 and that of the induction-coil only 30, the wires being about 
the same thickness. It follows that the magnetising force of 
the current on the rotating magnet was much weaker than the 
magnetizing force of the earth. As the induction-coil was used 
in various positions, and no effect dependent upon that position 
was ever observed, I conclude that the effect of the earth's in- 
duction was too small to be observed, and consequently that 
the permanent current could not have produced any sensible 
alteration in the magnetism of the rotating magnet. 

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Dr. A. Sebtuter^B Bsperiments on Ekotrieal Vibrations. 847 

Maay oihep observations agree witb this conclusion. When, 
for instance, the galvanometer of small resistance was employed, 
a current about eighty times stronger passed through the inaue* 
tion-eoil than when the usual galvanometer was used, It should 
be expected that if the effect were due to a magnetization of the 
magnet, it would be stronger in that case, if not eighty times, 
perhaps thirty or forty times. Yet the effect was hardly stronger 
than Dcfore, sometimes even not quite as strong. The num&» 
rical results obtained give additional evidence against the expla- 
nation which we have just discussed. 

rV. Two possible Eapphnations^ 

Aa we cannot explain the effect by anv known cause, we have 
to find another explanation, I can only account in two waya 
for the phenomenon which has to be explained; and my experi- 
ments give no due as to which of them is the correct explanationt 
The first, and perhaps the simplest assumption to be made, is 
that Ohm's law is not rigidly correct. Ohm's law says that tb^ 
resistance which a wire offers to an electric current going through 
it is independent of the strength of the current. I shall try to 
show now that my observations can be explained by assuming 
that the resistance decreases as the current increases, but that 
the deviation froih Ohm's law would be so small that it would 
not have been found out by any of the usual methods of veri- 
fying Ohm's law. Suppose the electromotive foroe of the rota- 
ting magnet to be +6 in one direction and — e in the other 
direction, and that the electromotive force sending the perma- 
nent current through the galvanometer-circuit is +2a?. If the 
permanent current and the electrical vibrations go* through the 
circuit at the same time, we have a current the electromotive 
force of which is a; + 6, counterbalancing another current the elect 
tromotive force of which is ;i?— 6. If the resistance for both cases 
is equal to r, we have as the resultant current affecting the galva- 

r r r 

We should therefore have the same effect as if only the perma- 
nent current went through the circuit. If, however, the resist- 
ance of the first current is r +{&*, we have for the whole effect 

x+e x—e 

If «&* is very small, this expression is equal to 
2x x+Sj 

7— -Is-A 

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848 Dr. A. Schuster's Experiments on Electrical Vibrations. 

If^ thereforCj^ dr be negative^ the deflection will be greater when 
the electrical vibrations and the permanent current are passing 
than when the permanent current alone is passing. This means 
that the experiments described above could be explained by as- 
suming that the resistance 'decreases as the current increases. 
As we can make e very large without introducing any difficulty 
in the way of experimenting^ we may produce a sensible effect 
although dr may be very small. It can be shown that with the 
instruments with which I worked I could have detected a differ- 
ence in the resistance amounting to yooToTq ^^ '^® whole resist- 
ance. The change in the resistance which we should have to 
assume in order to account for the effect observed is easily found. 
Supposing the current which passes when the constant electro- 
motive 2x acts alone to be c, the deflection will then be propor- 
tional to c or ac. Similarly the resultant current which passes 
when the constant electromotive force acts and the magnet 
rotates shall be designated by c', and the deflection observed 
consequently by «</• We have then 



r r* 

Dividing one of these equations by the other, we get 

dr ^ C'-cf ^ 2x 
r, "" c x+e 

In this equation x means the integral electromotive force 
of the battery acting during half a revolution of the magnet, 
while e means the electromotive force of the moving magnet 


during that time. The value of — -- in my experiments was 

generally about 0001 ; was found by experiments to be 

nearly 0*05. It follows from this that 

- = -000005. 


A change in the resistance amounting to such a small frac- 
tion of the resistance only could not have been detected by the 
methods which have been hitherto used to verify Ohm's law. 

I shall now pass to a second explanation of the phenome- 
non^ which is, however, a little complicated. If a current of 
electricity passing through a circuit is increased by any elec- 
tromotive force, an electromotive force in the opposite direction 

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Dr. A. Schuster^s Experiments on Electrical Vibrations, 349 

is set up in the circuit, owing to what we call self-induction. 
It is assumed that this electromotive force is proportional to 
the rate of increase of the current ; so that, if that rate is a 
negative quantity, an electromotive force in the same direction is 
set up. If we could imagine some state of things so that this 
self-induction would not depend merely upon the rate of in- 
crease of the current, but also in part upon the current passing 
through the circuit, my experiments would find an easy expla- 
nation. In order to fix our ideas I shall make certain hypo- 
theses, and show how the different facts can be accounted for 
by means of them. While the current increases it has to 
establish its own lines of force, and is therefore doing work. 
The weakening of the current due to selt-induction is assumed 
to be due to this work. The establishment of the lines of 
force may, however, not be the only work the current has to do. 
Suppose the current places the particles of copper in a certain 
way, and suppose that this magnetization of the copper par- 
ticles, as it may be called, approaches a maximum as the current 
increases. It is easy to see that in this hypothetical case the 
self-induction of a current will be smaller if the original current 
passing through the circuit was strong than if it was weak. It is 
also evident that the self-induction will be weaker when a cur- 
rent is increased than when it is decreased by a certain amount. 
A rotating magnet will therefore induce currents of unequal 
strength in a wire through which a permanent current passes, 
as the current induced in the same direction as the original 
current will be stronger than that induced in the opposite direc- 
tion. This would agree with the observed facts. 

V. Conclusion. 

It is impossible to decide by the experiments which I have 
made which of these two explanations is the correct one ; and 
it will be very difficult to decide this by further experimenta- 
tion. Whenever we use currents of varying intensity, both 
the causes suggested will give the same result. We should 
therefore have to use only constant currents. Unfortunately 
we have to meet great practical difficulties if we want to use 
constant currents. The greatest of these difficulties is the 
change of resistance by increase of temperature. I need not go 
into this any further here. 

The above paper was read in a slightly different form before 
Section A of the British Association at Belfast. As it is of some 
importance to see whether Ohm's law is rigidly correct or not, 
the. British Association has appointed a Committee for the pur- 
pose of verifving the law experimentally. If the result should 
be that the law is correct within the limits in which we should 

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850 Prof« Ghallit #ii the HyJrodynmmical Theory af thi 

expect a deriation from the experiments described in this paper^ 
we should hare only the second explanation to fall back upon. 

The experiments were made in the physical laboratory of the 
Unirersity of Oottingen ; and I hare to thank Professor Weber 
and Professor Riecke for the kindness with whieh they hare 
placed the necessary apparatus at my disposfdi 

XLVIII. 7^ Hydrodynamieal Theory of the Action of a Gahanie 
Coil on an external small Magnet. — Part II. By Professor 
Chaixis, M.A., F.R.8. 

[Continued from p. 200.] 

THE discussions of principles and proofs of propositions, coq«« 
tained in Part I. in the September Number, have prepared 
the way for a direct solution on hydrodynamicfd principles of 
the problem of the action of a galvanic coil on a small magnetic 
needle, which I now proceed to give. For the sake of conveni- 
ence in making references, the articles in this second Part are 
numbered in continuation of those of the first. 

43. From the reasoning contained in arts. 24-38 it has been 
concluded that the motion of a galvanic current along a uniform 
conductor whose axis is a complete circle, and whose transverse 
section is a small circle of given radius, consists of circular 
tnotion parallel to the axis and of circular motion about the 
axis in transverse planes, the result being q)iral motion, which, 
as shown in art. 42, may either be dextrorsum or sinistrorsum. 
A rectilinear axis being supposed to be drawn at right angles to 
the plane of the circular axis of the conductor through its centra 
let 11 be the distance of any point of the fluid from that axis 
and r the distance of the same point from the axis of the con- 
ductor. Then it has been shown in arts. 35-38 that the trans- 

verse circular velocity is -^ and the circular velocity parallel to 

the conductor's axis is ~, C| and e^ being arbitrary constants 

indeterminately related to each other. 

44. Now let a small magnet be so mounted that its osciIIa<> 
tions about a centre of motion, supposed fixed, shall be con^ 
strained to take place in the plane which passes through that 
centre and the centre of the conductor's axis, and cuts the plane 
of this axis at right angles. From what is proved in arts. 17- 
19, to find the direction which the galvanic current gives to the 
axis of the small magnet we have only to find the direction, at 
the centre of its motion, of the velocity of the current ^resolved 
in the plane of that motion } and it is permitted to consider 
separately the effects of the two motions which the current eon^ 

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Action of a Chzhanie Coil on an external small Magnet. 361 

Bists of. Bat it is evident that the motion of the cnrrent 
parallel to the axis of the condaetor has no effect in determining 
the angular position of the magnet^ inasmuch as it cuts the plane 
in which the magnet is compelled to more at right angles* 
Also the small secondary motions generated bv the reaction of 
the atoms against the portion of the current which flows in the 
interior of the conductori if they should be of sensible amount, 
would have no tendency to cause vibrations of the magnet, 
because the aggregate directive effects of those on the opposite 
sides of the plane of vibraiion would be just equal and opposite^ 
It remains only to consider the effect of the circular motions 
about the conductor in planes perpendicular to the plane of itsaxis» 
46. Now these motions will have a directive effect on the 
magnet in two ways, which will require separate considerations. 
First, the angular position of the magnet will be determined in 
part, and in a direct manner, by the circular motions about the 
two opposite points of intersection o£ the axis of the conductor 
by the transverse plane passing through the centres of the mag- 
net and of that axis. If A and B be these points and P be the 
given point, these motions, being in the same direction about 
the axis of the conductor, will be in opposite directions about 
the points A and B, and, according to the law stated in art. 43, 
will vary inversely as the squares of the distances AP and BP. 
Hence it is easy to calculate the sums of the resolved parts of 
the velocities in two rectangular directions^ one parallel to the 
before-mentioned axis through the centre of the conductor, which 
will be supposed to be the axis of z, and the other parallel to 
the intersection of the plane of the circular axis by the plane 
through the axis of z and the point P. If we suppose the latter 
plane to be coincident with the plane cror, the resolved velocities 
will be parallel to the direction of the axes of z and x* Hence 
if z be the distance OG of the centre G of the circular axis from 
the origin of coordinates^ and if/) and q be the coordinates of 
P parallel to the axes of z and x, and a be the radius of the cir^ 
cular axis, then, the two above-mentioned velocities being ex« 
pressed by 

and t^e sums of their resolved parts in the directions of the axes 
being X and Z, it will be found that 

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352 Prof. ChalUs on the Hydrodynamical Theory of the 

It 18 here supposed that the direction of the motion about the 
axis is such that at the centre C^ where the two motions have 
the same direction, the compound motion is in ^tpotitwe di- 
rection; for since at that point p=z and q^O, the formube 

giveX=0, andZ= + %- 

46. The above values of X and Z determine the direction the 
needle would take supposing it to be acted upon solely by the 
two motions considered in the preceding argument. To find the 
effect of a coil composed of any number of such circular rheo- 
phores all of the same magnitude, and having the axis of z for 
their common axis, it is required to find fX& and j^ii?, the in- 
tegrals being taken from one end to the other of the axis of the 
coil. If the length of the axis be 2/ and its middle point be at 
the origin of coordinates, the limits of the integration are 
j8r= — / and z= + /• Hence substituting, for the sake of brevity, 

n, for ((p-Q«+ (?-a)0"S «8 for ((p-/)*+(g + a)0"*. 
fh for ((i>+Q'+(?-«)0"*, n4 for ((;, + /)« + (?+«)«)-*, 
it will be found by effecting the integrations that 
*JXrfxr=*/i(n, —Ha— 113+114), 

k being the constant factor which converts the sum of the velo^ 
citie$mUy the sum of the directive /orce«. 

47. If instead of a single cylindrical coil we have any num- 
ber of such coils in juxtaposition and having a common axis, 
the directive action of this compound coil would be found by ob- 
taining the integrals 

^{k^lUzyta, ^{k^Zdz)da, 

between the limits of the least and greatest values of the radius 
a. Supposing a^ to be the mean value of a, and the least 
and greatest values to be a, — € and ai + €, the results of these 
integrations, if € be very small compared with a,, would be very 
approximately obtained by multiplying the previous integrals by 
26, putting ^1 in the place of a, and altering the constant k, 

48. The direct action of the transverse circular motions on 
the magnet having thus been calculated, we have now to take 
account of an indirect action, the hydrodynamical origin of 
which I proceed to explain. From hydrodynamics it is known 
that the steady motions of a mass of fluid of unlimited di- 
mensions, whether it be incompressible or highly elastic, may 
be supposed to coexist, and that, if U, Y, W be the sums of 

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Action of a Galvanic Coil on an external small Magnet. 353 

the resolved parts of the velocities in three rectaDgular direc- 
tions^ the pressure/} at any point is given by the equation 


In this equation U^ Y, W may represent the resolved parts of 
impressed velocities, such as the longitudinal and transverse 
velocities which, according to the pi*esent theory, constitute 
the galvanic current which is produced and maintained, by the 
action of a battery, along a fine cylindrical conductor. Hence, 
since the value of j9, by reason of these velocities, varies from 
point to point of space, they give rise to motions of the fluid 
which, for distinction, may be called secondary} and the varia- 
tions of pressure producing such motions, inasmuch as they result 
from impressed velocities, are to be regarded as externally im- 
pressed moving forces. The motions thus produced will be 
steady because the originating primary motions are steady ; and 
iu)nsequently these secondary motions can coexist with the 

49. In the problem before us U, V, W may be taken to ex- 
press the sums of the resolved parts of all the motions, as well 
those parallel to, as those transverse to, the axes of the conduct- 
ing wires. But it is evident that the former may be left out of 
consideration, because they tend to produce equal and opposite 
motions on the opposite sides of the plane of the axis of each 
circular conductor, and therefore, on the whole, have no effect 
in generating secondary motions. Thus we have only to take 
account of the transverse motions about the circular axes. 

50. Directing attention at first to a single circular rheophore 
'and to the motions about its axis which cross the enclosed plane 

circular area, it will be seen that at each point of this area two 
motions about two elements of the axis, which are at the extre- 
mities of a diameter passing through the point, have the same di- 
rection. The sum of the Velocities at or immediately contiguous 

to the centre is -^, and is a minimum : it increases from the 

centre up to the conductor ; but on the other side of the con- 
ductor in the extension of the same plane the two velocities 
are opposed to each other, and their sum rapidly decreases. 
Thus, the motion being steady, the mean of the motions cross- 
ing the circular area will be in excess, and the mean of the 
pressures in defect, within the area ; and the contrary will be 
the case outside. The consequence will be that a current of 
the circumambient fluid will set through the area, entering at 
one side and issuing at the other, as being necessarily a cir- 
culating current. Each circb of the coil will have the same 
Phil. Mag. S. 4. Vol. 48. No. 319. Nov. 1874. 2 A 

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854 Prof. Challifl on the Hydrodynamkal Theory of the 

effect ; and as the different circles may be astomed to prodooe 
independent effects, there will be in the interior of the ooil fron 
end to end impulses x>{ equal intensity analogous to those which 
were supposed in art. 7 to be generated in a magnet by a regular 
gradation of atomic density. The whole action being symme- 
trical with respect to the axis of the coil, the impulses may with 
dose approximation be assumed, for the same reasons as in the 
case of the magnet, to be concentrated along the axis, 8up« 
posing the shape of the coil to be that of a hollow cylinder^ 
and the radii of the interior and exterior surfaces to be smalL 

61. In fact, so far as regards the indirect action now under 
consideration, the hydrodynamical circumstanees doe to the ooil 
are exactly analogous to those due to a magnet, the force of the 
battery p^orming the part which was attributed to the grada* 
tion of atomic density of the magnet. Consequently the mathe- 
matical investigations contained in the Numbers of the Philoso- 
phical MagaEine for July 1869 and June 1872, and already ap- 
plied in the theory of the magnet given in arts 6-15 of the pre- 
sent essay, may with equal reason oe applied to the problem of 
the aetion of a galvanic coil, although in each case the adopted 
solution of the hydrodynamical problem can only be eonsiderodl 
to be approximately applicable. It suffices, however, for draw- 
ing the inference that the galvanic aetion of a cylindrical ecA 
approxieaates to the action of a cylindrical magn^ which eon- 
dnskm is eonfirmed by well-known experimenta made witk 
Amp^'s 9olemids. Accordingly the fomake obtained ia ait» 
15 for the directive action oi a lai^ magnet on a small mi^mflir 
needle will be considered to be equally applicable to the aetion 
of a galvanic coil on the needle, so far, at least, as regards the 
mdireet action of the coil. 

52. But experiment has also shown that there is a decided 
difference between the action of a magnet and that of a coil 
under the same circumstances. This fact has been speeiallj 
established by the experiments of the Astronomer Royal the 
results of which are given in the Philosophical Trsnsactionay 
vol. clxii. pp. 489-491. I propose to account for the difference 
by taking mto consideration the direct effect of the drcular 
motions treated of in arts. 45-47, to which there is nothing cor- 
responding in the hydrodynamical circumstances of the streama 
of a magnet. This explanation admits of being supported by 
the following argument. 

From results obtained in art. 15 it appears that if at any point 
P, the coordinates of which in the longitudinal and transverse 
directions are/> and ;, the directive force of a lai^ mamet of 
length 2/ on a small one in the longitudinal direction be Zp and 

that in the transverse direction be X|, 

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Action qf a Galvanic Coil on an external tmail Magnit. 355 

P-l P+l 

z C(y-/)'+g«)i C(f+/)'+g')^ 

^» ._ 2 ^ 2 ' 

the origin of the coordinates being the middle point of the axis. 
This ratio determines the direction of the magnetic current at 
the point P^ and, according to our theory, gives also the direc- 
tion of the current which would be produced at the same point 
if the magnet were replaced by a galvanic coil having an axis of 
the same length, so far, at least, as the current is due to what 
I have named the indirect action. If Z', and X\ represent the 
directive forces in the same rectangular directions due to the 
direct action of the coil, it follows from the results obtained in 
arts. 46 and 47 that 

z;. (^-')(^-^)-'.^-)(^-^) 

Substitnting now for fi„ n^ rtg, 114 the expresaions given in art, 
46, aftiBr putting a, for 0, and supposing that Ci is small comi? 
pared -with the distance of the point F from the extremity of thiB 
axia, wfaidi distance is ((j»^0'+?*)*' ^* ^^^ ^ found, by ex- 
panding the right-hand side of the above equation so as to in- 
clude only the first power of a^, that 

Since, as it is easy to see, the right-hand side of this equality 

is a positive quantity, it follows that <^ is greater than 

sj-. The B^aning of this result ib thjat tne lines of motion 

pertaining either to the current of a magnet or to the current 
indirectly produced by a galvanic coil, supposing the current to 
issue in the positive direction, are less bent from the axis than 
the lines of motion directly due to the circular motions about 
the axis of the coil. Hence it appears that the lines of motion 
due to the streams compounded or those resulting both from the 
indirect and the direct actions will be more bent from the axis 
than those of the magnet. These lines, therefore, supposing 
them to pass through all the points P of the circumference of a 
circle, the centre of which is on the axis of a and its plane per- 


Digitized by VjOOQ IC 

339 Prof. Challis on the Hydradynamical Theory of the 

pendicular to that axis, will apparently diverge from a point of 
the axis more distant from the origin O than the point of appa- 
rent divergence of those lines of motion of the magnet which 
pass through the same points P. Analogous considerations, 
applied to the entering streams at the other end of the coil, 
frould show that the points of apparent conoergenee of the lines 
of motion are more distant from O in the case of the coil than 
in that of the magnet. These inferences from the theory accord 
with the results of the experiments mentioned in art. 52. 

63. According to what is said in art. 20^ the velocities design 
nated by X|, X'|, Z^ Z'l are proportional to the directive forces 
of the coil in the transverse and longitudinal directions. The 

theory has furnished an expression for ^, which ratio de- 

termines at any point the direction given to the axis of the small 
magnet, either by the streams of a large magnet or by those due 
to the indirect action of a coil ; and it has also furnished the 


value of -^y which gives the direction that the axis of the small 

magnet would take if acted upon only by the transverse cir- 
cular movements of the galvanic current. But wc require to 
know the direction of the axis resulting from the total action 
of the coil, the expression for determining which, on the prin* 
ciple of the coexistence of velocities, will be ^ 


It is here to be remarked that, according to the conditions 
of the problem, there must be a certain hydi^vnamical relation 
between Z| and Z'„ as also between X| and X'i; but in the ex- 
isting state of hvdrodynamics it does not appear possible to 
ascertain these relations exclusively by theoretical investigation. 
Hence for calculating the above ratio recourse must be had to 
experimental data. Theory has advanced so far as to prove that 
Z,=CxM, X, = CxM', Z\=C'xN, X',=C'xN', M, M', N, 
W being quantities that can be calculated from known formulae, 
and C, C being unknown constants. . If, now, for a certain po- 
sition of the centre of the small needle the value of the ratio 
which determines the angular, position of its axis be found by 
experiment to be ^, we shall have 

^""X^ + X'," CM'+C'N' ""M' + CiN'' 
Ci being put for rj. Consequently C|= -mio^^ ' By taking 

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Actum of a Gahanic Coil on an external small Magnet. 857 

different positioDs we may calculate from this formula as many 
different values of Ci as we please ; and it will be a criterion of 
the truth of the theory to find that these values differ but little 
from each other^ Ci beings according to the theory^ absolutely 
constant. Taking the mean of the values of Ci thus obtained to 
be a sufficiently close approximation to its ti*ue value^ we may 
proceed to calculate for any given position of the centre of the 
small needle the angular position of its axis resulting from the 
total action of the coil, by means^of the formula 

Z, + Z', M + C,N 

Xi+X'i""M' + CiN'' 

M, N, M', N' being calculated for the given position by means 
of the known formulae. By comparisons] of angular positions 
of the needle calculated in this manner with a large number of 
observed positions, the theory may be fully tested. 

54. Since I arrived at this solution of the problem, I have not 
had leisure for going through the arithmetical calculation which 
would be required for making the above-mentioned comparisons, 
and I am consequently unable to say whether the theory is 
capable of satisfying such a test. This omission, however, does 
not materially affect the argument, because, as I shall afterwards 
show, the theoiy may be tested in another way. I have already 
intimated in arts. 5 and 24 that on the principles of the method 
of philosophy I have adopted it should be possible to account 
theoretically for the facts and hypotheses on which Amp^re^s 
galvanic theory of magnetism is founded. If this were effected 
by means of the hydrodynamical theory of galvanism, it is evi- 
dent that any confirmation which Ampere's theory might receive 
by satisfying an applied test, would at the same time be a con- 
firmation of the hydrodynamical theory. For instance, the com- 
putations undei'taken by Mr. Stuart for the purpose of account- 
ing for, on Ampere's theory, the results of the Astronomer 
Royal's experiments on the Directive Power of Galvanic Coils in 
their action on external small magnets (given in the memoir 
cited in art. 62), and the comparisons contiained in an Appendix 
to the memoir, might, in the case supposed, be claimed for the 
hydrodynamical theoi^. Accordingly I propose to give in a 
third part a theoretical discussion of the empirical foundations 
of Ampere's theory, with particular reference to its application 
in the problem of the galvanic coil. 

Cambridge, September 20, 1874. 

Postscript^ Oct. 7, 1874. — In the last paragraph of the fore- 

Digitized by VjOOQ IC 

858 Prof. Challis an the Hydrodynamed Theory of the 

going communicatiou I hare stated that I omitted^ from want of 
kisure, to compare the theory with observation by arithmetical 
calculations. Part II. was, m fact, finally written out for thfe 
press before I took any steps for making such compariaotti being 
deterred from the undertaking mainly by the apprehension that 
it would require more time and labour than I could spare for 
it. I have, however, since found that the theory could be 
suflBciently tested by an amount of calculation much less than 
that which I thought to be necessary ; and I now propose to give 
the results of such calculation. 

According to the proposed hydrodynamical theory the action 
of a cylindrical coil on an external small magnet consists of two 
parts, which I have named "direct'* and "indirect" The for- 
mulse for calculating the angle of nosition of the mi^^net, sup- 

Josing it to depend only on the inoirect action, are given in art. 
5 ; and those for calculating the position as depending only 
on the direct action are given in arts. 46 and 47. The theory 
is incapable of furnishing of itself formulse for calculating the 
effect of the simultaneous action of the two parts ; but it is shown 
in art. 53 how the calculation may be performed by the aid of 
experimental data. 

The first set of formulse were derived from the hydrodynamical 
theory of maonetic force, supposing the form of the magnet to 
be cylindrical, its transverse section small, and its ends to he Jlnt, 
on the principle that under these conditions the magnetic action 
may be supposed to be concentrated in an elementary tine of tmi« 
form magnetic intensity along the axis (see arts. 12--I4). Then, 
for the reasons given in arts. 60 and 61, the same supposition ift 
made relative to the galvanic coil; that is, as far as regards the 
indirect action, it is supposed to act exactly in the same manner 
as a magnet of the same length, having the lorm described above, 
pronded also its transverse dimensions be small compared with its 
length. This last condition was satisfied in the experiments 
about to be used for testing the theory, the interior radius of the 
coil being 0*45 inch, the exterior radius 0*7 inch, and its length 
13*4 inches. In calculating thus the indirect action the exact 
transverse dimensions do not come into account. 

It is evident that the action will be the same in all planes 
passing through the axis of the magnet, or coil ; and since the 
motion of the aether in any such plane is symmetrical both with 
respect to this axis and the transverse plane through its middle 
point, it will suffice to consider the lines of motion of the stream 
in only one of the quadrants. According to our theory the 
stream of sether issues from that end of a magnetic needle which 
is directed southward^ which, as represented in the diagram in 
the Philosophical Transactions, voU clxii. p. 488, is on the riffhi 

Digitized by VjOOQ IC 

Action of a Galvanic Coil on an external small Magnet* 859 

hand. The coones selected for consideration are those indicated 
hy the small magnets on the upper side of the right-hand half 
of the diagram'; and the longitudinal velocity will be taken to be 
positive in the direction of issuinff^ and the transverse velocity 
positive in the direction from the axis. Hence, putting /iX^ and 
fsYi for these velocities respectively, and substituting m, for 
((p-0*+«*)"*i and m, for ((;>+0* +?*)"*, we have by the 
formuke in art. 15, ; 

21 being the length of the coil, and j9, q the longitudinal and 
transverse coordinates of any one of the positions of the centre 
of the small magnet. If a line drawn in the direction opposite 
to that of the motion at any position cuts the axis of the coil at 
an angle of inclination <o reckoned always from the negative di- 
rection from the point of intersection, we shall have tan (o = — ^, 

and <» will in all cases be positive, varying from sero for a posi- 
tion on the transverse axis to 180^ for a position on the longitu* 

The calculation of w by means of the formula above gives the 
theoretical determination of the angle of position of the small 
magnet, so far as the action of the coil is the same as that of a 
magnet ; and the observed position is readily determined by means 
of the values of the longitudinal and transversal forces for a coil 
without core, given (in p. 491) in the memoir before cited. I 
have besides calculated the same angle by Amp^re^s theory^ 
availing myself for that purpose of the results of Mr. Stuart's 
theoretical calculation of X and Y contained in p. 497. The 
value of / for all the observations is 6*7 inches, and the values of 
the coordinates j9 and q for the different positions of the small 
magnet are those subjoined. Both the experimental and the 
theoretical values of <» were calculated to minutes of arc, but it 
was thought suflBciently accurate, considering the circumstances 
of the observations, to express them to the nearest tenth of a 
degree. After these explanations the following statement of the 
results of the calculations will be intelligible. 

Digitized by VjOOQ IC 

860 Prof. Chillis an the Ht/drodynamieal Themy of the 

No. of the 

Yalae of 

Value of Excess of 

Excess by 



w by ob- 

w by the obsenred 






































































































































KcspectiDg these results, it is first to be noticed thi^t the ob- 
served and calculated values of o> differ so little from each other 
(except in the instances of Nos. 7 and 13, which seem to bq 
affected by some incidental errors), that the differences scarcely 
exceed what might be attributed to unavoidable errors of obser* 
vation. It is evident, therefore, that the effect of not taking the 
direct action into account must be very small ; and I have conse- 
quently not thought it worth while to employ the calculation9 
indicated in art. 53 for ascertaining its amount. The reason 
that the direct action has comparatively so little effect I take to 
be, its being due only to the transverse circular motions about 
parts of the coil contiguous to the plane passing through the 
axis of the coil and the centre of the small magnet in a very thin 
slice i whereas the indirect effect results from the transverse mo- 
tions about all parts of the coil, and increases both with its length, 
and with the area of its transverse section. 

It may, however, be remarked that there is a preponderance 
of minus signs in the excesses of the observed values, and that 
this is the case in somewhat greater degree relatively to the by- 
drodynamical theory than to that of Ampere. The argument in 
art. 52 shows that, by taking account of the direct action, the 
angle o> would be diminished, so that the minus errors might 
thus be made less, and the calculated and observed values be 
brought into closer agreement. In the calculation of the direct 
action the transverse dimensions of the coil are explicitly taken 

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Action of a Galvanic Coil on an external smaU Magnet* 361 

iuto account (see art. 52) ; and in Ampere's theory the same 
thing is done by making the hypothesis of a magnetic sheet* 
This probably explains why that theory agrees with experiment 
in some degree better than the hydrodynamical theory when the 
latter does not include the direct action. 

The hydrodynamical theory admits also of the application of 
a different arithmetical test, based on the following considera* 
tions. The theoretical quantities ftX, and /iY^ are velocities of 
the aiher; and supposing X' and Y' to be the directive forces 
acting on the small magnet^ expressed numerically by inference 

Y Y' 

from the experiments, we have seen that quam proximi r«i =s ^7* 

This equality would be generally true if the ratio of Yj to Y' 
were the same as that of Xj to X', even if that ratio were differ- 
ent for different positions of the magnet. But the argument in 
art. 19 shows that the directive forces in the two rectangular 
directions are equal to the quantities X| and Y^ multiplied by a 
constant factor, which, although dependent on the dimensions 
and atomic constitution of the small magnet, is independent of 
its position and the direction of its axis. Consequently for each 
set of corresponding values we have Y'=*Y, and X'=*X„ k 
being absolutely constant ; and by summing all these equalities^ 


which equation may be supposed to give the value of k with as 
much accuracy as the character of the experiments allows of. 
By calculating X, and Y, from the expressions within brackets 
in the formulae of art. 15, taking X' and Y' as given numerically 
by the experiments, and using all the values of Xp Y|, X\ Y', I 
find that the value of k which satisfies the above equality is 6978'7. 

Assuming that in Ampere's theory X'ssA'X^, Y'=il'Y^ and 
that the values of X^, Yg are those obtained for X and Y by Mr. 
Stuarf s calculation, I have found, by a process exactly analogous 
to that indicated above, that A/= 1*6378. 

The values of the constant factors k and V being thus deter« 
mined, we may proceed to test both theories by comparing the 
several values of itX, and ilY,, and those of kHL^ and JfY,, with 
the corresponding values of X' and Y'. In this way the follow- 
ing results have been obtained : — 

Digitized by VjOOQ IC 

803 Adkn of a Oahnmic Coil on an $xiirml imtllMagn^l. 











+ 46 




+ 35 


- 16 





+ 26 


- 23 





+ 36 


- 29 





+ 30 


- 12 



- 80 


- 18 


+ 121 





+ 121 









+ 69 





+ 19 




+ 21 


- 15 





+ 28 


- 28 





+ 29 


- 39 







- 29 



- 67 


- 24 


- 68 



+ 100 


- 31 


- 62 





- 29 


- 36 





- 46 


- 2 





- 79 


+ 14 


The anomalies liere presented by Nos. 7 and 13, taken in 
oonnezlon with those in the former comparison, seem to point to 
errors concerned with the computing of Y, and observing of X^ 
The diflferences X'— ilX| and Y'~ilY| between the observed and 
calculated forces according to the hvdrodynamical theory, and 
the differences V^HX^ and Y'— ArY^ according to Ampere's 
theory, are perhaps not greater, when compared with the values 
of X' and Ir, than might from the circumstances of the observa- 
tions be expected. Relative to these differences it may be re- 
marked^ as before, that the hydrodynamical theory, restricted to 
the indirect action, does not agree so well with observation as 
the theory of Ampere. The totality, however, of the above com- 
parisons with the former theory prove that the value of k must 
at least be very approximately constant, and so far justify the 
theoretical conclusion that for the case of a coil, or a magnet, 
reduced to a Htu of magnetism, that factor is absolutely con- 

But at the same time the foregoing comparisons with Amp&re^s 
theory prove that the factor V is also verv nearly constant, 
although there is no d priori reason deducible from that 
theory why this should be the case. It is worthy of remark, 
too, tnat the differences between observation and calculation ex-, 
hibited above follow for the most part the same law for both 
theories, although they depend on very different processes of 
calculation. I cannot but regard these circumstances as confir- 
matory of the views maintained in the foregoing essayi according 

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Sir William ThomMm an Perturbaiioni of the Compasi. 868 

to which the receired empirical theories of galranism and mag- 
netism virtually have for their basis the hydrodynamical theory 
of these forees. 

I have not attempted to treat in like manner the other expe- 
riments the details of which are given in the same memoir^ 
because my analysis applies exclusively to a cylindrical magnet, 
or coil, of the same transverse section throughout. The action 
of a large bar-magnet, and that of an iron core in the form of a 
bar Within a coil, would require very different treatment, on ac- 
count of the forms not being symmetrical with respect to an axis. 
The experiments made with the edge and flat side of the large 
bar-magnet turned towards the small magnet showed that the 
action dq>end^ in some degree on the form presented to the 
latter* 1 take occasion to mention incidentallv that the great 
accession of magnetic force which was*observea to result from 
putting a soft-iron core in the coil is attributable, according to 
the hydrodvnamical theoij, to the transverse circular motions 
about the rheophore constituting the coil, which give rise to just 
such fbtherial streams as are proper for magnetising* (See 
' Principles of Physics/ pp* 619 ft 620.) 

The arguments^ and the evidence from numerical comparisons. 
Which I have now addui^ed, should, I thbk, suffice fbf coming 
to the conclusion that galvanic and magnetic forces are modes of 
pressure of the ttther in steady motion. 

XLIX. On the Pertwrhaiions of the Compass produced by the 
roWng of the Ship. By Sir W illiam Thomson, F.R.S.* 

THE ''heeling^rror,'' which has been investigated by Airy 
and Archibald Smith, is the deviation of the compass pro- 
duced by a '* steady heel'' (as a constant inclination of the ship 
round a longitudinal axis, approximately horisontal, is called). 
It depends on a horizontal component of the ship's magnetic 
force, introduced by the inclination ; which, compounded with 
the horisontal component existing when the ship is upri^t, 
gives the altered horisontal component when the ship is inclined. 
Regarding only the error of direction, and ^sregarding the 
change of the intensity of the directing force, we may define the 
heeling-error as the angle between the directions) for the ship 
upright and for the ship inclined, of the resultant of the hori- 
zontal magnetic forces of earth and ship at the position of the 
compass. These suppositions would be rigorously realised with 
the compass supported on a point in the ordinary manner, if the 

* Communicated by the Author, having been read in Section A. of th^ 
British Association at Belfast (1874). 

Digitized by VjOOQ IC 

864 Sir William Thomson on the Perturbattoniof the 

bearing-point were carried by the ship uniformly in a straight 
line. Tney are nearly enough realized in a large ship to render 
iDCOusiderable the errors due to want of perfect uniformity of 
the motion of the bearing-point, if this point is placed anywhere 
in the '' axis of rolling ^^* ; for in a large ship the compass, how- 
ever placed, is not considerably disturbed by pitching, or by the 
inequalities ,of the longitudinal translatory motion caused by waves. 
Hence, supposing the compass placed in the axis of rolling, the 
perturbation produced in it by the rolling will be solely that due 
to the variation of the horizontal component of the ship's magnetic 
force. Such a position of the compass would have one great 
advantage — that the application of proper magnetic correctors 
adjusted by trial to do away with the rolling-error, would per- 
fectly correct the heeling-error. To set off against this advan- 
tage there arc two practical disadvantages : — one, that the axis of 
rolling (being always below deck) would not be a convenient 
position for the ordinary modes of using the compass; the other 
(far more serious), that, at all events in ships with iron decks, 
the magnetic disturbance produced by the iron of the ship would 
probably be so much greater at any point of the axis of rolling, 
than at suitably chosen positions above deck, as to more than 
counterbalance the grand kinetic advantage of the axial position. 
But careful trials in ships of various classes ought to be made ; 
and it may be found that in some cases the compass may, with 
preponderating advantage, be placed at the axis of rolling. 
Hitherto, however, this position for the compass has not been 
used in ships of any class, and, as we have seen, it is not pro- 
bable that it can ever be generally adopted for ships of all classes. 
It is therefore an interesting and important practical problem 
to determine the perturbations of the compass produced by oscil- 
lations or other non-uniform motions of the bearing-point. 

The general kinetic problem of the compass is to determine 
the position at any instant of a rigid body consisting of the 
needles, framework, and fly-card, which for brevity will be called 
simply the compass^ movable on a bearing-point, when this point 
moves with any given motion. Let the bearing-point experience 
at any instant a given acceleration «, in any given direction. 
Let W be the mass (or weight) of the compass, and gVf the 
force of gravity upon it, reckoned in kinetic units. The position 
of kinetic equilibrium of the compass at that instant is the posi- 

* One way, probably the best in practice, of Andin^ by observation the 
position of the axis of rolling is to bans pendulums m>m points at differ- 
ent levels in the plane through the keel perpendicular to the deck, till one 
is found which indicates the same degrees of rolling as those found geo- 
metrically by observing a graduated scale (or "batten") seen against the 

Digitized by VjOOQ IC 

Compass produced by the rolling of the Ship. 363 

tion in which it would rest under the magnetic forces and a force 
of apparent gravity equal to the resultant of yWand a force aW 
in the direction opposite to that of a. Now the weight of the 
compass is so great and its centre of gravity so low that the level 
of the card is scarcely affected sensibly by the greatest magnetic 
couple experienced by the needles^. Hence in kinetic equili- 
brium the plane of the compass-card is sensibly perpendicular 
to the direction of the '' apparent gravity ** definea above ; and 
the magnetic axis of the needles is in the direction of the result- 
ant of the components; in this plane^ of the magnetic forces of 
earth and ship. Hence it is simply through the apparent level, 
at the place in the ship occupied by the compass, differing from 
the true gravitation-level, that the problem of the kinetic-equi- 
librium position of the compass in a rolling ship differs from the 
problem of the heeling-error referred to above. That we may 
see the essential peculiarities of our present problem, let there 
be no magnetic force of the ship herself or cargo. The kinetic- 
equilibrium position of the magnetic axis of the compass will be 
simply the line of the component of terrestrial magnetic force in 
the plane of the apparent level. Let k be the inclination of this 
plane to that of the true gravitation-level, and ^ the azimuth 
(not greater than 90°) from magnetic north of the line LL' of 
the intersection of the two planes (a diagram is unnecessary) ; 
also let H and Z be the horizontal and vertical components of 
the terrestrial magnetic force. The component of this force in 
the plane of apparent level will be the resultant of H cos 6 along 
LI/ and H sin ^ cos #c + Z sin k perpendicular to lAJ ; and there- 
fore^ if if>f denote the angle at which it is inclined to LU, we have 

Hsin^cosic + Zsin^ ^ , . Zsinic 


—J T = tan cfc cos ie+ ^f r* 

H cos ^ ^ H cos ^ 

If, as usual in compass questions, we reckon the directions as of 
forces on south magnetic poles (or the northern ends of the com- 
pass-needles), the direction of H cos if> is along LI/ northwards, 
and the direction of Z sin k, when the ship is anywhere north of 
the magnetic equator, is downwards in the plane of the apparent 

Now, as we are only considering the effect of rolling, the di* 
rection of the given " acceleration ^' of the bearing-point will 
always be in a plane perpendicular to the ship^s length ; and 
therefore LI/ will be parallel to the length. (It will in fact be 
the line through the "lubber-points^^ of the compass-bowl.) 
Hence, and as compass angles are ordinarily read in the plane 
of the fly-card, the kinetic equilibrium-error of the compass is 

* Generally no adjusting counterpoise for the compass is required when 
a ship goes from extreme north to extreme south magnetic latitudes. 

Digitized by VjOOQ IC 

866 Sir William Thomson on the PeriwrbatUn$ of the 

exietly equal to ^,-^^. When /c is a small fraetion et 67*'S 
(the '^raoian/' as the angle whose arc is equal to radius baa 
been called by Professor James Thomson), which is the case ex- 
cept in extreme degrees of rolling when the compass is properly 
placed*, we have approximately 

0/ — ^«ilCj7C0S^. 

The direction of this error is, for the northern ends of the needlea 
in the northern magnetic hemisphere or for the southern ends 
in the southern hemisphere, towartb the side on which the appa^ 
rent level i$ depressed— thtit is (as practically the compass is 
always above the axis of rolling), towards the elevated side of th0 
ship. It has its maximum value 


when ^==0 ; that is to say, when the ship heads north or south 
magnetic* To estimate its amount, consider perfectly iegul#r 
rolling ; wbicb in general fulfils approximately the simple h$f^ 
monie law, so that we may put 

ml sin 11^, 

where t denotes the indination of the ship at time t, and n and 
I constants. Let h denote the height of tne bearing-point of the 
eompass, vertically above the axis of rolling when the ship is ver* 
tieal« For Uie amount of its acceleration we have 


NoW; if / denote the length of a simple pendulum laoeiHronous 
with the rolling of the ship, we have 

and therefore 


The direction of «, being tangential to the circle described hy 
the bearing*point, is approximate] V horizontal; and therefore the 
direction of apparent gravity wiU be approximately Ithat of the 
resultant of 

ff vertioJ, 

* The " matt-head compass/' perniciously used in too many merchant 
•tenners, may, ib moderate enougli rolling, experience deviations of appa- 
rent level amounting to 20^ or 30^ on each side of tbe tnie gravitation-level. 

Digitized by VjOOQ IC 

dmpaa produced by the rolMng of ihi Ship. 867 


^Tt horizontal. 

KZK J t, approximately, 

Henee, when the ship heads north or souths the amount of th^ 
kinetic-equilibrium error is approximately 

Z A. 

Suppose^ for example^ the period of the rolling to be 6 seconds^ 
(or three times the period of the " secopds' pendulum '') ; / will 
be 39 feet (or nine times the length of the seconds' pendulum^. 
And suppose the compass to be 14^ feet above the axis of roll- 
ing. We have Ksz\i (so that the range of apparent rolling in- 
dicated by a pendulum hung from a point in the position of the 
bearing-point of the compass is greater by half than the true 
range of the roll). On these suppositions tne kinetic-equilibrium 
error amounts to 

IZ . 

About the middle of the British Islands the magnetic dip is 70^^ 

and therefore ^ (being the natural tangent of the dip) is equal 

to 2*76 nearly. Hence the kmetie-eqpulSmum error for the 
supposed case amounts in this locality to about a degree and 
three eigkths for every degree of roll. 

In an iron ship the equilibrium value of the rolling-error wiB 
be approximately the sum of the kinetic error investigated above^ 
and a heeling-error found by an investigation readily worked 
out from that of Archibald Smith in the ' Admiralty Compai^ 
Manual ' (edit. 1869^ Section IV. pages 82-89^ and Appendix^ 
pages 189--150), with modification to take into account the de- 
viation of the apparent levels at the place of the compass^ from 
the true gravitation-leveL 

I have used the expression '^kinetic-equilibraaia error'' to 
distinguish the eiror investigated above &wn that actnaUy exhi- 
bited by the compass. It is exactly the error which would be 
shown by an ideal eompass with inmutely short period of vihin- 
iion. A light i|«iek needle (either with silk-fihj?e snspeusionj o^ 

* Tkii would be the case for a ship of any aize expoied to xsgnlar waves 
of length 184 feet from crest to crest, and^ if moving through the wator^ 
moving in a line parallel to the lines of crests. 

Digitized by VjOOQ IC 

868 Sir William Thomson on Perturbatiom of the Compass. 

sapported on a point in the ordinary way) having a period of not 
more than about two seconds, shows the rolling-error very bean- 
tifully, taking at every instant almost exactly the position of 
kinetic equilibrium. I have thus found the rolling and pitching 
errors so great in a small wooden sailing-vessel that it became 
very difficult to make exact observations with the quick compass, 
either in the Frith of Clyde or out at sea on the Atlantic unless 
when the sea was exceptionally smooth. The well-known kinetic 
theory of forced oscillations'' is readily applied to calculate, 
whether for a wooden or an iron ship, the actual '' rolling-error" 
of the compass, from the ^'kinetic-equilibrium error'' investigated 
above. Thus let 

u be the deviation of the compass at any instant, from tbe 
position it would have if the ship were at rest and upright ; 

T the period of its natural oscillation if unresisted by any 
'^ viscous" influence (the dampina effect of copper, intro- 
duced by Snow Harris and used with good effect in the Ad- 
miralty standard compass, being included in this category) ; 

2/* a coefficient measuring the amount of viscous resistance ; 

E the extreme equilibrium value of the rolling-error ; 

T' the period of the rolling. 

For brevity put n= 7=-, and n'=: jp^. The differential equa- 
tion of the motion is 

gf +2/^-Hi«u=:n«Eco8ii'/. 

The integral of this proper to express the effect of regular rolling 

— -p n^cos(n^/+6) 


€=tan-' H. g * 

It would extend the present communication too far to enter 
on details of this solution. For the present it is enough to say 
that no admissible degree of viscous resistance can make the 
rolling-error small enough for practical convenience, unless also 
the period of the compass is longer than that of any consider- 
able rolling to which the ship may be subjected. Probably a 
period of from 15 to 30 seconds (such as an ordinary compass 
has) may be found necessary for general use at sea ; and it be- 
comes an important practical question how is this best to be 

Digitized by VjOOQ IC 

Dr. W. M. Watts an the Spectrum of Carbon. 869 

obtained coDsistently with the smallneaa of the compass-needles 
necessary for a thoroughly satisfactory application of the sys* 
tern of magnetic correctors by which Airy proposed to cause 
the compass in an iron ship to point correct magnetic courses on 
all points f 

L. On the Spectrum of Carbon. By W. Marshall Watts, 
D.Sc, Pht/sical-Science Master in the Gigglesunck School*. 

ALTHOUGH the different comets which have appeared in 
the northern skies since astronomers have been in pos- 
session of the spectroscope have been carefully examined by 
some of the best observers, the exact nature of the comet-spectrum 
is still a matter of doubt ; and the very important question 
whether comets give the spectrum obtainable from carbon-com- 
pounds, or only a spectrum of bands of nearly the same refran- 
gibility, is not decided. 

The explanation of the varying results of different observers is 
to be found, no doubt, in the extreme faintness of the light 
emitted by a comet^ and the great difficulty of measuring the 
positions of the lines by any arrangement which requires the 
bands to be seen together with cross-wires or spider-lines. The 
best chance of obtaining accurate results is probably to abandon 
micrometric measurements, and to work by eye-estimations of the 
distance of the bands from the known bands of some equally 
faint spectrum, made to occupy the lower portion of the field of 
view, provided a faint spectrum can be found possessing a suffix 
dent number of well-defined bands in the region of the spectrum 
to be mapped. 

In the case of the comet-spectrum we have just the reference- 
spectrum required in the well-known spectrum of carbon, which, 
if it be not identical with the comet-spectrum, has at all events 
bands of very nearly the same refrangibility, and can easily be 
obtained of any feeble intensity required. 

It seemed to me therefore of importance to determine the po* 
sitions of the lines of the carbon-spectrum with as much accu- 
racy as the spectroscopic means at my disposal allow. 

The spectrum was obtained from the flame of olefiant gas and 
oxygen, burnt together at the platinum nozzle of an oxyhydrogen 
blowpipe. • 

The spectroscope employed was Browning's automatic spec- 
troscope of six prisms, with a micrometer eyepiece furnished 
with two pairs of cross- wires. This eyepiece requires 12*49 
turns of the micrometer-screw to separate the wires by the in- 

* CommimiGated by the Author. 
Phil. Mag. S. 4. Vol. 48. No- 819. Nov. 1874. 2 B 

Digitized by VjOOQ IC 

870 Dr. W. M. Watts on the Spectrmn o/CdrboH. 

ierval between the lithium- orange line (6101) and the leaat* 
refrangible sodium-line (6895). 

The referenoe-lines employed were, as far as available, the 
Fraunhofer lines of the solar spectrum, and the lines of the 
spark-spectra of magnesium, leaa, air, antimony, cadmium, and 

The results are given in the following Table. Column I. 
gives the designations of the lines measured as given in ray 
< Index of Spectra ; ' column II. the wave-lengths as now de- 
termined in tenth-metres; column III. the number of obser- 
vations ; column IV. the difference of the highest and lowest 
results from the mean result. 







J 61-5 





+ 13,-14 
+0-5, -0-6 
+0*0, -0-0 


i 77-0 




+0-3, -0-5 
+1-0, -2-1 
+0-8, -0-8 


r 97-0 






+2-2, -8-« 
+ 15,-3^ 

The lines most exactly determined are those whose wave- 
lengths are 5165*5 and 5585'5. 

It may be well to repeat here that this spectrum is the spec- 
trum of carbon, and not of a hydrocarbon or any other compound 
of carbon. That it is so is proved by the fiact that it is common 
to compounds of carbon with oxygen, with hydrogen, and with 
nitrogen (Phil. Mag. S. 4. vol. xxxviii. p. 240) ; and this evi- 
dence does not rest only upon the use of vacuum-tubes, the 
results obtained from whicn are confessedly open to doubt. 
The spectrum is not only obtained from the flame of otefiant 
gas and cyanogen or oxygen, but also from the electric spark 
taken directly in a stream of cyanogen (or carbonic oxide) at 
the ordinary* pressure. 

Digitized by VjOOQ IC 

[ 371 ] 

LI. Researches in Acoustics. — No. V, 
By Alfred M. Mayrr, 

[Continued from p. 274.] 

8. Experinunts on the supposed Auditory Apparatus of the 
Culex mosqaito. 

OHM states in his proposition that the ear experiences a 
simple sound only when it receives a pendulum-vibration, 
and that it decomposes an^ other periodic motion of the air into a 
series of pendulum-vibrations, to each of which corresponds the 
sensation of a simple sound. Helmholtz, fully persuaded of the 
truth of this proposition, and seeing its intimate connexion 
with the theorem of Fourier, reasoned that there must be a 
cause for it^in the very dynamic constitutipn of the ear ; and 
the previous discovery by the Marquis of Corti of several 
thousand"*^ rods of graded sizes in the ductus cochlearis, indi- 
cated to Helmholtz that these were suitable bodies to effect the 
decomposition of a composite sonorous wave by their covibrating 
with its simple harmonic elements. This supposed function of 
the Corti organ gave a rational explanation of the theorem of 
Ohm, and furnished " a leading-thread " which conducted Helm- 
holtz to the discoveries contained in his renowned work Die 
Lehre von den Tonempfindungenf. In this book he first gave 
the true explanation of timbre, and revealed the hidden cause 
of musical harmony, which, since the days of Pythagoras, 
had remained a mystery to musicians and a problem to philo- 

It mav perhaps never be possible to bring Helmholtz's hypo- 
thesis of the mode of audition in the higher vertebrates to the 
test of direct observation, from the apparent hopelessness of 
ever being able to experiment on the functions of the parts of 
the inner ear of mammalia. The cochlea, tunnelled in the hard 
temporal bone, is necessarily difficult to dissect ; and even when 

* According to Waldeyer, there are 6500 inner and 4500 outer pillars in 
the organ of Corti. 

t " But all of the propositions on which we have based the theory of 
consonance and dissonance rest solely on a minute analvsis of the sensa- 
tions of the ear. This analysis could have been made bv any cultivated 
ear without the aid of theory ; but the leading-thread o£ theory and the 
employment of appropriate means of observation have facilitated it in an 
extraordinary degnee. 

''Above ail things I beg the reader to remark that the hypothesis on the 
covibration of the organs of Corti has no ii9mediate relation with the ex- 
planation of consonance and dissonance, which rests solely on the facts of 
observation, on the beats of harmonics and of resultant sounds.*' — Helm- 
holtz, Tonempfindungen, p. 342. 


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872 Prof. A. M. Mayer's Researches in Acoustics. 

a view is obtained of the organ of Corti, its parts are rarely 
m situ, and often the;jr have already had their natural structure 
altered by the acid with which the bone has been saturated to 
render it soft enough for dissection and for the cutting of sec- 
tions for the microscope. 

As we descend in the scale of development from the higher 
vertebrates^ we observe the parts of the outer and middle ear 
disappearing, while at the same time we see the inner ear 
gradually advancing toward the surface of the head. The 
external ear^ the auditory canal^ the tympanic membrane^ and 
with the latter the now useless ossicles, have disappeared in 
the lower vertebrates, and there remains but a rudimentary 

Although the homologieal connexions existing between the 
vertebrates and articulates, even when advocated bgr naturalists, 
are certainly admitted to be imperfect, yet we can hardly sup- 
pose that the organs of hearing in the articulates will remain 
stationary or retrograde, but rather that the essential parts of 
their apparatus of audition, and especially that part which re- 
ceives the aerial vibrations, will be more exposed than in higher 
organisms. Indeed the very minuteness of the greater part of 
the articulates would indicate this; for a tympanic membrane 
placed in vibratory communication with a modified labyrinth, or 
even an auditory capsule with an outer flexible covering, would 
be useless to the greater number of insects, for several reasons. 
First, such an apparatus, unless occupying a large proportion of 
the volume of an insect, would not present surface enough for 
this kind of receptor of vibrations ; and secondly, the minute- 
ness of such a membrane would render it impossible to covibrate 
with those sounds which generally occur in nature, and which 
the insects themselves can produce. Similarly, all non-aquatie 
vertebrates have an inner ear formed so as to bring the aerial 
vibrations which strike the tympanic membrane to b^r with the 
greatest effect on the auditory nerve-filaments* ; and the minute- 
ness of insects also precludes this condition. Finally, the hard 
test, characteristic of the articulates, sets aside the idea that they 
receive the aerial vibrations through the covering of their bodies, 
like fishes, whose bodies are generally not only larger and far 
more yielding, but are also immersed in water which transmits 
vibrations with 4i times the velocity of the same pulses in air 
and with a yet greater increase in intensity. For these reasons 
1 imagine that those articulates which are sensitive to sound and 
also emit characteristic sounds, will prove to possess receptors of 
vibrations external to the general surface of their bodies, and 
that the proportions and situation of these organs will comport 
♦ See Section 4 of this ])apcr. 

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Prof. A. M. Mayer's Researches m Acoustics. 873 

with the physical conditions necessary for them to receive and 
transmit vibrations to the interior ganglia. 

Naturalists^ in their surmises as to the positions and forms of 
the organ of hearing in insects^ have rarely kept in view the im- 
portant consideration of those physical relations which the 
organ must bear to the aerial vibrations producing sound, and 
which we have already pointed out. The mere descriptive ana- 
tomist of former years could be satisfied with his artistic faculty 
for the perception of form ; but the student of these days can 
only make progress by constantly studying the close relations 
which necessarily exist between the minute structure of the 
organs of an animal and the forces which are acting in the 
animal, and which traverse the medium in which the animal 
lives. The want of appreciation of these relations, together 
with the fact that many naturalists are more desirous to de» 
scribe many new forms than to ascertain the function of one 
well-known form which may exist in all animals of a class, 
has tended to keep many departments of natural history in the 
condition of mere descriptive science. Those who are not pro- 
fessed naturalists appreciate this perhaps more than the na- 
turalists themselves, who are imbued with that enthusiasm 
which always comes with the earnest study of any one depart- 
ment of nature ; for the perusal of those long and laboriously 
precise descriptions of forms of organs without the slightest 
attempt, or even suggestion, as to their uses, affects a physi- 
cist with feelings analogous to those experienced by one who 
peruses a well-classifiea catalogue descriptive of physical in- 
struments, while of the uses of these instruments he is utterly 

The following views, taken from the 'Anatomy of the Inver- 
tebrata ' by C. Th. v. Siebold, will show how various are the 
opinions of naturalists as to the location and form of the organs 
of hearing in the Insecta : — '^ There is the same uncertainty 
concerning the organs of audition (as concerning the olfactory 
organs). Experience having long shown that most insects per- 
ceive sounds, this sense has been located sometimes in this and 
sometimes in that organ. But in their opinion it often seems 
to have been forgotten, or unthought of, that there can be no 
auditory organ without a special auditory nerve which connects 
directly with an acoustic apparatus capable of receiving, con- 
ducting, and concentrating the sonorous undulations. (The 
author who has erred most widely in this respect is Mr. L. W» 
Clarke in Mag. Nat. Hist., September 1838, who has described 
at the base of the antennse of Carabus nemoralis, Illig., an audi- 
tive apparatus composed of an auricula, a meatus auditorius 
externus and intemus, a tympanum and labyrinthus, of all of 

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874 Frof. A. M. Mayer's Reietardui m AanuHa. 

which there is not the least trace. The two white convex spot* 
at the base of the antenne of Blatta orieniaHs, and which Tre- 
viranus has described as auditory <Hf;ans, are^ as Burmeister has 
correctly stated^ only rudimentary accessory eyes. Newport and 
Goureau think that the antennae serve bioth as tactile and as 
auditory organs. But this view is inadmissible^ as Erichaon 
has alr^^ stated, except in the sense that the antennse, like all 
solid bodies, may conduct sonorous vibrations of the air ; but 
even admitting this view, where is the andiUNry nerve f for it is 
not at all supposable that the antennal nerve can serve at the 
same time the function of two distinct senses.) 

'^ Certain Orthoptera are the onljr Insecta with which there 
has been discovered in these later times a single organ having 
the conditions essential to an auditory apparatus. This oi|;an 
consists, with the Acrididse, of two foss» or oonchs, surrounded 
by a projecting homy ring, and at the base of which is attached 
a membrane resembling a tympanum. On the internal sur&ce 
of this membrane are two homy processes, to which is attached 
an extremely delicate vesicle fiUed with a transparent fluid and 
representing a membranous labyrinth. This vesicle is in con- 
nexion with an auditory nerve which arises from the third tho- 
racic ganglion, forms a ganglion on the tympanum, and termi* 
nates in the immediate neighbourhood of tne labyrinth by a 
collection of cuneiform staff-like bodies with very finely pointed 
extremities (primitive nerve^bres f), which are surrounded by 
loosely aggregated ganglionic globules. (This organ has been 
taken for a soniferous apparatus by Latreille. J. MtLlkr was 
the first who fortunately conceived that with GryUuM kterogfy' 
phus this was an auditory organ. He gave, however, the inter- 
pretation only as hypothetical ; but I have placed it beyond all 
doubt by careful- researches made on Gomphoceroa, QldgHH/oy 
Podisma, CaJoptenus, and TVuxalii.) 

** The Locustid» and Achetide have a similar organ situated 
in the fore less directly below the coxo-tibial articulation. 
With a part of tne Locustid» {Meconema, Barbiiittes, Phanero^ 
ptera, Phylloptera), there is on each side of this point a fossa, 
while with another portion of this fiunily there are at this 
same place two more or less spacious cavities (auditory cap- 
sules) provided with orifices opening forward. These fossis 
and these cavities have each on their intemal surface a long- 
oval tympanum. The principal trachean tmnk of the 1^ 
passes between two tympanums, and dilates at this point into 
a vesicle whose upper extremity is in connexion with a gan- 
glion of the auditory nerve. This last arises from the first 
thoracic ganglion, and accompanies the principal nerve of the 
leg. From the ganglion in question passes off a band of ner- 

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Prof. A. M. Mayer^s Researches in Acoustics. 875 

vouft substance which stretches along the slightly excavated 
anterior side of the trachean vesicle. Upon this band is situ- 
ated a row of transparent vesicles containing the same kind of 
cuneifonn staff-like bodies^ mentioned as occurring with the 
Acrididse. The two large trachean trunks of the fore legs open 
by two wide infundibuliform orifices on the posterior border of 
the prothorax ; so that here, as with the Acrididse^ a part of this 
trachean apparatus may be compared to a tuba Eustachii. 
With the Achetidse there is on the external side of the tibia of 
the fore legs an orifice closed by a white silvery membrane (tym- 
panum), behind which is an auditory organ like that just d^ 
scribed. (With Acheta achatina and italica there is a tympanum 
of the same size on the internal surface of the legs in question ; 
but it is scarcely observable with A. sylvestris, A. domestica, and 
A* ctanpestris.y 

Other naturalists have placed the auditory apparatus of diur- 
nal Lepidoptera in their club-shaped antennse, of bees at the 
root of their maxilbe, of Mehhntha in their antennal plates, of 
Locusta vtridissima in the membranes which unite the antenna 
with the head. 

I think that Siebold assumes too much when he states that 
the existence of a tympanic membrane is the only test of the 
existence of an auditory apparatus. It is true that such a test 
would apply to the non-aquatic vertebrates ; but their homolo- 
gies do not extend to the articulates ; and besides, any physi- 
cist can not only conceive of, but can actually construct other 
receptors of aerial vibrations, as I will soon show by conclusive 
experiments. Neither can I agree with him in supposing that 
the antennse are only tactile organs ; for very often their posi- 
tion and limited motion would exclude them from this function*; 
and moreover it has never been proved that the antennae, which 
differ so much in their forms in different insects, are always tac- 
tile organs. They may be used as such in some insects ; in 
others they may be organs of audition ; while in other insects 
they may, as Newport and Goureau surmise, have both func- 
tions; for even granting that MttUer'slaw of the specific energy 
of the senses extends to the insects, yet the anatomy of their 
nervous system is not sufSciently.known to prevent the supposi- 
tion that there may be two distinct sets of nerve-fibres m the 
antennse or in connexion with their bases; so that the antennse 
may serve both as tactile and as auditory organs — just as the 
hand, which receives at the same time the impression of the 

* Indeed they are often highly developed in themselves while accompa- 
nied by palpiy which are properly placed, adequately organized, and en- 
dowed wkh a range of motion suitable to an organ intended for purposes 
of touch. 

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876 Prot. A. M. Mayer's Researehet in deau^ks. 

character of the aur&oe of a body and of its temperature— or like 
the toDgQCj which at the same time distinguishes the snr&ce, 
the forra^ the temperature, and the taste of a body. Finally, I 
take objection to this statement : — '^ Newport and Gk>ureau think 
that the antennae serve both as tactile and as auditory organs. But 
this view is inadmissible, as Erichson has already stated, except 
in the sense that the antennse, like all solid bodies, may conduct 
sonorous vibrations of the air.'' Here evidently Siebold had 
not in his mind the phvsical relations which exist between two 
bodies which give exactly the same number of vibrations ; for it 
is well known that when one of them vibrates, the other will be 
set into vibration by the impacts sent to it through the interve- 
ning air. Thus if the fibrillse on the antennse of an insect 
should be tuned to the different notes of the sound emitted by 
the same insect, then when these sounds fell upon the antennal 
fibrils, the latter would enter into vibration with those notes of 
the sound to which they were severally tuned > and so it is evi- 
dent that not only could a properly constructed antenna serve 
as a receptor of sound, but it would also have a function not 
possible m a membrane; that is, it would have the power of 
analyzing a composite sound by the covibration of its various 
fibrillse to the elementary tones of the sound. 

The fact that the existence of such an antenna is not only 
supposable, but even highly probable, taken in connexion with 
an observation I have often made in looking over entomolo- 
gical collections, viz. that fibrillse on the antennse of nocturnal 
insects are highly developed, while on the antennse of diurnal 
insects they are either entirely absent or reduced to mere rudi- 
mentary filaments, caused me to entertain the hope that I should 
be able to confirm my surmises by actual experiments on the 
effects of sonorous vibrations on the antennal fibrillse; also the 
well-known observations of Hensen* encouraged me to seek in 
aerial insects for phenomena similar to those he had found in 
the decapod the Mt/sis, and thus to discover in nature an appa- 
ratus whose functions are the counterpart of those of the appa- 
ratus with which I gave the experimental confirmation of 
Fourier's theorem, and similar to the supposed functions of the 
rods of the organ of Corti. 

The beautiful structure of the plumose antennse of the male 
Culex mosquito is well known to all microscopists ; and these 
organs at once recurred to me as suitable objects on which to 
begin my experiments. The antennse of these insects are twelve- 

i'ointed; ana from each joint radiates a whorl of fibrils; and the 
atter gradually decrease in their lengths as we proceed from 

* ** Studien iiber das Gebororgan der Decapoden," Siebold und Kolliker's 
Zeitschfytfur wissenschaftlicke Zooloffie, vol. xiii. 

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Prof. A. M. Mayer's Researches in Acoustics* 877 

those of the second joint from the base of the antenna to those 
of the second joint from the tip. These fibrils are highly elastic^ 
and so slender that their lengths are over three hundred times 
their diameters. They taper slightly^ so that the diameter at the 
base is to the diameter near the tip as 8 to 2. 

I cemented a live male mosquito with shellac to a glass slide, 
and brought to bear on various fibrils a one-fifth objective. I then 
sounded successively, near the stage of the microscope, a series 
of tuning-forks with the openings of their resonant boxes turned 
towards the fibrils. On my first trials with an Ut4 fork of 512 
vibrations per second, I was delighted with the results of the 
experiments ; for I saw certain of the fibrils enter into vigorous 
vibration, while others remained comparatively at rest. 

The Table of experiments which I have given is characteristic 
of all of the many series which I have made. In the first column 
(A) I have given the notes of the forks in the French notation, 
which Konig stamps upon his forks. In the second (B) are the 
amplitudes of the vibrations of the end of the fibril in divisions 
of the micrometer-scale; and in column C are the values of 
these divisions in fractions of a millimetre. 




Ut, . 

. 0*5 div. 

•0042 millim 

Ut3 . 

. 2-5 „ 

•0200 „ 

Mia . 

. 1-76 „ 

•0147 „ 

Sol, . 

. 20 „ 

•0168 „ 

Ut4 . 

. 60 „ 

•0504 „ 

Mi^ . 

. 1-5 „ 

•0126 „ 

S0I4 . 

. 1-5 „ 

•0126 „ 

Br . 

. 1-6 „ 

•0126 „ 

Ut« . 

. 20 „ 

•0168 „ 

The superior effect of the vibrations of the Ut4 fork on the 
fibril is marked ; but thinking that the differences in the ob- 
served amplitudes of the vibrations might be owing to differ- 
ences in the intensities of the various sounds, I repeated the 
experiment, but vibrated the forks which gave the greater ampli- 
tudes of covibration with the lowest intensities; and although I 
observed an approach toward equality of ampUtude, yet the 
fibril gave the maximum swings when Ut^ was sounded ; and I 
was persuaded that this specisd fibril was tuned to unison with 
XJt4 or to some other note within a semitone of it. The differ- 
ences of amplitude gi^en by Ut4 and S0I3 and Mi4 are con- 
siderable; and the Table also brings out the interesting ob- 
servation that the lower (Uto) and the higher (Utg) harmonics 
of Ut4 cause greater amplitudes of vibration than any interme- 
diate notes. As long as a universal method for the determina- 

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878 Prof. A. M. Mayer^s Researches m Acoustics, 

tion of the relative intensities of sounds of different pitch re- 
mains undiscovered^ so long will the science of acoustics remain 
in its present vague qualitative condition"*** Now^ not having 
the means of equalizing the intensities of the vibrations issuing 
from the various resonant boxes^ 1 adopted the plan of sounding 
with a bow each fork with the greatest intensity I could obtain. 
I think that it is to be regretted that Konig did not adhere 
to the form of fork with incUned prongs as formerly made by 
Marloye; for with such forks one can always reproduce die 
same initial intensity of vibration by separating the prongs by 
means of the same cylindrical rod^ which is drawn between 
them. Experiments similar to those already given revealed a 
fibril tuned to such perfect unison with Vt^ that it vibrated 
through 18 divisions of the micrometer, or *15 millim., while 
its amplitude of vibration was only 3 divisions when Ut4 was 
sounded. Other fibrils responded toother notes; so that I infer 
from my experiments on about a dozen mosquitos that their 
fibrils are tuned to sounds extending through the middle and 
next higher octave of the piano. 

To subject to a severe test the supposition I now entertained, 
that the fibrils were tuned to various periods of vibration, I mea- 
sured with great care the lengths and diameters of two fibrik, 
one of which vibrated strongly to Vt^, the other as powerfully 
to Ut^ ; and from these measures I constructed in homogeneous 
pine-wood two gigantic models of the fibrils, the one corre- 
sponding to the Utg fibril being about 1 metre long. After a 
little practice I succeeded in counting readily the number of 

* I have recently made lome experiments in this direction which show 
the possibility of eventually beins able to express the intensity of an aerial 
vibration directly in fraction of Joule's dynamical unit, by measuring the 
heat developed iu a slip of sheet rubber stretched between the prongs of a 
fork and enclosed in a eompound thermo-batterv. The relative intensitiea 
of the aerial vibration proauoed by the fork when eneaged in heating the 
rubber and when the rubber is removed, can be measured by the method I de» 
scribed in the Philosophical Magazinci 1873, vol. xlv. p. 18. Of course, if we 
can determine the amount of heat produced per second by a known fraction of 
the intensity, we have the amount produced b]^ the vibration with its entire 
intensity. Then means can be devised by which the aerial vibration pro- 
duced by this foriL can always be reproduced with the same intensity. 
This intensitv, expressed in firaiction of Joule's unit, is stamped upon the 
apparatus, which ever afterward serves as a true measure for obtaimng the 
intensities of the vibrations of all simple sounds having the same pitch as 
itself. The same operation can be performed on other forks of oiffeient 
pitch ; and so a series of intensities of different periods of vibration is ob- 
tained expressed in a corresponding series of fractions of Joule's unit. 
Recent experiments have given - ^^^^^^ of a Joule's unit as the approxi- 
mate dynamic equivalent of ten seconds of aerial vibrations produced by 
an Ut, fork set in motion by intermittent electromagnetic action and placed 
before a resonator. 

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Prof. A. M. Mayer's Re9earehes in Acoustics. 879 

vibrations they gave when they were ehonped at one end and 
drawn from a horizontal position. On obtiuning the ratio of 
these nnmbersj I found that it coincided with the ratio exist- 
ing between the nnmbers of vibrations of the forks to which 
covibrated the fibrils of which these pine-rods were models. 

The consideration of the relations which these slender, taper- 
ing, and pointed fibrils must have to the aerial pulses acting on 
them, led me to discoveries in the physiology of audition which 
I imagine are entirely new* If a sonorous wave falls upon one 
of these fibrils so that its wave-front is at right ang^ to the 
fibril, and hence the direction of the pulses in the wave are in 
the direction of the fibril's length, the latter cannot be set in 
vibration ; but if the vibrations in the wave are brought mcnre 
and more to bear athwart the fibril, it will vibrate with am- 
plitudes increasing until it reaches its maximum swing of co- 
vibration, when the wave-front is parallel to its length, and there- 
fore the direction of the impulses on the wave are at right angles 
to the fibril. These curious surmises I have confirmed by many 
experiments made in the following manner. A fork which 
causes a strong covibration in a certain fibril is brought near 
the microscope, so that the axis of the resonant box is perpendi- 
cular to the fibril, and its q)ening is toward the microscope. 
The fibril in these circumstances enters into vigorous vibration 
cm sounding the fork ; but on moving the dox round the 
stage of Hbk microscope so that the axis of the box always 
points toward the fibril, the amplitudes of vibration of the fibril 
gradually diminish; and when the axis of the box coincides 
with the length of the fibril, and therefore the sonorous pulses 
act on the fibril in the direction of its length, the fibril is abso- 
lutely stationary, and even remains so when the fork in this 
position is brought quite close to the microscope. These ob- 
servations at once revealed to me another function of these 
(MTgans : for if, for the moment, we assume that the antennae are 
really the organs which receive aerial vibrations and transmit 
them to an auditory capsule, or rudimentary labyrinth, then 
these insects must have the faculty of the perception of the 
direction of sound more highly developed than in any other class 
of animals. Hie following experiments will show the force of 
this statement, and at the same time illustrate the manner in 
which these insects determine the direction of a sonorous centre* 
I placed under the microscope a live mosquito, and kept my at- 
tention fixed upon a filnril which covibrated to the sound of a 
tuning-fork which an assistant placed in unknown positions 
^ around the microscope. I then rotated the stage of the instru- 
ment until the fibril ceased to vibrate, and then drew a line on 
a piece of paper under the microscope in the direction of the 

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880 Prof. A. M. Mayer's Ra^arches in Aeomtia. 

fibril. On extending this line I found that it always cat within 
5^ of the position of the source of the sound. The antennae of 
the male mosquito have a range of motion in a horizontal di- 
rection^ so that the angle included between them can vary con- 
siderably inside and outside of 40^^; and I conceive that this is 
the manner in which these insects during night direct their 
flight toward the female. The song of the female vibrates the 
fibriUse of one of the antenn» more forcibly than those of the 
other. The insect spreads the angle between his antennse^ and 
thus, as I have observed, brings tibe fibrilUe, situate within the 
angle formed by the antennas, in a direction approximately pa- 
rallel to the axis of the body. The mosquito now turns his 
body in the direction of that antenna whose fibrils are most 
afiected, and thus gives greater intensity to the vibrations of*the 
fibrils of the other antenna. When he has thus brought the vi- 
brations of the antennae to equality of intensity, he has placed his 
body in the direction of the radiation of the sound, and he directs 
his flight accordingly ; and from my experiments it would appear 
that he can thus guide himself to within 6^ of the direction of 
the female. 

Some may assume (as I did when I began this research), 
firom the fact of the covibration of these fibrils to sounds of dif- 
ferent pitch, that the mosquito has the power of decomposing the 
sensation of a composite sound into its simple components, as is 
done b^ the higher vertebrates ; but I do not hold this view, 
but beheve that the range of covibration of the fibrils of the mos- 
quito is to enable it to apprehend the ranging pitch of the 
sounds of the female.- In other words, the want of definite and 
fixed pitch to the female's song demands for the receivin^-q)pa- 
ratus of her sounds a corresponding range of covibration ; so 
that, instead of indicating a high order of auditory development, 
it is reallv the lowest, except in its power of determining the di- 
rection of a sonorous centre, in which respect it surpasses by far 
our own earf- 

* The shafts of the antenns include an ansle of about 40°. The basal 
fibrils of the antennae form an an^le of about PO^, and the terminal fibrils 
an angle of about 30^, with the axis of the insect. 

t Some physiologists, attempting to explain the function of the semi- 
circular canab, assume, because these canals are in three planes at right 
angles to each other, that they serve to fix in space a sonorous centre, just 
as the ^ometrician by his three coordinate planes determines the position 
of a pomt in space. But this assumption is fianciful and entirely devoid of 
reason ; for the semicircular canals are always in the same dynamic rela- 
tion to the tympanic membrane which receives the vibration, to be trans- 
mitted always in one way through