William Jackson Hooker.

The London, Edinburgh and Dublin philosophical magazine and journal of science online

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HARVARD
COLLEGE
LIBRARY



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THE
LONDON, EDINBURGH, and DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

CONDUCTED BT

SIB DAVID BREWSTER, K.H. LL.D. P.R.S.L. & E. &c.
RICHARD TAYLOR, P.L.S. G.S. Astr. S. Nat. H. Mosc.ficc.
SIR ROBERT KANE, M.D., F.R.S., M.R.I.A.
WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. P.C.S.
JOHN TYNDALL, Ph.D. F.R.S. &c.



*' Nee aranearum sane textus ideo melior qoia ex se fila gignunt, nee notter
▼Uior quia ez alienis Ubamiis at apes." Jubt. Lips. Polii. lib. i. cap. 1 . Not.



VOL. XII.— FOURTH SERIES.
JULY— DECEMBER, 1866.



LONDON.

TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Printers and Publishers to the Unhersity of London j

SOLD BY LONOM AN, BROWN, OREBN, LONOMANS, AND ROBEBT8 ; UlCmNy

MARSHALL AND CO.; WHITTAKEB AND CO.; AND PIPBB AND CO.,

LONDON : — BY ADAM AND CHARLES BLACK, AND THOMAS

CLARK, EDINBURGH; SMITH AND SON, GLASGOW;

HODGES AND SMITH, DUBUN ; AKD

FVTNAM, NEW YORK.



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HARVA.QL^

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Lz.^ARY



" Meditationis est pencrutari occulta; oontemplatioius eat adminri

penpicua Admiratio generat qusestionem, qiuestio investigationeiD,

investigatio inyentionem." — Hugo de S. Victore.



— " Cur Spirent venti, cur terra dehiscat.
Cur mare turgeacat, pelago cur tantus amaror.
Cur caput obacura Phoebus ferrugine condat.
Quid totiea diros cogat flagrare cometas;
Quid pariat nubes, Yeniant cur fulmina ccelo.
Quo micet igne Iris, superos quis conciat orbea
Tarn vario motu.**

/. B. PinelU ad Mazonium,



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CONTENTS OF VOL. XIL

(FOURTH SERIESO



NUMBER LXXVL— JULY 1856.

Pagt

Prof. Powell on the Demonstration of Fresnel's Formulas for

Reflected and Refracted Light ; and their AppUcations • . • . 1
Mr. A. Cayley on the Cones which pass through a given Curve

of the Third Order in Space 20

Mr. H. M. Witt on a peculiar Power possessed by Porous
Media (Sand and Charcoal) of removing Matter from Solu-
tion in Water 28

Prof. Tyndall's Comparative View of the Cleavage of Crystals

and Slate Rocks 36

Prof. W. H. Miller on the Form of an Alloy of Bismuth 48

The Rev. S. Haughton oo the Density of the Earth, deduced
from the Experiments of the Astronomer Royal, in Harton

Coal-pit 60

Dr. Atkinson's Chemical Notices from Foreign Journals. ... 61

Proceedings of the Royal Society - 69

Geological Society 68

On the Absorption of Heat by Decomposition, by Dr. Woods. . 74

On Heat as the Equivalent of Work, by M. Hoppe • 76

Explosive Action of Sodium on Water, by F. W. Griffin, Ph.D. 78

Meteorological Observations for May 1856 79

Meteorological Observations made by Mr. Thompson at the
Garden of the Horticultural Society at Chiswick, near
London; by Mr. Veall at Boston; and by the Rev. C.
Clouston at Sand wick Manse, Orkney 80



NUMBER LXXVn.— AUGUST,

Prof. Clausius on a modified Form of the second Fundamental
Theorem in the Mechanical Theory of Heat 81

Prof. H. Hennessy on the Influence of the Earth's Internal
Structure on the Length of the Day 99

Mr. W. J. M. Rankine on Heat as the Equivalent' of Work . 103

Prof. Powell on the Demonstration of Fresnel's Formulas for
Reflected and Refracted Light ; and their Applications. —
Part II 104-



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ir CONTBNT8 OF VOL. XII. — FOI7BTH IBIUM.

Pag*

Prof. Sylvester on Professor Galbraith's Construction for the

Range of Projectiles 112

Mr. H. M. Witt on the Variations in the Chemical Composition

of the Thames Water, during the year between May 1855

and May 1856 114

Mr. J. Cockle on the Resolution of Algebraic Equations of the

Fifth Degree 124

Mr. H. J. Brooke on a substance named Bleiniere in modem

Treatises on Mineralogy •. . 126

Mr. H. C. Sorby on the Theory of the Origin of Slaty Cleavage. 127

Prof. Tyndall's Observations on the preceding Paper 129

Sir W. Snow Harris on certaiu Phsenomena of Electrical Dis-

charge 136

Proceedings of the Royal Society 141

Geological Society 149

On the Heat absorbed in Chemical Decompositions, by J. P. Joule. 155
On the Cleavageof compressed WhiteLead,byWarrenDe la Rue. 167
On the Behaviour of Iodide of Silver towards Ammonia, by

Dr. A. Vogel, Jun 157

Electrolytical Investigations, by M. Magnus 157

Meteorological Observations for June 1856 159

Table 160



NUMBER LXXVIII-— SEPTEMBER.

Prof. Tyndall's further Researches on the Polarity of the Dia-

magnetic Force 161

Mr. C. Marett's Attempt to investigate the Causes of the Inter-
vals between High- water and Slack- water, and between the

turn of Tide near the Shore and in the Offing 184

Dr. Atkinson's Chemical Notices from Foreign Journals 188

Sir J. F. W. Herschel on Slaty Cleavage, and the Contortions

of Rocks 197

Dr. A. Matthiessen's Preliminary Notice on the Electric Con-
ducting Power of the Alkaline Metals 199

Dr. Schunck on Rubian and its Products of Decomposition. —

Part III 200

Prof. Stevelly on the Doctrine of Parallel lines considered in a

new Method 220

Prof. Airy on Scheutz's Calculating Machine 225

Proceedings of the Royal Society 226

Absorption of Heat by Decomposition, by Dr. Woods 283

Observations and Experiments upon the employment of Iodide

of Potassium as a Reagent for Ozone, by S. Cioez 237

Ou the Presence of Mercury in the native Argentiferous Copper

of Lake Superior, by M. Hautefeuille 238

Meteorological Observations for July 1856 239

Table 240



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COlinifTS OT TOL. XII. — FOVBTB UKIBI. T

NUMBER LXXIX.-OCTOBBR.

Page

Prof. Claosius on the Application of the Mechanical Theory of

Heat to the Steam-engine 241

Prof. Powell on the Demonstration of Fresnel's Formulas for

Reflected and Refracted Light.— Part III 266

Dr. Schunck on Rubian and its Products of Decomposition. —

Part III. (concluded) 270

Mr. J. P. Hennessy's Note on Professor Stevelly's Paper on the

Theory of Parallels 283

M. T. Plateau on the recent Theories of the Constitution of

Jets of Liquid issuing from Circular Orifices . . • 286

Dr. Atkinson's Chemical Notices from Foreign Journals .... 297

Proceedings of the Royal Society 805

Cambridge Philosophical Society 316

On the Heat absorbed inChemical Decompositions, by J. P. Joule. 32 1

On a Law of Electrical Heat, by Dr. P. Riess 322

Obserrations on Ozone, relating to a recent paper of M. Cloez,

by M. Bineau 324

Note on the Endosmose of Gases, by J. Jamin 325

Meteorological Observations for August 1856 327

Table 328



NUMBER LXXX.— NOVEMBER.

Prof. Challis on a Theory of the Composition of Colours on the

Hypothesis of Undulations 329

Prof. Clausius on the Application of the Mechanical Theory of

Heat to the Steam-engine (continued) 338

Mr. A. Cayley's Second Note on the TTieory of Logarithms . . 354
Dr. Debus on the Action of Nitric Acid on Alcohol at Common

Temperatures 361

Mr. J. P. Hennessy on a Solution of the Theory of Parallels,
from the Definitions of Euclid, without deviating from the

ordinary Principles of Geometrical Proof 371

Prof. Stevelly on the Doctrine of Parallel Lines 375

Mr. J. N. Hearder on a powerful Form of the Induction Coil,
with some new Statical and lliermal Effects of the Induced

Current 377

Mr. J. P. Joule on Prof. Clausius's Application of the Mecha-
nical Theory of Heat to the Steam-engine 385

Dr. Heddle on the " Davidsonite " of Thomson 386

Proceedings of the Royal Society 387

Cambridge Philosophical Society 397

Note on the Employment of Induction Apparatus. — The Mer-
curial Interruptor. By L6on Foucault 403

Note on Colonel Sabine's Periodic and Non-periodic I'empera-
ture Variations at Toronto, by S. M. Drach, Esq., F.R.A.S. 406



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Tl COBmNn OF VOL. XII. — POVETH BERIB9.

Page
On a Zeolitic Minend from the Isle of Skye, Scotland, by J. W.

MaUet, Ph.D 406

Meteorological Observations for September 1856 407

— ' Table 408



NUMBER LXXXL— DECEMBER.

The Rev. S. Haughton on Slaty Cleavage, and the Distortion
of Fossils 409

Prof. Stokes's Remarks on Professor Challis's paper, entitled
" A Theory oi the Composition of Colours/' &c 421

Prof. Clausius on the Application of the Mechanical Theory
of Heat to the Steam-engine (concluded) 426

Mr. J. N. Hearder on a new Arrangement of the Induction Coil. 443

Sir W. R. Hamilton's Memorandum respecting a new System
of Roots of Unity 446

Mr. P. J. Martin on the Anticlinal Line of the London and
Hampshire Basins 447

Mr. J. P. Hennessy on the Importance of an Adequate Defini-
tion in developing the Theory of ParaUel lines 452

Prof. Schonbein on the Oxidation of the Constituents of Am-
monia by Porous Media, with some Remarks on Nitrification. 457

Mr. H. Wedgwood's Remarks on a System of Geometry derived
from an Analysis of our ideas of Direction and Position .... 459

Prof. Clausius's Reply to a Note of Mr. Joule, contained in the
November Number of the Philosophical Magazine 463

Notices respecting New Books: — M. A. Delesse's Mat^riaux
de Construction de TExposition Universelle de 1855 464

Proceedings of the Royal Society 466

Geological Society 482

Note on the Optical Properties of Transparent Bodies submitted
to the Action of Magnetism, by M. Verdet . . 483

On the possibility of the simultaneous existence of opposite
Electrical Currents in the same Conducting Wire, by Professor
G. Belli 485

Measurement of the Speed of a Railway Train by means of
Electro-magnetism, by W. C. M'Rea 486

Meteorological Observations for October 1856 487

Table 488



NUMBER LXXXIL— SUPPLEMENT TO VOL. XII

M. V. Regnault on the Specific Heat of some Simple Bodies,
and on the Isomeric Modifications of Selenium 489

Mr. C. A. Bentley on an Improved Construction of Ruhmkorff 's
Induction Coil 519



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CONTENTS OP VOL. XII. FOURTH SERIES. TU

Page
Prof. Challis on the Transmutation of Rays of light ; with a
Reply to the " Remarks " of Professor Stokes in the Decern-

ber Number 621

Prof. Magnus on the Allotropic Conditions of Sulphur 526

Dr. Atkinson's Chemical Notices from Foreign Journals .... 531

Proceedings of the Ro3ral Society • 539

Note on the new Zeolite from Skye, analysed by Mallet, by

Dr. Heddle 562

Sir W. Snow Harris on Riess's Law of Electrical Heat 553

Index 566



ERRATA IN VOL XI.

Page 157, tine btfw half the side rtad the side.

— 159, — 24, /or 2,000,000 read 5200x10*; snd /or 8,200,000

r0a<2 21000 xlO«.

— t6. — 30, /or 10 tons r«id 53,600 X 10* ttms; and /or 42 tons!

read 874,000 x 10« tons I



ERRATA IN VOL XII.

Page 394, line 19, /or p r op ert y ttad (juality.

— 395, — 7 from bottom, /or a siTen result read given a result.

— 396, — 14 from bottom,/or that rwd iteel.



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THE
LONDON, EDINBURGH and DUBLIN

PHILOSOPHICAL MAOAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SEKIES.]



JULY1S5Q.



h On the Demonstration ofPresneVs Formulas for Reflected and
Refracted Light ; and their Applications, By the Rev. Baden
Powell, M.A., F.R.S. Sfc, Savilian Professor of Geometry in
the University of Oxford*,

h A QUESTION between two fundamentally different views

JljL of the theory of polarization, which has been long
agitated among inquirers into the undulatory theory, viz. as to
the direction of the plane of vibrations in relation to that of
polarization, has of late excited more peculiar interest, partly
from the announcemejat, a few years ago, of a remarkable crucial
experiment by Professor Stokes, and partly from several subse-
quent investigations, especially the recent elaborate discussion of
the general bearing of the experimental evidence by M. Haidinger.

The revival of this question recalls the attention of the studeni
to the very unsatisfactory condition in which the elementary de-
monstration of those parts of the theory on which it depends has
long been left, and from which recent speculations have done
little to deliver it*

2. The well-known and remarkable formulas originally given
by Fresnel to express the amplitudes of the vibrations, and thence
the intensities, of reflected and refracted rays of polarized light
(for singly-refracting media), which are found to represent so
beautifully all the observed changes, — in fact including the whole
doctrine of plane polarization, and thus invaluable as inductive
laws, — ^yet long remained confessedly defective as to their system-
atic deduction from theory.

8. Fresnel, indeed, with that marvellous sagacity for which
he was so conspicuous, satisfied himself of their truth by reason-

* Gommumcated by the Author.
Pha. Mag, S. 4. Vol, 12. No. 76. July 1856. B



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3 Prof. Powell on the Demonstration o/VresneVB Formulas

ing on assamptioDB in some instances confessedly empirical^ in
others dependent on analogies^ or hypotheses not me from doubt^
and at any rate little connected into a system.

4. This investigation, -whose questionable points are so &irly
stated, and ably grappled with, by Mr. Airy in his tract on the
Undulatory Theory (1831, art, 128 et seq.), has been since pur-
sued on different principles by M. Gauchy, and especially by the
late Prof. Maccullagh in his memoir '^ On th« Laws of Crystal-
line Reflexion and Refraction '^ (Mem. Roy. Irish Acad. vol. xviii.
1838), whose views have been ably but briefly expounded by
Dr. Lloyd in his Lectures on the Wave Theory (part 2. p. 30,
1841). More recently, Mr. Power has investigated the subject
by a systematic analysis, directed to other objects, but inclu<ung
an important element in these deductions ('^ On Absorption of
Rays,'' fee, Phil. Trans. 1854, part 1).

6. But among these distinguished philosophers there exists
considerable diversity, and even contradiction of views. Nor, so
far as I am aware, has the subject been so discussed as to enable
us to trace the source of these discrepancies, or fairlv to estimate
the claims of the opposing theories, or the force of the experi-
mental results which bear upon them. Thus it seems highly
desirable, that questions affecting so fundamental a part of the
undulatory theory should be cleared up and placed on an un-
assailable oasis.

Having lon^ ago thrown aside some investigations oh the
subject, in which I was then engaged, I have of late had my
attention recalled to the question, and have thus been induoed
to revise and extend those investigations, in the hope of contri*
buting towards the settlement of the points involved, or at any
rate of putting the whole discussion before the student in a con«
neeted point of view ; with which object I have been led to eom-
mence ab initio, so that those who have only an elementary
acquaintance with the theory may be enabled to follow the de*
ductions without difficulty, and may here be furnished with that
systematic elucidation which is not, as far as I am aware, to be
found in any existing publication. -

Theoretical Views,

6. The formulas for the amplitudes of the incident, reflected,
and refracted rays, as given by Prof. Maccullagh and later writers,
though closely corresponding with those of Fresnel, and frdfilling
gaierally the same conditions, yet differ from them in certain
cases as to the sign, and in others as to the values of the ex^
pressions.

7. But the main point of difference and difficulty consists in
this : Presnel investigates two sets of formulas ; one set (H) for



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ftir Reflected amd Refracted Light. S

the respective rays deduced on the supposition that the vibra-
tions are perpendicular to the plane of incidence^ another set (K)
on the supposition that they are parallel to that plane. Now
those of Maecollagh^ which correspond closely to FresnePs first
set (H), are deduced on the contrary supposition of vibrationer
parallel to incidence^ while those corresponding to Fresnel's
second set (K) are for vibrations /^^^Tu^tcu&^r to that plane.

8. In eidier investigation the formulas (K) are. those which
represent evanescence of the light at the polarizing angle, while
the formulas (H) represent brightness at that incidence.

But when a ray vanishes at the polarizing angle^ we know that
its plane^ of this second incidence^ must he perpendicular to that
of its first incidence or original polarization. Hence^ according
as the vibrations (K) may be parallel or perpendicular to thiii
second plane of incidence^ they must be respectively perpendicular
or partUlel to the first or plane of polarization. The questioi)
thus reduces itself to whether^ in polarized light in general^ the
vibrations exe parallel or perpendicular to the pluie of polariaation.

9. M. Cauchy^ in an earlier paper {Mem, Inatit. vol. x. p. 304}^
had inferred with Maccullagh^ from dvnamical views^ that the
vibrations are parallel to the plane of polarization. But in a
later memoir {Bull. Math. July 1830) he deduces formulas cor<i
responding to FresneFs on the hypothesis of vibrations perpen-
diadar to the plane of polarization, and even more formally
renounces his earlier opinion and returns to that of Fresnel. He
also connects similar equations with higher dynamical principles
in the Nouv. Exerciees Math, (liv. 7).

Synopsis of Formulas referred to.

10. FresneFs formulas for yihrBiiona perpendiculai: to the plane
of incidence (A being the amplitude of the incident, h! of the
reflected, and A, of the refracted rays, and dividing by h, i being
the angle of incidence, r of refraction),



^_ — sin (t— r) |, _ 2sinrcos> ,„.

'^" sin (i+r)^ '*'" trin(t-fr)' • • • W

and for vibrations para/&/ to the plane of incidence (similarly
designated by A, /?, and A^),

L/_ tan (t-r) f tan(tT) \ cost .„

tan(t+r)' '""\^ tan (f>r)/cosr' * ^^^
Theae last may be otherwise expressed thus :

1/— ^ ^*"" ^ ^^
"*" sin2t+ sin2r*



, ^ / 2sin2r \co8 « 4 sin r cos t
'^ \sin2i+ sin2r/i



sin2i+ sin 2r /cos r "* sin 2i -h sin 2r*
B2



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4 Prof. Powell an the Demomtraiim of Fresnd's Pammloi
11. Here we may observe, in the numerator of h^



and of kp



2 sin r cos ts - sin 2t :

28in2r^ = i2sin2t.
cosr ^



' 12. It is also desirable to notice, that these expressions are
the same as those given in Mr. Airfs Tract, § 129, under the
slightly different form in which they directly result firom the
pecnliar process there pursued, viz. writing sin (r — t) and
— tan (r— •).

Also the numerator of if is positive for all values of (t-^r),
which is necessarily less than 90^, while the denominator becomes
00 at (t+r)=:90^, which, according to Brewster's law, is the
polarizing angle, and for greater values continues negative,

13. Prof. Maccullagh's formulas are, —

for vibrations parallel to the plane of incidence,

A'=^ife^„ h,^-^^-, (HO

8m(t+r)' ' 8m(t-fr) ^ '

for ^i^r^iioxi^ perpendicular to the plane of incidence,

I'— ^^^^<'~sin2r _ tan {i'-^r)

"" sin 2i + sin 2r "" tan (i + r)'

2Bin2t _ tan(t-r) .^^

'"" 8in2t + 8in2r "" ^tan(t+r)* • ' " ^^^

These last are sometimes expressed under the forms

jj^ sin {i'^r) cos (»-Hr) , 8in2t

"" cos (t — r) sin (i + r)' '"" cos (t — r) sin (f + r) '

14. Comparing these formulas with FresnePs (distinguished
by using roman letters), we may observe from (11),

A'=-h', A,=h^,

Here also k^ undergoes the same change of sign at the incidence
of complete polarization.

Densities and Vibrating Masses.

16. In deducing these formulas, it is in all cases necessary to
express the ratio of the ^passes of sther simultaneously vibrating
without and within the medium; and the differences in the
respective formulas are mainly dependent on the very opposite
suppositions made by the several philosophers as to the density
of the tether in different media, — Fresnel supposing it mare dense



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/or Reflected and Refracted Light » 6

within the denaer medium; Caacby^2e«« dense; and Maccullagh^
equally dense in all media. The last-named writer has argued
that refraction cannot be dependent on the density of the aether
89 such. He especially observes^ that ''in doubIy*refracting /
crystals, the density, being independent of the direction, could (
not be conceived to vary with the refiractive index'* (p. 89). And \
Prof. Stokes has observed, that in the vibrations of sether, '' di«>
minution of velocity seems capable of being accounted for on j
several distinct hypotheses/' t

16. The expressions for the masses of sther vibrating in the \
same time without and within the denser medium, are obtained

on these different suppositions as to the density of the sther, as
follows :—

If V be the velocity of the incident ray, v^ that of the refracted^

and the index f^s — , then at a perpendicular incidence, the simul*

taneously vibrating masses will be simply

(m) ^ *> ^ _ sint

(m^) "" V| '"'^ "" sin r *

If the densities be 8, 8^, then, according to the view of Fresnelj
*,>S, and

8 _ sin^r _ 1

?;^sin«t •"/*»'

and we must multiply in this ratio, which gives

K) /**

If S^Sp according to the view of MaccuUagh,

(m)

K)

17. In either case, for oblique inddences we must multiply by
the rectangular breadth of the rays on the same base or section
of the surface, which will be as cos t : cos r, or

m _ (m) cos t
m^ "" (m^)cosr*
Thus, according to Fresnel,

w ^1 cost ^ sinrcost



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