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THE 


LONDON, EDINBURGH, anp DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


CONDUCTED BY 


SIR WILLIAM THOMSON, Kur. LL.D. F.R.S. &c. 
GEORGE FRANCIS FITZGERALD, M.A. F.R.S. 


AND 


_ WILLIAM FRANCIS, Px.D. F.L.S. F.R.A.S. F.C.S. 


‘Nec aranearum Sane textus ideo melior quia ex se fila gignunt, nec noster 
vilior quia ex alienis libamus ut apes.” Jusr. Lips. Polit. lib. i. cap. 1. Not. 


VOL. XXIX.—FIFTH SERIES. 
JANUARY—JUNE 1890. 


LONDON: 
TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, 


SOLD BY SIMPKIN, MARSHALL, TIAMILTON, KENT, AND CQ., LD.; AND WHITTAKER 
AND CO.;—-AND BY ADAM AND CHARLES BLACK, AND 'T. AND T. CLARK, 
EDINBURGH; SMITH AND SON, QLASGOW »--HODGES, FIGGIs, 

AND CO., DUBLIN ;—PUTNAM, NEW YORE 3—-VEUVBE J. BOYVEAU, 
PARIS ;—AND ASHER AND CO., BERLIN. 


“Meditationis est perscrutari occulta; contemplationis est admirari 
perspicua.... Admiratio generat queestionem, queestio investigationem, 
investigatio inventionem.”—Hugo de S. Victere. 


“Cur spirent venti, cur terra dehiscat, 

Cur mare turgescat, pelago cur tantus amaror, 

Cur caput obscura Phoebus ferrugine condat, 

Quid toties diros cogat flagrare cometas, 

Quid pariat nubes, veniant cur fulmina ccelo, 

Quo micet igne Iris, superos quis conciat orbes 

Tam vario motu.” 

J. B. Pinelli ad Mazonium. 


CONTENTS OF VOL. XXIX. 


(FIFTH SERIES). 


NUMBER CLXXVI.—JANUARY 1890. 


Page 

Mecdetayletohi on Dells..gr. Sse 6 uM NS BEL 6. af 
Ladislaus Natanson on the Kinetic Theory of the Phenomena 

Grebissocintionbim Gasesil.): kt Ws OS: Foe oN 18 
Prof. S. P. Langley and Mr. F'. W. Very on the Temperature 

CE WOS MCC ARN ae ae Oa eer eA Oni, SUPA, AL Be 31 


Mr. W.G. Gregory ona New Electric Radiation Meter.. 54 
Mr. J. Enright on Electrifications due to the Contact of Gases 


TEPID, TNCTOING IEA Se aoe ene mn renee Acs dart it a as, OU 56 
Mr. Herbert Tomlinson on the Effect of Repeated Heating 
and Cooling on the Electrical Resistance of Iron ........ 77 


Prof. Tait on the Importance of Quaternions in Physics .... 84 

Prof. T. Carnelley on an Approximate Algebraic Expression of 
the Periodic Law of the Chemical Elements. (Plate I.) .. 97 
Mr. A. L. Selby on two Pulsating Spheres in a Liquid ...... 113 

H. Nagaoka on Transient Electric Current produced by 

suddenly twisting Magnetized Iron and Nickel Wires. 
With Note by Sir W. Thomson. , (Plate II.) ............ 123 

Proceedings of the Geological Society :— 

Mons. F. M. Corpi on the Catastrophe of Kantzorik, 
ASIEN INVA EY APR ys Saya aS oat hots) aie cee Nel ek SxSE NE y's han 133 

Mr. RK. N. Worth on the Igneous Constituents of the 
Triassic Breccias and Conglomerates of South Devon . 134 

Capt. A. W. Stiffe on the Glaciation of parts of the Valleys 


of the Jhelam and Sind Rivers, Kashmir .......... hea 
The Magnetism of Nickel and Tungsten Alloys, by John 
Trowbrdee and SamuelSheldom, 5 4434). 15. 4)-..2)- te oe ds 136 
Note on the Application of Hydraulic Power to Mercurial 
Pumps, by ive. Hrederick Jj Smith, .)ySsehs aye. bec. 138 
On Evaporation and Solution as Processes of Diffusion, by 
ARO NmO OU CNA ic scieys a) cc e's Big Aide ws yp 0g 5 AD AIMS tro GOs 139 
On the Changes of Temperature resulting from the Torsion 
and Detorsion of Metal Wires, by Dr. A. Wassmuth .... 140 


lV CONTENTS OF VOL. XXIX.—FIFTH SERIES. 


NUMBER CLXXVIL—FEBRUARY. is 
age 
Mr. Carl Barus on the Pressure-Variations of certain High- 
Memperature Boiling-Poimts. .. 0... 2)... 0022 eee 141 
Mr. Shelford Bidwell on the Electrification of a Steam-jet .. 158 
Prof. Hermann Karsten on the Geological Age of the Moun- 


taims of Santa Marta 002 .0....0.. 03. 6.055, 0 163 
Mr. James C. M°Connel on Diffraction-Colours, with special 
reference to Corone and Iridescent Clouds ............ 167 
Lord Rayleigh on the Vibrations of an Atmosphere ........ 173 
Eric Gerard on a Process of Plotting Curves by the Aid of 
Photography 0.202 ev. ee Ls 21) cee ou ee 180 
Mr. Arthur Schuster on the Disruptive Discharge of Electri- 
ciby through Gases 2. 4. bs. ls ns oe rl 182 
Mr. C. A. Carus-Wilson on the Behaviour of Steel under 
Miecchanical Stress. (Plates LI.—V.) ...... 0 aoe 200 
Prof. A. Gray on Sensitive Galvanometers ................ 208 
Notices respecting New Books :— 
Rev. O. Fisher’s Physics of the Earth’s Crust ........ 211 


On the Resistance of Hydrogen and other Gases to the Current 
and to Electrical Discharges, and on the Heat developed in 
chesSparcks yoy lH: Villarit leig5) pe ap). choise alee eee 214 
Further Investigations on the Inert Space in Chemical Reac- 
momssaby ©. Iiebreich.. oo 2.0! ale ate = © one eels 216 
Lecture Experiment to prove the Existence of the Direct and 
Inverse Extra Currents, by M. C. Daguenet ........... 216 


NUMBER CLXXVIII—MARCH. 


Mr. A. W. Flux on the Form of Newton’s Rings.......... 217 

Prot. John Perry on Twisted ‘Strips! SY). 2 eee 244 

Mr. Spencer U. Pickering on a New Form of Mixing-Calori- 
meter-. (Plate VIL). 0.0/2 fees th ee 247 


H. E. J. G. du Bois on Kerr’s Magneto-optic Phenomenon .. 253 
Mr. Fred. T. Trouton on the Acceleration of Secondary Hlec- 


tromarnetic Waves. (Plate Vi.) G2, 23552): : See 268 
Sir William Thomson on the Time-Integral of a Transient 
Electromagnetically Induced Current .................. 276 


Proceedings of the Geological Society :— 
Prof. J. Prestwich on the Relation of the Westleton Beds 
or ‘ Pebbly Sands’ of Suffolk to those of Norfolk .... 280 
Prof. C. Lloyd Morgan on the Pebidian Volcanic Series 
Ob Ste Davids i363 ccs s 07 ce ee ee eee ko eee Cee 282 
Prof. T. G. Bonney on the Crystalline Schists and their 
Relation to the Mesozoic Rocks in the Lepontine Alps 284 


CONTENTS OF VOL. XXIX.—FIFTH SERIES. vi 


Page 
Messrs. G. A. J. Cole and J. W. Gregory on the Vario- : 
Inge Rocks. of Momt-Genevre . g0. 5) oie jhe dee eels 286 
Prof. John W. Judd on the Propylites of the Western 
Isles of Scotland, and their Relations to the Andesites 
and) Diovites oltheé Distri¢be, yc. ulema ih) via ad 287 
Note on the Gradual Alteration in Glass produced by altering 
its Temperature a few Degrees, by Spencer U. Pickering.. 289 
On a Telethermometer, by Prof. Dr. J. Puluj ............ 291 
On the Measurement of Electromotive Contact Forces of 
Metals in Different Gases by Means of the Ultra-Violet 
Serie rOee Nr RCL Sd ps"y es ap Saree + spaenlayecegeyete ca ie: Ceyevene\s 291 
Mr. Enright’s Experiments, by Oliver J. Lodge............ 292 


NUMBER CLXXIX.—APRIL. 


H. HE. J. G. du Bois on Magnetization in Strong Fields at 
Different Temperatures. (Plate VIII.)................ 293 

Messrs. J. S. Haldane and M.S. Pembrey on an Improved 
Method of Determining Moisture and Carbonic Acid in Air 306 

Dr.,J. R. Rydberg on the Structure of the Line-Spectra of the 


Dec raa Cal OTM ETIUS . "6 coe ancn-sn ax op onset, of viet shot ar 8A Nol epoh Sporades, WlaT Se 301 
Mr. Carl Barus on the Change of the Order of Absolute Vis- 

cosity encountered on. passing from Fluid to Solid........ O37 
Profs. T. Gray and C. L. Mees on the Effect of Permanent 

Elongation on the Cross Section of Hard-drawn Wires. 355 
Prof. J. J. Thomson on the Passage of Electricity through 

IELeS GRSeSHyS Oar Nene eRe Eee Sets Cor mar ar eee a 358 


Prof. Wyndham R. Dance and Mr. T. 8. Dymond on an 
Apparatus for the Distillation of Mercury ina Vacuum .. 367 
Notices respecting New Books :— 
Transactions of the Edinburgh Geological Society, Vol. VI. 
IP ph rca aca AS) sayy ttn sd cat sche bila Mra his oh ood ys orgs t us 372 


SLIGLEND 2a SO, Ce eer 2 ee een a ee See Pe 373 
Electrical Vibrations in Rarefied Air without Electrodes, by 

BAIT SONOS OTSA hn horn ae tse) 4 Sed casa do eis oi a lceiiekk © 375 
On the Formation of Ozone by the Contact of Air with Ignited 

Platinum, and on the Electrical Conductivity of Air ozonized 

by Phosphorus, by Profs. Elster and Geitel ............ 376 
Note in Connexion with Dropping-Mercury Electrodes, by J. 

EO ERM gl beta lls alo itty, tert assis oda ih oP MaL® Ge Sees 376 


vl CONTENTS OF VOL. XXIX.—FIFTH SERIES. 


NUMBER CLXXX.—MAY. Page 
Rev. Frederick J. Smith on a New Form of Electric Chrono- 
eraphe? (Plate TX) ).. 204 LO rrr 377 


Mr. Ward Coldridge on the Electrical and Chemical Properties 
of Stannic Chloride ; together with the Bearing of the Results 
therein obtained on the Problems of Electrolytic Conduction 
and Chemical Action.—Part I. Experimental Observations. 383 
Mr. Herbert Tomlinson on the Villari Critical Points of 


INiekelyand-Trom 0. Of ees 928 oe Oe er 394 
Dr. G. Gore on a New Method and Department of Chemical 
MRESCARGI --.1o vos wes oy 1s cate oe ow nce tee Se Sate ‘o's fo“ eile e's) 401 
Mr. Spencer U. Pickering on the Nature of Solutions ...... 427 
Mr. T. Mather on the Shape of Movable Coils used in 
Hlectrical Measuring-Instruments ......... 22. 434 
Mr. Shelford Bidwell on the Magnetization of Iron in Strong 
ICIS hots chleiecise phe enitc eee hbk os ooh errr 440 
Prof. J. J. Thomson on the Passage of Electricity through 
HOPG ASES 6 ce bso pe oe pine ets os Orr 441 


Notices respecting New Books :— 
Dr. G. Chrystal’s Algebra: an elementary Textbook for 
the higher classes of Secondary Schools and for Col- 
NOSOS bE ceere sie ool Wes ea hie rrr 449 
On Electrical Oscillations in Straight Conductors, by Prof. 
CHAM ee cipepe se dese hse eyo se ce eye ctae ose ceceieiee 9 ier 450 


CUNIOS, spe eieus dol ibiaiardtd ohaipte-n <ielalia.e pals G's Sle 452 


NUMBER CLXXXI.—JUNE. 


Mr. James ©. M’Connel on the Theory of Fog-Bows. 
CREO D5) SEMIN EHM Soo 453 

Prof. C. Runge on a Method of Discriminating Real from 
Accidental Coincidences between the Lines of Different 


Spechra sh. Vie te... ee 462 
Dr. G. Johnstone Stoney on Texture in Media, and on the 

Non-existence of Density in the Elemental Ather........ 467 
Prof. W. Ostwald on the Theory of Dropping Electrodes.— 

Reply do-Mr.Brown... 0.0... . 2.2. oer 479 


Mr. Ward Coldridge on the Electrical and Chemical Properties 
of Stannic Chloride; together with the Bearing of the 
Results therem obtained on the Problems of Electrolytic 
Conduction and Chemical Action.—Part II. Theoretical 
Wonsiderattons .).6 60. Vali st ee oe 480 
Mr. Spencer U. Pickering on the Theory of Osmotic Pressure 
and its bearing on the Nature of Solutions.............. 490 


CONTENTS OF VOL. XXIX.—FIFTH SERIES. vil 


Page 
Rey. Frederick J. Smith on a Mercury-still for the Rapid Dis- : 
micion ok Mercury im a Wacuum ......6...... 5526-005 501 
Mr. Charles A. Carus-Wilson on the Distribution of Flow in a 
SC MMENTSTIC SOG) 628k eae e eck ee he ee ec ees 503 
Prof. R. Threlfall on Sensitive Galvanometers ............ 508 
M. F. Osmond’s Considerations on Permanent Magnetism .. 511 
Notices respecting New Books :— 
Dr. A. Irving’s Chemical and Physical Studies in the 
Meiamorphismm Ob IOCKS)! ly os5 ec ssn eb eee est 514 
The Radiant Energy of the Standard Candle; Mass of Meteors, 
Pay MO MUG OMIMIS coo eee ee eo aa ee edn os 518 
Observations on Atmospheric Electricity in the Tropics, by 
Lo JURT SD 2g Bilge si can Gc cea eae neat ne nner 520 


PLATES. 


I, Illustrative of Prof. Carnelley’s Paper on an Approximate Algebraic 
Expression of the Periodic Law of the Chemical Elements. 


II. Illustrative of H. Nagaoka’s Paper on Transient Electric Current 
produced by suddenly twisting Iron and Nickel Wires. 


IIL-V. Illustrative of Mr. C. A. Carus-Wilson’s Paper on the Be- 
haviour of Steel under Mechanical Stress. 


VI. Illustrative of Mr. Fred. T. Trouton’s Paper on the Acceleration 
of Secondary Electromagnetic Waves. 


VII. Illustrative of Mr. Spencer U. Pickering’s Paper on a New Form 
of Mixing-Calorimeter. 


VIII. Lllustrative of H. E. J. G. du Bois’s Paper on Magnetization in 
Strong Fields at Different Temperatures. 


IX. Illustrative of Rey. F. J. Smith’s Paper on a new Form of Electric 
Chronograph. 


X. Illustrative of Mr. J. C. M°Connel’s Paper on the Theory of Fog- 
Bows. 


ERRATA. 


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2 ty ane 


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” » O& » VG » GJ 


THE 
LONDON, EDINBURGH, ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES. ] 


SANUARY 1890. 


I. On Bells. By Lord Rayunien, Sec. R.S.* 


«ier theory of the vibrations of bells is of considerable | 


difficulty. ven when the thickness of the shell may 
be treated as very small, as in the case of air-pump re- 
ceivers, finger-bowls, claret glasses, &., the question has given 
rise to a difference of opinion. The more difficult problem 
presented by church bells, where the thickness of the metal 
in the region of the sound-bow (where the clapper strikes) is 
by no means small, has not yet been attacked. A complete 
theoretical investigation is indeed scarcely to be hoped for ; 
but one of tue principal objects of the present paper is to 
report the results of an experimental examination of several 
church bells, in the course of which some curious facts have 
disclosed themselves. 

In practice bells are designed to be symmetrical about an 
axis, and we shall accordingly suppose that the figures 
are of revolution, or at least differ but little from such. 
Under these circumstances the possible vibrations divide 
themselves into classes, according to the number of times the 
motion repeats itself round the circumference. In the gravest 
mode, where the originally circular boundary becomes ellip- 
tical, the motion is once repeated, that is it occurs twice. The 
number of nodal meridians, determined by the points where 
the circle intersects the ellipse, is four, the meridians corre- 
sponding (for example) to longitudes 0° and 180° being 
reckoned separately. In like manner we may have 6, 8, 10.. 


* Communicated by the Author. 
Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. B 


2 Lord Rayleigh on Bells. 


nodal meridians, corresponding to 3, 4, 5... cycles of 
motion. A class of vibrations is also possible which are 
symmetrical about the axis, the motion at any point being 
either in or perpendicular to the meridional plane. But these 
are of no acoustical importance. 

The meaning here attached to the word nodal must be 
carefully observed. The meridians are not nodal in the sense 
that there is no motion, but only that there is no motion 
normal to the surface. This can be best illustrated by the 
simplest case, that of an infinitely long thin circular cylinder 
vibrating in two dimension3*. The graver vibrations are 
here parely flexural, the circumference remaining everywhere 
unstretched during the motion. If we fix our attention upon 
one mode of vibration of n cycles, the motion at the surface 
is usually both radial and tangential. There are, however, 2n 
points distributed at equal intervals where the motion is 
purely tangential, and other 2n points, bisecting the intervals 
of the former, where the .aotion is purely radial. There are 
thus no places of complete rest ; but the first set of points, or 
the lines through them parallel to the axis, are called nodal, 
in the sense that there is at these places no normal motion. 

- The two systems of points-have important relations to the 
place where the vibrations are excited. ‘‘When a bell- 
shaped body is sounded by a blow, the point of application of 
the blow is a place of maximum normal motion of the re- 
sulting vibrations, and the same is true when the vibrations are 
e: cited by a violin-bow, as generally in lecture-room experi- 
ments. Bells of glass, such as finger-glasses, are, however, 
more easily thrown into regular vibration by friction with 
the wetted finger carried round the circumference. The pitch 
of the resulting sound is the same as that elicited by a tap 
with the soft part of the finger; but inasmuch as the tan- 
gential motion of a vibrating bell has been very generally 
ignored, the production of sound in this manner has been 
felt as a difficulty. It is now scarcely necessary to point out 
that the effect of the friction is in the first instance to excite 
tangential motion, and that the point of application of the 
friction is the place where the tangential motion is greatest, 
and therefore where the normal motion vanishes” f. 

When the symmetry is complete, the system of nodal 
meridians has no fixed position, and may adapt itself so as to - 
suit the place at which a normal blow is delivered. If the 


* ‘Theory of Sound,’ § 232. 

+ ‘Theory of Sound, § 284, That the rubbing finger and the violin- 
bow must be applied at different points in order to obtain the same 
vibration was known to Chladni. 


Lord Rayleigh on Bells. 3 


point of application of the blow be conceived to travel round 
a circle symmetrical with respect to the axis, say, for brevity, 
_acircle of latitude, the displacement will make no difference 
to the vibration considered as a whole, but the effect upon an 
observer who retains a fixed position will vary. If the bell 
be situated in an open space, or if the ear of the observer be 
so close that reflexions are relatively unimportant, the sound 
disappears as nodes pass by him, swelling to a maximum 
when the part nearest to the ear is one of the places of 
maximum normal motion, which for brevity we will call 
loops. In listening to a particular note it would thus be 
possible to determine the number of nodal meridians by 
watching the variations of intensity which occur as the place 
of the blow travels round a circle of latitude. 

In practice the symmetry is seldom so complete that this 
account of the matter is sufficient. Theoretically the slightest 
departure from symmetry will in general render determinate 
the positions of the nodal systems. For each number of 
cycles n, there is one determinate mode of vibration with 2n 
nodes and 2n intermediate loops, and a second determinate 
mode in which the nodes and loops of the first mode exchange 
_ functions. Moreover the frequencies of the vibrations in the 
two modes are slightly different. 

In accordance with the general theory, the vibrations of the 
two modes as dependent upon the situation and magnitude of 
the initiating blow are to be considered separately. The 
vibrations of the first mode will be excited, unless the blow 
occur at a node of this system; and in various degrees, 
reaching a maximum when the blow is delivered at a loop. 
The intensity, as appreciated by an observer, depends also 
upon the position of his ear, and will be greatest when a 
loop is immediately opposite. As regards the vibrations of 
the second mode, they reach a maximum when those of the 
first mode disappear, and conversely. 

Thus in the case of n cycles, there are 2n places where the 
first vibration is not excited and 2n places, midway between the 
former, where the second vibration is not excited. At all 4n 
places the resulting sound is free from beats. In all other 
cases both kinds of vibration are excited, and the sound will 
be affected by beats. But the prominence of the beats 
depends upon more than one circumstance. The intensities 
of the two vibrations will be equal when the place of the blow 
is midway between those which give no beats. But it does 
not follow that the audible beats are then most distinct. The 
condition to be satisfied is that the intensities shall be equal 
as they reach the ear, and this will depend upon the situation 


B2 


ZI Lord Rayleigh on Bells. 


of the observer as well as upon the vigour of the vibrations 
themselves. Indeed, by suitably choosing the place of 
observation it would be theoretically possible to obtain beats 
with perfect silences, wherever (in relation to the nodal sys- 
tems) the blow may be delivered. 

‘There will now be no difficulty in understanding the proce- 
dure adopted in order to fix the number of cycles corresponding 
to a given tone. If, in consequence of a near approach to 
symmetry, beats are not audible, they are introduced by 
suitably loading the vibrating body. By tapping cautiously 
round a circle of latitude the places are then investigated 
where the beats disappear. But here a decision must not 
be made too hastily. The inaudibility of the beats may be 
favoured by an unsuitable position of the ear, or of the mouth 
of the resonator in connexion with the ear. By travelling 
round, a situation is soon found where the observation can 
be made with the best advantage. In the neighbourhood of 
the place where the blow is being tried there is a loop of 
the vibration which is most excited and a (coincident) node 
of the vibration which is least excited. When the ear is 
opposite to a node of the first vibration, and therefore to a loop 
of the second, the original inequality is redressed, and dis- 
tinct beats may be heard even although the deviation of the 
blow from a nodal point may be very small. The accurate 
determination in this way of two consecutive places where 
no beats are generated is all that is absolutely necessary. 
The ratio of the entire circumference of the circle of latitude 
to the arc between the points represents 4n, that is four times 
the number of cycles. Thus, if the are between consecutive 
points proved to be 45°, we should infer that we were dealing 
with a vibration of two cycles—the one in which the defor- 
mation is elliptical. As a greater security against error, it 
is advisable in practice to determine a larger number of 
points where no beats occur. Unless the deviation from 
symmetry be considerable, these points should be uniformly 
distributed along the circle of latitude*. 

In the above process for determining nodes we are sup- 
posed to hear distinctly the tone corresponding to the vibra- 
tion under investigation. For this purpose the beats are of 
assistance in directing the attention; but with the more 
difficult subjects, such as church bells, it is advisable to have ~ 
recourse to resonators. A set of Helmholtz’s pattern, manu- 
factured by Koenig, are very convenient. The one next higher 

* The bells, or gongs, as they are sometimes called, of striking clocks 


often give disagreeable beats. A remedy may be found in a suitable 
rotation of the bell about its axis. 


Lord Rayleigh on Bells. 5 


in pitch to the tone under examination is chosen and tuned by 
advaneing the finger across the aperture. Without the security 
afforded by resonators, the determination of the octave is in 
my experience very uncertain. Thus pure tones are often 
estimated by musicians an octave too low. 

Some years ago I made observations upon the tones of 
various glass bells, of which the walls were tolerably thin. 


A few examples may be given :— 
I. Goa tMeny; Ci. 
II. GAT Meh Ms ht" 
IT. oe eo. 

The value of n for the gravest tone is 2, for the second 38, 
and for the third 4. On account of the irregular shape and 
thickness only a very rough comparison with theory is 
possible ; but it may be worth mention that fora thin uniform 
hemispherical bell the frequencies of the three slowest vibra- 
tions should be in the ratios 

1 : 2°8102 : 5°43816 ; 
so that the tones might be 
c, f'#, jf”, approximately. 


More recently, through the kindness of Messrs. Mears and 
Stainbank, I have had an opportunity of examining a so- 
called hemispherical metal bell, weighing about 3 cwt. A 
section is shown in fig. 1. Four tones could be plainly heard, 


eb, pes CE Oe. 


the pitch being taken froma harmonium. The gravest tone 


has a long duration. When the bell is struck by a hard 
body, the higher tones are at first predominant, but after a 
time they die away, and leave ep in possession of the field. 
If the striking body be soft, the original preponderance of the 
higher elements is less marked. 


6 Lord Rayleigh on Bells. 


By the method above described there was no difficulty in 
showing that the four tones correspond respectively to n=2, 
3, 4,5. Thus for the gravest tone the vibration is elliptical 
with 4 nodal meridians, for the next tone there are 6 nodal 
meridians, and so on. ‘Tapping along a meridian showed 
that the sounds became less clear as the edge was departed 
from, and this in a continuous manner with no suggestion of 
a nodal circle of latitude. 

A question, to which we shall recur in connexion with 
church bells, here suggests itself. Which of the various co- 
existing tones characterizes the pitch of the bell as a whole ? 
It would appear to be the third in order, for the founders give 
the pitch as Hi nat. 

My first attempts upon church bells were made in Sep- 
tember 1879, upon the second bell (reckoned from the 
highest) of the Terling peal; and I was much puzzled to 
reconcile the pitch of the various tones, determined by reso- 
nators, with the effective pitch of the bell, when heard from 
a distance in conjunction with the other bells of the peal. 
There was a general agreement that the five notes of the 
peal were 


z, 9g z, az p) b, Ch, 


according to harmonium pitch, so that the note of the second 
bell was 6. A tone of pitch a# could be heard, but at that 
time nothing coincident with} or its octaves. Subsequently, 
in January 1880, the 6 was found among the tones of the 
bell, but at much higher pitch than had been expected. The 
five gravest tones were determined to be 


a’, alg, a", Gat, vs 

so that the nominal note of the bell agreed with the fifth 
component tone, and with no graver one. The octaves are 
here indicated by dashes in the usual way, the ¢c’ immediately 
below the d’ being the middle ¢ of the musical scale. 

Attempts were then made to identify the modes of vibra- 
tion corresponding to the various tones, but with only partial 
success. By tapping round the sound-bow it appeared that 
the minima of beats for d’ occurred at intervals equal to 4 of 
the circumference, indicating that the deformation in this 
mode was elliptical (n=2), as had been expected. In like 
manner g"¢ gave n=3; but on account of the difficulty of 
experimenting in the belfry, the results were not wholly 
satisfactory, and I was unable to determine the modes for the 
other tones. One observation, however, of importance could 
be made. All five tones were affected with beats, from which 


Lord Rayleigh on Bells. 7 


it was concluded that none of them could be due to symme- 
trical vibrations, as, till then, had been thought not un- 
likely. 

Nothing further worthy of record was effected until last 
year, when I obtained from Messrs. Mears and Stainbank the 
loan of a 6-ewt. bell. Hung in the laboratory at a convenient 
height, and with freedom of access to all parts of the cir- 
cumference, this bell afforded a more convenient subject for 
experiment, and I was able to make the observations by 
which before I had been baffled. Former experience having 
shown me the difficulty of estimating the pitch of an isolated 
bell, I was anxious to have the judgment of the founders 
expressed in a definite form, and they were good enough to 
supply me with a fork tuned to the pitch of the bell. By my 
harmonium the fork is d”. 

By tapp‘ng the bell in various places with a hammer or 
mallet, and listening with resonators, it was not difficult to 
detect 6 tones. ‘They were identified with the following 
notes of the harmonium *:— 


el, ef f"+, b"b, au. vie 
ey 4) (6) (6) (8) 


As in the former case, the nominal pitch is governed by 
the fifth component tone, whose pitch is, however, an octave 
higher than that of the representative fork. It is to be un- 
derstood, of course, that each of the 6 tones in the above 
series is really double, and that in some cases the components 
of a pair differ sufficiently to give rise to somewhat rapid 
beats. The sign + affixed to f” indicates that the tone of 
the bell was decidedly sharp in comparison with the note of 
the instrument. 

I now proceeded to determine, as far as possible, the cha- 
racters of the various modes of vibration by observations 
upon the dependence of the sounds upon the place of tapping 
in the manner already described. By tapping round a circle 
of latitude it was easy to prove that for (each of the approxi- 
mately coincident tones of) e’ there were 4 nodal meridians. 
Again, on tapping along a meridian to find whether there 
were any nodal circles of latitude, it became evident that 
there were none such. At the same time differences of in- 
tensity were observed. This tone is more fully developed 


* In comparisons of this kind the observer must bear in mind the 
highly compound character of the notes of a reed instrument. It is 
usually a wise precaution to ascertain that a similar effect is not produced 
by the octave (or twelfth) above. 


8 Lord Rayleigh on Bells. 


when the blow is delivered about midway between the crown 
and rim of the bell than at other places. 

The next tone is ¢’. Observation showed that for this 
vibration also there are four, and but four, nodal meridians. 
But now there is a well-defined nodal circle of latitude, 
situated about a quarter of the way up from the rim towards 
the crown. As heard with the resonator, this tone disappears 
when the blow is accurately delivered at some point of this 
circle, but revives with a very small displacement on either 
side. The nodal circle and the four meridians divide the 
surface into segments, over each of which the normal motion 
is of one sign. 

To the tone 7” correspond 6 nodal meridians. There is no 
well-defined nodal circle. The sound isindeed very faint, when 
the tap is much removed from the sound-bow; it was thought 
to fall to a minimum when the tap was about halfway up. 

The three graver tones are heard loudly from the sound- 
bow. But the next in order, b"p, is there scarcely audible, 
unless the blow be delivered to the rim itself in a tangential 
direction. The maximum effect occurs at about halfway up. 
Tapping round the circle, we find that there are 6 nodal 
meridians. 

The fifth tone, d!, is heard loudly from the sound-bow, but 
soon falls off when the locality of the blow is varied, and in 
the upper three fourths of the bell it is very faint. No 
distinct circular node could be detected. Tapping round the 
circumference showed that there were here 8 nodal meridians. 

The highest tone recorded, 7”, was not easy of observation, 
and I did not succeed in satisfying myself as to the character 
of the vibration. The tone was perhaps best heard when 
the blow was delivered at a point a little below the crown. 

All the above tones, except /", were tolerably close in pitch 
to the corresponding notes of the harmonium. 

Although the above results seemed perfectly unambiguous, 
I was glad to have an opportunity of confirming them by ex- 
amination of another bell. This was afforded by a loan of a 
bell cast by Taylor, of Loughborough, and destined for the 
church of Ampton, Suffolk, where it now hangs. Its weight 
is somewhat less than 4 cwt., and the nominal pitch is d. 
The observations were entirely confirmatory of the results 
obtained from Messrs. Mears’s bell. The tones were 

ép—2, d'—6, f' +4, b"pb—b", ae gi" 
(4) (4) (6) (6) (8) 
the correspondence between the order of the tone and the 
number of nodal meridians being as before. In the case of 
d' there was the same well-defined nodal circle. The highest 


Lord Rayleigh on Bells. 9 


tone, g!, was but imperfectly heard, and no investigation could 
be made of the corresponding mode of vibration. 

In the specification of pitch the numerals following the 
note indicate by how much the frequency for the bell dif- 
fered from that of the harmonium. Thus the gravest tone 
eb gave 2 beats per second, and was flat. When the number 
exceeds 3, it is the result of somewhat rough estimation and 
cannot be trusted to be quite accurate. Moreover, as has 
been explained, there are in strictness two frequencies under 
each head, and these often differ sensibly. In the case of 
the 4th tone, b"p—b" means that, as nearly as could be judged, 
the pitch of the bell was midway between the two specified 
notes of the harmonium. 

The sounds of bells may be elicited otherwise than by 
blows. Advantage may often be taken of the response to 
the notes of the harmonium, to the voice, or to organ-pipes 
sounded in the neighbourhood. In these cases the subsequent 
resonance of the bell has the character of a pure tone. Per- 
haps the most striking experiment is with a tuning-fork. A 
massive ep (é! on the c!=256 scale) fork, tuned with wax, and 
placed upon the waist of the Ampton bell, called forth a 
magnificent resonance, which lasted for some time after re- 
moval and damping of the fork. The sound is so utterly 
unlike that usually associated with bells that an air of mystery 
envelops the phenomenon. The fork may be excited either 
by a preliminary blow upon a pad (in practice it was the bent 
knee of the observer), or by bowing when in contact with 
the bell. In either case the adjustment of pitch should be 
very precise, and it is usually necessary to distinguish the 
two nearly coincident tones of the bell. One of these is to 
be chosen, and the fork is to be held near a loop of the cor- 
responding mode of vibration. In practice the simplest way 
to effect the tuning is to watch the course of things after the 
vibrating fork has been brought into contact with the bell. 
When the tuning is good the sound swells continuously. 
Any beats that are heard must be gradually slowed down by 
adjustment of wax, until they disappear. 

Observations upon the two bells in the laboratory having 
settled the modes of vibration corresponding to the five 
gravest tones, other bells of the church pattern can be suf- 
ficiently investigated by simple determinations of pitch. I 
give in tabular form results of this kind for a Belgian bell, 
kindly placed at my disposal by Mr. Haweis, and for the five 
bells of the Terling peal. For completeness’ sake the Table 
includes also the corresponding results for the two bells 


already described. 


E+2 G+9 2 9-9 Zo 
p+6 B+n o+#/ $6—6 E—qn 
q@ 8+ qa b+rqa 9+ ga 9+4ga 
Stag Gad 9192 aa b—to 
Gt Ho Uae 14 Sin e+ #0 €— he 
< 
= ! ‘9 SB 00} YF 07 poltofor You 
RQ 
Ss 
S 
oa 
= S+#,,2 GT 19 #0 9—#,,4 C— hud ee 
Be b+ t 0 (Ol) +#,4 9+, i9—# yP Cae. a? 
AC 9 8+ iP +42 9+9 9+ 2 [tf 
ag C+19 G— hi 9+/D F—#6 0 1P—#, 1? 
3 op 9—p e+Hp E+» g—6 7— P 
“UU TUOULLG FT Aq Youd [enjpovy 
‘6981 “GGLT ‘GG9T ‘OI8T ‘6841 T° 
‘TOULG AA, ‘LOULPLC ‘OAL ‘SIVOTAL ‘ULOgsQ weiss 
(T) surp1oy, “(G) SurpAoy, ‘(g) Surpaey, ‘(p) Surpsay, ‘(q) surpaay, set 


=} 
re 


B) D) 
D— qn qv 
p+qa + 4a 
9-9 qq 
G— #0 Pp 
ub has 
iP iP 
u9$—4149 quid 
buf tid 
9,2 iP 
Z—4q,a a 
‘8881 | ‘881 
‘uogdury ‘SLVOTAL 


Lord Rayleigh on Bells. 11 


It will be seen that in every case where the test can be 
applied, it is the fifth tone in order which agrees with the 
nominal pitch of the bell. The reader will not be more sur- 
prised at this conclusion than I was, but there seems to be no 
escape from it. Hven apart from estimates of pitch, an ex- 
amination of the tones of the bells of the Terling peal proves 
that it is only from the third and fifth tones that a tolerable 
diatonic scale can be constructed. Observations in the neigh- 
bourhood of bells do not suggest any special predominance of 
the fifth tone, but the effect is a good deal modified by 
distance. 

It has been suggested, I think by Helmholtz, that the aim 
of the original designers of bells may have been to bring into 
harmonic relations tones which might otherwise cause a dis- 
agreeable effect. If this be so, the result cannot be con- 
sidered very successful. A glance at the Table shows that 
in almost every case there occur intervals which would 
usually be counted intolerable, such as the false octave. 
Terling (5) is the only bell which avoids this false interval 
between the two first tones; but the improvement here shown 
in this respect still leaves much to be desired, when we con- 
sider the relation of these two tones to the fifth tone, and the 
nominal pitch of the bell. Upon the assumption that the 
nominal pitch is governed by that of the fifth tone, I have 
exhibited in the second part of the above Table the relation- 
ship in each case of the various tones to this one. 

One of my objects in this investigation having been to find 
out, if possible, wherein lay the difference between good and 
bad bells, 1 was anxious to interpret in accordance with my 
results the observations of Mr. Haweis, who has given so 
much attention to the subject. The comparison is, however, 
not free from difficulty. Mr. Haweis says * :—“ The true 
Belgian bell when struck a little above the rim gives the 
dominant note of the bell ; when struck two-thirds up it gives 
the third ; and near the top the fifth ; and the ‘true’ bell is 
that in which the third and fifth (to leave out a multitude of 
other partials) are heard in right relative subordination to the 
dominant note.” 

If I am right in respect of the dominant note, the third 
spoken of by Mr. Haweis must be the minor third (or, rather, 
major sixth) presented by the tone third in order, which it so 
happens is nearly the same interval in all cases. The only 
fifth which occurs is that of the tone fourth in order. Thus, 
according to Mr. Haweis’s views, the best bell in the series 
would be Terling (1), for which the minor chord of the last 

* ©Times,’ October 29, 1878. 


12 Lord Rayleigh on Bells. 


three tones is very nearly true. It must be remarked, how- 
ever, that the tone fourth in order is scarcely heard in the 
normal use of the bell, so that its pitch can hardly be of 
importance directly, although it may afford a useful criterion 
of the character of the bell as a whole. It is evident that the 
first and second tones of Terling (1) are quite out of relation 
with the higher ones. If the first could be depressed a semi- 
tone and the second raised a whole tone, harmonic relations 
would prevail throughout. 

Judging from the variety presented in the Table, it would 
seem not a hopeless task so to construct a bell that all the 
important tones should be brought into harmonic relation ; 
but it would require so much tentative work that it could 
only be undertaken advantageously by one in connexion with 
a foundry. As to what advantage would be gained in the 
event of success, I find it difficult to form an opinion. All I 
can say is that the dissonant effect of the inharmonious 
intervals actually met with is less than one would have ex- 
pected from a-musical point of view; although the fact is to a 
great extent explained by Helmholtz’s theory of dissonance. 

One other point I will touch upon, though with great diffi- 
dence. If there is anything well established in theoretical 
acoustics it is that the frequencies of vibration of similar bodies 
formed of similar material are inversely as the linear dimen- 
sions—a law which extends to all the possible modes of vibra- 
tion. Hence, if the dimensions are halved, all the tones should 
rise in pitch by an exact octave. I have been given to under- 
stand, however, that bells are not designed upon this principle 
of similarity, and that the attempt to do so would result in 
failure. It is just possible that differences in cooling may 
influence the hardness, and so interfere with the similarity of 
corresponding -parts, in spite of uniformity in the chemical 
composition of the metal; but this explanation does not 
appear adequate. Can it be that when the scale of a bell is 
altered it is desirable at the same time to modify the relative 
intensities, or even the relative frequencies, of the various 
partials ? 

Observations conducted about ten years ago upon the 
manner of bending of bell-shaped bodies—waste-paper baskets 
and various structures of flexible material—led me to think 
that these shapes were especially stiff as regards the principal 
mode of bending (with four nodal meridians) to forces applied 
normally and near the rim, and that possibly one of the 
objects of the particular form adopted for bells might be to 
diminish the preponderance of the gravest tone. To illustrate 
this I made calculations, according to the theory of the paper 


Lord Rayleigh on Bells. 18 


already alluded to, of the deformation by pure bending of 
thin shells in the form of hyperboloids of revolution, and in 
certain composite forms built up of cylinders and cones so as 
to represent approximately the actual shape of bells. In the 
case of the hyperboloid of one sheet (fig. 2), completed by a 


Fig. 2. 


crown in the form of a circular disk through the centre, and 
extending across the aperture, it appeared that there was no 
nodal circle for n=2. The investigation is appended to this 
paper. 

The composite forms, figs. 4 and 5, represent the actual bell 
(fig. 3*) as nearly as may be. At the top is a circular disk, 


Fig. 3. 


and to this is attached a cylindrical segment. The expanding 
part of the bell is represented by one (fig. 4), or with better 
approximation by two (fig. 5), segments of cones. ‘The cal- 
culations are too tedious to be reproduced here, but the results 
are shown upon the figures. In both cases there is a circular 
node N for n=2, not far removed from the rim, and in fig. 5 
very nearly at the place which represents the sound-bow of an 
actual bell. In the latter case there is a node N! for n=3 
near the middle of the intermediate conical segment. 


* Copied from Zamminer, Die “Musik und die musikalischen Instru- 
mente. Giessen, 1855. 


14 Lord Rayleigh on Bells. 


The nodal circle for n=2 has been verified experimentally 
upon a bell constructed of thin sheet zinc in the form of fig. 5. 
The gravest note, GZ, and the corresponding mode of vibra- 
tion, could be investigated exactly in the manner already 
described. In each mode of this kind there were four nodal 


Fig. 4. 


Fig. 5. 


meridians, and a very well defined nodal circle. The situation 
of this circle was not quite so low as according to calculation ; 
it was almost exactly in the middle of the lower conical 
segment. By merely handling the model it was easy to 
recognize that it was stiff to forces applied at N, but flexible 
higher up, in the neighbourhood of N’. 

It is clear that the actual behaviour of a church bell differs 
widely from that of a bell infinitely thin; and that this should 
be the case need not surprise us when we consider the actual 
ratio of the thickness at the sound-bow to the interval 
between consecutive nodal meridians. I think, however, that 
the form of the bell does really tend to render the gravest 
tone less prominent. 


APPENDIX. 


On the Bending of a Hyperboloid of Revolution. 
The deformation of the general surface of revolution was 
briefly treated in a former paper *. The point whose original 


* “Qn the Infinitesimal Bending of Surfaces of Revolution,” Proc. 
Math. Soc. xiii. p. 4 (1881). 


Lord Rayleigh on Bells. 15 


cylindrical coordinates are z, 7, d, is supposed to undergo 
such a displacement that its coordinates become 


z+6z, r+oér, 6+56¢. 


The altered value (ds+d6s) of the element of length traced 
upon the surface is given by 


(ds + dds)? = (dz + dbz)? + (r+ 6r)? (8h + dd)? + (dr + dér)?. 


Hence, if the displacement be such that the element is un- 
extended, 


dz déz+r°d¢ dbp + ror (dp)? + dr dbr=0. 


Now 
dé. ddz 
d8z= ae 47g 
| = Ore ddr 


oe 4, a 4 ae 


and by the equation to the surface 


dr, dp 
dr= But ag? 


in which, by hypothesis, dr/d@=0. Thus 
(de)? i >) +(d¢)° {7 cE tier \ 


ddz ne dr dé&r 
d aera yr 
ale of SS tee 0. 
If the displacement be of such a character that no line 
traced upon the surface is altered in length, the coefficients 
of (dz)”, (dd)’, dz dd, in the above equation, must vanish 
separately, so that 


déz . drdér 
ae To ee Sr Hew eae 


ddd 
Oe or Se eee a Pe 


ddz dd dr ddr : 


16 Lord Rayleigh on Bells. 


From these, by elimination of 67, 


déz dr dy ddd 
dz TENG 1¢)= 0). 
ddz , .ddh_ dr Pd 


db ee ae ie ae ‘ . Mee 2 (5) 


from which again, by elimination of 62, 


£( 8) _ 0 Ts agra .— ae 


For the purposes of the present problem we may assume 
that dd varies as cos sd, or as sin sp; thus, 


dd ae 
AG oP) 4 8 —35P=0 . . . » (7) 


is the equation by which the form of 6¢ as a /unction of < is 
to be determined. 
When application is made to the hyperboloid of one sheet 


ye 2 
eR ° ° ° ° ° ° e (8) 
we find, since 
dr az a Os 
‘a dé — 5» 
2d ( .ddd 
pi (aie). = o2' 540. 


The solution of this equation is expressed by an auxiliary 
variable y, such that 


e=biany, r=asecy . . ae 
in the form 


6¢6=A cossy+ Bsin sy. Seay 


In order to verify this it is only necessary to observe that 
hy (10) 
iC ae Oe 
Pf =— — 
dz bdy 


We will now apply this solution to an inextensible surface 


Lord Rayleigh on Bells. 17 


formed by half the hyperboloid and a crown stretching across 
in the plane of symmetry z=0 (fig. 2). The deformation of 
this crown can take place only in the direction perpendicular to 
its plane, so that 6r>=0, 56=0. ‘These conditions must apply 
also to the hyperboloid at the place of attachment to the 
crown. Hence 6¢ must vanish with z, or, which is the same, 
with y. Accordingly A=0 in (11); and dropping the con- 
stant multiplier we may take as the solution 


OP cil SViCOSsOn sane to ya uc!) (12) 
and in correspondence therewith by (2) and (3) 
Gh snicm syvisin s@y ka) a-P ol sola -oil) ese (18) 


2 
bz = — = {cos sy +stanysin sy} sinsd. . . (14) 


It is evident from these equations that, whatever may be 
the value of s, there is no circle of latitude over which both 
dd (or 67) and 6z vanish*. Hence there can be no circu- 
lar nodal line in the absolute sense. But just as there are 
meridians (sin s6=0) on which the normal motion vanishes, 
so there may be nodal circles in this more limited sense. The 
condition to be satisfied is obviously 


dr/dz = dr/dz ; 
or in the present case 


sin 2y + 2s tan sy (sin ?y+07/a7)=0. . . (15) 


In this equation the range of y is from 0 to $7; and thus 
there can be solutions only when tan sy is negative. 
In the case s=2 the equation reduces to 


1+2sin *y + 40?/a?=0, 


which can never be satisfied. 

When s=3, the roots, if any, must lie between y=30° 
and y= 60°. A more detailed consideration shows that 
there is but one root, and that it occurs when y is a little 
short of 60°. 


* A corresponding proposition may be proved more generally, that is 
without limitation to the hyperboloid. 


Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. C 


Eenee 4 


II. On the Kinetic Theory of the Phenomena of Dissociation 
in Gases. By Lapistaus NATANSON™. 


T is well known that the problem of the dissociation of 
gaseous bodies has been successfully attacked by several 
physicists by thermodynamic methods. If one attempts to 
apply the kinetic theory, it will be found difficult to make a 
complete calculation without introducing certain assumptions 
as to the mode of combination of the atoms in gaseous mole~ 
cules. Therefore the first task of the theory consists in making 
such assumptions as are either in agreement with experiment, 
or else, on the other hand, the most general possible. As this 
object does not appear to be sufficiently evident, I have allowed 
myself to enter into a more detailed consideration of a simple 
case. 

§ 1. In the space v there are present N, free atoms and N, 
diatomic molecules; every atom has the same properties. 
The total number of atoms is N=N,+2N,. If m is the mass 
of an atom, the mass of the gas will be mN; I shall assume 
henceforth that we are always dealing with unit mass. The 
problem which was usually considered was the determination 
of the ratio W (the dissociation ratio) as a function of the 
pressure and temperature ; and its object was attained some- 
what after the following manner. 

Let p, and p, denote the partial pressures of the two gases 
(molecular and atomic); let p be the total pressure, ¢ the 
common temperature, and H, and H, the mean values of the 
kinetic energy of a free atom and of the centre of mass of a 
molecule respectively. Apart from phenomena of dissociation 
let both gases be considered perfect. Then we may write 


Sp0=NiH,: 3p v=—N,E,;. p=pi tp =e 


Further, according to Maxwell’s law, H,=H,; and we use 
the magnitude of this energy as a measure of the temperature 


by assuming 
=o. ee (B) 
where AX is some constant. From (A) and (B) it will be 
found that 
8 pvu=(Ny + No). O. .  r 
Now let us introduce the condition for equilibrium. This 


* Translated from Wiedemann’s Annalen, xxxviii. p. 288 (1889) by 
James L. Howard, D.Sc. 


Kinetic Theory of Dissociation in Gases. 19 


will be reached when the number of molecules decomposed 
during any period of time is equal to the number formed 
during the same period. As shown in previous theories*, 
this equality is expressed by the equation 


areas ©) 


and hence (C) expresses the condition of equilibrium. Here 
j(é) isa function of the temperature whose form has never 
been successfully determined, so far as I am aware, either by 
kinetic or thermodynamic methods. From (1) and (C) we 
have further 
_ At(N?—Ny’) _ Aé(1—g’) 
TSONGA 


qg denoting the dissociation ratio shy If d is the density 


N 
of the partly dissociated gas, corresponding to the state qg, and 
5 the density of the completely dissociated body, then if the 
formula (1) holds good, we have . 


d _ N,+2N, 
Sr NSN ® e ° ° ° ° (3) 


whence, substituting in (2), 


d(d—6) ss DE 
Mo mar aay oi ee tea n call) 


which, for shortness, I shall call “ Gibbs’s Equation.” 

§ 2. Gibbs’s equation has been verified by various experi- 
ments ; among others by those on nitrous acidt. Since we 
leave the function a at present undetermined, we can prove 
the formula by calculating the: values of the expression 
p(26 — d)?/(d — 6) = a6, which should be constant for each 
isotherm. From our data it is clearly seen that the 
value of a does not considerably alter along any isotherm. 
The constancy is of course still more perfect if we calculate 
(for the isotherms H, F, H, J, loc. cit.) the expression 


byt hagelaad sed 


_ * To the kinetic or partly kinetic theories belong those of van der 
Waals, Verslagen en Mededeelingen d.kon. Ak. d. Wet.|2| xv. p. 199 (1880) ; 
Boltzmann, Wied. Ann. xxii. p. 89 (1884); and J. J. Thomson, Phil. 
Mae. [5] xviii. p. 233 (1884). It is impossible to enter upon these theories 
here ; I only remark that certain conclusions to which | have been led in 
§ 3 have already been indicated by Thomson. As for the rest I cannot 
agree with Thomson’s calculations. 

+ E. and L. Natanson, Wied. Ann. xxiv. p. 454 (1885), and xxvii. 
p. 606 (1886). 

C2 


20 Ladislaus Natanson on the Kinetic Theory 


p(26—d)?/(d—8,), where 8; may be greater or less than 4, 
and denotes a new isothermal constant*. Whether these 
critical values of the density of NO, are similar to the critical 
densities of chlorine and bromine gases (which, however, were 
found, not for p=0, but at atmospheric pressure), as Ostwald 
supposes ¢; or whether the proved deviations from Gubbs’s 
formula are attributable wholly or partly to the imperfect 
nature of the gas {—these appear to me difficult questions to 
decide, inasmuch as there exists no firm basis to work upon. 
It suffices us, for what follows, to know that Gibbs’s equation, 
with f(t) left undetermined, is always in general agreement 
with experiment. 

§ 3. Two atoms collide and form a molecule, which lasts 
for atime 7. It is required to know how often this happens 
during unit time in a given quantity of gas. The interval 7 
may depend on certain variables x, y,..., which we need not 
specify, and in unit time 

Loe, y,-+.)dudy... ...) ee 
collisions take place between the atoms, in such a manner that 
the variables lie between the limits 

gandetda; yand y+dy3... = =. 


Let us assume that 2, y,... in general have values lying 
between the limits 


yp and 23; Yo and y,3..-.. = ner 


and that Z is the total number of collisions between the atoms 
during unit time, so that 


NEW 
("| ...0(2,y,...) dzdy... =e 
Zo“ Yo 


Let us further assume that a collision of two atoms which 
is included in class (2) is followed by the formation of a mole- 
cule in case w, y,... lie between 


E, and a > No and Disses ° 2 aT (5) 


(Hach of these classes can also be subdivided into further 
simple ones.) Let us write 


& Ny ‘ 
( (iste, Sana ee > sn 


a’ &, “ Xo 


* Cf. p. 617 of the second paper. 

Tt Ostwald, Lehrbuch der allg. Chemie, ii. p. 699 (1887). 

{ Ostwald, op. cit. ii. p. 7384; Planck, Wied. Ann. xxxii. p. 484 (1887); 
J. s Thomson, ‘ Applications of Dynamics to Physics and Chemistry,’ 
p. 200. 


of the Phenomena of Dissociation in Gases. 21 


then we can say that in unit time aZ molecules are created, 
and @ is the ratio of the number of associating collisions to 
the total number. Now let us suppose that the gas has 
reached a state of equilibrium as regards dissociation. During 


time 7, 
TAO nes Oud nae ) Veliraiica 28) (0) 


molecules of class (2) will be formed, and they will each last 
for a time equal to 7, or differing from it by an infinitely 
small quantity. Therefore there will exist at any time as 
many molecules of class (2) as are given by (7) *. 

Hence the total number N, of existing molecules is 


e & 0 
se Ge 
{ ie TDC 16) Canady a) 
=aZ ss - =aZs, 
{ PINOKU Uae AL Ors... , 
0 e/ "0 


where 3 denotes the mean value of the interval during which 
a molecule remains intact. 

The conditions which are necessary in order that a molecule 
should be formed when two atoms collide are very different, 
according to the assumptions made respecting the mutual 
actions of the atoms. As hypothesis (#) we shall designate 
every assumption, according to which, as the result of a col- 
lision of two atoms, two opposite cases arise: either the 
collision is “associating,” the motion of the atom becoming a 
stationary one, and a molecule is formed ; or else “normal,” 
in which case the atoms rebound immediately and of their 
own accord, as happens in the collision of molecules in 
common gases. With this hypothesis («) we must also 
assume at the same time, that a molecule which has once been 
formed cannot be decomposed of itself, but only by the action 
of external force. As hypothesis (@) we shall, on the con- 
trary, designate any assumption in which the above distinction 
is wanting: two colliding atoms will sooner or later leave 
each other; only the interval during which they form a 
system can, according to the circumstances of the collision, 
be different in different cases. There is then no sharp dis- 


* The proposition made use of here, that “there exist at any time as 
many molecules, belonging to a given class, as are formed during the time 
of existence of a molecule (in case all molecules of that class exist for an 
equal time),” is often made use of in the kinetic theory. Cf Wied. Ann. 
XXxili, p. 683 (1888). 


22 Ladislaus Natanson on the Kinetic Theory 


tinction between a collision and the formation of a molecule ; 
during the time of collision the atoms form a molecule. 
Every collision is then an “ associating” one, every molecule 
must exist for a certain time and then decompose of itself. 

In order to bring calculation to bear on both assumptions, 
let us consider a new mean value of 7, namely @, which we 
define in the following manner :— 


yEn 
{ { ani TOE; Y,».~) 02 die 
SS ee) 
{ VDE, Yoo ==) OL OY eure 
@=a8,. .°-.-. |. 7 


Equation (10) will be found on remembering the definition 
of @ and also equation (4), and considering the condition that 
7 vanishes outside the limits & and &,, m) and 7, &. ; so that 


an 6 (°m 

{ { San Gee) Cay ae CHATS A ={ { ose TD( dy Ye nae tee ee 
Lg VY 0 Vv No 

From (10) it follows that : 


Ne—7iee: e ° . ° 5 . . (12) 


According to the (8) hypothesis, 0=3 and w=1; according 
to the («) hypothesis, @<4, because in the formation of $ all 
the molecules really formed must be taken into account ; but 
in that of @ every collision, associating and normal, must be 
reckoned ; and the latter contribute nothing to the sum of tT. 
Let the mean number of impacts of an atom against other 
atoms be C per unit of time. If we write CT=1, T is 
approximately the mean time which elapses between two 


successivé collisions*. On the other hand, Z=N, " and 


* In the space v let there be N equal molecules, whose velocities are 
distributed according to Maxwell’s law (with modulus «). If R is the 
smallest distance within which two molecules can approach each other 
without colliding, and if a molecule moving with a given velocity expe- 
riences B impacts per unit of time, the mean value of the time between 
successive Impacts 1s 


I 06505 v ke 
pe ee Migs Ne 

while 
1 i 1 v v 
== =(0:1995 2 
CB 2V27 NR*e NR?e 


Cf. Tait, Trans. R. 8S; E. xxxiii. p. 74 (1886). 


of the Phenomena of Dissociation in Gases. 23 


therefore 
oe eit es (13) 


According to the («) hypothesis, 3 is the mean time during 
which the molecules exist, and T/# the mean time during 
which a liberated atom remains free. According to the (8) 
hypothesis, on the other hand, @ has the former and T the latter 
meaning. In any casewe can easily calculate @/T or «3/T from 
2(d—S) 
(26—d) 
we have for N,O,, according to the experiments quoted in § 2%, 


Isotherm D. f p=26'°80 mm. . . 6/T=0:096 


this equation, since x. is equal to For example, 
i 


(449°7 0.) YU 497-75 1-069 
Isotherm HE. f p=49'65 mm. . . 0/T=0:058 
(+ 73°7 C.) 633°27 0°396 
Isotherm F.fp=11'73 mm. . . @/T=0-016 
(+99°8 C.) 132-51 0°139 
isotherm H. f p=35°99 mm. . .. O/T=0-011 
(+129°-90C.) 550:29 mm. 0:023 


At constant temperature we can put C proportional to a If 
2 

we write C= Ni) then Z= suey 

(12), 4 y 


; and, according to 
Ni? OwW(t 
i eS saps ues aie) 


We have thus obtained the condition (C) of § 1, but only in 
case 6 depends on the temperature alone, and not on the 
pressure or volume. If we assume that the course of an 
impact is not affected by the frequency of occurrence of the 
impacts, I do not see how this condition relative to @ is to be 
reconciled with the hypothesis (a). In that case @ would 
indeed depend on the volume, in the same way that the time- 
interval between consecutive impacts of a molecule does, 
From the above table, or from Gibbs’s equation, regarded as 
the outcome of experiment, it follows that w3/T varies greatly 


* For nitrous acid and other dissociable gases the absolute magnitude 
of Tis unknown. We can, however, take for granted that it is not essen- 
tially different from the length of the same time-period in such gases as 
oxygen, nitrogen, or nitrous oxide. We shall be within the limits when 
we say that the mean time of existence of the N,O, molecule in the 
experiments quoted was somewhere between 10~!° and 10—'° second. 


24 Ladislaus Natanson on the Kinetic Theory 


; N 
along any isotherm, and must in fact be proportional to 7 : 
Therefore a3 must be constant, and consequently $ also, since 
@ cannot be regarded as dependent upon v. 

This conclusion can also be arrived at in the following 


INS Fi(¢) 
VU 


manner. Let new molecules be formed during unit 


time. In unit time collisions of two atoms take 


IN 2 Cy Jt 
v 
place ; therefore F\(¢)=ac, Vt, where c, is a constant factor. 
Now let us calculate how many molecules are decomposed in 
unit time, if hypothesis (z) be true. During unit time there 
take place between the molecules on the one hand, and either 

J 2 F 
molecules or atoms on the other hand, Mio 
collisions. Again, if a, and a, denote the ratios of the 
number of dissociating collisions to the corresponding total 
number of collisions, and assuming that w, and aw, are indepen- 
dent of the volume, so that w2c,./ t= F(t), and @y2¢yp / t= Fy (A), 
the condition for equilibrium expressed in § 1 becomes’ _~ 


NF (é) =N.? F.(¢) + NIN. F io), 


which is quite different from (C) § 1. 

§ 4. The equation (B) of § 1 is also, as I believe, incom- 
patible with hypothesis («), and for this reason, that then 
Maxwell’s law loses its meaning. The true meaning of this 
law may be thus expressed :—“If two gases are mixed 
together, whose mean kinetic energies are different, an ex- 
change of energy takes place until the difference disappears ’’*. 

If two colliding atoms enter into combination, their energy 
divides into motion of the centre of gravity and relative 
motion. The molecules formed have therefore a definite 
mean yalue for the kinetic energy of the motion of the centre 
of gravity, which we shall call molecular motion. 

Now there are two cases possible :—(i.) The molecular 
energy may, just after the formation of the molecule, be 
equal to that of the free atoms; this is the case, for example, 
when aggregations are formed in imperfect gases, as I have 
already pointed outt. Then HE, and E, are equal, because 
this follows as a consequence of the laws of collision of atoms, 


* Tait, Trans. R. 5S. HE. xxxiil. p. 82 (1886); ef Wied. Ann. xxxiv, 
p- 970 (1888). 
+ Wied. Ann. xxxili, p. 687 e¢ seg. (1888). 


of the Phenomena of Dissociation in Gases. 25 


and not because Maxwell’s law makes them equal. (ii.) The 
energy. of the molecules formed may, on the contrary, be 
different from that of the free atoms, and then, according to 
Maxwell’s law, an interchange of energy will take place 
between the molecules and atoms ; every molecule will tend 
to regulate its velocity according to Maxwell’s law. This 
phenomenon happens during the collisions of the molecule ; 
after a few collisions the molecule will approximately fulfil 
the conditions of Maxwell’s law. If the molecule does not 
last longer than the time requisite for this process of equaliza- 
tion of energy, or if it lasts a shorter time, the equalization 
can only take place in part, and only a part of the difference 
of energy will be equalized. A stationary condition may 
therefore arise, in which the ratio of the molecular and atomic 
energies has a value which is intermediate between unity and 
the value obtained from the energy of the molecules formed 
and that of the atoms. 

Now I hope to be able to prove that the case (i.) corre- 
sponds to the hypothesis (8) of § 3, while case (11.) corresponds 
to the hypothesis («) of the same section. Let us assume that 
a is the most probable velocity of the atoms, so that ?ma? =H. 
The velocity of the progressive movement of a molecule, 
which is formed out of two colliding atoms, being V, let us 
choose V as one of the independent variables in the collision 
of two atoms. According to the rules laid down in § 3 of my 
paper ‘‘ On the Kinetic Theory of Imperfect Gases’ (loc. cit.), 
there will occur in unit time, 

N,? R/? V29-2V2/02 ii 
rere! C ND dats ON OU dyremme 1) Cl) 


collisions between atoms, in which the velocity of the centre 
of gravity of each lies between V and V+dV; and the 
remaining variables also lie between certain infinitely close 
limits, which we do not need to specify. In (1) N, is, 
as before, the number of atoms, v the volume, R, the charac- 
teristic distance determining whether a collision will or will not 
ensue between two atoms. We shall assume that in every 
collision of class G.) a molecule is formed. (According to 
hypothesis (@) this is always the case; but on the (a) hypothesis 
the variables w, 7,... must satisfy certain conditions.) There 
exist, then, at any time, 


N?R, 
U 


Nama lad ec Yy-»-)dVdedy... . (2) 


molecules of the class considered, whose duration is tr. The 


26 Ladislaus Natanson on the Kinetic Theory 


mean value V? is therefore for all molecules, 


panes { {f. eo TN ers or: Y; ee 3) dV dx dy eee 
We A EE eee Slee 
{ (j ee Dies CROP noo dV dx dy elewt 
0 


the limits of integration with respect to 2, y,... being a, a ; 
Yo) Yi 3 +» according to the hypothesis (@),and &, &; %, m... 
on the («) hypothesis. According to the (8) hypothesis, r is 
independent of V ; but on the other assumption (a), rT depends 
upon the time which elapses between the collisions, and there- 
fore on V. If we accept the (8) hypothesis as the true one, 
we obtain 


(3) 


Vaze; ) 1: 1) es 
whence 


Ho=mV*=gmeP=Hy. 2. (5) 


If, on the contrary, we take the («) hypothesis, we must 
write ?T for t, where T denotes the time between two succes- 
sive collisions of a molecule whose velocity is V ; and i+1 is 
the number of collisions which the molecule experiences before 
breaking up, reckoning as first collision that in which the 
molecule is formed. We can treat 7 as dependent on V only 
as T depends on V, and then 2 will be determined by the 
quantities v, y,.... We have then 


(OPV aV 
Vie Jo) 
T2222 gV 
e/ 9 


Now since the relation 7 
) UES ip — Fea) TV26e-2V7/2 dV 
0 0 


ie) 


2 ey TT 2 
= i) V3 So erate iV —F [ TV | 


0 


holds good for all values of T, and T must be finite at V=0 
and equal to zero at V=oo (as follows from the definition of 
T), we must have 


oes € 7 Ej 
Vi=ga*(1+ =) and B,=H, (1+ 3) - 2 @%) 


| of the Phenomena of Dissociation in Gases. 27 


in which 
: une Mgrs Ry te 
3 —2V2/a2 
\ V aV° d\ 


a (3) 
(reeeeay 
0 


— 


It will be seen that ¢ is negative, and consequently, on the 
hypothesis (a) V? <#e?, and H,<H,. We shall put H,=.H, 
and proceed to calculate yu. 

§ 5. As a first approximation we may make use of the fol- 
lowing method. Leta molecule which moves with velocity 
V meet B, atoms and B, molecules during the unit of time, so 


that 7 =B, + By. Let us also assume that Maxwell’s law 


holds among the molecules, the velocity-modulus being £, 
which is small; and that B=3pe’. We have then (taking the 
volume v equal to unity) 


Ee a ek ae 
BNR /a[ eet SA (Mw ae], © (Y) 
e' 0 


2 2 (*V/B = 
B=NReV/ a | Bev ( rede], . 2) 
2 0 

where Ry, R, are the characteristic radii for the collision of 
molecules with an atom or a molecule respectively. In order 
to calculate «, let us introduce into the two integrals mean 
values B, and B, instead of the variable quantities B, and B,. 
As mean values we take 


4 po eee 
Sve), BVM AVR INR ETE), ) 
0 


B= 
Pe yf  p* Ps m 
B= nie B,V2e-V4l? dV =2N,Ry/ 278, . (4) 


and obtain a 
_ 8 2(Jdit+de) 5) 
a® JV 7(By = Bs ( 


where 
,o 9 
ee, Oran & 4—V3/02 oes oe, { 
NR. va E é Hi v) ‘ 


ee) 2 vV/B 
T=NRE Va [pours go & \) eda | Vee-2V77 dV... (7) 
2 give ma a ( v) ; ( ] ( 


V 


/o 
oe da] Vee2V78 dV, (6) 


28 Ladislaus Natanson on the Kinetic Theory 


If we obtain the expression for the differential coefficient 
d : ue 
dv ON aes eN de A e } and apply it to the cases F(V) =} e- da 
j ; 0 
al rv)=| e-* da, we shall be able to calculate J, and J, 
0 


easily. Their values are 


I= nN Rv; °°. 


8V3 
T a” 
Je=9 NR,’ We (9) 


and substituting the values of B, and B, from (3) and (4) in 
the expression (5) for e, 


N,R,.?+ 


By 
ro) 


Ti 2 
J 3(2+p)N Ry? + V Gu NRE 


It follows from the definition of w (§ 4) that e=3(1—yp), and 
therefore equation (10) gives us a means of calculating the 
value of pw. As the general expression for wu is complicated 
we shall content ourselves with taking the two extreme cases. 
It can be shown that the minimum value of w corresponds to 
N,=0, the maximum value to N,=0. In the first case the 


equation for p is 
18n1+p)d—-p)=1; 
and in the second case, 
27(2+u)A—p)y=1 ; 


from which the value of w must always he between 0°805 and 
0°886. 

We can check this calculation in the following manner. 
The probability of a molecule having a velocity between V 
and V+dV is (from § 4) equal to 


EN2e= 2022 GN. 
( “DV2e-2V28 dV 
0 


(10) 


(11) 


Since (B,+ B,)T=1, we have 


een oN a © V7 2—2V2/a? 
= = S= leaf ad REN 1 If 
(+B,= Bais where J { B13, dV. 1) 


ae 
2J; 


of the Phenomena of Dissociation in Gases. 29 


If we put N,=0 in this equation, the value of B, is ob- 
tained as follows:—Let J, be the value of J when N,=0. 
It is easy to show that 


at we? daw 
= svt pe ° (13) 
ay 0 ven + (208-41) ( “o Ee =" da 
0 


In exactly the same way that Clark calculated the table given 
in Prof. Tait’s paper previously quoted, I have found as 
numerical value of the integral in equation (13), 


0°0605022. 
Hence B,=4°2706N,R,.?«; while previously (from equa- 
tion (3), putting w~=0°886 since N,=0) we found for B, the 
value 4°2584N,R,,.”«. Ina similar manner B, could be eal- 
culated. It will therefore be seen that the former method 
gives fairly correct results. 
There is one other method of calculating w, which I will 


again apply to the case N,=0. From the equation (6) of 
§ 4, we can show that 


le ( 3— d 
Sie By ak B, av : 
4 a Yee) ti ‘ 

Bi 


0 1 


Vs (14) 


—2V2/a2 dV 


The denominator is equal to J, and is therefore known. 
On writing V=az, we obtain 


08s. no-** + (2a"—1) | GE Ce 


oO”: 0 
B av. 3 oa (15) 
wen* + (20-41) { OSGi 

whence 


. t+ —_=* _____—___ 
we~™ + (Qa? + Hf eda we” + Qn" + DI poe 
0 0 


Applying Clark’s method, I have found for the numerical 
value of the integral (16), it 088139, which gives 


V?=0°67776 a2. 


ee) 
— 72 
if en ( é AX 


| ax. 


(16) 


30 Kinetic Theory of Dissociation in Gases. 


The previous calculation, with ~=0°886, gave the value 
ae PH 6? =0-66450 eh. 


This calculation can also be extended to the case N,=0, 
and I have worked it out for that case. We may conclude 
that if ~ represents the ratio of the energy of the molecules 
formed to the atomic energy, the value of w always lies be- 
tween # and 8; and the final ratio of the two energies, which 
remains stationary, lies between mw and 1. 

§ 6. The problem dealt with above appears to me to be of 
great interest in the theory of dissociation. If the mean 
values of the kinetic energies of a molecule and an atom are 
different, and do not even stand in a constant ratio to each 
other, it is difficult to decide which mean value should be 
taken as a measure of the temperature. As previously in the 
case of imperfect gases*, so also here it is seen that in the 
kinetic theory of heat we are far from possessing a general 
definition of temperature ; the usual one is applicable only to 
perfect gases. 

§ 7. Now since the hypothesis («) appears to be at variance 
with experiment in actual dissociation phenomena (dissocia- 
tion of iodine vapour, nitrous acid, &c.), and would only be 
applicable to phenomena of decomposition, which are due to 
secondary causes (e. g. the dissociation of hydriodic acid), it 
would be necessary to suppose that iodine atoms, NO, groups, 
&c., only combine into molecules during collision. Since all 
gases may probably dissociate under suitable circumstances, 
this assumption would have to be extended universally to all 
gaseous molecules. We should then have to make, for gases 
like oxygen, hydrogen, &c., the further supposition that 0/T 
is very large and nearly constant, or else free atoms would 
occur in impossible numbers in these gases. According to 
experiments hitherto made on atomic weights and densities of 
gases, it must be assumed that in these cases @ is far greater 


than 500 T. 


* L. Natanson, Wied. Ann. xxxiii. p. 693 (1888). I have formerly 
tried to prove that the energy of the “free” molecules should be taken as 
a measure of the temperature. In a paper which I know only by an ab- 
stract (Proc. R. 8. Ei. xvi. p. 69, 1889), Tait arrives at the same conclusion 
by quite another line of argument. 


feok 


Ill. The Temperature of the Moon. From Studies at the 
Allegheny Observatory by 8. P. LANGLEY, with the assist- 
ance of F. W. Vzery*. 


HIS memoir may be regarded as the completion of the 

investigation commenced in 1883, and continued during 

the next four years, and of which previous portions have been 

published in the Memoirs of the National Academy of Sci- 

ences, in a paper read Oct. 17, 1884 (vol. ili.), and in that 

read Nov. 9, 1886 (vol. iv.), the latter having been published 
in abstract in the American Journal of Sciencef. 

The original memoir, of which the following is a very 
succinct abstract, can, from its special character, hardly claim 
the attention of the general reader; but the latter may, 
perhaps, be here reminded that the main questions at issue 
are the temperature of an airless planet at the earth’s distance 
from the sun, the action of the atmosphere in modifying the 
temperature of such a planet, and, in general, the study of 
those conditions of radiation and absorption which have 
actually rendered life possible on our own. He may be re- 
minded also that it has been generally assumed hitherto that 
the temperature of the sunlit surface of an airless planet at 
such a distance, e. g. of the moon, would be excessively high. 
Thus Sir John Herschel, in his latest ‘ Outlines of Astronomy,’ 
says:—‘ The surface of the full moon exposed to us must 
necessarily be very much heated, possibly to a degree much 
exceeding that of boiling water.” The only experimental 
evidence obtainable appeared to lend support to this view, 
for though Lord Rosse did not undertake to directly deter- 
mine the lunar temperature (as he is often supposed to have 
done), any inference which can be drawn from his experi- 
ments appears to support the above views of Herschel, which 
he also cites {. 

It has also been almost universally supposed that our at- 
mosphere was nearly impervious to the lunar radiant heat, so 
that, if any existed, it could still not be perceived by us at 


* Memoir read to the National Academy of Sciences, November 1887. 
Communicated by the Author. 

+ For December 1888. See also ‘London, Edinburgh, and Dublin 
Philosophical Magazine,’ December 1888; also Ann. de Chemie et de 
Physique, July 1889. 

{ See Proc. Royal Society, xvii. 1869, p. 443; xix. 1870, p. 12; Trans- 
actions, clxiii. pp. 622-4. Having elsewhere shown that the lunar 
radiation consists of a small quantity of reflected heat and a compara- 
tively large quantity of heat emitted from its soil, Lord Rosse compares 


32 Prof. 8. P. Langley on the 


the sea-level. Thus Sir John Herschel says of the moon that 
“its heat (conformably to what is observed of that of bodies 
heated below the point of luminosity) is much more readily 
absorbed in traversing transparent media than direct solar 
heat, and is extinguished in the upper regions of the atmo- 
sphere, never reaching the surface of the earth at all.” 

The reader may also be reminded that these statements have 
remained unchallenged on account of the hitherto insuperable 
difficulties of experimental investigation, arising from the all 
but infinitesimal amount of heat which the moon sends us, 
and the added fact that this heat, small as it is, is necessarily 
of two essentially different kinds—that which the moon, acting 
as a mirror, reflects from the sun, and that which directly 
emanates from the substance of her own sun-heated soil, while 
it is only by an analysis of each of these two kinds of heat, 
each in its totality non-existent to the most sensitive ther- 
mometer, that we can expect to give an experimental answer 
to the question *, 

It was Melloni who, on Mt. Vesuvius in 1846, by the 
employment of a polyzonal lens, one metre in diameter, and 
the newly invented thermopile and galvanometer, first suc- 
ceeded in getting any certain indications of heat from the 
moon, though these were of the feeblest kind. It is Lord 
Rosse, employing the Parsonstown telescope with improved 
thermopiles and galvanometers, who has the credit of abun- 
dantly confirming Melloni’s observation of the fact of the 
moon’s radiant heat being perceptible, and further the great 
merit of making a preliminary investigation of its character, 
by showing by its imperfect passage through glass that it is 
chiefly non-reflected heat. Lord Rosse, however, as has been 


the total excess of this lunar radiation over that from the sky by means of 
that from two blackened vessels, one producing the same effect on his 
thermopile and galvanometer as the sky, the other as the moon, and finds 
that the observed galvanometer range is that due to a temperature of 
excess in the latter vessel, to be computed at 197°'5 F. if Dulong and 
Petit’s law of cooling is used, or at a still higher one if Newton’s is em- 
ployed. The effective sky temperature was about +20° F., so that if 
we suppose the result due wholly (instead of mainly) to the emitted 
heat, this would indicate a temperature of the lunar soil at any rate above 
that of boiling water. Lord Rosse, however,in view of the empirical 
character of the formula employed and of other considerations, is careful 
to state as his conclusion ‘‘ that the problem of the determination of the 
lunar temperature is nearly as far as ever removed from our grasp.” 

* In an appendix (No. 1) of the memoir referred to, will be found a 
historical account, believed to be fairly complete, of the labours of previous 
thinkers and workers in this subject. 


Temperature of the Moon. 3d 


said, concludes that the problem of the moon’s temperature is 
still indeterminate. 

At this point the question is taken up by the writer, who, 
with the aid of the bolometer, used directly in the lunar 
image, had already reached, in the first of the memoirs men- 
tioned above, the following inference among others of less 
importance, viz. that the sunlit surface of the moon is not 
far from the freezing temperature. 

This inference resulted both from observations in the direct 
beam and from a preliminary and partially successful attempt 
to form a heat spectrum, for this gave indications of two 
maxima in the heat-curve—the first corresponding to the heat 
from the solar reflected rays; the second (indefinitely lower 
down in the spectrum) corresponding to a greater amount of 
radiant heat emitted from a source at a far lower temperature, 
lower at any rate than that of boiling water, above which the 
temperature of the lunar soil has been hitherto supposed to 
not improbably be. This statement of the first memoir is put 
forward as inferential and probable merely, and not as con- 
clusively proven. 


The second memoir, on “ The Solar and the Lunar Spec- 
trum,” is chiefly devoted to the invisible spectrum of the sun, 
but incidentally describes the progress in the improvement of 
the apparatus employed so as to better fit it for the delicate 
task, 

(1) of measuring the already feeble lunar heat when diffused 
by expansion into a lunar spectrum ; and 

(2) of determining the possible existence and the exact 
position of the two heat maxima already described in the first 
memoir. 

We are now prepared to take up the present memoir, and 
give an abstract of its results. It contains researches pursued 
through several years with constantly improving instrumental 
means, and while the writer cannot feel that (owing to the 
extreme experimental difficulty of the subject) the results 
have obtained a certitude corresponding to the great labour 
bestowed upon tkem, he believes that this labour is justified 
by the fact that it has not been given to a question of merely 
abstract interest, but that the whole subjects of terrestrial 
radiation and the conditions of organic life upon our planet 
are intimately related to the present research. 


Spectroscopy has hitherto dealt almost exclusively with 
Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. D 


34 Prof. 8. P. Langley on the 


light, but in this new field we consider chiefly that great in- 
visible spectral region in which the entire radiation of the soil 
of our own planet is to be found, a region of which we have, 
until quite recently, known nothing. ‘To see how the question 
of the lunar heat affects our knowledge on the whole subject 
of our planet’s temperature, we must remember that, until a 
few years past, it had been assumed by all writers of repute 
that the earth’s atmosphere acted exactly like the glass cover 
of a hot-bed, and kept the planet warm in exactly the same 
way that the hot-bed is warmed, by admitting the light-heat 
of the sun, which was returned by the soil in the invisible 
radiation of greater wave-length to which the atmosphere was 
supposed to be impervious, and that thus the heat was stored, 
glass being till lately supposed to be practically athermanous 
to all infra-red heat. It was a necessary part of this assump- 
tion that all, or very nearly all, the infra-red was absorbed by 
our atmosphere; but in 1881, the observations of the Mount 
Whitney expedition, supplementing previous ones made at 
this observatory, showed that through the infra-red, as far as it 
had then been explored, the atmosphere transmitted the invisible 
rays with greater facility even than the luminous heat ; so 
that the ordinarily received idea must be essentially modified, 
and, if the absorption of the telluric radiation did indeed take 
place as supposed, it must be in spectral regions then entirely 
unknown. It is in an examination of these, till now, quite 
unknown regions beyond the extreme boundaries of former 
researches on the infra-red, and in the study of the radiations 
of corresponding wave-length emitted from the lunar soil, 
that we find the principal subject-matter of the present 
memoir *. 

It is, in introduction, again pointed out that the absorption 
of the earth’s atmosphere for these radiations, as for all others, 
is not simple, but eminently complex, and that the old for- 
mulze lead to gross errors in practice. Further, as the amount 
of radiation of a planet is, like that of any other body, de- 
pendent on that of its surroundings, reasons are repeated for 
believing that the so-called temperature of space (a term due 
to Fourier and afterwards adopted by Pouillet, who fixed its 


* The reader is reminded that the words “infra-red ” have obtained 
an extension of meaning, since we have been able to show in previous 
memoirs, not only the vast amount of the energy in this region (which, 
in the case of the sun, is over 100 times that in the ultra-violet), but 
that in this invisible infra-red there is every variety of condition, greater 
differences than there are e. g. between violet and orange light, and that 
Melloni’s anticipatory comparison of varieties of radiant heat to varieties 
of colour actually understates the truth. 


Temperature of the Moon. a5 


value at —142° Cent.) has no sensible existence, but may be 
here treated as that of the absolute zero. 

There is next given a description of the apparatus, which 
consists essentially of a siderostat, carrying an 18-inch mirror, 
and capable of sending a lunar beam of corresponding capacity 
horizontally into an adjoining dark room and keeping it 
fixed there during the night’s observations. In the path of 
the beam can be interposed a large double screen of blackened 
copper, ordinarily filled with water. The beam then falls on 
a condensing mirror, whose ordinary aperture of 8 inches 
does not, as may be seen, utilize the whole of the beam trans- 
mitted by the siderostat, but has been selected in reference 
to the capacity of the rock-salt train of lenses and prisms 
which forms the spectrum. This train is believed to consist 
of pieces of salt of hitherto unapproached perfection in work- 
manship, as at the time our investigation commenced no salt 
prisms were procurable giving a single Fraunhofer line in 
the solar spectrum; while with the actual rock-salt train, D 
is divided in the spectrum of the moon. The general con- 
struction of the spectrobolometer, and of the special bolometer 
employed with it, will be found given in previous papers*. 

There are three principal methods of investigation :— 

First, the measurement of the total heat of the moon 
with a concave mirror, admitting the interposition of a sheet 
of glass to rudely indicate the quality of lunar rays as com- 
pared with those of the sun. ‘This method, which was that 
employed by Lord Rosse, has been very thoroughly practised 
here with results which have been partly given in the previous 
memoir. 

Second, a method, practised here for the first time, and 
yielding quite peculiar results, has been to form, usually with 
this same mirror, an image of the moon, but to now let this 
fall upon the slit of a special spectroscope provided with the 
rock-salt train referred to; and after expanding this exces- 
sively minute heat in this way, it has been found possible, 
with late improvements in the apparatus, to measure by the 
bolometer the different degrees of heat in the different parts 
of this lunar heat-spectrum, both visible and invisible. The 
doing of this, with its results, forms the principal subject of 
the present memolr. 

Third, since such a mirror as that just mentioned, owing to 
its short focus, forms an extremely small lunar image, in cer- 
tain observations (carried on, however, only during a limited 

* See this Journal, xv. March 1883, and xxi. May 1886, For a descrip- 
tion of the improved form of bolometer and galvanometer see vol. xxii. 
August 1886. ae 


36 Prof. 8S. P. Langley on the 


time), we have taken advantage of the sensitiveness of our 
apparatus to directly explore a large lunar image with the 
bolometer, in spite of the diminished heat in such a one. For 
this purpose a special mirror, 303 millim. in diameter and 
3137 millim. focus, giving a lunar image of about 30 millim. 
diameter, has been employed. On the occasion of a lunar 
eclipse the last-named apparatus has also been used. 

We have already alluded (see Memoirs of the National 
Academy, vol. iii. p. 20) to the especial importance of the 
action of the screen in these observations. ‘This arises from 
the fact, as will be seen later, that we shall deal with lunar 
heat of a totally different quality from that of moonlight or 
sunlight. It is, in a large part, radiation emanating from the 
lunar soil, and of a quality, as we shall see, approximating 
to that of the screen itself. It must be evident, then, that the 
radiations from this screen assume here a wholly abnormal 
importance. 

An investigation of the theory of the screen accordingly 
occupies a chapter, for which the reader is referred to the 
original. We may remark here, in passing, that the investi- 
gation incidentally offers an explanation of the empirically 
known fact, that the velocity of cooling of a hot body at various 
temperatures of excess varies with that of the enclosure itself. 
The discussion also indicates what appears to be an inde- 
pendent method of determining the absolute zero; but the 
method, although apparently correct in theory, would demand 
observations more accurate than our own casual ones to give 
it practical value. It may be, however, worth mentioning 
that the observations, such as they are, indicate by this novel 
method the existence of an absolute zero at a point between 
— 250° and —300° Cent. 

A list of all the observations in the lunar spectrum extend- 
ing from October 1884 to February 1887 is then given, 
together with some collateral ones upon the “ great radiator.” 
This latter instrument may be briefly described as analogous 
to an immense Leslie cube, presenting as it does a blackened 
radiating surface at the temperature of boiling water and of 
1 square metre area. The object in giving it this extraordi- 
nary dimension is to enable it to still angularly subtend the 
whole field of view of the bolometer, while it is at such a dis- 
tance that the intervening column of air may be supposed to 
exercise a measurable absorptive effect. Its actual distance 
was 100 metres, and at this distance the absorption of the 
intervening air on the dark radiant heat, emanating from its 
surface at 100° Cent., was in fact manifest, and gave evidence, 
novel and interesting, both as to the actual absorption by our 


Temperature of the Moon. a7 


atmosphere for radiations from bodies of low temperature, and 
as to the spectral region where it chiefly occurred. 

This list includes, besides the described heat observations 
on the moon at every obtainable lunation, the following 
others :— 


(1) On the heat during a lunar eclipse. 

(2) On the quality of the heat in the lunar spectrum at 
different stages of the moon’s age. 

(3) On the direct heat observable from different regions of 
the moon’s face in an enlarged lunar image, and com- 
parisons of the heat radiated by the dark and by the 
bright regions of the moon. 

(4) A supplementary investigation showing that different 
percentages of the radiations from these dark and bright 
regions were transmitted by glass. 

(5) Observations giving the means of comparing the atmo- 
spheric absorption of lunar radiations in summer with 
that in winter for equal altitudes. 

(6) Very numerous observations of the spectrum of the mid- 
night sky. 

(These last are specially important here, where they 
are rendered necessary by the fact that this sky is the 
standard with which the lunar radiations are to be 
compared. ‘These last observations give, for example, 
certain evidence of a great “hot band” in the nega- 
tive sky spectrum, corresponding in position to the 
great cold band in the lunar spectrum, which is thus 
shown to be produced jointly by the absorption of the 
moon’s rays and by the absorption of the radiation of 
the bolometer due to the intervening air-column be- 
tween it and the moon.) | 

(7) Observations supplementary to the last, by comparative 
measurements of the sky radiation from the zenith to the 
horizon. 

(8) On further supplementary measurements made by com- 
paring the energy in the spectrum of a lampblack 
screen at 100° C. with that of the sky, showing the 
existence of several regions of atmospheric absorption, 
giving “ hot bands”’ in the negative sky spectrum. 

(We only allude here, in passing, to the important 
inference to be drawn with regard to the nocturnal 
radiations from the soil of our own planet, to which 
these observations show that our atmosphere is partially 
diathermanous. ) 


38 Prof. 8. P. Langley on the 


(9) On other measurements giving the means of estimating 
the total lunar radiation in terms of solar; 

but for these and many more subsidiary ones, the reader must 

again be referred to the original memoir. 

The only one of these subsidiary researches which needs 
further mention here is the measurement of the heat from 
different parts of the eclipsed moon, on the night of September 
23, 1885. 

The diameter of the lunar image was 28°3 millim., and of 
this only a limited portion (0°08 of the whole) fell upon the 
bolometer. As the penumbra came on, the diminution of 
heat was marked, being measured by the bolometer even before 
the eye had detected any appearance of shadow. The heat 
continued to diminish rapidly with the progress of the im- 
mersion in the penumbra, but at no time did the lunar radia- 
tion from the part in fuil shadow entirely vanish. At one 
hour before the middle of the total eclipse, the deflexion in 
the umbra was 8°8 divisions. Fifty minutes after the middle 
of the eclipse it had diminished to approximately 1°3 divisions, 
less than one per cent. of the heat from a similar portion of 
the uneclipsed moon, a deflexion so small that its significance 
may be somewhat doubtful. It need hardly be stated that 
this heat from the eclipsed moon was almost absolutely cut 
off by the interposition of glass. The rise of the temperature 
after the passage of the umbra was apparently nearly as rapid 
as the previous fall. The vicissitudes of the lunar climate in- 
dicated by these observations in the short time of a few hours, 
must exceed the change from our torrid zone to the greatest 
cold of an arctic winter. 

In this connexion it should be stated that repeated obser- 
vations on the dark side of the moon have given only the 
same heat-spectrum as shown by the sky away from the 
moon, the conclusion being that, so far as our present obser- 
vation carries us, the moon has no internal heat sensible at 
the surface, so that the radiations from the lunar soil, already 
spoken of, are to be understood as due purely to solar heat 
which has been absorbed and almost immediately re-radiated. 

The principal method employed in the present research for 
determining the temperature of the surface of the moon is 
founded on the fact, already experimentally established by 
the writer, that the position of the maximum in a curve, 
representing invisible radiant heat, furnishes a reliable crite- 
rion as to the temperature of the radiating (solid) body*, 


* Proc. Am. Assoc. for Adv. of Sci., 1885; also Phil. Mag. xxi. May 
1836, 


Dee 


Temperature of the Moon. 39 
and on the further fact, established by Mr. F. W. Very and 


the writer, that two distinct heat-maxima are observable in 
the lunar spectrum, one corresponding to the radiation 
reflected from the soil, the other to that emitted by it. It at 
first seemed, in accordance with what has just been said, that 
the accurate determination of the wave-length of this latter 
maximum would give acorrespondingly accurate determination 
of the temperature of the sunlit surface of the moon; and, 
accordingly, to this object the main portion of the observa- 
tions were given. We may anticipate what follows by here 
saying that by this method, a perfectly correct one in theory, 
the writer believes that the temperature of the lunar soil 
could be determined with great exactness, were it not for the 
intervention of the earth’s atmosphere, which exercises, in 
this part of the spectrum as in every other, a highly selective 
absorption, indicated here, however, not by fine lines like the 
Fraunhofer lines of the solar spectrum, but by enormously 
wide “ cold bands,” which vary in size and even in position 
from night to night *, rendering the exact position of this 
maximum in a corresponding degree indeterminate. 

Another chapter is occupied by an example of a single 
night’s work in detail, with a statement of some of the pre- 
cautions and corrections employed in practice. It may be 
observed here in general as to the apparatus, that while the 
rock-salt train, as already mentioned, is of such perfection 
as to show the Fraunhofer lines very completely in the lunar 
luminous spectrum, the accompanying bolometer and galva- 
nometer enable us to measure cold bands in the non-luminous 
lunar or air spectrum, whose heat is otherwise so inappre- 
ciably small that it corresponds to a radiation of zo o00000 
of a calorie per second, measured by the generation of a 
current of 0°000,000, 001 ampere. This is the amount of 
heat and current implied j in moving the galvanometer image 
over 1 millim. of the scale. In fact, the image is quite 
steady enough under favourable conditions to admit of the 
observation of less heat than this, giving deflexions of frac- 
tional portions of a millimetre ; but owing to fluctuations in 
the absorption of our atmosphere which transmits this radia- 
tion, rather than to any limitations of the instrument itself, 


* That an absorption- band may vary in magnitude will excite no sur— 
prise, but that it should vary sensibly in position may appear to some in 
contradiction with our knowledge of the fixity of lines in the upper 
spectrum. An explanation of the anomaly will be found in this Journal 
for Dec. 1888. 


4h 
-: 


40 Prof. 8. P. Langley on the 


it is generally found best not to note deflexions of less than 
1millim. Whathas just been said refers particularly to mea- 
surements of the diffused heat from the moon’s soil in the 
invisible lunar spectrum and to the corresponding spectral 
analysis of the reflected heat. When, however, we place the 
bolometer directly in the lunar image formed by the 8-inch 
aperture, the deflexion throws the needle at once off the 
scale, and is found on more careful measurement to corre- 
spond under favourable circumstances to a potential deflexion 
of about 1500 millim. divisions. Melloni, it will be remem- 
bered, obtained four or five divisions on his galvanometer 
with the thermopile and the metre polyzonal lens on Vesuvius, 
and the immense difference just noted is some indication of 
the advance of experimental physics in this matter since his 


day. 


Theory of Observation ; with typical example, 
showing Method. 


Every observation on the moon, whether on its total heat, 
as observed directly in the lunar image, or on its diffused 
heat in the spectrum, should consist in a comparison of its 
radiations with those of the adjacent sky on either side of it. 
If our thermometric apparatus had an absolute scale, and 
there were no intervening atmosphere, it appears, In accord- 
ance with what has already been said, that such apparatus, 
when directed not to the moon but to ‘‘ space’? more or less 
adjacent, should indicate the temperature of this space, which 
is sensibly that of the absolute zero; and then, when it is 
turned upon the moon, supposing it to receive only the 
emitted and not the reflected heat, it would give, also on the 
absolute scale, the temperature of the lunar soil. In fact, 
with such an absolute thermometer, the preliminary com- 
parison with space would be unnecessary. In reality, we use 
not an absolute apparatus with a natural scale, but a differen- 
tial apparatus with an arbitrary scale ; and if we could work 
without an intervening atmosphere, we should, even in this 
case, require to let the bolometer radiate to space in order to 
determine the point on our arbitrary scale which corresponds 
to zero. We should then observe a second point correspond- 
ing to the temperature of the lunar surface, and having 
determined the value of the units of our arbitrary scale in 
terms of the natural one, we should evidently have the 
quantity sought. 


7 


Temperature of the Moon. Al 


The above conditions are still of ideal simplicity. The 
great, the almost insuperable difficulty of actual observation, 
lies less in the minuteness of the actual radiation, or even in 
its two-fold character, than in the fact that it is masked to us 
by the changes of an always intervening atmosphere. The 
case of observations on the sun is totally different from the 
present one, and would be so even if the sun were withdrawn 
till it emitted no more heat than the moon; for in this latter 
imaginary case, the greater portion of the solar radiation 
would still lie in a spectral region totally distinct from that 
in which the radiations proper to the obscuring atmosphere 
are found, and it is the peculiar, unavoidable difficulty, at 
every stage of this long investigation, that since the moon 
and the air are both alike cold bodies, their invisible spectra 
are, in general, superposed in the same field. Let us add to 
this, that the (invisible) spectrum of the air is usually not 
fixed but fluctuating, and we shall see the desirability of 
having some separate standard with which to compare it from 
night to night. This we obtain most conveniently by filling 
a vessel of proper shape and size, either with water or with a 
freezing mixture at a temperature constant for the series, 
and making this vessel itself the screen which is interposed 
between the bolometer and the lunar rays. The bolometer 
must remain unmoved, and the direction of the heat-receiving 
apparatus to the east or west of the moon must always be 
understood to be obtained by a shght motion of the siderostat 
mirror. 

That the minute change in the angle of presentation of the 


- face of this mirror does not affect its own radiations appre- 


ciably might well be anticipated, but is a fact which has not 
been left unproven by direct experiment. The bolometer, 
then, enclosed in a non-conducting case which cuts off 
radiations from every object but the mirror or prism imme- 
diately in front of it, practically feels only the radiations 
from the moon, or from the sky immediately on each side of 
it, except when the screen is interposed. Mirrors and prisms 
do indeed radiate heat to it from their own substance, but 
these radiations may be considered as absolutely constant, 
and as therefore absolutely negligible during the brief cycle 
of a single observation. 

We confine ourselves here to the above general explanation, 
referring the reader who may be interested in the details of 
the observations to the original memoir, remarking, however, 
that the actual spectral position of a ray is given by a circle, 
reading to 10” of are, and that previous measures of our 


42 Prof. 8S. P. Langley on the 


own * enable us to convert this are into wave-length. This 
fixes the position of bands in the spectrum. The amount of 
heat in any portion of the spectrum is, within the narrow 
limits of errors of observation, strictly proportional to the 
deflexion on the galvanometer-scale (the conditions of the 
bolometer, battery-current, galvanometer, &c., remaining 
constant). As these degrees are arbitrary, they are converted 
into thermometric degrees by a process fully detailed in the 
original memoir. 

The preliminary record of the humidity, state of the sky, 
temperature, &c., is nearly self-explanatory. We need only 
explain that ‘ Rock-salt lenses at 387 centim.” refers to the 
fact that the focal length of these lenses increases from 35 
centim. in the visible spectrum to one indefinitely greater 
with heat of great wave-length, and that this focus accord- 
ingly needs to be adjusted for the particular part of the heat- 
spectrum under study. 

“ Deflexion per degree Centigrade” refers to the use of a 
constant determined for each evening, giving the actual 
deflexion the galvanometer produces, for each degree of 
excess of temperature in a certain standard Leslie cube at a 
certain standard distance from the bolometer. 

The order of observation consists first in noting the time. 
(We will suppose, in the example which follows, that the time 
is 95-08 M. T., on the evening of February 9, 1887) ; next, 
in noting the prismatic deviation corresponding to the actual 
position of the bolometer in the spectrum, which in this 
particular case is 41° 08’ 30", or that of the D line in the 
visible spectrum. Previously to observation the bolometer 
has been radiating through the spectroscopic train and mirror 
to the special screen described, which, on this particular 
evening, is at the constant temperature of + 18° Cent. 
Under these circumstances, the needle will take up some 
position representing radiation to the screen, which at this 
first exposure we will call A, its position here on our 
arbitrary scale being at the 215th millimetre. During this 
time the siderostat-mirror has been so placed as to be sending 
towards the bolometer radiations from the sky on the east of 
the moont: Call the effect of these particular sky radia- 
tions B. They have been intercepted by the screen, but 
now the screen is withdrawn, and the bolometer radiating to 
this eastern adjacent sky receives less heat than the screen 


* See Phil. Mag. xxii. August 1886. 
+ The area of sky observed is virtually the same as that of the moon. 


Temperature of the Moon. 43 


gave it (213°2). The siderostat-mirror is moved to throw on 
the image of the moon. Let us call the resultant deflexion 
C. The moon appears in this example very slightly warmer 
than the sky, for the image moves on to 213°4. Next, by 
another adjustment of the siderostat-mirror, the sky west of 
moon is thrown on. Call this result D. The image on the 
galvanometer-scale moves back to 211:9, indicating cold. 
Finally the screen is interposed the second time. Call this 
second interposition H. In an ideally constant apparatus, 
the second interposition of the screen should give the same 
reading as the first. Actually 210 divisions is obtained, 
instead of 215 as before, owing to the so-called “drift” of 
the needle during observation. The mean of the two readings 
for sky-east and sky-west is now subtracted from that for the 
moon and gives, under the column ga, the difference 


between the temperature of the moon and the sky in our 
arbitrary degrees. It will be seen from a comparison of all 
the numbers in this column that there are fairly accordant 
indications of a maximum near the prismatic deviation of 
39° 30’, which corresponds with the wave-length of 2":1, and 
approximately with the maximum of the solar-heat curve. 
There is another maximum of far greater magnitude near 
a7° 30’ (wave-length about 14”), corresponding to the 
maximum known to exist in the radiations of bodies at a 
temperature of about 0° Cent., and due, it would seem almost 
beyond doubt, to radiations from the sun-heated lunar soil. 
It will be seen also that all numbers in this column have one 
sion, 2. ¢. the positive, indicating that throughout this series, 
without exception, the moon has been found warmer than 
the adjacent sky. This, indeed, is to be expected, since, 
without the atmosphere, the temperature of this sky would be 
nearly that of the absolute zero, and at any rate lower than 
that of the moon. ‘The difference is so considerable that even 
the temperature fluctuations due to the interposition of the 
intervening atmosphere in no case this evening hide the fact. 

In order to compare the fluctuating radiation of the atmo- 
sphere with a constant source, we take the mean of the sky 
observations and compare it with the mean of the readings on 


B+D A+H 
2 2 
ference of but 01 division; but this is, as we have already 
observed, when the bolometer is directed towards the orange 


the screen. In this particular case, 


gives a dit- 


44 Prof. 8. P. Langley on the 


in the luminous part of the spectrum, and our cold screen, it 
need hardly be said, is not emitting any rays of orange light. 
We conclude, then, that the apparent deflexion of 0-1 div. 
here has no real significance ; but, as we go down the spec- 
trum towards the region of the radiation from cold bodies, we 
find, beyond deviation 39° (~=4":3), values which indicate a 
real excess of screen over sky radiations. 

We have selected the first number in our second series of 
Feb. 9, 1887, as the example, because this follows the normal 
course without marked instrumental disturbance. ‘The nature 
of these fortuitous disturbances and the methods adopted for 
their correction are explained in the original memoir. In 
many cases, as will be seen, they may cause the sky on one 
side or the other of the moon to appear momentarily warmer, 
although the mean of the two is colder. 

Comparisons of the sky and screen by directing the bolo- 
meter to the sky at the zenith and at the east and west horizons 
follow, and three double series at the most important points in 
the spectrum, made with the moon ata high, a low, and an 
intermediate altitude, give indications of the atmospheric ab- 
sorption. These, however, are not given here, but only the 
double series (No. 2), of which a literal transcript from the 
book of original entry now follows :— 


Station, Allegheny. 

Date, February 9, 1887. 

Wet bulb at 7h 80m=+11° 2 C. 
Dry bulb at 7h 30m=+16°-0 C. 
Temperature apparatus at 9h 45m= +19°8C. 
External temperature, near the freezing-point. 
State of sky at 8h 30m clear. Very good sky. 
Aperture of slit =3 millim. =27'°9, 

Prism used L,, : A==60° 00' 28”. 

Rock-salt lenses set at 37 centim. 

Spectrum thrown west. 

Galvanometer No. 3. 

Time single vibration=12 sec. 

Deflexion per degree Centigrade =17°8. 
Bolometer No. 1; aperture=35 millim.=27':9, 
Setting on D,=41° 08' 30”. 

Battery current =0:036 ampere. 

Reader at circle, J. P. 

Reader at galvanometer, F. W. Y. 


Internal. 


CE , SE eT 


Time. 


Series IT. 


bh mH 
9 08 


9 42 


9 45 


10 00 


10 20 


Devia- 
, tion. 


41 08 30 


38 


41 08 30 


Temperature 


213°2 
233 
183 
185 
193°5 
185°3 
196°2 
213 
183 
1846 
184 
170°8 
161 
165 
166°7 
169 
166°5 
174 
182 


of the Moon. 


Screen Moon 
ihe Sky B. C. 


——q“qgl—— oo _/ 


213°4 
235°6 
184°6 
188-2 
198°8 
188°4 
198°3 
214°5 
183°6 
186-7 
189:2 
180 

177-2 
1818 
182°8 
182 

176 

184 

184°3 


Sky D. 


2119 
234°8 


181 


184-2 


196 
186 


197°5 


212 


182-4 
186°7 
182°8 


167 


159-4 
161-2 


164 


1688 


166 


172°8 
179-6 


Screen 


—" 

ite) 

=] 
SHH OIE OS 


— 
J 
bo 
ee ee ee 
SHS) Ce) CCS 110.6) ION ee 
HOME BACH MDODONANH AND 


— 
J 
9 
iW) 
— 


Temperature of Screen=18°. 


190 
191 
199°5 
198-2 
189°5 
188-2 
189 
181-4 
173°6 
185 
195 
203 
209°7 
206 
210 
200°5 
206°4 
2145 
2214 


185 
190 
193-8 
190 
181°5 
182°4 
183°5 
176°3 
1728 
183°7 
195°9 
203°5 
208 
207 
211-4 
201°5 
209:2 
214-7 
222 


186-2 
201°3 
205°5 
203 

197-2 
200-2 
200°5 
188°8 
180°6 
185'8 
198 

205 

208°7 


211-2 | 


215 
205 
215 
217 


224°] | 


178:2| 181 4°6 
191°8| 197-6 10-4 
192°2| 200-9 125 
186°8} 195 14-6 
Iie |) SUS 17-5 
180 | 189°5 19-0 
Gey of ts 19:4 
175°4| 176 12°8 
175°9| 181 6:3 
185 | 188 1-4 
197°8| 199:7 12 
201 | 201 2°8 
206 | 205°8 17 
207°4 | 209 4:0 
210°5 | 210°5 4-0 
201 | 202°3 37 
211°6| 211-6 4:8 
214 | 215 2°7 
223°2 | 223 15 


E. ae el tal 


—7T9 
—86 


—I11 


b aeigpesos9 
—3-4 
_ 7-9 
8:2 
_86 
_7:9 
4-4 
~2-7 
—3:0 
91 
—0°6 
+02 
—0°7 
—0°3 
+0°7 
—0-1 
41:2 
—0-4 
+04 


The observations of this night may serve as a type of a 
They all show two maxima (see column 


great many others. 


B+ D 


C— 


pei 


whose apparent position differs little from that 


already given in the example, and it may b> added that in all 
eases the radically different character of the heat in these two 
maxima bears the proof of the independent test furnished by 


46 Prof. 8. P. Langley on the 


passing the rays through glass before measurement, the rays 
from the upper maximum passing freely, as rays belonging to 
the maximum of solar reflected heat should do; those in the 
lower maximum, on the contrary, being absolutely cut off by 
the glass, as rays of this wave-length from a source at a 
temperature below that of boiling water are known to be. 
This test of the glass employed by Lord Rosse in the direct 
lunar beam, is here, it will be observed, applied at different 
parts of the lunar heat-spectrum ; and its result in the latter 
case, corroborating that already obtained by the respective 
wave-lengths of the maxima, brings evidence of a radiation 
of heat from the lunar soil at a temperature at any rate below 
that of boiling water. 

Other observations furnish the means of computing the 
relative absorption of the earth’s atmosphere as exhibited in 
extended cold bands in the region of the lower maximum. 
Then, from a combination of the two, we are enabled to reach 
a certain approximation to the position and magnitude of this 
maximum as it would appear if the atmosphere had not inter- 
vened. The existence of some of the principal atmospheric 
cold bands in this region, due to the absorption exercised by 
an atmospheric column 100 metres in length, has been quite 
independently determined by means of the great radiator 
already referred to. During moist summer weather two prin- 
cipal maxima have been found in its spectrum—the larger at 
deviation 37° 15’, nearly agreeing with the lunar curve in 
summer, a second smaller maximum at deviation 38° 45’, and 
between them a cold band with its minimum at deviation 
38° 20’. Remembering that the unabsorbed spectrum: from a 
radiating surface of lampblack, at the temperature of boiling 
water, has its maximum at 38° 25’, or very near the deepest 
depression of the cold band, it will be recogized that we have 
evidence of a considerable absorption at this point. 

To this must be added the fact, shown by our observa- 
tions, that in the case of solids the greater part of the whole 
heat is always found below the maximum of the (unabsorbed) 
prismatic curve. If this law hold in the case of the sun, 
since little heat is found below its actual prismatic maximum 
(near deviation 39° 40'), the inference is that absorption in 
that region (2. e. the eawtreme infra-red), must have been 

reat. 
Arguments on these different lines, combined with another 
derived from a direct comparison of sun and _ electric-are 
radiation, which will be described farther on, enable us to 
present a curve (fig. 1) showing, with the degree of ap- 
proximation compatible to the first attempt in such a field, 
the atmospheric absorption in all parts of the spectrum. 


47 


Temperature of the Moon. 


Per cent. 


—-———--—-—— oe  e — — 
: —— 
Sy es 


a 


“ 


Transmission of Radiation by the Karth’s Atmosphere. 


Abscisse = Rock-Salt Deviations. 


oGG 


“SMOTXOTO(T Joyououvayesy) = 


SO}VUIPL() ‘SUOT}VIAGC] I[VQ-OOY =eessrosq V 


o96 


oL& 


08S 


‘QAING [VULT ve IVUWT oY} UL AdLoUTT FO WOINQITASI(] 
ol? och 


0 


OL 


OF 


OG 


Prof. Langley on the Temperature of the Moon. 49 


The final result of the measurements, extending over the 
three years from 1884 to 1887, is given in fig. 2, in which 
abscissee correspond to deviations of a rock-salt prism of 60°, 
vertical ordinates to directly observed heat from radiations, 
while the dotted curve indicates what seems to be the most 
probable position and amount of the lower maximum, as it 
would be observed were there no intervening atmosphere. 
The following remarks may serve to make the full meaning 
of this curve clearer. | 

The heat is a vanishing quantity at deviation 42° at the 
left of the scale (42° with a 60° prism at the temperature of 
+ 20° Cent., corresponding to a wave-length of 0:48, or that 
of “blue” radiant energy). Confining our attention to the 
solid curve, we observe that it reaches a maximum near 
39° 40’=1"'5, corresponding to rays of dark heat which are 
vet transmitted by glass, and which must be emitted from a 
source at a very high temperature. The maximum of the 
solar heat directly observed through the rock-salt train is 
found to be at the same point. ‘There is no reason to doubt, 
then, that this maximum is due to the solar heat reflected 
from the lunar surface, and its actual effect is to produce a 
deviation of rather less than 20 degrees on the arbitrary scale 
of the galvanometer from the small part of the spectrum 
covered by the bolometer. Continuing to go down the 
spectrum in the direction of greater wave-lengths, and passing 
with casual notice a depression at 39° 15! (A=3"1), which, 
it is probable, would be found in the direct lunar spectrum 
were there no intervening atmosphere, we come to a very 
large depression at 38° 30! (A=7"), due almost beyond doubt 
to the rays emitted from the lunar soil having been here 
absorbed by our atmosphere. The conclusive evidence that 
this is due to the atmosphere is derived, first, from the 
constant appearance of an analogous band in the heat spec- 
trum of the sky away from the moon, and, second, from the 
independent observation of the existence of this band in the 
invisible spectrum of a terrestrial object after absorption by 
100 metres of air. In the latter case it is always found 
distinctly marked in moist weather and can even be observed 
under circumstances favourable to its development, in the 
few metres of air within the length of the observing-room. 
lt is important here to remark that the maximum of the 
unabsorbed radiation of a Leslie cube, at a temperature a 
little below that of boiling water, is found at the deviation of 
38° 20! (A=8"), when observed by the same rock-salt train. 

Following the solid curve down the spectrum, we find it 
rise into its principal maximum just below deviation 37° 30’ 


Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. E 


ag se ee co a a > 
eee gee ee 


50 Prof. 8. P. Langley on the 


(A, about 14”), where it attains a height of about 43 degrees 
of our arbitrary scale*. It is again most important to 
remark that this point, just below 37° 30’, corresponds to the 
maximum of the unabsorbed radiation of a lampblacked 
surface at a temperature of about —10° Cent. Were it not, 
then, for atmospheric absorption, we should assert with confi- 
dence that, so far as the radiations of a lampblacked surface 
and the lunar soil are comparable, the temperature did not 
exceed —10° Cent. Below this point the curve falls off with 
interruptions by several cold bands, until evidence of heat 
disappears near deviation 33° of our rock-salt train; but of 
this latter portion of the solid curve we will not pause here 
to speak. The dotted line is an attempted reconstruction of 
the original curve of lunar heat as it would appear before 
atmospheric absorption. It is made by allowing for the 
amount of absorption directly observed in the sky radiation, 
and in the radiation from terrestrial objects at a low tem- 
perature, already referred to, supplemented by an estimate of 
atmospheric absorption in this region inferred from a com- 
parison of solar and electric arc radiation, to be presently 
described ; and this constructive maximum occurs near 
deviation 38° 15’, which corresponds to the maximum of 
unabsorbed radiations from a terrestrial source at a tempera- 
ture of a little over +50° Cent. 

Direct observation, then, of the lunar heat-curve indicates 
that the probable temperature of the lunar soil is between 0° 
and —20° Cent. This is subject to the effect of our atmo- 
sphere, which probably is to displace this maximum in some 
degree towards the position of greater cold ; but the highest 
temperature we can assign by an allowance for this is +50° 
Cent. Between these points, we believe it probable that the 
temperature of most of the lunar sunlit soil must lie. The 
temperature of the lunar poles has not been specifically 
determined, but direct observation indicates that it is still 
lower. 

The relative amounts of the reflected solar and the emitted 
heat could evidently be obtained with satisfactory accuracy 
by measurements within the respective portions of the solid 
curve, were it not for the distorting action of the terrestrial 
atmosphere already mentioned. We must refer to the original 


* Tt may be interesting to observe that we infer from our bolometric 
observations that the effect of the total and unconcentrated lunar radia- 
tion on a blackened thermometer would be something like ;,1,,° Cent. 


Temperature of the Moon. ol 


memoir for reasons for estimating the total amount of the 
reflected radiation as little more than } of that emitted *. 
The memoir, of which an abstract is here given, contains 
numerous subsidiary researches and observations for which 
we must refer the reader to the original, only here mention- 
ing two :— 
_ first. Temperature-correction of a rock-salt prism. This 
investigation of the change of refrangibility due to tempera- 
ture was carried only far enough to give such approximate 
accuracy as served our immediate purpose, giving a value of 
—13” of arc for each degree Centigrade; but subsequent 
measurements have materially modified this, and I give the 
value now adopted, which is — 9/5, the formula being 


de = day— (t—20) 10”, 


where d= deviation, and ¢ = temperature in Centigrade 
degrees. 

Second. Comparison of the intrinsic intensity of solar 
radiation with that of the electric arc in different parts of the 
spectrum. This observation of the comparative intensity of 
the sun and the electric light is given in the original memoir 
only so far as to show that it brings independent evidence of 
a large atmospheric absorption of the extreme infra-red rays 
and enables us to estimate approximately the amount of this 
absorption at each point in the spectrum. The observations 
were not repeated to obtain such a thorough comparison as 


* Lord Rosse found that 87 per cent. of all the solar rays were trans- 
mitted by a particular piece of glass which allowed 92 per cent. of solar 
light to pass, and 12 per cent. of the total lunar beam. He attempted 
from this to determine the relative amounts of the solar and lunar heat, 
but felt obliged, in the then state of knowledge, to make the assumption 
(which our subsequent researches have shown to be erroneous) that the 
glass absorbed all the invisible rays, or that the lunar radiation contains 
12 per cent. of luminous rays, instead of less than 5 per cent., which is 
more nearly the actual case; but when Lord Rosse’s own observations 
are reduced with the aid of the facts determined by the writers, and 
representing the actually large transmissibility by glass of the invisible 
rays of shorter wave-length in the infra-red, his expression for the relative 
yalue (which we will call 2) of the emitted part of the lunar radiation 
(whose transmission by glass is presumed from observations on a Leslie 
cube to be 1°G per cent.) becomes ae 
times the reflected solar part ; so that if Lord Rosse could have possessed, 
at the time his reductions were made, knowledge as to the diathermic 
properties of glass which has only been acquired since, his own observa- 
tions would have given results for the relative amounts of reflected and 
radiated heat in somewhat remarkable accordance with our own. 


i 2 


ES Thich w=7:2 
= 2, from which r=7:2 


52 Prof. 8. P. Langley on the 


would be desirable. As they have never been printed, 
however, and since, so far as we know, none other such exist, 
we will give them here under the caution that they are to be 
considered only first approximations. The light was that 
from the pit of the positive carbon of gas coke, one inch in 
diameter, with the current derived from a dynamo, actuated 
by an engine of ten horse-power, and therefore certainly at 
least as intrinsically hot and bright as any smaller arc-light 
in more common use, and presumably much more so. The 
apparatus was that already described in the memoir “On 
hitherto unrecognized Wave-lengths.” * 

The following Table gives the observed galvanometer de- 
flexions after applying a multiplying factor for the shunt, 
which had to be used for the larger readings :— 


if 2. 3. 4, 5 6. 
Deviation Cenc” Observed Caleulted Observed SS 
eflexion | se deflexion ; ratio of 
Rock Salt | Wave- f deflexion| ‘thout| T2410 84D), nabsorbed 
60° Prism. | length, || 223 ter are, Sl Without) 3d arc, |(Wnabsorbe 
absorption. absorption. sun and arc. 
et Le div div div. 
7 0-373 (is) 13 34 ris 26-0 
43 AT 0:398 115 15 38 767 21°8 
41 54 0-489 33°5 53 60 6°32 144 
41 05 0 587 104-0 10°5 115 9°90 itt 
40 45 0:663 204:0 22:0 204 9:27 10-0 
40 27 0-749 432°0 43°5 450 9°93 9-1 
40 05 0-96 1 073-0 2150 1 763 4:99 8-2 
39 54 113 1 783°0 459-0 3 534 3°88 a 
39 20 2°87 1 905°0 882'0 5 645 2°16 6:4 
39 =00 4:3 521:0 235°0 1 3563 2-22 a8 
38 45 56 75°0 1570 832 0:48 53 
38 00 | 10-4 19°5 39°0 156 0°50 40 


The result of the comparison of the (of course unabsorbed) 
electric arc with the radiation of the sun after absorption, as 
shown in the sixth column, is that this solar radiation in the 
orange and red is nearly ten times that of the are, while to- 
wards the violet end of the spectrum the relative superiority 
of the absorbed solar heat diminishes, evidently because of the 
progressive increase of the atmospheric absorption in that 
direction, which lessens the solar intensity without sensibly 
affecting that of the arc. The solar efficiency continues greater 
through all the infra-red spectrum known until very lately, 
while in the extreme portions, recently investigated, it falls 
below that of the are. Thisis partly due to the fact that radia- 


* See this Journal, xxii. August 1886. 


Temperature of the Moon. 53 


tion from a source at a lower temperature (the arc in this case) 
is relatively more powerful in the longer than in the shorter 
waves ; yet it can hardly be doubted that here also (that is, in 
the extreme infra-red) a very large atmospheric absorption has 
taken place. 

There is reason to believe that a considerable part of 
this absorption takes place in the first few metres of air ; 
while we conclude from all the evidence in our possession, 
that the real telluric absorption, being a locally selective one, 
is much greater than the comparison of high and low altitude 
observations alone would indicate. 

The import of this comparison will be still more evident 
from a consideration of the seventh column, where by means 
of the Allegheny tables of the solar absorption we have 
calculated the ratio of the arc heat to that of the sun before 
absorption by the earth’s atmosphere. Although a large ab- 
sorption by the solar atmosphere has already taken place, we 
see that in the ultra-violet the solar radiation is from 20 to 30 
times that of the arc, while that of the absorbed sun is only 
about 6 or 7 times. When we reach the region of the red and 
upper infra-red, we see that these ratios are nearly the same in 
the absorbed and unabsorbed solar radiation, showing that the 
terrestrial absorption in this region (which was once supposed 
to be its principal seat), is in fact very small, while in the 
regions of the extreme infra-red corresponding to temperatures 
not greatly exceeding that of the terrestrial soil (regions only 
revealed by quite recent investigation) the telluric absorption 
again becomes considerable. 

The general result of this comparison is to enhance our ideas 
as to the rate of solar radiation and as to the solar temperature. 
Comparisons of the total solar radiation with the total arc 
radiation have (it may be observed) been made before, but so 
far as | am aware, comparisons of the heat in different por- 
tions of their spectra are here presented for the first time. 


Principal Conclusion. 


Of the numerous conclusions to be drawn from this research, 
we here only direct the reader’s attention to what we consider 
the most important one, namely :—That the mean temperature 
of the sunlit lunar soil is much lower than has been supposed, 
and is most probably not greatly above zero Centigrade. 


Post Scriptum. 


I would ask to be allowed here to state that the very con- 
siderable expense for the special means and reduction of the 


54 Mr. W. G. Gregory on a New 


preceding series of lunar researches was born by one of the 
most generous and disinterested friends that Science has had 
in this country, the late William Thaw, of Pittsburgh. By 
his own wish, no mention of his name was made in previous 
publications in connexion with the results so greatly indebted 
to his aid. His recent death seems to remove the restriction 
imposed by such a rare disinterestedness. 


LV. Ona New Electric Radiation Meter. (Preliminary Note.) 
By W. G. Grecory, JL.A., Demonstrator in Physics at the 
Royal Indian Engineering College, Coopers Mill*. 


‘hae usual method of detecting electric radiations by ob- 
| serving the sparking across an air-gap in ihe wire used as 
uy a receiver admits of only a rough estimate of their intensity. 

The object of this paper is to describe an instrument by ! 
means of which definite quantitative measurements may be 
made. It is based on the measurement of the elongation of a 
wire when heated by the currents induced init by the rapidly 
varying field of force. 


It consists of a long glass tube A B cemented to a shorter 
piece of brass tubing B D. Within is stretched a platinum 
wire W fastened to the glass tube at A and to a Perry magnifying- 
spring at M, where there is a mirror to indicate the rotation 
of the spring by the reflexion of a beam of light upon a scale. 
At K there is a nut and screw for adjusting the tension. The 
brass tube is partially filed away in front of the mirror to 
form a window. The object of the brass tube is to compensate 

A the spring for general changes of temperature, the glass tube 
B serving the same purpose for the platinum wire. 

The wire employed was ‘0086 cm. in diameter, and 192 ems. 
long. The spring was about 25 cms. long and -007 em. 
in diameter. It was made out of a fine kind of tinsel -04 em. 
wide and ‘0015 cm. tbick, which can be obtained at fancy shops 
wound loosely on cotton. When removed from the cotton, it 
was already in the form of an irregular helix. It was then 
rolled tightly between the fingers to reduce the diameter as 
much as possible. A piece of silk was next attached to one 
end, and the spring extended almost to breaking-point, the 


* Communicated by the Physical Society: read November 1, 1889. 


eH pat Sse) z. ¥ Si hie Le 
ere ame ee is = 4 


Electric Radiation Meter. 55 


suk allowing it freely to untwist as much as it would. After 
this it was rolled between two hard surfaces and again pulled 
out. This was repeated till at last 10 revolutions per millimetre 
extension were obtained. 

The mirror was a ;%-inch worked concave one, and gave 
a very sharp image of a wire on ascale one metre off. Using 
an ordinary galvanometer-scale, it was easy to read to one 
division. This would correspond to an elongation of the wire 
of 000005 of a millimetre, and a rise of temperature about 
‘003 of a degree Centigrade. In spite of this sensitiveness, 
only one or two divisions’ deflexion were obtained with the 
oscillator 4 metres off. The oscillator used consisted of two 
brass rods ‘53 cm. in diameter supported horizontally and 
carrying two zinc plates 40 cm. square, capable of sliding along 
them so that the wave-length could be altered at pleasure. 
They were usually kept about 25 cm. apart. The terminal 
knobs were 2 cm. in diameter and the spark-gap about 2 or 3 
millim. It was noticed that one of the knobs blackened very 
quickly but remained quite cool, while the other, which altered 
little, became very hot. . 

The induction-coil employed to work it was 20 cm. long 
and 12 cm. diameter, and gave with the battery-power em- 
ployed sparks 4 cm. long between two points. To obtain 
greater regularity in the working of the coil, a tuning-fork 
mercury break, vibrating 86 times a second, was used. 

By employing a larger coil larger deflexions could, no 
doubt, be obtained and effects at greater distances observed. 

A method was tried for increasing the sensitiveness by 
weighting the mirror so that its centre of gravity was behind 
and rather above the axis of suspension. The tension was 
adjusted so that the spring kept the mirror near its position 
of unstable equilibrium. ‘The effect was to render the smaller 
deflexions nearly 10 times as great, while the sensitiveness 
diminished as the deflexions became larger. But the diffi- 
eulties of working with it were greatly increased, as the 
smallest draught of air would alter the zero-point. 

Wires of different materials were also tried which should 
theoretically give better results ; but, probably owing to their 
diameters not being sufficiently fine for the tension to which 
they were subjected, the results were not satisfactory. The 
convenience of being able to compensate the platinum wire by 
the glass tube seems, however, a great point in favour of the 
use of platinum, and has led me hitherto to keep to it. 


Ba aces 


V. On Electrifications due to the Contact of Gases with 
Liquids. By J. Hnricut, B.Sc.* 


A STUDY of Helmholtz’s theory of atomic charges led 

to the experiments I am about to describe. When one 
has got the idea that molecules are kept in their integrity by 
the mutual attractions of the oppositely charged atoms or 
radicals composing them, a question soon arises as to what 
part, if any, these charges play in ordinary chemical reactions. 
The theory precludes any other form of chemical affinity 
than that due to the mutual attractions of the opposite 
charges, and it occurred to me that since at the moment of 
reaction there must be disturbance and re-arrangement of 
them, some indication of their existence might be obtained 
by allowing reactions to go on in an insulated vessel properly 
connected with a quadrant-electrometer. Hven if a per- 
manent electrification could not follow, I thought it just 
possible that a momentary flutter of the “spot” might take 
place on account of the electric disturbance due to the inter- 
change of the charged ions. 

This consideration alone was sufficient to excite one to 
experiment, but if I tell the whole story I must say that I 
had had other expectations. According to theory the charges 
on monads are exactly equal. How then does it happen, if 
reactions bea result of the charges, that chlorine drives iodine 
out of potassic iodide? How, indeed, does it happen that 
any one molecule composed of a particular pair of monad 
elements is stronger,—that is to say, more stable than any 
other molecule composed of any other pair of monads? And 
soon. After pondering on such questions for some time, I 
could not suppress the thought that after all perhaps the 
charges might not be equal, and that the experiments I had 
determined to carry out might possibly throw some light on 
the matter. 

Then there were certain special reactions which appeared 
to afford an admirable opportunity for experimental study of 
the theory. I refer to cases in which the atomicity of ele- 
ments undergoes a change during a reaction, 


2Fe™SO,+ H,SO,4+ Clp = Fes(SO,)3 + 2HCI (Roscoe). 


Here four monad charges of positive electricity attached 
to the iron on the left change into eight monad charges on 
the same quantity of iron on the right. If the increment of 
positive electricity be produced by contact an equal charge of 


* Communicated by the Physical Society : read November 15, 1889, 


— 


Electrifications due to the Contact of Gases with Liquids. 57 


negative ought to be set free, and this ought to be easily 
detected by the electrometer. 

On the whole there appeared, to a strong believer in the 
theory, a fair and inviting field for experiment. My plan 
was to examine in the manner indicated instances of the four 
following types of chemical change :— 


(1) Combination of elements. 
(2) Displacement. 

(3) Double decomposition. 
(4) Change of valency. 


I may as well say at once that from (3) and (4) I got no 
result whatever, from (1) only an electrification of little 
importance, and that it was from (2)—instances of displace- 
ment—that the results I wish to call attention to were obtained. 

The electrometer was made rather sensitive. A high- 
resistance Daniell through which a current never passed gave 
a deflexion of 94 divisions either way. An insulated plate on 
which the reactions were to proceed was fixed so that it could 
be connected or disconnected at pleasure with the insulated 
pair of quadrants. The insulation of this plate was tested by 
giving to it a small charge, and connecting it then with the 
quadrants. The spot moved and came to rest 200 divisions 
from zero. It was watched for 3 minutes, during which it 
maintained its position. 

A porcelain dish containing about 20 c.c. of a strong 
solution of potassic iodide was placed on the insulated plate. 
About the same volume of a strong solution of chlorine in 
water was placed in a beaker to which was attached a handle 
of insulating material, and by means of this handle the 
chlorine water was poured into the potassic iodide. A heavy 
brown precipitate appeared. The insulated plate was now 
connected to the insulated quadrants. No deflexion resulted. 
The experiment was repeated without producing a movement 
of the spot. 

The porcelain dish was now half filled with distilled water, 
placed on the insulated stand, and a fragment of potassium 
east into it. The usual reaction ensued and the “spot” 
moved 160 divisions to the left, came to rest, and maintained 
its position. The quadrants were short-circuited, and the 
spot returned to within 2 divisions of zero. 

At first view this appeared exactly what I had expected to 
occur. On reflection, however, many possibilities suggested 
themselves and each had to be considered. Had I merely 
detected electricity in the air? May not the deflexion be 
due to the inductive action of the charged needle on the 


= 


fe T Bie SO) —a eS bn as D ge ee 
cheer ie ou arias ete are : 


58 Mr. J. Enright on Electrificateons due 


quadrants? Was the escaping hydrogen electrified, and if 
so what was the sign of the charge? I proceeded to repeat 
the experiment. 

The quadrants were short-circuited, and the insulated dish, 
after being momentarily put to earth, was, as before, con- 
nected to the insulated quadrants. A second fragment of 
potassium was tossed into the water in the dish. The spot 
moved 28 divisions to the left, then turned and moved up the 
scale to the right, coming to rest at 200 divisions from zero. 
The quadrants were once more short-circuited, and the experi- 
ment again repeated. The spot moved 40 divisions to the 
right. I could not possibly explain such irregular behaviour. 
I carefully looked up the connexions and tested the instru- 
ment. It was in good order. I again repeated, but with 
similar results. | 

Sodium was used instead of potassium, and although the 
deflexions with it were also irregular, the tabulated results 
showed a contrast. When sodium was used, 40 per cent. of 
the deflexions were first to the left; when potassium was used, 
70 per cent. were first to the left. Speaking broadly, this 
seemed to indicate that when potassium was used the dish 
received a negative charge, when sodium was used the dish 
took a positive charge ; and as I fancied that such a result 
would enable me to set up some theory with regard to the 
atomic charges, I tried very hard to eliminate what I then 
believed to be accidental exceptions and to prove that in 
reality such was the case. 

The porcelain dish was replaced (1) by a glass beaker, and 
(2) by a metallic dish, the experiment being repeated in 
every other particular, but without obtaining greater regu- 
larity in the deflexions. 

I wish to remark here that the method of testing the 
electrification by keeping the insulated vessel from which gas 
is escaping in connexion with the insulated quadrants daring 
the reaction is faulty, inasmuch as that under the cireum- 
stances a deflexion may be caused by the inductive action of 
the charged needle on the quadrants. It has, however, this 
great advantage, viz., that one can see distinctly every varia- 
tion that may take place during any interval. It will be 
noticed that throughout the inquiry I use this method for 
preliminary testing, and that I conclude nothing until I 
verify by the more rigid process of allowing the reaction to 
go on while the insulated plate is disconnected from the 
quadrants, and testing the electrification at its close. 

Having failed to get a definite and constant result with 
water, I proceeded to try other liquids. Sodium and dilute 


to the Contact of Gases with Liquids. 59 


sulphuric acid, sodium and nitric acid, and many other such 
combinations were tried, and eventually I found that sodium 
and strong acetic acid gave an invariable result, viz., a 
positive charge on the dish in which the reaction took place. 
This has not failed hitherto in a single instance. 

I reviewed the state of affairs. The first thing to do, as it 
appeared to me, was to ascertain whether or not the hydrogen 
carried a charge, and, if so, to determine its sign. I found it 
so difficult to work with sodium that after many unsatisfactory 
attempts I decided to search for another metal which would 
give a similar constant and definite result. One naturally 
turned to zine. 

A piece of zine was thrown into dilute sulphuric acid 
which was put into the insulated dish, the connexions being 
-as already described. The spot rapidly moved 36 divisions 
to the left, turned, went back. across zero and up on the other 
side 120 divisions. This was not encouraging. It seemed 
to be the beginning of another set of irregular deflexions. 
It, however, went to show that electrification was an accom- 
paniment of most chemical reactions. I repeated the experi- 
ment several times, varying the degree of dilution of the acid, 
but failed then to get constant results. I next tried hydro- 
chlorie acid. 

A small portion was placed in the insulated dish and a 
particle of zinc thrown into it. The spot rapidly moved off 
the scale to the left, indicating a negative charge on the dish. 
The quadrants were short-circuited, and the spot returned 
to zero. Repetition was followed by the same result, and 
fortunately this turned out to be as constant a deflexion to 
- the left as that from sodium and acetic acid was to the right, 
while it was much greater in quantity. 

I now concentrated my attention on zinc and hydrochloric 
acid. In this experiment, as in all others where a gas escaped 
into the air, it was possible, though not likely, that the resulting 
deflexions were due to atmospheric electricity, and I thought 
it as well to settle this point at once. A piece of sponge was 
saturated with alcohol and placed on the insulated plates. — It 
was then fired,and burned with a large flame. The insulated 
plate was connected to the quadrants when the sponge ceased 
to burn, and the spot at once moved 10 divisions to the right, 
indicating a small positive charge on the plate. The experi- 
ment was repeated in every particular except the burning of 
the sponge, but with the result of only a disturbance of the 
spot of a few divisions. 

The air in the neighbourhood of the insulated plate 
appeared to be slightly electrified, but as it was of opposite 


60 Mr. J. Enright on Electrijications due 


sign to the charge produced by the action of zine and hydro- 
chloric acid, it was certain that the latter was not due to any 
atmospheric cause. But a new point of great importance 
had arisen. Whence came the positive charge in the air 
near the instrument? The idea of its being due to the 
evoived hydrogen at once suggested itself. For some time 
before testing with the sponge, I had been repeating the 
experiment with zine and hydrochloric acid in order to satisfy 
myself as to its constancy, and a considerable quantity of 
hydrogen had escaped into the air. 

The charge on the evolved hydrogen opposite in sign to 
that on the insulated generator! If this were really the case 
I saw that I should have to give up certain ideas which I had 
been fostering while dealing with these experiments. The 
point had to be at once cleared up. 

A zine goblet was metallically attached, mouth downwards, 
to the insulated plate. A long-necked flask containing zine 
and hydrochloric acid was placed underneath in such position 
that the hydrogen found its way into the inverted goblet. 
In two minutes after so placing the hydrogen generator the 
goblet was tested by connecting it with the insulated quad- 
rants. The spot moved 78 divisions to the right, indicating 
that the hydrogen escaped with a positive charge—that is to 
say, as already suspected, its charge was opposite in sign to 
the acid and generator from which it was evolved. 

The experiment was several times repeated, and always 
with the same result, but it was noticeable that the positive 
charge on the hydrogen was much less in quantity than the 
negative charge on the generator. If they were in reality 
oppositely charged, the quantities, as in all such cases, would 
be exactly equal. J urged, in explanation, that the hydrogen 
moving over the moist glass of the long-necked generator 
must lose some of its charge. However, a confirmatory ex- 
periment was devised. 

A second insulated plate was set up and connected metal- 
lically with the first. A hydrogen generator, containing zine 
and hydrochloric acid, was placed on one, and a suitable pneu- 
matic trough was placed on the other, in such manner that 
the gas might be generated and collected on the insulated 
plates, which were connected to the insulated quadrants. A 
stream of hydrogen was allowed to pass, and by means of an 
insulating rod the delivery-tube could be placed so that the 
hydrogen might get into the air or be collected and retained 
on the insulated plates at pleasure. It was found that as long — 
as the gas did not escape the spot remained motionless, but 
that when it escaped from the plates into the air the spot 


to the Contact of Gases with Liquids. 61 


moved. This, [I took it, proved that the charges on the 
generator and evolved gas were equal in quantity, though 
opposite In sign. 

The state of the case was now, so far, pretty clear. When 
hydrogen was produced by zine and hydrochloric acid the 
hydrogen became positively, the generator negatively, charged. 
I set this fact up before my mind and examined it as care- 
fully as I could on every side. I turned it round and round, 
looking for some information as to the atomic charges, but I 
could find none. Had the charge on the escaping gas been 
of the same sign as that on the generator, I could have set 
up some hypothesis concerning them, but, as things were, 
nothing of the kind was possible. 

But what is the cause of this undoubted electrification ? 
I repeated the experiment many times. I varied the quan- 
tities of acid and zine, and noticed that with weaker acid 
or a larger quantity of zinc the deflexions were not so 
strong. During these repetitions I was in the habit of short- 
circuiting the quadrants when the spot came to the end of 
the scale, lest the suspending fibres of the needle should get 
a set from being twisted too much in one direction. On one 
occasion, however, being called away suddenly, I neglected 
to do so, and the electrification worked its will, so to speak, 
on the needle. On returning in about twenty minutes, I 
found that all the zinc was dissolved, and to my very great 
astonishment the spot was at rest at the extreme right of the 
scale. 

Up to that time the deflexion from zine and hydrochloric 
acid had been to the left ; and, as I had made the experiment 
a great many times with this unvarying result, I was much 
perplexed. ‘The uncertain behaviour of sodium and potassium 
was still fresh in my memory. 

However, what to do on the occasion was quite clear: I 
repeated the experiment in every particular, sat down, and 
watched it. The spot went rapidly off the scale to the left as 
usual. ‘The reaction proceeded. In eleven minutes the spot 
appeared again on the scale, went down 100 divisions rather 
slowly, then more rapidly, crossed the zero, and at a good 
pace went up the other side almost to the end of the scale. 
This was quite a new development. Frequent repetition, 
with the same result, proved that this behaviour, strange as 
it was, had a definite cause. I varied the strength of the 
acid and the quantity of zine, and found that by either making 
the acid weak or increasing the quantity of zinc I could 
hasten the reversal of the sign of the electrification of the 
generator. 


naeeatle 


62 Mr. J. Enright on Electrifications due 


I now concentrated my attention on this reversal of sign. 
I contrasted all the circumstances attending the deflexion to 
the left with all those attending the deflexion to the right, 
and could detect only one difference, and that was the pro- 
duction of chloride of zinc in the generator, and I could not 
fail to see that as the quantity of this salt increased the de- 
flexions to the right became stronger. 

From this change of sign of the generator, when a certain 
quantity of chloride of zinc got into solution, there suddenly 
appeared to come a ray of light which I thought dispelled 
the fog which hung round the earlier experiments. The 
nature of the liquid through which the hydrogen passed 
apparently determined the sign of the electrification. I 
paused again to review the events of my little enterprise. 

I set out in quest of some direct evidence as to the atomic 
charges. I had tried the four types of chemical change. 
From double decomposition and from cases of change of 
valency I had got no result whatever. From direct union of 
elements—from the combination of phosphorus and iodine, 
accompanied by a cloud of P,O;, and, I suppose, iodine vapour 
—I had got an electrification. From many cases of dis- 
placement I had got considerable electrifications; but from 
some, such as the displacement of iodine by chlorine, I had 
got nothing whatever. A careful examination of these re-— 
sults disclosed the fact that no electrification was obtained 
except when something escaped from the vessel in which the 
reaction occurred. ‘This circumstance I thought could not 
fail to have some meaning. Then there were the leading 
incidents, as I considered, of the inquiry :—(1) The escaping 
gases or vapours came off with a charge opposite in sign but 
equal in quantity to that on the generator. (2) The reversal 
of the sign of both generator and escaping gas when the liquid 
in the generator underwent a definite change. 

Such were the facts to be brought under some theory. I 
was reluctantly compelled to conclude that they had nothing 
to do with atomic charges, but for all that they afforded food 
for the most delightful contemplations, often for hours at a 
stretch, during the last two or three years. 

Reflect as I may on the reversal of sign of the electrification 
when a certain quantity of chloride of zinc gets into solution, 
I can find no explanation for it but the electricity of con- 
tact. Hydrogen is positive to hydrochloric acid, but nega- 
tive to chloride of zine. And, indeed, looking at the whole 
matter in this light, from my present standpoint, I can per- 
ceive how, in the earlier experiments, the nature of the liquid 


to the Contact of Gases with Liquids. 63 
through which the hydrogen passed decided the sign of the 


electrification. From hydrochloric acid it was positive; from 
acetic acid (or it may be acetate of sodium) it was negative. 
Hven the very whimsical deflexions from sodium and water 
become intelligible. As a piece of sodium careers about on 
the surface of water, the escaping hydrogen is one instant in 
contact with water, the next with caustic soda, the next with 
the side of the vessel, and, accordingly, on the theory of 
contact, the irregular deflexions are at once explained. 

In most of the experiments described above, the hydrogen 
was allowed to escape from an open dish or beaker, and not 
from a narrow delivery-tube, for it was found that the gas 
partially discharged itself when it passed through narrow 
openings. Whatever tended to electrically connect the 
charged liquid with the oppositely charged escaping gas, also 
tended to lessen the charges on both. And besides this, there 
was the possibility that the contact of the gas with the de- 
livery-tube might cause electrification. On the whole, it was 
found least ambiguous to half fill an evaporating-dish about 
6 inches in diameter and 2 inches high with HCl and drop 
into it a few fragments of zinc. The bubbles of gas then shot 
straight up through the middle of the liquid, and passed into 
the air without coming into contact with anything else. It 
was, however, a defect of this mode of proceeding that par- 
ticles of the acid were projected about in all directions, some- 
times beyond the dish. In order to get rid of any doubts on 
this head, a smaller dish was used and placed at the bottom of 
a beaker 7 inches high. I propose to give in detail one of 
several experiments made in this way with all possible care. 

The electrometer was not in a very sensitive state. The 
high-resistance Daniell gave a deflexion of 38 divisions on 
either side. A glass beaker 7 inches high and 5 inches in 
diameter was placed on the insulated plate. A porcelain dish, 
2% inches in diameter and 14 inch high, was nearly filled 
with a 10-per-cent. solution of HCl in distilled water, and 
placed at the bottom of the beaker just mentioned. Three 
small fragments of zinc were now dropped into the dilute acid in 
the small dish. <A very slight effervescence at once appeared, 
and it gradually increased, but never became violent. No 
trace of spray could be detected at the end of the experiment 
above the lower half of the beaker. In 4 minutes from 
dropping the zinc, the spot could be perceived moving, and 
in 44 minutes more it had moved 28 divisions to the lett, 
indicating the charge on the dish negative. J append the 
notes taken during the time the experiment lasted. 


64. Mr. J. Enright on Electrifivations due 


Time. Reading. 


——— 


| Zine dropped into acid. Insulated quads con- 
nected to insulated generator ............cecceseenees } 2 10 378 (zero) 


Ree Sa eee A 


_ Spot moving to left. Generator positive ......... 2 14 ol7 
Spot mmlovin s faster cajecsac.t a accicace <n sestonce = neienen ees 2 16 367 
Insulated d d 1 d re as 

nsulated quads and insulated generator discon- 1 

MCC LEGS» Lbph Ta cekanen MUNN, eoe e ee ter enree ak i ay Se | fe 
2 193 | 349 
Insulated quads and generator reconnected ......... 2 20 329 
2 21 322 
Spot stops and appears to return ................e000- 2 2hei\ ely 
2 23 328 
2 25 346 
2 26 366 
Spot Crossed Zero vcssehes Le aati st Th sce ete teloe ane 2 263 | 378 
2 28 388 
Quads and generator disconnected .........s00e0-... 2 314 | 458 
2 33 458 
Quads and generator reconneeted ........ ss Sere 2 333 | 5138 
TBIEITOTESNOS BUS GES 5 oo5dboodobonenocepesndesodeesocade> 2 35 550 
2 om 562 
2 40 568 

Quasdsrshorb-cincuntediwnreenedens ie. eocenescse meso 2 42 382 (zero) 


It may yet be urged that when hydrogen passes through 
hydrochloric acid, it carries with it both HCl gas and vapour 
of water, and that the electrification is due to these, and not to 
the hydrogen. In order to test the suggestion, I placed on 
the insulated plate a dish nearly filled with boiling concentrated 
HCl. Intwo minutes the plate was connected with the insu- 
lated quads, but the spot moved only 1 or 2 divisions. It was 
then watched for more than 5 minutes, but the spot did not 
stir although clouds of vapour were escaping from the acid. 

I cannot help remarking on the difficulty of neutralizing 
a gas—at all events, hydrogen. ‘The following experiment is 
well calculated to illustrate this properly, while it affords, I 
submit, a very stringent verification of the experiment to 
which the notes are appended. The large beaker with the 
small dish was set up in the manner described in the experi- 
ment just referred to. ‘The dish was nearly filled with a 16- 
per-cent. solution of HCl in distilled water. Three small 
fragments of zinc were thrown into it. A disk of sheet-zine 
with a circle one inch in diameter, cut from its centre, was 
placed as a cover on the beaker. Over the aperture in the 
centre were placed, one above the other, 4 flat pieces of per- 
forated zinc, the perforations being 7! of an inch in diameter. 
The hydrogen had to fight its way through this barrier, and 


to the Contact of Gases with Liquids. 65 


yet it carried with it the greater part of its charge, as the fol- 
lowing notes of the experiment prove. ‘The high-resistance 
Daniell gave a deflexion of 72 divisions either way. 


Time. Reading. 


— 


h m 
Zinc dropped into acid. Cover placed on beaker. 3 93 265 
4 flat zines placed over aperture ..............066- } 
3 25 364 
3 27 363 
3 28 308 
3 29 343 
Spot comes to rest and returns ..............sscseceee 3 30 330 
3 3l 330 
3. 382 343 
3 33 303 
3. 34 363 
3. 3d 373 
3 36 383 
3 37 383 
3 39 413 
IBPPOEVESCONCOCEASING! 15.2.0 seccckavesecisocdecsssseee| 3 42 413 
Slagieanis SWOrt-CIrCUIled, | ¢o.c0:. caasdcicneseanaceasod viel 3 43 368 


On examining the perforated zincs used in this experiment, 
each was found to have either spray or condensed vapour de- 
posited on it, but the quantity on the lowest one was greater 
than that on any of theothers. I was not, therefore, clear as 
to what part the spray played in the matter, and I set myself 
to consider what experiments I could make to clear up the 
point. Hventually I decided to make the following two, 
which I submit as decisive :— 

(a) Every one has noticed that when hydrogen escapes 
from a generator containing acid and zine, particles of the 
former are projected with considerable force from the vessel. 
I easily succeeded in catching these particles, or some part 
of them, on the metallic part of a proof-plane. I then touched 
the electrode of the insulated quads with the proof-plane, and 
found that the charge produced a deflexion to the left, indi- 
cating that the spray was of the same sign as the generator, 
and consequently opposite in sign to the charge carried by the 
gas. It also appears from this experiment that electrical re- 
pulsion among the particles themselves constitutes part of the 
force which causes their flight through the air. 

(b) The bottom of a metallic goblet was perforated with 
holes about } inch in diameter. Jt was then attached, mouth 
downwards, to the electrode of the insulated quadrants. A 
hydrogen-generator containing zinc and HCl was placed under 
it in such a position that the evolved gas passed right through 


Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. F 


N 


66 Mr. J. Enright on Electrifications due 


the goblet. Almost instantly the spot moved rapidly to the 
right, which I had expected. The generator was now with- 
drawn. The spot slowly returned to within 5 divisions of zero. 

Now if the electrification were due to spray, the goblet 
would retain its charge (the insulation was good) ; but being 
due to the hydrogen, which gradually passed through the 
perforations into the air, it very rapidly lost it. 

In the course of these experiments I had often cast about 
for means of measuring the difference of potential arising from 
the contact of zinc and hydrochloric acid, and on consideration 
it appeared to me that this experiment presented a possible 
method. Particles of matter charged with electricity, and 
impinging on an insulated conductor, to which they give up 
part or the whole of their charges, could not raise the conductor 
to'a higher potential than they had attained ; but they, in the 
course of time, ought to bring it up to that level. My notion 
was to allow the charged hydrogen to flow through the goblet, 
fixed as described, long enough to ensure its reaching the 
potential of the gas ; then to remove the generator, and allow 
the gas to pass away through the perforations. The perma- 
nent deflexion then obtained ought, I considered, to be the 
measure of the quantity in question. I carried out with all 
the care possible several experiments on these lines; but on 
account of the tenacity with which the gas holds its charge, I 
failed to get satisfactory determinations. 

At this stage of my inquiry, I felt that I had got a few defi- 
nite facts, that I had cleared up, at all events to my own 
satisfaction, many points which were at first doubtful, and 
that the theory of contact which I proposed was consistent 
with all the observations I had made. I proceeded to devise 
new experiments with the view of testing the truth, and de- 
termining the scope, of this theory. 

Hydrogen passing through HCl and H,SQ, takes a positive 
charge ; passing through the corresponding salts of zine it 
takes a negative charge. Then at any moment it ought to be 
possible to reverse the electrification by introducing into the 
vessel in which the reaction is going on acid or salt, as the 
case may be. ‘The old experiment was made. Hydrogen 
was escaping from a 16-per-cent. solution of HCl, and the spot 
had travelled 100 divisions when a strong solution of zine 
chloride was added. The spot went quickly back and up on 
the other side of the scale, showing that reversal had taken 
place. The addition of HCl produced a second reversal. 

I had found hydrogen positive to two acids, and a question 
as to whether this was general often floated before me. 1 had 


to the Contact of Gases with Liquids. 67 


no means of testing with nitric acid, because its action on 
metals does not give rise to hydrogen—at all events not in 
the final stage. I therefore directed attention to the other 
side of the question. Hydrogen was proved to be negative 
to chloride and sulphate of zinc. Was it possible that it was 
negative to other salts, or to salts in general ? 

I again made the old experiment with Zn+ HCl, and when 
a deflexion of 50 divisions was obtained a strong solution of 
ferric chloride was added, with the effect of reversing the sign 
of the electrification. I proceeded to try other salts, such as 
NaCl, AmCl, FeSO,, MgSO,, CaCl, and found that these also 
produced reversal. I found, however, a few salts which did 
not do so, notably Co(NOs)>. 

A wide principle thus appeared to be foreshadowed, viz., 
that hydrogen is positive to acids but negative to salts ; but 
the number of cases examined does not warrant one in laying 
it down absolutely. Moreover, I have found the hydrogen 
passing from acetic acid, whether by the use of sodium or iron 
filings, always comes off with a negative charge. I strongly 
suspect, however, that the reversal of sign in these cases takes 
place so rapidly that it escapes observation. I have had 
several instances of the spot moving a small distance to the 
left, suddenly turning, and moving far up on the opposite 
side of the scale. Occurrences of this kind leave no doubt on 
my mind that the first electrification (that due to the gas 
passing through the acid) is often small, owing, I think, to 
the rapidity with which the salt produced in the reaction 
diffuses. 

Is hydrogen among gases unique in becoming charged when 
it passes through acids? was the question that next presented 
itself. I considered what reactions were likely to give any 
information with regard to the matter, and made numbers of 
experiments in the manner already fully described. I found 
that as a rule electrification results from any reaction giving rise 
to an escape of any substance into the air. In many cases the 
electrification is very trifling, and the electrometer must be in 
a sensitive state in order to show it. Of all the reacting com- 
binations which I have tried, HCl+ Zn give by far the greatest 
difference of potential between generator and expelled gas. 
On the other hand, from H,SO,+ NaCl I failed to get any 
trace of electrification. I give in the following Table only 
those reactions which by frequent repetition I have found to 
give constant results. I also give the estimated difference of 
potential, but shall postpone to a later stage a description of 
the method of making the measurement. 


F 2 


Ve, eee Roe 
Y an . - . 


* ese a ao SURE ly ea a me 


a 


Poi Re 


a 


68 Mr. J. Enright on Electrijications due 
z Gas passing Ghantity 
Reacting substances. eae Through salt DP: in 
Through acid. solution volts. 
WOE int. a. ees dene e H + — 42 
2 tetael CaO, © a. 62c.teese CO, + _ 
BLES O st Na CO gees dons oar Co, - = 9 
fe SO NawsO, oo -.ceccr SO, + _ 
De Pi Cl-E NasSORee ines. ase SO, + = 
6. H,SO,+2Zmn (50°/, acid)} H a — 16 
ey ELC IEE HOS. Foose oo eiowinesest SH, + = 
Coa HeSO Nese s- ncn s-eee- SH, S - 
9. HCl+Bleaching-powder| Cl + - ‘ 
10. H,SO,+Bleach~powder| Cl 7” eanerets 
Could not get the 
11. HNO,+Bleach.-powder| Cl usual positive — 
deflexion. 
Could not get 
12>) FENO, CaCO), apc. s..-. co, | positive deflex- - 
ion. 
; CH. (\Could not in) \ ay 
13: 1 COROT N® -----e+--- H il methericte cena 
{| the normal) } 
CH | | positive deflex-| | uA 
14.4 Goo bE? ee Hie bial 
ou not get 
[HA eIESO. 8 CaCON NE. 2 co, sis { To eee 
1G ett O;- Nac 2. eicz: HCl Nil Nil | 


It will be seen that there are nine instances in which the elec- 
trifications occur normally—that is to say, in which the charge 
is of one sign when the ejected gas passes through acid, but of 
the opposite sign when the corresponding salt gets into solu- 
tion. J wish to direct special attention to the instances of 
abnormal behaviour, which I believe to be entirely due to the 
solubility of the salts produced in the reaction. When these 
get rapidly into solution and diffuse through the acid, the 
electrification due to the gas passing through acid cannot be 
obtained. There are two cases with HNO; and two with 
acetic acid where this happens, and we know that the salts 
derived from these acids are very soluble. On the other hand, 
there are two cases where H,SO, takes part in the reaction, 
in neither of which could the electrification due to the 
passage of the gas through the solution of salt be obtained. 
In both instances sulphate of calcium is formed, and we know 
that this is rather insoluble. The ejected gas therefore never 
passed through a solution of salt. My contention here 
derives great support from the fact that when Na,CQs is used 
with H,SO, to give CQ,, both deflexions are obtained. The 


to the Contact of Gases with Liquids. 69 


only difference between the two reactions is that Na,SO, is 
very soluble compared with CaSQ,. 

Taking a broad view of these experiments, they appeared to 
me to indicate that, in general, gases were positive to acids, 
but negative to solutions of salts. I could not, however, throw 
off a feeling of dissatisfaction which arose from my not being 
able to suggest a trace of any a@ priort reason for such a 
thing. I fancied I saw some reason why hydrogen should be 
positive to acids and negative to salts; but that the generaliza- 
tion should be so wide as to extend to all gases, seemed to me 
most improbable. I felt disposed to question my theory of 
contact altogether, and resolved to make experiments of a 
different kind for the purpose of testing it. 

If hydrogen be positive to hydrochloric acid, then, why not, 
I asked, prove it by a straightforward experiment such as 
passing a stream of the gas through the strong acid? Two 
insulated plates were set up near the electrometer and con- 
nected by a piece of copper wire. A beaker 2 inches in 
diameter and 5 inches high containing strong HCl was 
placed on one, and a hydrogen generator furnished with a 
narrow delivery-tube more than 12 inches long was set on 
the other. The delivery-tube was suitably fixed, and a brisk 
current of hydrogen passed through the strong hydrochloric 
acid. The hydrogen was found to come off with a positive 
charge, but on allowing it to get into the air direct from the 
delivery-tube it also came off charged in the same way. Here, 
then, | was balked. Of course the object of the long delivery- 
tube was to neutralize the gas before it touched the strong 
acid in the beaker. I have often remarked how firmly the 
hydrogen held its charge, but I was quite unprepared to find 
that it passed through more than 12 inches of wet glass 
tubing 4 of an inch in diameter and escaped strongly elec- 
trified. J next passed the hydrogen through a wash-bottle, 
but it again came off charged. I passed it through all manner 
of bent tubing, made all possible shifts in fact to de-electrify 
the gas in order to fairly carry out my experiment, but with- 
out success. In sheer desperation I snatched up a litre-flask, 
filled it with water, and displaced the latter at the pneumatic 
trough by hydrogen from Zn+ HCl. I then placed the flask 
mouth upwards and open on the insulated plate which was 
connected to the quadrants. The spot gradually moved to the 
left, and came to rest at a distance of 180 divisions from zero. 

This experiment yielded more food for thought. At first 
sight the deflexion appeared to be in the wrong direction, and 
I had to consider whether the hydrogen could, by any pos- 
sible process, be neutralized. 


Sdembsskteecbe ars : Sa Ee 


_ a ir a | 


70 Mr. J. Enright on Llectrifications due 


I refilled the flask with hydrogen from zine and hydro- 
chloric acid and corked it before lifting its mouth from under 
the water, set it on the table, left it for 1? hours, then uncorked 
it and placed it on the insulated plate. A deflexion to the 
left of 100 divisions was gradually produced as the hydrogen 
left the flask. By repeated trials I found that it required 
from four to six hours to neutralize a flask or even a metallic 
vessel filled with hydrogen from zinc and hydrochloric acid. 

But what of the deflexion in the wrong direction? On 
reflection, the explanation of the deflexion being to the left— 
that is to say, the insulated quadrants being negatively 
charged—very quickly appeared. The flask was held in the 
hand while being filled with hydrogen holding a positive 
charge. This acted inductively, repelling an equal quantity 
of positive to earth through my hand and body, and binding 
on the outside of the moist flask a charge of negative. When 
the flask was set on the insulated plate the hydrogen, owing 
to its lightness, gradually escaped into the air carrying its 
charge with it; and for every-portion of the positively charged 
gas which left the flask a corresponding part of the negative 
charge bound on its wet outside was set free and spread over 
the quadrants, causing the deflexion. In fact the wet flask 
containing the charged hydrogen constituted a veritable 
Leyden jar. 

I was anxious to verify this view. A hydrogen generator 
with a long neck and containing Zn + HCl was placed on the 
table. A large wide-mouthed wet flask was attached to an 
insulating handle, and, by means of this handle, was held 
mouth downwards in such position that the hydrogen from 
the long-necked generator filled it by displacing the air. It 
was then taken by means of the insulating handle near the insu- 
lated plate (which was connected to the insulated quadrants), 
when the spot moved along the scale to the right, indicating 
that the quadrants were positively charged by the inductive 
action of the charged gas. The flask was next touched on the 
outside by the finger and again held near the insulated plate, 
but the spot did not move. This was quite in accordance 
with the Leyden-jar view, for the bound charge on the out- 
side of the flask could have no effect on the insulated plate or 
the quadrants connected with it. The flask was now placed 
on the insulated plate, mouth upwards, and as the hydrogen 
escaped into the air the spot moved up the scale to the left, 
indicating that the bound negative charge on the outside of 
the flask was being liberated and charging the quadrants. 

This afforded an instance ofa kind of distribution of static 
electricity rather novel. I could only liken it to ground sul- 


to the Contact of Gases with Liquids. 71 


phur electrified by the grinding. Most instances of charged 
bodies are connected with surfaces, but here appeared a case 
where electricity pervaded an enclosed space. The only way 
in which I could figure it in my mind in connexion with the 
hydrogen was by furnishing each molecule of the gas with a 
charge with which it could not part until, in the ordinary 
movements of the molecules (according to the dynamical 
theory of gases) each came into actual contact with the 
moist inner surface of the flask containing the gas. This way 
of looking at it enables one to understand the slowness with 
which the electrified hydrogen becomes neutral ; and as the 
time required to neutralize a vessel of gas of given shape and 
dimensions must be a function of the average velocity of its 
molecules at the existing pressure, suitable experiments may, 
possibly, lead to a direct determination of this quantity. 
Musing over these experiments, the wet flask holding the 
charged hydrogen appeared, to me, not to differ materially 
from a soap-bubble blown with hydrogen from Zn + HCl. 
If there be anything in the notion, such a bubble should con- 
stitute a charged condenser with the binding charge com- 
pletely enclosed. During the process of blowing it the 
repelled charge would pass to earth through the wet delivery- 
tube and generator. Figuring such a condenser floating 
through the air, I speculated as to how it would behave itself. 
As long as it remained in its integrity, no manifestation of its 
electrical condition could be given. Should the film, how- 
ever, get fractured its nature would display itself. The gas 
containing the binding charge would instantly pass away, 
leaving the bound charge free on the water composing the 
shell, and it would pass to earth at the first opportunity. 
Accounts have been given from time to time of curious 
bodies which make their way into dwelling-houses during 
periods of electrical disturbance in the air. They are de- 
scribed as gliding about, apparently examining nooks and 
corners, and often going up the chimney exploding (as it is 
called) on the way. Now if we consider a portion of elec- 
trified air enclosed by a film of some substance such as water, 
it would in most respects behave like a soap-bubble blown 
with hydrogen from zine and hydrochloric acid. Being of 
nearly the same density as air, it would not rapidly ascend but 
move about, impelled by every slight draught. 1t would be a 
charged condenser, and the moment any rough or sharp 
prominence fractured the film, the bound charge would pass 
to earth, doing mischief in its track. Such an enclosure of 
electrified air might possibly be effected by an abnormal dis- 
tribution of heat similar to that indicated by the formation 


Tae ee He ML AT ue 
s | aN i = 9 re 


72 Mr. J. Enright on Electrijications due 


of hail during thunderstorms. So close did the resemblance 
between my soap-bubbles and those ‘‘fire balls,” as they are 
sometimes called, appear to me that I hastened to ascertain 
by experiment whether or not my speculations with regard to 
them comprised any truth. 

Soap-bubbles were accordingly blown by means of the 
generator containing Zn+HCl. Only small ones could be 
obtained, and these shot away towards the ceiling so quickly 
that it was not easy to touch them with the metallic part of 
the proof plane. Some few, however, were caught and the 
proof plane was found to be very slightly negatively elec- 
trified. Some better plan had to be tried. The end of the 
delivery-tube was placed under the surface of the soap solu- 
tion while gas was ecaping. A great mass of bubbles were 
produced on the surface, and some of them toppled over the 
side of the dish and fell towards the floor on account of the 
greater quantity of water in them. These were caught on the 
metallic part of the proof plane, and on testing the latter it 
was found to be strongly charged, the sign being negative, 
which bore out the idea of the bubble being a charged 
condenser. 

Another form of the experiment then occurred to me. The 
dish containing the soap solution was attached to an insulating 
handle and then set on the table. The end of the delivery- 
tube was once more dipped into the soap mixture, and a mass 
of bubbles was as before produced. ‘The delivery-tube was 
then withdrawn, and the dish lifted from the table by an insu- 
lating handle. It was kept thus insulated until, in the course 
of a few minutes, the bubbles broke up, allowing the hydrogen 
to escape. The dish was then tested and found to have a 
negative charge. The soap-bubble blown as described was 
thus proved to be a charged condenser. 

If by any process a mass of electrified air were enclosed by 
vesicles of water, or any other conducting material, a free 
charge would be developed on the outside which would cause 
the whole mass to be attracted or repelled according to the 
electrical state of proximate objects. In a recent number 
of ‘ Nature’ I find an account of a thundercloud behaving in 
a manner at once explained by this hypothesis. The observer 
describes it as appearing to detach itself from a mass of cloud, 
gradually descend, and immediately after draw itself up again. 
The descent would be due partly to the attraction of the earth 
and to the repulsion of similarly electrified clouds above it. 
On touching the earth the free charge would escape, and the 
clouds, which at first repelled, would now attract, it, causing 
its ascent. 


to the Contact of Gases with Liquids. 73 


If such an enclosure of electrified air as I suggest were to 
occur at a high temperature in the upper regions of the atmo- 
sphere, its potential would gradually rise as it cooled and 
descended towards the earth ; for the cooling of the mass of 
air, and the increase of pressure due to its less elevated 
position, would cooperate to lessen its volume, and, therefore, 
the surface of the enclosing film, while the quantity of elec- 
tricity would remain the same. 

Up to this stage I had used glass vessels in these experi- 
ments, but according to the view just set forth there could be 
no reason why a metallic vessel should not behave in precisely 
the same way. A tea-canister was accordingly filled with 
hydrogen by displacement of water from a generator con- 
taining zine and hydrochloric acid. It was then placed on the 
insulated plate, mouth upwards, and it was found that as the 
hydrogen escaped into the air the spot moved to the left, as 
had been expected ; and it was found on trial that everything 
that had been done with the glass flask could be done with 
one of metal. We have thus a condenser with only one con- 
ductor, and apparently without a dielectric; and, from the 
ease with which it can be charged, and most of the properties 
of condensers demonstrated by means of it, one which may 
turn out useful for teaching-purposes. 

A metallic flask filled with hydrogen by displacement of 
water from a generator containing Zn+HCl | found very 
instructive. It proved that hydrogen holds its charge with 
unexampled tenacity, for the vessel could be handled or left 
in communication with the earth for a considerable time 
without becoming neutral. It proved that spray or vapour of 
hydrochloric acid had nothing whatever to do with producing 
the electrification, for these were absorbed by the water over 
which the gas was collected. It also suggested a possible 
means of measuring the difference of potential due to the con- 
tact of hydrogen with hydrochloric acid. After a few trials, 
however, I gave it up, and decided to determine the quantity 
by Sir W. Thomson’s “ Water-dropper.” 

A metal funnel with a long stem was fixed to the insulated 
plate, which was as usual connected to insulated quadrants. 
The funnel was filled with water, and a series of drops fell 
from the nozzle of the stem. The drops broke away at a 
distance of 6 or 7 inches from the body of the funnel. An 
uninsulated dish 3 inches in diameter, containing Zn + HCl, 
was placed under the nozzle, so that the drops fell into it. 
As the hydrogen passed into the air, enveloping the nozzle 
and falling drops, the spot moved rapidly up the scale to right 
and off it. 1 withdrew some of the charge from the needle, 


Ses Se 
3 pee 


Het 


aa} oFy 


74 Mr. J. Enright on Electrifications due 


and repeated the experiment. It again went off the scale. 
I withdrew a considerable quantity from the needle, and 
eventually reduced the sensibility of the instrument to such a 
degree that the deflexion never amounted to 300 divisions. 

Fresh zine and hydrochloric acid were now placed in the 
dish. The spot rapidly went up to 130 on the scale, from 
zero, and began to return. The “‘ water-dropper ” was then 
quickly disconnected from the quadrants, and the spot stood 
at 125. The dish was again supplied with fresh acid and 
zine and placed in position, and when I could see by the fumes 
that the nozzle was enveloped in the escaping gas I again 
connected the quadrants to the “ water-dropper,’” when the 
spot moved up the scale higher. This was repeated as long 
as the spot could be forced to go higher. At 187 from zero 
it only oscillated right and left to the extent of 3 or 5 divi- 
sions, but could not be forced higher by the liberation of 
hydrogen near the nozzle from fresh acid and zinc. I took 
this number as measuring the potential above earth of the gas 
as it escaped from the acid. 

The reason for changing the acid so frequently is to be 
found in the fact, which I had already proved, that when 
hydrogen passes through a solution of ZnCl, it comes off with 
a negative charge; and on this account, if the measurement 
be not made when the gas is passing through at the first 
stage of the reaction, the result cannot be correct. And, 
indeed, no matter what precautions are taken the result must 
be a little too small. 

Several preliminary experiments of this kind were made, 
and when I was satisfied that the result was definite and con- 
stant I made very carefully the three following determina- 
tions. In each case the acid was changed nine times :— 


Zero. Deflexion. Division. 
(1) ear Pec 362 552 190 
Oy ee 359 544 185 
(3) Le het ee 358 545 187 
3)562 
187 


I knew that I had reduced the sensibility of the electro- 
meter very much, and when I proceeded to find the value of 
the scale-divisions in volts I found that the standard Daniell 
gave only a deflexion of from 3 to 6 divisions. Besides, this 
being very small I could not be certain of it to within a divi- 
sion, as the spot did not come precisely to zero. Of course, 


to the Contact of Gases with Liquids. 15 


{ could not attempt to base a calculation on so uncertain a 
quantity. 
To get over this little trouble I set up five Grove cells in 
series, which gave a deflexion either way of 40 scale-divisions. 
Therefore, 
187x5 
AQ 


18x187x5 


=D. P. in Grove cells. 


=D. P. in volts. 
A?-038= DD. Poin volts. 


The other numbers given were found in the same way. 
The potential of an electrified body depends on conditions, 
and the quantity I have determined may not be what I repre- 
sent it. At all events, | have found approximately the 
potential above earth of a point in space immediately above 
the surface of the hydrochloric acid, through which hydrogen 
is passing. The distance between the surface of the acid and 
the drops where they broke away separately was 2 inches. 
If this distance were lessened another source of error would 
arise (or increase), for the particles of acid propelled by the 
hydrogen from the acid generator would strike the stem of 
the funnel and lessen the electrification, because, as has been 
proved, they are opposite in sign to the escaping gas. 

But to return to my proposed straightforward experiment. 
I had intended to pass a current of neutral hydrogen through 
a column of strong hydrochloric acid, but found it impossible 
to neutralize the gas from a generator. However, I had now 
by trial become aware that a flask of hydrogen would become 
neutral after the lapse of some hours. 

Three half Winchester quarts were filled with hydrogen by 
the displacement of water from a generator containing zinc 
and HOl, and were left during the night to lose their charges. 
At 8 o’clock the next morning one was uncorked and placed 
on the insulated plate. The hydrogen escaped, but the spot 
did not move. I was then pretty certain that the gas in the 
other two vessels was neutral. 

A beaker, 7 inches high and 2 inches in diameter, was 
nearly filled with strong HCl, and a very slender delivery- 
tube, which had been attached to one of the vessels containing 
the hydrogen, was placed in it in such manner that any gas 
escaping from the vessel should pass right through a column 
of acid 6 inches high. An inverted metallic goblet was now 
attached to the insulated plate and quadrants, and placed in 
such position that any hydrogen issuing from the beaker con- 


ae. ot oe a oe an 
ja rag fe Sek eS 


ae ne tees 


76 ~~ Electrifications due to Contact of Gases with Liquids. 


taining the acid should pass into it and be retained until it 
got into the air by diffusion. The hydrogen in the half 
Winchester quart was next forced through the acid by a 
stream of water. The spot did not move. No electrification 
was produced by the hydrogen bubbling through the acid. 
The experiment was repeated with the remaining half Win- 
chester quart of hydrogen, but with the same result. 

IT had then to consider whether, in the face of this failure 
to electrify the neutral gas, I could reasonably stick to my 
theory of contact. I concluded that I could, and urge the 
following as sufficient grounds for my decision :— 

I had proved beyond doubt that hydrogen holds a charge 
with amazing tenacity, and that it only gives it up when each 
molecule individually, it would appear, comes into contact 
with a conducting body. Such contacts were also proved to 
be most difficult to effect, and whatever difficulty exists in 
discharging the gas, by bringing it into contact with other 
substances, must also exist, and in a magnified form, when 
one tries to make contact between the gas and any substance 
for the purpose of charging. The difficulty of making real 
contact is not a new one. In fact, I hold that when the 
stream of hydrogen was forced through the pure acid, real 
contact was not made. 

A very different state of things obtains when a piece of 
zine is thrown into a quantity of acid. Here each molecule 
of hydrogen escapes from the chlorine into the acid separately, 
and very likely takes its charge while in the nascent condition. 
One cannot imitate the circumstances attending this condition 
of things by any possible arrangement of delivery-tubes, 
however small. 

If it is proved that hydrogen or gases in general, in their 
nascent condition, take a charge when they come into contact 
with acids or solutions of salts, the fact, I should think, cannot 
fail to be of importance in the theory of the galvanic battery; 
and if it is proved that to make electrical contact between a 
gas and either metals or liquids is extremely difficult, what is 
known as “the air effect” in connexion with that theory 
appears to be negatived. 

In conclusion, I wish to acknowledge the help in making 
many of the experiments which I have received from Messrs. 
Horsnell and Leach, students at present passing through the 
college. 


St. Mary’s College, Hammersmith, 
November 1889. 


Pua] 


VI. The Effect of repeated Heating and Cooling on the Elec- 


trical Resistance of Iron. By HeErsert Tomuinson, 
PLS.* 


Soe of the physical properties of iron wire, even if it 

has been previously well annealed, can be considerably 
modified by repeatedly raising the metal to the temperature 
of 100° C., and suffering it to cool again. The internal 
friction, for instance, of a torsionally oscillating iron wire can 
be largely and permanently reduced by this process. Again, 
in a paper quite recently presented to the Royal Society, the 
author has brought forward an instance of an iron wire, which 
when made to go through magnetic cycles of very minute 
range, alternately at the temperatures of 100° C. and 17° C., 
was found to be permanently reduced, both in its molecular 
friction and its magnetic permeability, at each heating and 
cooling to such an extent that ultimately the former of these 
two physical properties became one quarter, and the latter less 
than one half of their respective original amounts. The large 
diminution of permeability and friction was also attended by 
a considerable lessening of the temporary effects of change of 
temperature on these properties. The object of the present 
investigation was to ascertain whether the electrical resistance 
and temperature-coefiicients of iron would also be altered by 
the heating and cooling process. According to Matthiessen 
the electrical resistance of metals can be expressed by the 
formula : 


R,= R, (1+ at+62), 


where R, and Ry are the resistances at ¢° and 0° C. respec- 


tively, and a and 0 are constants. For most pure metals the 
coefiicient a is not very far from ‘00366, and the resistance 
varies, therefore, approximately as the absolute temperature ; 
but with pure iron this coefficient is much greater. One of the 
questions which the inquiry was designed to answer was—Can 
the temperature-coefficient of iron be reduced by repeated 
heating and cooling to anything like ‘00366? This question 
has been answered in the negative, but, at the same time, it 
appears that the electrical resistance itself suffers a small but 
decided change. 

The iron wire examined formed part of a hank supplied by 


* Communicated by the Physical Society: read November 15, 1889. 

The Author begs to acknowledge, with thanks, the assistance which he 
has received, in this and kindred investigations, from the “ Elizabeth 
Thompson Science Fund.” 


aS 


eer ee 


Pe 


78 Mr. H. Tomlinson on the Effect of Heating and 
Messrs. Johnson and Nephew, and was specially prepared 


and annealed for the author by these makers; it was again 
annealed by the author himself in the following manner :— 
The piece of iron wire, together with several others, was 
placed in an iron tube about 130 centim. long ; the tube and 
its contents were then heated, in one of Fletcher’s new tube- 
furnaces, to 1000° C. This high temperature was preserved 
for several hours, and the wires were then allowed to cool 
slowly in the furnace. The above operations were repeated on 
three different days, so that eventually the wire was probably 
annealed as well as it could be by the ordinary method. In 
order to avoid any appreciable effect from the earth’s mag- 
netic force, the furnace was placed in a direction at right 
angles to the magnetic meridian. After the annealing the 
wire, which was about 120 centim. long and 1 millim. in dia- 
meter, was wrapped round with strips of paper, and wound 
double ina coil 5 centim. in diameter and 12 centim. in length. 
It was then placed in an air-chamber consisting of two co-axial 
copper cylinders (sce fig.) connected at their extremities, and 
enclosing between them an annular space filled with water. 
The whole arrangement is sufficiently shown in the figure. 


ae 


La LHe ry 


In this figure O O are two clamps grooved so as to receive 
the ends of the iron wire 2*, the clamps themselves being 
soldered to stout copper connecting-rods; a German-silver 
wire, y, is similarly connected, and placed ina glass vessel. 


* If the grooves, and the ends of the wire which fit into them, be well 
cleaned, clamping serves quite as well, for the purpose of connexion, as 
soldering, and is more convenient. 


Cooling on the Electrical Resistance of Iron. 79 


ab is a platinum-iridium wire of 745 ohm resistance ; R, is 
a resistance of 100 ohms, and R, a set of resistances from + 
ohm to 200 ohms; the india-rubber-covered connecting-wires, 
11, 7, have each a resistance of s ohm at the temperature 
of 17°C.; and isa sliding-piece which, by a suitable spring- 
and-catch arrangement, can be kept pressed on any part of 
ab. At the temperature of the room, the resistance of y is 
nearly equal to that of #, and R, as well as R, is nearly 100 
ohms ; consequently, any slight changes which may occur 
during the experimenting in the temperature of 7, 72, and ab 
do not sensibly affect the balance. The thermometers T, and 
T, register the temperatures of x and y respectively *; T, has 
its bulb in the centre of «#, and is enclosed by the glass tube 
G ; this tube is lined with india-rubber at the extremity out- 
side the air-chamber, so that the thermometer can, if necessary 
for the purpose of reading, be pulled out to any required ex- 
tent without causing any cooling ; the glass tube and T, are 
both slightly slanted upwards to prevent the column of mer- 
cury from breaking when the temperature is falling. 

For the purpose of preserving the temperature inside con- 
stant, the ends of the air-chamber are closed by corks, Qj, C,, 
and the vacant spaces inside are stuffed with cotton-wool (not 
shown in the figure). The water in the annular space W is 
heated by a row of burners, made by piercing pin-holes at 
equal intervals in a copper tube, closed at one end, and con- 
nected at the other with the gas. By adjusting the supply of 
gas or by altering the distance of the row of burners from the 
air-chamber, any required temperature up to 100° C. could be 
maintained nearly, if not quite, constant for a considerable 
length of time. In 15 minutes the water could be raised to 
100° C. ; and then, by diminishing the supply of gas so that 
the water only just boiled, this temperature could be kept up 
for 16 hours without adding more water ; when it was neces- 
sary to maintain the temperature at 100° C. for longer periods 
of time, the vessel was replenished with boiling water. 

It will be seen from the figure that there is a “ Wheatstone’s 
Bridge” arrangement for determining the resistance-ratio, 
z:y. The temperature of y varied by only a few degrees 
during the whole of the inquiry; and as both the actual resist- 


* Only one thermometer was used for T, in this particular investiga- 
tion, but the author generally employs, in work of this kind, three ther- 
mometers in turn. One of these thermometers is graduated from —5° C. 
to 30° C., the second from 50° C, to 65° C., and the third from 65° C. to 
100° C.; all three thermometers are divided into tenth degrees, and have 
been carefully compared with the Kew standards. 


ne hy ook oe BET 


80 Mr. H. Tomlinson on the Liffect of Heating and 


ance of the coil at 17° C. and its temperature-coefficient were 
known, the resistance of y at any other temperature could be 
calculated. 

It is usual in experiments with the “ bridge ”’ to close first 
the battery-circuit, and immediately afterwards that of the 
galvanometer ; but the author prefers to keep the galvano- 
meter-circuit always closed, and to observe the effect of closing 
the battery-circuit. It is true that in the latter case there is 
always a momentary throw of the needle due to self-induction 
in the wires, but this, with the arrangement shown above, is 
very slight; and with no more delay than that of two or 
three seconds, it can be easily ascertained whether the act of 
closing the battery-circuit causes any alteration in the difference 
of potential at the gulvanometer-terminals*. If, on the con- 
trary, the former of the two methods be employed, there 
arises more or less inaccuracy from the presence of thermo- 
electrical currents set up in one or more branches of the bridge 
by slight variations in the temperature of the air at different 
parts of the room. Besides, even if the air could be main- 
tained at perfectly uniform temperature throughout, thermo-. 
electrical currents are always produced by the act of pressing 
down the sliding-piece, 8S, on the wire ab, and by Peltier 
effects. 

The act of bending the wire into the form of the coil .pro- 
duced, as might be expected, a slight permanent change in 
its resistance, which was thereby increased by + per cent. ; 
doubtless a portion, but only a small one, of the whole reduc- 
tion of resistance, to be presently recorded, is to be attributed 
to the partial or complete removal of the effect of coiling. 

When everything was ready, and the wire had been left 
undisturbed for several hours, its resistance and temperature 
were determined ; the latter was then raised to 100° C., or 
very nearly to 100° C., and maintained thereat for at least 8 
hours t; and during this period the resistance of the wire was 
tested several times. The wire was then permitted to cool 
down, and its resistance was again determined about 16 hours 
afterwards. The same operations were repeated again and 
again, until the metal showed that no sensible change of re- 
sistance was produced by the heating and cooling. The results 
are given in the following Table :— 


* There is always a difference of potential at the galvanometer- 
terminals arising from thermo-electrical effects ; see what follows. 

+ The deviation from 100° C. never exceeded ;3,° C., and could in all 
cases be accounted for by changes in the barometric pressure. 


81 


Cooling on the Electrical Resistance of Iron. 


a nme eee ee 


Number of times Specific resist- 


hontadite ance in O©.G.S./tween consecu- 


100° C. units at 17°C. 
Ri 

0 11162 

I 10942 

2 10807 

3 10772 
10757 
10755 
10727 


Oo Oo 


7 10711 
8 10694 
9 10689 


eeeeee 


12 10688 


a ea gi he eo le ee ee ee 


Differences be- Specific resist- 


ance at 100° C. 


tive tee of 1Ron 
220 16029 
135 15796 
35 15789 
15 15747 

Dita AND Bee eens 2 
28 15724 
16 15679 
17 15674 

5 Soins 

a 15654 


cerca 


eeeeece 


Remarks. 


Kept at 100° O. for 8 hours; the bat- 
tery-current always applied in the 
same direction. 

Ditto. 


Ditto. 
Ditto. 


Ditto. 

Kept at 100° C. for 26 hours: the 
battery-current applied first in one 
direction and then in the opposite. 

Kept at 100° C. for 8 hours; the 
battery-current applied first in one 


direction and then in the opposite. 
Ditto. 


Ditto. 
Ditto. 
Ditto. 


Ditto. 


* For the mode of calculating the numbers in these columns, see what follows. 


G 


Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. 


82 Mr. H. Tomlinson on the Effect of Heating and 


It will be noticed that the specific resistance both at 17° C. 
and at 100° C. is diminished with each repetition of the 
heating and cooling process, until, finally, it becomes about 
4i per cent. less than at first. Thus, though the permanent 
effect on the electrical resistance is very much less than that 
on the permeability for very minute magnetizing forces, it is 
quite sensible. 

At the sixth heating the wire was kept at 100° C. for 26 
hours and, moreover, the battery-current was applied first in 
one direction and then in the opposite. These reversals of the 
current served to increase the rate of diminution of the re- 
sistance. 

The maintaining the temperature at 100° C. for 26 hours 
did not diminish the resistance as much as the next two 
heatings and coolings taken together ; evidently, therefore, 
the cooling exerts an influence as well as the heating. It is 
not, in fact, of much use prolonging each period of heating 
beyond 8 hours, whilst, on the contrary, a less time will hardly 
suffice, heating and cooling in rapid alternation being com- 
paratively ineffectual. 

Though the specific resistance of the annealed iron is per- 
manently diminished by the heating and cooling process, this 
is not so with the temporary change of resistance arising from 
change of temperature; the sixth column of the Table shows 
that the temporary increase of resistance produced by raising 
the temperature from 17° C. to 100° C. is not affected by the 
heating and cooling process, whilst the temporary increase of 
resistanve per unit becomes greater in proportion as the 
specific resistance itself becomes less. 

The values of Ryo) — Ry; and soy were calculated so 

17 
as to avoid, as much as possible, error arising from the per- 
manent changes consequent on the heating and cooling. Let 
C,, Cy, C3, &e., represent the resistances of the cold wire after 
the first, second, third, &c., heatings, and H,, H,, Hs, &., 
the corresponding resistances of the hot wire, then the num- 


bers in the sixth column were obtained from pee 
pews. ——— ——- &e., and those in 
the See column by dividing these by CG, as tee 
— &e., respectively. Of course, the temperature of the 


room was not always 17° C., but the resistance of x at 17° C, 
could be calculated from its actual resistance at the temperature 


Cooling on the Electrical Resistance of Iron. 83 


at the time by means of a formula ultimately obtained for the 
resistance of the wire at any temperature*. This formula 
was calculated from the results of a number of very careful 
observations at 17° C., 60° C., and 100° C., and after the 
heating and cooling process had ceased to affect the resistance. 
The formula thus obtained was :— 


R,= Ry (1 +'005131 ¢+°00000815 ¢”); 


whilst the formula deducible from Matthiessen’s results for 
pure iron annealed in hydrogen is 


R,= Ry (1 + °005425 ¢ + 0000083 27). 


The specific resistance at 0° C. (R,.,) of the author’s iron 
was 9808 eletromagnetic units, whilst that of Matthiessen’s 
pure iron (R,.,,) is given on the authority of the late Prof, 
Jenkin as 97187. It seems not improbable that this last value 
is from 4 to 5 per cent. too high; for it follows from Mat- 
thiessen’s researches that the resistances at any temperature of 
a pure metal and its alloy should be in the inverse ratio of 
the rates of increase of resistance at that temperature, so that 


Pee 005131 


=a should equal 05498? 


which, if the author’s result be assumed to be correct, would 
make R,.,, equal to 9277. 

Unfortunately, Matthiessen did not determine the absolute 
resistance of iron and many of the other pure metals exa- 
mined by him, and it appears from Prof. Jenkin’s own state- 
mentt that the calculated results for these metals cannot be 
depended on for any great degree of accuracy. The author, 
therefore, ventures to express the hope that the B. A. Hlec- 
trical Standards Committee may be induced to determine the 
absolute resistances and the temperature-coefiicients of those 
of the pure metals which are in ordinary use. 


* Similarly for the higher temperature of 100° C. 

+ The number actually given by Prof. Jenkin has been multiplied by 
‘9889 (the value of the B.A. unit in terms of the legal ohm). 

t See note on p. 250 of Prof. Jenkin’s book on ‘ Electricity and Mag- 
netism.’ 


G 2 


VII. On the Importance of Quaternions in Physics. 
By Professor Tart*. 


\ j Y subject may usefully be treated under three heads, 
ViZ.:— 

1. The importance of mathematics, in general, to the pro- 
gress of physics. 

2. The special characteristics required to qualify a caleulus 
for physical applications. 

3. How quaternions meet these requirements. 

The question has often been asked, and frequently answered 
(one way or other) in the most decided manner :—Whether 
is experiment or mathematics the more important to the pro- 
gress of physics? To any one who really knows the subject, 
such a question is simply absurd. You might almost as well 
ask :—Whether is oxygen or hydrogen the more necessary to 
the formation of water? Alone, either experiment or mathe- 
matics is comparatively helpless :—to their combined or alter- 
nate assaults everything penetrable must, some day, give up 
its secrets. 

To take but one instance, stated as concisely as possible :— 
think of the succession of chief steps by which Hlectromag- 
netism has been developed. You had first the fundamental 
experiment of Oersted:—next, the splendid mathematical work 
of Ampere, which led to the building up of a magnet of any 
assigned description by properly coiling a conducting wire. 
But experiment was again required, to solve the converse 
problem:—and it was by one of Faraday’s most brilliant dis- 
coveries that we learned how, starting with a magnet, to 
produce an electric current. Next came Joule and v. Helm- 
holtz to show (the one by experiment, the other by analysis) 
the source of the energy of the current thus produced:—in 
the now-a-days familiar language, why a powerful engine is 
required to drive a dynamo. Passing over a mass of import- 
ant contributions mathematical and experimental, due to 
Poisson, Green, Gauss, Weber, Thomson, &c., which, treated 
from our present point of view, would furnish a narrative of 
extraordinary interest, we come to Faraday’s Lines of Force. 
These were suggested to him by a long and patient series of 
experiments, but conceived and described by him in a form 
requiring only technical expression to become fully mathe- 
matical in the most exclusive sense of the word. This 


* Abstract of an Address to the Physical Society of the University of 


Edinburgh, November 14, 1889. See the Author’s Address to Section A 
at the British Association, 1871. 


On the Importance of Quaternions in Physics. 85 


technical expression was given by Clerk-Maxwell in one of 
his early papers, which is still in the highest degree interest- 
ing, not only as the first step to his Theory of the Electro- 
magnetic field, but as giving by an exceedingly simple 
analogy the physical interpretation of his equations. Next, 
the narrative should go back to the establishment of the Wave- 


theory of Light:—to the mathematics of Young and Fresnel, ~ 


and the experiments of Fizeau and Foucault. Maxwell’s 
theory had assigned the speed of electromagnetic waves in 
terms of electrical quantities to be found by experiment. The 
close agreement of the speed, so calculated, with that of light 
rendered it certain that light is an electromagnetic pheno- 
menon. But it was desirable to have special proof that there 
can be electromagnetic waves ; and to measure the speed of 
propagation of such as we can produce. Here experiment 
was again required, and you all know how effectively it has 
just been carried out by Hertz. It is particularly to be noticed 
that the more important experimental steps were, almost 
invariably, suggested by theory—that is, by mathematical 
reasoning of some kind, whether technically expressed or not. 
Without such guidance experiment can never rise above a 
mere groping in the dark. 

I have to deal, at present, solely with the mathematical 
aspect of physics; but I have led up to it by showing its 
inseparable connexion with the experimental side, and the 
consequent necessity that every formula we employ should as 
openly as possible proclaim its physical meaning. In presence 
of this necessity we must be prepared to forego, if required, 
all lesser considerations, not excluding even such exceedingly 
desirable qualities as compactness and elegance. But if we 
can find a language which secures these to an unparalleled 
extent, and at the same time is transcendently expressive— 
bearing its full meaning on its face—it is surely foolish at least 
not to make habitual use of it. Such a language is that of 
Quaternions ; and it is particularly noteworthy that it was 
invented by one of the most brilliant Analysts the world has 
yet seen, a man who had for years revelled in floods of sym- 
bols rivalling the most formidable combinations of Lagrange, 
Abel, or Jacobi. For him the most complex trains of formule, 
of the most artificial kind, had no secrets :—he was one of the 
very few who could afford to dispense with simplifications : 
yet, when he had tried quaternions, he threw over all other 
methods in their favour, devoting almost exclusively to their 
development the last twenty years of an exceedingly active 
life. 

Hveryone has heard the somewhat peculiar, and more than 


+,” ra De oe 


86 Prof. Tait on the Importance of 


doubtful, assertion—Summum jus, summa injuria. We may, 
without any hesitation, make a parallel but more easily ad- 
mitted statement :—The highest art 1s the absence (not, as 
Horace would have it, the concealment) of artifice. This com- 
mends itself to reason as well as to experience; but nowhere 
more forcibly than in the application of mathematics to phy- 
sical science. The difficulties of physics are sufficiently great, 
in themselves, to tax the highest resources of human intellect ; 
to mix them up with avoidable mathematical difficulties is 
unreason little short of crime. [To be obliged to evaluate a 
definite integral, or to solve a differential equation, is a neces- 
sity of an unpleasant kind, akin to the enforced extraction of a 
cube root; and here artifice is often requisite in our present 
state of ignorance: but its introduction for such purposes 
is laudable. It does for us the same kind of service which has 
been volunteered in the patient labour of the calculators of 
logarithmic tables. It is not of inevitable, but of gratuitous, 
complications that we are entitled to complain.| The in- 
tensely artificial system of Cartesian coordinates, splendidly 
useful as it was in its day, is one of the wholly avoidable en- 
cumbrances which now retard the progress of mathematical 
physics. Let any of you take up a treatise on the higher 
branches of hydrokinetics, or of stresses and strains, and then 
let him examine the twofold notation in Maxwell’s ‘Hlectricity.’ 
He will see at a glance how much expressiveness as well as 
simplicity is secured by an adoption of the mere notation, as 
distinguished from the processes, of quaternions. It is not 
difficult to explain the cause of this. But let us first take an 
analogy from ordinary life, which will be found to illustrate 
fairly enough some at least of the more obvious advantages of 
quaternions. 

There are occasions (happily rare) on which a man is 
required to specify his name in full, his age, height, weight, 
place of birth, family history, character, &e. He may bean ap- 
plicant for a post of some kind, or fora Life Policy, &e. But it 
would be absolutely intolerable even to mention him, if we had 
invariably to describe him by recapitulating all these parti- 
culars. They will be forthcoming when wanted ; but we must 
have, for ordinary use, some simple, handy, and unambiguous 
method of denoting him. When we wish to deal with any of 
his physical or moral qualities, we can easily do so, because 
the short specification which we adopt in speaking of him is 
sufficient for his identification. It ¢ncludes all his qualities. 
We all recognize and practise this in ordinary life; why 
should we outrage common-sense by doing something very 
different when we are dealing with scientific matters, especially 


Quaternions in Physics. 87 


in a science such as mathematics, which is purely an outcome 
of logic ? 

In quaternions, a calculus uniquely adapted to Euclidian 
space, this entire freedom from artifice and its inevitable 
complications is the chief feature. The position of a point 
(relative of course to some assumed origin) is denoted by a 
single symbol, which fully characterizes it, and depends upon 
length and direction alone, involving no reference whatever to 
special coordinates*. Thus we use p (say) in place of the 
Cartesian w, y, z, which are themselves dependent, for their 
numerical values, upon the particular scaffolding which we 
choose to erect as a (temporary) system of axes of reference. 
The distance between two points is 

T(p—p’), 
instead of the cumbrous Cartesian 
{(e—a!P + (yy! P+ (2-2) 
But the distance in question is fully symbolized as to direction 
as well as length by the simple form 
p—p'. 

If three conterminous edges of a parallelepiped be p, p’, p’” 

its volume is 
=Sego ps 

Even when advantage is taken of the remarkable conden- 
sation secured by the intensely artificial notation for determi- 
nants, Cartesian methods must content themselves with the 
much more cumbrous expression 


0 URE 
a! y! 2! 
a! pe eft 


As we advance to higher matters, the Cartesian complexity 
tells more and more; while quaternions preserve their sim- 
plicity. Thus any central surface of the second degree 1s 
expressible by 

Spgp=—1, or T¢p=1; 
while the Cartesian form develops into 
Aa? + 2B” ay + A’y? + 2B/2a + 2Byz+ AM? =1. 


The homogeneous strain which changes p into p’ is expressible 


* Note here that though absolute position is an idea too absurd even 
for the majority of metaphysicians, absolute direction is a perfectly defi- 
nite physical idea, It is one essential part of the first law of motion. 


88 Prof. Tait on the Importance of 


by a single letter :—thus 
p=p. 
Its Cartesian form requires three equations, 
x =axn+ by+cz, 
y' =deteyt+fz, 
Z=gethy+i. 
These may be simplified, but only a little, by employing the 


notation for a matrix. To express in quaternions the conju- 
gate strain, a mere dash is required : thus 


5 ae 

while with the artificial scaffolding we must write our three 
equations again, arranging the coefficients as below :— 

Ad. _0, 

b- eh 

ey ieee 
If we now ask the question, What strain will convert the 
:. ellipsoid above into the unit sphere, the answer will be some 
_ time in coming from the ponderous Cartesian formule. The 
¥ quaternion formula assigns it at once as ¢°. 


When Gauss gave his remarkable expression for the number 
of interlinkings of two endless curves in space, he had to print 


it as | 
= (a' — x) (dy dz! —dzdy') + (y'!—y)(dzda' —dx dz’) + (2 —z)(dady! eee | | 
ECE 1 C=) EC a | 


i What an immense gain in simplicity and intelligibility is 
a secured when we are enabled to write this in the form 

. zl (Seeder, S-p—pi dp dp, | 

es a pe 

<4 or as 

E - A) S dp ( Verdes 

e Tp —p1° 

t so that we instantly recognize in the latter factor the vector 
ra force exerted by unit current, circulating in one of the closed 
a curves, upon a unit pole placed anywhere on the other; and 
¥ thus see that the whole integral represents the work required 
i: to carry the pole once round its circuit. 

i Without as yet defining vy, I shall take, as my final 
e example, one in which it is involved. A very simple term, 


Quaternions in Physics. 89 


which occurs in connexion with the strain produced by a 
given displacement of every point of a medium, is 


Sey. S8@y1. Voo. 
Its Cartesian expression is, with the necessary specification 
o=1F +90 + kG, 


made up of three similar terms of which it is sufficient to 
write one only, viz., 


dyn d& dy =) nfan dg dn dt 
! ! — ——— = p+ 1 ag ar. aes 
(ab! —ba ) = dy dy dx we a) = dx dx 7 


dn dg dy =) 
ETN beth sale Sol ee: 
“ae Mer ea): 


Now, suppose this to be given as the 2-coordinate of a point, 
- similar expressions (formed by cyclical permutation) being 
written for the y and z coordinates. How long would it take 
you to interpret its meaning ? 

Look again at the quaternion form, and you see at a glance 
that it may be written 


V(Savy.c)(SBv.c), 
in which its physical meaning is more obvious than any mere 
form of words could make it. 

Or you may at once transform it to 

—38.(VaB) Vy. Voo, 
which shows clearly why it vanishes when a and 6 are 
parallel. 

I need not give more complex examples :—hecause, though 
their quaternion form may be simple enough (containing, 
_ say, 8 or 10 symbols altogether), even this unusually large 
blackboard would not suffice to exhibit more than a fraction 
of the equivalent Cartesian form. 


Any mathematical method, which is to be applied to 
physical problems, must be capable of expressing not only 
space-relations but also the grand characteristics (so far as 
we yet know them) of the materials of the physical world. 
I have just briefly shown how exactly and uniquely quater- 
nions are adapted to Huclidian space ; we must next enquire 
how they meet the other requirements. 

The grand characteristics of the physical world are :— 
Conservation of Matter, with absolute preservation of its 
identity ; and Conservation of Hnergy, in spite of perpetual 
change of a character such as entirely to prevent the recogni- 
tion of identity. The first of these is very simple, and needs 
no preliminary remarks. But the methods of symbolizing 


90 Prof. Tait on the Importance of 


change are almost as numerous as are the various kinds of 
change. The more important of them employ forms of the 
letter D :—viz. d, 0, D, A, 6, and v. 

From our present point of view little need be said of A, 
which is the equivalent of (D—1) or of (e/“—1), because 
the changes which it indicates take place by starts and not 
continuously. Good examples of problems in which it is 
required are furnished by the successive rebounds of a 
ball from a plane on which it falls, or by the motion of a 


light string, loaded at intervals with pellets. 


Various modes of applying the symbol d are exemplified 
in the equation 


aq=(@) da + (=) dy + (2) de. 


In the terms daz, dy, dz, the symbol d stands for changes of 
value (usually small) of quantities treated as independent. 
In the term dQ it stands for the whole consequent change -of 
a quantity which is a function of these independents. By 


the factors (=) &e. we represent the rates of increase of Q, 


per unit of length, in the directions in which 2, y, z are 
respectively measured. The contrast between the native 
simplicity of the left-hand, and the elaborate artificiality of 
the right-hand, member of the equation, shows at once the 
need for improvement. To express the rate of change per 
unit of length in any other direction, we have to adopt the 
cumbrous expedient of introducing three direction-cosines, 
and the result is given in the form 

AQ dQ dQ 

Us Ba ee: 

The above equation may be read as pointing out, at any 
one instant, how a function of position varies from point to 
point. ‘To express the change, at any one place, from one 
instant to the next, we write in the usual notation 


_ (22 
IQ=(F ) dt 
But if we have to express the changes, from instant to 
instant, of some property of a point, which is itself subject to 
an assigned change of position with time, we have to combine 
these expressions, and to indicate the relation of position to 
time. ‘Thus we build up the complicated expression 
__ (dQ dQ)\ dx dQ) dy dQ) dz 
1Q=(F) det (Fat (Fae dt+(F eae 


dx 


——— 


Quaternions in Physics. 91 


Here the symbol 9 is called in, to effect a slight simplifica- 
tion ; and we go a little further in the same direction by 
putting u, v, w for 

di dy dz 
TH ae aos 


which are obviously the components of velocity of the point 
for which : is expressed. Thus we write 


3 = (a) + Ge) +o) + #G) 


Of course you all know this quite well; and you may ask 
why I thus enlarge upon it. It is to show you how com- 
pletely artificial and unnatural are our recognized modes of 
expression. 

Fresnel well said :—La nature ne s'est pas embarrassée des 
difficultés danalyse, elle n'a été que la complication des 
moyens. Why should we not attempt, at least, to imitate 
nature by seeking simplicity ? 

The notation 6, as commonly used, is (like the d in dQ 
above) quite unobjectionable. At least we cannot see how to 
simplify it further. Its effect is to substitute, for any one 
point of a figure or group, a proximate point in space, so that 
the figure or group of points undergoes slight, and generally 
continuous, but otherwise wholly arbitrary displacement and 
distortion. It thus appears that d and 6 are entitled to take 
their places in a calculus, such as quaternions, where sim- 
plicity, naturalness, and direct intelligibility are the chief 
qualities sought. We have now to inquire how such expres- 


sions as 

AQ dQ, dQ 
can be put in a form in which they will bear their meaning 
on their face. 

It was for this purpose that Hamilton introduced his sym- 
bol y. No doubt, it was originally defined in the cumbrous 
and unnatural form 

edn. ciel d 
But that was in the very infancy of the new calculus, before 
its inventor had succeeded in completely removing from its 
formulee the fragments of their Cartesian shell, which were 
still persistently clinging about them. ‘To be able to speak 
freely about this remarkable operator, we must have a name 


92 Prof. Tait on the Importance of 


attached to it, and I shall speak of it as Nabla*. We may 
define it in many ways, all independent of any system of 
coordinates. Thus we may give the definition 


—Seyv == 


meaning that, whatever unit-vector « may be, the resolved 
part of 7 parallel to that line gives the rate of increase of a 
function, per unit of length, along it. From this we recover, 
at once, Hamilton’s original definition :—thus 


V=—«S«y—PBS8y —ySyv =2d.+ Bdg+yd,, 


a, B,y being any system of mutually rectangular unit-vectors. 
But, preferably, we may define Nabla once for all by the 
equation 


—Sdpy=4d, 


where d has the meaning already assigned. The very nature 
of these forms shows at once that Nabla is an Jnvarzant, and 
therefore that it ought not to be defined with reference to any 
system of coordinates whatever. 

Hither of the above definitions, however, shows at once 
that the effect of applying 7 to any scalar function of position 
is to give its vector-rate of most rapid change, per unit of 
length. 

Hence, when it is applied to a potential, it gives in 
direction and magnitude the force on unit mass; while from 
a velocity-potential it derives the vector velocity. From the 
temperature, or the electric potential, in a conducting body 
we get (employing the corresponding conductivity as a 
numerical factor) the vector flux of heat or of electricity. 
Finally, when applied to the left-hand member of the equation 
of a series of surfaces 

Z— 
it gives the reciprocal of the shortest vector distance from 
any point of one of the surfaces to the next ; what Hamilton 
called the vector of proximity. 

If we form the square of Nabla directly from Hamilton’s 
original definition, we find 


v=- {(@) +(@) *@) > 


* Hamilton did not, so far as I know, suggest any name. Clerk- 
Maxwell was deterred by their vernacular signification, usually ludicrous, 
from employing such otherwise appropriate terms as Sloper or Grader; 
but adopted the word Nabla, suggested by Robertson Smith from the 
resemblance of y to an ancient Assyrian harp of that name. 


Quaternions in Physics. 93 


simply the negative of what has been called Laplace’s Opera- 
tor :—that which derives from a potential the corresponding 
distribution of matter, electricity, Kc. 

Thus Laplace’s equation for spherical harmonics &c. is 
merely 

vu=0; 
and, as 1/T(p—«) is evidently a special integral, an indefinite 
series of others can be formed from it by operating with 
scalar functions of y, which are commutative with v, such as 
SB8y, e-S”v, &e. In passing, we may remark that if 8 be a 
unit vector, id-+jm+kn, we have 
d d d 


SCY eh cin da a a 
Sy tie Cee rede 


This is the answer to the question proposed a little ago. 


The geometrical applications of Nabla do not belong to my 
subject, and they have been very fully given by Hamilton. 
But, for its applications to physical problems, certain funda- 
mental theorems are required, of which I will take only 
three of the more important ;—an analytical, a kinematical, 
and a physical one. 

I. The analytical theorem is very simple, but it has most 
important bearings upon change of independent variables, and 
other allied questions in tridimensional space. Few of you, 
without the aid of quaternions or of immediately previous 
preparation, would promptly transform the independent vari- 
ables in a partial differential equation from 2, y, zto 7, 0,6 :-— 
and you would certainly require some time to recover the 
expressions in generalized (orthogonal) coordinates. But 
Nabla does it at once, Thus, let 

Lat ied d 
Wore ae Raa Se 
where 
a= E+ yn t+ ke, 
E, , § being any assigned functions of w, y, z. Further, let 
do = $dp, 


where @¢, in consequence of the above data, is a definite linear 
and vector function. Then, from the mere definition of 
Nabla, 

Sdov.= —d=Ndpy, 
which gives at once 


S.odpy.=5 .dpd'y.=NSdpyv. 


Nil t 
| 


94 Prof. Tait on the Importance of 
As dp may have absolutely any direction, this is equivalent to 


$'Vo=V) 
where ¢’ is the conjugate of ¢. 

II. The fundamental kinematical theorem is easily obtained 
from the consideration of the continuous displacement of 
the points of a fluid mass. (It is implied in the word “ con- 
tinuous” that there is neither rupture nor finite sliding.) 

If o be the displacement of the point originally at p, that 
of p+dp is 

o+do=ao—Sdpy .o; 
and thus the strain, in the immediate neighbourhood of the 
point p, is such as to convert dp into 


dp—Sdpy «co. 
Thus the strain-function is 
Wwr=T—Sty.o. 


If this correspond to a linear dilatation e, and a vector-rota- 
tion e, both being quantities whose squares are negligible, we 
must have 

wr=(l+e)7+ Ver. 
Comparing, we have 

—Sry .o=er-+ Ver, 
from which at once (by taking the sum for any three direc- 
tions at right angles to one another), 


vo= —d(e) +2; 
so that 

Sve represents the compression, 
and 


iVvc _ , 5 vector-rotation, 


of the element surrounding p. 

By the help of these expressions we easily obtain the stress- 
function for a homogeneous isotropic solid, in terms of the 
displacement of each point, in the form 


go= —n(Soy.c+ VSac)—(c—2n)o8qe ; 
where n and ¢ are, respectively, the rigidity and the resistance 
to compression ; and $ is the stress, per unit of surface, on 
a plane whose unit normal is o. 

III. The fundamental physical relation is that expressing 
conservation of matter, commonly called the equation of con- 
tinuity. We have only to express symbolically that the 
increase of mass in a finite simply-connected space, due to a 
displacement, is the excess of what enters over what leaves the 


Quaternons in Physics. 95 


space. This gives at once 


\\\Svods=\\SUveds, 


where Uy is unit normal drawn outwards from the bounding 
surface. If we put for o the expression wyv, where wu and v 
are any two scalar functions of position, this becomes Green’s 
Theorem. 

If the space considered be imagined as bounded by two 
indefinitely close parallel surfaces, and by the normals at each | 
point of a closed curve drawn on one of them, this is easily 
reduced to the form of the line and surface integral 


(WS . Uryods=|Scdp. 


The simplest forms of these equations are respectively 


ANN Vvuds ={\Uvuds ; 


\\WW(Ury)uds =\dpu, 


where uw is any scalar function of position. But it is clear 
from the mode in which it enters that u may be any quater- 
nion. And it is easy to build on these an indefinite series of 
more complex relations. ‘Thus, for instance, if o and 7 be 
any two vector-functions of p, we have 


\\\iew?r + Kyo.yr)ds =\\cUryrds, 
which has many important transformations. You will find it 
laborious, but alike impressive and instructive, to write this 
simple formula in Cartesian coordinates. It consists of four 
separate equations, containing among them 189 terms in all! 


In the three relations just given we have the means of 
applying quaternions to various important branches of mathe- 
matical physics, where Nabla is indispensable. But I must 
confine myself to one example, so I will take very briefly the 
equations of fluid motion. 

Let e be the density, and o the vector-velocity, at the point 
p ina fluid. Consider the rate at which the density of a little 
portion of the fluid at p increases as it moves along. We 
have at once, for the equation of continuity, 


Cg 


Di =eSyo 5 
which we may write, if we please, as 
de 


= = Sy(ec). 


96 On the Inportance of Quaternions in Physics. 


This is the result we should have obtained if we had considered 
the change of contents of a fixed unit volume in space. Next 
consider the rate at which the element gains momentum 
as it proceeds. We write at once, since momentum cannot 
originate or be destroyed by processes inside the element, 


Oc 
ox —eyP +\\pUrds, 
where P is the potential energy of unit mass at p, and Uv 
is the stress-function due to pressure and viscosity. We 
have already had the form of this function; so that the 
equation transforms at once into 
298 = —eyP—yp—nv7o+3VS8ve); 
which contains the three ordinarily given equations. Here 
n is the coefficient of viscosity, and the pressure p enters the 
equation in the form 
cSve. 


To obtain v. Helmholtz’s result as to vortex-motion, putn=0, 
and we deduce for the rate of change of vector-rotation of an 
element, as it swims along, 


ovyo=V.vV. oVV\0}. 


If the fluid be incompressible, this becomes 


ov yo= —S.V101V-¢. 
From either it is obvious that the rate of change of the 
vector-rotation vanishes where there is no rotation. But time 
forbids any further discussion of formule. 

Hydrokinetics, as presented by Lagrange and Cauchy, 
was rather a triumph of mathematical skill than an inviting 
or instructive subject for the student. The higher parts of 
it were wrapped up in equations of great elegance, but of 
almost impenetrable meaning. They were first interpreted, 
within the memory of some of us, by Stokes and v. Helmholtz, 
after we know not what amount of intellectual toil. The 
magnificent artificers of the earlier part of the century were, 
in many cases, blinded by the exquisite products of their own 
art. ‘lo Fourier, and more especially to Poinsot, we are 
indebted for the practical teaching that a mathematical for- 
mula, however brief and elegant, is merely a step towards 
knowledge, and an all but useless one, until we can thoroughly 
read its meaning. It may in fact be said with truth that we 


Periodic Law of the Chemical Elements. 97 


are already in possession of mathematical methods, of the 
artificial kind, fully sufficient for all our present, and at least 
our immediately prospective, wants. What is required for 
physics is that we should be enabled at every step to feel 
intuitively what we are doing. Till we have banished artifice 
we are not entitled to hope for full success in such an under- 
taking. That Lagrange and Cauchy missed the import of 
their formulz, leaving them to be interpreted some half- 
century later, is merely a case of retributive justice :— 


“, , . neque enim lex aequior ulla 
Quam necis artifices arte perire sua,” 


Lagrange in the preface to that wonderful book, the Mécanique 
Analytique, says :— 

“Les methodes que j’y expose ne demandent ni construc- 
tions, nl raisonnemens géométriques ou mécaniques, mais 
seulement des operations algébriques, assujéties 4 une marche 
réguliére et uniforme.” 

But note how different is Poinsot’s view :— 

‘“‘Gardons-nous de croire qu’une science soit faite quand 
on l’a réduite a des formules analytiques. Rien ne nous 
dispense d’étudier les choses en elles-mémes, et de nous bien 
rendre compte des idées qui font l’objet de nos spéculations.” 

No one can doubt that, in this matter, the opinion of the 
less famous man is the sound one. But Poinsot’s remark 
must be confined to the analytical formule known to him. 
For it is certain that one of the chief values of quaternions is 
precisely this :—that no figure, nor even model, can be more 
expressive or intelligible than a quaternion equation. 


VII. An Approammate Algebraic Expression of the Periodic 
Law of the Chemical Elements. By THos. CARNELLEY, 
D.Sc., Professor of Chemistry in the University of Aberdeen.* 


[Plate I.] 


EVERAL attempts have of late years been made to ex- 
press the atomic weights of the Elements by algebraic 
formule. Of these that of Dr. H. J. Mills (Phil. Mag. [5] 
XVlil. p. 893; xxi. p. 151) expresses the atomic weights by a 
logarithmic function | 
15(p—0°9375"), 
in which p and ¢ are whole numbers. 
Another attempt, referred to by Prof. Mendeljeff in his 


* Communicated by the Author. 
Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. H 


98 Prof. T. Carnelley on an Algebraic Hupression of 


Faraday Lecture of this year (Chem. Soc. Journ. lv. p. 642) 
as having been made by Tchitchérin in 1888, seeks to ex- 
press the relations between the atomic volumes of the alkaline 
metals by the formula A(2—0:00535 An), where A=the 
atomic weight and n=8 for Li and Na, 4 for K, 3 for Rb, 
and 2 for Cs. 

In a paper read at the Aberdeen Meeting of the British 
Association in 1885 (Chem. News, nos. 1875-1378, 1886), I 
proposed for the chemical elements the general formula 
A, Box+~@—«), In which n is the series and w the group to 
which the element belongs; A=12 and B= —2. 

Since that time, and for thirteen years previously, I have 
made frequent attempts to find a simple numerical expression 
for the Periodic Law, but so far without marked success. 
Early in the past summer, however, I obtained an expression 
which, though only approximate, may still be found of con- 
siderable interest. According to this 

1 
A=c(m+v7) or a + =4, 
m+ vz 


in which A=atomic weight, c=constant, m=a member of 
an arithmetical progression depending on the series* to 
which the element belongs, v=the maximum valency or the 
number of the group* of which the element is a member. 
After numerous trials it has been found that the best 
results are obtained when «=2, and 
m=O; 24; 5; 84; 12; 153; 19; 225; 26; 295m oe 
for 
Series Il.; Ul.; IV.3 V.j Vie; VH.3. VIL. ; 1X. K.5 ke 


So that 
Boa is 
m+Vv 
It will be observed that m is a member of an arithmetical 
series in which the common difference is 34, except in the 
first two cases, where it is only 23. 
In the following Table are given the values of ¢ calculated 
from the above equation. The atomic weights employed and 
iven in Column I. are taken from Clarke’s ‘ Recalculation 
of the Atomic Weights ’ (1882), corrections being made when 
rendered necessary by more exact determinations published 
since Clarke’s work. The atomic weights are given to the 
first place of decimals only. 


C. 


* These terms are employed in the sense in which Mendeljeff uses 
them in his Natural Classification of the Elements. 


the Periodic Law of the Chemical Elements. 99 


TABLE I. 


fy. EE 


EvEN SERIES. : ms 
Atomic (Cale.) 
A 


weight. 
A. = 
m+ N v 
Series II. m=0. (H=1) 
WAGE oo. cece seo 7:0 7:00 
Beryllium: ......... ot 6°45 
SOOM cas conosees! 10-9 6:30 
On 000 ae 12:0 6:00 
INTGROSCNY 2 <00200-3 14:0 6°25 
NET Ta ccain conde 16°0 6°53 
Plwuorime .........6.. 18:9 713 
Mean...| 6°52 
Series LV. m=5. 
Potassium .......<.- 39°0 6:50 
@alenamr® 0 .2.62406: 40:0 6:24 
Seandiumt -.50.5.0.. 44:0 6°54 
EATS Galea co sces 48:0 6°86 
Wang: .c.00e.0+ 51°3 7:09 
Chromium ......... 52:0 6:98 
Manganese ......... 54:0 7:06 
Mean...| 6°75 
Series Vi. m=12. 
EOL TUM , rs ee ces 85'3 6°56 
Strontium -.....:..- 87°4 6°52 
NCETM hye c cieics soe 89°8 6°54 
ARECOMMUM: 625.6600. 90°42 6°46 
INVODUWM: 5,55 ss000 0: 94-03 6:60 
Molybdenum ...... 95°5 6°61 


Series VIII. m=19. 


CSU oi. scceoacsas 132-6 6°61 
IBA) 6. s.ccesscc 136°8 6:70 
Lanthanum......... 138:0° 6:66 
Geri |... cecn cece 139-97 6°66 
DiC yMUN 6.0... 142-08 6:69 

Mean...| 6°66 


1 Marignac (1884). 
8 Meyer, Mod. Theor, p. 89 (1888). 
8 Cleve (1888). iL 


ig II. 


Opp SERIES. : é 
Atomic (Cale.) 
A 


weight. 
A. eather 
m+ Vy 
Serizs ITI. m=23. 
Soca pesos 23°0 6:57 
Magnesium......... 24-4" | 6:24 
/Vinramravnyia sp Gecaccss 27-0 6°38 
Silicomt consecceneee 28°37 6:29 
Phosphorus......... 31:0 6:54 
Sulphur “ose ees 32'0 6°46 
@hiorine 222).. esd. 35°4 6°87 
Mean...| 6°48 
‘Sans V. m=83. 
Copper s22s-cce4- 63°3 6°66 
Bin nc daseryee oui 65°3 6:59 
Gailltumiereeeces: so: 68°9 6°73 
Germanium ...... ORS 6°88 
sATSENIC! ade nhac. 74:9 6:97 
Selemmum: vs.es--0 78°83 7:20 
IBLOMING wet sassee cee 79'°8 7-16 
Mean...| 6°88 
Series VIT. m=153. 

Silkvierl ah. oxoscectees 107°7 6°53 
Cadmium 52%-.... 111°8 6°61 
sa Clavimas + gece aces ee 113°4 6:58 
PENaue eel yee 6°72 
PATTON) eclessees 119-64 6°74 
.Relitariand 425. 52.-< 125:0° 6:96 
ROGIMG’ je hhcscsecnnes 126°5 6:97 
Mean...| 6°73 


Series IX. m=223. 


Wanting. 


2 Thorpe & Young (1887). 
+ Cooke. 5 Brauner (1883). 
8 Cleve (18838). 


H 2 


100 Prof. T. Carnelley on an Algebraic Expression of 
Table I. (continued). 


I. ET us i, 
Even SERIES. Atomic on Opp SERIzEs. eee ae 
ee Me weight. A ; 
5 = A. ——— 
m+ Nv m+ Vv 
(H=1) 
: Szrtes X. m=26. Serres XI. m=293. 
Mantalum py <enss ss. 182:1 6°45 Gold’ pssecceceonnte 196-9° 6°46 
: Tungsten ......--. 183°6 6°45 Mercury: jccs.-eoee 199-7 6:46 
i | halitamy: ee.eecee 203°7 6°52 
j head oc... ucnnaee 206°5 6°56 
}| 


Mean...| 6°45 


Series XIT. m=383. 


5 if Thorium ......+.+++- 9319 | 6-6Qu 
Wrantum:...c2s..--s 238°5 6°72 
Mean... 667 General Mean=6:64. 


® Thorpe & Laurie (1887). 1° Marignac (1884). '! Kruss & Nilson (1887). 


From the above Table it will be seen that the values of c 
as calculated from the atomic weights of 55 elements, using 
; the equation referred to, lie between 6°0 and 7:2, with a 
‘ ae mean value of 6°64. The lowest value, 6:0, is obtained in the 
AP case of carbon, and the highest, 7:2, in that of selenium. In | 
the great majority of cases, however, the value lies much | 
nearer to the mean value than is indicated by the two extremes 
mentioned, thus :— 


In I case the value of ¢ lies at 6:0. 


q 0 » 0 lm.s«OG 1, 4. @, betiweenilig amigas 
Bi With one exception( 2 és 5 6:2, “s 6°15-6:25 
ai (Si), all these occur in} 3 Pi i. 6:3, E 6:25-6'35 | 
i Groups 1 to 3. 1 54 ie 6:4, 5 6:35-6:45 
a 15 . A mat 645-655 | 
= 3894 11 if 5 6:6, 3 6°55-6°65 } 
f 9 i ee ” 665-6°75 
Mis 0 # : 6°8, »  6°75-6-85 
a iv With one exception : 2 ae 2 Mees A 
4 i (Li), all these occur in 3 a2 2 FAL 22 7-05-7°15 
j : Groups 4 to 7. 2 - i 7:2, ee 7-15-7-20 

All the values of c, except that for carbon, lie between | 


; : 6:24 and 7:20. Of the 55 values of c, 35 lie between 6°45 
oH and 6°75. Of the other 20 values of c, which are farthest 
| from the mean, 11 occur in groups 5, 6, and 7, and of these 


the Periodic Law of the Chemical Elements. 101 


10 are higher than the mean, whilst of the 9 remaining 
values 5 occur in groups 1, 2, and 3, and of these five, four 
are lower than the mean, so that the high values of ¢ occur 
chiefly with elements belonging to the higher groups (viz. 5, 
6, and 7), while the low values occur chiefly with elements 
belonging to the lower groups (viz. 1, 2, and 3). Four of 
the values furthest from the mean occur in group 4; of these 
gr (Ti and Ge) are high, and two (C and Si) are low values 
of c. 

It will be observed that the elements of group 8 have 
not been included in the above table on account of the dif- 
ficulty of assigning a value to v in their case. This difficulty, 
however, is removed if v represents, not the valency, but the 
numerical order of the elements in the series to which they 
respectively belong, in which case ¢ has the following values 
in group 8 :— 


m=). m=12. m=19. m= 26. 


Fe...7:14 | Ru...6-98 OGD | mS Gs. 
Se || ei ae) nas 
Ni...7-18 | Pa...7-00 Pt...666 | v=10. 


Ir ...6°64 v= 9. 


For potassium m=5, so that the equation A=6°6(m+4/v) 
becomes A=6°6(5+4/v) for the elements of the potassium 
series; and since the common difference in the arithmetical 
series 5, 83, 12, 154 &c. is 34, therefore for any element in 
series IV. or upwards 


A=6°6[54+3:5(a—4) +/0] =6'6(3-5a—9 +/2), 


where a=the number of the series to which the element 
belongs, and v the numerical order of the element in its own 
series. 


The equation A= c(m+ Vv) becomes A=c(m+1) in the 
case of elements belonging to the first group. So that for 
potassium and silver, 


(1) c(m+1)=89, and (2) ¢e(m,+1)=107°7. 
Let # represent the common difference in the arithmetical 
Seles 74, 5, Mg, m7, &e. corresponding to the 4th, 5th, 6th, 
mm &e. series of elements. 
hen 


Mi=m,+3x (3). 


44 
i 
ea 
i 
ai 
it ‘ a 
il 1g 
i % 
: ; 
wee 
J pe 7 
heey 
b | ean 
} | Feo 
q y i] 
| ies 
1 4 
Wy 
1 a 
b | ae |" 
ie 
mae 
iow 
ae 
ee 
4 
{ 
| i 
aoe 
i 
ban 
Wa 
‘i 
‘ wi 
i aS 
i a 


102. Prof. T. Carnelley on an Algebraic Expression of 
By substituting (3) in (2) we get 
107:°7=c(m,+ 3x +1) =c(m, +1) +320. 
But 
c(m,+1)=39; 
“. 107°7=39 + 3x¢ or xc 22°90. 


By proceeding in a similar manner the following values of 
ae are obtained from the pairs of elements (all belonging to 


group 1) named :— 


From K and Cu xe=24°30 
» Kand Rb 2e=23°15 
Pe eS aad Ale. xc= 22°90 
Ca and Cs xe=23'40 
ny ake and an LO—=22°56 
oo Wand gabe xc= 22°00 
3 Cnand Ao: ee=22°20 
9) Cuand:Cs*.. L6—= 25 10 
em aire JA... LC=22°22 
5 | kb and are xc—= 22°40 
5 BRband Cs . xo=23°65 
5) | deb andr Agi Lo 22°32, 
peas ands =. xe=24°90 
» | Agiand Au . xe==22°30 
hac stand JAM <2 ze= 21°43 

Mean= 22°85 


Or, in other words, the difference between the atomic weights 
of any two elements in group 1 (from series Iv. upwards) 
divided by the difference between the number of the series to 
which each element belongs, gives a constant, or 
Bae = constant= 22°85, 

| ya: ary 
where « and y are the numbers of the series to which the 
elements A and B respectively belong. That is to say, the 
difference between successive elements of group 1 from 
series IV. upwards is practically constant and equal to 22°85. 

Now the constant 22°85 is very nearly identical with the 
atomic weight of sodium, which the most trustworthy deter- 
minations have shown to be 22°99. 

If ¢ boiBi, then c= -- 6-53, or if, in place eae 


ee 22-99 
we take the atomic weight of sodium, then c= 350 ne 


the Periodic Law of the Chemical Elements. 103 
a number which is very nearly identical with 6°64, which was 


obtained as the value of ¢ by applying the equation c= 
to all the atomic weights, as in Table I. 

Tf there be any truth in the above, then the atomic weights 
at present accepted for cesium (132°6) and copper (63°3) are 
rather too high, and that for gold (196°9) somewhat too low. 
Cesium should be about 131, copper about 62, and gold 
about 198. 


m+Vv 


In Table II. (pp. 104, 105) is given a list of the atomic weights 
calculated from the equation A=c(m+ Vv), ¢ being taken 
equal to 6°6. 

The Table shows that, of the 54 elements considered, the 
difference between the calculated and experimental atomic 


weights 
93 | in the case of 21 elements is less than 1 unit ) 
BS ¥3 12 »  itlies between 1 & 13 units | 
( 39 29 8 29 29 29 2&3 99 Mean 
9] ae 2” 3 ” 29 ” 3 & 33 2» r +19 
5 39 93 6 99 39 bP) 4 & 45. 99 | 
L 29 ” 4 29 9 9 6 & 62 29 


The considerable difference between the calculated and ex- 
perimental values in some cases shows that the expression 
At. wt.=6°6 (m+ Vv) is at best only approximate. The 
atomic weights calculated by it are, however, very much 
nearer the experimental values than those calculated accord- 
ing to Dulong and Petit’s law from the equation 

atomic heat Or4 
aE specific heat spec. ht. 
Thus of the 44 elements* of which the specific heats have 
been directly determined, the difference between the calculated 
and experimental atomic weights 


14 { in the case of 9 elements is less than 


1 
= <s 5 - it lies between 1 & 14 units 

G 9 99 a ” 9 9 ile & 2 ” 

| ” 9 5 99 99 ” 2&3 9 
93 9 9 5) ” 9 9 3.& 4 99 Mean 
4 99 39 4 99 99 29 4 & 5 99 +42 

| ” ” 2 ” 99 ” 5 &6 ” 

L ” ” 3) ” ry) 39 6 Cis. 

” 9 ” 2 9 9 ” i & 10 ” 

” ” 5) ” ” ” 10 & 15 ” 


* Exclusive of C, Si, B, N,O, F, and H, which are apparently such 
marked exceptions to Dulong and Petit’s law. 


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106 Prof. T. Carnelley on an Algebraic Expression of 


In Table II. is given not only the atomic weights as 
accepted by the best authorities and as calculated by the 
formula A = 6°6(m+ Vv), but also the specific gravities*, 
together with the specific volumes as calculated both from 
the experimental and from the calculated atomic weights, by 
dividing each of these respectively by the corresponding 
specific gravities. From the Table it will be seen that the 
specific volumes as found by each of these two processes agree 
closely. Further, if two curves be constructed in the manner 
first suggested by Lothar Meyer, by taking in the one case 
the experimental atomic weights as abscissee, and the corre- 
sponding specific volumes as ordinates, and in the other case 
the atomic weights calculated from A= 6'6(m+ Vv) as 
| abscissse and the corresponding specific volumes as ordinates, | 
i lines then the result represented in Diagram I. will be obtained, in 
| which the dotted curve, being constructed from the experi- 

mental atomic weights t, may be called the experimental curve; 
| while the continuous one, being constructed by using the cal- 
| culated atomic weights, may be called the calculated curve. 
It will be seen from both Table II. and from Diagram I. 
that the greatest differences between the calculated and ex- 
perimental atomic weights occur chiefly at the end of series 
IV., V., and VII., and at the beginning of series XI. 


: It has been shown that in the equation A=c(m+ 4/v) the 
a et constant c has a mean value of 6°6. Supposing that there is — 
| any truth in the equation, what is the meaning of the constant 
y 6:6? This number at once suggests the constant 6°4, obtained 
ae according to Dulong and Petit’s law, by multiplying the 
( ig atomic weight by the specific heat. If in the equation 

| A=c(m+ Vv) we assume that the constant ¢ represents the 
i atomic heat, then, 


Atomic weight = atomic heat x (m+ “/v) 


: = atomic weight x specific heat x (m+ Vv) ; 
: 1 = specific heat x (m+ VW v), 
% 

Rome 


2 r specific heat = ————— 

y oe m+ Vv 

t If the specific heats of the several elements be calculated 
by this equation, we find that in almost all cases the caleu- 
lated numbers agree very closely with the experimental specific 
heats. This will be seen from the following Table :— 

Be * Taken from Lothar Meyer’s Mod. Theories, p. 123; translated by 

i Bedson and Williams. 

i ) + It is identical with Lothar Meyer’s curve. 


Tg ee CSYS 


the Periodic Law of the Chemical Elements. 107 


Tas Le ITI. 
i Specific Heat 
Specific (experiment). 
Heat calcu- 
lated from 
1 


_ =. |_ Specitic Temp. of 
m+v°| Heat. |determin-/ Authority. 


ation *. 
Serres II. m=0. C. 
MERE MTU... <csicaiee ses 1-000 941 64° | Regnault. 
642 100 | Reynolds. 
Beryl 614% viescns- 709 582 257 | Nilson and Pet- 
terson. 
IBQEOME 252.0508 code 578 : (?) 600 | Weber. 
raphite c 467 978 - 
Carbon | Giamond om 459 | 985 | 3; 
INIEROREMY... 02 <2 - cere "446 36|t 
VPC Mey iaos7s tendon’ 408 [-25]t 
I EGOTIME, wi ancbh os vaeces OTT [-26]t 
Srrizs ITT. m=23. 
OGM osnis oc of ew cielo ‘286 "293 —14 | Regnault. 
Magnesium ............ "255 "250 60 5 
214 60 i 
Se : *225 ... | Mallet. 
ATOAIMTUIN 425) 00500 236 216 BOE NEE 
240 300 , 
CODY nadine ce o's ovdacte > 222 °203 232 | Weber. 
"189 20 | Regnault. 
Phosphorus (yellow) ‘211 °202 25 | Kopp. 
212 75 | Person. 
lifts) 67 | Regnault. 
188 ... | Dulong and Petit. 
Sulphur (rhombic)... "202 "202 ... | Regnault. 
"209 ... | Neumann. 
\ 235 134 | Person. 
OHIOKING Te sec dai veeses "194 "180t 
Srrizs IV. m=5. : 
IP OUASSTUIA <6... lais0.60. na 164 "166 —34 | Regnault. 
CWaleimy i. ce.cdecw oases "156 "170 50 | Bunsen. 
DAMM. cccdecrocees "148 "145t 
"112 50 | Nilson and Pet- 
PR CANTUND eae se +0 ols: "143 terson, 
"162 220 a8 Bi 
WGNAGIUMNG Sesccnsoves "188 124 
Chromium .secee<5: "134 122t 
Manganese (two : 122 = 
samples) ......... \ ISt { 133 } oo) pscenauits 


* These temperatures are the arithmetical mean of the extreme temperatures 
between which the specific heats were determined. 

Tt. Not determined directly, but by calculation from the experimental specific 
heats of the compounds. 6-4 


at. wt.° 


{ Calculated from Dulong and Petit’s law. Sp. ht.= 


108 Prof. T. Carnelley on an Algebrate Expression of 


Table ITI. (continued). 


Specific Specific Heat 
(Elss.& anilore (experiment). 
lated from 
pene ees : Temp. of | 
m+ Ny, ae determi- Authority. 
nation*. 
Serius V. m=83. C. 
if 093 35 | Kopp. 
7095 58 | Regnault. | 
24 093 50 | Naceari. | 
Copper cent eos Re 105 ‘ 099 300 : 
| ‘095 50 | Dulong and Petit. 
N ‘101 150 i “ 
( 093 33 | Kopp. 
094 50 | Bunsen. 
| 096 55 | Regnault. 
{D1 1 ORR A Re NES ARABS ‘101 < ‘094. 50 | Dulongand Petit. 
102 150 5 +3 
093 50 | Naccari. 
*104 300 is 
Gallina hecho ntece ‘097 ‘079 18 | Berthelot. 
Germanium............ 095 ‘076 270 | Nilson and Pet- 
terson. 
‘O81 55 | Regnault. 
Arsenic (crystalline) 093 ' 082 56 | Neumann. 
091 13 | Regnault. 
(crystal- | \ ( ‘076 59 é 
line) | | 
Chien en ' 091 { 086 61 | Neumann. 
| (amor- | | 095 ? | Bettendorf and 
|. phous) | / \ Willner. 
Bromine (solid) ...... 089 084 —51 | Regnault. 
Series VI. m=12. 
uabidiuma 2.62.0. - ee ‘077 ‘O77T 
SEOMtIIN fonts ‘O74 “O74t 
SCAT Cage ee ene ae ‘073 ‘O72t | 
PAAPCONTUTA ~5.52 foe /.0001 ‘071 ‘067 50 | Mixter and Dana. 
NaobiuaM 0 ,c2snenss. se ‘070 ‘068 
066 10 | Delarive and 
Molybdenum ......... ‘069 Marcet. 
‘072 55 | Regnault. 


* These temperatures are the arithmetical mean of the extreme temperatures 
between which the specific heats were determined. 

Tt Not determined directly, but by calculation from the experimental specific 
heats of the compounds. 


{ Calculated from Dulong and Petit’s law. Sp. ht.= = ; 


the Periodic Law of the Chemical Elements. 109 
Table III. (contenued). 


Specific Specific Heat 
Heat calcu- (experiment). 
lated from 
1 
oe Pacing : Temp. of 
m+n v, Ep ang debra Authority. 
eat. 55 18 
nation”. 
Series VII, m=153. O. 
(/ 056 =|50; 36 | Bunsen; Kopp. 
057 55 | Regnault. 
‘056 50 | Dulong and Petit. 
‘061 150 % 99 
SiBVer ecetisecccteccnste ‘061 4 ‘057 25 | Bystrom. 
‘061 150 5p 
056 50 | Naccari. 
061 300 3 
\ ‘063 ? | Potter. 
054 37 | Kopp. 
055 50 | Bunsen. 
"058 10 | Delarive and 
CadMiUM...0.0cde00008- ‘059 Marcet. 
"059 13 | Regnault. 
055 50 | Naccari. 
K 062 300 4p 
1 Lace Dt 058 ‘057 50 | Bunsen. 
055 34 | Kopp. 
056 50 | Bunsen. 
Ta, eee ee 057 "056 55 | Regnault. 
"055 58 | Bede. 
058 115 é 
( 050 50 | Bunsen 
051 55 | Regnault. 
052 31 | Kopp. 
“049 50 | Naccari. 
AMHAMONY “p.0.2000 000 056 054 300 55 
051 50 | Dulong and Petit. 
055 150 3 i 
(ordinary form) _ 050 17 | Pebal and Jahn. 
(explosive form) 056 17 9 ~ 
O47t 36 | Kopp. 
Tellurium (distilled) 055 “O4TT 55 | Regnault. 
(undistilled) 052T 55 A 
HOGING! <3 iotisascnes scies 055 "054 59 . 
Serres VIII. m=19. 
(CREST 943 Hos ocauobbns 050 “048+ 
arian be. dsmees. see 049 047 
Lanthanum ............ 048 045 50 | Hildebrand. 
: : 045 49 cs 
@erium. seis 048 { 05 Schuchardt. 
1D yighyralinyoay AaseeRoasoee 047 046 Hildebrand. 


* These temperatures are the arithmetical mean of the extreme temperatures 
between which the specific heats were determined. 

+ It is very doubtful whether the Tellurium employed was pure. Compare 
Brauner, Chem, Soc. Journ. ly. p. 382. 6-4 

¢ Calculated from Dulong and Petit’s law. Sp. ht.= at. wt. 


110 Prof. T. Carnelley on an Algebraic Expression of 
Table III. (continued). 


Shiga Specific Heat 
Hest Aiea (experiment). 
lated from 
ear ble ; Temp. of 
m+ 0° as © | determi- Authority. 
ae nation*. 
Srrizs IX. m=223. ae ting. 
Serizs X. jee 26. 
Pantalinas secccs see ece oe 035 °035t 
"0334 55 | Regnault, 
Z ‘035 11 | Delari d 
DUN ESM «svsnvie cee cde 0351 Mace 
0364 Regnault. 
Serres XI. m=293. 
Golde. 32 ian be eee 0328 0329 55 | Regnault. 
Mercury (solid) ...... 0323 0319 —59 + 
: : 0325 Lamy. 
Thallium eibid sWiclslelelelelelelvie 0320 { 0335 58 Regnault. 
( 0314 55 > 
| 0315 34 | Kopp. 
Tedd one 0317 1 cee vee 
0304 50 =| Naccari. 
{ 0338 300 he 
0305 34 | Kopp. 
IBISMIUENE eicnacsatsecest 70315 "0308 55 | Regnault. 
"0309 ? | Schmidaritsch. 
Series XII, m=83. 
CENOTIUIMN: veseeste nen ‘es 70285 ‘0276 50 =| Nilson. 
(Wramium seosceess. oe 0282 0277 49 | Zimmerman. 


* These temperatures are the arithmetical mean of the extreme temperatures 
between which the specific heats were determined. 6-4 
t Calculated from Dulong and Petit’s law. Sp. ht. = 


at. wt. 

The specific heats of nitrogen, oxygen, and fluorine have 
not been determined in the solid state, while the values 
obtained from the specific heats of their compounds are well 
known to be abnormally low, as are those of beryllium, boron, 
carbon, and silicon, which have been determined directly with 
the elements in the solid state. Even in the case of the latter 


elements, the values calculated from the expression ————= 
| m+ Vv 
are not very far from the experimental numbers, while in all 
others, except those of calcium, gallium, and germanium, the 
agreement is remarkably close. The experimental value for 
calciumis apparently too high, being greater than that of potas- 


the Periodic Law of the Chemical Elements. 111 


sium, whereas, according to Dulong and Petit’s law, it should 
be less. The experimental values for gallium and germanium, 
on the other hand, are, according to Dulong and Petit’s law, 
apparently much too low, being less even than that of bromine, 
although this element has an atomic weight about 10 units 
higher. The atomic heat of gallium is only 5°4, and that of 
germanium only 5:5; whereas the specific heats calculated 


from the expression = would give rather less than 6°7 
m 


I 
+ Vv 
and 6°9 respectively. 

It may be said that of the 55 elements with which the 
comparison can be made, the calculated specific heats agree 
very closely with the experimental values in the case of 45 of 
them, while the other ten are elements the specific heats of 
which, according to Dulong and Petit’s law, are more or less 
abnormal. 

The agreement becomes even more marked when the com- 
parison is made with specific heats determined at temperatures 
above those at which specific heats have been more commonly 
determined. 

Diagram II. shows graphically the close agreement between 
the calculated and experimental specific heats. It is con- 
structed by taking the atomic weights as abscissee and the 
specific heats as ordinates. The dotted curve is constructed 
from the calculated and the continuous one from the experi- 
mental specific heats. The specific heats used in the latter 
case are chiefly those given on page 89 of Lothar Meyer’s 
‘Modern Theories,’ translated by Williams and Bedson. If, 
however, those determinations which agree more nearly with 
the calculated numbers were used, the two curves would coin- 
cide even more closely. q 

In the equation A=c(m+ Vv) the constant ¢ is equal to 
6°6, and has been assumed to represent the atomic heat of the 
elements, whereas the atomic heat, on the basis of Dulong and 
Petit’s law, is usually taken to be 6:4. This latter value, 
however, is obtained because the specific heats employed are 
mostly those which have been determined between 0° and 
100° C., whereas if the specific heats obtained at higher tem- 
peratures (say 0° to 300°) be employed a somewhat higher 
value, approximating to 6°6, will be found for the atomic heat. 

As is well known, the specific heat, and therefore the atomic 
heat likewise, increases, though very slowly, with the tem- 
perature. If c, therefore, really represents the atomic heat, 
it is not strictly but only approximately a constant, being a 
function of the temperature. Consequently, in each of the 


) | 


112 Periodic Law of the Chemical Elements. 


equations 
A=c x spec. heat (Dulong and Petit’s law). 


A=c (m+ Vv), 


the atomic weight A is not exactly but only approximately 
equal to the expressions on the right-hand side, since the 
latter are a function of the temperature, whereas the atomic 
weight, so far as we know, is constant. 

According to Bettone the hardness of an element is 
inversely proportional to its specific volume. [If this be so, 
then hardness may be represented in terms of the specific 


gravity and the expression 6°6 (m+ /v), thus 


(esp. gr. 0) spate 
spec. vol. at. wt. 6°6(m+ 0) 


Hardness = 


The following Table gives the hardness of a number of 
elements as found experimentally by Bettone, and as calcu- 
lated by the above equation :— 


Hardness. 
Specific 
gravity. Calculated. 
ee Found 
bide rico 8 2) (Bettone). 
6°6(m-+ Nv). 
Carbon (diamond) ... 33 "250 301 
Manganese 22... -sem.4: 8-0 "158 "146 
Copper intsectadoes. eames 88 “140 "136 
VEiii Cha een teeter Pa 7-15 "109 108 
Silverre csccos ences arnene 105 70964 "099 
Gold: hsb ccetdacraseoeees 19:3 096 098 
AJnmInGuM: 3. c.cessene 2°56 "092 ‘082 
Madman e-ceo5: cece 8:65 077 076 
Magnesium ............ 1°74 ‘O71 073 
(I? on ae Ae ne 7-29 063 065 
Ponds Athan. eeaeeehe 11°38 "055 057 
Utval Mgt esis. cece soe ae 11°86 057 056 
Galen sans sere coe osae ee 1:57 037 041 
Sodmumglie.i.eeeese. cs: ‘97 042 ‘040 
PP OEASSIUM|/fencjesnstecene 86 022 023 


It should be noted, however, that Bettone’s values, on 
which he founds his law of hardness, do not agree in several 
cases with those found by other observers, 7. e. Calvert and 
Johnson. 


In the expression A=C(m-+ ¥/v) it has been stated that 
m is the member of an arithmetical progression. For even 


On two Pulsating Spheres in a Liquid. 113 


series mis a whole number, whereas in the odd series it is a 
whole number and a half, thus corresponding to the well- 
known difference between elements of even series on the one 
hand and odd series on the other. 

Again, in the arithmetical series, 


W255 3D 27 8h 5 12; lot 5 19; 224; 265.2925 33 


the common difference in the case of the first three members 
is only 24, whereas after that point it is 34; this corresponds 
to the statement of Mendeljeff that the 2nd and 38rd series 
(z.e. Li and Na series) of elements are more or less excep- 
tional in their character and not strictly comparable with the 
subsequent series. 


IX. On two Pulsating Spheres in a Liquid. 
By A. L. Sepsy, 1.A., Fellow of Merton College, Oxford *. 


A SPHERE is said to pulsate when it periodically dilates 
and contracts. 

If two pulsating spheres are immersed in a liquid, in- 
_ equalities of pressure in the liquid arise, and there is generally 
a resultant pressure on each sphere urging it towards or away 
from the other. 

An approximate expression of this is given in Basset’s 
‘ Hydrodynamics’ (vol.i. p. 255), but the proof is rather long, 
mone an integration of pressures over the surface of a 
sphere. 

By a somewhat different method I have obtained in § 5 an 
expression which may be carried further than Mr. Basset’s 
without much labour ; and in §6 I have applied the method 
to solve the more general problem relating to the case when 
the radial velocities on the surfaces of the spheres are Zonal 
Harmonics of the mth and nth degrees respectively, with the 
line of centres as their axis. 

A still more general solution can be derived from this ; for 
when the radial velocities on the spheres are any functions of 
the distance from the line of centres, each can be expressed as 
a series of Zonal Harmonics. 

Since I wrote this paper I have found one by Prof. Pearson 
(Trans. Camb. Phil. Soc. vol. xiv. part ii.) in which this 
problem ig investigated ; but numerical values of the constants 
involved are only given for Harmonics of low degree. 

In dealing with these questions some propositions on 


* Communicated by the Author. 


Pihit. Mag. S. 5. Vol. 29. No. 176. Jan. 1890. I 


114 Mr. A. L. Selby on two 


Images, due to Mr. Hicks, are required. His proofs will be 
found in the ‘ Philosophical Transactions’ for 1880; but in 
§$ 2-4 of this paper I give other proofs, in which the subject 
is considered from a slightly different point of view. 

The main interest of the problem of pulsating spheres is 
derived from its experimental illustration by Prof. Bjerknes. 

§ 1. Preliminary Dejfinitions.—A source of liquid of strength 
m is a point at which a volume of liquid 47m is supplied per 
unit time. A sink (or negative source) of equal strength is 
a point at which liquid disappears at the same rate. A com- 
bination of a source and sink of equal numerical strength m, 
at an infinitesimal distance d apart, is a doublet. As this is 
analogous to an infinitely smali magnet, I shall call md the 
moment of the doublet. The intensity of a doublet is its 
moment divided by its length; it is analogous to the intensity 
of magnetization of a bar of unit section. The axis of a 
doublet is the line from the sink to the source. 

The lines of flow due to any distribution of sources and 
sinks are the lines of force due to the corresponding magnetic 

oles. 

3 § 2. Let P, P! be a source m and sink —m on the straight 
line OL: 


TPL = 6; LP, =@? 32 P= 7 eee 


Then the flow through the circle (of which TT’ is the pro- 
jection) formed by revolving T round OL is 


2am (cos 6! —cos @). 


Let P! approach P so that PP! diminishes indefinitely, 
md retaining a constant magnitude uw. Then 


27m (cos 6!—cos 0) = 2rpsin? @. /r. 


__ If the source and sink are interchanged, the sign of the flow 
is reversed ; we may consider mw as negative in this case. 


j 


of 


Pulsating Spheres in a Liquid. 115 


Let a doublet of moment —p! be placed at Q, where uw > wp. 
If TQL=¢, TQ= 7’, the flow through TT’ due to this is 


—2ry! sin? hd. /'. 


The equation of a surface ot revolution across which there 
is no flow from the doublets at P and Q is 


2a(wsin? 0. /r—p! sin? d./7) = A, a constant. 
If A=0, this reduces to the line OL and the sphere 


= ee 
If C be the centre of this sphere and a the radius, 
CP. CQ=a@ and a=(e?—1)PQ/2z, 


where a? = p/p. 

Since the liquid is supposed to be “ perfect,” and the sphere 
is part of a surface of flow, we may make a material sphere 
occupy its place. 

Hence the effect of a sphere X (fig. 1) in disturbing the 
flow from the doublet w at P, distant 7 from its centre, is the 
same as if the sphere were removed and a doublet —pa?*/f° 
placed at Q. This doublet is called the image of yw in the 
sphere. 

§ 3. To determine the unage of a source p at P. 

This source is equivalent to a line of doublets of intensity 
extending from P to infinity along PO (fig.1). Its image is 
therefore a line of doublets from Q to C. 

If wd be the moment of a doublet distant a?/x from the 
centre, —ydx*/a® is the moment of its image. But the 
lengths of corresponding parts of Po and CQ are as a?: x”. 


Therefore the intensity of the image is —— supposing 
the axis along QC; or = , regarding it as along CQ. 


Now a magnet of length 7 and unit section, whose intensity 
of magnetization at a distance w from one end is Cz, is equi- 
valent (so far as concerns external action) to a quantity of 

“magnetic matter” Ci at the positive end, and a distribution 
of line-density —C along the axis. 

Therefore, from the analogy between sources and magnetic 
poles, the line of doublets is equivalent to a source pal arti: (). 
and a line sink of strength —,/a per unit length along CQ. 

§ 4. To jind the image of a system of doublets PQ ‘(fig. 2) 
of intensity wx, where x is the distance from Q. 

Let P’, Q! be the points inverse to P and Q. 

By §2 the image is a system of doublets lying between 
P’ and Q!. 

12 


j 
1 
ig! 
4 
| 
i 
i 


116 _ Mr. A. L. Selby on two | 


Let N be a point on PQ, N’ its image, QN=a, CP=/. 
By § 3 the image of a doublet of intensity wx at N is of 
intensity —yeCN'/a or —wCQ. Q'N'/a. 


Fig. 2. 


The image of the system PQ is therefore a line of doublets 
in which the intensity is proportional to the distance from Q'; 
and the image is similar to the system from which it is 
derived. 

This result is easily transformed by the process used in §3 
into the following :— 

The image of a source w at P and a line-sink PQ of strength 


—20 per unit length is a source w.a/f at P! and a line-sink 


IQ! Re ea 
P/Q! of strength F PIQl | 

It is clear that any system of sources and sinks of total 
strength zero distributed along PQ has for its image another 
such system distributed along P’Q!. For the given system 
can be reduced to a system of doublets. 

§5. To determine the stress between two spheres X, Y, 
pulsating m an infinite liquid. 


Fig. 3. 


Let A, B be the centres of the spheres (fig. 3); a, b the 
radii. Then a, d are the normal velocities at the surfaces. 


Pulsating Spheres in a Liquid. 117 


Let , be the velocity-potential in the liquid when A pulsates 
and B does not, ¢g the velocity-potential when B pulsates and 
A does not. Then ¢,+ 4p is the velocity-potential when both 
pulsate. 

For if m, n; are normals to X, Y, drawn into the liquid, 


d¢,/dm=4, dd,/dn=h, do,/dn,=0, dd,/dn,=0. (1) 
Therefore, if ¢,+¢,=¢, 
doé/dm =a and dd/dn, = b. 


Also ¢ satisfies Laplace’s equation, and vanishes at infinity. 
If T be the kinetic energy of the liquid, p its density, 


pS) ZY) paae 


x { {6% as, ( (048 as, hs 
the volume-integration extending through the liquid, and the 
surface-integrals being taken over Sy, 82, the surfaces of X 


and Y. 
But by the surface conditions (1) and by Green’s theorem, 


( (on a= | (oth as. ae) 


Substituting ,+¢, for @ in (2), and employing (1) and 
(5), we have 


2T/p = —a{( bsdS:—20\{ padSo—b ff ppdSe. . (4) 


Let P (fig. 8) be the inverse of A in the sphere Y; Q, C 
the inverses of P, B in X ; R, D the inverses of Q, C in Y. 

If Y were absent, the pulsations of X would give the same 
velocity-potential as a source a’a at A. 

The image of this in Y is a line of doublets BP; that of 
BP in X is a line of doublets QC ; that of QC in Y is a line 
of doublets RD ; and so on. 

Now the flow across the surface X due to BP, QC; RD,... 
taken in successive pairs is zero ; and the flow across Y due to 
A, BP; QC, RD; ... taken in pairs is also zero. 

¢, is therefore the velocity-potential due to these systems. 

It is simpler to transform each line of doublets into the 
equivalent source and line-sink. 

Let AB=c, and denote a?a by pu. 


) 
33 
1D. 
7 
eT! 
1; 
bE} 
i| 
#' 


= 


Birdie wae ae 


118 Mr, ALL. Selby on two 

The doublets BP reduce to a source wb/e at P and a line- 
sink ——*, along BP. 

The doublets QC reduce to a source pab/(c?—b) at Q and 


a line-sink (ofa along QC. 


We shall find that the doublets RD contribute a term of 
order c—!° to T; this we shall neglect. 

The lengths of successive line-sinks diminish very rapidly, 
a being to its predecessor in a ratio of the order a*/¢ or 
b?/c. 

Therefore, since BP=0?/c, the lengths QC, RD,... are of 
order c—*,c->..., and the strengths of successive sources 
ab) ..2..aro Ol oder, | cay eae e 

If a source v at distance r from A contribute a term ¢, 
to d,, it has been proved by Gauss that 


KY g,d8,= —Aza’v/r or —4mav, according as r> or <a. (5) 


[This may be proved in the following elementary way :— 
Let the sphere be an attracting shell of surface-density 
unity. 


iy ‘) , dS is the work done by a particle v if the sphere recedes 


to infinity. 

And—47a’v/r or —47avis the work done by the sphere 
when the particle recedes to infinity, according asr> or <a. | 

Excepting the source w at A, all the images within A are 
of total strength zero. 

An image outside A consists of a source of strength s 
distant p from A, and a line-sink —s/y per unit-length, with 
extremities distant p, p+ from A. 

This contributes to the coefficient of 47a? in —{\d,d8, 


the term 
fi Nis ss 
p oY pte 


2 § Y 

ne a l € 1 5 e ° . . . 

poe OS ( t ) (6) 
which is, approximately, 


syfip?—sy'/ap’. . . . « = 


or 


For the image PB, 
s=pb/e; y=Jle3; p=c—Be.. . . (8) 


Pulsating Spheres in a Liquid. 119 


Therefore this contributes 
[2 pee ee 
per i erage 
The source at R is of order c—?; RD is of order c—>; AR is 


of order e. 
Therefore RD contributes a term of order ¢~". 
Omitting terms of this order, 


; cel b iL Ce 
=f b. dS, = dma? | 7 + emo b log a 3 
—4\f h,dS82 can be written down by interchanging a and 0. 


It remains to form the term —\\ db, dSz in (4). 
A contributes a?a/¢ to the coefficient of 47b?; BP contri- 


butes nothing. 
For QC, oe —b’); p=c—a'c/(?—0"), p being 


here reckoned from 


2 


ab? 
7 (e—BP) shi. | eo init ei abmnh aLaees (9) 
sy’/3p° is of order ce}; 
a —s , 
Zoe ch N2 Ce 
RD contributes nothing, and further i images a are negligible. 
_ to terms of order ¢- inclusive, 


C2 
= Amati | —— > Flog 4, } 
1 Cc 
LAT 9 as fae Seen KS Maes pis Saale a 
+ 47rb*b bee log zt 


: 373 373 (42 2 
+ 8rabias {oS ee) 
6 Be ¢ 5) 


Now the force tending to increase ¢, required to maintain 
i Je yal da. 
¢ at 1tS given value, 1S mrs 
Therefore, if the spheres are free to move they behave 
feat a force —— 
de. 


brevity terms beyond ¢~*), 


0 


C 


Se iaee 2 


pdc C 


ayy 27,3 Qp2 Anrhth2q3 2 
Pot eS Oe) (ae is mbib'a (1+ 


Ce 


20° 


tended to separate them, and (omitting for 


{vit 
i 


= 


an 
Yo SY 
fe 
aS 
pi 
iM +d 
tt 
iT 
ih 
& 
* 4 
ih 
bie Yh's 

\ ; 
# : 
) ae aif 
{ \ i! 
re 
hi 
et 
1 
ti 
( 
Lie 


ana 
afm aba 25 


erect See ese 
aa sere et rere at a 


120 Mr. A. L. Selby on two 


If a, 6 be the mean radii of the spheres, T the period 
of vibration, «, 8 the amplitude of vibration, 


Bd = ; if 
azatea sin. a b=b-+Bsin 2a (ay +e); 


and, supposing the pulsations small, the mean value of the 
force is (after replacing a, b by a, b) 


87ra7b? ¢aB 7) 2areé 
_ ! 2 Ue 6 ) COS HR 


pl? 2 
27.2 
— (ba? + a8?) } ; 


If the spheres are not very near, terms after that involving 

c-2 can be neglected, and ¢ tends to diminish or increase 
: 27re . aaa ‘ , : 

according as Cos a 3s positive or negative—i. e. according 


a & (ac? +8?) + 


as the phases of vibration of the spheres approach more 
nearly to coincidence or opposition. 3 

§ 6. The above method is also applicable when the dis- 
placement on each sphere is a Zonal Harmonie with the line 
of centres as axis. 

Definition —If (f, 0, 0)(a, y, z) be the coordinates of two 
points C and P, at a distance r apart, a source at OC which 
gives a potential —yu = (-) at P is called a source of the 
nth order. oN 

A doublet is a source of the first order, and a source of the 
second order is derived from it in the same way as a doublet 
from a source of order zero (hitherto called a source). A 
source of the rth order is derived similarly from a source of 
the » —1th order. 

Let H (fig. 3) be the position of a doublet mu distant f from 
B along BA; and let V be the potential at (2, y, z) due to H 
and its successive images in Y and X. | 

Take a doublet w at H!such that BH'=/+d/, and a doublet 
—w at H. 


The potential at (a, y, z) due to H’ and its images is V + wrap. 
Therefore the potential due toa source uw of the second order 


and its images is = , and that due to a source # of the nth 


gd” 31V 
1 


order and its images is 


Pulsating Spheres in a Liquid. 121 


When the axes of the doublet and of the derived sources are 
; ; ee GES 
directed towards B, this becomes (—) 7 a= i 

Now let the spheres X, Y vibrate so that the normal 
velocities are Zonal Harmonics uP,, vP», having AB, BA as 
their respective axes. 


Then, since 
Gel N ane, 
eA!) 7 pith ‘ 


X, if it vibrated by itself, would behave like a source of the 


n+2 
a 


nth order of strength a‘ with its axis along AB. 


@ 
fae dl 
Let ¢, be the potential due to this source and its images. 


This is found by calculating successive images of the complex 
source H in Y and X, and making /=<c after all operations 
are completed. : 

It Y vibrated by itself it would be equivalent to a source 


m+ 2 


of the mth order, are and with its images it would give 


a potential 5. 
Then, as before, if both spheres vibrate, 


2T/p = —u\ \o,P,d8:—2v) [o,P_,dS.—v f { O,P, ds. (10) 


To evaluate i) \¢ al,,dSe, we proceed as follows :— 


2 ae : 
TM (with axis 


where yw is the potential due to a doublet oe 


along AB) distant / from B, and to the images of the doublet; 
the subscript ¢ denoting that after all operations are completed 
c is to be written for /. 

EO 


oH \5 bah ,dS2 7 ( 7 ye ae \\PP,,d8>. 


Now, if v be a source of order zero distant & from B, ¢, its 
velocity-potential, 
Amb” ty ’ Ade” y 


P CIS ee yg ee 
J my We (Qm+1)e"*" f (2m+1)b"-* 


according as §> or <b. 


122 On two Pulsating Spheres in a Liquid. 


Whence, for a doublet y at the same point, with axis 
— along AB, 
Amb” **y(m+1) Anme”—*y 
iP TS 
J mV, We (2m+1)é""? (Q2m+1)0"~-” 
vr, being the velocity-potential due to v. 


But taking >, the image of the doublet v is —v6’/E’, 
distant 6?/€ from B. 
The two doublets together give the term 


and it remains to evaluate 
is ae ey 
( A> eam => 
2y 


n+ 
where the summation extends to the doublet ——— (or “) 
ee 


and its images outside Y. For this doublet 


y=p, E=f. 
For Q, the next image outside B, 
a’b° af 


v= gv) = ae 


The succeeding image introduces a term of order c—? com- 
pared with that due to «; we shall neglect this. 
Making f=c after all operations are over, we have 


Ana” *? bh" wy m+n! 
—0 ff Pb. d= fe 


323 Caria’ Dae mat 2 
+ (14 Stee +h) 4 ] 
2c ¢ € 


ee © 
where 
p = (m4+2) (m+3)a'+2(m+ 2) (n+ 2)a°b? + (n+ 2)(n+3)64. 
It remains to find iy p,P_d8;, from which \) bpP,,dSe 
can be derived by symmetry. 
The source p» at A contributes a constant, which we need 


not write. 
The images P and Q contribute a term found by making 


y= pif, F=c—PIf 

The image R and its successor contribute only a small 
term; here € can be regarded as constant, since f only 
occurs in a term of order c~°; and vy is approximately 
mao sf *. 


On Transient Electric Current from Iron and Nickel. 123 


As far as terms of the order c~@"*1 inclusive, —ul\ P 6,48; 
is made up of the term 


ee n (n+2)? b? | (n+2)?(n+3)? 04 
2 | 


Cee ele? 412! G 
(n+2)?(n+38)?(n+4)? 0° 
== Ny ae ase a ae ead OL 
due to the images P and Q, together with the term 
Qara2"t 4Q3h ou? 
=e ligneor | 2 


due to the image R. 

By interchanging m and n, u and v, a and 6, the remaining 
term on the right-hand side of (10) can be found. 

If the vibrating spheres consist of liquid of density p’, the 
velocity-potential within X is ene and the kinetic 
energy of the sphere X is es 
holds for the other sphere. 

When ¢ is constant the principal term in the expression of 
the stress between the spheres varies as c~™*"*”) or ag c~ Gn ¥), 
Oimas, ct), 

If u, v are simple harmonic functions of the time, the 
average stress between the spheres is to be found as before. 

The case when m=n=1 has been discussed by Mr. Hicks 
(loc. cit.); for all other values of m and n the centres of the 
spheres are at rest. 


A similar expression 


X. On Transient Electric Current produced by suddenly twist- 
ing Magnetized Iron and Nickel Wires. By H. Nagaoxa, 
fiigakust, of Imperial University, Tokyo*. 

[Plate IL] 


N a recent number of Wiedemann’s Annalen, Herr 
Zehnder + communicated the result of his experiments 

on the transient current produced by twisting magnetized iron 
and nickel wires, in which he finds the direction of current in 
nickel to be opposite to thatiniron. The same result had been 
already known to me since July 1888. Being engaged in 


* Communicated by Sir William Thomson. 
+ “Ueber Deformationsstréme.” Wiedemann’s Annaler, Bd. xxxviii. 
p. 68. This number reached me on 14th October, 1889. 


124 H. Nagaoka on Transient Electric Current produced 


the investigation of the effect of twist in the magnetization of 
nickel and iron, I tried some preliminary experiments on the 
transient current produced by twisting magnetized wires. 
Thereby I hoped to trace some connexion between the transient 
current thus observed and the reversal of polarity* produced 
by twisting magnetized nickel wire, which is at the same 
time subjected to longitudinal stress. Though nothing striking 
was obtained in this direction, results not hitherto made known 
by the researches of Matteucci t and Ewing t were obtained. 
The following is the description of the experiments made in 
July and September, 1888. 

The wire to be examined was well annealed and hung in a 
magnetizing solenoid, The coil was 30 centim. long and 
wound in 12 layers of thick copper wire, giving a magne- 
tizing field of 36°7 units for a current of one ampere. ‘The 
upper end of the wire was held fixed, while the lower was 
attached to a twisting apparatus provided with a graduated 
‘circle and a pointer. The two extremities of the wire were 
electrically connected to a low-resistance ballistic mirror- 
galvanometer. The transient current was measured by the 
first swing of the galvanometer. The deflexion was read 
after suddenly twisting the wire between two extreme limits 
of twist. Generally, it was after a number of twistings in 
both ways from the initial position of no twist, that the 
transient current settled to its final value. 

Since the present investigation was undertaken with a 
view to ascertain the relation, if such exists, between this 
transient current and the reversal of polarity, the effect of 
eae longitudinal stress on the transient current was also looked 
Hoh into, as this played an important part in producing the re- 
He versal mentioned. 
| A nickel wire 30 centim. long and 0:5 millim. in radius 
was treated in the way above mentioned, the angle of twist 
amounting to 60° in both directions from the initial position 
of no twisting. The first experiment was performed under 
no longitudinal stress; the transient current produced by 
suddenly twisting the wire in various magnetizing fields was 
measured, the field being gradually increased from 0 to 110 


hone * See “ Effects of Torsion and Longitudinal Stress on the Magnetiza- 
fi ae tion of Nickel,” Journ. of the Coll. of Science, Imp. Univ., Japan, 
| ian vol. ii., or Phil. Mag. Feb. 1889; and also “ Effect of Twist on the Mag- 
he netization of Iron and Nickel,” Journ. of the Coll. of Science, vol. iii. 
| oa At the end of the latter paper a short sketch of the results on the transient 
ats current is given. 

ee + See Wiedemann’s Lectricitat, Bd. iii. § 771. 
iD | ee | { Proce. Roy. Soc. vol. xxxvi. 1884. 


by twisting Magnetized Iron and Nickel Wires. 125 


C.G.8. units (July 5, 1888). The following Table gives the 
readings of the first swing in different magnetizing fields :— 


Nickel wire (r =°5 millim., / = 30centim., T= + 60°). 


Unloaded. 
Reading of | Reading of 
S). ballistic S). ballistic 
galvanometer. galyanometer. 

“21 C 13°8 149 

"34 15 19:9 151 

71 26 17 152 
1-14 49 40-7 149 
2°01 89 48°8 145 
3°63 107 | 61-0 142 
4°74 122 756 136 
6°82 135 1100 124 
9°05 144 | 


The result is shown graphically in Plate II. fig. 1. Ex- 
amining the curve we see that the current increases rapidly 
in low magnetizing fields ; but as the magnetizing force be- 
comes greater the increase takes place very slowly, passes a 
maximum, and begins to diminish nearly in a straight line. 

On loading the wire and going through the same series of 
operations, the following readings of the deflexion were 
taken :-— 


Nickel wire (vr =°5 millim., / = 30 centim., r= + 60°). 


Loaded 3 kgs. Loaded 6 kgs. 
Reading of Reading of 
H. ballistic i. ballistic 
galvanomecer, galvanometer. 
“1A 3 1-1 ( 
10 8 36 16 
3°6 30 74 35 
6°8 64 16:8 87 
10-0 98 24-1 129 
19:9 140 31°8 146 
31°8 154 40:7 155 
41-0 159 51:0 165 
49-1 161 68:7 168 
60°6 160 85°8 167 
83:0 158 


The above readings are plotted in fig. 1, from which we 
see that although the essential form: of the curve is not 


126 H. Nagaoka on Transient Electric Current produced 


changed by loading, the maximum current is increased. 
At the same time, the point at which the current passes a 
maximum is shifted towards stronger field. The loading does 
not produce any remarkable change in the transient current. 

Similar series of experiments were performed on an iron 
wire 1:02 millim. thick and 30 centim. long (July 8, 1888). 
The following Table gives the readings taken in different 
magnetizing fields :— 


lron wire (r =°51 millim., / = 30 centim., r= + 60°). 


With no load on. Loaded 6°4 kgs. 

Reading of j Reading of 

H. ballistic H. ballistic 

galvanometer. galvanometer. 

34 18 “34 45 
ie 55 1:0 21 
18 92 2:1 36 
36 109 2°8 40 
4-7 114 4:7 AT 
6°8 108 79 50 
10-0 103 10:0 49 
20:1 74 19:2 39 
31°8 53 31:0 30 
41:0 44 41:0 24 


These and two others are shown graphically in fig. 2, A 
glance at these curves will show that the transient current 
at first increases rapidly as the field is increased, but soon 
reaches a maximum and then begins to diminish gradually. 
The application of longitudinal stress diminishes the current, 
while at the same time the maximum point is transferred 
towards higher magnetizing field. | 

Comparing the results obtained for nickel and iron, we 
notice a peculiar difference in the behaviour of these two - 
metals. The current which is produced by suddenly twisting 
the wire in the magnetizing field is, in the first place, 
opposite in direction. The direction* of the current in nickel 
is such that, the twist being applied like a right-handed 
screw, the current flows from south to north. In iron it is 
from north to south. This singular fact was also noticed 
later by Herr Zehnder. 

In the experiments hitherto described the magnetizing 
force was gradually increased, and the transient current pro- 
duced by suddenly twisting the wire at different magnetizing 


ee one + a rane. perme Se ee ae i A a Bites 5 aca sc i ope Ra 


ee 


Feiune oj 


* See Note by Sir W. Thomson appended to this paper. 


by twisting Magnetized Iron and Nickel Wires. 127 


fields was observed. There we see that both in iron and 
nickel the first increase of the field gives rise to rapid in- 
crease of the transient current. In unstretched iron this 
current attains its maximum strength at a field of about 
5 C.G.8. units. It then gradually decreases as the field is 
further increased. In nickel of nearly the same length and 
thickness as the iron this current attains its maximum value very 
slowly, so that it is difficult to ascertain precisely the strength 
of the field at which this point is reached. Moreover, this 
maximum, though not very distinct, occurs at a magnetizing 
field far greater than that for iron. 

The application of longitudinal stress produces opposite 
effects in the transient current in iron and nickel. The tran- 
sient current due to sudden twist in iron always decreases when 
acted upon by pulling stress, whereas in nickel it diminishes 
in low magnetizing field, but beyond a certain strength of the 
magnetizing force the current in stretched wire attains 
greater value than in the unstretched wire. Thus the maxi- 
mum transient current in nickel increases with the amount of 
longitudinal stress. 

The effect of pulling the wire changes, not only the amount 
of the current, but also the strength of the field at which the 
current attains its maximum value. The effect is similar in 
both iron and nickel, although the amount of shifting of 
maximum in the former is less than in the latter. 

That the transient current produced in twisting iron wire 
reaches a maximum was first noticed by Professor Ewing ; 
the method of procedure in his experiments being different from 
the one here described. He measured the current produced 
in a twisted wire by reversing the direction of the magnetizing 
force. In the present experiment the current produced by 
twisting the wire was observed. In one of Professor Hwing’s 
experiments the transient current induced in an iron wire 
34 centim. long and 1 millim. thick, and twisted through 60°, 
passed a maximum when the strength of the field was 15 or 
16 C.G.S. units. The wire used in the present experiments 
cannot be much different from the one used by Professor 
Ewing. ‘The transient current attained its maximum value 
for = 5. Whether the discrepancy between these two re- 
sults is due to the quality of iron wire or to the difference in 
the method of procedure, is a question not easily to be 
decided. 

A simple glance at the results hitherto obtained will show 
the similarity between the phenomenon here investigated and 
the Wiedemann effect. In the latter phenomenon the twist 
produced by magnetizing a circularly magnetized iron wire 


———EE———E_ 


128 H. Nagaoka on Transient Electric Current produced 


is in opposite sense to that of nickel. Moreover the 
maximum twist in iron occurs in lower magnetizing field than 
that in nickel. These facts closely resemble the transient 
current produced by twisting nickel and iron wires. In fact 
Professor J. J. Thomson* has shown that the existence of 
the Wiedemann eect necessarily leads to the production of 
electromotive force by twisting a longitudinally magnetized 
wire. According to Shelford Bidwellt the Wiedemann effect 
in iron comes out in the same sense as in nickel when the 
magnetizing force is sufficiently increased. In order to see 
if there is any such similarity in these two phenomena, the 
transient current produced in high magnetizing field was 
examined. 

Using the dynamo current, a magnetizing force of 300 or 
400 units was easily obtained, and observations made with 
nickel wire are as follows (July 11, 1888) :— 


Nickel wire (r =°5 millim., / = 80 centim.). 


| 


Reading of 

Sa ballistic Twist. 

galvanometer. 
300 5D +60 Under no load. 
409 43 +60 3 
339 66 +60 - Loaded 3 kgs. 
SYA 81 +60 phone 
333 91 +90 33) GO 


The transient current in nickel wire diminishes with the 
increase of the magnetizing force, as will be seen from the 
readings given above. Hven in a field of 300 units, the load- 
ing produces increase of the current-strength. 

With an iron wire 1°46 millim. thick and 30 centim. long, 
and twisted through 60°, the following readings were taken:— 


H. Reading. Twist. 
202 35 +60 
338 Inappreciable. +60 
404 z +60 
550 is +60 


* See ‘ Application of Dynamics to Physics and Chemistry,’ p. 70. 
+ Phil. Mag. September 1886. 


- 


by twisting Magneiized Iron and Nickel Wires. 129 


The current produced in iron wire caused an appreciable 
deflexion of the galvanometer in a field of 200 units, and in 
the same direction as for lower fields. On raising the 
magnetizing force to 300 or 400 units, no current of measur- 
able strength was produced. If the transient current becomes 
reversed in direction, the deflexion of the galvanometer 
becoming null in field of 300 units, an appreciable throw of 
the mirror should have been noticed in the opposite direction 
for 6=400 or =500. Judging from the fact that no such 
change is observed, it seems probable that the current never 
becomes reversed even by further increasing the magnetizing 
force. The current thus appears to decrease asymptotically 
with the increase of magnetizing field. Professor Ewing 
also arrived at a similar conclusion. 

The next point to be investigated was the effect of various 
amounts of twist on the transient current. There are two 
ways of examining the proposed problem. We may either 
vary the magnetizing field, while the twist is kept constant, 
and work out separately for different twists ; or we may keep 
the magnetizing force constant while the twist is made to 
vary. 

Both these cases have been tried. The first case was tried 
with iron wire of different thicknesses, and the result is 
shown graphically in fig. 8. The thinner wire was twisted 
through + 15°, + 20°, + 30°, and + 60° (September 25, 
1888). All these curves show that the current increases 
with the increase of twist. The maximum point remains 
nearly in the same magnetizing field for three small twists, 
- but is shifted toward stronger field as the twist is increased. 
A similar tendency will also be noticed in the curves obtained 
for the wire of °73 millim. radius (September 22, 1888). 
The rate of decrease of the current as the field is increased 
becomes more rapid for the thick than for the thin wire. 

Similar experiments performed on nickel wire of 0:43 
millim. radius are shown graphically in fig. 1 (dotted lines). 
They are for the twists of 30° and 60° respectively. The 
increase of the current with the increased twist is quite 
apparent, but nothing definite can be said about the shifting 
of the position of maximum transient current. After a 
certain strength of the magnetizing force, the current in- 
creases so gradually, that without very delicate measurement 
it is difficult to know exactly where the maximum point is 
situated. 


To examine how the current increases with the inerease otf 


twist, | had recourse to the second mode of investigation, @. e., 


Phal. Mog. 8. 5S. Vol. 29. No. 176. Jan. 1890. .K 


Es eee « 


1380 H. Nagaoka on Transient Electric Current produced 


changing the amount of twist while the magnetizing forceis 
kept constant. | | 

The following Table gives the readings of the first swing, | 
in weak as well as strong magnetizing fields. 


Tron Wire (r='51 millim., Iron Wire (r='73 millim., 
1=30 centim., )=2°45). 1=30 centim., H=112). 
Reading of Reading of 
ee ballistic ap ballistic 
galvanometer. galvanometer. 
a ae : -— 
10 4:0 15 o7 
15 15°9 20 61 
20 30°2 25 (gi 
25 43:4 30 9-1 
30 529 40 13:2 
40 63°5 50 16:1 
50 68:7 60 19-0 
60 (Nar 70 21°5 
ia 70 70-7 80 23°4 
ae 80 70°3 90 24-7 
hy 90 68:8 100 24°3 
The results of these and other experiments (September 
: 22-26, 1888) are plotted in fig. 4. 
iH Hxamining the curves obtained in weak magnetizing fields, 
; we notice that the transient current increases with the 


increase of twist at first very rapidly, but after passing the | 
Ht “Wendepunkt” becomes very gradual. The current ulti- 
a mately attains maximum strength, and then begins to diminish. 
; Ina strong magnetizing field the current is greatly diminished, 
a and the curve becomes less steep. The increase goes on 
| slowly with the increase of twist up to the maximum. Com- 
paring the results obtained in different magnetizing fields, 
we notice that the twist for which the current is maximum 
becomes greater as the magnetizing force is increased. In 
fact the maximum for the wire of radius ‘73 millim. occurs 
when the twist is about +60° for )=5-0, while for H=112 
the twist of 100° is barely sufficient to make the current 
reach the maximum strength. 

With nickel wire treated in the same way as above, the 
following readings were taken (October 1, 1888):— 


aa 2 : 


by twisteng Magnetized Iron and Nickel Wires. 131 


Nickel Wire (r=0°43 millim., /= 29-4 centim., H=27°'5). 


Reading of Reading of 
T. ballistic Tn ballistic 
galvanometer. galvanometer. 
ate ay Saas | ay fe) air, 

10 13 50 74 

15 21 60 77 

20 30 7U 79 

25 46 80 79-5 

30 57 90 80°3 

40 69 100 80°5 


The result is plotted in fig. 4 by dotted lines, where the 
ordinates are measured upwards for convenience, although 
they are actually below, as in fig. 1. The general feature of 
the curve does not differ much from those obtained for iron 
wires. The increase of the current beyond the ‘““Wendepunkt ”’ 
takes place very slowly, but it does not reach a maximum 
even for the twist of 100°. If the maximum exists, it must 
be for a larger angle of twist. 

Tt has been remarked by Professor Ewing that the produc- 
tion of the transient current is a natural consequence of Sir 
William Thomson’s * discovery, that solotropic stress gives 
rise to an olotropic magnetic susceptibility in iron. By 
twisting the wire, the lines of induction, originally parallel to 
the axis, are changed into helices. The component in the 
plane section, normal to the axis of wire, induces the transient 
current above described. Taking the Villari reversal into 
consideration, he also explained why the transient current in 
iron does not flow in the opposite direction, when the mag- 
netizing force is greatly increased. 

The development of eolotropic susceptibility by twisting 
the nickel wire, will similarly explain the production of 
transient current in that metal. The stress on twisting the 
wire is equivalent to extension and compression along lines 
perpendicular to the radius, and inclined at 45° to the normal 
plane section. According to the experiments of Sir William 
Thomson f and Professor Hwing f, the susceptibility in iron 


* Phil. Trans. 1878; or ‘Mathematical and Physical Papers,’ vol. ii. 
WL. c. 
t Phil. Trans. 1888, 


132. On Transient Electric Current from Iron and Nickel. 


is, by stretching, rendered less in the elongational line than 
in lines perpendicular to it. The result is that the lines 
of induction of twisted wire are no longer straight, but 
are changed into helical lines. They are inclined toward 
the direction of relatively increased magnetic susceptibility. 
The direction of the transient current will be thus deter- 
mined by that of compression. In iron, on the contrary, 
the direction of the current is that corresponding to stretching”. 
Consequently, the direction of the current in nickel must be 
opposite to that in iron. 

In nickel there is nothing corresponding to Villari reversal 
in iron. The magnetization of nickel is always diminished by 
stretching, while it is increased by compression. The conse- 
quence is that the circular component of the lines of induction 
is always on the increase as the twist becomes greater. ‘This 
will account for the reason why the transient current does 
not reach a maximum even when the angle of torsion 
amounts to 100°. 

Further investigations on the subject will be published in 
the Journal of the College of Science, Imperial University, 
Japan. 

Tokyo, Oct. 17, 1889. 


{ Note on the Direction of the Induced Longitudinal Current in 
Iron and Nickel Wires by Twist when under Longitudinal 
Magnetizing Force. By Sir W. THomson. 


To avoid circumlocutions suppose the iron or nickel wire 
to be vertical, and the magnetizing current to be in the 
opposite direction to that of the motions of the hands of a 
watch held with its face up. The undisturbed magnetization 
is downwardst. Now suppose a right-handed twist to be 


* For explanation of this see Note by Sir W. Thomson added below. 

+ Much of circumlocution is avoided, and of clearness gained, through- 
out dynamics and physics, by introducing the substantive noun ward (as 
has been done by my brother Prof. James Thomson in his lectures on 
Engineering, and in lithographed sheets put into the hands of his 
students, in the University of Glasgow) to signify line and direction in a 
line ;—that which is represented ordinarily by a barbed arrow. Taking 
advantage of this usage I now define the ward of magnetization as the 
ward in which the magnetizing force urges a portion of the ideal northern 
magnetic matter or northern polarity. By northern polarity, I mean 
polarity of the same kind as that of the earth’s northern hemisphere. It 
is that which is marked blue by Sir George Airy to distinguish it from 
southern magnetic matter or southern polarity, which he marked red. 
According to a usage condemned 300 years ago by Gilbert, but not yet 
quite dead, English instrument-makers still sometimes mark with an N 
the true south pole, and with an 8S the true north pole, of their steel bar- 
magnets. All confusion due to this unhappy mode of marking magnets 
is done away with by Sir George Airy’s red and blue. 


Geological Society. 133 


given to the wire. Its elongational spiral is right-handed, 
and its contractional spiral is left-handed. If the substance 
is iron, the lines of magnetization become left-handed spirals ; 
if nickel, right-handed. Now a downward current, in the 
downwardly magnetized wire, would, by the superposition of 
circular magnetization in the direction opposite to that of the 
hands of a watch, cause the lines of magnetization to become 
left-handed spirals. Hence the sudden right-handed twist 
induces in iron a current upwards, in nickel a current down- 
wards. Thus we have the following simple specification for 
the directions of the induced longitudinal currents in the two 
substances, without reference to “ up” or ‘‘ down.” 

From any point, P, on the surface of the wire, draw same- 
wards parallels to the current in the nearest part of the mag- 
netizing solenoid, and to the direction of the induced longi- 
tudinal current. Draw a helix through P making an acute 
angle with each of these lines. ‘This helix is of same name 


as the elongational helix for iron, and as the contractional 
helix for nickel.—W. T., Dec. 21, 1889. | 


XI. Proceedings of Learned Societies. 
GEOLOGICAL SOCIETY. 


[Continued from vol. xxviii. p. 493. ] 


November 20, 1889.—W. T. Blanford, LL.D., F.R.S., President, 
in the Chair. 


ee following communications were read :— 
1. “On the Occurrence of the Striped Hyena in the Tertiary 
of the Val d’Arno.” By R. Lydekker, Esq., B.A., F.G.S. 


2. ‘The Catastrophe of Kantzorik, Armenia.” By Mons. F, M. 
Corpi. 

The village is 60 kil. from Erzeroum, and 1600 metres above sea- 
level. Subterranean noises and the failure of the springs had given 
warning, and on 2nd August last part of the “ Eastern mountain ” 
burst open, when the village, with 136 of its inhabitants, was 
buried in a muddy mass. 

The author described the district as formed of Triassic, Jurassic, 
and Cretaceous strata, subsequently broken up and torn by granitic, 
trachytic, and basaltic rocks, which overlie or underlie the Secon- 
dary rocks, according to the nature of the dislocation. 

The flow was found to have a length from east to west of 7-8 kil., 
with a width ranging from 100 to 300 metres, and the contents were 
estimated at 50,000,000 cubic metres. It appeared as a mass of 
blue-grey marly mud, which, after the escape of the gases, soli- 
dified at the top; the inequalities projected to the extent of 10 
metres. The site of the village was marked by an elevation of the 


ere re 


134 Geological Soctety :— 


muddy mass, some of the débris of the houses having been carried 
forward. The lower part of the flow was still in a state of motion, 
and earried forwards balls of marly matter. 

It was difficult to approach the source of this flow on account of 
the crevasses in the side of the mountain. An enormous breach 
served as the orifice for the issue of the mud, which emitted, it was 
said, a strong odour. The violent projection of this marly liquid 
and ‘‘ incandescent ” (?) mass had carried away a considerable por- 
tion of the flanks of the mountain, whose débris might be recognized 
on the surface of the flow by the difference of colour. Great falls 
were still taking place, throwing up a fine powder which rose into 
the air like bands of smoke. There were also fissures and de- 
pressions of the ground at other localities in the neighbourhood. 


3. “On a new Genus of Siliceous Sponges from the Lower Cal- 
careous Grit of Yorkshire.” By Dr. G. J. Hinde, F.G.S. 


December 4.—W. T. Blanford, LL.D., F.R.S., President, 
in the Chair. 


The following communications were read :— 
1. “On the Remains of Small Sauropodous Dinosaurs from the 
Wealden.” By R. Lydekker, Esq., B.A., F.GS. 


2. “Ona peculiar horn-like Dinosaurian Bone from the Wealden.” 
By R. Lydekker, Esq., B.A., F.GS. 

3. ‘The Igneous Constituents of the Triassic Breccias and Con- 
glomerates of South Devon.” By R. N. Worth, Esq., F.G.S. 


During the investigation several hundred fragments were exa- 
mined, the largest occurring at Teignmouth, between which place 
and Dawlish the breccias are most varied in composition, and con- 
tain the greatest proportion of granitoid rocks. The igneous 
fragments were thus divided :—I. Granites ; II. Felsite group: a, non- 
schorlaceous, 6. schorlaceous; Il]. Andesitic group; IV. Miscella- 
neous. Of these, including in all 76 varieties, I., II. 6, and IV. 
are plainly of Dartmoor origin in gross, the schorlaceous and con- 
tact-altered rocks having belonged to the outer or to an upper zone ; 
III. can for the most part be identified with the zn-sztu “ felspathic 
traps ” of the neighbourhood. The non-schorlaceous division of II. 
differs but little from Dartmoor elvans; some may have been sur- 
face-portions of felsitic dykes, or even fragments of felsitic lavas. 
The igneous fragments of the breccias, as a rule, are not much altered 
structurally ; they are of local origin. 

The large blocks indicate the vicinity of high land abutting on a 
shore-line. Of this high land Dartmoorisarelic. The transporting 
power of water was perhaps supplemented by a glacial climate and 
voleanic activity. De la Beche considered that igneous action 
accompanied the earliest ‘‘red-rock” deposits. The “ felspathic 
traps” are known to be both antecedent to and contemporaneous 
with the breccias, and there is evidence which points to their being 
comprised within the period of igneous activity represented by the 
Dartmoor elvans. The author says that there isa preponderance of 


On the Glaciation of parts of Kashmir. 135 


volcanic over plutonic igneous rocks, and thinks that the existing 
remnants of ‘felspathic traps” are not sufficient to supply the 
quantity. He suggests that they must have come from an upper 
portion of Dartmoor. 

In conclusion, the author considered that he has shown that the 
igneous materials are of local origin, and that they consist of granites, 
felsites, and voleanic types, ranging from andesites to basalts ; thas 
the few igneous fragments not hitherto assigned to in-situ rocks are 
yet of a similar character ; that the conditions under which the “ fels- 
pathic traps” occur a situ lead to the inference that they are vol- 
canic phenomena which probably represent the final phase of the 
igneous activity of the Dartmoor region. Lastly, he expresses his 
opinion that the elevation of Dartmoor and the associated igneous 
phenomena took place at a period not earlier than the Permian. 


4, “Notes on the Glaciation of parts of the Valleys of the 
Jhelam and Sind Rivers in the Himalaya Mountains of Kashmir.” 
By Capt. A. W. Stiffe, F.G.S. 

After referring to the previous writings of Messrs. Lydekker, 
Theobald and Wynne, and Col. Godwin-Austen, the author gave 
an account of his observations made during a visit to Kashmir in 
1885, which appeared to him to indicate signs of former glaciation 
on a most enormous scale. 

A transverse valley from the south joins the Sind valley at the 
plain of Sonamurg, and contains glaciers on its west side. These, 
the author stated, filled the valley at no remote period, and extended 
across the main Sind valley, where horseshoe-shaped moraines, many 
hundred feet high, occurred, and dammed the river, forming a lake 
of which the Sonamurg plain was the result. The mountains which 
originated the above glaciers were described as being cut through by 
the Sind river, and the rocks of the gorge were observed to be 
striated, whilst rocks with a moutonnée appearance extended to a 
height of about 2000 feet. 

The whole of the Sind valley was stated to be characterized by a 
succession of moraines through which the river had cut gorges, whilst 
the hillsides were seen to be comparatively rounded to heights of 
2000 feet or more. 

The author had also formed the opinion that at Baramulla the 
barrier of a former lake occupying the Kashmir valley was partly 
morainic, before reading Prof. Leith Adams’s view of the glacial 
origin of some of the gravels of this point. 

The whole valley of the Jhelam from this point to Mozufferabad 
showed extensive glacial deposits, which had been modified by 
denudation and by the superposition of detrital fans, widely 
different in character from the glacial deposits. Relow Rampoor 
the valley was thickly strewn with enormous granite blocks resting 
upon gneiss, and the author believed that they had been transported 
by ice. 

In conclusion, it was noted that the existing torrential stream had 
further excavated the valley since Glacial times and, in places, to a 
considerable depth. 


P1386. =] 


XII. Intelligence and Miscellaneous Articles. 


THE MAGNETISM OF NICKEL AND TUNGSTEN ALLOYS. 
BY JOHN TROWBRIDGE AND SAMUEL SHELDON. 


Introductory. 


HE fact that different kinds of steel, alloyed in small propor- 
tions with tungsten or wolfram, and magnetized to saturation, 
increase in specific magnetism *, has long been known. Whether 
the same effect would result from the use of nickel alloyed with 
tungsten has never been investigated. This paper has for its 
object a partial answer to the query. It was instigated by Mr. 
Wharton, proprietor of the American Nickel Works, whose 
chemist, Mr. Riddle, kindly prepared the alloys which have been 
employed. These alloys were in two groups. The first, received 
in November 1888, consisted of three bars of the same shape, one 
being of pure nickel and the other two having respectively 3 and 
4 per cent. of tungsten in alloy. These bars were rolled from cast 
ingots, which were toughened by the addition of magnesium after 
Fleitmann’s method, the magnesium being added just before 
pouring. They were hot when rolled. The one of pure nickel 
was afterwards planed into regular shape. ‘Those containing 
tungsten were too brittle to allow of this manipulation. They 
were, however, of sufficient regularity to permit accurate measure- 
ments. This group contained also an octagonally shaped bar with 
8 per cent. of tungsten, which was prepared like the others, and 
was afterwards ground into shape. 

The second group, received in May 1889, contained bars which 
were simple castings, made without the addition of magnesium, 
and consisted of pure nickel and alloys with 1, 2, 3, and 6 per 
cent. of tungsten. All the bars in this group were extremely hard 
and brittle. In making them tungsten oxide, of weight calculated 
to yield the desired percentage of tungsten in the resulting alloy, 
was placed with adequate carbon in the bottom of a graphite 
crucible and covered by the proper weight of pure grain nickel. 
All was then covered with borax, the lid of the crucible was placed 
on, and the crucible was heated until reduction and fusion were 
completed. 

Method. 


As the suspected influence of the tungsten would be to affect 
the magnetic moment of the bars, these were magnetized to 
saturation and their specific magnetism then determined, 2. e., 
the magnetic moment for each gram of metal. 

The magnetization was effected by placing the bars separately 
in a hollow coil whose length was 15 centim. and outside and 
inside diameters respectively 6 and 3 centim. It consisted of 6 
layers of wire having 63 turns each. A dynamo current of 40 


* Journ. Chem. Soc. 1868, xi. p. 284, says 800 fer cent. 


Intelligence and Miscellaneous Articles. 137 


amperes was then sent through the coil for one minute, and the 
circuit then broken and the bars removed. 

For the determination of the magnetic moment, use was made 
of a reflecting-magnetometer, and deflexions were observed with a 
telescope and scale at a scale-distance of 100 centim. Measure- 
ments of the horizontal intensity, H, of the earth’s magnetism 
were first made. The results from these determinations by means 
of the first and second Gauss arrangements were, respectively, 

H=0°1724 Centim. G. 8. 

H=0-1720 i 
The freshly magnetized bars were then placed in the second Guass 
position relative to the magnetometer, and the angular deflexion 
determined. The specific magnetism, 8, was then calculated by 
the formula 


steal r° H tan @ 
mm t 
where 
7 == distance from bar to magnetometer = 72°68 centim. ; 


H = earth’s horizontal intensity = 0°1722; 
m = mass of the bar; 
@ = angular deflexion of magnetometer. 


Results. 


The mean results of two sets of observations on Group I., and 
also upon a similar bar of soft tool steel, are given in the following 
table :— 


Group I. 
Composition, Sizeincms. Massin grams. §[Cm.i G.-2 Sec.-?]. 
Pure Nickel 18 x 2:7 x 0°65 84: 1:23 
Ni+ 3p.c.W 45 - Ps 286°5 10°60 
Ni+4p.c.W es os . 283°5 10:40 
Tool Steel 15 x 25 x0°5 159°5 7:46 
Octagonal 
Ni¢8p.ew (13x15 144-0 5-25 
Group IL., of cast bars, gave the following results :— 
Group II. 
Composition. Sizeincms. Massin grams. §[Cm.2 G.-3 Sec], 
Pure Nickel 18x18x16 5) ; 
Ni+ 1p.c. W Sa Migs ees A455 1:92 
Ni+ 2p.c. W Sy east ss 454 1:70 
Ni+3p.c. W Bess hes) attdas 463 1°75 
Ni + 6p.c. W pO ETS, ce 465 115 


The bars of both groups were, subsequent to the above obser- 
vations, completely demagnetized, and then freshly magnetized. 
New determinations gave the same results as before. The de- 
magnetization was accomplished by placing the bars inside two 
coils, which were traversed by currents from an alternating 
dynamo. The coils were then slowly drawn apart, and the bars 
maintained at a position central between them. After treatment 


Phil. Mag. 8. 5. Vol. 29. No. 176. Jan. 1890. L 


— 


138 Intelligence and Miscellaneous Articles. 


in this manner, they showed no appreciable deflexion when placed 
in position relative to the magnetometer. 

The results tabulated indicate that tungsten greatly increases 
the magnetic moment of nickel, if the alloy be forged and rolled, 
but, on the other hand, has but small influence if it be simply 
cast. Furthermore, changes in the amount of tungsten do not 
appear to cause corresponding changes in the magnetic properties. 

To see whether the remarkable effect in bars 2 and 3, as com- 
pared with bar 1, of Group I., was owing to some molecular 
condition of their surfaces induced by rolling, two bars from the 
same steel, one rolled and the other pressed, were magnetized and 
then measured. The ratio of the specific magnetism of pressed to 
rolled was as 9 to 5, the rolled having the smaller amount. The 
existing difference, in this case, is probably owing to a differe.ice 
in hardness rather than to any molecular condition of the surfaces, 

The specific magnetisms of all the bars are small when compared 
with good steel magnets. Kohlrausch says that good magnets of 
common form should have S=40. The bar of ordinary tool steel, 
however, retained but 7°46. Still it was soft, and by tempering 
would doubtless have doubled this value. 

If forged nickel and tungsten can be made to maintain a specific 
magnetism of 10, it will form a useful addition to the resources of 
physical laboratories. From the high polish of which it is suscep- 
tible and its freedom from damaging atmospheric influences, it will 
be most hapily suited for the manufacture of mirror magnets where 
magnetic damping is to be employed.—Silliman’s American Journal 
of Science, December 1889. 


NOTE ON THE APPLICATION OF HYDRAULIC POWER TO MER- 
CURIAL PUMPS. BY FREDERICK J. SMITH, M.A., MILLARD 
LECTURER, TRINITY COLLEGE, OXFORD. 


In vol. xxv. p. 313, 5th series, Phil. Mag., a description is given 

of the application of hydraulic power to the working of mercurial 
umps. 

: ae the paper was written the author has ceased to use rubber 

tubes, and has, in their place, introduced flexible tubes made of 

steel. As the alteration has proved itself to be satisfactory, and 

may be of use to those who work with mercurial pumps, or similar 

apparatus, he ventures to add this note. 

The steel tube is made by the Flexible Metallic Tube Co. in 
the form of a hollow screw, or tube on which a screw-shaped 
indentation has been impressed. The outcome of the construction is 
that while the tube is under a great pressure it is quite flexible, 
behaving itself in much the same way as a strong rubber tube, with 
the advantage over the latter of being durable when subject to, 
constant motion. Several pieces of tube, made of steel and bronze, 
have been tested up to 200 lb. per square inch, without showing 
any signs of being injured. These have been used in the labora- 
tory for connecting together vessels which are subject either toa 


Intelligence and Miscellaneous Articles. 139 


high pressure or a vacuum. Sometimes the tube has been used 

for liquids which act upon the metal it is made of; when this has 

been the case, a rubber tube has been threaded through the metal 

tubes, so as to form a protective lining. 

ON EVAPORATION AND SOLUTION AS PROCESSES OF 
DIFFUSION. BY PROF. J. STEFAN. 


In a paper published in 1873 the author described experiments 
which he made on evaporation from narrow tubes. Those obser- 
vations led to the law that the velocity of evaporation is inversely 
proportional to the distance of the surface from the open end of 
the tube. The application of the theory of the diffusion of gases 
to this process led to the same law, and at the same time furnished 
a complete determination of the velocity of evaporation, which 
reuders it possible to calculate the coefficient of diffusion of vapours. 
These experiments have been extended by Winkelmann to several 
series of liquids, and have been used to determine the coefficients 
of diffusion of their vapours. 

Similar experiments to those on evaporation may be made on the 
solution of solids in liquids. A rectangular prism of rock-salt 
was made ; its height was 30 millim., and the two other dimensions 
were 7 and 9 millim. Glass plates were cemented by Canada 
balsam to the bottom and sides, so that only the top surface of the 
prism was free. In ore of the glass plates a scale is etched. If 
the prism, with its top upwards, is immersed in a large vessel of water, 
its solution takes place from the top and the process can be 
observed on the scale. After 1, 4,9, 16 days the solution had 
extended to 6°3, 12°6, 18°8, and 25 millim. ‘These depths areas the 
square roots of the times. Hence for this process the law holds 
that the velocity of the solution is inversely proportional to the 
distance of the rock-salt surface from the open end of the prism. 

If such a prism is dipped with the free surface downwards, the 
solution proceeds with almost uniform velocity. In one hour 17:1 
and in 14 hours 25:6 millim. were dissolved. A prism of a metre 
in magnitude requires for its solution from upwards 70 years, and 
downwards 23 days ; the former times increase with the magnitude 
in a quadratic, and the latter in simple ratio. 

Experiments of the first kind may be used for investigating the 
diffusion of salts through their solvents. It is necessary for this 
to represent the process in a form which can be calculated from 
the theory of diffusion. This gives a new method for determining 
the coefficient of diffusion of salts. The method is not restricted 
to such bodies as can be obtained in large crystals. If a uniform 
mixture or a magma is formed of the powder and its saturated 
solution, and if a graduated tube is filled with it, the progress of 
the solution can be as well observed by it as with a prism of rock- 
salt. The law in this case is the same as in the former ease, 
though the absolute value of the velocity with which the plane of 
separation of the solution and of the magma moves downwards 


140 Intelligence and Miscellaneous Articles. 


is greater, and the more so the smaller the quantity of undissolved 
salt in the magma. 

The mathematical part of the paper consists of four divisions. | 
In the first, the equations of the theory of diffusion of gases 
are developed. In the second, they are applied to evaporation. 
The solution of this problem in the former paper was only an 
approximate one, yet quite sufficient for calculating the experi- 
ments. In the present paper the exact solution of the problem 
is communicated. Their establishment forms a fresh application 
of the equations which the author has developed in the theory of 
the formation of ice. In the third section the differential equations 
of the diffusion of gases are transformed into the equations which 
serve for calculating the diffusion of liquids. The last section 
contains the applications of these equations to the calculation of 
experiments on diffusion.— Wiener Berichte, Nov. 21, 1889. 


ON THE CHANGES OF TEMPERATURE RESULTING FROM THE 
TORSION AND DETORSION OF METAL WIRES. BY DR. A. 
WASSMUTH. 


In the year 1878 Sir W. Thomson (Phil. Mag. vol. v. p. 19) 
deduced from the mechanical theory of heat the principle that a 
twisted wire must become cooled when the torsion is suddenly 
carried further. 

In the above research it is proved for iron, brass, and particularly 
for steel that the phenomenon in question actually occurs; and the 
opposite one on detorsion, that the cooling or heating increases 
with the angle of rotation, and that the change of temperature 
observed for a steel wire agrees very well with the calculated one. 

In these experiments thermoelements were soldered to six steel 
wires connected with each other by pieces of wood, and slightly 
stretched horizontally, in such a manner that this wire arrangement 
could both be stretched and twisted. It was possible in this way 
to compare the very small changes of temperature on torsion and 
detorsion with the much larger ones due to stretching, and which 
indeed can be done in two ways. For the cooling @ which occurs 
on the torsion of a wire of length 7 from the angle w, to w, it was 
calculated 


2 2 
gai, Bt luinu, 
EO Apa er ort oe 
in which m was the weight, 7 the radius, SEED the modulus of 


torsion, T0! its relative decrease with the absolute temperature 7, 


c the specific heat of the wire, and J the mechanical equivalent 
of heat. There was thus obtained for 6, 

Calculated 195:10-5 of a degree Centigrade ; 

Observed 191°10-4 - ks me 
Several further experiments likewise showed agreement with what 
has been said.— Wiener Berichte, Noy. 7, 1889. 


tS C10) 


LONDON, EDINBURGH, ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] 


in Bere Cee ae ESO. 


XII. The Pressure-Variations of certain High-Temperature 
Boiling-Points. By Cart Barus *. 


t. i the following pages I briefly describe a practical 

method for the calibration + of thermocouples by aid 
of boiling-points, and then apply it in measuring the vapour- 
tensions of zinc, cadmium, and bismuth. During the course 
of the work a neglected principle of Groshans{ is advan- 
tageously employed. I must state at the outset that it is not 
the object of this paper to furnish accurate values for boiling- 
points. My purpose is to investigate the probable nature of 
the relation of boiling-point to pressure, throughout very 


* Communicated, with the permission of the Director of the U.S. 
Geological Survey, by the Author. 

+ The literature of the subject, which is very voluminous, may be 
omitted here, because I give a full account of it in the Bulletin of the 
U.S. Geological Survey, no. 54, pp. 28 to 55, 1889. Among recent 
authors H. Le Chatelier (cf. Bull. Soc. Chim. Paris, n.s. xlv. p. 482, 
1886; zd. xlvii. pp. 2, 300, 1887; C. R. cil. p. 819, 1886; Jorn. de 
Physique, vi. p. 23, 1887, and elsewhere) is particularly active in pro- 
moting thermoelectric high-temperature research. In the ‘ Bulletin’ 
I describe methods of standardization by aid of boiling-points (pp. 84 to 
125), and by direct comparison with Deville and Troost’s porcelain air- 
thermometer (pp. 165 to 248). I also submit an independent method of 
my own, based on the high-temperature viscosity of gases (pp. 248 to 
306). Experiments made conjointly with my colleague, Dr. William 
Hallock, on capacious high-temperature vapour-baths, are discussed in 
another part of the ‘ Bulletin’ (pp. 56 to 83). 

t Groshans, Pogg. Ann. Ixxviu. p. 112, 1849. 


Piul, Mag. 8. 5. Vol. 29. No. 177. Feb, 1890. M 


142 Mr. Carl Barus on the Pressure- Variations of 


wide ranges of temperature, with the hope of stimulating 
speculations on the subject, somewhat more rigorous than that 
of Groshans (§16). It is clear that if a law can be found by 
which the normal (76 cm.) boiling-point of a substance can 
be predicted from an observed low-pressure boiling-point, 
then a more complete knowledge of high temperature boiling- 
points can be arrived at than is now available. More than 
this: by varying pressure, boiling-points of different metals 
may be made to overlap each other. Hence a thermocouple 
calibrated as far as the boiling-point of zinc, for instance, 
may be used to measure a low-pressure boiling-point of bis- 
muth (say) ; and the couple then may be further calibrated 
by the normal boiling-point of bismuth, predicted by aid of 
the law in question. The process may obviously be repeated. 
The couple whose calibration interval has been enlarged in 
the manner given may now be used to fix the low-pressure 
boiling-point of some other suitable metal, and then in turn 
be further calibrated by aid of its boiling-point. The limit of 
such a method is the fusibility of platinum. The fact that at 
high temperatures the vapours to be used will be either mon- 
atomic or diatomic enhances the interest of the project (cf. 
Biltz and V. Meyer, § 15, below). 

2. The platinum /iridio-platinum thermocouple used in 
this work had on another occasion* been tested for poly- 
merization anomalies, by minute comparison with the porce- 
lain air-thermometer, and between about 400° and 1300° 
none were found. ‘The alloy contained about 20 per cent. of 
iridium. Unfortunately I could not avail myself of the former 
air-thermometer comparisons, nor was it expedient to repeat 
the work. M. Le Chatelier t rejects the iridio-platinum 


couple because of irregularities of the kind referred to. Dr. | 


Hallock and I have also found them pronounced in other 
iridio-platinum couples {. In the present couple slight irre- 
gularities between 350° and 450°, equivalent to about 5°, had 
to be allowed for. When the range of temperatures is very 
large, the Avenarius-Tait equation is insufficient ; but this 
equation subserves a good purpose when interpolations be- 
tween two fixed temperature-data are called for, the data lying 
anywhere on the scale, but not too far apart. 


Apparatus. 
3. Boiling-points below 500° may be studied in a closed 


glass tube, aaaa, fig. 1, within which a thin-walled tube, dd d, 
open at both ends, passes coaxially quite through. Jn the 


* Bull. U.S. Geol. Survey, no. 54, p. 208 e¢ seg., 1839. 
+ Le Chatelier, 7. c. 
¢ Bull. U.S. G. 8S. no. 54, pp. 80, 114 e¢ seg., 1889. 


certain High-temperature Boiling-points. 143 


bottom of the annular space between the tubes, the ebullition 
liquid, & k, is placed, and it is heated by Wolcott Gibbs’s ring- 


Fig. 1.—Longitudinal section of boiling-point tube. Scale 3 to 3. 


\ 
\ 
N 
i\ 
N 
x 
\ 
\ 
\ 
\ 
\ 
~ 
N 
N 
\ 
\ 
\ 
\ 
\ 
N 
N\ 
\ 
N 
NY 


SS SSAA FESS SSS SE SASS SEE ELE ASRO 


burner, 77. A conical asbestos screen, nn, protects the 
upper part of the tube from direct radiation. Other screens 


M2 


fre re Bihe ayTe 
3 alle; ; 


144 Mr. Carl Barus on the Pressure- Variations of 
and jackets, pp pp, are suitably added. The upper end of 


the tube, aaaa, is in communication with the air-pump, 
through the lateral tubulure h. Finally, to obviate breakage, 
the lower end of the tube is protected by a metal jacket, mm. 

The thermocouple to be calibrated, « 0 8, is introduced into 
dd from below, and raised until the junction o is slightly 
above the plane of ebullition of the liquid, kk’. The upper 
part of the tube is closed with asbestos wicking (not shown) 
as far down as o. The wires of the couple pass through 
parallel canals in a rod of fire-clay, xy, and are thus well 
insulated. The boiling-points of most organic substances, 
mercury, sulphur, &., are conveniently obtained in this way, 
provided the pressure be not too low (§§6,7). The vacuum 
boiling-point of cadmium is also easily reached. In general, 
boiling may be kept up for any length of time—often a great 
desideratum. If the substance kk be very volatile, like 
methyl alcohol for instance, a condenser is added at h. By 
using diphenylamine and a thickly jacketed tube, I found no 
difficulty in keeping the whole column (80 em. long) at 
a practically constant temperature (310°). When normal 
boiling-points (76 cm.) only are wanted, it saves breakage to 
leave the tube aaaa open above, and to close it with a 
cork *. 

4. In the case of boiling-points above 500° it is more conve- 
nient to use glazed porcelain or fire-clay crucibles, resembling 
uebbfa, fig. 2. In some forms I run the central tube bcd 
quite through the crucible, so as to project at the lid; but 
this makes the apparatus very much more fragile. Usually 
the closed tube 66 of the figure is satisfactory. The ebul- 
lition liquid is shown at kk, and the thermocouple «o£ is 
again introduced from below. dd is the fire-clay insulator. 
To vary the pressure under which boiling takes place, the 
tube a is connected with an air-pump. Finally a tight joint 
at ef is secured by calking with asbestos fibre, and then filling 
up the annular space left above the asbestos with fusible 
metal. 

The crucible aebbfa is amvednded by a small furnace of 
Fletcher’s composition, F F FF, and heated by one or more 
blast-burners, AB. Products of combustion escape at D. 
If the flame impinges directly on the cold crucible the latter 
is apt to get broken ; but such breakage may be prevented by 
surrounding the crucible with a conical shell of asbestos. 
Unfortunately crucibles can be used but once, for they are 


* For details of construction, manipulation, degree of constant tem- 
perature, burner, insulators, &c., see the ‘ Bulletin’ (54) cited, pp. 80 to 
89, 94 to 97. 


certain High-temperature Boiling-points. 145 


usually fractured by the cone of solidified metal 4 k on heating 
a second time. Any single ebullition, however, may be 
Fig. 2.—Longitudinal section of boiling-point crucible. Scale 4. 


a 


1) See ee eee we es ee 


ey IF 
4 
Wf 
Gj 3 


IAL 


I 


prolonged almost indefinitely, that is half a day or more. 
found no serious difficulty in obtaining vacua of two or three 


- * ¥ erat 
> fey hg if ‘ 
% a ig 
a we 
4 t 


146 Mr. Carl Barus on the Pressure- Variations of 


millimetres, at extreme white heat. The crucible must be 
well glazed internally ; and it is probable that the work will 
be facilitated by using tubular forms made in a single piece, 
2. €. without the joint ef. In such a case the crucible ebb fa 
may be reduced in size, and placed wholly withzn the furnace, 
the tube a leading out of it. The charge will then be more 
effectually heated. A charge of granulated metal is easily 
introduced through a. When normal boiling-points are 
wanted, smaller crucibles of fire-clay are preferable *. 

5. The thermoelectric powers can best be measured by a 
null-method, in which the thermoelectric constants are 
expressed in terms of a given Latimer-Clark’s cell. Recali- 
bration is then rarely necessary, and calibrations made at 
different times may be compared. But the adjustments and 
computations, if they occur in great number, are incon- 
venient. In this respect the torsion-galvanometer } offers 
decided advantages. I constructed an apparatus of this kind 
in which the thermoelectromotive forces are directly ex- 
pressed in terms of the twist of a platinum fibre. 

The description of the galvanometer must be omitted here. 
Its chief points are an astatic, aperiodic magnetic system, 
the needles (two bundles of four each) of which are of glass- 
hard steel, consecutively annealed at 100° in order to secure 
stability both against changes of temper and of magnetiza- 
tion ft. The instrument is 135 cm. high, and is read off by 
the observer standing. The magnetic moment of each needle 
(10 cm. long) being intense, only a moderately thin platinum 
fibre (-018 cm.) suttices ; and as the needles are brought back 
to the fiducial zero of the instrument by torsion of the wire, 
the directive effect of the terrestrial or local magnetic fields 
is quite eliminated. The torsion-circle is sharply divided in 
single degrees ; the fractions are read off by telescope and 
scale, a mirror being attached to the needle. Both telescope 
and scale are compendiously fixed to the galvanometer. 
Thermoelectromotive forces are therefore expressed in terms 
of a fixed standard, the torsional rigidity of the platinum 
wire, and hence they are comparable even after the lapse of 
time. Any temperature between 100° and intense white heat 
may be measured without further adjustment. These desi- 
derata, added to convenient manipulation and the durability 


* For details, particularly with regard to superheating, see Bull. U.S. 
G. 5S. no. 54, pp. 89 to 94. 

t The priority of adapting Coulomb’s torsion-balance for thermo- 
electric measurement is due to Schinz (Dingler’s Journal, clxxv. p. 87, 
1865 ; ibid. clxxix. p. 436, 1866). Cf. Bull. U.S. G.S. no. 64, p. 48. 

t Cf. Strouhal and Barus, Wied. Ann. xx. p. 683, 1880; or Bull. U.S. 
G. 8. no. 14, chap. vi. 1885. 


certain High-temperature Bowling-points. 147 


of the instrument against wear and tear, constitute the advan- 
tages of the galvanometer constructed. 

M. Le Chatelier * recommends the Deprez-D’Arsonval gal- 
vanometer. 

From what has been stated, if D be the twist corresponding 
in a given instrument to the temperatures T and ¢ of the 
junctions of the given thermocouple, D=a (T—t) +6 (T’—?’). 
Again, if d=a (t—20)+6 (?— 207), it follows that 


Dev == d=a(T—20) + b(T?—20°). 


Hence a small table for d is to be computed, for tempera- 
tures t between 10° and 35°. A short preliminary calibration 
suffices for the purpose. In this way the observer may at 
once deduce Dy) from D, where Dy is a function of T, the 
temperature of the hot junction only. By aid of known 
melting-points (Le Chatelier), or boiling-points (water, mer- 
cury, sulphur, cadmium, zinc, bismuth), the quantity Do) may 
then be graphically constructed as a function of T. Inter- 
mediate points between two consecutive boiling-points, T, 
and T., are filled in by using the constants of the equation 


D,—D,=a a — T;) + b (T,? —T,’). 


From a chart of this kind, the temperature T corresponding 
to any twist D is taken with facility. 


Observations. 


6. In the above apparatus the normal boiling-point (76 
centim.) of mercury is sharply determinable; but there is 
considerable difficulty in determining the low-pressure boiling- 
points. Unless the heat be regulated to a nicety, the lower 
layers boil under the pressure of the upper layers. Again, 
since the agitation of the mercury nearly ceases in approxi- 
mate vacua, a flame of reasonable intensity presupposed, the 
rate of evaporation is much decreased. In the case of a 
liquid of small specific heat, of relatively large cohesion, 
films of which do not adhere uniformly to glass, it is there- 
fore to be suspected that both liquid and vapour will be super- 
heated in relatively very large degree at low pressures. If the 
flame be intensified so as to produce violent ebullition at low 
pressure, the liquid can be superheated to such an extent that 
its direct radiation on the junction of the thermocouple may 
increase its temperature as much as 10° above the boiling- 
point. 


* Le Chatelier, Se’ziéme Congrés Soc, Industr. du gaz, 1888. 


148 Mr. Carl Barus on the Pressure-Variations of 


Accordingly [ was not surprised to find that the tempera- 
tures obtained in the static method by Regnault, Hagen, 
Hertz, Ramsay and Young™, are as a rule decidedly below the 
corresponding boiling-points of the present dynamic method. 
It is only by taking great pains in the adjustment of burner 
and apparatus, that my temperatures began te coincide with 
those of Regnault. But this nice adjustment introduces 
arbitrary conditions; hence the low-pressure boiling-points | 
of mercury are to be rejected. At high pressures the un- 
satisfactory circumstances mentioned fall away, and the rate 
at which boiling-point changes with pressure is very much 
reduced. Fig. 3, § 15, will show the difficulties which I 
strove to overcome ; but as my data, even in the final work, 
are not of exceptional accuracy, I will omit them here. 

7. The behaviour of sulphur is peculiar. On removing 
pressure to about 1 centim., the substance passes into the 
treacle state, and the full ebullition observed under atmo- 
spheric and other pressures changes into sticky frothing. 
Hxact temperature data cannot therefore here be expected. 
The following Table is an example of the earlier results 
obtained, P being the pressure in centimetres of mercury, 
and T the correspending boiling-point in degrees Centigrade. 


= 


TaBLE £.—Boiling-points of Sulphur. 


P. 7. P. T. P. T. 
eentim.| °C. centim. oC. centiin. ce: | 
0 218 48 298 21-2 374 | 
| | 
0 205 70 316 || 398 410 | 
24°) 263 | Tne 4 887°) 1 76-07 eg 
! 


The next Table contains results of a later date, in which 
much care was taken to guard against the difficulties men- 
tioned. Dy, the twist in degrees of arc, has been added to 
show the sensitiveness of the torsion-galvanometer. 


* Ramsay and Young, Journ. Chem. Soe. xlix. p. 37, 1887; Landolt 
and Boernstein’s Tables, p. 58 (Berlin, Julius Springer, 1883). I may 
advert in passing to the discussion between Ramsay and Young and 
Kahlbaum. The former, corroborating Regnault’s law, maintain that 
vapour-tensions, whether obtained by the static or the dynamic mode of 
measurement, are identical. Kahlbaum claims to have found a differ- 
ence, and he is sustained by O. Schumann (Chem. Ber. xviii. p. 2085, 
1885). Both authors make use of Landolt’s vapour-tensions. 


certain High-temperature Boiling-points. 149 


TaBLE [].-—Boiling-points of Sulphur. 


i. Dy: a. xT. lee Die oy x T. 
centim. a cc: 20. centim. 3 ae: 2 ¢: 
79°84 | 27-976 | 446 448 655 | 18°30 316 324. 
55°36 | 26°57 428 429 4:06 | 16°80 295 305 


55°41 | 26°59 429 429) || ————— | —_—_| —_—__}— —- 
54:75 | 26°49 427 428 75:87 27°999| 448 448 
48°30 | 25°87 420 422 30°69 23°65 389 396 
47°78 | 25°64 416 421 30°70 23°65 389 396 
37°59 | 24-51 402 407 13:01 20°18 342 bo4 
37°57 | 24:39 399 407 12:93 20°18 342 354 


28°67 | 23°44 386 393 5°61 17°28 302 317 
28:80 | 23°51 387 394 5°91 17°51 305 320 
20°68 | 22:23 370 376 6:14 17°62 306 321 
20°70 | 22:25 370 376 3°29 15°55 278 295 
14:37 | 20°76 349 358 3°44 15:51 277 297 
14:49 | 20°73 348 399 1-67 11-21 228 275 
11:15 | 19°66 339 346 1°39 11:85 | +2238 266 
125 19°77 336 347 1:05 11°33 | +215 260 


GLP | 718'05 313 | 32] 0-75 10:76 | +206 252 
6°35 | 18°20 315 | 323 


| 
\ 


* Extrapolated by Regnault-Bertrand’s formula. + Sulphur sticky. 


These results agree fairly well with those of the earlier 
Table. I have added values of T extrapolated graphically § 
from Regnault’s data by aid of the Dupré-Bertrand equation 
(§ 12) log p = 19710740 — 4684-49/0 — 3-40483 log 6, which 
holds between @ = 663 and @= 843 absolute degrees Centi- 
grade. It will be seen by comparison of my values with the 
data predicted by this formula that there is much error at low 
pressures. 

8. Table ILT. contains data of four sets of experiments with 
zine. ‘The first of these were made in the glass tube (fig. 1) 
at low pressure. Although in this case there was profuse 
volatilization, I did not observe any ebullition. In the table 
the result marked x is the only datum of this work inserted. 
Change of temperature with pressure was not obvious. The 
remaining data of this part of the table are legitimate and 
were obtained from crucible experiments (fig. 2). The 
criterion of boiling-point is change of temperature with 
pressure. In the second and third parts of the Table, I aimed 
at greater accuracy. Hach of the values given is a mean of 
two or three distinct measurements. + refers to low position, 
and { toa high position of the thermocouple in the central 
tube bcd, figure 2. 


§ I computed the inferior prolongation of the curve, and plotted the 
results. From the chart the values of T were taken correct to I degree. 


150 Mr. Carl Barus on the Pressure-Variations of 


TaBxie I11.—Boiling-points of Zine. 


1B pT 1e mT, P, 4 ip 
centim. ClO: centim. OC. centim. dt Os 
1:0 582 4-2 710 26 675 
—|—— 3°5 699 6°7 Tol 
40 710 | SS 684 || 15°8 792 
6°5 732 6:2 736 26°4 833 
9°6 [57 9:9 758 37:5 864 
1071 772 166 802 47°3 884. 
156 78 26°4 838 57:0 Y04 
27°71 837 36°8 863 65:4 916 
34:5 857 ATT 884 WICA 933 
42:5 873 SOT 900 
53-5 897 65°3 914 | 
76:4 933 his +928 
| Mle 1922 | 
| \ 


9. Table IV. contains three sets of experiments with 
commercial cadmium, the first of which were made in the 
glass tube. Hbullitionin vacuum was obvious ; but inasmuch 
as the limit of heating-power of the ring-burner is not much 
above 500°, the remaining thermal data are too low. 

The experiments of the 2nd and 3rd parts of this table 
were made in the porcelain crucible. They are legitimate ; 
change of temperature taking place with every change of 
pressure. I was unable to make the crucible satisfactorily 
tight. Mean values of somewhat varying pressure had to 
be inserted. Again, cadmium is more easily superheated than 
zinc, so that the present temperatures are probably high. 
Repetitions of the experiment failed from breakage of the 
crucible. 


TasiE LV.-—Boiling-points of Cadmium. 


P. Tee opel tes mn B: ris 
centin. OT | centim. ONCE centim. S13 
00 444 Ee ah 702 6:3 606 
2°75 526 29-2 706 8-4 622 
5:25 549 35°95 724 226 686 
7°70 562 > Biseil 729 27°4 704 
aS ee |, 48:9 745 ; 84-2 G22, 
De, 549 yal af 750 | 51-0 752 
DiS 552 62:4 760 563 760 
2°6 565 64-4 766 63°6 770 
372 574 65°6 766 65 6 772 
We 620 756 772 TaD 786 
10°5 639 hy af O10 770 15:5 788 
apes 667 i 7x 7174 75°5 781 
189 681 || 


certain High-temperature Boiling-points. 151 


10. Table V. contains results for bismuth. In the first 
part of the Table temperature does not change with pressure. 
Hence a boiling-point is not reached. In the second part of 
the Table temperature certainly oscillates with pressure. 
Hence the temperature corresponding to the lower values of 
pressure (3 centim. to 4 centim.) are boiling-points. The 
temperature corresponding to the higher values of pressure 
(9 centim. to 10 centim.) are below the corresponding boiling- 
points ; for I found that on further increasing pressure the 
temperature did not increase. The temperatures observed 
are therefore the limit of the heating-power of the furnace. 
At least 5 minutes must be allowed for each observation. 
The top of the crucible should be filled with asbestos to 
diminish loss of heat by radiation. 


TaBLE V.—Boiling-points of Bismuth. 


P. si be PP TT, Regan 2 mT. 
ee || Je 5} tees) SE eos 4 

centim. OR centim., Oe: centim. ZC 
2-6 1152 3:2 1199 9-5 1236 
5:8 1164 || 86 aT! 3-4 1207 
2-6 1165 9-7 1207 4-0 LY 
8-1 te2) i | 3:2 1206 9-7 1260 
8-8 1186 Bi On alle 3:4 1206 
2-7 1188 || 42 1915 5 ell <3 -9 1221 
9-8 1194 3:7 1247 || 96 +1258 
9-4 Mise | 3:9 1213 3:3 1215 
3:4 1204 4-9 1233 


* Flame intensified ; B.P. criterion satisfied. 
Tt Limit of burner-power. 


11. In the above Tables I. to V., the criterion of boiling- 
point has been change of temperature with pressure. When 
this was not observed the data were rejected. The method 
of obtaining low boiling-points from liquids is @ priori ob- 
jectionable, because of the liability to superheating. In 
special measurements made with zinc*, however, I found the 
error thus introduced to be negligible. There seems to be 
less superheating in case of metals and high temperatures, 
supposing the temperature of the environment to be reason- 
ably near the boiling-point (say 200° or 300° above it). In 
case of bismuth and metals of higher boiling-points, the 
difficulties of experiment are such that I do not think a 
capacious vapour-bath for low pressures feasible. 

Experiments with antimony failed from breakage of 
crucible. 

* Bull. U.S. G.S. no. 54, pp. 108, 109, 1889. 


152 Mr. Carl Barus on the Pressure- Variations of 


Inferences. 


12. Equations expressing tension of saturated vapour in 
terms of temperature have been invented in great number. 
Among them the simple form of Magnus and the more elaborate 
exponential due to Biot, and applied by Regnault, are given 
in most text-books. A remarkably close-fitting exponential 
is investigated and tested by Bertrand*. Quite recently 
M. Ch. Antoinet has devised and applied a new form. 
Following the early suggestions of Bertrand} and of J. J. 
Thomson §, I have used the equation of Dupre |, 

log p= A— B/O— Clog 0, . i: Gaeeeeey 
where p and @ are corresponding values of pressure and 
boiling-point in absolute degrees Centigrade, and A, B, and 
C are constants. Hquation (1) has been independently 
interpreted by Thomson. Its immediate meaning appears 
more clearly in the differential form 


dp/d0= —p(C/@— BYa); 


d0/dp =(@/p):(1/B/(L—@C/B’)), 
with reference to which it is to be observed that O/B’ is a 
small quantity. 
Applying equation (1) to the results of the Tables I. to V., 
I found the following set of constants by direct computation. 


or 


TasLe VI.—Constants for Boiling-point and Pressure. 


| | 

| Metal. A. B. C. 
Sulpliie * c4aceveaters —3d°969 — 3661 —13:066 
| Cadmuunin, A0--. ree — 30°567 + 13891 —11:180 
| 

| 


VEEL OS eRe ene ne | +42°265 | +11435 +10:022 


pi eee ee Se Smee eee 
* When these constants were computed, the data of Table I. only were in 
hand. 


The results are irregular, even as to sign. Other direct 
methods gave similarly irregular constants, which need not 


* Thermodynamigue, pp. 104 to 162 (Paris: Gauthier-Villars, 1887). 

t C. R. cvii. pp. 681, 778, 836, 1888. 

{t ZL. c. pp. 90 to 102. 

§ ‘ Application of Dynamics, &c.,’ pp. 158 to 161 (Macmillan, 1888). 

|| Théorie mécanique de la chaleur, pp. 96 to 120 (Paris: Gauthier- 
Villars, 1869). 


certain High-temperature Boiling-points. 153 


be entered here. Little can be learned from them, as might 
have been expected. ‘To get comparable values for the con- 
stants of a complex equation, the data must either be very 
fine or in great number. 

13. Bearing in mind therefore that it is my object to 
detect possible relations, anc that my high-temperature 
boiling-points are necessarily somewhat crude, I will facilitate 
computation by observing that in Dupré’s data the prevailing 
value of A is between 15 and 20. Assuming A=20, the 
following set of constants were obtained, in which, of course, 
there is greater uniformity. Water is added from Dupré 
and Bertrand. 


TaBLeE VII.—Constants for Boiling-point and Pressure. 


Substance. A. B. C. 
WN SCRE |). Saks. ta0sase8 19°324 2795 3°868 
Sal PMY. «fens ocerosas ese 20 4379 4217 
Pad maw so s.6: c<<. fan 20 7467 3°6438 
PATIO sagen eae ee 20 8433 3°603 


* Bertrand (/.c. p. 93) inadvertently puts A=17-44324, in which case, 
however, pressures are measured in atmospheres instead of millimetres of 
mercury, which is his usual standard. The same constant is repeated by J. J. 
Thomson. 


14. From an inspection of Table VII., I was led to suspect 
better agreement in making © constant throughout, and A 
variable. This step is further suggested by assuming, con- 
formably with the indications of Table VII., that for any two 
substances 8 and WV the boiling-points 6 and @', corresponding 
to a given pressure 7, will follow the relation B/B!=0/@' =1/n, 
where n is constant for the given pair of substances. This is 
virtually the principle of Groshans, and postulates a funda- 
mental equation of the form (1), from which all others are 
derived by substitution as follows :— 


German —a/O—-Clow ests As sted os CL) 
=A—nB/nO—C log n64+ C log n, 
iG! OGG es Oe el  (Q) 


The constants of Table VIII. are obtained by supposing 
C to be constant for all the substances. As to a choice of 


154 Mr.,Carl Barus on the Pressure- Variations of 


value, I noticed that the mean C of Table VII. is nearly the 
same as Bertrand’s C for water. Hence it was selected. 


TABLE VIII.—Constants for Boiling-point and Pressure. 


| Substance. A. B. | C. 

Water {7 Seeeeer es _— :19°824 | 2795 | 3°868 
| Sulphur sees cesses: | 19°77 | 4458 3-868 
Cadi Me Ft | 20-63 | 7443 | 3:68 
[ae ee eo ie | 2098 | 8619 | 3868 
hiBismnath |. fees | 2151 | 12862 | 3868 


These constants could be improved by successive trials ; 
but further work would be wasted. The data for sulphur in 
Table II. (‘7 em. to 76 cm.), which coalesce pretty well with 
Regnault’s data (27 cm. to 3888 cm.), suggest a calculation of 
constants including both sets of results. I will supply this 
elsewhere, since it is not essential here. Extrapolation by 
aid of the sulphur constants, Tabie VIII., does not reproduce 
Regnault’s high-pressure data. 

15. In order to exhibit the point of view taken, it is 
necessary to plot the results graphically. This is done in 
fig. 3, in which the abscissee are pressures in centimetres of 
mercury, and the ordinates boiling-points in degrees Centi- 
grade. Inthe case of mercury I have inserted the vapour- 
tension curve of Regnault, showing that, conformably with 
§ 6, it is uniformly lower than the present data. Points 
computed by the constants of Table VIII. are marked. It 
appears from an inspection of the chart that the agreement 
between observed and computed results is nearly in keeping 
with the errors of observation. 

The results for bismuth are particularly interesting. Un- 
fortunately it was impossible for me to calk the crucible 
quite tight. Hence the low-pressure boiling-point of bismuth 
does not overlap the normal boiling-point of zine, which 
limits the calibration interval of the thermocouple. The 
chart shows the interval of extrapolation to be about 270°. 
This makes the bismuth results less certain; and the normal 
boiling-point of bismuth deduced by Groshans’s principle, 
1550°, is possibly too high. Carnelley and Williams *, using 


* Carnelley and Williams, Journ. Chem. Soc. London, xxxvy. 1879, 
p- 065 : 


certain High-temperature Boiling-points. 155 


Fig. 3.—Chart showing the relation of Boiling-point and Pressure, for 
Water, Mercury, Sulphur, Cadmium, Zinc, and Bismuth,and the re- 
lation of corresponding Boiling-points at 76 centim. and 4 centim. 


1500 If 


1200 


Age | 
AVA 


NK 


156 Mr. Carl Barus on the Pressure- Variations of 


a fusing-point method, give 1450° as the maximum tempera- 
ture for boiling bismuth, which means, however, that it is 
short of the melting-point of nickel taken at 1600° (Wan der 
Wyde). In my own experiments * with a Fletcher furnace 
like fig. 2, I signally failed to boil bismuth f in a number of 
trials, in which I used three blast-burners. The boiling- 
point criterion in the present results is beautifully exhibited. 
When pressure increases, the group of points B on the chart 
passes into group A ; hence the group B are boiling-points. 
When pressure increases further, the group A do not 
increase in temperature ; hence the group A are not boiling- 
points {. The zine and the later sulphur results are most 
satisfactory. Irregularities in the cadmium observation for 
the higher pressures I attribute to leakage of the crucible 
(§ 9). 

The straight lines running obliquely across the chart 
exhibit the approximate truth of Groshans’s principle. The 
abscissee are boiling-points, @, at 76 cm., the ordinates boiling- 
points at 76 cm. and 4 cm. respectively, all expressed in double 
absolute degrees Centigrade ; 2. e. the chart shows the varia- 
tions of #/2. Mercury and sulphur fall below the line of 
proportionality. Inasmuch as it is possible that the 4 centi- 
metre data for zinc and cadmium are slightly superheated, the 
general agreement of data may be better than it here appears. 
It is by aid of this diagram that the bismuth constants in 
Table VIII. were computed. 

16. Bertrand computes the constants of Dupré’s formula 
for 16 substances, and shows its admirable agreement with 
observed data throughout. The constants in such a summary 
vary largely : A between 4 and 21 (pressures being expressed 
in centimetres of mercury); C between —9 and +5. In 
any such grouping of constants as I have very roughly 
attempted, the agreement of the formula with facts would 
therefore be lost. It is worthy of remark, however, that in 
10 of the 16 substances, A lies between 15 and 21°5, and in 
| one half of the substances C lies between 3°2 and 4:2. 
fey When, however, the errors left in any attempt to group 
. the constants are considered, not so much with reference to 

the small range of temperatures of a single substance, but 
rather with regard to the relatively large range of tempera- 


* Bull. U.S.G.S. no. 54, pp. 116-118, 124. 

+ In determining the vapour-density of bismuth, Biltz and V. Meyer 
heat bismuth up to 1700° (Chem. Ber. xxii. p. 725, 1889), but the tem- 
perature is purposely chosen high. . 

{ Very interesting experiments on the volatilization of metals in vacuo 
and at low temperatures (Cd at 160°, Zn at 184°, Sb and Bi at 292°, Pb 
and Sn at 360°) are due to Demarcay, C. R. xev. p. 183, 1882. 


__ a Cs 
f . 2 
Ed eg 


certain High-temperature Boiling-points. 157 


ture exhibited by the phenomena as a whole, and by a 
diagram such as fig. 3, for instance, then the errors in 
question assume much smaller importance. In the above 
pages I have presumed to believe that at the outset the wide 
temperature comparison is the one which ought first to be 
made, and some fundamental relation applicable to the whole 
range of temperature investigated. After this has been done, 
the said relation may be modified to-suit the individual case. 

I can state this more clearly as follows :—Groshans’s deri- 
vation of his principle * is sufficiently simple. If vapours 
have identical coefficients of expansion, 1/273 say, and their 
densities be expressed relatively to the density at the normal 
boiling-point in each case, then the ratio of absolute boiling- 
temperatures corresponding to any two given pressures will 
be the same for all vapours. This inference is incorrect, just 
in proportion as the application made of the Boyle-Charles 
law is incorrect. 

However, Dupré in deriving his formula makes virtually 
the same assumption +. Again, J. J. Thomson f{ introduces 
Boyle’s law into the mean value of the Lagrangian function 
investigated for the occurrence of maximum vapour-tension ; 
but since the form of an arbitrary function of temperature is 
here determined by experiment, the insertion of Boyle’s law 
suffices Thomson’s purposes. Following the model of his 
work, I hoped to find some suggestion as to a modification of 
Dupré’s equation, such that it may be the outcome of an 
original type for all substances, by inserting Van der Waals’s 
law instead of Boyle’s law into the proper term. It seemed 
plausible that Dupré’s equation could thus be corrected by 
aid of constants, a and b, the molecular interpretation of 
which has already been given by Van der Waals.  Per- 


forining the operations, I find, rigorously, 


Ef Po ap po 
an equation which, though capable of simplification, essen- 
tially involves &, and is therefore not suggestive. 


Physical Laboratory, U.S. Geological Survey, 
Washington, D.C., U.S.A. 


* Somewhat similar approximate relations are investigated from Reg- 
nault’s data by Dupré (/. c. pp. 115-117). Groshans used data for water 
and carbonic acid gas. An older principle due to Dalton (Lit. Soe. 
Manchester, v. p. 550) is incorrect. The work of Kopp and of Bartoli 
on corresponding boiling-points has special reference to volumes. 

{+ Bertrand, 7. ¢. p. 101. t Thomson, Z. ¢. p. 158. 


Phil. Mag. 8. 5. Vol. 29. No. 177. Feb. 1890. N 


Fle. 


XIV. The Electrification of a Steam-jet. 
By SHeLForRD BipweLL, M.A., F.AS.* 


fee boiler used in these experiments consists of a small 

tin bottle capable of holding about fifteen fluid ounces, 
which is supported upon a tripod above a Bunsen burner. 
Its neck is fitted with a cork, through which passes 
a glass tube 7g in. in diameter, terminating in a nozzle 
with an opening of about =; in. At a point four inches 
above the cork, the tube is bent to an angle of 100 or 
110 degrees, and the nozzle may be formed at a distance of 
five or six inches from the bend. In this case its direction 
will, of course, be nearly horizontal. When it is desired to 
have a vertical nozzle, the tube is again bent in an upright 
direction at a distance of not less than five inches from the 
first angle, the nozzle terminating two or three inches above 
the second bend. The nozzle is made by simply drawing out 
the tube to a point in a flame, and cutting off its end at the 
proper place. 

I have given these dimensions in detail, not, of course, be- 
cause they are absolutely the best possible, but in order that 
anyone who wishes to repeat the experiment may be enabled 
to obtain good results without trouble. The object aimed at 
is to keep the tube as free as possible from water, whether 
arising from ebullition or from condensation, so that the jet 
of steam may be regular and uniform ; at the same time, it is 
essential that the end of the nozzle from which the steam issues 
should not be directly above the gas-burner, or the experiment 
cannot succeed. 

The tin bottle is charged with four ounces of water, and 
when it boils the burner is adjusted until the steam-jet is as 
vigorous as is possible consistently with steadiness ; if the 
ebullition is too violent, the water thrown up into the tube 
will produce jerks, masking the effect to be looked for. 

The jet is most conveniently observed by means of its 
shadow projected upon a white screen. For this purpose a 
lime-light is desirable, but any good source of light may be 
employed. The shadow of the jet will be seen to be of feeble 
intensity and of a n&utral tint; the jetis,in fact, nearly trans- 
parent, and does not appear to exercise any selective absorp- 
tion upon the light. Hf now a sharp point, or, better, a small 
bundle of points, in connexion with one of the terminals of 
an influence-machine (such as a Voss), is brought near the 


%* Communicated by the Physical Society : read December 6, 1889. 


On the Electrification of a Steam-jet. 159 


base of the jet, the machine being worked slowly, a startling 
change instantly comes over the shadow. It becomes dark 
and dense, at the same time assuming a marked orange-brown 
tint. By removing the point, or simply connecting it to earth, 
the shadow can be immediately caused to resume its original 
appearance, again becoming almostinyisible. This operation 
may be repeated as often as desired, one of the most remark- 
able things about it being the extreme rapidity with which 
the changes are produced. 


The point need not necessarily be directed to the origin of 
the jet ; it is nearly as effective when placed in the steam at 
a ence of a foot or more from the nozzle; and in sucha 
case the whole of the steam-jet is equally acted upon from its 
origin onwards, even when the direction of the point is the 
same as that of the jet. A ball may be used instead of a 
point, but it operates only when actually within the jet, 
whereas a point may be outside it. The effect may also be 
produced by directing the jet upon an electrified metal disk, 
supported at a considerable distance from the nozzle. 

I have examined the absorption-spectrum of the steam-jet. 
When the jet is not electrified, its action upon the spectrum 
is small, the intensity of the whole being slightly diminished 
in an apparently equal degree throughout. Possibly the 
violet is dimmed in a somewhat greater proportion ion the 
other colours. Electrification of the jet causes the violet to 
disappear completely, while the luminosity of the blue and 
the more refrangible part of the green is materially decreased. 
The orange and red are, I believe, quite unaffected. 

From these facts it may be concluded that electrification 
causes an increase in the size of the water particles contained 
in the steam-jet. In the unelectrified condition the majority 
of these particles are small in relation to a wave-length of 
light; under the influence of electrification they become larger, 
and attain a diameter of something like a fifty --thousandth 
part of an inch. 

The idea naturally suggests itself that the phenomenon 
may be of the same nature as that observed by Lord Rayleigh 
in the case of water-jets*. A stream of water issuing in a 
nearly vertical jet from a small orifice is found to break up 
into separate drops at a certain distance above the orifice. 
Under ordinary conditions these drops collide with one 
another, and, again rebounding, become scattered over a con- 
siderable space. But when subjected to the influence of an 
electrified body, as a rubbed stick of sealing-wax, brought 
near the point of resolution, the colliding drops no longer 

* Proc. Roy. Soc. 1879. 


N 2 


& 
; ; 
4! é 
2 
aS .' 
by 
“chet 
_ wey 
o 
ee $ 


160 Mr. Shelford Bidwell on the 


rebound but coalesce, and the entire stream of water, both 
ascending and descending, appears to become coherent. Now 
it seems to me certain that the innumerable minute particles 
of water generated in the steam-jet, each consisting perhaps of 
only a few molecules, must necessarily come into frequent 
collision with one another; for we cannot suppose that they 
all travel with equal velocities and in exactly the same direc- 
tion; and there is no reason why they should not behave 
just in the same manner as the larger drops of the water-jet, 
rebounding when they are not electrified, coalescing into 
larger drops when they are. It is true that the degree of 
electrification required to produce the phenomenon in the 
case of the steam-jet is apparently much greater than in the 
other, a rubbed stick of sealing-wax being altogether inopera- 
tive. Perhaps this is a consequence of the different sizes of 
the drops in the two cases. That the actual electrification of 
the particles in the steam-jet is really very small indeed, is 
proved by the fact that if two electrified steam clouds are 
generated in close proximity to each other, they exhibit 
little, if any, evidence of mutual repulsion when they are 
similarly electrified, or of attraction when their electrifications 
are of the opposite kind. 

Lord Rayleigh shows cause for believing that if the elec- 
trifications of the drops in the water-jet were strictly equal, 
the phenomenon in question would not occur; and the reasons 
why they are not, in fact, equal would just as well apply to 
the case of the steam-jet. How unequal charges of electricity 
of the same name are operative in bringing about coalescence 
Lord Rayleigh does not explain, nor am I prepared to hazard 
a conjecture on the point. 

Lord Rayleigh concludes his paper by referring to the 
importance of the investigation from a meteorological point 
of view. I may do the same. It seems certain that the 
steam-jet experiments go far towards explaining the cause of 
the intense darkness which is characteristic of thunder-clouds, 
as well as of the lurid yellow light by which that darkness is 
frequently tempered. 


I had made the above described experiments and drawn 
the above stated conclusions concerning them, and had just 
requested the Secretary of the Physical Society to accept the 
present communication, when Prof. Silvanus Thompson, 
whose knowledge of scientific history is proverbially encyclo- 
peedic, was good enough to bring to my notice the fact that 
experiments upon the electrification of a steam-jet had been 
recently made in Germany by the late Robert Helmholtz. 
An account of these experiments, which are of the greatest 


Electrification of a Steam-jet. 161 


interest, is given in Wiedemann’s Annalen, vol. xxxii. p. 1. 
The author appears never to have examined his jets by trans- 
mitted light, and makes no mention of the marvellous increase 
of opacity under electrification, to which I have called atten- 
tion. His observations were all made against a dark back- 
ground, the illuminating beam of light coming obliquely from 
the front, but shaded from the eyes. When the jet is elec- 
trified, he says, it is at once seen more clearly and sharply 
against the background ; it also assumes diffraction colours, 
like those seen in strata of fog. Very strong electrification 
produces a deep blue colour, indicating the formation of very 
small mist drops. On slowly diminishing the electrification 
the blue tint at first becomes gradually paler, which points 
to the formation of larger drops; and it is then succeeded 
by tints of purple, red, yellow, green, and finally, when the 
discharge is very feeble, by pale blue tones again. Under 
certain circumstances all these several tints may be seen at 
once in different portions of the jet. 

I, too, had observed these diffraction colours, which were 
sometimes very beautiful; but having convinced myself that 
they undoubtedly occurred at times when no electrical in- 
fluence (that I knew of) was operating, I did not follow up 
the observation. 

Helmholtz found that these condensation phenomena could 
be just as well produced by some other causes as by electrifi- 
cation, and especially by the agency of flame. All the ex- 
citing causes in question involve some continuous chemical 
action inside the steam-jet. He conjectures, therefore, that 
the sudden condensation may be due to molecular tremors or 
shocks, which upset the unstable equilibrium of the super- 
saturated vapour, just as a small disturbance will sometimes 
cause the sudden crystallization of a supersaturated saline 
solution ; and after showing that. chemical reactions may occur 
freely even outside the visible portion of a flame, he states 
his opinion that similar dissociations and recombinations take 
place among the molecules of the air affected by an electric 
discharge, as evidenced, for instance, by the formation of 
ozone. 

A very striking illustration of the effect of combustion is 
afforded by holding beneath the jet a piece of burning touch- 
paper, made by soaking blotting-paper in a solution of nitrate 
of lead. The jet at once becomes quite as opaque as if elec- 
trical influence were employed, and the same hissing noise is 
also heard. The burning touch-paper suggested itself as 
more convenient than the actual flames used by Helmholtz 
for the purpose; for these cannot be brought underneath the 
jet without causing its immediate dissipation ; and it is there- 


162 On the Electrification of a Steam-jet. 


fore necessary to hold them on one side, and direct their 
heated gases upon the jet by blowing or fanning. 

After reading Helmholtz’s paper it naturally occurred to 
me to try the effect of combustion upon the water-jet. In 
this case the objection to the use of an actual flame does not, 
of course, apply. I therefore introduced the flame of a 
Bunsen burner into the jet, and found that, if the air-holes 
were stopped up, and the fame thus rendered luminous, a 
decided effect was produced upon the jet. Often, indeed, it 
became just as completely coherent throughout its length 
as if it were electrified, though I have not yet succeeded in 
obtaining this result with perfect certainty; but in every case 
~ when the burner was held a little below the point of resolu- 
tion, a considerable diminution of the scattering was observed. 
If the air-holes were opened and the flame made non-luminous, 
it failed to act Im any way whatever upon the jet. It is to 
be remarked that Helmholtz found certain non-luminous 
flames (of which, however, a gas-flame was not one) to be 
devoid of influence upon the steam-jet. 

Can the effect here also be due to electrification*? It 
can hardly be attributable to heating, because the flame of 
a Bunsen burner is certainly hotter when it is non-luminous 
than when it is luminous. On the other hand, it is known 
from many experiments that flame is electrified. If, for 
example, we place a luminous flame between the positive and 
negative ball-terminals of a Voss machine in action (the ter- 
minals being too far apart for sparks to pass), we find that 
the flame, or at least the upper part of it, is repelled by the 
positive and attracted by the negative ball. This seems to 
denote positive electrification of the flame. 

In conclusion, it should be mentioned that Helmholtz 
suggests another hypothesis as an alternative to that of mole- 
cular shock, though he does not appear to attach much impor- 
tance to it. It is that the electrical discharge, the flame or 
other exciting agent, whatever it may be, acts by introducing 
into the steam-jet minute particles of solid matter which serve 
as nuclei upon which the water-vapour may condense, as in 
Aitken’s experiments on the formation of fog. 

It is possible that several different causes may be competent 
to produce the condensation phenomena. 


* In replying to the discussion which followed the reading of the paper, 
I suggested the possibility, which had occurred to me after it was written, 
that the flame might act simply by coating the separate particles of water 
with certain products of combustion, Lord Rayleigh having found that 
the addition of a little soap or milk to the water prevented the scattering. 
Perhaps the action of flame upon the steam-jet may be similarly explained. 


7. 


plese 


XV. The Geological Age of the Mountains of Santa Marta. 
By Professor Hermann Karsten, J.D." 


HE Geological constitution of the mountain-mass of 
Sta. Marta has until recently remained quite unknown. 
lt was only in consequence of my Report of 1852 upon ‘ The 
neighbourhood of Maracaybo and the North coast of New 
Granada ” (Karsten’s Archzv, 1853), in which the geological 
age of these mountains was touched upon, and after the pub- 
lication of the nearly simultaneous investigation of this region 
by Acosta (Bull. Soc. Géol. Fr. sér. 2, vol. ix. p. 396, June 
1852), that these questions have been dealt with more in detail, 
both in my subsequent geological writings and in those of my 
successors. 

Acosta, like myself, describes the Geological constitution of 
the Sierra Nevada de Sta. Marta as Plutonic, consisting of 
Granite, Gneiss, Syenite, Diorite, Hurite, &c.,and of Porphyries 
traversed by veins of malachite. Neptunian strata, from 
which the age of the mountain-mass might be inferred, are 
not cited by Acosta; but he concludes, from the complete 
isolation of the massif, and from its Hast and West direction. 
that it existed long before the upheaval of the Cordillera, 
which runs North and South. 

In my discourse upon “The Geological Constitution of 
New Granada” (Amilicher Bericht der Versammlung der 
Naturforscher, 1856, Vienna 1857) I also describe the Sierra 
Nevada de Sta. Marta in more detail as a distinct mountain- 
system which abuts with its south-eastern declivity upon the 
chain of Ocaiia striking northward from Bogota, and by sub- 
sequent upheavals there was united therewith by means of a 

narrow and low connecting range (p. 81). This mountain- 
mass of Sta. Marta consists of alternating beds of crystalline 
rocks :—Granite, Gneiss, Protogine, Syenite, Hornblende-, 
Chlorite- and Quartz-schists,—which have a general strike 
from 8.W. to N.E. In the periphery of this formation there 
are readily weathering Diorites, Porphyries, Syenites, Gra- 
nites, &. Towards the east and south-east beds of the 
Cretaceous formation bound these rocks, a continuation of 
those which compose the mountains of Ocaiia (Perija). The 
lowest of these Neptunian beds is a red sandy laminated marl 
in which Ammonites santafecinus, D’Orb., occurs, and which 
alternates upwards with dark, bituminous limestones and 
siliceous schists containing Ammonites and Jnocerami. These 
are covered by lght- blue limestone- beds, in which Lwogyra 


* Communicated by the Author. 


164 Prof. H. Karsten on the Geological Age 


Boussingaultii is plentiful. Upon the neighbouring south- 
east foot of the Plutonic rocks of the Sierra Nevada are de- 
posited correspondingly stratified but unfossiliferous cal- 
careous and aluminous rocks, in part crystalline and schistose. 

In the valleys of this Cretaceous formation Tertiary strata 
are deposited up to at the outside 200 metres. These appear 
to be entirely wanting on the northern slope, where, however, 
according to the statements of the natives, limestone contain- 
ing Belemnites occurs. 

In opposition to Acosta, Hettner (Petermann’s Geogra- 
phische Mittheil. 1885, p. 92) concludes from the direction of 
the centre of the mountains from 8.8.W. to N.N.E., that the 
mass is a continuation of the Central Cordillera, which is like- 
wise furnished with a nucleus of Plutonic rock, and to which 
this line of strike under 8° N. lat. leads eastwards from the 
river Nechi; an opinion which is in harmony with the deve- 
lopment of these Colombian mountain-chains as deduced by 
me from the nature of the Neptunian strata, although the 
contemporaneity of the two existing mountain-systems is not 
thereby proved. 

In my Viennese address on New Granada (Amtlicher 
Bericht, 1856), as well as in a more recent memoir on the 
Geology of the three northern Republics of South America*, 
in which [ have brought together all that was observed by me 
in those countries, or that has been published by other travel- 
lers, I concluded that the mountains of Guiana are the central 
point of the different mountain-systems of Colombia, by 
which the direction of these mountain-chains was prescribed, 
having been elevated as the northern ( Venezuela) and western 
(New Granada and Heuador) borders of a great semicircular 
fissure which was formed in the solid crust of the earth around 
this primitive centre of upheaval, which, although it was not 
then recognizable in its whole extent by prominent mountain- 
masses, nevertheless traced out the direction of contempo- 
raneous and subsequent eruptions. 

The elevatory force which gave origin to this fissure in the 
periphery of the central mountain-mass already in existence 
appears to have acted from the east to the west and south, 
and indeed on the greatest scale in the north, gradually | 
becoming weaker towards the south. On the contrary, the 
last considerable upheaval, that of the Tertiary epoch, followed 
the opposite direction ; its greatest force was exerted in the 
south. 

In the north the Plutonic mountain-chains which bound the 


* Géologie de Vancienne Colombie Bolivarienne, Vénézuéla, Nouvelle 
Grenade et Ecuador.—Berlin, Friedlander, 1886. 


a 


of the Mountains of Sta. Marta. 165 


sea (Caracas, Sta. Marta) attained nearly their present eleva- 
tion above the sea-level at their first upheaval, and were only 
a little further uplifted at the close of the Cretaceous* and 
Tertiary epochs, while the present Cordillera, extending south- 
wards, remained still covered by the sea, and only attained its 
present form and elevation in this direction by means of the 
eruption of the trachytic masses and lavas, which occurred 
most powerfully in the south (Hcuador) and diminished 
eradually northwards (Gévlogie, p. 51). 

The existing Sierra Nevada de Sta. Marta, like the moun- 
tains of Caracas, was already almost completely upheaved 
above the Cretaceous sea and still more completely above the 
sea of the succeeding Tertiary formation, as may be recog- 
nized from the conditions of stratification of the Neptunian 
deposits. 

Whilst the Cordillera of New Granada and Ecuador, espe- 
cially in its trachytic portions, is generally overlain nearly to 
the highest summits by strata of the Tertiary epoch, the two 
Plutonic mountain-masses of the north coast bear Tertiary 
deposits only up to small elevations (Géologie, pp. 12, 23, 52). 

The two geographers, Simons and Sivers, the latest writers 
upon the Sierra Nevada, do not enlarge our "knowled ge of this 
geological question. 

Simons (Proc. Roy. Geogr. Soc. 1879, 1881, and 1885), as 


_ the fruit of his investigations of the Sierra Nevada extending 


over several vears, gives us an excellent geographical Map, 
the first and best of the original maps of this region founded 
upon personal surveys (Proc. R. G. 8. 1881), as a com- 
pletion of the admirable “work of Codazzi, who, as is well 
known, perished under the deadly climate of the plains at the 
commencement of the survey of this province. 

Upon the geological characters of the Sierra Nevada Simons 
saysnothing. The traveller Sivers, who followed him (Zettschr. 
der Gesellsch. fir Erdk., Berlin, 1888), adheres, as regards 
geology, to the results obtained by me (p. 07), saying upon 
the age of this mountain-massif, “It appears, therefore, that 
the Sierra Nevada de Sta. Marta isa very old piece of the 
earth’s crust which had enjoyed a long continental period 
when the flooding of its margins by the Cretaceous sea com- 
menced. After these deposits had lasted throughout the 


* Steinmann’s statement that the Jurassic formation also occurs in 
New Granada (Neues Jahrb. der Min. &c., 1882) has proved to be erro- 
neous. The Jurassic formation indicated by me, in consequence of Stein- 
mann’s publication, in my Map in the “ Géologie, &c.” is consequently to 
be altered to Cretaceous. 


166 The Geological Age of the Mountains of Sta. Marta. 


whole Cretaceous period, 
a folding of them took 
place in Tertiary times, 
by which the Sierra de 
Perija was produced, 
&c.” , 
The accompanying 
profile surveyed by me 
in the district of Papaijal 
on the river Rancheria (5) 
(Rio Hacha) and com- 
pleted near Tomarazon 
in the west, and passing 
through the mountains 
Cerrejon (2) and Potrero 
de Venancio (3), gives 
an indication of the stra- 
tification of the rocks be- 
tween the Sierra Nevada 
(4), and the Cordillera 
of Ocafhia (Perija) which 
terminates here (1).— 
a, a, a, Red marly sand- 
stoneand laminated marl, 
alternating above with 
calcareous Cretaceous 
beds*; 6. Tertiary strata; 
c. Porphyry with copper 
ores; d. Red quartz- 
porphyry; e. Plutonic 
rocks, such as also form 
the nucleus of the Sierra 
Nevada. 


Lao 


q99 


fr 


* In the uppermost, pale- 
blue limestone beds of the 
younger Cretaceous there are, 
in this district, near Chorrera, 
towards the summit of the 
hill, the so-called “ Geologi- 
cal organs,’—perpendicular, 
cylindrical shafts, in parts 
10-12 m. high and 4-5 m. in 
diameter, which I have fully 
described in the Zettschr. d. 
Geol. Gesellsch. 1862, and in 
Westermann’s Monatsheften, 
1863. 


. 
4 
(a8 
} 
+} } 
ay 
h 
i 


pe 16n 


XVI. On Diffraction-Colours, with special reference to Corone 
and ‘Iridescent Clouds. By James C. M*Connet, JA., 
Fellow of Clare College, Cambridge.* 


| Concluded from vol. xxviii. p. 289. ] 


3. CORRECTIONS AND ADDITIONS TO THE First PAPER. 


N the article which I wrote two years agof on this sub- 
ject occur some actual blunders and some points which 
require fuller explanation. The most important blunder has 
been already mentioned {. In accordance with the usual 
statement of treatises on Optics, I imagined the central spot 
of the diffraction diagram to be white, whereas, as a matter 
of fact, it is coloured with tints similar to those of Newton’s 
first order. Hence what in the calculation I called the first 
spectrum should really have been called the second; for 
second spectrum should be written third, and so on. This 
does not affect the force of the argument against the theory 
of thin plates, but it makes a considerable difference in the 
size of the particles deduced from observation. My first 
inkling of some error in the previons es{imate came from the 
comparison of the sizes of lycopodium seed deduced from 
measurements of the diffraction-rings round a candle and 
from actual observation under the microscope. Applying the 
true theory of observation, it appears that the diameters of the 
filaments which produce the brightest colours average 0-008 
millim. I have measured corone produced by filaments vary- 
ing in diameter between 0:01 and 0-045 millim. 

My statement that purple only occurs at the junction of the 
first two spectra is not strictly correct, for a good purple fre- 
quently follows the second red. But the two colours are not 
likely to be mistaken for each other. The first, in general, 
inclines much to blue; the second to red. For further 
description of the colours see the preceding section. 

With regard to the distinction between coronz and irides- 
cences, it is probable that no hard and fast line can be drawn. 
The optical explanation of the colour is exactly the same, the 
only difference lying in the character of the cloud. Still, 
with ice-clouds at any rate, I have never been in doubt in 
which class to place the colours. In corone the rings are 
complete and perfectly circular, but the tints are in general 
comparatively poor ; whereas in iridescences we have glow- 


* Communicated by the Author. 
+ “On the Cause of Iridescence in Clouds,” Phil. Mag. Nov. 1887. 
t See vol. xxvii. pp. 274, 280. 


axes 


168 Mr. J. C. MeConnel on Diffraction-Colours, 


ing colours arranged in scattered patches or, at best, broken 
rings. It is clear, however, that if the observer could only 
move close up to one of these patches of glowing colour, a 
complete system of rings would be developed. 

There is a trifling slip in the expression I gave for cos ¢', 
in the discussion of reflexion from thin plates. In that for- 
mula 2 should be replaced by n+4. It will be observed that. 
this change does not affect any part of the argument. 

The short paragraph on ditfraction-colours seen nearly 
opposite the sun is founded on a miscalculation, and must be 
withdrawn. These colours appear to be produced in both 
water- and ice-clouds. Mr. Omond has sent me a list of several 
cases in which such glories were seen from Ben Nevis, at 
temperatures far below the freezing-point *. Their theory 
seems to be in the most unsatisfactory state. I have come 
across five different explanations, none of which do I consider 
satisfactory. 

These are the only corrections I have to make, but I find 
that my description of iridescent clouds has given rise to some 
misapprehension. Wishing to bring out forcibly the ten- 
dency of the colours to arrange themselves symmetrically 
with regard to the sun, which is one of the main arguments 
against their being due to thin plates, I used the words: 
“ Within a circle round the sun, radius about 2°, the clouds 
are white, or faintly tinged with blue. ‘This circular space is 
surrounded by a ring of yellow, passing into orange.” This 
led some readers to think that these circles were always to be 
seen ; whereas, of course, the yellow is not seen unless there 
is a cloud of suitable density in a suitable position. The 
yellow ring is often fairly complete, as every one must have 
noticed round the moon, but it is very seldom a regular circle 
like those of corone. 

The greatest distances from the sun at which I have been 
able to detect colour, since the date of my first paper, are as 
follows :—St. Moritz, Oct. 20, 1887, 25°; Jan. 9, 1888, 34°; 
March 10, 29°; Davos, Dec. 27, 37°. But these extreme 
colours are only faint pinks and greens. In Colorado irides- 
cences have been observed up to “ more than 45° from the 
sun” (‘ Nature,’ April 21, 1887). 

Since I became interested in these colours I have had few 
opportunities of observing from the sea-level. Still I have 
seen enough to feel confident—and this view is supported by 
the testimony of others—that the phenomenon is nearly as 


* It is at least possible that in such cases the mists consisted of fine 
drops of water; and the Ben Nevis observations of fog-bows at all tem- 


- peratures lend support to this suggestion. 


with reference to Corone and Iridescent Clouds. 169 


common in England as in the Alps, though fine displays are 
rare. Common though it be, it has been seen by few. The 
observer should arm himself with dark spectacles, and, shading 
his eyes from the direct sunlight with the hand, or preferably 
with some distant object, such as a building, carefully examine 
any clouds within 10° of the sun, and he will seldom fail to 
see colour. A curious illustration of this fact is that irides- 
cences are so frequently seen when the brightness of the sun 
is reduced by an eclipse, and recorded as remarkable pheno- 
mena. To meteorologists these colours should be especially 
interesting, as manifesting the actual size of the cloud par- 
ticles*. The following table will be found convenient. To 
calculate the diameter in millimetres of the average filament 
in an ice-cloud or of the average drop in a water-cloud, divide 
the number in the first or second column respectively by the 
angular distance of the colour from the centre of the sun 
expressed in degrees. 


Filaments.| Drops. 

MMSE VellOwas 6s acs eve oe ccesees: 0:022 0-028 
PRAT CCM cere n sia dats Sao. 0 hk owerions 0:028 0-035 

Pe DUG DIOR fe ancaetia sists snes sed 0031 0:038 
ECONO sONWe! cenciancse senses ease 0:035 0:042 
Mee PERCE Monsen cau wanene tae ones 0-045 0-052 

Rar WellOwiaryhehecetiifne tne 0:051 0-058 

Bile BECO soit c(t ce stateroom ester 0:057 0-065 

Ties MG DIC cosce -ceseen ccna rine ds 0-062 0-069 

MP MIGEVECTI GE cass iecdscaotncsceseee 0 076 0°083 
MMe REG ke lerianaiiotlstiolriieat cere 0-087 0:095 
IMOMEL MVOC yseocntiiseeee se deqacs- 0106 O-113 
Fah th @LCUL. ciseisacieoijs!siiseis aiestnis ete sh 0-124 0-131 


A convenient and, in general, sufficiently accurate method 
of measuring the angle is to find the corresponding length on 
a pencil held at the full stretch of the two arms. The distance 
from the eye to the pencil varies only slightly with the posi- 
tion of the body and the altitude of the sun, and can be 
measured at leisure. 

Hiven when there is no trace of colour we generally see in 
moderately translucent clouds a great increase of brightness 
near the sun. With water-drops this might be produced by 
ordinary refraction, but in frozen clouds it must be attributed 


* Fifty years ago Kaemtz used Fraunhofer’s results to determine the 
diameter of the vesicles, as he supposed them to be, of fog (Kaemtz, 
‘ Meteorology,’ translated by Walker, p. 111). But the method seems to 
have been since neglected. 


170 Mr. J. C. M°Connel on Diffraction-Colours, 


mainly to diffraction, and from the extent of the bright region 
we can form a rude idea of the size of the particles. The 
absence of colour will present no difficulty to anyone who has 
noticed the overpowering brightness of the white central 
space compared with the surrounding rings of corone. It is 
easy to believe that if there be any considerable variety of 
size, or if, on the other hand, the majority of particles have 
any shape other than those approximating to spheres or long 
cylinders, there will be such blurring of colour that nothing 
but the bright central white space will survive. As to the 
size of particle, suppose, for example, the white glow, up to 
the circle where the brightness is about one fourth of that close 
by the sun, have a radius of 4°. Taking the number appro- 
priate to the first yellow for filaments and dividing by 4 we 
obtain 0°0055 mm. We can then assert with some confidence 
that there are a considerable number of crystals in the cloud 


at least as thin as 0°005 mm. The estimate is rough, but ~ 


rough estimates often prove useful. If there is no percep- 
tible increase of brightness in the cloud near the sun we can 
assert positively that the vast majority of the particles are in 
no dimension as thin as 0°1 mm. 

Unusually vivid iridescences were seen in Hngland and Scot- 
land during the winters 1884-5 and 1885-6, and called forth 
a number of letters to ‘Nature.? The clouds seem to have 
been of a special type, suspended at a great height in the air, 
and recognizable even when not coloured *. The bright and 
varied colours described occurred at distances of over 30° 
from the sun, so the ice-filaments must have been as fine as 
0-001 millim. in diameter. Colours similar, though not so 
bright, were seen nearly opposite the sun. But the region 
between 50° and 180° from the sun seems to have been 
colourless, showing that this was not a case of the action of 
thin plates. 

If cloud-colours are ever formed by thin plates of ice, they 
may be distinguished by their strong polarization in the plane 
of the sun. Let us imagine the reflected light to be divided 
into two parts polarized respectively in and perpendicular to 
the plane through the sun. Even at 10° from the sun the 
ratio of these parts is 0°74, at 20° 0°53, at 30° 0°37. In the 
case of diffracted light the polarization is of the same nature, 
but not nearly so strong. It probably varies as the square of 
the cosine of the angle of diffraction. This gives the ratio at 
10° 0°97, at 20° 0°88, at 80° 0°75. Thus at 10° the polariza- 

* See especially letters by Mr. T. W. Backhouse, Feb. 19, 1885, and 


Mar. 25, 1886. One cloud, from simultaneous observations at different 
places, was found to be at least 11 miles high. 


tiie 


i 


with reference to Corone and Iridescent Clouds. 171 


tion of diffraction-colours could not be detected with a nicol 
prism, though readily seen in thin-plate colours. At 20° the 
var iation of brightness, as the nicol is rotated, should in one 
case be in the ratio 4:1, in the other 4:3; at 30°, 7:1 and 7:4 
respectively. As [have pointed out before, thin-plate colours 
are most likely to be seen at 20° or 30° from the sun. 

I have recently looked up Fraunhofer’s own account of 
his observations on the light diffracted by a slit*. I find 
that, though in his formulated statement he says that the 
deviations of the red bands are in the ratio 1:2:3... Sel 
what he actually measured were the boundaries between suc- 
cessive spectra. He describes the first spectrum as ending 
with red, and the second as commencing with indigo, blue, 
&c., and remarks that each spectrum fades by insensible 
degrees into the next. He measured the extreme limits of 
the first four spectra, and found they corresponded to “ 
tardations 7’ of 0°0000211 Paris inch or 0:000057 centim. 
multiplied respectively by 1, 2, 3,4. By referring to the 
continuous curve in my diagram, it will be seen that the first 
three of these points lie nearly on the line from W to the 
violet corner, while the fourth would lie nearly in that line 
produced. Thus he evidently included what I have called 
purple in the red. 


4, BisHop’s Ring f. 


One of the most interesting examples of a diffraction-corona 
was the great ring round the sun produced by Krakatoa dust. 
In the report of the Krakatoa Committee of the Royal 
Society there is a section devoted to this subject, in which 
two serious blunders occur, and some important consider- 
ations are omitted. Soa few remarks on the subject may not 
be out of place. 

The corona is generally described as “a whitish silvery 
patch surrounded by a brownish fringe,” or in similar terms f. 
Prof. Cornu studied the colours carefully and says that in 
favourable circumstances the order was, ‘‘ Proceeding from the 
centre outwardly, clear azure blue, neutral grey, brown- 


* Schumacher’s Astronomische Abhandlungen, vol. ii. 1823. 

+ Since this section was written I have received from Dr. J. Pernter 
a copy of his paper “Zur Theorie des Bishop’schen Ringes ” (Meteoro- 
logische Zeitschrift, Nov. 1889), in which some of my remarks are 
anticipated. Pernter deduces the size of the particles from Fraunhoter’s 
measurements of the diffraction pattern of a circular aperture, and obtains 
results not very different from mine. In this case also Fraunhofer 
measured the boundaries of the spectra and included my purple in the 
ned. 

{ Krakatoa Report, p. 233. 


« I -- ” 
a ae 


at 
“a: 
Bp 
F 
ia 

. 

. Bt 
i 
at 
x 
iat 

3 
ce) 
ie 
} 1 
. 


oe emt el eR em ne PY ont hes . ee i Ae 


eer erence ret waren 
= 


so Nee ee oe 
ial eloekate 


rs 
: ae 


172 Mr. J. C. MeConnel on Diffraction-Colours. 
yellow, orange-yellow, coppery red, purple-red, and dull violet, 


which is analogous to the succession of the colours of the first 
ring of diffraction-coronee presented by thin clouds” *. This 
evidence will probably be considered conclusive. 

Some observers thought the red ring had some connexion 
with an ice halo, as it happened to “have about the same 
radius ; and it may be remarked that, when the ice prisms are 
small, diffraction” must greatly modify the appearance of a 
halo. The narrow beam of light, which passes through the 
two faces of a hexagonal prism in the position of minimum 
deviation, must behave as if it had passed through a narrow 
slit in an opaque screen. Thus I find that a beam of red 
light which traversed a prism of 0°03 millim. greatest diameter 
would be spread out by diffraction to an angular breadth of 
5°, and other colours less in proportion to their wave-lengths. 
This spreading out would probably be fatal to such an in- 
distinct phenomenon as an ordinary halo. Still, if the mass 
of prisms were of great depth, the halo might survive with an 
aspect very different to its usual one. One thing that enables us 
to say with certainty that Bishop’s ring was a corona and not 
a halo, is that, however a halo be moditied, the brightness 
outside the red ring will be greater than that inside, while in 
a corona the reverse holds good, and re ring was the 
outer border of a bright space. 

Mr. Douglas Archibald, from a consideration of all the 
observations, selects the following radii: for the inner border 
of the red ring 10° 30!, for the middle 15° 10’, for the outer 
border 22° 45’. Taking 15° 10’ and applying the figure 
given in the table above for the first red with spheres, we “find 
the average diameter of the particles to be 0:0023 millim. 
The ring was evidently broadened out by the irregular dia- 
meters of the particles. Assigning the outer border of the ring 
to the first purple and using the radius 22° 45’, we find for 
the diameter of the particles 0°00167 millim., and we can 
assert that there were a considerable number as small as this. 
It does not follow that smaller sizes were not well represented. 
The brightness of the diffracted light is proportional to the 
fourth power of the diameter of the particle, so the smaller 
sizes are severely handicapped. With regard to the upper 
limit of size, we may perhaps take the first yellow as the inner 
border of the brownish or reddish ring, which gives 0°0027 
millim. By using the value for the red, we find that there 
were certainly not many particles broader than 0-0033 millim. 

Mr. Douglas Archibald ¢ used the formula sin (radius) = 
NA/d, where d is the diameter of the particle and N a constant. 


* DT. c. p. 282. qe 6p. 257. 


On the Vibrations of an Atmosphere. 173 


It is apparent from the context that he intends to use the 
value of N which gives the first bright ring in homogeneous 
light. - This is the very mistake into which I myself fell. 
But there is another mistake. Through some oversight the 
value of N, with which he was supplied by Prof. Stokes, is 
0°7655, which applies to the first dark ring when the diffracting 
aperture itself is a narrow ring of diameter d*. When the 
diffracting aperture is circular or, what comes to the same 
thing, the diffracting obstacle is spherical, the value of N for 
the first bright ring is 1°64. It happens that the two errors 
nearly compensate each other; so that he obtains d=0-:00162 
millim. 

If the diffracting particles had been very thin circular 
disks floating with their planes horizontal, the ring would 
only have been circular when the sun was in the zenith. 
When the sun was at an altitude of 30°, the vertical angular 
diameter of the ring would have been about twice as great 
as the horizontal. Nothing like this was observed, so we 
must suppose the particles to have been either nearly spherical 
or else lying with their planes in all positions at random. 
A small dilatation of the ring was observed about sunset, 
especially of the vertical radius, amounting to 3° and 6° at 
zenith distances of the sun 85° and 90°; but it is difficult 
to conceive any shape or orientation of the particles which 
would explain this. 

As the sun gets low the higher regions of the air become 
relatively brighter, so that if these contain smaller particles 
the radius of the ring will increase. On the other hand, as 
the red rays become relatively more powerful, the red ring 
will become brighter and broaden out towards the sun. ‘This 
seems to agree with what was observed. 


Hotel Buol, Davos, 
November 30, 1889. 


XVII. On the Vibrations of an Atmosphere. 
By Lord Rayueien, Sec. k.S.F 


1 order to introduce greater precision into our ideas 
respecting the behaviour of the Earth’s Atmosphere, it 
seems advisable to solve any problems that may present them- 
selves, even though the search for simplicity may lead us to 
stray rather far from the actual question. Itis proposed here 
to consider the case of an atmosphere composed of gas which 
* Encye. Brit., Wave Theory, p. 482. 

t+ Communicated by the Author. 


mil. Mag. Ss a..Vol, 29, No. 177. feb. 1890. O 


174 | Lord Rayleigh on the 


obeys Boyle’s law, viz. such that the pressure is always pro- 
portional to the density. And in the first instance we shall 
neglect the curvature and rotation of the earth, supposing 
that the strata of equal density are parallel planes perpen- 
dicular to the direction in which gravity acts. 

If p, o be the equilibrium pressure and density at the 
height z, then 


d 
~- — —09; e e e e s e e (1) 
and by Boyle’s law, 


2 


p=, . 2... Ce 
where a is the velocity of sound. Hence 
do g . | 
Bae = — a? ee. Hea Sees (3) 
and 
oC=d9 Fai ss oe ° (4) 


where gy is the density at z=0. According to this law, as is 
well known, there is no limit to the height of the atmosphere. 

Before proceeding further, let us pause for a moment to 
consider how the density at various heights would be affected 
by a small change of temperature, altering a to a’, the whole 
quantity of air and therefore the pressure p, at the surface 
remaining unchanged. If the dashes relate to the second 
state of things, we have 


= —g2/a2 fe 12 
O=—d0é g2/ ) g =a, € g2/u ; 


hil P=poe FI", p= poe", 
While 


Coj—@ Op 
If a’ —a?=6a?, we may write approximately 


Pp aay 2 == ba’ gé e—82/a?, 
Po a” a 

The alteration of pressure vanishes when z=0, and also when 
z=0. The maximum occurs when gz/a?=1, that is when 
p= pole But relatively to o, (p’—po) increases continually 
with z. 

Again, if p denote the proportional variation of density, 

ao’ —o 


oO 


Oh is 
p = ar aka tga _ 1), 
If a’>a’, p is negative when z=0, and becomes + when 
zg=o. The transition p=0 occurs when gz/a?=1, that is at 
the same place where p’—p reaches a maximum. 


Vibrations of an Atmosphere. 175 


In considering the small vibrations, the component velo- 
cities at any point are denoted by u, v, w, the original density 
o becomes (o+¢p), and the increment of pressure is 6p. On 
neglecting the squares of small quantities the equation of 
continuity is 


or by (3), 
dp ,du , dv , dw_ gw _ 5 
an dy at OE ple Le eh os (C5) 
The dynamical equations are 
dip __du dip __dv_  ddp 


CORALS Camas se 
de ° dt’ dy Falta [dtiabidests °°. Sgn: din’ 
or by (3), since 


am, dis ee aes 
We will consider first the case of one dimension, where u, v 
vanish, while p, w are functions of zandt only. From (5) 


and (6), 


de dw gw 

eae ae 
dp dw 

De sy os ° ° e ° e e e 
dz aan (8) 


or by elimination of p, 
il -dw ao go aw 


ee 

The right-hand member of (9) may be written 
d 2 2 

(cae)? aa® 
and in this the latter term may be neglected when the varia- 
tion of w with respect to z is not too slow. If 2% be of the 
nature of the wave-length, dw/dz is comparable with w/)d ; 
and the simplification is justifiable when a? is large in com- 
parison with gd, that is when the velocity of sound is great in 
comparison with that of gravity-waves (as upon water) of 
wave-length >». The equation then becomes 


d?w a d g Vw 
ae. der ne : 


bo 


oR af 


176 _ Lord Rayleigh on the 
or, if 
w= Werle, . . ite 
GN gia NV 
dt? Su dz ’ (11) 


the ordinary equation of sound in a uniform medium. Waves 
of the kind contemplated are therefore propagated without 
change of type except for the effect of the exponential factor 
in (10), indicating the increase of motion as the waves pass 
upwards. ‘This increase is necessary in order that the same 
amount of energy may be conveyed in spite of the growing 
attenuation of the medium. In fact w*c must retain its value 
as the waves pass on. 
If w vary as e’”’, the original equation (9) becomes 


Cw gdw., nw 


dz es ae ae oe =(). * e e e (12) 


Let m,, mg, be the roots of 


Ft . so that 
BF Gt (9° —4'e? 
Ege?) oo 
then the solution of (12) is 


w= Ae™* + Bem*, : (14) 


t | A and B denoting arbitrary constants in which the factor e”4 
i may be supposed to be included. 

il The case already considered corresponds to the neglect of 
a g? in the radical of (13), so that 

; Ab + 2naz 

a and 


we ele — Rede) + Bent cia) | 
A wave propagated upwards is thus 
wes cosn(t—zja), . .” 7) (tb) 
and there is nothing of the nature of reflexion from the upper 
atmosphere. 
A stationary wave would be of type 
= poge/a = de 
w= ere cosntsin—, . . re 


w being supposed to vanish with z. According to (17), the 


Vibrations of an Atmosphere. 177 


energy of the vibration is the same in every wave-length, 
not diminishing with elevation. The viscosity of the rarefied 
air in the upper regions would suffice to put a stop to such 
a motion, which cannot therefore be taken to represent any- 
thing that could actually happen. 

When 2na<g, the values of m from (13) are real, and are 
both positive. We will suppose that m, is greater than 
m,. If w vanish with z, we have from (14) as the expression 
of the stationary vibration | 


COG ne eM — Ere Vee in vide (L8) 
which shows that w is of one sign throughout. Again by (8) 


; emz ome 
ap=nsin ni} = - SRE ECTS 
m Mg 


1 


Hence dp/dz, proportional to w, is of one sign throughout ; 
p itself is negative for small values of z,and positive for large 
values, vanishing once when 


Care all Mose Wists i), Aiea oni 20)) 
When vn is small, we have approximately 


G7 ne Oe 
ie a2 aiuone eka OR 0 5 5 ° (21) 
so that p vanishes when 
2 
92/0? — — + as eaeaamerveian ton 22) 
‘or by (4) when 
Gi Gp (AO oe anice a ees (OG) 


Below the point determined by (23) the variation of density 
is of one sign and above it of the contrary sign. The inte- 
grated variation of density, represented by li op dz, vanishes, 
as of course it should do. 

It may be of interest to give a numerical example of (23). 
Let us suppose that the period is one hour, so that in C.G.S. 
measure n= 27/3600. We take a=33 x 10*,g=981. Then 


1 
7/90= 9993 


showing that even for this moderate period the change of 
sign does not occur until a high degree of rarefaction is 
reached. 


Bes Maia | 


178 - Lord Rayleigh on the 


In discarding the restriction to one dimension, we may 
suppose, without real loss of generality, that v=0, and that 
u, w, p are functions of # and z only. Further, we may 
suppose that x occurs only in the factor e*; that is, that the 
motion is periodical with respect to w in the wave-length 
27/k; and that as before ¢ occurs only in the factor e”. 
Equations (5) , (6) then become 


: 2 
rent, 9 Sr epee ta eees 


Oe 


inp +ikus & —2 =0, Me 24) 


akp=—nu, . « . . «| =e 
adpldz=—imw; . . 2. =e 


from which if we eliminate u, w, we get 


- ' o . “ _ 
‘ 
Oe ee 


@p gdp, jm_, ; 
qa ae tae P= o \e. ie (27) 
an equation which may be solved in the same form as (12). 
One obvious solution of (27) is ofimportance. If dp/dz=0, 
so that w=0, the equations are satisfied by 


=P. 2. | 2 SS) 


Every horizontal stratum moves alike, and the proportional ) 
variation of density (p) is the same at all levels. _ The possi- ; 
bility of such a motion is evident beforehand, since on account 
of the assumption of Boyle’s law the velocity of sound is the 
same throughout. 


In the application to meteorology, the shortness of the 
more important periods of the vertical motion suggests that 
an “equilibrium theory” of this motion may be adequate. 
For vibrations like those of (28) there is no difficulty in taking 
account of the earth’s curvature. For the motion is that of 
a simple spherical sheet of air, considered in my book upon 
the ‘Theory of Sound,’ § 333. If r be the radius of the 
earth, the equation determining the frequency of the vibration 
corresponding to the harmonic of order A is 


wr=hh+l1)d, . . . 


the actual frequency being n/27. If 7 be the period, we 
have 
277 


ee 
a Vh(h+1) 


For A=1, corresponding to a swaying of the atmosphere 


(80) 


Vibrations of an Atmosphere. 179 


from one side of the earth to the opposite, 


2rr 
7) a/2’ ; . ° . 6 ° e (31) 


and in like manner for h=2, 
eer. OT 

To= V6 = Wes . coon ese © (32) 
To reduce these results to numbers we may take for the 
earth’s quadrant 

tar=10° cm. ; 
and if we take for a the velocity of sound at 0° as ordinarily 
observed, or as calculated upon Laplace’s theory, viz. 33 x 10° 
em./sec., we shall find 
eo ey 

Ey 2335010" 


On the same basis, 


- seconds = 23°8 hours. 


T,—=13°¢ hours. 


It must, however, be remarked that the suitability of this 
value of ais very doubtful, and that the suppositions of the 
present paper are inconsistent with the use of Laplace’s 
correction to Newton’s theory of sound propagation. In a 
more elaborate treatment a difficult question would present 
itself as to whether the heat and cold developed during atmo- 
spheric vibrations could be supposed to remain undissipated. 
It is evidently one thing to make this supposition for sonorous 
vibrations, and another for vibrations of about 24 hours period. 
If the dissipation were neither very rapid nor very slow in 
comparison with diurnal changes—and the latter alternative 
at least seems improbable—the vibrations would be subject to 
the damping action discussed by Stokes *. 

In any case the near approach of 7, to 24 hours, and of 7, 
to 12 hours, may well be very important. Beforehand the 
diurnal variation of the barometer would have been expected 
to be much more conspicuous than the semi-diurnal. The 
relative magnitude of the latter, as observed at most parts of 
the earth’s surface, is still a mystery, all the attempted ex- 
planations being illusory. It is difficult to see how the 
operative forces can be mainly semi-diurnal in character ; 
and if the effect is so, the readiest explanation would be ina 
near coincidence between the natural period and 12 hours. 
According to this view the semi-diurnal barometric move- 


* Phil. Mag. [4] i. p. 305, 1851. ‘Theory of Sound,’ § 247. 


eer tan 


180 Prof. E. Gerard on the Process of 


ment should be the same at the sea-level all round the earth, 
varying (at the equinoxes) merely as the square of the cosine 
of the latitude, except in consequence of local disturbances 
due to want of uniformity in the condition of the earth’s 
surface, 


Terling Place, Witham, 
ec. 1889. 


XVIII. Process of Plotting Curves by the Aid of Photography. 
By Hric Gerard, Professor of Electricity at Montefiore 
University, Liege™. 


‘hoih eee eh of registering automatically are being em- 
ployed more and more in the “technique” of natural 
sciences. The indicator serves as a faithful and patient 
observer when it has to register phenomena of slow move- 
ment. It is also possible to make use of it to note displace- 
ments which are too rapid for our senses to observe. The 
registering of rapid movements is most often effected by a 
style fastened to a movable arm, which traces on a rotating 
cylinder covered with lampblack. When the movement of 
the cylinder is not perfectly regular, and when the law of 
displacement in terms of its duration is required, the time is 
registered by the aid of an electric chronograph regulated by 
a tuning-fork. This process has led to important results; but 
it is not easily applied when it is required to mark the path 
described by very light moving arms, or indicators, with very 
small forces to move them. In such cases the optical method 
by mirror-galvanometer, with lamp ; and with the traces fixed 
by means of photography, is available. This has been done for 
curves measuring variable electric currents, which have been 
the subject of research in the laboratory of the Montefiore 
Hlectro-technical Institute in the University of Liege. 

For this purpose we require an extremely delicate deadbeat 
galvanometer, with a movable coil of little inertia (electro- 
magnetic system of MM. Despretz and D’Arsonval). A beam 
from an electric lamp was thrown upon a small concave 
mirror fixed to the movable part of the galvanometer, so as to 
give an image, focused by a lens upon a registering cylinder, 
which was covered beforehand with a sheet of paper sensitized 
with a gelatine emulsion of bromide of silver. The time was 
recorded simultaneously on the cylinder by means of a second 
beam of light thrown on a movable concave mirror, the axis 
of which was placed on the prong of an electric tuning-fork. 


* Communicated by Sir W. Thomson. 


- 
Ae 
. aa 


Plotting Curves by the Aid of Photography. 


A simplification of this method by which 
the need for the separate time-curve is done 
away with has been worked out success- 
fully and has given us good results, in the 
Montefiore Institute. The photographie 
record is produced by a spark obtained 
from a Ruhmkorff coil of ordinary dimen- 
sions. The induction-spark passes between 
a strip of magnesium and a carbon-point, 
like that which is used in an arc-lamp. 
The two electrodes are fixed less than 1 
millim. apart. The spark is thrown ona 
concave mirror attached toa galvanometer- 
needle, or other body whose motions are 
to be observed, and reflected thence to the 
sensitized paper, covering either a rotating 
cylinder, or a frame descending between 
guides. The periodicity of the spark de- 
termined by the elasticity of a spring used 
in the inductive break-make, shows natu- 
rally the time-interval by divisions on the 
curve corresponding to equal accurately 
known intervals of time. The breaks are 
effected by an electric tuning-fork of known 
period. <A single circuit is then formed, 
including the battery, the primary wire, 
and the coil of the tuning-fork. 

A short white spark is obtained, the 
position of which is invariable, by connecting 
the terminals of the secondary coil to the 
coatings of a Leyden jar. Besides, it is 
well to reduce the image of the spark by 
introducing a double concave lens in the 
path of the reflected ray. 

By way of illustration of the method we 
give a curve representing the variation of 
magnetic field in the air-space of an electro- 
motor. A short length of straight insu- 
lated wire was fixed to the armature pa- 
rallel to the axis. This wire was connected 
at its end to rings, insulated and fixed 
on the axle of the motor. Brushes press- 
ing on the rings were connected to a 
galvanometer, of which a description is 
given above. The ordinates of the curve 


181 


Saar 
~<_ 


182 Mr. A. Schuster on the Disruptive Discharge 


are proportional to the currents induced in the movable 
wire, and hence represent the intensity of field traversed by 
the wire in the successive positions which it occupies around 
its axis. The time-intervals between the ordinates corre- 
sponding to the dots forming the curve are hundredths of 
a second. 


XIX. The Disruptive Discharge of Electricity through Gases. 
By ARTHUR ScHusTER, /.R.S.* 


ae phenomena connected with the disruptive discharge 
of electricity through gases present some special diffi- 
culties which have hitherto withstood all efforts to form a 
consistent theory. Some time agof I presented to the Royal 
Society an outline of a general theory of electric discharge, 
which has been so favourably received by nearly every one 
who has been working at the subject { since, that Iam en- 
couraged to trace out its consequences in various directions. 

Prof. Chrystal § concludes an interesting paper on the dis- 
ruptive discharge as follows :— 

‘¢ With the same end in view, IJ think it would be desirable 
to reduce the experiment of Baille and others with spheres, in 
cases where the surface-density can be calculated, and to 
examine the values of the dielectric strength in these cases. 
Until this or something equivalent is done, it is clear that we 
have really no experimental ground for asserting the exist- 
ence of such a constant as the dielectric strength of a medium, 
and therefore cannot take the very first step towards a physical 
theory of the disruptive discharge, which appears to me to be 
the next great advance to be made in the science of electricity.” 

The present paper is divided into two parts. In the first 

lace I have reduced the numerical results obtained by Baille 
and Paschen for the discharge between spheres. The result 
quite justifies Prof. Chrystal’s caution, for it appears that the 
so-called dielectric strength of a medium depends on so many 
circumstances that there seems to be no sufficient reason to 
consider it at all as a special property of the medium, except, 
perhaps, in the case of a perfectly uniform field. In the 


* Communicated by the Author. 

t+ Proc. Roy. Soc. xxxvii. p. 317 (1884). 

{ Dessau, Wied. Ann. xxix. p. 362 (1886); Warburg, Wied. Ann. 
Kd. y 545 (1887); Elster and Geitel, Wied. Ann. xxxvii. p. 315 
(1889). 

§ Proceedings Royal Society Edinburgh, 1881-82, p. 487, 


of Electricity through Gases. 183 


second part of the paper I have discussed the discharge from 
the theoretical point of view, and although no very definite 
results are arrived at, owing to our ignorance of the properties 
of a gas in the layer which is in contact with the solid, I 
hope the discussion may serve to point out the direction in 
which further experimentation is at present desirable. 


Part I.— Calculation of the Disruptive Tension at the Surface 
of a Sphere. 


Whatever idea we may form of the nature of a disruptive 
discharge, it seems natural tosuppose that the spark passes when 
the normal force at some point of a conductor has reached a 
certain value. If the discharge takes place between two equal 
spheres, the point for which the normal force R has to be cal- 
culated is on the line joining the centres, where RB has its 
greatest value, for it is there that the spark will pass. I shall 
use the equations in the form given them by Kirchhoff*; and 
treat of the case only in which one of the spheres is at poten- 
tial zero: the problem then consists in finding the potential 
of the other sphere when the normal force, where it is greatest, 
has reached a certain value. 

If ais the radius of the spheres, ac the distance between 
the centres, R the normal force at that point of the sphere 
having a potential V which is nearest to the sphere of zero 
potential, we have the equation 


R= Micra sh iuactad ol emer) 


where y is a function of ¢. 


Writing 
2g=c— VC—4, ©) 
m—1 
= al I a 2) dq? 7¢ mg 2 2 
| Oa ae eae 1—g ae ={—g™ (3) 


we obtain easily from Kirchhoff’s equations, 


y= Do fe areas ta aa C'S) 


When the spheres are near each other so that ¢ is nearly 
equal to 2, and therefore g is nearly one, the series (3) con- 
verges very slowly, and the potential has to be calculated in 


* Collected Works, p.78. There is a misprint in the equation for 
d°U/d¢? on p. 99. The factor on the right-hand side of the equation should 
be 4 instead of 3. 


ee 


Oey 
a4 


184 Mr. A. Schuster on the Disruptive Discharge 


some other way ; but the above series will be the most con- 
venient to use whenever the shortest distance between the 
spheres is greater than the tenth part of the radius of either. 
The Tables I have prepared will, however, save future observers 
all trouble of calculation. The following remarks will suffi- 
ciently explain the way in which they have been calculated. 
If, in the general term of series (3), the value of g” has be- 
come sufficiently small to be neglected compared to unity, the 
remaining terms can be added up without further trouble ; for 
m+1 m—1 
(m—2)q *? +mq ? 
+9? 


When the distance between the spheres is small, it is found 
more convenient to change the form of series (3) so as to 
render it more quickly convergent. We may expand each 
term of the series in powers of g and add up all the first 
terms, V1Z. :—— 

1—39+59¢’—Tq + ae 
she cea 

Treating the second and subsequent terms similarly, we 
obtain 

0-9) GOED et-)) e 
Aaah ek * are? 1 


Here, again, the terms may be added up as soon as g4”*! can 
be neglected. Finally, we may transform the equation still 
further by multiplying numerator and denominator with 
(1—g‘"*1)?, finding thus 


JUS Oe Mire) gaa 
AD= Top Fag? * =e 

In this equation the denominators very quickly approach 
the value unity. [ have given the series in its various forms 
as I find that individual computers differ much in their pre- 
dilections for particular forms, and as the relative trouble of 
calculating the different series differs according to the degree 
of accuracy required. 

Table I., which I have calculated for the objects of this 
paper, may be useful to others. The first column gives the 
distance between the centres in terms of the radius of either 
sphere, which is the value called c above. 

The second, third, and fourth columns give g, f(g), and y, 
defined by equations (2), (8), and (4). Column 5 gives a 
quantity, 2, which will be found useful for purposes of inter- 


m—l1 m+1 m+3 


=mg 2 —(m+2)q 2 +(m+4)q ? —... 


of Electricity through Gases. 185 


polation when yis wanted for spheres which are near together 
and for a value of ¢ not directly given in the Table. If e is 
the smallest distance between the spheres, that is the explo- 
sive distance, w is defined by the equation 


SG ah Settee tt ae aad (5) 


If the normal force were to vary uniformly between the 
spheres we should have h’/=V/e, and a is the numerical factor 
which has to be applied to R’ in order to obtain the true value 
R. Column 5 shows that # varies with sufficient uniformity 
to render interpolation easy. 


TABLE I. 
ie II. IIT. IV. V. 
1 2 
c. q- fa. | a IQ)= x 
q , 
21 7298 9331 10-335 10335 
22 ‘6417 ‘7099 5842 10684 
2:3 5821 ‘6157 3°687 11061 
2-4 ‘5367 5641 2-875 11500 
2-5 5000 5829 2398 1:1990 
2°6 4693 5135 2-089 12534 
Oy ‘4431 5018 1876 1-3132 
2:8 “4202 4953 1-723 13784 
2-9 -4000 ‘4918 1607 1:4463 
3-0 3820 ‘4908 1517 15170 
35 3139 5059 1-273 19095 
4-0 2680 5324 1:169 2-338 
5:0 2087 ‘5870 1-084 3-252 
6-0 1716 "6338 1-050 4-200 
70 1459 6723 1-034. 5172 
8-0 1270 ‘7037 1024 6-144 
9:0 1125 7299 1-018 7-126 
100 ‘1010 ‘7519 1-014 8-112 
100-0 0400 "8892 1:002 


When the explosive distance becomes less than the tenth 
part of the radius of the spheres, the series given above can- 
not be used with advantage. Plana™ has written an elaborate 
memoir on the distribution of electricity on two spheres which 
are near together. Unfortunately he expresses everything in 
terms of the total charge of the spheres, which itself is un- 
known ; and his formule are not, as far as I can see, useful 
for our present purpose. Kirchhoff+ has given an equation 


* Memorie della reale accademia della scienze di Torino, tomo yii. 


845. 
+ Collected Works, p. 96. 


=o 


— 


ree < 


Oe 


Se a 
3 Sees 


, 
{ 
if 
vest ip 
SBE 
cae 
ovat 1 ’ 
Os 
a 
ey 
oe 
‘ 
at 
at 
va 
is 
ae 
=I 
iI 
1 
t 


PST at) IW 2S RAT Seon Ad 
% an! ~ 

TMI LOT PPI SEI IA SE PLIES LITE LSE ION 

ace = ve 


186 Mr. A. Schuster on the Disruptive Discharge 


in which the quantity called y above is expanded in powers 
of log g. Ifthe spheres are near together so that g is nearly 
equal to one, the higher powers of log g become sufficiently 
small to be neglected. Kirchhoff’s formula is, however, very 
inconvenient for purposes of caiculation, as the determination 
of factors of the series is very complicated. It is of use only 
when the spheres are so near together that the first two terms 
are sufficient. 

I have transformed the equation so as to render it more 
easily applicable to the problem I am discussing, and have 
deduced a very simple expression which will give accurate 
results, if the explosive distance is less than the fifth part of 
the radius of the spheres. If the spheres are further apart, 
the series (3) or Table I. must be used. 

Kirchhoff’s equations applied to the case of two equal 
spheres are as follows:— 


fi—Viyjo, lee | A OE le 


ee Cee 
y 2(1-9) Vg log g™ 


dU 


B au 
Ws 089 ae + 7-5 (log 9)? 


de 
B 2-0 
Seg ae (0g 9) "7px tea 


The factors B are Bernoulli’s numbers and 
U=1/(e + e-°5), 
=flogg. . .9. 1) — 


In order to apply the equations to any special case, we 
have first to obtain qg from equation (2), {from equation (8), 
al “ai 
de? d2 &e. The 
labour of calculation is very great even for a few terms, 
and it is found that the coefficients in the series (7) become 
very large, so that many terms of the series are necessary 
even for comparatively small distances between the spheres. 

I shall transform the equations in the first place by ex- 
panding the differential coefficients of U in terms of log “q.m 
start from the equation (De Morgan, ‘ Differential and Inte- 
gral Calculus,’ p. 249) 


and next to find the numerical values of U 


of Electricity through Gases. = Lee 
2 2 4 
2 oe 2s © 


2/(e + e-%) = 2U =1— 


2! 4! 
_ 61.9.0 , 1885.28 ¢ _ 5021. 21.40 
6! 8! Ilr: 


This series is differentiated with respect to ¢, and the 
differential coefficients are expressed in terms of log qg by (8). 
It will not be necessary to give all the steps of the numerical 
transformations. The result is the series :— 


QO =} + Ag(log 7)? + As(log g)*+ Ac(log g)"+... (9) 


where 
Hi 
As a 02083, 
A= = 003038 
= Oe ; 
1891 
A, ='000494, 


A= "000523. 


It will be seen that A,)is greater than Ag, and it is impossible 
to say how large the A coefficients may ultimately become. 
If we compare together the values of y obtained by means of 
(6) and the series (7) with those obtained by the series (3), 
we find that if log g is so small that all terms higher than 
the second in the series may be neglected, the agreement is 
perfect ; for larger values of g, although the series seems to 
converge, it only yields approximate values of y. The con- 
vergence of Kirchhoff’s series does not necessarily imply the 
convergence of the series (7), and we must confine ourselves 
therefore to the use of the latter for such values of log g only, 
for which the series can be shown to give correct results with 
a moderate number of terms. If the explosive distance is small, 
we may obtain a very simple formula by a further trans- 
formation. We call e the explosive distance, and express 
the normal force in the form Va/e as in (5). Let 2 now be 
expanded in a series proceeding by powers of & where k?=e/a; 
a being as before the radius of the sphere. The function of 
g occurring in the equation (6) is to be expressed in terms 
of k. Remembering that ca is the distance between the 


188 Mr. A. Schuster on the Disruptive Discharge 
centres of the spheres, we obtain 

GO SAU? 

ela=c—2=F’, 
Also from (2), 
c=(1 +) /g=r +2, . . eee) 
P= (1—g)*/g, or k=(1—9)/ vq. | 
From (10) it follows that | 

+4=(14+9)%/q, | 
and therefore that | 


SOS eh a aE EE 


and hence 


(+4) = 
— k2+4 hee k / 2 aes nee 
Equation (6) now becomes | 

as oma 
Y=— Flog q* 


(11) 


and the series (7), after substitution of Ny in terms of lo 
becomes = wee 


ee ee (ee 1891 Janae | 
O/og I= Fogg * A882 + 9304'S 4 * To3gg60 BF > 9) 


We have still to express log g in powers of k. | 
Differentiating (10) we find ) 


dq (1— =) = Idk, | 


Ldq_ 2gk y 


- = = — —.—— from (11); 
qd P—l Rrenmeis css | 
dlogq _ 2 i ; 
dk mi 2 Q) i 
Vk? +4 Ws ees 
i 
— 184 =1-3(5) aay 3 (Kk) -3 3.5 aes 
dk ; DD ae 5:55 aie 
ag ke ou oe oh! & 
—logig: =m ta grog” aro gi” te 
3 ips : 
BL ak oy Sag Me z aah +. 


24° 640 7168 


of Electricity through Gases. 189 


From this series we may obtain 1/logq and any power of 
rae q in terms of &. Retaining £ as far as the fifth power, I 
nd :— 


Ei ato6 us. 
Iflogq= 7 [1+ oq — 5760" — 967680" ] 


k 
sain (log q)° =k — 3? 


—(log g)’=—F’. 


Therefore 
ii a ol sagt LG3e as 
—hOjlog g= 5 + 94 + Tagg" + ga7560" 
and hence 
ke +A a 
2S 
As R=Vy/a and e=k’a, 


Kamada Neailids akts 


and finally, 


R=7[1+3-° estes er ae 


Fa erin se sia ve |. (12) 


This series converges rapidly as regards the first few terms 
if e/a is small, and the results obtained from it may be com- 
pared with the values of # givenin Table I. Table II. shows 
the comparison. 


TABLE II. 


e—2=e/a. | «x from Series (12). x from Table I. 


——— 


‘1 1:0335 1:0335 
“2 1:0676 1-0684 
9) 1:1725 1:1990 


The equation (12) gives a result therefore which is too 
small by 3 per cent. if the distance between the spheres is 
equal to half their radius ; but the result is correct to less than 


Phil. Mag. 8. 5. Vol. 29. No. 177. Feb. 1890. PP 


; Ne sen 
ook ipsa sian 


ans ig 


+ 


Se ge ea gre ergs 
RSET RI SS 


Ps ASA 


ee 2 ten ens 


STR UPS) nh we NT a oe 
—s andl 


an PNR AY TEE 


saat ae cee ade aa 
esnips ee eh 


~ 
ETA NIE ft 


THE 


190 Mr. A. Schuster on the Disruptive Discharge 


one part in a thousand if the distance is equal to the fifth 
part of the radius. This accuracy is quite sufficient in the 
reduction of any actual observations. 

For values of e/a which are smaller than *2 the last term 
of the series may be neglected, and the equation 


if 2 
R= [1435+ Be | 
é a 


may be used; while for distances between the spheres smaller 
than the tenth part of the radius, 


is correct for all practical requirements. For large distances 
Table I. must be used. 

By the help of this preliminary investigation the reduction 
of all such observations as Baille’s becomes an easy matter. 
Table IIL. gives the values of R at which the spark begins to 
pass according to Baille between spheres of various diameters 
at different distances. If the so-called dielectric strength is 
a constant these values should all be equal to each other. 


TaBLE IIJ.—Values of R for Spark Potential between 
Spherical Surfaces, in Electrostatic Units. 


Radius of Spheres in centimetres. 


Explosive 

distance in Planes. 

Ron re: 3 | 15] 05 | 08 | o17s | 005 
0-05 i) 180 | 186 190 197 206 292 
0°10 147 149 | 153 163 176 198 376 
0-15 135 188 | 141 157, 170 206 425 
0:20 127 igi 137 | 154 170 219 460 
0°25 122 127 | 184 | 154 180 236 478 
0-30 118 124 | 130 | 156 189 253 494 
0-35 116 122) || 129 3) S59 ey 263 516 
0-40 113 12%- | 129 164 204 272 528 
0-45 112 1206) 127 2 iGo 214 278 540 
0-40 112 18) | 124 1.15 Oy, 268 539 
0:45 110 119 | 122 167 206 275 578 
0°50 109 Ae | S125 166 218 296 608 
0-60 106 WG il 2b eas 233 327 639 
0:70 106 7 126 | 188 234 339 667 
0-80 106 123 | 1380 | 192 250 349 685 
0:90 105 120) tag | POL 255 349 708 


1-00 106 | 128 | 188 | 194 | 258 | 349 | 7338 


of Electricity through Gases. 19 


TABLE [V.—Values of R for Spark Potential between 
Spherical Surfaces in Electrostatic Units. 


: Radius of Spheres in centimetres. 
Explosive 
distance in 
centimetres. 1 0:5 0-25 
0-01 336 347 372 
0:02 258 262 277 
0:03 224 236 240 
0:04 206 213 222 
0:05 194 202 215 
0.06 184 190 202 
0:07 175 183 193 
0:08 172 179 192 
0:09 165 174 187 
0-10 164 171 187 
O11 160 167 183 
0-12 159 167 185 
0-14 154 164 187 
0:10 166 175 190 
0-15 155 . 165 190 
0-20 148 162 198 
0:25 145 161 204 
0:30 143 163 215 
0:35 143 166 226 
0:40 142 170 236 
0°45 142 174 249 
0°50 144 180 256 
0°55 145 184 265 
0°60 145 190 272 
0-70 148 196 281 
0:80 151 205 288 
0:90 a3: a 298 
1-00 set ie 301 
1:20 site fis 312 


1°50 one nae 327 


In Table IV. Paschen’s* recent observations have been 
similarly reduced. I have taken the values which Paschen 
gives for the potential necessary to produce the first spark, 
which, according to him, are slightly larger than those for 
the subsequent sparks. 

Tables III. and IV. will be found to agree with each other 
in their main features ; and considering the many disturbing 
influences to which such difficult measurements are subject, 
the individual numbers also compare well with each other. 
The main facts which, whatever their causes, can be deduced 
from the Tables are as follows:— 


* Wiedemann’s Annalen, xxxvii. p. 69 (1889). 
6 


P 2 


al wae 
wate 


192 Mr. A. Schuster on the Disruptive Discharge 


(1) For two similar systems of two equal spheres in which 
only the linear dimensions vary, the breaking-stress is greater 
the greater the curvature of the spheres. 

(2) If the distance between the spheres is increased, the 
breaking-stress at first diminishes. 

(3) There is a certain distance for which the breaking- 
stress 1s a minimum. 

Let us consider how far all or some of these results may be 
due to disturbing influences. 

I do not think there can be a doubt as to the reality of the 
influence of curvature, as that influence shows itself persist- 
ently at all distances and under all circumstances. Sparks 
taken between two concentric cylinders show the same effect, 
as appears from the experiments of Gaugain and Baille. The 
former™, in a valuable paper, came to the conclusion that when 
the spark passes, the surface-density is independent of the 
radius of the outer cylinder. This was to be expected, and 
shows that Gaugain’s method of measuring potential, which 
does not quite come up to our present standard, was sufficiently 
accurate for the purpose in view ; that is to say, that the indi- 
cations of his electrometer were really proportional to the 
potential to be measured. The density o on the inner 
cylinder increased, however, with its curvature, and Gaugain 
found that the relation could be approximately represented by 


the equation 
o=atB/y/r, 
where, with the units employed by him, 
o— iO andor OZ. 

Baille has compared Gaugain’s equation with his own experi- 
ments, but the values for the surface-density calculated by 
Baille do not all agree with the numbers deduced by Gaugain 
himself from the same formula. ‘The cause of the discrepancy 
is found in the fact that Baille, by an oversight, took r in the 
above equation to be the radius measured in centimetres, 
while in the original memoir it stands for the diameter 
measured in millimetres. I have recalculated Baille’s num- 
bers, and the result is given in Table V. 

Column v. in that Table shows a decided though not very 
regular increase of R for diminishing radii of the interior 
cylinder. This increase comes out more clearly in Gaugain’s 
observations, as he worked with cylinders of much smaller 
radius. We may use the last column of this Table to reduce, 
at any rate approximately, Gaugain’s numbers to absolute 
measure. Taking 1°25 as the ratio by means of which Gau- 
gain’s numbers are to be divided in order to reduce them to 


* Annales de Chimie et de Physique, viil. p. 75 (1866). 


of Electricity through Gases. 193 


electrostatic units, we must multiply his surface-density with 
Arr/1-25, or very nearly with 10, in order to obtain R. The 
result is given in Table VI., in which r is the radius of the 
inner cylinder, in centimetres, and R the normal force when 
a spark begins to pass. 


TABLE V. 
Values for Spark-potential between Cylinders. 
P. Dy Inne IV. V. VI. VII. 
Diameter | Diameter o from ele 
of internal of external Explosive Baille's 4no=R.| Gaupain’s o'/o. 
cylinder. | cylinder. | distance. | observa- ae 
2r. 2R. tions. De ae 
6:28 6°86 29 7:24 91 9:03 1:25 
5 GO 56 8:44 106 9:20 1:09 
5:50 68 8°73 110 9-32 1:07 
4°92 ‘97 9:07 114 9°60 1:06 
4-92 532 | 20 9-07 | 114 9-60 1-06 
4-50 “41 8:33 105 9°72 leat 
4-40 46 8:25 104. 9°84 1:19 
4-00 66 8:59 108 10:07 117 
3°66 83 9-92 125 10°30 1:04 
4-00 4-45 23 8:23 103 10:07 1:22 
3°66 “40 8:60 108 10°30 1:20 
3°10 68 8:95 112 10°74 1:20 
2-49 98 9-65 121 11°35 1:18 
2-49 3:00 26 8:46 106 11°35 1:34 
2°20 ‘40 8°74 110 11:73 1:34 
1-78 ‘61 9°76 1.23 12°40 1:27 
1:25 88 10:99 138 13°62 1:24 
TABLE VI. 
r R. 
1:5 110 
5 145 
25 168 
05 282 
013 451 
010 491 
OU6 600 


Comparing these numbers with Table IT., we find that the 
disruption-stress is for two coaxial cylinders not very far 


mi 
a er 


194 Mr, A. Schuster on the Disruptive Discharge 


different from that found for two spheres placed at such a 
distance that the disruption-stress is a minimum. Without 
attaching too great an importance to this apparent coincidence, 
I think we may safely conclude that the explosive distance is 
really a function of the curvature of the surface. 

The second result which may be deduced from Baille and 
Paschen’s observations is, in my opinion, also well established. 
The fact that the breaking-stress diminishes for increasing 
distances between two planes has been known since Sir 
William Thomson’s observations ; and it is well brought out 
in the case of spheres, especially with the larger ones and at 
small distances, that is, just where the disturbances are 
smallest. I shall point out in the second part of this paper 
that the breaking-stress may possibly depend, not only on the 
state of the field at the point where the spark passes, but m 
surrounding portions also. The further the spheres are apart, 
the more nearly will all points of their surface reach the cri- 
tical density at the same time ; and this, in the way to be 
explained, may help the spark to pass. 

I feel much more doubtful as to the reality of the third 
conclusion, that the explosive stress reaches a minimum with 
increasing distances and then increases again; but on the 
whole I believe the evidence to be in its favour. 

There are two causes which tend to increase the observed 
difference of potential when the distance between the spheres 
is larger. There may in the first place be an appreciable 
leakage between the electrometer and the electrodes, and the 
potential registered will in consequence be too high. That 
leakave actually took place in some of Baille’s observations 
is rendered probable by his observations on cylinders. For a 
given surface-density on the inner cylinder the state of the 
medium must be the same whatever the distance of the outer 
cylinder; and there can be no reason therefore that the break- 
ing-stress will depend on the diameter of that outer cylinder. 
Gaugain arrived experimentally at the result which was to be 
expected ; but Baille’s results, as given in Table V., show a 
decided tendency towards a larger apparent normal force for 
greater striking distances, the inner cylinder remaining the 
same. ‘This seems to me to point to a leakage effect. 

The second disturbing cause tending in the same direction 
is the electrification of the leads. Baille gives us no informa- 
tion as to the disposition of his experiments and the size of 
the leads, and seems to consider the difference of potential 
between the electrodes to be the determining cause of the 
spark and not the rate of fall at their surface. There is no 
evidence in Baille’s paper that he realized the importance of 
avoiding the presence of electrified surfaces in the neighbour- 


of Electricity through Gases. - 196 


hood of his spheres. In the absence of any statement re- 
garding the thickness of leads, we can attach no importance 
to Baille’s results as far as his smallest spheres are concerned. 
When their diameter is only one millimetre, we may take it 
for granted that the effect of the wires conveying the charge 
was considerable. 

Paschen has taken this point into consideration, and it 
follows from the information he gives that with spheres of 
5 millimetres in diameter and cylindrical leads of about 3 
millimetres diameter the disturbing effect becomes apparent 
when the sparking distance is greater than 5 millimetres. 
The leads cannot be reduced in size beyond a certain point 
with the usual arrangement of the experiments, as the spheres 
are moved together by a micrometer arrangement, and must 
of course be kept rigidly in their place. 

Making full allowance, however, for the possible effects of 
leads and leakage, I cannot altogether resist the feeling that 
the ultimate increase of potential with increasing distance is 
not altogether due to these causes. My chief reason is the 
good agreement between Paschen and Baille’s results in this 
respect. 

For spheres having a radius of *5 centim. Baille finds the 
minimum of R to take place when the distance is about half- 
way between *20 and :25; while Paschen finds the same dis- 
tance almost exactly the same, though a trifle nearer to'25. It 
seems difficult to believe that a disturbing cause should affect 
both observers in exactly the same manner. Tor the smaller 
spheres the distance at which the spark potential is a mini- 
mum is equal to nearly half the radius of the spheres. This 
is shown in the following Table :— 


TABLE VII. 


Explosive distance for smallest normal force. 


Radius of spheres. 


Baille. Paschen. 
centim. vr ee 
3 “60 
15 “45 
LOL TA ee HID "42 
5 29 "25 
3 oi 
eT en ec 11 
"175 10 


196 Mr. A. Schuster on the Disruptive Discharge 


Part [l.— Theoretical. 


The attraction between electrified bodies involves a tension 
along the lines of force in the medium which, with the usual 
notation, is equal to KR?/8z. The specific inductive capacity 
K of gases is nearly equal to one, and the stress is therefore 
not much affected by the presence of the gas. It follows that 
the stress is due to a strain in the interstellar medium, and 
that the particles of air have nothing to do with it except in 
so far as we consider them to be conductors which can deflect 
the lines of force in their neighbourhood. We may imagine 
the distribution of electricity on each molecule to be regulated 
by the same law as the distribution on conductors ; and in 
that case the forces tending to produce a passage of electricity 
between the particles of a gas will be proportional to R?, but 
we do not know how large or how small its value may be. I 
adopt the theory that the atoms of a molecule carry the same 
charges as the ions in an electrolyte, and that a spark passes 
as soon as the forces are sufficient to dissociate the molecules. 
I take this opportunity to mention that Mr. Giese has in the 
year 1882, that is, two years previous to the paper in which I 
first applied this theory to the continuous discharge under re- 
duced pressure, explained by the same hypothesis some of the 
electric phenomena of flames. The problem of finding the 
effect of the electric field on the molecules carrying their 
electric charges is very similar to the problems we meet with 
in the theory of magnetism. It is usual to consider two 
vectors inside a magnetized body, the so-called magnetic force 
H and the magnetic induction B, which are related by the 
equation 

B=H+47l, . ... 3 eee 


where I stands for the intensity of magnetization. In the 
problems of induced magnetization I is taken to be pro- 
portional to the magnetic force defined as the force at the 
centre of a thin hollow cylinder inside the magnet. It would 
be more correct to take the magnetizing force as equal to 
the force at the centre of a space left vacant by the removal 
of a molecule; and this force could be expressed in terms of — 
the magnetic force as usually defined and the magnetic in- 
duction. Let the force within the space left vacant by the 
removal of one molecule be G ; we may write 


G=—HFal,.. »... —e 


where n is anumerical quantity, which, if the space left vacant 


of Electricity through Gases. 197 


is spherical, will be 47/3, as already given by John Hop- 
kinson*. Combining the equations (14) and (13) we find 


B=G+ (4r—n)I, 
and if 

Seo as Pee. ee Mists & nG15) 
it follows that 

B=G(1+(47—n)k)=AG, . . . (16) 


which gives the relation between the force G on which the 
magnetization depends and the magnetic induction. 

Let now B stand for the electric induction, and G for the 
electric force tending to separate the ions. The ions will 
separate when G, and therefore B/A, has reached a certain 
value, which value may, however, be different according as 
the molecule is near the surface of the body, or within the 
space occupied by the gas. In the case of electrolytes no 
finite force is required to separate the ions; and it is at any 
rate possible to imagine that if there is a condensed layer of 
gas on the surface of the electrode, the critical value of B/X 
may not be as great as if the particles were altogether inde- 
pendent of each other. 

The most remarkable fact connected with the disruptive 
discharge seems to me to be the apparent diminution of 
dielectric strength with a diminution of pressure. Imagine 
the state of a molecule in the gas just before the spark passes 
at atmospheric pressure ; next imagine half the number of 
molecules to be suddenly removed. Why should the discharge 
now pass? What difference can the removal of some mole- 
cules make in the state of those which are still left? None, 
as far as I can see, unless a great change in the inductive 
capacity has taken place. But no sufficient diminution of 
inductive capacity is observed within the bulk of the gas; and 
unless our present ideas are altogether wrong, I can see no 
way out of the difficulty except by assuming a surface-layer 
of gas in contact with the solid having a large inductive 
capacity. If the layer is thin the electric displacements will 
not be materially changed by its presence; and if the discharge 
begins within the layer we have to substitute in B/A, for \ the 
inductive capacity not of the gas itself, but that of the con- 
densed layer. If is large in equation (16) above, » will be 
nearly proportional to the density of the layer, and will there- 
fore diminish with the pressure. There seems to me to be no 
difficulty in imagining the value of & in a gas to be large 


* Phil, Trans. clxxvi. p. 468 (1886). 


198 Mr. A. Schuster on the Disruptive Discharge 


close to the surface of the solid; and if we once admit the 
possibility of such a contact-layer which diminishes in 
density by a reduction of pressure, some of the most 
puzzling tacts of the disruptive discharge admit of explana- 
tion. One objection, which occurs to me, must be answered. 
It may be said that if is large near the surface of the solid, 
the spark will start wherever B/A is largest, and therefore not 
within the condensed layer, but between it and the remainder 
of the gas. This objection would be justified if we take the 
discharge to be a passage of electricity between the molecules; 
but according to the theory I advocate the dissociation of the 
molecules may, as already explained, take place more easily in 
the condensed layer, and probably soonest in direct contact 
with the metal. 

Let us see how far the theory is capable of dealing with the 
known difficulties of the discharge. I think it will be found 
sufficient to explain the fact that when the planes or spheres 
are near together, the normal force sufficient to produce a 
spark diminishes with increasing distance of the conductors. 
No explanation which has as yet been suggested can deal with 
this fact. Prof. Chrystal, in the paper quoted above, has 
really disposed of all suggestions except one proposed by him- 
self, which, however, does not seem to me to be supported by the 
observations on spheres. According to the views of this paper 
the polarized particles within the surface-layer of the gas can 
slide along the surface of the electrode, and will do so under 
the action of the electric forces. They will crowd together 
where the field is strongest, that is to say at that point at 
which the spark is about to pass. The increased number of 
particles will increase A, and will therefore introduce an 
additional impediment to the formation of the discharge. As 
the conductors are removed, the field will become more and 
more uniform all round, the particles will no longer crowd 
together to the same extent, and the spark will pass more 
easily. 

The increased stress required to produce a spark when the 
striking-distances are small are due therefore, if Iam correct, 
to the inequality of the field along the surface of the con- 
ductor. In the case of plane surfaces which are opposed to 
each other, the inequality lies between the back and front of 
the plates, and the surface-particles will be drawn from the 
back to the front. A fact which seems to me to support the 
idea that some such thing may take place has been deduced 
by Mr. G. Jaumann* from a large series of experiments. 


* Wrener Berichte, July 1888. 


of Electricity through Gases. 199 


Mr. Jaumann comes to the conclusion, which appears well 
supported by the evidence he gives, that the potential required 
to produce aspark is the greater the more slowly the potential 
is raised to its final value. If the potential is raised quickly, 
so that, according to our view, no time is given for the par- 
ticles to move along the surface of the conductor, the spark- 
potential has much smaller values than those usually given. 

I am not very confident that a satisfactory explanation of 
the observed effects of curvature can at present be given. IEtf 
a surface-layer such as I imagine really exists, forces of the 
nature of surface-tensions may modify its properties. But it 
is also possible that the density of the layer may depend, not 
only on the inequality of the field at different points of the 
surface, but also on the inequality of the field along the nor- 
mal to the surface. Particles may be drawn by the electric 
forces from the gas into the surface-layer whenever there 1s a 
rapid variation of the field along the normal. If the polarized 
particles point in the direction of the lines of force, they will 
tend to move along them under the action of a force propor- 

2 
a where V is the potential ; and this quantity is 
the larger for the same value of R the greater the curvature 
of the surface. It is possible that this is the explanation of 
the greater spark-potential required for small than for large 
spheres. The two effects combined may explain the fact 
that when the spheres are moved away from each other, the 
breaking-stress at first diminishes and then increases again. 
For small distances the inequality of the field along the sur- 
face causes a crowding of the molecules, and for large distances 
the inequality of the field along the normal produces the same 
effect. At intermediate distances it is probable that either a 
maximum or a minimum of the normal force should take 
place, but which it should be it is impossible to predict theo- 
retically at present. 

I do not attach very much importance to some of the sug- 
gestions I have made in order to explain a quantity of very 
puzzling facts; butitseemed to me to be worth while to place 
them before the public, as others may be induced to join in an 
experimental investigation which promises to yield results of 
importance. 

I have to thank Mr. H. Holden for much assistance in the 
numerical calculations contained in this paper. 


tional to 


Rit 


fs 2OOw | 


XX. On the Behaviour of Steel under Mechanical Stress. 
By C. A. Carus-Witson, B.A., AML C_E., Demonstrator 
in the Mechanical Laboratory at the Royal Indian Engineering 
College, Coopers Hill”. 

[Plates III.—-V.] 


HE effect of uniform longitudinal stress on a steel bar is 
threefold —— 
(i.) The molecules are strained. 

(ii.) The elements are strained. 

(ui.) In virtue of the straining of the elements “ flow ”’ is 
produced. 

The strain usually observed is the elongation due to flow, 
which may be recoverable or irrecoverable. ‘The strains of 
an element can be shown to bea uniform dilatation combined 
with a uniform shear about an axis parallel to that of the bar ; 
hence the elongation due to flow consists of a sliding combined 
with an increase of volume. 

The state of strain of an element may be conveniently 
described by defining the shape, size, and orientation of the 


strain quadric, which is a sphere of radius ay / : combined 
with an hyperboloid of two sheets whose principal semi- 


diameter is a: “ and axis parallel to that of the bar ; where 


p is the intensity of longitudinal stress, n the rigidity, and 


k the bulk modulus. 

Up to a certain stress the elastic properties of the steel are 
such that the strain produced is recovered when the load is 
removed, but at that stress the elastic resistance is overcome, 
and the molecules slide over one another, the strain being 
permanent. , . 

This sliding beyond the limit of elastic resistance does not 
continue. The elastic resistance is raised by the sliding, and 
consequently the sliding is limited. 

A stress-strain curve can be drawn which shows the in- 
crease of the limit of elastic resistance p with sliding; the 
rate of increase of the former at any point may be measured 
by observing the angle which the tangent to the curve at that 
point makes with the axis of strain; I will call this angle @. 

The initial value of p is often taken as an indication of the 
“hardness ”’ of the steel, and when p is raised by permanent 
strain the steel is said to be “ hardened ” thereby. This, how- 
ever, conflicts with a measure of hardness usually employed, 


* Communicated by the Physical Society : read December 6, 1889. 


Behaviour of Steel under Mechanical Stress. 201 


namely the amount ef permanent strain caused by performing 
a given amount of work on a bar. 

Thus if a hard steel edge attached to a weight is allowed 
to fall on the surface of a steel bar, the depth of the indenta- 
tion is taken as a measure of the softness of the metal. 

If we draw the stress-strain curve O P for the steel under 
examination, the work done in producing a permanent strain 
O Dis the area OP D. If OQ represent the stress-strain 
curve of a harder bar, the same amount of work, OQC will 
clearly produce less permanent strain, O C. The hardness 
then is evidently determined by the form of the curve; but 
this depends upon the rate of increase of p with permanent 
strain, 7. e. upon the value of d. Hence tan@d is the true 
measure of the hardness; but tan¢ is not constant, it dimi- 
nishes : therefore the initial value of tang must be taken as 
the measure of hardness. It will be seen that p cannot be 
taken as a measure of the hardness, for p is the same at R and 
P for the two bars, but the former is obviously the harder*. 

We can say, then, that permanent strain raises the limit of 
elastic resistance, but diminishes the hardness—defined as the 
rate of increase of p with permanent strain. 

I imagine itis because the harder steel has the greater value 
of initial p that p has been taken as a measure of the hardness. 

If a bar of soft steel be taken and cut in four pieces; No. II. 
“hardened” in oil; No. ILI. in water [alkaline]; No. IV. in 
water [acid]; if each piece is now tested we shall obtain stress- 
strain curves as in fig. 1, Plate III. A curve can be drawn 
through the points OABCDEF, which I will call the 
“vield-line”’; this will be the locus of all points such as A 
and EF for pieces of the same bar “ hardened” to different 
degrees. ‘The points A, B, C are called the “ yield-points.”’ 

As the piece is harder the yield-point—or initial limit of 
elastic resistance—is higher, and the yield A F is lessf. 

When the yield begins it continues until p is raised by a 
given amount ». If we could show that » was the same for 
each piece, then it would follow that the yields as AF, BE, 
C D are direct measures of the hardness of the piece. 

If there is any inequality or want of homogeneity in the 
bar due to unequal stresses in the manufacture, there may be 
one plane or planes along which the limit of elastic resistance 
is less than along any other. 

Hence when this resistance is overcome sliding will take 
place throughout the bar parallel to that plane or planes until 


* If tang@=0, the bar at that point is perfectly plastic. 

+ Fig. 2, Plate III. is a facsimile of an autographic diagram thus 
obtained: the steel bar was cut in three pieces; A was soft, B hardened 
in oil, and C in acid. 


202 — Mr. C. A. Carus- Wilson on the Behaviour 


the limit of resistance along that plane has been raised, by the 
sliding, to that of the rest of the bar, when the sliding will 
henceforth be uniform. 

In a bar cut into pieces the required increase is the same 
in each piece, only in the harder bar less permanent strain is 
required than in the softer. Hence A is the same in each 
piece and the yield is a measure of the hardness. 

Steel bars and plates can be shown in which the permanent 
strain at the yield-point has clearly taken place as a sliding 
parallel to one plane only. 

It would seem that there was an apparent discontinuity in 
the form of the stress-strain curve at the yield-point. 

The question arises whether the curve may not actually be 
continued through a double inflexion, and be one with the 
rest of the curve as shown by the dotted lines, fig. 1, Plate ILL. 

Let us imagine a solid model made so as to represent at 
any point of its surface a particular condition of the bar with 
respect to stress, strain, and hardness. Let the curves L., II., 
III., 1V. (fig. 1, Plate 1II.) be placed parallel to one another 
at distances from the plane X O Y proportional to the hardness 
which each curve represents, with their origins in the axis O Z 
(perpendicular to X O Y), and let the surface of the model 
be made to pass evenly through all these curves and other 
similar curves which would be obtained at higher and lower 
degrees of hardness. 

We see that from the curve which just passes outside the 
yield-line there is a part of the solid figure entirely wanting. 
It would seem a much more natural view to suppose that in 
some sense the successive curves are theoretically continuous, 
as shown by the dotted line above. 

Such a supposition involves a state of affairs in which the 
limit of elastic resistance decreases as the permanent strain 
increases. 

This would be the case if the sliding at the yield-point 
instead of taking place simultaneously over the whole bar 
parallel to one plane only took place as a strain wave passing 
up or down the bar with a definite velocity without any 
further increase of load. 

This is what actually takes place. Sliding is started at 
one end and takes place along a definite plane, generally at 
A5° to the axis; this disturbs the equilibrium of the mole- 
cules in the parallel plane next to it, and sliding is indueed in 
this plane, so that a wave of strain passes the whole way up the 
bar; or sometimes starting from both ends two waves meet 
in the centre. 

The velocity of the wave varies greatly with the quality of 
the steel; sometimes the wave appears to be instantaneous, 


of Steel under Mechanical Stress. 203 


sometimes so slow that it may take 30 seconds to pass up a 
10-inch bar, in which case the pencil drawing the stress-strain 
curve is seen to follow the wave; in the former case the 
pencil drops as if the bar had broken. 

When the wave starts from one end a plane in the centre 
experiences no permanent sliding until the wave has reached 
the plane next to it, so that while originally the resistance to 
sliding was greater than the stress, now it is less; in other 
words, permanent strain (in an adjacent plane) diminishes the 
resistance to permanent strain. 

The most reliable stress-strain curves are those drawn by 
Prof. Kennedy’s apparatus, and these show a rapid and irre- 
gular inflexion at the yield-point (see fig. 3, Plate III.). In 
these diagrams the record of stress is unaffected by the inertia 
due to the load. 

These stress-strain curves indicate the condition of strain 
in a steel bar as, by gradually increased stress, the steel is 
converted from an elastic solid to a viscous fluid. It is inter- 
esting to compare such curves for steel of different hardness 
with the stress-strain curves of a gas at different temperatures 
(see fig. 4, Plate III.). 

We have the effect of increased 1¢ aban doing 

leld |}: 

inset line. Also 
the strong probability that in both cases the apparent discon- 
tinuity is really a double inflexion due toa change taking 
place piecemeal throughout the substance, and inconceivable 
if the substance be supposed homogeneous (cf. Prof. J. 
Thomson, Proc. Roy. Soc. 1871, no. 130). 

[The stress-strain curves shown in the diagram are from 
Dr. Andrews’s paper (Phil. Trans. vol. clix. 1869, p, 575).] 

Thus far the strains considered have been those due to 
relative displacements of the molecules, but it is impossible to 
conceive that this can take place without the molecules them- 
selves being strained, 7. e. without a displacement of the atoms. 

Such a displacement of atoms, if permanent, would alter 
the chemical and physical condition of the iron. Hence we 
must look to the straining of the atoms to account for the 
change that takes place when a bar is permanently strained, 
2. e. to account for the increase in the value of p with per- 
manent strain. 

Osmond has proved almost beyond a doubt that the so-called 
“hardness ” of steel is due essentially to the existence of an 
allotropic modification of iron ; that the molecules of iron may 
be either («) soft, or (6) hard. (Cf. Osmond’s ‘ Htudes Me 
tallurgiques, Paris, Dunod, 1888.) 


away with the discontinuity at the 


~ “po 


i a 


Rr 3 


204 Mr. C. A. Carus- Wilson on the Behaviour 


Hence the change induced in steel by permanent strain 
must be due to a permanent straining of the atoms in the 
molecule. 

We should then expect to find evidence of a straining of an 
entirely different order and nature to that due to a molecular 
disturbance. Such evidence is forthcoming. 

It has long been known that if a steel bar lying in a mag- 
netic field of limited intensity be subjected to tension in the 
direction of the magnetizing force, the magnetization of the 
bar will be increased. 

I have made a series of experiments on this subject, and 
find that the intensity of magnetization increases regularly 
with the load up to the yield-point. 

The following experiments were made :— 

The bar to be tested was turned in the lathe, and a screw 
cut on each end; it was placed vertically in the testing- 
machine ; to each end was screwed a nut, the top one (A) of 
gun-metal, the lower one (B) of steel (see fig. 1, Plate IV.). 
The former was of gun-metal so as to remove the free upper 
extremity of the bar as far as possible from the neighbourhood 
of large masses of magnetic material. These nuts rest on 
steel collars, C C, which have conical surfaces to fit into coni- 
cal holes in the main shackles, D D, of the testing-machine. 
The bearing of the nuts on the collars is spherical, so as to 
allow of a free movement of the specimen, and to ensure a 
direct pull. A short distance above the upper end of the bar 
a small magnet, EH, is hung by a silk fibre, the suspension of 
which is rigidly attached to the upper shackle, so that any 
small motion of the latter involves the same motion of the 
needle ; a silvered mirror is attached to the needle, which 
reflects a beam of light from a lamp, F, onto a horizontal scale, 
G ; His a controlling-magnet. 

A small displacement is given to the magnet (i.) when 
there is no load on the bar, and the time of 20 complete 
oscillations observed ; (ii.) the same with a small load on; 
(iii.) the load is then removed, and the time of 20 oscilla- 
tionsagain observed. ‘The results are recorded in the accom- 
panying Table. 

Experiment I.—Bar of soft steel, never loaded before: cross 
sectional area 0°306 square inch, 19°5 inches long; elonga- 
tions measured on 10” by a vernier and microscope reading 
to thousandths of an inch. 

An automatic stress-strain diagram was taken (see curve A, 
Plate 1V.). The time of 20 oscillations of the needle was first 
observed with the bar out—102°6 seconds. From this was 
deduced 2”, the square of the number of oscillations per 
minute, and this was deducted from N?, the same when the bar 


of Steel under Mechanical Stress. 205 


was in place. The resultsare plotted on fig. 1, Plate V.as two 
curves, the upper one, A,, being the curve of temporarily- 
induced magnetism, with load on, and the lower one, Ag, that 
of permanent magnetism, with load off. The arrow shows 
the yield-point. The two curves cross one another twice, and 
coincide in a third point. The third curve, Ag, is the curve 
of extensions from the second column of the Table, 186 times 
full size. Curve A,isthe curve of permanent set, same scale 
as As. This bar was broken. The last observation was after 
the fracture. 

Kaperiment II—Bar of soft steel never loaded before : 
cross-sectional area 0°308 square inch, 19 inches long; diagram 
measures elongations of 10”; square of number of oscilla- 
tions per minute with bar out 121; ditto, bar in, no load on, 
1849. The results are plotted as a curve in fig. 2, Plate V. 
The arrow shows the yield-point. The observations at this 
point were taken after the set. The stress-strain diagram is 
shown at B, Plate IV. This bar was broken. 

Haperiment LI[.—W rought-iron bar never loaded before : 
cross-sectional area 0203 square inch. The extensions on 
the diagram, C, Plate IV., are on a length of six inches. The 
results are recorded in the Table, and plotted on fig. 5, Plate IIL., 
the ordinates here representing simply the square of the num- 
ber of oscillations per minute. The arrow shows the yield- 
point. The curves intersect twice. This bar was not broken. 

The circles show the loads at which observations were made. 

From the curves on Plates III. and V., it is evident that 
the magnetic induction is increased in a regular way by 
increased stress, and that the effect is largely permanent ; a 
point is reached, before the yield-point, where the effect 
produced is wholly permanent. The two curves continue 
side by side up to the yield-point, when the large permanent 
set which then takes place completely upsets the former con- 
dition of the bar, as might have been expected. The temporary 
effect is roughly proportional to the elastic extension below 
the yield-point. 

The conclusions to which I am drawn by these experiments 
are :— 

Gi.) Mechanical straining produces an “atomic disturb- 
ance” in a bar which increases regularly with the stress. 

(il.) For small stresses the disturbance is only partly per- 
manent, but as the yield-point is neared it becomes wholly 
permanent. 

(iii.) The magnetic properties of a loaded bar are in general 
different from those of the same bar unloaded, but there is a 
certain stress or range of stresses over which the bar has the 
same magnetic properties whether the load be on or off. 


Phil. Mag. 8. 5. Vol. 29. No. 177. Feb. 1890. . Q 


Seeetieeetieeemeeessn esau 


= 


206 Mr. C. A. Carus-Wilson on the Behaviour 


In Experiment I. the range of stress referred to in (iii.) is 
about 15 to 22 tons per square inch, the latter being the 
yield-point ; and in Experiment III. it is about 10 to 15 tons 
per square inch, the latter being the yield-point. In HExperi- 
ment II. the critical stress appears to coincide very nearly 
with the stress at the yield-point. 


It is interesting to compare these results with those obtained : 


by Joule. In his ‘ Scientific Papers,’ pp. 253-256, Joule 
shows that an iron or steel bar elongates on being magnetized, 
but that if the bar is strained, the effect is reduced until, at 
a certain load, no effect is observed, and if the load be further 
Increased, magnetization produces a shortening of the bar. 
These experiments were made with soft iron and steel wires. 

Joule’s experiments show that magnetization produces a 
minute elongation of a bar, those quoted above show that 
mechanical stress increases the magnetization of a bar, 2. e. 
mechanical stress produces a change similar to that pro- 
duced by magnetization. It would seem, then, that Joule’s 
critical point of no elongation (+ or —) must be reached 
when the molecular elongation produced by the mechanical 
stress is the same as that which would be produced inde- 
pendently by a certain given intensity of magnetization. For 
at that point, the molecular elongation having already been 
produced by mechanical stress, the effect of the given magne- 
tization would be nil, z. e. there would be no further elonga- 
tion (+ or —). Now, taking an intensity of magnetization, 
denoted by 5 in Joule’s experiments, we see that this produces an 
elongation in a 12 inch length of soft iron wire (0°25 in. diam.) 
of j5,9 in.3 assuming Young’s modulus for the iron at 13 x 10° 
tons per square inch, the mechanical stress required to pro- 
duce this elongation would be about 0-03 ton per square inch. 

According to Joule’s experiments the critical stress is at 
about 6 tons per square inch, 7. e. in order to produce this 
molecular elongation by mechanical means we require an 
elongation of the bar 200 times as great as that which accom- 
panies the same effect produced by magnetization. 

We are thus dealing with two distinct kinds of elongations— 
firstly, that produced by a relative motion of the molecules; 
and secondly, that produced by a straining of the molecules 
themselves. 

It is clear that if the atomic displacement should be perma- 
nent, there would be a permanent change in the physical and 
cheinical properties of the iron; and as there certainly is a 
change produced by permanent set, it is highly probable that 
we must look to such a straining of the molecule to account 
for it. 


—————— 


ee 


of Steel under Mechanical Stress. 207 


Thus, taken in conjunction with Osmond’s experiments, 
those quoted above would seem to show that the increase in 
the value of the limit of elastic resistance with permanent 
strain is due to a permanent straining of the individual mole- 
cules. 

Experiment I.—Steel Bar. 


| = ‘ E s a1 © 
Peet aS bow |) a |} aoe < 
oes eee et i=) 8 lees ek) Ne 
5 & |Hse | 4 = S |HSF] @ 
= Bie, = ZS 
qn ex) 
00 L417, | 249 218 0-0 1-418 18-9 389 
Ol 1-417 24°85 219 5-4 1:457 18°7 398 
0-2 1-417 25°0 217 0-0 1:418 18:7 398 
0-4 1-418 248 221 0:0 1-418 18°65 400 T 
0°0 1-417 24°85 219 5°6 1-458 18-65 400 
0°6 1420 } 24°75 221 0-0 1-418 | 186 403 
08 1-420 | 246 224 58 1-463 | 18-7 398 
1:0 1-422 | 24:55 225 0-0 1-420 18°5 407 : 
0:0 1-417 24°9 219 6-0 1-465 18:3 416 | 
1-2 1-424 | 24-1 234 0:0 | 1:420 18:5 407 | 
14 | 1°425 23°7 243 6:2 1-465 18°35 414 
16 1426 | 23°35 250 0-0 1-420 18-4 412 ; 
18 1-427 22°4 273 6-4 | 1:467 18:2 421 
2°0 1-428 | 21:3 289 CORP iAa2ZL 18°55 405 
0-0 1-417 22°6 268 6°6 1-469 18:3 416 
0-0 1-417 | 22°5 Pals 00 | 1-421 18:3 416 
2°2 1:430 | 20°9 316 68 | 1-470 18-0 431 
2-4 1:431 20°55 327 OO i421 18-6 403 
26 | 1483 | 20-4 332 70§ 
28 | 1434 | 203 336 0-0 | 1:455 18°8 394 
30 | 1:436 19°85 352 70 § 
OOM) LAV) 1207 322 0-0 | 1-507 19-2 377 
0-0 1-417 | 20°75 321* || 7T-0§ 
32 | 14387 19°6 361 00 | 1:538 19°4 369 : 
34 | 1-438 19°5 365 0-0 | 1:538 19°5 365 ft 
36 | 1:489 19°65 359 T7 | 2:095 17-95 433 | 
3°8 | 1-440 19°6 361 00 | 2°036 | 25°35 210 
40 | 1442 | 19°45 367 SOs 278 16°5 515 
OOF) 4li-| 20:05 344 OOM 2 25205 216 
0:0 | 1417 19°9 300* || 83 | 2323 | 168 497 
4:2 | 1°444 ISP I 381 0:0 | 2:248 | 25°45 209 : 
0-0 1-417 19°75 309 86 | 2-455 16°65 506 
4-4 1-446 19°15 379 O70 | 2:374 | 25:7 204 
0-0 1°417 19°45 367 90 | 2692 17-05 482 
4°6 1-451 19-1 381 00 | 2616 | 264 193 
0:0 1-418 19°5 365 93 | 2-981 16:8 497 
4°8 1°452 18:8 394 00 | 2893 | 26°35 194 
00 | 1418 18:9 389 LOOMIS ROARS 17-4 462 
0-0 1-418 18-9 SSO |e OOM eaewer 27°5 Les 
50 1-453 18°85 391 BORD 5 (les. s 5 17°35 465 
0-0 1-418 19:05 383 O10) abl gers 6 28:0 170 
5:2 1455 18°65 400 LOSZ ian: 18:1 426 || 
* After 10”. § Load removed after small permanent set. 
Tt After 5". || After fracture. 


+ After 17 hours. 


PO a ee ee 


7 
4 
7 


208 Professor A. Gray on 


Experiment I1].— Wrought-iron Bar. 


' wt. | i. 
| Time in | i Timein | 
orm seconds of n= AP | he seconds of a? 
|20 vibrations. "|20 vibrations. 
0-0 17-25 336 o0 | 182 574 
05 168 354 27 | 1325 | 570 
00) 171 342 00 | 1285 | 606 
00} 169 30* || 301] 130 | 592 
O7 | 1525 430 G4) 83h 565 
10} 1405 507 312} 12°75 615t 
00} 147 463 00 | 1485 453 
15.) 1305 587 je RR Bee | 615 
16 13-15 578 One | 1725nF 433 
0-0 13°5 549 .38c). 1gsa ky 606 
2-0 12-95 596 4-2 | 1355 | 545 
0-0 12-95 596 0-0 16-25 379 
2-2 13-1 583 | 44) 1355 545 
0-0 13-4 | 557 00 | 15°95 393 
| 24 128 610 
* After one hour. + After the permanent set. 


XXI. On Sensitive Galranometers. 
By Prof. A. Gray, IA. 


To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 

HAVE read with interest and also some surprise the re- 
marks made by Prof. Threlfall in his paper in the Phil. 
Mag. for December last on the galvanometer invented by my 
brother and myself, and described by us in the ‘ Proceedings of 
the Royal Society,’ for 1884 (vol. xxxvi.). The notes of our ori- 
ginal observations on the sensitiveness of that instrument are 
I believe in the possession of my brother, who is now in the 
United States, and are at present therefore beyond my reach. 
I have, however, set up the instrument, and am now able to 
state some results I have obtained with it in its present state. 
The sensitiveness I have attained is not so great as that stated 
in our paper; but I feel certain, that with the same delicacy of 
adjustment and suspension as was formerly given to it by my 

brother, the former degree of sensibility would be regained. 
But first as to Prof. Threlfall’s statements and calculations. 
He says, speaking of the galvanometer of our type which he 
constructed, and which had a resistance of 15,852 ohms :— 
“The test for sensitiveness was made by running a large 


Clark cell through 10,000 legal ohms, and a certain small 


Sensitive Galvanometers. 209 


resistance taken out of an ordinary bridge-box. The ter- 
minals of the bridge-box were coupled up through the gal- 
vanometer toa megohm.... In the final test the period of 
vibration of the magnet system was 80 seconds, and the re- 
sistance out of the bridge-box was 100 ohms. The H.M.F. 
acting through the megohm and galvanometer and 100 ohms 


was therefore ae Clark cells, say ‘0145 volt. The current 
therefore —°7—— = 1-26 x 10-T amperes.” Lower d 
was therefore —Gp09 = amperes. ower down 


Prof. Threlfall says that this gave a double deflexion of 5 
divisions, and that therefore the current per division was 
«2-5 x 10-8 amperes.” 

Now this calculation, if I understand the arrangement 
(and taking the statement that °0145 volt worked “ through 
a megohm, the galvanometer, and 100 ohms,” there seems 
no room for mistake), is evidently erroneous. The current for 


the 5 divisions’ double deflexion was really 7 any ampere, or 


1:43 x 10-§ ampere nearly, and the current per division 
2°85 x 10~® ampere, or 5°7 x 10—* ampere per division of single 
deflexion. Thus Prof. Threlfall, by an error in arithmetic, 
makes the sensibility of his instrument only about } of what 
it was in reality, according to the data which he gives. 

For this sensibility it is to be noted the period of vibration 
of the needle system was 80 seconds, the suspension (two 
silk fibres) 16 centimetres long, and the distance from the 
galvanometer-mirror to the scale 155 centimetres. 

Prof. Threlfall then describes an instrument of another form 
which he constructed with the coils of the unsuccessful instru- 
ment of our form, and begins his next paper with the follow- 
ing statement of its sensibility :—‘‘ The galvanometer having 
been brought to a state of sensitiveness of 5 scale-divisions 
for 10~! amperes, the measurement of the resistance of the 
sample of sulphur in question became a tolerably easy matter.” 
One naturally infers from this statement that the sensibility 
of the galvanometer in the experiments thereafter described 
was 2x 10-” ampere per division of deflexion. However, 
calculating from the table on p. 472, we find that it was 
really about 3x 10-" ampere per division of s¢ngle deflexion. 
If a double deflexion is meant in the statement above, this is 
only about — of the sensibility stated, or, if a single deflexion 
is meant, >4 of the sensibility stated. That the instrument 
was working near the limit of its sensibility seems evident 


a 


Ne rg as 
setae a) 


ELIE Oe si taeda 
Spain re oS 
aati iS 


210 On Sensitive Galvanometers. 


from the fact stated by the author that the zero was “ always 
on the move.” 

It is to be noted that in this instrument the suspension was 
a quartz fibre 85 centim. long, and that the distance of the 
scale from the mirror appears (p. 466) to have been 3 metres. 
(Hence for a scale at a distance of 1 metre from the mirror 
the current for 1 division of single deflexion would be 9 x 10~" 
ampere. ) 

Thus in his comparison of the two instruments Prof. Threl- 
fall evidently states the sensibility of his own instrument as 
either 15 or 7:5 times its real amount, and certainly makes 
the sensibility of the trial instrument of our form only about 
4, of what it was according to his own observations. 

In my own experiments the arrangement was as follows:— 
A circuit was made of a Daniell’s cell (freshly prepared) and 
two resistances, one of 22,000 ohms and the other of 100 ohms. 
The terminals of the galvanometer were applied at those of 
the resistance of 100 ohms. The galvanometer had a free 
period of 23 seconds, and the double deflexion produced was 
88 scale-divisions each gy of an inch. Hence the current was 
nearly 1:°5x10-‘ampere. For one half millimetre single 
deflexion the current therefore was 2°7 x 10—-* ampere. 

To compare this with Prof. Threlfall’s result with the same 
type of instrument, we ought to reduce to a scale 1°5 
metre from the mirror. ‘The current for 1 division would 
then be 1°85 x10-* ampere as against 5°7x 107° for Prof. 
Threlfall’s; or, with only 23 seconds period, my instrument 
has 3 times the sensibility his had with a period of 80 seconds. 
With the latter period (and that with even a longer period, the 
instrument can be readily used, I am certain from our former 
experiments) the current would be about +4, of that stated, or 
1°5 x 10-° ampere per division ; that is, the instrument would 
have about 36 times the sensibility of that made by Prof. 
Threlfall. The silk fibre was a little less than 3 inches long, 
and was by no means so fine as it might be made. 

A previous set of experiments, after which the fibre was 
broken down, and the instrument dismounted for resuspension, 
gave greater sensibility. The electromotive force of the cell 
used was, however, in that case a little uncertain. 

I ought to state that the sensibility of the instrument 
depends very much on its state of adjustment. As the time 
at my disposal for these experiments was very limited, and I 
am not able to apply anything like the degree of skill which 
my brother used in the management of the instrument, and 
in the arrangement of a delicate silk-fibre suspension, the 
sensibility is not now so great as that which we formerly 


— ——————————Ee—v 


Notices respecting New Books. 211 


obtained. Were everything in its former state (and in a little 
time I hope to put it so), I am confident that our former 
estimate of the limit of practical sensibility, viz. 1 x 107" 
ampere per division, would be found not far from the truth. 

I can only rejoice if Prof. Threlfall, or anyone else, makes 
an instrument of a higher sensibility. I hold, however, 
that our instrument possesses special advantages in point 
of astaticism, steadiness of zero, &c. Its principal disadvan- 
tage is its long period of free vibration owing to the large 
moment of inertia of the needle system. If, however, we were 
to construct a new instrument, this would be very greatly 


diminished. I am, Gentlemen, 


University College of N. Wales, Your obedient Servant, 
January 1890. A. Gray. 


XXII. Notices respecting New Books. 


Physics of the Earth’s Crust. By the Rev. Osmond Fisner, M.A., 
F.G.S., &c. Second Edition, altered and enlarged. 8vo. Pages 
i-xvi, 1-391. Macmillan and Co., London and New York. 
1889. 


ee excellent book comprises a complete and critical digest 

of the various results of researches made by very many 
Physicists in the nature and character of observed phenomena 
and calculated probabilities relating to the structure and con- 
ditions of the Crust and Interior of the Harth. Its value, how- 
ever, is greatly increased by the Author’s own observations and 
calculations, especially as revised and augmented in this Second 
Edition. <A nearly lifelong experience in Geology has afforded the 
Author good guidance in the application of his mathematical 
studies, and has been a better basis for his researches than the 
merely hypothetical data submitted generally to mathematicians 
wishing to solve such terrestrial problems as come within the 
limits of Physical Geology. Many diagrams and some plates are 
given as illustrations. 

With reference to the new features of this Second Edition*, it 
is stated in the Preface that “possible explanations of some of the 
difficulties left unsolved in the first edition have since occurred to 
me. Investigations have also been carried on by others, which 
appear to strengthen and support some of the conclusions already 
arrived at; these needed to be followed up and embodied..... A 
great part of the book has been rewritten; and, while there are 
many additions, there are some omissions. Some portions have been 
omitted because they seem uncalled for in the present state of 
Geological opinion; and some because they would not have ac- 
corded with the results arrived at in the new portions. At the 


* The First Edition was published in 1881. See Phil. Mag. ser. 5, 
vol, xv. p. 56, 


212 Notices respecting New Books. 


same time these results appear to be the legitimate deductions 
from generally received geological data, now for the first time 
submitted to mathematical treatment. The most important ad- 
ditions will be found in Chapters V., VI., VIII., IX., XV., XVII, XVIIL., 
4 Kako X KG 
siz I. Under ground temperature is the subject of the opening 
chapter. The general law of its average rise on descent into the 
earth, and the probability that it does not remain unaltered for all 
fe depths, are discussed. 
i Il. Internal densities and pressures. Chief points :—the Earth 
iB probably once wholly melted; now consisting of concentric shells ; 
‘a mean and surface densities; internal pressure; numerical value of 
the densities according to Laplace’s and Darwin’s laws,—both 
satisfying the geodetic and astronomical tests, but the former 
iZ being the most probable expression of the facts; for, ‘‘if the den- 
' sities of the substances in the central parts of the earth are due 
z rather to their intrinsic nature than to condensation by pressure, 
4 it is clear that Laplace’s law is the more probable representation 
- of the reality; for it must be remembered that, although based 
i: upon a supposed relation between density and pressure, it does not 
necessarily imply that the density is the result of the pressure.” 
IIl. The condition of the Interior is next considered. ‘The 
question as to whether the Interior of the Earth is at the present 
time solid or fluid, or partly solid and partly fluid, apart from geo- 
logical considerations, may be attacked in two ways. The first of 
these is by inquiring what would be the difference of effect that 
bodies exterior to it, namely the sun and moon, would have upon 
the motions of the Earth in either case; and, secondly, by con- 
Pe sidering the sequence of events according to which a molten globe, 
such as the Earth once was, may have passed into its present state.” 
In the first case arguments have been based on the phenomena of 
qi the Precession of the Equinoxes and the Tides. These are briefly 
discussed and disposed of in Chapter III., no appreciable tide in 
| the body of the Earth being produced by the attraction of the 
ij moon and sun. ‘The change of density on solidification is illus- 
trated by many collected calculations and observations; and the 
existence of a cooled crust over a molten mass is regarded as 
possible. 

It is then argued that a liquid substratum might dissolve water- 
gas, according to Henry’s law of the absorption of gases by liquids, 
and that there would be a very considerable quantity of steam 

re emitted from this substratum if it gained access to the atmosphere 
he in voleanos. Moreover, the high temperature of the gases (chiefly 
i water-gas) passing up through the lava would support its tem- 
perature, and would also account for amygdules in the deep-seated 
igneous rocks of many dykes. This hypothesis of absorbed gases 
is regarded as accounting for the alleged absence of bodily tides 

within the Earth. 

Chapter VI., with its text,—‘“‘a thin crust implies an energetic 
substratum,’—goes to prove that this substratum must be affected 
by convection-currents, upward and downward, according to local 


Notices respecting New Books. 79 


alterations of temperature and level, as the currents are disturbed, 
producing changes in the motion of the liquid. Hence occur 
changes of level on the Earth’s crust over different areas of surface. 
It is also remarked that ‘the extreme slowness with which 
the accretion of fresh solid matter at the bottom of the crust 
takes place [the molten substratum dissolving it nearly, but not 
quite as fast, as it solidifies] would lead us to expect that its con- 
stitution would, from the first, be crystalline and not vitreous. In 
this respect it would differ from erupted igneous rocks, which are 
in some cases at first vitreous, and in which a crystalline structure 
is induced by subsequent metamorphism” (page 78). 

IV. The crumpling and contortions of strata, and the inequali- 
ties of the surface resulting from lateral stresses, are considered 
in Chapters VII. to X.; and the existence of a yielding, fluid 
substratum, holding water-gas in solution (that is, a magma in a 
state of igneo-aqueous fusion), beneath a thin crust (about 25 miles 
thick), is regarded as proved and in accordance with geological 
evidence. The conditions of the existence of the water-substance 
in a gaseous state, in both the primitive and the present stages cf 
the Harth’s history, are discussed in Chapter XI. It is explained 
in Chapter XII. that the crust is not so flexible as to yield by 
bending and folding only to lateral pressure; but that the yielding 
must take place through a crushing together and local thickening 
of the crust. Chapter XIII. comprises the conditiens of a dis- 
turbed tract, with the formation of a mountain-range and its root, 
downward protuberance, or equivalent subterranean mass,—also 
the local results of denudation and sedimentation. Researches 
with the plumb-line, pendulum, and thermometer are severally 
considered in their bearings on the condition of mountain-masses 
and of the crust generally (Chapters XIV.-XVI.). The attraction 
of mountain-masses, and the rate of increase of temperature 
within them, are both much less than would be the case if the 
heavy, hot, molten liquid from below had risen into their anticlines. 

Oceanic areas and the suboceanic crust form the subject of 
Chapter XVII. Oceans occupy depressions, definitely below the 
spheroidal surface of the Earth; and these have probably resulted 
from a greater density of the crust (somewhat thicker there than 
beneath the Continents); the soft substratum being not quite 
so dense as that beneath the land. The permanency of the ocean- 
basins is accepted. Prof. Darwin’s speculation of the Moon having 
broken away trom the Earth some 50 million years ago is regarded 
with favour. 

The thickness of the crust below the ocean—when the water is 


one mile deep may be........ 2°15 miles, 
two miles ,, PANY Wh DG aM 49°3 . 
three ,, ,, Behe ht 14°90") Vs 


Its density is also calculated (2°80 to 2:95). At the rare depth of 
five miles the density might be so great as to allow the crust to 
lose heat more rapidly and to sink slowly,—as, for instance, near 
Japan, where the frequent earthquakes may be due to this cause. 


Phil. Mag. 8. 5. Vol. 29. No. 177. Feb. 1890. R 


O14 Intelligence and Miscellaneous Articles. 


The peculiarities of island attraction (gravity) are succinctly ex- 
plained in Chapter XVIII. The density of the crust in general is 
2°68, and that of the fluid substratum 2-96; and the pressure of 
the crust upon this liquid substratum is about 10,000 tons on the 
square foot. 

In judging the cause and amount of compression in the Earth’s 
crust (Chapter XIX.), the Author thinks that a mean compression 
ot 4 per cent. (of the linear dimensions) may have elevated the 
continents from the sea-level to their present height (p. 260). 
Cooling of the crust and contraction of the interior may have been 
causes of the compression,—also, to a slight degree, extravasation, 
from beneath the crust, of the water new com; osing the ocean. It 
is also pointed out by the Author that the expansive magma (with 
its included water-gas) forced up from below would widen cracks, 
thus causing some compression; and that such rocks as whinstone 
and granite when solidifying would swell, as water does in 
freezing. 

V. Chapters XX. to XXIV., appropriately following the dis- 
cussion of hypotheses and phenomena in the earlier chapters, are 
rich with facts and inferences concerning Physical Geology. Dis- 
turbance of rocks; folding, crumpling, shearing, faulting; fissures, 
volcanic dykes, mineral veins; geological movements generally ; 
volcanos, volcanic action, and distribution of volcanos, are subjects 
of great interest and are here well handled by a master. Chapter 
XXV. gives an interesting speculation as to the origin of ocean- 
basins,—comprising Prof. Darwin’s hypothesis. 

VI. At pages 342-381 we have a concise summary of the objects 
and results of each Chapter in the book, forming a most valuable 
résumé, which both physicist and geologist will fully appreciate. 
An excellent Index completes this elaborate work. 

The careful references to all observers who have treated of the 
physics of the Earth’s crust, and straight-forward expositions of their 
views, enhance the value of the book; and we may remark that all 
the different authors and their opinions have been treated in a 
characteristically considerate and courteous manner. 


XXIII. Intelligence and Miscellaneous Articles. 


ON THE RESISTANCE OF HYDROGEN AND OTHER GASES TO THE 
CURRENT AND TO ELECTRICAL DISCHARGES, AND ON THE HEAT 
DEVELOPED IN THE SPARK. BY E. VILLARI. 


a arc-lieht between carbon points of 1 centim. diameter is 
well known to be shorter in a horizontal than in a vertical 
direction ; and the arc is somewhat longer in a vertical position with 
an ascending current than with a descending one, doubtless owing to 
the greater heat of the anode, which must become more strongly 
heated when it is uppermost. 
Are-lights were furmed in glass bulbs which were filled with dry 
gases. ‘The carbon electrodes were superimposed in a vertical 
position, and were then drawn apart from each other until the arc- 


Intelligence and Miscellaneous Articles. 213 


light disappeared. Two arc-lights were each time produced in two 
glass bulbs, one of which was inserted in the circuit. The strength 
ot the current was measured by an ammeter. 

The are was found to be far shorter in hydrogen than in carbonic 
acid, and in the latter, again, shorter than in air; the ratio of the 
lengths was about 3-9: 7-4: 8:5. In nitrogen, with an ascending 
current, it is about 7 times as long as in hydrogen, and with a de- 
scending current it is 25-7 times as long. With decrease of pres- 
sure the are lengthens in nitrogen, hydrogen, and coal-gas; in the 
two latter, however, it never attains the same length as that of the 
arc In alr. 

With platinum electrodes the lengths of the arcs in carbonic 
acid, nitrogen, coal-gas, and hydrogen at ordinary pressures were 
in about the ratio 16:19: 4°6: 2°8. 

The production of heat at the electrodes was determined for 
various gases with sparks from a Ruhmkorff’s inductorium. The 
electrodes were thermoelements of iron and German silver. The 
heating was investigated in two globes filled with various gases, in 
which the distance between the electrodes was almost identical. 

The heating of the negative electrode was greater than with the 
positive; the difference of the heating effect seemed also to be 
greater in nitrogen than in hydrogen. A globe filled with hydrogen or 
with nitrogen was next used, through which the induction-spark was 
passed, and the strength of the current measured by a well insu- 
lated galvanometer. The induced discharge was more enfeebled 
by a layer of hydrogen than by an equally thick one of nitrogen. 
Moreover equally thick layers of hydrogen and nitrogen enfeebled 
the discharge as much as columns of water of 99 and 59 millim. 
respectively. 

In order to diminish the induction-current by the same amount, 
the length of the spark in hydrogen was 33 millim., in nitrogen 
48 millim., and in carbonic acid greater than 49 millim. Hence the 
resistances were in the order—carbonic acid, nitrogen, hydrogen. 
The heating of the electrodes increases with the rarefaction. 

The spark was then made to pass over the bulb of a mercurial ther- 
mometer in various gases. The temperature increased more strongly 
in nitrogen than in hydrogen both for the induction-spark and for 
the spark from the battery-discharge. The heating with both was 
much smaller in hydrogen than in nitrogen, so that in passing 
through hydrogen the discharge has a much smaller electromag- 
netic and thermal intensity than in passing through nitrogen. By 
substituting for the spark other resistances the same result was ob- 
tamed. A layer of nitrogen 47-6 millim. in length enfeebles the 
intensity of the induced current to the same extent as a layer of 
hydrogen 36°95 millim. in length; and a layer of carbonic acid 49 
millim. in length as much as a spark 33 millim. in length with the 
battery-discharge. The negative electrode is almost as strongly 
heated with the discharge in hydrogen as in nitrogen. With the 
discharge of the condenser it is more heated in nitrogen. 

The spark was finally produced in glass tubes which were sur- 
rounded by small calorimeters filled with oil of turpentine. Under 


i ae 


216 Intelligence and Miscellaneous Articles. 


similar conditions the spark in hydrogen develops more heat than 
in nitrogen, which is just the opposite to what occurs in the 
measurement of temperatures. The same holds also for the dis- 
charge of cascade batteries —Rendiconti della R. Ace. det Lincei, 
y. p. 730, 1889; Besblatter der ae xii. p. 1016, 1889. 


FURTHER INVESTIGATIONS ON THE INERT SPACE IN CHEMICAL 
REACTIONS. BY O. LIEBREICH. 


The phenomenon of the inert space observed and described 
by the author (Phil. Mag. xxiii. p. 468) has been further fol- 
lowed, and a series of experiments with the chloral mixture are 
described, which are illustrated by figures showing the influence of 
the surface of the liquid and of the sides of the vessel on the shape 
of the inert space. It is thus shown that the evaporation of chlo- 
roform cannot be the cause of the phenomenon, nor are immersion 
and convection phenomena sufficient to account forit. The experi- 
ments with iodic acid and sulphurous acid were also extended, and 
it was more especially shown experimentally that the process of 
the reaction in narrow spaces is retarded, and in spherical spaces 
occupies a central position. Analogous phenomena were also ob- 
served with the use of vessels of rock crystal, so that the alkali of 
the glass cannot be adduced as the cause for the occurrence of the 
inert space. The conclusion forces itself that the physical influence 
of the side and the varying tension of the surface of the liquid play 
the predominant part. The hypothesis is not inadmissible there- 
fore that the occurrence of every chemical reaction only becomes 
possible above a certain magnitude of the space in which it occurs. 
Transferred to biological processes this leads to the conclusion that 
chemical processes in cells are also bound up with a certain magni- 
tude of the cells, unless a process of a different kind occurs, which 
in a certain sense may, in comparison with the normal, be re- 
garded as a degenerative one.—Stizungsberichte der Akad. der Wiss. 
zu Berlin, 1889, p. 169; Berbldtter der Physik, xii. p. 998, 1889. 


LECTURE EXPERIMENT TO PROVE THE EXISTENCE OF THE 
DIRECT AND INVERSE EXTRA CURRENTS. BY M. C. DAGUENET. 


The existence of the direct and inverse extra currents may be 
easily demonstrated by means of a Wheatstone’s bridge. In one 
of the branches is inserted a high linear resistance, an incandescent 
lamp for instance, while in the other is a long coil of wire of 
small resistance. When the normal state of the current is at- 
tained the resistances are balanced; then the curcuit is opened 
or closed, and the needle is seen to be deflected either in one direc- 
tion or the other under the influence of the extra currents, and then 
return quickly to its position of equilibrium. This experiment is more 
easily made than that either of Faraday or of Edlund, especially 
for the current on closing.—Journal de Physique, viii. p. 285, 1889. 


THE 
LONDON, EDINBURGH, ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] ‘| 


MARCH 1890. 


XXIV. The Form of Newton’s Rings. By A. W. Fivx, 
B.A., Fellow of St. John’s College, Cambridge*. 


és following essay deals with the formation of the equa- 

tions of Newton’s Rings, when the inclination of the 
surfaces concerned in their formation is taken into account, 
not merely with regard to its effects in producing a gradually 
varying thickness of the intervening medium, but also in 
deflecting the rays so that, though parallel at incidence, they 
are no longer so on emergence. 


om: 


SO a a 


Owing chiefly to the finite size of the sources of light avail- ; 
able, in spite of the use of the best collimating instruments, . 
the incident light is not a single plane wave, but consists of 
an infinite series of such waves having their fronts inclined at 
small angles. Hach incident wave will produce a series of 


colour-effects at any point in the field of view, but these are 
in general masked by the effects due to other waves; only in 
the neighbourhood of a certain surface does there exist distinct : 
coloration. The main result of the calculations of this paper | 
is the determination of the surface on which the colour-ettects 
are most clearly defined. This has been effected both for i. 
reflected and for transmitted light. 

The conclusions arrived at are the following :— 

(1) The rings lie on a certain ruled surface of the third 
order, which cuts the planes through the central spot parallel 


* Communicated by the Author. 
Phil. Mag. 8. 5. Vol. 29. No. 178. March 1890. S 


Se 


218 Mr. A. W. Flux on the 


and perpendicular to the plane of incidence, in two straight 
lines, which cross each other without intersecting. 

We shall refer to these lines as the ‘‘ Principal” line and 
the “ Transverse ”’ line. 

(2) The rings are the curves in which this ruled surface is 
intersected by a set of coaxial cylinders, which are oblique 
cylinders on circular bases. 

In the case of the transmitted system the rings are not 
rigidly coaxial, though for ordinary angles of incidence the 
defect could only be detected by means of very refined in- 
struments. 

(3) The rings are symmetrical with regard to the first of 
the two planes mentioned in (1), both in shape and distinctness. 

(4) The principal line being inclined to the surfaces of the 
plate of glass used in producing the rings, after the ring of a 
determinate order, every ring will lie partially above the upper 
surface of the plate. Similarly every ring beyond another 
determinate limit will lie partly below the lower surface. 

(5) The points of the principal line are always clearly 
defined. In all other directions the clearness varies with the 
incidence, decreasing as the angle of incidence increases, in | 
general. 

Every ring whose order does not exceed a certain limit, de- 
terminate for each angle of incidence, will have, however, a 
pair of points quite clearly defined. These points lie sym- 
metrically on the side of the rings furthest from the incident 
light. Further, the rings are always more clearly defined on 
this side than on the other. 

(6) Any point in a certain line intersecting the principal 
and transverse lines, and lying between these lines, may be 
taken as the central spot, which is therefore, to that extent, 
indeterminate. 

The analytical methods of this paper are, for the most part, 
derived from an article in Band xii. of Wiedemann’s Annalen 
der Physik und Chemie, by Herr Wangerin. Experimental 
evidence supporting the theory may be found in the first 
article in that volume. 

The results attained by Wangerin are in all respects iden- 
tical with those of this paper. I have endeavoured to profit 
by some changes in Herr Wangerin’s method, developed in 
later articles, and to modify these and combine them so as to 
derive a method which seemed to me to be satisfactory. 

The results for transmitted light have been given by Herr 
Gumlich in Band xxvi. of Wiedemann’s Annalen. 


Form of Newton’s Rings. 219 { 


Part J].—NewrtTon’s Rines In REFLECTED LIGHT. 


Section I. Calculation of the Relative Retardations. 


Suppose a plate of plane parallel glass to be in contact at 
the point O (fig. 1) with the surface of a lens, whose upper 
surface is convex and of radius 7. ) 


Fig. 1. 


Let d be the thickness of the glass, w its refractive index. 

Let LABCDEG be the course of a ray incident on the 
plate at A and reflected at the lens at C. 

Let L’ A’ B’ Hh’ G’ be the course of a ray belonging to the 
same incident wave-front and reflected at the lower face of 
the plate at B’. 

Suppose the pair of rays so chosen that their directions after 
emergence intersect at the point F. 

Let the interval between plate and lens be supposed to 
contain the same medium (air) as the space above the plate. 

Let O be taken as origin, the common normal to lens and 
plate, drawn on the side towards the plate, as axis of z, and 
let axes of x and y be taken in the lower face of the plate. 


RN i aR gem 


Take 
E, n, € as coordinates of F. 
Ei, my oi ” ” C. 
E,, Ne, &o ” ” B. | 
u, v, O ” ” By. 
Let - 


1, m, n be the direction-cosines of AL or CB, 
hy my, ny ” ” ” BA or BA’, 


am Meg 

l 9 m ) nr ” sy) ” CD, 

Et Soe, Pade 

Ly’, my’, % ” ” ” DE. 
S 2 


) 
a eee eee ee 


220 Mr. A. W. Flux on the 
Then 


—l,, —m,, n, will be the direction-cosines of B/H’. 
/ 
aig ” ” ” BG’, 
/ / i/ 
Uy m,n ” ” ” HG. 


If we refer C to spherical coordinates with the radius 
through O as polar axis, ¢, ~ being those coordinates, 


E=rsingdcosy, =rsindsiny. | 
f _ (i.) 


¢=—r+rcos é=—2r sin* aa q-P 


The normal at C has Pata, 
sing@cosy, singsiny, cosd. 
’ =—l +2U sind cosy, 
mn’ = —m-+2U sin dsinwy, 
n=—n +2U cos; 


where 
U=lIsin dcosy+msin pd siny +neosd 
2 
= Ipcos+md sin yy tn(1— £) to the 2nd order; 


lv =—l +2ndcosy +2¢? cos p[lcosw+msin ¥1)) 
m= —m-+ 2nd sin p +2¢’ sin pl lcosw+msinw], (i1.) 
v= n+2¢[lcos+msin p]—2nd’. | 
We have also 
L =l/p, m=m/n, nm =/ uw? —1 +r? Iu, 
i= /u, ml=m'/p, nf=J/ 1 ne. 


W hence 
2 | 
nm ne oe | 
ae a B rs [ae -1] (lp cos + md sin oe sa 
iii. 
5 = *fi- = — (Id cos + md sin Wr) + 2¢? 


| 
+ Sig cos +m¢ sin +). 


Form of Newton’s Rings. 221 


Again, 
l 
oa Ce jee = ue ae — (F—6,), 
Sola a pee eee 
where 
= pn ate 
i, =a [1 =. 
And 


Eset" “(d =i 2d = 2r sin of, 
2 


Inserting the above expressions for the various direction- 
cosines in terms of /, m, n, h, yr, and writing 


a|1- l= 


we “~ to the 2nd order of ¢, 


m=n+— de ae 6) — mat oat 


f= E+ © (3) 24 cos y(E—8,) — (6-4) 
(lh cos r+ m¢ sin yr) + : 2r sin? 2 | 
| 
=u—2¢ cos H(C—8:)— = (Ie cos r+ m¢ sin yr) | 
(iv.) 
(6-8) +4" rts 


7, =v—2 sin  (E—6,) — 22 (Id cos wr+md sin yr) | 
(6-8) +4 = rg’. | 
J 


Comparing these values with those in equations (i.), we find 
that, to the first order, 
POeOs ur — > a sini “9. So are (Ve) 


Using this approximation in the terms of 2nd order, 


222 Mr. A. W. Flux on the 


poop — 2h pg 2 etme y_5y pg Ee | 


¢siny=? — 2v 5 = ae Eo 1 mu — | 


Also, from the a 


. l mu e 
i : f=E+3— rd’, 12=M +37". » + (vii) 


| Now, if a plane be drawn through B, perpendicular to BA 
'g and B’A’ and cutting the latter in H, the vibration in the 
two rays will be in the same phase at B and H. 

& If, then, A denote the retardation of phase at F of the 
f vibration in FE, relative to that in FH’, 


| A=BC+CD+4,DE—EF—[yHB’ +pB/E —PF’) 


= 2r sin? © E 4 = + wal = ae = | Hage) [>- =] ~ dA | 
i Now | 
|. pBH! = pl (E—u) +m(m—v)] 
=| [a—ut3 ore] +m| —v+ 4g? |. 
Inserting the values of & and 7 in (iv.) and using in (viii.) 
the values in (ili.) of if and os and the values of ¢cos+, 
d sin y in (vi.), we deduce from (viii.) the following :— _ 


1 Re rd hone Ee +? 42 econ) 1 


n 


ie - w+ +v?  2rlu+ : 
\ =n one > ch a (¢—8,) > G) 


+ (lu-+mv)— ule 
Correct to the third order, inclusive. 

I This is the result obtained in equation (8) p. 211, 
i Band xii. of the Annalen der Phystk. 


Section II. The same in the general case. 


Before proceeding to the use of the evaluation of the 
retardation in Sect. I., we shall determine in a similar manner 


Form of Newton’s Rings. 223 


theretardation when one of the rays ABCB, C,.... 
Ch-1 = E G (fig. 2) is reflected & times at the stitace of this 


Fig. 2 


lens, and k—1 times at the lower surface of the plate, the 
other ray being only reflected at B! as before. 


Take now 
&, n, € as coordinates of F, 
oe Nry fe 99 of C,-1[ 7 <a k], 
BP Sk 34 of B, 
U, Vv; 0 99 of IBY 


Let the spherical coordinates of C, C,...C,... be gd, W; 
Pi, Wy. 23 Pr Yor... 5 
and let 


l,, mr, My be the direction-cosines of C,_1B,. 


Then 
> —™M,r, nr are the se 
Let 


’, m’, vn’ be the direction-cosines of BA and B’A’ ; 
—l', —m’, 1’ are those of B/H’. 

Lit Nin. ne ol i 
—l, —m, n oy) SOL wGe. 
sou Oly NG. 


of (OF Br. 


ly, Mk, MN; 


Also 
=p’, m=pwm!, Vw—l+n,? =pny'. 


If we write down the coordinates of B,, deriving them from 
the coordinates of C first, and then from those of A , we obtain 


>sin d cos w ae 4 a cin’? =?” sin d, Cos w- 2 - ae sin? = os 


r sin ¢ sin p+ — mer sin? =rsin ¢; sin W,— mad sin? 


294 Mr. A. W. Flux on the 
. To the first order, 

p cos p=, cos Pi, 

And therefore to the second order, 


g; cos W,=¢ cos p— - rd’, 


o sin p=¢, sin yy. 


¢; sin ¥, =¢ sin p— rg? 


Similarly, we have 
I if 
go cos ro=¢, cos, + ae cos pe df”, 


dy Sin Wy= dd; sin Wy + 7 =o sin p—2— ¢?. 


And, generally, 
dz cos Wre=Gh cos p—k. tgs, | 
m gs ( (i.) | 


gz sin ~z=—dsin p—k. : 4 


Recalling the results of (ii.) section I., we have :— 
| fo=1,+2n, E cos yw— ~$'| — 29,’ cos Wl, cos +m sin W] 
= —1+4nd cos p— 21g? + 8¢ cos [1 cos +m sin ] ; 


Mg= —m+ 4nd sin y—2mg? + 8d sin Y[/fh cos + mgsinw | ; 
1—n’ 
n oS 


nm,=n+4 [ld cos +m sin py] —8nd? —2 
Proceeding thus, we find that 
| ] 


L,= —14+ 2k ng cos p—k(k—1)l¢’ 
+2h’6 cosw[ lp cosr+ mo sin W], 


me= —mt 2k nd sin w~—k(k—1)mg? 
+ 2k sin wld cosh +mé¢ sin], r (il.) 


m=n-t 2k 1d cosp+m¢ sin f]—2k nd? 
—k(k—1) = $?+2 = [/p cos f+ md sin y]?. j 


| Form of Newton’s Fings. 228 
Whence . 
=~ [1-2 cc kein sin he aa | 
WN ee 1) a cosy + mp sinyp)” |; e 

(iii.) 
e- 1 2Qnk 
ark = i Phony nbn d) 4 | 
1—n’? 2k? 
+ ae Ak 1)¢?+ oP (=, eri cos+md¢ sin |. j 
Also, from the ide aay of Cz- b 
r sin dy_1 Cos Wy_-1=§ + *(a- f)— bi ee sin? ~ =e, 


Mz 


r sin dz-1 Sin Wr_-1= 7) ie ae ea per ——= 
Whence, by means of é a (ii.), and Git. Nh 


$ cos p= — 2k %(¢—8)— 2%, 1lu-+me) (8) + Eg 


We k—1 
— 2r sin? m : 
Nk 2 


$ sin po — 2k 5(6—8,)—  ym(lu + mv) (8-8) + (k- 3) a 
) We have also 
OG pa hel | 
g=e+ Aca Oe = d+5[¢ 35 *.) 
+$2(—L— 2) +... to # terms | 
my f (v.) 


tant (df) — “hat 5 [ g(2—" 
Clee 
+o aoe + ...to bi | 
(2-2). ] 
Drawing the plane BEL ah i to BA and B’A’ as 


before, the retardation at F of the vibration in FE relative 
to that in FH’ is 


=B04CB ak On D+ud [=— ~ | +(-¢ ¢)[-— =|- 2,8 eee 
And 
w. BH=pl,(E'—u) + wm(n'—») ) 
=1(€'—u) + m(n'— - 
Also oe (vil.) 


BC+CB, +... +Cy- iD=5/ 4°(; +744 (+ ~)+.. “terms J. 


226 Mr. A. W. Flux on the 
Using the values obtained in (ii.), (iii.), (iv.), (v.), (vil.) in 
evaluating A in (vi.) we obtain 


Q 2 D p2 Q 
Ana nrkg?-+ 2k + (¢—5,) + (Mme _ay) | 


2 
ue + v2 
v2 


! 7 Sse 
Piss: \ (viii.) 
—1f an" sata | 


—k(k—1) (lu+mv), 


uz +r? 
ik 


=kn 
r 

a2 u2+ a 
? 7 : 


nN 


2 (etm 8,)— (lume) : 


Section III. Determination of the Equations of the Rings. 


If we now determine the axes of x and y so that the plane 
xz is parallel to the incident light, and if @ be the angle of 
incidence, 

1=sin OY Gn=0;, .n=cos 0. 


y= [l= ay 1 8,=d| 1 sea |e 


bcos 6, pcos? b, 


Also 


where 
sin? =wsin 6,, u=E+tan 6 (€—6,), v=. 
And with this simplification 


2442 hk eos 
=k eos 9~ = — aay 


OSE [Bu +0*)(8-2) 


+2 u? tan? 6(¢—6,) —u tan 8 (u?+0v7)]. (7.) 
We shall find it convenient to refer the system to a new 
origin and new axis of z, keeping the axis of x and y parallel 
to the directions just chosen. 

The new axis of z is inclined at an angle @ to its old 
direction, 7.e. is parallel to the emergent light which has 
been but once reflected at the surface of the plate. The new 
origin is the point (& &), where 

°0 
fo=—d(w—1) tan, G=d/1—-“" |. . ii) 
pb. cos’ 6, 
The formule of transformation are :— 
E=£,+a—zsin 8, 


€=6,+2 00s 6. (See fig. 3.) 


Form of Newton’s Rings. 227 


Fig. 3. 


C 


eae. 
We shall also write 


2 
LN ET epee on? @: 
z, cos = (6,—6,) sin vai oo cos @ sin? 0; 


ie yo —- M1 ge pag ~ Dra 
Ve on eas Oy cos 0, 


(iv.) 


With the assistance of this change of symbols, we shall con- 
sider the retardations of systems of incident rays slightly in- 
clined to the incident rays hitherto considered. 

If @ be the angle between such rays (@ being small) and 
af the angle which the plane through the two rays makes with 
the plane wz, we have 


1 = sin 0—cos @. d cos , 
m= dsiny, se stilier. Ce) 
n = cos@+sin 8. dcos wp. 


ene =p?—1+7n?=p? cos? 0,+2 sin 6 cosO.dcosw+.. 


MP Hee civil [ _ sin cos 0 
pn) pcos 0, 2” cos® 0, 


cos ¥ |. 


228 Mr. A. W. Flux on the 
*. The new pe of 6, 
6,/=d| 1— — 
: I Bry 
cos 0 sin 0 cos 0 
=4d[1-— os 0, (+00 sanp( y 
cos @ cos 8 sin 0cos07 
=d|1— | a oe 0, $ os ae 6, 
sin 0 q 
=6, — ag bos vr, 
=6 —<g pcos es ll 
uxt + ays ) 
: cos 
=&+2e—zsin @ + tan 6(1— os) 
as COs a ae cos Wp), 
= —1) tan’ 6, 
ae ti cons Ea ind sin? @ ose de 
=2——y cosy. . Se ee ee - . (ay 
vent (6-8), 
go sinw 6 : a. 
es: (e+2,)cos@=y+(ze+z,)Gsinw . (viii.) 
Therefore 
=" (cos 0+sin 0. cos Wr) ety" 
DUZ : 
-_— ae cos W+ 2y(z+z%) ¢ sin + 
Sa 
— ef aa +9) (e+) 
+22 tan? 6(z—z cot? 6) — z oe ety) | 


to the 3rd order of small quantities, x, y, z, z, 6 being of the 
1st order; 


=A +2 ((y") sin 6-222) ¢ cos 
+: . 2y (¢+2,) cos @.¢ sin y, 
=A+Bdcosyt+C.gsiny (say), . . . . (ix) 


Form of Newton’s Rings. 229 


This expression varies least from its mean value A, as > 
and vf vary, the former from zero to a small value, the latter 
from 0 to 27, when B?+C? is least, 7. e. when 


oB cle 
B.— +C.—=0, 
Oz 1 Oz 
10. | 
Qu [(a%+y?) sin O—2xz|—4y? cos? 6 (z+2,)=0, 
or 
a (x?+y?) sin O—22%2z—2y? cos* 6 (2+ 2,)=0, 
or 


2 (a2 +?) (2+2) cos? 64 2x? sin? 0 (z—z, cot? A) 
—asin 0 (a?+y?)=0. . (x) 
When (x.) holds, the value of A; in (i.) becomes 
Ar= "cos 0 (u? +07), 


i.e. the A of equation (ix.) 
24 42 

Z <4 =18, where ue (@2-y?),. <n ee oni) 
With this value, corresponding closely with that given in the 
ordinary theory of Newton’s Rings, we can determine the 
equations of those rings at once. The ordinary methods used 
for thin plates by Glazebrook or Airy furnish the result that 
the equations are (for the dark rings) :— 


cos @ 


=k cos 6 


(2? + y?) =hn, 


ae Pt ye= ™ at (say)... «(aii 
i.e. The rings lie on this set of coaxial elliptic cylinders. 

They also lie on the surface of the 3rd order (x.). 

The principle which we have employed to determine the 
position of the rings is both simple and satisfactory. Though 
any pair of intersecting rays received into the eye may be 
regarded as producing interference-results, yet only such need 
be considered as have their effect neutralized in the least 
degree by that of other pairs of interfering rays. 

Since, in every case of experiment, the incident light is not 
a simple plane wave, but consists of many plane waves, only 
limited in direction by the size of the pupil of the eye or 
object-glass of the observing-instrument, and therefore in 
general but little inclined to one another, we shall only be 
able to observe those colour-effects in which these various 
waves combine to the most complete extent. 


TE TE A EERE me eg 


230 Mr. A. W. Flux on the 4 


These lie on the surface (x.), where it is intersected by the 
series of coaxial elliptic cylinders (oblique cylinders on cir- 
cular bases) (xii.). 


Section IV. The Surface of Interference. 


We have now to examine the surface whose equation is 
given in (x.) of the last section. 
We shall use the form 
a (a2?+y?) sin 0—2x?z —2y? cos? 8 (z+z)=0 . (i) 
The points of the surface which we have to consider are its 
intersections with 
2 +ypPaars).. -.) oh lad Ce 
EN Aa 2h+1 rr 
o ~ c08 8 2 cos? 
according as we are considering dark or bright rings. 
Where (i.) is intersected by y=0, 


gsin0—22=0. . . . J hina 
The intersection is therefore a straight line through the 
origin. 
If w be the angle made by this line with the axis of a, 


where 


a g— 7% — 2 sin @ 
~ «& cos (d—o)’ 


__ sin 6 cos O 


tan @= aces) ° reece (iv.) # 


Fig. 4. 


We may notice that when €=0 and when 0= > tan w vanishes, 


It attains a maximum value when tan 0= +/2, 


Form of Newton’s Rings. 231 
2. e. when 8=54° 44! 8"-2 (about). 
For this value w=19° 28! 16"-4 (about). 


This is the greatest value of w, which varies from zero when 
@ is zero to this greatest value, and then decreases to zero 
again as @ approaches a right angle. We notice that the 
value of w is entirely independent of the shape, thickness, 
and material of the lens and plate employed. 

The extreme points of any ring in this line are by (ii.) 
— a. 

The actual diameter of the ring is therefore 

cos 6 _, sin 0 cos 0 
“cos (0—@) sin @ 


= ON Me iCOS" Cau. 2c.) ale ee CVS) 


The diameter, as seen projected on the horizontal, is the 
distance froumc—a,z—0, to c= —ea, z=0, 2. e) 2a! 

Let us now consider the intersection of (i.) with y= +a. 

Since, so far as the rings are concerned, equation (ii.) is 
also to be considered, so that z=0, we see from (i.) that 


2. e. the intersection of this plane with the ring-system is also 
a straight line, and, moreover, a line parallel to the surfaces 
of the glass plate. 

We may write (i.) in the form 


ee a) el) es) 
= BEI CosG Pee ane G) cr) 
Thus, when # and y vanish, z lies between zero and —z,, 
the exact value depending on the vanishing ratio of « to y. 
Thus this portion of the axis of z lies entirely in the 
surface. 
Again, we may write the equation (i.) in the form 


(2? + y?)(# sin 0—2z) + 2y? sin? 6 [z—z, cot? 0]=0; 


and hence we see that the line 


ef] cot? 0 
Peis 22 2 cos? @ e e e e (vii.) 
Wen Msimee 


lies wholly in the surface. 
This is a line parallel to the axis of y. 


ne 


232 Mr. A. W. Flux on the 
If we take a plane 
xz sin O—2z2+2X(ze—z, cot? €)=0 


passing through the line (vii.), it cuts the surface in the pair 
of straight lines 


Xr 
ee ir/s sin? 0—r 
It cuts the axis of z where 
ru 
cS] cot? Coma ° 
Denoting this value of z by zo, we see that 


2, 
+2 

gives the pair of lines in which the above plane meets the 
surface. 


It appears, therefore, that the surface is generated by pairs 
of lines intersecting the axis of z between the origin and 


J— 4 sec 6 
ra 


z=—z,, and also intersecting the line (vi.). If we denote 
the origin by P (fig. 5), z=—z, by Q, and z=—z, by M, 
Fig. 5. 


and also the line (vii.) by RN, R being its intersection with 
the plane zz, and N its intersection with one of the above 
pair of lines, 


22, cos? 0 PM 
RN= Fin 3igd e ste sec 0 MQ 
2 cos O PM 


= + sin? 0 a MQ’ 


giving the law of the generators. 


Form of N erten’s Rings. Da 


Section V. Some Points about the Rings. 


From these details concerning the “surface of interference’ 
we may learn something about the rings. 

It is evident that since the plane xz cuts the rings in a 
straight line inclined to the surfaces of the plate, we shall, by 
proceeding far enough in either direction, at last reach rings 
which lie partially above or partially below the plate. 

The upper surface of the plate is 


z= (d—&) sec 8 


=d sec —z,. 


’ 


The lower surface is z= —z,. 

Hence the line (iii.) in the last section intersects the upper 
surface of the plate where 
2(d—z,cos@) = 2d cos’ O 

sn @cos@ ~~ wsin @ cos? 0,’ 


and the lower surface where 


—2z 21°. 
f= = — sin G, 
sin 0 pe cos? 0, 


since the order of the ring in this direction (y=0) is 
given by 


@=+a=+ \/ 5 for the dark rings, 


Cc 


2 (2h +1) dr oDees 
ar yy pe ee: the bright rings. 
: 4d? cos? 8 

z te aa eae 

the dark ring of order h has points above the upper surface of 
the glass plate. 


If ee tere 
‘Xp pw? sin? 6 cos? 6,” 


the bright ring of order / lies partially above the upper 
surface of the glass plate. 


4d? (u* —1)? sin? @ cos 0 


i ao nr pe cos? 0, 


3 

the dark ring of order h lies partially below the lower surface 

of the glass plate; and if h+4 be greater than the quantity 
Phil. Mag. 8. 5. Vol. 29. No. 178. March 1890. ft 


2 
z 


rc eg 


234 Mr. A. W. Flux on the 


just written, the bright ring of order 4 lies partly below the 
glass plate. 
If we denote the line (iii.) of the last section, viz.: 


asin @—2z=0 
gaa 
the principal line, and the plane 
z sin 0—2:=0, 
the principal plane. 
The rings lie wholly below the principal plane so long as 
x sin 0 
ae 
The greatest value of z determined from equations (i.) and 
x sin 6 
2 
(u?—1) cost @ | 
pe sin? @ cos® 6, ° 
Ad? (u?—1) cos” @ 
Xr pF sin? 6 cos? 6, 


It will be observed that this value of A and the first two of 
those just given is greater as @ is smaller and decreases as @ 
increases. | 

It is otherwise with the number determining the order of 
ring lying below the lower surface of the glass plate. 

It was found that the axis of < lies entirely in the surface 
between z=0 and z= —2). 

Thus there arises a certain degree of indeterminateness 
with regard to the central black spot, any point between these 
limits being seen with equal clearness. This difficulty is 
actually found in the course of the experiments undertaken in 
connexion with this more exact theory of Newton’s Rings. 


Section VI. Relative Distinctness of Different Portions of | 
the Ring-system. 


Z< 


(ii.) of the last section is less than 


so long as 


a? < 4d? 


1. é. h< 


We shall now consider where and under what conditions 
the rings are formed most distinctly. 

In Sect. ILI. (ix.) the expression found for the retardation 
was 


A, =A+B ¢ cos f+C ¢ sin yf, 
=—A+ 7 B?+C? ¢ cos (w—«), where tan a=5. 


When B?+ C? is a minimum, 


A= cos 6 (a? + y?). 


Form of Newton’s Rings. 235 
Also b= : | (a* + y?) sin 0— 2a : 


o=" 2y cos 8 (2 +2). 


We have hitherto not considered the effect of the term in- 
volving ¢, but since the minimum of B?+C? is not always 
zero, we cannot pass these terms over without notice. 

When y=0, and w sin 9@—2z=0, Band C vanish, and there- 
fore the points on the line in the plane wz are always formed 
clearly. 

The only reason why we cannot see rings of a very high 
order in this plane is that the rings of different colours over- 
lap to such an extent as to obscure the result if the incident 
light be not strictly monochromatic. 


When «=0, and z=—z,, © vanishes, but B does not; in 

fact, 

(ieee 

B=- y’ sin 6, 
;. 
=" hrr tan 0; 
hrr 

Bee a 
since y’ =a =, when «=0. 


Therefore, the distinctness depends on the magnitude of 
hx» tan 6. This quantity increases as h increases, and there- 
fore the outer rings in the direction of the axis of y are always 
less distinct than the inner. Further, as 0 increases, tan 0 
increases; and when the incidence is nearly grazing, very 
few rings can be formed distinctly, since small variations of 
are sufficient to cause large variations of B, and taking also 
into account the variations of @, the colours overlap so as to 
cause all trace of variation of intensity or colour to disappear. 

Since B? + C? is unchanged by the substitution of —y for y, 
the rings are equally distinct on the two sides of the plane 
ae. 

Again, since @ lies between 0 and =, when p is greater than 
unity (2. e. in general) z, is positive. Hence 

(2? +y?) sin 0+ 222, 
is decreased by the substitution of —2 for a. 

Thus the part of the rings on the side of the plane yz 
which is nearest the incident light is less distinct than the 
other part. 

With the help of the equation of the “ surface of inter- 
ference,” we find that 

T 2 


Ls PPLE PEELE LEI O LI 


FY a 


, } | > CONSENS tae 
} ? 
. 


236 Mr. A. W. Flux on the 


2y Cos WN 1) ,/)2 cee 
v 


V/ B2+ C?= 


This vanishes when (vz? +? cos? @)/« vanishes. 


Now 
2 (a? + y? cos? @) (2+2,)=2 [ (a? +y”) sin 0+ 2x2; | 
=| a? sin 0+ 222], 
.. “B?+C? vanishes when 
~ _@ sin 0 
: Soe 


and since w?+y?=a?, this requires that «pa, 


| a a sin oe 1 
tr” 224 , 
Az? cos 0 
or = 
Ar sin? O 
: Ad? (u2—1)? sin? 
ae pee (mw )? sin? @ cos gy 


Mr pe cos® 0, 


For all rings of lower order than the limit so determined 
there are two points quite distinctly visible, symmetrically 
situated with regard to the plane «#z, and on the side of th: 
plane yz farthest from the incident light. 

To obtain the required criterion for bright rings it is only 
necessary to write +4 for h in the above. 

If the rings are examined by means of a microscope, the 
breadth of the visual pencil is much greater than if the naked 
eye were used. ‘Thus much greater values of ¢ are possible, 
and the obscurity is consequently increased. 

For purposes of exact measurement, however, a microscope 
is necessary, In spite of the consequent greater indistinctness 
in the phenomena observed. . 


Part II.—NewrtTon’s Rives In TRANSMITTED LIGHT. 


Section I. Calculation of the Relutive Retardations. 


We now proceed to consider the case of transmitted light. 
We shall take the axis of z in the opposite direction from that 
before used in Part I., viz. drawn towards the side on which 


the lens lies (fig. 6). 


Form of Newton’s Rings. 237 
Fig. 6. 


c 


G 


The direction-cosines will be similar to those used in 
Sect. II. Part I., so far as the two cases coincide, viz.:— 


The direction-cosines 
of LA, L'A’, BC, B'C! are —l, —m, n; 


of AB, A’B! are —I!, —m’, nl ; 
of B,C are 1,, m,, m1; of B,C, are —1,, —m, 1, ; 
Xe. ec. 


of Bz,Cy-1, are lz, mz, nz ; of Br, Creare —l,, —mz,n4. 
Also we shall take as direction-cosines of 
C,D, lpn (Sy oan © CHB =e, = 8 y3 
FD, —lise, —tr2, M423; FD', —e, —B, y. 
The rectangular and spherical coordinates of 
C are &, M1) OL and d; Ws 


C, are &, M2) &2y and Q, vi 3 
&e. 
Cy are Fp41, Me+1y Se+1, and py We ; 
C' are €', 7/, ?', and d/, w'; 
while F is &, y, €. 


The thickness of the lens at its centre will be denoted by d, 
while 7 is the radius of its convex surface. The direction- 


a 


ETN Een re a ile Og conte 


— Sa See . 


238 Mr. A. W. Flux on the 


cosines of the normal at ¢, y are 


sing@cosy, singsiny, —cos ¢. 
We have 


lL, =1 —2hnd cos w+h(h—I lp? 7 


—2h’d cos Willd cos r+m¢ sin], 
my=m— 2hnd cos w+ h(h—1)m¢? 


—2h’¢ cos ¥| Id cos Pi + ee sin +], 
n= n+ 2h(ld cos w + md sin w) 102) = a 


+ ae “Llp cos + m¢ sin “sa ng? 


Pi 
mn, on 


[1 = (ig cos y+ ing sin wp) +H (h— | 
a sie cosy ee sin 4 f zie? | 


x 


Putting 
U=lIsin ¢! cos wp! +m sin ¢' sin y+ cos 


'Q 
=n+/¢' cos +m! sin yank 5 eos 


a= — J [sin gl cos yt vF=IF UU} +0) 
dl oe ae ip ta SATE 
ie [sing’siny’{ 7 y?—14 U2?—U} +m], >(ii-) 


1 = ts Mee sae 
y= en [cos p! § /u?—1+4 U2—U} +2]. 
And 
a=pal, B=pB, y= V1—w+p'y?; 
v. a=l —(n—pi')¢! cos = aay? cos af! 
(/d! cos py! + mq! sin w'), 
B=m— (n—pn') ¢' sin wy! — (1-7 sin yy! 


(/! cos y' + m¢! sin W’) ; 
pey!? =? —1 +n? —2(un'—n) (ld! cos W! + md! sin W’) 


— (un —n)?d'? + yee” (Id! cos Wy! + m®¢! sin w’)?. 


Form of Newton’s Rings. 239 
Again, 
1 
E— : Caos a (d—£') =2'=rd! cos p, 
I 
ae 2 (d—¢) + = (d—€')=7!=r¢' sin W’. 
Therefore, os 


to (§—8,), v=at F(t-8);. CG) 


v yy 
j=a/1— 7], = ena 


a 
u——_t'=rd'cos w! 
eS =rgleos 


where 


we have 


v— Stang sin w’. 


 Pgtau2+r2— gue aie 
ei a een , aut Bu u?+v? 
C= ee 20 ga 2 a ae on 
21 2 2 
Hoosyat yet yy, eee | 
py or (Degg op r iv) 
iv. 
: v B w+? B autPvuw?+v 
g! sin Woes ee ea ses eye 0 ae | 


We shall now proceed to connect ¢, ~ with ¢!, W. 
Writing 


: n . re n 
eee gmat (A gal 
l m 
m=é ate < (Go) Yy=n+ ak (¢—6,'), 
(p it 
aeh——, ef =h——. 


Now /,42, M42, Me+2 are derived from 1, mz, nz as a, B, y are 


from /, m, n, $! w' being replaced by dx Wx - 
l 
Now od; cos Wz=¢ cos p—k = ¢*, 


$, sin W.=¢ sin p—k < o?. 


240 Mr. A. W. Flux on the 


Therefore 
Le49=l,—(ne— pene!) by CoS Wry 


-(1 = a) pr cos We [lady cos Wr + mug: sin Wz], 
ke 


=1—nele41 6 cos wt he! ld?— | 2h + Qhk+1 


— (2k+1) | #008 (ld cosw+mé¢ sin), td 
nesg=m—nesr sin y+ ke! mo? — | 24 42hk+1 7 
— (2k+1) aa] # cos (1d cos +me¢ sin fp), | 

n*,49=n? + Qneox+1 (lh Cos ice sin wr) —2ke;! (L—n?) 6? +2 | 22 
+2k+1— —2k+1 | (lb cos +m sin W)?—ne7o.41 b, | 


Leso=ble+1, MEe+o=HMNg41, KBNe~1= Vp? —1+np+2 J 
Therefore 
1 ] l sl] 1—n? 
=—| l—eln+1 ee Sect Sah + ke! a p? + 3e°on4+1 Pp? 
Ne+g 7 7 v7 


+ Ea —[2i2+2k+1 - +12] | (+= ee 


it 1 1 neon +1 k »l—n? n 1 Ff ate? 
Je ae, 7 252 + he! pen — 73 P +3 Gin ns $+ = 4 2,/2 
_ 


Ne+1 7 en pn 
—(2i*+22-+1-2h+1™,)| | 1p cos y+-me sin wp)? 
=I 


The values of J, m, in terms of a, 8, y may be dedaced 
from those of «, 8, y in terms of /, m, n. 


They are :— 


] u? +2 u aut Bo | 


i 
r 


l=atye, ~+ha bes 


u at v aut Bo 
r 


m=B +6 — e +168 Gee 


Be . 2—T ( Y ae 
n=y—eE Age ee (eee 
¥-G 2 ¥ py re 
ny (Ate) 3 yes? reed) 
¥ r r y r 
pn! = pry! — ey ale ae &e. 


‘pyr 


Form of Newton’s Rings. 241 
=, f1- =] =) ay 
pen y? 


 m=Eto(C-8)3 


tg e-8) +a te 8y, 
r 7” 
g z } (vil.) 
5 ; -- 
etn ey eB hryeany 
Again, 


rp cos p= f= F— cae as Gees ts eat) | a 
Ne+2 k+l h=1 Mh \. (vill.) 

Myp+9 a ee | 

‘ 0) sin — ee ae (d— ¢) + eee C41) +38 (Gt Chi). J 


Ne+2 


Using the values already found in (v.) for the direction- 
cosines, we have 


4 


MICO) lal lu, +mv,—6,/ 


b cos p= | —elyy UH ee ae = 3 Cat F Fe 
2 2 
ae | 24— |" seen 
n pn ’ 
ne) 
=" 2" SSo 24 Oo +32 [2%— y )u ue 
, r r r Y bY , 

: ee Wie —Oy ee ne oe 24.42 
fee, 2h +47 [2h a Six.) 
And | 

au+ Bv u2+v? 
pipe an SB te | 
yP if 
Let! nee oO — 4p (A+ Be)" C0), ! 
7 (ie r yr ? | 
21 12 
+[%—2 |e = 2 te an a 


f* is obtained by putting h=0 
and 
¢’7is obtained by putting k=0 as well as h=0. 


Ifa plane be drawn through B perpendicular to B’A’ and 
BA, and cutting the former in H, the points B, H are in 
the same wave-front which is incident in the direction LA. 


242 Mr. A. W. Flux on the 


Also the coordinates of B’ are:— 
each pee a! Be 
EF (dt) + 5d-0) + 2, 
EP 2) Ad p crcl . Mga 
n—F (d-)+ 5 (df!) + Bo; 


and those of B are:— 
l 
E+ Pate + — 613 


£., m being given in (viii.). 
The difference of path (measured in air) of the two rays, at 
F is 


i as iS Siar se E “<3 * 
“Latte =e —* + wB'H| | 


, Ap Mia 
=-[4- g|— ea ee pas ae re) 
me E42 + MMy+2— (d—£) | ) 


NE+2 


ie llke+1 + mmys41— Gea aaues ae ¢) 


Ne+1 
+ yn artes tae 
Now ” 
2a = —n-+2nd order terms, 
and P 
Gt tn = 5 [Pat git]arg?— (h—1) AEE EEN, 


z. e. is of the 2nd order, and therefore we need not calculate 
lla +mmn—1 
Ny ( 
Hvaluating the other terms by means of equations (iv.) 
(v.) (vi.) (ix.), we obtain the following result :-— 
ur+v? fe ies pant eat BY u?+v 
pyr’ “ - 


= & raat G8) +2 (ASE) g—5) SE es ty] 


as given by Herr Gumlich in Wiedemann’s Annalen, xxvi. 


p. 361. 


the 2nd order terms in 


Form of Newton’s Rings. 243 


Section II. The Shape of the Rings. 


The only difference between this expression and that of 
equation (vili.) of Sect. Il. Part I. is in the 2nd term, 
a, 8, y taking the place of J, m, n. 

It is evident that the same process as that adopted in the 
former part of the paper will give similar results. 

Putting 

smo, U0 ...c0s O=+, 

(@ is the angle of emergence) 
the equation of the ‘‘ surface of interference,” referred to a 
system of axes of which the z-axis is in the direction of 
emergence, and the substitutions are those of Sect. III. 
Part L., is 


x(x? + y”) sin @—2a?z—2y? cos? O(z+2,)=0. . . (i) 
__ keos@ we—lL (a+ y?) 


oo : 
i; ze cos 0; ie d 


(2? +y?) +k 


ee 2 w pi—l 
== (x? + y”) cos 0 [1+ a cow tn & |. 
The other equation to the rings is, therefore, 
ae 2 | 
eae Cos 0 | 1+ Ke = tan, | =I ee 
r PCosG 2 


according as we consider the bright or dark rings. 


Taking the former and putting a? for sca this becomes 
§ 


2 
paat Deak zy 

r+ y =o | reer as 0, |. Sa sci igall.G (it.) 
Thus in this case the rings lie on elliptic cylinders which are 
not co-axial, 

The distance of the centre of the Ath bright ring from 

the central spot, from the origin, is 

ot we—1 pw?—1 


SU ee rama esse aah 
20" ost tan 6,=thrx anes a tan 6. 


This increases with / and with A, but is of the order AS unless 
@ be nearly = when these differences would become very 


perceptible. In ordinary cases the difference is not ob- 
servable, and the rings are practically co-axial. 

The shape of the surface of interference is exactly the same 
as that considered in the earlier part of this paper, and the 
conditions of distinctness remain unaltered. 

December 1889. 


a ge 


nS hc Par title SOS AT OEE IE oe OM 


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aOR es 


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XXV. Twisted Strips. 
By Professor JoHN Perry, /.R2.S.* 


N a paper read at the British Association Meeting this 
year, and also at a former meeting of the Physical Society, 
I referred to the curious behaviour of a twisted strip. The 
twisted strip must not be confounded with what has been 
called the Ayrton and Perry Spring. It is a straight strip of 
metal to which a permanent twisted appearance has been 
given, a twisting moment being applied about the axis of the 
strip to give it the permanent twist, care being taken to pre- 
vent the axis of the strip from lateral motion. In fact the 
axis remains straight, and is the axis of all the spiral lines now 
formed by the lines which were originally straight and parallel 
to the axis. When an axial force is employed to elongate a 
twisted strip, a slight elongation takes place accompanied by 
a large relative rotation of the ends of the strip. The only 
simple hypothesis on which, as I told the Society on a former 
occasion, I could see my way to building a possible theory 
was to consider in any very short length of the strip any two 
spiral filaments equally distant from the axis as two threads 
in a bifilar suspension. Under the action of any axial force 
these two threads tend to produce untwisting, and the sum of 
all these untwisting moments is equal to the torsional rigidity 
of the cross section multiplied by the angle of untwist. 

The phenomena are so complicated that I never hoped to 
explain them all by this or any other hypothesis. I was 
seeking for a roughly correct theory only. 

The breadth being 6 and thickness ¢, we may roughly 
assume that the section remains rectangular; and as 6 is 
always more than ten times ¢, we may take the torsional 


rigidity as 2 bi?. If then @ is the angular amount of un- 


twisting produced per unit length of the strip, the moment of 
torsional resistance is 

N 3 

3 bt°0. 

Let w be the axial force. If ¢ is the twist of the strip per 
unit length, then for a filament whose horizontal section is 
¢. dv, at the distance # from the axis (as ¢ is small compared 
with 6 I take the filament as extending quite across the sec- 
tion), if p is the vertical tensile stress on the section, it is 


* Communicated by the Physical Society: read November 1, 1889. 


- ee —_—— 


Prof. J. Perry on Twisted Strips. 245 


obyious that the part of the untwisting moment due to one 
filament is tpa’d. dx; so that 


Ne as. 2 
y= 16 | 


5 
Lb 
wtf pear we Vee (2) 


I explained on the former occasion that, for a working theory, 
it ought to be sufficient to take p constant over the section. 
Hence, from (2), 


DEOL Pew ois) es (1) 


also 


= bt? ° ° ° . . . e ° (3) 
and inserting this value in (1), we have 


N 


3 tO = pth’ 7 


or 


b 
a ee) 


If @ is small in comparison with q, it is allowable to take } 
as the twist of the strip when no axial load is acting—that is, 
its permanent twist. 

Now I announced on the former occasion that careful expe- 
riments made upon large twisted steel strips of various dimen- 
sions did not by any means agree with my result. It is true 
that 8 was proportional to w; but it seemed rather indepen- 
dent of ¢, and instead of being proportional to b, @ seemed to 
get less as b was greater; and, again, instead of ¢ in the 
denominator some power of ¢ between 2 and 3 ought to be 
taken. ) 

Under these circumstances I asked members of the Society 
for assistance in obtaining a working theory, but hitherto 
I have not obtained any. 

I wish now to announce that the experiments I referred to, 
made very carefully by Mr. Still, of the Finsbury College, 
under my direction, were not sufficiently exhaustive. Mr. C. 
Hj. Holland has lately been kind enough to make an experi- 
ment for me ona very small strip of platinum silver. He finds 
that when ¢ is large his results agree very closely with the 
former results; but as @ is made less and less, the law con- 
necting @ and @ becomes more and more nearly what is given 
by (4). The experiments were carried out upon double- 
twisted strips. That is, a straight strip was taken with its 


——- 
i EE TE IRE A II me Sl AI erie 


A OI Oe res, 


246 Prof. J. Perry on Twisted Strips. 


ends fastened in a frame ; it was caught in the middle and 
there a twisting-couple was applied, so that one half of it took 
a right-handed and the other a left-handed permanent twist. 
Beginning from almost the condition ¢=0, by giving more 
and more permanent twist to the strip and applying loads in 
each case, it was seen that, for a given axial load, @ was nearly 
proportional to @ at first, but as @ became greater and 
greater the increase of @ was less rapid, @ eventually remain- 
ing nearly constant, although ¢@ was increased. ; 

T now know that Mr. Still’s experiments were carried out 
upon strips in which there existed so much permanent twist 
as to resemble the strips in the condition in which they were 
towards the end of Mr. Holland’s twisting operations, and 
hence 6 seemed independent of ¢. 

Now if, instead of taking p constant and using (3), we take 
p as getting less for filaments at greater distances from the 
axis, it is obvious that we shall arrive at a result which, 
although more complicated than (4), will represent much 
better the results of experiments. 

Thus, as is probable enough, if the tensile strain in every 
filament is such as to keep a section at right angles to the 
axis parallel to itself, it is easy to show that, instead of p 
being constant, we must take 


k 
pa t(1 + x?) . e e e ° e (5) 
Using this in (2), we find 


c 
we . 
i 


itt 
+3 
AR 
1. 
ra 
4 
3 


pia! ope awe 
2 tan—'$bo 
Substituting (5) in (1) we find, on simplifying, 


3w il i 
es ae ae 
It is obvious that, except when d¢@ is great, (6) becomes 


a Oe 
0= aye gh— 4, +P I, e e. e (7) 
which agrees with (4) for small values of $d. : 
And evidently from (6), as bf gets greater and greater, 
6 reaches more and more nearly the limiting value, 
po 
Né’ar 


Making p any other likely function of 2 than that given in 
(5) will merely modify the constants in (7). 


A New Form of Mixing- Calorimeter. 247 


Professor Ayrton and I have used these strips in weighing- 
machines, instruments in which forces require to be measured, 
and instruments in which small motions require to be mag- 
nitied. We are now using the double-twisted strip of constant 
length, but with initial pull in it, as a thermometer and as a 
galvanometer. It is my opinion that it only requires to be 
better known to be largely used ; and although I seem to 
have spent rather in vain a considerable amount of time in 
trying to get a working theory, I do not think the time has 
been really wasted. It is no mere curious puzzle, it is a 
problem of practical importance. 

The two great difficulties are—(1) What is the law of p over 
the section? (2) to what extent is it wrong to regard the 
section as resisting untwisting with the moment 


Hy bt? ? 

3 
that is, to what extent has the original twisting given initial 
shear strains to the material ? 


XXVI. A New Form of Mixing-Calorimeter. 
By Spencer U. Pickerine, W.A.* 


[Plate VII.] 


HE methods which have been employed in recent calori- 
, metric work for mixing two liquids are two in number. 
Berthelot (Wéc. Chim. i. p. 171) places one liquid in the 
calorimeter, and adds the other from a flask, which is handled 
by the help of wooden clips; while Thomsen (Thermochem. 
Untersuch. i. p. 19) has a metal calorimeter for each liquid, 
one of them being placed above the level of the other, and 
communicating with the lower one by means of a metal tube, 
which is stopped by a plug till the temperatures have been 
ascertained. Berthelot’s method is inapplicable in cases where 
delicate thermometers with large bulbs have to be employed ; 
and there are various other objections both to his and to Thom- 
sen’s method, of which the most serious is that the two liquids 
before being mixed are not at the same temperature, and the 
results obtained are, therefore, dependent, not only on the 
accuracy with which the two thermometers have been com- 
pared with each other, but also on an accurate knowledge of 
the heat-capacities of the two liquids. 
In devising a new form of mixing-calorimeter, the chief 
improvement which I aimed at was to obviate this source of 


* Communicated by the Author. 


248 Prof. 8. U. Pickering on a New Form 


error by starting with the two liquids in the same vessel : the 
other objects to be considered are, however, numerous, and 
create considerable difficulty in obtaining a satisfactory appa- 
ratus. The volumes of the liquids to be mixed are generally 
required to be equal, and should not exceed 500 cub. centim. in 
each case: this gives very little spare room, when each liquid 
contains a thermometer with a large double bulb, and stirrer. 
No part of the apparatus must be removed, nor must any- 
thing be introduced into the liquids to effect the mixing. 
Whatever operation is necessary to mix the liquids must be 
performed quickly, so as to avoid the disturbing influence of 
the experimenter ; and must be consistent with the calori- 
meter not being held in its position, but with its resting on 
pointed wooden supports. Finally, the mixing of the liquids 
must not occupy more than one minute. 

The apparatus which I ultimately adopted, after many un- 
successful trials, consisted of an oblong platinum vessel (figs. 
land 2, Plate VII.), measuring 14 by 8 centim. and 10 centim. 
deep, with a frame, F, in the middle, against which small 
folding-doors, D, close, and divide the vessel into two equal 


compartments. A thin slip of sheet indiarubber, I, is sewn on . 


to the edges of these doors, and a small beading, B, running 
round the doors and round the partition against which they 
close, affords a good bedding for the indiarubber, and prevents 
the leakage, which it was found impossible to obviate when 
the surfaces of the doors and frame were flat. Hach door is 
kept closed by the pressure of two pairs of bow-shaped pieces 
of iridio-platinum, 8, which act as springs. One of these is 
at the bottom of the doors, and is attached to a rod, R, of the 
same alloy, rising vertically above the top of the calorimeter ; 
the other is at the top of the doors, and is worked by being 
attached to a-metal tube, T, through which the above- 
mentioned rod passes. The rod and tube each terminate in 
ebonite knobs, EH; and, when these knobs are pressed together, 
the lower spring is lowered below the door, while the upper 
one is raised above it, and the latter consequently opens, and 
permits the liquids to mix. ‘To allow for the removal of the 
lower spring in this manner, the doors do not come within 
5 or 6 millim. of the bottom of the vessel, and this also allows 
the stirrer to work freely at the bottom of the liquid. 

Under the bottom of the vessel there are four small cup- 
shaped projections which help to steady it on the pointed 
supports on which it rests. 

‘The various parts of the apparatus are all distinct, and are 
easily unscrewed and removed for the purpose of cleaning and 


drying. 


of Mixing- Calorimeter. 249 


. Although the principle of this apparatus is extremely 
simple, it required the utmost skill in workmanship and the 
greatest attention to minute details to produce anything which 
would work really satisfactorily*. 

The stirring-apparatus which I use with my single calori- 
meter consists of a fan-screw with three blades revolving at 
the bottom of the liquid, and worked by means of an electro- 
motor (Chem. Soc. Trans. 1887, p. 293). This apparatus was 
doubled, so that each half of the mixing-calorimeter should 
have a separate stirrer, and in each half also one of the most 
delicate thermometers is suspended, these being tapped con- 
tinuously on the upper end by the clockwork-tapper (2bid.). 
Fig. 3 represents the whole apparatus. 

In working this calorimeter it is first of all put in position 
with the doors closed, and the thermometers and stirrers in 
their places. The two liquids are then measured or weighed 
out from flasks into the two compartments, the temperature 
of each being slightly below that selected for the initial tem- 
perature of the experiment. The stirrers and tappers are then 
started, and the temperature of two liquids raised to the 
required temperature by touching the outside of the calori- 
meter with some heated object. ‘The temperatures of the two 
liquids are in this way easily and quickly brought to within 
0°:02 of each other. 

The thermometers are then read through a telescope at 
intervals of one minute, till the rate of cooling in each case is 
perfectly regular: this occurs in a minute or two, and the 
temperatures of the liquids may then be assumed to be iden- 
tical. The rate of cooling is then determined for three or 
four observations ; after which the doors of the calorimeter 
are opened without stopping the stirrers; the thermometers 
are again read, and the readings repeated at intervals of one 
minute, as before, in order to determine the correction for 
cooling at the final temperature. 

Although it is not absolutely necessary to have a thermo- 
meter in each liquid, it is not only advisable as a precautionary 
measure, but it gives the method a very important advantage 
over previous methods; for the heat evolved being measured 
independently by two different instruments, a single experi- 
‘ment has nearly the same value as the mean of two separate 
ones. 

The temperature, as has been mentioned, may be obtained 
identical in each division of the vessel before the doors are 


* To the ingenuity and perseverance of W. Peover, of Leigh Street, 
W.C., I am indebted for success in this work. 


Phil. Mag. 8. 5. Vol. 29. No. 178. March 1890. U 


(ery eee 


ol ae 


Fae Re 


LITIF Bg im oe 


ashi 


== = sae a ‘ 


en 


250 Prof. 8. U. Pickering on a New Form 


opened ; but I have found it convenient, and often necessary, 
not to wait till absolute identity is attained, but to open the 
doors when there may be a difference sometimes of as much 
as 0°:003 between the two temperatures. This difference, when 
unavoidable, was entirely due to local circumstances which 
are independent of the apparatus itself, chiefly to its position 
with regard to the windows in the room, one division of it 
being nearer the window than the other. The correction ne- 
cessary on account of this difference (often nl) is so insigni- 
ficant that it does not require any knowledge of the heat- 
capacities of the liquids,and necessitates an accurate comparison 
of the readings of the two thermometers throughout but a very 
small portion of their scales (only two or three millimetres), 
since the initial temperatures in the individual experiments of 
any series need never differ by more than this amount. 

The following details of an experiment will render the 
method of procedure clear. 


Left-hand Division, | Right-hand Division. 
Water. Thermometer 761. CaCl, sol. Thermometer 708. 
Rate of Rate of 
Time. Reading. sola Time. Reading. ood 

i | 

0 6 | 145°65 mm.* | 030 | 151-33 mm.* 

48 28 
[OLA | Patz 130 | 15105 _,, 

27 | 25 
20 | 14490 ,, =27| 230 | 15080 _,, = 23 

27 20 
3 0 | 14463 _,, | 830 | 15060 ,, 
530 | 198-95. ,, | 6 0 | 19550. ,, 

‘60 ) 0) 
630 | 19835 ,, | MF FO 1195-800 oe 

70 $ =-62 50} =-48 
730 | 19765 _,, 8 0 | 19450 _,, 

‘55 45 ) 
830 | 19710 _,, 9 0 | 194-04 ,, 


* | millimetre represents about 0°-01 C. 


The rate of cooling here became constant after 1’ 0”. The 
last reading of the thermometer for the initial temperatures 
was taken at 3’ 30”, and the doors were opened by 4/0” Up 
to this time the first-determined rates of cooling would hold 
good, and the reading of thermometer ’61 at this moment 
would be [144°9 (the mean of the three previous readings) 
=—(*27 x 2)=] 141°36 millim.; while that of °08 would be 


of Mixing-Calorimeter. 251 
[150°82— (23 x 1:5)=] 150°48 millim. But, according to 


the previous comparison of the thermometers, the reading of 
708 which corresponds to 144°36 of ’61 is 150-28 millim. ; 
hence the initial temperatures corrected for this difference 
will be, according to ’08 (150°48—-10) millim., and according 
to “61, (144:36 + (10 x 193)) millim. ; the fraction 193 repre- 
senting the relative values of 1 miilim. of the scale of the two 
instruments. 

The liguids had entirely mixed in this experiment at 5’ 0”, 
and the readings of the two instruments at this moment would 
be [197-99 (mean of the last four readings) + (*62 x 2) = |199°23 
millim. in the case of 761, and [194°76 + (48 x 2°5) = |195°96 
millim. in the case of 708. During the one minute while the 
liquids were mixing, the rate of cooling is taken to be the 
mean between the rates at the initial and final temperatures, 
necessitating the further addition of ‘44 and 36 millim. to the 
readings last mentioned. The only other corrections to be 
then applied are those for the effect of the temperature of the 
surrounding air on the mercurial columns, and the calibration 
corrections. 

Where one liquid is very much more dense than the other, 
as in mixing water with salt-solutions of a density 1:3 to 1°7, 
two special difficulties arise: the temperature of the salt- 
solution rapidly rises to an appreciable extent above that of 
the water, owing to the greater friction of the stirrer in the 
former ; and, secondly, the two liquids mix very slowly when 
the doors are opened, taking, in extreme cases, nearly 30 
minutes todo so. This latter is not, however, entirely due to 
the viscous nature of the liquid, but to the fact that the two 
stirrers in my present apparatus rotate in opposite directions, 
whereas for the purpose of rapidly mixing the liquids they 
should rotate in the same direction. 

These objections are, however, of no great importance. 
They do not exist in cases where there is a difference of *2 or 
less in the densities of the solutions, and in very few cases 
would the difference reach this amount. 

The exactitude of the method may be estimated by the fact 
that the difference in the rise or fall of temperature as mea- 
sured by the two thermometers in all the experiments which I 
have yet performed with the apparatus (omitting those in which 
the liquids were too dense to mix in less than three or four 
minutes) is, on the average, only 0°:0008, and only on three 
occasions did it exceed twice this amount. This quantity 
represents a sum total of °07 millim. error in all the readings 
of the two thermometers, and represents a difference of 0°6 
cal. in the heat measured, taking the actual quantities used 

U2 


252. A New Form of Mixing Calorimeter. 


(on that calculated for gram-molecular proportions); an error 
only one seventeenth as great as that experienced by Thomsen, 
its average error in duplicate experiments being +9 cal. from 
ee mean, or a difference of 10 cal. between duplicates sind 

1p. 21). 

When dealing with very strong solutions it is madvisable™, 
and often impracticable, to make the determination in the 
mixing-calorimeter. 

The method which I have adopted in such eases is very 
simple. It consists of putting 20 to 50 grams of the liquid 
into test-tubes on feet, placing these in an air-bath surrounded 
by a water-jacket till they have attained the temperature of the 
surrounding air, and then pouring their contents into 600 cub. 
cent. of water in the calorimeter (a platinum beaker) ; thus 
the heat of dissolution is determined as in the case of a solid. 
The chief precaution to be observed here is, that the tubes 
be left sufficiently long in the air-bath before being emptied 
into the calorimeter. This is necessary owing to the heat- 
capacity of a liquid being generally higher than that of 
a solid, any error in the determination of its temperature 
making therefore a greater error in the heat of dissolution 
determined. About three hours in the air-bath at a constant 
temperature (that is, within 0°-05 of the required temperature) 
were generally allowed, and greater pains were taken to bring 
this temperature to exactly that of the calorimetric water than 
in the case of solids. If the temperature of the air in the 
room is satisfactorily constant, and nearly identical with that 
in the bath, a comparison of the temperatures of the latter 
and that of the water in the surrounding jacket will indicate 
the time when the test-tubes have attained the former (and 
the latter) temperature; and if left under these constant con- 
ditions for nearly ancther hour, satisfactory results will be 
obtained. Success in this is entirely a matter of practice. 
The correction which has to be applied to the heat of disselu- 
tion, owing to differences in the initial temperature of the 
solutions and the calorimetric water, averaged only about 
0°-002, and the heat-capacity of the strong solutions necessary 
for its calculation need therefore be known approximately 
only. All splashing on pouring in the solutions is entirely 


* In mixing acids and alkalies the results obtained are more aceurate 
in proportion as the solutions are more dilute. In determining the heat 
evolved on diluting strong solutions, the experimental errors increase in 
a very rapid proportion “if the determinations are made by diluting the 
solutions with successively equal volumes of water. Further details will 
be found in a paper on the Nature of Solutions, in the current number 
of the Journal of the Chemical Society. 


On Kerr’s Magneto-optic Phenomenon. 253 


obviated by the use of the wire-gauze tray suspended just 
below the surface of the water. 

When dealing with liquids, where dissolution takes place 
almost instantaneously, the “uncertain interval” when the 
temperature is between the initial and final points is practi- 
cally nzl, and may be overlooked. The process in making 
the determination therefore consists in ascertaining the rate 
ef cooling at the “initial temperature,” and correcting the 
last reading of this so as to give its value at the moment of 
the addition of the solution (15 seconds generally after this 
last reading), and dating the commencement of the rate of 
cooling at the “final temperature”’ from this moment. Three 
or four readings at intervals of one minute generally suffice 
to determine this latter rate satisfactorily. 

I now invariably read the thermometers without stopping 
the stirrers and tapping-apparatus, and I believe that greater 
accuracy in the results is thereby obtained. 


XXVIT. On Kerr’s Magneto-optie Phenomenon. 
By H. H. J. G. pu Bots, of the Hague*. 


§ 1. YPNTRODUCTOR Y.—Dr. Kerr has shown, in 1877, 

that the mode of vibration of light is in general 
affected by reflexion from a magnet. Hitherto this phenome- 
non has been almost exclusively studied from an optical point 
of view {; in particular, the complicated behaviour of light, 
obliquely reflected from magnets, has been much discussed. 
A magnetic curve was, however, given by Prof. Kundt, from 
which I drew the following conclusion}: for light normally 
reflected, the rotation is probably proportional to the magneti- 
zation, as it is for light transmitted through magnets. Start- 
ing from this, I have now further investigated the phenomenon 


* Translated by the Author from Wied. Ann. xxxix. p. 25 (1890); a 
synopsis of results had been communicated to the British Association, 
Neweastle. See Proceed. of Sect. A, Sept. 17, 1889 Report. 

t Literature:—Kerr, Phil. Mag. [5] iii. p. 821 (1877), and v. p. 161 
(1878) ; Kaz, Dessert., Amsterdam (1884); Kundt, Wied. Asn. xxiii. 
p. 228 (1884), and xxvii. p. 198 (1886); Righi, Ann. de Chim. et Phys.|6] 
ly. p. 433 (1885), ix. p. 65 (1886), and x. p. 200 (1887). 

Theoretical papers:—Fitzgerald, Proc. Roy. Soc. xxv. p. 447 (1876) ; 
Phil. Mag. [5) ii. p. 529 (1877); Phil. Trans. clxxi. p. 691 (1880); Wied. 
Ann. xxv. p. 186 (1885). Rowland, Phil. Mag. [5] 1x. p. 482 (1880), and 
xi. p. 254 (1881). H. A. Lorentz, Versl. en Mededeel. Amsterdam, xix. 
p. 217 (1883), and Arch. Néerl. xix. p. 123 (1884). van Loghem, Des- 
sert,, Leiden, 1883, and Wied. Berbl. viii. p. 869 (1884). Voigt, Wied. 
Ann. xxiii. p. 493 (1884). Ketteler, Theor. Optics, Brunswick, 1885. 

ft du Bois, Wied. Ann. xxxi. pp. 965, 974 (1887). 


ey a ee 


LS ea eee a epee eS er 


et 

tig 
he 
4 
} 
We 


{ 
4 
{ 
| 


254 - H. E. J. G. du Bois on Kerr’s 


in its intimate connexion with magnetization. Optical com- 
plications were purposely avoided by working at almost normal 
incidence. I have also determined the effect of temperature, 
the rotational dispersion, and the characteristic absolute 
constants. 


§ 2. Method —Light from a Linnemann’s burner (incan- 
descent zirconia disk) was made to pass horizontally in suc- 
cession through red glass, a lens, a Lippich’s penumbral 
polarizer ; it then reached the vertical mirror of the magnet, 
by which it was reflected into the analyser and telescope. By 
special constructive devices the parts of the apparatus, passed 
through by the light before and after reflexion respectively, 
could be fixed on a common base so near to each other 
as to have their optical axes inclined at but 2°; this angle is 
halved by what I shall call the apparatus’s medial line. The 
observer's eye was, of course, carefully screened from the 
burner. The medial line was adjusted normal to the mirror. 
By this arrangement practically normal incidence (at 1°) was 
ensured ; in fact, Righi* noticed hardly any change in the 
phenomenon up te 15° of incidence. | 

The same physicist has found that with plane-polarized light, 
normally incident, the reflected vibrations are exceedingly 
oblong ellipses, the azimuth ef whose major axis naturally 
differs from that of incidence. I saw no reason for making 
measurements of ellipticity; working with a penumbral 
polarizer, the azimuth of the major axis is what is actually 
observed. When using good mirrors and avoiding alli dit- 
fused light, the alternative extinction of each half of the field 
of vision proved satisfactory, thus showing the ellipticity to 
be very small. The analyser’s azimuth was measured by a 
modification of Poggendorff’s mirror-and-(vertical)-scale 
method t+. The arrangement and dimensions of lenses, dia- 
phragms, the telescope, &., had been calculated beforehand 
with a view to obtain the field of vision as bright and uniform 
as possible, | | 

§ 3. The metallic cores principally used were ovoids (pro- 
late ellipsoids of revolution) of different material, on to which 
small reflecting-planes had been ground in various positions. 


* Righi, Ann. Chim. et Phys, [6 sér.] ix. pp. 120 and 132 (1886). 

+ [This was separately described (Wied. Ann. xxxviii. p. 494, 1889) in 
order not to encumber the present paper with details, and does not pre- 
tend to anything beyond a mere laboratory expedient. It has since come 
to my notice that other experimenters have used similar devices. ] 


Magneto-optic Phenomenon. 255 


I desire to thank Messrs. Hartmann and Braun, of Bocken- 
heim and Frankfort, and their foreman, Mr. G. Troll, who 
executed this difficult job for me with perfect success. The 
ovoids were magnetized ina coil of 1080 turns, 30 centim. 
long. In order to let light pass, small looking-tubes (-7 
centim. diam.) had been fixed between the wire during wind- 
ing. These lay in meridian planes through the coil’s axis, 
and inclined at various angles to it. 

§ 4. Notwithstanding the resulting slight irregularity of 
winding, the field was sufficiently uniform over the space 
to be covered by the evoids. This was tested by the mag- 
netic rotation in bisulphide of carbon, measured at different 
points on the coil’s axis. At the same time the field could 
thereby be determined in absolute measure ; and a numerical 
factor deduced, by means of which the readings of an ampere- 
meter in the coil’s circuit were afterwards reduced to fields. 
The ovoids’ moment was magnetometrically determined in 
the ordinary manner, the coil’s action on the magnetometer 
being compensated by that of asecond coil. Apart from ovoids, 
I have also worked with small reflecting disks, fixed between 
the poles of a Ruhmkorff electromagnet. Certain other 
arrangements will be described in due time. 


§ 5. Notations, often recurring :—, intensity of coil’s 
field; J, magnetization, and Sy’, mean magnetization of 
-ovoids ; 2a, 26, their major and minor axes; n=D/a, axial 
ratio ; Xt, outward normal to mirror; «, angle ¢(3, 2). K, 
Kerr’s constant (see § 24) ; 0, temperature ; X, wave-length; 
€,, rotation on “ polar” reflexion ; ¢, rotation (according to 
§ 2 this is to be understood as meaning the angle between the 
incident rectilinear vibration and the major axis of the reflected 
ellipse). Of course, 2 was in the first place determined ex- 
perimentally by reversing the current, generally as a mean 
of from 10 to 30 observations of azimuth. In every case 
below, however, the values of ¢ are given in minutes, radian 
measure being still too little usual in such work. Otherwise, 
wherever the contrary is not expressly stated, all quantities 
and scales of diagrams are given in C.G.S, units. Wherever 
the sense of rotations has to be expressed with reference to 
vectors, I shall use the system of the vine and Huropean 
“right-handed screw” *. Accordingly, the sign of Kerr’s 
effect, e. g. for iron, is negative, the sense of rotation having 
to be referred to the direction of magnetization. 


* Maxwell, Treatise, 2nd ed. i. p. 24, 


ey 
SF 


256: H. du Bois.on Kerr’s Magneto-optic Phenomenon. 


First Part. 


sng 6. I begin by describing the experiments with the ovoids. 


The polarizer consisted of a nicol and a Hartnack-Prazmowski’s 
semi-prism (see § 16). The zirconia disk stood in the focus of 


the first lens, which thus projected parallel rays on to the 


mirror. Distance of vertical scale about 175 centim. 


_§ 7. Normal temporary magnetization.—The 5. ovoids used - 
in this case were provided at one end with circular mirrors. 
perpendicular to the axis of revolution, and were magnetized 
parallel to the latter. In this case, therefore, the reflexion, 
polar,” 7. e. the. 
metal is magnetized normally to the mirror (¢=0).. An: 


according to Dr. Kerr’s nomenclature, is ‘ 
g ’ 


ellipsoid (particular cases : sphere, spheroid, ovoid) i is known 
to be the only finite figure in which iron is uniformly mag- 


netized when subjected to a uniform field. In particular, no 
figure bounded by planes exists, for which this might be the 
case otherwise than approximately. Instead of such of vanish-. 


ing size I had to use mirrors whose dimensions were only so 
far reduced as was consistent with sufficient intensity of the 
reflected beam. The ovoidal shape was necessarily disfigured 
by the missing segments ; and the magnetization, uniform on 
the whole, must be differently distributed in the neighbour- 
hood of the small planes ; it 1s easy to see that it must be less 
than with an infinitely small mirror. 

§ 8. Some preliminary trials were made to show that this 
is the correct view of the case. On turning down the mirror 
of one ovoid successively from *7 to ‘5 and then to ‘3 centim. 
diam., the rotation increased each time, ceterts paribus. 
Another ovoid, provided with mirrors at both ends, showed 
the lesser rotation at the larger mirror. Lastly, an ovoid 
was fitted as one pole-piece into an electromagnet, with the 
result that the rotation, for about the same estimated mean 
degree of magnetic saturation, proved considerably larger than 
when the ovoid was magnetized in the coil. The second 
bored pole-piece acts in the same manner as Kerr’s “ sub- 
magnet,” i. e. it prevents the self-demagnetizing action of the 
plane end. In the final experiments the observed rotation 
may be estimated at 60 to 75 per cent. of that which would 
occur were the mirror of vanishing size (by data of § 19). 

- § 9. The rotation, evidently a local action of magnetiza- 
tion, was now directly compared with the magnetometer- 
deflexion, apparently an action at a distance. The quotient 
(moment/volume) gives the mean magnetization Sj of the 
ovoid, plotted in the broken curves of fig. 1 as a function of 


{/ 5 
A Auxilio TY axts of abs 
| for Steel 


10U y : 4UU 5UU 6UU (UU SUU YUU 


I, Glass-hard English Cast Steel (tem- III. Cast Iron : 
pered at 100°), 2a=12'6;, 26=1°8; 2 
2a=10; 26=2; n=}. IV. Cast Cobalt: 
II. Soft Swedish Iron (annealed) : Qa=10; 26=2; n=}. 
20=12:00 2o= 8s n=. V. Hard-drawn pure Nickel : 


Qa=10; 2=2; n=j. 


258 H. E. J. G. du Bois on Kerr’s ee: 
the magnetizing field. The rotation ¢, proved very nearly 


proportional to “¥’; for each ovoid the mean m of the ratios 
€,/§ was therefore calculated. By marking the values of 


¢,/m in the figure, and joining these points ©, lines are 


obtained consisting of straight parts nearly coinciding with 
the broken curves, so as even partly to overlap in the small 
diagram. Proportionality is now seen to exist between € 
and ‘¥! at the first glance. The optical phenomenon, however, 
can evidently only depend upon the magnetic condition imme- 
diately behind the mirror ; the foliowing conclusion therefore 
appears justified: Within the comparatively narrow range of 
fields applied (§ between 100 and 900 C.G-S.), the distribu- 
tion remains unchanged ; accordingly, S}, the magnetization 
at the mirror, is proportional to Sj’, the mean magnetization 
throughout the ovoid. 
I. This gives the Law of Proportionality : 


ee KS; 
where K is a constant. 
In order to give this result a solid experimental foundation 
I have worked with 5 ovoids of different metals and various axial 
ratios. Accordingly each curve is seen to exhibit its peculiar 
character between the extremes of steel and nickel, though 
in each case verifying the proportionality to be proved. 


§ 10. Inclined temporary magnetization.—All researches 
hitherto published refer either to ‘‘ polar” («=0) or to 
equatorial” («=90°) reflexion. The case of magnetization 
inclined to the mirror’s normal remains to be investigated. 
On to a large ovoid (2a=15; 26=3; n=1/5) of soft 


Swedish iron small elliptical mirrors (minor axes ‘25 centim.) 


were vround under different angles to the axis of revolution. 


These were so small in comparison with the ovoid that the 
latter’s longitudinal magnetization might be considered uni- 
form. Accordingly the rotation observed may be estimated 
(by data of § 19) at 90 to 95 per cent. of that with an in- 


finitely small mirror. The inclinations of the mirrors to the 


axis of revolution were measured in the lathe; the angles 
are their complements. 

§ 11. The rotation was now measured for 4 mirrors with 
the same current flowing in the coil, and the beam of light 
passing forwards and backwards through the looking-tubes 


mentioned in § 38. The value zero for equatorial reflexion at 


normal incidence is taken from previous observers. 
The numbers in the last line were calculated by analogy to 
Verdet’s cosine law. The apparatus for these last experi- 


ee 


_Magneto-optic Phenomenon. 259 


Polar, € . Inclined. Equat. 


UES eSB Ramer ne CF 0° 39°°4 50°'5 77°°2| -90° 
Rotat. observ. ¢....... —16"5 | —12°6 | — 9"7 |—4'6| 0 
Rotat. caleul.e,cosa| —16"5 —12'8 —10'5 | — 3"7 0 


ments having been difficult to construct, many sources of error 
occurred ; considering these, the observed and calculated 
values of e sufficiently agree. 

Il. This leads to the Cosine Law 

3 e=e, cos (J, St). 

It must still be remarked that the plane parallel to the 
mirrors normal and to the direction of magnetization may 
be called a “magnetic principal plane.” In the above 
experiments this principal plane and the plane of polarization 
of the incident light were both horizontal. Experiments with 
a cobalt mirror, obliquely magnetized, proved that the same 
rotation is obtained whether one plane is perpendicular or 
parallel to the other. The effect is therefore independent 
of the azimuth of incidence. Equally good extinction was 
observed with inclined magnetization as on polar reflexion. 


§ 12. Normal residual magnetization.—In order to obtain 
this an elongated ovoid (2a=18 ; 26=1°2 ; n=1/15) of glass- 
hard English cast steel, tempered at 100°, had to be used. 
This, on the other hand, offered the disadvantage that the end 
was considerably disfigured by grinding on a mirror. The 
magnetic distribution must therefore differ considerably frem 
a uniform one. I succeeded in obtaining a residual rotation 
in the shape of a change of the analyser’s zero on impressing 
reversed residual magnetizations ; it could be measured as a 
mean of 30 observations. The influence of magnetic history 
was each time eliminated after the manner of Gaugain, 
Auerbach, Maxim, Hwing, and others, by gradually diminish- 


ing reversals. Results follow :— 


. su ery €,/S". 
MPeSTCMal i580... cecwernes 0 180 —0'6 —°0033 
Mesidual 6.0 dec 0 250 —0'8 —°0032 


260 H. E. J. G. du Bois on Kerr’s 


§ 13. On account of the slight rotation no very sharp con- 
clusions can be drawn from these numbers. The ratios of the 
last column are certainly all of the same order of magnitude ; 
the first two, corresponding to residual rotations, appear to 
be equal and less than the third. This is easily explained by 
the plausible assumption of a residual distribution differing 
from the temporary one in giving comparatively less mag- 
netization near the mirror. ‘The result appears to me to lead 
to the following interpretation :— 

For the law of proportionality it matters not whether the 
magnetization be residual or kept up by external induction. 

This would tend to prove that the rotation is an immediate 
effect of magnetization and depends upon it alone*. 


§ 14. Effect of temperature.—The ovoids could be fixed in 
a brass tube closed at one end, and fitted at the other with a 
number of diaphragms, through the central apertures of which 
the mirror remained visible. This tube was heated by a 
horizontal perforated burner; the necessary draught being 
obtained by two waterjet-exhausters, which thus acted lke 
chimneys. ‘This arrangement could be introduced inside the 
coil, separated from it by an asbestos jacket. With a current 
of 30 amperes the coil and its contents could be electrically 
heated up to 170°; by means of the burner the ovoid could 
be raised to higher temperatures still. Magnetic and optical 
observations were then made simultaneously during cooling. 
The rate of cooling could be modified at will by regulating 
the enclosing coil’s temperature by the current. The 
temperature was given with sufficient approximation by a 
thermometer having its bulb near the mirror and stem pro- 
jecting from the apparatus. Of course the metals were heated 
only for a short time and never beyond the temperature at 
which they begin to show surface-colours ; as the least film 
of oxide on the mirror completely modifies the phenomena f. 

§ 15. The results are given in Table I. The numbers for 
eobalt, iron, and steel on the whole lead to the conclusion 
that the value of €)/%}/ is but little variable with temperature. 
At the same time ‘SY’ varies so little { with @ that the distribu- 
tion may be safely considered constant. Consequently € 9/5 
(=K) is proportional to €)/7s', 2. e., by the above, practically 
constant. 

For nickel, however, %/ diminishes considerably while @ 


* du Bois, Wied. Ann. xxxi. p. 973 (1887). 
+ Kundt, Wied. Ann. xxvii. p. 199 (1886). 
{ See footnote ¢ next page. 


Magneto-optec Phenomenon. 261 


TABLE I. 
Q. | Ey. | x", | yi Sie Pea: | se | y", | €,/S'. 

Cobalt. §=930. Steel. $—930. 
99°| —10:9 | 894 | —-0121 ||. 31°] —10-7 | 983 | —-o109 
Gee!) ico tsge 0193. || 101. | £108°.| *.9794 | 0111 
leg | Sikes \ so4) = -9196' | 147 ‘| =10-7+|. 964 “| =-o111 
990 | —11-2 | 897 | —-0125 

Nickel. §=820. 

Be), D780: 7° | =49 | 472° | —-0103 
97°) 13:0 | 1528 |) —-0085 || 99 |. 54 | ~452' | —-oi18 
73 | —123 | 1594 | —-o080 || 162 | —52 | 426 | —-0123 
120) 2191 | 1523 | =-0080 .|.945 | —4:8. |. 330 )|—-0146 
164 | —136 | 1517 | —-0090*!| 282 | —3-2 | 198.°| —-0163 


increases: the self-demagnetizing action thereby decreases 
at higher temperatures, so that the distribution approaches to 
uniformity, and the values of 5 and ¥’ tend to become equal. 
It follows that even if €)/-} be constant, €)/S’ will none the 
less increase with 0, and this is what the numbers for nickel 
actually do. Hxperiment therefore does not contradict the 
highly probable assumption that K is practically constant for 
nickel as well as for the other metals. At temperatures above 
280° no more data could be obtained with sufficient accuracy. 
But on further heating I observed a rapid decrease of both 
rotation and magnetization until both vanished for tempera- 
tures above 335°, only to reappear simultaneously on cooling. 
This qualitative experiment affords a convincing instance of 
the close relation between both quantities. The result of this 
paragraph may be thus expressed :— 

Ill. Lhe variation of the constant K with temperature is 
practically zero ; it is certainly less than a few per cent. per 
100°, and therefore much below that of the electric resistance 


* It is quite possible that a thin colourless film of oxide begins to 
cover iron about 164°, which would explain the larger rotation here given ; 
the temperature corresponding to a pale yellow is stated to be about 220° 
on heating fora short time. See Loewenherz, Zettschr. f. Instrum. Kunde, 
ix. p. 316 (1889). For cobalt, and especially for nickel, these temperatures 
happen to lie much higher. 

+ It may not be superfluous to remark that from the values of $’ given, 
nothing more than a qualitative conclusion may be drawn as to the 
thermomagnetic behaviour of the metals; for the self-demagnetizing 
action of the rather short ovoids tends to diminish any temperature- 
variations of their magnetization. For quantitative determinations in 
thermomagnetism the metals have to be used in forms fulfilling the con- 
dition of perfect or approximate endlessness. 


262 H. E. J. G. du Bois on Kerr’s 


and index of refraction*. It may also be remarked that Dr. 
Sissingh f has not been able to observe any change in the two 
ordinary constants of reflexion for iron between 20° and 120°. 


SECOND PART. 


§ 16. The experiments in which the electromagnet was 
used remain to be described. Polarizer and analyser now 
consisted of genuine Lippich prismst. Working with a 
parallel beam of light was now given up, and an image of 
the zirconia disk thrown on the analyser’s diaphragm instead ; 
by this artifice of Lippich’s the disturbing effect of any 
flickering of the source of light on the accuracy of observa- 
tion is counteracted. Distance of vertical scale is 400 centim. 
nearly. These improved arrangements, together with the 
mounting of the optical apparatus on a pillar, separate from 
the electromagnet, considerably increase the accuracy of the 
results stated below above that hitherto attained. 

§ 17. Other active substances.—Besides the three metals, 
exhibiting negative rotation on reflexion, I have detected 
Kerr’s effect on common magnetic iron-ore. <A piece of 
loadstone, ground and polished, showed a slight rotation be- 
tween the poles of an electromagnet. Its numerical value 
varies over the mirror, but it is always positzve. For quanti- 
tative measurement this material is of no use on account of its 
heterogeneous structure. 

I therefore got a mirror ground parallel to the octaheder 
(11 1) ofasmallerystal of magnetite (Fe;,0,, holohedr. tesseral). 
With a strong current in the electromagnet this gave a 
rotation ¢= +95’ for red light; the extinction was perfect, 
proving the ellipticity to be quite negligible. The rotation 
proved independent of the azimuth of incidence relatively to 
the crystal’s principal directions ; I therefore abstained from 
having other mirrors ground on in different positions, mag- 
netite evidently behaving like an isotropic body. It would 
be interesting to observe the effect on transmitted light. 
However, hitherto I have not been able to find any method of 
procuring transparent films of this highly opaque substance. 

§ 18. I have further tried the following much less magneti- 


* Kundt, Berl. Berichte, Dec. 1888, p. 1393. 
+ Sissingh, Dzssert., Leiden, 1885, p. 186; Arch. Néerl. xx. p. 216 
1886). 

: t Lippich, Wren. Ber. xci. 2, p. 1081 (1885). These prisms, as made 
by Dr. Steeg and Reuter, of Homburg, give a perfectly uniform field of 
vision with a well-defined line of demarcation ; unfortunately, the linseed- 
oil used in their construction requires months for drying, so that I could 
not use them from the beginning. 


263 


zable, though powerfully absorbent, substances, but without 
any positive result—sulphide of iron (FeS, amorphous), and 
oxide of iron (Fe,O3, rhombohedr. hemihedr. hexagonal ; 
mirror normal to principal axis). The fact that a measurable 
Kerr’s effect has hitherto been detected only on the strongly 
magnetizable opaque substances Co, Ni, Fe, Fe3Q,, points 
once more to the important part which magnetization plays 
in the phenomenon. I am much obliged to Prof. Biicking 
for kindly supplying me with these minerals. 


Magneto-optic Phenomenon. 


§ 19. Absolute constants.—After having considerably im- 
proved the accuracy of the optical observations, as pointed 
out in $16, I could venture to apply them in their turn to 
magnetic measuring purposes. ‘This application of the law of 
proportionality I shall describe* in detail; at present I will 
only mention that by means of it I was able to find the 
magnetizations corresponding to the rotations ¢, given below. 
By division the absolute values of the constant K are ob- 
tained for “ red” light in minutes per unit magnetization. 


Cobalt. Nickel. Iron. Magnetite. 
Gpates. —20'-97 —7'25. | —22'-99 
SX Sae aeee 1060 453 1669 
Le ee — 0198 — 0160 | —-0138 +012 


The value for magnetite is approximate ; the others refer 
to the massive metals free from oxide; I could not detect any 
effect due to the polishing material. Thick electrolytic films 
gave about the same rotation under the same circumstances, 
but in general this depends on their thickness and surface 
condition; such films are, therefore, hardly suited for absolute 
measurement. 


§ 20. The rotational disperston of Kerr’s phenomenon is 
anomalous, but only for iron is it sufficiently developed to 
interfere with working in white light. For quantitative 
measurement I applied spectral analysis in connexion with 


Lippich’s{ penumbral method. By means of a prism “a 
vision directe ”’ a solar spectrum was thrown on a small screen. 


* In the April number of this Magazine. 
+ See Kundt, Wied. Ann. xxvii. ae 199 (1886). 
{ Lippich, loc. cit. p. 1070; and Wied. Ann, xxxvi. p. 767 (1889). 


AES ps ee wo . 


ee 


SS ee 


LLL, LLL ALLL LLL LLL LLL LO 


PES I REEL EO A Se 
ae y _ = 0 go ts batic = = a 


264 H. E. J. G. du Bois on Kerr’s 


All parts of this combination were rigidly put together, and 
its optical axis adjusted perpendicular to the medial line (§ 2) 
of the optical apparatus. Instead of Lippich’s slitted screen 

“slitted mirror ”’ of adjustable breadth was set up vertically 
at 45° to the spectral screen in about the same place where 
the zirconia disk previously stood. This mirror, therefore, 
projected a sufficiently homogeneous beam of light into the 
polarizer. 

§ 21. The positions of the lines Li a, D, 6b, F, G were 
marked on the spectral screen and checked by means of 
spectra of Li, Na, and H. The slitted mirror was afterwards 
set to these. The “red” light used in the preceding experi- 
ments was not quite homogeneous, but owing to the slight 
dispersion sufficiently exact measurements could be made 
with it. Strictly speaking a definite wave-length cannot be 
assigned to the “red” light. But in order to allow a re- 
duction of the spectral measurements to absolute values the 
question arises: which part of the spectrum is rotated through 
the same angle as was found for the ‘‘red” light? To this 
a definite answer may be given; by trial and interpolation I 
found for the wave-length X¥= 62 x 10-° centim. 

§ 22. The rotation was determined with each metal for six 
colours, each angle being obtained from thirty observations. 
The values of K (Gn minutes per unit magnetization) are 
given in Table II. ; the numbers marked with an asterisk are 


TaBLeE II. 

| Colour.| Line. |AX106em. || Cobalt. | Nickel. Iron. Mages 
Red. Lia 67°71 — 0208 = O173*| —'0154 | +:0096 
Red lf? ity Tike 62 —'0198*| —-0160*; —-0138*| +--0120* 
Yellow D 58:9 — 0193 | —:-0154*| —-0130 | 4:-0133* 
Green b 51°7 —°0179 | —:0159 | —-O111 | +-0072*| - 
Blue. EF 48°6 — 0181 | —:0163*| —:0101 | +-0026* 
Violet. G 43:1 —°0182*| —:0175*| —-0089 


the means of two separate series of observations. In plobenae 
K=funcet. (A) perfectly continuous curves of dispersion are 
obtained, showing the following characters :— 

IV. Cobalt has a faintly pronounced minimum for bluish 
green. Nickel a minimum for yellow. The iron curve runs 
almost straight down from red to violet. Lastly, for magnetite 
a maximum occurs in the yellow. 


= 


Magneto-optic Phenomenon. 265 


Unfortunately quantitative observations with the poorly re- 
flecting magnetite could not be pursued beyond blue. Further 
measurements might have proved the more interesting, as the 
rotation appeared almost to vanish for violet. I donot deem 
it impossible that the rotation passes through zero and changes 
sign in the ultra-violet, though this point appears difficult to 
decide. 

TuirD Part. 


§ 23. The combined expression of both experimental laws, 
€,= KJ and e=e, cos (3, MN), leads to the general law :— 


e=K% cos (9, N)=KF,, 


where %, stands for the component magnetization normal to 
the mirror. This relation was found for red light, but may 
evidently be extended to radiations of all wave-lengths ; it 
may be thus expressed :— 

V. The rotation of the major axis of vibration of radiations 
normally reflected from a magnet is algebraically equal to the 
normal component magnetization, multiplied into a constant K. 

Poisson, as is well known, has shown how any arbitrary 
magnetic distribution may be replaced, without prejudice to 
its internal or external action, by fictitious magnetic fluids, 
distributed in a definite manner throughout the magnet and 
on its surface*. The surface-density 3 of the latter portion 
is given by the equation $=J,. By the above we now 
have the rotation proportional to the surface-density, and it 
would thus appear theoretically possible to determine the 
latter by purely optical means. It would, however, be of no 
practical use to introduce the fictitious quantity § into the 
physical equation ; it has no meaning beyond that of a purely 
mathematical symbol. 

§ 24. The constant K is a quantity of dimension [L? M-?T] 
in electromagnetic measure. For four substances it is given 
in Table II. as a function of the wave-length; it hardly varies 
with temperature. I venture to propose calling it ‘Kerr's 
constant; for another quantity, which I have previously 
defined and denoted WT, the name “ Kundt’s constant”’ 


* Not to be confounded with Gauss’s surface distribution, the action of 
which may be substituted for that of the magnet only for points external 
to it. Both distributions do not coincide except in the particular case of 
solenoidal magnetization. 

+ The constant ¥ for radiations of definite wave-length is algebraically 
equal to the rotation which the plane of polarization of such radiations 
would experience on normal transmission through a plate of unit thick- 
ness and unit normal magnetization; du Bois, Wied. Ann. xxxi. p. 968 


(1887). 
Phil. Mag. 8. 5. Vol. 29. No. 178. March 1890. X 


ot. 


at 


ate Ree a Rn ca ni aera mera mao cainstet-anecrinicSoatimenlcr Oeaeetie pee SU Gj MIE RT MCX 7 ) ee oe eee 
een se = a = sf ne EET "9 
Farriee a aey lai DO pipe as A ee Sm lage act the geet ee ele ae = Sse a 


wets 


pe ee SU ee een ae 


teh eee pee 


266 H. EH. J. G. du Bois on Kerr’s 


appears suited. ‘These names are formed analogously to that 
of another magneto-optic quantity, viz. ‘‘ Verdet’s constant,” 
which is quite generally accepted; they recall the names of 
the discoverers of the corresponding phenomena, and are not 
limited to any particular language. I therefore believe that 
no objection can be made against their introduction, which 
appears desirable in order to avoid confusion among three 
essentially different constants of nature. 


§ 25. Conclusion.—To my mind the experiments discussed 
leave no doubt but that the peculiar phenomena connected 
with reflexion from magnets solely depend upon the magneti- 
zation existing immediately behind the mirror; and I believe 
that no theory ought to ignore this fact. They also supply an 
experimental proof, which, however, is hardly required, for 
the assumption that at least part of the incident radiation 
penetrates below the surface and is there acted upon by mag- 
netism, to be reflected out again afterwards. For, supposing 
the ray’s path to lie entirely outside the metal, the action 
could only depend upon the magnetic condition of the air, 
which, however, is not the case. | 

I have been able to show, on a former occasion, that mag- 
netization also is the quantity upon which the effect on trans- 
mission of radiations through magnets depends ; this of course 
is intimately related to Kerr’s phenomenon. The latter is 
doubtless the more complicated of the two phenomena, and 
differs from the former in sign and in the character of its dis- 
persion*. I believe the following simple kinematical ex- 
planation may be given for this difference; in doing so the 
dynamics of both phenomena are left aside as a remoter 
question. 

§ 26. On normal transmission through a magnetic film the 
resulting difference of phase between the two opposite cir- 
cularly polarized rays depends on their different velocity of 
propagation only; for the geometrical path is the same for 
both, viz. the film’s thickness. On normal reflexion, however, 
the “optical path” t in the metal (=retardation of phase) is 
proportional for each ray to the quotient of the geometrical 
path by the velocity of propagation. Now the latter as well 
as the geometrical path (in consequence of the different depth 


* The rotation is known to be positive on transmission through Co, 
Ni, and Fe; its dispersion is anomalous, but according to Dr. Lobach 
(Dissert., Berlin, 1890) it shows neither maxima nor minima. 

+ “Optical path ”=geometrical path xindex of refraction; a con- 
venient expression used by some authors. 


Magneto-optic Phenomenon. 267 


of penetration *) is different for the two circular rays. Ac- 
cordingly it is easily seen that the difference of optical path, 
and therefore the difference of phase, may have the opposite 
sign for reflexion or transmission respectively. In fact it is 
only necessary that the swifter circular ray penetrate so much 
deeper than the slower one, that the acceleration of phase, 
which it would otherwise acquire, be thereby changed into a 
retardation behind the phase of the slower ray. 

Generally speaking it is therefore possible that the rotations 
on reflexion or transmission respectively have the same or 
opposite signs. The former might even have different signs 
according to wave-length, and vanish for particular values of 
X. Hxperiment seems to point to a case of this kind with 
magnetite (§ 22). The curves of dispersion for reflexion and 
transmission of course need not show any analogy; in any 
particular case this depends upon the properties of the sub- 
stance. The above considerations were hinted at by Voigt, 
though in a different form; but they are not limited to any 
particular optical theory, whether electric or elastic. They 
are of a purely kinematical nature; the hypothesis of circular 
birefraction and “ biabsorption,” on which they are based, 
must, however, be retained. 

The contents of this paragraph have therefore to be con- 
sidered apart from all that precedes; with this sole exception 
I have striven to cling to experiment and its immediate con- 
sequences, free from any additional assumption. In conclusion, 
I beg to tender my best thanks to Prof. F. Kohlrausch, in 
whose laboratory these experiments were carried out. 


Phys. Inst. of Strasburg Univ., 
Oct. 20, 1889. 


* The most general assumption is that part of each circular ray is re- 
flected in the surface itself. The rest then penetrates into the metal, and 
every elementary sheetof its substance again reflects a “circular element,” 
with amplitude the less, the greater the depth at which reflexion ensues. 
The reflected pencil now consists of one circular vibration and an infinity 
of circular elements vibrating in the same sense. Kinematic integration 
gives a single circular vibration in this sense. This consideration, there- 
fore, leads to the same result as the assumption, made above, of direct 
penetration of the pencil as a whole, and subsequent reflexion at a defi- 
nite depth. The two resulting opposite circular vibrations now possess 
difference of phase, thence rotation, and slight difference of amplitude, 
thence slight ellipticity in the reflected ray. (Compare the geometrical 
zp hod of circular elements by Dr. Wiener, Wied. Ann. xxxy. pp. 3-5, 

5) 
t Voigt, Wied. Ann, xxiii. p. 508 (1884). 


X 2 


— oe 


a 


XXVIII. On the Acceleration of Secondary Electromagnetic 
Waves. By Frep. T. Trouton*. 


[Plate VI.] 


[ is well known that if, after the manner of Huygens’s 

construction, the effect of a wave-surface at any point be 
determined by summing up the individual effects of the 
secondary wayes obtained, by supposing the surface divided up 
into elementary portions, each element of surface acting as an 
independent source, it becomes necessary to assume that an 
elementary portion egies its effect at the point with an 
acceleration of phase of + period in advance of the effect pro- 
duced at the point by the general wave-surface, otherwise the 
sum of the secondary effects would possess a phase + period 
in error. 

As ordinarily considered f, it is somewhat surprising that 
there should be this change of phase in a wave coming from 
an element of surface. But the consideration of this question, 
in the light of Hertz’s investigations on the radiation emitted 
from an electromagnetic “vibrator”? or discharging con- 
denser, seems to be particularly suggestive. 

At first the magnetic component of the wave will be taken, 
as it can be more simply dealt with. Considering, for 
the moment, points situated along a line at right angles to, 
and starting from, the centre of a “vibrator,” Hertz’s ex- 
pression t for the magnetic component of the electromagnetic 
wave at a distance r is 


P= 2 { sinan(<— \4e~ cos 2r (7 —<) }. 


At points near the “ vibrator”? the vibration is easily seen to 
depend almost entirely on the latter term, or 


= a cos tm (> —* : 


while at a distance it depends in like manner on the first 
term, or, as it may be written, 


P=S cos2n} 5 — BG +z}. 


* Communicated by the Author. 
+ The complete Elastic Solid Theory contains this acceleration. See 
Enc. Brit., art. “ Wave Motion,” p, 458. 


t Wiedemann’s Annalen, January 1889; also ‘ Nature,’ February 21, 


1889. 


— ‘ 


On the Acceleration of Secondary Waves. 269 


This at once points to an acceleration of phase of } period at 
distances remote from the “ vibrator.” 

The rate at which the magnetic component of the disturbance 
is propagated can be determined by taking a definite position 
on the wave and finding how v varies with respect to ¢ on tra- 
velling out with the wave in this phase. If P=0, then 


tan (mr—nt)= —1/mr. 


Here m stands for 27/d, and n for 27/r. From this we get 
for the velocity of the wave, 


Bedi eee te 
(ecdian my" 

where V is the normal velocity, or that at a great distance 
from the “vibrator.” When r=0, v has an infinite value, 
but on going outwards rapidly approximates to V. Hertz 
has pointed out that the true interpretation of this great 
value for the velocity at points near the origin involves the 
idea of the energy radiated really coming from points in the 
surrounding medium, the true seat of the oscillations. 

Thus, from the consideration of velocity an acceleration in 
phase is observed to occur. ‘To find its amount, the time the 
disturbance takes to reach a point at distance NA from the 
origin can be easily found and compared with the normal 
time. Thus 


Nidp 1 Ae LE Lape 
{ TT UN gel NaS 


When N isa large number this approximates to the value 
Nzr—7/4, and is an acceleration corresponding to one quarter 
period. 

If the position of maximum or minimum value of P 


(G6. oe =(*) be taken on the wave instead of the zero value, 


we shall have tan (mr—nt)=mr, and the same expression for 
the velocity is found. The circular electric-line of force in 
Hertz’s diagrams of the disturbance, here reproduced for 
convenience of reference, also spreads out with this velocity. 


* It is to be particularly observed that in the neighbourhood of the con- 
ductor, unlike in normal wave motion, the position on the wave where 


P ‘ ; a 
qG = is not the position on the wave of maximum displacement; this 
state of the wave will be found like the electric force to originate at 
\/4:4, having a very similar expression for the rate of its propagation. 
On plotting the curve P at a series of stated epochs this is well shown, 


Zo 3 Mr. F. T. Trouton on the Acceleration 
The electric component of the wave* 


ll Z { a a cos (mr—nt) Sin (mr—nt) 


mr mr" 


may in like manner be considered. Similarly to before, if 
z=0, it is necessary everywhere along the line considered that 


mr 
1—m?*r? 


From this we get for the velocity, 


m7* — m7? +1 


m?r"(m?r? — 2) 

In this case v has an infinite value both at the centre and at 
distance \/47V 2—roughly A/4:4. At intermediate points it 
is negative or towards the centre. As the wave passes out- 
wards it is at this point \/4°4 that the zero value of ¢ is first 
reached (at about ‘127 before it becomes zero at the centre, 
which occurs at 7/2), whence it spreads both outwards and 
inwards. On the diagrams this appearance of the zero value 
of z is easily traced, and its subsequent outward movement at 
the centre of the small circles ; these of course are the cross 
sections of a vortex-ring, as it were, thrown off by the 
TeVIOLAtOI.. 

For determining the time to reach any point, we have 


(2 & ice epee at » +const. i ; 
. m J 


tan (mr—nt) = 


C= 


cree jm atecaerse eer Petsing= nee nein SPE RSE oe ee 1 Te pete ae Bb aon RRR = eens eet Pa tS 


oe. 3 
iste 


DS ge a ieee Tee ee FS 


pe ac nas 


ee aN 1 —m?r" 


This between NA and A/4°4, when N is a large number, gives 
as the time taken, 

| 7(N—1/4:4) —7/27.. tan7'V 2, 

the first part being the normal time. 

If we wish from this to determine the period elapsing 
between the arrival of the wave in this phase at the point NA 
and the time of zero value of the electric force at the centre 
which occurs at the epoch of fig. 1, Plate VI., we must add 
the epoch of the appearance at A/4°4. This will be found to 
afford N'T, the normal time. But if we reckon from the time 
the zero value, uaving appeared at )/4°4, travelling inwards 
reaches the centre, we obtain NT —7/2, an acceleration of one 
half-period. In neither case, it is to be observed, does it 
represent the time of passage between two places. The zero 
value of z at the centre in fig. 1 ought really to be referred 


* Wiedemann’s Annalen for 1889. 


| 


of Secondary Electromagnetic Waves. 271 


to the previous swing. This will be better understood by 
recollecting that at the conductor, when the electric force is 
at its greatest development, the current is zero, and conse- 
quently so, too, the magnetic force, while in radiation the 
electric foree and the magnetic force simultaneously reach 
their maximum value. This is beautifully shown in Hertz’s 
diagrams. In fig. 1, at the centre the electric force is zero, 
while the magnetic force is about at its greatest development. 
The latter travels outwards with such a velocity at each point 
(the same as that of the circular line of force in the diagrams) 
that there is an acceleration of + period ; while the former 
vanishes at the centre but reappears at /4°4, as is seen in 
fig. 4, so as to be now one quarter wave-length behind. In 
this way the necessary readjustment of the relative phases 
of the electric and magnetic components is effected. 

If the position on the wave of maximum or minimum value 
of z (that is to say, the “crest ””) be taken instead of the zero 
value, the condition at any point is that 

mr? —1 
tan (mr—nt) = ae 
and the same expression for the velocity as before is obtained, 
so that the position at distance \/4°4 may be considered the 
point from which the electric disturbance originates, and not 
the centre. As the energy in the neighbourhood of the con- 
ductor turns from its magnetic to its electric form*, it is at this 
point that the maximum value is first reached, and is in 
advance of the “normal epoch” 7/4, or that of the “ crest” 
at the centre by about $7. The maximum value spreads both 
outwards and inwards from ’/4°4, reaching the centre at 7/4, 
the epoch of fig. 3. 

As in the case of the zero value of z, so here also, if the 
period elapsing between the arrival at any point and the time 
of greatest electric development at the centre, which occurs 
at the epoch of fig. 3, be calculated, an acceleration of 7/2 on 
the normal time is found. This virtual acceleration of 7/2 is, 
however, due to the combined effect of the “ crest” or maxi- 
mum value of z, (1) starting from the point \/4°4 instead of 
from the centre, (2) at a time about }7 previous to the 
normal epoch 7/4 or that at the centre, (3) as well as to the 


* In the curves obtained by plotting z for a series of epochs the forma- 
tion of the wave at A/4°4 is clearly observed. The wave after springing 
here into existence above the zero-line, lengthens out in both directions, 
and then beginning to sag in the centre, finally splits into two at this 
point, as the force reaches zero, again to pass over to the other side of 
the zero-line. 


ae MPLS Beha 


as 


(aR 


RAH Ng a inept aghrcmen ah ae pest hae Fea rary 0 hag 
= ide e903 wall \ waa “ 
sek eerey o 7 7” e ‘ » : 


kee De. 


aoe 


tn ea 


ay hare ak» «ae. 


Soe 


aan od 


ro 


272 Mr. F. T. Trouton on the Acceleration 


increased velocity. As mentioned before, the acceleration of 
the rate of propagation of the electric component of the dis- 
turbance must differ by 7/4 from that of the magnetic com- 
ponent in order to provide the necessary readjustment of their 
relative phases. 

The question now arises if, on the whole, the elementary 
disturbance to be supposed in Huygens’ construction* may 
not fairly be considered as being of the same character as that 
produced by a Hertzian “vibrator.” Such an elementary 
disturbance as is there assumed, in the absence of neighbour- 
ing ones, would have apparently uncompensated ends or poles 
equivalent to the opposite electrifications on a “ vibrator.” 
Of course the only way we know of producing an elementary 
disturbance is by the presence of matter, so that it seems 
natural to take the disturbance assumed in Huygens’ con- 
struction to be similar in its effects. It might perhaps be 
objected to this that a “vibrator” is a conductor, and that 
there are conduction-currents to be dealt with ; but as against 
this the fact is to be considered that, as we shall see, a non- 
conductor such as glass can act by reflexion so as to be the 
source of such an elementary disturbance. 

Some experiments were described in ‘ Nature’ (August 22, 
1889) in which this acceleration in phase was actually observed 
to take place in the reflexion from a small surface. It was 
there described how, in Hertz’s experiment of “loop and 
nodes,” if a small sized reflector be employed, the magnetic 
node, instead of being at + from the reflector, is found to 
be nearly 42% further out. This evidently corresponds to a 
change of phase of + period in the reflected wave, for the 
distance 3X has to be twice traversed. 

The way in which this change in phase is brought about is 
perhaps most conveniently considered by supposing the small 
reflector to be itself resonant, or equivalent to a second 
vibrator having the requisite phase with reference to the inci- 
dent wave. And indeed that something such as this occurs 
may even be noticed by touching the mirror with a small 
piece of metal; for bright sparks can be drawn from the two 
edges running at right angles to the electric force, while little 
or no effect is obtained from the central parts. 

Let the magnetic component of the wave incident vertically 
on the reflector, and supposed a parallel beam, be taken as 


t vi 
P=A cos 27 fe =e =) 3 
Tie ON: 
* In the case of sound, the divergency of the direction of motion of 


the particles from an element of surface affords the analogous reason for 
the acceleration. 


} 
oO : 
im 3 : 
| & ? 
| < 
5 
} 
| Se 
= | 7 ; 
- 4 —_ 


of Secondary Electromagnetic Waves. 273 


where 7 is the distance to the reflector, and A is the ampli- 
tude of the magnetic force. The magnetic component of the 
reflected wave, supposed as above to be from a second “ vibra- 
tor,” will be given by* 


An 2H 5 ,. t r af t 
— 2 pole es fa 3 ee py Vier Xa 
P= - 4 sin aan ( = )+ 5} cos aT (- ne 


as this has the same phase at the reflector as the incident 
beam. Here + EH is the maximum value of the electrifica- 
tion induced by the incident wave on the second “‘vibrator,” and 
lis the equivalent distance apart of the positive and negative 
charges, which, taken roughly, is the length in the direction of 
the electric displacement of the reflector supposed rectangular. 
An approximation for H may be easily obtained from the 
value for the induced current arrived at, by assuming that the 
magnetic force parallel to the reflector due to the induced 
current is such as to neutralize the effect of the direct radia- 
tion immediately behind the reflectort. If cis the amount 
of the current per centimetre cross section in the reflector, 
the magnetic force due thereto parallel to the reflector and 
close up to it is 27c ; that is to say, it is assumed equal to the 
force due to an infinite current-sheet of intensity ¢ per centi- 
metre cross section. (See Maxwell, chap. xii.) This is to be 
put equal to the magnetic force of the direct radiation at the 


reflector A cos a=, Recoliecting that ¢ is in electromag- 


netic units, we have for the amplitude of the total charge 
along the edge & of the reflector, 


7/4 7/4 
H=kV edt=tV |Z cos dn dt= Ele 
Be aT T An” 
This neglects the end irregularities in the electrification. 

At any point in front of the reflector the disturbance is the 
sum of P and P’, and we have a series of stationary waves, 
complicated, however, by the fact that the velocity and the am- 
plitude of one of the components are functions of the distance. 


P4-P’=Bcos 2a ( = +2) 
Th 


represents the stationary waves when 
kl Te > kl\? Pes 

ay i a za VA pepe 
B=A 4 geo mG AT rae, COs Am x) i & | 1+ ) 


* Wiedemann’s Annalen, January 1889. 
+ This, as a method of evaluating the electrification, was pointed out 
to the author by Prof. Fitzgerald. 


—— 


i SiS GORA Ha cory ctor: 
Ra ESR AS a 


af yng: - << 
1 Ree artis 


So i ae ae 
coe ge Parnes 9: 8 Perrtaeg Smnget ms 
ee ee an oe are ae Oe 


be aR rte lt bee cae 
Bn soo a ee eae te 


- a 


Se dS TE Eo FES iy 
as i 4 — on 


274 Mr. F. T. Trouton on the Acceleration 


Practically the quickest method for determining the positions 
of maxima and minima for B is to plot the curve represented 
by this equation in each particular case. The curve shown in 
fio. 5, Pl. VI. is that where k=30 ec, 1=22c, and X=72¢. The 
abscissa represents the distance, measured in centimetres, from 
the reflector to the point, while the ordinate multiplied by A? 
represents the intensity or square of the amplitude of the 
magnetic force of the stationary wave at the point. The 
dotted line indicates the intensity of the direct radiation, to 
which the curve is seen to approximate as 7 increases in value. 
The curve is seen to be going off the limits of the paper on 
the side next the reflector; but it must be remembered that 
in this region the formule used have but an indirect inter- 
pretation as the finite size of the reflectcr becomes important, 
and that there is involved the idea of the ether here being in 
special commotion, so that reflexion may in a certain sense be 
looked upon as taking place before really reaching the mirror. 

On examining the curve the first minimum will be seen to 
occur at about 24 c¢ from the reflector, which agrees suffi- 
ciently well for an approximate method of calculation with 
tne result of experiment, which for a wave-length of (2 ¢ 
gives the first minimum at about 25 ¢.* And in fact we 
might expect, on looking at the curve, that the experiment as 
made would always tend to give the minimum a little beyond 
its true position ; for if the spark-gap be set to just observe a 
spark of, say, the direct waves’ intensity, and if the distance 
be bisected between the positions to right and left of the 
minimum where sparking is observed to commence on moving 
along the “receiver,” this point will be too far out, owing to 
the portion of the curve to the left being steeper than that to 
the right. This is well marked when working with the spark- 
gap comparatively open ; that is to say, various positions are 
then obtained for the minimum according to the width of the 
spark-gap. This was experimentally noticed before the curve 
was plotted. 

The curve indicates at once the reason why it is difficult to 


* In this Table the results of experiments with different wave-lengths 
are shown in the third column. 


d 2n. Min 
G2 | Pai 25 
68 25°5 24 
60 22°5 21 
56 21 19 


of Secondary Electromagnetic Waves. 275 


observe even the second minimum. It will also be noticed 
from the curve that the second minimum is at a distance from 
the first slightly greater than the half wave-length ; so that 
if the curve were continued further out we might very well 
expect the minima to be shifted out the complete $A, as in 
fact may be seen to be the case from the equation of the 
eurve. Thisin ordinary wave theory would be referred to the 
necessity for the point to be at a proportionate distance before 
a given surface can be considered as truly sending out a 
secondary wave. Some experiments were made which cer- 
tainly tended towards showing that this lengthening of the 
distance between the first and second minimum exists ; but 
the experiments were unsatisfactory, for the second minimum 
is very slightly marked, and experimentally indeed seems to 
be even less so than one would expect from the curve. How- 
ever, it is most likely that the Hertzian stationary waves are 
never so well marked as they would ordinarily be calculated ; 
for it seems most probable that primary “ vibrators ’”’ do not 
send out strictly “ monochromatic light,” but send out a num- 
ber of wave-lengths of nearly the same period—a “ band- 
spectrum,” so to speak, the centre of which no doubt may be 
by far the strongest, and correspond with the “period” as 
would be calculated for the “ vibrator ;” also that “ secondary 
vibrators’ or resonators may in like manner be forced so as to 
take up, in some degree depending on the discrepancy, any 
member of a ‘‘ band-spectrum”’ special to each resonator, its 
“eriod’ corresponding to the centre*. Thus the marking 
of a node belonging to the central wave-length will probably 
be weakened, owing to the presence of the other members of 
the “band ”’ whose nodes on the whole will occur elsewhere. 
An observation which has proved of use in the course of 
these experiments on secondary waves was made during the 
autumn, namely that glass absorbed Hertzian radiations com- 
paratively rapidly ; in fact on account of this property it was 
found quite impracticable to determine the velocity of “ light” 
in glass by the method} of interposing a sheet of the 
substance in front of a reflector affording stationary waves, 
because the front surface of the glass itself gave a well-marked 
series of loops and nodes. A comparatively thin piece of 
glass, say of one centimetre, will afford an observable reflexion. 
This must be due chiefly to the reflexion from the second sur- 
face being weakened by absorption, so that it is insufficient to 


* The author hopes shortly to publish an account of experiments made 
during the autumn which have led to these conclusions. 
+ ‘Nature, August 22, 1889. 


276 Sir W. Thomson on the Time-integral of a 


seriously interfere with that from the front, but also no doubt 
to reflexions from points situated in the substance of the glass. 
A sheet of glass two centimetres thick gives fairly good 
reflexion, while a sheet of paraffin of that thickness would 
give almost no effect. ; 

Thus by using glass it was comparatively easy to obtain 
stationary waves by reflexion from a small surface of a non- 
conducting substance, in order to compare the effect thus 
produced on the position of the stationary waves with that 
produced by employing a small metallic reflector. The first 
node was found to be shifted out nearly $4, as in the case of 
metallic reflexion. That reflexion from glass is not of the 
metallic sort was proved by obtaining polarized reflexion. 
In this case the two opposite edges of the nonconductor may 
be looked upon as undergoing variations of apparent electrifi- 
cation. 


XXIX. On the Time-integral of a Transient Electromag- 
netically Induced Current. By Sir Wi.L1am THOMSON, 
Jip gyohes 


T has hitherto been generally supposed that, in ordinary 

apparatus for electromagnetic induction, with or without 

soft iron, the oppositely directed transient currents, in the 

secondary circuit, induced by startings and stoppings of 
current in the primary circuit, have equal time-integrals. 

I have recently perceived [been wrongly led to imagine] 
that this may be far from being practically the case by 
the following considerations. The starting and stopping 
of the current in the primary circuit was, in Faraday’s 
original discovery of this kind of electromagnetic-induction 
(ixp. Res. Series I. Nov. 1831), and is generally in ele- 
mentary illustrative experiments, produced by making and 
breaking a circuit consisting of a voltaic element or battery 
and the inductor-wire. In this arrangement the starting 
of the inductor-current is generally much less sudden than 
the stopping. Hence a thicker shell of the secondary wire 
(or portion inwards from the outward boundary) is utilized 
for conducting the secondary current, on the make, than 
on the break+. Hence the effective ohmic resistance in 


* Communicated by the Author. 

+ [In reality the whole cross sectional area of the secondary conductor 
is utilized, equably in all its parts, in conducting the secondary current. 
See Postscript of February 23. | 


Transient Electromagnetically Induced Current. 277 


the secondary circuit is less to the current induced by 
the make than to the current induced by the break; and 
the time-integral of the former current is correspondingly 
greater than the time-integral of the latter. 

Faraday in his first experiment found the current induced 
by the make to be greater than that induced by the break, 
but he explained it by the running down of his voltaic battery 
during the time the current was passing through the primary, 
in consequence of which the magnitude of the current stopped 
on the break was smaller than that of the current instituted 
onthe make. This was undoubtedly a vera causa, and probably 
one of considerable potency, considering that Faraday had 
then no Daniel’s battery and had no storage-cells to serve him 
in his work. Another vera causa is the heating of the 
circuit, which, even with a battery of constant H.M.F., may 
render the current started very considerably greater than the 
current stopped in ordinary experiments. Faraday, in his 
original experiments*, had only magnetization of steel wires 
to discover the induced currents by, and to test their magni- 
tude ; and he had no galvanometer in the primary circuit. 
If he had had a ballistic galvanometer in his secondary 
circuit, and any suitable galvanometer for steady currents in 
his primary circuit, he might possibly have found that the 
time-integral (as shown by the ballistic galvanometer) of the 
primary current exceeded that of the secondary current by 
a greater difference than could be accounted for by the 
current being suddenly started and the current suddenly 
stopped in the primary. So far as I know no one, from 
1831 till now, has made any experimental examination of the 
question suggested in Faraday’s Exp. Res. Series I. 16; and 
his idea that the two currents are equal has been generally 
accepted{. Ihave therefore asked Mr. Tanakadaté to make 
some experiments on the subject in my laboratory. He 
immediately obtained results § seeming to demonstrate a con- 


* Exp. Researches, Series I., 1831. 

+ [No. On the contrary, he would have found that his first idea, of 
perfect equality of the two currents, was perfectly true! February 23. ] 

t See Maxwell’s ‘ Electricity and Magnetism’ (1878), vol. ii. §537, 

ol7als ; 

r § But these results we find are quite untrustworthy because of the 
susceptibility of the steel needle of the galvanometer to magnetic induc- 
tion, which with the currents produced through its coil by the induced 
currents due to the make and break in the primary circuit, may largely 
alter its effective magnetism. It is in fact well known that ballistic gal- 
vanometers with steel needles give very erratic results if they are used in 
attempting to find time-integrals of very intense transient currents of very 
short duration. 


278 Sir W. Thomson on the Time-integral of a 


siderable excess in the time-integral (as shown by a ballistic 
galvanometer) of the secondary current on the make above 
that on the break. A magneto-static galvanometer in the 
primary circuit showed the current before the break to be 
always a little less than immediately after the make. This 
difference was due to heating of the primary circuit, because 
a potential galvanometer applied to the two terminals of the 
voltaic element used, which was a large storage-cell, showed 
no sensible drop of potential during the flow of the current 
in the primary circuit. It was, however, insufficient to account 
for the large differences found between the ballistic deflexions 
produced by the induced currents on the make and on the 
break. A rapid succession of makes and breaks has given 
large irregular permanent deflexions of the ballistic galvano- 
meter, sometimes in one direction, sometimes in the other, 
which we have found to be chiefly due to magnetic sus- 
ceptibility of the steel needle of the ballistic galvanometer : 
and we find that this cause has probably vitiated the observa- 
tions on the effects of single makes and breaks. I have there- 
fore arranged to have experiments continued, with a coil of 
very fine wire bifilarly suspended, instead of the steel needle 
of the ballistic galvanometer ; a steady current through the 
fine wire being maintained by an independent voltaic battery. 

Hitherto the make and break have been performed by hand, 
dipping a wire into and lifting it out of a cup of mercury. 

Various well-known methods may be used to render either 
the break or the make so gradual that we may be sure of the 
induced current running practically full-bore through the 
secondary. On the other hand, very sudden breaks may 
be effected by separating two little balls or other convex 
pieces of copper by the blow of a hammer. The experiment 
may be varied by short-circuiting the ends of the inductor 
and allowing the current from the battery to continue 
flowing through electrodes of sufficient resistance not to 
allow an injuriously great amount of current to flow. 
These electrodes, between the voltaic element and the ends 
of the inductor-wire, may have large self-inductance given to 
them by coiling them round a closed magnetic circuit of soft 
iron. The starting of the current in the inductor-wire will 
thus be rendered much more sudden than the stopping ; and 
the induced current in the secondary will no doubt be found 
stronger on the stoppage than on the start. Mr. Tanakadaté 
is continuing the experiments with these modifications in 
view. 

The mathematical foundation of the common opinion that 


Transient Electromagnetically Induced Current. 279 


the time-integrals of the induced currents on the make and 
break are equal is as follows*. 

Let 8 and y be the currents at time ¢ in the primary and 
in the secondary circuits respectively ; J the self-inductance 
of the secondary circuit ; and M the mutual inductance of the 
two. We have 


__ yeh _7%. 


Hence if y=0 when ¢=0, and if we suppose R to be constant, 
ve M J 
ydt= = (Qo—-B)— sy: 
\ ike a 


Now let T be any value of ¢ so large that @ has become 
sensibly constant, and y has subsided to zero. We have 


ie dt= as (8>—Br). 


This shows that the time-integral of the induced current in 
the secondary circuit would depend solely on the difference of 
values of the current in the primary at the beginning and end 
of the time included in the reckoning, and would be quite 


[* February 23.—Worked out more perfectly it shows, as follows, that 
the common opinion is correct! 

Imagine the whole secondary conductor divided into infinitely small 
filaments of cross-section dQ: and let & be the current-density, at time ¢, 
in any one of these. Instead of y in the text take dQ, and instead of R 
take //(cdQ) ; o denoting the specific conductivity of the material, and / 
the length of the circuit. We have 


dB , d&dQ 
Fo am eer ees 

where S denotes the sum of effects due to the risings and fallings of cur- 
rent in the different parts of the secondary conductor. Their time-integral 
from 0 to T is essentially zero; as is also that of the infinitesimal middle 
term of the second member. Hence we have 


lo-1\ “dt é=M(B—B,); 


which shows that the time-integral of the current, dQ, in each filament 
of the secondary conductor, is exactly equal to that which is calculated 
according to the ordinary elementary theory! The whole details of the 
fallacy in the text are now clear !] 


ae ne ee > ae 
= ne ee ~A _- 


280 Geological Society :-— 


independent of suddennesses, 7/ the effective ohmic resistance 
were constant. But this supposition is not true ; and that it 
is very effectively untrue for copper wires of a millim. dia- 
meter or more, and times of change in the primary less than 
3h, of a second, we see readily by-looking to the diffusional 
curve and the time-number, 5}, of a second for curve 10, 
corresponding to the diffusivity of copper for electric currents 
(which is 131 square centimetres per second) given and ex- 
plained in my short article on a Five-fold Analogy, in the 
British Association Report for Manchester, 1888 (to be found 
also in the Electrical Journals, and ‘ Nature’). 


| Postseriet, February 23, 1890.—The thermal analogy, 
which is very simple for the case of electric currents in 
parallel straight lines, has, as soon as I have considered it, 
shown me the fallacy pervading the text; and has led me to 
make the corrections in the insertion and footnotes enclosed . 
in brackets [ ], all of which are of the date of this postscript. 
Prelimmary experiments with the suspended coil instead of 
the steel magnet, in a ballistic galvanometer now nearly com- 
pleted by Mr. Tanakadate, have already disproved the large 
differences which I expected between the time-integrals of 
the secondary currents on the break, and on the make; andas 
far as they have yet gone are consistent with the perfect 
equality which I now find proved by theory. | 


XXX. Proceedings of Learned Societies. 
GEOLOGICAL SOCIETY. 
[Continued from p. 135.] 
December 18, 1889.—W. T. Blanford, LL.D., F.R.S., President, 
in tne Chair. 


(pee following communications were read :— 
1. “On the Occurrence of the Genus Girvanella, and remarks 
on the Oolitic Structure.” By EK. Wethered, Esq., F.G.S. 


2. “On the Relation of the Westleton Beds or ‘ Pebbly Sands’ of 
Suffolk to those of Norfolk, and on their extension inland, with some 
observations on the Period of the final Elevation and Denudation of 
the Weald and of the Thames Valley.”—Part II. By Prof. Joseph 
Prestwich, M.A., D.C.L., F.R.S., F.G.S. 

The author having, in the first part of this paper*, discussed 
the relationship of the Westleton Beds to the Crag Series and to 


* Phil. Mag. [5] xxviii. p. 142. 


On the Westleton Beds of Norfolk and Suffolk. 281 


the Glacial Deposits, proceeded in the present contribution to con- 
sider the extension of the Westleton Beds beyond the area of the 
Crag, and described their range inland through Suffolk, East, West, 
and South Essex, Middlesex, North and South Hertfordshire, South 
Buckinghamshire, and North and South Berkshire, noticing their 
relationship to the overlying Glacial beds, where these were deve- 
loped, and the manner in which they reposed upon older deposits. 
He gave an account of the heights of the various exposures above 
Ordnance Datum, and mentioned the relative proportion of the 
different constituents in various sections, thus showing that in their 
southerly and westerly extension they differed both in composition 
and in mode of distribution from the Glacial deposits. Distinction 
was also made between the Westleton Beds and the Brentwood 
Beds. 

Attention was next directed to the occurrence of the Westleton 
Series, south of the Thames, in Kent, Surrey, and Hampshire, and 
their possible extension into Somersetshire was inferred from the 
character of the deposits on Kingsdown and near Clevedon. 

In tracing the deposits from the east coast to the Berkshire 
Downs it was noticed that at the former place the beds lay at sea- 
level, but ranging inland, they gradually rose to heights of from 500 
to 600 feet; that in the first instance they underlay all the Glacial 
deposits, and in the second they rose high above them, and their 
seeming subordination to the Glacial series altogether disappeared ; 
thus at Braintree, where the Westleton Beds were largely developed, 
they stood up through the Boulder-clay and gravel which wrapped 
round their base, whilst further west, where they became diminished 
to mere shingle-beds, they attained heights of from 350 to 400 feet, 
capping London-clay hills, where the Boulder-clay lay from 80 to 100 
feet lower down the slopes, the difference of level between the two 
deposits becoming still greater in a westerly direction, until finally 
the Boulder-clay disappeared. 

The origin of the component pebbles of the beds was discussed, 
and their derivation traced (1) to the beds of Woolwich age in Kent, 
N. France and Belgium, and possibly to some Diestian beds, (2) to 
the older rocks of the Ardennes, (3) to the Chalk and older drifts, 
and (4) to the Lower Greensand of Kent and Surrey, or in part to 
the Southern drift. 

The marine nature of the beds was inferred from the included 
fossils of the type-area, and the absence of these elsewhere accounted 
for by decalcification. 

The southward extension of the beds was shown to be limited by 
the anticlinal of the Ardennes and the Weald, and the scanty pale- 
ontological evidence of the nature of that land was noted, and the 
possible existence of the Scandinavian ice-sheet to the north was 
referred to in connexion with the disappearance of the beds in that 
direction. 

From the uniform character of the Westleton shingles the author 


Phil. Mag. 8. 5. Vol. 29. No. 178. March 1890. ¥ 


bf t< worn, et ee ding MEE ee 
_ a 


282 Geological Society :— 


maintained that they must originally have been formed op a com- 
paratively level sea-floor, and that the inequalities in distribution 
had been produced by subsequent differential movement to the ex- 
tent of 500 feet or more to the north and west above that experienced 
to the east and south, where the chronological succession remained 
unbroken, also that the inequalities below the level of the Westleton 
beds had been produced since the period of their deposition, as, for 
instance, the gorge of the Thames at Pangbourne and Goring, and 
most of the Preglacial valleys in the district ; furthermore, evidence 
was adduced in favour of the formation of the escarpments of the 
Chalk and Oolites since Westleton times, whilst certain observations 
supplied data for estimation of the relative amounts of pre- and 
post-glacial denudation of the valleys. 

It was stated, in conclusion, that the time for the vast amount 
of denudation was so limited that it was not easy to realize that 
such limits could suffice, but the author did not see how the con- 
clusions which he had arrived at could well be avoided. 


January 8, 1890.—W. T. Blanford, LL.D., F.R.S., President, 
in the Chair. 


The following communications were read :— 


1. “On some British Jurassic Fish-remains referable to the 
genera Hurycormus and Hypsocormus.” By A. Smith Woodward, 
Esq., F.G.S. 


2. “On the Pebidian Volcanic Series of St. Davids.” By Prof. 
C. Lloyd Morgan, F.G.S. 


After a brief sketch of the principal theories that have been pro- 
pounded, the author concluded that our knowledge of this series 
has not yet reached ‘a satisfactory position of stable equilibrium.” 
His own communication was divided into three sections. 

The Relation of Pebidian to Cambrian.--There are four localities 
where the junction is described—Caerbwdy Valley, St. Non’s Bay, 
Ogof Golchfa, and Ramsey Sound. The stratigraphy of the second 
of these was given with much detail, and illustrated. The author 
concluded that here, together with clear signs of local or contem- 
poraneous erosion, the general parallelism of the strike of Pebidian 
and Cambrian ismost marked. There is no evidence of any bending 
round of the conglomerate against the strike of the Pebidians. The 
stratigraphical evidence in each of the localities having been con- 
sidered, together with the evidence offered by the materials of the 
Cambrian conglomerate and local interstratification with the volcanic 
beds (the interdigitation at Carnarwig being well marked), he con- 
cluded that there was no great break between the conglomerate and 
the underlying Pebidians. The uppermost Pebidian already fore- 
shadowed the sedimentary conditions of the Harlech strata, and the 


Pebidian Volcanic Series of St. Davids. 283 


change emphasized by the conglomerate was one that followed 
volcanic conditions after no great lapse of time. 

Hence the relation of the Pebidian to the Cambrian is that of a 
volcanic series, for the most part submarine, to succeeding sedi- 
mentary strata—these strata being introduced by a conglomerate 
formed in the main of foreign pebbles borne onward by a current 
which swept the surface of, and eroded channels in, the volcanic 
tuffs and other deposits. He was disposed to retain the name 
Pebidian as a volcanic series in the base of the Cambrian system. 

The Pebidian Succession.—With the exception of some cinder-beds, 
which appear to be subaerial, the whole series was accumulated 
under water. There is no justification for making separate sub- 
divisions ; the series consists of alternating beds of tuff of varying 
colour and basicity, the prevailing tints being dark green, red-grey, 
and light sea-green. In the upper beds there is an increasing 
amount of sedimentary material, and more rounded pebbles are found. 
Basic lava-flows occur, for the most part, in the upper beds. Detailed 
work, laid down on the 6-inch Ordnance map, appears to establish a 
series of three folds—a northern anticline, a central syncline, and a 
southern anticline—folded over to form an isocline, with reversed 
dips to the 8.E. The axis of folding is roughly parallel to the axis 
of St. David’s promentory. The total thickness is from 1200 to 
1500 ft. 

The author devoted a considerable number of pages to further 
details concerning this series of deposits. He failed to find the 
alleged Cambrian overlap. ‘The probabilities are that it is by 
step-faults between Rhoson and Porth Sele, and not by overlap, 
that the displacement of the conglomerate has there been effected.” 
Also at Ogof Goch it does not rest upon the quartz-felsite breccia 
and sheets (group C, of Dr. Hicks), but is faulted against them. A 
section was devoted to the felsitic dykes, and it was suggested that 
they may be volcanic dykes of Cambrian age. 

The Relation of the Pebidian to the Dimetian.—The author has 
not been able to satisfy himself of the existence of the Arvonian as 
a separate and distinct system. He notes the junction of Pebidian 
and Dimetian in Porthlisky Bay and the Allen Valley at Porth 
Clais, at neither of which places are there satisfactory evidences of 
intrusion. At Ogof Llesugn the intrusive character of the Dimetian 
was strongly impressed upon him. He criticised the mapping 
of Dr. Hicks, and pointed out the difficulties which present them- 
selves in the way of mapping the Dimetian ridge as Pre-Cambrian. 
He pointed out that not a single pebble of Dimetian rock, such 
as those now lying on the beach in Porthlisky Bay, is to be found 
in the conglomerate. He concluded that the Dimetian is intrusive 
in the southern limb of the isocline, and that there are no Archwan 
rocks a situ. 


284. . Geological Society :-— 


January 22.—W. T. Blanford, LL.D,, F.R.S., President, 
in the Chair. 


The following communication was read :— 

“‘On the Crystalline Schists and their relation to the Mesozoic 
Rocks in the Lepontine Alps.” By Professor T. G. Bonney, D-Sc., 
LL.D., F.R.S., F.G.S. 

In the debate upon the paper “On two Traverses of the Crystal- 
line Rocks of the Alps” (read Dec. 5, 1888) it was stated that rocks 
had been asserted on good authority to exist in the Lepontine Alps, 
which contained Mesozoic fossils, together with garnets, staurolites, 
&c., and thus were undistinguishable from crystalline schists re- | 
garded by the author as belonging to the presumably Archean 
massifs of that mountain-chain. In reply, the author stated that 
he regarded this as a challenge to demonstrate the soundness or un- 
soundness of the hypothesis to which he had committed himself. 
The present paper gives the result of his investigations, undertaken 
in the month of July, 1889, in company with Mr. James Eccles, 
F.G.8., to whom the author is deeply indebted for invaluable help. 
The paper deals with the following subjects :— 


baal! 


(1) The Andermatt Section. 


By the geologists aforesaid, a highly crystalline white marble which 
occurs on the northern side of the Urserenthal trough, at and above 
Altkirch, near Andermatt, is referred to the Jurassic series (mem- 
bers of which undoubtedly occur at no great distance, almost on the 
same line of strike). The author describes the relation of the 
marble to an adjacent black schistose slate, and discusses the signifi- 
cance of some markings in the former which might readily be con- 
sidered as organic, but to which he assigns to a different origin. He 
shows that there are most serious difficulties in regarding these two 
rocks as members of the same series, and explains the apparent 
sequence as the result of a sharp and probably broken infold, as in 
the case of the admitted band of Carboniferous rock at Andermatt 
itself. That the section is a difficult one on any hypothesis the author 
admits, but in regard to the former of these, after a discussion of the 
evidence, he concludes ‘‘ that tendered on the spot demands a ver- 
dict of ‘ not proven ’—that obtainable in other parts of the Alps will 
compel us to add, ‘ not provable.’ ” 


_ == —— 


SS eee : = ; ee : = ee 
SS I IE Sa we mrp es SS Foi 2 ae a —~ 


(2) The Schists of the Val Piora. 


These schists, already noticed by the author in his Presidential 
Address to the Society in 1886, occur in force near the Lago di 
Ritom, and consist of two groups :—the one, dark mica-schists, some- 
times containing conspicuous black garnets, banded with quartzites, 
the other, various calc-mica schists ; between them, apparently not 
very persistent, occurs a schist containing rather large staurolites or 
kyanites. On the north side is a prolongation of the garnet-actino- 


aN es 


AI aia GNSS hE A 


Sait ree 
» ‘ 
exes 


On the Crystalline Schists of the Alps. 285 


lite (Tremola-) schists of the St.Gothard and then gneiss; on the south 
side gneiss. There is also some rauchwacké. This rock, at first 
sight, appears to underlie the Piora-schists, and thus to be the lowest 
member of a trough. If so, as it is admittedly about Triassic in 
age, the Piora-schists would be Mesozoic. The author shows that (1) 
the latter rocks do not form asimple fold; (2) they are beyond all 
question altered sediments ; (3) they have often been greatly crushed 
subsequent to mineralization; (4) the garnets, staurolites, Wc. (if 
not injured by subsequent crushing) are well developed and charac- 
teristic, and are authigenous minerals. 


(3) The Rauchwacké and rts Relation to the Schist. 


(a) The Val-Piora Sections.—The author shows that the rauch- 
wacké, which at first sight seems to underlie the dark mica-schist, 
is inconstant in position (on the assumption of a stratigraphical 
sequence); that its crystalline condition does not resemble that of 
the schist-series, but is rather such as is common in a rock of its 
age; that it contains mica and other minerals of derivative origin, 
and in places rock-fragments which precisely resemble members of 
the Piora-schist series. 

(6) The Val-Canaria Section.—This section, described by Dr. 
Grubenmann, is discussed at length. It is shown that the idea of a 
simple trough is not tenable, for identical schists occur above and 
below the rauchwacké ; that there is evidence of great pressure, 
which, however, acted subsequently to the mineralization of the 
schists ; and that in one place the rauchwacké is full of fragments 
of the very schists which are supposed to overlie it. 

(c) Nufenen Pass gc.—Other cases, further to the west, are 
described, where confirmatory evidence is obtained as to great 
difference in age between the rauchwacké and the schists, and the 
antiquity of the latter. The apparent interstratification is explained 
by thrust-faulting, 


(4) The Jurassic Rocks, containing Fossils and Minerals. 


The author describes the sections on the Alp Vitgira, Scopi, and 
the Nufenen Pass. Here indubitable Belemnites and fragments of 
Crinoids occur in a dark, schistose, somewhat micaceous rock, which 
is often very full of “knots” and “prisms” of rather ill-defined 
external form, something like rounded garnets and jll-developed 
staurolites. These rocks at the Alp Vitgira appear to overlie, and 
in the field can be distinguished from the black-garnet schists. In 
one place the rock resembles a compressed breccia, and among the 
constituent fragments is a rock very like a crushed variety of the 
black-garnet mica-schist. These Jurassic ‘‘schists” are totally 
different from the last-named schists, to which they often present 
considerable superficial resemblance ; for instance, their matrix is 
highly calcareous, the other rock mainly consisting of silicates, 


286 Geological Society :-— 


Some of the associated mica may be authigenous, but the author 
believes much of it and other small constituents to be derivative. 
There is, however, a mineral resembling a mica, exhibiting twinning 
with (?) simultaneous extinction, which is authigenous. The knots 
are merely matrix clotted together by some undefinable silicate, and 
under the microscope have no resemblance to the “black garnets.” 
The prisms are much the same, but slightly better defined; they 
present no resemblance to the staurolites, but may be couseranite, 
or a mineral allied to dipyre. Hence, though there is rather more 
alteration in these rocks than is usual with members of the Mesozoic 
series, and an interesting group of minerals is produced, these 
so-called schists differ about as widely as possible from the crystalline 
schists of the Alps, and do not affect the arguments in favour of the 
antiquity of the latter. In short, they may be compared to rather 
poor forgeries of genuine antiques. Incidentally the author’s 
observations indicate (as he has already noticed) that a cleavage- 
foliation had been produced in some of the Alpine schists anterior 
to Triassic times. 


February 5.—W. T. Blanford, LL.D., F.R.S., President, 
in the Chair. 


The following communications were read :— 

1. “ The Variolitic Rocks of Mont-Genévre.” By Grenville A. 
J. Cole, Esq., F.G.S., and J. W. Gregory, Esq., F.G.S., F.Z.S. 

The following conclusions were arrived at by the authors as the 
result of their observations :— 

The gabbro or euphotide south of Mont-Genevre is associated with 
serpentines, which were originally peridotites, and were not derived 
from the alteration of the gabbro. These coarsely crystalline rocks 
probably form a considerable subterranean mass, but have little 
importance at the surface. 

They were broken through by dykes of dolerite and augite-ande- 
site, and are now overlain by a great series of compact diabases and 
fragmental rocks, which has no direct connexion with the gabbro. 

The Variolite of the Durance occurs i situ as a selvage on the 
surfaces of contact of these diabases among themselves, as blocks 
in certain fragmental rocks, which are regarded by the authors as 
tuffs, and occasionally as a selvage to the diabase dykes. 

This product of rapid cooling was originally a spherulitic tachy- 
lyte, and has become devitrified by slow secondary action. Variolite 
thus stands in the same relation to the basic lavas as pyromeride 
does to those of acid character. 

The eruptive rocks in the Mont-Genevre area are probably Post- 
Carboniferous, but their exact age cannot at present be determined. 

There are several other areas of similar variolitic rocks among 
both the Alps and the Apennines of Piedmont and Liguria. 

The best modern representatives of the conditions that produced 


Propylites of the Western Isles of Scotland. 287 


these rocks are to be found in the great volcanoes of Hawaii, and there 
is nothing either in their fundamental characters or in their mode of 
origin that cannot be paralleled among the products of causes now in 
action. 

The authors expressed their indebtedness to Professors Bonney and 
Judd, as well as to those who have preceded them upon the classic 
ground of Mont-Genevre. 


2. “The Propylites of the Western Isles of Scotland, and their 
Relations to the Andesites and Diorites of the District.” By Pro- 
fessor John W. Judd, F.R.S., F.G.S., &c. 

The “ Propylites ” of von Richthofen and Zirkel constitute what 
has been aptly characterized by Rosenbusch as a “ pathological 
variety ” of the andesites. ‘The relations of rocks of this type to 
the andesites and diorites in Eastern Europe and in the Western 
Territories of the United States have been made known to us by the 
researches of Dolter, Szabo, Becker, Hague and Iddings, and other 
petrographers. 

The ‘“felstones ” described by the author of the present memoir 
as constituting the oldest series of the Tertiary volcanic rocks in 
the Western Isles of Scotland are now shown to belong to this 
interesting type. When found in an unaltered state, these rocks pre- 
sent remarkable analogies with the andesites of Iceland and the Faroe 
Islands, which have been so well described by Zirkel, Schirlitz, Osann, 
and Bréon. In the altered condition in which they usually occur, 
however, the Scottish rocks resemble in a not less striking manner 
the “ propylites ” of Hastern Europe and Western North-A merica. 

The rocks in question vary in colour from white to dark grey, various 
shades of green usually prevailing among them. They have a specific 
gravity ranging from 2:4 to 2:9; the density diminishing as the silica 
percentage and the amount of glassy material in them increase; a 
lowering of the density of the rocks being also the result of extreme 
alteration. In their chemical composition these rocks were shown to 
agree with the pyroxene- and amphibole-andesites of other areas, 
and with propylitic forms of those rocks. 

Very striking and remarkable is the amount of change that many 
of these Tertiary rocks have undergone—change that has equally 
affected their porphyritic constituents and the ground-mass in 
which these are imbedded. The felspars are never fresh, but are 
more or less kaolinized, and not unfrequently converted into epidotes 
and other secondary minerals; the ferro-magnesian silicates are 
almost always changed into isotropic “viridite,” or into various 
chlorites; while the titano-ferrite and magnetite have been con- 
verted either into ‘ leucoxene”’ or into sulphides. The glass and 
microlites of the original ground-mass have in nearly all cases dis- 
appeared as the result of secondary devitrification. 

The propylites are the oldest of the Tertiary lavas in the Western 
Isles of Scotland. They exhibit every gradation in minute struc- 


A - S Sr. a : == = = ———— ~ = 
7 " — — — et _— —— —< — -- = -e2 a II nr ee a eee ee ee bs = ans sae ce MAE pa =o ita immed We” a PS =r 
~ — aa eR SSS TVET S ~ 2 ie ares eo ox o ae a SS SES, ERE SF oe TE, Bren’ Freee ey a > 
arent ila ee eee ;* eke Se ae Te es Set “ ened 7 area ae eee ae Se ater: Seales A eat era ee ee a Re te Aj 2 (eS ee ee 
bl fi ie a pig ow i — ~ ie tages» on = - op gr Ss ae. ree i 5 ai pty Ne as pha se es he eae a> ‘ * - x = “ 


gai ARMS Ral a SSG SETS 


288 Geological Society. 


ture, from holocrystalline forms (diorites) through various ‘ grano- 
phyric” and “ pilotaxitic” types into true vitreous rocks (“ pitch- 
stones”). They are found constituting lava-streams, which are 
usually short and bulky; eruptive bosses or ‘“‘ Quellkuppen;” and 
lenticular intrusions or “ laccolites.” 

By carefully following in the field the much-altered rocks to points 
where they retain some of their original characters, the propylites 
can be shown to represent various interesting types of andesite and 
diorite. The amphibolic and micaceous rocks include hornblende- 
andesites, hornblende- and mica-andesites containing enstatite, 
diorites, and quartz-diorites. Among the pyroxenic rocks the most 
noticeable varieties are the labradorite-andesites, the pyroxene- 
andesites—of which both ‘trachytoid” and ‘ vitrophyric” forms 
occur,—as well as examples of what have been called “ dial- 
lage-andesites ” (the nature of the pyroxene in which was fully dis- 
cussed); these rocks are found passing into augite-diorites, and 
quartz-augite-diorites. 

A microscopic study of these rocks enables us to investigate the 
processes by which they have acquired their peculiar characters. The 
chief and most widely operating cause of change is thus demonstrated 
to have been solfataric action; and this was shown to haye accom- 
panied the intrusion into the andesites of masses of igneous material 
of highly acid composition (granites and felsites). This solfataric 
action has been developed around each of the five volcanic centres 
described in 1874. A smaller and much more local cause of change 
—some of the results of which are strikingly contrasted with those 
of the wide-spread solfataric action—is found in the contact-meta- 
morphism resulting from the intrusion into the andesites of masses 
of igneous rock of basic, intermediate, or acid composition. 

The much-altered propylites of Tertiary age were shown to have 
their exact analogues among the older (Paleozoic) lavas of Scotland 
and other districts. These rocks, which have been called “ fel- 
stones,” ‘‘ porphyrites,” &c., are andesitic lavas, some of which have 
suffered only from the action of surface-waters, while others among 
them must have been profoundly affected by solfataric action and 
converted into propylites, prior to the operation of the surface- 
agencies of change. 

Forming a very striking contrast with the older Tertiary andesites 
(propylites), are the numerous scattered and generally small masses 
of rock which belong to a late period in the Tertiary, and constitute 
the youngest volcanic rocks of the British Islands. These rocks are 
found intersecting, in the form of dykes, the great sheets of olivine- 
basalt ; or where poured out at the surface (as at the Sgurr of Higg 
and Beinn Hiant in Ardnamurchan), lie upon their greatly eroded 
surfaces. The rocks in question, which have the mineralogical 
constitution of augite-andesites, are remarkable for the wide 
variations in their aspect and chemical composition; and this 
was shown to result from differences in the proportion of the crys- 


Intelligence and Miscellaneous Articles. 289 


talline and glassy constituents to one another. Holocrystulline 
aggregates, of basic-composition, are found passing, as the quantity 
of acid glass increases, into various “ ophitic,” “ intersertal, ” and 
“‘ pilotaxitic ” types, finally assuming the “ vitrophyric” form of 
‘¢ pitechstone-porphyries ”—rocks which have a distinctly acid com- 
position. The rocks of the Tertiary dykes in Southern Scotland and 
the North of England, which have been described by Dr. A. Geikie, 
Mr. Teall, and other authors, were shown to agree with these later 
Tertiary andesites, both in their mineralogical constitution and in 
the peculiar phases which they present to us. The latest Tertiary 
ejections were shown in 1874 to bear the same relations to the five 
grand volcanoes of the Western Isles which the chains of ‘“ puys ” 
Auvergne do to the great central volcanoes of that district; and this 
conclusion is strikingly confirmed by petrographical studies of which 
the results were given in the present memoir. 


XXXI. Intelligence and Miscellaneous Articles. 


NOTE ON THE GRADUAL ALTERATION IN GLASS PRODUCED BY 
ALTERING ITS TEMPERATURE A FEW DEGREES. BY SPENCER 
U. PICKERING, M.A.” 


(THE alteration experienced by glass when heated to tempera- 

tures above 50° C. is well known, but I do not think that it 
has previously been noticed that a rise or fall of even a few degrees 
at ordinary temperatures will produce an appreciable alteration of 
a similar nature. 

That such is the case, however, the following experiments will 
show. During the course of a series of density-determinations, in 
which the apparatus. used consisted of an ordinary 25 cub. cent. 
density-bottle with perforated stopper—but of which the stopper 
was so accurately ground that it made the instrument thoroughly 
reliable—the water-contents of the bottle were frequently deter- 
mined. Between November 1887 and May 1888, during which 
time the temperature of the laboratory had been kept at about 13°, 
no appreciable alteration in the capacity occurred, the values all 
being within -0002 grm. of 25:0070 grm., and this in spite of the 
fact that the bottle had been temporarily heated to temperatures as 
high as 38°. But during November and December of the latter 
year the temperature of the laboratory had been maintained 10° 
lower than during the previous twelve months, and the effect of 
this lowering on the bottle was such that its water-contents, mea- 
sured at the same temperature, were ‘001 gram less. Although the 
amount of this contraction is small, the following values will, I 


* Communicated by the Author. 
Phil. Mag. 8. 5. Vol. 29. No. 178. March 1890. Z 


290 Intelligence and Miscellaneous Articles. 


think, place its existence beyond doubt: they were determined, as 
will be seen, at various temperatures between 6° and 28°. 

The gradual contraction does not appear to have ceased at the 
end of the seventeen days’ exposure of the bottle to 8°, nor does it 
seem to have been affected by the temporary heating of the bottle 
to the higher temperatures at which its contents were deter- 
mined. 

In the last column is given the weight of the bottle itself on the 
various dates: it shows a slight gradual decrease owing to wear; 
but this wear, even if it took place entirely on the inside, would 
not be sufficient to account for a tenth part of the decrease in the 
weight of the contents. 


Alteration in the Capacity of Glass Bottle while being kept at 8°, 
after it had been previously kept at 18°. Contents measured 
at t°. 


io Bottle 
t= 6°. Sue 10 128: a iesig: 
INOW ie Om ies ence Dy OSU MAAS Stow soe Walaa es 157192 
Dec. 3 ZOOM ONT Coeeoee 25°0288 25:°0245 15 7188 
oe CHS a aie aeeee 200293" | satees, lh eeaeee 15-7188 
i iG 25°0311 25-0289 25°0264 25:0228 15-7187 
Seek boo Pumeacieeicn,. | al ih Me eee 2550269 wialny eapene 15-7186 
(= 14°. 14°.* 162% 28°. 
INGVe 0 ral oo teak ciel tn moee iy =i eocceeee 24-9535 15°7191 
Dec. 3 25-0916 7 liueseec toe ele weceere 24°9532 15-7188 
Sy ads Ny Marre ee 44 4345 436239 24-9519 15°7187 
jut he 250182 44-4309 AS: GAD Tar 82s 2 15°7186 


* The bottle contained sulphuric-acid solutions instead of water in these 
cases. 


Just as cooling the bottle for a few degrees induces a gradual 
contraction, so does heating it induce a gradual expansion. After 
the contents measured at 28° had been reduced on December 7 to 
24-9519 grams, they were found to have increased to 24-9532 
grams by April in the following year, the bottle in the mean time 
having been kept at the higher temperature of 12°-15°. Again: 
on December 3, 1889, after the bottle had been exposed for some 
time to a temperature of about 10°, its contents at 18° were found 
to be 25:0066 grams; it was then heated at 30°-35° for three days, 
after which they had increased to 25-0073 grams. 

The maximum alteration in capacity noticed in any of the above 
experiments is ‘0001 of the total volume, and an alteration of this 


Intelligence and Miscellaneous Articles. 291 


magnitude occurring in the bulb of a thermometer would mean a 
displacement of the zero-point by ;/;°. 


ON A TELETHERMOMETER. BY PROF. DR. J. PULUJ. 


The author gave the following abstract of a long paper on this 
‘subject :— 

The present paper contains the description and theory of an 
apparatus, which renders it possible to transfer to a distance the 
indications of any given temperatures. The construction of the tele- 
thermometer depends on the use of two conductors, the resistance of 
which varies with the temperature in opposite directions, and which 
form the thermometric part of the apparatus. The latter consists 
of a small glass tube closed at both ends, which contains a carbonized 
strip and a spiral of platinum wire, and which is filled with 
hydrogen in order to conduct the better. The carbon strip and 
the iron spiral form two branches of a Wheatstone’s bridge, and 
‘by means of three wires are connected with a measuring-scale which 
has an empirical scale of temperature in Centigrade degrees. The 
resistance of the carbon strip decreases with the temperature, while 
that of the iron increases, and in accordance with this the zero of 
the difference of potential is altered. The temperature may be 
determined either by means of an astatic galvanometer, or by a 
telephone with a microphonic contact-breaker in such a manner 
that contact with the measuring-wire is deferred until the galvano- 
meter shows no deflexion, or the telephone gives no sound. The 
telethermometer renders it possible to determine temperatures at 
a distance of 1 km. to within 0*1 C. 

In the theoretical part of the paper the displacement of the 
contact along the wire is calculated, and the graduation of the 
telethermometer is completely discussed; this is followed by a 
calculation of the correction of the scale for temperature, and the 
proof is given that a rise of temperature of the wire bridge has no 
influence on the indications of the telethermometer. It is shown in 
conclusion how the telethermometer may be used as an indicator 
of temperature, which automatically gives the temperature at any 
instant.— Wiener Berichte, Oct. 10, 1889. 


ON THE MEASUREMENT OF ELECTROMOTIVE CONTACT FORCES OF 
METALS IN DIFFERENT GASES, BY MEANS OF THE ULTRA- 
VIOLET RAYS. BY A. RIGHI. 

Since, as is shown by the earlier experiments of the author, ultra- 


violet rays bring to the same potential bodies which are very close 
to one another, the differences of potential of contact can by this 


292 Intelligence and Miscellaneous Articles. 


means be very conveniently measured. It is only necessary to 
measure the deflexion in the electrometer connected with the plate 
after it has been put to earth for an instant while ultra-violet rays 
have been allowed to fall on the plate through the net. The light 
of a zinc-carbon arc-lamp was always used. ‘The plates of ordinary 
metal and carbon were in air, or in a bell-jar filled with gases or 
moist air. The net was of zinc, brass, or platinum. From the 
differences of the observations with the same net and different 
plates the differences of potential between the latter can be de- 
duced. Jn dry and moist air and in carbonic acid they are the 
same; in hydrogen they are so for C, Bi, Sn, Cu, Zn, but different. 
for Pt, Pd, Ni, Fe. When hydrogen is gradually allowed to enter, 
these metals behave as if they were gradually oxidizable in air: 
For platinum against a zinc net the difference of potential reduces 
from 1:12 in air to 0°69 in hydrogen. On the fresh addition of 
air the electromotive force returns in the opposite directien to its. 
original value. Metals such even as tinand bismuth behave in am- 
moniacal air as if they were less oxidizable, and therefore the opposite 
of what obtains with hydrogen. Here also in air the initial electro- 
motive force is restored. In coal-gas, carbon, copper, and platinum 
behave like oxidizable metals. With a platinum net and a copper 
plate the sign of the electromotive contact-force is changed when 
coal-gas is admitted instead of air.—Rendic. Lincei [5] p.860, 1889 ;. 
Beiblatter der Physik, xiv. p. 69: 


MR. ENRIGHT S EXPERIMENTS. 


To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN,. 


When Mr. Enright described his attempts to prove that 
contact could electrify hydrogen, in ‘ Nature,’ August 18, 1887, I 
wrote to that Journal (vol. xxxvi. p. 412) to point out that all 
he had observed could be expressed in a few lines as due to the 
well-known frictional electrification of spray. The length of his 
communication to the Physical Society, printed in your January 
number, may perhaps have deterred a critic from reading it. But 
he makes no serious attempt to meet my obvious objection, and 
so far as experiments so crude can negative anything they negative 
his own contention.. 

Yours faithfully, 
Ouiver J. Lopex. 

Liverpool, February 15, 1890. 


THE 
LONDON, EDINBURGH, ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] 


AGE eS O(). 


XXXII. On Magnetization in Strong Fields at Different Tem- 
peratures. By H.H. J. G. vu Bors, of the Hague*. 


[Plate VIII] 


SL, [XY TRODUCTOR Y.—Prof. Rowland, in summarizing 
his well-known magnetic researches (1873), thus 
carefully expresses himself :— 

“ (7) Iron, nickel, and cobalt all probably have a maximum 
of magnetization, though its existence can never be entirely 
established by experiment, and must alwavs be a matter of 
inference ; but if one exists, the values must be nearly as 
follows at ordinary temperatures. Iron when 8=17500 or 
when 3=1890; nickel when 8=6340 or when J=494 ; 
cobalt when 8=10000 (?) or when J=800(?)” t. Until 
lately, nothing decisive was done in the matter, apart from 
occasional announcements of £§ having been found > 1890 for 
iron; and Rowland’s values had to be adopted by experi- 
menters, including myself (Phil. Mag. Nov. 1887)t. Mr. 
Shelford Bidwell’s experiments on the lifting-power of 
divided ring-electromagnets (up to §=585) furnish important 


* Paper read before the Physical Society of Glasgow University, Nov.8, 
1889 ; a synopsis of results had been communicated to the Brit. Assoc., 
Newcastle (see Proceed. Sect. A, Sept. 17, 1889 Report). 

t Rowland, Phil. Mag. [4] xlviil. p. 389 (1874); reduced to C.G.S,. 
units. 

{ Compare Fromme’s comments, Wied. Ann. xxxiii. p. 234 (1888), 


Phil. Mag. 8. 5. Vol. 29, No. 179. April 1890, 2A 


294 H. E. J. G. du Bois on Magnetization in 


evidence for the continual increase of the Induction, propor- 
tional to the square root of the weight supported. However, 
I cannot quite agree with the author's way of calculating the 
curve of magnetization *. Quite recently “Messrs. Ewing and 
Low ¢ published the final results obtained with their i ingenious 
“isthmus ” method, which disprove the existence of a limit to 
$, the induction having been forced up to over 45,000 C.G.S. 
The authors further conclude that the ma cnetization remains 
sensibly constant throughout the extensive range of mag- 
netizing field (2000 to 20, 000 C.G.S.) which they were the 
first to ‘apply. 

§ 2. Mainly with a view to check these results by an alto- 
gether different method, and toe obtain more accurate data 
than the isthmus method, as developed at present, appears 
capable of supplying, | undertook the experiments to be de- 
scribed. Excepting Mr. Bidwell’s 585 C.G.S., fields over a 
few hundred units hardly appear to have been applied in 


coils; I therefore began with a powerful coil giving up to 


1300 C.G.S. Thence upward to 13,000 an optical method, 
based on Kerr’s phenomenon 1, was used. I have also studied 
the effect of temperature with these strong fields ; considerable 
interest having been lately attached by various authors to 
theoretical thermoma gnetic speculations; and thermomagnetic 
motors having been proposed by Thomson-Houston, Schwe- 
dofi, Stefan, Edison, and others §. In conclusion, the important 
part played by magnetization in affecting the properties of 
matter is discussed. 
_ Throughout this paper I shall as usual denote by: , mag- 
netic intensity; S,induction ; when the values of these quan- 
tities inside the metal are considered, they are denoted by 5‘ 
and %$’; S$, magnetization; D, density ; ; G6=3/D, specific 


_ = The magnetic intensity 5 in the thin air-films between the halves of 
the ring evidently equals $', the induction in the iron. Now the tractive 
force a unit section is sequal to the tension in the se of force 


— ig y= 7 =2a9°+S5' +57 on ; Te =$'+455] 
(for ee see : es This adaptation of Maxwell's formula by Row- 
land, Mr. Bidwell (Proc. Roy. Soc. xl. p. 492, 1886) finds “ clearly erro- 
neous,’ though I fail tosee why. He adopts the formula 
G=2- ¥+S5'; 

the missing term "/8z appears, from the action-at-a-distance point of 
view, to correspond to the mutual electrodynamic attraction of the two 
half-coils, neglected by Mr. Bidwell. 

| Ewing and Low, Phil. Trans. clxxx. p. 221 (1889). 

i See du Bois, Wied. dun. xxxix. p. 25 (1890); transl., Phil. Mae. 
ante, p. 253, the paragraphs of which will be referred to as loc. cit. 

§ See Stefan, Wien. Berichte, xcvii. 2, p. 70 (1888). Kitiler, Hand- 
buch ae “Serres -otecknik, i. p. 47 G520). 


-_ & 


i 


Strong Fields at Different Temperatures. 295, 


magnetization, 7. e. moment per unit mass ; 0, temperature ; 
€,, rotation of plane of polarization ; K, “ Kerr’s constant.” 
C.G.S. units are tacitly assumed, wherever the contrary is not 
expressly stated ; compare loc. cet. § 5. 


I. MAGNETOMETRIC OBSERVATIONS. 


§ 3. Apparatus.—FYour elongated ovoids (prolate ellipsoids 
of revolution) of length 18 centim. and diameter °6 centim. 
(ratio 1/30) were prepared and could be uniformly magnetized 
in the coil. On account of their non-endlessness a correction 
of -C52 S* had to be subtracted from the field 5 of the coil 
in order to obtain the real magnetic intensity §’ inside the 

ovoid. The following metals were tested :— 

(a) Soft Swedish iron, carefully annealed : D=7-82. 
ae Hard English cast steel, yellow-tempered at 230°: 

= 7°78; 

(c) Hard-drawn best nickel wire: D=8-°82 (from the 
“ Nickelwalzwerk’”’ in Schwerte, Westphalia) ; stated by the 
makers to contain 99 per cent. Ni, besides SiO, and traces of 
Fe and Cu. 

(d) Cast cobalt : D about 8°0 (from Messrs. Johnson and 
Matthey). My friend Dr. Serda kindly analysed this for me 
with the following result :—Co 93:1 per cent., Ni 5°8 per 
cent., He -8 per cent., Cu ‘2 per cent., Si ‘1 per cent., C3 
per cent. Rather unsatisfactory brittle material ; the ovoid 
broke in the lathe ; it was thought best to scrape the frac- 
tured ends truly plane, and to hold them tightly pressed toge- 
ther in a brass tubular screw-and-nut arrangement f. 

The coil was wound to the following dimensions: length 
30 centim.; inner diameter 4 centim.; outer diameter 12 
centim.; 12 layers, each of 90 turns, of double cotton-covered 
shellacked wire, °25 centim. in diameter ; resistance cold ‘9 
ohm. It could be surrounded by an ice-jacket; with a 
dynamo-current of 32 amp. almost a kilo-watt of activity was 
being dissipated in it, sufficient to melt a kg. of ice every five 
minutes. In other cases the coil was electrically heated. 

§ 4. The ovoids, fixed inside the coil, could be maintained 
at O° or 100° by ice or steam properly applied. The arrange- 
ment for heating them over 100° and the mode of deter- 
mining the fieldiane described, loc. cit. §§ 4 and 14. The 
whole of this apparatus was placed in Gauss’s ‘first position,” 
about 185 centim. due east of a magnetometer. It was 

* See Maxwell, Treatise, 2nd ed. ii. § 438, form. (14). 


epee Jn ae Thonmeen aul Newall, Proc. Cambr. Phil. Soc. vi. p. 84 
(1887) ; Ewing and Low, Phil. Mag. [5] xxvi. p. 275 (1888). 
29A2 


296— H. E. J. G. du Bois on Magnetization in 


attempted to compensate the very considerable action of the 
coil alone by that of another similar one, placed due west and 
in the same circuit. Great difficulty was experienced with 
this, principally due to heating of the coils and parasitic action 
of distant current leads. Finally the idea of total compensa- 
tion had to be given up, and the remaining difference was 
each time carefully determined and corrected for. The earth’s 
horizontal intensity at the magnetometer’s site was measured 
once for all; its fluctuations being followed with one of Prof. 
F. Kohlrausch’s local variometers. Thus the magnetic 
moments of the ovoids could be accurately obtained in abso- 
lute measure. 


§ 5. Preliminary trials.—I began by trying whether there 
was a perceptible influence of magnetic history in general; or 
of the hysteresis, due to its latest phases, in particular. The 
ovoids were therefore made to pass through various magnetic 
ordeals, as descending or ascending currents, reversals, &e. 
None were found, however, to have an appreciable effect, except 
with fields below 150 C.G.S., say, where such an influence 
occurred, though slightly. The reasons for this are no doubt:— 
(1) the ovoids had too little of endlessness to exhibit much 
hysteresis in any case ; (2) the slightly pulsating machine- 
current effectually counteracts it by its shaking action ; and 
(3) probably hysteresis really comes less to the foreground 
with such strong magnetizing fields. 

However this may be, I was thereby free to magnetize in 
whatever manner I chose; as a rule, two magnetometer- 
readings were taken with currents reversed. The moment for 
a given temperature may thence be plotted in a loopless curve 
as a function of .§’ only, provided the latter exceed 100 C.G.S. 
say. Neither was I sensibly troubled with the well-known 
acyclic shaking-in action of temperature-variations ; perfectly 
consistent results being obtained with strong fields whether on 
heating or on cooling. Accordingly the moment due to a 
given magnetic intensity may be considered a function of the 
temperature only. | 


§ 6. Magnetic curves——After much hesitation I decided 
not to plot § as usual, but the specific magnetization ©. The 
principal reason for this was that the results became more 
comparable by thus eliminating the density, which depends on 
temperature and other physical conditions of the material, and 
could moreover not be determined for the electrolytic metals 
tested (§ 8). In fact, magnetism being an essentially mole- 
eular phenomenon, it is for certain purposes more rationally 


Strong Fields at Different Temperatures. 297 


referred to unit mass, which always contains the same number 
of molecules, than to unit volume, which does not. In PI. VIII. 
fig. 1 the long curves represent 6=funct. (.§’) over a range 
evident from the scale of abscisse. The origins do not occur 
in the diagrams, excepting that for nickel, which is joined 
to the first experimental point © in a manner approximately 
estimated from known data. From these curves others may 
readily be calculated ; in particular, those representing $= 
funct. (8), which will be referred to below. 


§ 7. Hifect of temperature.—The upper curves of magneti- 
zation for iron and steel correspond to O°. It will be seen 
that at first they almost coincide with those for 100°, but that 
the difference increases towards larger abscissee. For §! con- 
stant*, equal to about 900 C.G.S., G=funct. (@) was then 
determined. It is represented by the short temperature- 
curves to the left of fig. 1, plotted to the separate scale of 
abscissee. They all show a decrease of © ; the latter evidently 
always being above its critical value, below which it is known 
to increase on heating. The nickel curve falls off less abruptly 
than it is known to do for weaker magnetizing fields. 
Hence in an infinitely strong field the magnetization of all 
these metals would probably begin by decreasing at a quicker 
rate still; then to fall off without any abruptness towards 
practically vanishing values (see § 13), 

On the hypothesis of magnetic molecules, this case corre- 
sponds to the temperature-variation of the indiwidual molecular 
moments, because the supposed infinite field would direct the 
axes of all the molecules parallel to itself. It is the simplest 
case ; the abrupt changes and other complications observed 
with ordinary fields being due to the action of temperature 
on the direction of the molecular axes. All this was theoreti- 
cally pointed out by Prof. G. Wiedemann. As far as I 
can see, my results nowhere contradict any previous thermo- 
magnetic researches, conducted with much lower fields, though 
partly at higher temperatures, by G. Wiedemann, Rowland, 
Baur, Wassmuth, Hwing, Berson, Ledeboer, Tomlinson, 
J. Hopkinson, and others. 


§ 8. Additional experiments were made on material slightly 
differing in condition or quality from that above defined 
Gn §3). Annealing the hard-drawn nickel caused the 


* Of course it was the current, and with it the field §, which was 
actually kept constant ; but the increase of '=—-0529, amounts to but 
2 per cent. even when, as with nickel, § falls off from 500 to 0, 

t Lehre v. d, Llektrizitit, iii, § 892. 


298 H. HE. J. G. du Bois on Magnetization in 


magnetic curve to rise much more rapidly at first without, 
however, attaining in the end to values beyond those of the 
unannealed metal. The yellow-tempered hard steel was further 
tempered dark blue and finally annealed at red heat without 
any very marked change in the general character of the curve 
ensuing. 

The values of G, found for iron and nickel, are 216°1 and 

54-0 respectively at 25°, as interpolated on the temperature- 
curves of fig 1. Thin sheets of electrolytic iron and nickel 
were now prepared in the shape of oblong ellipses and 
weighed. They were subjected (at ordinary temperature) to 
a field of 900 C.G.S., and their moments approximately 
measured with the following results :— 
a. Iron, about -05 centim. thick, originally intended for 
printing Russian banknotes, and kindly given to me by 
Prof. F. Kohlrausch : @=211°4, 30 per cent. of which was 
residual. 

b. Iron, about ‘005 centim. thick, which I electrolytically 
obtained from the so-called Varrentrapp bath: G=213°7, 
50 per cent. of which was residual. 

c. Nickel, about -015 centim. thick, from citrate of nickel : 
©=53'5, 20 per cent. of which was residual. 

Hlectrolytic cobalt could not be got in films sufticiently 
thick for this purpose. The results appear to warrant the 
conclusion that with these very strong magnetizing fields 
much does not depend on the quality of the metal, as long as 
it is tolerably pure. Nor has its condition, as resulting from 
the mechanical and thermal treatment previously applied, 
any sensible influence. Of course the experiments in this 
paragraph are meant to be novel only with respect to the 
strong fields applied. 


II. MAGNETO-oPTIC OBSERVATIONS. 


§ 9. Method and Apparatus.—As the isthmus method is 
based on the principle of tangential continuity of § and dis- 
continuity of B (6'/=H and B!>%B3), so the method to be 
described may be said to rest on the normal discontinuity 
of § and continuity of B (.6'<§ and B’=%3). In addition, 
the normal component of 3 is measured by the rotation 
impressed upon plane-polarized light normally reflected from 
the magnetized metal. In order to obtain the former the 
latter has only to be divided by a factor, which I have 
_ proposed to call “ Kerr’s constant ” (doc. cit. § 24). 

The optical apparatus used for accurately measuring the 
rotation of red ight has been described at length (loc. cit. 


EL 


Strong Fields at Different Temperatures. : 299 


§§ 2, 16). Small disks M were turned out of the same 
material as that above defined ($38), and polished on one 
side. These mirrors were fixed to one pole P, of a Ruhm- 
korff electromagnet (see Pl. VILI. fig. 3, full size). On its 
way towards the reflecting surface and back the light passed 
through the narrow bore of the other pole Ps, which thus 
screened off all but a small central patch of the mirror. 
Here the lines of induction evidently issue normally from the 
metal for reasons of symmetry. P, and M could be kept 
very nearly at 100° by means of a steam-jacket JJ. 

§ 10. A very thin standard glass-plate G, silvered (S) at 
the back, could be placed immediately in front of the mirror. 
The light then being reflected in it suffers a double magnetic 
rotation in the glass ; this affords a measure for the field § 
directly in front of the metal, equal, by the principle of 
continuity alluded to, to the induction 3’ immediately inside 
it. The glass plate had previously been magneto-optically 
standardized by comparison with bisulphide of carbon, whose 
Verdet’s constant is known from the determinations of Lord 
Rayleigh and Koepsel ; such standards are very convenient. 
Owing to Ruhmkorff’s well-known construction the ray has 
to pass through one of the coils on its way to and from M 
through P,. The ensuing very slight double rotation in the 
magnetized air must be proportional to the current, and may 
be calculated from the data of H. Becquerel, Kundt and 
Rontgen. It was in every case corrected for, the maximum 
value being +°3'; I have actually observed about this rota- 


-tion with a silver mirror. 


$11. Results—The first thing experimentally obtained 
was the curve é)=funct. (3”), whose ordinates must be and 
were actually found proportional to those of J=funct. (23') ;- 
the latter being calculated from @=funct. (.§’), as far as this 


goes (see §6). In order further to exemplify the somewhat 


complicated mode of calculation the numbers for cobalt and 
nickel are given in Table I. Here the italics are the three 
highest corresponding values of 3 and 3’, indirectly given 
by the magnetometric method ; the ordinary type refers to 
the five highest corresponding values of €) and 3", obtained 
magneto-optically with all possible accuracy t. The value of 
ss marked * is interpolated from those above and below ; it 
corresponds to the rotation €) printed to its left; the ratio of 


+ I. e. from 30 observations of the analyser’s azimuth; the smaller 
values of e, were based on 4 observations and measured only in order to 
approximately check the whole method by the proportionality of ordinates 
above alluded to. 


300 A. E. J. G. du Bois on Magnetization in 


TABLE I. 
Cobalt. Nickel. 

Q. Doe Eo. S: 6. $8’. Eo. S. 
100 | 27720 |)" Ga058 * 100 |" 5980 °| nee 
100 | 14180 |—20:97| zo60* || 100 | 6420 | —7-25 | 453* 
HOO Gl HUTOw es. co 1070, 100 | 6490: 11, eee 456 
MOO sl IG5O | ace 108A WN AG's 681054 eee 461 
100 | 16750 | —22'45 | 1134+ || 100 | 9920 | —829 | 518+ 
100 | 19550 | —23:24 | 1174+ || 100 | 12850 | —836 | 522+ 
100 | 21710 | —23:38 | 1181+ || 100 | 16250 | —843| 527t 
100 | 23330 | —23:60 | 1192+ || 100 | 19290 | —840 | 525t 


0° 23330 | —24'39} 1232x|| O° | 19290 —9"27| 579x 


both quantities gives Kerr’s constant for red light, in minutes 
per unit magnetization, as follows :— 


Cobalt. Nickel. Steel. Tron. 
Exe us a0 OF —7'°25 —24"81 —22'99 
aes 1060 453 L531 1669 
K. . —:0198 —°(0160 —°0162 —'0138 


Inversely the four remaining values of e) were now divided 
by K, thus giving $=funct. (3’) marked f in the Table. 
From this again G=funct. (.§') could be calculated, which 
thus forms a continuation of the curves obtained before 

in $6). 

: ‘ § 12. In fig. 2 the results of both methods are combined 
into continuous magnetic curves, now extending, at least 
in the case of nickel, from §/=150 to §’=13,000 C.G.S8. 
The scale of abscissee is ten times smaller than in fig. 1, and the 
additional points © are those derived from the optical method. 
As the strongest field § of the Ruhmkorff attained about 
25,000 C.G.S. it is evident that the maximum intensity S|, 
obtainable inside the metal (.6’=§—47%), is less the more 
strongly magnetic the metal used. Thus in fig. 2 the 
abscissee extend to 8500 for cobalt, to 4500 for steel, to but 
2500 for iron ; the latter’s curve is therefore not continued 
beyond §=1200, the point reached in fig. 1; the more so as 
the iron gave somewhat irregular results on account of the 
‘mirror’s polish not being perfect. The rotational dispersion 
being much greater for iron and steel contributed to make the 


Strong Fields at Different Temperatures. 301 


optical measurements with the only approximately homo- 
geneous “red” light less accurate than for cobalt and nickel 
(loc. ett. § 21) ; another reason for attaching most importance 
to these latters’ curves. 

§ 13. Nearly all optical observations were made, with steam 
on, at 100°; cooling to 0° would not do on account of the 
dew condensing on the mirror. A few measurements were, 
however, made with the strongest fields at ordinary tempera- 
ture; the rotations proved greater than at 100° in every 
ease, and their values for 0° were obtained by simple extra- 
polation ; they are given at the bottom of Table I. The 
values of § marked x were calculated on the assumption of 
absolute invariability of Kerr’s constant with temperature, 
whereas I have only shown the variations to be jess than the 
limit of experimental errors (a few per cent. per 100°, loc. cit. 
§ 15). The corresponding values of © are marked x 0° in 
the diagrams of fig. 2 for steel, cobalt, and nickel. From a 
comparison with the short temperature-curves of fig. 1 it 
would appear (always on the above assumption) as if the 
decrease of magnetization from 0° to 100° were much more 
marked for fields of thousands of units than for lower ones. 
The conclusion of § 7 is based on this inference. 


§ 14. Magnetite (see loc. cit. § 17).—-Curve I. of fig. 4 
represents ¢y,=funct. (23), experimentally determined for a 
small crystal of magnetite by purely optical observations (at 
ordinary temperature) ; its ordinates must be proportional to 
those of $= funct. (33’). Now the latter function is unknown 
for this material, but it may be asserted to start from the 
origin very nearly as a straight line J=3’/4cr*. On in- 
spection of curve I. the two observed points © nearest the 
origin are accordingly seen to lie almost in line with it. 
Now multiplication of these two values of ¢ into the corre- 
sponding ones of 477/23’ is easily seen to give Kerr’s constant 
as +°0122 and +:°0115 for the two points respectively ; the 
mean value +°012 will be sufficiently near the truth for our 
present purpose. 

We consequently divide the ordinates of «y= funct. (B’) by 
"012 and thus obtain J=funct. (23’) in absolute measure. 
Thence $=funct. (.§’) is easily calculated and plotted as 
curve Il. (fig. 4). The magnetization evidently tends 
towards a limit not much above 350 C.G.S., somewhat less 
than that for nickel. Our magneto-optic method has thus 
given an absolute magnetic curve, at least approximately, 


* du Bois, Wied, Ann, xxxi. p. 952 (1887); Phil. Mag. Nov. 1887. 


302 -H. E. J. G. du Bois on Magnetization in 


without any magnetic observations having been made. In 
fact these are quite out of question in the present case ; and 
accordingly no absolute data have ever been given for mag- 
netite or loadstone that I am aware of. 


ILI. Concuvusion. 


§ 15. There can be no doubt that the curves of fig. 2, 
especially those for cobalt and nickel, show a tendency to 
a limiting value of magnetization. This of course can never 
actually be observed, but the values of J can hardly exceed 
1630, 1200, 530 C.G.S. respectively for the steel, cobalt, 
and nickel used (at 100°). Though, as explained in § 12, iron 
unfortunately happened to give the least trustworthy results, I 
may infer from my observations that the value 1750 cannot 
be far from the truth (also at 100°). As regards the im- 
portant question whether the approach is an asymptotic one, 
or whether 3 reaches a maximum with finite values of §, 
thence to rediminish*, I cannot pretend to decide it any 
more than Messrs. Ewing and Low. The apparent slight 
decrease in the case of nickel (see Table I., $=525) is within 
the range of experimental error. 


Accordingly the general type of the well-known suscepti- 
bility curves «=funct. ($) has the point of inflexion I, as 
was indeed first shown for iron by Fromme and Haubner 
(see § 1, footnote). Its continuation beyond the final ex- 
perimental point P is a matter of inference. If there be an 
-asymptotic limit to $, the curve will cut the axis of abscissee 
in a point Q, and the shape of the end PQ will depend on 
the law of approach of 3; e.g. if the approach be ike that 


* See Maxwell, Treatise, ii. § 844. It may be well to observe that even 
in a field of 35,000 C.G.S. the magnetization of bismuth, the most 
‘diamagnetic metal known, would reach but —‘5, 2. e. —7’5 per cent. of 
the limiting value for nickel, so that its superposition on the latter would 
probably escape observation. ‘ 


Strong Fields at Different Temperatures. 303 


of a hyperbola towards its asymptote P Q will be very nearly 
I P tangentially produced. These curves of course have 
nothing to do with those representing the permeability, 
w=funct. (93), which have been shown by Messrs. Hwing 
and Low to tend towards the asymptote w=1, for B’=ox. 

§ 16. The general conclusions of these physicists are 
entirely corroborated by the present experiments, conducted 
on altogether different lines. I believe all doubts, that have 
occasionally arisen as to the existence of a limit of Magnetiza- 
tion, will thereby be dissipated. In fact this quantity appears 
about to regain its physical importance, which has lately been 
perhaps too much transferred to Induction. This I will 
now endeavour to show, without thereby in the least wishing 
to contest the great advantages of induction in the mathe- 
matical theory, as well as in the practical applications of 
electromagnetism. 

In 1842 the late James Prescott Joule * enunciated the 
law that the elongation of unstrained iron is proportional to 
the square of the magnetization applied. The same has 
recently been shown by M. Goldhammer to hold for the 
decrease of electric conductivity |; and it can hardly be 
doubted that thermal conductivity varies in the same manner. 

I have shown the optical rotation to be entirely dependent 
on and directly proportional to the magnetization on reflexion 
as well as on transmission (oc. cet. § 23, and Phil. Mag. Nov. 
1887). Hall’s effect probably follows the latter law {, and it 
is natural to suppose that the three analogous phenomena 
discovered by Messrs. v. Httingshausen and Nernst will prove 
no exceptions. 

§ 17. I therefore entirely agree with M. Goldhammer, 
where he points out the probability of this general law :— 

‘‘ Magnetization affects all physical properties of metals in 
a way generally depending on. its direction. Whenever the 
ensuing changes are odd functions of the magnetization (both 
simultaneously reversing their sign), they are simply propor- 
tional to it. In the case of even functions (always having 
the same sign), they are proportional to its square.” 

This statement is an expansion of ideas put forth by Sir 

* Joule, Reprint of Papers, 1. p. 246. 

+ Goldhammer, Wied. Ann. xxxvi. p. 823 (1889); Procés-verbaua, 
Paris Electr. Congress, Aug. 80, 1889. 

t This statement, well worth safely establishing by experiment, is 
based on the following evidence :—1. By Hall, curve for Ni, Phil. Mag. 
[5] xu. p. 166 (1881); 2. Residual effect in steel, Phil. Mag. [5] xix. 
p. 419 (1885) ; 8. Behaviour of conducting strips of various thicknesses, 

‘Sillim. Journ. [3] xxxvi. p. 131 (1888); 4. By v. Ettingshausen and 
Nernst, table for Co and Ni, Wien. Ber. xciv. 2. pp. 585, 587 (1886). 


304 H. B. J. G. du Bois on Magnetization in 


W. Thomson in 1855*. The relation assumed to exist be- 
tween the optical phenomena and Hall’s effect (as extended 
to displacement currents) by Messrs. Rowland, H. A. Lorentz, 
and van Loghem} appears in a certain sense as one of its 
particular cases. In conclusion, it may be remarked that the 
above phenomena are not actions at a distance, but actually 
occur on the selfsame spot as the magnetization, which thus 
appears to be their common cause, and to have a real physical 
existence. 


APPENDIX. 


On Manganese Steel. 


The optical method having proved a valuable aid in the 
case of magnetite, it occurred to me to apply it for scruti- 
nizing the behaviour of manganese steel. A piece of bar and 
some wire was kindly supplied to me by Mr. Hadfield, of the 
Hecla Works, Sheffield. Chemical analysis, for which I am 
again indebted to Dr. Serda, gave 87:1 per cent. Fe, 11°8 per 
cent. Mn, °3 per cent. Si, and some C. It is susceptible of 
an excellent polish, rather better than that on ordinary steel. 
However, I find it somewhat more liable to rust; after some 
months the polished surface showed small specks of oxide 
under the microscope. Rough magnetometric measurement, 
with the strong fields of the coil, gave an apparently con- 
stant susceptibility of only -001, or permeability 1-013 f; 
about 25 per cent. of the magnetization being residual. 

On magneto-optic examination, in the manner above de- 
veloped, negative rotation was found in every case, But its 
numerical value varied considerably according as different 
patches of the same polished surface were made to reflect, or 
as different mirrors, ground on to the same piece, were tried. 
The rotation on a given patch was not proportional to the 


* Sir W. Thomson, Reprint of Papers, ii. p. 178, 

t See Wied. Berdblitter, viii. p. 869 (1884), 

t Literature on p. 34 of Mr. Hadfield’s paper read before the Iron 
and Steel Institute, Edinburgh, 1888; further, Barrett, Proc. Roy. Soe, 
Dubl. vi. p. 107 (1888). Results of experiments made at the German 
marine observatory of Wilhelmshaven are given in Ann. d. Hydrogr, 
xvi. p. 177 (1889), though not in absolute measure ; however, on con- 
sidering the data given, the susceptibility may be estimated at :005 for 
the thin bar, and ‘0015 for the thick bar used. Ewing and Low, loc. cit., 
find the permeability much larger, viz. 1-4, and constant for magnetizing 
fields between 2000 and 10,000 C.G.S. This seems to show that the 
magnetic properties of manganese steel are exceedingly variable from one 
sample to another. [The same conclusion is arrived at by Dr. Paul Meyer, 
in an article published quite recently (Llektrotechnische Zeitschrift, x. 
p- 582 (1889) after the reading of the present paper. | 


Strong Fields at Different Temperatures. 305 


field of the Ruhmkorff, as the constant permeability at first 
led me to expect, but tended towards a limit. The largest 
rotation obtained was about 4 of the maximum for iron. All 
this appears to me to show the material to be essentially he- 
terogeneous, relatively strongly magnetic layers being inter- 
posed between the feebly magnetic mass. Probably the 
structure on the whole is laminar, and so fine-grained that to 
ordinary chemical mass-tests it appears per fectly homogeneous. 
The ultimate heterogeneousness is only revealed by the mag- 
neto-optical method, in which the action is restricted to a 
surface patch a few millim. in diameter and a fraction of a 
wave-length in thickness. Microscopical examination of a 
mirror showed a faint indication of streaks in the polished 
surface, and the specks of rust alluded to appeared to be 
arranged in definite configurations. The crystallographic 
method of corrosive etching was now resorted to: a drop of 
dilute nitric acid produced a peculiar network of microscopical 
surface figures, not revealed by a common steel mirror after 
the same treatment. This affords another proof for the hetero- 
geneousness of manganese steel, which thus appears to be 
rather an unsatisfactory alloy for the physicist to deal with”, 
however interesting it may be to the engineer. 

I believe great care should be taken in drawing conclusions 
from the greater or less attraction of manganese steel filings 
by strong magnets, this attraction proving an altogether false 
criterion. I have not been able to file my samples; but 
small particles scratched off with a glass-cutting diamond 
were readily attracted by any magnet. A piece of wire was 
then drawn out to 4 millim. diameter, and a number of small 
bits, about 1 millim. long, cut off. These also behaved like a 
heap of filings, and were attracted by a magnet as long as 
separate. But on kneading them together with very little 
wax, the lump was as unatfected by the magnet as a larger 
piece of wire or bar. 

I think all this is only due to the diminutive dimensions 
of the particles, and to nothing else, because they may thus 
come very near the edges of the steel magnet. Here the 
space-variation of .§’, on which the attraction depends, pro- 
bably is considerable. In connexion with this it may be re- 
membered that mineralogists extract ferruginous minerals, 


* In fact the ordinary theory of magnetic induction ceases to be ap- 
plicable to heterogeneous solids; all results obtained by the magneto- 
meter, isthmus, Quincke’s, or any other method must therefore be re- 
garded as untrustworthy. If, for example, the laminz are, on the whole, 
perpendicular to the field, the constant permeability, found by Messrs. 
Ewing and Hem, comes out quite naturally. 


306 Messrs. Haldane and Pembrey on an Improved Method 


though quite unmagnetic in large lumps, out of the crushed 
rocks with magnets. Magnetic ore-separators are also said 
to be used on a practical scale. 

In conclusion I may mention that M. Heusler, of the 
Isabellenhiitte, Dillenburg, kindly sent me an alloy which he 
defined as foilows :—93-93°5 per cent. Mn, 1-1-2 per cent. 
Fe, -2—5 per cent. Si, and carbon. This gave not the 
slightest trace of an attraction by the pole of a steel magnet 
or of the Ruhmkorff, whether in a piece or pounded almost 
to dust. 

I beg to tender my best thanks to Prof. F. Kohlrausch, in 
whose laboratory these experiments were carried out. 


Phys. Inst. of Strasburg Univ., 
Noy. 1, 1889. 


XXXII. An Improved Method of Determining Moisture and 
- Carbonic Acid in Air. By J. 8. Hatpanz, WA., W_D., 
and M. 8. Pemprey, B.A., Fell Hahibitioner of Christ 
Church, Oxford. (From the Physiological Laboratory, 
Oxford.) * 


Wt were originally led to undertake the present investi- 
gation by difficulties experienced in measuring the 
respiratory exchange of oxygen and carbonic acid in animals. 
In the method which we wished to employ the results depend 
on an accurate determination of the difference in the per- 
centage of moisture and carbonic acid in the air entering and 
that leaving a ventilated chamber in which the animal is 
placed. As the ventilation current is large, the difference to 
be measured is a small one, and errors of analysis are corre- 
spondingly important, especially m short experiments. 

Although the object of our work was thus originally physio- 
logical, we have been guided chiefly by regard to the wider 
applications, particularly in meteorology, of the methods in 
question. 

I. The Determination of Moisture. 

Of the various methods in use for determining moisture in 
air the “chemical” method is generally acknowledged to be 
the most accurate when properly carried out. This method 
consists in the aspiration of a known volume of the air 
through one or more weighed tubes filled with a substance 
‘which absorbs moisture, such as anhydrous phosphoric acid 
_or pumice soaked in sulphuric acid. The increase in weight 
_of the absorption-tubes gives the weight of moisture contained 
-in the air. The great disadvantage of this method as used 


* Communicated by Prof. Odling, F.R.S. 


of Determining Moisture and Carbonic Acid in Air, 307 


hitherto lies in the fact that for an accurate analysis a very 
long period of experiment is necessary. The changes in the 
amount of moisture which in ordinary cases occur during 
the period of experiment are thus not indicated, and the 
method is rendered useless for many purposes, besides being 
very inconvenient. 

The details of the method have recently been reinvestigated 
by Shaw, in a research undertaken at the request of the 
Meteorological Council*. He found that with a U-tube filled 
with pumice and sulphuric acid and weighing about 170 
grammes, the absorption was complete with a rate of aspira- 
tion of about 8 or 10 litres per hourft. With double this 
rate there was a considerable escape of moisture through the 
first absorption-tube t. Thus, with the faster rate of aspira- 
tion, the increase of weight of a second absorption-tube had 
to be added to the result. But since it was found that be- 
tween the weighings the second tube frequently varied con- 
siderably in weight from accidental causes, the advantages of 
the faster rate were neutralized. 

_ We have endeavoured to improve the method in three 
directions :—(1) by reducing to a minimum accidental varia- 
tions in the weight of the tubes; (2) by increasing the 
efficiency of the absorbing tubes, and thus making a very 
rapid rate of aspiration possible; and (8) by making the 
apparatus more convenient. 

Big 


——>+ 


| 
ee 


0 Ui 
Se Ujones aes SOREL 
83 OS RoPae, 220. fh 
S RoR 202 BLE SOOO. 
<i SeatiscstSts ee ee ee 


Py @ 
2,02, 
See 


Absorption apparatus for Moisture and Carbonic Acid, x3. 
a. Tubes filled with pumice soaked in sulphuric acid. 6, Tube filled with 
soda-lime. ce. Plug of cotton wool. 
The absorption apparatus which we finally adopted is shown 
in fig. 1. We shall describe it in detail because, as will be 


* Phil. Trans. vol. A, 1888, p. 73. Tt Ibid. p. 84. ¢ Ibid. p. 88. 


308 Messrs. Haldane and Pembrey on an Improved Method 


seen below, the disadvantages of the chemical method, as 
ordinarily used, are dependent on a want of attention to 
details. It consists of a pair of test-tubes, containing pumice 
soaked in sulphuric acid. The test-tubes are 4 x 1 inch, 
and made of thin glass. Hach tube is provided with a 
double-bored cork about 4 inch thick, which is fitted with 
glass tubing of about 33, inch internal diameter, and in the 
form shown in the figure*. The tubing must fit firmly. The 
corks are covered with a layer of hard paraffin inside and out. 
They are pushed down a very little below the tops of the 
tubes, the end of each tube being first wiped inside free of 
acid, and then warmed to soften the paraffin on the cork and 
so facilitate its entrance. To enable the longer limb of the 
tubing to be pushed down, a passage should first be cleared 
in the pumice with a piece of glass rod. A layer of paraffin 
is spread smoothly over the top of the cork until it is just 
level with the edges of the tube. The apparatus must be 
absolutely tight, and should allow air to pass perfectly freely 
when suction is applied. It should finally be carefully 
cleaned with a wet cloth to remove any traces of acid, and 
then dried. 

The pumice is sifted through a wire sieve with about 7 
meshes to the inch, and shaken in a fine one to remove the 
powder. It is then heated to redness by playing on it 
with a large blowpipe-flame, and thrown still hot into “ pure 
redistilled”? sulphuric acid. The superfluous acid is then 
poured off, and the pumice preserved for use in a stoppered 
bottle. Before using the tubes for experiments we have 
always taken the precaution of washing them out with air, 
as the air passed through them at first usually tastes slightly 
of sulphurous acid. 

Each pair of tubes when filled weighs about 80 grammes, 
and can therefore be weighed on any ordinary balance. 

To diminish to a minimum errors arising from accidental 
variations in weight of the tubes, we adopted the plan of 
weighing against a counterpoise consisting of a similar 
absorption-tube, and of about the same weight. This coun- 
terpoise is always kept in the same place as the absorption- 
tubes. Since during an experiment the absorption-tubes will 


* The longer piece of glass tubing in the first sulphuric acid absorption- 
tube is made somewhat shorter than the corresponding tubing in the 
other absorption-tube. The inconvenience arising from the collection of 
water in the first tube is thus avoided. 

Since writing the above we have been supplied by Messrs. Gallenkamp 
with pairs of tubes made in one piece. These are more brittle, but other- 
wise very convenient. 


of Determining Moisture and Carbonic Acid in Air. 309 


have been warmed above the temperature of the counterpoise, 
the weighing must be deferred for half an hour, so as to allow 
their. temperatures to become equal again. The tubes are 
weighed unstoppered. If several tubes are to be weighed 
the stoppers* are removed before weighing from the whole of 
the tubes, including the counterpoise, and not replaced until 
the last tube has been weighed. No absorbent is kept inside 
the balance-case. The tubes should be lifted by the wires 
attached to them for hanging on the balance. 

We found the following form of aspirator very convenient, 
especially when the apparatus had to be carried to a distance. 
Two bottles (fig. 2), each holding about 3200 cub. cent. up toa 
mark in the neck, were arranged as shown in the figure, and 
connected together by a piece of stout, non-collapsing rubber- 


Fig. 2. 


\\ 


SSAAASAASSASTS TS SSAA SON 
The Ut lati pia 


y 
A= 
= 
Z 


tubing provided with a screw-clip for regulating the rate of 
aspiration. The burette clips are for starting or stopping 
the flow. The bottles are covered outside with a layer of felt, 
to keep the temperature of the air and water equal during an 
experiment, and also to prevent breakage. A vertical strip on 
each bottle is, however, left uncovered, so that the height of 
the water may be watched during the experiment and the 


* The stoppers used are the ordinary ones, consisting of a short piece 
of black rubber about 3 inch long, closed at one end by a piece of glass rod. 


Phil. Mag. 8. 5. Vol. 29. No. 179. April 1890. 2B 


310 Messrs. Haldane and Pembrey on an Improved Method 


reading of the thermometer taken. It is convenient to 
graduate the bottles roughly by pasting strips of paper at 
intervals of half a litre up the uncovered strip of glass. 
With the help of this graduation it is easy to ascertain if the 
aspirator is running at about the proper rate. 

‘l'o graduate the aspirator, one of the bottles is allowed to 
drain for a minute, and is then weighed accurately. The two 
bottles are now connected and the weighed bottle is filled 
with distilled water to the mark, the tubing also being 
filled with water. The cork of the weighed bottle is then 
removed, care being taken to let no water escape from the 
end of the long piece of glass tubing. The bottle filled with 
water is then weighed again ; and by deducting this weight 
from that of the empty bottle and allowing for air displaced 
&c., as in the graduation of a measuring-flask, the amount of 
water held by the bottle filled to the mark with the tubing in 
it, is obtained. The difference between this amount and some 
round number of cub. cent., such as 8000, is then measured 
into the bottle, which has been previously emptied and 
drained for a minute. The cork is then replaced, care being 
taken, as before, not to spill any of the water in the tubing. 
The aspirator is now ready for use, and measures off with the 
utmosé exactness 3000 cub. cent. of air each time it is 
reversed. 

We are now in a position to consider the advantages of the 
method as thus modified. As regards, firstly, errors of weigh- 
ing, we found, in accordance with previous observers, that 
an absorption-tube, when left to itself, varies considerably in 
weight from hour to hour. The same is true of a tube 
through which dry air from another absorption-tube is passed *. 
There is usually a gain in weight, but sometimes a loss. This 
may be due partly to variations in temperature and barometric 
pressure. It is also due to gradual penetration of moisture 
into the tubes and to the varying amount of moisture de- 
posited on the surface of the glass. The amount of this 
variation in weight was often two milligrammes or more, 
both in Shaw’s experiments and our earlier ones with other 
absorption-tubes. With the method just described the tubes 
did not vary in apparent weight by more than three deci- 
milligrammes in a day; and these slight variations were in 
part accounted for by small imperfections in our set of weights. 

The advantages of using a counterpoise are illustrated by 
an experiment in which weighings with the counterpoise 
were compared at intervals with ordinary weighings during 


* Cf. the data on this point given by Shaw, loc. cit. p. 84. 


of Determining Moisture and Carbonic Acid in Air, 311 


several days. The differences found are shown in the follow- 
ing Table :— 


Intervals between weighings. | 20 hours. | 3 hours. | 43 hours. | 42 hours. 
Counter- j Ordinary ......... +0:0012 | +0:0010 | +0:0008 | +0-0024 
poise tube (66°923C grms.) 
| Ordinarysm 2 b-4538) 9 s0-0. +0:0009 | +0:0008 | +0°0018 
Tube 1 (77-7075) 
Comparative ccs.) 2... +0:0000 | +0:0000 | —0:0004 
(10-7840) 
Ordinary... saccah<o- +0:0007 | +0:0015 | _...... +0:0023 
(87-6274) 
Bo} Coniparativesn sii... —0-0001 | +0:0002 |... +0:0002 
(20-7041) 
Ordinary, oe. 55: +0:0009 | +0:0010 | +0:0006 | +0-0018 
Tube 3 (69-6367) 
Comparative......... +0:0000 | —0:0002 | +0:0000 | —0:0005 
(2°7136) 


With regard, secondly, to the rate of aspiration possible 
and the lasting powers of the tubes, we made a number of 
experiments. 

When a single absorption-tube was used, instead of the 
double ones described above, the absorption in the first tube 
was perfect (at least with rates up to two litres per minute) 
for a considerable time, as shown by the following expe- 
riments. 

Haperiment No. 1. 


90 litres of air were aspirated at a rate of 1 litre per 
minute through two single absorption-tubes connected to- 
gether by a very short piece of rubber tubing. The aspirator 
in this and the following experiment was a glass filter-pump, 
the air being measured by a gas meter :— 


Pilea. 7 ceed ce Oso Ae 
Pubec2 5% ans - + 0:0000; 


Haperiment No. 2. 


90 litres aspirated at 1 litre per minute. 
Aub! iy owing hs (yeh e047 12. 
Aberin Wepre cid 0002. 


EHaperiment No. 3. 
50 litres aspirated at 12 litres per minute. 
tibet a UEOOT. 


Onis, sxhiectos ue oo a OOOO L, 
2 B2 


7 7? a) 4 a 


312 Messrs. Haldane and Pembrey on an Improved Method 


Experiment No. 4. 


21 litres aspirated at 2 litres per minute. 
Tuber eee... Oicoore 
Tube 27oc8 3 . +:0:00005 


Haperiment No. 5. 
50 litres aspirated at 1 litre per minute. 


Tubes Ses. os | (+ Oras 
Tubes. .2 < —O:000s 


The same tubes were not used through all these experi- 
ments, as tube No. 1 had become spent in the middle of the 
series. The use of double tubes enormously increases the 
lasting powers, so that, as shown by the following experi- 
ment, a double tube may be used for 300 determinations or 
more without being recharged. 


Experiment No. 6. 


The number of analyses possible without refilling a double 
absorption-tube was determined by aspirating air through 
two of them at a rate of 1 litre a minute, and weighing the 
second pair at intervals. 120 litres had previously passed 
through pair No. 1. 


Litres of Air Variation in Weight 
Aspirated through Pair 1. of Pair 2. 
235 —0:0005 * 
Bd4 —0-0002 
418 + 0°0000 
568 —0-:0001 
753 —0-0003 
1046 + 0:0000 
1225 
1346 +0:0001 
1588 +0:00038 
1767 —0:0002 
1994 _ +0°0000 
2200 —0-:0001 


At the end of the experiment the first pair had absorbed 
12°8255 grammes from 2820 litres of air. Although this 
pair was still absorbing moisture completely we did not con- 
tinue the experiment further, on account of the inconvenient 
accumulation of dilute acid in the first tube. 

As in determining moisture we have generally made a 
carbonic-acid determination simultaneously, our usual rate of 


* Weighed by mistake five minutes after experiment. 


of Determining Moisture and Carbonic Acid in Air. 318 


aspiration has (for reasons given, p. 821) been about 1 litre 
per minute. The following were test experiments with faster 
rates -— 

Faperiment No. 7. 


25 litres aspirated at 3 litres per minute. 
lea (AL) heer a ekg een 
aM) st. O0004, 


Haperiment No. 8. 
25 litres aspirated at 4 litres per minute. 


arenes ysis ice, 073453. 
Rama) o ee 42020008. 


Experiment No. 9. 
21 litres aspirated at 7 litres per minute. 


Rann) sty ites + 02142. 
rain (@)) er. tote a AO000L. 


The rate of aspiration may thus be, if required, 7 litres per 
minute. 

With the view of determining whether there is any appre- 
ciable constant error due to incomplete absorption of moisture 
by the first tube, we have added up the variations in weight of 
the second tube in all our experiments in which a second 
absorption-tube was used. 


Total moisture absorbed Sum of variations 
by first tube. of second tube. 
13:0522 grms. —0:0007 grms. 


The mean variation in weight of the second tube was thus 
only 0-0065 per cent. ; and a constant error of this order would 
be quite inappreciable in ordinary experiments. 

Additional evidence of the accuracy of the method is afforded 
by the fact that in the simultaneous determinations recorded 
below (pp. 322 and 327) the two sets of results are practically 
identical. We have also made for another purpose two ex- 
periments in which air dried by sulphuric acid was passed 
through a weighed vessel containing water, and then again 
through a drying apparatus. The apparatus used was on a 
much larger scale, and the rate of aspiration was in one case 
7 and in the other 15 litres per minute. The balance em- 
ployed weighed to centigrammes. The vessel containing water 
lost 4°86 and 3°62 grammes, and the drying vessels gained 
4°86 and 3°61 grammes respectively. 

If the modified method described above be compared with 
the old method as investigated by Shaw, it is seen that by the 


314 Messrs. Haldane and Pembrey on an Improved Method 


modified method the rate of aspiration may be more than 20 
times as fast and the accidental errors in weighing are reduced 
to a sixth or less. Thus for a given duration of experiment 
the error in the modified method is less than a hundredth of 
that by the older method. In other words, an experiment of 
one minute’s duration by the modified method is equal in 
accuracy to a two hours’ experiment by the older method.. 

It is perhaps hardly necessary to refer to the great con- 
venience of the modified method. For experiments in the 
open air sets of weighed tubes can be carried even for long 
distances in a box with places arranged for the tubes. We 
have found that no variation in weight is caused by the 
shaking, &e. (see p. 817). No precautions beyond the very 
simple ones above mentioned are necessary in weighing ; and 
with a good short-beam balance not more than three minutes 
are occupied in the whole of the manipulations connected with 
weighing. Once an absorption-apparatus is filled it is always 
ready for use, and may be used every day for nearly a year, 
The fact that only a small quantity (usually about 6 litres) of 
air is needed for an analysis makes it possible to use an easily - 
portable aspirator, such as that described above. 


Il. Comparative Experiments with the Dry- and Wet-Bulb 
Psychrometer and the Apparatus described above. (Made 
at the Radcliffe Observatory, Ozford, by M. 8. P.) 

This series of experiments was undertaken with a view to 
test the degree of accuracy attainable by ordinary observa- 
tions with the dry- and wet-bulb psychrometer ; and also with 
the object of obtaining independent evidence as to the 
accuracy of the different tables used in connexion with the 
psychrometer. 

The chemical method has been recognized by Regnault 
and others as the standard with which to compare all other 
hygrometers. How important the first of these observers 
considered the method is shown by the following extracts 
from his Etudes sur l Hygrométrie:—“. . . jattachais 
un grand intérét a rendre cette méthode éminemment 
pratique et facile a employer dans toutes les expériences 
hy grométriques.” * 

“ La méthode chimique convient éminemment & la vérifica- 
tion des autres méthodes hygrométriques et a la détermination 
des constantes numériques que plusieurs d’entre elles exigent. 
J’en ai constamment fait usage, a ce point de vue, dans les 
recherches qui font objet de mon premier Mémoire.” fF 

* Annales de Chimie et de Physique, xv. p. 152 (1845). 
* Thid. xxxvii. p. 257 (1853). 


of Determining Moisture and Carbonic Acid in Air. 315 


Although Regnault proved by experiment that the absorp- 
tion of moisture was complete with the chemical method, yet 
he was prevented from bringing it into general use in hygro- 
metry by two difficulties. ‘These were the inaccuracy of the 
weighings, and the slow rate at which the air could be 
aspirated through the absorption-tubes *. All other observers 
who have used the chemical method have had to encounter 
these same difficulties. Hven the mercury-joints and glass- 
stoppered absorption-tubes used by Shaw have not removed 
the errors arising from these causest. Hach determination 
made by these observers required about one hour, and generally 
longer. By what simple means these serious errors can be 
avoided has been shown above. 

I must here express my hearty thanks to the Radcliffe 
Observer for giving me every facility to carry out these 
experiments. ‘To his assistants Messrs. Wickham, Robinson, 
and Bellamy, my thanks are also due. 

Two determinations were made each time and as nearly 
simultaneously as possible. ‘Two aspirators similar to the one 
described above were used. Four pairs of absorption-tubes 
were employed each time :—pair 1 for determination A ; pair 
2 for determination B; pair 3 as a test pair to show if any 
alteration in weight was caused by carrying the tubes from 
the Physiological Laboratory (where the tubes were weighed) 
to the Radcliffe Observatory and back ; whiist pair 4 was the 
counterpoise. 

The tubes were carried in a small box with partitions of 
copper wire to prevent them from knocking against each 
other. The entrance tube, by which the air to be examined 
passed into the pair 1 (or 2), was fixed through a small per- 
foration in a rubber partition covering a hole in the box, so 
that there was no possibility of air being taken from the inside 
of the box. The box and its tubes were placed about 1 foot 
below the wet and dry bulbs. That the air in this position 
might be fairly compared with that in the shed containing 
the psychrometer is shown by experiment 6, in which pair 2 
was placed in the shed close to the bulbs, and pair 1 in the 
usual place below. 

In making a determination the following was the order of 


* Ann. de Chim. et de Phys. xv. pp. 153 and 164. ‘“ La méthode 
chimique est trop embarassant, et elle exige une manipulation trop longue 
pour qu’on puisse employer souvent dans les observations méteorolo- 
giques.” 

+ Shaw on Hygrometric Methods, Phil. Trans. 1888, A, pp. 83 and 
84, The variations in weight range from —:0009 to +0028 gram. or still 
higher. . 


316 Messrs. Haldane and Pembrey on an Improved Method 


procedure. The wet and dry bulbs were first read off; the 
absorption-tubes, pairs 1 and 2, were then connected by two 
long pieces of rubber tubing with their respective aspirators, 
and the air was drawn through them at as equal a rate as 
possible. The readings of the thermometers in the aspirators 
were now taken. When one known volume (2900 cub. cent.) 
had been drawn through, the aspirators were quickly reversed 
and started again until 5800 cub. cent. of the air had been 
taken for each determination. The thermometers in the 
aspirators were now again read ; the readings of the wet and 
dry bulbs entered'; the apparatus disconnected; and the absorp- 
tion pairs 1 and 2 stoppered. Everything was easily done 
in twelve minutes, whilst the actual period of aspiration 
was only about half this time, as shown by the Table of 
experiments. | 

How closely the two determinations agree Table I. will 
show, and there is no doubt that could they have been strictly 
simultaneous the agreement would have been still closer. 
This is well shown by a comparison of the first five or six 
experiments with the last four, in which the determinations 
were almost exactly simultaneous. 

To show that no practical error was introduced in the 
weighings by carrying the tubes about, the variation of the 
test pair 3 is given in Table I. 

In calculating the results for the psychrometer in Table I. 
I have taken the mean of three readings—one at the beginning, 
one at the middle, and one at the end of each period of 
aspiration (7. e. one reading about every two minutes). These 
readings were obtained from a continuous photographic 
record of the wet and dry bulb taken at the Radcliffe 
Observatory. ‘This record can be read off to two minutes and 
one tenth of a degree Fahrenheit, and its accuracy has 
been proved by years of use and comparison with eye- 
readings. The volume of air drawn through the tubes has 
always been corrected for temperature, aqueous vapour, and 
barometric height. In calculating the tension of aqueous 
vapour from the chemical determinations I have used the 
table given by Shaw in his paper on Hygrometric Methods*. 

The mean of all these gravimetric determinations compared 
with the mean of the amounts of moisture calculated from 
the psychrometric readings is ‘0551 to 0549 grm., or less 
than + 4 per cent. Thus although the psychrometric result 
varied from the standard chemical method in the above series 
by + 6 per cent. to — 5 per cent., the mean difference is 
insensible. 

* Phil. Trans. 1888, A, pp. 78, 79. 


a a es 


TABLE I. 
~ | 
a Weight of | Dorcent Variations of 
Corrected | Gain in Gain in | vapour calcu-|" 4:6 ee test pair 3, show- 
ewes Time during volume of | weight of | weight of | lated from | | 2 ae Dry bulb | Wet bulb | ing that carry- 

£ aes 2 Date. which air was | air aspira- | pair 1, de- | pair 2, de-| readings of a ooro"! (mean of | (mean of | ing the tubes 
<= one aspirated. ted through|termination |termination| psychrometer aa 2 al 3 readings).|3 readings).| about intro- 
x each pair. A. B. by Glaisher’s eee duced no error 
Ss Tables, 7th ed. 2s of weighing. 
aS cub. centim.) grm. grm. erm. per cent. a é grm. 
“Se 1. | 16July 1889 | 11.39-11.48 a.m. 5723 0421 ‘0430* "0450 +53 61°6 53°0 +0001 
& | 

S Qe SP, 0» 11,39-11.45 a.m. 5722 0529 0524 0552 +5 58:3 54°59 +0002 
nS 

S 3. | 18 # 11.10-11.16 a.m. 5723 0516 0512 ‘0520 +1 61:3 54:9 — ‘0002 
<5) 

3 4, |19 “ 11.6-11.12 a.m. 5780 0502 ‘0508 0519 +3 63°7 56°0 +0002 

x By, AW) i 11.45-11.52 a.m. 5681 0613 ‘0610 ‘0600 —2 579 56:0 +0003 

x 

$ 6. | 22 5 12.138-12.16 p.m. 5732 0440 0435 "0452 +3 615 53°0 —°0002 
S i 5 Aug. 1889} 11.52-11.58 a.m. 5707 ae ean 0687 ‘0668 —3 65°6 60°7 — ‘0005 
> Sera 6s 11.48-11.54 a.m. | 5709 bee 0564 0548 —3 62:5 56:5 +0000 
a 9. 7 .9 11.21-11.27 am. | 5756 "0510 0510 ‘0495 = 63°0 50°2 +°0002 
s 10. 8 S 11.0-11.7 a.m. 5776 ‘0575 ‘0572 "0552 —4 64:1 57-0 +0001 
al ite 9 Fr 11.24-11.80 a.m. 5731 0678 ‘0675 ‘0678 +0 61:0 58°9 +-0002 

7 12. | 10 5 11.32-11.39 a.m. 5755 "0583 ‘0585 0553 —5 64:6 57-4 —-0001 


* The rubber of one of the stoppers was found to be split on reaching the Observatory, and this accounts for the slight excess in weight of 
this pair of tubes. , 


318 Messrs. Haldane and Pembrey on an Improved Method 


During some experiments the psychrometer was very 
steady; at other times it showed considerable fluctuations. 
As examples may be given the readings of the wet and dry 
bulbs for the experiments 1 and 5. 


Exp. l. Dry. Wet. || Exp. 2. Dry. Wet. 
fil SOACN ae 61:4 BOO || 11.45 aa. 2...) 59 559 
HMB SY AS 61:8 Hoel A9n. 5, cete 57°9 56:0 
Tbe pede ae Se 61:6 Ocal epee oe 58-0 56:0 


It is to be noticed that a difference of two or three tenths 
of a degree Fahrenheit in the reading alters greatly the 
percentage error. 

I have also calculated out the tension given by the chemical 
method, and have compared it with the results calculated 
from the psychrometer by means of Glaisher’s, Haeghen’s, 
Guyot’s, and Wild’s Tables. 


Tasze IT. 
= Chea | Psychrometer. 
xperiment. Method. <> _ : 
"| Glaisher. | Haeghens.| Guyot. Wild. 
mm | 
i siiascaccane 743 776 Meo ‘ler orice T4 
DP Bleep. 9°15 9°55 9°54 9°51 9°5 
OnE eiesi see 8-99 9-00 8°88 8°87 8-9 
Le ae epee 8-78 8:99 8°74 8:77 88 
Deh ste a cae 10-70 10°72 10°75 10°76 10-7 
La ae Sa ee 763 WOE! oho T34 74 
Ton anes ieee 12sto) eg a Als 11:80 1tG 
Sone oae Bee 9°91 | S65 7! 2 9:5y 9°57 9°6 
Oe sia ste 8-90 8°68 8°45 8:43 8:5 
MOS Pe cacet 1000 _ 99752 9:38 9-41 9-4 
Place seston 11-82 | Bt alos 11°93 11-9 
| are ee 10°23 9°67 | 9°55 9°57 95 
Mean! 2.5. 9°64 9°57 9°44 9°44 9°44 


This Table shows that Glaisher’s Tables are the most 
correct as far as my experiments go. These tables were 
prepared by Glaisher from the Greenwich factors and Reg- 
nault’s Table of pressures, and are in general use in England. 
Haeghen’s Tables, which are used in France and _ Italy, 
Guyot’s, which are almost identical with the last and are 
employed in America, and Wild’s, which have been adopted 


of Determining Moisture and Carbonic Acid in Air. 319 


by Germany and Russia, are all reduced from Regnault’s 
table of pressure and psychrometric formule. 

In conclusion may be given the results obtained by other 
observers, who have compared the psychrometer with the 
chemical method. Regnault *, who made 106 experiments 
under very varied conditions, obtained for the mean per- 
centage error 2, whilst the extreme percentage error varied 
from + 12 to— 10. In order to calculate out the results 
from the readings of the dry and wet bulbs, Regnault 
determined the values for the constant A in each series of 
experiments. Hach experiment lasted about one hour ; the 
readings of the psychrometer were taken every five minutes, 
and from the mean of these the result was calculated. M. 
Izarn made 34 comparative experiments in the Pyrenees. 
These are given by Regnault in his paper +. The extreme 
percentage differences are + 2 and —3in the first series, 
and + 10 and — 10 in the second. 

Shaw made comparisons in a room with a current of air 
passing over the instruments ; he does not, however, consider 
them satisfactory. The tensions calculated from the psychro- 
meter by Glaisher’s Tables were generally higher than those 
given by the chemical determination, the variations ranging 
from + 380 per cent. to — 7 per cent. f. 


Ill. The Determination of Carbonic Acid. 


The method adopted by us for carbonic acid is similar in 
principle to that for moisture. The absorption-apparatus 
(see fig. 1) consists of a pair of test-tubes arranged in the 
same way as was described above (p. 307) §. The first tube is 
filled with soda-lime, and the second with sulphuric acid and 
pumice. The air must arrive perfectly dry at the absorption- 
tube for carbonic acid, and is therefore passed through the 
previously described absorption-apparatus for moisture. The 
connecting piece of rubber tubing should be as short as 
possible. 

The soda-lime we have hitherto used was made by heating 
together in a copper vessel 1200 germs. of caustic soda in 
strong solution, and the product obtained by slaking to a fine 
powder 1000 grms. of quicklime. The heating was continued 
until the soda-lime became capable of being broken up into 
fragments ina mortar. The fragments were rapidly sifted 


* Annales de Chimie, xxxvii. pp. 264-285 (1835). 

+ Ibid. pp. 275-272. 

{ Phil. Trans. 1888, A, p. 111. 

§ The same counterpoise is used for the carbonic acid as for the 
moisture determinations. 


a ae 


320 Messrs. Haldane and Pembrey on an Improved Method 


in a wire sieve with about 12 meshes to the inch, and the 
product freed from powder by a finer sieve. We have also 
tried commercial soda-lime similarly sifted, and found that 
it absorbed CO, well (see p. 821). As a precaution against 
blocking of the tubing by soda-lime during the process of 
fitting, a small plug may be placed in the end of the tube 
and afterwards be withdrawn bya string attached to it. The 
figure shows that a piece of cotton-wool is placed between 
the surface of the soda-lime and the cork ; the object of this 
is to prevent soda-lime being carried over in the form of 
owder by a rapid air-current. 

The method was tested in the same way as that for mois- 
ture. As regards accidental errors of weighing, what was 
said above with regard to the apparatus for moisture applies 
equally to that for carbonic acid. With respect to the efficiency 
of the absorption, we may first quote the results of two 
experiments in which the soda-lime and sulphuric-acid tubes 
were weighed separately. In the subsequent experiments 
the double absorption-tubes just described were employed. 


Experiment No. 1. 


The tubes were arranged in the following order;—1 and 2, 
sulphuric acid; 3, soda-lime; 4, sulphuric acid; 5, soda- 
lime ; 6, sulphuric acid. 90 litres aspirated at a rate of 
1 litre per minute. 


Bea ar o-o405 f together +0°0868. 
” 7 ms 
BY ie ho  aeay 
” jee: 
4 6 te 00220 together —0-0001. 


Experiment No. 2. 
Repetition of No. 1; 90 litres aspirated at a rate of 1 litre 
per minute. 


Tube 3. . +0-0360 

ee + 0.0838 | +0°1198. 
Sp ROSS 

ve Osea 10-0832 | +0°0004. 


Experiment No. 3. 
90 litres aspirated at a rate of 1 litre per minute. 


Soda-lime, pairl . . +0°1615. 
y +0:0001. 


”? 9 


of Determining Moisture and Carbonic Acid in Air. 321 


Haperiment No. 4. 
50 litres aspirated at a rate of 1} litres per minute. 


Soda-lime, pairl . . +0°0558. 
ss Sey an 2 tO OOO, 


Experiment No. 5. 
21 litres aspirated at a rate of 2 litres per minute. 
Soda-lime, pairl . . +0°0339. 
A ee ge TOTO Mar 


Experiment No. 6. 


In this experiment commercial soda-lime (Hopkins and 
Williams) was used. 

The soda-lime contained much more water than ours, as 
shown by its appearance and the amount of water it gave up 
to dry air. 50 litres aspirated at a rate of 1 litre per minute. 


Soda-lime, tube1. . . . —0:055 
Sulphuric acid, tubers tO: 10923 ytogether + 0:0871, 
Soda-lime, pair2 . . . . +0°0000. 


Experiment No. 7. 


The same soda-lime tube was used as in the previous 
experiment. 50 litres aspirated at a rate of 2 litres per 
minute. 


Soda-lime, tubel. . . . —0:0478 acai 
Sulphuric acid, tube3 . . +0-:0893 6 +9°04I5. 
Soda-lime, pair2. . . . +0°0013. 


A rate of 1 litre a minute is thus well within the limit of 
safety, so that even should the aspiration be temporarily 
faster, there is no risk of appreciable non-absorption of either 
moisture or carbonic acid. 

The number of analyses possible without refilling the 
carbonic-acid tubes was determined in the same way as for 
the moisture-tubes, 7. e. by passing air through two pairs at a 
rate of 1 litre per minute, and weighing the second tube at 
intervals. 


EHaperiment No. 8. 
120 litres of air had already been passed through pair No. 1. 


Litres of air aspirated Variation in weight 
through pair 1. of pair 2. 
235 + 0:0003 
304 —0:0001 
418 +0:0010 


968 + 0:0049 


we ianeaieniall 


SLEEPS ELE EE EAT RR TE SG AE I EA 


ES TS Fe SN RE SS ee A EE EA a ee eee Ee 
= SS a es = 


322 Messrs. Haldane and Pembrey on an Improved Method 


At the end of the experiment pair No. 1 had absorbed 
0:4371 gram of carbonic acid from 688 litres of air. We 
concluded that 500 litres of air might be safely passed 
through an absorption-apparatus. Other experiments con- 
firmed this conclusion. 

The mean error of the method for carbonic acid was 
estimated in the same way as with the method for moisture 


(p. 311). 


Total CO, absorbed by tubes No.1 . . 06464 
-Sum of variations of tubes No. 2 . «) sO0008 


The mean error was thus about 0:1 per cent. 

The method is thus exceedingly accurate, in this respect 
far exceeding, as will be shown below, the other methods 
in common use. 

For free air about 20 litres or more, according to the 
accuracy aimed at, will be required for an analysis. For 
vitiated air, such as that of schools, 3 to 6 litres will suffice. 

The result of a pair of simultaneous experiments made out 
of doors may be quoted here. 18 litres of air were aspirated 
in each case. 

No: bl 


Sulphuric acid pair. . . . +0°0820 
Soda-lime pair . . . . . +0°0109 


Now; 


Sulphurieacid pair. .) -) = =20;08n9 
Soda-lime pair. ...... .. « | #00103 


The methods just described have now been in use in this 
laboratory for nearly a year. They have also been used for 
some months in experiments out of doors at the Radcliffe 
Observatory here, and in the country in Scotland. So far as 
our own experience of them goes they have successfully 
stood the test of every-day use. 

We may now review shortly the literature bearing on the 
determination of carbonic acid in air, and record some experi- 
ments which we made with a view to testing the two methods 
at present in common use in this country. 

The first attempt at a quantitative analysis of the carbonic 
acid in free air seems to have been made by A. von Hum- 
boldt *. His numerous results were, curiously enough, 
entirely illusory, since he concluded that about 100 vols. per 
10,000 of air were usually present. In 1802 Dalton fT, who 


* Gilhert’s Annalen, iii. p. 79 (1800). 
+ Manchester Lit. Phil. Soc. Mem. 1802. 


of Determining Moisture and Carbonic Acid in Air, 323 


made the first approximately correct analyses, reduced the 
amount to 6°8 vols. ; and De Saussure * had, about 1830, 
brought it down to a mean of about 4:1 vols. for country air. 
This result was confirmed by Watson (1834) and Boussin- 
gault (1844), who used other methods, and for long was 
supposed to be nearly correct. Still more recent researches, 
particularly those of Angus Smith f in Scotland, Schultze in 
Germany, Reiset{ in France, and Miintz and Aubin in 
France§ and other countries, have gradually reduced it by 
about a third more. 

There still, however, exists a considerable amount of ap- 
parent contradiction on the subject. Not only are the mean 
results of different observers different, but there is perhaps 
still greater want of agreement as regards the limits within 
which the proportion of CO, varies. That the uncertainty 
and want of agreement which prevails is probably due to the 
imperfection of some, at least, of the methods employed will, 
we believe, be evident from the experiments to be recorded 
below. The subject of the variations in the carbonic acid of 
free air will, however, be taken up in a future paper. 

The methods at present in use for the determination of 
carbonic acid in air are, practically speaking, of two kinds : 
(1) those in which the CO, is absorbed by standardized 
baryta-water, which is afterwards retitrated; (2) those in 
which it is absorbed by potash, and afterwards liberated by 
acid and measured in the form of gas 

The method best known in this country is that of Petten- 
kofer{], or, more correctly, of Dalton** and Pettenkofer. In 
this method a large bottle is pumped full of the air to be 
examined. A measured quantity of standardized baryta- 


* Annales de Chinue, xliv. p. 5. 

+ ‘Air and Rain,’ p. 59. 

t Annales de Chimie, xxvi. p. 145 (1882). 

§ Ibid. xxvi. p. 222 (1882), xxx. p. 238 (1883). 

|| A valuable critical account of the methods hitherto used is given by 
Blochmann, Liebig’s Annalen, cexxxvii. p. 39 (1887). 

{ Abhandl. der techn. Commission der Bayer. Akad, ii. p. 3 (1858) ; 
and Liebig’s Annalen, Suppl. ii. p. 23 (1861). 

** ‘The form finally given to Dalton’s method is described in a paper by 
Watson, communicated by Dalton to the British Association (Brit. 
Assoc. Report, 1854, p. 585). Watson used a large bottle, which he 
filled with air with the help of a pair of bellows. He then added lime- 
water, and after shaking allowed the bottle to stand for several days, at 
the end of which time he filtered off the carbonate, and titrated with 
dilute sulphuric acid. Pettenkofer independently invented a similar but 
improved method. He introduced baryta-water as an absorbent, and 
turmeric as an indicator, and avoided the filtration. Watson’s mean 
result for country air (4'1 vols.) was about the same as that obtained by 
the earlier observers who used Pettenkofer’s method. 


324 Messrs. Haldane and Pembrey on an Improved Method 


water is then added, and the bottle closed and shaken, so as 
to bring the air in contact with the baryta. After a certain 
time the baryta solution is again titrated, and the CO, esti- 
mated from the loss of alkalinity of the baryta-water. 

For certain cases where the bottle method is not suitable, 
Pettenkofer recommends that a measured quantity of air 
should be allowed to bubble through a long tube placed nearly 
horizontally, and containing a known quantity of baryta-water. 
The CO, absorbed by the baryta is estimated in the same way 
as in the first method. Pettenkofer found that about 5 litres 
per hour is the maximum rate at which the air can be passed. 

Reiset* has recently devised an apparatus which allows 
large quantities of air to be aspirated through baryta-water. 
With this apparatus he was able to aspirate as much as 100 
litres through 300 cub. cent. of baryta-water in an hour. The 
absorption of CO, appears to have been complete. Hach 
experiment lasted several hours. He used an enormous 
aspirator, mounted on a cart, and capable of holding 600 litres 
of water. 

The method in which the CQ, is absorbed by potash, and 
afterwards liberated by acid and measured in the form of gas, 
was in its first form used by Mangon and Tissandier{ for 
balloon experiments. A rough form of this method has been 
for some years in use at the Paris Observatory. The method 
has been brought to great perfection by Mintz and Aubin {, 
whose test-experiments show that an accuracy to about 2 per 
cent. of the CO, estimated may be attained when 200 litres of 
air are used. For absorbing the CO, they use tubes about a 
metre long, filled with pumice soaked in caustic-potash solu- 
tion free from CO,. After the experiment the CO, is liberated 
by the addition of acid, and collected over mercury with the 
help of a mercury-pump. The apparatus and manipulations 
required are very complicated, so that the method is not likely 
to come into general use. Miintz and Aubin confirmed and 
extended Reiset’s conclusions, and found that the mean pro- 
portion of CO, in country air is about 2°85 vols. per 10,000, 
and that it very seldom rises above 3°1 or falls below 2°6. 
The experiments of these three observers are certainly the 
most reliable of any hitherto published. 

Gravimetric methods of determining CO, in air were at one 
time much employed, although they have been practically 
disused since the introduction of Pettenkofer’s method. In 


* Loe. cit. p. 164. 
+ Comptes Rendus, |\xxx. p. 976 (1875). 
t Annales de Chemie, xxvi. p. 222 (1882). 


of Determining Moisture and Carbonic Acid in Air. 825 


1832 Brunner* described a gravimetric method. He aspi- 
rated the air at a rate of about 30 litres an hour through two 
absorption-tubes. The first contained asbestos soaked in sul- 
phuric acid ; and the second, which was 38 feet long, was filled 
in the first two thirds with moist slaked lime, and in the last 
third with sulphuric acid and asbestos. He tested the com- 
pleteness of the absorption of the CO, by allowing the air to 
bubble afterwards through baryta-solution, which remained 
clear. The increase in weight of the first tube gave the mois- 
ture, that of the second the CO, in the air aspirated. He 
says he always obtained for free air results lying between 
De Saussure’s maximum and minimum (3°7 and 6:2 vols. per 
10,000). 7 

Brunner’s method, with various modifications, has been 
used by a number of subsequent observers. The most reliable 
results were those of Boussingault, who obtained with large 
volumes of air a mean of 4°0 vols. per 10,000 for Paris airf. 
The results of several other observers were certainly quite 
unreliable. 

In 1856 Hlasiwetz { published a paper in which he criticised 
adversely the gravimetric method. He made a number of 
analyses by different forms of this method, and found that not 
only did analyses simultaneously made often entirely disagree, 
but that in eleven out of fifty-six analyses the absorption- 
apparatus for CO, actually lost in weight. These results he 
set down partly to unavoidable “errors of weighing,’ and 
partly to the fact that CO, is absorbed by sulphuric acid. 
Hlasiwetz’s criticisms appear to have been generally accepted 
as conclusive ; and since the publication of his paper the 
gravimetric method has been almost entirely given up, though 
still described in some text-books. 

Soda-lime has for long been in use as an absorbent for CO, 
in combustions. It was first used by Mulder§ in 1859, and 
Fresenius || has shown its superiority to potash-solution &c. 
Its successful use by one of us in a new form of animal- 
respiration apparatus] suggested the working out of the 
method described above. 

We have made experiments with a view to testing by our 


* Annalen der Physique, xxiv. p. 570. 

t Annales de Chimie, x. p. 456 (1844). 

{ Srtzber. der Wiener Akad. (Math.-nat, Ki.) xx. p. 189. 

§ Zertschr. fiir Anal. Chem. i. p. 3. 

|| Zbed. v. p. 89. . 

4, A full account of this apparatus will shortly be published. A pre- 
liminary paper on the subject was published in the ‘ Proceedings of the 
Oxford University Junior Scientific Club’ for October Term, 1888. 


Phil. Mag. S. 5. Vol. 29. No. 179. April 1890. 20 


ie SAW AS? 


a ee 


Batre AE in shin 


4G 
1 
i 

| 
ty 
: 


oa S 
ap 


826 Messrs. Haldane and Pembrey on an Improved Method 


gravimetric method the bottle method and also the tube 
method of Pettenkofer. 

The bottle method is in general use in this country and in 
Germany, and is in many ways exceedingly convenient. 
There are reasons, however, for suspecting that even in expe- 
rienced hands it may give seriously inaccurate results for free 
air. Thus although the French experiments referred to above, 
and a series at present in progress by our own method, show 
that the real proportion of carbonic acid is, as a rule, under 
3 vols. per 10,000, and fluctuates within pretty narrow limits ; 
yet with the Pettenkofer method a very different average 
proportion is often obtained, and the apparent limits of fluc- 
tuation are, as a rule, much greater. 

We may quote a few recent instances. Marcet and Lan- 
driset* found at two country stations near Geneva 2:7 to 4:9 
vols. per 10,000, mean 3°76 vols. Carnelley, Haldane, and 
Anderson}, who titrated with the barium carbonate in sus- 
pension, found in the outskirts of Dundee and Perth 1:7 to 
3°5 vols., mean 2°9.  Feldtt, who also titrated with the car- 
bonate in suspension, found in Dorpat 1°85 to 3°65, mean 
2°66 vols. The results of pairs of simultaneous analyses made 
by him sometimes disagreed by as much as 30 per cent. 
Uffelmann§, in Rostock, found a mean of 3°5 vols., whereas 
Schultze at the same place had previously obtained an average 
of 2°9 vols. Yet these three observers seem to have used very 
nearly the same modification of Pettenkofer’s method. All 
titrated straight into the absorption-bottle, the carbonate being 
still in suspension. 

In the following comparative experiments, which were 
nearly all made within doors, every care was taken to obtain 
the air from the same place in the room, and at the same 
time in each pair of determinations. The bottles were 
pumped full of air when the aspiration through the tubes was 
half over. 

For the Pettenkofer analyses we used two large bottles of 
10,680 and 10,800 cub. cent. capacity, with ground-glass 
stoppers ||. Before each analysis these bottles were washed, 
first with tap-water, and then with distilled water, and dried. 
They were not washed with acid. The air was pumped into 
the bottle with a bellows, 100 cub. cent of baryta-water 


* R. Meteorol. Soc. Journ. xiii. p. 167 (1887). 

+ Phil. Trans., B, 1887, pp. 66, 68. 

{ Der Kohlensatiregchalt der Luft zu Dorpat, 1887. 

§ Archiv fir Hygiene, viii. p. 252 (1888). 

|| India-rubber caps are objected to by Blochmann, Liebig’s Annalen, 
CCXXXV1i. p. 39 (1887). 


327 


of Determining Moisture and Carbonic Acid in Air. 


Ss a ea ae ee ee Se ee 


Gravimetric Method. Pettenkofer Method. 
Number, | Litres of air a cHeeE ee Hoon ees ioa,.o8 0, Eo ae a Baia ep 
aspirated. | moisture pairs. | acid pairs. atc se Ee ge metric result. | determinations. 
eae 12 say 0-0115 4°63 5138 11 per cent. 
OF eee en 12 —, 0:0108 * 4:35 467 (aaa, 
(a) 12 0:0920 0:0218 } 9:30 | i 
(a) 18 0:1095 0-0211 \ 42 
4 @eecccesesces { (BS ee 0:1040 ee t] 5 67 il 640] 14 99 1 99 
(a) 18 0:0960 0:0175 \ ; 
5 uececteccee 1 18 0:0962 0:0176 4-74 | 548 | 13 9 5 9 
eee 12 7s 0.0079 S17 1. 308} ieee i es 
Pee es cca 12 oe 0:0083 3:33 3°89 ae ait 
Bt Seat ae 18 oe 0:0106 2-84 | 390} ies 5 jes 
Open onvieer ee 0-0928 25-09 joe peek oe Once 
* 2:97 
HOV eral necks ra = des. | 390} pte as 
291 
MG Pees hi vetoes nae ee ee { 3-10 f a Goes 
3:04 
Why ee nema ere — sei ae 1 3:00} — et 


* A second carbonic acid pair used in this experiment and No. 3 (0) varied by +0:0001 and —0-:0002 in the two experiments. 
+ The two Pettenkofer experiments were not quite simultaneous, and so cannot be compared together. 
{ The aspirator leaked, and the volume aspirated had to be calculated from the moisture found. 


2 C2 


ae A < 
es es SF Rc seta os pal = 

SS ae ee ° 7 > = ty Seo 
Gy - x 2 nt ee 


he ‘ mAh +> . “ ree 
I EN TEM ERS 


328 Messrs. Haldane and Pembrey on an Improved Method 


added, and the bottle allowed to stand, with occasional 
shaking, for at least two hours. The baryta-water was then 
removed to a clean and dry cylinder, corked up, and titrated 
after the carbonate had subsided. We used as a rule either 
30 or 40 cub. cent. of the baryta-water in the titration, which 
was performed twice with the ordinary oxalic-acid solution 
(1 cub. cent. ="001 gram. of CQG,), rosolic acid or phenol- 
phthaléine being used as an indicator. The end reaction was 
always sharply defined, and the two results never differed by 
more than 0:1 cub. cent. 

The above Table shows that with air containing a small 
proportion of carbonic acid the Pettenkofer method gave 
résults from 8 to 27 per cent. higher than those given by the 
gravimetric method. As the proportion of carbonic acid 
rises (Experiment No. 9), the difference tends to disappear. 
Judging from these experiments the result for outside air 
would usually be about 15 or 20 per cent. too high by the 
bottle method. a 

It will be seen that the pairs of determinations made with 
the gravimetric method agree with the utmost closeness, both 
for moisture and carbonic acid. 

We have not succeeded in tracing satisfactorily the reasons 
for the inaccuracy of our results with the bottle method. 
Although these results were all too high, other observers 
have, as before mentioned, obtained results which were often 
almost certainly too low. 

We at first thought that the error might be due to contact 

of the baryta-water with air during the manipulations in- 
volved. In the first four or five analyses we had simply 
followed Pettenkofer’s plan of pouring the baryta-water out 
of the large bottle through a funnel into the narrow vessel 
used for allowing the carbonate to settle. To avoid the 
exposure to air implied in this operation, we in the later 
experiments removed the baryta-water with a pipette pro- 
vided with a piece of rubber tubing for applying suction. 
As the pipette was washed first with some of the baryta, it 
was free from carbonic acid. Our results, however, were 
little, if at all, better. | 

Another possible source of error is the state of the glass 
walls of the bottle. Pflitiger* found in making the titrations 
for Kjeldahl nitrogen determinations that it was impossible 
to titrate accurately in flasks which had previously been 
washed with acid. The glass seemed to retain some of the 
acid in spite of washing, and give it up again slowly during 
the analysis. We made several experiments with a bottle 

* Pfliiger’s Archiv, xxxvi. p. 105. 


of Determining Moisture and Carbonic Acid in Air. 329 


which had been washed with mineral acid and then allowed 
to stand full of water fora day; but the result was not always 
higher with this bottle. | 

In the bottle experiment No. 6 (6), which gives the worst 
result of all, a smaller bottle of about 3 litres capacity was 
used. In Parkes’s ‘ Hygiene,’ 7th edition (1887), p. 711, it 
is stated that the results by the bottle method vary with the 
different sizes of bottle. It seems likely that as a rule the 
results will be less correct the smaller the bottle used. 

When the results are too low this is as likely to be due to 
insufficient time being given for the carbonate to settle out 
as to incomplete absorption. If the attempt is made to titrate 
too soon, the result may be much too low, and the end reaction 
will be very indefinite. 

It is no conclusive test of the correctness of the bottle 
method that two simultaneous experiments give the same 
result. If the conditions are kept the same in the two 
experiments, the results must be the same whether right or 
wrong. In the above experiments we usually varied the 
conditions somewhat as regards details supposed to be un- 
essential. In experiments where the conditions were carefully 
kept the same, results were practically identical. There are 
doubtless several sources of error, which may neutralize one 
another more or less, The subject is complicated by the fact 
that nearly every observer introduces, often unconsciously, 
some new modification of the method. 

We have come to the conclusion from the above experi- 
ments that the bottle method in its ordinary form is of very 
limited use for experiments on free air, though usually quite 
accurate enough in the case of vitiated air. 

Blochmann™* has recently described a modification of the 
bottle method which enables him both to avoid all possibility 
of contact of the baryta-water with air, and at the same time 
to titrate with perfectly clear baryta-water. For want of the 
special apparatus required we have not yet tested this method. 

We used Pettenkofer’s tube method in some of our 
earlier experiments for the purpose of testing the efficiency 
of the absorption of carbonic acid by soda-lime. Before we 
had overcome the difficulty caused by errors of weighing, we 
believed that any carbonic acid which had escaped absorption 
by the soda-lime would be indicated best by Pettenkofer 
tubes filled with baryta-water. Accordingly in different 
experiments the air was passed through one or more Petten- 
kofer tubes after it had passed through the soda-lime. We 
always found that the baryta-water had lost distinctly in alka- 

* Liebig’s Annalen, cexxxvii. p. 72 (1887). 


330 Determining Moisture and Carbonic Acid in Air. 


linity after the experiment. There were, however, several 
reasons for doubting whether this was really due to escape 
of carbonic acid through the soda-lime. We therefore made 
the following experiment. 

A current of air, after passing through sulphuric acid and 
soda-lime absorption-tubes, was divided by means of T-tubes, 
and passed through six Pettenkofer tubes placed beside one 
another on a board. The loss of moisture from the baryta- 
water in these tubes was determined by means of a sulphuric 
acid absorption-tube placed in the air-current beyond them. 
The moisture which had collected in the tubing connecting 
the Pettenkofer tubes and this absorption-flask was washed 
into the flask by means of a current of dried air. 60 litres 
of air were aspirated in one hour. 

In addition to the six Pettenkofer tubes through which the 
air was passed six others were taken, and charged with the 
same quantity of baryta solution in exactly the same way as 
the first set. These dummy tubes were kept stoppered 
during the experiment. . 

All the tubes were washed before the experiment, first 
with dilute nitric acid, then three times with tap-water, and 
finally with distilled water. At the end of the experiment 
the baryta from each set of tubes was poured into a small 
flask, and at once corked and allowed to stand for a time. 
During these manipulations every precaution was taken to 
avoid unnecessary contact of the baryta-water with air. The 
results are given in full. 

Sulphuric acid, pair 1. +0°4183. 
Soda-lime, pair 1. +0°0554. 

Baryta-waterfrom ( (1) 40c.c. =39°9 c. c. standard oxalie. 
first set of Peten} 7 
kofer tubes. CS ARSE ees Zs 

Loss of water from same tubes by evaporation 0°8408 gram. 

Baryta-water from ( (1) 40 c.c. =39°65 c.c. standard oxalic. 
dummy set of Pe} 
tenkofer tubes. (2) onal 1S 
Mean . . 39°7 
Standard baryta-water 40 c. c. =40°25 standard oxalic. 


Therefore 


zy, 33 3) 


loss of alkalinity in 1st set=6 x 0°35=2°1 c. c. standard oxalic 
and loss by evaporation = 0°84 > < 
2°94 


loss of alkalinity in 2ndset=6 x 0°55=3:3 


Structure of the Line-Spectra of the Chemical Elements. 331 


The dummy tubes had thus actually lost slightly more in 
alkalinity than the tubes through which the air had passed. 
This loss is about equal to what would be caused by the 
absorption of the carbonic acid contained in 6 litres of pure 
air. 

It follows from this and the other experiments just referred 
to that the error with the tube method may be considerable, 
at least in experiments of not more than two or three hours’ 
duration. 


XXXIV. On the Structure of the Line-Spectra of the Chemical 
Elements. By J. R. Rypsere, Ph.D., Docent at the 
University of Lund*. 


(PRELIMINARY NOTICE.) 


: researches, the most important results of which are 
given in the following pages, will be published 
with pull details in the Svenska Vetensk.-Akad. Flandlingar 
Stockholm. They have extended hitherto only to the 
elements which belong to the groups I., II., III. of the 
periodical system ; there is, however, no reason to doubt but 
that the laws I have found can be applied in the same way > 
to all elements. : 
In my calculations I have made use of the wave-numbers (n), 
instead of the wave-lengths (A) ; n= 10°. X-, if A be expressed 
in Angstrém’s units. ~ As will be seen, these numbers will 
determine the number of waves on econiian! in air (760 millim., 
16° C. according to Angstrém), and are proportional, within 
the limits of the errors of observation, to the numbers of 
vibrations. 

1. The “long” lines of the spectra form doublets or triplets, 
in which the difference (v) of wave-numbers of ther correspond- 
ing components is a constant for each element. 

This law, found independently by the author, has already 
been announced by Mr. Hartley for Mg, Zn, Cd. The values 
of the constant differences (v) vary from v=3:1 in the spec- 
trum of Be to v=7784:2 in the spectrum of Tl. In each 
group of elements the value of v increases in a somewhat 
quicker proportion than the square of the atomic weight. 
For instance :— 


* Communicated by the Author. 


eee nN ‘ - > area ne aaa 
Se eee Jee < 


=~ ee es 
ea, ee 


38382 ~——-Dr. J. R. Rydberg on the Structure of the 


Element ...| 3B. Al. Ga. In. 1 
Prot 109 | 2704 | 699 | 1134 | 2037 
ee 105 | 1096 | 8236 | 22124 | 77842 

= 84 | 1499 | 1686 | 1720| 1876 


In accordance with analogy, the spectral lines of Li (the 
one element, besides H, in which only single lines are ob- 
served) ought to be double with v=0°8, corresponding, for 
instance, in the red line (A=6705°2) to a difference in A of 
0-36 tenth-metre. The most refrangible of the components 
should also be the strongest. 

The elements of the groups I. and III. (atomicity odd) 
have only doublets; triplets are found in the elements of 


group II. (atomicity even). As examples may be cited the 


doublets of Tl and the triplets of Hg. 
Thallium. 


> 


...| 5849°5| 3528-3] 3229-0) 2921-3) 2825-4] 2710-4) 2669-1] 2609-4] 2552-0) 2517-0 


1 


8 


..| 7792°6 | 7796°6 | 7794°9 | 7785°5 | 7766°1 | 7773:9 | 7783-1 | 7781-2 | 7794-2 | 7780-7 
Nay ons s1156 2767-1) 2579-7) 2380-0} 2317-0) 2238-7| 2210-0) 2169-0) 2128-6| 2104-8 


Mercury. 
Nereneees 5460°5 | 3662°9 | 3841°2 | 30210 | 2925-2 | 27985 
Bh poe 46330 | 4644-0 | 46380 | 46029 | 4644-7 | 4626-6 
Nh aone 4358°0 | 3180-4 | 2892°9 | 2652-2 | 2575-3 | 2477-7 
rcstes ‘17634 | 17661 | 17764 | 1761-9 | 1759-0 
Nee eee 4047°0 | 2966-4 | 2751°5 | 25338 | 2463-7 


With the triplets the ratio of the two constant differences “4 
v 


2 
increases from 2°01 in Mg to 2°63 in Hg. Also with these 
elements (of group II.) there are doublets, which follow the 
same rule as the others; the value of the difference Vp in these 
doublets is about 2°2 times as great as the first difference , 
of the triplets in the same element. For example, we have:— 


Line-Spectra of the Chemical Elements. 333 
Ca. Zn. Cd. 

yi eee 2232 876-5 2483'8 

Di) ccsce 103-2 3884 11725 

Oh ee 2:16 2:23 2-12 

oa 


These doublets contain the strongest lines of the elements 
of group II. 

2. The corresponding components of the doublets form series, 
of which the terms are functions of the consecutive integers. 
Each series is expressed approximately by an equation of the 


form 
No 


N=N, Gee a ae ee (1) 
where m is the wave-number, m any positive integer (the 
number of the term), N,=109721°6, a constant common to 
all series and to all elements, mp and w constants peculiar to 
the series. It will be seen that n, defines the limit which the 
wave-number n approaches to when m becomes infinite. 

Messrs. Liveing and Dewar were the first to remark the 
existence of the series, as well as their different appearances. 
They are of three kinds: diffuse, sharp, and principal series. 
The first two are formed by the above-mentioned doublets or 
triplets ; in the elements of the groups I. and III. there are 
consequently four different series of these two kinds, in the 
elements of group II. there are six. I have named them 
jirst, second, and third diffuse or sharp series. The lines of 
the first series of each kind are the strongest and the least 
refrangible. 

Hitherto I have found the principal series only in group I. 
They are double, but the doublets are not of the same kind as 
those described in section 1; the components approach each 
other when m increases (see section 3). I name the stronger 
of the two series, which is also the most refrangible, first 
principal series. The principal series contain the strongest 
lines of the spectrum (in group I.), then come the diffuse 
series (the individual lines of which are in reality double ; ¢/r. 
section 4), the sharp series are the weakest. In the individual 
groups the intensity decreases as the order of the series 
increases, in the same way as the lines grow weaker in the 
individual series with increasing m. 


Se 


oo os -_ — - 
a a I en 
i ° 


Sr ree 


334 Dr. J. R. Rydberg on the Structure of the 
As an example of the series and their calculation, the prin- 
cipal series of Li is as follows :— 
109721°6 


Formula: n=434877— (m+0°9596)? 


$$ 


ee Ee leaky 3. 
ree 


| 

-—|—— SoH Ue. 

[A obs. | 6705-2] 3232-0 27410 2561-5) 2475-0 2495-5 23945) 2373-5 2359-0 

I eale.| 6704°8) 3229°8 27. “ 25623) 2475°3 2425-9, 2394-9) 2374-1, 2359-5 

| | 
3. The different series of the elements are related to each 

other ina way which proves that they all belong to one system’ 


ef vibrations. .To show these relations, I will cite as an 
example the formule of the diffuse and sharp lines of Na :-— 


| i | | ~ 
ae —0-4 —22 —05 +08 +03 +404 +04) +06 +05 
| : 


Diffuse Group. Sharp Group. 
“ae Z : 109721°6 4 109721°6 
Ipst Series ......... — ee eee ere = JAAS OU —. = ee eee | 
First series nu—24A4818 (m£09887)? m—=24485 (m4+0645P 
109721°6 | 


791-2 i 
Second series ...... n=24496:4— 109721°6 | 


go Sik yo Tica .—94500-5 — 
(meoges7y | *— 2008 


(m+0- 65)" 

The series of the same group (diffuse or sharp) have the 
same value of 4; the difference of their values of ng is equal 
to v or (y, and y,). This follows from the fundamental pro- 
perty of the doublets. With Na we have v=14°6. 

The series of the same order (first, second, third) have the 
same value of No in the different groups; they are distinguished 
by the values of uw. The difference, for instance, of the num- 
bers 24481°8 and 24485°9, which are perfectly independent of 
each other, amounts only to 0°7 tenth-metre. We find in all 
the revised spectra the same accordance when we calculate 
the values of ng, using only the last terms of the series. For 
example, if we denote the values obtained from the diffuse 
series by mn, and those from the sharp series by ny :-— 


| | 


WE wees _ 28601-1 397799 | 407891 414865 


| | | 
Element ...) Li. Mg. | Cd | i 
| | 
fh, foes | 285985 | 397779 | 407759 | 414859 
| 


Wha 4. 


Line-Spectra of the Chemical Elements. 335 


Between the principal and the sharp series there is also a 
very close relation. Tor if we write the equation (1) in the 
more symmetrical form 


n 1 i 
2N) (ate Gatm? 7 7 
it is found that this equation, without varying the constants my, 
and fa, will represent a principal series or a sharp series, ac- 
cording as we assume the one or the other of the integers m, 
and m, to be variable ; tothe number which is left unchanged 
we must assign the value 1. 

To calculate with great approximation the spectrum of one 
of the alkaline metals, we use only four constants (with Li 
but three), the common constant No not included. 

By the proposal of a system of notation for series and 
lines, I have tried to show a way by which we can indicate 
shortly the connexion of the different parts of a spectrum 
with the whole system of vibrations, and which at the same 
time allows the correspondence of the lines of different ele- 
ments clearly to appear. A few examples will suffice to show 
the arrangement and the use of this system. K [D,,4] 
denotes the fourth line of the first diffuse series of the spec- 
trum of potassium (A=5801) ; Mg [8.] the (whole) second 
sharp series of Mg (A=5172°0, 8331°8, 2938°5, 2778°7, 2695, 
2646): Rb [P,,2] the second doublet of the principal group 
of Rb (A=4202 and 4216); the single lines are denoted by 
Rb [ P,, 2] and Rb | P., 2] respectively. 

A. The wave-lengths (and the wave-numbers) of corresponding 
lines, as well as the values of the constants v, m, mw of corre- 
sponding series of different elements, are periodical functions of 
the atomic weight. 

As an example, the wave-lengths of the second term (m=2) 
of the diffuse series may be taken together with the values of 

v (with the triplets v, and v.), which are given in smaller 
ates in their respective places between the wave-lengths. 
These values of vy are means from the differences of the wave- 
numbers of all doublets which have been employed in the 
calculation. ‘The components of the doublets are themselves 
double; the less refrangible of the secondary components is 
the weaker, but corresponds to the constant difference, and is 
consequently to be reckoned as the true component of the 


doublet. 


Bee 
a 
ty 

{ 
ue 


——. 
DE 


TS: 


2 Fa CS 
os 


3836 Structure of the Line-Spectra of the Chemical Elements. 


Group of . 
rs Li. Na. K. Cu. Ag. ae 
pe Seow. |. , |{54700| (58620 
pee ee hoa poo 12330 || 52271 |] 5460-0 { 3836-0 
F vy |(O8ecale)}| 146 56-4 242°2 917-2 38195 
eee ee BAe | ask. 51526 | 5208-7) 4792-0 
Be. Mg. Ca. Zn. Cd. Hg. 
j 9 | (44552 , | £36118] / 3662-9 
(} Ax | 31303 | 3837-9 | abe oo { 36004 | 36544 
| limes 41*4 103-2 388-4 | 11602 | 46373 
m4]. ao aon (4858) soe | Sa 
| Vos uillieeracier 206 ol4 187°4 538°4 1766°0 i 
| eae 3829-2 | 4425-0] 8281-7) 34027| 2966-4 
i, B. ie In, | TL 
SANG Ae 32578 = 
tis Nal 2497-0 | (3001Sr ls le | prreried 
v 10°5 OD: Giee | ein eeatete’ato|||l nl ateteterere 2212°4 7784:°2 
de 49GB) BOBL2 reece | soe 30387 | 2767-1 


The lines of Li and K are, in all probability, double like 
the others, but their components have not yet been separated. 

The periodical variation of the constants allows of calcula- 
ting by interpolation the spectrum of an element when the 
spectra of the adjacent elements in the periodical system are 
known. Toshow how far such an interpolation can go, I will 
cite the wave-lengths of the first terms of the diffuse and 
sharp series of Ga. They are calculated without making use 
in any way of the (two) measured lines of this element, or 
even having them present in the calculation. 

The interpolated constants are (cfr. section 3) :— 


Np. Vv. H. 

First series ......... 47547°1 } Diffuse group ...... 0:8363 
831-6 

Second series ...... 48378 °7 Sharp group....... .. 01568 


and the thereby calculated wave-lengths :— | 


Diffuse group. Sharp group. | 


7] MORES ip Uy. 3h De 3. 4, 


First series ...| 6663-4 | 2949-2 | 24943 | 4173°7 | 2787:0 | 2427°-4 
Second series...) 6313°5 | 2878°6 | 2443°6 |) 4033-7 | 26761 | 2379:3 


Absolute Viscosity of Solids and Liquids. 887 


The sharp doublet (m=2) is nearly coincident with the two 
lines which hitherto have been measured. The wave-lengths 
of these lines are, viz :-— 


After Lecog de Boisbaudran. After Deville and Mermet. 
4170 4171 
v=&26°9 v=820°3 
403] 4033 


The accordance is even better than could well be expected. 

Finally, I will remark that the hypotheses of Mr. Lockyer 
on dissociation of the elements are quite incompatible with 
the results of my researches. The observations of Lockyer 
within the spectra of Na and K prove only that, with lumi- 
nous atoms as with sounding bodies, the relative intensity of 
the partial tones may vary under different circumstances. 
For the lines in question belong, without doubt, to the same 
system of vibrations. 


Lund, February 1890. 


XXXV. The Change of the Order of Absolute Viscosity encoun- 
tered on passing from Fluid to Solid. By Cart Barus. 


ii. i? my knowledge nobody has thus far defined the dif- 

- ference between the solid state and the fluid states 
quantitatively. In the case of liquids and gases viscosity can be 
absolutely expressed with facility, and the data have therefore 
to be stated with considerable rigour. This is not true for 
solids, where the results are relative throughout. 

The present paper submits two methods for the coordination 
of the viscous behaviour of solids and of liquids. In deseri- 
bing the differential method applied by Dr. Strouhal and 
myself+, we incidentally pointed out the way in which the 
relative viscosity of two solids may be stated in terms of the 
respective sectional areas, by which the motion at the junction 
of the two counter-twisted wires or rodsis annulled. Suppose 
that one of the wires is a solid, whereas the other is a very 
viscous liquid. Then if the viscosity of the latter can just be 
measured by transpiration-methods (§§ 4, 5), it follows that 
the viscosity of the true solid with which it was counter- 
twisted may also be absolutely expressed. This indicates the 
first method of the present paper (§§ 8, 9). 


* Communicated by the Author. 
+ Barus and Strouhal, American Journal, xxxili, p, 29 (1887). 


838 Mr. C. Barus on the Change of the Order of Absolute 


My second method for measuring the viscosity of solids 
absolutely is direct. It is capable of yielding results of any 
desirable accuracy, supposing the necessary facilities for an 
adjustment free from vibratory disturbances are given 


(§§ 12, 18). 


Gases and Vapours. 


2. Results for the viscosity of gases and vapours are given 
by many observers*. The data present some curious aspects 5 
thus, for instance, the viscosity of vapours? is frequently 
smaller than the viscosity of gases. The order of viscosity 
(n) is about 10~‘g/cs (cf § 18.). Results for the viscosity of 
substances in the neighbourhood of Andrews’s critical tempe- 
rature are not available. Such an investigation would be 


highly desirable (§ 18). 


Liquids. 


8. The literature contains extensive researches and is 
systematized in Landolt and Boernstein’s Physical Tables f. 
The data are easily expressed absolutely, by aid of Slotte’s § 
values of the viscosity of water between 0° and 100°. If 
water at 20° be taken asa type liquid, 7=:01(g/ces) (of. $18). 


Viscous Liquids. 

4, Data are wanting. 

My experiments were made with marine glue||. The 
method is simple. A fairly wide capillary tube, abc, pro- 
vided with a cylindrical open reservoir, a, at one end, was 
half filled with marine glue, the thread extending from the 
reservoir, a, as far down as the middle, 0, of the tube. The 
other (open) end of the tube was inserted into the flask, dddd, 
from which the air was then exhausted. Thus a pressure of 
about | atm. is continually brought to bear on the reservoir a 
of the tube, the other end, c, being in vacuo. A lateral arm, 
e, closed by fusion, facilitates the exhaustion. A small vacuum- 


* Summarized in O. E. Meyer’s Die kinetische Theorie der Gase, 
Breslau, 1877, pp. 138 et seq. 

t+ The most complete set of data are those of Puluj, Phil. Mag. [5] vi. 
p. 157 (1878). Lothar Meyer, E. Wiedemann, and others have contri- 
buted to the subject. 

{ Physikalisch-chemische Tabellen: Berlin, J. Springer, 1883, p. 153. 

§ Slotte, Wied. Ann. xx. p. 267 (1888). References to other researches 
(O. EK. Meyer, Poiseuille, Rosencranz) are there given. 

|| A valuable cement being (nominally) a specially prepared mixture of 


rubber and shellac, It has a pitchy consistency, and can be thickened 
by adding shellac. 


Viscosity encountered on passing from Fluid to Solid. 339 


gauge, gg, held in place by a 
layer of paraffin, h, shows the 
observer to what degree the 
vacuum is maintained in the 
lapse of time. A number of 
tubes, abc, may be inserted 
side by side, and it is always 
necessary to coat the stopper 
with cement. 

5. The transpiration-equa- 
tion due to Poiseuille, theoreti- 
cally corrected by Hagenbach”*, 
has the form 


mTPr* m 1 
a= ep ts gapey p> CL) 


where 7 is the absolute visco- 
sity of the liquid, v the volume, 
and m the mass transpiring 
through the capillary length / 
and radius 7, in the time t. 
In the present case of exces- 
sively slow transpiration the 
correction may be neglected. 
P is the pressure-excess, in 
dynes per square centimetre. 
All magnitudes are to be ex- 
pressed in C.G.S. units. 

In the above form of appa- 
ratus (fig. 1) / isnot constant, 
and v is measured in terms of 
the increase of length of the 


capillary thread ab (fig. 1).: 


Hence the differential equation 
corresponding to (1), since 
dv=mr'dl, is 


Fig. 1.—Apparatus for the Secular 
Transpiration of Viscous Liquids. 


w/ b 


il 
a 
be 


Pr? dt 
n= or aie ° ° . ° e . (2) 


Integrating between 0 and ¢, and between J, and Jy, 
Mf leadas th Wacicalen Ru Rad chins sily eaeishus¥ eta Gey) 
Here 1, is the original length (t= 0), and 2, the final length 


* Pcge. Ann. cix. p. 858 (180). 


This reference is incidental, or I 


should have to refer to Poisson, Navier, Stokes, Stefan, Helmholtz, and 


others. 


aris 


SO 
Pee, pane na tree oe en 


= ee a8 eae en, ee ie SA RE ‘Gaeeeenel oe at > “TR 
pone * a caper intr lie Sir. pare, Per ay ee gh aed? fey oles eee RO ot tel ; ns .' 
Fcc Cece EMER SORE R calla ne Bia ag aah ne a ai NA gaty EERE RR ped One, TEN, SEL AT SO a So> se 


ate i ae 


ae 


— nag 
= ‘ — oo gyms “. 
Seine ey 


340 Mr. C. Barus on the Change of the Order of Absolute 


of the thread of marine glue. The effect of the cylinder of 
viscous fluid in the reservoir a may be neglected from its 
large radius. 
5a. By way of digression I may add another similar case ; 
viz. that of a viscous liquid like glycerine, transpiring in a 
vertical capillary tube, in virtue of the weight of its own 
column only. In this case P=(L+1)ég, 5 being the density 
of the liquid, g the acceleration of gravity, L the initial head 
of the column. Inserting these quantities and integrating, 
equation (2) becomes 
égr* 


= : 
8(—h+L In 


bad). 
L+l, 


An example of results obtained in this way is given in the 
following Table. The observations, though made upon a 
single descending thread at the end of each half minute, are 
grouped in two batches. The tube was dry ; perhaps a moist 
tube (adhering thin film of glycerine) would have been 
preferable. 


HXAMPLE.— Viscosity of Glycerine. 
7r="0505 centim.; Li=1°35 centim.; 6=1:°26 = Ags 20 eee 


t l n t. l n 
sec em g/cs. sec em g/cs. 
150 20°30 390 38°60 

60 12°72 300 31°95 
180 | 29-75 } 507 || 490 | 40:83 } 5-46 

90 15°30 ; 330 34:20 
210 25°10 J 


To account for the difference of 7 in the two sets of results 
is beyond the present purpose. It is noteworthy* that each 
measurement of 7 occupies but two minutes, even admitting 
that the tube is unfavourably wide ; for in the case of viscous 
liquids the temperature-effect is of great importance, and this 
expeditious method therefore has some advantages. The 
experiment may be varied by observing the descending upper 


* Cf. Graham, Phil. Trans. cli. p. 382 (1861) :—“ The liquid (glycerine) 
is too viscous to be transpired by means of the bulb and capillary em- 
ployed in these experiments.” I am not aware that the viscosity has 
been measured since. 


Viscosity encountered on passing from Fluid to Solid. 341 


meniscus, while the lower end of the capillary is submerged 
in glycerine. 

6. By applying equation (3) I obtained the » expressed in 
the following Table :— 


Tas Le I.—Transpiration of Marine Glue. 
P=108 dynes ; r=-0406 centim.; temperature (say) = 25°. 


Date. Ui, l. 7 x<107 e 
| sec. em. c/gs. 
May af) LS8Q0I2h GR 8 0 i 
Ween 7 USO wo epee. 18°5 x 10° 7:2 200 


This is a striking result, remembering that a sphere of the 
cement, if placed on a plane surface, will run out to a flat 
eake in a few months. Nevertheless this type of viscous fluid 
is 20 billion times as viscous as water at the same temperature. 

After long continued transpiration the thread of marine 
glue shows two strata. The advance portion is amher-coloured 
and less viscous, the rear portion brown, clearly containing 
most of the shellac. Hence the observed 4 is probably some- 
what low. (Cf. § 10.) 

7. Paraffine (melting-point 55°) treated in the same way 
showed no transpiration. The tube (29=°082 centim.) was 
nearly of the same bore as above, and the length of thread in 
the most favourable case 2°2 centim. The motion, if any, 
must have been below :01 centim. Hence the viscosity of 
the paraffine must be greater than 2 x 10"g/ces at about 25°. 
It is nearly impossible to insert a capillary paraffine thread in 
a tube, free from the vacuum-bubbles due to contraction on 
cooling. 


Sole. 


8. Having obtained the result in § 6, I proceeded to use it 
for obtaining the viscosity of hard steel by the method of 
comparison indicated in § 1. The apparatus was essentially 
like that of my earlier experiments”. To secure additional 
safety + I introduced the principle of substitution, whereby 
the steel wire and the rod of marine glue were consecutively 
subjected to known torsion-couples, in ways otherwise iden- 
tical. From the enormous viscosity of steel, as compared 


* From the context it appears that the method of substitution is pro- 
bably necessary. 
+ American Journal, xxxiv. p. 2 (1887). 


Hil. Mag. S. 5. Vol. 29. No. 179. Aprel 1890. 2D 


342 Mr. C. Barus on the Change of the Order of Absolute 


even with marine glue, a beam of this substance, say a deci- 
metre thick, would show about the same deformation initially 
as a steel wire only a millimetre thick, cwé. par. So large 
a mass of the cement is inconvenient to handle. I therefore 
used a rod about 4 centim. thick and suitably apportioned the 
torsion-couples in the two cases. The results are given in 
Tables II. and III., where 2p is the diameter, / the length, of 
the similarly twisted rods. This twist 7 is given in the first 
column, and is proportional to the applied couples. N de- 
notes the viscous motion at the index, at the time specified, 
and is given in scale-parts (distance between mirror and scale 
200 centim.). Reduction of N is not necessary, since the 
present purposes are comparative. The steel wire is twisted 
alternately in opposite directions to allow for the accommo- 
dation. In Table II. this precaution is superfluous, the sub- 
stance being a fluid. The three sets of data are merely given 
to show the behaviour more fully. Other experiments made 
with the cement may be omitted here. 


TaBLE I[].—Viscous Deformation of Hard Steel. Wire No. 1. 
= 0°40 centim. ; / = 30 centim. 


Toe bime: » | eNGlO?: ive Time. | Nx 10?. im Time: NSC tO", 
© |minutes.| cm. o |minutes.| cm. o |minutes.| em. 
+5°7 0 |Twisted.|| —5°7|. O | Twisted.) +58 0 | Twisted. 

2 0 2 =) 2 0 
3 70 3 — 71 4 40 
4 115 4 —125 3 72 
6 187 6 — 200 6 122 
8 235 8 — 258 8 160 
10 278 10 —301 10 190 
12 315 12 — 840 12 212 


TABLE III1.—Viscous Deformation of Marine Glue. 
p = 2 centim.; / = 30 centim. 


72 |) came: IN 107. r. | Time. | NX107.|| +r. .| Eimep a eon: 
> |tainutes.; cm. o  |Mminutes.| em. o |Minutes.| em. 
¥1°4 0 0 1-4 0 0 , 0 0 
2 260 2 250 2 220 
3 480 3 450 3 420 
4 710 4 700 4 610 
5 910 5 900 5 810 
6 1010 


* This refers to the applied couple. The initial twist of the bar of marine 
glue is practically zero. 


Viscosity encountered on passing from Fluid to Solid. 3438 


9. From these Tables the mean rate of motion of marine 
glue appears as 2 centim. per minute, whereas the corre- 
sponding mean motion for hard steel is (say*) ‘4 centim. per 
minute, for the three cases. The couple acting on the cement 
is 1-4.z, while the couple in the other case is 5°7.z. Since the 
cement is a fluid, the rate of motion for identical couples 
would be 8 centim. 

The principle given in § 1 may now be applied, whereby 
viscosities are inversely as the fourth power of the radii, 
cet. par. Let 7! and 7 be the viscosities of marine glue and 
hard steel respectively. Then 

2°00\* 8-0 
n= (pr Sy SH AOR Lidia) 


From Table I., 7/=200 x 10°; hence the mean viscosity of 
originally untwisted glass-hard steel, during three consecutive 
alternate twists of 12 minutes each, just within the limits of 
rupture is at least 


Me ADEA eo OiSCn ppt Ay et tons AR MO) 


10. The present results subserve their chief purpose in 
furnishing an estimate of the order of viscosity of glass-hard 
steel ; for the unavoidable errors encountered in a comparative 
method like the present are not insignificant. In the first 
place the thread of marine glue observed for transpiration in 
§ 6 during half a year is not identical with the rod of this 
material which is twisted (§ 8), neither as to temperature nor 
composition (cf. remarks end of § 6). Possibly better results 
might be obtained with old pitch. Again, the rod of marine 
glue, while it is being twisted, is also being appreciably 
stretched by its own weight. This complicates the angular 
measurement. Finally, the sectional error of an opaque rod, 
not necessarily free from air-bubbles, is considerable. Hqua- 
tion (3) must therefore be looked on as assigning an order to 
the viscosity of hard steel above 10'* g/cs. 

11. Before giving the results of the following direct method, 
it is expedient to insert a paragraph on the viscosity of solids 
generally. In § 8, while the steel wire is strained by the 
couple almost as far as the limits of elasticity permit, the rod 
of marine glue is initially scarcely strained at all. In the 
latter case, however, the unstable configurations essential to 
viscous motion are supplied in relatively great numbers by 
the ever changing distribution of the heat-agitation within the 
body. In a homogeneous solid free from strain (soft steel) 

* The viscosity of solids being a function of time, strain, and tempera- 


ture. This distinction is beyond the purposes of the above paragraph, 
but will be fully carried out below, in §§ 11 e¢ seg. 
2D 2 


344 Mr. C. Barus on the Change of the Order of Absolute 


such configurations practically vanish as tonumber. I doubt 
whether in soft steel the viscous deformation due to instanta- 
neous exceptionally intense molecular motion at different 
points within the solid, could be recognized at ordinary tem- 
peratures. The case is different when the solid is under stress. 
Any twist, no matter how small (?), is accompanied by a pro- 
portionate amount of permanent strain, with which a cor- 
responding amount of instability is necessarily associated. 
Hence it must be borne in mind that the viscosities expressed 
absolutely below refer to steel in a condition of strain just 
within the elastic limits. 

I can here merely allude to the very recent and suggestive 
paper of C. H. Carus-Wilson (Nature, xli. p. 213, 1890), in 
which the behaviour of steel near the elastic limits is inter- 
preted in analogy with the well-known circumflexed iso- 
thermals of condensible gases, due to James Thomson. 

Now it is clear that if stressed steel be left to itself, the 
number of unstable configurations becomes rapidly less as the 
time after twisting increases. nergy is dissipated. The 
viscosity of solids is therefore essentially a time-function as 
well as a strain-function. 

12. The apparatus with which the following absolute results 

Fig. 2.—Apparatus for measuring the Absolute Viscosity of Solids. 

a 


were obtained is shown in fig. 2. AA ard BB are two 
massive torsion-circles, the hollow cylindrical shafts, oo, of 


Viscosity encountered on passing from Fluid to Solid. 345 


which are firmly clamped to supports projecting from the 
wall of the room. The steel wire, ww, to be tested is tensely 
drawn between the cylindrical cores, al, a‘ l’, and clamped 
without torsion. To accomplish this the ends of the wire are 
bent hook-shaped, and inserted in flat fissures at the ends of 
the rods al, a’l/, the clamp-screw (shown at a’) passing 
through the hooks of the wire. The middle part of ww 
carries a. pair of plates, bc, held together by four screws in 
such a way as to clamp the wire firmly between the plates. 
A brass rod of screw-wire, dd, is soldered to the upper plate, 
and when in adjustment is horizontal and at right angles to 
the axis of ww. Thus the rod dd is virtually the beam of a 
balance, and two small nuts, mm’, symmetrically placed near 
the ends of dd, are provided with hooks from which a scale- 
pan, Ah, may be suspended. The latter carries a light hori- 
zontal disk, vv, to be submerged in water (not shown), with 
the object of deadening vibrations when the apparatus is in 
adjustment. The upper plate bc also carries an adjustable 
mirror, N, for angular measurement, as well as an index, fg, 
moving across a stationary graduated dial (not shown) by 
which the amount of twist holding the weight, P, in equili- 
brium is roughly registered. 

In adjusting the apparatus, the scale-pan hh is removed 
and the rods al so placed that the lever dd is vertical. After 
clamping al (care being taken to avoid twisting ww) the 
scale-pan is attached at m’, and additional weights P added to 
hold the lever dd horizontal. Hence the two halves of the 
wire ww are twisted 90° each for the whole length. Other 
twists may be applied by rotating the torsion-circles together 
Git would be necessary to connect them rigidly for this pur- 
pose) and adding suitable weights P. 

To fasten the wire securely between the plates the lower 
one is clamped horizontally in a vice. If there were rota- 
tional sliding possible here it would be detected in examining 
very viscous wires. Some difficulty is experienced in fixing 
ww in place quite free from initial torsion. There is also 
some flexure ; but for wires of the radius given these discre- 
pancies may be disregarded. When A A and BB are rigidly 
connected, the twist of the wire ww may be expressed in 
terms of the load P. 

13. To complete the results obtained with this apparatus, 
let 2 be the amount of angular viscous motion*, in radians, 
of any right section of the wire relative to another right 
section, whose distance from the first is the unit of length. 
Suppose, furthermore, that in the plane of a right section 


* The factor 2 is supplied conformably with my earlier notation. 


wap pane 


346 Mr. C. Barus on the Change of the Order of Absolute 


there is no shearing. Then 2d¢/dt=2C; is the common 
angular velocity, per unit of length, with which the shear is 
increased. Consider an elementary cylindrical shell whose 
length / is the effective length of either half of the wire ww 
(fig. 2), and whose right section is2a7dr. Then the amount 
of force distributed uniformly over 277rdr will be 


faa, (1207). . <a 


Multiplying by r, and integrating between 0 and p, the radius 
of the steel wire, 


4 
4PA=n, 5-20, _ » 9) 2s 


where P/2 is the weight at the end of the lever-arm A, per 
effective half of the wire. Inany given adjustment PA/mp*=A 
= constant. Hence 


TN Ce 


In these equations it has been assumed that Sar’ dr=m\r dr. 


Hence under all circumstances 9, is a mean value defined by 
these integrals. 

14. Results obtained with the apparatus § 12, are given in 
Tables 1V. to VII. Here p is the radius, / the length of each 
effective half of the steel wire. P is the total force (being 
the weight plus the weight of the scale-pan) acting at the 
end of the lever A (see fig. 2). The rate of twist is given 
under r, and 2 @ is the total yield during the interval of 
experiment. N denotes the actual scale-reading observed by 
the telescope (scale-distance from mirror, R = 200 centim.) 
at the time given; and 2 @ is the viscous angular motion 
between two right sections of the steel wire 1 centim apart. 

In the second half of the tables, 2 C;is the time-rate of 
change of 2, computed for consecutive intervals of 500 
seconds each. The final column contains the corresponding 
absolute viscosity. All times are reckoned from the moment 
of twisting. ‘To obtain 2C, I availed myself of graphic 
methods *, these being in conformity with the mean accuracy 
of the work. Table LV. contains results for the wire No. 1, 
already tested in Table I. Three twists are applied, alter- 
nately in opposite directions. In Table V. the same wire is 
similarly examined, after it has been softened by heating to 


* Of course a set of smoother values might be obtained by computing 
the constants of the curves @ from Kohlrausch’s exponential formula, and 
the tangents from the values obtained. : 


Viscosity encountered on passing from Fluid to Solid. 347 


redness and cooling in air. Table VI. contains data for a 
new glass-hard steel wire, originally free from stored twist. 
Table VII., finally, contains the viscous behaviour of a wire 
tempered at 450°, which was used as a normal in my former 
differential experiments. 


Taste L[V.—Absolute Viscosity of a Glass-hard Steel Wire. 
No.1. Fourth Twist. 


{—12°9 centim.; p="0405 centim.; P=82x981 dynes; 
A= 9-43 centim. | 


re 


Time. |Nx102.} 29x10 || Time. | 20;x10%. |mx107 


2 o. 
Radians 
Radians., Sec. | Centim. | Radians per Sec. | per centim. g/cs. 
centim. per sec. 
12 O | Twisted. 
420 0 *0 500 735 22 
720 104 202 1000 462 194 
1020 180 349 1500 310 291 
1860 320 621 2000 222 405 
2220 360 698 2500 183 491 
2820 417 808 3000 150 600 
3480 465 901 
No. 1. Glass-hard. Fifth Twist. 
—'12 O | Twisted. 0 
009 480 *0 *O 500 *910 99 
840 120 232 1000 474 190 
1320 235 456 1500 347 259 
1860 329 638 2000 270 300 
2400 402 779 2500 230 3891 
2940 464 900 3000 210 28 
3480 520 1008 
No. 1. Glass-hard. Sixth Twist. 
12 0 | Twisted. 0 
—°009 360 0 0 500 467 193 
960 120 OS} 1000 265 339 
1260 160 310 1500 193 466 
1800 210 407 2000 156 57 
2340 250 485 2500 138 652 
3120 - 306 593 3000 126 715 
3900 353 684 


* The minus signs, being without interest in this and the following similar 
series, are omitted tor brevity. 


gd a at tie * 


348 Mr. C. Barus on the Change of the Order of Absolute 


Taste V.—Absolute Viscosity of Soft Steel, being Wire 
No. 1, heated to redness and cooled in air. First Twist. 


1=13-0 centim.; p=*0405 centim.; P=82x981 dynes; 
A=9°43 centim. 


ov, | Time. |Nx10%] 2pXx10% | Time. | 20,x10°. |nex10 ai 
Radians 
‘Radians. Sec. Centim.| Radians Sec. | per centim. g/cs. 
per centim. per sec. 
12 O | Twisted. 0 
| —-007 490 0 0 500 220 409 
900 40 717 1000 89 1010 
1500 63 121 1500 63 1430 
2100 80 154 2000 47 1920 
2700 92 177 2500 34 2650 
3380 98 188 3000 26 3460 
3780 103 198 
No. 1. Softened. Second Twist. 
—12 O | Twisted. 0 
010 360 ) 0 500 164 550 
1020 50 96 1000 116 776 
1500 70 135 1500 59 1520 
1983 82 158 2000 40 2250 
2520 Qe 179 2500 30 3000 
3120 100 192 3000 15 6000 
No. 1. Softened. Third Twist. 
12 O | Twisted. 0) 
—-007 240 8) 0 200 138 652 
840 42 81 1000 70 1290 
1560 64 123 1500 40 2250 
2100 74 142 2000 28 3210 
2520 76 146 2500 17 5300 
2640 78 150 3000 14 - 6400 


3120 81 156 


Viscosity encountered on passing from Fluid to Solid. 349 


TaBLE VI.-—Absolute Viscosity of Glass-hard Steel. 
First Twist. 


No. 2. 


Wire 


1=13:0 centim.; p='0405 centim.; P=82x981 dynes; 
X=9'°43 centim. 


ae Time. | NX107.} 29x10°. Time. | 2C;x10°. | 7x 10 
: Radians Radians 
Radians.| Sec. | Centim. per centim. Sec. |percentim. ges. 
per see. 
al O | Twisted. 0 
—-009 120 0 0 500 660 136 
420 186 358 1000 325 Niel 
720 270 520 1500 230 391 
1080 335 644 2000 180 500 
1620 410 789 - 2500 140 6438 
2100 458 881 
2580 495 952 
3000 518 996 
No. 2. Glass-hard. Second Twist. 
—13 O | Twisted. 0 
"010 240 ft) 0 500 683 131 
600 144 De 1000 $92 229 
900 220 423 1500 285 316 
1260 288 554. 2000 240 310 
1800 365 702 2500 205 439 
2100 404 TA 
2460 450 865 
2700 470 904 
3000 502 965 
No. 2. Glass-hard. Third Twist. 
O | Twisted. 
240 0) 0 
600 ley 225 


Wire breaks spontaneously. 


= ees ee 


350 Mr. C. Barus on the Change of the Order of Absolute 


Taste VII.—Absolute Viscosity of Steel, annealed at 450°. 
Wire No. 15. Twisted indefinitely. 


1=13°6 centim.; p=:0405 centim.; P=82x981 dynes; 
A=9-43 centim. 


T | time. |Nx102.| 29x10% || Time. | 2C,x10.|,x10 


2. 

| Radians 
Radians.| Sec. | Centim.| Radians Sec. |percentim.| g/cs. 

| per centin. per sec. 

12 0 | Twisted. 0 

— 002 240 0 0 500 177 508 
720 51 94 1000 69 1300 
1200 71 131 1500 40 2250 
1860 86 158 || 2000 32 2810 
2520 95 175 2500 25 3600 
2000 101 186 3000 20 4500 


No. 15. Tempered at 450°. Next Twist. | 


No. 15. Tempered at 450°. Next Twist. 


12 0 | Twisted. 0 
—°003 240 0 0 500 180 500 
660 48 88 1000 | 82 1100 
1260 78 143 1500 57 157 
1740 92 169 2000 48 1870 
2520 112 206 2500 45 2000 
3120 126 232 3000 42 2140 


Some irregularities are apparent, largely introduced by 
vibrations against which our laboratory facilities afford no 
adequate protection. Vibrations increase the rate of twist 


Viscosity encountered on passing from Fluid to Solid. 351 


periodically, and thus supply a greater number of instabilities 
than correspond to the mean twist (position of equilibrium) in 
question. They may also have a more direct molecular effect 
in decreasing viscosity. When the rate of twist in the two 
wires is unequal, viscous motion will also be in excess of the 
true value. This also applies in case of slightly different 
lengths, /, of the two effective halves of the wire. In the case of 
No. 15, which had become somewhat worn by use, the load P 
probably strained the wire too near the elastic limits. This I 
infer from the observed successive reduction of viscosities 
from twist to twist, clearly indicating that an excess of insta- 
bility is being supplied. It is therefore better to accept the 
behaviour of No. 2 (soft) as typical of No. 15; for the normal 
viscosities of the two states of temper are identical. 


Discussion. 


15. Turning first to the values of ¢, it is seen at once 
that they substantiate the inferences of my earlier papers 
throughout*. They therefore need no further comment here. 
Tables V., VII. contain data for my normal wire, by aid of 
which the differential results of the earlier papers may be 
reduced to absolute values. I have endeavoured to make the 
angles t of nearly the same value in all cases, so that $/7 
may be comparable. 

16. The spontaneous breaking of the glass-bard wire in 
Table VI. deserves mention. It occurred during the third 
twist, and at a time when the wire was in no way interfered 
with. This corresponds to the spontaneous explosion of hard 
projectiles frequently observed. It also corresponds to the 
spontaneous rupture of stressed glass, whether the stress be 
stored internally or applied externally. I have observed this 
interesting phenomenon in glass under a great variety of 


* Phil. Mag. xxvi. p. 183 (1888) ;- cbed. xxvii. p. 155 (1889). 

In the deductions of the former paper (p. 189) I neglected the elastic 
motion, in virtue of which, at every stage of viscous yielding, the rate of 
twist is maintained constant throughout the system. After correcting 


for this, 
Ly=2!' {3(8—V) + o(a—B)+$,(L—a)} —2/g7 ; 


which under the simplified conditions of experiment becomes p=/(¢— 9’). 
Hence it follows that the data (6—¢’') of the two papers cited are 
relative, and must be multiplied by In2 to reduce them to the dimensions 
defined in the text. Beyond this the error is without importance, the 
data applying at once to rods initially somewhat harder than those 
actually observed. 


# 
~ ia 


ie ee er RA ne ROR ARI 


A wey EN oye Eee ee 
wv; EER ITT ee 
BP he —— 


Se eae EOI AI = ” 
5 eB Rel ey Diheg aA Fed F Y 


_| Mean viscosity at 500 sec. 14010" | Mean viscosity at 500sec. 57010" 


302 Mr.C. Barus on the Change of the Order of Absolute 


conditions. In all cases there is gradual molecular change, 
and the solid finally breaks without any apparent cause. 

17. The chief results of Tables IV. to VII. are the values 
m:, Whether they be regarded as time-functions, or as ex- 
ponents of the solidity of steel. In fig. 3 these data are 
constructed graphically. An inspection of the figure shows 
at once that both solid viscosity and its rate of increase with 
time are magnitudes which increase together (Tables IV., VI. 
compared with Tables V., VII.). After about an hour has 
elapsed since twisting, the viscosity of hard steel may be quite 


-as large as the initial viscosity of soft steel ; but at corre- 


sponding times the viscosity of soft steel continues to be 


more and more pronouncedly the greater. 


The curves are not consistent as to curvature. This may 
be best inferred from the hard wires, where the viscosities 
are smaller, the deformations large, and the observations there- 
fore as a whole much more accurate (Tables IV., VI). 
Hence I regard the promiscuous irregularities of fig. 3 as due 
to errors of observation and construction. According to the 
law of F. Kohlrausch*, —dd¢/dt=ad/t,, where a and n are 
constants. In case of small torsions or short times, —dd/dt 
=ad/t suffices. Thus for the purpose of deducing the time- 
rates, x, of increase of solid viscosity, it is permissible to re- 
gard the curves of fig. 3 as essentially linear. 

This is done in the following table. 


Taste VIII.—Mean time-rate of increase of the absolute 
Viscosity of Steel, hard and soft. 


|] 
Hard Steel. ! Soft Steel. | 
Twist No.| «xX 10722: | Twist No.| «x 10774: 
g/cs*. | | g/cs? 
Table IV.... 4 20 | Table V... 1 1200 
— Ho; 140 ! = 1400 
5 fie 240 3 1900 
1 Table VI... 1 230 | Table VII. 1 1500 
ey 140 | —— 1200 
3 1000 
Mean rate k..... sesesesee-e- 194x1uU!? | Mean rate © ceeccccceessees 1400 x 10! 


* Kohlrausch, Pogg. Ann. cXxviil. p. 216 (1866). 


Viscosity encountered on passing from Fluid to Solid. 353 


Fig. 3.—The Absolute Viscosity of Hard Steel (Tables IV., VI.) and of Soft 
Steel (Tables V., VII.), considered in its variation with the time 
elapsing after twisting. 


1000 2000 8000 1Luv0 2000 8000 


354 Absolute Viscosity of Solids and Liquids. 


The general explanation of these results has been indicated 
in § 11. Ina liquid or a viscous fluid under moderate stress 
the instabilities are supplied by the mere thermal agitation at 


ordinary temperatures, at the same rate in which they are 


used in promoting viscous motion. Hence viscosity 1s con- 
stant at a given temperature. In a solid under stress the 
instabilities are expended at a rate decidedly greater than the 
small rate of continuous supply. Thus viscosity decidedly in- 
increases with time. Suppose, therefore, a solid of initially 
greater viscosity starts on its viscous deformation at an instant 
when the viscosity of a solid of initially smaller viscosity has 
been increased by time to the initial value of the former case. 
This can actually be realized by twisting a soft steel rod about 
an hour later than a hard steel rod (fig. 3). Then, in suc- 
ceeding times, even though the substances start at a state 
where both are equally viscous, the viscosity of the initially 
more solid body will rapidly overtake the other; for the 
supply of instability due to temperature alone is continuously 
greater in one case than in the other. 

18. Summarizing the results of the above paragraphs, the 
viscosities of the three states of aggregation may be expressed 
in terms of the absolute g/es scale as follows :— 


TaBLe IX. y, considered in its Variations with the 
State of Aggregation. 
| And 5 | 
narewss | . : 
Gases and Vapours. “critical state. | + Liquids. 
Sub- | 
Substance. n. ae nee 1. | Substance. 4. 
° ar fe) me! 
* Ether, O 6°38 x10 ? ? || Ether, 30...; 9x10 
2H ia 87 M10: Ether, 10...| 19x10” 
*Air, 0 | 175x10~ Water, 97...) 30x10 
+O, O | 212x10* Water, 20... 1:0x10> 
: '§ Glycerine...| 5 
Range ......... 10 “ to? ? to ? Range ...... ?tol0 
* Puluj, Zc. t+ O. E. Meyer, Z. c. p. 142. 


t Landolt and Boernstein’s Tables, 7, c., and Slotte, 7. ¢. 
§ A rough measurement of my own, § 5@. Graham's results, ‘ Phil. Trans.’ 
1861, p. 373, refer to dilute glycerine. 


Permanent Elongation of Hard-drawn Wires. 355 
Table [X. (continued). 


Viscous Fluids. Solids. 
Substance. n. Substance. . 
Marine glue......... 2x 108 oo. at 20° (m.p. \ 219" 
10"” to 
t Hard steel, glass &e. 6x10" 
17 
it Softisteelnt ascmp at saan { ae IGE te 
MEG °c cc ecarctne? 10? to 1011 Paes eotcn sees tana 10" to 107° 


Tt During the first hour (500 to 3000 seconds) after twisting just within the 
elastic limits, 


The limits here defined are somewhat arbitrary. They will 
be made more definite when a greater number of substances 
lying on the boundary between the classes have been examined. 
Information is lacking and particularly desirable in the 
neighbourhood of Andrews’s critical temperature. From 
Table IX. it does not seem improbable that the critical tem- 
perature may be definable by a narrow limit of viscosity, quite 
apart from the substance operated on. What this limit may 
be I do not venture to assert, seeing that the viscosity of gases 
decreases on cooling, whereas that of liquids increases on 
cooling. 

Table LX. gives the positively astounding range of varia- 
tion of 7, the chief variable of our material environment—a 
variable which throughout the whole enormous interval in 
question nowhere fails to appeal to our senses. 


Phys. Lab., U.S. Geological Survey, 
Washington, D.C., U.S.A. 


XXXVI. On the Effect of Permanent Elongation on the Cross 
Section of Hard-drawn Wires. By Professors T. Gray 
and ©. L. Mrxs*. 


N the course of a series of experiments on the torsional 
rigidity of metals, forming part of the course of instruc- 

tion in elasticity in the mechanical laboratory of the Rose 
Polytechnic Institute, we were somewhat surprised to find a 


* Read before the Physical Society of Glasgow University, February 28, 
1890. Communicated by Th. Shields, M.A., Secretary. 


356 Profs. Gray and Mees on the Effect of Permanent 


hard-drawn iron wire increased in total rigidity by being 
slightly stretched above its elastic limit. Slight changes in 
the modulus of rigidity, due to stretching, are of common 
occurrence ; but we had not previously noticed, nor heard of 
anyone else having noticed, such a change as to overbalance 
the effect of increased length and probably diminished section. 
The result seemed to make it probable that there was an 
actual increase of diameter produced by pull when the elastic 
limit is reached. As to whether actual permanent stretch is 
necessary to produce this effect we are not yet certain; but 
there seems, from subsequent experiments, little doubt but 
that, for several metals, hard-drawn wires do expand laterally 
when they begin to take a permanent longitudinal set. 

The observation here referred to seemed so interesting, 
that we instituted careful observations on the effect of slight 
stretching (that is to say, permanent stretching of from ly to 
fo of 1 per cent. of the original length) on the density of 

ard-drawn iron, brass, German silver, and pianoforte-steel 
wires. The results indicate that for an elongation of less than 
+ per cent. the section of the wire is slightly increased, above 
which the section diminishes. ‘The experiment is, however, 
by this method exceedingly tedious and difficult, and hence 
the exact elongation which gives the greatest increase of sec- 
tion has not been determined. One or two of the results are 
quoted below mainly for the purpose of indicating the mag- 
nitude of the quantities concerned. These changes are very 
small; and as they enter into the experiments on density 
determined by weighing in water as the differences between 
quantities of comparatively large magnitude, we cannot 
assume the results to be more than an indication confirmatory 
of the result obtained from the elasticity experiments. It 
may be remarked, however, that experiments on this subject 
were made by several members of the senior class both on 
soft and hard wires, with the consistent result that they ob- 
tained sometimes a gain, sometimes a loss of density for the 
soft wire, but always a loss of density in the hard wires. 
The specimens which showed most decided results were 
cut from two coils of very hard wire, one brass and the 
other German silver. The brass is so hard as to render 
it difficult to obtain permanent stretch without fracture. 
The results with iron and steel have not been quite so 
conclusive, owing to difficulties with oxidation during the 
density-determinations. A pianoforte-steel wire does, how- 
ever, show signs of slightly increasing in volume just before 
breaking. The difference between the elastic strength and 
the rupturing strength is not great in pianoforte-wire, and it 


Elongation on the Section of Hard-drawn Wires. 357 


is difficult to avoid fracture. We hope, however, to make a 
more systematic investigation, and to get over these difficulties 
by improved apparatus and methods of experiment. 

Confining our attention to the brass and German-silver 
wires, the results indicate that if the stretch does not amount 
io more than from =) to 4 of 1 per cent. the diameter 
increases. The elastic effect previous to the point where 
stretching is about to begin is for those wires in accordance 
with other well-known results of experiments on this subject, 
in so far as the diameter diminishes with increase of length ; 
but we have not yet got a means of measuring with such 
accuracy as to give quantitative results as to the ratio of con- 
traction to extension. The change from contraction to expan- 
sion seems to take place very near to the limit of elasticity, if 
not after that limit has been reached. A short distance 
beyond this limit contraction again sets in; and if the exten- 
sion be as much as half of 1 per cent., the diminution of 
density, although noticeable, is not sufficient to produce 
increase in diameter. 

The method of experiment which was used for the observa- 
tions on which we base some of the above remarks on the 
effect of elastic stretch, was to pass the wire along 
the axis of a glass tube about 5 millimetres in dia- 
meter, which was hung on the wire in the manner 
indicated in the sketch by means of a rubber stopper s. 
The tube was then filled with water, and the position 
of the surface of the water read on a scale fixed on 
the back of the tube. The wire was then stretched 
and the fall or rise of the water observed. A dimi- 
nution of volume was observed until the wire reached 
about the elastic limit, at which point the water rose, 
slightly indicating a swelling of the wire. We have 
made several attempts to increase the sensibility of 
the above arrangement by means of index-tubes 
fused into the side of the main tube, aided by narrow 
contractions in the tube, itself filled with mercury, 
from which the wire was protected at that point by 
a thin coating of shellac varnish. As yet, however, 
we have not been perfectly successful. The unstable 
condition of the mercury in the narrow contraction 
of the tube renders this method unsatisfactory. 
Should mercury-tubes prove superior, however, in 
experiments with iron and steel, we will platinize the 
other metals and use mercury. 

The following are a few of the results obtained by the 
measurement of density before and after stretching, the 


Phil. Mag. S. 5« Vol. 29. No. 179. Aprnit-1890. 235 


Ne Ss 


me Poa TEP PS ae ay Me a Sane 


ne 
ae 


aaah sana 
°F nae * i 


398 Prof. J. J. Thomson on the Passage 


method being the determination of the loss of weight when 
immersed in water. Very careful precautions were taken to 
eliminate all trace of air from the wire and from the water by 
placing the vessel in the receiver of an air-pump and working 
the pump continuously for an hour or more. Care was also 
taken to minimize the effect of capillarity, and to correct for 
temperature in the measurements. Boiling the water by 
passing a stream of steam through it, causing a current to 
play on the wire, was also tried, with the result that the iron 
and steel wires tarnished too much to render the results of 
any great value. The effect of stretching was slightly dim1- 
nished, a result which might possibly be due to annealing. 


_ Percentage | Areas of section Areas of section 
| Kind of Metal. permanent | before stretching, after stretching, 
| 


elongation. | in square centim. in square centim. 


| ih 
| | 0-10 0-01262 0-01268 | 
IMBrass* -:. 4.288 Seer 
| 0-20 001261 0-01269 | 
| | ota 0008255 0008300 | 
| German-silver ... | | 
| | 0-20 0:00827 | 000834 


XXXVIT. On the Passage of Electricity through Hot Gases. 
By J. J. Tuomson, MA., F.RS., Cavendish Professor of 
Ezperimental Physics, Cambridge*. 


-ASES exhibit the most remarkable differences of be- 
haviour with respect to the passage of electricity through 
them: the same gas under different circumstances may be 
either an insulator and require the electromotive intensity to 
exceed a certain value before any electricity at all can pass 
through it, or it may be a conductor and unable to insulate even 
a difference of potential as small as ;>55 of a volt (Blondlot, 
C. &. civ. p. 283). The study of the changes in the condition 
of the gas which accompany these remarkable changes in its 
electrical properties can hardly fail to afford most interesting 
information as to the method by which electricity passes 
through gases, and possibly through solids and liquids as 
well. As one ofthe simplest changes which can take place in 
the condition of a gas is that occasioned by a rise in tempe- 


* Communicated by the Author. 


of Electricity through Hot Gases. 309 


rature, | have during the last year made a series of experi- 
ments on the changes which take place in the electrical 
properties of gases when they are heated. 

Before describing these experiments I will sketch briefly 
the electrical properties of a gas, such as air, at the tempera- 
ture of about 16° C. In order to get electricity through the 
air at atmospheric pressure, the electromotive intensity has to 
exceed 30,000 volts per centimetre ; as the pressure of the 
air diminishes, the electromotive intensity required to produce 
discharge diminishes almost exactly in the same proportion. 
This goes on until the electric strength of the air reaches a 
minimum, after which any further diminution in the pressure 
causes the electric strength to increase; the pressure at which 
the electric strength is a minimum depending on the size and 
shape of the vessel in which the air is contained. 

These results are, I think, in accordance with the view of 
the electric discharge through gases which I gave in the Philo- 
sophical Magazine for June 1883, and which, I think, derives 
great support from some of the experiments described below. 
According to this view, the provision of a supply of atoms by 
the splitting up of the molecules is the essential accompani- 
ment of the electric discharge through gases. We may regard 
the atoms in the molecule as being in oppositely polarized 
states ; one atom behaving as if it were charged with a quantity 
of positive electricity, the other as if it were charged with an 
equal quantity of negative. When the atoms are together 
in the molecule they neutralize each other’s action at points 
outside the molecule, which behaves as if it were electrically 
neutral; but as soon as the atoms separate, since each one is 
essentially polarized, the gas acquires energetic electrical pro- 
perties, and by the motion of its atoms electricity can be carried 
from one part of the gas to another. The ease with which 
the gas can be made to conduct electricity depends upon the 
ease with which its molecules can be split up into atoms. 

Let us consider what, according to this theory, happens 
when a spark passes between two parallel plates. In some 
one or more of the molecules near the negative electrode the 
atoms separate, the positively charged atom goes to the nega- 
tive electrode and the negative atom is repelled. If F is the 
value of the electromotive intensity between the plates, d the 
distance of the molecule which is ultimately split up from 
the electrode, the work done by the electric field on the posi- 
tive atom when it reaches the negative electrode is F'de, where 
e is the charge on the atom ; the work done in the same time 
on the negative atom will not be greater than this, so that 
the whole work done on the atoms in the molecule will not 


2H 2 


360 Prof. J. J. Thomson on the Passage 


be greater than 2Fde. But if the molecule is split up by 
the electric field, the work done by the field must equal the 
difference between the energy of the molecule and its atoms, 
a constant quantity if the temperature remains constant. 
Thus Fd is constant, so that F must vary inversely as d. Now 
the effects produced by the collisions between molecules are 
probably so vigorous, that the electric forces trying to split 
up the molecules will have to commence their work afresh 
after each collision: in this case d is the free path of a 
molecule in the neighbourhood of the electrode, and the force 
required to produce discharge varies inversely as the free path 
and therefore inversely as the density. This investigation, or 
a similar one, will hold if we suppose that the splitting up of 
the molecules is helped by the presence of an “ electric double 
sheet’ near the surface of an electrode, corresponding to a 
definite difference of potential between the electrode and the 
gas, or whether we suppose short “ Grothaus chains” to be 
formed, and the splitting up to pass from one molecule in 
the chain to another, being helped by the chemical forces 
between the molecules. 

If we suppose the charges on the atoms to be the same as 
those deduced from electrolytic considerations, the force be- 
tween the atoms in the molecule is so much greater than the 
force tending to separate them, in a field of 30,000 volts 
per centimetre, that it seems almost necessary to assume that 
the decomposition is helped in some such way as has just been 
suggested. 

The increase in the strength when the density of the gas 
falls below a certain value may be accounted for by the 
diminution in the number of atoms available for carrying the 
electricity, by the interference of the vessel with the free path, 
and it may be by the increased difficulty of forming a 
“ Grothaus chain” in a rare gas. 

We onght also to notice that since Fd must be constant, 
and since d cannot be greater than the distance between the 
plates, the electric strength must be infinitely great when the 
distance between the plates is indefinitely small. 

According to this view, the molecules of a gas are essen- 
tially electrically neutral, and any electrification in the gas 
must be due to the presence of free atoms. Now the most 
careful experiments seem to show that air is incapable of 
receiving a charge of electricity ; for Nahrwold’s experiments 
(Wied. Ann. xxx1. p. 448) show that apparent exceptions to 
this rule may be explained by the presence of dust, either 
originally present in the gas or given off from the electrodes. 

Perhaps the most conclusive evidence of the impossibility 


_ of Electricity through Hot Gases. 361 


of communicating a charge of electricity to a gas in a normal 
state is afforded by Blake’s discovery (Wied. Ann. xix. p. 518), 
confirmed by Sohncke (Wied. Ann. xxxiv. p. 925), that the 
vapour arising from an electrified liquid is not electrified. 

The effect on the electric discharge of the disintegration of 
the electrodes seems to have been too much neglected. Me- 
tallic electrodes give off particles of the metal freely under 
many circumstances. Thus, for example, it has been known 
for a long time that they do so when they glow; and the 
recent experiments of Lenard and Wolff (Wied. Ann, xxxvii. 
p. 443) prove that they do so when exposed to ultra-violet 
light. Now a gas when exposed to ultra-violet light allows 
electricity to pass through it. This might either be due to 
the decomposition of the gas by the ultra-violet light (of which, 
however, there does not seem any direct evidence), or the 
discharge may be carried by the particles which the electrodes 
give off under the influence of ultra-violet light. The dis- 
covery by Wiedemann and Kbert, that electricity will not 
pass through the gas unless the cathode is illuminated, how- 
ever brightly the rest of the field may be illuminated, points 
to this explanation ; as Lenard and Wolff found that a posi- 
tively charged plate does not give off particles of metal when 
illuminated, though a negatively electrified plate does so freely, 
and an uncharged one also, though not to so great an extent as 
a negatively electrified one. 

Dr. Schuster has lately found (Proc. Roy. Soe. xli. p. 371) 
that a gas through which an electric discharge is passing is 
unable to insulate the smallest electromotive intensity due to 
a source independent of that producing the discharge. This 
is easily explained on the preceding view ; for the discharge 
splits up the molecules, provides a supply of atoms, and thus 
turns the gas into a conductor. In this case the atoms are 
supplied by the splitting up of the molecules hy the electric 
field. There are, however, other ways of splitting up the 
molecules, of which raising the temperature is one; it is 
therefore interesting to study the effect of heat on the elec- 
trical conductivity of gases. The following experiments were 
made for that purpose. 


Results of previous Haperiments. 


Previous experiments on the electrical conductivity of hot 
gases have given apparently conflicting results. Thus 
Becquerel, whose experiments have been confirmed by Blond- 
lot, found that hot air conducted ; while Grove could not 
detect any conduction between white-hot platinum wires sur- 


362 Prof. J. J. Thomson on the Passage 


rounded by steam ; and neither Maxwell nor Hittorff could 
find any trace of conduction through hot mercury-vapour. I 
have repeated all these experiments and verified the results. 
Hittorff found, too, that the conductivity of a fame was very 
much increased by putting volatile salts, such as the chlorides 
of sodium and potassium, into it, and that the increase in the 
conductivity depended on the nature of the salt. 


Methods of Hxaperimenting. 


I have used three different methods of investigating the 
conductivity of hot gases, as the method which is the most 
convenient for one gas is not always so for another. In all 
these experiments the conductivity of the gas was sufficiently 
large to enable the current sent through a centimetre or two of 
the gas by a few Daniell’s cells to be easily measured by a gal- 
vanometer of about 4000 ohms resistance. The galvanometer 
method, when available, is much more convenient and easy to 
use than the much more delicate one in which a leak through 
the gas is detected by an electrometer. Whatever method is 
employed it is essential that the current measured really 
passes through the gas, and is not due to the defective insula- 
tion of the electrodes which carry the current into it. The 
effective insulation of these electrodes requires considerable 
care, because no substance is known whose insulation can be 
trusted even at temperatures very much lower than those used 
in these experiments. It is therefore necessary to keep the 
places at which insulation is essential quite cool. The only 
really effective way of doing this is to keep such places well 
away from the hot gas and well screened from currents of hot 
air. In the following experiments this was done by making 
the upper part of the electrodes pass through vertical glass 
tubes, to which two long horizontal pieces of glass tube were 
fused; these pieces were about 8 inches in length, and were 
supported at the ends away from the electrodes by passing 
through holes drilled in solid pieces of ebonite, supported by 
retort-holders. These pieces of ebonite remained cool even 
when the gas had been kept at a white heat for some hours, 
and though they were tested repeatedly they were never found 
to leak. The electrodes were connected with the battery by 
long overhead wires insulated by pieces of sealing-wax placed 
so far from the hot gas that they never became appreciably 
warm. 

In the greater number of experiments the gas to be investi- 
gated was contained in a platinum tube made by Johnson and 
Matthey. It was 7 inches long and 1 inch in diameter. Into this 


of Electricity through Hot Glases. 363 


tube the terminals insulated in the way just described dipped. 
The platinum tube was wrapped round with asbestos tape, 
then placed in an iron tube, and the whole arrangement put 
into one of Fletcher’s muffle-furnaces, fed by 1-inch gas-pipe 
and a large air-blast worked by bellows such as are ordinarily 
used for forges. 

If the substance experimented on was solid or liquid at 
ordinary temperatures, the gas was produced by dropping the 
solid or liquid into the tube and allowing the vapour from 
it to drive the air out; if the substance was gaseous at ordi- 
nary temperatures, a stream of it was conducted through 
the stem of a clay tobacco-pipe to the bottom of the tube 
and allowed to run until it had driven the air out. 

The method of procedure was very simple. The electrodes 
in the tube were placed in series with the galvanometer and 
with a large Daniell’s battery arranged in boxes with twelve 
cells in each ; a reversing-key was placed in the circuit. When 
the gas had reached the requisite temperature, the supply of gas 
to the furnace was stopped, the battery put on one way, and 
the deflexion of the galvanometer read ; the battery was then 
reversed and the deflexion again read. Though the deflexions 
are given in some cases the results must be considered as 
qualitative rather than quantitative, as the temperature was 
only fixed by describing the glow from the tube as dull red, 
bright red, yellow, bright yellow, and white. 

It was found as soon as different gases were tested that 
they differed enormously in their power of acquiring con- 
ductivity by heating. Some of them, such as air or nitrogen, 
only acquired it to a very small extent; and I shall afterwards 
give reasons for believing that most of this can be accounted 
for by convection-currents produced by the disintegration of 
the electrodes. In other cases, however, notably for hydriodic 
acid gas, iodine vapour, bromine vapour, the vapour of sodium 
chloride, hydrochloric acid gas, the vapours of sodium and 
potassium, the gas acquired very considerable conductivity 
when the temperature exceeded a red light; so much so in fact 
that at a white heat two or three Leclanché cells were sufficient 
- to throw the light reflected from the galvanometer-mirror 
right off the scale. The difference between the conductivity 
for the two classes of gases is so great that it suggests that 
the method by which the electricity is conveyed from one 
electrode to the other is not the same in the two cases. 

It ought to be mentioned that even in the case of those 
gases which conduct best, there was not sufficient conductivity 
to produce a current that could be detected by the galvano- 
meter until the electrodes began to glow; and from some 


NN lS 


364 Prof. J. J. Thomson on the Passage 


experiments which I shall describe later I am inclined to think 
that in order for the electricity to get with ease from the 
gas to the electrodes the latter must be glowing (and there- 
fore disintegrating ?). 

The results obtained by using the platinum tube are given 
in the following table. The results for metallic vapours are 
not given here, as with this arrangement the temperature 
could not be raised high enough to volatilize many metals, so 
that a different method had to be used for these. 


Behaviour when heated to a 


Sulphur (surrounded by nitrogen). 
Sulphuretted hydrogen (ditto) 


Substance. yellow heat. 
J NTU er ae Pp OE A eee Small deflexion, about 10 or 12 di- 
visions for 156 Daniells. 
ETO EM cts e oaths cements Much the same as air. 
@anbonig acidy) i. es... eke ee Rather less than air. 
PAMIINONI cits eee ne KAR RIA Rather less than air. 
SLAM m0 .oh ns Sysop mips yeh ts Considerably less than air. 
Hydrochloric acid....... pide t Large deflexion ; spot driven right off 
scale by 12 Daniells. 
ny ditodic ACId, wiecia ssa e he vee .. Very large deflexion indeed; larger 
2 than for HCl. 
Sul plouricvacid Grice cruciate ks Small deflexion; very little more 
than air. 
NLA CACC crauste's «6 ae ole se ate Mee About the same as air. 
JOGMER 50066. 509505 5.0.0 2.08 Very large deflexion; comparable 
with HI. 
LS TONITE rca etssn: 0), 6 reg stay apes eear eke Large deflexion. 
POCASSUUM VORNDE cnn sinin vo nienn » Conducted fairly well, but not so 
well as HI, HCl, or I. 
SAI-AMMONIGCT 0.0.62 ht. ee Conducted well. 


Small deflexion. 
Very small deflexion until the tem- 


perature was raised to a white 


heat. 

IMETCUIY AS ait aie sie cre milo eee Very small deflexion indeed; much 
smaller even than air. 

Sodium chloride... .secssessees .. Large deflexion. 

Potassium chloride......0 sssses Large deflexion. 


In this table the gases which conduct well are printed in 
italics. Several of these are known to dissociate at high 
temperatures ; thus iodine and bromine are known to do so 
to a very large extent, and the dissociation of the vapour of 
hydriodic acid, perhaps the best conductor in the list, is 
rendered very striking by the change in the colour of the 
vapour, which is brown at low temperatures and purple at 
high. There are, however, many substances in the list whose 
dissociation has not been observed, and in some cases cannot 
be great: thus the experiments on the vapour-density of 


of Electricity through Hot Gases. 365 


hydrochloric acid at high temperatures, and Scott’s determina- 
tion of the vapour-density of KI, show that there cannot be 
any very great amount of dissociation for these substances. 
I thought, however, it would be interesting to test whether 
or not there was any dissociation of the KI and HCl, since they 
conducted electricity when raised to a red heat. The po- 
tassium iodide was tried first. The stem of a long clay tobacco- 
pipe was placed in the platinum tube, one end reaching down 
to the bottom (the hottest part) of the tube, the other end 
connected by a glass tube with a bulb filled with a solution of 
starch; another glass tube was fixed on to this bulb and con- 
nected with a water-pump, so that when the pump was 
working, the gas from the bottom of the platinum tube bubbled 
rapidly through the starch solution: it thus passed very rapidly 
from avery hot to a cold place, so that if any dissociation 
took place in the platinum tube the constituents might not have 
time to combine before passing through the solution, where 
the presence of free iodine would be detected. On trying the 
experiment, a very distinct blue coloration of the solution 
was obtained, though no such coloration was produced by 
driving hot air through the bulb just before the KI was put 
in the platinum tube. The experiment was repeated several 
times, always with the same results; and we may therefore 
conclude that free iodine was present, in other words, in the 
KI which conducted the electricity there was dissociation. 

A similar experiment was then tried with the hydrochloric- 
acid gas, the only difference being that the bulb now contained 
a solution of starch and iodide of potassium instead of a 
solution of starch alone. If the HCl is dissociated into H and 
Cl, and if these gases can be withdrawn from the hot platinum 
tube so quickly that they have not time to recombine, on 
bubbling through the solution the free chlorine will set free 
iodine from the potassium iodide and produce a blue colora- 
tion of the solution. On trying the experiment, the solution 
began to change colour as soon as the gas commenced to 
bubble through, and in less than a minute became almost 
black. This was not due to any oxide of nitrogen, because 
the coloration did not take place when air from the bottom 
of the hot platinum-tube was sacked through the solution, 
nor was it due to any impurity in the hydrochloric acid, for 
it did not occur when the HCl was allowed to bubble through 
the solution without being heated. 

A similar experiment was tried with NaCl, and free chlorine 
was found in the hot vapour of this gas, though the effects 
produced by it were not so large as in HCl, where the solution 


pa 


IEEE TOE “ART — 
bn af ie ae J 0 y a 


366 On the Passage of Electricity through Hot Gases. 


became black at once. Sal-ammoniac, another good con- 
ductor, is known to dissociate into ammonia and hydrochloric 
acid. In fact, whenever a gas became a good conductor when 
heated, I was able to detect dissociation by purely chemical 
means. 

The converse statement is not, however, true; there are 
many cases in which dissociation takes place without the gas 
acquiring the power of conducting electricity. Thus, take the 
case of ammonia; this at high temperatures is known to 
dissociate into nitrogen and hydrogen; but ammonia heated 
to a temperature above that of dissociation, the dissociation 
being proved by the absence of any effect on litmus-paper of 
the hot gas rising from the tube, was an excessively bad con- 
ductor, being worse than air. Again, steam at high tem- 
peratures dissociates into hydrogen and oxygen ; but steam 
even at these temperatures does not conduct electricity. The 
dissociation of the steam which woald not conduct was proved 
by sucking the hot gases quickly from the platinum tube; when 
a series of electric sparks were passed through the gases thus 
sucked over, a large condensation took place. 

There are, however, two kinds of dissociation—the one 
where atoms or unsaturated bodies are produced, as in the 
dissociation of iodine, bromine, chlorine, hydrochloric acid, 
hydrobromic acid, and hydriodic acid; the other where a 
complicated molecule is merely split up into simpler mole- 
cules, as for example ammonia, which at temperatures below 
that at which the molecules of nitrogen and hydrogen dis- 
sociate, dissociates into nitrogen and hydrogen molecules ; or 
steam, which at temperatures below that of the dissociation 
of hydrogen and oxygen dissociates into molecules of these 

ases. 

; It is the first kind of dissociation which is always accom- 
panied by conduction, while the second kind has little if any- 
thing to do with it. This is just what we should expect if we 
accept the view of the passage of electricity through gases 
given above, for in the first case we have the charged atoms 
which can carry the electricity, while in the second we have 
merely neutral molecules which have no such power. 


[To be continued. | 


Pnse7 >] 


XXXVIII. On an Apparatus for the Distillation of Mercury 
ina Vacuum. By WynpuAm R. Dunstan, M.A., F.C.S., 
Professor of Chemistry to the Pharmaceutical Society of 
Great Britain, and T. 8. Dymonp, F..C., #.C.S.* 


[From the Research Laboratory of the Pharmaceutical Society. | 
ISTILLATION of impure mercury constitutes the best 


method of removing foreign metals, and distillation in a 
vacuum is the only feasible plan of conducting the operation 
in the laboratory. It is doubtful whether mercury can be 
completely freed from zinc by distillation, and it is therefore 
safer to remove this metal, before distillation is resorted to, 
by agitating the mercury with warm concentrated hydro- 
chloric acid. 

Different forms of apparatus for distilling mercury in a 
vacuum haye been described by Weinhold, Weber, Wright, 
and Clark. The action of these different pieces of apparatus 
is primarily dependent on the same principle; but that de- 
scribed by Clark (Phil. Mag. 1884, xvii. p. 24) is undoubtedly the 
most convenient and is the form which is ordinarily used. It 
possesses, however, several disadvantages. It is inconveniently 
long, being at least 5 feet in length, and needs a special place 
in the laboratory where it must be permanently fixed. More- 
over the apparatus is only applicable when a comparatively 
large quantity of mercury is available, since at the con- 
clusion of the operation there remains in the apparatus 
between one half and one quarter of a litre of undistilled 
mercury, the amount being chiefly dependent on the diameter 
of the distillation-tube. To this residue more mercury must 
be added before distillation can be recommenced. 

The still we are about to describe does not entail these dis- 
advantages. It is easy and inexpensive to construct, and 
when once started is automatic in its action. It is rather 
more than a metre long, and when required for use can 
immediately be clamped on a retort-stand and may be as 
readily dismounted again. ‘The residue of undistilled mer- 
cury which remains in the apparatus is less than 20 cubic 
centimetres. 

The apparatus is constructed in the following manner:— 
A bulb A is blown on one end of a piece of thick-walled soft 
glass tubing B, and is made to assume somewhat the shape of 
an oblate sphercid, so that nearly the whole of the mercury may 
be distilled out of it. The other end of the tube has a small 


* Communicated by the Physical Society: read March 7, 1890. 


== SS ee 
PTT CEN NET meer | 


) 


368 Messrs. Dunstan and Dymond on an Apparatus 


elbow-bend to admit of its connexion with the reservoir H by 
means of the stout rubber-tubing G. The diameter of the 
bore of this glass tube is 3 millim., and its length 1 metre, 
measured from the point at which it joins the bulb to the 
bend at the other end. To the summit of the bulb is sealed 


(k 
D 
Te [—se II] 
B 
C 
G 
= F 
—— “Uf 


a plece of tubing which is bent round one side of the bulb 
and terminates in the limb C, which acts as a Sprengel pump. 
The length of the tube from the lower surface of the bulb to 
the bend at its other end is about 1 metre, and the bore has a 
diameter of 1:5 millim. The upper part of this limb, at a dis- 


ray 
) ij 


for the Distillation of Mercury in a Vacuum. 369 


chamber D for the condensation of the mercury vapour ; this } 
chamber is 1 decim. long and 1 centim. wide. The other end 1] 
of the limb is for convenience bent twice at right angles F, 


i 
tance of about 5 centim. from the bulb, is expanded to form a i 


and beneath it is placed a receptacle for the distilled mercury. 
The movable reservoir H, attached by means of at least | 
1 metre of stout rubber-tubing, known as “ pressure” tubing, 1 
to Hi is a large tap-funnel having a capacity at least twice . 
as great as that of the bulb A. It is provided with a tightly- 
fitting indiarubber cork carrying a small tapped tube K, which 
projects just below the cork, and a thistle-funnel L which . 
extends to the bottom of the reservoir. The apparatus is | 
supported by a clamp immediately below the chamber D, . 
and it rests on the bend E of the stout limb B. | 
Before the still is set in action it must be thoroughly dried. ) 
The reservoir H is then filled with dry mercury and raised | 
until the liquid has ascended to the summit of the bulb A, and . 
has commenced to fall over into the limb C. The reservoir 
is now slightly lowered, and by means of the tap J the flow | 
of mercury is checked until it falls only moderately fast (as 
in a Sprengel pump) down the limb C. In about five minutes 
the chamber D will have been exhausted of air. As soon as 
the sharp “click” of the falling mercury is heard and the 
descending column in C is almost continuous, the reservoir is 
lowered until the bulb A is about half full. The reservoir H 
is now adjusted to act automatically in maintaining a constant 
level of mercury in the bulb A. The stopcock J having been 
shut, the bulb is heated and the distillation allowed to proceed 
for about half an hour until the vapour-pressure of the 
mercury for the maximum temperature to which the bulb will 
be raised has been attained. Air is then sucked out of the 
tube K until bubbles pass up through the mercury, when the 
tap in K isinstantly closed. The tube of the funnel L now con- 
tains no mercury, the pressure of the air and of the mercury in 
the reservoir being exactly equal to the atmospheric pressure 
acting through L. The level of the mercury in the reservoir 
must now be adjusted until the surface of the mercury in the 
bulb is distant from the bottom of the reservoir (above J) by the 
height of the barometric column less the vapour-pressure of 
mercury for the temperature at which distillation occurs. This 
temperature having been ascertained, the adjustment may be 
made after direct measurement of the mercurial column. It may 
also be effected perhaps more readily by raising the reservoir 
little by little until on momentarily opening the stopeock J air 
is observed to bubble through the mercury. As soon as this 
occurs, the stopcock J is left open. The mercury from the 


) 


370 = Messrs. Dunstan and Dymond on an Apparatus 


reservoir H will now be automatically supplied to the bulb A. 
As the mercury distils out of the bulb more rises from the 
reservoir to take its place, and air enters from the funnel L 
and bubbles through the mercury in the reservoir into the 
closed space above. Through this action of the reservoir the 
level of the mercury in the bulb will remain the same until 
the whole of the mercury contained in the reservoir has been 
distilled. 

In order to heat the bulb A the tubes just below it are 
surrounded by the ring-burner M, which may be a circular piece 
of metal or glass tubing perforated at regular intervals with 
small holes; the flames proceeding from these perforations 
should be very small, and must on no account be allowed to 
impinge on the bulb or on either of the tubes. The bulb is 
now enclosed on all sides so that a hot air-chamber may 
result. This is best done by cutting a circular disk N, whose 
circumference is somewhat greater than that of the ring- 
burner, out of asbestos millboard, incisions being made to 
correspond with the tubes so that the disk may slide under 
the bulb and rest on the burner itself. On this disk as a 
base a cylinder of the same material, or of glass, is placed, 
the cylinder being wider and taller than the bulb. The 
cylinder is closed at the top by a rather larger and circular 
piece of asbestos millboard, in the centre of which a small 
round hole should be cut. By partially or entirely cover- 
ing this hole with a small disk of millboard, it is easy to 
regulate the admission of air to the chamber. The cylinder 
is prepared from the millboard by thoroughly wetting it and 
rolling it round a bottle or wooden block of the proper size. 
When dry the cylinder is removed and secured by twisting a 
piece of thin copper wire round it. The bulb is thus heated 
in the air-chamber, and not by direct contact with the flames, 
and the bulb is effectually protected from the disastrous 
effects of draughts of cold air. 

The temperature of the air-bath when distillation is pro- 
ceeding ranges between 200° and 300°C. Since fresh mer- 
cury is automatically supplied to the bulb the still requires 
no attention, and may safely be left at work day and night 
provided that the gas pressure is almost constant. This may 
of course be ensured by fixing a gas-regulator in the air-bath. 
We have found, however, that an ordinary Sugg’s dry governor 
introduced between the gas supply and the burner answers 
the purpose sufficiently well. 

When the still is started for the first time the air-film on 
the glass is detached and passes away down the limb C. The 
distillation consists in continuous evaporation from the 
liquid surface unaccompanied by actual ebullition, or by the 


Jor the Distillation of Mercury in a Vacuum. 371 


“bumping ” and spirting which are so noticeable when mer- 
eury is distilled under the ordinary atmospheric pressure. 

The rate of distillation is mainly dependent on the capacity 
of the bulb A. We have generally worked with a bulb 
rather smaller than that described above, because it is easier 
to blow it of sufficient thickness. As the still is automatic 
in its action and needs no attention the quick distillation of 
a large quantity of mercury is not a point of much importance. 
It has frequently happened that the distillation has come to 
an end during the night, both the reservoir and the bulb being 
discovered nearly if not quite empty. This, however, has oc- 
casioned no inconvenience ; it is only necessary to introduce 
more mercury into the reservoir and from thence into the bulb. 
This can be done without extinguishing the burner. ‘The 
stopcock J is closed and the tap K is opened. Mercury is then 
poured through the funnel L. The stopcock F is now opened 
very oradually, so that cold mercury may not suddenly rush 
against the hot glass, until the bulb is half full, when the stop- 
cock J is closed again. A piece of rubber-tubing i is now attached 
to K, and air is sucked out until bubbles begin to rise through 
the mercury in the reservoir, when K is shut ; after the lapse 
of about half an hour the stopcock J is opened. When a dis- 
tillation has been finished and the apparatus is not further 
required for the present, it may be left standing with the 
stopcock J closed, and the end F dipping into mercury or 
otherwise sealed ; it can then be started again at any moment. 
To empty the still, F is closed and the apparatus is carefully 
tilted so that the mercury remaining in CU may flow into the 
chamber D. If now the end F be cautiously unclosed air will 
enter the apparatus through the empty limb C., 

When this apparatus is at work in a dark room the re- 
markable phenomenon of the “flashing”? of mercury is 
observed. Itis seen in the condensation-chamber D. As the 
mercury liquefies flashes of green light are produced, which 
exhibit the spectrum of mereury. It would seem that this 
is an electrical effect arising from friction between mercury 
and glass. We have noticed that it is enormously intensified 
when one of the dischargers of a Wimshurst machine is 
brought near the chamber ‘D. Under these circumstances the 
entire chamber becomes illuminated with a magnificent green 
light. 

The apparatus may also be conveniently employed for 
observing the electrical discharge through mercury-vapour at 
different temperatures. For “this purpose the ascending 
column of mercury in B and the descending column of mer- 
cury in © are used as electrodes. One terminal from the coil 
dips into the mercury in the reservoir H, the other into the 


— ee ES a pe eats Ea eee Pee =a 
GS Pe ew 1 > , “ap 
oe we 


Ee er 


— Se 


———— 


eee 


Te eT AS ARE Ee es 


oe 


372 Notices respecting New Books. 


distilled mercury which has collected in the receptacle under 
I’, and below the surface of which the extremity of the tube 
C is immersed. 

We are now making observations on the character of the 
discharge which occurs under these conditions, in the absence 
of any foreign metal. 


XXXIX. Notices respecting New Books. 


Transactions of the Edinburgh Geological Society. Vol. VI. Part 1. 
8vo. Edinburgh: 1890. 


I. ME: RALPH RICHARDSON, W.S., in an Inaugural Address 

gives a detailed and at the same time a comprehensive view 
of “ Darwin’s Geological Work,” and warmly insis's on the good 
results of his researches and published views: and he appends a 
list of Darwin’s geological writings. II. “The Classification, 
Determination, Distribution, Origin, and Evolution of the Normal 
Micas,” is the title of a paper by Mr. A. Johnstone, F.G.S. He 
arrives at the conclusion that—as the mica in recent igneous rocks 
is almost always biotite, and that this must therefore have been a 
product of igneous fusion,—and, as the micas of the older rocks 
are referable to biotite, hydrobiotite, muscovite, and hydremuscovite, 
the first may be safely considered as the original mica, and the 
others as varieties derived from it by water, CO,, and other natural 
agents. III. The supposed High-level Shell-beds in Easter Ross 
are shown by Mr. Hugh Miller to be only recent mussels and lim- 
pets thrown out on the blown sand which has now invaded the 
village. ‘IV. Mr. John Henderson treats of “‘ The Succession of the 
Lower Carboniferous Series to the West of Edinburgh, with special 
reference to the district around Cramond.” This is in continuation 
of former researches, and is to be followed by remarks on higher 
beds in a future paper. V. “An Old Manand Woman; or Human 
Bones in a Scrobicularia-bed at Newton Abbot, Devonshire,” are 
described by W. Pengelly, F.R.S., in a paper of remarkable per- 
spicuity and interest, every point of observation and treatment 
being well and clearly dealt with. The conclusion arrived at is 
that ‘‘the man and woman represented by the relics under notice 
were as old as the era of the deposition of the Raised Beaches of 
Devonshire, and therefore older than the period of their upheaval ; 
but for this we are by no means unprepared, as the mollusks of the 
said beaches limit them to a Post-glacial age; and the caverns of 
the neighbouring Torbay district have undoubtedly established for 
Devonshire Man a very early Post-glacial, if not, as I believe, a 
Pre-glacial Antiquity.” VI. “Improvements in the Methods of 
determining the Composition of Minerals by Blowpipe-Analysis,” 
by A. Jobnstone, F.G.S., is a very careful mineralogical paper, 
treating of the improved and newest methods and results, as 
more particularly set forth under the headings (A-J) in Tables of 
the operations of qualitative blowpipe-analysis at pages 47-52. 
VII. This is the Anniversary “Address on Recent Progress in 


a 


Intelligence and Miscellaneous Articles. 373 


Paleontology as regards Invertebrate Animals,” by Prof. H. A. 
Nicholson, M.D., D.Sc., F.G.S. After pointing out the false 
position taken by those who would suppress Paleontology as an 
independent branch of Biology, he proceeds to mention the dis- 
covery of the probably Foraminiferal structure of some oolitic 
grains,—of the probable occurrence of Radiolaria in Ordovician 
chert of South Scotland, and of the possible proof of fossil Radio- 
larian deposits being of deep-sea origin,—of the recent advances 
in our knowledge of fossil Sponges,—of the Stromatoporide and 
the true Hydrocorallines,—of the true Coral groups and other 
Coelenterata,—the Monticuliporoids also, and the fossil Echino- 
derms, Annelides, Crustaceans, Arachnides, Insects, and Polyzoa. 
The Brachiopoda and Mollusca proper are slightly touched on, 
except the fossil Pteropods, which are more especially treated of. 
In conclusion Dr. Nicholson states “that the ascertained facts of 
Paleontology indicate, with an ever-increasing clearness, the exist- 
ence of some general law of Evolution, by the operation of which 
new forms of life have been successively introduced upon the earth. 
As to the precise modus operandi of this general law, Paleontology 
does not, in my opinion, at present afford a decisive answer. That 
one great factor in the process has been the operation of ‘Natural 
Selection,’ as explained and defined by Darwin, does not, I think, 
admit of reasonable doubt. That ‘Natural Selection’ has been 
the sole agency at work is, however, a different and more doubtful 
point; and Paleontology, at any rate, does not seem to me to be 
yet in the position to supply the final solution to this most difficult 
and complex problem.” 


XL. Intelligence and Miscellaneous Articles. 


ON ELECTRICAL VIBRATIONS IN STRAIGHT CONDUCTORS. 
BY PROF. J. STEFAN. 


HE distribution of a constant electrical current in a conductor, 
or its branching into several conductors, takes place in such a 
manner that, for the same strength of the total current, the disen- 
gagement of heat, according to Joule’s law, isa minimum. ‘This 
principle has been demonstrated by Kirchhoff for conductors ot 
any given shape. It holds, however, only when the individual parts 
of the conductor contain no special electromotive forces ; it does 
not hold therefore for variable currents in which inductive actions 
occur in the conductors. 

In currents of rapid variability, particularly with periodical 
currents of very high number of vibrations, the influence which the 
resistances exert on their regulation becomes less In comparison 
with those of the inductive actions ; and with periodic currents to 
the greater extent the higher the number of vibrations. In solving 
many questions relating to the behaviour of such currents we can 
entirely neglect the resistance of the conductors, and can use 
equations which hold for currents in conductors without resistance. 
G. Lippmann was the first to direct attention to these equations 
and their application. 


Phil. Mag. S. 5. Vol. 29. No, 179, April 1890. ap Oh 


Sy r= a, 
SEERA 
ee 


374 Intelligence and Miscellaneous Articles. 


From these equations we may deduce the following principle :— 
The branching or distribution of a variable current takes place in 
such a manner that for any time its electrodynamic energy is a 
minimum for the same magnitude of the total current. As this 
energy may also be represented as a magnetic one, which has its 
basis in the magnetization of the conductor and of the medium 
surrounding it, the principle may also be so expressed. The dis- 
tribution of the current takes place in such a manner that for the 
same magnitude of the total current its magnetic energy is a 
minimum. 

In a straight conductor of circular section, which is exposed 
to no lateral actions, electrical currents can only be symme- 
trically arranged about the axis. In whatever manner the 
density of the current may vary from the axis towards the surface, 
the external magnetic action of the conductor is the same as if the 
entire current was concentrated in the axis. The minimum of 
magnetic energy is determined, therefore, by the fact that this 
energy has the smallest value in the space occupied by the con- 
ductors. This smallest value, and indeed the value zero, is attained 
when the entire current is condensed in an infinitely thin layer on 
the surface of the cylindrical conductor, for such a current-tube 
has no magnetic force on the space enclosed by it. 

If the section of the conductor is not circular there is also a dis- 
tribution of the current on the surface which makes the magnetic 
action at any point in the interior equal to zero, and corresponds 
to the minimum of magnetic work. ‘This distribution is conform- 
able with that which an electric charge acquires when it is on the 
conductor in a condition of equilibrium. Just as the resultant of 
the electrical forces of such a charge is zero at any point of the con- 
ductor, this is also the case with the resultant of the various cur- 
rent-filaments lying in the surface, if the density of the current 
along the periphery varies in the same manner as the density of 
the statical electrical charge. If, for instance, the section of the 
conductor is bounded by an ellipse, the densities in the various 
points of the ellipse will be as the perpendiculars which fall from 
the centre on the tangents to these points. 

In his last published. experiments H. Hertz has given very 
striking proofs that electrical vibrations of very high frequency 
can only move along the surface of the conductor. It also follows 
from his observations on such movements in band-shaped conductors, 
that the density of the current at the edges of the band is far 
ereater than that in the middle of the broader side. 

It may here be observed that the principle of distribution pro- 
pounded not only serves for estimating the deportment of vibra- 
tions, but may also be applied to rapid electrical impulses, such as 
hghtning-flashes, or constants of very short duration. 

The velocity with which electrical waves travel in a conductor 
depends on the product of two factors—the coefficient of self- 
induction, and the capacity, both referred to unit length of the 
conductor. With the distribution of the current-density on the 
surface of a conductor, described above, the magnetic energy, and 


Intelligence and Miscellaneous Articles. 378 


therefore also the self-induction, is independent of the magnetic 
nature of the substance. In consequence of this, electrical waves 
of high periods travel in an iron wire with the same velocity 
as in one of copper. According to an experiment made by Hertz 
this, as a fact, is the case. Hertz explains this by the assumption 
that the magnetism of iron cannot follow such rapid vibrations. 
According to what is here stated the matter is much simpler: the 
iron remains free from any magnetic action of these vibrations. 
From the experiments of H. Hertz, it results that the propaga- 
tion of electrical waves in thin and thick wires takes place with 
the same velocity. According to the distribution of such waves on 
the surface of a conductor, it follows that this velocity in a straight 
conductor is independent, not only of the magnitude, but also of 
the form of the section. The coefficient of self-induction may be 
expressed by twice the potential ef the electrical charge on itself 
divided by the square of the quantity. [fin calculating the potential 
of the current we take the formula propounded by Neumann for the 
potential of two elements of current, this, in a straight conductor in 
which only parallel elements occur, reduces to the potential of two 
elements of the statical charge. If now the current-density as well 
as that of the charge in the surface are divided according to the 
same law, the same calculation must be made to determiné the two 
potentials. Both are in like manner dependent on the size and 
shape of the section; and accordingly the product of the coefficient 
of induction and the capacity, as well as the velocity of propagation 
of the waves, are independent of the size and form of the section. 
The identity in the form of the electrodynamic and electrostatic 
potential has the consequence that the distribution of the current 
on such conductors as are parallel, and not connected with each 
other, may be determined by the rules of electrostatics. Here the 
potential of a conductor, which is only evoked by the induction of 
the other, must be called zero.— Wrener Berichte, January 9, 1890. 


ELECTRICAL VIBRATIONS IN RAREFIED AIR WITHOUT 
ELECTRODES. BY JAMES MOSER. 


Incited by the view of Heaviside and Poynting, that electrical 
vibrations penetrate inte a wire from the surface, and influenced 
by Hertz’s experiments with the wire cage*, the author has used 
rarefied spaces without electrodes as conductors in which electrical 
vibrations occur. 

A glass tube which contained a gas of constant rarefaction was 
surrounded with a wider tube, and the rarefaction varied in this 
by means of the air-pump. The following results were obtained :— 

(a) At the ordinary atmospheric pressure in the outer tube the 
inner tube becomes luminous. 

(6) With a sufficient rarefaction of the outer tube the pheno- 
menon is reversed; the inner tube becomes dark and the outer one 
luminous. Here there is obviously a screening action. 


* Wiedemann’s Annalen, xxxvil. p. 395. 


ee 


376 Intelligence and Miscellaneous Articles. 


In the course of the preceding research the rarefaction was 
pushed still further, and 

(c) The outer tube was again dark, the inner one luminous ; so 
that to the eye this third stage was like the first one. 

The more perfect vacuum exerts therefore no screening action ; 
it has lost the power of conducting the electrical current.— Wener 
Berichte, January 9, 1880. 


ON THE FORMATION OF OZONE BY THE CONTACT OF AIR W1TH 
IGNITED PLATINUM, AND ON THE ELECTRICAL CONDUCTIVITY 
OF AIR OZONIZED BY PHOSPHORUS. BY PROFS. ELSTER AND 
GEHITEL. : 
The authors sum up the results of their investigations in the 

following terms :— 

(1) Incandescent surfaces of platinum ozonize the surrounding 
air, even when combustions are excluded. 

(2) When air is ozonized by contact with moist phosphorus 
it is seen to conduct electricity in the same manner as the gases of 
flame do. 

(3) It could not be found that this process of ozonization had 
any electromotive force, or that the air which had been subject to 
it had any unipolar conductivity. ; 

(+) The mere presence of ozone already formed, as well as the 
bie production of clouds from ammoniacal salts in the vicinity of phos- 

phorus, are not connected with the origination of the conductivity 
of the surrounding air, or at any rate only to a subordinate extent. 

ai | —Wiedemann’s Annalen, March 1890. 


Se hee 
n 


= ve 
>= 


= = = < ———— —— ie! a = aaa ee er 
— = we = Spt ale ra hb yaar oy ae a NE ee « 
Le ale GEG ram. SS pa ee SO ame See aera ag Ee RE Ce 
ip png lee Ae aga ey NTA, gel Oe ES a OS F Cn ear a 


be antl Listed. 
a el 


NOTE IN CONNEXION WITH DROPPING-MERCURY ELECTRODES. 
i BY J. BROWN. 
if i ; In the Zeitschrift fiir physikalische Chemie, iv. p. 577, there is a 

i reference by Prof. Ostwald to my paper on ‘‘ Helmholtz’s Theory 
of Mercury-dropping Electrodes,” communicated to the Philoso- 
. phical Magazine for May 1889 by Dr. Lodge, as secretary to the 
Electrolysis Committee of the British Association. 

Prof. Ostwald, however, considers only one of my experiments, 
. viz. that which deals with the current in a wire connecting the 
“fee dropping mereury with the mercury resting on the bottom of the 
vessel containing the electrolyte in which the drops form. My 
experiment shows that this current varies in a direction inverse to 
the change of resistance of the electrolyte, and is therefore con- 
ducted by the electrolyte, and does not consist of charges carried 
down by the drops as assumed by Helmholtz. 

It is perhaps unnecessary to refer to Prof. Ostwald’s criticism 
further than to point out that his method of explaining away my 
ne conclusion is inconsistent with the fact brought forward by me, 
“ee but apparently not considered by Prof. Ostwald, that the current 

flows just the same whether the drops fall into the resting mercury 
Wee or not, provided they form in the electrolyte in contact with the 
As resting mercury. 


THE 
LONDON, EDINBURGH, ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES. ] 


HEA Ye 03830: 


~XLI. A New Form of Electric Chronograph. By Rev. 


Freperick J. SmitH, W.A., Villard Lecturer in Mechanics 
and Physics, Trinity College, Oxford™. 
[Plate IX. | 


URING the last two years a research has been carried 
on by me on the subject of the acceleration-period of 
explosionst. In order to deal with the time-measurements 
which arose out of the investigation, it was found necessary 
to devise a chronograph which would register a large number 
of events following each other after small periods of time. As 
the chronograph used in these experiments has been found to 
be of use in other branches of scientific work, viz. in deter- 
mining the velocity of shot, and many physiological time- 
measurements, I beg to offer an account of its construction 
and use to the readers of the Philosophical Magazine. The 
instrument has been called the Hlectric Tram Chronograph, 
because the moving surface is carried upon wheels running 
on rails. 

The instrument has, in common with other forms of time- 
measuring instruments, a moving plate on which traces are 
made by means of electromagnetic styli. In other respects it 
greatly differs from other forms of time-measuring instruments. 

In order that an electric chronograph may be of general 


* Communicated by the Author. 
+ Proceedings of the Royal Society, xlv. p. 451, 


Phil. Mag. 8. 5. Vol. 29. No. 180. May 1890. 2G 


——- Sia NET onenos z oS ee ee ae re a mon a CS eke = ae 


. ~~ 
paisa avi 
he Sep ser ent oe 


LASTS NTE gfe. toa 
TLE ey ee : a 
BPs ake y ee ee Man ih eg 


7 eee 
' 


378 Rev. F. J. Smith on a New Form 


use, several conditions have to be complied with; some of 
these are as follows :— 

(1) The moving surface on which the time-traces are made 
should be both long and wide. It should be long, so that 
periods greatly differing in their duration may be recorded 
on the same surface close together. It should be wide, so 
that a large number of time-determinations may be made and 
compared side by side on the same plate. 

(2) The experimentalist should be able to vary the velocity 
of the moving surface. 

(3) The surface should so move that all the time-traces may 
be in straight lines, and the velocity of the surface should be 
uniform during an experiment. The necessity for uniform 
movement is forced upon one by the experience of the diffi- 
culty found in subdividing a tuning-fork trace as recorded 
by a pendulum-chronograph. When a time-record is made 
on a surface which is moving at a uniform velocity, the diffi- 
culty of accurately subdividing a single vibration at once 
disappears. 

(4) The marking-points of the electromagnetic styli, 
actuated by springs, when released from an electromagnet, 
should make a sharp and definite mark ; also the time between 
the breaking of the circuit and the marking should be as 
short as possible, and it should be constant in value. 

These ends have been attained in the following manner :— 
To a vertical carriage, running upon wheels, between two rails, 
a sheet of smoked glass is fixed. The carriage is impelled by 
means of a cord attached to a weight ; after the weight has 
acted upon the carriage through a certain length of fall it is 
arrested, and the carriage moves with the velocity it has 
attained : this velocity is found to be practically constant for 
the whole length of the trace. It will be noticed that this 
arrangement embodies the principle of the Atwood machine. 
It will also be noticed that the impulse given by means of the 
falling weight gives a maximum velocity at the point where 
its pressure is taken off. With respect to pressure given by 
a spiral spring, as used in the well-known shooter employed 
in physiological work, exactly the opposite of this takes place. 
The writing-points of the electromagnetic styli and the tracing- 
point of the tuning-fork are placed so as to mark the moving 
surface. 

The distance between the markings of the styli is obtained 
in terms of the length of the vibrations of the fork : from this 
the time between two or more markings is determined. This 
will become clear from the consideration of the following 
detailed description of the instrument. 


of Electric Chronograph. 379 


The rails.—Two steel rails, A B and C D, each 2 metres long 
(Plate IX. fig. 1), are attached to three cast-iron standards : 
two of these, Mand N, are shown. WHach standard is fur- 
nished with two levelling-screws. The upper rail is adjustable, 
so that it may be placed parallel to the bottom rail, and at a 
correct distance from it for the width between the wheels of 
the carriage. (The rails are slightly inclined from D to C.) 

The carriage, EF, is built up of bars (which are not shown) 
so as to be both light and rigid. It runs upon three wheels, 
each wheel being carried on two steel points ; the points are 
adjustable, so that the face of the carriage can be placed 
parallel to the plane of the rails. To the front of the carriage 
a sheet of smoked glass is fixed with clips and screws. The 
carriage is furnished with a catch which engages with a detent 
at H ; by this it is held back against the pull due to the weight, 
W, until required to run past the styli. A projection at the 
back of the carriage engages with a leather brake-band. 

The brake.—A band of leather, L, is fixed to the standard, 
M, and also to a strong spiral spring at the back of the upper 
rail: the projection previously mentioned rubs under the band 
and brings the carriage to rest without any concussion. 

The weight.—A gut-band or cord, passing over the pulleys, 
Q, P, R, is fixed at G ; it is provided with a small ball which 
engages with a fork fixed to the back of the carriage. The 
weight impels the carriage until it is arrested by contact with 
an adjustable table T; the carriage then runs on with the velo- 
city acquired. The velocity is found to be practically uniform 
throughout the whole length of a time-trace. The cord, if 
free, has a velocity approximately double that of the driving- 
weight. 

eRe omingnstic stylii— These are shown at AA (fig. 2). 
An electromagnet of peculiar construction is mounted upon a 
brass plate, which carries a T-shaped lever ; to this a writing- 
point of aluminium, mica, or parchment-paper is attached. 
The lever is held by the electromagnet, as long as a current is 
acting upon it, against the pressure of a spring: when the 
current is broken the lever rises and gives its marking. The 
electromagnet is so constructed and wound that its period of 
“latency” is exceedingly small, and also constant within 
close limits. By means of a flat rectangular spring the stylus 
is attached to a pillar furnished with a sliding-holder B: each 
stylus can be easily adjusted to a vertical line for experiments 
in which a large number of markings are required in succession. 

The pillar-support.—lt has been found that, unless the sup- 
port of the styl is free from vibration, the trace produced by 
them is not worth much. The pillar used in connexion with 


2G 2 


art 
— Se 


EE ea. Eee ee 
: * ae 7 


380 Rev. F. J. Smith on a New Form 


the instrument consists of a heavy iren casting, C C (fig. 2) 
fitted with a slide, B, the slide can be raised or lowered by 
means of a screw with a milled head, the styli are attached 
to the slide B. By raising the slide after each experiment a 
large number of traces can be made side by side, and by the 
addition of an extra carrier as many as 10 stylican be carried. 
The pillar can be rotated on a triangular base, which is sup- 
ported upon three levelling-screws. The screws rest after the 
method of Sir W. Thomson, viz. in a hole, a groove, and ona 
plane, on the slab which supports the chronograph. The 
points of the styli are adjusted to the face of the glass by a 
screw. A simple pillar, A’, can also be used when only one 
set of traces is required. 

The tuning-fork.—A tuning-fork T is carried upon a pillar, 
which slides upon a block in which a V-groove is cut; a screw- 
stop limits its position against the glass. The fork may be 
driven electrically, or it may be excited otherwise. In the 
experiments on explosions the fork was started by means of a 
wedge, which kept the prongs apart, being suddenly with- 
drawn by means of an electromagnet. 

The latency of electromagnetic styli— While going through 
a large number of papers upon investigations in which electro- 
magnets were used for measuring time, it was found that in 
nearly all cases it had been assumed that the armature of an 
electromagnet was detached at the instant of the circuit being 
broken ; also, that in two instruments of similar construction 
the armature was released at the same instant. Several electro- 
magnets of chronographs were examined: in some cases, where 
much iron was used in the cores, the time between breaking 
and release of the armature was as much as 0°04 second ; also 
two apparently similar shaped electromagnets with similar 
windings, equal currents being used, differed in their action by 
some hundredths of a second. The experiments showed in a 
very definite manner that some electromagnets were not to be 
depended upon for close and accurate work. 

In order to produce an electromagnetic stylus free from 
these evils a large number of experiments were gone through 
on the relative proportions of the cores and their yoke, also 
upon the winding. It was found that the yoke should be made 
large as compared with the cores; the dimensions finally 
adopted were :— 


Cores) 5 0. 2 millim. diam. ; 10 million 
Yoke . .°. . 20 miilim. x5 millim. x5 mall 


The method of measuring the period of delay spoken of, 
which may be called the latency of the stylus, is as follows, it 


of Electric Chronograph. 381 


may be taken as an example of the way in which the instrument 
is used (see fig. 3) :—A piece of warm glass is smoked over 
the flame of a paraffin lamp furnished with a wide wick ; it 
is then attached to the carriage, and the stylus to be tested is 
adjusted to the surface of the glass, also the tuning-fork is ad- 
justed so that its writing-point lightly touches the glass ; an 
electric circuit is then completed through the break I (fig. 2), 
and the stylus prepared for giving a signal. The carriage is 
then brought slowly past the stylus, the result of which is that a 
vertical mark I H (fig. 3) is produced; the carriage is then 
held back by the detent, the stylus is again prepared, by the 
armature being caused to touch the poles of the electromagnet, 
the fork is excited, and the carriage released: the markings 
K N ML and A B are then produced. The tuning-fork point 
is brought against the glass so that a straight line may be 
drawn by it, the intersections of this with the curved line deter- 
mine the limits of any vibration. The length of the traverse 
I N, duly turned into time, is the latency of the stylus. Lines 
are drawn by a needle’s point through the points I and N, cut- 
ting A Bin EF; the value of H Fis then determined by means 
of a micrometer microscope, constructed as shown in fig. 4, 
In all cases of estimating time the fork is excited for each 
observation, the writing-point of the fork being placed verti- 
cally above the writing-points of the styli, so that the velocity 
of the moving surface is common to both the fork and the 
stylus. The needle-point for scribing the vertical lines is 
carried on a kind of dividing-engine. The styli are found to 
have a latency of almost perfect constancy, its value being 
0:0003 second. The first stylus constructed by me, and used 
in the Physiological Laboratory of the University, was not 
proportioned as the later ones have been; it was tested by 
Prof. G. F. Yeo, and his result published in the ‘Journal of 
Physiology, vol. ix. nos. 5 and 6, gave as a value of latency 
000062 sec. The improved result, viz. 0°0003, has been 
arrived at by a careful selection of the iron used, and a modi- 
fication of the winding of the bobbins ; by the reduction of 
the latency the marking is rendered much more definite and 
readable. The two facsimile tracings (fig. 5) show the nature 


of the markinys of a time-trace of a slow explosive wave. BA 
or BA equals 0:00227”. 

The micrometer-microscope is mounted on a bridge HF 
(fig. 4) attached to an inclined table A B; it is carried by means 
of a slide, which permits movement parallel to the trace which is 
put under it; the slide is moved by a screw having 40 threads 
to the inch ; the screw has a micrometer-head divided into 25 
large divisions, each of these is again divided into 4 parts, so 


enn warn get 


382. On a New Form of Electric Chronograph. 


that 25 x 74) =aobo of an inch can be read with ease. The 
microscope is furnished with a fine fibre which is brought 
over the trace to be measured; a rod of rectangular section 
HK is attached to two links or rods, L H, M K; the links 
being equal and moving about the points M, cause the rod to 
move always parallel to itself; upon the rod the trace rests; 
any part of the trace can be brought under the microscope. 
The markings appear as rather wide lines of light; a V-shaped 
scale in the field of the instrument enables one to bisect these 
lines. Fig. 3 gives an illustration of its use. The centre of 
the field is brought over C, the index of the micrometer-screw 
being at zero; then the microscope is moved by the screw till 
the centre coincides with D. The length CD is then re- 
corded, let it be L; then the micrometer is brought to zero 
again, and E is brought under the centre, and H F is then 
measured in the same manner as CD, let it bel; then, if 
az denote the time of traverse over E I’, and ¢ the time of one 
vibration, 
| Dien ea oh ce 


and 

nee 
or 
Fractions of a vibration can thus be easily estimated with 
great accuracy. This proportional method of subdividing the 
vibrations depends upon the fact that the velocity of the 
carriage is practically uniform. 

The method of preserving time-traces.—After the smoked 
glass has received records of time-traces it may be preserved 
by being varnished. It is a somewhat difficult matter to 
cover a smoked plate with photographic varnish without 
making either streaks on the plate or removing a good deal of 
the carbon surface ; but if the varnish be diluted with about 
25 times its volume of strong methylated spirit, it may be 
poured over the plate without injuring the trace. When it 
has dried off ordinary photo-varnish may be applied without 
any risk of doing harm. In the first case the plate should 
be cold, in the second it may be a little heated before a fire 
previous to the application of the thicker varnish. The traces 
can then be used as negatives to print from in the usual way. 
Eastman’s bromide-paper in rolls has been found to be most 
convenient for reproducing the traces. One of these is shown 
at fig. 5. The lines are thicker than those usually made, as 
a thicker deposit of carbon was used to get a very dense 
negative to make a print for this communication to the Philo- 
sophical Magazine. 


Electrical and Chemical Properties of Stannic Chloride. 3838 
I wish to add that Mr. A. W. Price has greatly assisted 


me in the manufacture of the new instrument. The method 
of increasing the velocity of the carriage by the introduction 
of a pulley attached to the driving-weight is due to him. 


XLII. On the Electrical and Chemical Properties of Stannie 
Chloride; together with the Bearing of the Results therein 
obtained on the Problems of Electrolytic Conduction and 
Chemical Action.—Part 1. Haperimental Observations. 
Part Il. Theoretical Considerations. By WARD COLDRIDGE, 
B.A., Scholar of Emmanuel College, Cambridge*. 


INTRODUCTION. 
l E \HE germ from which this work has been developed was 


found in Faraday’s statement that Stannic Chloride is 
a nonconductor. In the first instance this led to an investi- 
gation of the lower-limit of its conductivity ; the result which 
is here recorded was submitted to the Meeting of the British 
Association at Bath in 1888 by my friend Mr. W. N. Shaw, 
Fellow of Emmanuel College, who experimented with me on 
this point: in the second instance I examined the condition 
‘requisite for the development of electrolytic power; the 
results obtained are here for the first time recorded. 

It is claimed that, by taking advantage of the suitable 
chemical and physical properties of stannic chloride, a defi- 
nite advance has been made towards the resolution of the 
ambiguous statement that “‘ heterogeneity is necessary for the 
development of electrolytic power,” and that the results of 
Part I. throw light on the nature of an effective impurity, 
and in so striking a manner exhibit the parallelism between 
the chemical and electrical properties that the conviction 
arises of an ultimate explanation common to both. I have 
endeavoured to arrive at a single consistent view which shall 
explain the phenomena observed ; and in stating the idea I 
have carefully abstained from wandering into disquisitions on 
other ideas, as that of Arrhenius’s vagrant atoms, which, 
according to my notion of the stability of the fundamental 
chemical molecule, are untenable. 

The field of research from which these results have been 
gathered is a fertile one. Incidentally some opportunities 
are mentioned: I am conscious that pure pentachloride of 
antimony, inter alia, would yield interesting results. 

With much pleasure I acknowledge my indebtedness to 


* Communicated by the Author 


a ne a A 


Se Te PIE Mal eet ao Bye Sos en 


384 Mr. W. Coldridge onthe Electrical and 


Professor J. J. Thomson, F.R.S., for the suggestion of ex- 
amining the conductivity of the chloride at the boiling-point ; 
and to W. N. Shaw, Hsq., as well for the use of his room at 
the Cavendish Laboratory as for the interest he has kindly 
evinced in my results ; and, lastly, to Professor Dixon, F.R.8., 
who has kindly read my manuscript. | 


Part I.—ExPERIMENTAL OBSERVATIONS. 


Preparation of Stannic Chloride.—Stannic chloride was 
prepared by passing a current of dry chlorine gas over melted 
tin. The collected distillate was a yellow powerfully fuming 
liquid ; the yellow colour was due to an excess of chlorine, 
which was removed by allowing the liquid to stand for two 
days over granulated tin. After decantation it was distilled 
from a fresh quantity of granulated tin. The liquid then 
boiled at a perfectly fixed temperature of 112° C., which is 
accurately the boiling-point observed by Andrews, and differs 
considerably from Dumas’s value of 120° C. The liquid thus 
obtained is perfectly colourless : it exhibits a great attraction 
for moisture, combining to produce a white crystalline solid, 
SnCl,.5H,0 (Lewy), insoluble in the chloride. 

Electrical Conductivity of the Pure Chloride.—The conduc- 
tivity of the pure stannic chloride was examined by placing 
it ina V-tube with platinum electrodes: in the circuit were 
included a high-resistance galvanometer (4000 ohms), and 
twenty secondary cells of electromotive force of 40 volts. On 
completing the circuit by depressing a key not the slightest 
effect was observable; the insulation was absolute within 
these limits of delicacy, and was in marked contrast to the 
conductivity of a pencil-streak of black-lead on paper, for, 
with the latter in circuit instead of the former, the spot of 
light immediately moved off the galvanometer-scale. 

In order to test whether the insulating power was appre- 
ciably affected by elevation of temperature, the containing 
V-tube was heated in a bath of aniline. But as the tempera- 
ture rose to 20°, 80°, 40°, 100°, and even to the boiling-point 
when the stannic chloride was distilling freely—and this last 
observation 1s of particular import because the physical homo- 
geneity of the liquid agitated now with bubbles of vapour 
has been disturbed—no conductivity could be observed. To 
arrive at some concept of the degree of insulating power, 
the following experiment was performed. The same galvano- 
meter was placed in circuit with the resistance of one meoohm 
and supplied with the electromotive force of one Daniell cell : 
the deflexion then observed was thirty-five of the scale- 
divisions of the galvanometer. An electromotive force of 


Chemical Properties of Stannic Chloride. 385 


forty volts would give this deflexion through a resistance of 
forty megohms. Thus, then, the lower limit to the value of 
the conductivity of the above column of pure stannic chloride 
cannot be less than one thousand and six hundred megohms. 
There is thus in this chemically homogeneous liquid a high 
degree of insulating power, and one admirably adapted for 
the study of the influence on its electrical conductivity of the 
destruction of that homogeneity. The agents used to produce 
the required heterogeneity may be classified :— 


A. Dry gases. 
B. Liquids. 
C. Solids. 


Class A. The Effect of Dissolved Gases on the Conductivity. 


I. Chlorine Gas.—A specimen of stannic chloride ofa yellow 
colour was prepared as above, save that the excess of chlorine 
was not removed by granulated tin. The experiments above 
described, using the yellow liquid with the excess of chlorine, 
were again performed, and precisely the same results were 
obtained ; so that the dry chlorine gas was without effect on 
the conductivity. It will suffice to note that no compound of 
tin and chlorine exists in greater proportion than one atom of 
tin to four atoms of chlorine. 

Il. Dry Hydrochloric-Acid Gas.—The hydrochloric acid 
was carefully dried by sulphuric acid. It was then passed 
for a quarter of an hour through a V-tube containing the 
tetrachloride. An absorption of the gas was indicated by the 
fall in temperature of the liquid through four to five degrees, 
which may, however, have been due to the evaporation of the 
stannic chloride, and on tightly corking both arms of the 
V-tube the liquid rose to different levels. 

The accompanying diagram illustrates the arrangement of 
apparatus which I used both here and in subsequent experi- 
ments to detect the existence of a polarization effect. The 
battery used to electrolyse this tetrachloride saturated with 
hydrochloric-acid gas consisted of twenty-five storage-cells. 
On making the primary circuit, a small direct current passed, 
producing a deflexion of thirty scale-divisions. The cell had 
thus a resistance of above 5 x 10’ohms. Calculating from the 
magnitude of this direct current, it was not to be expected 
that a polarization-current would be observed: in fact, after 
passing the primary current for half an hour, no current was 
detected on making the secondary circuit. 


386 Mr. W. Coldridge on the Electrical and 


Diagram of the Electrical Apparatus used in these experiments. 


s— Storage 


— cells 


Reflecting 


be examined 
Subs. class A. 
sa Ls 


- C 


After resaturating the tetrachloride with hydrochloric-acid 
gas an increased conductivity was registered. 

An additional experiment was then made to determine 
whether this conductivity was merely a residual phenomenon 
due possibly to the incomplete drying of the acid gas. But 
the same order of conductivity was observed on saturating a 
fresh quantity of the tetrachloride with the acid gas, which 
had been completely dried by sulphuric acid and a column of 
phosphorous pentoxide. Now the pure tin tetrachloride is at 
least a comparative insulator, and liquid hydrochloric acid 
exhibits the same property. Yet when dry hydrochloric-acid 
gas is dissolved in the tetrachloride, some conducting-power 
is developed. Now it is known that a compound, 2HCl. 
SnCl, 6 H,O exists ; and, further, compounds 2 NaCl. SnCh, 
&c. are of frequent occurrence and of a common type; there 
can therefore be but little doubt that a compound, 2 HCl. SnCL, 
is formed on passing the dry acid gas into the tetrachloride, 
and to the presence of this compound must the developed 
conductivity be due. The observed development is accurately 
analogous to that with which Moissan endowed liquid hydro- 
fluoric acid by dissolving in it the freely soluble, thoroughly 
dried hydrogen-potassium fluoride. In the one case 

2HCl.SnCl, is dissolved in SnCl,, 
in the other 
HF, KF 15, m eh. * 

Til. The Effect of Dry Sulphuretted Hydrogen.—Sul- 

phuretted hydrogen was generated and washed in the usual 
* Comptes Rendus, 1887. 


Chemical Properties of Stannic Chloride. 387 


way, and then thoroughly dried by the use of tubes containing 
calcium chloride and by a column of phosphorus pentoxide. 
The gas thus carefully dried was passed for an hour into the 
tetrachloride. The only alteration in appearance was due to 
the separation of some white crystals, resembling in appear- 
ance the hydrate SnCl,5H,O. After filtration the colourless 
liquid, which smelt strongly of hydrosulphuric acid, and 
fumed in the air as the original unaltered liquid does, was 
tested for conductivity. But within the limit of these experi- 
ments the conductivity was unaltered by the presence of the 
hydrosulphurice acid. In striking contrast with this result is 
the effect observed on merely placing a few drops of absolute 
alcohol on one of the platinum electrodes, shaking it until no 
more than a mere film adhered and then replacing it; a de- 
flexion is immediately registered and stannic sulphide is 
formed on the electrode. 

These observations at once raised a question of considerable 
chemical interest as to the nature of this nonconducting pro- 
duct: had there or had there not been chemical action? In 
Watts’ ‘Dictionary of Chemistry’ the following statement 
Is given on the great authority of Dumas :— 

“Stannic chloride quickly absorbs sulphydric-acid gas, 
giving off hydrochloric acid, and forming a stannic sulpho- 
chloride, 


SnS,. 2 8nCl,. 


The compound obtained by the perfect saturation with sul- 
phydric-acid gas is a yellowish or reddish liquid heavier than 
water. When heated it gives off SnCl, and leaves SnS,.” 

This abstract is in accord with the account of Dumas’s 
observations, given in Frémy’s Encyclopédie Chemique. 
According to these dicta, the answer to the above question 
must be that there is chemical action. Assuming for a 
moment that the statement is categorically correct and com- 
plete, and that the liquid is indeed a chemical compound, 
Sn8,.28nCl,, then even this compound is a nonconductor. 
But this point is hardly worthy of expression ; because the 
fundamental assumption, the existence of the liquid compound 
SnS,.2SnCl, can be completely disproved. Attention was 
directed to the following points in the above statement :— 

(a) “That sulphydric-acid gas is quickly absorbed and 
that hydrochloric-acid gas is evolved.” 

The idea is obviously that the following changes oceur:— 


(1) SnCl,+ 2H,8 =Sn8,+4HCl. 
(2) SnS, +2S8nCl,=Sn8,. 28nCl,. 


388 Mr. W. Coldridge on the Electrical and 
(b) “ The product is a yellowish or reddish liquid heavier 


than water.”’ 

It was noted that no mention is made of the white crystal- 
line compound. 

(c) “On heating the liquid, SnCl, is evolved and Sn8, 
remains.” 

This observation as to the residue of stannic sulphide was 
verified, and beautiful specimens of the ‘‘ mosaic gold” were 
obtained. Butit should be noted that the liquid has been 
heated. 

The following experiments were then made :— 

(a) The fumes which are evolved on passing in dry hydro- 
sulphuric acid smell strongly of the sulphuretted hydrogen 
even when the gas was slowly delivered, and immediately 
blacken moist lead-acetate paper: they are moreover acrid, 
and distinctly smell of the tetrachloride rather than of hydro- 
chloric acid. But to establish the presence of the tetrachloride 
vapour, a test more reliable than the sense of smell was 
required. The following was devised :—A glass rod with a 
drop of water at the end was held in the fumes; after a 
minute, whilst the dry liquid below remained colourless and 
clear, here in the drop of water stannic sulphide was deposited. 
The fumes therefore contain the vapour of the tetrachloride 
and sulphuretted hydrogen, which are caused to combine by 
the action of the water. Thus, then, the statement that hydro- 
chloric-acid gas is evolved, if it be in the least degree posi- 
tively true, is fatally incomplete. 

(b) The liquid compound, the supposed stannic sulpho- 
chloride, was next distilled. The warming was gently regu- 
lated ; as the temperature rose gradually to 50°, 60°, 70°, 
sulphuretted hydrogen was copiously evolved in such quantity 
that the liquid assumed the appearance of boiling, whereas 
distillation had not commenced. At 112° C., the boiling- 
point of stannic chloride, a free distillation commenced, and 
the greater portion of the tetrachloride was thus recovered. 
Finally the temperature rose, a solid residue melted, and 
stannic sulphide remained, though, from a gravitation expe- 
riment, in less quantity than was required by the hypothetical 
constitution “SnS,..28nCl,.”’ A veritable compound stannic 
sulpho-chloride could not at low temperatures evolve sul- 
phuretted hydrogen copiously and then distil at the ordinary 
boiling-point of stannic chloride. 

(c) The presence of the residue of stannic sulphide proved 
that, on passing dry hydrosulphuric-acid gas into the chloride 
and then subsequently heating, some reaction occurred. But 
the question remained as to how far this production of the 


Chemical Properties of Stannic Chloride. 389 


sulphide was a function of the temperature-change. Was its 
formation induced by the elevation of temperature? It was 
noticed that, on warming up the product obtained by passing 
the dry gas into the liquid, the white crystals dissolved and 
the liquid became yellow ; there was thus a probability that 
these white crystals would prove the key to the change. 
Some of the crystals were separated and heated ; they then 
evolved sulphuretted hydrogen, hydrochloric acid, and left a 
residue of stannic sulphide. But it still remained to examine 
whether the unheated saturated stannic chloride contained 
any stannic sulphide. This point was determined by evapo- 
rating the saturated liquid to dryness without heating it, an 
operation which could be effected by taking advantage of the 
volatility of the tetrachloride. A current of thoroughly dried 
air was steadily driven into the saturated tetrachloride: fumes 
of the tetrachloride mixed with sulphuretted hydrogen were 
evolved ; but in the end, when all the liquid had disappeared, 
it was found that not a trace of stannic sulphide had been 
formed, and that in its place was a residue of the white crys- 
talline solid. Therefore, then, dry sulphuretted hydrogen 
may be passed into the tetrachloride, and, if the temperature 
be not raised, not a trace of stannic sulphide is formed: b 

far the greater part there is no combination, to the smaller 
extent these crystals are formed. The transformation which 
these crystals undergo when heated fully explains the forma- 
tion of the stannic sulphide observed by Dumas. The com- 
position of these crystals was determined. A small tube was 
weighed and about ten grams of the tetrachloride were placed 
in it, and saturated with dry sulphuretted hydrogen ; the 
liquid was then evaporated to dryness by a current of dry air. 
In this way, in two experiments, were obtained in the tube, 


(1) 1:15 gram of the compound SnCl,, nH,S8. 
(2) "926 7) = »P) 9 
The tubes were then carefully heated by a spirit-lamp. The 
solid melted and evolved sulphuretted hydrogen ; and next, 
as the heating was continued, hydrochloric acid, and a residue 
of stannic sulphide to the amounts respectively, 
(1) :48 gram, 
(2) 365. ,, 


which numbers correspond closely to the value n=5. These 


white crystals, which are the sole product of the action of 


dry sulphuretted hydrogen on stannic chloride, are thus 
SnCl, .5H,8, analogous to SnCl,. 5H,O. 
The reaction which occurs on heating is thus :— 


SnCl,. 5H,8=Sn8, +4HCl+ 3H,8. 


—— FOG SW oF cast 
SS sa 
ra - wma. 


Oe OL LLG LLLL ALE, OE 


390 Mr. W. Coldridge on the Electrical and 


The effect of adding a drop of water to these crystals is to 
produce stannic sulphide ; and this action is thus in harmony 
with that described above of holding the drop of water in the 
mixed vapours*. : 

Judging, then, from the fact of the unaltered boiling-point of 
the liquid, and from the analogy of SnCl, 5H,S to SnCl, 5H,0, 
and from the fact that the former as well as the latter separates, 
the conclusion that the sulphuretted hydrogen is merely 
mechanically mixed with the chloride is strongly supported. 


Class B. The Effect of various Liquids on the Conductivity. 


I. Chloroform.—Chloroform was first taken because of the 
similarity of its chemical structure to that of stannic chloride. 

The conductivity of chloroform was found likewise to be 
nothing within the range of these experiments. The tetra- 
chloride mixes perfectly with the chloroform. In the first 
instance the proportions taken were two volumes of the former 
to one of the latter. The conductivity of this mixture was 
nothing. In the next experiment one volume of the tetra- 
chloride was diluted with five of the chloroform. But there 
was still no conductivity. 

In each instance the result was checked by placing a streak 
of black-lead on paper in circuit instead of the mixture. 

There would seem @ priori to be no chance of a reaction 
between so stable and saturated a compound as chloroform 
and stannic chloride; as an experimental fact the mixture 
does not conduct. The test was applied of passing in dry 
sulphuretted hydrogen ; no precipitation of stannic sulphide 
resulted; the behaviour was the same as if no chloroform had 
been present, and in marked contrast to the influence of water 
or absolute alcohol. 

II. Absolute Alcohol_—Rectified spirit of good quality was 
dried by standing over lime and by subsequent distillation 
from lime. The phenomenon observed on adding a drop of 
this alcohol to stannic chloride is analogous to that which 
occurs when water is added. A white beautifully crystalline 
compound is formed and much heat isevolved. By adjusting 
the quantity of alcohol and cooling the vessel with water the 
whole of the liquid can be transformed into a mass of these 
crystals, which dissolve again on adding more alcohol. This 
alcoholate has probably the constitution SnCl,.5C,H;OH, as 
would be concluded from its analogy to the amyl alcoholate 
described by Bauer and Klein (Zeits. 7. Chemie [2] iv. p. 370). 

* My best thanks are due to the authorities of Exeter Grammar School, 
who placed their laboratories at my disposal during the Christmas vaca- 


tion, and to my friend Mr. J. M. Martin, who helped me in the manipu- 
lation involved in the examination of the above change. 


Chemical Properties of Stannic Chloride. 391 


The solution of the alcoholate conducts with facility ; and 
that electrolysis is proceeding is shown by a polarization- 
effect of considerable magnitude. The electrolyte remains 
clear and colourless. There were no signs of an evolution of 
gas at the anode, and no tin was deposited at the cathode ; 
but the difference between the electrolyte before and after the 
passage of the current was shown by its behaviour towards an 
alcoholic solution of mercuric chloride. The unelectrolysed 
solution of the stannic chloride gave no precipitate of calomel, 
but that through which the current had passed at once preci- 
pitated calomel. In one experiment, when a concentrated 
solution of the tetrachloride was electrolysed for two hours, 
the whole was converted into a magma, and some of the solid 
adhering to the electrode when dissolved in alcohol gave the 
reaction for the stannous salt. In this experiment a copper 
voltmeter showed that a current of between ‘1 and °15 of an 
ampere had passed. 

The production of calomel in the electrolysed solution shows 
that the current has transformed the stannic salt into a stan- 
nous salt, stannic chloride into stannous chloride. The 
absence of an evolution of chlorine gas is accounted for by 
the certain action of electrolytic chlorine on the alcohol. 

Qualitatively it has been proved that alcohol added to 
stannic chloride induces such a condition of instability as to 
render it capable of electrolytic conduction. Moreover this 
power of electrolytic conduction is closely analogous to the 
power of sulphuretted hydrogen to precipitate stannic sulphide. 
Mention has been made of the fact that the placing of a mere 
film of absolute alcohol on one of the platinum electrodes 
produces in the stannic chloride saturated with sulphuretted 
hydrogen a slight conducting power and the precipitation of 
stannic sulphide. When more alcohol is added, there results 
a copious precipitation of stannic sulphide; and when sul- 
phuretted hydrogen is passed into the alcoholic solution of 
stannic chloride an immediate precipitation of stannic sulphide 
occurs. 

Ill. The Effect of Dry Ether—Advantage was next taken 
of the curious fact that ether combines with stannic chloride 
to form a compound, SnCl, 2(C,H;),0, which is soluble in 
excess of ether. Absolutely dry ether was prepared in the 
usual way. On adding the ether to the chloride a mass of 
white crystals are formed, which are difficultly soluble in the 
ether at the temperature of the laboratory. LHther was added 
to the crystals and shaken ; the cell was then placed in circuit; 
a deflexion of sixty scale-divisions was registered. But on 
concentrating the solution by placing the cell in warm water, 


Ae eee ait Con es = 


392 Mr. W. Coldridge on the Electrical and 


the conductivity improved and became comparable with that 
of the alcoholic solution. 

After passing the direct current for thirty hours, a slowly 
diminishing polarization-current was registered producing at 
first a deflexion of thirty scale-divisions. The electrolysed 
product contained some stannous salt. 

On passing dry sulphuretted hydrogen into the cold ethereal 
solution an emulsion is formed, and the tetrachloride separates 
at the bottom of the ether. The distinction between the 
action of ether and of alcohol under these circumstances will 
be adverted to in Part II. 

IV. Effect of Strong Aqueous Solution of Hydrochloric 
Acid.—Instead of taking, as in the previous experiments, a 
V-tube for the electrolytic cell, a cell of the same pattern was 
used as that described and devised by Mr. Fitzpatrick (Brit. 
Assoc. Reports). Itis a glass cylinder closed at the ends, 
where wires leading to the circular platinum electrodes enter; 
and midway between the electrodes there is an open tube 
fused into the cylinder. A drop of strong hydrochloric acid 


was poured down the central tube on to the surface of the 
chloride : as long as it remained unmixed the effect was nil, 
but on admixture the cell conducted. The same H.M.F. was 
used as in B. I, II., III., viz. that of twenty-five storage 
secondary cells and a polarization-current of approximately 
2x 10-7 C.G.S. units, which is equivalent to a scale-deflexion 
of sixty scale-divisions. The act of mixing was accompanied 
by the evolution of heat and by the formation of a subsequently 
dissolved gelatinous substance. This reverse current was con- 
stant at the temperature of the'room for nearly an hour: this 
constancy and its high H.M.I’. led me to observe it at differ- 
ent temperatures. The primary current ran for three minutes; 
at a temperature of 31° the polarization-current gave a de- 
flexion which diminished from 77 scale-divisions to 56 in the 
course of fifteen minutes ; at a temperature of 41° it fell from 
79 to 63 scale-divisions in twelve minutes; at 51°, from 79 to 
55 in ten minutes ; at 71°, some hydrochloric acid boiled off 
explosively ; at 90° more was expelled, the polarization was 
a and decayed from 55 to O scale-divisions deflexion at 
go- €. 


Chemical Properties of Stannic Chloride. 393 


“2 WV. The Effect of Absolute Alcohol on the Tetrachloride 
saturated with Sulphuretted Hydrogen.—Incidentally, in de- 
seribing the effect of sulphuretted hydrogen on the alcoholic 
and ethereal solutions of stannic chloride, I was compelled to 
‘state some of the results which would naturally have fallen 
‘under this heading. It has been recorded :— 

(1) That stannic chloride saturated with sulphuretted hy- 
drogen does not conduct. 

(2) That a mere film of absolute alcohol adhering to one 
‘electrode is sufficient to endow such a solution with some 
conductivity. 

To amplify (2): the actual deflexion observed was forty 
scale-divisions. On pouring a little alcohol down one arm of 
-the cell the conductivity increased so that a 150 scale-division 
deflexion was registered. Directly the alcohol reached the 
solution there was a vigorous interaction and stannic sulphide 
was precipitated. After a similar quantity had been added to 
the other arm and the cell shaken, the current through the 
galvanometer was sufficiently great to turn the mirror at 
right angles to its original position. 


Class C. The Effect of Solids on the Conductivity of the 
Tetrachloride. 

The endeavour to destroy the chemical homogeneity of the 
stannic chloride was a failure, owing to the insolubility of the 
solids that were tried. Attempts were made with 

(1) The crystalline hydrate, 

SnCl, ° 5H.O. 

(2) The crystalline sulphydrate, 

SnCl, .5H,S8. 

(3) Dry sodium chloride. 

(4) Moist sodium chloride. 

(5) The double ammonium stannic chloride. 

After failing to obtain other than a negative result with 
sodium chloride, it seemed possible that if the chloride of the 
alkaline metal was first combined with stannic chloride the 
double salt might dissolve. The success that Moissan enjoyed 
by adding to the liquid hydrofluoric acid, the double potassium 
hydrogen fluoride, suggested this attempt. Some quantity of 
the double ammonium stannic chloride, (2NH,Cl.SnCl,), was 
prepared according to the directions given by Bongartz and 
Classen (Ber. xxi. p. 290), who determined the atomic weight 
-of tin by. electrolysing a solution of this salt in the acid am- 
monium oxalate. The double chloride was perfectly dried by 
standing over phosphorus pentoxide in a desiccator. A gram 
of this dry salt was added to the stannic chloride in the V-tube. 
Phil. Mag. 8. 5. Vol. 29. No. 180. May 1890. 2H 


394 Mr. H. Tomlinson on the Villari 


The effect on the conductivity, even after heating to and at 
the temperature of 100° C., was nothing. A drop of water 
added to the double chloride before adding it to the stannic 
chloride was powerless to promote conductivity. 

The fact, then, is that neither the crystalline hydrate, nor 
sulphydrate, nor moist nor dry sodium chloride, nor the moist 
nor dry ammonium stannic chloride have any influence on the 
conductivity of the stannic chloride. The solids remain out- 
side the sphere of action: and, like the drop of strong hydro- 
-chloric acid as long as it was unmixed with the stannic 
chloride, and like the perfectly dissolved chloroform and the 
-gases chlorine and sulphuretted hydrogen, having produced 
no effect on the chemical homogeneity of the stannic chloride, 
which remains stannic chloride, they were without influence 
-on its electrical conductivity. 

[To be continued. | 


XLIUL. The Villari Critical Points of Nickel and Iron*. 
By Hersert Tomunson, F.R.S.F ~~ 


WE owe to Villari the discovery that the magnetic per- 

meability of iron is increased by longitudinal traction 
provided that the magnetizing force does not exceed a certain 
limit, but beyond this limit the traction produces decrease of 
permeability so that for a certain value of magnetizing force, 
known as the Villari’s Critical Point, longitudinal traction has 
no effect in either direction. Several experimenters have 
verified and extended Villari’s discovery, notably Sir William 
Thomson and Prof. Ewing, but, as far as the author is aware, 
no observer has been as yet. able to find a similar critical 
point for nickel. If, however, we confine ourselves to the 
consideration of the temporary magnetization}, aVillari critical 
point in nickel can be detected with comparative ease. In the 
present investigaticn the ballistic method of observation has 
been emp'oyed, the arrangements of which have been already 
described§. The nickel wire used contains nearly 98 per 
cent. of nickel and only 0°7 per cent. of iron; the iron wire 
is also, judging from its small specific resistance, nearly pure. 
The mode of conducting the experiments may be illustrated 
by the aid of fig. 1; this figure refers to a piece of well- 


* Communicated by the Physical Society: read March 21, 1890. 

+ The author begs to acknowledge with thanks the assistance which he 
_ has received in this investigation from the Elizabeth Thompson Science 
. Fund, U.S.A. 

t The magnetization which disappears on the removal of the magneti- 
zing force. : 

§ Phil. Mag. xxv. p. 572. 


Critical Points of Nickel and Iron. B95 


annealed iron wire | millim. in diameter. The wire was in the 
first instance loaded with 12 kilos (the highest load employed 
in the experiment), and was subjected to a magnetizing force 
of 15°5 C.G.S. units which was alternately applied (always 
in the same direction) and removed until the deflexions of the 
ballistic galvanometer became constant. The load was then 
entirely removed, and the same force was again applied and 
removed as before. A load of 2 kilos was now put on the wire, 
Fig. 1.—Iron. 


\ FAS 
EES 


aue 
aepoed 
. eV 
NEE ae 

NCC 


Percentage alteratiou* of permeability; + siynifles increase, — decrease. 


and the same operations were repeated with this and the sub- 
sequent loads upto 12 kilos. Next the load was again entirely 
removed, and a similar series of observations was made with a 
magnetizing force of 10°5 C.G.S8. units, and so on until the 
force had diminished to 2°8. The entire set of experiments was 
then repeated with ascending forces up to 15°5; this set did not 
sensibly differ from the one taken with descending o& magnetizing 
forces. As might be expected, each change ot Toad produced 

* If P, and P, represent respectively the permeability with no load 


and a load of x kilos, the percentave alteration of permeability is taken to 
pee Ronit aha) + 100(Pr—F P,) 


according as the permeability is de- 


ee or  inerenteu by ae ae 
eel a gee 


_ 896 Mr. H. Tomlinson on the Villari 


, an alteration in the residual magnetization, but this alteration 
does not concern us, and only “the temporary changes, 2.@. 
; those which take place after repeated application of the force 
: and when the deflexion on closing the battery-circuit is equal 
. to that on opening it, are recorded in the figure. 

It may be noticed that the Villari critical point depends 
upon the load, the greater the load the smaller the critical 
‘value of the force. This fact has been already observed by 
Sir William Thomson, but for a given load the Villari er itical 
point is much lower when only tbe temporary magnetization 
is taken into account than when, as in Sir W. "Thomson’s 
experiments, the whole magnetiz: ation is observed. It occurred 
therefore to the author that though it might not be possible 
to reach the critical force for nickel as far as the total-mag- 
netization is concerned, such a value could nevertheless be 
found for temporary magnetization, and this has proved to be 


the case. wat 2.—Nickel. 


—40 


Percentage alteration of permeability ; + signifies increase, — decrease. 
, ; 
3 


| 
| 
| 
{ 
| 
| 


| COCs sh 
—70 | | 
 KBBESREVEERS Sane 


Fig. 2 refers to a nickel wire of °8 millim. diameter, onal 
shows Villari critical points quite as striking as those of iro a, 
but with this difference, that the critical value is greater the 


Critical Points of Nickel and Iron. 397 


greater the load, and for a given load is much greater in 
nickel than in ircn. 

With iron wire the curves may, and do, sometimes cut the 
load line ¢wice, so that for a given value of magnetizing force 
there may be two loads which have no effect on the temporary 
magnetization. In fig. 1 none of the curves actually cut the 
load-line a second time, because the loading was not carried. 
quite far enough ; but with subsequent experiments made 
with the same wire and with the same loads at a temperature 
of 200°C. the two points of cutting were easily obtained, 
within certain limits of magnetizing force, whilst the meet 
figure shows that with greater loads the second point can be 
reached at the ordinary temperature of the room. 


Fig. 3.—Iron*, 


+30 |i 


+20 |tee 


+- 
te 
=) 


Oo 


Seer 
oe 
ROE 


LVERZEREP 24 
INNCECCCV CEP, 
aipceeter’ cade 


| 
LS) 
> 


|ZEe eran an 


| 
re) 
S 


Percentage alteration of permeability ; + s'pnifies increase, — decrease. | 
Up 
fo) 


Fig. 3 illustrates. the effect of loading on an iron wire 
of -077 millim. diameter, ‘which in the “fitst instance was 


.*.Tn this experiment: a load of-2 kilos was left pe rmanently on the wire, 
r0 that the initial load is 2 instead of 0. 


398 — Mr. H. Tomlinson on the Villari 


well annealed, but was subsequently loaded to very nearly 
its breaking-point, and was in consequence permanently 
lengthened by about 10 per cent., whereas the wire referred 
to in fig. 1 was not loaded sufficiently to produce any sensible 
permanent extension. For a magnetizing force of 3 C.G.S. 

units the curve cuts the load-line twice, but for higher forces: 
the first cutting-point disappears and we have only the 
second one. 

The maximum decrease of permeability is greater the 
greater the magnetizing force up to a certain limit of the: 
latter, which limit other experiments (nut illustrated by the’ 
figure) proved to be about 16 C.G.S. units. Beyond this 
limit the maximum decrease begins to become slowly less, as 
is shown by the dotted curve of the figure for which the 
magnetizing force was 73. 

The curves for nickel can never be made to cut the load- 
line twice, for the wire of fig. 2 was stretched within one or 
two per cent. of its breaking-point, suffering thereby a per- 
manent elongation of about five per cent. of its original 
length. The curves, however, show a maximum decrease of 
permeability with a load of about 24 kilos. 

The observations hitherto recorded were only made at the 
different stages of loading, but subsequent ones showed that 
with nickel the readings on unloading were very nearly the 
same as those cn loading, there being very little lagging of 
mechanical strain behind stress. Prof. Ewing has pointed 
out also that nickel exhibits very little magnetic hysteresis. 
With iron there is a very sensible lagging of mechanical 
strain behind stress, but the only effect of taking a mean 
between the observed changes on loading and unloading 
would have been to make the curves more parabolic in ee 
and not to alter their main character. 

For the next two figures observations were made both on 
loading and unloading, and though the magnetizing force 
employed was here very minute, the curves show pretty 
nearly the same amount of lagging of mechanical strain 
behind stress which is experienced when much higher forces 
are used. For these very minute forces, of course, the. 
apparatus had to be made much more sensitive, and the 
number of turns in the secondary coils was very great. 
Fig. 4 refers to the same kind of wire as that used in the first 
experiment. The wire in this case was, however, previously 
loaded to nearly its breaking-point. Ifthe mean be taken of 
the percentage alterations of permeability on loading and: 
unloading, the curve becomes exactly parabolic, with its axis 
vertical and its vertex at the point where the vertical from 


Critical Points of Nickel and Iron. 399 
aa: 4, Paton: 


Percentage alteration of permeability. 


the load 16 kilos. cuts the curve. Both the loading and un- 
loading curves lie entirely above the load-line, and there is no 
point of cutting this line. 

Fig. 2 deals with a nickel wire of the same degree of 
purity as the first but 14 millim. in diameter. The stress 


Fig. 5.—Nickel. 
Kilos on lever. 


Percentage alteration of permeability. 


1 kilo on the lever ea ecants a stress of 2°68 kilos per sq. millim. 
was carried by the aid of a lever to very nearly the breaking- 
point of the wire. There is in this case no perceptible lagging 
of mechanical strain behind stress, the curve on loading being 


400 The Villari Critical Points of Nickel and Iron. 


identical with that on unloading. ‘With nickel the curve lies 
entirely below the load-line and never cuts the line. | 

In figures 4 and 5 the curves are described as having been 
obtained with a magnetizing force of 0-03 C.G.S8. units ; 
but other experiments showed almost precisely the same 
curves to be obtained for any force between 0°03 and 0°3 
C.G.S. units. Between these limits of force the whole of the 
magnetization is practically temporary provided the wires 
have been stretched to the extent these were. 

From what has been said and from the figures it is easy to 
see what would be the general character of the curves, show- 
ing the relation between change of temporary permeability 
and change of load for any magnetizing force whatever. If 


a piece of iron wire be tested with loads nearly up to the 


breaking-point, then for magnetizing forces ranging from 0 
to somewhere about °3 C.G.S. units the curves will be zdentz- 
cal with those of fig. 4, and will not cut the load-line. Fora 
value of force above °3 the curves will cease to be identical, the 
maximum increase of permeability will become less and less 
as the force increases until for a certain force the curve begins 


to cut the Joad-line. As the force increases beyond this value — 


the point of cuttmg approaches nearer and nearer to the origin 
of coordinates, and the curve begins eventually to cut the 
load-line in iwo points. The first point of cutting, as the 
force increases still further, gets nearer and nearer to the 
origin, whilst the second point gets further and further away 
from it ; and when the magnetizing force reaches a value but 
little over 3C.G.S. units, the first point vanishes and the 
second point only remains. Finally, with a sufficiently high 
force it would seem that the second point also cannot be 
reached and the curve now lies entirely beneath the load-line, 
whereas for very minute forces it lies entirely ubove this line. 

With nickel the curves for very minute magnetizing forces 
are, like those of iron, exactly the same for different values of 
the force, but instead of lying above the load-line lie entirely 
below it. Beyond a certain limit of the force the curves 
cease to be identical and the maximum decrease of per- 
meability begins to become less and the curve near its origin to 
bulge more and more towards the load-line, until for a value of 
force a little over 21 C.G.S. units the permeability begins to in- 
crease with small loads and to cut the load-line in one point, 
which gets shifted further and further away from the origin 
as the force increases. | 


Mp MOE 4] 


XLIV. fae ediien Method and pean orem of Chemical 
Research. By Dr. G. Gort, F.R.S.* 


CONTENTS. . PAGH 
WipeEBGGE WVGREKING £2. (52 oeeoee cb libs docsletihdte sce. PRS CTT co eee ate od Ay We ee RR 401 


CurvEs oF ELECTROMOTIVE FORCE. . 
we By Varying.the Strength of the Solution at Both Metals. 
Strength of Solution. 


Substance. Water. 
Curves of Chlorine, Bromine, and Iodine ...... 001 to ‘01 grain in 155 grains. 403 
i, HCl, HBr, and HI. Weak............ (001 to ‘Ol ,, FP 405 
is HNO,, and H,SO, Wea @asds- ocr OOl to -O1.,, 5) 406 
“ H,SO, at 60° Cl. | aa, eee ‘OOl,to OL | 4s, 407 
A HCl, HBr, aud HI. Strong aN pala tion tou ah Bs 409 
5 HCl with Cadmium as Positive Metal. :1 tol A * 409 
" ME Cle K Bry ade Wb: hiss. ccsseedcen gues os 1), tol i BS 410 
. LEB a ROS O82 Ree Re Wa toyl a ie 4l1l 
6 Nai, NaBr, and Nal : ................ 1 cont % ce 412 
SSHeClO.; KBrOv and KIO, J... 2.20.5 tons] i, 3 413 
Sse SOoand: Nags@) (oho. ..ices-- ddeo- ip tol 93 ‘2 414 
x KC1-LKI, mat KCl4NaCl sauaas ees ‘1 tol 3 és 415 
a Hsomieri¢ SOMtHONS ~..:.... -20..-s.+s 701 to ‘1 4 416 
B. By Varying the Strength of the Solution at One Metal only. 
Guryedercar NaCl, and KCl s.o205..:... oceessnonaes onent tes ‘1 grain in 465. 417 
C. By Varying the Temperature of the Solution at Both Metals. 


Gurve ot ERC! from 10° toW00? Co. el ‘03 grain in 465. 419 
D. By Varying the Temperature of the Solution at One Metal only. 


Curve of Cold Zine and Hot Platinum from 17° to 100°C. 39 grains in 465. 420 
Cold Platinum and Hot Zinc from 15° to 100° C. 39 grains in 465. 420 


E. General and Theoretical Considerations. 


MeErHop or WoRKING. 


rN an investigation “ On the Change of Potential of a Voltaic - 
Couple by Variation of Strength of its Liquid” (Roy. Soe. 

Proc. 1888, xliy. p. 296), I showed that by i immersing a small - 
pair of unamalgamated zinc and platinum plates in distilled 
water, then adding to the water successive small and equal 
quantities of a particular halogen, acid, or salt, until a more 
or less saturated solution was formed, and measuring by the 
method of balance with a galvanometer i in the circuit, with a 
suitable thermoelectric pile (see Proc. Birm. Phil. Soc. 
iv. p. 130; also ‘The Hlectrician,’ 1884, xii. p. 414), aided 
when necessary by a zinc-platinum distilled water- cell, or a 
Clark’s standard cell, the degrees of electromotive force pro- 
duced by each addition of substance, the changes of that 
force did not vary by a regular gradation. And I stated that 


* Communicated by the Author. 


ey 


402 Dr. G. Gore on a New Method and 


“by plotting the quantities of dissolved substance as ordinates 
to the degrees of electromotive force as abscissee, each sub- 
stance or mixture of substances yielded a different curve of 
electromotive force on uniformly changing the degree of 
strength of its solution.” And that “with a given voltaic 
couple at a given temperature, the curve was constant and 
characteristic of the substance.” The examples given in this 


paper illustrate these statements, and the measurements were 


made by the above method. 

Instead of employing a thermopile, the following plan with 
the “ voltaic balance” might be adopted :—1st. Balance two 
small zinc-platinum voltaic cells with distilled water in each, 
and a galvanometer of 100 ohms resistance in the circuit, then 
add gradually sufficient of the exciting substance to one of the 
cells to just visibly upset the balance, and note the quantity 
added. 2nd. Balance the cells with a very weak solution 
containing one unit quantity of the substance in each cell ; 
then add a sufficient excess of the substance to one cell to 
again upset the balance, and note the amount of excess. 3rd. 
Balance the cells with a two unit quantity solution, and upset 
the balance again in like manner. And so on through suca 
a series of strengths of solution as may be desired to obtain 
acurve. The proportions of excess of substance added to the 
amount of water in the cell represent the relative amounts of 
voltaic energy of the different strengths of liquid. 

This method is very much more sensitive than the one with 
the thermopile, for whilst the latter only divides the range of 
difference of potential between water and chlorine for example 

='753 volt), in practical working into about 15,000 parts, 
the former divides it into 1200 millions. On the other hand, 
whilst by the thermopile method the values of the unit of 
measurement are equal throughout a series, those of the 
numbers obtained by the voltaic-balance one vary with the 
degree of strength of the solution. The following instance 
illustrates this :— 

The liquid employed was a solution of potassium sulphate, 
and the balancing couples were formed of zinc and platinum. 


The table shows the degrees of strength of the solution, and. 
the proportions of additional salt required with each to upset 


the balance. 


Strength of Solution. Excess of K,SO,. 
K,SO,. Water. K,SQ,. Water. 
1:0 grain 155 grains. 30 grain = Lantelg 
HOT 5 ri es ea nate 25 2, = 1lin600 ~ 
SS Ia EA 520 conysp «ak mee 


Department of Chemical Research. 403°-- 


The degree of sensitiveness of the balance therefore in- 
creased directly as the degree of dilution of the solution. 


A. CURVES OBTAINED BY VARYING THE STRENGTH OF THE 
SoLuTION AT BOTH METALS. 


Nearly all the measurements of electromotive force given in 
this paper were made with highly pure substances, and in sec- 
tion “A,” with the exception of one instance only (see fig. 8), 
each curve starts from the potential of unamalgamated zinc 
and platinum in distilled water at about 16° C.=1°127 volt. 
The quantity of distilled water employed as the solvent was 
in nearly every case 155 grains, and the series of degrees of 
strength of the solutions of each substance were usually such 
as could best be worked by the process, 7. e. neither too strong 
nor too weak, and were with different substances either the 
same Or so arranged as to best enable comparisons to be made 
between the results of the different series of measurements ; 
they were not always sufficiently strong to fully develop the 
most characteristic curves. 

For each separate measurement, with the solutions of the 
halogens and the strong ones of the acids, a fresh portion of 
the original liquid was taken ; with those of other substances 
the zine was so feebly acted upon and the liquid so slightly 
altered in composition, that this was not found necessary. With 
solutions of salts, the presence of films of oxide upon the zinc 
was tested for by replacing the saline liquid by distilled water, 
and then observing whether the cell was still exactly balanced 
- by a zinc-platinum water one. No trouble was experienced 
from polarization caused by hydrogen in the platinum plates, 
nor by atmospheric air dissolved in the water. 


1. Curves of Chlorine, Bromine, and Iodine. 


The range of strength of the, solutions of each substance 
was from ‘001 to °01 grain in 155 grains of water. With 
solutions of these substances the degree of electromotive force 
increased somewhat with the period of immersion ; this diffi- 
culty was due to the great chemical energy of the substances, 
and was overcome by making the fluctuations of the gal- 
vanometer-needles equal on each side of zero. 

These curves show :—1st. An increase generally of electro o- 
motive force attending increased strength of solution. 2nd. 
A much greater increase caused by the first amount of sub- 
stance added than by the subsequent additions. 3rd. A 
gradation of degree, both of first increase and of maximum 

electromotive force in the three curves, varying inversely as” 


Volts. 
2-000 


1975 


1950 | 


1°925 


1:900 f 
1 875 | 
1-850 ! 
1°825 + 
1°800 
L7i5 
1-750 § 


1°725 


1-700 | 
1°675 | 


1-650 | 


1°625 
1°600 
l‘d7o 


1°550 | 
1°525 | 
1-500 | 
1°475 | 


1°450 


1°425 } 


1-400 
1°375 


1°350 | 


1°25 
1-300 
1-275 
1°25t 
1°226 
1-200 
1175 
1°150 


1:125 | 


1100 


Grains. 


"0010 


‘Vv015 


Dr. 


"0020 


G. Gore on a New Method and 


Fig pac teas d 


Curves of Cl, Br, and I. 


' 
i] i 
om om) Oo. 8 oS WO So 2 
222222222 3 § 2223 8 
> S$ SS$-3SS535 SS SESERB RS 


Department of Chemical Research. 405 


the magnitudes of the. atomic weights: of the substances. ‘th. 
A general similarity of form, sufficient to show a graduated 
degree of likeness. And 5th. A sufficient degree of difference 
of form to characterize each individual sees 


2. Curves of HCl, HBr, and HI. 
a. Weak Solutions. 


Each acid was pure and colourless.. The solutions were of 
the same range of degrees of strength as those of the halogens, 
in order to compare the effects of the two groups of sub- 
stances ; and the curves are all drawn on the scale of magnitude 
imseauh direction as those of the halogens. 


Fig. 2 
Curve of HCl at 10° C.— Weak Solution. 


Fig. 2) 


HBr. 


HI. 


J Sie eet au sak oon ee i alt = 

om SS 6 S us =) oD Oo od a SOF inte mW © we = 

seo oe eS Se ee ee SS 
Gaim, 5825 3.355955 $5 SSEBSESBS SS 


‘406 Dr. G. Gore on a New Method and 


The curves show :—Ist. That the union of hydrogen with 
the halogens greatly diminished the electromotive force. 2nd. 
A feeble increase of electromotive force, greatest at the-com- 
mencement, especially with hydrochloric and hydrobromic 
acids, attending increased strength of the solution. 3rd. A 
less degree of family likeness than in the curves of the halo- 
gens. 4th. The substance of largest molecular weight gave 
the smallest increase of electromotive force. And 5th. Hach 
substance gave a characteristic curve. The general feeble- 
_ness of character of the curves was due to the weakness of 
_the solutions (compare fig. 7, of curves of solutions 100 times 
stronger). 

3. Curves of HNO; and H,SQ,.- 

The acids were pure and the range of degrees of strength 

of their solutions was the same as those of the weak ones of 


hydrochloric, hydrobromic, and hydriodic acids. 


Fig. 4. 
Volts. Curve of HNO, at 14° C.— Weak Solution. 
1°350 |r bas ia Se alo a ee T T T SS 


L ie Il. 
S29, So S46 - Sb Se we Ss S 1) OL, DSO. eae 
BeOS RA cw) ea ca AD a ee SS or Cos ae 
Grains © 2 22 oS 6 7S) 5 S96 806 5S 6 Ss Seog 
(De pe (oO isto Ss oS 'S- 5 6S S S Ss Saisegone 


Department of Chemical Research. 407 


The curves are drawn upon the same scale as those of the 
weak solutions of the above-named acids. Ist. They are very 
greatly different from those of the halogens, and show very 
much smaller degrees of electromotive force. 2nd. Their 
differences from those of hydrochloric, hydrobromic, and 
hydriodic acid of the same range of degrees of strength are 
also quite conspicuous. And 8rd. They are sufficiently unlike 
to be characteristic of each substance and to be clearly dis- 
tinguishable from each other. The solutions employed were 
too weak to fully show the characteristic forms of the curves ; 
the degrees of strength were chosen chiefly to enable the 
curves to be compared with those yielded by the halogens and 
by their acids. 


4. Curve of H,SO, at 60° C. 


The range of degrees of strength of the solution was the 
same as in the previous case, viz. from ‘001 to ‘01 grain of 
the substance in 155 grains of water. 


Fig. 6. 
Curve of H,SO, at 60° C.— Weak Solution. 


By comparing the curves obtained at the two different 
temperatures, we find that a rise of temperature caused a 
general increase of electromotive force, greatest at the com- 
mencement, and quite sufficient to distinguish the one curve 
from the other. The difference would probably be much 
greater with stronger solutions (compare figs. 9 and 10 of 


KBr at 18° C. and 60° Us): 


Dr. G.-Gore on a New Method and 


et Fig. 7. 
Curves of HCl, HBr, and HI.—Strong Solutions, 


| HClatj4°C. 


| 
HBr at 14°C. 


HI at 11° C.} 


Department of Chemical Research. 409 


d. Curves of HCl, HBr, and HI. 


b. Strong Solutions. 

_These solutions were one hundred times stronger than the 
previous ones in order to fit them for comparison with those 
of the corresponding salts ; they contained from *10 to 1:0 
grain of substance in 155 grains of water. The degrees of 
electromotive force of the solution of hydrochloric acid were 
variable, and those of the other two acids less so. 

These curves are drawn upon a scale 2°92 times as large 
vertically as those of the previous ones, in order to fit them 
for comparison with those of the corresponding salts. They 
show :—Ist. A general increase of electromotive force attend- 
ing gradually increased strength of liquid. 2nd. A much 
larger increase produced by the first amount of substance 
added than by the succeeding ones. 38rd. A gradation of 
degree of general increase of such force varying inversely as 
the magnitudes of the molecular weights of the substances, 
And 4th. A great dissimilarity of form characteristic of each 
individual substance. 

By comparison with the curves yielded by the weak dole 
tions of the three acids, those of the strong ones show :—Ist. 
A much greater increase of electromotive force, both on the 
addition of the first amount of the substance and by the subse- 
quent additions. 2nd. A more distinct relation of those 
increases to the magnitudes of the molecular weights of the 
substances. 3rd. Much more characteristic curves. And 4th. 
A’ much greater degree of irregularity of form of curve ; this 
greater irregularity of form was a genuine effect, and was not 
due to temporary fluctuations of the current... 


6. Curves of HCl with Cadmium as Positive Metal. 


The range of degrees of strength of the solutions in this 
case was the same as that of the “ strong” solution of the 
same acid in the immediately previous group of acids, and the 
scale of magnitude upon which the curve is drawn is the 
same. ‘The “electromotive force was variable, owing to the 
strength of the solutions, and of course started from a lower 
point than when zinc was used as the positive metal. 

On comparing the curve with the one yielded by zinc in the 
same degrees of strength of solution of the same acid, we 
find :—I1st. Quite a different form of curve. 2nd. A ee lor 
increase of electromotive force on adding the first portion of 
acid. 3rd. A general decrease of that force by the further 
additions. And. 4th. A curve characteristic of the substance. 


Phil. Mag. 8. 5. Vol. 29. No. 180. May 1890. a 


ee ~—— 


410 Dr. G. Gore on a New Method and 


Fig. 8. 
Curve of HCl with Cd at 14° 0.—Strong Solution. 


Z Oo) 119 12 o w 
Grains, ST oF YW RF PB Oo ww 


7. Curves of KCl, KBr, and KI. 


Ail the substances were highly pure, colourless, and inodo- 
rous ;- the iodide was very faintly alkaline. The solutions were 
of the same range of degrees of strength as the strong ones of 
the corresponding acids, viz. from ‘1 to 1:0 grain of substance 
in 155 grains of water. The electromotive force of the zinc- 
platinum couple increased somewhat with the period of immer- 
sion. The absence of solid films upon the zinc was proved 
by occasionally replacing the saline liquid by distilled water, 
and observing whether the cell was still exactly balanced by a 
zinc-platinum water ono. 


Department of Chemical Research. 411 


Fig. 9. 


1:26 & KCl at 15° C. 


zy KBr at 18°C. 


KI at 10°C. 


wo 
Be 


I re een ee 
—) 

et 

5 : 


G rains. AQ S 8 

The curves of these substances are all drawn upon the same 
scale of magnitude as those of the ‘“‘ strong” solutions of the 
corresponding acids. They show:—lst. A much greater 
increase of the electromotive force caused by the first amount 
of substance added than by the subsequent ones. 2nd. A 
gradation of degree of first increase and of maximum electro- 
motive force, varying inversely as the magnitudes of mole- 
cular weight of the substances. ard. Large differences of 
form, characteristic of each individual substance. And 4th. 
The substitution of potassium for hydrogen in the correspond- 
ing acids lowered the electromotive force in all three cases, and 
the amount of this reduction varied inversely as the magni- 
tudes of the molecular weights of the substances ; the union 
of potassium with the halogens had similar effects, but in 
much greater degrees (compare the respective figures). 


8. Curve of KBr at 60° C. 


The range of degrees of strength of the solution in this case 
was the same as in the previous one when the liquid was at 
18° C., and was from ‘10 to 1:0 grains of substance in 155 
grains of water. 

21.2 


412 Di.-G. Gore on a New Method and 


Fig. 10. 
Curve of KBr at 60° C. 


; One comparing the two curves obtained at the two tempera- 


tures we find considerable differences, viz. :—Ist. A great 
unlikeness of general form. 2nd. A general and large 
diminution of electromotive force at the higher temperature. 
And 3rd. A much smaller increase of that force on the 


addition of the first portion of the substance. The differences 
would probably have been less conspicuous if the solutions 
in each case had been much weaker. These results support 
the conclusion that potassium bromide behaves to a certain 


extent like a different substance at each different temperature. 


9. Curves of NaCl, NaBr, and Nal. 


The chloride contained a trace of sulphate, and the bromide 


and iodide were very faintly alkaline. The solutions were 
of the same range of degrees of strength as the corresponding 


salts of potassium ; and the curves are drawn upon the same 


scale of magnitude. 


These curves show:—1st. A general increase of electromotive 


force by increase of dissolved substance. 2nd. A great 


difference of form, and strongly characteristic curve in each 
case!’ Ard’ 8rd. The substitution of sodium for potassium in 


each ‘salt considerably reduced the degree of. electromotive’ 


force produced by the first addition of the substance, and the- 


amount of this reduction varied inversely as the molecular 
weights of the salts. The curves are widely different in form 
from those of the corresponding salts of potassium, and this 


is no doubt entirely due to the difference of metallic base ; in’ 


each group, however, the curve of the chloride intersects that 
of the bromide. | 


Department of Chemical Research. 413 


Fig. 11. 
Curves of NaCl, NaBr, and Nal. 


NaBr at 13° C. 


NaCl at 15° C. 


Nal at 11°C. 


tts S19 1S) 16! SS 
Grain. (@ TF NN DB & 


10. Curves of KC1O3, KBrO3, and KIOs. 


The chlorate contained a trace of chloride. In consequence 
of the degrees of electromotive force produced by solutions of 
these salts being so little greater than that produced by water 
alone, viz. 1127 volt, it was necessary to use much stronger 
solutions than those of the previous substances ; the ones 
employed contained from ‘7 to 1:7 grains in 155 grains of 

water. 


Fig. 12. 
Curves of KC10;, KBrO,, and KIO . 


| KIO, at 16°0. 


KBrQ, at 18°C, 
KC10q at 13°°5 C. 


414 Dr. G. Gore ‘on a New Method and 


The curves show :—lst. A striking similarity of general 
form, very different from that of the corresponding chloride, 
bromide, and iodide; this was probably chiefly due to the 
general feebleness of the action. 2nd. A very small increase 
of electromotive force in each case on adding the first portion 
of substance, and on subsequent additions ; and the amounts 
of these increases, contrary to what happened with other 
groups of substances, varied directly as the magnitudes of the 
molecular weights of the salts, but the degree of reversed 
action was not conspicuous. 3rd. A sufficient difference of 
form to characterize each substance. And 4th. The chemical 
union of oxygen with the three corresponding halogen salts, 
reduced the general electromotive force in each case, and the 
amount of reduction varied inversely as the magnitudes of the 
molecular weights of the salts (compare fig. 9). 


11. Curves of K,SO, and Na,SO,. 


The potassium salt was very pure; the sodium one con- 
tained traces of chloride. The solutions were of the same 
range of degrees of strength as those of the halogen salts of 
the same metals, viz. from ‘1 to 1:0 grain of salt in 155 grains 
of water. : 


Fig. 18. 
Curve of K,SO, at 14:5° C. 


Department of Chemical Research. 415 


Fig. 14. 
Curve of Na,SO, at 17°C. 


These two curves are largely alike, due to their being those 
of closely allied salts of the same acid ; but somewhat different 
in consequence of difference of their metallic bases. They are 
both considerably different from those of the chlorides, bro- 
mides, and iodides of the same metals. 


12. Curves of KO1+ KI, and KC1+ NaCl. 


The measurements of electromotive force of these were 
made to ascertain the influence of more complex compounds 
upon the amount of that force. The salts were mixed in the 
proportions of their molecular weights, and the proportions of 
mixtures taken were the same as those of the same salts 
separately in previous experiments, viz. from ‘1 to 1:0 grain 
in 155 grains of water. | 


Fig. 15. 
- Curve of KC1+KI at 16°C. 


416 Dr. G. Gore on a New Method and 
Fig. 16. 
Volts. Curve of KCl1+ NaCl at 18° C. 
1°20 T 2 a ae 


1-19 
1:18 
117 
1:16 
1°15 
114 
113 
¥-12 


Oo 16 
oe co | 


O19 3: = 1975 4O 2 ao 1S 19S IBY O16) oS ae 
Grains UE GPRS apa Stary ne 2S) SE 8 ES ES 


1:00 


Ist. Each of the curves is strikingly unlike in general 
form each of those of the constituent salts of the compound, 
and the form is not in either case an average of that of the 
two ; each of them also shows a great reduction of electro- 
motive force due to the chemical union of the two constituents. 
2nd. In each case an increase of strength of solution is 
attended by an increase of electromotive force. 38rd. The 
two curves are each characteristic of the individual substances. 
' * The amounts of voltaic energy of the dissolved salts separately 
before chemical union were :—KC] = 699,803, NaCl= 207,589, 
and KI=16,361; and after the union those of the compounds 
were :—KCl+ KI=7,571, and KC1+ NaCl=5,959 (see “ Re- 
lative Amounts of Available Voltaic Energy of Aqueous Solu- 
tions,” Proc. Birm. Phil. Soe. vii. part i.). T 


13. Curves of Isomerie Electrolytes. 


I have already shown (see Phil. Mag. October 1889, 
p. 289, “On the Molecular Constitution of Isomeric Solu- 
tions ”’) that aqueous isomeric electrolytes yield different 
amounts of voltaic energy with a zinc-platinum couple. In 
the present case I employed the same pair of mixed aqueous 
solutions as were used in that research, viz. an unstable one 
“A” having a composition represented by the formula 
Na,SO,+2HNO,, and yielding an average voltaic energy 
= 77,446; and its stable isomer “B” represented’ by 
2NaNQ;+H,SO,, and yielding 32,722. The degrees of 
strength of the series of solutions employed were those which 
were the most easily worked, and were from ‘01 to ‘1 grain of 
the mixture in 155 grains of water. The constituent solutions 
of “A,”’ previous to being mixed, contained ‘01 grain of 
substance per cubic centimetre ; if they were stronger than 
this there was risk of the liquid undergoing a chemical change 
during the mixing. 


‘Department of Chemical Research. 417 


Fig. 17. 
Volts. Curves of Isomeric Electrolytes. 
-1°26 ge = = = — 6c A. ” 
Na,80,+2HNO, 

1:25 at 11°C. 
1:24 
1:23 SOBs 

x 2NaNO,+H,S0, 
1°22 at 14° C. 


1:21 
1:20 
1:19 
1:18 
1-17 
1:16 
1:15 
1:14 
1°13 
1:12 


: S 
Grains. S 


eS i © 
ie) = & fo 0) 
SS 6 Ss 


Ney 
oO 
> 


015 
020 
025 
030 
035 
040 
045 
050 
055 
060 


These-curves-show much more completely than any single 
pair of measurements of voltaic energy could do, the con- 
siderable differences between the molecular and chemical 
constitutions of the two liquids. Nearly throughout its entire 
range the curve of “ A” shows a greater degree of electro- 
motive force than that of “ B.” 

As the unstable liquid “A” is readily changed into the 
stable one ““B” by merely heating it to nearly "100°C. in a 
stoppered glass flask during fifteen minutes, and then would 
give the curve of “ B,” it is evident that the method of exami- 
ning aqueous solutions by means of curves of electromotive 
force is applicable for detecting and measuring chemical and 

molecular changes in them. 


B. CurvES BY VARYING THE STRENGTH OF THE SOLUTION AT 
OnE METAL ONLY. 


The kind of apparatus employed is shown by the annexed 
sketch, and is formed of glass. A weak solution, containing 
1 grain of the substance in 465 grains of water, was put, 
‘together with the negative metal, platinum, into the short lege 
of the tube, and successive portions of solution, of regularly 
decreasing strength, in 465 grains of water, were put, to- 
gether with the positive metal, unamalgamated zine, into the 
long leg, and the electromotive force with each strength of 
solution. was measured. The positions of the met: als were 
then reversed, and the measurements repeated. The glass 


418 Dr. G. Gore on a New Method and 


tap was closed during the process of changing each strength 
of liquid. In consequence of the much greater conduction 
resistance in the constricted portions of the solutions, the 
degrees of electromotive force were all much smaller than if 


ee 


the two metals had been near each other in thesame leg, The 
following are the results obtained with solutions of KBr and 


NaCl :— 
Fig. 18. 


Curve of KBr, by Varying Strength of Solution at One Metal only, at 
Volts. 162-5. 


1:22 
1°21 
1:20 
1°19 
1-18 
1:17 
1°16 
1:15 
114 | 
113 | 
1-12 | 


Zn only. 


Pt only. 


i By variation at 


) By variation at 


Department of Chemical Research. 419 


. Fig. 19. 
Curve of NaCl, by Varying Strength of Solution at One Metal only, 
Volts. at 15° C 
1 f| By variation at 
1°06 Pt only. 
Sige By variation at 
1:04 Zn only. 
1:03 
1-02 


1:01 


1°00 | 
“99 Ad pe 
a © 5 © 
=; N 
Grains. = = 10 st = Ss Bs a 3 = 
. ei ton) fe | et 


The curves show that the variation of strength of the liquid 
had a large effect upon the electromotive force at the surface 
of the zinc, but scarcely any such effect at that of the pla- 
tinum ; and we may conclude that when such variation of 
strength occurs at both metals simultaneously, the effect upon 
the electromotive force, and consequently also upon the form 
of the curves, is nearly wholly due to changes of chemical 
action at the surface of the zinc, and but little to such changes 
at the platinum. 

In a third similar oxperitient, with a solution of 1 part of 
potassium chloride and 465 parts of water at 15°°5 C. in the 
short leg, and one of the same salt, varying in strength equally 
in nine successive portions. from 3 to 147 grains, in 469 grains 
of water in the long leg, the changes of strength had no per- 
ceptible influence upon the electromotive force, which re- 
mained constant at 1°1544 volts whichever mee was in the 
longest leg. 


C. CurvEs By VARYING THE TEMPERATURE OF THE SOLUTION 
AT BotH MEtTALs. 
Curve of Dilute HCl. 

The solution contained ‘01 grain of HCl in 155 grains of 
water, and the electromotive force was measured every five 
Centigrade degrees from 10°C. to 100° C. 

| Fig. 20. 
Volts” Curve of dilute HCl. 


ss ie L 
3 a on oR eo MW oe 
Centisrade 3S FE SS 2 8 2S BS SF Bh S 2 .S S 


degrees. 


420 Dr. G. Gore on a New Method and 


This curve shows :—l1st. That the electromotive force varies 
with the temperature. And 2nd. That a regular variation of 
temperature of the solution is attended by an irregular change 
of electromotive force. It is probable that the curve obtained 
by varying the temperature is characteristic of the substance, 
and would be different with every different substance and 
degree of strength of its solution. 

In a similar experiment with a solution of ‘027 grain of 
chloride of ammonium in 465 grains of water, the electro- 
motive force of the zinc-platinum couple remained constant 
at ‘9084 volt at all temperatures between 14° and 100°C., 
and then very slightly increased. 


D. CurRVE BY VARYING THE TEMPERATURE OF THE SOLUTION 
AT Ong METAL ONLY. 


In these measurements the large bent glass tube was em- 
ployed (see section ‘B’’). The liquid consisted of 39 grains 
of potassium chloride dissolved in 465 grains of previously 
boiled distilled water. In one series of measurements the 
zinc was immersed in the heated portion of liquid and the 
platinum in the cold portion; and in the other series the 
reverse. The following are the curves obtained :— 


Fig. 21. 


Curves of KCl Solution. 


Volts. 
1°10 
1:09 

1-08 


1°07 


Zn at 17° C. 
1-06 Temperature of 
1-05 Pt varied. 
1°04 
1-03 
1°02 
101 
1:00 | 
“99 
“98 
3 Pt at 185° C. 
OF 
Lemperature of 
-*96 
“95 Zn varied. 


Centigrade S$ 2 8 SSS eR 
degrees. ij 


60 
70 


Department of Chemical Research. 421 


_ The two curves are very different. The greatest variation’ 
of electromotive force was.at. the zinc, and was = °108 volt, 
whilst that at the surface of the platinum was only = ‘04 volt. 

The results show that the change of electromotive force 
which occurred on gradually heating an electrolyte and the 
two metals in it is a concrete effect of two influences, one of 
which is situated at the surtace of the positive metal and the 
other at that of the negative one. Hach of these two in- 
fluences itself would also probably be a compound effect. of: 
the separate actions of heat upon the metal and upon the 
liquid. : 
Bitose general effects of variation of temperature described: 
in sections ‘ C ” and “ D” are very similar to those of change. 
of strength of liquid given in sections “ A” and “ B.” 


EH. GENERAL AND THEORETICAL CONSIDERATIONS. 


The evidence obtained by this research shows :—l1st. That. 
every different electrolytic substance when in aqueous solution 
gives, by varying the degree of strength of its solution (or by 
varying its temperature), a different curve of electromotive, 
force. 2nd. That this curve is characteristic of the substance. 
3rd. That under these conditions, substances which constitute 
a recognized chemical group yield a series of curves which 
usually exhibit a gradation of likeness of form. 4th. That. 
the degrees of electromotive force of such a group usually 
vary in magnitude inversely as the amounts of the atomic 
and molecular weights of the substances. 5th. That a much 
greater increase of electromotive force is usually caused by 
the first amount of substance added to the water than by the 
subsequent amounts. 6th. That the chemical union of two. 
substances to form a soluble salt is attended by a definite 
decrease of electromotive force and a definite change of form 
of curve. 7th. That the substitution of one halogen, acid, or 
metallic base for another in the composition of a soluble 
electrolytic salt, is accompanied by a definite amount of change 
of that force and of the form of its curve ; and it will be 
possible to trace, by means of these changes, the presence of 
each halogen, acid, and metal in the various solutions of its. 
salts. 8th. That isomeric solutions of electrolytic substances 
give different curves under the same conditions, and may thus 
be distinguished from each other. 9th. That molecular and 
chemical changes and their rates, in electrolytes, may be 
examined and measured by this method, And 10th. That if 
the solutions of the substances are too weak, the characteristic 
forms and differences of the curves are not fully developed, 


——————= 


422 Dr. G. Gore on a New Method and 


and if they are too strong the measurements of electromotive 
force are more difficult to make. As the measurements. were 
made at the null point when no current was passing, the 
curves represent the electromotive forces and molecular 
motions which exist under that condition; when the current 
passes, the molecular movements are greatly altered. 

_ The changes of electromotive force and forms of curve 
obtained,—I1st, by the same variations of strength of the 
same solution at two different temperatures; 2nd, by vary- 
ing the temperature of a solution without changing its 
strength ; and 3rd, by varying its temperature at the posi- 
tive metal only, or at the negative one only,—support the 
general view that each substance becomes more or less a 
different substance at each different temperature, and that the 
degrees of property of each substance at different tempera- 
tures are practically infinite in number. 

_ The results in general support the kinetic theory that the 
most fundamental attribute of matter is motion, that a mass 
of matter is a mass of motion, that each substance consists 
essentially of a collection of molecular motions, and that the 
chief properties of bodies are consequences of such motions. 
Changes of volta-electromotive force are now generally 
recognized as being due to those motions, and as being dis- 
turbances of the universal ether which pervades all bodies 
and all space. Hach degree of such force may also be 
regarded as a concrete result of an extensive series of mole- 
cular vibrations of extremely varied degrees of amplitude ; 
this series being characteristic of the particular material 
combination producing it, analogous to the collection of 
vibrations producing a beam of light of a particular burning 
substance. The curves represent in addition the changes in 
amount of these motions ; and by observing these changes in 
a single substance under a sufficient variety of conditions, a 
more or less complete graphic delineation of them as repre- 
senting that particular substance might be obtained. When 
we are able to fully interpret the language or meaning of 
thexe curves, we shall learn a very great deal respecting the 
internal motions and changes of substances, and the conditions 
of conversion of potential into kinetic energy. 

As each curve is a geometrical and quantitative representa- 
tion of.a series of such changes, a complete collection of such 
curves, yielded by all kinds of aqueous solutions, would con- 
stitute an extensive system of representations of the molecular 
motions of substances somewhat like that of the luminous 
spectra of bodies ; and the magnitudes and harmonic relations 
of the degrees of electromotive force represented by the 


Department of Chemical Research. 423 


curves will form a very large basis of study for mathema- 
ticians, such as the spectra of bodies now afford. The entire 
subject appears to be nearly as large as that of spectrum 
analysis, and is not altogether unlike it. 

The whole system of curves may be viewed as being in 
some respects analogous to the absorption-spectra of liquids, 
and in a less degree to the spectra of gases. The relations 
between the different curves are probably more complex than 
those between the spectra of liquids, because the electrodes 
take part in the action ; and still more complex than those 
between the spectra of gases, because of the influences of the 
solvent and of the electrodes, and because each dissolved 
substance is in the liquid state and under the influence of 
cohesion. 

As the magnitudes and forms of the curves are manifestly 
related to the atomic and molecular weights of the dissolved 
substances, they are doubtless also related to the periodic 
series, and in this direction a study of them by mathematicians 
will lead to the acquisition of new knowledge. And as they 
reveal the kinetic changes which isomeric and other sub- 
stances undergo when they pass from one state of chemical 
equilibrium to another in cases of chemical union, substitu- 
tion, and decomposition, &e., they are evidently related very 
intimately to Newton’s third law of motion. 

With regard to the latter suggestion, in several researches 
(see “ Relative Amounts of Voltaic Hnergy of Electrolytes,” 
Roy. Soc. Proc. November 1888, xlv. p. 266; “‘On Loss of 
Voltaic Energy of Electrolytes by Chemical Union,”’ Proc. 
Birm. Philos. Soc. December 1888, vi. p. 225; “ Relative 
Amounts of Available Voltaic Energy of Aqueous Solutions,” 
ibid. vii. part 1; “ Examples of Solution Compounds,” ibid. 
and ‘Chemical News,’ April 1890), I have largely shown, 
by means of the “voltaic balance”’ method, that chemical 
union in definite proportions by weight of substances whilst 
in aqueous solution together is apparently universal; that 
elements unite with elements, with all kinds of acids, and 
with all classes of acid, neutral, and basic salts; that acids 
unite with ‘acids, each with every other one, and each 
acid with every salt; and salts with each other in almost 
- endiess variety ; and apparently that all kinds of dissolved 
chemical compounds, with but few if any exceptions, unite 
together more or less distinctly, in those definite proportions 
indiscriminately and without limit of kind, provided no sepa- 
ration of substance by precipitation or otherwise occurs. 
Also, by repeatedly doubling the molecular weight of a 
‘solution compound” by successive additions to it of other 


“A424 Dr. G. Gore'on a New Method and 


dissolved substances of equal chemical value, each addition 


‘producing a new. state of chemical equilibrium, in which 


chemical action and reaction are equal, [ have by the same 
method shown that chemical union of substances whilst: in 
aqueous solution together extends to large aggregates of 
molecules of the most varied kind and of considerable degrees 


-of complexity (Proc. Birm. Phil. Soc. vi. p. 225). This 


universality of chemical union of substances whilst in solution 
together indicates the existence of an equally general cause 


-of such union, and that cause must be a molecular one. 
__“'The theory most consistent with these facts is a kinetic 
‘one, viz. that metals and electrolytes are throughout their 
‘masses in a state of molecular movement. That the molecules 


of these substances, being frictionless bodies in a frictionless 
medium, and their motion not being dissipated by conduction 
or otherwise, continue in motion until some cause arises to 


prevent them. That every different metal and_ electrolyte 


has a different class of motions, and that the molecular motion 
of each substance varies at a different rate by rise of tem- 
perature.” This theory has been employed by me to explain 
certain thermoelectric phenomena in electrolytes (see Roy. 
Soc. Proc. 1883, xxxvl. pp. 54-55). “In accordance with 
this theory chemical action is an effect of molecular motion, 
and is one of the modes by which that motion is converted into 
electric current.” ‘‘ These statements are also consistent with 


‘the view that the elementary substances lose a portion of 
‘their molecular activity when they unite to form acids or salts, 
and that electrolytes have usually a less degree of molecular 


motion than the. elements of which they are composed ” 


(ibid.). 


A kinetic theory must agree with mechanical laws ; we 
cannot create motion or energy, all motion arises from pre+ 
existing motion, every efficient cause of material change is a 
kinetic one ; the immediate source of all chemical change is 
the latent molecular motion of the combining or mutually 
acting substances. As neither mere difference of substance, 
nor union in definite proportions by weight, is in itself an 
active influence, neither can it be the immediate:kinetic cause 
of chemical change; but as both these circumstances in- 
variably: attend. chemical union, and no such union occurs 
without them, we may conclude that they are necessary con- 
ditions of the union. . 

By adopting. the above theory, “that electrolytes are 
throughout their masses in a state of. molecular movement : 
that. the molecules of: these substances, being frictionless 
bodies in a frictionless medium, and their motion not being 


Department of Chemical Research. 425 


dissipated by conduction or otherwise, they continue in- 
cessantly in movement until some cause arises to prevent 
them,” and associating it with Newton's third law of motion, 
viz., that “the actions of bodies upon one another are 
always equal and in opposite directions,” we are driven to the 
inference that, what we term “ chemical affinity,” or the 
_ immediate active cause of chemical union, is latent or potential 
molecular motion and the mutual impact and momentum of 
the molecules of the uniting substances. When two dissolved 
substances are brought by admixture of their solutions into 
mutual contact, a portion of the molecular motion of the one 
_ substance is neutralized by an equal amount of opposite 
_motion of the other, and the two portions are converte 1 into 
free heat, electric current, or other form of energy, and the 
molecules thus brought into nearer proximity retain their 
new positions and distances: this agrees with the usual evolu- 
tion of heat, loss of voltaic energy, depression of electromotive 
_ force, and frequent increase of density, which occur during 
chemical union. According to this view, every dissolved 
chemical compound is an instance of balanced molecular 
-motion, and it is the neutralized. portions of motion which 
_ escape as heat and electric current. How far there is any 
originality in these ideas I leave to other persons to decide. 
Many of the facts evolved by the several researches I have 
referred to point towards the conclusion that measurements 
of volta-electromotive force and voltaic energy are esgentially 
measurements of “ chemical affinity’ between the dissolved 
substance and the positive metal. An analogous idea has 
already been suggested by other investigators. H. F. Her- 
_roun, adopting a view of Helmholtz’s, has inferred that ‘the 
electromotive force of a voltaic cell is a measure of the actual 
transformation of free energy,’ and concluded that it “ fur- 
nishes a more accurate measurement of the free energy, and 
therefore of true chemical affinity, than data derived from 
calorimetric observations” (Phil. Mag. 1888, xxvii. pp. 230, 
233). The amounts of voltaic energy lost by two substances 
during their act of chemical union clearly indicate to a large 
extent the quantities of opposite molecular motion neutralized 
by their union. For instance, a much larger amount of such 
motion is neutralized by the union of sodium with chlorine to 
form sodic chloride than by that of hydrogen with chlorine to 
form hydrochloric acid; and no doubt, by investigating the 
losses of electromotive force and voltaic energy attending the 
chemical union of substances in aqueous solution, we may 
learn a very great deal respecting the quantitative relations 
of ‘chemical affinity ” between metals and electrolytes ; but 
Phil. Mag. 8. 5. Vol. 29. No. 180. May 1890. 2K 


426 New Method and Department of Chemical Research. 


a great obstacle to making accurate measurements of such 
“affinity ’” by this method is the unmeasured portion of energy 
lost by ‘‘local action.” It may be further remarked that, 
disregarding “local action,” this chemical union and neutrali- 
zation of opposite molecular motions only occurs whilst the 
circuit is closed ; and that at the instant of closing the circuit, 
potential energy is converted into kinetic energy, and a multi- 
tude of electromagnetic waves of very varied lengths are 
generated and radiated into space: the conversion of energy, 
therefore, in this kind of case depends upon closing of the 
circuit. 

The results obtained by varying the strength or the tempe- 
rature of the liquid at each metal separately support the con- 
clusion that, in an ordinary voltaic cell, nearly the whole of the 
energy is due to action at the zinc, and but little to that at the 
platinum ; and that the latter acts nearly wholly by obviating 
the greater counter electromotive force which would occur by 
using a more corrodible metal,and by diminishing the resist- 
ance which a less conducting substance would offer. The 
mere absence of an obstacle to a change cannot be an active 
cause of that change; and any substance which takes an 
essential part in any physical or chemical action, and (like 
the platinum plate) remains exactly the same in every respect 
after the action as it was immediately previous to it, cannot 
have been a real cause of that action, or of any loss or gain of 
energy attending it. The presence of the negative metal is 
only a static permitting condition ; it enables, without any 
expenditure of energy on its own part, the opposite potential 
molecular motions of the positive metal and the liquid to 
neutralize each other and to be converted into voltaie current. 

The method described in this paper is not merely a technical 
one of detecting substances, nor is it specially fitted for such 
a purpose ; but it is an extensive new department of chemical 
and molecular research, and a general system of representation 
by means of geometrical curves, not only of individual sub- 
stances, but of some of the fundamental changes of molecular 
motion of substances which are inseparably related to their 
chief chemical properties; and it will in this way supply 
mathematicians with a new and extensive series of facts, 
representing, in terms of electromotive force, the degrees of 
volta-chemical action of metals and electrolytes upon each 
other. One of the chief uses of it as a method of research 
will be to examine the molecular structure and chemical com- 
position of dissolved substances, to detect differences and 
changes in them caused by heat, light, chemical union, sub- 
stitution, or decomposition, &.; and to detect and measure 


The Nature of Solutions. 427 


molecular and chemical differences in isomeric liquids. It 
may be used to detect and measure the changes gradually 
produced by light and heat in chlorine water and bromine 
water, the influence of light upon nitric acid, the degrees of 
retarding effect of coloured glass screens &c. upon various 
chemical changes caused by light, the gradual oxidation of a 
solution of sulphurous anhydride by exposure to air, the 
spontaneous decomposition of aqua regia, the rate of de- 
composition of a solution of potassic iodide by chlorine water, 
the speed of displacement of one acid by another, &., &c. 
The examples given and researches suggested are sufficient 
to indicate the very great extent of the subject. 


XLV. The Nature of Solutions. 
By Spencer UMFREVILLE Pickerine, M.A.” 


N the March number of the Journal of the Chemical 
Society there was published a paper by the present writer, 
“On the Nuture of Solutions,” which had been honoured by 
an adverse criticism from Prof. Arrhenius (Phil. Mag. 1889, 
XXVill. p. 86) eight months before its appearance zn extenso. 

It is impossible to answer the objections raised by Prof. 
Arrhenius without giving some account of the work itself ; 
and, as this work is of a character calculated to interest many 
physicists, it may be advisable to give here a somewhat fuller 
résumé of it than would otherwise be necessary. 

Solutions of sulphuric acid formed the subject of the inves- 
tigation. Series of density-determinations with solutions of 
different strengths were made at 8°, 18°, 28°, and 38°, each 
series consisting of 50 to 100 determinations. A still more 
elaborate series of determinations of the heat of dissolution at 
18° were made, as well as some of the heat-capacity of solu- 
tions up to 12 percent. in strength. From the density-results 
at 18° the contraction on mixing was calculated, and these 
values treated independently. The density-results, moreover, 
at the four different temperatures gave the means of calcula- 
ting the expansion by heat for various intervals of temperature ; 
and, finally, F. and W. Kohlrausch’s determinations of the 
electric conductivity were re-examined, the first examination 
of them having been made by Crompton (Chem. Soc. Trans. 
1888, p. 116). 

Different solutions were for the most part used in investi- 
gating the different properties, and the total number of deter- 
minations made amounted to 600 or 700. 

The results were examined by plotting them out, and by 

* Communicated by the Author. 


ed at, HP He 


ee. 


428 Mr. 8S. U. Pickering on the 


differentiating them; the differentiation being performed ~ 
_ either on the experimental values themselves or on the smooth 


curves representing them, generally on both. 

For a direct differentiation the difference between the values 
obtained for the densities, or any other properties, of two solu- 
tions was divided by the difference in their percentage com- 
position. The result gave the first differential coefficient; that 
is, the rate of change in density between these two percent- 
ages, or, as it has ‘to be less perfectly expressed, at a point 
intermediate between the two. If the densities themselves 
form a continuous and regular curve, the differential deduced 
from them will form either another continuous curve or a 
straight line ; whereas, if the densities are represented by 
several different curves, the differential will consist of as many 
other curves or straight lines. Thus, differentiation was used 
primarily as a means of rendering more apparent any sudden 
changes of curvature in the figure representing the experi- 
ments ; but it generally indicated the nature of the component 
curves of the latter, since parabolic curves of the second order 
give straight lines as their first differential. Im all cases 
either the whole or else the greater part of the first differential 
figures obtained were curvilinear, but, on proceeding to a 
second differentiation, a rectilinear figure was obtained. 

The only case in which the second differentiation could be 
performed on the first differential values themselves was that 
of the electric conductivities ; in the other cases the magnitude 
of the errors of the experiments approached too nearly to that 
of the quantities constituting the second differential to render 
such a method practicable. In such cases it was necessary to 
reduce the error by plotting out the first differential points, 
drawing a smoothed curve through them, and performing the 
second differentiation on readings taken from this. Prof. 
Arrhenius objects to such a process : but it is one which every 
physicist uses to reduce experimental error, and objection 
might as well be made against taking the mean arithmetically 
of several determinations at the same point, as against taking the 
mean of a curve diagrammatically from several determinations 
along its course. To say that 1 in such a case the mean value 
taken, or the mean curve drawn, “ entirely lacks experimental 
foundation,” and still more, to say that I admit that it does so, 
is certainly incorrect. 

In all cases, except that of the densities and olen con- 
ductivities, the first differentiation was applied to the smoothed 
curve drawn to represent the experiments, as well as to the 
experimental values themselves: the two first differential 
figures thus obtained were treated separately and the results 
compared. 


Nature of Solutions. 429 


It was found impossible to draw any of the figures obtained 
with the help of a bent ruler, except in different sections. In 
some cases these sections cut each other on prolongation, 
this is so with the heat of dissolution and the expansion- 
results ; in others they meet tangentially, this is so with the 
first differentials of the densities and conductivities ; while in 
one case, that of the heat-capacities, they do not meet at all. 
But this want of continuity is probably only apparent. In all 
cases therefore, except the last mentioned, the whole figure is 
continuous. The fact that it can only be drawn in separate 
sections does not prove that it is made up of so many separate 
curves. This is only rendered probable by the fact that each 
section is shown by subsequent differentiation to be within 
experimental error a parabolic curve, and is proved by the 
fact that all the very different figures representing the differ- 
ent properties all require to be drawn in the same number of 
sections, and give the same number of lines for the second 
differentials, thus showing changes of curvature in the original 
figures at the same points. : 

Prof. Arrhenius attacks me on the subject of this smoothing 
of the curves, remarking that if“ Mr. Pickering had ‘smoothed’ 
his curve properly he would evidently have removed these 
angular points or sudden changes of curvature.’ The ques- 
tion hinges on the interpretation of the word “ properly.” 
Prof. Arrhenius seems to think that the “ proper” amount of 
smoothing to be made is such that all sudden changes of curva- 
ture should be obliterated ; and this, too, in an investigation the 
sole object of which is toascertain whether there are suchsudden 
changes or not. I must beg to differ from him. The “proper” 
amount of smoothing I take to be such as will allow but little 
more error in the experimental points than the known errors 
of the determinations, or than that which seems to be the 
probable error according to the irregularities of consecutive 
points in the figure. If with such smoothing we are led to 
conclusions which are obviously false, or which are at variance 
with the results obtained from independent sources, then and 
then only must we admit some further unknown source of 
error, and increase the smoothness of our drawings. 

Hven excessive and unwarrantable smoothing will not help 
us in reducing the whole figure to one regular curve, but 
results only in emphasizing the more marked changes of cur- 
vature as the less marked ones disappear. This was found to 
be so even in the case of the curve for the heat of dissolution 
of solutions from 5 per cent. in, strength upwards ; a curve 
which, of all the instances examined, was that in which the 
changes were the least marked, and in which the figure 
presented the greatest seeming regularity. 


430 Mr. 8. U. Pickering on the 


There can be no question but that the method of analysing 
results by differentiation presents many difficulties, and must 
be used with extreme caution ; nor can it be denied that many 
of the changes of curvature which I consider to be probable 
are but faintly marked, and are by no means beyond question. 
This must inevitably be the case if these changes are due to 
changes in the unstable and partially dissociated hydrates 
constituting the liquid. Their existence can be established only 
by the concordance of the indications obtained from many 
independent sources, and can scarcely be refuted by a hasty 
criticism (such as Prof. Arrhenius’ s) of results which had not 
been published. 

Figs. 1, 2, and 3 give rough illustrations of the six experi- 
mental curves examined. They show how very-different the 
figures are in the different cases, and how improbable it would 
be that they should all split up by mere chance into the same 
number of sections, and exhibit changes at the same points*. 
Illustrations of the first differentials derived from them would 
lead to the same conclusion. 


Fig. 1. 


Per cent. H,SOx. 


* Diagrams representing on a larger scale the portions below 10 per 
cent. would show the differences in’a still more striking manner. 


Nature of Solutions. 431 


Fig. 2. 
Heat % 
Diss. 
20,000 
Elect. 
Conduct. 
6000 15,000 
4000 10,000 
2000 5,000 
0 
0 20 40 60 89 luu 
Per cent. H,SO,. 
Fig. 3, 
Expansion 
for 3y°. 
"03 
“02 
“01 


0 20 40 6U 80 100 
Per cent. H,SQ,. 
Notrr.—Points have been inserted in these diagrams through error ; 
they do not represent the experiments, which are very numerous, 


432 Mr. 8S.’ U. Pickering on the 


_ The number of more or less sudden changes of curvature 
noticed amounted to seventeen, and, of the eight separate 
series of determinations, | 


1 showed 1 of the changes, 


2 ” 1 ” ” | 
3 ” 1 ” ” 
a: ” 4 ” ” 
g) ” 1 ”? ” 
6 ” @ ” ” 
q ” 2 ” ” 


and it may be fairly stated that in no case did any of the 
series fail to show a change except through lack of sufficien 
data. . 

_ The concordance, moreover, of the actual position of the 
changes shown by the various properties was certainly better 
than might have been expected, considering the great difficulty 
in determining the exact point at which any two constituent 
curves cut or touched each other. The average difference 
between their position as shown by the different individual 
properties (or by the same property at different temperatures) 
and by the mean results was only 0°388 per cent., and in only 
nine cases did it reach or exceed 1 per cent. ; 

Another point which adds confirmation to these results is, 
that in every case where the hydrate indicated is sufficiently 
simple to admit of its composition being determined accu- 
rately (that is, where a difference of 2 to 11 per cent. would | 
be caused by the addition of one more water-molecule), the 
changes occur at a point corresponding, within the oe 
limits of error, to a definite molecular composition*. There 
are seven such cases available, and the found and calculated 
values show an average difference of only 0:226 per cent., or 
about 0-057 H,O ; the maximum reaching but 0-48 per cent., 
or 7th H,0. te 

A comparison of the density-results at the four different. 
temperatures is very instructive. The first differentials show 
gradual changes in their general character as the temperature 
alters, the curvature in the various portions becoming more 
marked as the temperature is lower; yet, in spite of these 
alterations in general appearance, the points at which definite 
alterations in curvature occur remain unalteredt. The con- 


* Prof. Arrhenius implies that they do not; but as my found values 
were not published at the time when he wrote, I do not see how he was 
in a position to judge. 

‘i Tn attacking Mendeléeff, Prof. Arrhenius falls into the error of con- 
founding changes in general direction, especially positions of maximum 


‘Nature of Solutions. 433 


tractions also are. well worth attention.. They are deduced 
from the densities, but form a figure totally unlike the density- 
curve (fig. 1); and the first differential obtained from them 
is also totally unlike that from the densities. Yet the second 
differential figures in the two cases exhibit a similarity of the 
closest description, not only in general appearance, but in 
the inclination of almost every line constituting them, as well 
as in the position of the changes which they show. 

Prof. Arrhenius attempts to dismiss the argument based on 
the concordance of my results from independent sources, by 
stating “that Mr. Pickering with his multitudinous arbitrary 
constants can fix the points ‘where the breaks occur’ just where 
he chooses.” Had Prof. Arrhenius waited to see my results 
before he attacked them he would have found that, so far from 
working with “ multitudinous arbitrary constants,” I worked 
with no constants at all*; and he would also have found that 
an attempt to place the breaks by means of constants, or drawn 
curves, at points other than those at which they really occur 
led to a signal failure, even when the attempt was made on a 
portion of the density-curve where the true breaks or changes 
of curvature were but feebly marked (see p. 78, loc. cit.). 

The multiplicity of the hydrates as well as the complexity 
of the highest ones (containing as much as 5000 H,O) may 
no doubt prove a stumbling block to others as well as to Prof. 
Arrhenius. But till we have gained some slight knowledge 
of the constitution of solutions, it is surely well not to turn 
our backs on any evidence which may be forthcoming, and 
brand it as a reductio ad absurdum before it is produced. 
Organic chemistry would be non-existent had it met with 
such a reception. : 

Prof. Arrhenius’s attack reaches a climax when he states 
that ‘‘ Mr. Pickering has deduced from the specific gravity 
quite different hydrates from Mendeléeff, and from the. elec- 
tric conductivity quite different hydrates from Crompton.” 
This statement is certainly a most unfortunate one; for, 
though I altogether disagree with Mendeléeft’s views as to 
the nature of the density first differential, and though I think 
that Crompton’s conclusions were scarcely justified by the 


elevation, with definite changes of curvature (p. 34). It is obvious that 
the highest or lowest point in a curvilinear figure may occur in the middle 
of the most regular portion of it, and such points have nothing to do with 
the changes of curvature here dealt with. 

* I prefer imagining that Prof. Arrhenius really did think that I 
-worked by fitting equations with arbitrary constants on to my curves; 
but it is rather difficult to reconcile such a view with his previous 
remarks. : 


434 Mr. T. Mather on the Shape of Movable Coils 


facts at his disposal*, yet the hydrates which I mention as 
existing include those which both Mendeléeff and Crompton 
mentioned, thus:— 


gn, ll 
From Densities. || From Conductivities. ta 


sources. 
Mendeléeff. | Pickering. || Crompton. | Pickering. Pickering. _ 
About 84°5 | At 84-48 || About 845 | At 840 84:24 per cent. 
ye fod 1, TOF yy tod »» 403(?) 1304) ay 
Be FO Ol sont OU oe » 476 49-92 ete 
» 18°5 72185 189241 BS 


et Pane 5 ey BD! 7 BD. 7 || 
| 


I have mentioned above that the second differential is reeti- 
linear in every case ; but I do not by any means think that it 
has been proved to be absolutely so. The investigation was 
purely experimental in its nature; and the point of chief 
importance was that the lines ultimately obtained by differen- 
tiation should be straight within the limits of experimental 
error, for their being so proves that each of them is derived 
from an independent curve, which, within these same limits, is 
regular. 


XLVI. On the Shape of Movable Coils used in Electrical 
Measuring-Instruments. By T. Matuer, Assistant in the 
Physical Department, Central Institution f. 


[ is with some diffidence that I venture to bring the sub- 


ject of this note before the Society, because it concerns 
such a fundamental point in the construction of measuring- 
instruments having movable coils, such as d’Arsonval galva- 
nometers, electro-dynamometers, wattmeters, &c., that it is 
almost certain to have been worked out before. However, as 
the matter is not touched upon in the ordinary text-books, I 
bring it forward in the hope that it may serve to recall atten- 
tion to a subject which, judging from the construction of such 


* It is not difficult to see how both Mendeléeff and Crompton arrived 
at partially right conclusions from erroneous or insufficient premisses (doc. 
cit. pp. 79, 86, 125). 

+t Communicated by the Physical Society : read March 21, 1890. - 


used in Electrical Measuring-Instruments. 435 


instruments as are in common use, has been almost entirely 
ignored. — : 

In a paper “On Galvanometers,” by Prof. Ayrton, Dr. 
Sumpner, and the writer, read before the Society on Jan- 
uary 17th, it was pointed out that the coils of d’Arsonval 
galvanometers should be narrow and long, and that there 
should be no internal core. Mr. C. V. Boys had evidently 
arrived at the same conclusion long before the date referred 
to, for the coil of his radio-micrometer is a proof of this. 

The object of this paper is to determine the best shape of 
the section of the coil perpendicular to the axis about which 
it turns. 

The subject will be dealt with as concerning coils suspended 
in uniform fields, but similar reasoning may be applied to 
other instruments in which movable coils are used. 

Let the point O (fig. 1) represent in plan Fig. 1. 
the axis about which the coil turns,and assume A 
it is placed in a magnetic field whose direction | 
is perpendicular to A B. 

Let P be an element of the section of the | z 
coil, then the deflecting moment exerted by unit | Le 
length measured at right angles to the paper is re 

| 
| 
I 
! 


CARS Soca” gain Sy) ay al) 


where H is the strength of field, C the cur- 
rent-density per unit area, a the area of the 
element, and r its distance from the axis. B 


The moment of inertia of the element about O will be 
WOT Meal vanne ae ones Oe? 2) 
where w is the mass per unit cube. 

Now in ordinary commercial instruments it’ is important 
that the period of oscillation should not be inconveniently 
long, and that the power consumed by the instrument should 
_ be as small as possible ; then, since for a constant period the 
controlling moment at unit angle must be proportional to the 
_ moment of inertia, the problem resolves itself into finding the 
_ shape of the section such that the total deflecting moment for 

a given total moment of inertia is a maximum. 


The ratio of the Deflecting Moment to the Moment of 
Inertia for the element above considered is 


HCarsind — , ot SIG 


5 d. é. ee b 
war ’ , 


since H, ©, and w may be considered constants. 


436 Mr. T. Mather on the Shape of Movable Coils 


The ratio see thus is a measure of the efficacy of the 


element and its position. 


If we now draw a curve whose polar equation is 
7r=2; sin, 


then, as in Maxwell (vol. ii. p. 332), it may be shown that a 
given length of wire wound within this space is more efficient 
than if wound outside it. Hence the curve r=a;, sin 0, 
i. e. a circle tangential to AB at O, is the best form of the 
section of a movable coil, just as in the case of sensitive gal- 
vanometers the best shape is given by 


(ir SIMO! 


The complete section is given in fig. 2, 
and ,consists of two circles touching at O. 
The circles C and D have section-lines 
in different directions to indicate that the 
current passes in opposite directions in the 
two. 

The problem may be treated in another 
way ; for it resolves itself into finding the (777 
shape and position of an area having a W/7 
given moment of inertia about a point in 
its plane such that the moment of the area 
about a coplanar line through the point is 
a maximum. 

Taking the point as pole, and the line as the line of refer- 


-ence, the expression 


ig sin 0dr dé is to be a maximum, 
whilst 
iy) r® dr dé@ is constant. 


‘This may be solved by the Calculus of Variations with the 
result above obtained. By this method Dr. Sumpner (to 


whom the writer suggested the problem) arrived at the solu- 


tion some time before the author considered the subject from 


the first point of view. 

In order to illustrate the sort of improvement obtained by 
winding coils to this shape, a table is appended, the first 
column of which shows various shapes of section, the 
second column the value of the ratio moment of area 
— moment of inertia of area, and the fourth column the 
deflecting moments of the various shapes all having the unit 


used in Electrical Measuring-Instruments. 437- 


moment of inertia. From this last column it may be seen 
that the ordinary Siemens dynamometer type of coil, and those 
of d’Arsonval’s galvanometers and wattmeters, are far from 
being the most efficacious. | 

The numbers in column 4 are obtained on the assumption 
that the coils are long in proportion to their breadth ; and 
when this condition is not fulfilled (as it very seldom is), the 
numbers would be still further reduced, for the parts of the 
wire at right angles to the axis of suspension add to the 
moment of inertia but not much to the deflecting force. 

This consideration is of importance where the coils are of 
sections such as (4), (7), (8), (9); for as the coils are-wide, 
the useless moment of inertia sometimes amounts to one fifth 
the useful. In such a case as (8) the real numbers represent- 
ing the efficacy of the coil, as compared with one made to 
section (1) of the same moment of inertia, would be about 1 
to 38. These latter numbers represent approximately the 
efficacy of the coil of an ordinary Siemens dynamometer 
reading up to 60 amperes, as compared with that of a coil 
made to thé best shape. It is thus possible to increase the 
deflecting moment for a given current threefold by changing 
the shape of the movable coil and arranging the fixed coils to 
produce the same strength of field as at present used. 

Of course the new coil would be heavier than the old one, 
and would therefore require a stronger suspension which 
might introduce more vagueness of zero; but as the friction 
at the mercury-cups is considerable, the necessity for using a 
stronger suspension would not seriously interfere with the 
accuracy of the instrument. 

It will be noted that in the preceding part of this paper the 
moment of inertia of the suspended coil has been assumed 
constant; it is perhaps desirable to give reasons why this 
assumption is made. a 

In most instruments having movable coils which are in 
ordinary use, the current is led into and from the coil either 
by mercury-cups, or by wires which also serve as the control, 
or by flexible wires independent of the control. 

Taking the first case of mercury-cups, it may be noted that, 
owing to friction and viscosity, a certain minimum contro} 
is necessary to give the requisite definiteness of zero. As 
time is generally of importance in making commercial mea- 
surements, the period. of oscillation may be taken as constant. 
Therefore, as both control and period are determined by 
circumstances other than those affecting the shape of the coil, 
the moment of inertia may be taken as constant. 

When the current is led into the coil by the torsion-wires. 


ia = sail bed ; *) | — “s - ne ey Se ly a a 
ee oe == = ae aE 3 2 io ee". EP mt - Seer = ie pee on fee | 
RS RET 5 = =z TT Se a ee o—= : ; ie ret ae = ate = BS ee a ce eg Lt — c a s = 
aed = ex > = Ss Sa er eee = She hey iy om wore oe nw = < . . = 
: Se aad —= = een aie a tis a Gi ee TN nS en 
ee ee to Cai > Se -sleeis tote 2 PRE ERIE Pein, ecw es we > ee Se mows 3 ee ~~ 
- —— - + aE em ~~ eee 2 ee == eget rae 


Aare as 


jan al 


438 Mr. T. Mather on the Shape of Movable Coils 


the smallest size of the latter is usually determined by con- 
siderations of heating, and their length is limited by questions 
of portability, compactness, and resistance. This means that. 
the control cannot be diminished below a certain minimum, 
and hence, by reasoning as in the last paragraph, the moment 
of inertia of the coil must not exceed a certain value. 

The third case, where the leading-in wires are independent 
of the control, the conditions are somewhat similar to those 
in the first case ; for the size of these wires is determined by 
considerations of heating by the current to be measured, and 
they necessarily possess some viscosity or internal friction, 
which requires a certain control to give definiteness of zero. 

In addition to the assumption of constant Moment of 
Inertia, the field in which the coil swings is taken to be uni- 
form and parallel; and consequently the reasoning will not 
apply to radial fields which exist in instruments such as the 
new d’Arsonval milliamperemeter, having a range of 180°. 
In such case it would be advantageous to make the coil of 
a section similar to that in No. 4 (see table), keeping the 
radius 6 as small as possible. 

The shape given in No. 1 of table cannot be imitated 
exactly in practice, for insulation-space is required between 
the two halves, and unless the coil is used in a zero-instrument, 
parts near the axis might oppose the rest when a considerable 
deflexion exists. Shapes (3), (5), and (6) are also open to 
the same objection, but this is easily surmounted by allowing 
a small space to exist about the axis ; in fact some such space 
is almost necessary to enable the coil to he wound conveniently. 

Again, in Siemens dynamometers for fairly large currents 
it would be difficult to make the coil of the best shape, owing 
to the space required for the mercury-cups being considerable; 
but a much closer approximation to this shape than the one 
often employed could be used. 

In ordinary d’Arsonvals, which deflect through a consider- 
able angle, the shape should be modified so that no part of it 
crosses the line A B (fig. 2) even at the maximum deflexion, 
for any such part would oppose the rest of the coil. The 
resulting figure would be lemniscate-shaped. There are some 
cases, however, such as deflexional dynamometers, where it is 
advisable to make the coil of such a shape as to cross the line 
AB when deflected ; for then the deflexion would increase 
less rapidly than the square of the current, and hence the 
instrument would have a greater useful range for a given 


length of scale. 


$ 
e 


€<26-> 


used in Electrical Measuring-Instruments. 


Shape of Section. 


ISSN] 
ahaa ae a 
oO 


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t 
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4 


Deflecting moment | Proportions in 
Moment of inertia |particular cases. 


= 
a Bie olden 
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Cw 0—45°. 
8 
Snb @orteeceos 
4s8in 6 6,7—b,§ Weigel pew cle 
50) Uae Pien? a= Toby 
30 2a=—b. 
2(6?-4.a?) 4a=b. 
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4b aretayersucistale 
1 1 
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2 2 2 
(?+a7+36 Ee, 
Vaten. OG 
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439 
Deflecting 
moment 
per unit Instrument. 
Moment 


of inertia. 


1:02 
0°91 
0:95 
0:80 

Low-resistance 
0-44 { d’Arsonval. 
0:97 
0-91 
0:79 

Jolin’s 
: High-resistance 

0-47 d’ Arsonval. 


{ | Wattmeter (Ganz | 
0°38 { and Co.), 60 | 


amperes. 


Dynamometer 
(Siemens), 60 
amperes. 


| ae 
{ Dynamometer 
| 

| 


(Siemens), 500 | 
amperes. 
Wattmeter 
(Siemens), 500 | 
amperes. 


f 440 J 


XLVII. The Magnetization of Iron in Strong Fields. 
By SHELFORD BipWeL., J.A., P.RS.* 


N the Philosophical Magazine for April 1890, p. 293, 
Mr. Du Bois takes exception to the equation 


Wo=27l?+ HI, | 
which I employed (Proc. Roy. Soc. no. 245, 1886, p. 486) 


in calculating the curve of magnetization from observations 


of the pull between two halves of a divided ring-electro- 
2 


magnet. He objects that a term = ought to have been added 


for the mutual attraction of the two half coils of wire. 

In point of fact this attraction was found to be quite in- 
significant, and was purposely neglected. Within the limits 
of the magnetizing forces used it would have no effect what- 
ever upon the calculated values of I as given in my table. 
The greatest magnetizing force employed was 585C.G:S. units, 
when the weight supported was 15,905 grammes per sq. centim. 
Substituting these values for H and W, and putting g=981 
and 7=3'14, we get from my equation 


l=15304: 
2 
If we add the term — the solution is 


87 
T=1530°2. 


The value given in my table (in which decimals are dis- 
carded) is 
iea=1530) 


For the greatest value of H the error is therefore only 2 in 
the first place of decimals: for smaller values it would of 
course be less ; and it is clear that, whatever the results of m 
experiments may be worth, they are not affected by the 
omission to which Mr. Du Bois calls attention. 

I regret that, through a mistake, I found fault with Row- 


2 
land’s expression Wg= = It would certainly have afforded 


a better and more direct_method than my own of arriving at 
the values of B. 


* Communicated by the Author. 


ier res 


XLVI. On the Passage of Electricity through Hot Gases. 
By J. J. Tuomson, W.A., F.RS., Cavendish Professor of 
Haperimental Physics, Cambridge. 

[ Continued from p. 366]. 


Conductivity of Hot Metallic Vapours. 
O vaporize such metals as silver or tin a higher tempera- 
ture is required than can be produced by the arrange- 
ment which sufficed for the substances hitherto described. 
The method used to determine the conductivity of metallic 
vapours was as follows:—In a brick made of “ ganister”’ a 
vertical channel was bored, into which an earthenware crucible 
was placed ; this vertical channel was in communication with 
a horizontal one which conveyed the flame of a large oxy- 
hydrogen blowpipe. The terminals conveying the current 
dipped into the crucible, which was kept full of nitrogen 
when the metal used was one that readily oxydized. In this 
furnace silver could be volatilized, and the electrical conduc- 
tivity of it and most of the metals more volatile than it were 
tested. 

The metals tried were sodium, potassium, thallium, cad- 
mium, mercury, bismuth, lead, aluminium, magnesium, tin, 
zinc, and silver. Of these the vapours of mercury, tin, and 
thallium did not seem to conduct at all; at any rate their con- 
ductivity is less than that of air; the vapours of the other 
metals conducted very much better than air, the best con- 
ductors being the vapours of sodium and potassium, which 
conducted even better than ‘iodine. 

The difference between the behaviour of the vapours of 
mereury, tin, and thallium and that of the other metallic 
vapours is very remarkable. I thought at first it was con- 
nected with the behaviour of the salts of these metals when 
used as electrolytes, as the chlorides of mercury are such bad 
conductors as hardly te deserve the name of electrolytes, while 
one of the chlorides of tin is a non-conductor ; however, Mr. 
T. C. Fitzpatrick, who kindly determined for me the con- 
ductivity of thallium chloride, found that it was normal, so 
that the behaviour of the metallic vapours does not seem neces- 
sarily connected with the conductivity of the salts of the metal. 

The vapour-densities of most of the metals seem to show 
that the molecules of metals are monatomic ; if we suppose 
the atom is able to possess and give up a charge of electricity, 
this fact would explain the conductivity of their vapours. 

If tin and thallium were found to be exceptions to the rule 
that the molecule of a metal is monatomic their want of con- 
ductivity would be explained. The vapour-density of mercury 
shows that if its molecule is diatomic all the compounds ot 


Phil. Mag. 8. 5. Vol. 29. No. 180. May 1890. 2 L 


—————oeoorr rr SS 
ee 


waiek! 
8 iO IO Pi PE PPR INET 


Saeed 
sat — pili eR. 
aaa he 


442 Prof. J. J. Thomson on the Passage 


mercury we know are molecular compounds—that is, they 
contain the molecule of mercury and not the atom ; the other 
alternative would be that the atoms of mercury differ from 
other atoms in not being charged. 


Further Experiments on the Conductivity of Arr. 


Some experiments, in which the arrangement was slightly 
altered, seem to throw light on the way in which air conducts 
electricity : the electrodes, instead of being placed as in the 
previous experiments in a platinum tube closed at one end 
and heated by a furnace, were placed at opposite ends of a 
vertical thin platinum tube open at both ends, which could be 
made white hot by passing the current from a large number 
of storage-cells through it. With this arrangement it was 
found that the current through the hot air was very different 
according as the upper terminal was positive or negative. 
When the upper electrode was negative there was hardly any 
deflexion, but when it was positive there was a deflexion of 
70 or 80 scale-divisions. In this experiment there is no 
appreciable difference of temperature between the top and 
bottom of the tube; there is, however, a rush of heated air up 
the tube; and the experiment shows that the positive current 
of electricity travels much more easily against the current of 
hot air than with it, indicating I think that the current is 
largely due to convection and that the particles carrying the 
current travel from the negative to the positive pole. This 
seems in accordance with the experiments of Lenard and 
Wolff already mentioned, for they found that negatively 
charged platinum disintegrated much more readily than un- 
charged or positively charged platinum. 

When the tube was placed in a bell-jar, filled with one of 
those gases which conduct electricity well, such as hydro- 
chloric-acid gas, it made but little difference to the current 
whether the top or bottom electrode was negative, though on 
admitting the air this difference was at once detected. This 
indicates, I think, that the main part of the current through 
air is carried in a different way from that in which it is 
carried through one of the better conducting gases. 


Laws of Conduction through Hot Gases. 


It is known that the conduction through hot air does not 
obey Ohm’s law (Blondlot, Journal de Physique, 2° série, t. vi. 
March 1887). The following experiments, although they 
cannot lay claim to any very great accuracy, show that the 
conduction through those gases which conduct electricity 
well does not depart very much from Ohm’s law. The great 
difficulty in these experiments is to keep the temperature 


of Electricity through Hot Gases. 445 


constant. I found it impossible to do this for any length 
of time, and so endeavoured to make the experiments as 
quickly as possible. For this purpose a series of small storage- 
cells were arranged within easy reach of the observer, and 
connected in such a way that the number of cells in the 
circuit could be altered by lifting a wire from one mercury 
cup and putting it in another. The following are the results 
obtained in this way with hydrochloric-acid gas at a yellow 
heat, the observations made within a short time of each other 
being enclosed tn brackets :— 


Number of Cells. Deflexion. Deflexion per Cell. 

J | a) ang) 

3 13 43 

9 j 35 3°9 

3 13 Aloe 

5 45 9°0 

4 35 8°75 

Z, 20 10:0 

4. 30 8°75 J 
8 39 4-4. 

4 ‘i 20 } 5:0 } 


These experiments seem to indicate that these gases obey 
Ohm’s law. 


Influence of the Temperature of the Electrode on the Passage 
of Electricity through Hot Gases. 

The condition of the electrodes exerts a most powerful 
influence on the passage of electricity through the best 
conducting gases. This was proved by several experiments 
in which cold electrodes were suddenly dipped into a gas 
maintained at a temperature sufficiently high to make it 
conduct. This experiment was tried in three ways—first, 
with the platinum tube heated by the furnace ; secondly, with 
the tube heated by the current; and, thirdly, with the cru- 
cible heated by the oxy-hydrogen blowpipe. In all these 
cases an arrangement was fitted up which enabled the 
observer to lift the electrodes (or one of them in the case of 
the tube heated by the current) out of the hot gas, allow 
them to cool, and then rapidly replace them. It was always 
found that however hot the gas might be no deflexion of the 
galvanometer occurred when the cold electrodes were first 
placed in the hot gas, and that the time when the mirror of 
the galvanometer began to move was just the time the elec- 
trodes began to glow. The experiment was repeatedly tried 
both with thick and thin platinum wires, and with thin carbon 
filaments and thick carbon rods. The cooling of the gas by 
contact with the electrode does not seem sufficient to explain 


A444 Prof. J. J. Thomson on the Passage 


this effect, as before the hot gas can be cooled it must come 
into contact with the electrode ; and as there is a strong up 
current of hot gas fresh supplies of it are continually coming 
into cuntact with the electrode ; so that if the hot gas could 
give up its electricity to the cold electrode there would be a 
current through the gas. The difficulty with which cold 
metals get electrified by hot gases is also shown by the 
following experiment:—two platinum electrodes were im- 
mersed in iodine at a yellow heat, and a piece of platinum 
foil, whether insulated or uninsulated is immaterial, was 
arranged so that it could be lowered between the electrodes 
or raised from the hot gasat pleasure. Initially the platinum 
foil was out of the iodine and a current was flowing through 
the hot gas; the foil was then lowered into the hot gas and 
at once stopped the current. As soon, however, as the foil 
began to glow the current recommenced, and the system finally 
conducted as well as before the introduction of the foil. These 
experiments seem to show that for electricity to get from the 
gas into the electrode, or in other words for the atoms to give 
up their charges to the electrodes, the latter must be at least 
red hot. Whether this is due to the disintegration of the 
electrodes at a red heat, or to the increase in the temperature 
of the electrode producing an increase in that action between 
the gas and the metal which manifests itself in the case of 
some gases and metals as chemical action, is a point which I 
hope to investigate more fully. 


Influence of the Material of the Electrode. 

Hlectrodes of platinum, iron, carbon, gold, and aluminium 
were tried ; the experiments with the aluminium electrodes 
were not, however, satisfactory, as the electrodes melted as 
soon as the temperature was high enough to make the gas 
conduct. The resistance of a conducting gas, such as iodine, 
seemed practically the same whichever of the first four sub- 
stances were used. Copper electrodes seemed also to behave 
in the same way until they got covered with a coating of 
oxide. 

Symmetry of the Conduction. 

There does not seem to be in the conduction of electricity 
through those hot gases which conduct the most readily, that 
dissimilarity in the properties of the positive and negative 
electrodes which is found in the discharge through vacuum 
tubes and in the more closely analogous case of conduction 
through flames. This was tested by using two electrodes, A 
and B, which were very unlike in shape and size: in most of the 
experiments A was a piece of platinum foil, while B was a thin 
platinum wire. The deflexion of the galvanometer was observed, — 


of Electricity through Hot Gases. 445 


first when A was the positive and B the negative electrode; and, 
secondly, when B was the positive and A the negative elec- 
trode. No difference could, however, be observed between the 
two cases. This is in striking contrast to the resuits of a 
similar experiment made by Hankel (Wiedemann’s Llektrici- 
tat, iv. p. 891) with different-sized electrodes immersed in a 
flame ; for Hankel found that the deflexion of the galvano- 
meter when the largest electrode was negative was greater 
than when it was positive in the proportion of 294 to 34. 
We must remember, however, that though a flame is no doubt 
very hot gas, the condition of this gas is not nearly so simple 
as that of the hot gas which was the subject of our experiments. 
For, in the first place, the temperature of the flame varies 
greatly from place to place, and, secondly, there seems to be 
a separation of the electricities in the flame, so that the nega- 
tive electricity is in one part of the flame and the positive in 
another. In the hot gas with which we had to deal the 
temperature was very much more uniform than in the case of a 
flame, and there was no evidence of the positive electricity 
being in one part of the gas and the negative in another, as is 
the case in the flame ; this separation of the electricities might 
easily give rise to a want of symmetry in the conduction. 

Another way in which the symmetry of the conduction was 
tested was by raising one electrode out of the hot gas and 
keeping it out until it was cool, then suddenly plunging it 
into the hot gas again. In this case it was found that there 
was no conduction until both electrodes were glowing, how- 
ever the signs of the hot and cold electrodes were changed. 
The same thing was tried in a slightly different way by 
having two earthenware crucibles at a white heat connected 
by a strip of platinum foil with one electrode dipping into one 
crucible and the other into the other; a gas which conducted 
well was put into one crucible, while the other crucible con- 
tained air. No difference in the deflexion of the galvanometer 
could be detected when the signs of the electrodes were 
reversed. 


Polarization. 


A great many experiments were made with various hot 
gases, such as iodine, hydricdic acid, hydrochloric-acid gas, 
and the vapours of sodium and potassium, to see if the passage 
of the electricity through these gases produced any polarization 
of the electrodes. The result of these experiments was that 
when all the sources of disturbance were eliminated no effect 
of this kind could be detected. In the first set of experi- 
ments a commutator was used which first sent the current 
through the gas, the galvanometer being out of circuit ; on 


446 Prof. J. J. Thomson on the Passage 


reversing the commutator, the battery was thrown out of 
circuit and the galvanometer in. In this case no deflexion of 
the galvanometer was obtained though the current from 150 
Daniell’s cells had passed through the gas for several minutes. 
As, however, it seemed possible that the polarization of the 
electrodes, if it existed, might have disappeared in the short 
time taken to reverse the commutator, another experiment was 
tried. In this a very large resistance, formed by rubbing 
graphite on a piece of ebonite, was put in parallel with the 
hot-gas resistance. The graphite resistance was so large that 
practically all the current went through the hot gas; and the 
galvanometer-needle was so still that any disturbance of it 
could easily have been detected. On breaking the battery 
circuit, however, no kick of the galvanometer could be 
detected, though as before the current from a battery of 150 
Daniell’s cells had been flowing through the hot gas for 
several minutes. 

Hlectrolytic polarization is connected with the work re- 
quired to split up the electrolyte into itsions. In the case of the 
hot gas on our supposition the molecules are already split up 
into their ions, so that the absence of polarization in this 
case is not inconsistent with its presence in electrolysis. 

At first sight it might seem that the fact that those gases 
which dissociate conduct electricity on a scale altogether 
different from those which do not, points to the theory that 
the conductivity of electrolytes is due to the presence in the 
liquid of free ions, the number of these being very large, in 
some cases so large that it corresponds to a dissociation of 
more than 90 per cent. of the electrolyte. I think, however, 
that a closer examination of the case will lead to the opposite 
conclusion. Let us take the case of iodine for example, 
which at high temperatures is known to dissociate largely. 
The specific resistance of iodine vapour at a yellow heat is 
comparable with +1, of a megohm, or about the same order of 
magnitude as that of glass at the temperature 300°C. This 
resistance is enormously greater than that of a solution of 
potassium iodide for example, containing the same number of 
molecules per unit volume as the gas; on the hypothesis of 
free ions, with definite electrical charges, we should expect the 
opposite result, as we cannot suppose that the resistance to the 
motion of the free ions is as great in the gas as it is in the 
liquid. The agreement between the conductivity of a salt 
solution and the effect produced by the presence of the salt on 
the freezing-point and vapour-pressure does not seem to be 
at all a conclusive argument as to the existence of these 
free ions ; for exactly the same result would follow on the hy- 
pothesis that the conductivity was proportional to the chemical 


of Electricity through Hot Gases. 447 


action between the salt and the solvent, if the thermal effect 
accompanying this action were to follow the logarithmic law, 
that is if the thermal effect produced by increasing the 
quantity of water by unity were inversely proportional to the 
quantity of water already present. 

From the consideration of the preceding experiments we 
may deduce, I think, the conclusion that it is the atoms, as 
distinct from the molecules, which are instrumental in carrying 
electricity from one place to another, and that the molecules 
are electrically inactive. 

Many interesting questions arise as to how the atoms effect 
this transference of electricity. Does each atom, for example, 
carry a charge equal to that (10—" in electrostatic units) 
deduced from electrolytic considerations, and is this charge 
unalterable ? 

In this connexion it is important to notice that all that 
electrolysis teaches us is that each ion which comes up to the 
electrode receives from it a definite and calculable charge. 
It does not, however, give us any information about the 
charges on ions under other circumstances. If we adopt the 
view enunciated by v. Helmholtz, inthe Faraday lecture, that 
chemical forces are electrical in their origin, we must suppose 
that the charges on the atoms are susceptible of change, tor 
the hydrogen ascending from the kathode is in the molecular 
condition, each molecule consisting of two atoms with equal 
and opposite charges ; the charges on one or both of these 
atoms must have undergone some change, for when the atoms 
were in contact with the kathode they were presumably in the 
same electrical condition. It seems probable that when two 
atoms come very near together they may affect the charges on 
each other, the gain of the one being equal to the loss of the 
other. ‘To fix our ideas we may imagine that the electric 
charge is measured by the momentum corresponding to some 
coordinate helping to fix the configuration of the atom, and 
that when two atoms come quite close together their momenta 
change, the one gaining as much as the other loses. 

If we had a collection of charged atoms of this kind, even 
though the charges might not all be numerically exactly 
equal, if combination began the molecules formed would be 
electrically neutral, for the potential energy, other things 
being the same, is a minimum when this is the case. 

It may perhaps give a clearer idea of the theory we are con- 
sidering if we take the particular case of a charged metal plate 
and consider what are the conditions under which it can lose its 
charge. According to our view the charge on the plate implies 
the presence of atoms of the metal of which the plate is made; 
and in order for the plate to lose its charge, these charged 


aoe Sen 
a 


a 


ao 


paaes 


448 Passage of Electricity through Hot Gases. 


atoms must be neutralized by combining with equal and 
oppositely charged atoms, or perhaps by acting on atoms 
quite close to them. In any case, for the charge to diminish 
there must be atoms in the neighbourhood of the plate. If 
the electric intensity in the neighbourhood of the plate is 
sufficient, these may be supplied by the splitting up of the 
molecules by the electric field, and we have the electric dis- 
charge; or the atoms may, as in our experiments, be supplied 
by the dissociation of the molecules by heat. Besides the 
mere existence of the atoms, the conditions must be such that 
they come into intimate contact with those of the metal. 

A possible way of supplying the atoms necessary to get rid 
of the charge might be by chemical action of the gas on the 
electrodes. In this case, however, the leak would be much 
less than if the whole body of the gas contained free atoms, as 
in the preceding experiments. I tried some experiments on 
the conductivity of gases which slowly acted on the elec- 
trodes, and also of mixture of gases, such as chlorine and 
H.8, which slowly act upon each other, these experiments 
being made at a temperature less than 100° C. I was not able 
to be sure of any leak by the galvanometer method, and a 
similar remark applies to an experiment when the electrodes 
were made white hot while the gas was cold. It must be 
remembered that the galvanometer method, although more 
convenient, is not nearly so sensitive as the electrostatic 
method; so that these results only show that the conductivity 
in these cases is not comparable with that of some hot gases. 
It is known that the leak from a hot platinum wire can be 
detected with an electroscope. 

The connexion on this view between the conductivity of 
metals and their tendency to assume the atomic condition, 
which is exemplified by the abnormal vapour-densities of 
these substances, will at once occur to the reader. 


Unsaturated Compounds. 


It is very interesting to see whether the molecules of un- 
saturated compounds possess the same electrical properties as 
atoms or not. I accordingly examined the electrical pro- 
perties of two gases, which on the ordinary electrical theory 


- of chemical action would be unsaturated, viz. NO, and ozone, 


prepared by passing air through a tube in which the silent 
discharge was taking place. I could not ascertain that these 
gases behave in any way differently from air. They transmit 
electrostatic induction: for example, a gold-leaf electroscope 
will work perfectly well inside a glass vessel filled with NO 
or ozone, and the leaves will be attracted by an electrified 
body outside the electroscope. A current from a battery 
containing a moderate number of cells will not pass through. 


Notices respecting New Books. — 449 


these gases when cold, nor will a current go through NO 
when the electrodes are made to glow by insulated batteries ; 
so that in this case the want of conductivity cannot be due to 
the electricity being unable to get from the gas into the elec- 
trodes. These experiments show that the molecules of those 
gases are electrically neutral. This cannot be the case if we 
suppose the atoms to be charged with definite and equal 
quantities of electricity ; for if this were so, O3, the molecule 
of ozone, would have a resultant charge. We must therefore 
either suppose that the charges on the atoms are capable of 
variation, or else that the resultant effect of the charges on 
the atoms is to be got by combining the charges like vectors 
and not like scalars, for if this were so it would be easy to 
explain the neutrality of Qs. 


- ALIX. Notices respecting New Books. 


Algebra: an elementary Textbook for the higher classes of Secondary 
Schools and for Colleges. By G. Curystat, LL.D. Part Il. 
(Edinburgh: Black. 1889. Pp. xxiv+588.) 


a this splendid volume we have the fulfilment of the Author's 

promise, and, we presume, the completion of his labours upon 
Elementary Algebra. Of what sort this work is will be recog- 
nized by readers of the first volume when they are assured that the 
present instalment is even more worthy of praise, if that be pos- 
sible, than its predecessor. There is no shirking of difficulties, for 
our Author is a past master of his subject; and from a large 
acquaintance with what has been written upon it, both recently 
and long ago, is able to bring forth things new and old out of his 
ample store. Still he does not exhibit his wares from a vain 
desire to show off, but has ever an eye to what will be useful to 
the student subsequently. Hence in his chapter on Probability 
he omits “matter of doubtful soundness, and of questionable 
utility,” and fills the place usually occupied therewith with “a 
useful exposition of the principles of actuarial calculation.” There 
is a very full analytical Table of Contents which puts the student 
easily in possession of the heads of the matters discussed in the 
text. There are, as before, valuable historical. notes, and to 
crown all there is a full Index of Names of Mathematicians whose 
works have been cited in the two volumes. Much time has been 
devoted to the construction of the work; this is evident on the 
most cursory examination, but we feel convinced that Dr. Chrystal 
has an ample reward in the admiring gratitude of his readers. 
They feel that if the Author has given so much of his valuable 
labour to make the path, if not smooth for them, at least plain, 
and has collected so many objects of interest for their inspection, 
it is but meet that they should not flinch from doing their best 
to master what he has put before them. Our Author, it is well 
known, has clear and pronounced views on the teaching of Mathe- 
matics, and in his preface he comments on points to which we will 
now briefly refer. The practice of ‘hurrying young students inte 


Phil. Mag. S. 5. Vol. 29. No. 180. May 1890. 2M 


450 Intelligence and Miscellaneous Articles. 


the manipulation of the machinery of the Differential and Integral = 
Calculus before they have grasped the preliminary notions of a 
Limit and of an Infinite Series” he pronounces to be to a large 
extent an “educational sham,” which is a “sin against the spirit 
of mathematical progress.” Hence, after devoting the two opening 
chapters to the subjects of Permutations and Combinations, and 
the general theory of Inequalities, he discusses very fully and 
adinirably in the following two chapters the doctrine of Limits 
and the convergence of infinite series and of infinite products: 
these are followed by chapters applying the previous results to 
Binomial and Multinomial series for any index, and to Exponential 
and Logarithmic series. All this forms a good introduction to the 
theory of Functions, such as has been opened up by the labours of 
Cauchy, Riemann, Weierstrass, and others, and will enable the 
student who assimilates the results to get an intelligent hold upon 
the Calculus. This account of the function-theory is further illus- 
trated in other three chapters, in which the Author treats of 
Graphs of the circular functions, Riemann’s surface, hyperbolic 
functions, Gudermannian functions, the numbers of Bernoulli and 
Euler, anda host of other choice matters, succeeded by explana- 
tions of the method of finite differences, Recurring series, and a 
group of miscellaneous methods. The concluding five chapters are 
devoted to Continued Fractions, properties of Integral Numbers, 
and, as we have already mentioned, Probability. This is a very 
scanty account of much admirable work, but the analysis of one 
chapter would occupy too much space. The dip we have made 
here and there (on the ex pede Herculem theory) will be enough 
to assure those of our readers who have not yet got the book that 
there is a rare treat in store for them if they will but get it. The 
“ set-up” and other features make the volume a handsome addition 
to one’s book-shelf. 


L. Intelligence and Miscellaneous Articles. 


ON ELECTRICAL OSCILLATIONS IN STRAIGHT CONDUCTORS. 
BY PROF. STEFAN. 


E a variable current is transmitted through a wire which is sur- 

rounded by a concentric metal tube, a current is induced in this 
tube. The direction and magnitude, as well as the distribution in the 
tube, may be directly deduced from the principle of least magnetic 
energy when the current in the wire is supposed to be given. The 
minimum of this energy is obtained by the following arrangement 
of the currents :—The central current is condensed in an infinitely 
thin layer on the surface. The induced current flows in an infi- 
nitely thin layer on the inner surface of the tube, and has at any 
instant the same intensity as the current in the central wire, but 
the opposite direction. With this arrangement magnetic forces 
are only effective in the space between the surface of the wire and’ 
the inner surface of the tube. The interior of the wire as well as 
that filled by the mass of the tube, and in addition the whole 
external face, are free from magnetic forces. ot 


Intelligence and Miscellaneous Articles. 451 


~ The tube laid round the wire neutralizes also its inductive action 
in the entire outer space; it forms a complete screen for the indu- 
cing as well as the magnetic forces of the wire surrounded by it. 
The screening action of the tube, according to this view, consists in 
the fact that the actions of the central current are neutralized by 
those of the induced current in the tube. : 

This case is completely analogous to the electrostatic problem of 
the distribution of electricity on two concentric cylinders, of which 
the inner one is insulated and the outer put to earth. In like 
manner the problem of the distribution of the current, even when 
the wire and the tube are not concentric, and have other than 
circular section, is to be solved by the analogous problem in elec- 
trostatics. The screening action of the tube is complete even under 
these altered conditions. 

The influence of the screening-tube on the velocity of propaga- 
tion of waves in the wire results in the following manner :—By 
restricting the magnetic field to the space between the wire and the 
tube, the self-induction in the wire is considerably diminished. For 
a circular section and concentric positions this diminution may be 
easily given. An increase of the velocity of propagation corre- 
sponds to this, if the capacity is almost the same, which, according 
to electrostatic rules, is the case so long as the tube is insulated. 
But if this is put to earth, the capacity of the inner wire is increased 
in proportion as the self-induction is diminished, and consequently 
the velocity of propagation remains unchanged. 

The capacity may, however, be considerably increased by filling 
the space between the wire and the tube with a stronger dielectric 
than air; by interposing, for instance, a glass tube between the wire 
andthe tube. This glass tube has no influence on the self-induction, 
but the capacity is almost doubled. The velocity of propagation 
sinks thus in the ratio of V2 to1. Sir W. Thomson has already 
remarked this influence of the insulating medium on the velocity 
of propagation. 

If a current is divided at two equal wires, one of which is sur- 
rounded by a tube but the other not, the former will take a far 
greater part of the current than the second, owing to the greater 
ae of the self-induction, which is due to the enveloping 
tube. 

If, now, a second straight wire is placed parallel to a conductor 
through which acurrent is passing, the primary current distributes 
itself on the surface of the first, and the induced one on that of the 
second conductor, in the same way as a given charge would be dis- 
tributed on the first, and the induced one on the second conductor, 
if the Jatter were put to earth. If the first conductor has a circular 
section, the current is not distributed uniformly over its surface, but 
has a greater density on the side nearest the second conductor than on 
that away from it. If this condensation is visible, as in a Geissler’s 
tube, it presents the phenomenon of an attraction of the current 
towards the approached conductor. As a matter of fact, there is 
an electrodynamical repulsion between the conductor of the pri- 
mary current and the approached conductor, which is observed at 


452 Intelligence and Miscellaneous Articles. 


a higher degree of rarefaction, and therefore at an increased resist- 
ance, in which the apparent attraction no longer occurs. 

- A conductor also which does not encircle the one carrying the 
current partially exerts a screening action, and to a greater extent 
the longer it is. Prof. Hertz has shown that a system of parallel 
stretched wires may also act as a plane-shaped conductor. Such 
a system of wires can, however, only exert a screening action if 
the primary current can induce currents in those wires; such 
wires form, therefore, no screen when they are placed at right 
angles to the primary conductor. Induced currents form also an 
essential condition that a conductor can reflect inducing actions. 
The reflected actions are the actions of the currents which are 
induced on the surface of the reflecting conductor.— Wzener Berichte, 
January 16, 1890. 


ON THE OSCILLATIONS OF PERIODICALLY HEATED AIR. 
BY DR. MARGULES. 


Prof. Hann’s investigations on the Daily Oscillation of the 
Barometer led the author to calculate the variations in pressure 
which result from periodical changes of temperature in the air. 
Plane waves of temperature progressing in a plane stratum of air 
produce pressure-waves of equal period, the amplitude of which is 
greater the nearer the velocity of propagation of the constrained ap- 
proximates to that of the free vibrations. If the atmosphere were cut 
into a great number of zones each of which was traversed by a daily 
wave of temperature, the zones near the equator would have waves of 
pressure in which the maximum coincided with the maximum of 
temperature; near the poles the phases would be opposite, at 50° of 
latitude the amplitude would be very great, and in two adjacent zones 
of opposite phase. The magnitude of the differences of pressure be- 
tween two separate zones which thus results shows that the transfer- 
ence to annular spaces of the calculation which holds for plane waves 


as not sufficient, and that the movements of the air upon the globe 


must be calculated without diaphragms, if waves of temperature 
travel from meridian to meridian. The calculation for the spheroid 
at rest shows, as already demonstrated by Lord Rayleigh in a 


recent paper (Phil. Mag. February 1890), that the semidiurnal 


waves of pressure on the earth are far smaller than the diurnal 
ones, even if the corresponding waves of temperature are of the 


‘same amplitude. But the semidiurnal variations of temperature 


(which are obtained by decomposing the daily curve of temperature 
by the method of periodic series) are small compared with the 
diurnal ones. How, notwithstanding this, the relatively large semi- 


‘diurnal variations of pressure may be explained, has incidentally 


been indicated by Sir W. Thomson. The calculation for the rota- 
ting spherical shell, made in a manner analogous to that for La- 


place’s calculation of ebb and flow, confirms Thomson’s supposition. 


Small semidiurnal variations of temperature are sufficient, with a 
corresponding choice of the mean temperature, to produce very 
great variations of pressure.— Wiener Berichte, March 6, 1890. 


THE 
LONDON, EDINBURGH, ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES. ] 
JUNE 1890. 


LI. The Theory of Fog-Bows. By James C. M°Conne., 
M.A., Fellow of Clare College, Cambridge™. 


[Plate X.] 
“heen supernumerary bows often seen within the ordinary 


rainbow received their first explanation, bordering on 

the truth, from Thomas Youngf. In the principal plane 
through the centre of the drop, as we increase the angle of 
incidence from zero to a right angle, the deviation of the rays 
from their original direction at first diminishes, gradually 
reaches a minimum, and finally increases again. So for any 
deviation slightly greater than the minimum there are two 
emergent rays which have travelled paths of slightly different 
length and are ina condition to interfere. By the interference 
of such Young supposed the supernumerary bows to be formed. 

Now the wave theory in its essence knows no such thing 
as rays, and they should be regarded merely as convenient 
symbols for obtaining approximate results when the wave- 
surfaces are spherical. Inall ordinary cases the wave-surfaces 
may be treated as spherical, but the rainbow is an exception. 
The wave-surface of the emergent light changes the sign of 
its curvature at a point corresponding to the ray of minimum 
deviation; and thus we have diffraction phenomena, depend- 
ing merely on the peculiar shape of the wave-surface, without 
any limitation by screens. 

* Communicated by the Author. 

+ Phil. Trans. 1804; or Encyc. Brit., eighth edition, art. “‘ Chromatics.’ 
Phil. Mag. 8. 5. Vol. 29. No. 181. June 1890. 2N 


454. Mr. James C. M¢Connel on the 


On these lines Sir George Airy* worked out the true 
theory ; showing not only that the light attains a principal 
maximum in one direction and a series of lesser maxima in 
neighbouring directions, but also that the principal maximum 
does not, as Young supposed, fall exactly in the direction of 
minimum deviation. The amount of its divergence is de- 
pendent on the diameter of the drops. The smaller the drops 
the smaller is the rainbow, and the further are the supernu- 
merary bows separated from the principal bow and from each 
other. 

When the sun is shining on fog or mist, a bow is often 
seen differing considerably in appearance from the ordinary 
rainbow—far broader and, though quite bright, nearly colour- 
less. The breadth may be as much as 6° or 7° instead of 14° 
as in the rainbow, and the colouring seldom surpasses “a 
faint dull red and orange at the outer border and a slight blue 
tinge” at the inner. The mean radius is a few degrees less 
than in the rainbow. Verdetf considers this to be a degraded 
form of the primary rainbow. According to Airy’s theory 
the radius would be diminished by smallness of the drops; 
and Verdet attributes the whiteness (1) to the faintness of 
the illumination, and (2) to the irregularity in size of the 
drops. There can be little doubt that the main contention is 
correct, and more satisfactory reasons may be adduced for the 
want of colour, as we shall see. 

At the top of Ben Nevis there are many opportunities for 
seeing fog-bows, and the observers there are provided with a 
special instrument{ for taking their angular dimensions. 
Mr. Omond has kindly sent me a list of such observations 
from May 1886 to October 1887, extracted from the Proceed- 
ings of the Royal Society of Edinburgh for 1887. Those 
relating to fog-bows are quoted below. The temperatures 
(Fahr.) were taken in a Stevenson screen at the times named. 


1) “ October 7, 1886. Temp. 89°°8. At 12 h. a solar foo- 
Pp & 


bow. No colours, only a broad white band. 


Radius to inside of bow . . . 30 20 
-f outside _,, fe MASTS 


(2) “October 22. Temp. 31°°5. Fog-bow seen at 11 h. 
25m. Colours as in fig. 1.” [They are, from the outside 
inwards, brownish red, pale green, pink, light blue, red, 

* Trans. Camb. Phil. Soc. vi. p. 879; vill. p. 595. 

+ Legons d’Optique Physique, 1. p. 422. 

{ This instrument, named a stephanome, consists of a graduated bar, 
at one end of which the eye is placed and on which slides a cross bar 
carrying certain pointed projections. With its aid faint objects, for 
which a sextant would be useless, may be measured to within 5’. 


Theory of Fog-Bows. 455 


light blue, red.] ‘‘ No measurements were got. The pink 
was a badly-defined space, not a true band. <A coloured 
glory was seen at the same time. 

(5) “ November 12. Temp. 27°9. Double fog-bow seen 
at 13 h.; outer bow white, inner bow red and blue, red being 
inside. 

(4) “ November 16. Temp. 22°°0. Fog-bow seen at 11 h.; 
red outside and white inside. A fainter bow was seen inside 
this one at times. 

(5) “ December 16. Temp. 15°7. Glory and fog-bow 
seen at 15 h., too fleeting to measure. The glory was double 
with reds outside; the fog-bow a broad whitish band, with 
occasionally another bow inside it more sharply defined and 
coloured, but the order of its colours was not observed. 

(oi December 26. Temp. 18% 9 At’ 12h. 30m. misty 
glory and double fog-bow seen ; outer bow had red outside 
and inner bow red inside. No measurements got. 

(7) “ December 30. Temp. 24°°2. Double fog-bow seen 
at 11 h. Red outside outer bow and inside inner bow. The 
following rough measurements were got :— 


Radius of outside of outer bow . . 4} 99 


te middle of Serato. 20 
- inside - iy eh OH BO 
= outside of inner bow . . 34 44 
i. inside 3 Eye on 0. 


The first and last measurements give the radii of the outer and 
inner red respectively. 

(8) “January 2, 1887. Temp. 20°3. Lunar fog-bow 
seen at 18° h. Radius about 38° 40’. 

(9) “February 6. Temp. 22°5. Lunar fog-bow seen at 


Bi: ilmside radiug 7: ™) ¥, 33 56 
Outside _,, 57a il AOR 20 


(10) “February 13. Temp. 28°1. Double fog-bow seen 
at 12h. Trace of red outside outer and inside inner bow. 
No measurements got. 

(11) “April 5. Temp. 16°°3. Fog-bow (faint) seen at 
3h.” [ Lunar. | 

(12) “June 29. Temp. 42°0. Fog-bow, occasionally 
double, observed at 5 h. and 6 h. 

(13) “July 21. Temp. 46°°5. A double fog-bow seen at 
times. Red inside inner bow and outside outer bow; the 
rest of the bows were white. 

(14) “ August 19. Temp. 37°°8. Fog-bow seen at 9h. 45 m. 

(15) “September 18. Temp. 45°°0. Fog-bow observed 
at 13h. 80 m., measuring 35° 16’ (to inside of bow ?). 


2N2 


456 Mr. James C. M¢Connel on the 


(16) “October 4. Temp. 43°°0. Lunar fog-bow at 23 h. 
Radius to inner edge (about) 38° 5’. 

(17) ‘October 5. Temp. 86°1. At 2h. fog was begin- 
ning to blow across the hill-top, and on it a distinct lunar 
fog-bow was seen with traces of a faint second bow outside it. 
The following measurements of the inner bow were got :— 


Radius toinsideedge .. . 35 4 
5 outsideedge . . . 410 


“Temp. 34°3. A similar lunar fog-bow was seen at 3 h. ; 
there appeared to be a faint trace of red about the outer edge 
of the inner bow. 

“Temp. 34°1. The fog-bow was seen again at 4h. and 5h. 
The following measurements were made at 4 h. :— 


Radius to inside of inner bow . . 36 3 
, outside ofinner bow . . 41 0 


(18) “October 15. Temp. 25°9. At 14h. double fog- 


bow and glories observed ; no measurements got.” 


A remarkable feature of this list is the number of double 
fog-bows. Out of eighteen bows no fewer than ten were 
double. In one case (17) the outer bow was probably a form 
of the secondary rainbow ; for the inner bow, according to the 
measurements, extended at one edge almost up to the normal 
radius of the primary rainbow. But in the other case, in 
which measurements were taken (7), both bows were within 
this radius, and in (3), (6), (7), (10), and (13) the inner bow 
had the red inside. Assuming that the two bows are the 
primary bow and its first supernumerary, the reversal of the 
normal order of the colours in the inner bow is a direct result 
of Airy’s theory, and my main object in writing the present 
article is to point this out. 

The divergence of the principal bow from its normal 
position, and of the first supernumerary from the principal 
bow, depends on the ratio of the radius of the drops to the 
wave-length of the light. As it is greater with a given kind 
of light the smaller the drops, so with given drops it is greater 
the greater the wave-length. For red light it is greater than 
for blue. As long as it is small for both, it only brings the 
red bow rather nearer the blue; but, when it is greater, it 
may bring the red bow to coincide with the blue; and it may 
become so great—with the first supernumerary at any rate— 
as to put the red bow well within the blue. This is the essence 
of the explanation ; but, to treat the matter properly, a fuller 
statement of Airy’s results is required. 


Theory of Fog-Bows. 457 


The intensity of the light in any direction is proportional 
to the square of the expression 


w= cos 5 (w?—muw) deo, Pes anieaane (89) 
0 


where m is connected with the angular separation y of that 


direction from the geometrical bow by the equation 
Z 


es. Wee ee ore yet (2) 
XL" 2 


q was left by Airy an undetermined constant. It has recently 
been shown by Boitel* and Larmory that, for the primary 


bow, 3 9 en” 


q ~ 4096 (uw? —1)*" BU ON unpies neon (3) 


Thus g, which may be treated as constant for different colours, 
=0°465 nearly. 

Hverything turns on the value of W?. Airy, calculating by 
quadratures, found that, for negative values of m, W’, starting 
from a small value at m=O, rapidly and continuously de- 
creases and becomes very soon insensible ; but on the positive 
side W* has an infinite number of fluctuations, vanishing 
between the successive maxima. Selected values are given in 
the following table :— 


mM. Ww?. 
—4:00 0:000009 

— 1:00 0:0745 
0:00 0:357 
0:80 0:940 
lst maximum ... 1:08 1:006 
1:20 0:995 
2°50 0-000 
2nd maximum ... 347 0-615 
4°36 0:000 
3rd maximum ... 5:14 0:510 
5:89 0-000 
4th maximum ... 6:58 0-450 
7:24 0:000 
5th maximum ... 787 0412 
8-48 0-000 


* Comptes Rendus, 1888; or Phil. Mag. August 1888. Boitel points 
out that Airy’s equation to the wave-surface is only a first approximavion, 
and has found experimentally some small discrepancy between theory and 
observation which he attributes to this. But Larmoy’s analysis of Miller's 
observations on fine jets of water shows no discrepancies greater than 4’, 
up toly—l05 

t+ Proc. Camb. Phil. Soc. vi. p. 283 (1888). 


458 Mr. James ©. MeConnel on the 


Airy’s calculation extended from m= —4tom=+4, Out- 
side these limits the calculation by quadratures becomes al- 
most impracticable, but Sir George Stokes* has found a 
rapidly convergent series for W in descending powers of m. 
From this follow simple approximations. For the dark bands 
m=8 (i—4)3, where 7 is given the values 1, 2, 3... successively. 

2 
For the maxima, m=3 (¢—?)# and W?= Ae. These are 
accurate enough for most purposes when 7>1. 

The variations of W? with m are exhibited graphically in 
Pl. X. fig. 1. It will be observed that the first band is much 
broader as well as higher than the others, and that the intensity 
at m=x=0 is by no means negligible. Thus, putting the 
question of colour on one side, the effect of diminishing the 
size of the drops is to spread out the principal bow in an 
inward direction, leaving its outer edge but little affected. 
After the third band the brightness diminishes very slowly. 
Even the 30th maximum at m=28°5 has the value W?=0°217. 
Of course the irregularity of the drops would prevent any 
colour-effects or distinct bands as far out as this, and we should 
only look for white light ; and this is exactly what is observed. 
The space within the primary rainbow is strikingly brighter 
than that outside; and Mr. Backhouse describes the glare 
within a fog-bow he witnessed as being not much inferior in 
brightness to the bow itself. 

Some idea of the colour-effects in two cases may be gleaned 
from fig. 2. I have taken as the representative red and violet 
of the spectrum, light of wave-lengths 0°000615 millim. and 
0000455 millim. It happens that the radii of the geometrical 
bows for these colours are 42° and 41°. The curve represent- 
ing the brightness of the red is set out in accordance with 
equation (2), 42° being taken as equivalent to m=y=0. 
In the curve for violet, which is dotted in the figure, 
41° is taken as equivalent to y=0. The upper pair of 
cu.ves represent the case when 2a, the diameter of the 
drops, is 0°3 millim., the lower pair the case when 2a=0:024 
millim. In the former the drops are of about the size 
adapted to give the most vivid colours possible in the 
principal bow and the first two supernumeraries. When the 
drops are very large, say 5 millim. in diameter, it is true 
that the principal maxima for red and violet are better sepa- 
rated, but the principal violet maximum gets entangled with 
a number of the smaller red maxima. ‘Thus, when we take 


* Trans. Camb. Phil. Soc. ix. 1850, or Collected Papers, ii. p. 329. 


Theory of Fog-Bows. 459 


the blurring due to the finite diameter of the sun into account, 
it is clear that the violet would be far more diluted with red 
and other colours than in the case illustrated. There is an 
intermediate stage in which the green would reach its maxi- 
mum purity, but the violet would be poor. 

This first case would be realized in a rainbow formed by 
unusually fine drops. The other case might be described by 
an observer as a double fog-bow, the outer bow being broad— 
extending from 424° to 3844°—and colourless except for a 
reddish tinge on the outer edge; and the inner bow—extend- 
ing from 32° to 274°—being brightly coloured with the red 
inside. This figure shows that the whiteness of the outer 
bow is sufficiently explained (1) by the immense breadth of 
the bow even when formed by homogeneous light, and (2) by 
the approximation of the red to the violet maximum. In this 
case they are about }° apart. The fact of the third bow being 
so seldom observed can hardly be due to its faintness, so we 
must attribute it to irregularity in the size of the drops. 

Thus far we have only treated of two special wave-lengths. 
In fig. 3 may be seen the relative positions of all the different 
colours in bows of various radii. The abscisse are wave- 
lengths and the ordinates radii of the bows. The top curve 
gives the geometrical bow, calculated by the formulee 


3cos? d=yw?—1, sind=pusin¢’, radius=4o'—2¢, 


from the values of w for water at 0° C., quoted by Landolt and 
Bornstein. The indices for He, HS, Hy are from Wiillner, the 
other three from Riihlmann. I have drawn the curve on the 
supposition that the small difference between the results of the 
two sets isconstant. The other curves are separated from this 
by distances proportional to \3 and to 3, 5, 6, 7,10, and 12 
respectively, and may serve to represent either the rainbow or 
any of the supernumeraries. The two dotted vertical lines 
indicate roughly the boundaries of the bright part of the 
spectrum. The temperature-effects are triflmg and may be 
disregarded. At 60°F. all the radii are some 4’ larger. 
Below 32° F. the indices of refraction and, consequently, the 
radii are almost constant. 

Nowhere is the superposition of colours perfect. But about 
36° 45! they may be all contained within 15’, so that any 
supernumeraries near that radius must be colourless. At 32° 
the spread of the colours is nearly as great as in the geometrical 
bow, and in the reverse order. In practice, however, we 
cannot expect the same vivid colouring under the most 
favourable circumstances, as the first supernumerary, for 


Ae 


460 Mr. James C. M¢Connel on the 


example, when its maximum is at 32°, must have a breadth of 
over 5° in homogeneous light (see fig. 2). 

We are now in a position to understand the observations 
better. The most complete measurements are those of (7). 
Here the mean radius of the dark space between the two 
bows is 85° 40’. This is 6° less than the mean radius of the 
geometrical bow. Assuming this is given by m=2-50, the 
values of m corresponding to the radii observed are as 
follows :— 


Mm. 
Outside or red of outer bow . . . . O12 
Middle a \) ales 
Inside ye _ os « \emezple 
Ontside of inner bow ..+ . .) .ae2zaee 
Inside or red oo : . ares 


The agreement with fig. 1 is as good as could be expected. 
Also by fig. 8 the inner bow is small enough to be distinctly 
coloured. The drops are larger than in the second case of 
fig. 2. We find indeed for equation (2), taking y as 67/180, 
g as 0°465, m as 2°48, and » as 0°00056 millim., that their 
average diameter is 0°041 millim. 

In (1) the outer radius is greater than that of the geo- 
metrical bow. ‘This finds its explanation in fig. 2. 

(2) seems to be a transition stage between a rainbow and 
an ordinary fog-bow. 

(5) By fig. 1 the first supernumerary is much narrower 
than the main bow. 

Taking the radius of (9) as 37° 8’ we find the average 
diameter of the drops 0°018 millim. 

In (17) the measurements of the inner bow show con- 
clusively that it was the main primary bow, the drops being 
much the same size as in the second case of fig. 2. So the 
faint outer bow must have been a modified form of the 
secondary rainbow. It may be remarked that the effect of 
the drops being small on the secondary rainbow is similar to 
the effect on the primary, except that the supernumeraries 
are outside and the radii are made larger instead of smaller. 

It will be observed that the air-temperature in (3), (4), 
(5), (6), (7), (10), and (18) is below freezing-point ; in (5) 
as low as 15°-7 F. I have nevertheless assumed throughout 
that the phenomena are due to drops of water and not to any 
form of ice. The correctness of this assumption is established 
by the agreement of observation with Airy’s theory, as well 
as by the identity of the phenomena above freezing-point; 


Theory of Fog-Bows. 461 


(12), (13). The suggestion that we have to deal with perfect 
spheres of ice may be put on one side. In the first place, I 
have never heard of such being observed ; and, secondly, if 
such were to exist for a moment, either evaporation or 
deposition would soon destroy the perfection of form. Nor do 
I think it probable that such small drops could be raised much 
above the temperature of the air by the sun’s radiation. 
Indeed I have often seen the air in Davos, when only a few 
degrees below freezing-point, filled with floating crystals of 
ice sparkling in the brilliant sunshine. I am thus led to 
think that these drops on Ben Nevis were originally formed 
in air above the freezing-point, and, being free both from jars 
and from contact with foreign bodies, have been cooled far 
below 32° F. without congelation. Drops of water suspended 
in oil of the same density have been cooled by Dufour to 
—4°F. If this opinion be correct, the drops on striking any 
object should freeze instantaneously. 

I quote the following from an article in ‘ Nature’ (April 9, 
1885), by Mr. Omond :—‘“ In addition to the actual fall of 
snow, hail, &c., there is on Ben Nevis a form of solid precipita- 
tion scarcely known on lower ground, but of almost daily 
occurrence here. In ordinary weather the top of the hill is 
enveloped in drifting fog, and, when the temperature of the 
air and ground is below freezing, this fog deposits small 
crystalline particles of ice on every surface that obstructs its 
passage. ‘These particles on a wall or large sloping surface... 
combine to form long feathery crystals; bat on a post or 
similar small body they take a shape more like fir-cones with 
the point to windward.” The deposit only forms on the wind- 
ward side of each object. Its rate of growth may exceed an 
inch per hour. As far as I can judge from the above descrip- 
tion the deposit is just what might be expected from liquid 
particles below 32° F., drifting with the wind. If the fog 
particles were dry ice, how should they stick together to form 
the feathers? I may suggest further, that in the upward de- 
flexion of the wind by the slopes of the mountain we have an 
excellent reason for the cooling of the air after the drops were 
formed. 


- Hotel Buol, Davos, 
April 1890, 


Fae. wl 


LIT. On a Method of Discriminating Real from Accidental 
Coincidences between the Lines of Different Spectra. By 
C. Runes, Professor of Mathematics at the technische Hoch- 
schule, Hanover *. 


ie the Philosophical Magazine for January 1888 EH. F. J. 
Love gives a method of discriminating real from acci- 
dental coincidences between the lines of different spectra. 
The method is as follows:—The differences between the 
wave-lengths of the lines compared are arranged in groups, 
each group containing those observations the errors of which 
lie within certain narrow limits. The number of observations 
in each group is then plotted as an ordinate of a curve, the 
average error of the group being the abscissa. It seems 
allowable to assume that this curve will have the form of the 
curve given by the law of error y=ae~*” in case the coin- 
cidences are real and not merely accidental. Any serious 
divergence from the form of the latter curve will therefore 
indicate that the coincidences are accidental. So far, I 
think, one may agree with the author. But he argues 
further:—If the plotted curve resembles the curve given by 
the law of error, the coincidences are not accidental. I do 
not see the necessity to draw this conclusion. On the con- 
trary, I am able to show that for a certain distribution of lines 
in one spectrum the plotted curve must always resemble the 
error curve for any lines that one pleases to take as lines of 
the other spectrum. Let Xo, 4, . . . An be the wave-lengths of 
any spectrum, A, the smallest and A, the largest. What then 
is the probability that an arbitrary number A between d, and 
A, does not differ by more than « from the nearest of the wave- 
lengths Ao, Ay, -- + An? To find this probability one must add 
together all the parts between A, and 2, that differ by not more 
than v from one of the numbers Ag, Ay... An. This sum divided 
by An»—Ap is equal to the probability in question. Let 
d,, d,...d, signify the differences of two consecutive wave- 
lengths in such order that d| <d, <d3... < d,, and let 
dy41 be the first of these quantities, that is not smaller than 
2z, so that dy» 2% ~<dy4;. Then all the intervals d,, do, . . 
d, have to be included in the sum, whilst for each of the 
intervals d,y41, dy42,.+. dn only a part equal to 2x has to 
be added. We find therefore the probability in question 


* Communicated by the Author. 


Coincidences between the Lines of Different Spectra. 463 


equal to 
dj tdg+ ...+de+2(n—v)x 
Ven 


From this expression one may deduce a simpler one for the 
probability that the difference between the arbitrary number 
r and the nearest of the wave-lengths Ao, 4)... A» lies between 


dy Ay+1 . 
3 and 3° It is 
dj +dat 16. +dp+(n—v) doy, — drtdgt... t+hat(m—vtl)d, 
RE) An— No 
or 
(n—v) (dy14—dy) 
Ne ken 
k ay alg dg ! 
Let us take g? grt g a abscissas, and let us draw a rectangle 
F 2 dy Ay +1 ‘ dys+1—dy nV 

over the interval 5 to 9 with ma ke base and 2 =n, 


as height. Then the area of this rectangle will represent the 
probability, that the difference of > from the nearest wave- 
= (for “v= 00 write “dy = 0). 


length lies between = and — 


Thus we get what we may call a curve of difference analogous 
to the curve of error. The curve of difference forms the pro- 
file of a staircase, the steps of which may be of different 
height and depth. If n is a large number and the scale of 
the drawing not too large, the staircase will resemble a 
smooth curve ; and it may be seen from the following applica- 
tion that there are cases where it closely resembles the curve 


2 Soape 
v= Se if one is allowed to choose the constant c 
T 


accordingly. 

I have taken as an example the first five ultra-violet bands 
of the water-spectrum as observed by Liveing and Dewar™*. 
They consist in 598 lines extending from 2268 to 3203°5. 


* Phil. Trans. of the Roy. Soc. 1888. 


464 Prof. C. Runge on Real and Accidental Coincidences 


Abscissa. | Ordinate. || Abscissa. | Ordinate. Abscissa. | Ordinate. 


00 to-05 | 1-28 ‘90 to 95 | -85 1:85 to 1:90 | -05 
05,10 | 1:28 95 ,, 100} 32 1:90 ,, 2:00] -04 
I, SP ae 1:00 ,, 1:05 | -28 2:00 ,, 205 | 04 
15,20 | 1:26 1:05, 1:10] 25 205 ,, 210] -04 
20 ,,°25 |- 1:24 || 110,115] -23 210 ,, 215 | 03 
25 ., 80 | 1:18 115 ,, 1:20] -20 215 ,, 220] -03 
7 aH | ee) 1:20 ,, 1:25] 18 2:20 ,, 225 | -038 
Boye 4014] 1-02) | 125 esON) .-15 2-25 ,, 2:30} 02 
40 ,, 45 96 130, 1:35 | 138 2:30 ,, 2:35 | 02 
45, -50 G0. ll ica5 Sett00) etd 2:35 ,, 250 | 02 
50 ,, 55 82 || 140,,145] ll 2:50 ,, 265 | 02 
5B ,, 60 74 || 145 ,,150] 1 265 ,, 280] Ol 
60 ,, 65 67 || 1:50,, 1:55 | 09 2:80 ,, 305] OL 
65 ,, "70 59 1:55 ,, 1:60 | -08 3-05 ,, 335 | -O1 
70 ,, 75 57 || 160, 1:65 | -07 335 ,, 3°65 | -Ol 
75 ,, 80 50 «|| 1:65 .,, 1:75 | -06 3:65 ,, 380 | Ol 
80 ,, *85 44 11-75, 1-80| -06 380 ,, 5°70 | -00 
85 ,, 90 39 1:80 ,, 1:85 | -05 570 ,, 670 | 00 


In order to compare these values with those given by the 
law of error, I have for the sake of simplicity interpolated the 
values of the ordinate for 2=0:1, 0°2, &c., by taking the 
mean of the two neighbouring ordinates. The third column 


9 
contains the ordinates of the curve = Tati for'e«=1:148, 
a 


The table shows the close agreement between the two curves, 


Ordinate | Ordinate Ordinate | Ordinate 
Abscissa. curve of curve of Abscissa. | curve of curve of 
difference. error. difference. error. 
0 1:28 1°30 1:3 lial 14 
it 1:28 1:28 14 sat 10 
2 25 1:23 1°5 10 ‘O7 
3 1°14 1-15 16 08 04 
4 ‘99 1:05 lerf 06 03 
5 86 93 18 06 02 
6 ‘70 Pail 1:9 05 ‘Ol 
74 58 68 2-0 04 ‘Ol 
8 ‘47 56 2°5 “02 00 
2g By "45 30 ‘O1 00 
1:0 30 515) 3°D Ol ‘00 
ibe “24. 26 4:0 00 700 
1:2 “19 19 


With the spectrum of the water-bands we may now compare 
any other spectrum we please that lies between the extreme 
lines of the water-bands. We must expect to find the number 


between the Lines of Different Spectra. 465 


of differences between certain limits equal to the area of our 
eurve of difference between the same limits multiplied by the 
number of lines of the second spectrum. And if a curve is 
plotted in the manner indicated by Love, it evidently must 
resemble the curve given by the law of error, whatever the 
second spectrum may be. In this case, therefore, the method 
of Love cannot give us any information whether the coinci- 
dences between the lines of the two spectra are real or 
accidental. But we may derive some information by con- 
sidering the value of the constant in the formula given by the 
law of error. Supposing the coincidences to be real ones, the 
differences between the lines compared must be distributed 


2 
according to the formula y= rae . If now we can make 
uy 


an estimate of ¢ and find it considerably larger than 17148, 
the distribution of differences ought to show a divergence 
from the distribution given above. If the divergence is not 
shown, the coincidences must be accidental. Only when ¢ is 
not found considerably larger than 1°148 we are left without 
an answer. The distribution of differences would then be the 
one given above, and would afford no reason to think the coin- 
cidences real ones. 

The most important verification of A. Griinwald’s far- 
reaching speculations on the composition of the elements 
he believes to be afforded by the agreement between the 
wave-lengths of the lines in the spectrum of water, as de- 
duced by him from those of the hydrogen spectrum, and 
their values as obtained by observation. But I find that the 
distribution of differences is in perfect accordance with the 
one expected for an equal number of wave-lengths chosen at 
random. ‘To show this more clearly, I have taken the man- 
tissas of log sin from 9° 43! to 12° 4', and of log tan from 
19° 20’ to 19° 38’ for each minute abbreviated to five 
figures. These numbers lie between the extreme wave- 
lengths of the water-bands. ‘The distribution of differences 
between each of these numbers and the nearest wave-length 
of the water-spectrum does not show any serious divergence 
from the distribution corresponding to the wave-lengths 
calculated according to Griinwald’s theory by multiplying the 
wave-lengths of hydrogen by 3%*. 

The first column of the following table contains the limits 


* IT have taken Hasselberg’s measurements, Mém. de Acad. de St. 
Pétersbourg, 1882, as Griinwald has preferred these to the more complete 
measurements of 1883. I have abbreviated the halves to five figures, 
adding a unity to the fifth figure when it was even. 


466  Corncidences between the Lines of Different Spectra. 


of the differences, the second gives the expected number of 
differences within these limits, the third the observed number 
corresponding to the wave-lengths calculated from hydrogen, 
the fourth the observed number corresponding to the said. 
mantissas of log sin and log tan. 


Limits of | Expected | Observed Limits of | Expected | Observed 
differences. | numbers. numbers. differences. | numbers. | numbers. 
00 to -05 10°4 12 6 2:05 to 2°15 06 9 i 
05 ,, 15 20°6 16 26 || 215-.,, 2:25 0:5 

Al Ges eh O25) 20:2 19 16 2°25 ,, 2°35 0-4 

SU is ED) 18-4 Pl 16 2°35 ,, 2°45 

*ODl,51) 45 160 19 15 ZY LOPS) ! 0-9 1 
hot, =69 11:3 ig 12 PA OYa) Ry ea (COR 5 1 

SOD ea ai) 9°3 8 9 2°75 ,, 2°85 O:'7 

S715) pay tol) UD fa ill ROOM OOM 

85 ,, ‘95 59 5 12 2°95 ,, 3°05 1 

95 ,, 1:05 4:9 6 il 3:05 ,, d°15 | 06 1 1 
Ogee oly 3°8 1 Den oslo vez 

ete ee aval ie: Wey oe eaeaye) 1 

1 5e ABH 2:2 5 3 33D ,, v4D 0-4 

135, 145 1:8 ] 2 3°45 ,, 3°55 

NEAT ype mec) 1:6 3 DPD) oe COMED) 

ea 5 GD tell iy. | OOD)», Oo LO 0-4 

EGS, elehs 1:0 a WE PSO 4.038 

Leeroy een ier) 0-9 2 Di cilia Gon., D129 1:0 1 ] 
SoM elo 0-7 sah 525. ,, O75 0-7 } 

IS) 5, PAYS 0-7 2 il 


As the distribution of the differences corresponding to the 
wave-lengths calculated from hydrogen is in accordance with 
the expected distribution, it follows either that the coincidences 
are accidental or that their probable error is not smaller than 
the one corresponding to c=1:148. The probable error for 
c=1-148 is 0°42. That is to say, 0°42 x 10-7 millim., as 107-7 
millim. is the unit of the wave-lengths. It seems to me not im- 
possible that the probable error of the difference between Liveing 
and Dewar’s measurements and the halves of Hasselberg’s is as 
much as 0°42. One cannot therefore, without more exact 
measurements, safely infer that Griinwald’s coincidences are 
accidental. However, one can say that the distribution of 
differences gives no more reason to believe the coincidences 
real than to believe in a connexion between the mantissas of 
log sin and the spectrum of water. 


pabdieT hs 


LILI. On Texture in Media, and on the Non-existence of 
Density in the Elemental Atther. By G, JOHNSTONE 
Stoney, a Vice-President of the Royal Dublin Society, 
Mee. DSc... FS.” 


N the investigations of ordinary dynamics—the dynamics 
of secondary t motion—integrations have to be ex- 
tended throughout the bodies with which we are dealing, or 
over their surfaces. Now whenever we employ this operation, 
assumptions are tacitly made which do not accord with what 
exists in real objective nature. 

Suppose that the problem is to obtain the pressure of water 
against a sluice ; to ascertain the amount and distribution of 
the pressure, we integrate over the surface between the water 
and the sluice, and in doing so assume :— 

(1) That the boundary is a surface ; and 

(2) That the elements into which we conceive this surface 


* Read before the Royal Dublin Society, February 19, 1890, and 
reprinted by permission from a proof of the paper in the Scientific Pro- 
ceedings of the Society. 

+ In the computations of ordinary dynamics, we conceive the portion of 
space occupied by the body with which we are dealing to be divided into 
elements of volume (the dz dy dz’s), which elements of volume we regard 
as movable. Each of these we multiply by a coefficient called the den- 
sity, and call the product the element of mass (dm=p.drdydz). These 
elements of mass we picture to ourselves as acting on one another, or as 
being acted upon by external forces; and from the laws of these actions 
we endeavour to deduce the motion of the element of volume, carrying 
its contents with it, and in some cases changing its form or volume. 

In this process we take no notice of any motions which may be going 
on within the element of volume, except so far as that some imperfect 
account may perhaps be indirectly taken of them when we multiply the 
element of volume by a density. Nevertheless, in all the real cases that 
occur in nature, there are, as a matter of fact, very active motions of 
various kinds going on within the element of volume: motions of the 
molecules which it contains, and still more deep-seated motions within 
the portion of the element of volume occupied by those molecules, or in 
the interspaces between them. 

Accordingly the motions with which we deal in our ordinary dynamical 
investigations are merely drifting motions—the drifting about of elements 
of volume, within each of which, as events really occur in nature, there 
are elaborate subsidiary motions going on. Now, secondary motion is to 
be defined as the motion which consists in the drifting about, with or 
without changes of size and form, of elements of volume within each of 
which there are subsidiary motions. 

If the subsidiary motions consist exclusively of irrotational motions in 
an incompressible and perfectly fluid medium, they cannot contribute to 
the density by which the element of volume in which they occur is to be 
multiplied. It is, however, otherwise if there are any rotational motions 
present. j 


468 Dr. G. J. Stoney on Texture in Media, and on the 


divided for the purposes of the integration may be made as 
small as we please without ceasing to be subjected to the law 
in heavy liquids of pressure proportional to the depth below 
the upper surface of the water, plus that due to the superin- 
cumbent atmosphere. 

Both these assumptions continue approximately true when 
the elements into which we suppose the surface divided are 
diminished till they are as small as, or even a good deal 
smaller than, the smallest speck that can be distinguished with 
the most powerful microscope ; but they utterly break down 
if we suppose the subdivision carried so much further as to 
reach or even approach the scale of molecular magnitudes. 
If, for instance, the elements into which we suppose the sur- 
face divided were reduced to a square tenth-metret * in size, 
a patch of surface which is the millionth part of the utmost a 
microscopist can see, we should have got well within the 
range t of molecular differences. The boundary between the 
water and sluice would cease to be a surface: it would be the 
continually shifting boundary between molecules on both 
sides in energetic motion, acting individually on each other 
in their own special ways ; which happen to be such that when 
immense numbers of these individual operations are lumped 
together they produce approximately, as the outcome of all 
that is going on, that law of pressure proportional to depth 
with which we are familiar. 

Thus, what we regard as a physical property of the medium 
—in this case the law of pressure in a heavy liquid—is in 
reality a statement of what is the drift of a vast number of 
individual events, grouped together by a kind of statistical 
process. This we may briefly describe by saying that the 
dynamical properties of the medium are due to its texture, 


* The decimetre is the first of the metrets (z. e. decimal subdivisions of 
the metre), the centimetre is the second, the millimetre is the third. The 
tenth-metret is the tenth of this series. It is a metre divided by 10°. 
The waves of visible light have lengths varying from 3900 to 7600 of 
these tenth-metrets. 

+ According to Professor Loschmidt, who first published an estimate 
of the interval within which the centres of two molecules must approach 
to act sensibly on one another, this interval is about a ninth-metret 
(Proceedings of the Mathematical Section of the Academy of Vienna, Oct. 
1865, p. 404). The mean of such intervals may, perhaps with more pro- 
bability, be taken as lying nearer to the tenth-metret. It is very impro- 
bable that it is as small as the eleventh-metret. In the present paper 
I assume it to be about the tenth-metret. If, however, it lies nearer the 
ninth-metret, though we shall have to change almost all the numbers of 
the computation in the text, we shall arrive at a conclusion not materially 
differing from that on p. 472 below. 


Non-existence of Density in the Elemental Atther. 469 


meaning by the texture of a medium whatever is going on in 
it at close quarters. 

It is the same with the other recognized physical properties 
of media, such as what are called gaseous laws—the laws con- 
necting the density, temperature, and pressure of gases, the 
laws of their diffusion, the law of viscosity, and so on. Simi- 
larly with the properties of solid bodies: all are the outcome 
of vast numbers of very diverse individual events that occur 
between or within the molecules of the bodies, or between 
them and the luminiferous ether. 

In order to penetrate to this world of individual actions, we 
must not only descend to magnitudes that are comparable to 
the intervals at which the centres of molecules are spaced 
from one another, but we must also consider periods of time 
that are not too vast in reference to the motions that go on 
among them. A second of time is “out of all whooping” too 
long*; but a period which is definite and of suitable brevity 
is that for which I have elsewhere proposed the symbol 7, 
viz. the time that light takes to advance one millimetre in vacuo. 
The velocity of light being 30 quadrants per second, and the 
quadrant (the length of a meridian from the Harth’s equator 
to the pole) being 10° millimetres, we find that 

__ 1 one second 

ore C10 a 
i. é. it is one third of the eleventhet f of a second of time. In 
this fragment of time, visible light makes from 1300 to 2600 


* See the Philosophical Magazine for August 1868, p. 140, footnote. 
Readers of the paper here referred to are requested to change the square 
of 16 in the second paragraph into the square root of 16. In that paper 
(p. 141) I estimated the number of molecules in a cubic millimetre of a 
gas, at atmospheric temperatures and pressures, as about a uno-eighteen 
(101%), without being aware that a similar estimate had been obtained for 
solids and liquids by Professor Loschmidt in 1865 (Proceedings of the 
Mathematical Section of the Academy of Vienna for October 1865, p. 405). 
In March 1870 Sir William Thomson, doubtless also without knowing of 
what had been done before, published a paper in ‘Nature’ on the ‘size 
of atoms,” and arrives at substantially the same estimates as Professor 
Loschmidt and myself. 

The earliest determination of a molecular magnitude, so far as I am 
aware, was that made by Professor Clerk Maxwell of the mean length of 
the “free paths” of the molecules of certain gases in their excursions 
between their encounters. See Philosophical Magazine for January 1860, 
p- 32, and for July 1860, p. 31. See also Philosophical Transactions for 
1866, p. 258. 

+ The eleventhet means a unit in the eleventh place of decimals. It 


1 
accordingly is a name for the fraction 0:000, 000, 000, 01, or yon: 
Phil. Mag. 8. 5. Vol. 29. No. 181. June 1890. 20 


470 Dr. G. J. Stoney on Texture in Media, and on the 


vibrations according to its colour, so that the mean frequency 
of vibration of light is about 2000 vibrations during each 7*. 
[This mean is the actual frequency of that green ray whose 
wave-length in vacuo is 5000 tenth-metrets. | 

We may now get some insight into the physical events that 
occur in the world into which we have passed. The pressure 
of air in this room against the walls is, according to the 
kinetic theory of gases, due to the walls beg bombarded by 
molecules of air as they fly about like missiles. It is an 
elementary proposition f in the kinetic theory of gases that the 
momentum communicated to the wall is substantially the same 
when, as actually happens, the molecules frequently encounter 
one another throughout the room, as it would be if the aerial 
missiles could be divided into three equal squadrons, one of 
which should travel uninterruptedly up and down between the 
floor and ceiling, another squadron travelling horizontally 
from side to side, and the third squadron from end to end of 
the room ; and all moving with a velocity whose square is the 
mean of the squares of all the actual velocities of molecules in 
the room. This “velocity of mean square,” as it has been 
called, depends on the molecular mass and on the temperature 
of the gas; and in the case of the air in this room it is about 
500 metres per second{. Let us then suppose the wall to be 
struck by one third of the molecules in this room, rushing 
backwards and forwards between it and the opposite wall at 
this pace; and let us endeavour to form an estimate of how 
often one of the superficial molecules of the wall will be sub- 
jected to an encounter. 

The number of molecules in a cubic millimetre of the air is 
known to be about a uno-eighteen (10'%)§; and there are of 
course 500,000 times this number in a column 500 metres 
long and a square millimetre in section, 7. e. there are 5 uno- 
twenty-threes in this column. One third of all the molecules 
in the column are the squadron that we are to regard as tra- 
velling lengthwise, half of these advancing towards one end 
and the other half retiring from it. It thus appears that the 
number of molecules within the column to be taken as travel- 


ling at any instant towards one end is S. 20, This accord- 


* See British Association Tables of Oscillation-frequency, B. A. Report 
for 1878, p. 40. 


Tt See Maxwell’s ‘ Heat.’ 
{ Phil. Mag. 1857, xiv. p. 124; or Maxwell’s ‘ Heat.’ 
§ See footnote *, p. 469. The uno-eighteen means the number repre- 


sented by 1 with eighteen cyphers after it. It accordingly is the same as 
Ol: 


Non-existence of Density in the Elemental Aither. 471 


ingly is the number that will strike against a square millimetre 
of the wall in one second. Now the time 7 being, as we have 


found, 3 of an eleventhet of a second G x a of a second), 


it follows that = x10" is the number of downright blows 


that would be delivered by these molecules upon one square 
millimetre of the wall in the time 7. 

This is on the supposition that the molecules are divided 
into three squadrons. They are not so divided in reality, and 
accordingly all the strokes delivered against the square milli- 
metre of the wall are not downright blows, but are many of 
them oblique. An easy computation shows that this will 
increase the number of blows in the ratio of 3 to 2*; so that 


* If N be the number of downright blows delivered on a surface s in 
the time T, and if « be the momentum communicated by each blow, then 
the pressure they will occasion 


— —__, , r 


ue) 


If, on the other hand, the blows arrive from all quarters indifferently, 
and if dn’ be the number reaching s from inclinations between 6 and 6+d6, 
6 being measured from the normal, then will 


dni—Ti1s CoS@. 2rd cos.) (2) 1s sae ye (2) 


where & is such that &. do is the number of blows coming from directions 

lying within an element do of solid angle, that would be received in the 

time T, by a unit of surface presented perpendicularly to the shower. 
These dn' molecules communicate to s a momentum 


=2 cos 6. 2rks cos 6dcos 6. 


Therefore the whole momentum communicated in this way from all 
inclinations 


=2rkse \} cos? 6d cos 6 =" wkse 5 


and the pressure thus caused 
2 whe 


Rp te ee B 


This is to be equal to the pressure produced by N downright blows ; 
whence, equating (1) and (3), 


Nis aaltag bo (2 yagi yo fit A) 


_Again, N’, the number of blows that reach s, when molecules fly in all 
directions, 


= J dn! =2msk : i, cos 6d cos 0; 
whence N'=msk . 


(9) 
Comparing (4) and (5), we find that 
eee 
as in the text. N 2’ 


202 


7* sin A eas 
Mf eee ae 
* ca 


472 Dr. G. J. Stoney on Texture in Media, and on the 
the real number of blows delivered upon the square millimetre 


. 5 e 
is about 13 sels. 


Next consider the distance within which the centres of two 
molecules, one a molecule of the air and the other a molecule 
of the wall, must approach in order that they may sensibly 
act on one another. A circular disk, with this distance as 
radius, may be considered as a target towards which the centre 
of a molecule of the air must be directed in order that this 
particular molecule of the wall may be reached. Now the 
distance within which the centres of the molecules must ap- 
proach lies more probably in the neighbourhood of a tenth- 
metret than in the neighbourhood of either a ninth-metret or 
an eleventh-metret*. Let us for the purpose of an estimate 
assume that it is a tenth-metret. The size of the target, sup- 
posed flat, will then be about three square tenth-metrets. 


This is 8 fourteenthets of a square millimetre (3 x a of a 


1 
square millimetre). Accordingly the number of encounters 
this molecule will receive in the time 7 will be approximately 
5. 10° x 3 eae 
12° OT 80) 
target to be struck is a disk, whereas it is in reality a sphere. 
This will doublet the number of blows it will be subjected to 
in the time 7; whence, finally, we may take this number to 


This is on the supposition that the 


be about - : in other words, this molecule of the wall is struck 
on the average at intervals of about 40 times 7. If the colour 
of the wall be green, the molecular motions which occasion 
this colour are repeated in the molecule 2000 each 7, and 
therefore something like 80,000 in the intervals between the 
shots to which the molecule is subjected by the aerial artillery. 
This serves to explain why the incessant bombardment by the 


* See footnote t (p. 468). 
+ N’, the number of blows that reach a circular disk of radius a, is, 
according to equation (5) of footnote * (p. 471), 


mre bik on Ps 5) 4% pe 


Again, proceeding as in equation (2) of footnote * (p. 471), we find that 
the number N” which would reach a sphere with radius a, 


a i, k. wa”. 2rd cos 6, 
ONO Te, pe fey + | oe) nye be 
Comparing (6) and (7), we find that 
N°=2N* 


Non-existence of Density in the Elemental Atiher. 473 


air does not alter the colour of the wall. Between the en- 
counters long intervals elapse: intervals so long compared 
with the motions of light, that any small * disturbance in the 
periodic time which may be caused by the encounter probably 
lasts for but a very trivial part of the long intervals of respite. 

Thus in both liquids and gases, what are called the dyna- 
mical properties of the medium do not exist when we come to 
close quarters ; and, accordingly, investigations based on these 
dynamical properties, and carried out by integrations, will 
yield results that are valuable only when the integration 
(\\\ dC, y,2) dedydz) furnishes a result nearly identical 


with that which would be furnished by a summation 
(2$(4, y, <) Az Ay Az), where each of the blocks Ax Ay Az is 
sufficiently large to include an enormous number of the indi- 
vidual operations that are in reality what actually go on in the 
medium. 

We come upon the same result when we make a similar 
inquiry with regard to solids. But I forbear going into 
numerical details in this branch of our subject until I can 
publish investigations on which I was engaged some years 
ago, by which it appears that the form and dynamical pro- 
perties of many crystals can be connected with their chemical 
constitution. When this subject is gone into, it becomes plain 
that the dynamical properties of solids also, such as their 
power of propagating shearing-stresses, are, like those of 
liquids and gases, due to events of an utterly different kind 
that occur between parts so close, and in periods of time so 
brief, that enormous shoals of these events occur in a very 
small fraction of a second, within elements of volume many 
times smaller than the most tiny speck the microscope can 
show. Accordingly, what we regard as dynamical properties 


* Probably but small; since the periodic time seems to depend much 
more on the relation which subsists (and acts without intermission) be- 
tween ponderable matter and the luminiferous ether, than upon the 
occasional events which occur in the grappling of molecules with one 
another. 

This view is borne out by observations made by the author on 
the absorption-spectrum of the vapour of chlorochromic anhydride 
(CrO,Cl,), the lines of which were found to have sensibly the same ap- 
pearance whether air was or was not present with the vapour. It was 
expected that the spectrum might exhibit an appreciable difference in 
these two cases, since when air is present the molecules of the vapour are 
subjected to a largely multiplied number of encounters—notwithstanding 
which no alteration in the appearance of the lines of the spectrum could 
be detected. 

For an account of the very remarkable spectrum of this vapour, see a 

aper by Professor Emerson Reynolds, F.R.S., and the Author, in the 
Philosophical Magazine for July 1871, p, 41. 


474. Dr. G. J. Stoney on Texture in Media, and on the 


of solids, such as their power of propagating tensile, compres- 
sive, shearing, and twisting stresses, are an outcome of what 
I have called the texture of the medium; and only appear 
between blocks so large that, in considering the effect of one 
of these large blocks upon its neighbours, we need only take 
account of the general outcome that emerges when vast num- 
bers of the individual events that are actually going on are 
combined, and ther general drift obtained by a statistical 
method. 

It is especially instructive in this connexion to consider 
the problems of that branch of dynamics which is called Rigid 
Dynamics—such as the investigation of the motions of a top, 
or hoop, or of the precessional motion of the Earth. In these 
inquiries the integral calculus isemployed. But the integra- 
tions are all such that the calculated motions of such bodies 
would come out almost precisely the same, whether the abso- 
lute limit, as furnished by the integrals, be taken, or a sum- 
mation for which the volume of the rigid body is regarded as 
divided into blocks as large as the smallest specks visible in the 
microscope. It is desirable, however, that we should bear in 
mind that there is the widest difference between the physical 
assumptions underlying these two methods of procedure. 

If we proceed by integration, it is tacitly assumed that the 
stresses characteristic of a solid body prevail between elements 
of the volume however small, and differ, according to the law 
laid down as the law prevailing in the medium, at situations 
in the body however near. This is not true. 

On the other hand, if we proceed by summation, it is 
assumed that the forces acting on each little block are distri- 
buted equally and without any variation of direction to the 
several equal portions into which its little mass may be con- 
ceived to be divided, however minute this subdivision may be. 
If this were the case, the internal stresses of a rigid body would 
be powerless to induce rotation in any one of these blocks, or to 
alter any rotation that may have pre-existed in it. Accordingly 
each of these blocks would not rotate round the instantaneous 
axis: it would merely revolve round it*. These, which are 
the real physical meanings of the assumptions made in the two 
cases respectively, are specially instructive. 


About fifty years ago Professor MacCullagh announced his 
great discovery that the phenomena of light could be accounted 
for, if we suppose light to be an undulation in an incompres- 


* The proper inference from this is that our equations have only taken 
into account a part of the forces that are really acting: and this is true. 


Non-existence of Density in the Elemental Aither. 475 


sible medium of uniform density, endowed with those dyna- 
mical properties which are embodied in his fundamental 
equations. These properties are not very unlike the properties 
attributed to an ordinary solid body ; and the question now 
arises, whether these properties (or whatever are the real 
dynamical properties of the medium in which are propagated 
light, radiant heat, and other waves of electromagnetic stress) 
are fundamental properties of the medium ; or whether, like 
the properties of solids, liquids, or gases, they are the outcome 
of events of a wholly different character happening at inter- 
vals so short that the elements of volume (the dz dy dz’s of 
MacCullagh’s formule) contain vast numbers of them. Now 
the dynamical properties of the luminiferous medium— 
whether we use MacCullagh’s or Cauchy’s fundamental 
equations——sufficiently resemble those of media which we 
know to be “ textured,’ to make the latter supposition the 
more probable, after what we have found to be the real nature 
of solid, liquid, and gaseous media. And this probability is 
very much strengthened by the discovery made by Helmholtz 
about a quarter of a century ago, of the persistence and dyna- 
mical behaviour of vortex-rings and other vortex filaments in 
a perfect incompressible fluid, and by the investigations to 
which this discovery has led. 

One result of these investigations has been to suggest to Sir 
William Thomson that the chemical atoms of which ponderable 
matter consists may be simply vortex tangles in sucha medium; 
and to suggest to Professor FitzGerald that the luminiferous 
ether may be a medium of this kind permeated by straight 
vortex filaments in all directions. Investigations are being 
actively pushed forward with a view to ascertaining how far 
these suppositions can be corroborated. Other hypotheses 
which may be classed with these have been advanced by 
Professor Hicks and others, but I select Professor FitzGerald’s 
and Sir William Thomson’s, both because they seem, in our 
present imperfect state of information, the best of their class, 
and in order to give definiteness to what further I have to say. 

Let us then imagine this room to be permeated by three 
systems of wires. Let the first be a set of vertical wires from 
the ceiling to the floor in rows parallel to the walls, and at 
intervals from one another of one inch. Let a similar system 
cross the room from side to side, passing midway between the 
wires of the first set: and let a third system of wires run 
from end to end of the room threading their way along the 
middle of the clear passages that lie between the wires of the 
other two systems. Let these wires represent straight vortex 
filaments in a uniform incompressible medium devoid of 


476 Dr. G. J. Stoney on Teature in Media, and on the 


any stress that resists change of form, and let the alternate 
vortex filaments of each row rotate in the same direction, 
while the intermediate ones rotate in the opposite direction, 
but let the vortex filaments be in other respects similar. 

Such would be the simplest case of a medium of the kind 
that Professor FitzGerald has conceived*. Let us next 
imagine the whole space within the room to be divided into 
large blocks of a cubic yard in size. One of these blocks will 
include a great number of the vortex filaments, and all the 
large blocks will closely resemble one another; insomuch 
that if an undulation consisting of shallow waves each a 
quarter of a mile long were to traverse the medium, the 
blocks would appear to act on one another ina certain definite 
way. This corresponds to the way in which Professor 
MacCullagh’s elements of volume, his dw dy dz’s, are in his 
formule assumed to act, and the waves correspond to his 
waves of light. But if the whole space were divided into 
much smaller blocks, suppose into cubes of half an inch, 
great differences would be found to prevail between these 
small blocks, and equally great differences in the way they 
act on one another; and the difference would become more 
striking if the subdivision were carried so far as to render 
the blocks small in comparison with the thickness of the wires 
that represent vortex filaments. 

If, now, we further conceive small vortex tangles travelling 
about in this medium, the long vortex filaments opening to 
let them pass, and acting in front, sideways, and behind upon 
them in such a way as to urge them equally forwards and 
backwards, so long as their journey is along a straight path 
with uniform speed—we shall have a first sketch of what con- 
stitutes ponderable matter and the luminiferous eether, accord- 
ing to these speculations. 

The particular hypotheses which are here described may 
perhaps not have quite hit the mark ; but, though we have as 
yet only a glimmering of this great subject, it is pretty certain 
that either these hypotheses, or something like them, are the 
true ultimate account of material Nature. 

We must, therefore, carefully distinguish between the 
elemental and the luminiferous ethers. The elemental ether, 
until motions create differences in it, is absolutely alike and 
undistinguishable in all its parts; and in the mathematical 
investigation of motions in it, wherever in any of the 
equations of dynamics an element of mass appears, we must 


* “Nature, May 1889, xl. p. 32. 


Non-existence of Density in the Elemental Atther. 477 


write everywhere the element of volume instead. It is itself 
the integral of these elements of volume ; in other words, it 
is space under a new aspect. In the geometrical way of 
conceiving space, the parts into which it may be conceived 
to be divided are thought of as they would be if at rest 
relatively to one another. In the kinematical way of con- 
ceiving space, which alone is in accordance with what ob- 
jectivelyy exists, we are to recognize that each portion of 
volume is pervaded by the motions that actually subsist 
within it, and that it can travel about carrying those motions 
with it. In fact the volume occupied by a block of iron differs 
from an equal volume occupied by air, only by the motions 
that are going on within the one volume being different from 
those that pervade the other. In every other respect they 
are as exactly alike as one stationary portion of space is to 
another. One such portion of space is not another: but it 
is exactly like it; and there 2s no limit to this resemblance 
however small the portions compared may be. There is no 
“texture ” until there is motion. 

On the other hand, when, in investigating the motions of 
ponderable matter, we have occasion to conceive the bodies 
we are dealing with divided into small portions, it is only ¢f 
we stop short in our division so that the blocks we form do not 
fall below a certain size, that we are justified in treating them 
as resembling one another. When we thus stop short, the 
blocks are in reality accumulations of more minute internal 
motions ; and if we do not stop short, but carry the division 
sufficiently far, we shall come down upon the individual 
motions themselves, between which of course the most marked 
differences would be found. 

It appears to be the same in regard to the luminiferous 
gether. It is only when we do not subdivide too far, that we 
are justified in speaking of the blocks as resembling one 
another. The luminiferous «ther seems to be a textured 
medium like ponderable matter. But in the elemental sether 
—in space itself regarded as movable—there are no such 
limits. Its portions, however small, resemble one another 
with mathematical exactness* ; except so far as there may be 
different motions prevailing within those portions. 


* Empty coreless vortices involve the hypothesis of a medium that is 
discontinuous and has boundaries; or else (in the case of some coreless 
vortices) of a medium which obeys two laws of motion, one for the part 
of the medium that is interned on one side of a closed vortex sheet, and 
another for the rest of the medium. Now it seems very improbable that 
the objectively existing elemental xther—space under its kinematical 


ma oe 


478 Dr. G. J. Stoney on Texture in Media. 


It thus appears that the distinction between different parts, 
which is implied by the term density, does not exist* in the 
elemental eether, and that in it the element of volume is the 
element of mass. There is, accordingly, no such physical 
quantity as density in the dynamics of the ultimate motions 
of the elemental sether. It is only when accumulations of 
these primary motions are lumped together, and where what we 
are investigating is merely the drifting about of these accumu- 
lations—it is only in this branch of dynamics that we find the 
need and the advantage of the conception of density as a 
substitute for having to take separately into consideration some 
of the motions that are really going on. In fact, if any such 
hypothesis as Sir William Thomson’s is true, the density of a 
lump of iron, 7. ¢. the coefficient by which the elements of its 
volume have to be multiplied in order to get their masses, is 
nothing but a mere function of the primary or elemental motions 
prevailing inthat portion of spacet, and which alone make that 
portion of space differ from one in which other elemental 
motions are going on. 


aspect—is of either of these kinds; and accordingly it is improbable that 
empty coreless vortices are any part of real Nature. This is a kind of 
objection which may raise an improbability, even a great improbability ; 
but we should be rash to rely on it as finally decisive, for the reality of 
things is not limited by our way of conceiving them. 

The objection, such as it is, would not le against the presence in 
nature of coreless vortices lined with a vortex sheet and filled in with a 
part of the medium devoid of rotational motion; but such vortices would 
in some respects behave differently from empty coreless vortices. 

* This conclusion is confirmed by an important ontological proposition 
which is susceptible of demonstration, viz. that nothing that we suppose 
to exist in nature can be “real,” unless zt 7s a syntheton of perceptions 
actual, potential, or conceivable. Thus, motions and space relations may 
be “ real,” for they are such syntheta; but a “ thing to move” is not real 
except in those cases in which the motion we are considering is the 
drifting motion of volumes within which subsidiary motions prevail. In 
such cases the subsidiary motions are often thought of, and may, perhaps 
without objection, be spoken of as a thing that moves. 

+ That is, on the supposition that the luminiferous ether is of uniform 
texture throughout its whole extent, as seems to be the case. If, how- 
ever, the fact be otherwise, we must regard the density of the iron as a 
function both of the elemental motions pervading its volume and of the 
elemental motions in the adjoining part of the luminiferous ether. The 
density of the iron would then depend on its situation in the material 
universe. 


LIV. On the Theory of Dropping Electrodes.—Reply to 
’ Mr. Brown. By Prof. W. OstwaLp*. 


EF the April number of the Philosophical Magazine, Mr. 

Brown raises objection to a remark, which I made in the 
Zeitschr. f. ph. Ch. iv. pp. 547, 578, about his supposed dis- 
proot of v. Helmholtz’s Theory of Dropping Hlectrodes. | 
must regret not having expressed myself clearly enough in 
that remark, as Mr. Brown has not considered its essential 
part at all in his note. 

Mr. Brown ascribes to v. Helmholtz the opinion that the 
cause of the galvanic current observed when a mass of mer- 
cury dropping in an electrolyte is connected by means of a 

galvanometer with the mercury collecting at the bottom of 
the vessel, is the ‘‘ charges carried down by the drops.” Ido 
not know on what passage of Helmholtz’s writings Mr. Brown 
supports this statement; any such is unknown tome. Helm- 
holtz’s assumption is, that every drop on its formation becomes 
covered with an electrical double layer similar to the charge of 
a Leyden jar. This double layer contains positive and nega- 
tive electricity in equal quantities ; 1ts motion cannot theretore 
give rise to anything that is similar to a galvanic current. 
From this it follows, conversely, that the galvanic currents 
produced in this way have no connexion whatever with the 
motions of the drops. 

Such a connexion, however, exists with the formation and 
the destruction of the drops. Hvery drop that is produced 
takes positive electricity from the mercury, and negative from 
the electrolyte, in order to form its double layer. On the 
union of the drop with the mass of mercury lying at the 
bottom, the positive electricity goes over to the latter while 
the neg vative electricity remains in the electrolyte, and moves, 
in case the process continues, to the point of formation of the 
drops, to produce there new double layers. This latter move- 
ment is of course dependent on the resistance of the electrolyte, 
and Mr. Brown’s observation therefore is not, as he believes, 
in contradiction, but in complete agreement with the theory 
of Helmholtz. 

Against this, Mr. Brown objects that currents are also ob- 

tained if the dropping mercury is connected with a secondary 
mercury electrode which receives no drops. It seemed to me 


unnecessary to develop the above-given explanation also for 


this case, since every one who understands that can also here 
apply it. On Mr. Brown’s account I will, however, again 


* Communicated by the Author. 


See ee ee 


FER ee mee 


480 Mr. W. Coldridge on the Electrical and 


expressly state, that also in this case double layers are formed 
on the drops, whose negative electricity comes from the elec- 
trolyte. The supply of this electricity depends therefore on 
the conductivity of the electrolyte. ‘The process can, however, 
no longer be a lasting one, because the secondary electrode is 
immediately polarized. Mr. Brown can easily convince him- 
self (if he has not already noticed it), that the current pro- 
duced under such circumstances is much weaker than the one 
earlier mentioned, and that it becomes continually weaker 
owing to the polarization, while the other current can be kept 
for days at its original strength. 

Finally, it follows from the theory of v. Helmholtz, that a 
diminishing current of opposite direction must be obtained if 
the secondary electrode is connected, not with the dropping 
mercury, but with that collecting on the bottom of the vessel. 
This current can also easily be observed. According to Mr. 
Brown’s ideas, if I have correctly understood them, in this 
case no current whatever could be produced. 


Briider Strasse, Leipzic. 


LV. On the Electrical and Chemical Properties of Stannic 
Chloride; together with the Bearing of the Results therein 
obtained on the Problems of Electrolytic Conduction and Che- 
mical Action.— Part I. Huperimental Observations. Part II. 
Theoretical Considerations. By Warvd Coupringr, B.A., 
Scholar of Hmmanuel College, Cambridge. 


| Concluded from p. 394. | 
Part [I.—THEORETICAL CONSIDERATIONS. 


fier first problem that presses forward for consideration is 

that involved in the nonconductivity of stannic chloride. 
It is a truism to write that its insulating-power is a function 
of its constitution ; but it has hitherto been difficult, from the 
lack of experimental observations, to advance beyond that 
truism. The fact is that a column of stannic chloride, some 
three to four centimetres in length with a cross section of one 
to two square centimetres, has a resistance the lower limit of 
which is certainly not less than 1600 megohms. This pheno- 
menon is not an isolated one. Other pure liquids—water, 
hydrochloric acid, hydrofluoric acid—are also nonconductors, 
but liquid hydrocyanic acid is said to be an electrolyte ; and 
the fused salts, of which the silver halogen compounds may be 
taken as typical, easily electrolyse. Wherein, then, do these 
liquids which are nonelectrolytes differ from those which are 
electrolytes? In order to progress towards a solution of this 


Chemical Properties of Stannie Chloride. 481 


question a review will now be made :—of the chemical cha- 
racteristics, as far as they are pertinent, of those compounds ; 
of the possible influence of their physical aggregation ; and, 
lastly, of the conditions under which the power of electroly- 
sability can be developed. 

To take the liquids seratim :— 

Water is characterized by its stability and by its large heat 
of formation. If it could be directly oxidized to hydrogen 
peroxide, the change would involve a large absorption of 
energy, 


(H,0, 0) =23,100 cal. 


Thus it is not possible for pure water to become nonhomo- 
geneous through the formation of any peroxide: the only 
other w ay in which water could become chemically nonhomo- 
geneous, save through the formation of molecular as 
of varying complexity, would be by its dissociation in part 
into hy ‘drogen and oxygen atoms ; but this is a most remote 
speculative chance and a practical impossibility. 

Hydrofluoric Acid is the only compound of hydrogen and 
fluorine. There is neither a perfluoride (HF,) nor a sub- 
fluoride (H,F). Moissan examined the product of the elec- 
trolysation of liquid hydrofluoric acid, rendered a conductor 
by the presence of dissolved potassium hy rdrogen fluoride, and 
found no evidence of such a change as 


H,F,=yH+H,-,F., 


and established that the ions, as liberated, are simply hydrogen 
and fluorine. 

Hydrochloric Acid is the only compound of hydrogen and 
chlorine. I think that no one has endeavoured to perform 
with liquid hydrochloric acid experiments analogous to those 
of Moissan’s for the sake of their electrolytic importance. 

Stannic Chloride in the vaporized condition can exist per- 


fectly as a collection of like unit particles, molecules f SnCl, | 


There is a lower compound, stannous chloride; but the forward 


Changes SnCl, + Cl, = SnCl,, 


occurs with the utmost readiness. A strong presumption 
therefore exists against the possibility of the reverse dissocia- 
tion, except at high temperatures ; and there is no evidence 
in support of such an hypothesis. 

Thus, then, water, hydrofluoric acid, hydrochloric acid, 
stannic chloride, agr ee in their chemical homogeneity. 

Whilst there is the closest resemblance between the above 


482 Mr. W. Coldridge on the Electrical and 


nonconducting liquid acids and the conducting liquid hydro- 
cyanic acid, in point of their physical properties, it may yet 
be possible to distinguish it chemically : at least it is worthy 
of note that 


(H, C, N)= —28,400, 


for such a large endothermic formation is suggestive of a 
tendency towards instability. 

The observations of Bleekrode and De La Rue (Proc. Roy. 
Soe. xxv. p. 323), showing its power of electrolysing, are 
worthy of confirmation, provided all possible precautions be 
taken to ensure the use of an absolutely anhydrous specimen. 

In considering the phenomena presented by the fused salts, 
it is necessary to recall the warning given by Prof. Armstrong 
as to the scantiness of accurate data at the command of the 
inquirer into the properties of fused pure substances. Having 
noted this warning, a statement made by Faraday is very 
apposite. In the first volume of his ‘ Experimental Researches 
in Electricity, § 690, when he is discussing the results he 
had obtained with fused antimony trichloride, he suggests 
that the conductivity he had observed “ might be due perhaps 
to a true protochloride consisting of single proportionals 
(SbCl).” In a word, Faraday surmised that the fused com- 
pound was not quite homogeneous. A similar suggestion 
may be advanced: that silver chloride, silver iodide, selected 
as two of the best examples of Faraday’s law of Liquido- 
Conduction, are not homogeneous compounds in the fused 
state. Photo-salts—whether they be definite compounds or 
mixtures is of no import—exist and are characterized by the 
extreme facility of their formation. Probably with more 
accurate information at command it will be possible to advance, 
in explanation of the electrolytic conduction of fused sub- 
stances, this view of the imperfect homogeneity, itself sup- 
ported by separate and nonelectrical considerations ; and to 
establish as an expression of a complete uniformity that no 
homogeneous liquid is an electrolyte: electrolisability involves 
an antecedent condition of heterogeneity. 

But in such a statement as that no homogeneous liquid is 
an electrolyte it is necessary to accurately determine the sig- 
nificance of the word “homogeneous.” Without hesitation, 
for example, pure liquid stannic chloride would be spoken of 
as homogeneous. The statement would be accurate if the 
whole of the stannic chloride were composed of precisely similar 
unit molecules. But a view has been expounded in a pro- 
found paper by Prof. Armstrong, “On Electrolytic Conduction 
in relation to Molecular Composition; Valency and the Nature 


Chemical Properties of Stannie Chloride. 483 


of Chemical Change ; being an attempt to apply a Theory of 
Residual Affinity’ (Proc. Roy. Soc. 1886, p. 268), that 
stannic: chloride is not thus simply constituted, but that a 
condition of more complex aggregation is attained of which 
the particles could be represented thus :— 


ae (GaineeaaeN (a 
[ Sncl, | (.SnCl, | ( SnCl, | ; 
a ee ~~ ep 


where w, y, ¢ may or may not have the same value, and are 
probably of considerable magnitude. He considers that these 
groups are built up in virtue of the “ Residual Affinity ” 
which he holds to be characteristic of the negative elements. 
Such a group represented graphically would appear thus :— 


—C]l——- |. cl 
er ae ol 
ey ee CE 
_ des eo ee a1 
Bosh _ch_cl_C__1_Ba_01— 

hy aR EE LE Sek le Poel yea ob a 


| | | | 


This process of construction would be continued according to 


the value of x in | SnCl, ie 
GE 4) 
Ifa value of «=6 be assumed, the aggregation might be 
completely represented thus :— 


meee ae a a ee ee eee ee ee 


484 — Mr. W. Coldridge on the Electrical and 
Another group might be (SnCl,)193 another (SnCl,)1.; &e. 


Then to call stannic chloride homogeneous, if thus composed 


of aggregates of varying complexity, is to use the term in an - 


approximate and statistical sense, or subject to a reservation 
that it applies only to the ultimate molecules and not to the 
ageregates they form. The main purpose of this conception 
is the vivid realization of a condition of elephantine stability, 
one that shall afford a foundation for the dissociation processes 
which are associated with electrolytic conductivity. Thus, 
when Armstrong discusses the effect of water on the conduc- 
tivity of the halogen acids, he submits the view that the 
dilution improves the conductivity by decomposing the more 
complex molecules; and generally he concludes, when the 
molecular conductivity is low, then there are big molecular 
agoregates. The liquid stannic chloride would consist of 
massive groups. This conception is fruitful, and explains 
many phenomena. But a simpler explanation may serve 
these purposes as effectively. It thus becomes of interest to 
consider whether it is necessary to adopt this view of the com- 
plex aggregates in the place of the simple molecular compo- 
sition, whether stannic chloride is composed 


; ClLapiwee (ey EN (ae 
(a2) | SnCl, | | SnCl, ; SnCl, | 
ussaeanerns 7) \ sb ner | ee eo / 
or 
(Gisstia (Gana (3; a 
(B) | SnCl, | | SnCl, | | SnCl, | 
SS. as (oh ey 


lA 
& 


In consideration of this question, it may be advanced that 
stannic chloride in the gaseous condition does consist in 
molecules represented as in («). 

But it may be urged that some gases which have at high 
temperatures simple constitutions have at lower temperatures 
more complex ones. Thus nitrogen peroxide is ‘ NO,” at 
high, and gradually passes into “ N,O,” at low temperatures. 
Mallet has observed that hydrofluoric acid is ‘“ HF,” just 
above its boiling-point. ‘The density of acetic-acid vapour 
corresponds to a molecule C;H,O0; within a few degrees of its 
boiling-point, and then, as the temperature rises, rapidly dimi- 
nishes to a density which gives the molecular weight of 60. 

Do, then, these observations lead by induction to the result 


i . Ps 3 
that, as the vapour of | SnCl,| is condensed into a liquid, the 
Na. See) 


molecules coming nearer and nearer coalesce into complex 
aggregates? If this induction be correct, then the liquid 
must have the constitution £. 


ia - ee 


Chemical Properties of Stannic Chloride. 485 


But the induction is based upon a fallacy. It does not 
follow, in the cases cited, because the densities rapidly increase, 
relative to hydrogen, as the temperature falls, that therefore 
the molecules have also become greater. For these molecular 
weights are determined on the assumption that Avogadro’s 
law is applicable to these substances in a vaporized and imper- 
fectly gasified condition. Such an assumption is untenable ; 
it is, as Prof. J. J. Thomson emphasizes in his lectures on the 
Properties of Matter, more rational to conceive that the va- 
pours do not contain equal numbers of molecules. The state- 
ments that nitrogen peroxide is “ N,Qy,,” that hydrofluoric acid 
is “ H,F,,” that acetic acid is C;H,03*, are tainted with this 
fallacy ; and the taint vitiates the induction that leads to the 
conception (@) as the constitution of liquid stannic chloride. 

Moreover, positive evidence in favour of the simpler concept 
is supplied by the simplicity of the results obtained for the 
molecular weights of solids and liquids, as determined by the 
extent to which they lower the fusing-points and the vapour- 
pressure of solvents (Raoult). 

On this ground the statement made as to the constitution 
of gaseous stannic chloride may be extended so as to include 
the liquid condition, provided of course a necessary degree of 
cohesion sufficient to account for the viscosity of the liquid be 
allowed between these simple material particles the molecules 


gar eo 
| SnCl, | 
eS eae 


And, again, it may be maintained that the condition (g) 
presents a prospect of greater stability than (@). For an 


inspection of the graphic representation of the group { SnCl, 
Inspection OF the graphic representation of the group ena) 


shows that, whereas according to («) the chemical homogeneity 
is preserved solely by the attractions of the respective atoms 
of tin for their four respective atoms of chlorine, according to 
(8) this attraction is opposed “ by the straining of the chlorine 
atoms at the chlorine atoms of the adjoining molecules.” 
Thus, then, on account of the greater stability represented 
in the simpler view, on account of the evidence in its favour, 
on account of the absence of satisfactory arguments to prove 
the existence of the hypothetical complex aggregates, the 
simpler view («) will here be taken and the stannic chloride 
will be considered as strictly homogeneous; sic wqualiter for 
the other-mentioned nonconductors. And it is advanced that 
every substance thus strictly homogeneous is a nonelectrolyte 
on account of that very homogeneity. This homogeneity isa 


* Horstmann, Annalen, clxviii. VI. sup. 53. 


Phil. Mag. 8. 5. Vol. 29. No. 181. June 1890. 2P 


A86 Mr. W. Coldridge on the Electrical and 


function of the chemical stability. Indeed the problem of 
electrolysis is at its foundation a chemical one; but at this, its 
foundation, the chemical problem resolves itself into an ante- 
rior physical one, namely the laws that govern the interaction, 
the attraction of atoms at atomic distances. ‘The scientific 
aim of the theory of electrolysis has been stated by F. Kohl- 
rausch to consist in the reference of electrochemical phenomena 
to mechanical or electromechanical laws”’* : herein must be 
the solution of the problem of chemical affinity. 

To the question whether there is some physical property 
of pure water, pure hydrochloric acid, hydrofluoric acid, &e. 
which endows them with insulating-power, and the absence or 
difference of degree of which in fused salts admits of conduc- 
tivity no successful answer has been given, though a great 
variety of attempts have been made. Doubtless viscosity is 
a factor in the result, and Faraday’s law of liquido-conduction 
is a statement of that fact. But the influence of viscosity is 
secondary rather than primary : all the electrolytes must have 
a degree of limpidity, and as the limpidity decreases so will 
the resistance increase. As examples, Kohlrausch’s experi- 
ments on Silver lodidet, Arrhenius’s investigations of the 
actions of Fluidity on the Conductivity of Electrolytest ; 
though these would have been improved by the use, as sole 
solvent, of some oily polyhydric alcohol. But limpidity, as is 
seen in the various nonconducting pure liquids, does not 
involve electrolysability. The destruction of the physical 
homogeneity, and generally the change of physical properties 
which must occur when stannic chloride is heated from 16° C. 
to 112° C., its boiling-point, has not apparently any influence, 
and certainly not within the limits of delicacy of my experi- 
ments, on its nonconductivity. 

To sum up: Ithas been advanced that the fact that stannic 
chloride is homogeneous, chemically homogeneous, accounts 
for its nonconductivity : similarly for the other nonelectro- 
lytes. To continue: It will be demonstrated how the results 
obtained show that where this chemical homogeneity is de- 
stroyed, where the whole or part of the stannic chloride enters 
into combination so that molecular interchanges, akin to those 
which Williamson so vividly portrayed in his epoch-making 
papers on the Theory of Ktherification, can occur, then the 
power of electrolytic conductivity is developed. The validity 
of this conclusion will be most cogently established by answer- 

* Report on the Present State of our Knowledge in Electrolysis and in 
Electrochemistry. W.N. Shaw, M.A. (Brit. Assoc. 1889), 

+ Pogg. Ann. 1876, p. 159. 

{ Kongl. Vetenskaps-Akad. Fordhandlingar, 1885. 


Chemical Properties of Stannic Chloride. 487 


ing the following question: Whereas hydrochloric-acid gas, 
alcohol, ether, aqueous hydrochloric acid, sulphuretted hy- 
drogen and alcohol, render stannic chloride an electrolysable 
liquid, why do not chlorine, sulphuretted hydrogen, chloro- 
form, the various solids mentioned in Part I., exert a similar 
influence ? 

The answer is, that the former enter into chemical combina- 
tion, the latter do not. To quote the concluding sentence of 
Part I., the latter class of substances ‘“ producing no effect on 
the chemical homogeneity of the stannic chloride, which 
remains merely stannic chloride, are without influence on its 


electrical conductivity :” a collection of unit particles, [ SnCl, | : 
Ss 


even where mechanically interspersed with foreign substances, 
do not conduct. But when hydrochloric-acid gas, alcohol, 
ether, hydrochloric-acid solution, sulphuretted hydrogen and 
alcohol, are added, electrolytic power is developed. Here, 
however, there is no longer chemical homogeneity. 

The stannic chloride charged with hydrochloric-acid gas 
must contain a collection of molecules of the double chloride 
2HCl.SnCl, interspersed amongst molecules of stannic chlo- 
ride. There is here manifestly the potentiality of a continual 
condition of interchange between the combined and uncom- 
bined stannic-chloride molecules ; a condition of dynamical 
equilibrium maintained by changes of this nature :— 

(SF 


ameice Y (ae ak, 
(PESTA (ee (Fa Kaye DRY (20. (i SMG a eae 
| SnCl, | | 2HCl| | + | SnOl, | |'SnCl, | + | | 2EHCH| SnCl, | 
Ne ee) See | NOE SE Ss Rea eee ee SY) 


tts SS = 


a B Y & B 4 
The similar phenomenon is repeated under the influence of 
absolute alcohol; here the alcoholate SnCl,.2C,H;OH is 
formed and dissolved in the excess of alcohol. The equili- 
brium would depend on, here, the interchange of the com- 
bined alcohol molecules for the uncombined :— 


4 SE a ae eee 
GEren. Nae. seoae™ oN ae = ae (Ck NG (eee ee 

| [ SnO1, | |20,1,0H | | 4+ | Sn0l,| > | SnCl, | + | | SnCl, | {2C,H,OH | | 
eh a Se) eee) Se ee eas = eee 

Sa ———— a 

a p Y a 6B Y 
Similarly for the etherate SnCl,. 2(C,H;),0 :— 
ec © praia =a 


i 


(aka cae, ——— | (Tape ar) | (FL Lea a oe 
[ Suc, [2(C,H,,),0] | + [ Suc, } > [ sncl,} + | | 2(C,H,),0 | |Snet, 
Neate) | ei Cee) Se ot a ne aes 


eS 


a B Y a B aie 
Pe Pa 


488 Mr. W. Coldridge on the Electrical and 


The idea of examining the influence of these liquids pro- 
ceeded from a study of Moissan’s* work on liquid hydrofluoric 
acid ; it seemed that the conductivity he developed was due 
to such an interchange as :— | 


tae j= “aE 
SEAT (_) =a (=| a Can 
Gar) + | (ee) Gr) || Gar) | + (a) 
ee ee) | a) | eee ee) EEE Kuen 
Were Sa a ee 
a 6 y a 6 7 


and it was conceived that if a similar condition of dynamical 
stability could be produced in stannic chloride, conductivity 
would be developed. The results have justified the induction. 
The delicate observations made by Kohlrausch on the resist- 
ance of pure water, and the effect of exposing it to the atmo- 
sphere of a room charged with tobacco-smoke, are explicable ~ 
on the same lines; the water would absorb traces of carbonic 
acid and of the basic products, which in turn would form 
hydrates, and then there would result a similar condition of 
interchange. 

The generalization may now be provisionally stated :—that 
such an antecedent condition of dynamical equilibrium is 
absolutely essential to the development of the power of elec- 
trolytic conductivity. With no great difficulty, it would be 
possible in terms of 


(1) the number of such interchanges per unit of time, 
(2) the degree to which the stability of the original unelec- 
trolysable molecule is disturbed by each interchange, 


to establish a dynamical theory to explain the influence of 
(a) the concentration, (b) the temperature, on the conductivity 
of electrolytes; and for this purpose would be needed accurate 
measurements of the resistance of solutions (say, of the tetra- 
chloride in alcohol, in ether, and of their temperature-coefii- 
cients). The results would emphasize the great value of some 
dynamical explanation of chemical action, and the influence 
of mass and temperature on its course. 
The differences observed in the action of 


(1) dry sulphuretted hydrogen on stannic chloride, 

(2) dry sulphuretted hydrogen on stannic chloride in chlo- 
roform solution, 

(3) dry sulphuretted hydrogen and stannic chloride on water, 

(4) absolute alcohol on sulphuretted hydrogen and stannic 

: chloride, 

(5) dry sulphuretted hydrogen on ether and stannic chloride, 


* An account of Moissan’s work is given in ‘ Nature,’ vol. xxxvii. 
(1887-8) ; Moissan considers the potassium fluoride to be the electrolyte. 


Chemical Properties of Stannie Chloride. 489 


cannot fail to be suggestive. At present it may be noted 
that “where there exists an aptitude for directed decompo- 
sition,” such as is involved in the above dynamical cone:ptic n, 
and such as exists in the aqueous or alcoholic solution of 
stannic chloride, there sulphuretted hydrogen at once precipi- 
tates stannic sulphide ; whereas between the dry sulphuretted 
hydrogen and stannic chloride there is found only a small 
quantity of addition compound (SnCl,.5H,8), which, when 
agitated into a condition of instability by elevation of tempe- 
rature, gives the stannic sulphide observed by Dumas. This 
influence of alcohol on stannic chloride and sulphuretted hy- 
drogen is typical of that of catalytic agents in general; and 
the explanation here suggested is of wide application. The 
phenomena discovered by Prof. Dixon, to whom I am indebted 
for a complete list of the published papers on the action of dry 
substances, are of a parallel nature. He found that the com- 
bination of dry carbon monoxide and dry oxygen, 
2C0O + Oo = 200 

occurs only in the path of the spark, but that when the gases 
are moist the combination is explosive. Again, Dixon has 
shown that, in the combustion of carbonic oxide and hydrogen, 
the influence of the steam is not of a physical but of a che- 
mical nature}. The inactivity of dry hydrochloric acid and 
dry oxygen, of dry hydrobromic acid and dry oxygen, and 
their activity in the presence of water is of the same nature t 
(Richardson). The observation, made by Pringsheim §, that 
dry chlorine and dry hydrogen do not combine in sunlight, 
but that the presence of a small quantity of water is sufficient 
to determine their combination, is quite parallel. Baker has 
proved that some dry solids are incombustible in dry oxygen, 
though he finds that others are combustible ||. 

It cannot be maintained as a law of nature that no two pure 
substances, AB, DC, combine ; either 


(1) AB+DC=AB.DC, 
(2) AB+DC=AD+BC, 
possibly passing through the stage 
AB.DC>AD+ BC. 
As an example of such a change, we have 
SnCl,+ 5H,S =SnCl,. 5H8, 
SnCl, 5H,S ~ Sn8.+4HC1+3H,8 : 


* Phil. Trans. 1884. + Journ. Chem. Soc, 1886, p. 94. 
{ Journ. Chem. Soe. li. p. 803, § Wied. Ann. xxxil. p. 384. 
|| Phil. Trans, 1888, “A.” 


490 Mr. Pickering on the Theory of Osmotic Pressure 


but here, as in all the above cases, the catalytic agent, by 
producing a condition of dynamical equilibrium, greatly 
facilitates the change. 

Further instances of the precise similarity between the 
action of catalytic agents and of those substances which are 
capable of endowing nonconducting liquids with the power of 
conduction will doubtless be found, and further proof analo- 
gous to those advanced here in the case of stannic chloride of 
_ the strict parallelism between the phenomena, of the birth of 
electrolytic power and of enhanced chemical activity, will 
trace these effects back to an identity of cause, the setting up 
of a condition of dynamical equilibrium. 

Emmanuel College, Cambridge. 


LVI. The Theory of Osmotic Pressure and its bearing on the 
Nature of Solutions. By SPENCER UMFREVILLE PICKERING, 
VAS 


‘ATO one can doubt the mathematical correctness of the 

conclusions which Arrhenius, van’t Hoff, Ostwald, and 
others draw from the premisses with which they start in their 
arguments respecting osmotic pressure, nor can we doubt the 
value of connecting numerous actions with one and the same 
cause, or that there are a large number of instances in which 
the observed facts are in substantial agreement with their 
conclusions. But we may, I think, legitimately doubt 
whether the premisses of the arguments are sound, whether 
the conclusions harmonize as well as they should with ex- 
perimental data, whether the theory is more than a mathe- 
matical exercise, or more than a convenient working hypo- 
thesis of a rough character, instead of being, as its supporters 
maintain, an hypothesis established so firmly that we may 
build upon it a physical theory of solution. 

The direct measurement of osmotic pressure has been made 
in but a few cases, and those cases are ones in which the 
substances examined are eminently unfitted for showing the 
presence of any chemical action which may be present. Of 
the phenomena correlated with osmotic pressure, the lowering 
of the freezing-point of a solvent by the addition of foreign 
substances is the one which has received the greatest atten- 
tion, thanks to Raoult’s classical work, and is the one which 
forms the main support of the theory. 

In examining the experimental facts the following ques- 
tions must be asked, and if the theory is correct they must be 
answered in the affirmative. 


* Communicated by the Physical Society: read March 7, 1890. 


and its bearing on the Nature of Solutions. 491 


(1) Is the molecular depression—using this term to meat 
the lowering of the freezing-point produced by one foreign 
molecule on 100 molecules (not parts by weight) of the solvent 
a constant, whatever the foreign substance is, provided 
that the amount of the latter is not greater than that which 
would give a pressure equal to that produced by it in the 
gaseous state at the same temperature ? 

(2) Are such deviations from regularity, as are observed 
in exceptional cases, in the direction in which they should be 
according to the theory ? 

(3) Is the depression a constant whatever the solvent is? 

(4) Is the depression constant when the proportions of 
the solvent and dissolved substance are varied within the 
limits mentioned in (1)? 

(5) When stronger solutions are taken, is the deviation 
from regularity in the direction in which it should be 
according to the theory ? 

(6) Is the deviation always in the same direction, and 
always regular? 

I believe that I can show that the answer to every one of 
these questions is an unqualified No. 

The main facts of the case as elucidated by Raoult’s work 
are that, when various substances are dissolved in 


Benzene, 
Nitrobenzene, 
Hthylene dibromide, 
Formic acid, 

or Acetic acid, 


the molecular depression is about 0°63, though there are a 
few substances in each case which give an abnormal depres- 
sion of about half this amount. 

With water the molecular depression is generally 2°06, 
but in many cases approximates to 2°61, values which 
Raoult takes to be three and four times 0°63 (1°89 and 
2°-52) respectively. Abnormally low values are in the same 
proportion to the normal ones as with other solvents ; they 
are about 1°:03 (half of 2°-06), and are obtained with some 
inorganic substances, and with the majority of organic sub- 
stances at present investigated. 

All these determinations apply to solutions containing about 
1 molecule to 100 molecules of the solvent, and are, therefore, 
three or four times stronger than they should be in order to 
be comparable with gases under ordinary conditions. We 
shall have to decide whether the discrepancies which they 


492 Mr. Pickering on the Theory of Osmotic Pressure 


show are such as could be reasonably attributed to increasing 
the pressure from one to three or four atmospheres. 


Influence of the Nature of the Dissolved Substance. 


The half values obtained in many cases are explained by 
the duplication of molecules, owing to the solutions not being 
sufficiently dilute ; that is, an additional pressure of two or 
three atmospheres will cause the vapour-densities of hydro- 
chloric acid *, methyl, ethyl, amyl, and butyl alcohols f, 
benzol, and many other substances to double themselves 
(assuming that they retain their gaseous condition). This 
may be so, but direct determinations cannot be, or have not 
been, made. 

Leaving these abnormal values for the present, we find 
that, the normal ones exhibit the following variations:— 


Sie eee ae Variation in the value | 
investigated of the depression f. 
PACELIC TAGIC, a, ere tone.» -scasecceneesen: 57 30 per cent. 
BEL GETINTC ACIC ee ete aee aes saseurnaces oss 9 14; 
FSCNZONE ies nee eta tn seedeednaasene aes 4] a 
INWOBEN ZENE Fie .e.r Wants: cos catterdenses 15 1% 
Hthylene dibromide..........:0...c.-+.< 5 PDE F- | 
BRMere oh cere at ots te | 59 60§ ,, | 
»» (with organic substances) ... 29 AQ ate. | 


‘These variations appear somewhat too large to be attributed 
to the fact that we are working at two or three more atmo- 
spheres of pressure than we should be. 

It is noticeable that the organic solvents, except acetic 
acid, give comparatively constant results, but that, as soon as 
we come to the inorganic solvent water (which we know shows 
a much greater tendency to form “ molecular” compounds 
than the other liquids), we get a much larger variation, and 
the following values || will justify the assumption that when 
other solvents of a similar nature are examined, still greater 
variations will be observed. 

* Solvent, Acetic acid (Raoult, dunn. Chim. Phys. {6] xi. p. 72, from 
which paper this and other values quoted here are taken). 

+ Solvents, Benzene, &c. 

t Percentage on the lowest value. 

§ Omitting borax, where the value is exceptionally high. 

|| Chem. Soc. Trans. 1890. The values selected refer to solutions of 


the same strength as those used by Raoult. The results with calcium 
nitrate and chloride are as yet unpublished. 


and its bearing on the Nature of Solutions. 493 


Depres- 


| 
Solvent. Dissolved substance. | io nx. | Variation®. 
| | e Per cent. 
_Tetrahydrate of sulphuric | Water. 0:08 } | 
acid. 100 
| Do. Sulphuric acid. 0-04 
Monohydrate of sulphuric Water. 0-02 
acid. | 100 
| Do. Sulphuric acid. 0-01 
Sulphuric acid. | Water. PerOUs inl i500 
Do. Sulphuric anhydride. 0°42 
Hexahydrate of calcium) Water. 0-003 
chloride. | 233 
Do. Anhyd. cale. chlor. 0010 
Tetrahydrate of calcium} Water. en C007) 
nitrate. | | 100 
Do. Anhyd. cale. nitrate. | 0:015 


As an instance of a similar character we may quote 
Heycock and Neville’s determinations of the depression of 
the freezing-point of sodium by various metals f. 

Metal added. Molec. depression. 


CONG latin) vahtes 
halliamari. Oe Ve) 2 eas 


Mercury Ad 
Cadmammaeyes 417 3°0 
Rotassiumre: Woll; 0°. Os or6 
Lithium 1:3 
Lead 4°6 
Imei: 248.3% a) 


The variation here is 260 per cent. 

If such variations are not too great to be attributed to an 
excess of two or three atmospheres’ pressure (and I certainly 
think they are), they are undoubtedly too great to permit of 
a theory being founded on the assumption that they are 
constant. 

It may be noted also that Heycock and Neville’s deter- 
minations with indium, gold, and thallium extended to 
solutions as dilute as the gases from these metals would be 
Gf their molecules are diatomic), and that even with these 
“ideal ” solutions the variation amounted to 60 per cent. ; 
had lithium and cadmium been similarly investigated we 
should, no doubt, have found as greata variation as that quoted 
above with the stronger solutions. 


* Most of these values are but approximations. 
+ Chem. Soc. Trans. 1889, p. 667. The values refer to solutions con- 
taining as near as possible one atom of the foreign metal to 100 Na, 


4 


a 


Se 


oe 


494 Mr. Pickering on the Theory of Osmotic Pressure 


Direction of the Deviations with Dissolved Substances 
which give Abnormal Values. 


The abnormally low values (i.e. half values) which some 
dissolved substances give are attributed, as has been men- 
tioned, to the polymerization of their acting molecules, and 
the abnormally high values which some solvents give are, in 
the same way, attributed to a polymerization of the solvent 
molecules. This view is accepted by both the supporters 
and the opponents of the osmotic pressure theory. 

In the case of dissolved substances which give abnormally 
high values (i. e. double values), the supporters of the theory 
hold that these substances are dissociated into their ions, and 
in this view their opponents cannot agree with them. 

The first point to settle, is whether there are any abnormally 
high values (given by dissolved substances), and it appears to 
me that there certainly are none. 

In the case of the five organic solvents examined, the 
substances giving the higher and lower values are in the 
proportion of 100 to 16, and here there can be (and is) no 
question as to which are the normal ones; even if in the case 
of water these proportions were reversed, it would be incon- 
sistent to term the lower values the normal ones; but the 
proportions are actually not reversed, the substances giving 
high values being to those which give the lower ones in the 
proportion of 100 to 76. I fail to see therefore what grounds 
there are for saying that there are any abnormally high 
(double) values at all, or what need there is for calling in 
such a theory as that of dissociation into ions *. 

Indeed, there is a distinct difficulty, if not impossibility, in 
calling the lower values (1°03) the normal ones; for the 
normal value with other liquids is 0°°63, and the excess in the 
case of water could only be explained by the water molecules 
being more complex than those of other liquids in the pro- 


* Van’t Hoff’s statement as to Raoult’s position respecting the high 
and low values of substances in water is certainly remarkable; he says 
(Phil. Mag. 1888, xxvi. p. 99), “‘ Raoult did not discover the existence of 
so-called normal [meaning small] molecular depression of freezing-point 
and lowering of vapour-pressure until he investigated organic compounds ; 
their behaviour is almost without exception regular.” As a matter of 
fact, Raoult investigated organic substances first (Ann. Chim. Phys. 
1883 [5] xxviil. p. 183), and when he subsequently (cbid. 1884 [6] xi. 
p. 81) found that inorganic substances gave higher values, he did not 
hesitate to call these latter the normal ones. 

If we reverse the application of the word normal, we shall have to 
admit that of the 150 substances examined in water, not one gaye an 
abnormally low value. A most improbable admission. 


and its bearing on the Nature of Solutions. 495 


portion of 1-03 to 0°63; in other words, that the water molecule 
is 14 H,O, and that the atomic theory is wrong. 

The theory of dissociation into ions is, for many reasons, 
inacceptable to most chemists, and its application to the 
results at present under discussion affords, I think, some of 
the strongest arguments against its acceptance. 

If the higher values in the case of water are due to dissocia- 
tion, we must conclude that all the stronger acids (e. g. 
hydrochloric, sulphuric, and nitric acids) are nearly entirely 
dissociated, whereas the weaker ones (e.g. hydrocyanic, sul- 
phurous, and boric acids) are not so; and similar conclusions 
must be drawn respecting the alkalies and salts. In fact, we 
shall be driven to conclude that the more stable the compound 
is the more easily is it dissociated, and that too by an agent, 
water, which has, ex hypothesi, no action beyond the dilu- 
ting effect of its mass. Is it possible to maintain that sul- 
phurous acid ewists intact in solution, while sulphuric acid, 
which is formed from it and molecular oxygen, with the 
evolution of 55,000 cal.*, and which must, therefore, be by 
so much the stabler body of the two, is entirely dissociated ? 
Is it possible to maintain that hydrochloric acid is entirely 
dissociated at a pressure of three or four atmospheres when 
we know as a fact that it can exist undissociated at a pressure 
of only one atmosphere f ? 

Indeed, it appears to me that if we acknowledge such a 
dissociation we must deny the principle of the conservation 
of energy. Thus, to take one instance out of many, the 
molecules of hydrogen and chlorine must {t be formed from 
their constituent atoms with a considerable development of 
heat, say +z and +y cal. respectively, and they react with 
each other to form 2HCl with a further development of 
44,000 cal. ; if this 2HCl, when dissolved in water, be entirely 
dissociated into its atoms, it must absorb 44,000 +2+y cal., 
whereas, as a matter of fact, it evolves 34,630 cal. : hence there 
has been a creation of (78,630 + x + y) cal. out of nothing, 


* If atomic oxygen were taken, asit should be, the heat evolved would 
be much greater. 

+ In acetic acid hydrochloric acid is, according even to the supporters 
of the theory, not only not dissociated into its ions, but even not dis- 
sociated into its fundamental molecules, it being present as 2HCI. 

t I think that we may say “must.” Ifthey were formed with absorp- 
tion of heat it would mean that the atoms repel each other, and such 
atoms would, therefore, never combine. When we call a molecule endo- 
thermic, we merely mean that it is formed from its constituent atoms 
with a smaller development of heat than some other compound of the 
same atoms, not that it is formed from these atoms with an absorption 
of heat. 


496 Mr. Pickering on the Theory of Osmotic Pressure 


and that, too, through the agency of the water, which is as- 
sumed to have no action at all. 


Influence of the Nature of the Solvent. 


It is found that the nature of the solvent, instead of being 
without influence on the results, as it should be according to 
the osmotic-pressure theory, is one of the main factors in 
determining them. 

Thus, for instance, sulphuric and hydrochloric acids give 
the normal high values when dissolved in water, but solutions 
of the same strength in acetic acid show the abnormal half- 
values : formic and benzoic acids, methyl, ethyl, butyl, and 
amyl alcohols, as well as phenol, all give normal depressions 
with acetic acid, but abnormal ones with benzene. Many 
other instances of a similar character may be selected from 
Raoult’s data, but none of them show the influence of the 
nature of the solvent in such a forcible manner as the fol- 
lowing :— 

Molec. Depress. 
ce) 
H,O dissolved in 100 H,SO, . . .. -> See 


x = 100 '(H,S0,H,0). . 2 2 ae 
55 - 100 (H,SO, 4H,0) . aie 
‘ . 100. (CaCl, 6H,O) . 3). 90300 
% i, 100 (Ca(NO;).4H,O). . 0:007 
i " 100: (CH;COOH) » 2 ae 


The variation of this constant (?) calculated on the smallesi 
value amounts to 35,600 per cent. Again, 


H,SQ, dissolved in 100 H,O . . i Bas 


” ‘: 100 (H,S0,H 0). . 4! Opa 
35 39 100 (H,S0, AH. 30) e e 0:04 
o : 100 (CH,COOH) . . 0-31 


Extreme variation 21,400 per cent. Similarly, 


CaCl, dissolved in 100 H,O . . . 2S 
“ A 100 (CaCl, 6H, 0). . -« Se 


Variation 27,600 per cent.; and 


Ca(NO3;), dissolved in 100 H,O . . “ie BU 
‘) 7 100 Ca(NO3), 41,0. 0:015 


Variation 16,600 per cent. 


and its bearing on the Nature of Solutions. AQT 


Such numbers can certainly not be accepted as constants, 
and the values are certainly largely dependent on the nature 
of the solvent*. 

In the present instance the variation cannot always be 
taken as a proof of the incorrectness of the osmotic-pressure 
theory, for it may be perfectly legitimate to attribute it some- 
times to the various complexity of the molecules of the solvent. 
But we cannot, however, do so in all cases, as for instance 
that of formic &e. nels in benzene and acetic acid, where 
the two solvents have been proved to act normally with 
the majority of dissolved substances. Yet, in any case, the 
absence of constancy means the absence of ‘what would have 
been a strong argument in favour of the theory, and this 
absence must be felt all the more because there appears to be 
no simple numerical relationship between the very different 
values given above. 


Influence of Proportions taken with very Weak Solutzons. 


My own recently published results (Chem. Soc. Trans. 1890, 
p. 881) with sulphuri ic-acid solutions form, I believe, the only 
_ series of determinations as yet made which would, from their 
number and precision, be at all likely to settle whether the 
molecular depression is really constant or not with very weak 
solutions ; and the results here can leave little doubt but that 
it is not so. : 

Between 0 and 9 per cent. solutions the results are repre- 
sented by what would with rough determinations appear to be 
a single line of typical straightness. The deviations from 
straightness in regions below 4 per cent. (about 0°8 H,SO, to 
100 H,O) are less than 0°02, and would, therefore, not have 
been revealed by determinations such as have been made by 
other investigators. From 4 per cent. to 0 the determinations 
(each being the mean of several observations) which I made 
show mean error of 0°:0008 at most, and the number of points 
determined is about 80; and the results obtained leave no 
doubt but that the apparently straight line is really composed 
of four distinct lines, three of which are straight, meeting at 
(generally) well marked angles at the percentages of 1:0, 
0-35, and 0:07 respectively. 

The relative magnitude of these changes is best illustrated 
by drawing a straight line from the freezing-point of water 


* Combining the variations due to different solvents with those due to 
different dissolved substances, we get a variation of 153,000 per cent. 
(4°°6 to 0°:003). 


498 Mr. Pickering on the Theory of Osmotic Pressure 


to that of a 2°5 per cent. solution (H,SO, to 200 H,O ; this 
was selected merely because at this percentage the dia- 
gram attains the highest relative point) and plotting out the 
deviations of the observed freezing-points from this line. 
The accompanying figure illustrates the result. The deviation 


Deviation of the Freezing-points of weak solutions of Sulphurie Acid 
from regularity. 


Deviation. 


U 


0°02 


0-04 


0°06 


0°08 2 = - 
0 1 Z 3 = 5 
Per cent. H,SO,. 


from straightness amounts to at least 20 times the mean 
experimental error, and 28 per cent. of the total depression. 
Even if we draw our straight line from a solution of 0°44 
(08 H,SO, to 100 H,O) per cent. strength—in which the 
sulphuric acid would be as much expanded as it would when 
a gas at ordinary pressures—the aberration, at 0-7 per cent., 
amounts to 0°:008, or 20 per cent. of the total depression. 

The molecular depression calculated from these results, 
together with others obtained with stronger solutions, are given 
in the following table:— 


and its bearing on the Nature of Solutions. 499 


pe eression of the Freezing-point of Water produced by the 
addition of Sulphuric Acid. 


Mols. H,SO, to Molecular 
ee tE SO, 100 1,0. elec depression. 
fo) fe) 
0-068 0:0125 — 0:0369 2°95* 

03618 0:0667 — 0°1580 2°37 
0°44 0-0811 — 01874 2°31 
1-057 0:1961 — 04214 2°15 
2°500 0:4708 —- 09825 2:09 
4021 0-7692 — 1-600 2°08 
6-000 1-1855 — 2°520 2°15 
8585 1-724 — 3456 2°00 
18-492 4°167 —11:83 2°84 
29°526 7-692 —34:00 374 
37-701 ebb —72°63 6°54 


The depression with solutions weaker than H,SO, to 100 
H,O varies between 2°°08 and 2°°95, 42 per cent., and even be- 
tween 0°44 and O per cent. it varies from 2°31 to 2°95, 
a variation of 28 per cent., numbers which can give no grounds 
whatever for the statement that the depression, even with these 
very weak solutions, is independent of the strength. 

The only other determinations which, so far as I know, 
exist with solutions containing less than one dissolved mole- 
cule to 100 of the solvent, are those of Heycock and Neville 
(loc. sup. cit.) with certain alloys. Selections from those 
series which were most fully investigated supply the following 
data :— 


Solvent. Dissolved substance. Molecular depression. 
100 Na 0-114 Au 545 

9 0°296 ” 4°74 

a 0-966 ,, 4°54 

5 0-097 Cd 3°92 

3 0-391 ,, 3°71 

- 0648 ,, 317t 


* With still weaker solutions the molecular depression is somewhat 
ereater: with a 0-005 per cent. solution (‘0009 H,SO, to 100H,O) the 
value found was 3°-4, but the total depression here is so small that I have 
not included it or similar values in the table. 

+ With thallium, mercury, sodium, and indium, the depression was 
more constant, but the data were less complete. 


Sig 


A TI LOLOL EN AE 


—— 


Lag eA OE RT 


ee 


500 On the Theory of Osmotic Pressure. 


Direction of the Deviations from Constancy with Stronger 
Solutions. 

According to the theory of osmotic pressure the propor-— 
tionality between pressure (lowering of freezing-point) and 
amount of substance dissolved will hold good, as has been re- 
marked, only for very weak solutions. With stronger solutions 
the dissolved molecules will be brought within the sphere of 
each other’s attraction and will, therefore, exert an abnormally 
small pressure; that is, they will lower the freezing-point of 
the solvent to an abnormally small extent*. 

But in every case at present known exactly the reverse is 
the case. Stronger solutions exhibit an abnormally large 
depression, and the freezing-points fall at an increasing instead 
of a diminishing rate. The table given above illustrates to 
what extent this takes place in the case of solutions of sul- 
phuric acid in water, the molecular depression increasing 
from 2°08 to 6°54 (213 per cent.), and the examination of 
six other curves from the sulphuric-acid series, and two of a 
series with calcium nitrate, supplies us with eight other in- 
stances of a similar character. The results may be summarized 
thus :— 


Solvent. Dissolved substance.| Molec. depression. | Increase. 

Se a | ee 
| Oo {e) 

100 H,SO, 1 to 33 H,O 1072 to 1-253 | 17 percent. 
100 H,SO, 1 to 58 SO, | 0422 to 0-634 "| aaa 
100 (H.,,SO,H,O) 1 to 50 H,O | 002. to0<31 | TAO 
100 (H,SO,H,O) 1to50 H,S0O, | O01 to 0197 1, O70 pee 
100 (H,SO,4H,O) 1to 400 H,O+ | 0-078 to 0-108 OO oe 
100 (H,SO,4H,0) 5 to 60 H,SO,+t 0-27 to 0-42 Dome 
100(Ca(NO,),4H,O); 1 to 150 H,O 0-007 to 0°326 = 45,600 __,, 
100(Ca(NO,),4H,O)) 1 to 33Ca(NO,), | 0-015 to0179 {11,000 _,, 


It is true that these results have only recently been placed 
at the disposal of the supporters of the osmotic-pressure 
theory, but it is otherwise with the following values in the case 
of alcohol (Raoult, Compt. Rend. xe. p. 863) and calcium 
chloride (Hammerl, Wien. Sitzungsber. Ixxviii. p. 59) §:— 


* The same will hold good if we attribute dissolution to the balancing 
of the physical attractions of (1) solvent for solyent molecules, (2) dissolved 
for dissolved molecules, and (3) solvent for dissolved molecules. The 
stronger the solution the greater will be (2), and, consequently, the less 
will (1) be counterbalanced. 

+ With 60 H,O the depression is 0°:067, so that it first decreases and ° 
then increases. 

t With 1 mol. H,SO, it is 0°40. 

§ In each case I give the values as determined from my own results, 
but these are in good accord with those referred to above. 


yy aie ae. . 


| 
4 
| 
| 


Mercury-still for the Rapid Distillation of Mercury. 501 


| 


Solvent. | Dissolved substance. | Molec. depression. Increase. 
100 H,O | 1 to 7 CaCl, 2773 to 69 150 per cent. 
100 (CaCl,6H,O)| 1 to 800 H,O 0:003 to 0:099 3200s, 
100 H,O |  1to13C,H,O PUL tof teks 6 %9 


| 


The increase in the case of alcohol is small, but still there 
is an increase, and not a decrease ; while in the case of water 
in the hydrate of calcium chloride the increase is almost the 
greatest at present known. 


Trregularity of the Deviations with Weak Sotutions. 


That the deviations from constancy are not regular, and are 
not even always in the same direction, will be seen on referring 
to the results with sulphuric acid dissolved in water (p. 499) 5 
the depression in the freezing-point of the tetrahydrate, both 
by water and sulphuric acid, supplying two other instances of 
a similar character. 


Since every fact which can be used to test whether the theory 
of osmotic pressure is a true explanation of the nature and 
behaviour of solutions, either fails to give any evidence in its 
favour, or else gives evidence directly opposed to it—evidence, 
often, of the strongest possible character—this theory can 
certainly not yet be regarded as established. 


LVI. A Mercury-still for the Rapid Distillation of Mercury 
ma Vacuum. By Freperick J. Sito, I.A., Millard 
Lecturer in Mechanics and Physics, Trinity College, Oxford”. 


oy GEN mercury is distilled in a vacuum, in the usual 

apparatus, a large portion of it when vaporized, on 
reaching the internal domed surface of the bulb in which the 
operation is conducted, forms itself into minute spheres, which 
grow heavy and run down the inside of the bulb ; and only a 
small quantity of the metal finds its way into the central tube, 
from which it is caught for use. 

The advantage of the new form of vacuum mercury-still, of 
which I venture to give an account, is that all the mercury, 
which condenses in the head of the bulb, is prevented by its 
shape from returning to the mercury from which it has been 
separated by heat. ‘This is not the case in the mercury-still 
of Weinhold, or Clark, or in those stills in which only the 
mercury which collects in the eduction-tube is caught, as in 

* Communicated by the Author. 
Phil. Mag. 8. 5. Vol. 29. No. 181. June 1890. 2Q4 


Scien aaa ine lire Tie ee Drama eects aug see norte toe tet 


502 = Mercury-still for the Rapid Distillation of Mercury. 


the beautiful new form of apparatus, devised by Messrs. 
Dunstan and Dymond, for the purification of small quantities 
of mercury (supra, p. 867). In the former of these instru- 
ments, some portion of the mercury-vapour condenses on 
the surface of the bulb and then falls back to the mass 
of mercury from which it has just been separated. The 
mercury-still which is described in the following lines has 
been constructed with a view to obtain a more rapid yield of 
pure mercury than stills of this class have hitherto been 
capable of producing. The yield of mercury from the new 
form of still is about four times as great as that from one of 
the old pattern, the consumption of gas in each case being the 
same. The construction and method of using the still are as 
follows :—B K is a bulb and tube about 34 inches long, sup- 
ported on a stand not shown; the bulb has a ring-shaped 
channel, C C, round its upper end ; into this channel a piece 
of “ Sprengel” tube, D, is fused. This is furnished with two 


taps of glass, H and F; E is in connexion with a water-jet 
pump, F is terminated ‘with a piece of bent tube. A is a 
cistern for holding the mercury which is to be distilled. H is 
a ring of gas-jets. 


Distribution of Flow in a Strained Elastic Solid. 508 


The method of using the still is as follows:—The tap E 
is opened, F is closed ; a water-pump then exhausts the whole 
system, and the mercury to be acted on rises from the cis- 
tern A. The cistern being large and shallow, only a slight 
change takes place in the height of the mercury in the bulb, 
when the level of the mercury in the cistern changes. While 
the pump is exhausting the ring of gas-jets is lit, and in 
about ten minutes, in the case of the still in our laboratory, 
the mercury fills the tube D, any metal which comes over 
being caught in the bulb G. The tap E is then closed and 
F opened ; the still then continues to work by virtue of the 
vacuum formed by its own mercury. It has been found 
necessary to place a gas-regulator on the pipe which supplies 
the jets, as the change of pressure in the gas-mains is cons!- 
derable. An automatic arrangement, depending for its action 
upon the height of the mercury in the cistern, shuts off the 
gas when the surface of the mercury falls below a certain 
point. In using stills of this class the mercury before distil- 
Jation should be carefully freed from moisture, as a minute 


quantity of water will often cause a fracture in the heated tube 
or bulb. 


LVIII. On the Distribution of Flow in a Strained Elastic Solid. 
By Cuarues A. Carus-Wiison, B.A., AILLCE., De- 
monstrator in the Mechanical Laboratory at the Royal Indian 
Engineering College, Coopers Hill*. 


F a metal bar of uniform section throughout its length be 

subjected to uniform longitudinal stress, the elements of 

the bar will become distorted ; if the strain should exceed the 
limit of elasticity the distortion will be partly permanent. 

In consequence of the straining of the elements, every ele- 
ment will experience a displacement relative to three fixed 
axes in the bar ; say ow parallel to the length of the bar, oy 
parallel to one side, and oz parallel to a second side, both oz 
and oy being at right angles to ow: such displacement is 
generally spoken of as “ flow.” 

It is clear that if the metal be homogeneous, the stress 
uniform, and the section at right angles to the axis every- 
where the same, an element will experience a displacement at 
right angles to the planes woz, y oz proportional to its distance 
from these planes; since such displacement depends on the 
straining of the elements between it and these planes. Hence 
a bar with its sides originally parallel to ow will remain so 


* Communicated by the Physical Society: read May 2, 1890. 


2Q2 


504 Mr. C. A. Carus- Wilson on the Distribution 


after a certain amount of flow has taken place, and lines 
drawn on the sides respectively at right angles to and parallel 
to ow will remain so, since the displacement parallel to o # will 
be proportional to the distance from the plane yo. 

The question I propose to discuss is how to determine the 
distribution of flow when the section at right angles to 0# 
varles In any way as we pass along ow. 

I will for simplicity consider a plate in which the thickness 
parallel to oy is considerable compared with the thickness 
parallel to oz, and I will consider the displacements in the 
plane woy. 

We may take a plate in which there is a gradual reduction 
of section, in which there is what is commonly called a 
“shoulder,” as in fig. 2. 

It is required to determine the displacements in the plane 
of the paper—the plane xoy: in other words, supposing the 
plate covered with a series of lines parallel to ox and to oy 
respectively, it is required to determine the curvature of these 
lines due to flow. 

The distortion of the elements is caused by the shearing- 
strain induced in the bar when subjected to longitudinal stress. 
Since this shearing-strain is a maximum at 45° to the axis 0a 
of the bar, it will be convenient to consider the bar divided 


Fig. 1. 


into a number of small elements with sides making angles of 
45° to the axis ow. Every such element as abcd (fig. 1) will 


of Flow in a Strained Elastic Solid. 505 


be subject to a shearing-strain of amount f i. é. the angle 
bad will be diminished by an amount, where p is the inten- 


sity of the shearing-strain on the element, and 1 is the 
coefficient of rigidity of the metal. The effect of this shearing- 
strain on the element may be described as a rotation of ad 
through an angle s,, and of ad through an angle so, where 


3 +5= = s, and s, may be equal, when the displacement of 


e will be wholly parallel to ow; or they may be unequal, 
when ¢ will have a displacement parallel to 0 and a resolved 
displacement parallel to oy, which will be + ve or —ve accord- 
ing as s; is less than or greater than s,, and which will be a 
maximum if either s; or ss=0. © 

The value of s, +9, and the ratio of s, to s, for any element, 
appears to be determined by the following considerations. 
If a side ab of the element be produced in both directions so 
as to cut the sides of the bar, there is seen to be a tendency 
of that part of the bar below this line to slide over that part 
which is above. Assuming the resulting shearing-strain to 
be uniform over the length J, of this oblique section, the 
shearing-strain at any element in this direction, 2. @ 5, will 
clearly be inversely proportional to J, ; s. will also be inversely 
proportional to /,, where J, is the length of an oblique section 


L+/ 
parallel to ad, and s,+-s, will be proportional to a 2—say 
1 sg 

to =: 


Suppose, now, we take a series of elements, a 0, ¢ d;— 
Gy be ¢2d_ touching one another and lying across the bar. - If 
we imagine the points aj, dp, a3, &c. fixed on a line parallel to 
oy, it is clear that the displacements of ¢, ¢2, ¢3, &e. will be pro- 
portional to the sum of the shearing-strains in each element. 
If s;+s, is the same for each element, and s;=s,, the points 
€4,€2, 3, &c. will remain on a line parallel to oy. If, however, 
s,+s, becomes greater as we approach the middle, and less 
again towards the further side, the points c, ¢, cs, &c. will 
be found on a line concave upwards; if s;+s, diminishes 
towards the centre these points will lie on a line concave 
downwards. Ifthe strains should exceed the limit of elasticity 
the line through ¢, ¢, cs, &c. will be permanently curved. 

If the points a, a, a3,..., instead of being in one straight 
line have unequal downward displacements, the form of the 
curves obtained as above may be modified. 

If, now, we consider a series of consecutive elements, 
ay by ¢ dy—ay by cy da, lying in aline parallel to o x, if s;=s, for 


506 Mr. C. A. Carus- Wilson on the Distribution 


each element the points ¢, c:, c3, &c. will continue to lie on 
a line parallel to oz, since the displacement of each of these 
points, due to the distortion of the corresponding element, is 
parallel to ow. But ifas we descend from the first element 
we find s, becoming greater than s,, the points ¢, ¢3, &e. will 
have a displacement to the left which increases as we descend, 
so the line passing through ¢,, ¢, ¢3, &c. will be bent; andif | 
the shearing-strains become equal again on the lowestelement, 
this line will be concave to the right. 
It thus appears that any 
horizontal line will be curved 
concave downwards if the sum 
of s,; +s, is greater at the end 
of the line than in the centre, 
and vice versa, but that the line 
will remain straight if s,+s,1s 2 
constant along its length, and 
$1 = Sq. 

Also that a vertical line will 
remain so if s,; is everywhere 
equal to s.; but if s; is >, 
the line will be curved and 
concave towards the right, and 
vice versa. 

We can now proceed to de- 
termine the curvature of the 
lines in the case before us. jt 

Commencing at the upper 
extremity of the bar, fig.2,a 9? 
line such as ab will remain 
straight, because p is every- 
where constant, and J, = J. 
Theline cdef will be curved 
concave downwards, since from 
c to d and from e to/ p is less 
than it is from d to e (where it 
is constant and /;=/,) ; de will 
therefore remain straight, and 
ed and ef curved as shown. 
The line g hz will be concave 
downwards and curved along 
its entire length, since p gets 
less as we move away from h 
on both sides. 

The line jklmn_ will ole oe 
remain straight from 7 to &, 
since p is there constant and /,=/,; from k to p becomes 


Fig. 2, 


ges EX 


ES 


I 
K 
\ 


of Flow in a Strained Elastic Solid. 507 


less and greater again from Fig. 3. 
1 to m, kl m is theretore con- a PEEP aegge | 
cave upwards ; this line is PERE eee HHH 
straight from m to n, since p | aE00000000000000000000 
: =) A (SESE PE SEMEN ERLE 
is constant and 4=h. a co 
i i ry Bane 

The line o p q is curved PEERS re 

concave upwards throughout EERE SRE ECE 


the entire length, since p di- 
minishes from o to p and in- 
creases from p to q. 

The line r s¢ will be concave 
downwards, since p diminishes 
from 7 to s and increases from 
s to ¢. 

The line u v will remain 
straight, since p is constant 
and —-. 

To turn now to the curva- 
ture of the vertical lines. If 
we consider one of these as 
weaeyz, from wto d l=, at : 
£l,is <t,, while at 2 l=l, ATL 
again, sothat from d to w’ this BERBERS au 
line will be curved in convex |i ggamGRGC@HDENG 
towards ow. Again, at y /, is 
<l,, and at z 1,=1,, therefore 
x’ y zis also curved in convex 
towards 0 x. 

It would appear then that | 
the horizontal lines will have |Baaaame ee 
three distinct changes of cur- (ies HE 
vature, while the vertical lines A 
will be pinched in above and below the shoulder. 

To test the accuracy of these conclusions, I prepared a 
copper bar as shown in the following way. The sides and 
faces were very carefully planed and polished, and on one 
face I inscribed a series of vertical and horizontal lines in a 
lathe. I then strained the bar so as to produce a considerable 
permanent set. An impression was then taken from the bar, 
which is reproduced in fig. 3*. 

By placing the eye very nearly in the plane of the paper 
and looking along the lines, the curvatures can be seen to 
follow very closely those sketched on fig. 2. I would specially 
draw attention to the partial curvature of such lines as cdef 
and jklmn. 


* The diagonal lines in fig. 3 were ruled on the impression to serve as 
lines of reference. 


SS 


[08.4 


LIX. On Sensitive Galvanometers. By R. THRELFALL, M.A., 
Professor of Physics, University of Sydney, N.S. W. 


To the Editors of the Philosophical Magazine and Journal. 


GENTLEMEN, | 
foe I expect the matter will have been almost for- 

gotten when this reaches England, I still desire, if 
possible, to meet some of the criticisms which have been 
levelled at me by Professor Gray in the Philosophical Maga- 
zine for February 1890, and by Professor Ayrton at the 
Physical Society on January 17th. Of Professor Ayrton’s 
criticisms I have only as yet seen a report in ‘Nature’ for 
January 30, but since they appear in the main to coincide 


with Professor Gray’s as nearly as I can judge, I will endeavour 


to reply to both at once. 

In the first place, then, I must of course plead guilty to 
having made a mistake in arithmetic (to my shame be it said), 
and must express my thanks to Professors Ayrton and Gray 
for pointing it out. It now appears that instead of my success 
with the Gray galvanometer being a thousand times less than 
Professor Gray’s, it is only about a hundred times less as 
compared with the performance in 1884, and three times less 
as compared with his results in 1889. As the matter is one 
which purely depends on instrument-making and experiment- 
ing, I can only say that Lam very glad to find myself approach 
so nearly to Professor Gray. With respect to the much graver 
and more important charge that I have overestimated the per- 
formance of another type of galvanometer, I can only say that 
the mistake rests entirely with my critics, though very likely 
through my own fault in endeavouring to achieve conciseness 
of statement. That the galvanometer described did actually 
attain the sensitiveness quoted, viz. 5 divisions to 10—" ampere 
of current, a fresh reference to my notebook amply proves. 
Neither in my paper on “ The Measurement of High Specific 
Resistances,” nor in the following one on the Specific Resist- 
ance of an Impure sample of Sulphur, have I given any data 
from which this value was computed. How, then, can Pro- 
fessors Ayrton and Gray have concluded that I was in error? 
Professor Ayrton, as I imagine, and certainly Professor Gray, 
have obtained their data from the resistance-measurements 
quoted ; but itis purely gratuitous on their part to assume 
that these were the data used by me, and as a matter of fact 
they were not. In writing the paper, which pretended to be 
an account of an absolute measurement, I gave the maximum 
sensitiveness reached by the galvanometer in order to show 
that I had a good margin in the actual experiments, and was_ 


Prof. R. Threlfall on Sensitive Galvanometers. 509. 


not using the galvanometer at its limit of sensitiveness. Surely 
it is not necessary to remind such well-known experimentalists 
as my critics that an absolute measurement. depending on the 
indications of an instrument at its extreme sensitiveness are 
always liable to objection. I find in fact from my notebook 
that the sensitiveness mentioned having been obtained, it was 
reduced (by lowering the control magnets) to meet the 
requirements of the work in hand. The resistance of the 
sulphur turned out to be much less than I had anticipated, 
for I had got three hundred and sixty small storage-batteries 
ready for the work, as well as some forty Clark-cells; so I 
reduced the number of cells and the sensitiveness of the galva- 
nometer in what appeared to me at the time as the most 
advantageous manner. On reading the paper, however, I see 
that I was not so explicit (for the sake of brevity) as I might 
have been. I welcome a discussion on sensitive galvano- 
meters, however, though it has been raised somewhat at my 
own expense, because I believe that the galvanometer-method 
has several advantages over the electrometer-method in high- 
resistance measurements. To this, however, I will not now 
refer, but will instead make some further remarks anent sen- 
sitive galvanometers. 

My friend Mr. Boys, at the Physical Society some time 
ago, said that my quartz fibres were too long and thick. 
Well, that is a matter of opinion. I used the finest fibres 
that I could manipulate; and as I saw that I could handle a 
yard of them almost as well as an inch, I did not see why I 
should not reap the advantage of length. I saw Mr. Boys’s 
fibres, and I do not think that he mounts much finer ones than 
I do, though as it is purely a matter of manipulatory skill I 
daresay Mr. Boys can mount finer fibres than I can. If I 
can persuade Mr. Gray to use quartz instead of silk as a 
means of suspension, | am sure he will live to bless me. 
While I am on this subject I will add, that if Professor Gray 
will reread my paper he will find he has been unjust to me in 
stating that I must have used the galvanometer near the limit 
of sensitiveness as the zero was “always on the move.” He 
will find that the whole sentence runs thus :—“ It is practi- 
cally impossible to get a galvanometer of this degree of sen- 
sitiveness to work with a silk fibre, the zero being always 
on the move.” Since I gave this as one reason for having 
adopted quartz, Professor Gray will, I think, see that his 
argument, in so far as it depends on the galvanometer being 
at its limit of sensitiveness, is baseless, and that his stricture 
is unmerited. 

With respect to quartz fibres, | may say that I am forward- 
ing a paper on this subject to you; but meanwhile I desire to 


£5 


510 Prof. R. Threlfall on Sensitive Galvanometers. 


state here that I have gone back to Mr. Boys’s method of pre- 
paring the quartz, which (as might have been expected) is much 
better than mine. I wonder how many people have any real 
idea of what a sensitiveness of “five divisions to 10-1! ampere”’ 
really means. From the glibness with which we talk of sensi- 
tiveness, I fancy the conception has not generally been really 
grasped. Let me give an illustration. We all look on the 
eye as perhaps our most sensitive organ. Inthe Philosophical 
Magazine for January 1889 is a paper by Professor Langley, 
in which an estimate is made of the minimum rate of expen- 
diture of energy (by radiation) which can affect the eye. The 
estimates are of course rough and not very concordant, and 
there is some obscurity arising from the hoary-headed diffi- 
culty of distinguishing between work and rate of working. 
However, it follows from the data given, that an expenditure 
of work at the rate of 2°6 x 10-® C.G.S. per second will affect 
the eye so as to produce vision when the light has a wave- 
length nearly that of the line A; while an expenditure at the 
rate of 2°6x10-" (or 5°7x 10-' from another part of the 
paper) will produce the same effect if the light is green. 
Now the galvanometer I described had a resistance of nearly 
16,000 ohms; and since 10-" ampere produced a deflexion of 
five divisions, we may say that we could detect a current of 
10-"? ampere (giving a deflexion of half a division). In this 
case a simple calculation (without arithmetical error) shows 
that the galvanometer absorbed work at a rate of about 
1-6 x 10-9 ergs per second. Consequently the sensitiveness 
of the galvanometer may be said to stand half way between 
that of the eye for crimson and green light respectively. 

I never intended to institute a comparison between Prof. 
Gray’s form of galvanometer and the Thomson form: what I 
wanted was to get a workable instrument as easily as possible, 
and I found the Thomson form most easily manageable. 
Though the Gray form may be workable at the hands of such 
exceptionally skilful manipulators as its inventors, I do not 
think that tor the ordinary run of experimentalists it is to be 
compared with the older form, and I certainly do not pin any 
faith to silk fibres a few inches long. Though, as Professor 
Gray remarks, his form of galvanometer possesses “solid 
advantages,”’ as it certainly does, still it possesses also solid 
disadvantages, and these will, 1 think, in the long run be 
found to predominate. 

I am, Gentlemen, 
Yours obediently, 


University of Sydney, N.S.W., RicHARD THRELFALL. 


March 7, 1890. 


po edb 34 


LX. Considerations on Permanent Magnetisn. 


By M. F. Osmonp*. 


RON possesses at least two molecular states, aand 8. a is 
soft iron, that is iron which has been annealed and cooled 
slowly. It changes into 6 during heating, at a certain critical 
temperature, and in part preserves this state during cooling, 
the more so the quicker the cooling and the larger the pro- 
portion of carbon, manganese, and tungsten that it contains. 
Some 6 iron is also produced during cold hammering. Iron 
deposited electrically is also of the B variety. 

A bar of steel, allowance being made for the carburets 
and other compounds simply in mixture, can then be looked 
upon as an intimate mixture of airon and @ iron in rela- 
tive proportions, which can change from point to point but 
are determinate at any point. That being so, let us con- 
sider 8 as forming in a steel bar a porous framework, not 
changing under the influence of currents and of magnets. 
On the other hand, let us look upon « as composed of particles 
polarizable under such influences. (The actual mobility of 
such particles, admitted by Hughes, appears from the sounds 
and changes of volume which take place during magneti- 
zation.) The particles a so polarized will form so many small 
elementary magnets, which the magnetizing force has dis- 
placed from their former normal position of equilibrium, and 
which tend to take up this position again so soon as the ex- 
ternal force ceases to act. 

But in presence of the rigid network of iron £ these po- 
larized particles a are conceived as catching in the pores of 
the 6 structure, and immovable in this position, thus resulting 
in a permanent magnet. The temporary magnetism and the 
permanent magnetism determined by the action of a certain 
magnetizing force ata point of a bar will be therefore a func- 


tion of the relation = at this point. 


As an attempt to represent these ideas graphically, let 
there be a square, O A X Y, of which the side represents 100 


parts. Hvery line mn parallel to the axis of Y meeting in p 


the diagonal O A represents a steel containing = of iron a, 


i =a of iron B. 
At saturation the temporary magnetism, or rather the sum 


* Communicated by the Physical Society: read April 18, 1890, 


512 M. F. Osmond’s Considerations 
of the polarized particles, will be exactly equal to the whole 
1 
of the iron a, 7.e. to mp. «@ varying from 0 to 700° the 
temporary magnetism will be represented by the diagonal O A. 
4 zi ea 


Qo. Cane xX 
As to the permanent magnetism, in regarding it as the 
relative number of particles of a which remain polarized after 
the cessation of the magnetizing force, it will be a fraction of 


mp, all the greater as =~ is smaller for the steel under consi- 


deration. In other words, the polarized particles @ will be 
more immovable the closer the network 6. 

Under the supposition that the quantity mr of the particles 
a which remain polarized after the interruption of the 
magnetizing force (that is to say, the permanent magnetism 


as defined) is proportional to the percentage of iron 8, ae 
we can write 

ei 

100’ 


K being a numerical coefficient equal to or less than unity. 
Since 


mr=mp x K 


mp = moO — wv, 
np=100—mp=100—m0O, 
=100-—2, 
100—«x 


pee S00? 


x 


Accordingly the permanent magnetism is represented by a 
portion of a parabola whose axis is parallel to that of Y, It 


on Permanent Magnetism. 513 


vanishes for a=0, B=0 (as could be foreseen from the 
properties of the irons a and 6, which have served as the 
grounds of the argument), and is a maximum for a=8. 

The number of the particles capable of remaining polarized 
after the interruption of the magnetizing force will at most 
form a quarter of the whole mass of the iron. 

If the magnetizing force be too feeble to produce saturation, 
the lines OA, OrX will take up a position indicated ap- 
proximately by the dotted lines. 

These considerations agree fairly well with many observed 
facts. 

Thus all causes which tend to open, even temporarily or 
only in certain directions, the network of the iron 6 (expan- 
sion, shocks, vibrations) set at liberty some of the polarized 
particles of a, and diminish the permanent magnetism. 

The greater the proportion of 6 iron the more difficult 
becomes the polarization of a, in the diminished pores, and 
the greater must the magnetizing force be to produce satura- 
tion. 

When the proportion of carbon or of manganese is so 
great that the whole of the iron on quenching or even without 
this takes up the state 6, a substance will result which is 
incapable of taking up magnetism ; for example Spiegel-iron 
containing 25 per cent. of manganese and upwards, and Had- 
field’s steel. Since hardening takes place more energetically 


at the surface than in the interior of a bar, the relation 3 will 


always be smaller there. The permanent magnetism remain- 
ing after saturation will therefore be stronger at the surface 
if a>, which is the common case. It would be more feeble 
if B>a. | 

Magnets formed of laminz are in general more powerful 
than those of the same volume in a single piece, because 
the laminze are more hardened. But the contrary should be 
the case with metals in too hard a condition. 

It is difficult after a bar has been magnetized to saturation 
in one direction to bring it to a moment of the same value in 
-an opposite direction, because certain particles of the a metal 
being held immovably cannot be displaced, &c. 

The iron 8 can also be looked upon as a medium whose vis- 
cosity increases as its percentage in the mixture is greater. 

We can compare these ideas with the experiment of 
Hughes, who has obtained permanent magnets by mixing 
iron filings and wax and melting the latter, which in setting 
held fixed the polarized portions of iron. 


2 ae 


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ee 


ee a renee 


J 


LXI. Notices respecting New Books. 


Chemacal and Physical Studies nv the Metamorphism of Rocks, based 
on a Thesis (with Appendices) written for the Doctorate in Science 
in the University of London. By A. Irvine, D.Sc., B.A., F.GS. 
8vo. 1388 pages. Longmans & Co., London. 


OCK-METAMORPHISM, considered from the chemical and 
physical side, introduces the subject, which, after a definition 
of “ metamorphism,” as here meaning “ only changes in the internal 
structure of rock-masses,” is divided into three divisions—paramor- 
phism, metatropy, and metataxis. The first refers to atomic, that 
is chemical, changes; the second to molecular, that is physical, 
changes ; and the third to mechanical conditions. In one ease the 
process is, as it were, the dissociation of a molecule into atoms; in 
the next, the breaking up of a solid into a liquid and then into a 
gas, the cohesion of the mass being gradually overcome until it 
becomes divided into molecules; in the third case, we have molar 
division, by pressure, percussion, cr grinding. Such a change in a 
rock as is due to the introduction of a new, or the removal of an 
old mineral, and referred by many to metamorphism, is here 
separately noticed as hyperphorie change. 

I. Paramorphism, or mineral change, divides itself into—1. 
Primary paramorphism (Genesis of Rocks), which leads to the 
recognition of a universal glowing magma at an early stage of the 
Earth’s Evolution :—2. Secondary paramorphism, brought about by 
the action of saline (marine) waters in producing secondary 
minerals, derived from the primary minerals of the rock and not 
altermg the composition of the rock when tried by bulk-analysis. 
Examples referred to are separation-products in slates and shales, 
—siliceous cements in volcanic tuffs and sarsen stones,—calcite in 
some igneous rocks,—quartz in the quartz-porphyries of Bozen,— 
facts published by Judd, Allport, Bonney, Becker, and others. 

II. Metatropy is defined and illustrated. The conversion of 
coal into anthracite and graphite, with a slight change in chemical 
composition, may be metatropic ; the formation of palagonite and 
hydrotachylite from the glass of basalts by hydration,—the change 
of anhydrite into gypsum, of arragonite into calcite by dry heat, 
and of calcite into arragonite by solution and heat,—the results 
of contact metamorphism by heat, as some grauwackes and shales 
into hornstone and porcellanite,—of coal into coke,—sandstone 
into quartzite,—and limestone into marble, are metatropic. Poly- 
morphism is included in metatropy; and this variation of crys- 
talline form is brought about by :—1. Temperature, as with carbonate 
of lime; 2. Molecular water, as with native hydrates of alumina 
and in some silicates of copper; 3. An accessory mineral, as with 
carbonate of lime tainted with some carbonates of the alkaline 
earths; and here the author suggests that these may have the 
rhombic system of arragonite rather than the hexagonal for their 


Notices respecting New Books. 515 


normal crystalline system ; he refers also to the concretions in the 
Magnesian Limestone of Durham. 

The vitrification and devitrification of rock (e.g. obsidian and 
tachylite) belong to metatropy. Sulphur and phosphorus, each 
being allotropic, are taken in illustration, as also arsenious oxide, 
metaphosphoric acid, silica, borax, and calcium fluoride. The 
author states that with regard to devitrification the following in- 
ductions seem to be warranted :—1. The vitreous state of a body 
represents a more primitive and simple molecular structure, witha 
corresponding low degree of stability. 2. There is a latent heat of 
vitrification, the loss of this being accompanied by the building up 
of more highly complex and more stable molecules, with a tendency 
to assume a crystalline form. 3. In some cases hydration or de- 
hydration, as the case may be, appears to be a factor in the process 
of devitrification. 

The behaviour of artificial glasses under various conditions is 
next considered with respect to devitrification, also the behaviour 
of flint under certain conditions. 

Viewing the relative densities of the different allotropic forms 
of the same mineral, the author states that, as the maximum 
density and stability of molecular structure is identified with the 
crystalline form, pressure, by way of compression, is favourable to 
crystallization. Pressure crushing a rock may allow freer access 
and circulation of water with minerals in solution, and so prepare 
the way for paramorphic changes, but cannot induce direct meta- 
tropic change—therefore, continues the author, mere deformation 
of rocks by pressure may have had too much attributed to it as a 
factor in metamorphism. 

The passage of minerals through this solid-liquid “ critical state ” 
(z.¢. the state in which they were neither solid nor liquid), as 
exemplified by certain flattened masses of quartz, is illustrated 
with facts observed by the author and others. The access of water 
to rocks along their junction-planes is noted, and the consequent 
decomposition of such rocks, which, if subsequently compressed in 
deep earth-movements, might present appearances considered to be 
characteristic of ‘regional metamorphism.” Hence the author 
remarks that sometimes the further inference is drawn—“ that the 
Archean schists, &c., may be only instances on a grander scale of 
such transitional development.” 

III. Metataxis. 1. Cleavage is first considered, with critical 
observations on the theories of Mr. Harker and Mr. O. Fisher ; 
with the latter our author does not agree. Lateral pressure, con- 
tinued after folding and faulting have been effected, is the ac- 
knowledged cause of cleavage, but the author does not regard the 
accessory crystalline minerals on the cleavage-planes of many slates 
as the result of paramorphic changes induced by the pressure. 

2. Crumpling and gnarling of the folia of some gneisses 
and schists; and 3. The Foliation of schists are briefly noted. 
4, Metataxic work by solar and lunar tides in a primeval condition of 
the globe is suggested, thus “the feeble foliation of the fundamental 


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516 Notices respecting New Books. 


Gueiss ” may have been associated with “the earliest solar tidal 
waves, and the more pronounced foliation of the Archean schists 
with the subsequent dunar tidal waves of the magma.”. . 
“Then as now the tidal action would vary (within much wider 
limits, however) with the relative positions of the Sun, the Earth, 
and tue Moon, the maximum effect beimg produced when the 
Moon was in‘meridian.’ Pfaff (Algem. Geol. als. ex. Wiss. p. 188 et 
seg.) has discussed the action of tidal movements in the magma 
upon the earliest rind of the Earth, initiating the first permanent 
inequalities upon its surface. If the Archean schists (taken as a 
whole) represent this first-formed rind, their materials as they 
accumulated by precipitation from the heavy atmosphere being bathed 
through and through with H,O in a highly superheated condition, 
we seem to have at once an explanation both of the frequent 
recurrence of gneiss (in a subordinate degree) among the schists as 
a result of tidal movements, and of those lithological characters by 
which they have misled the Neptunists into regarding them ‘as 
sediments.’ The author takes his favourite subject of glacier- 
ice as an example of the several results of the physical forces act- 
ing on such a magma. 

IV. Hyperphoric change is illustrated by dolomitization, some 
amygdaloids, some masses of rock-salt, and the production of 
selenite from pyrites in fossiliferous clays. 

VY. Contact-metamorphism, combining paramorphic, metatropice, 
metataxic, and hyperphoric changes, is treated in stages—1. Direct 
effects of heat and pressure. 2. Effects of the circulation of 
superheated water between the intrusive mass and the adjacent 
rocks. 3. Changes following upon the cooling of the igneous 
intrusive mass. 

The General Remarks treat of the meaning and application of 
several words relating to metamorphism and metaphoric rocks,— 
such words and applications as the author would or would not 
approve of ; also of Archean, Cambrian, and some other old rock- 
stages. In his Conclusions he insists on the complex nature of 
metamorphism, and the different processes by which the results 
are effected ;—on the incomplete explanation hitherto given of 
‘regional metamorphism ;”—that “ uniformitarianism” really ought 
only to apply to the fact of the Earth having always been subject 
to the same universal laws as the other cosmical bodies ;—and that 
the mass of the Earth and its Atmosphere has remained the same 
from the beginning. He accepts the theory that there was a 
pre-oceanic stage, and that the Archean gneisses and schists were 
essentially diagenetic, rather than metamorphic ; and warns us that 
“such phrases as ‘ the highly metamorphised Archean gneisses and 
schists ’ must be relegated to an obsolete nomenclature of geological 
science.” The author winds up his Conclusions by stating that 
‘as the mists and clouds thus diperse, our intellectual vision begins 
to descry a boundary to geologic tume, and the physical geologist 
begins to feel that over this question he can join hands with the 
astronomer and the natural philosopher.” 


Notices respecting New Books. 517 


In the Appendices is presented a large mass of chemical notes, 
and of collected and original information bearing on the multi- 
farious subject-matters of the forezoing pages. 

This is a remarkable book, full to overflowing with carefully 
collected notes on every kind of metamorphosed rock, and results 
of personal research. The author’s happy acquaintance with 
German literature has been utilized by him in getting every avail- 
able German idea on metamorphism into his Essay ; and indeed 
this is a valuable and praiseworthy feature, certainly bringing us 
nearer to our Continental brethren ; for, though in micropetrology 
they are quoted often, yet in the broader field of rock-changes and 
the theories thereto belonging, their views, though known to those 
interested therein, have not been brought together so closely before. 
French and British geologists have not, it seems, helped the author 
much. With regard to the latter, some here and there get very 
“bad marks” indeed; he readily runs them down, and among 
their wreckage he floats high and disdainful. Indeed his egotism 
is very distasteful, and not least so when he quotes small observa- 
tions made by himself in the field, as if no one else, not even the 
tyro and the amateur, had seen the common thing and been told of 
its evident lesson again and again ; for instance, the selenite in clay 
near Grantham, &e. 

The American Geologists he treats respectfully ; and indeed he 
expresses regret at not having known more of Mr. T. Macfarlane, 
some of whose views, as well as some published by Dr. 8S. T. Hunt, 
he now finds that he has inadvertently taken as his own. 

In this Essay, of course, we meet with many facts and ideas 
already well known to both teachers and students; but certainly 
some are put aside as insecure, and some are authenticated and 
more clearly defined than heretofore. This is work in the right 
direction, and our thanks are due to the industrious, and indeed 
enthusiastic, author, who has brought his chemical and physical 
knowledge to bear on the advancement of Geology, by the elucida- 
tion of the Harth’s development, according to the views and theories 
that seem best to him after an earnest and conscientious study of 
rocks and rock-changes. | 

If the Second Edition be called for, and well it might, the 
author should, if possible, be less dogmatic, and endeavour to 
make himself less prominent in the language and style of the 
book ;—he should incorporate his more important notes as far as 
possible in the text, and above all make a good Index of both 
names and things,—for this would be very valuable for reference 
to the many good facts and notions in the book, and to the 
observers and authors who have treated of them. 


Phil. Mag. 8. 5. Vol. 29. No. 181. June 1890. 2R 


i. B18 .J 


LXII. Intelligence and Miscellaneous Articles. 


THE RADIANT ENERGY OF THE STANDARD CANDLE ; MASS OF 
METEORS. BY C. C. HUTCHINS. 


__ following investigation was undertaken with the primary 

object of finding, if possible, more trustworthy data for deter- 
mining the mass of shooting-stars; but a reliable determination of 
the radiation of the standard candle cannot fail to be of value for 
other purposes. 

The apparatus employed in making the measurements was my 
thermograph*, the constant of which was found in the two follow- 
ing ways. 

First method.—A copper Leslie cube, holding about 3 kilog. of 
water, was placed behind an opening of 16 square centim. in a 
wooden screen, which opening was closed by a movable shutter, by 
opening which the thermograph, one metre distant, could be 
exposed to the radiation from the cube. 

The following quantities were then determined :—dimensions of 
cube; weight of water contained in cube ; water-equivalent of cube ; 
mean of the galvanometer-deflexions taken during the interval that 
the cube and its contents were falling 5° from a temperature about 
65° above that of the air; time in seconds occupied by the cube in 
falling the 5° as above. 

Knowing these quantities, we can evidently compute in ergs per 
second the radiant energy passing through the square centimetre 
of surface containing the thermal junction, and such that it will 
produce a deflexion of one division of the galvanometer-scale. A 
number of trials showed that 16-9 ergs per second was the quantity 
required. 

Second method.—The constant was found by passing the rays of 
the sun through openings of 0°394 and 0-23 centim. diameter, and 
observing the galvanometer-deflexions when the thermograph was 
exposed in the divergent beam at a point where the diameter of the 
beam was 4:2 centim., and then computing the deflexion for the 
undiminished sunlight. Simultaneously with the above measures 
the radiation of the sun was observed with Pouillet’s pyrheliometer. 

The mean of several sets of measures by this method gave the 
constant 17:02; agreeing better than could have been expected 
with the results of the first method. The candle employed was 
the ordinary sperm candle, six to the pound. It burned in still 
air, without snuffing, 7°37 grm. per hour. The radiation of the 
candle was measured by placing it behind the screen in place of the 
cube employed in finding the instrumental constant, the exposures 
being made in the same manner as for the cube. The deflexion 
given varied very much with the length of the wick of the candle, 
constantly increasing for a half hour or more after lighting. It 
therefore was necessary to observe the deflexion at what was con- 


* Proc. American Academy, 1889. 


Intelligence and Miscellaneous Articles. 519 


sidered to be an average condition of the candle-flame, that is about 
fifteen minutes after lighting, when a deflexion of 75 scale-divisions 
was obtained. 

This number, multiplied by the constant previously found, gives 
the radiant energy which from the candle passes through each 
square centimetre of a surface everywhere one metre from the 
candle, provided we assume that the candle radiates equally in 
every direction. To find the total radiant energy, we must, as a 
first step, know the area of cross section of the candle-flame in a 
plane perpendicular to the direction of the flame to the opening of 
the thermograph. To learn this, an image of the flame was pro- 
jected upon 400 square centim. of paper, taking care to have the 
projecting lens midway between the candle and paper. It was 
then easy to trace about the image of the flame with a pen; and 
this having been done ten times upon the same sheet, the whole 
sheet was weighed, and then the tracings cut from it and also 
weighed. In this manner the section of the candle-flame was found 
equal to 1°308 square centim. 

We now have the whole radiant energy of the candle, 


ow At X10P x75 x17 
hi 1-303 


To find what portion of this total energy lies in the visible spec- 
trum could be satisfactorily accomplished only by measures made 
in every part of the spectrum of the candle. Such measures have 
been made by Langley* in the spectrum of an argand gas-lamp 
with a glass chimney. He finds 2-4 per cent. of the total radiant 
energy to be visible. It is easy to compare the candle with such a 
lamp. At a certain distance from the thermograph an argand 
lamp, whose light was that of ten candles, gave a deflexion of 238 
scale-divisions. When the lamp was replaced by the candle the 
defiexion was 29. Hence we see that very nearly 2 per cent. of 
the radiant energy of the candle is visible: or the visible part is 
2:46 x 10° ergs per second ; about 10:9 ft.-lbs. per minute. 

We may now proceed to find the mass of a meteor, first upon 
the supposition that its rays have the same ratio of visible to total 
energy as have those of the candle, and later correct, if possible, 
the value thus found. 

Let the meteor at a distance of 50 miles have a light equal to 
that of Vega; let it continue for 2 seconds with a velocity of 
25 miles per second. From the best data we find that if the 
meteor were at 1 metre distance, the log of its candle-power would 
be 3°9851. Hence to find the energy e, we have :— 


= 1-23 x 10° ergs per second. 


log candle-power ........ 3°9851 
log energy of candle ...... 8:0899 
NOt ates it Saat os ois: che SS Se 0:3010 

TOS} Gs) 4:01. sated: 12:3760 


* Science, vol. i. p. 482, 


520 Intelligence and Miscellaneous Articles. 


We have for the mass, m= i ; and employing the data assumed 
U 


above we find m=0:2936 grm. 

If the meteor in burning produce, fora given expenditure of 
energy, more light than does the candle, then a less mass than the 
one found would serve to produce the light given by the meteor. 
From what has been observed of the spectra of meteors, it is safe 
to conclude that their light is mainly due to incandescent vapours 
of the materials composing the meteors. It is also known that the 
spectra of these substances remain unchanged throughout very 
considerable changes of temperature, and we may therefore be 
permitted to draw conclusions from laboratory experiments upon 
these substances in the state of vapour. 

A lump of the Emmett Co., lowa, iron meteorite was placed 
upon the lower carbon of an arc-lamp and vaporized by the passage 
of the current. The light given by the meteor-vapour was found, 
on the average, equal to that of 40 candles. The galvanometer- 
deflexion by the meteor at a certain distance from the thermo- 
eraph was 223°2 scale-divisions. At the same distance the candle 
gave a deflexion of 55°4 divisions. From this we see that, for a 
given expenditure of energy, the arc of meteor-vapour gives ten 
times the light of the candle. Dividing the value of m obtained 
above by 10, we have m=0:029 germ. for the mass of a meteor 
giving the light of a star of the first magnitude, moving with nearly 
the parabolic velocity and lasting for two seconds.—American 
Journal of Science, May 1890. 


OBSERVATIONS ON ATMOSPHERIC ELECTRICITY IN THE TROPICS. 
BY F. EXNER. ; 


In order to investigate the relations of atmospheric electricity to 
the moisture of the air within certain limits, the author has made 
observations of the fall of atmospheric potential in countries with 
high relative moisture, particularly in the Indian Ocean between 
Aden and Bombay, in Bombay itself, and in Ceylon both on the 
coast and in the interior. The measurements were made with the 
well-known transportable apparatus invented by the author. The 
present paper contains only the total material of observation in 
tables, which comprise the date and hour of the observation, the 
temperature, absolute and relative moisture, the fall of potential, 
and meteorological observations. The discussion of the conclusions 
to be drawn from these numbers is reserved for a second paper. 
Tt need only be mentioned that all the values of the fall of potential 
were positive. Near the coast the finely-divided spray arising 
from the breaking of the waves exerted an increased action on the 
fall of potential. On the other hand, measurements made in the 
course of this journey in Cairo and the vicinity showed that there 
the dust of the air exerted a lessening influence on the fali of 

otential, which with a strong wind was so marked that the sign 
of the fall of potential became negative.— Wvener Berichte, xeviii. 
p. 1004 (1889); Bezbldtter der Physik, xiv. p. 144. 


INDEX to VOL. XXIX. 


—<—<—jp—_ 


ASTHER, on the non-existence of 
density in the elemental, 467. — 
Air, on a method of determining 
moisture and carbonic acid in, 306; 
on electrical vibrations in rarefied, 
without electrodes, 375; on the 
oscillations of periodically heated, 
452. 

Atmosphere, on the vibrations of an, 
173. 
Atmospheric electricity in the Tro- 
pics, on, 520. re 
Barus (C.) on the pressure-variations 
of certain high-temperature boil- 
ing-points, 141; on the change of 
the order of absolute viscosity en- 
countered on passing from fluid to 
solid, 337. 

Bells, on, 1. 

Bidwell (S.) on the electrification of 
a steam-jet, 158; on the magneti- 
zation of iron in strong fields, 440. 

Bishop’s ring, on the nature of, 171. 

Boiling-points, on the pressure- 
variations of certain high-tempe- 
rature, 141. ; 

Bonney (Prof. T. G.) on the crystalline 
schists of the Lepontine Alps, 284. 

Books, new :—Fisher’s Physics of 
the Earth’s Crust, 211; Transac- 
tions of the Edinburgh Geological 
Society, Vol. VI. Part 1, 372; 
Chrystal’s Algebra, Part II., 449 ; 
Irving’s Chemical and Physical 
Studies in the Metamorphism of 
Rocks, 514. 

Brown (J.) on dropping-mercury 
electrodes, 376. 

Calorimeter, on a new form of 
mixing, 247. . 

Candle, on the radiant energy of the 
standard, 518. | 

Carbonic acid in air, on a method of 
determining, 306. 

Carnelley (Dr. T.) on an algebraic 
expression of the periodic law of 
the chemical elements, 97. 


Carus-Wilson (C. A.) on the be- 
haviour of steel under mechanical 
stress, 200; on the distribution of 
flow in a strained elastic solid, 
505. 

Chemical action and electrolytic con- 
duction, on the problems of, 383, 
480. 

reactions, on the inert space in, 

216. 

research, on a new method and 
department of, 401. 

Chronograph, on a new form of elec- 
tric, 377. 

Clouds, on diffraction-colours with 
special reference to iridescent, 167. 

Coldridge (W.) on the electrical and 
chemical properties of stannic 
chloride, 385, 480. 

Cole (G. A. J.) on the variolitic 
rocks of Mont-Genévre, 286. 

Contact-forces, on the measurement 
of electromotive, of metals in dif- 
ferent gases by means of the ultra- 
violet rays, 291. 

Coronee, on diffraction-colours with 
reference to, 167. 

Corpi (F. M.) on the catastrophe of 
Kantzorik, Armenia, 133. 

Current, on the time-integral of a 
‘transient electro-magnetically in— 
duced, 276. 

Currents, experiment to prove the 
existence of the direct and inverse 
extra, 216. 

Curves, on plotting, by the aid of 
photography, 180. 

Daguenet (C.): experiment to prove 
the existence of the direct and 
inverse extra-currents, 216, 

Diffraction-colours with reference to 
corone and iridescent clouds. 167. 

Ditfusion, on evaporation and solu- 
tion as processes of, 139. 

Dissociation in gases, on the kinetic 
theory of, 18. 

Dubois (H. E. J. G.) on Kerr’s mag- 


a Pe i a 


: ee ee ee ee ed ee ee a eee 
eh a a el a ee SSS ees 
<a = 


7 "3 
eo aN tT Serer 


LEC 


lee act 


rte 


st 


aa 


“ RSI LT 


ee ee 
naa pron aes ee per 
es eS uae ie 


Dae 


522 


neto-optic phenomenon, 253; on 
magnetization in strong fields at 
different temperatures, 293. 

Dunstan (Prof. W. R.) on an appa- 
ratus for the distillation of mercury 
in a vacuum, 367. 

Dymond (T. 8.) on an apparatus for 
the distillation of mercury in a 
vacuum, 367. 

Electric chronograph, on a new form 
of, 377. 

current, on transient, produced 

by twisting magnetized iron and 

nickel wires, 128; on the direction 
of the induced, by twist when 
under longitudinal magnetizing 
force, 182; on the resistance of 
hydrogen and other gases to the, 

214. 

radiation meter, on a new, 54. 

Electrical measuring-instruments, on 
the shape of movable coils used 
in, 434. 

oscillations in straight conduc- 

tors, on, 450. 

resistance of iron, on the effect 
of repeated heating and cooling 
on the, 77. 

Electricity, on the disruptive dis- 
charge of, through gases, 182; on 
the passage of, through hot gases, 
358, 441; on atmospheric, in the 
Tropics, 520. 

Electrification of a steam-jet, on the, 
158. 

Electrifications due to the contact of 
gases with liquids, on, 56, 292. 

Electrodes, on the theory of drop- 
ing-mercury, 376, 479. 

Electrolytic conduction and chemical 
action, on the problems of, 383, 480. 

Electromagnetic waves, on the acce- 
leration of secondary, 268. 

Elements, on an algebraic expression 
of the periodic law of the chemical, 
97; on the structure of the line- 
spectra of the chemical, 351. 

Elster (Prof.) on the formation of 
ozone by the contact of air with 
ignited platinum, and on the elec- 
trical conductivity of air ozonized 
by phosphorus, 376. 

Enright (J.) on electrifications due 
to the contact of gases with liquids, 
56. 

Exner (F’.) on atmospheric electricity 
in the Tropics, 520, 


INDEX. 


Flux (A. W.) on the form of New- 
ton’s rings, 217. 

Fog-bows, on the theory of, 453. 

Galvanometers, on sensitive, 208, 508. 

Gases, on the kinetic theory of dis- 
sociation in, 18; on electrifications 
due to the contact of, with liquids, 
56, 292; on the disruptive dis- 
charge of electricity through, 182; 
on the resistance of, to the current 
and to electrical discharges, 214; 
on the passage of electricity through 
hot, 358, 441. 

Geitel (Prof.) on the formation of 
ozone by the contact of air with 
ignited platimum, and on the elec- 
trical conductivity of air ozonized 
by phosphorus, 376. 

Geological Society, proceedings of 
the, 133, 280. 

Gerard (Prof. E.) on plotting curves 
by the aid of photography, 180. 
Glaciation of the valleys of the 

J helam and Sind rivers, on the, 135. 

Glass, on the alteration in, produced 
Ly pial variations of temperature, 

Gore (Dr. G.) on a new method and 
department of chemical research, 
AOI. 

Gray (Prof. A.) on sensitive galva- 
nometers, 208. 

Gray (Prof. T.) on the effect of per- 
manent elongation on the cross 
section of hard-drawn wires, 355. 

Gregory (J. W.) on the variolitic 
rocks of Mont-Genévre, 286. 

Gregory (W. G.) on a new electric ~ 
radiation-meter, 54. 

Haldane (Dr. J. 8.) on a method of 
determining moisture and carbonic 
acid in air, 306. 

Hydrogen, on the resistance of, to 
the current and to electrical dis- 
charges, 214, 

Hutchins (C. C.) on the radiant 
energy of the standard candle, and 
on the mass of meteors, 518. 

Tron, on the effect of repeated heat- 
ing and cooling on the electrical 
resistance of, 77; on the magneti- 
zation of, in strong fields, 440; 
on the Villari critical point of, 394. 

a an ee electric cur- 
rent produce twisting mag- 
netized, 123 ; anf dae of 
the induced current in, 182. 


INDEX. 523 


Judd (Prof. J. W.) on the propylites 
of the Western Isles of Scotland, 
287. 

Karsten (Prof. H.) on the geological 
age of the mountains of Santa 
Marta, 163. 

Kerr’s magneto-optic phenomenon, 
on, 253. 

Langley (S. P.) on the temperature 
of the moon, 51. 

Liebreich (O.) on the inert space in 
chemical reactions, 216. 

Liquid, on two pulsating spheres in 
a, 113 

Liquids, on electrifications due to the 
contact of gases with, 56, 292. 

Lodge (Prof. O. J.) on electrifica- 
tions due to the contact of gases 
with liquids, 292. 

McConnel (J. ©.) on diffraction- 
colours with special reference to 
coronz and iridescent clouds, 167 ; 
on the theory of fog-bows, 453. 

Magnetism, on permanent, 511. 

Magnetization in strong fields at dif- 
ferent temperatures, on, 293, 440. 

Magneto - optic phenomenon, on 
Kerr's, 255. 

Manganese steel, magneto-optic ex- 
amination of, 304. 

Margules (Dr.) on the oscillations of 
periodically heated air, 452. 

Mather (T.) on the shape of movable 
coils used in electrical measuring- 
instruments, 454. 

Media, on texture in, 467. 

Mees (Prof. C. L.) on the effect of 
permanent elongation on the cross 
section of hard-drawn wires, 355. 

Mercury, on an apparatus for the dis- 
tillation of, 367, 501. 

electrodes, note on dropping-, 
376, 479. 

Metallic vapours, on the conductivity 
of, 441. 

Meteors, on the mass of, 518. 

Moon, on the temperature of the, 31. 

Morgan (Prof. C. Ll.) on the Pebi- 
dian of St. Davids, 282. 

Moser (J.) on electrical vibrations in 
rarefied air without electrodes, 
575. 

Nagaoka (H.) on transient electric 
current produced by twisting mag- 
netized iron and nickel wires, 123. 

Natanson (L.) on the kinetic theory 
of dissociation in gases, 18, 


Newton’s rings, on the form of, 217. 

Nickel, on the Villari critical point 
of, 394, 

wires, on transient electric cur- 

rent produced by twisting mag- 

netized, 123; on the direction of 

the induced current in, 132. 

and tungsten alloys, on the 
magnetism of, 136. 

Osmond (M. IF.) on permanent mag- 
netism, 511. 

porn pressure, on the theory of, 

0. 

Ostwald (Prof. W.) on the theory of 
dropping electrodes, 479. 

Ozone, on the formation of, by the 
contact of air with ignited pla- 
tinum, and on the electrical con- 
ductivity of air ozonized by phos- 
phorus, 376. 

Pembrey (M. 8.) ona method of de- 
termining moisture and carbonic 
acid in air, 306. 

Periodic law of the chemical ele- 
ments, on an app*oximate expres- 
sion of the, 97. 

Perry (Prof. J.) on twisted strips, 244. 

Photography, on plotting curves by 
the aid of, 180. 

Pickering (S. U.) on a new form of 
mixing-calorimeter, 247; on the 
alteration in glass produced by 
small variations of temperature, 
289; on the theory of osmotic 
pressure and its bearing on the 
nature of solutions, 427, 490. 

Prestwich (Prof. J.) on the Westle- 
ton beds of Norfolk and Suffolk, 
280. 

Propylites of the Western Isles of 
Scotland, on the, 287. 

Puluj (Dr. J.) on a telethermometer, 
291. 


Pumps, on the application of hy- 
draulic power to mercurial, 138. 
Quateynions, on the importance of, 

in physics, 84. 
Radiation meter, ona new electric, 54. 
Rayleigh (Lord) on bells, 1; on the 
vibrations of an atmosphere, 173. 
Righi (Prof. A.) on the measurement 
of electromotive contact-forces of 
metals in different gases by the 
ultra-violet rays, 291. 

Runge (Prof. C.) on coincidences 
between the lines of different 
spectra, 462. 


nie ETRES. 


Bo, Se ae 


524 


Rydberg (Dr. J. R.) on the structure 
of the line-spectra of the chemical 
elements, 351. 

Santa Marta, on the geological age 
of the mountains of, 163. 

Schuster (A.) on the disruptive dis- 
charge of electricity through gases, 
182. 

Selby (A. L.) on two pulsating 
spheres in a liquid, 113. 

Sheldon (S.) on the magnetism of 
nickel and tungsten alloys, 136. 
Smith (Rey. F. J.) on the applica- 
tion of hydraulic power to mer- 
curiai pumps, 138; on anew form 
of electric chronograph, 577; on a 
mercury-still for the rapid distilla- 
tion of mercury in a vacuum, 501. 

Solid, on the distribution of flow in 
a strained elastic, 503. 

Solutions, on the nature of, 427, 490. 

Spark, on the heat developed in the, 
214. 

Spectra, on the structure of the line-, 
of the chemical elements, 531; on 
real and accidental coincidences 
between the lines of different, 462. 

Spheres in a liquid, on two pulsating, 
113. 

Stannic chloride, on the electrical and 
chemical properties of, 383, 480. 
Steam-jet, on the electrification of a, 

158. 

Steel under mechanical stress, on the 
behaviour of, 200. 

Stefan (Prof. J.) on evaporation and 
solution as processes of diffusion, 
139; on electrical vibrations in 
straight conductors, 873, 450. _ 

Stiffe (Capt. A. W.) on the glacia- 
tion of the valleys of the Jhelam 
and Sind rivers, 159. 

Stoney (G. J.) on texture in media, 
and on the non-existence of density 
in the elemental ether, 467. 

Strips, behaviour of twisted, 244. 

Tait (Prof.) on the importance of 
quaternions in physics, 84. 

Telethermometer, on a, 291. 

Thomson (Prof. J. J.) on the passage 
of electricity through hot gases, 
308, 441. 


INDEX. 


Thomson (Sir W.) on the direction 
of the induced longitudinal current 
in iron and nickel wires by twist 
when under longitudinal magne- 
tizing force, 132; on the time-in- 
tegral of a transient electromag- 
netically induced current, 276. 

Threlfall (Prof. R.) on sensitive gal- 
vanometers, 508. 

Tomlinson (H.) on the effect of re- 
peated heating and cooling on the 
electrical resistance of iron, 77; on 
the Villari critical points of nickel 
and iron, 594. 

Torsion and detorsion of metal wires, 
on the changes of temperature re- 
sulting from the, 140. 

Trouton (F. T.) on the acceleration of 
secondary electromagnetic waves, 
268. 

Trowbridge (J.)on the magnetism of 
nickel and tungsten alloys, 136. 
Tungsten and nickel alloys, on the 

magnetism of, 136. 

Vibrations of an atmosphere, on the, 
173. 

on electrical, in straight con- 
ductors, 373; in rarefied air with- 
out electrodes, 375. 

Villari (E.) on the resistance of hy- 
drogen and other gases to the 
current and to electrical discharges, 
and on the heat developed in the 
spark, 214. 

Villari critical points of nickel and 
iron, on the, 394. 

Viscosity, on the change of the order 
of absolute, encountered on passing 
from fluid to solid, 337. 

Wassmuth (Dr. A.) on the changes 
of temperature resulting from the 
torsion and detorsion of metal 
wires, 140. 

Wires, on the changes of temperature 
resulting from the torsion and de- 
torsion of metal, 140; on the effect 
of permanent elongation on the 
cross section of hard-drawn, 356. 

Worth (R. N.) on the igneous con- 
stituents of the Triassic breccias 
and conglomerates ofS, Devon, 154. 


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