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THE
: LONDON, EDINBURGH, axp DUBLIN  PHILOSOPHICAL MAGAZINE
JOURNAL OF SCIENCE,
CONDUCTED BY
/ LORD KELVIN, LL.D. P.R.S. &c.   GEORGE FRANCIS FITZGERALD, M.A. Sc.D. F.BS.
AND
WILLIAM FRANCIS, Pu.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.” Just. Lies. Polit. lib. i. cap. 1. Not.
iS
VOL. XL.—FIFTH SERIES. J ULY—DECEMBER 1895.
LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.
SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD.; WIILTTAKER AND CO. AND BY ADAM AND CHARLES BLACK ;—T. AND T. CLARK, EDINBURGH ; SMITH AND SON, GLASGOW ;—HODGES, FIGGIS, AND CO., DUBLIN ;—— PUTNAM, NEW YORE 5—VRUVE J. BOYVEAU, PARIS ;—
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4
“Meditationis est perscrutari occulta; contemplationis est admirari perspicua.... Admiratio generat queestionem, queestio investigationem, investigatio inventionem.”—Hugo de S. Victore. 
;
 ‘Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, : Cur caput obscura Phoebus ferrugine condat, : Quid toties diros cogat flagrare cometas, : ) Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes
Tam vario motu.” J. B. Pinelli ad Mazonium.
CONTENTS OF VOL. XL.
(FIFTH SERIES).
NUMBER CCXLII—JULY 1895.
Mr. William Sutherland on the Fundamental Atomic Laws of _ USISTLGC 1 SUIDIS 1g Renee ROP eee oe
_ Mr. W. G. Rhodes on a Theory of the Synchronous Motor..
Ly

).
Mr. C. Chree’s Contribution to the Theory of the Robinson PME OU el ee. ssi ole avo toch Gi mine Aya odes FIs mp 8
Prof. KE. F. Herroun on the Use of an Iodine Voltameter for
the Measurement of Small Currents .................. Profs. James Dewar and J. A. Fleming on the Thermoelec tric Powers of Metals and Alloys between the Temperatures of the BoilingPoint of Water and the BoilingPoint of Liquid Air. ‘(Plates TAG om tert et Nt: eee Cy %.,  Dr. Meyer Wildermann’s Experimental Proof of Van’t Hoft’s Constant, of Arrhenius’s Generalization, and of Ostwald’s Law of Dilution in very Dilute Solutions .............. Notices respecting New Books :— Mr. J. F. Blake’s Annals of British Geology, 1893 ... Prof. N. Story Maskelyne’s The Morphology of Crystals.
fer esecemes of the Geological Society :—
Mr. HE. A. Walford on the Lias Ironstone around Ban LSE + oy bt ietiet atl eal el Aa es WAU eee a aaa ea Mr. W. F. Wilkinson on the Geology and Mineral Re Seuvees or Anatolia (Asia Minor) 2. ... 02 26..65 5. Mr. A. Harker on Carrock Fell—A Study in the Varia momo loncome IWOCKMasses 6... ee Mr. F. R. Cowper Reed on the Geology of the Country around Misheuard (Pembrokeshire), .............. Mr. J. L. Lobley on the Mean Radial Variation of the HELOIOD os, cage GSA a St OR she lege mee gen ala ea ae Prof. E. Hull on the Physical Conditions of the Medi terranean Basin which have resulted in a Community of some Species of Freshwater Fishes in the Nile and Pee ALCIS et ae eta hE ee a le eee
lv CONTENTS OF VOL. XL.—FIFTH SERIES.
Page © Messrs. S. B. J. Skertchly and T. W. Kingsmill on the Loess and other Superficial Deposits of Shantung
(Northern China).............: 205 eee 150  Dr. J. W. Gregory’s Contributions to the Paleontology  ph and Physical Geology of the West Indies .......... 151  Mr. J. D. Kendall on the Whitehaven Sandstone Series. 152 © On the Double Refraction of Electrical Rays, by K. Mach .. 152
NUMBER CCXLIII.—AUGUST.
{
Mr. J. Y. Buchanan on the Use of the Globe in the Study  of Crystallography «..... 2 5..2+.¢ 30 153 Dr. Kuenen on the Condensation and the Critical Phenomena
of Mixtures of Ethane and Nitrous Oxide.............. 173 § Mr. W. G. Rhodes on a Theory of the Synchronous Motor.. 195 fF Mr. F. W. Bowden on an Electromagnetic Effect.......... 200  § Dr. K. Olszewski’s Determination of the Critical and the :
Boiling Temperature of Hydrogen .......: 2 eee 202 Messrs. John Trowbridge and William Duane on the Velocity
of Hlectrie Waves .. oi... ee ee ee eee rll a  Messrs. J. Alfred Wanklyn and W. J. Cooper on Fractional Distillation applied to American Petroleum and Russian Kerosene $i. te clk vas eect kee eee 225 Proceedings of the Geological Society :— Prof. J. B. Harrison and Mr. A. J. JukesBrowne on the
Chemical Composition of some Oceanic Deposits .... 229 Dr. C. 8S. Du Riche Preller on FluvioGlacial and Inter glacial Deposits in Switzerland ....”. 7 eee 229 Mr. 8. 8. Buckman on the Bajocian of the MidCottes : WOIAS 5. 6. esa bia oh ole eelulels @ 0 tale se er 230 On the Magnetism of Asbestos, by Dr. L. Bleekrode ...... 231 ©
NUMBER CCXLIV.—SEPTEMBER.
Mr. Shelford Bidwell on the Electrical Properties of Selenium. 233 
Messrs. Alfred W. Porter and David K. Morris on the Mea  surement of Varying Currents in Inductive Cireuits .... 256 
Profs. Liveing and Dewar on the Refraction and Dispersion of Liquid Oxygen, and the Absorption Spectrum of Liquid ONT Gigs i ica ee sy eee nie ace os es 6) oR ae ee 268
CONTENTS OF VOL. XL.——FIFTH SERIES. Vi,
4 Page Dr. Ladislas Natanson on the Critical Temperature of Hydro gen, and the Theory of Adiabatic Expansion in the Neigh Bemumeodsor the Critical Point .. 02... se eet ee ee 272 _ Mr. Henry F. W. Burstall on the Measurement of Cyclically ferme Vemperature. (Plates I. & Il.) ............. 282 Profs. C. Runge and I’. Paschen on the Constituents of PN MSS fe 21S a Sa dieidn, vehi sine aoe eee es 297
 Notices respecting New Books :
Profs. James Dewar and J. A. Fleming on the Variation in the Electrical Resistance of Bismuth, when cooled to the @emperaiure o: Solid Air. (Plate V.) ........... oe 303
Dr. Joseph Prestwich’s Geological Inquiry respecting the Waterbearing Strata of the Country around London, with Reterence especially to the Water Supply of the Metropolis; and including some Ke
SE MSOMMOUMINGS sc we se nc eins ois hc we ye ee 31l
Geological Survey of Canada, Annual Report, New Series, Wor Vio Neports A (1892), A (1893), J, Q, RB, S, Oe ee Mag ha) Sin SS dru ys, whip «ol Hens 312
Proceedings of the Geological Society :— Major H. de Haga Haig on the Physical Features and
Pre eOore Oe WAMEIDIUS, 2... yuk cease ce eee es 313 Mr. W.N. Gresley on IcePlough Furrows of a Glacial
ee UT os hs ean ee, a ais wee LR ad +> 313 Sir H. H. Howorth on the Shingle Beds of Eastern East
A LUSLIS), yer atale Ops eet aa aa an feada,. «ea gee 314 Prof. W. J. Sollas on an Experiment to illustrate the
Svlind= ot Flow of a Viscous Flnid .... .....:4.. 314 Mr. H. W. Monckton on the Stirling Dolerite ........ 315 Mr. J. Postlethwaite on some Railway Cuttings near
1 SETTC Rd gle SS a eo a me 315
Mr. D. Bell on the Shelly Clays and Gravels of Aber deenshire considered in Relation to the Question of
“cA SMOG DSTA es RA Nee ae PSO ra 316 Mr. G.S. Boulger’s Geological Notes of a Journey round the Coast of Norway and into Northern Russia .... 317
Messrs. G. J. Hinde and H. Fox on a wellmarked Horizon of Radiolarian Rocks in the Lower Culm Measures of Devon, Cornwall, and West Somerset .. 317
Messrs. G. F. ScottElhot and J. W. Gregory on the Geology of Mount Ruwenzori and some adjoining ine rione Ole Mematorial Atmicay acd. .G i ddes. dees oss 319
Mr. <A. Strahan on Overthrusts of Tertiary Date in AVG IRE Gir ous eae oe On cn One Oe 319
V1 CONTENTS OF VOL. XL.—FIFTH SERIES.
NUMBER CCXLV.—OCTOBER.
Page Mr. Walter Hibbert on the Gladstone “ Law” in Physical Optics, and the True Volume of Liquid Matter ........ 321 Dr. Louis Trenchard More on the Changes in Length pro  duced in Iron Wires by Magnetization soe eee 345 Dr. George Johnstone Stoney on the Kinetic Theory of Gas,  reparded as illustrating Nature ...:_.... 7) oe 362  Mr. Harry C. Jones on the Cryoscopic Relations of Dilute  Solutions of CaneSugar and Ethy] Alcohol .......... 383  Notices respecting New Books :—  Dr. Andreas Fock’s Introduction to Chemical Crystallo praphy .....0.c ete ees ee 393 Proceedings of the Geological Society :— Mr. G. W. Lamplugh on the CrushConglomerates of the Isle of Man: :.:)22..2: 1.2. 3. ros 394  A Simple Method of Meteraniis the Duration of Torsional . Oscillations, by BR. W. Wood ........... =. eee 395 On the Inconstancy of the Potential required for a Spark, by G. Jaumann 2.0... ee eee ee ee De rrr 396
NUMBER CCXLVI.—NOVEMBER. Mr. R. A. Lehfeldt on the Properties of a Mixture of
Wiguids . 6 wesc hve eee eas ere 397 Mr. F. A. Waterman on an Improv ed Calorimeter for the Application of the Method of Mixtures. .. . 2222 = eee 413
Mr. William Sutherland on the Viscosity of Mixed Gases .. 421 Mr. E. H. Griffiths on the Thermal Unit. (Plates VI. &
WIE.) ad. ee es > 431 Thaddeus Estreicher on the Pressures of Saturation of OXYGEN 2s... oe eee ee we cee wee a 5 454
Dr. Charles H. Lees on a Simple Geometrical Construction © for finding the Intensity of Illumination at any Point of a Plane due to a Small Source of Light symmetrical about A an Axis perpendicular to that Plane ........ 0) sean 463  Mr. Henry Wilde on Helium, and its place in the Natural \ Classification of Elementary. Substances. (Plate VIII.) .. 466 Mr. Spencer Umfreville Pickering on Selfrecorded Breaks in the Properties of Solutions ................. enn 472  Measurements with Alternating Currents of High Frequency,  by Dr. Joset Toma’... ..... 2... saa wen) 476 
CONTENTS OF VOL. XL.—FIFTH SERIES. vil
NUMBER CCXLVII.—DECEMBER.
Page ‘Mr. William Sutherland on Molecular Force and the Surface MePegmrOr SOLUTIONS... 22... ee ee Pe Pe eee AT7 Prof. S. W. Holman on Galvanometer Design. Waste Space ps RULE ty GREE SI ete Oats eit sie eee 494 Prot. T. Mizuno on Tinfoil Grating as a Detector for Ne ahs els CA ote ea ne des ge 497 Prof. John Perry and Mr. H. F. Hunt on the Development RIOT ITICUIONS 6. i lk ee ee ee 506 Prof. J. J. Thomson on the Relation between the Atom and Baes@haree of Blectricity carried by it ................ 5k
' Proceedings of the Geological Society :— Sir Henry H. Howorth on the Chalky Clay of the Fenland and its Borders: its Constitution, Origin, MemimemM, AMG AGO i. yw kan te on eee wales 544  Mr. T. Crosbee Cantrill on the Occurrence of Spirorbis Limestone and Thin Coals in the socalled Permian Rocks of Wyre Forest ; with Considerations as to the Systematic Position of the “ Permians” of Salopian
: Mae te ol on ME tly he wig se vv e's be 545  Prof. T. G. Bonney on the Serpentine, Gneissoid, and i Hornblendic Rocks of the Lizard District .......... 546  Dr. J. W. Gregory on the ‘“‘ Schistes Lustrés ” of Mont 758) OS anne 7) eee ea 2 pe 547 On the Wavelength of the D, Helium Line, by A. Deforest tne. Ue ea 547
dex Sr fia hy ho Sint ES ten Vogt gt a  Jade Hae. 549
)
PLATES.
I. & II. Mlustrative of Mr. H. F. W. Burstall’s Paper on the Measure ment of Cyclically Varying Temperature.
Ill. & IV. Illustrative of Profs. J. Dewar and J. A. Fleming’s ee on the Thermoelectric Powers of Metals and Alloys. 
V. Illustrative of Profs. J. Dewar and J. A. Fleming’s Paper on the Variation in the Electrical Resistance of Bismuth, when cooled to the Temperature of Solid Air.
VI. & VIL. Tlustrative of Mr, E. H. Griffiths’s Paper on the Thermal Unit.
VOT. Illustrative of Mr. H. Wilde's Paper on Helium, and ite place in the Natural Classification of Elementary Substances.
j

SE aa =
a a Yn
THE
LONDON, EDINBURGH, anp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES. ]
aU 13e0%
I. The Fundamental Atomic Laws of Thermochemistry.
By Witu1sM SUTHERLAND *.
a data of Thermochemistry have been made the subject of many general suggestions as to relations and laws holding amongst them, but these suggestions have for the most part remained undeveloped and uncoordinated. It is true that Thomsen and Berthelot, to whom we owe the greater part of the splendid accumulation of experimental material, have ever had in view the deduction of generaliza tions from their data wherewith to enrich chemical philosophy on the side of energetics: thus Berthelot discovered his principle of maximum heat; and Thomsen marshalled the
facts of the thermochemistry of carbon ¢ompounds into an
orderliness in which he was able to show the operation of some beautifully simple principles. Unfortunately a few
Invalid assumptions and speculations introduced by Thomsen  into his theoretical systemization of carbon thermochemistry
seem to have made many chemists afraid that they have involved his whole system in their invalidity. But in reality
these assumptions are quite unnecessary, and when banished from Thomsen’s system leave his discoveries a grand un obstructed main road into the region of thermochemical law.  Thomsen’s generalizations relate to the carbon compounds
* Communicated by the Author.
_ Phil. Mag. 8. 5. Vol. 40. No. 242. July 1895. B
2 Mr. W. Sutherland on éhe Fundamental i
only, although by his experiments he also put upon a satis  factory footing the only general principle that has yet been discovered in organic thermochemistry ; namely, the principle practically enunciated in different forms by Hess, Andrews,  and Favre and Silbermann, that in the formation of salts in solution from their elements each atom contributes an amount of heat which is approximately independent of the other atoms with which it is associated. More recently Tommasi ( Comptes Rendus) and others have occupied themselves with this law, which indeed has for some little time been installed in text books as the one generalization of value that the thermal branch of chemistry has yet contributed to the science. Quite recently Dieffenbach (Abst. Journ. Chem. Soc. 1890, p. 1206) has tried to show that also in entering into the molecule of an organic compound, an atom of an element always produces the same amount of heat; and there is no doubt that this has been a fair enough hypothesis with which to investigate the accumulating store of experimental material, but it will be made manifest in this paper that this hypothesis must be abandoned in favour of one which provides for a dependence of the atoms on one another in the matter of heats of com bination.
The present paper embodies an attempt to unfold the fundamental atomic thermochemical laws in operation both amongst inorganic and organic compounds. In the First Part, after an introductory chapter, the laws regulating the thermochemistry of the haloid compounds of the metals are developed ; and in the Second Part Thomsen’s theoretical systemization of carbon thermochemistry will be gone over step by step with a view to eliminating a few principles that seem untenable, and to restating his discoveries in terms harmonious with the principles which will be shown to rule the greater part of thermochemistry.
One of the chief conditions which contributed to Thomsen’s success in the handling of the data of the thermochemistry of the carbon compounds, was that he studied the heat of for mation of the compounds in the gaseous state. The ideal condition in which the data of thermochemistry should be presented is that in which they relate to the heat of formation at constant volume of the gaseous product from gaseous elements ; for these would be the pure heats of formation of the compound molecule from the elementary, unmixed with latent heats or heat spent in external work. In the thermo chemistry of the carbon compounds the latent heat of vapori zation of carbon is unknown, so that Thomsen was not able to put his data actually into the ideal condition, although he
 — Atomic Laws of Thermochemistry. 3
lid so as nearly as he could. But considerable progress can (9e made in the thermochemistry of carbon compounds without  ‘ knowledge of the heat of vaporization of carbon; for  mnany different types of compound involving the same number of carbon atoms in their molecules can be studied, and in the differences of their heats of formation the unknown quantity disappears. Still, in striving for more comprehensive results, Thomsen made certain assumptions in order to obtain, as a single known quantity, the unknown latent heat of the carbon molecule plus its heat of formation from atoms. These have been a stumblingblock to many chemists on account of their arbitrary nature; and although Thomsen seems to have abandoned them and the value of the latent heat plus heat of formation of the grammemolecule of carbon as unsound, a certain distrust of even his sound conclusions still lingers. In the second part of this paper Thomsen’s analysis of the thermochemical data of carbon compounds wiill be restated in a brief form, with removal of the few unwarranted and unnecessary parts.  But in the thermochemical data of inorganic compounds, which will be studied in the first part of the paper, the cause of the little progress that has been made in the discovery of general principles amongst them is the fact that it bas not been possible to get them into the ideal state—that is, referred to the gaseous condition of both the agents and the products. Of course for a certain number of inorganic compounds the data can be obtained for the gaseous state, but these have been too few to give aclue to any general thermochemical law ; and the data for the compounds of most of the metals hitherto available are not pure thermochemical data at all, but contain, as it were, unknown amounts of impurity in the shape of unknown latent heats. It is obvious, therefore, that the pure thermochemical laws cannot be discovered until these latent heats are known: that is, for instance, until the heat of combination of gaseous Na with gaseous Cl to produce gaseous NaCl is known. Notwithstanding recent progress in chemical manipulation at high temperatures and the promising _ possibilities of the electric furnace, it may be some time yet before actual experimental values of the latent heat of vapori  zation of a metal like copper, or of a compound like sodium chloride are available. But in the course of a series of ‘researches on molecular force and of another research on a kinetic theory of solids, I have been led to results which enable approximate values of the latent heat of vaporization ‘of the metals and their compounds to be calculated. The ‘details of the reasoning by which the methods of calculation B2
4 Mr, W. Sutherland on the Fundamental 
are established can be followed in my different papers om Molecular Force and on a Kinetic Theory of Solids in the Philosophical Magazine; but for the convenience of chemical readers, I will reproduce here briefly the essential steps of th« reasoning, with the formule necessary for thermochemical — applications. This will form the Introduction to Part I1.; — which will deal with inorganic compounds, Part II. relating to organic. : INTRODUCTION.
The startingpoint in the application of Dynamics to mole cular physics is the Virial equation of Clausius. If a number of molecules (forming, say, a unit mass) are confined in a volume v at pressure p, and if 4mV? is the kinetic energy of translatory motion of any one, and ¢(%) the force acting between any two at distances r apart, then the Virial equation
ay 3pu=DsémV2—4.4>>rG(r7)3_ « . « CA) where the single } denotes that the values of }mV? for all the molecules are to be added together, while the double symbol > denotes first that all the values of r@(s) are to be added for the forces between one particular molecule and all the rest, and then that all such sums for all particular mole cules are to be added together. The best known attempt to transform this equation to a form suitable for physical appli cations is that which resulted in the now famous equation of van der Waals, namely, b a
po=RO+ Ro —> ie (2) the separate terms of which are to be interpreted as follows:— 6 is absolute temperature, RO stands for 2>4mV*, and R6b/(v—b) stands for two thirds of that part of —4.3 > >7¢(r) which results from the forces of repulsion that act during the collisions of molecules, while —a/v stands for two thirds of that part of —4.4>>7rd¢(r) resulting from the steady attrac tion of the molecules which produces the cohesion of liquids and solids. The experiments of Amagat, and later of Ramsay and Young, proved that the equation of van der Waals cannot represent the facts of the vapours of compounds ; and from these experiments I showed that the equation of van der Waals applies, so far as we know at present, only to the gaseous state of hydrogen, oxygen, nitrogen, and methane, and that a different form represents the main facts of most compound vapours. The point of most importance in this form for, present applications is that the part of —4.42>>7r¢(7)
 {  
_ ape
Atomic Laws of Thermochemistry. 5 resulting from the attractions of molecules for one another aS.
takes the form — 3 eae
tical volume, and / is a constant for each substance but different for different substances (a parameter); at volume & this becomes — 3//2k, and for volumes below &, that is for the liquid state, the term retains the form —31/2v. The con stant / is thus an important measure of molecular attraction amongst like molecules, and five chief methods along with some subsidiary ones are given for calculating its value from  available data, a large number of values being tabulated (Phil. Mag. 5th ser. vol. xxxv. March 1893) in the form MZ, where M is the ordinary molecular mass (weight) of the substance. The equation of one of these methods throws light on the matter in hand ; it is that of the third method,
Ml/v,=665MA—101T,, . . . . (3)
where A is the latent heat of vaporization of a gramme of liquid at its ordinary boilingpoint T, reckoned from absolute zero, v; being the volume of a gramme in cubic centimetres at that temperature: with 2 in calories this equation gives / in terms of 10° dynes as unit of force. In connexion with this equation it is shown that for a large number of liquids _ the approximate relation MA=19°4T; holds; that is, the molecular latent heat is proportional to the absolute boiling point, a relation discovered empirically by Pictet in 1876. Using this to eliminate Ts from our equation, we have ap proximately
where & is nearly equal to the cri
He edi ee ee: (4)
This shows how, if we can obtain values of /, we can derive the latent heat of vaporization of the substance as liquid. The latent heat of fusion of solid to liquid is for most bodies only a fraction of the heat of vaporization of the liquid ; so that if in the last equation we replace v,, the volume of the liquid at its boilingpoint, by v the volume of the solid, we shall have an approximate equation for the heat of vaporization of the solid. The problem of finding the latent heat of vapo  rization of solids is thus reduced to that of finding values of J.  The fifth method of finding / given in the Laws of Molecular _ Force is the only one of the five which is applicable to exist te data for solids: the equation of that method is
[SS TE) ae SR a ae ae
i where is the surfacetension of the liquid measured in _ rrammes weight per linear metre at two thirds of the absolute
6 Mr. W. Sutherland on the Fundamental ae
critical temperature, v the volume of a gramme at that tem perature, and M the molecular mass, ¢ being a constant the same for all bodies. Now the surfacetensions of a number of solids at their meltingpoints, or, more accurately, of a number of liquids at their solidifyingpoints, were measured some time ago by Quincke (Pogg. Ann. cxxxv. p. 138), and quite recently by Traube (Ber. der Deut. Chem. Ges. xxiv. p 8074). Quincke’s data relate to a number of metals and a few salts, and Traube’s to a number of salts of Na and K. It is obvious that there must be a certain amount of roughness in the measurements at the high temperatures of the melting
points of these bodies, and there is also an inaccuracy in the
equation by which Quincke calculates the surfacetensions from the experimental measurements ; but there is a com pensating cause at work, and it may be said that both Quincke’s and Traube’s data give a fairly accurate estimate of the surfacetension at the meltingpoint, if all the difficulties of the measurements are allowed for. Now in our last equa
tion (5) the surfacetension is supposed to be measured at — 
twothirds of the absolute critical temperature, though with a different value of ¢ it might be taken at any constant fraction of the critical temperature. Meltingpoints are hardly likel
to be proportional to critical temperatures ; but still, as high meltingpoints on the whole mean high critical temperatures, there is a rough proportionality between meltingtemperature and critical; so that if we denote the surfacetension at the meltingpoint by @,, and the value of a gramme at ordinary temperatures by 1/p, we can replace the last equation by the
approximate form lL=¢'dm(1/p)?7/MU, eG)
where c’ is a constant to be determined. The value of ¢ in (5) is 2 x 5930 when 10° dynes is the unit of force ; for c’ I have adopted the value 9300. To get values to join on naturally with those tabulated in the ‘Laws of Molecular Force,” where the unit of force used is,10’* dynes, we can write our present relation in the form
M?7=9300 x 1082 (M/p)®.. 2. . (7)
N.B.—Here and hereafter the unit of force is 10” dynes.
By this equation, then, we can get approximate values of J for. the metals and salts of Quincke’s and Traube’s experi= ments, and so deduce approximate values of their latent heats of vaporization; but as for thermochemical applications we require the latent heats of a larger number of substances,

i, i  i 
 i) iia : ; i
; we will proceed with an account of another method of obtain
Atomic Laws of Thermochemstry. 7
ing more numerous values of J. This second method is founded on a Kinetic Theory of Solids (Phil. Mag. 5th ser. vol. xxxii.). The fundamental equation there established relates to a collection of equal monatomic molecules of diameter 1) or distance Hi between the centres of two mole cules when they are in contact, e being the average distance apart of two adjacent molecules, so that e—H is the distance through which a molecule swings between an encounter on one side and an encounter on the opposite side; with the  same meaning as before for the other symbols, the equation
for a solid free from external force is
2>4mV? 1 oe Be (e— EB) 7 ga r=ro(r)=0. Bi) aig ie (8) This equation applies to the metals: as before, 22rd(r)/6 reduces to Jp, where p is the density, and e®=/p, so that ImDimV2 (M
Ws Frey (a) RS ere
(it should be noticed that m denotes the actual mass of a molecule, M its ordinary molecular mass (weight) referred to hydrogen). Now %3mV?’ is the kinetic energy of the oscil latory translatory motion of the molecules in unit mass, which is equal to 2Jc@ if the internal energy of the molecules is negligible, where @ is the temperature, c the specific heat, and J the mechanical equivalent of heat, and ¢e?(e—H) = H?(e/H—1) approximately: if the molecules are invariable with tem perature, e/H—1=00, where 6 is the coefficient of linear expansion of the metal. But it was shown in “A Kinetic Theory of Solids” that the metals behave as if E diminishes with rising temperature in such a way as to make e/H—1 = 760 approximately, and as H?=m/p nearly, we have
3). 2SeM(M/p) MIs =e we (10)
In this cM, by Dulong and Petit’s law, is nearly 6:4 for all the metals: the values of b have not been found experimentally for several of the most important metals, but can be obtained by an empirical relation given in “ A New Periodic Property of the Elements” (Phil. Mag. [5] xxx.; also xxxii. p. 540), namely, if T is the absolute meltingpoint, bTM‘/*=044;
8 Mr. W. Sutherland on the Fundamental
with 4:2x 10’ as the value of J, we get finally with 10”   dynes as unit of force, 
M2]=58(M/p)TM2*x10. . . . . (11) 
Thus J, and therefore the latent heat of vaporization of  nearly all the metals can be found ; but we also require a  similar equation for the compounds of the metals. 
The establishment of such an equation is sketched in  section 9 of “ A Kinetic Theory of Solids,” but inaform which  is not correct without a strained interpretation of some of  the symbols: the correct equation for a compound whose  molecule contains n, atoms of mass m, and nz of mass mz and  so on, the diameters of the atoms being H,, H, and so on, and  the. mean distances from their neighbours(centre to centre) €}, €2 and so on, 1s 
1 n,m, V ,? NyMz V 9” )= 1 wou es 4 q Saa(poet AS 12h, +. = Garzrhlr), : (12)
where as before e* is the domain of a molecule, that is, its share of the total space occupied by the solid, and (7) is the force between two molecules. The values of Hy, E,, ¢, e, and so on are unknown, but it is reasonable to suppose that for approximate purposes 1—H,/e, and so on can be replaced by a single mean value proportional to 60, where 6 is the linear coefficient of expansion of the solid compound: thus we replace each by ab@, corresponding to the 7b@ for metals, then we have the sum 3 (nym, V,?+ 2 m_V.?+ ...) of which the value is 2J Mc@, M being the molecular mass and ¢ the specifie heat of the compound. ‘The only unknown quantity remain ing is b, which has been found for very few compounds ; in the case of metals we eliminated it by the relation bTM’®=:044. Let us assume that a similar relation holds for compounds, namely that b1M**is constant, then merging this constant and the unknown a into a single coefficient we finally reduce the last equation to the form
MU=5'8 x 10K, N° (M/p) TM®, me yore ales) where k& is a parameter to be determined for each type of compound. I have found that k=} for such binary com pounds as NaCl, KI, and so on; and according to the principle of Joule and Kopp that the molecular specific heat of a com pound is the sum of the atomic specific heats of its atoms, Me for these binary compounds is 2x6°4. Thus for com pounds of this type the equation (13) simplifies down till it is
~ Atomic Laws of Ther beepaa Us )
Bcentical. with (11), which was established for the metals ; and I have found this same equation to hold for compounds of the types RS,, RS;, RS,, such as CaCl,, AICI, and SnCl,.
When S instead of being an atom is a compound radical a as NO:, the equation (13) does not become so simple, but in it we must put the value of Mc and take k as we have already implied that it is, namely the reciprocal of the number of radicals in the molecule. Thus in equation (13) a second
method of finding / has heen established, depending only on
density and meltingpoint. There is still another approximate method which comes in
useful for anumber of compounds which are liquid at ordinary
temperatures and for which only density and boilingpoint are known; it is
M21=1190x 108(M/p)T;. . . . « (14)
We have now to determine in what way we ought to pass from the values of / given by the three equations (7), (11), and (13) to the total latent heat of vaporization of the solid at ordinary temperatures, say 15°C. We have seen that for the latent heat of vaporization of a liquid at its ordinary boilingpoint (4) holds when the unit of force is 10° dynes ; with 10” dynes as unit it becomes
Ml/v,; = 61:3 x 10°Mn.
But in thermochemical experiments we have, as a rule, to do with the heat given out when the reagents are taken at about 15°C., and the products are brought back to the same tem perature, and in most cases the latent heat at 15°C. will be larger than at the boilingpoint. Under these circumstances it seems to me best to regard the matter in the following way : Ivi is the potential energy of the molecules of a gramme occupying volume v, due to their mutual attractions ; hence if v is the volume of the gramme when solid, and vis a large volume into which it is supposed to be vaporized, the change of potential energy, due to the separation of the molecules in a grammemolecule, is M//vp— MJ/v3. Now the second term is so small compared to the first that it can be neglected, when we have Ml/v, which when expressed in calories becomes M//upd.
It is this potential energy which constitutes the main part of the latent heat of vaporization; and it is this M//v,J, which ean be written .M/p/J; that. I propose to use in place of the actual heat of. vaporization at 15°C. The. manner in which the latent. heat is to be used in connexion with thermochemical data is. as follows :—Suppose a solid..element R to combine
10 Mr. W. Sathenaad on the Fundamental
with the solid element S to produce the solid compound RS  with evolution of heat g, then, to obtain the evolution of heat _ when § as gas combines with Ras gas to produce gaseous RS, we must add the latent heat of vaporization of R and of S and subtract that of RS: denoting these latent heats by L(R),  L(S), and L(RS), and the required heat of combination of  the gases by H(RS) we have 
H(RS)=q—L(RS)+L(R)+L(8). . . (15)
There remains now only to give tables of the experimental data and the valucs of M?/ calculated from them by equations (7), (11), and (18), and of Mlp/J or L, the latent heat per grammeatom or grammemolecule due to molecular force; L is given in kilocalories. As the application of (11) to the metals brings out some immediately interesting results, the values for the metals will be taken first. In the metals the ordinary atomic mass (weight) is taken for M.
TABLE I, 
First family and Copper subfamily.
Li. Na. Ke Rb. Cs, Cu. Ag. Aux. >a DE Ae cond er 453 569 335 sll 300 1330 1230 1310 MB Orcas see velon ass 19 «69387 45:4" 56" 706 72, 10:2 102 Me neck ates 41 $6° 162 912  27:6 Gi 159 18°7 (Teal) 2 )ocdscee 8°3 8:6 8:5 9:0 9:3 36'6 387°0 43°5
Second family and Zine subfamily. Be. Mg. Ca. Sr. Ba. Zn. Cd. Hg.
/ US a ee ee 1230 1023 900 #8 800 748 690 590 234 Mois eit cata cece 56 138 234 349 36:5 91 12:9 14:7 J Eps eed SN 58 139 245" > 34:0 ea59 73 9:7 48 Ti(keal.); 2.3: hss 945 989 93:0 “232 > 2a a 179 78 Third family and Gallium subfamily.
Al. La. Ga. In. 7.
I Gaus aah eas cee lacs nb 1933) hit > Bee 710 303 449 563 Miami herteco.:), 106 ida) ee 23 17 153 184 NTR E EOE CRON Le hs ic L129) nets eee 23°5 4°1 88 143 VG ee i) i alae? ane 26S + EN See 25:2 8:4 136 188
Fourth family and Tin subfamily.
Ce. Sn. Pb.
MEE Peek: tite dehwas Aaatacniee Fl: chauase \ segagtar do eee 100065 (as 503 599 Ar tte fae Rend Gat Ry alk sven csash cas ce DOs (Sve 161 181 1 CA eee ae peer ns ates oie ee Py fe Rae ee 10°9 15°3
rE a Oe eR Sbo ogee 161 201
Atomie Laws of Thermochemistry. 11
Table I. (continued). Fifth family and Arsenic subfamily.
Di. Was 82 Shi. 4: Bi. 7 1200 773 710 540 1 a 22:3 132 179 211 2) ee 85:7 122 164 161 a 382 219 218 182
Highth family—lIron, Palladium, and Platinum groups.
Fe (Ni Co). Pd (Ru Rh). Pt (Os Ir). i 2080 1775 2050 i ee 72 92 91 MIO c.cc0 169 206 261 Pi(Keal.): ..:....0: 56'1 532 682
The first fact deserving attention in this table is that in each main family M/p/J or L, the latent heat of vaporization per grammeatom due to molecular force, is constant. Thus, in
 the first family it is about 8°7, and in Cu and Ag about 37 or
about four times the value in the main family ; in the second family the value is about 23°6, and for Zn and Cd about 18°5,
_ which is much nearer to the value for the main family than
was the case with Cu and Ag, a fact that is probably con nected with the greater chemical similarity of Zn and Cd to the main family than is the case with Cu and Ag. The third main family is represented in the table by only two members, Al and La, which have practically the same value for L, the mean being 26:0, while in the related subfamily Ga has a value which is one third of this, just as that for Hg is one third of that in its main family ; In has a value which is nearly a half of that in the main family. At the fourth family we reach a point of transition, after which the sub families have more the character of main families than the main families themselves. In the fourth main family we have but the one value, that for Ce, about 32, of which the value 16 for Sn in the subfamily is one half. In the fifth sub family As, Sb, and Bi have nearly the same value, about 21, which is nearly one half of the 388 for Di in the main family. For Fe, Pd, and Pt the values are about 60. It is interesting to note how the latent heat per grammemolecule due to
_ molecular force increases with the valency or order of the
main family. To bring this out more clearly the following little table is drawn up, containing in the first row the mean yalues of L, the latent heat per atom in each main family, and
digs Mr. W. Sutherland on the Fundamental
in the second row the latent heat per equivalent, taking the  familynumber as the valency of the family. 
es j TABLE la. amvhy aumaber .)24.2.4.2.aventes senses 1. 26.2), . ater ene 8. Latent heat per grammeatom ............ 87 .23:6..26°0 32:0. 40 60 Latent heat. per grammeequivalent ...... 87 118. (89 SSG ye) ia
These numbers in the second row show that the latent heat — of vaporization per grammeequivalent due to molecular force is nearly the same in all the main families, except the second, where it is half as large again as in the other main families ; as regards this relation the subfamily. Zn and Cd  would appear to take the place of the main family, for the  value per equivalent is 9°2. As it has already been pointed  out that the values per grammeatom of most. members of the subfamilies are simple multiples or submultiples of those in the main family, the general principle can be enunciated for the metals :—The latent heat of vaporization per gramme equivalent due to molecular force is approximately a constant: or a simple multiple or submultiple of the constant. te
The fact that we have been led to a general result such as this shows that the method of calculation has probably yielded correct relative values of the latent heat of vaporization due to molecular force ; it remains to see whether these are of about the right absolute magnitude. The only metal whose latent heat of vaporization we can determine independently by means of existing data is mercury; for all the terms in the thermodynamical relation JA=(v3—v,)@ dp/d@ are known for mercury, dp/d@ being the rate of variation of the saturation pressure of the liquid with the temperature, v, and vy