" Nee aranearum sane textus ideo melior quia ex se fila gignunt, nee noster vilior quia ex alienis libamus ut apes." Just. Lips. Polil. lib. i. cap. 1. Not.

a s






" Meditationis est perscrutari occulta ; contemplationis est admirari perspicua .... Admiratio generat quaestionern, qusestio investigationem,

investigatio inventionem."

-Hugo de S. Victore.

" Cur spirent venti, cur terra dehiscat,

Cur mare turgescat, pelago cur tantus arnaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas, Quid pariat nubes, veniant cur fulmina coelo, Quo micet igne Iris, superos quis conciat orbes Tarn vario motu."

/. B. Pinelli ad Mazonium,






Page Mr. William Sutherland on the Fundamental Atomic Laws of

Thermochemistry 1

Mr. W. G. Rhodes on a Theory of the Synchronous Motor. . 56 Mr. C. Chree's Contribution to the Theory of the Robinson

Cup-Anemometer 63

Prof. E. F. Herroun on the Use of an Iodine Voltameter for

the Measurement of Small Currents 91

Profs. James Dewar and J. A. Fleming on the Thermo-elec- tric Powers of Metals and Alloys between the Temperatures of the Boiling-Point of Water and the Boiling-Point of

Liquid Air. (Plates III. & IV.) 95

Dr. Meyer Wildermann's Experimental Proof of Van't Hoff's Constant, of Arrhenius's Generalization, and of Ostwald's

Law of Dilution in very Dilute Solutions 119

Notices respecting New Books :

Mr. J. F. Blake's Annals of British Geology, 1893 .... 144 Prof. N. Story Maskelyne's The Morphology of Crystals. 145 Proceedings of the Geological Society :

Mr. E. A. Walford on the Lias Ironstone around Ban-

j bury 147

Mr. W. F. Wilkinson on the Geology and Mineral Re- sources of Anatolia (Asia Minor) 148

Mr. A. Harker on Carrock Fell A Study in the Varia- tion of Igneous Rock-masses 148

Mr. F. R. Cowper Reed on the Geology oL' the Country

'. around Fishguard (Pembrokeshire) 148

Mr. J. L. Lobley on the Mean Radial Variation of the

Globe 149

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 the Jordan Waters 149


Page Messrs. S. B. J. Skertchly and T. W. Kingsmill on the Loess and other Superficial Deposits of Shantung

(Northern China) ; 150

Dr. J. W. Gregory's Contributions to the Paleontology

and Physical Geology of the West Indies 151

Mr. J. D. Kendall on the "Whitehaven Sandstone Series. 152 On the Double Refraction of Electrical Kays, by K. Mach . . 152


Mr. J. Y. Buchanan on the Use of the Globe in the Study

of Crystallography 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

Mr. F. W. Bowden on an Electromagnetic Effect 200

Dr. K. Olszewski's Determination of the Critical and the

Boiling Temperature of Hydrogen 202

Messrs. John Trowbridge and William Duane on the Telocity

of Electric Waves 21 1

Messrs. J. Alfred Wanklyn and W. J. Cooper on Fractional Distillation applied to American Petroleum and Russian

Kerosene 225

Proceedings of the Geological Society :

Prof. J. B. Harrison and Mr. A. J. Jukes-Browne on the

Chemical Composition of some Oceanic Deposits .... 229 Dr. C. S. Du Riche Preller on Fluvio-Glacial and Inter- glacial Deposits in Switzerland 229

Mr. S. S. Buckmau on the Bajocian of the Mid-Cottes-

wolds 230

On the Magnetism of Asbestos, by Dr. L. Bleekrode 231


Mr. Shelford Bid well on the Electrical Properties of Selenium. 233 Messrs. Alfred W. Porter and David K. Morris on the Mea- surement of Varying Currents in Inductive Circuits .... 256 Profs. Liveing and Dewar on the Refraction and Dispersion of Liquid Oxvgen, and the Absorption Spectrum of Liquid Air * 268



Dr. Ladislas Natanson on the Critical Temperature of Hydro- gen, and the Theory of Adiabatic Expansion in the Neigh- bourhood of the Critical Point 272

Mr. Henry F. W. Burstall on the Measurement of Cyclically

Varying Temperature. (Plates I. & II.) 282

Profs. C. Runge and P. Paschen on the Constituents of

Cleveite Gas 297

Profs. James Dewar and J. A. Fleming on the Variation in the Electrical Resistance of Bismuth, when cooled to the

Temperature of Solid Air. (Plate V.) 303

Notices respecting New Books :

Dr. Joseph Prestwich's Geological Inquiry respecting the A\ ater-bearing Strata of the Country around London, with Reference especially to the Water- Supply of the Metropolis ; and including some Re- marks on Springs 311

Geological Survey of Canada, Annual Report, New Series, Vol. VI. Reports A (1892), A (1893), J, Q, R, S,

1892-93 312

Proceedings of the Geological Society :

Major H. de Haga Haig on the Physical Features and

Geology of Mauritius 313

Mr. W. S. Gresley on Ice-Plough Furrows of a Glacial

Period 313

Sir H. H. Howorth on the Shingle Beds of Eastern East

Anglia 314

Prof. W. J. Sollas on an Experiment to illustrate the

Mode of Flow of a Viscous Fluid 314

Mr. H. W. Monckton on the Stirling Dolerite 315

Mr. J. Postlethwaite on some Railway Cuttings near

Keswick 315

Mr. D. Bell on the Shelly Clays and Gravels of Aber- deenshire considered in Relation to the Question of

Submergence 31*6

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 well-marked Horizon of Radiolarian Rocks in the Lower Culm Measures of Devon, Cornwall, and West Somerset . . 317 Messrs. G. F. Scott-Elliot and J. W. Gregory on the Geology of Mount Ruwenzori and some adjoining

Regions of Equatorial Africa 319

Mr. A. Strahan on Overthrusts of Tertiary Date in Dorset 319



Page Mr. Walter Hibbert on the Gladstone " Law " in Physical

Optics, and the True Volume Liquid Matter 321

Dr. Louis Trenchard More on the Changes in Length pro- duced in Iron Wires by Magnetization 345

Dr. George Johnstone Stoney on the Kinetic Theory of Gas,

regarded as illustrating Nature 362

Mr. Harry C. Jones on the Cryoscopic Relations of Dilute

Solutions of Cane-Sugar and Ethyl Alcohol 383

Notices respecting New Books :

Dr. Andreas Eock's Introduction to Chemical Crystallo- graphy 393

Proceedings of the Geological Society :

Mr. G. W. Lamplugh on the Crush-Conglomerates of

the Isle of Man 394

A Simple Method of Determining the Duration of Torsional

Oscillations, by E. W. Wood 395

On the Inconstancy of the Potential required for a Spark, by G. Jaumann 396


Mr. E. A. Lehfeldt on the Properties of a Mixture of

Liquids , 397

Mr. E. A. Waterman on an Improved Calorimeter for the

Application of the Method of Mixtures 413

Mr. William Sutherland on the Viscosity of Mixed Gases . . 421 Mr. E. H. Griffiths on the Thermal Unit. (Plates VI. &

VII.) 431

Thaddeus Estreicher on the Pressures of Saturation of

Oxygen * 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

an Axis perpendicular to that Plane -. 463

Mr. Henry Wilde on Helium, and its place in the Natural

Classification of Elementary Substances. (Plate VIII.) . . 466 Mr. Spencer Umfreville Pickering on Self-recorded Breaks in

the Properties of Solutions 472

Measurements with Alternating Currents of High Erequency,

by Dr. Josef Tuma 476




Page Mr. William Sutherland on Molecular Force and the Surf ace- Tension of Solutions 477

Prof. S. W. Holman on Galvanometer Design. Waste Space

near the Needle 494

Prof. T. Mizuno on Tinfoil Grating as a Detector for

Electric Waves 497

Prof. John Perry and Mr. H. F. Hunt on the Development

of Arbitrary Functions 506

Prof. J. J. Thomson on the Relation between the Atom and

the Charge of Electricity carried by it 511

Proceedings of the Geological Society :

Sir Henry H. Howorth on the Chalky Clay of the Fenland and its Borders : its Constitution, Origin,

Distribution, and Age 544

Mr. T. Crosbee Cantrill on the Occurrence of Spirorbis- Limestone and Thin Coals in the so-called Permian Rocks of Wyre Forest ; with Considerations as to the Systematic Position of the " Permians " of Salopian

Type . . . t , 545

Prof. T. G. Bonney on the Serpentine, Gneissoid, and

Hornblendic Rocks of the Lizard District 546

Dr. J. W. Gregory on the " Schistes Lustres " of Mont

Jovet (Savoy) * 547

On the Wave-length of the D3 Helium Line, by A. Deforest Palmer, Jr 547

Index 549


I. & II. Illustrative of Mr. B. F. W. Bui-stall's Paper on the Measure- ment of Cyclically Varying Temperature.

III. & IV. Illustrative of Profs. J. Dewar and J, A. Fleming's Paper on the Thermo-electric 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. & VII. Illustrative of Mr. E. H. Griffiths's Paper on the Thermal


VIIT. Illustrative of Mr. H. Wilde's Paper on Helium, and its place in the Natural Classification of Elementary Substances.






JUL Y 1895.

I. The Fundamental Atomic Laws of Thermochemistry. By William Sutherland *.

THE 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 compounds 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 Thomson'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. S. 5. Vol. 40. No. 242. July 1895. B

2 Mr. W. Sutherland on the Fundamental

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. Ohem. 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 re-stating 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 lie could. But considerable progress can e made in the thermochemistry of carbon compounds without ^ knowledge of the heat of vaporization of carbon ; for many 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 stumbling-block 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 gramme-molecule of carbon as unsound, a certain distrust of even his sound conclusions still lingers. In the second part of this paper Thomson's analysis of the thermochemical data of carbon compounds will 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 has 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 a clue 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 Gl 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 vof the metals and their compounds to be calculated. The ^details of the reasoning by which the methods of calculation

B 2

4 Mr. W. Sutherland on the Fundamental

are established can be followed in my different papers on- 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 formulae necessary for thermochemical applications. This will form the Introduction to Part L. which will deal with inorganic compounds, Part II. relating to organic.


The starting-point 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 ^mY2 is the kinetic energy of translatory motion of any one, and <£(V) the force acting between any two at distances r apart, then the Yirial equation

where the single § denotes that the values of J mV2 for all the molecules are to be added together, while the double symbol %% denotes first that all the values of r<j>(r) 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,

pv = Ue + Rd—.i :--, (2)

the separate terms of which are to be interpreted as follows: 6 is absolute temperature, R0 stands for fSi771^2? an(^ R,#&/(v b) stands for two thirds of that part of %.%%'%r(p(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 ^.^E2^0W 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 i>i%%r<j>{r)

Atomic Laws of Thermochemistry. 5

resulting from the attractions of molecules for one another takes the form § r, where k is nearly equal to the cri- tical volume, and I is a constant for each substance but different for different substances (a parameter) ; at volume k this becomes §Z/2&, and for volumes below k, that is for the liquid state, the term retains the form— ^l/2v. The con- stant I 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 M% 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,

M//^ = 66-5MX-101T6, .... (3)

where X is the latent heat of vaporization of a gramme of liquid at its ordinary boiling-point Tb reckoned from absolute zero, Vj being the volume of a gramme in cubic centimetres at that temperature : with X in calories this equation gives I in terms of 106 dynes as unit of force. In connexion with this equation it is shown that for a large number of liquids the approximate relation MA,= 19'4T6 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

Mi/^ = 61'3MX. (4)

This shows how, if we can obtain values of I, 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 boiling-point, 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 I. The fifth method of finding I given in the Laws of Molecular .Force is the only one of the five which is applicable to exist- yig data for solids : the equation of that method is

IssceafrfM}**; (5)

where a. is the surface-tension of the liquid measured in grammes weight per linear metre at two thirds of the absolute

6 Mr. W. Sutherland on the Fundamental

critical temperature, v the volume of a gramme at that tem- perature, and M the molecular mass, c being a constant the same for all bodies. Now the surface-tensions of a number of solids at their melting-points, or, more accurately, of a number of liquids at their solidifying-points, were measured some time ago by Quincke (Pogg. Ann. cxxxv. p. 138), and quite recently by Traube [Ber. der Deut. Chem. Ges. xxiv. p. 3074). 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 surface-tensions 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 surface-tension at the melting-point, if all the difficulties of the measurements are allowed for. Now in our last equa- tion (5) the surface-tension is supposed to be measured at two-thirds of the absolute critical temperature, though with a different value of c it might be taken at any constant fraction of the critical temperature. Melting-points are hardly likely to be proportional to critical temperatures ; but still, as high melting-points on the whole mean high critical temperatures, there is a rough proportionality between melting-temperature and critical ; so that if we denote the surface-tension at the melting-point by am and the value of a gramme at ordinary temperatures by 1/p, we can replace the last equation by the approximate form

l = Cfam{\lp)^jWI^ (6)

where c' is a constant to be determined. The value of cin (5) is 2 x 5930 when 106 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 islO12 dynes, we can write our present relation in the form

M2Z = 9300xlO-6* (M/p)5'3 (7)

N.B. Here and hereafter the unit of force is 1012 dynes.

By this equation, then, we can get approximate values of / for v 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,


Atomic Laws of Thermochemistry. 7

we will proceed with an account of another method of obtain- ing more numerous values of I. 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 E or distance E 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— E is the distance through wrhich 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

&*(<?-E) 6e3

This equation applies to the metals : as before, 22r$(r)/6 reduces to lp, where p is the density, and e3=m/pj so that

(it should be noticed that m denotes the actual mass of a molecule, M its ordinary molecular mass (weight) referred to hydrogen). Now 2-JmV2 is the kinetic energy of the oscil- latory translator^ motion of the molecules in unit mass, which is equal to 2 Jc0 if the internal energy of the molecules is negligible, where 6 is the temperature, c the specific heat, and J the mechanical equivalent of heat, and e2(e— E) = E3(^/E 1) approximately : if the molecules are invariable with tem- perature, <?/E l = bd, where b 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/E 1 = 7b6 approximately, and as W = m/p nearly, we have



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 melting-point, &TM1/6=*044;

8 Mr. W. Sutherland on the Fundamental

with 4*2 x 107 as the value of J, we get finally with 1012 dynes as unit of force,

M2Z=5-8(M/p)TM1/6xlO-4 (11)

Thus I, 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 in a form which is not correct without a strained interpretation of some of the symbols : the correct equation for a compound whose molecule contains nY atoms of mass mY and n2 of mass m2 and so on, the diameters of the atoms being El7 E2 and so on, and the mean distances from their neighbours (centre to centre) ely e2 and so on, is

v 1 / n^Yf n2m2Y2* \ 1 ^ . > .

where as before ed is the domain of a molecule, that is, its share of the total space occupied by the solid, and <£(r) is the force between two molecules. The values of E1? E2, ely e2, and so on are unknown, but it is reasonable to suppose that for approximate purposes l 'E1/e1 and so on can be replaced by a single mean value proportional to bd, where b is the linear coefficient of expansion of the solid compound : thus w^e replace each by abd, corresponding to the Ibd for metals, then we have the sum %(n1m1Y^ + n2m2Y2^-{- . . .) of which the value is :l JMc#, M being the molecular mass and c the specific 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 iTM1/6 = ,044, Let ns assume that a similar relation holds for compounds, namely that 6TM1/6 is constant, then merging this constant and the unknown a into a single coefficient we finally reduce the last equation to the form

M2/ = 5-8xl0-^.^(M//O)TM1/6? . . . (13)

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, Mc for these binary compounds is 2 X 6*4. Thus for com- pounds of this type the equation (13) simplifies down till it is

Atomic Laws of Thermochemistry, 9

identical with (11), which was established for the metals; and I have found this same equation to hold for compounds of the types RS2, RS3, RS4, such as CaCl2, A1C13, and SnCl4. When S instead of being an atom is a compound radical such as ]ST03, 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 I has been established, depending only on density and melting-point.

There is still another approximate method which comes in useful for a number of compounds which are liquid at ordinary temperatures and for which only density and boiling-point are known ; it is

M2Z = 1190xlO-6(M//o)T6 (14)

We have now to determine in what way we ought to pass from the values of I 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 boiling-point (4) holds when the unit of force is 106 dynes ; with 1012 dynes as unit it becomes

M/M = 61'3xlO-6MX.

But in thermochemical experiments we have, as a rule, to do with the heat given out when the reagents are taken at about 15° G., and the products are brought back to the same tem- perature, and in most cases the latent heat at 15° G. will be larger than at the boiling-point. Under these circumstances it seems to me best to regard the matter in the following: way : l/v is the potential energy of the molecules of a gramme occupying volume v, due to their mutual attractions ; hence if v0 is the volume of the gramme when solid, and vB is 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 gramme-molecule, is ~M.l/v0 Mljv^ Now the second term is so small compared to the first that it can be neglected, when we have M//r0, which when expressed in calories becomes M//»oJ.

It is this potential energy which constitutes the main part of the latent heat of vaporization ; and it is this M.l/v0 J, which can be written M.lp/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 It to combine

10 Mr. W. Sutherland 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 S as gas combines with R as 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) = ?-L(RS) + L(R) + L(S). . . (15)

There remains now only to give tables of the experimental data and the values of M2Z calculated from them by equations (7)_, (11), and (13) , and of Mlp/J or L, the latent heat per gramme-atom or gramme-molecule 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 sub-family.

Li. Na. K Bb. Cs. Ou. Ag. Au.

T 453 369 335 311 300 1330 1230 1310

M/p 11-9 237 45-4 56*1 70-6 72 10-2 102

M.H 4-1 8-6 16-2 21-2 276 111 159 187

L(kcal.) 8-3 8*6 8-5 90 9-3 366 37-0 435

Second family and Zinc sub-family.

Be. Mg. Ca. Sr. Ba. Zn. Cd. Hg. T 1230 1023 900 800 748 690 590 234

M/p 5-6 138 25-4 34-9 365 91 12-9 14-7

M.H 5-8 139 24-5 340 35-9 7'3 97 4-8

L(kcal.) 24-5 239 23-0 23-2 23'4 191 179 7'8

Third family and Gallium sub-family.

Al. La. Ga. In. Tl.

T 1123 710 303 449 563

M/p 10-6 22-3 11-7 15-3 181

MH 11-9 235 4-1 8-8 143

L(kcal.) 268 25-2 8'4 136 18-8

Fourth family and Tin sub-family.

Ce. Sn. Pb.

T 1000 503 599

M/p 21-0 16-1 181

M22 279 109 15-3

L(kcal.) 31*6 16'1 20\L

Atomic Laws of Tliermocliemistry . 11

Table I. {continued).

Fifth family and Arsenic sub-family.

Di. As. Sb. Bi.

T 1200 773 710 540

M/p 22-3 132 179 21*1

M.H 357 12-2 164 161

L(kcal.) 38-2 21*9 21'8 18'2

Eighth family Iron, Palladium, and Platinum groups.

Fe (Ni Co). Pd (Eu Eh). Pt (Os Ir).

T 2080 1775 2050

M/p 7:2 92 91

Wl 16-9 206 26-1

L(kcal.) 56-1 53-2 68*2

The first fact deserving attention in this table is that in each main family MIp/J or L, the latent heat of vaporization per gramme-atom 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 familv 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 sub-family 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 sub-family 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 38 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 gramme-molecule 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 values of L, the latent heat per atom in each main family, and

12 Mr. W. Sutherland on the Fundamental

in the second row the latent heat per equivalent, taking the family-number as the valency of the family.

Table la.

Familynumber 1. .. 2. 3.... 4. 5. 8.

Latent heat per gramme-atom 8*7 23'6 26*0 32'0 40 60

Latent heat per gramme- equivalent 8*7 . .11 '8 8*7 80- 8*0 7*5

These numbers in the second row show that the latent heat of vaporization per gramme-equivalent 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 sub-familv 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 gramme-atom of most members of the sub-families 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.

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 J\=(v3 v2)# dp/dO are known for mercury, dp/d0 being the rate of variation of the saturation pressure of the liquid with the temperature, v2 and v$ the volumes of a gramme of the substance as liquid and saturated vapour under the vapour-pressure at 0. With Regnault's data and the assumption that at the boiling-point of mercury a gramme-atom or 200 grammes of mercury would occupy the same volume as 2 grammes of hydrogen at the same temperature and pressure, Berthelot has calculated the atomic latent heat of mercury as 15*5 kilocalories. With the values of dp/dd given by Ramsay and Young (Phil. Mag. 5th ser. vol. xxi.) I have calculated that 14 kilocalories would be the value, still on the above assumption as to the volume of saturated mercury vapour, but this volume is obviously too large ; and as it is a difficult enough matter to measure the true saturation volume of an ordinary vapour, it is evident that the experimental determinations hitherto made of the density of mercury vapour cannot be used in place of the

Atomic Laws of Thermochemistry . 13

above assumption. From what is known of the saturation densities of ordinary vapours, it is likely that with the true volume of mercury vapour the value 14 for the latent heat would be reduced to at least 13, of which about one eleventh part is due to doing external work ; so that the pure latent heat of liquid mercury is about 12 kilocalories for the gramme-atom. The latent heat of fusion of 200 grammes of solid Hg is *6 kilocalories ; so that the latent heat of vaporiza- tion of solid mercury is about 13 kilocalories per gramme- atom. The value calculated in Table I. for the latent heat due to molecular force is 7*8, and therefore the total latent heats would appear to be 1*6 times the tabulated values.

When the values of I are calculated for the metals by equa- tion (7) with Quincke's values for the surface-tension, certain discrepancies with the values in Table I. appear, which were remarked on in " A Kinetic Theory of Solids " in an indirect manner. These discrepancies now appear to be due to varying molecular complexity in a few of the metals, and it would lead us too far to discuss them at present. In the case of com- pounds the two equations (7) and (13) give accordant results, to which we will proceed. We will first give a table for those binary compounds for which the data for both methods are available, so that the two sets of values for M2/ may be compared. In the following table the values of the suriace- tension am are given in gTammes weight per metre, and when taken from Quincke are denoted by Q and from Traube by T. The melting-points here and in the following table are taken chiefly from Carnelley (Journ. Chem Soc. xxix., xxxiii., xxxv., and xxxvii. ; Phil. Mag. 5th ser. vol. xviii.), and the densities from Clarke's ' Constants of Nature ' and Landolt and Bornstein's Tabellen.

Table II.

LiOl. NaCl. NaBr. KF. KOI.

*IU 121 Q. 11-6 T. 10-5T. 14-2T. 100T.