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356 between the same limits by only o-ooi cal. C., which is loo times smaller than the limit of accuracy of observation; whereas the change of total heat at constant volume between the same limits in the case of water exceeds that of intrinsic energy by 21 cals., approxi- mately; but the correction from constant volume to constant pres- sure is very uncertain, even in the best known cases. It therefore appears to be more logical to employ a formula giving the specific heat at constant pressure directly, in place of applying an uncer- tain correction. It should be observed, however, that (9) assumes the mean frequency v m to be independent of T, as in Debye's formula, which may be a good approximation in many cases, but cannot be exactly true if the molecule changes its state. Curve (9) reaches s = 3R a little above 6=2, and attains a maximum 3-195 R at = 4, after which it falls with comparative rapidity to 3-048 R at = 5, tending to a limit 3R at =. The fall is of the right order of magnitude to explain the diminution of specific heat in the case of water, mercury and sodium. The distribution postulated in (8) appears to apply fairly to most of the metals, but it fails notably for many other substances. Such cases might be treated empirically by modifying the distribution, or assuming special frequencies, but such hypotheses would be of little value unless their physical meaning could be interpreted with reference to other properties of the substances.

In 1910 the very attractive theories of P. Drude and H. A. Lorentz were still commonly maintained, and were continually being applied to the explanation of electrical and thermal effects. According to their views a metal contained a number of free electrons moving in all directions with velocities corresponding to those of gas-molecules on the kinetic theory. Drude showed that this assumption led to an approximately correct value of the ratio of the thermal to the electric conductivity in the case of pure metals, and Lorentz showed that it accounted for the long wave radiation from hot bodies. There were numerous other applications of the theory which appeared to correspond in a remarkable manner with experimental facts, but there were also serious difficulties which appeared to render the adoption of such a theory premature.

The fluid state of scientific opinion on the subject in 1911 is well illustrated by the views expressed about that time by J. H. Jeans, one of the leading exponents of mathematical physics. In the report of the Solvay Congress, 1911, On the Theory of Radiation and Quanta (Gauthier Villars, Paris, 1912), assuming that there were two free electrons per atom of the metal, Jeans took the view that the specific heat of metals was entirely due to the movement of free electrons and not at all to the move- ments of the atoms, " a hypothesis which accords well with our knowledge of the internal movements of solids." On the other hand, in his report on the quantum theory (Phys. Soc., London, 1914), he adopted the theory of Debye (according to which the specific heat was entirely due to the movements of the atoms) as probably " destined to be final," and concluded that the free electrons do not contribute sensibly to the specific heat. Sir J. J. Thomson, Corpuscular Theory of Matter (Constable, 1907), had already pointed out that the number of free electrons required to explain thermal and electric conductivity was too large to reconcile with the facts of specific heat on the assumption that the electrons possessed the same energy of agitation as gas- molecules at the same temperature, and had proposed an alter- native theory (loc. cit., p. 86) previously suggested in his Appli- cations of Dynamics to Physics and Chemistry (1888). According to this view, the metallic atoms, owing to their close proximity in the solid state, were capable, under the influence of an electric field, of forming Grotthus chains, along which they could exchange electrons. There were no free electrons in the sense contemplated by Drude and Lorentz, with velocities depending on the temperature and contributing to the specific heat, but the thermal agitation of the atoms tended to break up the chains, so that their number and length varied with the electric field in the manner required to explain the relation between electric and thermal conductivity and many other effects. In a later paper (Proc. Phys. Soc., 27, p. 527, 1915), the same theory was applied to explain the striking phenomena of superconductivity dis- covered by Kamerlingh Onnes, who found that at very low temperatures, in perfectly pure metals, a current once started might continue for days instead of stopping almost instanta-

neously on the cessation of the exciting field. According to J. Thomson's theory, it would naturally follow that, below a cer-1 tain point, the thermal agitation would be insufficient to break up the chains when once they were formed, which would explain why it is that the electric resistance of most pure metals tends to vanish (apart from impurities) at a temperature above the absolute zero. A working hypothesis of this kind is very useful to the experimentalist as affording a mental picture of the physi- cal conditions, and may help to explain the remaining diffi- culties with regard to the specific heats.

Conductivity of Gases. Prof. Knudsen, who has made so many admirable contributions to the kinetic theory of gases on the experi- mental side, drew special attention (Solvay Report, p. 133) to the data for the thermal conductivity of gases, as being more scarce and discordant, owing to experimental difficulties, than determina- tions of other properties, and as requiring attentive examination for the elucidation of the law of action between molecules. Thi hot-wire method of T. Andrews (Phil. Trans., 1840) offers sped facilities for relative measurements, such as the comparison of coi ductivities of different gases, or of the same gas at different tempei tures, and has frequently been applied with this object in rece years. It has also been improved by introducing the usual co pensation for end-effects, and employing more accurate methods electrical measurement. But it remains liable to the difficulty depending on the small dimensions of the wire, and the uncer- tainty of the corrections for convection and radiation. For these reasons the parallel plate method, adopted by E. O. Hercus and T. H. Laby (Proc. R. S., A, 95, p. 190, 1918) for measuring the absolute conductivity of air, deserves special mention, owing to the great care with which the method was applied, and the complete elimination of convection effects. They also give a very complete reduction of previous results for different gases with the view of testing the value of the numerical coefficient / in the relation, k =fys, between the conductivity k, the viscosity ?;, and the specific heat J at constant volume. According to the theoretical investiga- tions of S. Chapman (Phil. Trans., A, 211, p. 433, 1911) the value of the coefficient / should be 2-5 for a gas constituted of spherically symmetrical molecules, which agrees with Maxwell's theory based on the inverse fifth-power law of force, and also with experiment for monatomic molecules. Unfortunately the variation of viscosity with temperature does not satisfy the fifth-power law, which requires that the viscosity should be directly proportional to T. The conclusion is that monatomic gases may have sphericall; symmetrical molecules, but that the law of force is different. Theor gives no clear indication with regard to the appropriate value of for other types of molecules. Experiment gives approximately linear relation, /=2-8i6-K 2-2, between / and the ratio of t specific heats. This gives / = 7/4 for diatomic gases, which she fair agreement with each other. The experimental values for pol atomic gases are much less certain, and suggest the need of furth investigation. The paper gives fairly complete references.

THERMODYNAMICS

Since the general principles of thermodynamics have not undergone any material change for the last 50 years, it will readily be understood that such progress as there is to record relates chiefly to matters of expression or convention, and to the practical application of the principles to engineering prob- lems. The evolution of the steam turbine and the internal-com- bustion engine, along thermodynamical lines, has illustrated the importance of an exact and consistent theory of the conditions limiting the efficiency, and of an accurate experimental study of the properties of the working fluid in either case. Thus the improvement of the internal-combustion engine has depended greatly on the extension of the thermodynamical efficiency of the cycle by using higher compression-ratios, which has neces- sitated careful attention to the reduction of heat-losses, to the properties of various fuels in respect of detonation, and to the specific heats of the products of combustion at high tempera- tures. The displacement of the reciprocating engine by the turbine for large power units has similarly depended on the possibility of improving the economy by utilizing high vacua. The high speed of the turbine has directed special attention to the importance of losses due to friction and supersaturation, which depend on the rapidity of expansion. The turbine realizes the ideal condition of steady flow with an exactitude unattain- able by the reciprocating engine. This has made it worth while for engineers to adopt the thermodynamical definition of total heat first proposed by Callendar in the loth ed. of the E.B., in place of Regnault's definition, which had sufficed for many