22 Prof. F. A. Lindemann on the 



Hence logj? = 



HT~ ~RT~ + ~Tl~ l08 i+ "R~ i+ • • • 



It is clear that every term of this series is a pure number 

 with the exception of the third, which has the dimensions of 



the logarithm of a temperature to the power -~ — -. One 



must conclude, therefore, that the dimensions of C are those 



of the logarithm of a pressure divided by a temperature to 



., &! — rti 



the power - — ^— . 



Now bi and a v are clearly the atomic heats of the gas and 

 the solid at the absolute zero, and there seems little doubt 

 that «], and for that matter a 2 and a 3 , are zero. Therefore, if 

 the value of b 1 — a i can be found it will be a measure of the 

 atomic heat of the gas at the absolute zero. 



Assuming the chemical constant C to depend only on m, 

 the mass of the atom, k, Boltzmann's constant H/N, and li y 

 Planck's constant, a simple dimensional consideration shows 

 that it must be of the form 



Log 



m 3/2£5/2 5 / 



P 







Therefore it must be possible to represent it by an expression 

 of the form 



C=K + 3/21ogA + (5/2-/> 1 /R + a 1 /R)log(9, 



where K is a constant, A the atomic weight, and 6 some un- 

 known temperature which can only depend upon the tempe- 

 rature at which according to the " degradation " theories the 

 gas laws cease to hold. 



Unless 6 is equal for all elements * 3 and this is scarcely 

 conceivable in the case of substances of such divergent 

 characteristics as say mercury and argon or cadmium and 

 hydrogen, a study of C should enable one to form some idea 

 of the value of b x since ai = 0. Now it has been shown that 

 C may be represented within the limits of error by 



C=K+3/21ogA. 



* This assumption was made in the case of isotopes in a recent paper 

 (Phil. M-Rg. xxxvii. 1919, p. 523). It is readily seen that the question 

 there considered, i. ?.,the difference of the chemical constants of isotopes, 

 is unaffected by which of these -views is taken. 



