Latent Heats of Fusion. 445 



values of n much higher than 3 have to be assumed (e. g. 

 6forKF, 7£orPbCl 2 ). 



It is to be expected on theoretical grounds that the energy 

 content of molecules at the fairly high temperatures of fusion 

 would be more satisfactorily given by the formula of Debye 

 than that of Einstein (see Partington, 'Thermodynamics/ 

 p. 535 : Jeans, ' Dynamical Theory of Gases,' 2nd edit, 

 p. 422). On Debye's theory the energy content E corre- 

 sponding with three degrees of freedom is given per gram 

 molecule by 



r C 3/3,/Tn 



|c ft J* 



E = fRT 



The values of E/T for given values of /3v/T are tabulated 

 by Nernst (Grundlagen des neuen Warmesatzes, p. 206, 1918), 

 and greatly facilitate the calculations. The values of E/T 

 taken from these tables may be regarded as giving the values- 

 of 3Ey/T, where Eyis the energy per degree of freedom for 

 rotation. A comparison of E//2T with ML/2T (observed) 

 will then give the value of n, the number of degrees of 

 freedom of rotation it is necessary to assume for the liquid, 

 molecule. 



The following example will illustrate the method of 

 calculation : — 



Benzopkenone.— M = 182. T m = 321. d (density) = 1-098. 

 .-. v from Lindemann's formula = 0*7447 x 10 12 . 

 .-. /3iv = 36-2. .-. /3v/T m =-1128. 



Value of 3E//T m corresponding with /3y/T = from Tables- 

 = 5-709. Observed ML/T TO = 12-28=nE / /2T TO =12-28. 



.-. n = 12'9. This, it will be observed, is much higher 

 than any value recorded by Honda. This example also 

 serves to bring out the complete failure of Wayling's rule : 

 " molecular number " of benzophenone = 96. .-. nL/T m = 6'5, 

 whereas the number of atoms in the molecule is 24. 



In the table are given the values of Ey/2T,„ calculated by 

 Debye's formula, with the values of ML/T m from the experi- 

 mental results of various investigators. For convenience in 

 applying other quantum formulae the values of /3v from 

 Lindemann's formula are also included. It will be seen that for 

 many elements and simple compounds the modified theory of 

 Honda which has been proposed is fairly satisfactory, although 

 in some cases the interpretation of values of n greater than 

 3 is not yet clear. It is possible that the large values of n 

 represent intramolecular vibrations ; at least it seems to be- 



