444 Mrs. K. Stratton and Prof. J. R. Partington on 



different constants are nsed for ortho-, meta-, and para- 

 compounds. The value of k in Baud's formula, for 1 gram 

 molecule, Narbutt gives as 272' d. Narbutt attempts to apply 

 the Nernst-Lindemann formula, the frequency being calcu- 

 lated by Koref 's rule (see Partington, ' Thermodynamics/ 

 pp. 527, 530), but with unsatisfactory results. 



H. Gr. Wayling (Phil. Mag. xxxvii. p. 495, 1919) proposes 

 the rule ?iL/T TO = N ; in this equation N" = number of atoms 

 in molecule, n is the " molecular number," i. e. the sum of 

 the atomic numbers of the atoms in the compound (H. S. 

 Allen, Trans. Chem. Soc. cxiii. p. 389, 1918). In the case 

 of salts containing water of crystallization, and in the few 

 organic compounds considered (except formic acid and 

 chloroform), this rule breaks down. 



The most attractive theoretical investigation we have met 

 with is that of K. Honda (Sci. Rep. Tohuku Imp. Univ. 

 vii. p. 123, 1918), which is based on the quantum theory. 

 The atoms or molecules in the solid are allocated an amount of 



energy e=hv (e% -l\ =k/3 ' (e^ -l\ or B./3 / (e^ -l\ 



per gram molecule. The constants h and k are Planck's 

 constant and Boltzmann's constant, respectively, /3 = h/k is 

 an absolute constant =4- 8 63 x 10 ~ n , and R = N /c is the gas 

 constant per gram molecule. Rotational energy in the solid 

 is assumed to be small, except at very high temperatures. 

 The molecules set free on liquefaction are assumed to retain 

 the energy referred to, but to acquire also rotational energy 

 corresponding with 2 or 3 degrees of freedom, the energy 

 per degree of freedom being -Je. The total energy acquired 

 on fusion will then be, per gram-molecule, jST e = E or -|E, 

 according as the liquid molecules have an axis of symmetry 

 or not. Thus ML = ^mE, where, n = 2 or 3. The value of E 

 is calculated by Einstein's formula (given above) with a 

 value of v, the frequency, given by Lindemann's equation : 



v=3-08xl0%/|!r 



This formula is applied both to elements and compounds, 

 and it is noteworthy that although n is 2 in the case of many 

 elements, the value 3 is also required for some elements 

 (e. g. zinc) usually assumed to be monatomic. Honda 

 obtains a fairly satisfactory agreement for a number of 

 elements and compounds, although in some of the latter 



