Frequency and Atomic Number. 487 



has been made for want of accuracy in the formula or in 

 the experimental data, it still appears probable that the same 

 element may have different frequency numbers according to 

 the physical conditions and the particular modification of 

 the solid state that is under examination. 



It has usually been assumed that the various frequency 

 formulae are equivalent to one another. 



Thus, if the formulae of Einstein and of Lindemann give 

 the same frequency, 



W(V*/KA) = £ LV /(T s /AV»), 



and therefore V/KT 5 should be constant for different elements. 

 The experimental values, however, are in agreement with 

 this conclusion only in particular cases *. A reason for this 

 may now be assigned. Instead of identifying the frequencies 

 given by the two formulae, Ave must put 



Ny E = n E ,/ A and Nv L = ? W 



where the subscript 15 or L refers to the author of the 

 formula employed. 



Hence v E n E 



n 2 Y 



from which it follows that 9 ^ must be constant for 



different elements. It is only in those cases in which 

 n L = n v ^hat ^ ie simpler expression can legitimately be 

 employed. 



§ 8. Conclusion. 

 The frequency formulae here considered, unlike the formula 

 of Debye discussed in a former paper, have an undetermined 

 constant, the value of which must be found experimentally. 

 The formulae themselves are to some extent empirical, and 

 it cannot be -*aid with certainty that they are applicable to 

 all elements without modification. It is, therefore, the more 

 remarkable that for the majority of elements the frequency 

 calculated by these formulae conforms to the relation 

 Nv=??v A . It appears from the results that, for a particular 

 element, the frequency number, n, is conditioned by the 

 physical state of the solid. Broadly speaking, the number n 

 varies in a periodic way with the atomic number, but the 

 discussion of the dependence of the value of n on the place 

 in the Periodic Table is deferred till it can be dealt with 

 more completely. 



* Einstein, Ann. d. Physik, vol. xxxv. p. 679 (1911) ; Griineisen, 

 Ann. d. Physik, vol. xxxix, p. 300 (1912) ; Richards, Journ. Am. Chem. 

 Soc. vol. xxxvii. p. 1643 (1915). 



