Frequency and Atomic Number. 481 



An examination of the figures in the last column of the 

 table shows a maximum divergence of about 3 per cent, 

 from the mean value of v A . This is too large to be accounted 

 for by uncertainty as to the experimental data (T S} A, V) 

 used in the calculation of the frequency, so that we are 

 forced to conclude either that Lindemann's formula is not 

 exact*, or that the proposed relation Nv = nv A is only an 

 approximation. 



A comparison of the two columns of integers in bold type 

 reveals the unexpected result that the integer required for 

 the frequency determined from the specific heat is not in all 

 cases the same as the integer required in connexion with 

 Lindemann's formula. For Al and Zn the same integer 

 appears in both columns of the table ; in the other cases 

 there is a difference of one unit between the figures in the 

 two columns. There does not appear to be any obvious 

 regularity in the relative position of the larger unit. 



This surprising result at first produced some degree of 

 scepticism as to the trustworthiness of the relation in question, 

 but similar results have been found in such a large number 

 of different cases that it is almost impossible to doubt the 

 general accuracy of the relation. 



The atomic frequency has been calculated by means of 

 Lindemann's formula for all elements for which data are 

 available. The results are given in the following Tables. 

 Where the data are uncertain the frequency is in brackets. 

 In such cases the value of Nv is to be regarded merely as 

 giving the most probable value of the integer n, which may 

 be called the frequency number. 



An examination of the figures in the column headed 

 Nz^xlO -12 makes it difficult to escape the conclusion that 

 the product. Nv may be expressed as an integral multiple of 

 a constant frequency of about 21 x 10 12 sec. -1 It is true 

 that little weight can be attached to those cases where the 

 product has a large value, for then it is always possible to 

 choose the integer to give a suitable value for v A ; but even 

 if we exclude all elements for which the frequency number 

 is greater than 10, sufficient instances remain to make 

 our conclusion secure that the coincidences cannot be 

 accidental. 



At the same time we must admit that for 14 elements not 



* A conclusion reached from theoretical considerations by Griineisen, 

 Ann. d. Physik, vol. xxxix. p. 298 (1912). The same result would follow 

 from Sutherland's argument if t&T g were constant only for similar 

 elements. 



