262 



Dr. J. W. Nicholson on the Number of 



half integers. In the following table the nearest integer, 

 and the percentage difference from it, is shown in each case. 



Table VI. 



Metal. 



Nickel 

 Cobalt .... 



Silver 



Copper .... 



Gold 



Magnesium 





Nearest 



p- 



semi- 





integer. 



1-87 



2 



2-45 



Oi 



~2 



2-49 



2| 



2 63 



2* 



2-52 



2* 



314 



3 



Per cent, 

 difference. 



65 



2 



04 



52 



08 



466 



Metal. 



riatinum . 



Lead 



Cadmium . 



Tin 



Zinc 



Aluminium 





Nearest 



p- 



semi- 





iuteger. 



310 



3 



4-48 



^2 



4-24 



4or4£ 



4 92 



5 



4-87 



5 



5-89 



6 



Per cent, 

 difference. 



33 

 0-44 



1-6 

 26 

 1-8 



Now the percentage difference between successive half 

 integers is 8J, even for the case of aluminium. For nickel, 

 which gives an apparently large difference, the percentage 

 from the half integer on the other side is about 20. Our 

 differences are all very small, and they are always within the 

 experimental limit of accuracy. The only exception is cad- 

 mium, and in this case it is significant that p = 4*24, or 

 exactly a quarter of an integer. 



The closeness of the value for silver to 2-^ is very striking, 

 especially when its behaviour in other respects is taken into 

 account, together with the detail of Drude's experiments 

 w r ith it. 



It is not proposed to say more about these numbers at 

 present, as the results of another paper, shortly to be pub- 

 lished, on the dispersion of light by metals, confirm these 

 results in some det;iil. But it would appear that the exact 

 number of free electrons per atom in a metal can be found, 

 and results obtained which may tend towards a comprehension 

 of the structure of the atoms of the elements. 



It is evident that the assumption of a dielectric capacity 

 of 1*8, and of five free electrons for every two atoms of 

 silver, gives a mathematically precise account of its behaviour 

 towards sodium light. We shall afterwards prove that the 

 same assumptions can explain its behaviour towards red light. 

 Drude's theory does not lead to conclusions so exact, although 

 these conclusions are a complete vindication of the ideas from 

 which Drude started. His experimental results are funda- 

 mental to the conclusions. 



It is to be noted that the actual value of p is proportional 

 inversely to the assumed value of elm for the negative 



