402 Dr. L. Silberstein on the 



Hence, making use of (7), 



2/0 (t — u \ - «2 2 — «3 2 — **/) = ^p('0Uill 2 + J) 



or 2jo{»l 2 + ^2 2 + w 3 2 + u i 2 + 12w^ 2 } =0. 



Now, by (6), 



i.e. %pu 1 u 2 ——^Sp i 



and therefore, n i2 = Zp(-± + i)=0, 



so that, by (7), fl a ^ — fl aa = for all values of the suffixes, i. e. 



0=0, 



for any direction of the operand. 



In plain language, the resultant action of all doublets in an 

 unlimited * diamond lattice is nil. 



Equation (1) thus becomes, for any i, 



as if there were no interaction between the carbon atoms. 



If pi is the refractive index and dl the number of carbon 

 atoms per unit volume of the crystal, then 



and therefore 9 -, 9?i? 

 /x 2 =l+ , 



Yo-7 



as in the elementary theory of dispersion. 



If X be the incident wave-length (in vacuo) and, similarly, 

 X the free wave-length belonging to the electron of the 

 carbon atom, then 



7 =4ttV/\ 2 , 7o = 47r 2 6- 2 /X 2 , 



c being the velocity of light in vacuo. Thus, with the 

 abbreviations 



M ~X 2 ' a ~47r 2 c 2 ~ JC 47r 2 c 2 ' " " • W 



* Sucli an assumption is physically equivalent to the limitation of 

 the investigation to portions of the crystal distant enough from its 

 surface. Deviations from the said simple behaviour will occur only in 

 surface-layers whose thickness is comparable with the elementary 

 spacings. It would be interesting to investigate them. 



