Dispersion of Diamond. 397 



squared frequency 7, the equation of motion of the i-th 

 electron gives, for an}- arrangement of equal centres, 



(7o-7)R- C 2"J [3u(up,)-p 7 .]=i?G, 



where y is the squared free frequency, common to all 

 the electrons, u the unit vector drawn from the i-th towards 

 the j-th centre (or vice versa), r the mutual distance of these 

 centres, and G the force on the i-th electron, per unit charge, 

 due to the external field E and due to all those doublets not 

 already taken account of under the sign of summation. 



If the sum, in our case a triply infinite series, embraces 

 all the centres, that is to say, all " neighbours " of i, no 

 matter how distant, then the force G- reduces simply to E. 

 For, according to the opinion generally held, electromagnetic 

 phenomena are influenced by particles of matter only so far 

 as these contain electric charges. Now, in the case of our 

 present problem it will be easy to exhaust all centres. 



Thus, 



7 V /p ^Sr5 7 k^(^)-P;]=E. . . (1) 



According to Bragg, diamond consists of the superposition 

 of two face-centred cubic lattices, one of which is obtained 

 from the other by translating it rigidly along a cube diagonal 

 one-quarter of the length of the diagonal *. Each point of 

 both lattices is occupied by a carbon atom. The result of 

 this superposition is that each carbon atom occupies the 

 centre of a regular tetrahedron whose four corners are 

 occupied by the four nearest neighbours of that atom. The 

 relation of this tetrahedron to the original face-centred 

 lattice is well-represented in fig. 1, drawn in perspective 

 (for which I am indebted to Mr. E. Hatschek). The lattice 

 points are the centres of the five spheres drawn so as to be 

 in contact with one another. The rough sketch, fig. 2, corre- 

 sponding to Bragg's photograph on Plate III. of his work, 

 represents a number of centres linked up by straight lines 

 to their four nearest neighbours. (The actual distance of 

 nearest neighbours, i. e. centres, or in usual notation f <r7 1]1} 

 is 1'54 . 10 ~ 8 cm. This, however, is irrelevant for our present 



* W. H. and W. L. Bragg, ' X-Rays and Crystal Structure/ London, 

 Bell Q915), pp. 105 et seq. A beautiful construction of the "funda- 

 mental domains " of Bragg's diamond lattice was given by L. Foppl in 

 Phys. Zeitschrift, vol. xv. p. 191 (1914). 



