396 



Dr. L. Silberstein on the 



= 0-40. 



c = 0-50. 



u. 



u. 



r. 



Usin0. 



u. 



U. 



r. 



Usin (j>r 



•02 



1-091 



11-2 



1-091 



•02 



1104 



100 



1-093 



•04 



1-127 



814 



1-106 



•04 



1-149 



7-25 



1-148 



•06 



1155 



6-72 



1-153 



•06 



1-184 



5-97 



1-151 



•08 



1177 



5-87 



1-138 



•08 



1-213 



5-20 



1-089 



•10 



1-195 



5-32 



1-086 



•10 



1-238 



4-71 



1-102 



•15 



1-229 



4-46 



1122 



•15 



1-289 



3-96 



1-230 



•20 



1-255 



3-95 



1-199 



•20 



1-328 



3-49 



1-308 



•25 



1-273 



3-68 



1-240 



•25 



1-357 



3-26 



1-352 



•30 



1-284 



3-46 



1-267 



•30 



1-380 



303 



1-380 



•35 



1-289 



331 



1-281 



•35 



1-398 



2-88 



1-396 



•40 



1-291 



3-20 



1-285 



•40 



1-406 



2-77 



1-399 



•45 



1-289 



310 



1-289 



•45 



1-412 



2-69 



1-399 



•50 



1-285 



3-02 



1-285 



•50 



1-414 



2-62 



1-396 



•55 



1-279 



2-97 



1-279 



•55 



1-414 



2-57 



1-390 



•60 



1-269 



2-93 



1-268 



•60 



1-413 



2-53 



1-384 



•70 



1-248 



2-86 



1-246 



•70 



1-392 



2-47 



1-356 



•80 



1-222 



283 



1-220 



•80 



1-368 



2-44 



1-324 



•90 



1-195 



2-81 



1-192 



•90 



1-337 



2-42 



1-295 



1-00 



1-167 



2-81 



1-164 



100 



1-306 



2-415 



1-260 



XXXIV. On the Dispersion of Diamond. By L. Silberstein, 

 Ph.D., Lecturer in Mathematical Physics at the University 

 of Rome*. 



THE object of the present paper is to apply the concept 

 of electrical interaction of atoms, developed in previous 

 papers f , to the refractive properties of diamond considered 

 as a known assemblage of fixed "atomic centres/' each 

 containing a single dispersive electron and becoming a 

 doublet in presence of an external electric field. The 

 assumption of the mutual immobility of the " centres " 

 themselves, i. e. of the whole atoms, need not be given up until 

 one comes to contemplate the infra-red free frequencies ; 

 the ultra-violet ones, which chiefly interest us for the present, 

 can all be thrown upon the electrons. 



Consider a space lattice of points, indefinitely extended in 

 all directions. Let all these points be occupied by the 

 centres of equal atoms, each containing a single electron 

 whose charge and mass are e, m. Write D = e 2 jm, and 

 denote by the vector p; the electric moment of the doublet 

 produced at the i-th centre by the electric force E of the 

 incident light-wave (and by the co-operation of all the 

 remaining doublets). Then, for monochromatic light of 



* Communicated by the Author. 



f For what follows it will suffice to consult the second paper on 

 " Refractivity and Atomic Interaction," Phil. Mag. vol. xxxiii. p. 521 

 (1917), more especially the general formulae (2), (3) on p. 522. 



