﻿and its Relation to the Quantum Theory. 857 



performed, (10) becomes to terms of the 7th order in w : 



^ 2 [1 - l-5to cos 2 B; + -375w 2 cos 4 Bt + -0625m; 8 cos 6 B* 



+ 'Q2344i0 4 cos s B* + "01172w; e cos 10 Bt + '00682m; 6 cos 12 Bt] 

 + /oj/875 + 7'5w cos 2 B^ - 4-12510 2 cos 4 B; + 1 '9375m; 3 cos 6 B* 



-F96094m> 4 cos 8 B* + -78516^ cos 1 * B* 4 -69830m; 6 cos 12 B*] 

 -fp[-3w-l-5M? 2 cos 2 Bi-l-125^ 3 cos 4 B«--9375^ 4 cos«B^ 

 -•82031m; 5 cos 8 Bt - -73824m; 6 cos 10 Bt] 

 = [C-'S15 + w--0625ivcos 2 Bt-'015625w 2 cos i Bt 



- -0078 13«? 3 cos 6 B* - -004882it' 4 cos 8 B* 



-•003417m; 5 cos 10 B*-'002563ti- 6 cos 12 B£--002016z*; 7 cos 14 B*] 



4-sm^cos Btf[3 — 6m; cos 2 B£ + 3m; 2 cos 4 B£] 



+ % [— 3 + 3to cos 2 B*] + /o 2 [ - 4'5m; cos 2 B* 



— 12ic 2 cos 4 B* + 4'5io 3 cos 6 Bt - 3m> 4 cos 8 Bt - 3m; 5 cos 10 B*] 

 + p 2 [3iu + 3i^ 2 cos 2 B^ + 32y 3 cos 4 B^ + 3ie 4 cos 6 Bi + 3^ 5 cos 8 B^] 

 + 5 2 [l-5-10-5wcos 2 B^+16-5io 2 cos 4 B^-7-5w 3 cos 6 B^] 

 + psicico&Bt[ — S+ 19-5^— 23'625m; 2 cos 4 Bt 



4-5-4375i<r 3 cos <5 B*4- > 8672z<: 4 cos 8 B£] (12) 



Similarly, equation (11) becomes 



4- +s=3pwi cos B* [1 - -'5w cos 2 B* - -125010 s cos 4 B* 

 B 



- -0625m; 3 cos 6 B* - -03906m; 4 cos 8 Bt - -02734m; 5 cos 1o B* 



-•02051m; 6 cos 12 Bt] 

 H- dies cos 2 Bt + phv* cos Bt[-6 + 7* 5io cos 2 Bt] 



+ * 2 [4-5ti^ cos B* - t-5ufl* cos 3 Bt] 

 4ps[3-15iucos 2 B(][l--5z<;cos 2 B£--125Ot0 2 cos 4 B* 

 -•0625m; 3 cos 6 B^-'0390iu 4 cos 8 Bt- '0273m; 5 cos 10 Bt] 

 (13) 



Let us now assume that p, s, and G can be expanded as 

 Phil Mag. S. 6. Vol. 44. No. 263. JS 7 ov. 1922. 3 K 



