574 Dr. A. C. Crehore on an Atomic Model 



Hence the value of (RA 2 ) -3 is obtained in terms of u and 

 and the constant, s, as follows : — 



lRA,)-«=.-«[a +3/3 2 Q + fi/3/(j) 2 +10/8,'Q 



-(3/2 + 6 



„ + 15 „ 



+ 30 



55 



....)« 



+ (15/8 + 9 



„ +105/4 „ 



+ 60 



55 



. . . i 



. . .)« 2 

 (29) 



J 



The equations (20) and (29) furnish the material for the 

 investigation in terms or circular motion. But we shall 

 restrict ourselves to tho-e terms only in the final result 

 which at great distances vary inversely as the square of 

 the distance, r. Contrary to the result using the Larmor- 

 Lorentz equations, there are no terms here of any lower 

 order than the inverse square. Terms were found in the 

 inverse first power of the distance, using their theory, which 

 are difficult of physical interpretation. 



In restricting ourselves to the inverse square terms certain 

 simplifications may be made immediately in the general 

 equation. First, it is only necessary to use the first line of 

 (29), since each succeeding line raises the order in r because 

 of the n, u 2 , etc. 



Except for the R that appears indirectly in (20) through 

 the sines and cosines (see (7)), it is correct to use the approxi- 

 mation that Ji = s —r at great distances. Also all those terms 

 not containing x, y, ~, or R in (20) may be omitted as con- 

 tributing nothing to the inverse square terms. With these 

 simplifications, and writing for x, y, and z the direction 

 cosines, X, Y, and Z, equal respectively to x/r, y/r, and z i\ 

 the force in (20) becomes 



+ /3A(S 1 S 2 Y+ SAY cos *)}i 

 + [-Y-fAS 2 



+ /3 1 /3 2 (S 2 C 1 X + CAY cos a)]j 

 + [ — Z — /5 2 C 2 sin a 



+ AA(SAYsin« + S 1 S s Z 



+ CA (X sin a + Z cos «))] k j r(RA s ) ~ 3 , 



. . . (30) 



