570 Dr. A. 0. Crehore on an Atomic Model 



term shows that the force (2) is in a direction opposite to the 

 direction of motion of the second point. 



Since the Saha notation differs from that employed by the 

 writer, let the above equations be converted into the symbols 

 heretofore used. The subscripts, 1 and 2, are preferred to 

 the prime letters. The vector r in (1) is equivalent to the R 

 denoting the vector from the position of <? 2 at the time t—~R/c 

 to that of e x at the time t. The scalar uv cos 6 may be 

 replaced b}^ q { . q 2 . The Saha j3 and ft' may be replaced by 

 J — ft 2 and 1 — y8 2 2 , where fii and j3 2 are used in their 

 common sense as the ratio of the velocity of the point to that 

 of light. The Saha X is defined as l — Vr'/c, which is taken 

 to be a misprint for 1 — XJ'r/c. This quantity is the equiva- 

 lent of the expression that we have denoted by 



A 2 = l— q 2 .R/cR, 



and similarly A x = 1 — q 1 . R/cR 



is the equivalent of his 1 — JJr/c in (2h Making these 

 changes in notation the two Saha equations, (1) and (2), 

 combine iuto the single equation 



-"■ y(i- / 3 i 2 )»l (1_ ? qi - qi)E — T q2 r (i) 



(RA,)' 



The investigation of the problem may be divided into three 

 stages (1) to express the instantaneous force upon one ele- 

 ment of the first ring due to one element of the second ring 

 in terms of the circular motion ; (2) to integrate these forces 

 around each ring ; (3) to average the force for all orienta- 

 tions of the axes of the rings on the assumption that all 

 -directions are equally probable. 



I. 



The Instantaneous Force upon One Point Charge in Circular 

 Motion due to a Second Point Charge in Circular Motion. 



Let 0] and 2 represent the fixed centres of the orbits of 

 the point charges <? x and e 2 , and let the vector, r, represent 

 the constant distance Ox0 2 . Let there be two sets of rect- 

 angular axes, i,j, and k, having origin at Oi and i',f, and h r 

 with origin at 2 . The h and k' axes are each perpendicular 

 to the planes of their respective orbits, the positive directions 

 along each being defined so that the revolution is clockwise 



