﻿752 Dr. A. 0. Crehore on the Construction of 



Expressing all distances in some convenient small unit %, 

 such as the radius of the orbit in the single electron atom, 

 instead of in centimetres, and letting m and n represent the 

 radii of the orbits and x*, y%, and z# the coordinates in these 

 units, we have 



#=a*j?*; y=a*y*\ z = a%z#; a = ma*; a' = na*. (10) 



The value of s in (5) becomes 



or, denoting the radical by A -1 , we have 



s = a*A~\ (11) 



and from (4) 



R- 3 =a- 3 A 3 (l + u)-t (12) 



Hence, substituting in (7), (8), and (9), 



F x = - ^L-A»(* # -mS + nS' cos a)(l + u)~% . (13) 



P 1 =-^-A«(y.-mO + nC'Kl + «)~*;, • • (^) 



06 



Ka! 



A^+nS'Bin.Xl+u)" 1 *. . . (15) 



This completes that part of the mechanical force which 

 arises from the first or electrostatic component. It remains 

 to consider the magnetic effect, which is derived from the 

 three component forces given by equations (2), (3), and (4) 

 of the former paper *. 



It has been previously shown f that the last two of these 

 terms when integrated contribute nothing to the transla- 

 tional force of the one charge on the other, so that the total 

 force will be obtained by considering, in addition to the 

 preceding, the force 



F 2 = + ^(q.q')E 06) 



Here the new quantities are /a, the magnetic permeability of 

 the medium, and q and q', the vector velocities of the charges 

 respectively. It was shown in the former paper that 



q .. q' = aa W( (XT cos a + SS'), . . . (17) 



* Loc. cit. p. 58. 

 t Loc. cit. p. 63- 



