﻿Construction of Cubic Crystals with Theoretical Atoms. 751 



R is the vector from the charge e to e' varying with the time, 

 and F x is the first component force which the second charge 

 e exerts upon e. Using the abbreviations 



S = sin(a>* + 0); S' = sin («'*+ ! )\ C = cos [cot + 6) ; 



C'=cos(ft>'* + 0'), . . (2) 



where g> and to' are the angular velocities of the charges and 

 6 and & their phase angles respectively, referred to fixed 

 rectangular axes, it follows that 



R=(^_aS)i + (y-aC + a / C , )i + ^ + a'SV, . (3) 



where i, j, and k, i', f, and k' form two systems of rect- 

 angular axes, referred respectively to the centres of the 

 orbits of e and e'. k and k' take the directions of the axes 

 of revolution of the electrons, each being clockwise when 

 observed from the positive side or pole, j and f each take 

 the direction of the line of intersection of the planes of the 

 orbits, the positive direction along each being defined by the 

 vector kx k'. i and i' lie in th« planes of the orbits respec- 

 tively in such directions as to make the two systems of axes 

 each have the conventional cyclic order i,j, k and i' 9 f 9 k\ 

 in the counter-clockwise rotation when viewed from the 

 positive side of each. 



Hence K 2 = s\l + u), (4) 



where 5 is a constant, 



* , =^+^+fl , +o?, .... (5) 



as, ?/, and z being the coordinates of the centre of the orbit 

 of the second charge, a and a the radii of the two orbits 

 respectively, and u a function of the time such that 



u= - 2 1 — ad-S — at/C + a'zS 1 sin a -f a'yC + a'.rS' cos a 

 5 \ \ 



— aa'SS' cosa — aa'CC'l. . . (6) 



If the force in (1) is resolved into three rectangular com- 

 ponents along the i, j 9 and k axes, which may be done by 

 taking the direct or dot products with i,j, and k in turn, we 

 obtain, observing that i'.i= cos a, and /'./• = sin a, 



¥i — — y ,y 3 ( .?■ — rtS + o'S' cos afi, . . (7) 



F -- - 



>3 (y-aO+a'C'Jj (8) 



Fi = -^(* + a'S'sin«)* (9) 



