Fundamental Law of Electrical Action. 359 



The form is Lagrangian, and the expression for (X, Y, Z, L) 

 comes out in the form originally pointed out by Clausius. 



We therefore prove that the force-tour-vector on (A) can 

 be put into the Lagrangian forms 



Ox citKowJ 



Y = 





dr\diu 2 / 



(9) 



dt dr\owJ 



.^ 



Similarly, if R = perpendicular distance of the point 

 B(a, b, c, \) from the axis of motion of: (A) (a, y, z, I), 



i.e., W = (x-ay+(y-by+{z-cy + (l-\y 2 



+ [(# — &)w x + {y— b)w 2 -\- (z — c)ic d + (l — \)iu 4 ] 2 , 



and <!>' denotes the expression 



-^r (wiWi 4- «0 2 w 2 ' + ^3^3' + ^4^4') > 

 the forces exerted by A on B are given by the equations 



da dT'xdwi) l$b dT\~dw 2 '/ I 



* " Be aV\Bw 3 7 ~ d* MW/J 



>-. (10) 



8. Two Electrons in Motion. 



In the foregoing sections we treated the case of two point- 

 charges. We shall now take the case of two electrons when 

 these are in a state of motion. It will be shown that the 

 same equations would hold if instead of the rest densities 

 /°o> Po'» we substitute the in variant charges (e, e'), and suppose 

 the whole charge to be concentrated at the centre of each. 



The electron occupies the space 



where (#, y, z) are the space-components of any point within 

 the electron, (# , y , z ) the corresponding quantities for the 

 centre, and r is the radius. 



