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XXV. A Method of finding the Scalar and Vector Potentials 

 due to the Motion of Electric Charges. By Prof. A. Anderson*. 



LET the coordinates of a moving electron be 3s = ^>(t), 

 y = TJr(t), z = x{t). Let AQ be its path, and Q its 

 . . r 

 position at time t : also let Q' be its position at time t , 



c 



Fij?. 1. 



" ■ X 



where r— Q'P, and c is the velocity of light ; then the co- 

 ordinates of Q' are a; = </>(£ — J, y = ijr(t — ), £ = %(£ ■). 



In what follows, we shall use the symbols (f>, ^, x t° denote 



these functions of t — • Thus the component velocities of Q' 

 are <£', yfr', X f - 



Let %= [(f)'(x — </>) +^ / (y — yfr) +%'(«— x)]/ c '• we want to 



show that if A = ^, A satisfies the equation of wave- 



. r — £ 



propagation, * 



VA c*W 



0. 



Since r % = (x— <£) 2 + (y— -ty-f+ [z— %) 2 , we have 



<* 



and 



Bf 



x>- 



3* ~ r-f 



Br _ 



c)£ r — f 



where A, denotes the quantity 



[*"(»-*)+f(»-^+/.M^ 



* Communicated by the Author. 



