L. Page — Fundamental Relations of Electrodynamics. 67 



Consider two charges e l and e 2 at A and B (fig. 3) respec- 

 tively. Let the charge at B be at rest relative to the observer 

 in K (0), and the charge at A be moving to the right with the 

 velocity v. While e i is at A the acceleration /"is applied to it 

 in the direction of its velocity v. Let AB = r = rf. BE is 

 an arc with A as center and ct as radius, CD an arc with A as 

 center and c (t — dt) as radius. If, as before, we define the 

 intensity as proportional to the density of the lines of force at 

 the point considered, the force just to the left of B will be 



e, e. 



0-v) 



sin a 



provided v is small compared to c. So the intensity at the same 

 point due to e, will be 



„ / «* \ 3 sin a 



If we denote by E„ and E 7 the components of E parallel to 

 and perpendicular to the radius AB, 



E *(-*) E ±$ , 



»' ( 1- — -sin 2 01* r» (l - -j sin 5 j * 



So we see that the component of the force parallel to the 

 radius AB is continuous through the pulse. 



, T ft sin 6 . . v . 



JNow cot a = it — is small. 



c c 



E = — sin 6 



re' t. v* . , \ 

 sin 6 



If we replace e, by a current element ids 



(l --£*,-»)* 



<& sin 

 ' dt r v 



in electromagnetic units. 



