446 Mr. H. T. Flint on the Applications of 



Thus if _ , T _ dio p.— 



p=E + VuH, ^-=— SEu, 



and making use of the Principle of Relativity, the physical 

 laws being unaltered by transferring to S'. 

 We have 



p' = E' + V(yiT), ~ = -SE'u'. 



On making the appropriate substitutions in (xvi.) and 

 (xvii.) and remembering that 



, u + v(l-/3)Suv-/3w , ... N 



U = - o/i o N • • • • (xvin.) 



We find 



E'+v(I-£)SE'v = /9(E-t<VHv), . . (xix.) 



and this contains the well-known formulae 



E; = E Z , E/=/3(E y -*,H,), E; =/ 8(E r + v H y ). 



On application to the expression (H — VuE) we obtain in 

 the same way 



H X ' = H„ H/=£(H, + t>EJ, H/=£(H, + t?E,), 



or H' + v(l-/3)SHV=/3(H + ^VEv). . . (xx.) 



10. The Field due to a uniformly moving electron. 



The case of the uniformly moving electric charge can be 

 easily dealt with by means of equations (xvi.) and (xvii.). 



The problem is to determine the field at a point in 

 system S due to a charge moving with velocity vv. If the 

 system S' moves with this velocity the charge is at rest in 

 that system, and from the point of view of 8' observers the 

 case is electrostatic. 



Consider a charge, e, at rest in S' and suppose there is a 

 unit charge at a point P' moving with velocity u'. We shall 

 ultimately write u'=— vv, so that P' is at rest in S. 



The force on P' is 



. e i € . 

 p' = 7 j - . ri = -,3 . r', 



where r/ is the unit vector in the direction from e to P'. 

 Let e be situated at the origin for convenience. Also 



dw' e , 



where r' % means the cube of the tensor of x' . 



