4:14 Prof. S. R. Milner : Does an Accelerated 



Cartesians, the flux becomes 



H-W§}s«yiy. . . . (14) 



■m 



Esin0 



47T 



Here # and y are the co-ordinates of a point of constant ^ 

 on the surface (5), which is bodily moving through space 

 and at the same time altering its shape since f and ft are 

 functions of t. To effect the integration we substitute 



, _ fix "bw ~d^r\ j doe _fix , ~&x ~d^r \d% 



etc., and use the transformation equations (3). On writing 

 for E and H, X, W, and 6 their values (4), (12), (13), and 



(9), and substituting for yfr, — ^- , -— everywhere their 



values in terms of x and f obtained from (5), and then 

 expressing by (1) f in terms of A afid ft, (14) becomes a 

 determinate function of %, which, integrated from to ir, 

 gives the net flux outwards from the boundary. On finally 

 taking the limiting value when a is indefinitely small, it 

 reduces to 



ke 2 (l-ft 2 ) 2 C JT {l + 2 coa 2 x + ft 2 ^^x) sin X d X 

 4«£ Jo (1-/8* sin 8 X )* 



ftce\l-ft*) C* sin X <fr 

 3a£ J (l-^siii 2 ^; 



The first term represents the flux corresponding to the 

 electronic field E, H alone, the second the additional flux 

 due to the superposition of the field X. On integration 

 the net flux outwards becomes 



B^ 1 -^ (15! 



The internal energy is given by (7), and its rate of 

 decrease with the time, in the existing state of motion (1), 

 is identical with the expression (^15) for the net outward 

 flux. 



It follows that the total energy of the system is conserved. 

 As the electrons are being brought to rest, a continual 

 process of conversion of magnetic energy into electric is 

 going on in the field, and at the same time field energy is 

 being transferred into the nucleus, where it shows itself as 



