80 Mr. S. B. McLaren on the Emission and 



dN above and using these last results, it becomes 



is 



r*rt. ■» . 



<'^Jiy;ci{j>>.v,*.«. 



- X7 X H. VrfW^tdv^ + Covj. (42) 



dv b = dfc 1 dK 2 dfc$, dY h = dK 4i dK 5 d/CQ. 

 Also dvdY = dv b dY b ; 



*i? *2> K 3 are the coordinates at t b ; 

 and /e 4 , # 5 , k & are the momenta. 



If the equations of dynamics hold everywhere, then these 

 coordinates of position and the momenta are extended at any 

 time all over the radiating body. The first set of terms in 

 (42), being perfect differentials, vanish. 



In the second term of (42) 



Vp5 r .Vr*-V r H.Vp* = V r *.J + V,,*^from(7)&(8). 



__~d$ d<f> 



~ cK dt ' 



where -^ is the total differential of with respect to t, and 

 ~~-ij is the explicit differential. 



t -f -(-+w^|(^-- w, )+ ^- b y <«> and ( 33 >- 



And inserting this in (42) it reduces to 



... (43J 

 On integration by parts (43) becomes 





(« 9 +/S 2 ) 

 ip 



* * V + ^SM f(H) ir h ft*''*'' **) dt dtt lN + Co »J u 8' ates - («) 



