422 Some Fundamental Concepts of Electrical Theory. 



To discuss the first case we must find the condition that 

 the generalized fields of two moving point charges may be 

 incident. In other words, we must find the condition that 

 there may be a relation between %, t, % > and t , where % 

 and t refer to the second point charge. 



Writing 



Z-£+c(t-T)> 



b = 



x — %—i(y — rj) 



%= 



and remembering that « depends only on a and t, we may 

 write 



^-T)[^ , (a + 6)-V / (a-/>) + r / (l-^)]+(l + a5)(c 2 -r 2 -V 2 ~t 2 j 

 «(*— T)[%\a + b) — iriXa-b) + Z(l-ab)-c(l + db)\ 



+ F(a,r) + F»(6,-T). 



The expression for % is similar to this ; on the other hand, 

 we have 



_ f+e(i _ T) ^. =fo+c( ,_ To) ^±| o - 

 *= f+^- T) - 1 _ fe = &+C ( i _ To ) T __ 



Let us write 



f~ fo-r^t?? — %)=>, ?~f — i (v-Vo) = q, 



?-?o + c(t— T ) = r, ?— ? - c ( T — T o)=«, 



pq-i-rs = fc 



then we find from equations (13) that 



2c(£ — T)[a£ + 5p— aftr-f 5]+/c(l + a6)=0, 



2c(£ — T ) [«g + ftp — «&y + s] + (</a + 5) (p& + 6') 



+■ (rb — q) (ra ~p) = 0, 



pb + s , _qa + s 



rb — q ra—p 



Now put 



£ +?'?7 =X, £ — IT} =fJL, f +CT =V, £ — CT =/J, 



fo + ^o = ^o> ?o— ^7o=/a , ?o-+ct = v , ?o — ^o = Po; 



