158 ME. GEORGE W. WALKEK ON THE INITIAL ACCELERATED 



When f(t) = we get the equations for the case of uniform motion, and as a 

 solution of these equations independent of time, we get 



_ A o .. 7,<ty,, , 3/ 



a u > Po A* -p ) 7o I* -p , 



V t-( l-*\ ^ V tyo 7 3l// 



*'"a' "fy' Z = "IT' 



where <// is a solution of 



/ , p\ 3 a / , 3 2 <Ao , aVo _ n 



\ A * / "K 9 1 ^ -J > -- ^ o " 



7 2 3 2 



In order to pass to a disturbed motion, we may assume f(t) to be small, and that 

 the electric and magnetic forces differ from the steady values by X, Y, Z, a, /8, y, 

 which are small of the same order as f(t). 



Hence, neglecting squares and products of small quantities, the fundamental 

 equations are 



^ ^ O ^ ^ *^ /~) ^ \ -| / *~\ ^v _// / , \ f\ 



tj 8^ ra fy d^ da\._ 1/3 ,^8 , , y y , _/ () 8 



'f-i, Sz' a7~^' a^ e^/"c\8T" " 



r.y az ?z r-x ax ay\ i /a 





c 



= , 



8x dy dz 



ax 3Y az 



"5 -- r ~ -- r "^~ u - 



do; cy dz 



When condition (l) is used it is convenient to assume the system 



a- 0, 



1 5V 7 . 

 C 3 3 



^2 i ^2_I 



Y - _ /I _7-^ /- y" _ ^_? _ 



j/ 

 v _ / 3 2 (/> n 





3*32;' 

 where </> is a solution of 



