of Telegraphic Electromagnets. 183 



Also 



F=ra, 



where F is the magnetizing force, and 

 Gr = 47ra 2 (,# — y). 

 To make F a maximum, n being variable, we found 



EG 



Therefore 



F = 



% 



Substituting 

 we have 



\A('+S> 



V P l(x 



pl{x+y) 



^ )R forG 



Stt(x- y)W 



F 2_ P l (x+y) 



~*>( i+ t) 



Now 



W 



., L 2 m 2 Lm . , . 



1 H — ^2~ — ~"o~ approximately, 



= 2m7r *_y 24 W> 



Therefore 



12E 5 



F 2 = 5l 



Zm(^ 2 + 2xy + 3w 2 + 24tt^ 2 ) + ^ ^ 



1/17 J zir x—y 



Now the magnetization of the core is proportional to the mag- 

 netizing force ; and the attractive force between the core and 

 a soft-iron armature placed close to it is proportional to the 

 square of the magnetization and to the cross section of the 

 core. Therefore, if A is the attractive force, 



A <* 1 . (U) 



lm(x 2 + 2ay + % 2 + 24™* 2 ) + °f~ — 



J u - Z7r x—y 



