COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 431 



7^ = / dx = VX+ — — - / — = + de I 



C J x * J VX J xVX 



(147) (120) (142) 



where the numbers refer to the formulae used. In the use of (142) the 

 product de or (c — a) (c — b) must be positive ; this is true, as a and b 

 both lie on the same side of a and the differences are either both positive 

 or both negative. Hence we have 



,— ( VX+Vde t d+e 1 \ 

 As a check on this formula, put a = b ; we obtain 



a; 



— = (t — «) + (c — a) log (< — c ) + const., 

 O 



which is the same as special case (b). 



To apply this to our problem, put a = a, b — 0, c = 1 ; then we 

 have 



C 



Vt(t-a) + 2 -Y^\og(Vt(t-a) + t-\ + 2 ~Y^) 



\/t(t — a) + -v/l — « 2 — a 1 



Vl " -f=T- - + — vr^a.' + r - 



Using when convenient m = Vl — «> this equation may be transformed 



into 



wr 



jj=Vt(t-a) + -^— log 



+ i . (V't + Vt- «) 2 



, ( \/m- 1 + V< — «) 

 -'"'°° 2, .(,-1) +r - < C > 



