436 PROCEEDINGS OF THE AMERICAN ACADEMY. 



When d = or m = 1, the amouut of electricity on the sharp edge is 



9 = i ^logl=0 



and we find there is none. 



To find the quantity of electricity on the upper surface of the upper 

 plate, we find the quantity which lies on the plate from the corner B, at 

 which t = 0, to a point P on the upper surface such that the correspond- 

 ing x is a large multiple of h. 



We must, however, agree to keep a small so that we can neglect it in 

 comparison with the value of t we choose. From the general equation 

 (a) we have 



z w 2 + 1 . _ , . . (m + l) 2 



m 2 + 1 , m 2 — 1 m 2 — 1 

 2-log— 2- + ™log — ^-; 



a; m 2 + 1 , . . m ! +l, . 



" c = ' ~~f~~ g ' + "I - " g 



o log (m - 1) = log (m + 1) 



and very approximately since 1 1 1 is large. 



x m 2 + 



1— *=1 + 7,+ 



- ^g ^1 + ^J - * ^ log (m - 1) 



and 



C ' 2 



(m + l) 2 ffl 2 +l, , 



- V 2 log (m + 1) + - 2 — log 4 (e) 



1 n-m 



C~ h ' 

 The quantity of electricity on the upper plate from t = to t = P is 



9 = 4~7 2 [log ( ' ~ 1} " iv l = HT 2 log (1 ~ t) ' 



