24 TransarMons of the Royal Society of South Africa. 
The equation of motion is — 
m d^^y _d'\J 
e dt^ dx ' 
mv dy 
but 4-85D = Uo, + A, 
tyiv du 
therefore - — -| = U _ Uo, + 4-85 D. 
7/, = CD I 1 + /31ogl + - 1 + /? - ilogn -t- /8 - 41-81 X 14-2 D 
e " ^ 
.9 
- y., = 373-3 CD - 593-5 D. 
The deflection at Q is given by — 
— 2/ = — + 7/,) = 470-6CD - 609-4D. 
If X be the electric intensity between the plates — 
27rD - 0-69 X, 
and we have seen that 27rC = 0-69, 
then = - 61-2 X 
e 
(5) Check Calculations . 
(a) Instead of integrating from P to 0^ in the first instance we might 
have integrated from P to O.,. In this case — 
1 + ,/?P - - 35-50, 1 + /3o, = 0, 1 + /iQ = _ 87-82, 
log 3-57, log (1 + f3o,) = - 36-96, log 1 + /:^q := 4-47. 
Then- 
mi;^ 
e 
and 
e 
= CD[i + /8 log 1 + /5 - 1 + /3 - I log- 1 + /^Jp'- 3-57 x 8-35 D. 
y, - CD [l + log r+ /3 - - i log'^ r+A'J ^ - 41-81 X 10-25 D. 
The total deflection is given by — 
e 
y = ^{yi + y-^ = - ^^05 cd - 457-1 d, 
y = - 61-1 X. 
e e 
mv 
(h) Let us integrate from P to a point M midway between and O.,. 
The value of log (1 + fti) is approximately — (^2^ ~~ 
therefore— log (1 + [3^) = - 18-98. 
(l + /:?p) =-35-50, (1 +/9m)=0, 1 + /?q = 87-82, 
log l + /8p = 3-57,. log (1 + /5m) = - 18-98, log (1 + ^q) =: 4-47. 
