UNITS IN THE ELECTROMAGNETIC UNIT OF ELECTRICITY. 
709 
The Dissipation Function 
=i { bx" + a (, x — (y- + z) f + c(y- + s) 2 +#z 3 + d(rc - yf } 
The Potential Energy 
where C is the capacity of the condenser. 
Thus if E be the electromotive force of the battery, we have, neglecting the self- 
induction of the resistance coils in the circuit, 
hx+a(x — (y + z)) + d(x — y) = E 
— a{x—(y+z)}+c(y+z) — d{x—y) + j -t=0 
- a ( x ~(y+' z ))+ c i i/+ z ) +gz =o 
or 
(« + b + d)x — (a + d)y—az— E 
— (a + d)x + (ct -f- c + d)y + ( a + c)z-\- ~ — 0 
—ax + (a- + c)y + («+ c+ g)z = 0 
To solve these equations, assume 
x—n-\-pe~ M 
y=qe-* y=~{ l-e" w ) 
z=w+re-*i 
where t is measured from the instant when the moving piece P first touches S. 
Substituting we get 
_«E_ 
(a 4- c + g)(a + b + d) —a 3 
{a + c+[))¥, 
(a + c + g)(a 4 b 4 d) — a? 
_£_ {(a + d)(a + c+g) — (ci + e)a}'& 
AC (a 4 c 4 f/)(ci + b + d) — or. 
r 
therefore 
r 
A ' 
MDCCCLXXXIJT, 
q{(a + b + d)(a + c) — ci(a 4 d )} 
a 3 — (a -HJ 4 d)(«. 4 c 4 g) 
CE{(« -\-b-\-d)(a- l r c) —a(ct 4d)}{ {ct 4 d)(ct 4c4 d) — ci(a 4c)} 
{{a + c+g){a + b-\-d) — a 2 } 3 
4 Y 
