Oscillatory Discharge of a Leyden Jar. 
15 
This equation has in it no term involving loss of energy by friction or 
a similar cause. 
The solution of 
dP 
+ iT { =0 
depends on the form of i. If i be real and positive 
r^=zA sin Ji.t +B cos y/i.t 
if real and negative 
r,—Ae/ ^ +Be 
J—i.t 
These solutions indicate oscillatory motion of the elastic medium, or 
gradual subsidence to rest, according to the value of i. 
Now as far back as 1842 Prof. Joseph Henry recognized that the dis¬ 
charge of a condenser might be oscillatory. Helmholtz seems to have 
so considered it in 1847 in his famous essay on the conservation of 
energy. In the Phil. Mag. for June, 1847, Sir William Thomson showed 
that when a condenser is discharged through a resistance having self 
induction L (or electro-dynamic capacity, as he termed it) and electro 
static capacity C of the condenser; being loaded originally with the 
charge q where q- 
■■CV and — —i= current at any instant, = ~ 
dt a 
by 
Ohm’s law in the case of steady currents, then 
d^q R dq 1 _ 
dtp + ~L ~dt + 'LC q ~° 
The general solution of such an equation is of the form 
.^4 + /V-i) (a*-/V~*> 
, R , * / 1 -R 2 
where u= —— and 
This equation reduces to one of the the form ( \ q + -=—=0 when the 
dP LC 
resistance of the discharging circuit can be neglected in comparison 
with the self induction coefficient of the same. The discharges 
are then strictly oscillatory, the, time of a complete oscillation, being 
27t^/LC. When R=^ the motion has just ceased to be oscillatory or 
is dead beat. For sufficiently large values of R in comparison with L 
the value of fi becomes imaginary, and there is no proper oscillation. 
