274 
Mr Sears, On the Longitudinal Impact 
through the galvanometer up to the instant when the rods 
separate, as though the condenser circuit were not there. At the 
same time the condenser will be discharging itself through the 
resistance, R 2 , at the same rate as if the galvanometer circuit did 
not exist. At the instant when the rods separate, however, the 
conditions change. The current which is flowing through 
the galvanometer is not now suddenly reduced (as in the normal 
experiment) but is simply diverted to the path XR 2 G 2 Y, and 
flows into the condenser, so that no spark is produced. Current 
continues to flow through the galvanometer into the condenser 
until the latter is once more charged to its original potential. All 
these events follow one another within a very small fraction of a 
second, so that there is no time for leakage currents to produce 
any effect. The galvanometer will, therefore, register a fling which 
is the same as that obtained in the normal experiment (less the 
part, if any, due to spark) plus that due to the quantity discharged 
by the condenser round the circuit G 2 K 2 X r 2 r± YG 2 . 
Consider this latter part. 
If x be the charge on the condenser at any instant, we have : — 
sc n . x 
7 = — UoX or x + 
G 
whence x— VG 2 e R2 ° 2 , 
VG 2 being the initial charge. 
If, then, the duration of the impact be T, the whole quantity 
discharged will be 
T 
VC.Al-e ... (=t/, say). 
Hence 
C.R 
12 = 1 - 
y 
vc 9 
or 
T=-C,S,]og t (l-^j = C,R, log , - (3). 
To determine the value of the spark effect by this method, it is 
T 
only necessary to make Go R 2 so small that, in the above, e Cq1<2 
is negligible compared with unity. We then have y, — VC 2 
simply, so that, if we take two galvanometer readings, one, Q, with 
the normal form of experiment, and one, Q', with the condenser, 
we shall have : — 
Q' = Q — Spark + y 1 or Spark = Q + VC 2 — Q' 
(4). 
