ELECTRICAL WAVES AND SOME OF ITS APPLICATIONS. 
13 
magnetic force due to the oscillation acting on the needle A is equal to the 
maximum value due to the oscillation on /3. 
Let be the maximum values of the current in the first and second half¬ 
oscillations respectively. 
Let be the number of turns per centimetre on solenoids A and B respectively. 
Then, since 
47rniyi = 4.TTn.2yz, yjyi = 
the ratio of the second to the first half-oscillation is therefore known, and the 
damping is thus deteimined. The actual resistance in the circuit may also be 
deduced. 
Now yi = 'pO'YQe where T = period of complete oscillation andy) = 
1 
(LC)^ ’ 
y3 = pCVoe-®'^^-^^A 
Therefore 
Therefore 
^,-E/2L.T/2 
72 
7i 
Pj, say. 
log Pi = 
R T 
TL' 2 
( 1 ). 
Since L and T are known from the constants of the discharge circuit, and p^ is 
determined by experiment, E. is known. 
In practice, in order to avoid the necessity of determining the constants of 
the discharge circuit, an additional known resistance ?■ is introduced into the 
circuit. If an electrolytic resistance of zinc suljDhate with zinc electrodes be used, 
the resistance will be found to be practically the same for steady as rapidly 
alternating currents, as the sjDecific resistance is very great. 
Let p^ be the ratio of the amplitudes of the two half oscillations when E -f- r is in 
the circuit 
, 11 + r T 
logft=- 2L.2 
Dividing (2) by (l) 
It -f r_ fa 
11 “ log Pi 
( 2 ). 
E is therefore determined in term of r, a known resistance. 
The method of two solenoids was not adopted in j^ractice, but one theoretically 
equivalent enqiloyed. 
A narrow piece of sheet zinc ABC was taken (fig. 4) and bent into almost a 
complete circle of 7 centims. diameter. This was fixed on a block of ebonite. At the 
centre of the circle a thin glass tube OM was placed, which served as the axis of a 
