Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/392

 

these three quantities $R$ can be determined in electromagnetic measure.

These methods involve the determination of the period of vibration of the galvanometer magnet, and of the logarithmic decrement of its oscillations.

Weber's Method by Transient Currents^[1].

760.] A coil of considerable size is mounted on an axle, so as to be capable of revolving about a vertical diameter. The wire of this coil is connected with that of a tangent galvanometer so as to form a single circuit. Let the resistance of this circuit be $R$. Let the large coil be placed with its positive face perpendicular to the magnetic meridian, and let it be quickly turned round half a revolution. There will be an induced current due to the earth's magnetic force, and the total quantity of electricity in this current in electromagnetic measure will be

$Q={\frac {2g_{1}H}{R}}$,

(1)

where $g_{1}$ is the magnetic moment of the coil for unit current, which in the case of a large coil may be determined directly, by measuring the dimensions of the coil, and calculating the sum of the areas of its windings. $H$ is the horizontal component of terrestrial magnetism, and $R$ is the resistance of the circuit formed by the coil and galvanometer together. This current sets the magnet of the galvanometer in motion.

If the magnet is originally at rest, and if the motion of the coil occupies but a small fraction of the time of a vibration of the

magnet, then, if we neglect the resistance to the motion of the magnet, we have, by Art. 748,

$Q={\frac {H}{G}}{\frac {T}{\pi }}2\sin {\frac {1}{2}}\theta$,

(2)

where $G$ is the constant of the galvanometer, $T$ is the time of vibration of the magnet, and is the observed elongation. From these equations we obtain

$R=\pi Gg{\frac {1}{T\sin {\frac {1}{2}}\theta }}$

(3)

The value of $H$ does not appear in this result, provided it is the same at the position of the coil and at that of the galvanometer. This should not be assumed to be the case, but should be tested by comparing the time of vibration of the same magnet, first at one of these places and then at the other.

1. Elekt, Maasb.; or Pogg., Ann. lxxxii, 337 (1851).