OF ELECTROSTATIC UNITS IN THE ELECTROMAGNETIC UNIT. 
413 
netism, and the deflections due to equal and opposite currents were as nearly as possible 
equalized. 
If it had been possible to adjust the magnets so as exactly to counterbalance the 
directive component of the earth’s magnetism, these deflections would have been exactly 
equal ; but a slight discrepance between the deflections remained after the adjustment 
of the magnets. This remaining discrepance was eliminated in the calculation by taking 
the mean between the two deflections. 
These deflections, which were measured according to the usual method by reflection, 
were read off on a scale (Plate XXXII. fig. 3,/) (divided to fortieths of an inch) placed at 
a distance of 3 or 4 metres from the coil. The light (from a gas-lamp constructed like 
a paraffin-lamp with glass shade &c. supported on a wooden frame attached to the table 
on which the electrodynamometer stood) was reflected from a light circular mirror (m) 
cemented to the lower part of the front of the movable coil. The lamp («) was placed 
about midway between the electrodynamometer and the scale, the reflected rays passing 
under it from the mirror away to the scale. The rays reached the mirror after passing 
through a condensing-lens ( c ) attached to a long telescope-tube (b), the position of which, 
relatively to the lamp and mirror, was adjusted by moving the tripod stand (d) to which its 
supports were attached. The lamp carried a metal screen with slit and fine wire stretched 
across the slit ; and the deflections were noted, as in reflecting galvanometers and electro- 
meters, from the positions of the shadow of this wire in the reflected image. 
To render these deflections available for absolute measurement, it was necessary to 
know in mechanical units the force required to maintain the coil deflected through any 
given angle. This force is given by the equation of oscillations in terms of the period 
of vibration and the moment of inertia of the coil round its vertical axis. The period 
of vibration of the coil was determined from a series of 110 periods. The times of the 
first 10 and the last 10 having been noted, and the differences of the times of the 1st 
and the 101st, the 2nd and the 102nd, &c. having been taken, the average period of 
vibration for the whole series was very accurately determined. As the deflections to be 
observed in the actual measurements were made in a magnetic field with the coil deflected 
from its zero-position, these observations of the period were repeated with the coil 
deflected under the influence of the current about to be used in the comparison. A 
result differing by nearly \ per cent, was sometimes obtained. This determination of 
the period of vibration of the coil was generally repeated before any lengthened series 
of observations. 
The moment of inertia of the coil round its vertical axis was obtained from a com- 
parison of its vibrations with those of a symmetrical body of the same weight vibrating 
under the same conditions. The coil having been carefully weighed, a vibrator of the 
same weight was constructed. The vibrator consisted of a cylindrical brass ring (radius 
5 centims.) and a light brass bar attached at its extremities to the ring. This was made 
to vibrate, in an enclosed space protected from currents of air, round an axis perpen- 
dicular to the plane of the ring, the suspending-wire being attached to the centre of the 
