414 ME. DUGALD M‘KICHAN ON THE DETEEMINATION OF THE NUMBER 
cross bar. The image of a light reflected from a galvanometer-mirror fixed to the vibrator 
at its axis allowed these vibrations to be easily counted. The period of vibration was 
determined from a series of oscillations extending through 110 periods. The vibrator 
having been removed from the suspending-wire, the coil was substituted in its place (care 
having been taken that the wire was not subjected to any stretching in the interval) ; and 
a similar series of observations was made to determine the period of vibration of the coil. 
The moments of inertia of any two bodies of equal weight around any axis being pro- 
portional to the squares of their periods of vibration round these axes, the ratio between 
the moment of inertia of the suspended coil and the moment of inertia of the ring- 
vibrator was given by this comparison. 
The dimensions of the vibrator were accurately known, and the summation w 7 as made 
for all its parts. This, together with the ratio just obtained, gave the moment of inertia 
of the movable coil round a vertical axis through its centre in centimetre-grammes. This 
moment of inertia, combined with the period of vibration of the coil after it was sus- 
pended in the electrodynamometer, gave the absolute measure of the couple required to 
hold the coil deflected through unit-angle or any fraction of unit-angle. The length of 
a scale-division and the distance of the scale from the mirror being known, the angular 
value of a deflection through any number of scale-divisions was known, and conse- 
quently the deflecting couple corresponding to each reading on the electrodynamometer 
scale. 
The electromagnetic measure of this couple was obtained in terms of the strength of 
the deflecting current from a consideration of the number of turns of wire in the coils 
and the area they enclosed, the distance of the movable coil from the fixed coils, and other 
quantities entering into the equation below. These two values, the mechanical and 
the electromagnetic (which for any given deflection must be equal to one another), having 
been equated, the strength of the current Avas obtained in mechanical or absolute elec- 
tromagnetic units, the unit strength of current being defined, in a purely mechanical 
way, as “ that current of which the unit of length placed along the circumference of a 
circle of unit radius produces a unit of magnetic force at the centre.” 
The methods of obtaining the corresponding absolute measurement of the resistance 
of the circuit and the electrostatic measure of the electromotive force have been already 
mentioned. These three measurements afford the data from which the ratio v is to be 
obtained. 
Mathematical Theory of the Comparison. 
I. Absolute Electrometer (see “ Reprint ” above referred to, § 362). 
Let F = force (determined by experiment) required to displace the movable disk of 
the electrometer through a known distance. 
A = mean of the areas of the disk and the aperture of the guard -ring which sur- 
rounds it. 
V = difference of potentials between the disk and the opposed plate connected 
with one of the poles of the battery. 
