ELECTROMAGNETIC UNIT OF ELECTRICITY TO THE ELECTROSTATIC UNIT. 585 
not be accurately circles. The effect on the capacity of a slight departure from circu¬ 
larity is calculated below, so that this effect may be corrected. (3) The conductors 
may not be true cylinders but swell or contract slightly as we proceed along their 
lengths ; we show, however, below, how to correct for an effect of this kind. (4) The 
existence of the air space between the guard ring and the middle cylinder will cause 
the distribution of electricity near the ends of this cylinder to be irregular, and there 
will also be some electricity on the cross section of the cylinder; we have, therefore, 
found the distribution of electricity in a case so nearly resembling this as to allow us 
to use the result as a correction. In the arrangement we used the jiotential of the guard 
ring differed slightly from that of the middle cylinder, the very small correction due 
to this is, however, easily calculated. Since we know the corrections, the capacity of 
the condenser can be calculated in terms of its dimensions, and the only errors to 
which we are liable are those which may be made in the determination of these 
dimensions. The lengths which have to be measured with great accuracy are the 
length of the middle cylinder, its radius and that of the outer cylinder, and the 
distance between the cylinders. The first three of these are long enough to be 
measured by the ordinary methods of measuring length, without danger of an error 
greater than one part in 3000, the fourth, however, is too small to be measured with 
so great an accuracy by these methods, it was determined, therefore, by finding v, the 
volume of water required to fill the space between the two cylinders, then d the 
distance between the cylinders is given by the formula 
nvl {a -f b ) 
where I is the length of the middle cylinder and a and h the radii of the two 
cylinders. In this way the percentage error of d was not greater than those of a, h, 
and 1. Since an accuracy of one part in 3000 can be obtained in the measurements of 
the dimensions of the cylinders, and since the electrostatic measure of the capacity is 
of the dimensions of a length, this measure of the capacity can be obtained correct to 
one part in 3000. 
We now pass on to the determination of the capacity in electromagnetic measure. 
This was determined by balancing, in a Wheatstone’s bridge, a discontinuous current 
produced by rapidly charging the condenser against a steady current derived from the 
battery which charged the condenser. In order to calculate the electromagnetic 
measure of the capacity it is necessary to know accurately the number of times per 
second the condenser is charged, and to keep this number constant. The charging 
and discharging of the condenser were effected by a commutator driven by a Thirlmere 
Water Motor, the water being obtained, not from the main, but from a cistern at the top 
of the Laboratory. The number of revolutions per second made by the commutator 
was compared by a stroboscopic arrangement wdth the frequency of an electrically 
driven tuning fork. The observer (G.F.C.S.) ■was able, after practice, to govern the 
MDCCCXC.—A. 4 F 
