584 PROF. J. J. THOMSON AND MR. G. F. 0. SEARLE ON THE RATIO OF THE 
the ca,pacity of the guard ring condenser, by using a complicated commutator which 
worked both the guard ring and tlie condenser. At first we tried one where the contacts 
were made by platinum styles attached to a tuning fork, but as the results were 
not so regular as we desired, we replaced the tuning fork commutator by a rotating 
one driven by a water motor. A stroboscopic arrangement was fixed to this commu¬ 
tator so that its speed might be kept regular and measured. With this arrangement, 
which worked perfectly, we got values for the electromagnetic measure of the capacity 
of the condenser distinctly less than those obtained by the old method. We then 
endeavoured to find out the cause of this difference, and after a good deal of trouble 
discovered that in the experiments by which the equality of the capacities of the 
guard ring and auxiliary condensers was tested by Maxwell’s method, the guard 
ring did not produce its full effect. When the guard ring of the standard condenser 
was taken off, and its capacity made equal by Maxwell’s method to the capacity of 
the auxiliary condenser, the two methods gave identical results; but the effect of 
adding the guard ring was less in the old method than in the new. We found also, 
by calculation, that the effect produced by the guard ring in the old method was 
distinctly too small, while that determined by the new method agreed well with its 
calculated value. As the new method was working perfectly satisfactorily, and as it 
possesses great advantages over the old one, inasmuch as we get rid entirely of the 
auxiliary condenser, and can also alter the speed of the rotating commutator with 
very much greater ease and considerably greater accuracy than in any arrangement 
where the speed is governed by a tuning fork, we discarded the old method and 
adopted the new one which we now proceed to describe, beginning by considering 
the errors to which this method is liable. 
Advantages of the Method of Determining “ v.” 
The best way of discussing the advantages of this method is to consider the 
c[uantities which have to be measured and the accuracy which can be obtained in their 
measurement. The investigation naturally divides into two parts (1) the determina¬ 
tion of the capacity of a condenser in electrostatic measure; (2) the determination 
of the capacity of the same condenser in electromagnetic measure. Let us begin by 
considering the first part. The condenser consisted of two co-axial cylinders, the 
inner cylinder being provided with a guard ring. If the distribution of electricity 
on the middle part of the inner cylinder were the same as that on an equal length, /, 
of an infinite cylinder whose radius is a, surrounded by a co-axial infinite cylinder of 
radius h, the electrostatic measure of the capacity would be ^ //log h/a. The actual 
case may differ from this ideal one in some or all of the following w'ays. (1) The two 
cylinders may not be quite co-axial; this, howmver, is not important if we know the 
distance betwen the axes, as we can find the capacity of the system got by placing 
one cylinder anywhere inside another. (2) The cross sections of the cvlinders may 
