Quadrant-LElectrometer. 303 
The capacity 93; of the needle and the coefficient of in- 
duction of the needle on either quadrant 4¢33 are also of no 
use, but the method by which they may be obtained is worth 
noting. Let quadrants A be connected to the case, and let 
B be insulated, diminish the charge of the jar slightly by the 
replenisher, and suppose the consequent deflection be ¢. Let 
py. and yw’ be the values of w before and after the diminution of 
charge, as ascertained by applying a known potential-dif- 
ference between the two pairs of quadrants; we have 
— 9330 = + 932B —q330’ —Bu'd, 
where o=—p'B, 
933, C—O") = (Gan + Bu”) B, 
which determine g33, since C and ©’ are known from 
pand p’. 
Of course the values of the constants of an electrometer are 
of no value for any instrument except that for which they are 
determined in the state of adjustment at the time. Tor any 
particular use of the instrument it is best to determine exactly 
that combination of constants which will be needed. Nor is 
there anything new in principle in the discussion or expe- 
riments here given; they are merely for the most part the 
application of well-known principles to methods of using the 
electrometer given by Sir William Thomson himself. The 
method of determining the capacity of a condenser by charging 
it and connecting it to an insulated quadrant has been used by 
Boltzmann. But the invention of the quadrant-electrometer 
by Sir W. Thomson may be said to have marked an epoch in 
Electrostatics, and the instrument from time to time finds new 
uses. It therefore seems well worth while to make known 
observations made upon it in which the instrument itself has 
been the only object studied. Some practical conclusions 
may, however, be drawn from the preceding experiments. 
Before using the formula 
g=(A—B)(0—* 55) 
it is necessary to verify that it is sufficiently nearly true, or 
to determine its variation from accuracy. Unless it be 
sufficiently accurate through the range experimented upon, 
the electrometer cannot be applied by the methods well 
known for determining alternating potentials and the work 
done by alternating currents. 
~My pupil, Mr. Paul Dimier, has very efficiently helped me 
in the execution of the experiments of verification. 
Y2 
