294 Dr. J. Hopkinson on the 
We may now consider the methods of varying the sensibility 
of the instrument (see Reprint of Sir W. Thomson’s papers, 
p- 280). The methods dealt with are those of Sir W. Thomson, 
somewhat generalized. 
(c) The quadrant B is connected with an insulated con- 
denser, capacity 5, whilst A is connected to a source of elec- 
tricity :— 
O=—G2A+ (b+ Yo) B—a8C, 
aN CAE) 
therefore 
7 
p= GA eae) A-3q)—26C; 
so asl Pye 
: "6+ du) =a 
If b=0, we have the first reduced sensibility given by Sir W. 
Thomson. 
(d) All methods of using the inductor may be treated under 
one general form. Let the quadrants A and B be connected 
with insulated condensers, capacities a and 6; then connect 
the inductor to a source, potential V; | 
@) = (gi + a)A— 2B — G14V + afC, 
O= —gA + (G22 +b) B—quV —abC, 
0=r(A—B)O; 
(+ 9y1922— 924 + 1900 + bu + ab) (A—B) 
+ Gia G12— Y22— 8) — Goal G2 G11 — 2) }V 
+ {29+ Geet qitb+afalC=0 ; 
whence we have an expression for V proportional to @. Bya 
proper choice of a and 6, we can make the sensibility as low 
us we please. 
Now the whole of these formulze rest on the same reasoning 
as the equation 
A+ ] 
9) 
I have mentioned that, in my instrument at least, this equation 
quite fails to represent the facts when C is considerable. It be- 
comes a matter of interest to ascertain when the formula begins 
to err toa sensible extent. Ifa constant battery of a large num- 
ber of elements were available, this would be soon accomplished. 
I have at present set up only 18 Daniells. I have therefore 
been content to use the electrometer to ascertain its own charge 
6—r(A—B) (o- 
