292 Dr. J. Hopkinson on the 
2W = gu’ + Job? + 330” + 44D?” ) 
— 291,AB = 29;3AC = 2¢u4AD t Ry (2) 
—2q23BC —29.4BD | 
— 29340 D 
Equations (1) and (2) are perfectly general, true whatever be 
the form of the four bodies. 
If the four quadrants completely surround the needle, 
qu=0, 
O14) Qoay aNd Quy are independent of | ee 
J33= 913 + Jo3 
Now when the electrometer is properly adjusted, the needle 
will not be deflected when A=B, whatever C and A may be. 
Hence A—B isa factor of gil , and we have 
dqu Ades ea 9 tgs 
dé d6 ~~ ~dé» 
Aqs3__ i 
Fae 
| 
) 
whence 
adW | dqu Adee dqis 
279 =A BY AGg Bag — C8): 
This should be true of any electrometer having the above 
adjustment correctly made. 
But by suitably forming the three bodies A, B, C, further 
relations between the coefficients may be obtained. The 
condition of symmetry would give us ae =— ae ; but it is 
not necessary to assume symmetry. If the circumferential 
termination of the needle be a circle centre in the axis of 
suspension (at least near the division of the quadrants), if 
the needle turn in its own plane, if the quadrants are each 
approximately a surface of revolution about the axis, and if the 
radial terminations of the needle be not within the electrical 
influence of the quadrants within which they are not, conditions 
closely satisfied in Sir W. Thomson’s electrometer, 
dqu _ 1 @9s 
Hoe 8 ale) 
dgog _ _ 1 4913 
de = dO 
p) 
