peeeer 7 
XXXII. On the Quadrant-Electrometer. 
By J. Horxinson, D.Sc., F.R.S.* 
N Professor Clerk Maxwell’s ‘ Electricity’ (vol. i. p. 273) 
it is proved that the deflection of the needle of a 
vaver 
2 
C is the potential of the needle, and A and B of the two pairs 
of quadrants. Desiring to ascertain the value of the standard 
charge of my instrument, I endeavoured to do so by the aid of 
this formula, and also by a more direct method. ‘The results 
were quite discordant. Setting aside the special reasoning by 
which the formula is attained, we should confidently expect 
that the sensibility of a quadrant-electrometer would increase 
continuously as the charge of the jar is increased, until at last 
a disruptive discharge occurs. In my instrument this is not 
the fact. As the charge was steadily increased by means 
of the replenisher, the deflection of the needle due to three 
Daniell’s elements at first increased, then attained a maximum, 
and with further increase of charge actually diminished. On 
turning the replenisher in the inverse direction the sensibility 
at first increased, attained the maximum previously observed, 
and only on further reduction of charge diminished. 
Before giving the experimental results, it may be worth while 
to briefly examine the theory of the quadrant-electrometer. 
Let A, B, C, D be the potentials of the quadrants, the needle, 
and the inductor which is used for measuring high potentials 
(see Reprint of Sir W. Thomson’s papers, p. 278). Let Q,, 
Q., Q3, Q, be the quantities of electricity on these bodies 
respectively, and @ the angle of deflection of the needle, mea- 
sured in terms of divisions of the scale, on which the image of 
the lamp-flame is projected. We have the equations 
Qi= ee ee 
Qo= —q2A + Go2B—Go3C —quD, 
3= —GisA— qosB + qs2C — ga.D, | 
Q.= — uA —qzaB—GouC ae guD. ) 
, where 
quadrant-electrometer varies as (A—B) (c — 
(1) 
gx, &c. are the coefficients of capacity and induction. They 
are independent of A, B, C, D, and are functions of @ only. 
As above written, they are all positive. Let the energy of 
electrification be W:— 
-* Communicated by the Physical Society, having been read at the 
Meeting on March 14th, 1885. 
