EXPERIMENTAL EXAMINATION OF THE INDICATIONS OF THE PROOF PLANE. 447 
Table IX. 
Quantity of electricity = 
i = 8° of electrometer. 
d. 
e. 
g- 
P- 
?• 
f 
F. 
/• 
F. 
/■ 
F. 
/• 
F. 
/• 
F. 
c . . 
7 
4 
10 
10 
14 
25 
15 
25 
21 
81 
c'. . 
9 
8 
15 
32 
20 
55 
22 
70 
21 
81 
E . . 
14 
25 
16 
36 
20 
55 
22 
70 
21 
81 
Supposing the given distance d = 10° to be one of those (14.) which would admit 
of the repulsive forces being considered proportionate to the quantities of electricity 
in the respective points of the body touched, we have, in taking the square roots of 
the respective forces, at 10°, the following results. 
Table X. 
Quantity of electricity 
= i 
= 32° 
of electr. 
a. 
b. 
c. 
d. 
e . 
g- 
V- 
9 ■ 
c . . 
i — 
1-6 
2 
3 + 
5 
7-4 
13 
18 
c'. . 
1-4 
2-2 
2-8 
5 
7-4 
15 
18- 
18 
E 
1-8 
3 + 
5 
7 + 
9-5 
15 
18- 
18 
Table XI. 
Quantity = 
i = 8° of electr. 
d. 
e. 
g- 
p‘ 
9- 
c . . 
2 
3 + 
5 
5 
9 
c'. . 
2-8 
5*6 
7-4 
8 + 
9 
E . . 
5 
6 
7-4 
8 + 
9 
42. On examining these results we observe, 1°. In the horizontal column c. 
Table VIII., where the quantities of electricity are less considerable, the respective 
forces/ F are in the first four cases, a, b, c, d, in an inverse ratio of the distances, or 
nearly so : thus we have for plate b force at 5° : force at 10° : : 5 : 2 5 : : 2 : 1. This 
law, however, begins at last to change, and become irregular when the quantity of 
electricity increases, a phenomenon already observed in Table IV. (14.). A similar 
result ensues in the horizontal column c', except that as the quantities of electricity 
are more considerable the law begins sooner to change, as at the plate d. The same 
result is seen in the column e ; but here the quantity of electricity being greatly in- 
creased, the law changes still more early, as at the plate c. In Table IX. we observe 
similar effects ; thus verifying in great measure the principles and conclusions we 
have already arrived at (14.). When, therefore, we begin to reduce these results so 
as to obtain the ratio of the quantities of electricity supposed to be distributed on the 
charged cylinder, we should expect to find them more or less disturbed by the variable 
inductive action between the repelling bodies. We accordingly perceive, on referring 
to Table X., that the ratio of the centre c to the extremity e is at first, with plates a 
and b, as 1 : 2, or nearly so ; being a similar result to that obtained by Coulombe *. 
Under plate c this ratio tends to change, as more clearly shown in Table VIII. : in 
fact, it is at this point the law for the plate c, touched at the extremity, begins to 
* Biot, tom. ii. p. 275. 
