INQUIRIES DEPENDING ON REPULSION LIABLE TO FALLACY. 
435 
column B, where the force is again nearly as in the case of the distances being 
small, as at 9° and 4°5. We also perceive in one instance, that where the distances 
are as 4 : 1, the forces are as 6 : 1, as in the distances 18° and 4 0, 5 of column B. 
20. These facts are of great consequence to every species of electrical inquiry de- 
pending on any instrument whose indications are derived from repulsion. Coulombe 
found, for example, that the balls of his balance were repelled with only one half the 
force at a given distance when the quantity of electricity in one of them was reduced 
F 
to one half, and further concludes that the whole repulsive force expressed by jj 2 
diminishes for the same distance, D, as the absolute quantity of electricity in each of 
the repelling bodies considered as points. This principle he applied extensively, with 
a view of detecting the ratios of the quantities of electricity accumulated in charged 
bodies or in any given point of them. The electricity of the given point he considered 
as transferable to a small insulated disc, first applied to the body, and subsequently 
placed in his balance, the ball of the needle being already charged with a certain 
quantity of the same electricity. The insulated disc has been termed a proof plane : 
when this plane is placed upon any part of a charged body, it is supposed to be 
identical with an element of the surface, so far as relates to the distribution of the 
accumulated electricity ; and hence, on removing it to the balance, it is assumed to 
operate just as the element would do under similar circumstances. Admitting, how- 
ever, this identity, the indications of the instrument may not in all cases be directly 
proportionate to the quantity of electricity in the proof plane, since on the principles 
just explained, and as seen in Table IV., the respective quantities of electricity are 
not always as the repulsive forces : if the particular cases in which this happens be 
not first ascertained, we may possibly arrive at erroneous conclusions. It appears, 
for instance, from Coulombe’s researches with the proof plane, that the relative elec- 
trical capacities of a solid or hollow sphere and a circular plane of equal area, each 
side to each side, are as 2:1; that when electricity is accumulated on a globe, either 
hollow or solid, it is only found upon the exterior surface ; hence in expanding the 
globe into a plane circular area of the same superficial extent, each side to each side, 
we double its capacity by giving it another exterior surface*; twice the quantity of 
electricity may therefore now be placed on it under the same intensity. 
21. This point is of some importance to an exact electrical theory, and deserves 
attention. The experimental evidence in support of it is principally the following. 
1°. When a small insulated body is plunged within a hollow sphere charged with 
electricity, it does not, on being again withdrawn, exhibit any electrical indication ; 
whereas on touching the exterior surface, the insulated body becomes vigorously 
electrified. 
2°. Coulombe found, by means of his proof plane, that when a charged sphere had 
* Biot, Traite de Physique, tom. li. p. 275. 
3 K 2 
