Fig. 2. Represents another balance of the same kind, but still more simple. The four vertical and square plates of glass, rise from a groove in a piece of well baked wood. Instead of the semicircle t, 0, ur, a band of paper m n is pasted on one of the glass plates, and on both sides from 0 is divided into degrees, according to the tangents of a circle, whose centre is the suspend ing fibre.
The micrometer m, at the top of both these balances, does not differ materially from that which has been re presented in a former Figure. The head of it consists of two circles, the lowest of which has a space of five de grees divided into single degrees, while the other circle is divided into spaces of five degrees each. These two circles are intended to adjust the needle to the zero of the scale. The suspending fibre in both these balances was a copper wire of the diameter No. 12. in com merce.
In using the preceding apparatus, Coulomb employed two methods for determining the manner in which the electric matter distributed itself between two bodies in contact. In the first, he placed the electrified body in the balance, after having electrified in the same manner the small circle of gilt paper at the end of the needle. The needle being repelled through a certain distance, was then brought back by means of the micrometer to any distance from the electrified body: and the angle of tor sion given by the micrometer, added to the distance of the needle from the zero of the scale, measured the re pulsive force which the bodies exercised at that distance. The electrified body placed in the balance, was then touched by the body with which it was to divide its elec tricity; and in untwisting the suspending fibre, the nee dle was brought back to the same distance from the body as formerly, and then the angle of torsion added to the distance of the needle from zero, measured the quantity of electricity which was left in the body by the other, to which part of its electricity was distributed. In this method, unless the weather is very dry, it is necessary to take into account the dissipation Ivhich happens dur ing the interval of observation. The preceding method was employed by Coulomb, when he wished to determine the relation between the quantities of electricity in two bodies ; but, in order to measure the electric density in each point of a conductor, he had recourse to the follow ing ingenious method.
In the small balance with which he made his first ex periments, he suspended his needle by a fine silver wire. He then formed a cylinder of gum lac, bent as at c d e in Fig. 3. and of the thickness of a hair, and to the end of it he attached a circle of gilt paper e. After having electrified the disc carried by the needle with an insulated pin as before, he electrified the body upon which the ex pel iments were to be made, and then touched the circle e with the point of the body, whose electrical density he wished to ascertain. He then placed this circle in the balance, and ascertained the quantity of its electricity. Now as this circle is only five or six lines in diameter, and the 18th part of a line thick, the electrical density which it acquires by the tangential contact, is either the same with that of the point which it touches, or propor tional to that density. Hence by making this circle touch different points of a conductor in succession, and by pre senting it after every contact to the needle of the balance, taking care that it shall always have the same position, Coulomb was' enabled to ascertain the electrical densi ties of different points of conductors.
In the comparison of succeeding observations, we must obviously take into account the dissipation of electricity by the contact of air, and the method by which this has been done by Coulomb is remarkably simple and inge nious. In order to compare the electrical density of two points, he first touched one of the points by the paper circle, and determined its density by placing the circle in the balance as before. He then touched the second point, and determined its density in a similar manner ; and after an interval equal to that which had elapsed be tween the two touchings, he touched the first point anew, and again determined its density, which was of course less than before, from the effect of dissipation. He then took the mean between the two densities found for the first point, which was therefore the real density at the instant of the second observation, so that the two densi ties thus measured were free from any error arising from dissipation.