The small lever being supposed thus freely sus pended and balanced, if we attempt to turn it any number of degrees in the horizontal plane in which it is situated, this cannot be done without twist ing in the same degree the metallic wire SC, to which it is attached. But this wire, by virtue of its elastic reaction, will resist the torsion with a force, depending on its dimensions, on its nature, ' and on its physical constitution ; and, according to Coulomb's experiments, so long as its state of ag gregation has not received a permanent alteration, by twisting, its resistance will be exactly proportion al to the angle by which we withdraw it from its na tural position of rest ; proportional, therefore, in this case, to the angle which we cause the small horizontal lever ab, to describe. (See Biot, Traitg de Physique Experimentak, Tom. I. and IL) We have othy, therefore, to produce this angular de viation by means of the electrical repulsion, and the torsion of the wire will measure its effect. For this purpose, the lever ab, being in that position of rest to which the na tural equilibrium of the wire tends to carry it, we place beside the ball a, a nother ball A, (fig. 3.) of the same or of a different diameter, but fixed upon an immoveable and insulating support, formed also of a short and very fine thread of gum lac. The two balls be ing now in contact, We touch the fixed ball A, with the extremity of an elec trified tube. The electricity then di vides itself between the two balls, the one fixed, the other moveable ; these fly from each other, and this repulsion forces the lever, ab, to turn round its centre, (fig. 3.) until the repulsive force, weakened by the distance, is ex actly balanced by the force of torsion of the suspending wire SC. Hence arises a state of equilibrium which is attained after several oscillations. We now observe, upon a divided circle which surrounds the ap paratus, the arc Aa, which the lever has described ; and turning the button S, by which the wire is sus pended, and which is itself divided on the circumfer ence, we twist it round a certain number of degrees, until the angular distance of the balls becomes the half, the fourth, the eighth, or any other fraction of what it was at first ; and then by comparing the degrees of torsion with the angles where the ball a stops in every case, we obtain the relative values of the repulsive force at various distances. In this manner it has
been found by Coulomb that this force, like that of the celestial attraction, is rigorously proportional to the quantity of free electricity upon each body, and reciprocally as the square of their mutual distance. An experiment of a similar kind de monstrates, that the same law extends also to the attractive force of the bodies charged with dinrent electricities ; and the sensibility of the apparatus is such, that no doubt can remain of the accuracy of the result. The only source of error would arise from the waste of electricity which is continually going on, through the air, and through the sup ports of gum lac, which, though highly insulating, can never be obtained in this respect altogether per feet. But the above mode of experimenting may it self serve to estimate the effects of these two causes. For we have only to leave the two bodies a and A near each other for a considerable time, several hours for example, taking care to untwist, from time to time, the wire SC, in order to diminish its resistance, and replace the balls at the same distance from each other, m proportion as their repulsive force diminish es by the progressive waste of the electricity which covers them. It is easy to conceive that experi ments of this nature, properly varied, ought to show the law of the waste of electricity through the air and along the supports. It was, accordingly, in this manner that Coulomb determined it ; he was thus enabled to correct all his results, and to bring them up to the mathematical case of air perfectly dry, and of supports completely insulating; and it is with these corrections that the law of the squares of the distances comes out with the utmost rigour, as above enunciated. The apparatus employed by him for this purpose, and which we have explained (fig. 3, 8), he called the electrical balance.