It is plain, that in the time allotted to me I cannot conduct you over all the long and tortuous paths which the science has actually pursued, that it will not be possible at every step to remind you of all the little precautions for the avoidance of error which the early steps have taught us. On the contrary, I must make shift with the simplest and rudest tools. I shall conduct you by the shortest paths from the facts to the ideas, in doing which, of course, it will not be possible to anticipate all the stray and chance ideas which may and must arise from prospects into the by-paths which we leave untrodden. * * * * * Here are two small, light bodies (Fig. 27) of equal size, freely suspended, which we "electrify" either by friction with a third body or by contact with a body already electrified. At once a repulsive force is set up which drives the two bodies away from each other in opposition to the action of gravity. This force could accomplish anew the same mechanical work which was expended to produce it.[27] [Illustration: Fig. 27.] [Illustration: Fig. 28.] Coulomb, now, by means of delicate experiments with the torsion-balance, satisfied himself that if the bodies in question, say at a distance of two centimetres, repelled each other with the same force with which a milligramme-weight strives to fall to the ground, at half that distance, or at one centimetre, they would repel each other with the force of four milligrammes, and at double that distance, or at four centimetres, they would repel each other with the force of only one-fourth of a milligramme. He found that the electrical force acts inversely as the square of the distance. Let us imagine, now, that we possessed some means of measuring electrical repulsion by weights, a means which would be supplied, for example, by our electrical pendulums; then we could make the following observation. The body _A_ (Fig. 28) is repelled by the body _K_ at a distance of two centimetres with a force of one milligramme. If we touch _A_, now, with an equal body _B_, the half of this force of repulsion will pass to the body _B_; both _A_ and _B_, now, at a distance of two centimetres from _K_, are repelled only with the force of one-half a milligramme. But both together are repelled still with the force of one milligramme. Hence, _the divisibility of electrical force_ among bodies in contact _is a fact_. It is a useful, but by no means a necessary supplement to this fact, to imagine an electrical fluid present in the body _A_, with the quantity of which the electrical force varies, and half of which flows over to _B_. For, in the place of the new physical picture, thus, an old, familiar one is substituted, which moves spontaneously in its wonted courses.