The Æpinian theory of electricity and of magnetism was modified and presented in a new form (in 1788) by Coulomb, with two fluids instead of one. His first task, before reducing the theory to calculation, was to determine the law of the forces involved—not being satisfied, for example, with Newton’s assumption that the attractive force of magnetism is inversely to the _cube_ of the distance. Mayer in 1760, and Lambert a few years later, had found the law to be that of the inverse square. Coulomb desired experimental confirmation of this law before accepting it as established. This he secured by means of his torsion-balance (about 1784).[20] It was in pursuance of this investigation that Coulomb brought to light for the first time the fact that the directive magnetic forces which the earth exerts upon a needle is a constant quantity, parallel to the magnetic meridian, and passing through the same point of the needle whatever be its position. Barlow, who had adopted the two-fluid hypothesis, showed that the magnetic “fluids” were collected at the surface of spheres (of iron), the surface being the only part in which there could be detected any magnetism. He demonstrated that a shell of iron produces the same effect as a solid ball of the same diameter. Poisson’s later analysis (1824) showed that this was a consequent to be expected. Merz has well said that what Laplace did for Newton was done by Poisson (1781-1840) “for Coulomb’s elementary law of electric and magnetic action, and on a still larger scale by Gauss, who worked out the mathematical theory and applied it to the case of the magnetic distribution on the earth’s surface. In England, already before Coulomb’s researches were published, Cavendish had, likewise by a combination of experiment and calculation, established the elementary formulae and properties of electrical phenomena.”[21] Benjamin Franklin, the first American to gain international renown as a scientist, adopted and developed a “one-fluid theory of electricity.” On this supposition the parts of the fluid repel each other, and the excess in one surface of the glass—for example—repels the fluid from the other surface. The fluid itself was regarded by Franklin as positive, the part of the other (negative electricity) being taken by ordinary matter, the particles of which were supposed to repel each other and attract the positive fluid, just as the particles of the negative fluid did on the two-fluid theory.