Exp. 5. Having electrified, positively, a globe eight inches in diameter, and also the needle of the balance, he found the electrical density of the globe to be 144°, by means of a small globe one inch in diameter, and then touched the globe with a circular plane 16 inches in diameter and ith of a line thick, so that a diameter of the globe was perpendicular to the plane at the point of contact. He again determined the electrical density of the globe by the small one-inch globe, and found it equal to 47°. The electricity of the globe being re duced from 144° to 47°, the plane obviously carried off 144-47-97° ; so that the quantity taken by the plane was double that which it left in the globe. Now, since the area of a globe of eight inches in diameter, is=201.6, and the area of both the surfaces of the circular plane long, its electricity was divided with a globe of eight inches in such a manner, that their mean densities were almost exactly in the same ratio of 1.30 to 1.00, as in the preceding experiment. When the diameter of the globe, however, was very large compared with that of the cy linder, and when the cylinder had very little length, then the mean density of the cylinder, relative to that of the globe, was much less than when the length of the cylin der was considerable.
Exp. 3. \Vhen a small cylinder, five or six lines in length, and two lines in diameter, was put in contact with'a globe of eight inches, the mean density of the electric fluid on the surface of the cylinder was to that of the globe nearly in the ratio of two to one ; but when the cylinder was only two lines in diameter, and six inches long, the mean density of the cylinder was to that of the globe as 8 to 1.
Exp. 4. When the globe was eight inches in diame ter, and SO inches long ; then, = 403.2, which is exactly double of the former, it fol lows, that the electricity is distributed between the plane and the globe, in the ratio of their surfaces.
The preceding result was obtained in a great number of other experiments made with globes and planes of different sizes ; and the ratio above mentioned was al ways more exact when the plane was small in propor tion to the surface of the globe. A plane, for example, six lines in diameter, when made to touch tangentially a globe of eight inches, takes upon each of its surfaces an electrical density equal to that of the globe, or, what is the same thing, the small plane is charged with a quantity of electricity double that of the portion of the surface of the globe which it touches.
E2p. 6. Having insulated an electrified globe A, eight inches in diameter, and also two equal globes b, c, two inches in diameter, placed at a distance from it, b being insulated upon a cylinder of glass coated, and sur mounted by four branches of gum lac, and c being insu lated by a vertical support, the same as in Plate CCXLV. Fig. 3, the needle of the balance and the globe A being electrified positively, the attractive force upon the needle of the globe c was found to be exactly equal to the repulsive force of the globe b.
Exp. 7. If we place an uninsulated cylinder at differ ent distances from an electrified globe, so that its axis points to the centre of the globe, we shall have the fol lowing result. The electrical density of the extremity of the cylinder nearest to the globe, will be a little be low the of the inverse ratio of the distance of this extremity from the globe.
Exp. 8. In placing successively two cylinders of dif ferent diameters at the same distance from an electrified globe, the electrical densities of the extremity of the two cylinders were to one another nearly in the inverse ratio of the diameters of the cylinders, provided that their diameters were much smaller than the diameter of the globe.
Exp. 9. In placing an uninsulated cylinder of a great length at a given distance from an electrified globe, Coulomb found that the electrical density of different points of the surface of this cylinder, were inversely as the square of the distance of these points from the cen tre of the electrified globe.
This law, however, does not hold upon a part of the cylinder near the globe, equal to four or five diameters of the cylinder. In this portion, the electrical density increases towards the extremity of the cylinder in a ra tio much greater ; and, if the cylinder is terminated by a hemisphere, the density at the extremity of the axis nearest the globe is nearly double that of a point whose distance from the extremity of the axis is equal to the diameter of the cylinder.
Exp. 10. If an uninsulated cylinder is placed at the same distance from the centre of two electrified globes of different diameters, then, supposing the electrical density of the globes to be the same, Coulomb found that the density of points of the cylinder placed at the same distance from the centre of the two globes, was as the square of the radii of the globes.
By combining the results in the four preceding expe riments, Coulomb has found, that the electrical densities of a hemisphere which terminates different cylinders presented to an electrified globe, are of a contrary na ture to that of the globe, and in the direct compound ra tio of the density of the globe's surface, and the square of the globe's diameter, and in the inverse compound ra tio of the power 4 of the distance of the centre of the globe from the extremity of the cylinder, and of the ra dins of the cylinder. Thus, if 1) be the positive elec trical density on the surface of the globe, whose radius is R ; r the radius of the c)linder ; a the distance. be tween the centre of the globe and the extremity of the cylinder ; then, if d be the negative electrical density of the extremity of the cylinder, we shall have d = r(11-1-a)f Now, the constant quantity in was found by experi ment to be m=2.07v(1 inch); hence, if the values or a, r and R be reduced to inches, we shall have d = The application of this formula, deduced directly from experiment, to the explanation of the effects of conductors, will be pointed out in the next Chapter.