This method, though in general the most convenient and simple, as well as the most exact. is nevertheless affected with an error in practice, arising from the gum lac not being perfectly impenetrable to the electric mat ter. This error is greatest in damp weather, and with, impure gum lac, the least clear being generally the most impenetrable by the electric matter. In order to get rid of this error, it is necessary always to try its non-con ducting power, by touching the electrified body with the extremity e, and observing if it has any effect upon the needle of the balance; if any sensible change is pro duced upon the needle, the cylinder of gum lac must be rejected. With these precautions, Coulomb made the following experiments.
4. On the Distribution of Electricity between two Globes of different Diameters, and in Contact.
Having placed in the great balance, Fig. 1, an elec trified globe six inches and three lines in circumference, he observed the force of torsion which was necessary to bring back the needle to a distance of thirty degrees from the globe. He then immediately touched the first globe with another globe 24 inches in circumference, and observed a new force of torsion necessary to bring it back to the same distance : The following were the results which he obtained.
Now, as the quantities of electricity before and after contact, are proportional to the angles of torsion, it is very easy to ascertain these quantities. In the first ex periment the force of torsion, for a distance of 30°, was 145 before contact, and 12 after contact ; so that the quantity of electricity taken by the large globe will be 145-12=133, only 12° being left to the small globe ; hence the quantities of electricity possessed by the two globes are as 1:33 to 12, or as 11.1 to 1.0. In the same manner it will be found that this is nearly the ratio in the other four experiments. Now, the surfaces of two globes, six inches and a quarter, and 24 inches in diameter, are in the ratio of 1.48 to 1.0; hence we may conclude, that the globes are not charged with electricity in a ratio as great as that of their sur faces.
In order to find the electrical densities of the two globes, we must divide the ratio of their surfaces by the ratio of the quantities of fluid which they contain, and the quotients by the ratio of the densities. Thus, in the present case, the electrical density of the small globe will be to that of the great one as 14.8 to 11.1, or as
1.33 to 1.
In this manner Coulomb has obtained the electrical densities For globes of various sizes, and has given the general result of them in the following Table. The mean results were obtained from experiments made by both the methods which we have already described.
If any two globes, for example, have radii of 10 and 40 inches, then the ratio of these numbers are as 1 to 4, so that the ratio of their electrical densities will be as 1 to 130 ; it being always supposed that when they are se parated the electricity is distributed uniformly over their surfaces.
5. On the Density of the Electricity in different Points of two Globes in Contact.
In order to determine the density of the electric mat ter in different points of two globes in contact, Cou lomb employed the small balance represented in Plate CCXLI V. He placed a small circle of gilt paper e, Fig. 7. four or five lines in diameter, at the end of a thread of gum lac c d e, fixed to a cylinder of glass or of well baked wood c b, coated with a non-conducting var nish. This cylinder moves up and down in the hole b, (Plate CCXLV. Fig. 3.) of the piece of wood A b, and can be fixed in any position by means of the screw s. In comparing the electricity of any two points, the circle of tinsel on the needle of the balance was electrified, and the circle of gilt paper, after touching one of the points, was put into the balance, and the quantity of its electricity measured as before. The electricity of the second point was determined in a similar manner. The electricity of the first point was again determined, after an interval equal to that between the first and second ob servations, and the mean between the two determinations adopted, as free from the effects of dissipation.
Exp. 4. frith the same Globes. When the globes are touched at 23°, or at any point below it, no electricity appears.
By comparing the 2d, 3d, and 4th experiments, we shall have for the ratio of the electrical densities at 30 and 90, 4.33, the mean of which and 4.72 formerly found, is 4.78.
The following Table will show at one view the results of the preceding experiments.
When the globes were unequal, and the one half the diameter of the other, the density of the small globe was almost nothing till the distance was SO°.