Although Coulomb had satisfied himself that his re sults were not affected by any dissipation along the sup porting fibre, yet lie made the following experiment to put this point beyond a doubt. He touched the ball by four fibres absolutely similar to those which supported it, so that if there was any electricity lost by the sup porting fibre, there ought to have been five times as much lost by the five fibres. He could not perceive, however, any dissipation by the five fibres; so that we arc entitled to conclude, that there is no error in the ex periments arising from imperfect insulation.
On the Dissipation of Electricity along imperfectly in sulating Electrics.
Ix the preceding experiments, it was necessary to in sulate the electrified body in the most perfect manner, in order to obtain the unmingled effect which was due to the contact of the air. In measuring, however, the dissipation arising from imperfect insulation, it is ne cessary to insulate the balls by electrics so imperfect, that the dissipation arising from this cause may be ex tremely great, when compared with that which arises from the contact of the air. But when this relation is very great, the electrified body will lose its electricity so rapidly, that it would be impossible to make several consecutive observations before the electricity was com pletely dissipated. Coulomb was therefore obliged to make use of supports, which did not permit a very rapid diminution, and to determine by calculation the part which was lost by contact with the air, and that which was lost by imperfect insulation.
In this way he constructed the following Table, upon the same plan as the former. The only difference in the apparatus was, that the ball introduced into the hole nz, (Plate CCXLIV. Fig. 7.) for the purpose of repel ling the ball a of the needle, instead of being insulated as formerly by a small cylinder of gum lac, from 15 to 18 lines long, was supported by a single fibre of silk as it comes from the worm, and lines in length. The experiments were made on the same days with those in the last Table; so that, from a comparison of the two Tables, we may readily determine the quantity of elec tricity dissipated at every instant along imperfect insu lators.
It appears from the preceding Table, that the diminu tion of electricity is at fit st much more rapid when the electrical density is considerable, than it ought to be if it were produced solely by the contact of the air; and when this density is reduced to a certain degree, the di minution of electricity becomes precisely the same as it is when the insulation is perfect, or as it is when the dis sipation is entirely due to the contact of the air.
It follows, therefore, from this observation, that the silken fibre 15 inches long is a perfect insulator, when the reciprocal action of the two balls is measured in the first set of experiments in the preceding Table by a force of torsion of 40° or under, since the loss of electricity is then only per minute, the very same dissipation that took place on the same day, and that was due sole ly to the contact of the air.
It results, likewise, that in the second set of experi ments in the above Table, the silk fibre 15 inches long insulated perfectly when the repulsive action of the two balls was 70° or under, for then the dissipation was Atli, the very same that was obtained on the same day, and that was due solely to the conducting power of the air.
Since the repulsive forces are measured at a constant the product of the densities of the two equal balls, the next object of Coulomb was to ascertain the relation between the primitive density, and the different degrees of density of the ball supported by the silken fibre, when the silk fibre begins to insulate the ball in .t perfect manner.
In the first set of experiments in the preceding Ta ble, the two balls were equally electrified. The ball a upon the needle insulated by means of gum lac lost 2 of its electricity per minute, solely by the conducting power of the ambient air. The other ball supported by the silken fibre, dissipated its electri city not only by the contact of the air, but also by its imperfectly insulating support ; and it was not till 10h 40' that the silk liore hewn to insulate completely the second hall, at which time the repulsive force of the two balls was d(r. But at the beginning of the experiment, the repulsive force of the two balls equally electrified was 1130°. Since the action at a con stant distance is always proportioned to the product of the densities. and since the densities at the first expe riment were equal, the electric density of each ball is proportional to ./180 at ()'. But tt e hat e already seen, (p. 269. col. 1.) that the dissipation of electricity from the contact of air = ur t, where ci is the sity at the cud of any time t, and in col.