The repulsion between two small bodies charged respectively with, and units of electricity is numerically equal to the product of the charges divided by the square of the distance.
Dimensions of the Electrostatic Unit of Quantity.
42.] If is the concrete electrostatic unit of quantity itself, and , the numerical values of particular quantities; if is the unit of length, and the numerical value of the distance; and if is the unit of force, and the numerical value of the force, then the equation becomes.
![{\displaystyle [Q]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32d2453284fa72720da205f53dd91aedcaac8e35)
![{\displaystyle [L]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1eba88cad4b17de726ed2c779b29eecdf5819a2)
![{\displaystyle [F]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2495ec47ff372dabec343f9ef436e1bc8622d055)
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![{\displaystyle {\begin{aligned}F[F]&=ee'r^{-2}[Q^{2}][L^{-2}];\\~[Q]&=[LF^{\frac {1}{2}}]\\&=[L^{\frac {3}{2}}T^{-1}M^{\frac {1}{2}}].\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e1b11523ebb373be6423115028e37e6e4189cee)
This unit is called the Electrostatic Unit of electricity. Other units may be employed for practical purposes, and in other departments of electrical science, but in the equations of electrostatics quantities of electricity are understood to be estimated in electrostatic units, just as in physical astronomy we employ a unit of mass which is founded on the phenomena of gravitation, and which differs from the units of mass in common use.
Proof of the Law of Electrical Force.
43.] The experiments of Coulomb with the torsion-balance may be considered to have established the law of force with a certain approximation to accuracy. Experiments of this kind, however, are rendered difficult, and in some degree uncertain, by several disturbing causes, which must be carefully traced and corrected for.
In the first place, the two electrified bodies must be of sensible dimensions relative to the distance between them, in order to be capable of carrying charges sufficient to produce measurable forces. The action of each body will then produce an effect on the distribution of electricity on the other, so that the charge cannot be considered as evenly distributed over the surface, or collected at the centre of gravity; but its effect must be calculated by an intricate investigation. This, however, has been done as regards two spheres by Poisson in an extremely able manner, and the investigation has been greatly simplified by Sir W. Thomson in his Theory of Electrical Images. See Arts. 172-174.
Another difficulty arises from the action of the electricity induced on the sides of the case containing the instrument. By
