7. of the first set of experiments in the preceding Table.
D 0.4343 Now the fluent of the above formula is log.— =, d 82 D being the primitive density of the ball, and 0.4343 the modulus of the common logarithms. Hence we shall have log. d=log. D— 0.4343 82 t. Now if we wish to know the density D after 40 minutes, when the silk fibre begins to insulate perfectly, we shall find for the ball a supported by gum lac, and perfectly insulated during the whole of the experiment, D being equal to V 180=13.416, Log. =7.291.
Hence the electrical density of the ball of the needle at 10h 40', which at 10h 0' was equal to is now equal to 7.291. But as the action of two balls is always proportional to the product of the density, if we call A the density of the ball supported by the silk fibre when it insulates perfectly, or when the action of the two balls is measured by 40°, then 7.291A=40°, 7. 401 = — and A — 5.49. Hence it follows, that the elec — 29 trical density of the ball supported by the silk fibre is 5.49, when the fibre begins to insulate perfectly, the distance of the two balls being 30".
Making use of the preceding formulae, Coulomb found, from a comparison of several experiments, that a small cylinder of gum lac 18 lines long, did not cease to insulate perfectly till the ball was charged with a degree of electricity nearly triple that of the silk fibre, that is, assuming 5.49 for the electrical density of the ball when supported by the silk fibre 15 inches long; when it begins to insulate perfectly, we must triple this density, to have the density at which the guill lac cylinder 18 lines long commences its perfect insula tion.
Our author next endeavoured to find the relation between the electrical density and the length of the supports at which they begin to insulate perfectly ; and he found from experiment, that the electric density, when a silk thread, or hair, or any fine cylindrical elec tric commenced its perfect insulation, was proportional to the square root of the length of the support ; that is, if a silk fibre, whose density is D, and whose length is one foot, begins to insulate perfectly, a fibre 4 feet long will be necessary to insulate perfectly when the density is double, or 2 D. This experimental result
Coulomb has shown to he quite comformable to theory, hut we cannot venture to follow this ingenious author into the field of speculation.* We shall merely lay before the reader the principle upon which he pro ceeds.
Ile supposes that the imperfect insulating power of electrics depends on the distance of the conducting molecules which compose the imperfectly insulating support, or which are spread over its surface, and there fore, in order that the electric matter may pass from one conducting molecule to another, it must traverse a small non-conducting space of a greater or less mag nitude, according to the nature of the body. Ile sup poses, likewise, that this non-conducting space opposes a resistance constant for the same body, because the conducting molecules are uniformly distributed, or at ;he same distance from one another. These supposi tions being admitted, Coulomb demonstrates the two following propositions. 1. That in a very delicate conducting fibre, the electric fluid is uniformly distri buted throughout all its length. And, 2. That if the fibre has a certain degree of non-conducting power, the action which each point experiences will depend solely on the electrical density of the molecule in contact with this point, and that the action of the rest of the fibre may be regarded as nothing.
WHEN any conductor receives electricity from an exWhen any conductor receives electricity from an ex- cited electric, this electricity is instantly distributed over the body; for every part of the conductor exhi bits electrical properties. It is therefore a most inte resting enquiry to discover the cause by which this distribution is effected, to determine in what parts of the conductor the electricity resides, and in what man ner the distribution takes place, between two or more bodies in contact, and in bodies of various forms.