ELECTRICITY. 



449 



the modulus of the cemmen logarithms. Hence we shall 

 have log. d = log. D 



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 

 ^180=13.416. 



Log. rf=l. 12762 26482=8628=7-291. 

 Hence the electrical density of the ball of the needle 

 at 10 h 40', which at 10 h 0' was equal to v/18f=13.416, 

 is now equal to 7.291. But as the action of two baits 

 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 7-291 A=40, 



=5.49. Hence it follows, that the elec- 



and A = 



40 



7^291 



U elation 

 between the 

 electric*! 

 ilcnity and 

 the length 

 of supports 

 when they 

 insulate 

 perfectly. 



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 5.4'J 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 gum 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 iierfect insulation, was proportional 

 to the square root of the length of the support ; that 

 is, if a silk fibre, wlm-c density is D, and whose length 

 i> one foot, begins to insulate perfectly, a fibre 4 1'eet 

 long will be necessary to insulate perfectly when the 

 density is double or 2 I). This experimental result 

 Coulomb has shown to be quite conformable to theory, 

 but 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. 



He supposes that the imperfect insulating power of 

 electrics depends on the distance of the conducting 

 molecules which compose the imperfectly insulating 

 Mipport, or which are spread over its surface, and there- 

 fore, in order that the electric matter may pa^s 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. He sup- 

 poses likewise, that this non-conducting space opposes 

 a resistance constant for the same body, because the 

 conducting molecules are uniformly distribute;!, or at 

 the 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 rlectric fluid is uniformly distri- 

 buted thoughout all its length. And, i!. 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. 



SECT. XI. On the Distribution of Electricity. 



WHEN any conductor receives electricity from an ex- 

 cited electric, this electricity is instantly distributed dcctticity . 

 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. 



The apparatus employed by Coulomb to determine ^* T 

 these important points, is nearly the same as what we ^ - ? 

 have already described. The only change which he 

 made upon it, was to remove the divided band of pa- 

 per - q, and to substitute in its place a wooden circle, 

 like the horizon of a globe, resting on four pillars, and 

 having a diameter nearly double that of the cylinder. 

 This circle is placed in such a manner, that its centre 

 may coincide with the axis of the wire or fibre which 

 suspends the needle, and that the first division on thr 

 wooden circle may be in the same line with the fibre of 

 suspension, and the centre of the ball a when the needle 

 a g is at rest. 



I. OH the Cause of the Distribution of Electricity. 



In order to determine whether electricity was distri- On the cause 

 buted over conductors by an affinity or electric attrac- of the dis- 

 tion for one body in preference to another, or merely tnbution f 

 in virtue of a repulsive force, Coulomb instituted the e ' 

 following experiments. 



E.tp. 1 . Having suspended in the hole m of the ba- Fig. T. 

 lance, by means of a cylinder of gum lac, a small ball 

 ot copjier, so as to touch the ball a of the needle 

 as before, he placed the centre of this ball in a 

 straight line with the suspending fibre and the zero 

 of the scale on the wooden circle. The ball a of the 

 needle which touched the copper ball was then distant 

 from the position where the torsion was nothing by the 

 sum of the semidiameters of the two touching balls. 

 The two balls were then electrified by the insulated pin 

 CAB, as in the former experiments, and the ball a was 

 repelled to the 48th degree upon the scale. The sus- pj g . u. 

 pending fibre was then twisted 120 by the head of the 

 micrometer, in order to bring back the ball of the 

 needle into contact with the copper ball as before, and 

 as soon as the oscillations of the needle ceased, it stop- 

 ped at 28'. At this instant Coulomb quickly brought 

 another pith ball of the same size as the copper ball, 

 and insulated with gum lac, into contact with the cop- 

 per ball, and upon removing the pith ball, the ball a 

 approached the ball of copper. In order to brhig it 

 back to its first distance of 28, it was necessary to un- 

 twist the fibre, so that the micrometer marked 120" be- 

 fore contact, and only 44 after it. 



Kjtp. 2. In place of the ball of copper, Coulomb 

 now substituted a circle of iron, 10 lines in diameter, 

 suspended by a cylinder of gum lac, and having its 

 vertical plane passing through the zer on the wooden 

 scale. He then electrified the ball a and the iron disc, 

 as in the preceding experiment, and the ball a was re- 

 pelled. In order to bring back the ball a into contact 



VIII. PART It- 



See Men*. Atad. Par. 1T85, p. 6S3. 



8 L 



