44* 



E L E T T R I C I T V. 



Coulomb 1 ! 

 CMthodor 

 determining 

 the Uw of 

 the repul. 

 ie force. 

 Kin. 11. 



Into the other hole w, is introduced a small cylinder 

 ElwovitT. mr i t the lower part of which, x t, is formed of gum 

 1 ic, and carries a pith ball (. At six inches from the 

 bottom of the glass cylinder there is pasted round its 

 circumference a band of pajx-r : c/, divided into 360 

 degrees, so as to be on a level with the needle at;. 



In order to adjust this instrument for use, the hole 

 m is made to correspond to the zero of the scale z o q. 

 The index o i of the micrometer is then placed upon 

 the xero of its graduated circle o p, and the whole mi- 

 crometer ii turned in the tube fh, till, in looking pa-t 

 the vertical silver wire P /, HIM! the centre of the ball, 

 the needle a e; shall conv-pond with the zero of the 

 scale :q. The other ball t is then introduced, so that 

 it may touch the ball n, and so that a line joining the 

 centre of the silver wire, and the ball /, may also point 

 to the zero of the scale r q. 



Cotilomb'i Method of determining Utc Lan of the Rcpul- 

 tive Force. 



When the instrument was thus adjusted, Coulomb 

 applied it in the following manner to determine the law 

 of the repidsions of the two balls t, a. Having provi- 

 ded a brass pin AB, F'ig. 1 1. with a large head, he stuck it 

 into a handle AC of sealing-wax, and having electrified 

 it he introduced it through the hole m, Fig 7- and touch- 

 ed the ball ( in contact with n. The electricity of the pin 

 was thus communicated to the two balls, which of course 

 possessed the same kind of electricity ; and as soon as 

 the pin was withdrawn, the balls mutually repelled 

 each other to a distance which is measured by obser- 

 ving the degree on the circle tOq, which is pointed 

 out by a line joining the silver wire and the ball a. If 

 the index o of the micrometer is now turned in the di- 

 rection p n o, the silver wire / P will be twisted, and 

 .til produce a force proportional to the angle of 

 torsion^ which is requisite to make the ball a return to 

 the ball /. By this means he observed the distance at 

 which different angles of torsion bring back the ball a 

 to the ball / ; and in comparing the forces of torsion 

 with the corresponding distances of the balls, he obtain- 

 ed a measure of their repulsive force. 



Kip. \. The two balls bein^ electrified with the 

 head of the pin, and the index of the micrometer being 

 set to zero, the ball a was repelled by the ball t to the 

 distance of 36 degrees. 



]'..r]>. 2. The silver wire being twisted by turning the 

 index of the micrometer 126 degrees, the ball a ap- 

 proached to t, and stopped at the distance of 18 de- 

 grees from it, having moved backwards tlirough an arch 

 of 18. 



Ejcp.S. Having again twisted the silver wire through 

 an arch of 567", the two balls approached, and stopped 

 at the distance of 8^. 



Now, as the force of torsion, or the force which is 

 capable of keeping a thread twisted to a certain de- 

 gree, go as to hinder it from turning round its axis, and 

 recovering its natural state, has been shewn by Cou- 

 lomb to be proportionjd to the angle of torsion, or the 

 arch through which it has been twisted, we have in 

 the first experiment a force of torsion equal to 36 ; and 

 in the second experiment, when the distance of the balls 

 wi 18, the angle, and consequently the force of tor. 

 ion, was 126+ 18= 144; so that the repulsive force, 

 at the distance of 36, was 36 ; and the repulsive force, 

 at the distance of 18, was 144, or quadruple at half 

 the distance. In the third experiment, when the dis- 

 tance of the balls was 8 J, the force of torsion was 567; 



Coulomb'* 

 experi- 

 ment!. 



so that, nt a quarter of the distance, the repulsive force r> 

 was nearly ci;;l.t times as great. II ,,.-, that *' ''^'"'"'T- 



the repulsive force of tno small globe* r ~~*~l~ m 



jwitivtly or HCgalivi-ly, ix in the inverse till id of the 

 Kfiiarcs of the distance of the centres </ the two pi lid. 



In the preceding experiments, UK- wire \'l was 28 

 inches long, and ,'^th of a grain in weight, and tho 

 force necessary to twist it through an iiiiijc of 

 when at the distance a P, or four inches from the wire, 

 is T T.th of a grain, as calculated from the formula 1 gi- 

 \ m by Coulomb in his Memoir on the force of Torsion. 

 Hence the real forces in the preceding expet imtnts were, 



of 



Ike BniU. 



36 

 18 



and Force* 

 uf Tonion. 



36 

 144 



676 



Abiolvtc force* 

 graim. 



-r^thofagrain. 



M. Coulomb has remarked, that with a silver wire, 

 so fine as that which he used, and which requires only 

 a force of r-j^^ part of a grain to twist it through an 

 angle of .V , it is impossible, with every precaution, to 

 .in the position of the needle to \\ithin 2 or Is' 

 when the force of torsion it nothing. He recommends 

 therefore, after electrifying the balls, to twist the wire 

 30 or 40, which, joined to the observed distance of the 

 two balls, will give a force of torsion so great as to re- 

 move any sensible error arising from the uncertainty of 

 2 or 3 already mentioned. He recommends also the 

 use of a wire nearly double in diameter to that which 

 he used, as it was liable to break with the least agita- 

 tion. A wire of this thickness should also be stretched 

 for two or three days by a weight equal to half of that 

 which is nece.asary to break it, and should never be 

 twisted through an arch of more than 300. 



It must have already occurred to the reader, that 

 while these experiments are making, the balls were 

 losing their electricity. Coulomb found, that when 

 they repelled one another through un arch of 30, they 

 reapproached one another about one degree in three 

 minutes; but as he was able to make the experiments 

 in two minutes, he did not consider it necessary to 

 make any correction for the loss of electricity. By ob- 

 serving, however, the rate at which the electric matter 

 is dissipated during every minute, a correction may be 

 applied when the air i* very moist, or when the dissi- 

 pation happens to be considerable. 



In the preceding experiments, the distance of the 

 balls was measured by the angular distance to which 

 they were separated, which is greater than the chord, 

 or the correct distance; but this is in a great degree 

 compensated by an opposite error, arising from ma- 

 king the lever, by which the force acts, equal to the 

 radius, or half the length of the needle, whereas it 

 is equal only to the cosine of half the angular distance 

 of the balls. This compensation is sufficiently correct, 

 when the distance of the Iwlls does not exceed 25 or 30 

 degrees ; but, at greater angles, the distance between 

 the balls and the length of the lever must be accurately 

 computed. 



Coulomb's Method* of determining the Law of the Attrac- 

 tive Force. 



The next object of M. Coulomb was to determine the On the l 

 law which regulated the action of two oppositely elec- '' thc > 

 trifled bodies ; but in employing his apparatus for this Tf 

 purpose, he encountered a practical difficulty which he 



