ELECTRICITY. 



443 



rk-i<- ; puvi 



Electricity 



PLATE 

 CtXLIV. 



1 had not anticipated. When the two balls, one of which 

 ia electrified positively, and the other, negatively, ap- 

 proach each other by then- mutual attraction, the at- 

 tractive force which (as will be afterwards seen) in- 

 crease in the inverse ratio of the square of the distance, 

 often increases in a greater ratio than the force of tor- 

 sion, which only increases as the angle of torsion, so 

 that it is only after many experiments that one succeeds 

 n preventing the attracting balls from coming into 

 mutual contact, by opposing an electric obstacle to the 

 motion of the needle a g ; the adhesion of the needle, 

 however, to the electric obstacle disturbs the results, 

 and occasions a delay, during which a part of the elec- 

 tricity is dissipated. 



Coulomb has shewn, in a more particular manner, 

 the difficulties which attend this method ol making the 

 experiments, and has pointed out the limits within 

 which we may place confidence in the results. 15y 

 carefully attending to every circumstance, he arrived 

 at the conclusion, that the attractive force of two small 

 plobes, one ofvhich is clccliified positively nni the other 

 negati-i-cli/, is in the inverse ratio of the squares of the 

 distance of the centres of the globes. In order to inspire 

 more confidence in this result, he employed another 

 method of making the experiments, which, though less 

 simple and direct than the first, requires fewer precau- 

 tions, and is less liable to error. It lias also the advan- 

 tage of admitting the use of balls of a very great dia- 

 meter. 



The apparatus which he employed for this purpose 

 K represented in Plate CCXLIV. Fig. 12. where AB is 

 a horizontal arm of wood, which can be fixed by means 

 of the nut A, at any height upon the vertical stand AC, 

 and which has a scale of inches on one of its sides. The 

 arm ABcarries a piece of wood, EF, which, by the screw 

 nut E, can l>e fastened on any part of the arm. The 

 lower part of the piece EF carries a little flat bit of 

 wood, st, well dried in an oven, and covered with gum 

 lac or sealing-wax ; and to its extremity is attached a 

 single fibre of silk xe, such as comes from the silk- worm, 

 which again suspends a horizontal needle of gum lac, 

 Ig, 15 lines long; at one extremity of this needle is a 

 small circle /, seven lines in diameter, cut from a sheet 

 of gilt paper, and placed perpendicular to the needle, 

 while at its other extremity the gum lac is formed into 

 a round little ball g. The remaining part of the appa- 

 ratus consists of a globe of copper G, a foot in diameter, 

 or a globe of paper covered wiui tinfoil, resting on four 

 glass pillars, coated with sealing-wax, and terminating 

 above in four pieces of sealing-wax th-ee or four indict 

 long. These pillars are fixed in a plate with a vertical 

 axis, which can be raised or depressed by means of the 

 screw nut N. 



The globe G is now raised by the nut N, till its ho- 

 rizontal diameter G r is in a line with the centre of the 

 circle /, and the stand upon which the globe rests is pla- 

 ced in such a position that when the moveable piece E 

 is at the zero of the scale of inches on the arm AB, the 

 circle / may just touch the globe G in the point r. The 

 piece EF is now placed at three inches on the scale, so 

 that the distance r I wiH be exactly three inches, and 

 G /, the distance from the centre of G, nine inches, and 

 the globe G is then electrified by the spark from a Leyden 

 jar. By presenting a conductor to the plate /, the electri- 

 fied globe G will communicate the opposite electricity to 

 the circle /, so that upon removing the conductor, we 

 hall have the globe G and the circle / in a state of mu- 

 tual attraction. Let the needle Ig be now made to oscil- 



late, so that the amplitude of the oscillations is not more Descriptive 

 than 20 or 30 degrees from the line where the force of Electricity.^ 

 torsion is nothing, and observe the number of oscilla- ""V""" 

 tions performed in a certain time. Again, place the piece 

 EF at 12 inches, and then at 18 inches on the scale 

 AB, so that the distance G I may be 18 inches and 24 

 inches successively; and observe,in both these cases, the 

 time in which the same number of oscillations is perform- 

 ed. The following were the results obtainedby Coulomb. 



Number of seconds in 



which these oscillations 



were performed. 



20" 

 40" 

 60" 



From these experiments we may now deduce the at- 

 tractive force of the globe G at the distances 9, 18, and 

 24; for the oscillations of the needle (abstracting the 

 effect of the force of torsion) are produced solely by 

 the action of that glol>e, in the same manner as the os- 

 cillations of a pendulum are produced by the action of 

 gravity. As the circle / is only 7 lines in diameter, we 

 may safely suppose all the lines drawn from the centre 

 of G to every part of the plate as equal and parallel, 

 and the whole of its action united in its centre /. If 

 we now call F the attractive force, and T the tune in 

 which a given number of oscillations are performed, we 



shall have T proportonal to -7-=; but if we make rf= 



v F 



G /, the distance of the centres of the circle and globe, 

 and suppose the attractive force to be inversely as the 



squares of the distances, or as rp , then it will follow 



that T is proportional to the distances d; so that if this 

 law is correct, the time of any number of oscillations 

 should be as the corresponding distances between the 

 centres of the globe anil the circle. \ow, 



The distances are as thr- number* 3 G 8 



The times in which 15 oscillations arc per- 

 formed by experiment 20 41 60 



The times in which they are performed by 



theory ". 20 40 54- 



The difference between the theory and the experiment 

 is almost at the distance of 18 niches, but at the dis- 

 tance of 21- it is nearly T V. A correction, however, re- 

 mains to be applied to the experimental result ; for as 

 four minutes were spent in the experiments, the globe 

 and the plate had lost a portion of their electricity. 

 Coulomb found that the action was diminished ^ of 

 the whole per minute, and therefore ^ in 4 minutes. 

 Consequently, in order to obtain the correct number 

 instead of 6'0", we have t/10 : v/9=60" : 57", which 

 differs only ^, from the number 60" determined expe- 

 rimentally. Hence it follows, that the law of the in- 

 verse ratio of the squares of the distances is correct 

 also, for the attractive forces of oppositely electrized 

 bodies. 



We have already stated, and the reader must him- 

 self have made the remark, that the oscillations of the 

 needle Ig are partly due to the force of torsion, and 

 are not produced solely by the mutual attraction of the 

 globe and the gilt circle. Coulomb, however, has shewn, 

 that the force necessary to twist through a whole arch 

 of 360, a silken fibre 6 inches long, an3 acting at the 



