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 globe, in the same manner as the os cillations of a pendulum are produced by the action of gravity. As the circle 1 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 1. If we now call F the attractive force, and T the time in which a given number of oscillations are performed, we shall have T proportional to — but if we make G 1, 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 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 and the circle. Now, The distances are as the numbers . . . . 3 6 8 The times in which 15-oscillations are per formed by experiment 20 41 60 The times in which they are performed by theory 20 tO The difference between the theory and the experiment is almost 0 at the distance of 13 inches, hut at the dis tance of 24 it is nearly A correction, however, re mains to be applied to the experimental result ; for as feur 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 -A- in 4 minutes. Consequently, in order to obtain the correct number in stead of 60", we have v10 : 8/9=60" : 57", which dif fers only from the number 60" determined experi mentally. Hence it follows, that the law of the inverse ratio of the squares of the distances is correct also, for the attractive forces of oppositeiy electrified bodies.
Wre have already stated, and the reader must himself have made the remark, that the oscillations of the nee dle /g 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, and acting at the end of a lever of 7 or S lines, does not exceed the of 120,000 a grain, and therefore when the whole oscillations arc not greater than 40 or 60, the force of torsion is 1080,000 or 72 --, a quantity so small, that it can have 0,000 no perceptible influence on the duration of the oscilla tions, and consequently on the results of the experi ments.
The preceding method may be applied without any change to the determination of the repulsive forces of similarly electrified bodies; but the method already adopted by the use of the torsion balance is much more simple and exact.
WHEN any electrified body is insulated in the most When any electrified body is insulated in the most perfect manner, the quantity of electricity which it pos sesses is found to stiffer a gradual, and sometimes a ra pid diminution, till the whole of its electricity is com pletely dissipated. It becomes a matter of the greatest importance, therefore, to determine the law according to which this dissipation takes place, and we arc fortunate ly able to lay before our readers a series of beautiful ex periments which have been made by Coulomb, by means of the very delicate apparatus which we have already described.
When any insulated electrified body dissipates its electricity; the effect is produced by three causes; 1. By the conducting power of the air which surrounds the electrified body ; 2. By the deposition of humidity on
the surfaces of the elect•ics, which are employed to in sulate the electric body ; and, 3. By the imperfect insu lation produced by the best non-conductors. The last of these causes has probably the smallest share in the dissipation of the electric fluid, and cannot easily be estimated separately from the rest.
In measuring the dissipation produced by the two first causes, the reader must see, that there is some dif ficulty in separating the effects of the one cause from those of the other ; for as the electrified body must al ways be insulated by imperfect conductors, the real quantity of electricity dissipated during a given time must be owing to both causes, Coulomb, whose inven tive genius overcame every difficulty, has succeeded completely in separating the two effects. He saw, that if the portion of the surface of the electrified body, avhich communicated with the insulating support, was made extremely small, the loss of electricity along this support must be immeasurably minute, in comparison with the loss which was due to the humidity of the am bient air. He therefore put this idea to the test of ex periment, and found, that when the electrified body did not possess much electricity, such as a pith ball 5 or 6 lines in diameter, he could insulate it completely by a cylinder of sealing-wax, or gum lac, about half a line in diameter, and 18 or 20 lines long ; that a very fine silk thread, penetrated with melted wax, and covered with wax, so as to form a cylinder of a line in diame 'er, had the same insulating power when it was 5 or 6 inches long ; and that an equal degree of insulation could not be procured by a fine thread of glass 5 or t, inches long, or by a hair, or by a fibre of silk, unless when the air was uncommonly dry, or the electric sity of the ball very weak.
Having suspended a pith ball similar to that upon the needle a g, (Plate CCXLIV. Fig. 7,) to a %cry line silk fibre, covered with sealing-wax, and terminated with .1 cylinder of gum lac 18 or 20 lines in diameter, Cou lomb introduced it through the opening m in his torsion balance, so as to touch the pith ball a, as in the former experiments. By means of the conductor, Fig. 11. he communicated the same kind of electricity to the two balls, which immediately repelled one another to such a distance, that the repulsive force was equal to the force of torsion. Let us suppose that the angular distance of the balls was 40°, then twisting the thread of suspension through Coulomb brought the ball back to 20°. He next observed the instant when this ball pointed ex actly to 20°. As the electricity was dissipating, the balls approached one another some minutes after the opera tion ; so that, in order to be able to observe always at the same distance of 20°, he twisted the thread of suspen sion 30° by means of the index, and as the force of tot sion was diminished by these 30', the bails repelled a little more than 20°. He then waited the instant when the ball of the needle art ivcd at 20°, and counted, with great exactness, the time which elapsed between the two operations. Suppose that this time was three minutes, then it will follow, that at the first observation the dis tance of the balls was 20°, and the repulsive force 140+ ; that three minutes after, the repulsive force at the same distance of 20°, was only 110°+20°=130°, or was diminished SO°, or 10° per minute. Hence, as the mean force between the two observations was 160°+130° 2 and diminished 10° per minute, it follows that the electric force of the two balls diminished per minute.