It must have already occurred to the reader, that while these experiments are making, the balls were los ing their electricity. Coulomb found, that when they repelled one another through an arch of 30°, they re approached one another about one degree in three mi nutes ; but as he was able to make the experiments in two minutes, he did not consider it necessary to make anv correction for the loss of electricity. By observing, however, the rate at which the electric matter is dissi pated during every minute, a correction may be applied when the air is very moist, or when the dissipation hap pens 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 making 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 correct, when the dis tance of the balls 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 Methods of determining the Law of the tractive Force.
The next object of M. Coulomb was to determine t!le law which regulated the action of two oppositely rice trifled bodies; but in employing his apparatus for this purpose, he encountered a practical difficulty which he had not anticipated. When the two balls, one of which is electrified positively, and the other negatively, ap proach each other by their mutual attraction, the attrac tive force which, (as will be afterwards seen) increases in the inverse ratio of the square of the distance, often in creases 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 in 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 elec tric obstacle disturbs the results, and occasions a delay, during which a part of the electricity is dissipated.
Coulomb has shewn, in a more particular manner, the difficulties which attend this method of making the ex periments, and has pointed out the limits within which we may place confidence in the results. By carefully at tending to every circumstance, he arrived at the conclu sion, that the attractive force of two small globes, one of which is electrified positively and the other negatively, is in the inverse ratio of the squares of the distance of the centres of the globes. In order to inspire more con fidence in this result, he employed another method of making the experiments, which, though less simple and direct than the first, requires fewer precautions, and is less liable to error. It has also the advantage of admit
ting the use of halls of a very great diameter.
The apparatus which he employed for this purpose is 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 vet tical stand AC, and which has a scale of inches on one of its sides. The arm AB carries a piece of wood, EF, which, by the screw nut E, can be fastened on any part of the arm. The lower part of the piece EF carries a little flat bit of wood, s well dried in an oven, and covered with gum lac or seal ing-wax; and to its extremity is attached a single fibre of silk, s e, such as comes from the silkworm, which again suspends a horizontal needle of gum lac, 1g, 15 lines long ; at one extremity of this needle is a small cir cle 1, seven lines in diameter, cut from a sheet of gilt pa per, 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 apparatus consists of a globe of copper G, a foot in diameter, or a globe of paper covered with tinfoil, resting on four glass pillars, coated with scaling-wax, and terminating above in four pieces of sealing-wax three or four inches 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 hori zontal diameter G r is in a line with the centre of the circle I, 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 I 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 will be exactly three inches, and G I, the distance from the centre of G, nine inches, and the globe G is then electrified by the spark from a Ley den jar. By presenting a conductor to the plate 1, the electrified globe G will communicate the opposite elec tricity to the circle 1, so that upon removing the conduc tor, we shall have the globe G and the circle 1 in a state of mutual attraction. Let the needle LT be now made to oscillate, so that the amplitude of the oscillations is not more than 20 or 30 degrees from the line where the force of torsion is nothing, and observe the number of oscillations performed in a certain time. Again, place the pike Eli' at 12 inches, and then at 13 inches on the scale AB, so that the distance G 1 may be 18 inches and 24 inches successively ; and observe, in both these cases, the time in which the same number of oscillations is performed. The following were the results obtained by Coulomb.