145 In this way Coulomb constructed the following Ta ble, which contains the observations made on the 28th May, the 29th May, the 22d June, and the 2d July, which lie selected from a multitude of others, as on these four days the variation of the humidity of the air was very great, while its temperature was very nearly the. same.
In this Table, the first column represents the instal,: of observation ; the second, the distance of the balls; the third, the degree of torsion given by the microme ter ; the fourth, the time which elapsed between two consecutive observations ; the the loss of the else uric force during that time ; the sixth, the mean force of repulsion between the two observations, as measured by the mean torsion indicated by the micrometer added to the distance of the two balls; and the seventh, the ra tio of the electric force lost in one minute to the tota' force.
ft will appear by examining the seventh column, that the ratio or the electric force lost to the total force is a constant quantity during the same day, or while the air has the same degree of humidity; from which it follows, that the loss of electricity is always proportional in the same state of the air to the electrical density.
From these experiments, Coulomb has shewn how to determine the electricity of the two balls after any given time. Thus from the first set of experiments in the Table, when the dissipation is every minute, he has slim!), that if we make t= the interval of time, d= the electrical density of each ball, and D the pi imitive density of the electric fluid in each ball, and ft. the modu lus of the logarithmic system, then we shall have 2 t=log• d • n 2 but as the distance is constant, is proportional to the primitive action, and to the action while the time is • —t. Hence in using the ordinary table, where the mo dulus fc=0.4343, we shall have 0.4343 , 41 d` If we now seek from this formula the value of d in the first experiment, it will be found that at the first experiment and that at the 6th ex 150 periment 345 t=loz.— 50 –= log. 3, and consequently t= 41 log. 0.4343 45 by the experiment.
Now the first experiment commenced at 6h 32' 30" and the sixth at 7h 17', the difference of which is 44'30" in stead of as found by the experiment.
Coulomb has also shewn, that the ratio of the force lost in a minute to the total force, is double of the ratio of the loss of the density of each body to the total den sity. For calling d their electrical density, and a their
distance, then since the two balls are equal, and receive at first the same quantity of electricity, their reciprocal action will be represented and consequently its a momentary diminution will be proportional to 2dd a Hence the ratio of this variation of repulsion to the 2 d repulsion itself, will be, neglecting equal to .
But is the relation of the loss of density of each ball to its own density, and consequently the dissipation is only one-half of the diminution of repulsion. Thus in the ex periment of the 28th of June, the diminution of repul sion was from which it follows that the dissipation was s2 per minute.
Our author made a great number of experiments of a similar kind with balls of different magnitudes, and when the quantity of electricity, as well as the electrical den sity of each ball, were very different, he always found, that the ratio of the dissipation of the electric force du ring a minute, to the total force, was uniformly a con stant quantity. On the 28th June, for example, though he presented to the ball a a ball double the size, and though he communicated to this ball a degree of elec tricity greater or less than that of the ball a, yet the loss of the electrical force was constantly per minute.
The most important result, however, which lie ob tained, was, that when the air was dry, and the degree of electricity not great, the ratio of the decrease of the electrical density to the density itself, wars always a constant quantity, whatever was the form, and %vhate% r the magnitude of the electrified body. This expel iment was made with a globe a foot in diameter, and with cy linders of all lengths and magnitudes: he even ted, in the place of the balls, circles of paper and of ; and, on a day particularly dry, he armed one of the balls with a small copper wire WI of a line in diameter, and 10 lines long ; and in measuring the dissipation of its electricity, he found that every body which he used on that day lost part of its electricity in a minute. It must be carelully observed, however, that this equality of dissipation exists only when the electric density has been reduced to a eel tain point ; for, when the electricity is very strong, all angular bodies dissipate their elec tricity according to a law which will afterwards be deter mined.