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that the loss is 10° a minute. Moreover the mean repulsive

force between the two experiments, was

160° +130°

2

or 145o.

Comparing this with the observed diminution, we see that the electrical force of the two balls diminished on this day by

1

10 or a minute, on account of the contact of the air only. 145 141

By experiments of this kind, Coulomb constantly found that on the same day, and with the same state of the air, the loss of electricity for a short time was proportional to its intensity, and that thus the ratio of these two elements is invariable. But this ratio changes with the state of the hygrometer, and consequently with the quantity of aqueous vapour suspended in the air.

21. A greater number of experiments on this subject would serve to discover the ratio between the quantity of aqueous vapour, and the greater or less rapidity with which the dispersion of electricty takes place. We might thus determine also whether this vapour is the sole cause of the phenomenon, or whether the pressure and temperature of the particles of the air itself are not also concerned. If we were able to estimate the influence of these different causes, we should perhaps find the electrical balance to be the most exact and sensible of all hygrometers. We might at least, from the simple indications of meteorological instruments, assign the proportional loss of electricity sustained. For want of these data we are obliged to determine this proportion directly by experiment for each particular time, when we have occasion for exact experiments on the intensity of electrical forces.

22. It is very fortunate for us in our experiments, that the law of decrease happens to be so simple; since, for the same state of the air, it is proportional to the repulsive force, we have occasion only for a single experiment each time, in order to apply the necessary correction to any number of cases. Moreover, the law which we have discovered, enables us, when the intensity of an electrical force and its rate of decrease are once determined, to calculate it for any other given moment. By examining the results thus obtained, we learn that the same law of decrease is applicable to cases where the two bodies acting upon each other, are of unequal magnitudes, and charged with

unequal quantities of electricity. Indeed, whatever be the magnitude of the fixed ball compared with the moveable one, and whatever be the quantity of electricity at first given to them, whether they are electrified simultaneously, or one after the other, and in whatever proportion, the momentary decrease of their whole repulsive force, measured at the same distance, is always in the same proportion to its intensity; and thus our experiments are all equally suited to the purpose of finding this common ratio. Moreover, this ratio is still the same when we employ balls of different substances. The nature of the substance has absolutely no influence on the loss of electricity occasioned by the contact of the air, at least with respect to the portion which acts at a distance by attraction and repulsion; and this confirms the observation which we have before made, that material bodies do not seem to retain the electric principle by any proper affinity, but by the effect simply of the resistance which is opposed to it by the surrounding air. For example, in weather when the electricity was decreasing at the rate of a minute for each of the pith balls of the balance, Coulomb found that it decreased also when he substituted for one of these balls a ball of copper; and, which will appear still more extraordinary, the decrease was also for a ball of sealing wax, which had been charged with electricity, by bringing it in contact with a body strongly electrified; and thus the surface of such a body opposes no difficulty, to the transmission of the electric principle, and has no influence in retaining the portion of this principle, which manifests itself by its reaction, when once it becomes free.

23. We have as yet considered only bodies of a globular shape; but whatever may be the figure of the electrified body, whatever its magnitude and the distribution of its repulsive force, if the air is very dry and the electricity communicated not very intense, the momentary decrease of the repulsive force is always. the same, and preserves always the same ratio to its intensity. This was demonstrated by Coulomb with a globe of a foot in diameter, and with cylinders of all diameters and all lengths. He substituted for the balls of his balance, circles of paper or metal; he also, in one instance, armed one of them with a copper wire of an inch in length, and in diameter; and he

found that, at the time of his experiments, the repulsive force of all these bodies, although so different in form, decreased by the same quantity, namely, in a minute. But it is necessary to remark, that this equality of decrease for bodies of different forms takes place only when their electricity is already considerably reduced, and reduced so much the more, according as the air is more moist. For all angular bodies, when possessed of a strong electricity, lose at first this excess by a much more rapid decrease, as we shall have occasion to show hereafter, when we come to speak of the electricity of points. This phenomenon may be rendered evident to the senses, without the aid of the balance, by connecting the prime conductor of an electrical machine with a metallic bar, having sharp angles or points. For, upon putting the machine in motion, the experiment being performed in the dark, the electricity communicated to this bar, will produce, as it flies off from the points, beautiful tufts of light. I do not mean to say that this fire is itself the electricity, for herein is involved a question to be examined hereafter; but as light always attends the rapid escape of electricity, it is at least a sign and indication of this escape. It would be well worth our attention to inquire whether, the state of the air being the same, the two kinds of electricity are dissipated at the same rate. I have made the examination, and find that this is in fact the

case.

24. The law of the gradual dispersion of electricity, produced by the mere contact of the air, being thus known, Coulomb proceeded, according to the same method, to determine that occasioned by the imperfect insulation of the supports.

The course which first suggests itself, is to choose such substances for supports, that the loss arising from this cause shall be very great, compared with that depending upon the contact of the air. But this very rapid decrease would be attended with a serious inconvenience. For every time we touch the balance, either to give the balls their first electricity, or to change the torsion by means of the graduated circle, the needle does not return to a quiet position till after several oscillations. It is therefore necessary that the insulation should be pretty perfect, that the electricity may not sustain in this interval very great variations of intensity, and that we may be able to make several experi

ments of this kind successively, without giving to the balls a new charge. Accordingly, Coulomb instead of suspending the fixed ball of the balance to a cylinder of gum lac, attached it to a single fibre of silk, as it comes from the silk worm, of about fifteen inches in length. The moveable ball at the end of the needle was always insulated as perfectly as possible, and made equal in magnitude to the other. Coulomb measured, as before, the repulsive force of the two balls at different times, and hence calculated the decrease of the electricity. He found this decrease to be much more rapid than that produced by the air alone, when the intensity of the repulsive force was considerable, but that it became gradually less rapid as the intensity diminished; and thus at a certain point, the ball, supported by the silk fibre, lost precisely as much as when it was insulated in the most perfect manner; and this limit being once attained, the same equality continued through the lowest degrees of intensity. We hence learn, that at this point the thread begins to insulate perfectly.

In these experiments, the moveable ball can lose its electricity only by the contact of the air. We may therefore calculate for any instant, the state of its electrical action from the law of decrease above established; and as the whole repulsive force, obtained by observation, for this instant, makes known the amount of the reciprocal electrical action of the two balls, we can thence deduce, for the same instant, the electric action of the fixed ball. By this calculation, therefore, the effect of imperfect insulation is determined. Applying it to the experiments we have mentioned, Coulomb was able to fix the degree of electrical action at which each of the supports used by him began to insulate perfectly; and he found that the intensity of this action was proportional to the square root of their respective lengths; in other words, that for the same state of the air, a quadruple length of support insulates perfectly a double quantity of electricity; it being well understood that this proportion is restricted to supports of a cylindrical form, which differ only in respect to length. When the substance or its figure is changed, it is necessary to deduce the ratio from the formula itself. Calculating in this way, from experiment, the intensity of the electrical action, at which perfect insulation begins, in the case of threads of gum

lac and of silk of the same length and diameter, we find that it is ten times greater for the first substance than for the second. By similar calculations we may compare together the conducting power of all substances which transmit electricity imperfectly.

In order thus to compare one substance with another, it is by no means necessary that the balls of the balance should be observed at the same distance in the two series of experiments; it is enough that this distance be constant in each series, and that we substitute its value each time in the formula. It is equally immaterial what degree of electricity we give to the balls. But it is always necessary that they should be equal and simultaneously electrified; it is also necessary that they, as well as the torsion wire, should be the same in all the experiments; otherwise the ratio of the torsions to the repulsive forces would not be the same in the different series, which would render the comparison of them more difficult and less direct. These are the only indispensable precautions to be observed.

Of Electricity in a State of Equilibrium in insulated Conducting Bodies.

25. Knowing how to reduce the electrical action of bodies to a constant state, notwithstanding the continual loss which takes place by the contact of the air, and along the supports, we are prepared to inquire into the mode in which electricity distributes itself among the different parts of the same body, both in its interior and at the surface.

Now, from what we have already learned upon this subject, it would seem very probable that the electricity is confined entirely to the surface of conducting bodies, and that their interior particles have no effect in retaining it; otherwise, it is not easy to perceive how the mere circumstance of equality of surface in the case of two bodies in contact, should produce between them an equal division of electricity, whatever be the substance of the bodies themselves, or how this equality should take place when one of the bodies is solid and compact, and the other hol

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