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into account, and which arise from our not being able to touch, at the same moment of time, the two points of an electrised conductor whose electric reactions we are desirous of comparing now, during the time that has elapsed between the instant when one of the points was touched, and that when the other was touched, a portion of the electricity with which the body was charged has escaped, either by the air, which is always more or less moist, or by the supports, which are never perfectly insulating. It follows that the experiment gives, for the second point touched, an electric reaction relatively more feeble than that which should have been recognised.

Coulomb endeavoured to take into account this cause of error by estimating beforehand what the loss should be. With this view he distinguished the part of the loss that is due to the ambient air, from that arising from the imperfection in the insulating property of the supports. With regard to the influence of the former cause, he found that it depended on the degree of the humidity of the air; and he succeeded in drawing out tables, which give for each degree of the hygrometer the corresponding loss of electricity; namely, the relation existing between the quantity which the body loses in one minute, and that which remains to it after this minute. In order to estimate the part played by the supports in the loss of electricity, he made various experiments with threads of different substances, such as silk, glass, wax, gum-lac, &c., all of the same diameter and of variable lengths. He discovered that the insulating property of these threads varies for each with the intensity of the electricity and with their proper length, —that there exists consequently a certain degree of intensity of electricity, for which they are perfectly insulating: but that this degree depends upon their length and their nature. Thus, a thread of gum-lac insulates a quantity of electricity ten times greater than can be insulated by a silk thread of the same diameter. A thread of any nature whatever insulates a quantity of electricity which is proportional to the square root of its length.

These laws are not general, for they are only verified if the supports are long and slender like threads; moreover, they are often altered by the property that supports of a

certain nature possess, such as those of glass, to attract moisture from the air upon their surface, which notably diminishes their insulating property.

To take account of the loss of electricity, it is therefore better to employ another method, which is that employed by Coulomb in preference in his experiments; it is the method of alternatives or means. It consists in this: we first touch one of the points of the surface of the electrised body with the proof-plane, and convey it to the torsion balance; then, at the end of a certain time, as short as possible, we touch another point and operate in like manner: we touch a second time the first point at the end of a time equal to that which elapsed between the two experiments. We take the mean of the two angles of torsion that were obtained by touching the first point of the surface twice: this mean angle is the same as that which would have been obtained directly by experiment, had we been able to touch the first point at the same instant that we touched the second. In fact, the loss of electricity being approximately uniform during a certain time, the same quantity must have been lost in the interval that separated this third experiment from the second, as in that which separated the first from the second. The mean of the results of the first and the third experiments represents, therefore, an experiment made with an electric state similar to that under the influence of which the second was made.

Among the experiments of Coulomb, of which we have already spoken, I choose the following, which will very well enable us to understand the method of alternatives. It refers to an insulated steel plate, 12 inches long, 1 inch wide, and 2th inch thick. The proof-plane was 1 inch wide. Coulomb first applied the proof-plane to the middle of the plate, then to 1 inch distance from the extremity; and he obtained the following results:

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whence we conclude that the relations between the electric reactions of the middle of the plate, and of the part 1 inch from the edge, are as 347° to 417°5, or as 1 to 1.20.

Employment of the Proof-plane in the preceding Experiments.

The employment of the proof-plane for determining the relative quantities of electricity that are found on the different points of the surface of the electrised conductor, has given rise to various remarks and to certain objections, which we cannot pass by in silence. We have admitted that as this plane becomes, so to speak, a part of the surface upon which it is superposed, to take it away is virtually to take away this part of the surface, and also the electricity with which it is charged. This manner of regarding the part played by the proof-plane is contested. Coulomb admits that it is charged in all with a quantity of electricity double that possessed by the part of the surface with which it is placed in contact, so that each of its two faces has as much. He bases his assertion upon the fact, that if an electrised and insulated sphere is touched with an insulated but unelectrised disc, of which one of the two surfaces is equal to that of the sphere, the latter, after the contact, has only one third of the electricity that it had before; the disc, therefore, has taken the double of what remained, an effect that is due to its two surfaces, which are each equal to that of the sphere, becoming each charged equally with electricity. This is exactly the case with the proof-plane, which is itself merely a disc. We must observe, however, that if this disc is sufficiently small to be confounded. with the element of the surface upon which it is applied, the former mode of regarding its effects is more accurate than the latter, which supposes a disc of the same surface as the body with which it is placed in contact.

But whatever may be the absolute quantity of electricity that the proof-plane takes, the important matter is, that it always takes a quantity proportional to the electric reaction of the part of the surface with which it is placed in contact. But this actually does take place, as is proved by many of

Coulomb's experiments, especially the following. We take two insulated conducting cylinders, perfectly similar. We electrise one of them, and determine with the proof-plane the relation existing between the electric reaction of a point situated at the middle of its length, and that of a point situated at its extremity. We then touch the electrised cylinder with the one that is not electrised; it is evident that the total electricity must be divided between the two with perfect equality; consequently, the one that was electrised has in each of its points only one half of the electricity that it had formerly; but the relation between the electric reaction of the point taken at the middle and of the point situated at the extremity, must still remain the same. The proof-plane confirms this conclusion; a proof that, whatever may be the absolute quantity of electricity, it takes from it a quantity proportional to that possessed by the part of the surface upon which it is applied.

We may add, that the absolute quantity of electricity that the disc carries away is always very small in relation to what the electrised body possesses: so that, without sensible error, we may affirm that the contact of the plane, when it has only been repeated for an inconsiderable number of times, in no degree modifies the electric state of the body.

More serious objections have been made by Sir Wm. Snow Harris to the employment of the proof-plane: numerous experiments have proved to him that the quantity of electricity, taken away from the surface of a body by means of a small and thin insulated disc, may be influenced by the position of the point of application, independently of the quantity of electricity possessed by this body at the point touched; so that the same quantity may exist in two different points, and yet the proof-plane may be charged unequally when it is put in contact with these two points. It may even happen that, by the effect of the action of the neighbouring points, the proof-plane is not at all charged, even when the element of the surface with which it is placed in contact is strongly electrised. These singular anomalies are due to the effect of action at a distance, or the induction exercised by

the electrised bodies upon those that are not so; phenomena, the study of which forms the subject of the following chapter. But before terminating this, we may add that Sir W. Harris's objections cannot shake the confidence that philosophers place in the results obtained by Coulomb, at least in the more simple cases, such as those which concern the distribution of electricity in conducting bodies of a regular form. Perhaps where bodies of irregular form, or where many bodies in contact, are concerned, there might be a new study to make; but what process can we employ if we must reject this of the proofplane? I will permit myself to point out one, which, if it has not the precision nor the sensibility of the latter, has at least the advantage of manifesting to the eye in a direct manner the law that is followed in the distribution of electricity. It consists in taking a simple electroscope or electric pendulum, the very small and very light ball of which is charged with the same electricity as the body to which it is brought near. We then see, in presenting it to the different points of the surface of the body, that it is more or less repelled, according to the points in front of which it is placed. Thus, with an ellipsoïde, the distance to which it is repelled goes on increasing from the extremity of the small axis to the extremity of the large. With a sphere, it is everywhere equally repelled. The slightest differences in the electric reaction are shown in a very sensible manner by this process, which, although it is not in itself free from all the objections presented by the employment of the proof-plane, would perhaps be susceptible of being usefully perfected.

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