quantity; the second is, that the trial plane, considered as infinitely small in relation to the whole surface of the conducting body, takes always at each point of the surface a quantity of electricity proportional to that of the point touched.

Proceeding in this way, each contact of the plane diminishes somewhat the absolute quantity of electricity of the body which it touches, and consequently we ought, strictly speaking, to take account of this diminution, if we would bring our successive trials into exact comparison; but this is rendered unnecessary by making the plane so small, that the quantity of electricity taken off by it, shall be inconsiderable in comparison with that of the whole surface of the body. If, in addition to this precaution, we would reduce the error still more, we have only to carry back the plane to the surface of the body without discharging it. Care should be taken also to support the little planes by threads of very pure gum lac, having the greatest insulating power.

31. As these experiments always require to be several times repeated, it is necessary, in comparing them with each other, to take notice of the loss of electricity occasioned by the contact of the air. This may be done according to the laws of decrease above given; but we may dispense with this correction, also, by combining the experiments in such a manner, that they shall rectify each other. For this purpose, if it is proposed to compare the electrical action of two points a and b, we first touch a with the little plane, and observe the action which results. We then touch b, and observe the corresponding action. If there be a certain interval between the first and second observations, as three minutes, for example, we should touch a again three minutes after the second observation, and take the arithmetrical mean between the two actions. We should thus have the same result as if the two contacts of a and b had been made at the same moment. This method of correction is to be preferred to any other. It even corrects the effects of loss along the supports, provided it is small, as it always is when they are well chosen and well prepared.

32. To give an example of the method of alternate contacts, I shall select the following experiment, which I find among the manuscript minutes of Coulomb.

He proposed to discover how electricity distributes itself upon a thin insulated plate. For this purpose, he insulated a plate of steel 11 inches in length, 1 inch in breadth, and of an inch in thickness. In order to touch it through its whole breadth, he made a trial plane an inch in length and of an inch in breadth. He first applied this plane to the centre C of the plate, and afterwards at an inch from the extremity, and he obtained the following results;

Fig. 10.

That is, upon equal spaces, taken throughout the breadth of the plate at the centre, and at an inch from the extremities, the quantities of electricity are to each other as 1 to 1,2, and therefore nearly equal.

Coulomb repeated the experiment, placing the trial plane exactly at the extremity, but resting wholly upon the surface, and he obtained the following results;

Observed Mean tor-Mean tor- Ratio of
torsions. sions at the sions at the the mean

In this case the ratio of the quantities of electricity is much greater than in the preceding. Thus we see that while they are nearly constant from the centre to within one inch of each extremity, beyond this the electricity increases very rapidly.

Coulomb made a third experiment, placing the trial plane across the end of the plate at D so as to come in contact with both surfaces at once; he then obtained the following results;

Thus the trial plane being placed across the end of the plate, receives just double the electricity which it acquired at this extremity when it touched but one surface.

The experiment being repeated with a plate 22 inches long, that is, of twice the length of the preceding, and otherwise of the same dimensions, gave exactly the same ratios between the intensities at the centre and at the extremities.

53. Hence Coulomb infers; (1.) That in the contact upon the surface of the plate, the trial plane shares the electricity of only one of the two faces, which is that to which it is applied; (2.) That beyond a certain length of the plate, so considerable that the electricity shall be nearly uniform over the greater part of its surface, any prolongation has no sensible influence upon the ratios of the quantities of electricity accumulated at the extremities and at the centre, the first being always double the second.

To understand the full import of this remark, let AB be a Fig. 11. plate whose length exceeds the limit just mentioned. Suppose the electrical state of the different points of its surface to be examined, and represented by the ordinates CE, PM, QN, AA', BB'. These ordinates will not differ sensibly from each other until we arrive within about an inch of one of the extremities, after which they will go on rapidly increasing through the remaining portion, so as to form the curve A'M or B'N. Now, since the ratio of AA' to PM or to CE is the same in all plates whose length is very great in comparison with their breadth, and as the same constant ratio obtains for the intermediate ordinates, it follows that the curve A'M or B'N preserves the same form for all these plates, and it is merely placed at the two extremities upon the uniform lamina, whose thickness is CE; and thus it is easy to foresee the electrical state of all plates of this description, when that at the centre is once known.

This rapid increase of the electricity towards the extremity is not peculiar to plates; it is found to take place generally in all elongated prismatic and cylindrical bodies; and it is more rapid according as they are more thin.

34. The tendency of electricity to the surface of conducting bodies, and the manner in which it distributes itself there, may be rendered evident by a very curious experiment. Let AB Fig. 12. represent an insulated cylinder moveable about a horizontal axis, and made to revolve by means of the glass winch M. About this cylinder is wrapped a thin metallic sheet R, which terminates in a semicircle, and is attached to a cord of silk F. This apparatus is made to communicate with an electroscope, composed of two linen threads ƒ, f, supporting pith balls. The instrument being electrified, the threads f, f, diverge; we then gradually unrol the sheet of metal, lifting it off by the cord F, and holding it suspended in the air. As it is extended, we see the linen threads approach, indicating a gradual diminution of action. If the sheet is sufficiently long, compared with the electrical charge given to the apparatus, the divergence will diminish till it becomes almost insensible; but it will increase again, if, upon turning the winch M, the sheet of metal is again wrapped about the cylinder; and then the action of the threads becomes the same as at first, allowance being made for the loss occasioned by the contact of the air.

Of combined Electricities, and their Action at a Distance.

35. We have thus far considered bodies as electrified by friction or communication. We come now to make known a class of phenomena in which the electrical state is produced without contact, and by the mere influence of electrified bodies at a distance.

We take a cylindrical conductor B, insulated in a horizontal Fig. 18. position, the two extremities being hemispherical. We attach to it at small intervals linen threads, to which pith balls are suspended. After touching this conductor, to make it certain that it is not charged with electricity, we bring it toward the electrified

body A, holding it by its insulating supports, and placing it always at such a distance from A that the electricity cannot be communicated by a direct discharge. We shall then observe the following phenomena;

(1.) The threads placed at the extremities of the cylinder B diverge, and thus show that it is electrified.

(2.) This divergence goes on diminishing toward the middle of the cylinder, and there is a point at which there is no repulsive force whatever.

(3.) This unelectrified point varies in its position upon the cylinder, according as it is moved from or toward the electrified body.

(4.) If we present along the cylinder a pith ball, unelectrified and suspended by a thread of silk which insulates it, it is attracted throughout, except at the intermediate point of which we have just spoken.

(5.) But if this pith ball be electrified, it is attracted by one extremity of the cylinder and repelled by the other, which shows that they are charged with different electricities.

(6.) Indeed, if we touch these two extremities successively with a small insulated conducting body, and examine the electricity thus obtained, we shall find that at the extremity next to the electrified body A, it is of a different nature from that of the body A; and that it is of the same nature at the opposite extremity.

(7.) The signs of electricity cease if we remove the cylinder by its insulating supports, to a great distance from the electrified body A, or if we deprive the body A of its electricity.

(8.) With the exception of this last case, the body originally electrified loses no part of its electricity by the influence which it exerts. No part of its electricity is transmitted to the cylinder; for if we measure its electrical action before the cylinder is brought toward it, and after it is withdrawn, we find that it has suffered no loss, except what is naturally due to the mere contact of the air.

(9.) This constancy obtains only while it is beyond the influence of the insulated cylinder. For while it is near an electrified body, if that be a conductor, the action at its surface is disturbed, as may be ascertained by means of the trial plane,