or part in judging of the proportion of the quantity of redundant fluid in two bodies. I imagine, however, that it will not often happen that the error will amount to as much as 32

262] I do not very well know what this irregularity proceeded from. Part of it might arise from the difference in the strength with which the vials were charged, but I believe that part of it must arise from some other cause which I am not acquainted with. For greater security I always compared each body with the trial plate 6 or 7 times running.

263] It appears from the description of the electrometer fastened to the wire Pp that the vials were charged extremely weakly in these experiments, (they were indeed charged so weakly that if tried by Lane's electrometer they would not discharge themselves, if the distance of the knobs was more than of an inch,)* and it perhaps may be asked why I chose to charge them so weakly, as it is plain that the stronger the vials are charged the less alteration in the size of the trial plate would it have required to produce the same alteration in the separation of the pith balls.

264] My reason was this, that the electricity seems to escape remarkably faster from any body, both by running into the air and by running along the surface of the non-conductor on which it is supported, when the body is electrified strongly than when it is weak, which made me afraid that if I had charged the vials much stronger the experiment might have been too much disturbed by the diminution of the quantity of redundant fluid in B and the deficience in the trial plate between the lifting up of the wires Rr and Mm and letting fall the wires Dd and DS, and also by the diminution of the charge of the vials between lifting up the wire bt and lifting up the wires Rr and Mm; and indeed it seemed, from some trials I made with a heavier electrometer fastened to Pp, as if the experiments were not more exact, if so much so, when the vials were charged stronger, as when they were charged in the usual degree.

I now proceed to relate the experiments I have made.

265] Exp. III. This experiment was made with a view to discover whether the quantity of redundant fluid communicated to

* [Difference of potentials about 11-8. See Art. 329 and Note 10.]

the body B was different according to the different situations in which it was placed in respect of the vial A, or according to the different shape of the wire sSRr by which it was touched, or according to the different parts in which it was touched by that wire. The body which I used for this purpose was a square tin plate, 12 inches each way, and the different ways in which it was tried are drawn in figure 17, which represents a plan of the disposition of the whole apparatus, in which the letters B, d, D, 8, t, m, M, N, a, A, S, R and r represent the same things as in fig. 14.

266] 1st Way. The tin plate was placed in a vertical plane so as to be represented in the plan by the line bẞ, the wires Rr and Dd when let down resting on the edge of the plate as in the figure.

2nd. The tin plate was placed horizontal, as represented by the square Befg, the plate being placed so that the wire Rr touched it near the middle. N.B. The wire Rr was bent at right angles about of an inch from the end r, so that of an inch was in a vertical situation, and the rest horizontal. Consequently the wire touched the plate only by its extremity.

3rd. The same as the last, except that the wire Rr touched the plate not far from the side fg, and pretty near the middle of that side.

4th. The same as the last, except that a cross wire ee was fastened horizontally across the wire Rr, so as to be parallel to the side fg, and about one inch distance from it.

5th. The plate in the same situation as before, but the wire Rr was bent into an arch, like tTR, only the plane of that arch was vertical. The wire touched the plate near the middle.

6th. The plate in the same situation as before, but the wire Rr was removed into the situation yx, the communication between y and S being made by the wire yzS bent into an arch, as in the figure, the plane of which was vertical. The wire yx touched the plate near the middle.

N.B. In all these ways the tin plate was supported on silk lines.

267] The charges of the plate in the different situations were found to be to each other in the following proportions*:

The plate was tried in some of these situations another night, when the charges came out in the following proportions +:

268] It should seem from these experiments that the charge of the tin plate is not exactly the same in all the ways of trying it, as the extremes seem to differ from each other by above part, which is more than could arise from the error of the experiments; but, excepting the 4th and 6th ways, the others seem to differ by less than This I think we may be well assured of, that no sensible error can arise in the following experiments from any small difference in the manner in which the bodies are touched by the wire.

269] Exp. IV. These experiments were made with intent to see whether the charge of a body of a given shape and size was

* [Art. 470, Dec. 17, 1771. The numbers there found are here multiplied by

a constant, so as to make the result by the 3rd way equal to 12.]

+ [Art. 468.]

the same whatever materials it consisted of, as it ought to be according to Prop. XVIII.*, and also to see how far the charge of a flat plate depended on its thickness +. The substances used for this purpose were all flat plates about one foot square. of the experiments are given in the following Table ‡:

The results

N.B. The three pieces of stone were all ground flat, and of an uniform thickness.

270] As it would have been difficult to try the following substances by themselves, I coated panes of crown-glass with them on one side and tried them in that manner, which, as glass does not conduct electricity, seems as unexceptionable as it would have been to have tried them by themselves, supposing it had been possible to have done so.

Names of substances with which the glass Mean side Thickness Thickness was coated.

Reduced

of square.

of glass. of coating.

Charge. charge.

The last mentioned substance was quite fluid, but had sufficient tenacity to prevent its flowing immediately to the lowest part of the plate. In those substances in which the thickness of the coating is not set down it was not measured, but the thickness was small.

271] All these things were supported on the pillars of baked wood and waxed glass described at [Art. 255]. The panes of glass were laid on these pillars with their coated sides uppermost, so that the wires Rr and Dd fell on their coated sides. As many of the substances used were but imperfect conductors of electricity, I fastened bits of tin-foil about an inch square on the places on which the wires Rr and Dd touched the plate in order to make the electric fluid spread more readily over it, and I satisfied myself beforehand that with this precaution they conducted readily enough for my purpose, as I found by discharging a Leyden vial, and making these substances part of the circuit.

272] It appears from these experiments that the charge of a thick plate is greater than that of a thin one of the same base, as might be guessed from the theory*, and it seems to be equal to that of a very thin one whose side exceeds that of the thick one by about 14 of its thickness. Let us therefore increase the mean side of each of these plates by 13 of its thickness, where that quantity is worth regarding, and alter the charge found by experiment in the ratio of 12 inches to the side thus increased, which will give us the charge of a plate of the same materials and shape whose increased side is 12 inches, when the charge of each substance will stand as in the last column of the preceding Table. These numbers do not differ from each other by more than what may fairly be supposed owing to the error of the experiment, and therefore I think we may conclude-firstly, that the charge of a body of a given shape and size is the same whatever materials it consists of, and, though the experiment was tried only with square plates, yet I think there can be no doubt but the case will be the same with bodies of any other shape; secondly, that the charge of any thin plate is very nearly the same whatever its thickness may be, provided its thickness is very small in respect of its breadth or smallest diameter; and there can be no doubt also but what this will hold good in thin plates of any shape, though it was tried only

* [Note 20.]