276] TWO SMALL CIRCLES AND ONE LARGE ONE. 133 wire for making a communication between them and the trial plate; Ee is the large circle placed half way between the two small ones, and Rr the wire by which it is electrified. But it must be observed, that in trying the large circle the two small circles and the wires Rf and Rg are taken away and the wire Rr put in their room; and in like manner, when the small circles are tried, the circle Ee and the wire Rr are removed. 274] It must be observed that the charge of the two small circles together will not be as much as double the charge of one circle, unless the distance of the two circles from each other is extremely great. In order, therefore, to know better what allowance to make on this account, I tried the experiment with the two small circles placed at three different distances, namely, at 18, 24, and 36 inches from each other, the circles being always placed so that the middle point between them was at the same distance from D. Their charges came out in the following proportion * : 275] I repeated the experiment in the same manner, except 1st, that the distances of the vials from the circles and trial plate were different from what they were before, namely, in the foregoing experiment the distance Ta from the middle of the trial plate to the vial a was 87 inches and eA, or the distance from the center of Ee to the vial A, was 106 inches, whereas in this experiment Ta was 98 inches and eA 63 inches; the distance Te was 83 inches in both experiments; and 2ndly, that I placed a frame of wood about 5 feet square under the circles 14 inches from the ground. The reason of these alterations will be shewn by and by t. Their charges came out as follows: 276] Let us now endeavour to find out what proportion the charges ought to bear to each other by the theory on the abovementioned supposition of their being connected by canals of in[Arts. 452, 454, 472-475.] [Arts. 277, 339, 474 and Note 17.] compressible fluid, and of the electrical attraction and repulsion being inversely as the square of the distance. This cannot be done exactly without knowing the manner in which the redundant fluid is disposed in the circles, which I am not acquainted with, but if we suppose the fluid to be spread uniformly over the plates, it will appear, by calculating according to Prop. XXX. [Art. 141], that their charges should be in the following proportion : If we suppose that the whole redundant fluid is collected in the circumference, they should be as follows: and if we suppose that of the whole redundant fluid is collected in the circumference, and the remainder, or 14, spread uniformly, they should be as follows: 277] I think this latter proportion of the charges much the most likely to agree with the truth*, as it appears from an experiment which will be mentioned hereafter, that the charge of a circular plate bears the same proportion to that of a globe that it would do if the fluid was disposed in that manner. But it must be observed that in these calculations the circles are supposed to be placed at an infinite distance from the vial by which they are electrified, and also from any other over- or under-charged body, whereas in these experiments the circles were at such a distance from the vial that their repulsion on the canal by which they communicated with it was sensibly less than if it was infinite, and moreover the attraction of the under-charged trial plate on the * I would not be understood by this to suppose that the fluid is actually disposed in this manner in a circular plate, but only that the charges will bear the same proportion to each other that they ought to do on this supposition. 278] COMPARISON WITH THEORY. 135 wire mMNn has some tendency to increase the quantity of fluid in the circles, and the repulsion of the circles tends to diminish the quantity of fluid in the trial plate, and moreover the floor and walls of the room will be made under-charged near the circles and over-charged near the trial plate, which will also have some tendency to alter the quantity of fluid in the circles and trial plate. It was with a view to find out what error could proceed from these causes that I tried the experiment in the two different ways above mentioned. It will be shewn, however, in the appendix*, that the first two of these causes cannot produce any sensible alteration in the experiment, and that it is not likely that the last should. This is also confirmed by the near agreement of the results in both ways of trying the experiment, as the difference in the proportion of the charges in these two ways of trying the experiment was not greater than what might well be owing to the error of the experiment. 278] It seems reasonable to conclude, therefore, that the proportion which the charges ought to bear to each other in the theory on the supposition of their being connected by canals of incompressible fluid, and of the electrical attraction and repulsion being inversely as the squares of the distances, must be nearly as in the last Table, and therefore it should seem that the observed charges of the two small plates were rather less in proportion to that of the large one than they ought to have been by theory on the above-mentioned supposition; but the difference is not great, and perhaps not more than what may be owing to our not being able to compute the true proportion with sufficient accuracy, and to the error of the experiment, though I am more inclined to think that the difference is real. This, however, can by no means be looked upon as a sign of any error in the theory, but, on the contrary, I think that the difference being so small is a strong sign that the theory is true. For it cannot be expected that the charges of bodies connected together by wires should bear exactly the same proportion to each other that they should do if they were connected by canals of incompressible fluid; and, indeed, the third experiment shews that they do not, as the charge of the tin plate was found to be a little different according to the situation in which it was placed and the disposition of the wire by which it * [Art. 188, and Notes 17 and 21.] was touched, which should not be the case if it was connected to the vial by a canal of incompressible fluid. 279] Exp. VI. This experiment was made with the same view as the last, and consisted in comparing the charge of two brass wires together, with that of a single one of twice the length and thickness. The small wires were 3 feet long and th of an inch thick; they were placed horizontal and parallel to each other, as represented by the lines Bb and Cc in fig. 18, and were tried at three different distances from each other, viz.:-18, 24, and 36 inches. The long wire was 6 feet long and th of an inch in thickness, and was placed in the same direction as the small ones, as represented by Ee. They were electrified by the same wires. and in the same manner as the circles, only they were placed so as to be touched by the wires fR, rR, and gR, very near their extremities b, e, and c. Their charges were as follows :— 280] The charges of the two small wires at the several distances of 36, 24, and 18 inches ought by theory to have been to that of the long wire in a proportion between that of 923, 905, and 883 to 1 and that of 893, 860, and 835 to 1, supposing them to be connected to the vial by canals of incompressible fluid, but, as it should seem from the next experiment, ought in all probability to approach much nearer to the former proportion than the latter. The observed charges were actually between these two proportions, but approached much nearer to the latter, so that they agreed as nearly with the computation as could be expected*. 281] Exp. VII. Being a comparison of the proportional charges of several bodies of different shapes: the result is as follows:A globe 121 inch in diameter.... 1.000 *992 957 An oblong tin plate 17.9 inches by 134 inches...... .965 *937 A tin cylinder 54.2 inches long and '73 in diameter. 951 •999. * [Arts. 453, 476, 477, 683, and Note 13.] 285] GLOBE, CIRCLE, SQUARE, OBLONG, CYLINDER. 137 The globe was the same that was used in the first experiment. The wire and cylinders were placed in the same manner as the large wire in the preceding experiment, and were touched in the same manner *. 282] Remarks on this experiment. First, the proportion which the charge of the circular plate bears to that of the globe agrees very well with the theory, for by Prop. XXIX. [Art. 140] the proportion should be between that of 76 to 1 and that of 153 to 1, and the observed proportion is that of 992 to 1. We may conclude also from this experiment that the charge of a circular plate is to that of a globe of the same diameter as 12 to 18, which by the above-mentioned proposition is the proportion which ought to obtain if of the whole quantity of redundant fluid in the plate was spread uniformly [over the surface], and the remainder, or 1, was spread uniformly [round the circumference], that is, if the value of p in that proposition equals it. 283] 2ndly. The charge of a square plate is to that of a circle whose diameter equals the side of the square, as 1:53 to 1, or its charge is to that of a circle whose area equals that of the square as 1.02 to 1. 284] 3rdly. The charge of the oblong plate is very nearly equal to that of a square of the same area, and consequently as the length of the trial plates used in these experiments never differed from their breadth (whether the trial plate was more or less drawn out) in a greater proportion than those of this oblong plate do, and as the charges of similar bodies of different sizes are as their corresponding diameters, or sides, I think we may safely conclude that the charges of these trial plates were as the sides of a square of the same area, agreeable to what was said in [Art. 247]. 2L 285] 4thly. By Prop. XXXI. [Art. 150] the charge of a cylinder whose length = L and diameter = D is to that of a globe whose diameter = L in a ratio between that of 1 to log, and that D 4L of 2 to log, D and therefore the charges of the brass wire, long [Arts. 478, 682.] [Arts. 654, 681, and Note 2.] [Arts. 479, 682, and Note 22.] |