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 andth 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:The long wire....... 1.000, 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 12.1 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. 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 181, 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, was spread uniformly [round the circumference], that is, if the value of p in that proposition equals lit. 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]. = 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 2L diameter = L in a ratio between that of 1 to log, and that D 4L D' and therefore the charges of the brass wire, long of 2 to log. * [Arts. 478, 682.] + [Arts. 654, 681, and Note 2.] [Arts. 479, 682, and Note 22.] cylinder and short cylinder, should be to that of the globe, supposing them to be connected with the vial by which they were electrified by canals of incompressible fluid, in a ratio between that of 894, 896 and 887 to 1 and that of 1·619, 1-573 and 1469 to 1. The observed charges are as 966, 980 and 1·028 to 1, which are between the two above-mentioned proportions, but approach much nearer to the foriner than the latter, as might have been expected; so that the observed charges agree very well with the theory*. 286] 5thly. If we suppose that the redundant fluid is disposed in the same manner in a cylinder, whether the length is very great in respect of the diameter or not, it is reasonable to suppose that the charges of the brass wire, long cylinder and short cylinder, should be to each other in a proportion not much different from that of 894, 896 and 887, or that of 966, 968 and 959. The observed charges do not differ a great deal from that ratio, only the charges of the two cylinders, especially the shorter, are rather greater in proportion to that of the brass wire than they ought [to be], so that according to this supposition the observed charges do not agree exactly with computation. But if we suppose that the redundant fluid is spread less uniformly in a cylinder whose length is not very great in proportion to its diameter than in another, that is, that there is a greater proportion of the redundant fluid lodged near the extremities, which seems by no means an improbable supposition, the observed charges may perhaps agree very well with what they should be by theory, if they were connected by canals of incompressible fluid. 287] With regard to the small disturbing causes mentioned in [Art. 277], as the length of the brass wire bears so great a proportion to its distance from the trial plate and to its distance from the ground, it is possible that its effect in increasing the deficiency of fluid in the trial plate may be sensibly less, and also that the increase of charge, which it receives itself from the ground near it being under-charged, may be sensibly different from what it would be if it had been of a more compact shape, so that perhaps some alterations may have been made in the experiments by these two causes. I should imagine, however, that they could be but small. It must be observed that the first of these two causes tends to make the charge of the wire appear * [Note 12.] greater than it really was, and consequently to make the observed charges appear to agree nearer with the theory than they really did. Which way the second cause should operate I cannot say. On the whole it should seem as if the true charge of a cylinder whose length is L and diameter D is to that of a globe whose diameter is L nearly as to natural logarithm 2L D or as 489 to 288] Exp. VIII. Let AB, ab and eg (Fig. 19) be three equal thin parallel plates equidistant and very near to each other, and let Cf, the line joining their centers, be perpendicular to their planes, and let all three plates communicate with each other and be posi Fig. 19. B tively electrified: it may easily be shewn that according to the theory the quantity of redundant fluid in the middle plate will be many times less than that in either of the outer plates, or than that which it would receive by the same degree of electrification if placed by itself. I therefore took three tin plates, each 12 inches square, and placed them as above described, and electrified them by means of a wire fixed to a Leyden jar, the end of the wire being formed in such manner as to touch all three plates at once. As soon as the electrifying wire was taken away I drew away the outer plates, and at the same time approached a pair of cork balls to the middle plate in the same manner as I did to the globe in the first experiment and observed how much they separated, care being taken to take away the electricity of the outer plates as soon as drawn away. I then removed the outer plates and, by the same means that I used in the first experiment, made the quantity of redundant fluid in the jar less than before in a given ratio, and by means of this jar electrified the middle plate by itself and approached the cork balls as before. In this manner I procceded |