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 1028 to 1, which are between the two above-mentioned proportions, but approach much nearer to the former 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.]

288]

THREE PARALLEL PLATES.

139

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 2L

diameter is L nearly as to natural logarithm or as 489 to

2L Tabular log. D'

D

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 proceeded

till I found how much it was necessary to diminish the quantity of redundant fluid in the jar in order that the corks might separate as much as before, and consequently how much less the quantity of redundant fluid in the middle plate when placed between the two other plates was than that which it would have received by the same degree of electrification if placed by itself *.

The result was that when the distance of the outer plates was (1.15

1.65

inches, the quantity of redundant fluid in the middle plate

was about

7

times less than it would be if electrified in the same degree when placed by itself.

289] It is plain that according to the theory the quantity of redundant fluid in each of the outer plates should be the same, and that the quantity in the middle plate should be such that the repulsion of AB and ab together on the column of shall be equal to that of the plate eg thereon in the contrary direction, and the redundant fluid in each of the outer plates is not much more than one-half of that which it would receive by the same degree of electrification if placed by itself. Now it will appear by computing, according to the principles delivered in Prop. XXX. [Art. 141], that the quantity of redundant fluid in the middle plate will be so excessively different according to the different manner in which the fluid is disposed in the plates that there is no forming any tolerable guess how much it ought to be; but if we suppose that part of the redundant fluid in each plate is spread uniformly and the rest collected in the circumference, and that in the outer plates. the part that is spread uniformly is of the whole, as we supposed in Experiment V., the quantity of redundant fluid in the middle plate when the distance of the outer plates is 1·15 inches will not agree with observation, unless we suppose that not more than the 21st part of it is spread uniformly; but if we suppose that of the redundant fluid in the outer plates is spread uniformly the quantity in the middle plate will agree with observation, if we suppose that about of it is spread uniformly and the rest collected in the circumference.

When the distance of the outer plates is 165 inches there is no need of supposing so great a proportion of the fluid in the middle [Art. 542 and Note 23.]

*

291]

CHARGES OF BODIES.

141

plate to be disposed in the circumference in order to reconcile the theory with observation.

N.B. The more uniformly we suppose the fluid to be spread in the outer plates and the less so in the middle, the greater should be the quantity in the middle plate.

The above computations were made on the supposition that the plates were circles of 14 inches diameter, that is, nearly of the same area that they actually were of.

290] It will appear by just the same method of reasoning that was used in the remarks on the 22nd Proposition [Art. 74], that a vastly greater proportion of the redundant fluid in the middle plate will be collected near its circumference than would be if the outer plates were taken away, and perhaps this circumstance may make the fluid in the outer plates be spread more uniformly than it would otherwise be, so that it seems not improbable that the fluid in the plates may be disposed in such manner as to make the experiment agree with the theory.

The circumstance of its being necessary to suppose a greater proportion of fluid in the middle plate to be lodged in the circumference when the plates are at the smaller distance from each other than when they are at the greater agrees very well with the theory, for it is plain that the nearer the outer plates are to each other the greater proportion of the fluid in the middle plate should be lodged in the circumference.

On the whole I see no reason to think that the experiment disagrees with the theory, though the middle plate was certainly more overcharged than I should have expected.

GENERAL CONCLUSION.

291] The 1st experiment shews that when a globe is electrified the whole redundant fluid therein is lodged in or near its surface, and that the interior parts are intirely, or at least extremely nearly, saturated, and consequently that the electric attraction and repulsion is inversely as the square of the distance, or to speak more properly, that the theory will not agree with experiment on the supposition that it varies according to any other law.

292] The 2nd experiment shews that this circumstance of the whole redundant fluid being lodged in or near the surface obtains also in other shaped bodies, as well as in the globe, conformably to the supposition made in the remarks at the end of Prop. IX. [Art. 41]. These two experiments, at the same time that they determine the law of electric attraction and repulsion, serve in some measure to confirm the truth of the theory, as it is a circumstance which, if it had not been for the theory, one would by no means have expected.

293] From the 4th experiment it appears, first, that the charge of different bodies of the same shape and size, all ready conductors of electricity, is the same, whatever kind of matter they are composed of; and secondly, that the charge of thin plates is very nearly the same whatever thickness they may be of, provided it is very small in respect of their breadth or smallest diameter; but if their thickness bears any considerable proportion to their breadth, then their charge is considerably greater than if their thickness were very small. These two circumstances are perfectly conformable to the theory, and are a great confirmation of the truth of it.

294] The remaining experiments contain an examination whether the charges of several different sized and different shaped bodies bear the same proportion to each other, which they ought to do according to the attempts made in different parts of these papers to compute their charges by theory, supposing, as we have shewn to be the case, that the electric attraction and repulsion is inversely as the square of the distance: with regard to this it must be observed that, as in computing their charges I was obliged to make use of a supposition, which certainly does not take place in nature, it would be no sign of any error in the theory if their actual charges differed very much from their computed ones; but, on the other hand, if the observed charges agree very nearly with the computed ones, it not only shews that the actual charges of different bodies bear nearly the same proportion to each other that they would do if they were connected by canals of incompressible fluid, but is also a strong confirmation of the truth of the theory. Now this appears to be the case, for, first the charge of a tin plate was found to be nearly, though not quite, the same in whatever part it was touched by the electrifying wire, or in whatever direction it was placed in respect of the jar by which it was electrified.