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

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 cf 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 1.65 inches there is no need of supposing so great a proportion of the fluid in the middle

* [Art. 542 and Note 23.]

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.

Secondly, the charge of a single plate or wire was found to bear nearly, though, in the first case, I believe, not quite the same proportion to two similar plates or wires of half the diameter or length which it ought to do according to computation. Thirdly, the proportion which the charges of a thin circular plate and of three cylindrical bodies of different lengths and diameters bear to that of a globe agree with computation; but it must be observed that, as the proportion of the charges of the bodies to that of the globe is determined by the theory within only very wide limits, their agreement cannot be looked upon as so great a confirmation of the theory as it would otherwise be, yet as their shapes are so very different I think that their agreement, even within those limits, may be considered as a considerable confirmation of it.

PART

[EXPERIMENTS ON COATED PLATES.]

295] This part consists chiefly of experiments made to determine the charges of plates of glass and other electric substances coated in the manner of Leyden vials. The method I used in doing this was nearly of the same nature as that by which I determined the charges of the other sort of bodies in the preceding part, but the apparatus was more compact and portable and is represented in Fig. 20, where Hh is a horizontal board lying on the ground, Ll and Ll are two upright pillars supporting the two horizontal bars Nn and Pp, both at the same height above the ground, and parallel to each other.

To these two bars are fastened four upright sticks of glass covered with sealing wax; they are represented in the figure and shaded black, but are not distinguished by letters to avoid confusion. To these sticks of glass are fastened four horizontal pieces of wire Aa, Bb, Dd, and Ee, and to Bb is fastened another wire mM supported at the further end by a stick of waxed glass.

Rr is a wooden bar reaching from the wire Ee to the pillar Ll, and along the upper edge of this bar runs a wire, one end of which is wound round the wire Ee and the other reaches to the ground and serves to make a communication between Ee and the ground. Cc and Kk are two wires fastened firmly together at k serving to electrify the plate. They are moveable upon K as a center where they communicate with the inside coating of one or more large glass jars, and the same electrometer that was used in the former experiments is fastened to the prime conductor by which the jars

* [Not numbered by Cavendish.]