break through, is directly proportional to the quantity of matter; (exp. 10) and inversely proportional to the surface. (exp. 11.) If therefore we increase the matter and the surface in the same ratio, the interval remains the same; (exp. 12)—but if as we increase the matter we diminish the surface, then the interval will be directly as the square of the quantity of matter; (exp. 13)—and if we represent the quantity of matter by ; the interval by 1, and the surface by s, we obtain by

Q

(exp. 12) the following equation 1= from which we get

S

Q=s1 and thus derive another means of estimating the relative quantity of matter thrown upon a given surface, supposing the surface to be either in a divided or undivided state, and all other things remaining the same.

19. I repeated the above experiments, by insulating the jars and electrometer on the principle represented in figs. 13 and 16, so as to measure the quantity of matter by means of the explosions of a jar, charging from the outer coating; (exp. 9) and it is not difficult to obtain in this arrangement, such a distance between the balls of the jar, (b fig. 13) as will accurately measure the accumulation corresponding to a given explosion of the jar (A.) Thus the balls of the electrometer attached to the jar, (b) and the balls of the electrometer attached to the jar, (A) being set to given intervals, it may observed, that some given number of explosions of the jar (b,) correspond to one explosion of the jar (A,) and thus by varying the distance between the balls of the electrometer connected with the jar (A,) whilst the balls of the electrometer attached to the jar (b,) are preserved always the same. We are enabled to investigate the force of the free action as before.

be

20. We come now to consider the second method of investigating the law of the free action, as regards the attractive force or tendency to discharge.

Exp. 14. A single jar containing five square feet, being

connected with the conductor, and with the insulated ball (b) of the instrument already described; (6) and the connection with the negative coating completed, as represented in fig. 15, the insulated ball (b) was depressed from contact with the suspended ball, through an interval of half an inch, and a weight of sixteen grains placed in the small pan suspended from the opposite arm of the balance.* When five turns of the plate were completed, the attractive force was sufficient to tip the beam. The accumulation being discharged, the insulated ball (b) was depressed through a second interval of half an inch, making the whole distance one inch. A weight of four grains, or part of the former weight, being now placed in the pan, the beam was again depressed with five turns of the plate: so that the distances being as 2: 1 the corresponding weights were as 4: 1. The accumulation being discharged, and the insulated ball (b) depressed through a third interval of half an inch, and one-ninth part of the first weight placed in the pan; the beam was again depressed with five revolutions of the plate. We may therefore infer, that the attractive force between the balls, varied in an inverse ratio of the square of the distance of the points of contact.

Exp. 15. The distance between the balls being adjusted to an interval of an inch, and a weight of four grains placed in the pan; the beam was again depressed with five revolutions of the plate. The quantity of matter being now doubled, that is to say, ten turns of the plate being allowed to accumulate, sixteen grains were requisite to balance the attractive force: the attractive force therefore, all other things remaining the same, increases directly as the square of the quantity of matter. This became further evident by placing a weight of thirty-six grains in the pan; in which case the beam was depressed with about fifteen turns of the plate.

* The position of the suspended ball (a) is carefully adjusted by means of the three levelling screws attached to the base of the instrument, so that it may hang vertically over the insulated ball (b) when the beam is perfectly horizontal.

This result is a necessary consequence of the law which seems to govern all these forces; for let two balls be connected with the opposed surfaces, and be separated by any given interval, and let the accumulation proceed until the free action can pass this interval: call the quantity at the time of the explosion 1 and the attractive force at the same instant also 1, and let the number of revolutions of the plate necessary to produce the accumulation be expressed by n. If we suppose the interval to be doubled, then the attractive force, all other things remaining the same, will be reduced to, since the force varies in an inverse ratio of the square of the distance between the points of contact, (exp. 14)—the discharge therefore, with the same quantity of matter, cannot occur at this new interval; but we have seen by (exp. 10) that with 2 n turns of the machine, that is with double the matter, the explosion will again pass at a double interval. If therefore, when the interval between the balls is doubled, we double the matter, the discharge will again take place; but in this case, the attractive force must necessarily be as great at the greater interval, as it was at the lesser interval, without which the explosion could not happen, that is to say, it must have increased from to 1, or if measured at the first interval, it must be equal to 4; in either case, with double the quantity of matter, it must be four times as great, all other things remaining the same.

Exp. 16. A weight of 16 grains being placed in the pan, and the interval between the balls again adjusted to an inch, the beam was again depressed with 10 revolutions of the plate: a second equal and similar jar being added, that is to say the surface being doubled; ten revolutions of the plate were still requisite to depress the beam, when only four grains were placed in the pan: thus it may be perceived, that the same matter, disposed on a double surface only, exerts part of the attractive force: the distance between the balls being constant. I repeated these experiments, the apparatus being insulated, and the quantity of matter measured by the explosions of a