while the part BS attracts it with the force F' m'z: A will therefore be attracted or repelled by B, according as F m' x' is greater or less than F f'z'; that is, according as m' z' is greater or less than f'z. This, again, depends on the proportion of f' to m', and on the proportion of ≈ to z'. The first depends on many external circumstances, which may occasion a greater or less redundancy or deficiency of electrical fluid; the second depends entirely on the law of electric attraction and repulsion, or the change produced in its intensity by a change of distance. As we are, at present, only aiming at very general notions, it is enough to recollect, that all the electric phenomena, and indeed the general analogy of nature, concur in shewing that the intensity of both forces (attraction and repulsion) decreases by an increase of distance; and to combine this with that circumstance of the hypothesis which states the repulsion to be equal to the attraction at the same distance; therefore both forces vary by the same law, and we have always greater than 2'. The visible action of B on A (which, by the 3d law of motion, is accompanied by a similar action of A on B) may be various, even with one position of B, and will be changed by changing this position.

First, We may suppose that B contains, on the whole, its natural quantity, but that part of it is abstracted from BS, and is crowded into BN. This is a very common case, as we shall see presently, and it will be expressed in our formula, by making f'm'. In this case, therefore, we have F'f'z greater than F'm'z, because z is greater than z'. A will therefore be repelled by B, and will repel it; and the repulsion will be Fƒ' × —z'.

It is evident, that if A be placed on the other side of B, the appearances will be reversed, and the bodies will attract each other with the force F'f' X z

z'.

It is also plain, that if A be as much undercharged as we have supposed it overcharged, all the appearances will be reversed; if on the undercharged side of B, it will be repelled; and if on the overcharged side of B, it will be attracted.

39. Second, If the redundancy and deficiency in the two portions of B be inversely proportional to the forces, so that

f'z

F': m'z' : %, we shall have ƒ' z= m' z', and m' = In this case these two actions balance each other, and A is neither attracted nor repelled when at this precise distance from the overcharged side of B. B may be said to be NEUTRAL with respect to A, although A and the adjoining side of B are both overcharged.

40. But if A be placed at the same distance on the other side of B, the effect will be very different: For because f'

m' —-—-3, and m' z' is now changed into m′ z, and ƒ' z into

=

m'

%

ƒz', we have the action on A = F' × (———ƒ' %), =

F'f' x

22- 8/2

; that is, A is strongly attracted.

In like manner, ƒ' and m' may be so proportioned, that when A, containing redundant fluid, is placed near the undercharged end of SB, it shall neither be attracted nor repelled, B becoming neutral with regard to A at that precise

%

And if A

distance. For this purpose m' must be = be now placed at the same distance on the other side of B,

it will be repelled with the force F' f'

Thus, when the overcharged end is rendered neutral to an overcharged body, the other end strongly attracts it; and when the undercharged end is rendered neutral to the same body, the overcharged end strongly repels it.

Similar appearances are exhibited when A is undercharged.

These cases are of frequent occurrence, and are important, as will appear afterwards.

41. It is easy now to see what changes will be made on the action of B on A, by changing the proportion of f' and f' z

m'. If m' be made greater than A will be attracted in

the situation where it was formerly, neutral; and if m be made less, A will be repelled, &c. &c.

Therefore, when we observe B to be neutral, or attractive, or repulsive, we must conclude that m' is equal to

fz

or greater or less than it, &c.

We have been thus minute, that the reader may perceive the agreement between this action on a body containing redundant fluid, and the action on the superficial fluid formerly considered in § 21, 22, 23, 24. When these things are attended to, we shall explain, with great ease, all the. curious phenomena of the electrophorus.

42. There is another circumstance to be attended to here, which will also explain some electrical appearances that seem very puzzling. We limited the inactivity of B to a certain precise distance of the body A. This inactivity required' If A be brought nearer, both s and ' are increased. If they are both increased in the same

that m' should be =

fz

proportion, the value of —— will be the same as before, and the body A will neither be attracted nor repelled at this new distance. But if % increase faster than z', we shall have ƒ" z greater than m' z', and A will be repelled; and if z increases more slowly than 2', A will be attracted by bringing it nearer. The contrary effects will be observed if A be removed farther from the overcharged end of B. This explains many curious phenomena; and those phenomena become instructive, because they enable us to discover the law of electric action, by shewing us the manner in which it diminishes by a change of distance. Electricians cannot but recollect many instances, in which the motion of the electrometer appeared very capricious The general fact is, that when an overcharged pith ball is so situated near the overcharged side of the electrophorus as to be neutral, it is repelled when brought nearer, but attracted when removed to a great dis

tance.

This shews that z increases faster than z' when A is brought nearer to B. Now, since the bodies may be again rendered neutral at a greater distance than before, and the same appearances are still observed, it follows, that the law of action is such, that every diminution of distance causes to increase faster than z'. We shall find this to be valuable information.

43. Let us, in the last place, inquire into the sensible effect on A when it also is partly overcharged and partly undercharged. This is a much more complicated case, and is susceptible of great variety of external appearances, according to the degrees of redundancy and deficiency, and according to the kind of electricity (positive or negative) of the ends which front each other.

44. First, then, let the overcharged end of A (fig. 5.) front the undercharged end of B, they being overcharged in N and n, but undercharged in S and s. Let F and ƒ be the quantity of fluid natural to each; and let F' and ƒ' be the redundancy in N and n, and M' and m' the deficiency in S and s. Moreover, let Z and Z' represent the intensity of actions of a particle in N on a particle in n and s; and let ≈ and z' represent the actions of a particle in S on a particle in n and in s; or, in other words, let Z, Z, z, z', represent the intensity of action between particle and particle, corresponding to the distances Ns, Nn, Ss, Sn.

Proceeding in the same manner as in the former examples, we easily see, that the action of B on A is = F' m' Z-F'f' Z'M' m' z + M' f' z'

Ff

; the attractions

are considered as positive quantities, having the sign + prefixed to them, and the repulsions are negative, having the sign

This action will be either attractive or repulsive, according as the sum of the first and last terms of the numerator exceeds or falls short of the sum of the second and third: And the value of each term will be greater or less, accord

ing to the quantity of redundant fluid and matter, and also according to the intensity of the electric action. It would require several pages to state all those possible varieties. We shall therefore content ourselves at present with stating the simplest case; because a clear conception of this will enable the reader to form a pretty distinct notion of the other possible cases; and also, because this case is very frequent, and is the most useful for the explanation of phenomena.

We shall suppose, that the redundant part of each body is just as much overcharged as the deficient part is undercharged; so that F' M', and f'm'. In this case, the Z' 8+8') formula becomes

F' f' (Z

Ff

Here we see that the sensible or external effect on A de. pends entirely on the law of electric action, or the variation of its intensity by a change of distance. If the sum of Z and 'exceed the sum of Z' and z, A will be attracted; but if Z' + ' be less than Z' + %, A will be repelled. This circumstance suggests to us a very perspicuous method of expressing these actions between particle and particle, so that the imagination shall have a ready conception of the circumstance which determines the external complicated effect of this internal action. This will be obtained by measuring off from a fixed point of a straight line portions respectively equal to the distances N s, N n, S s, and S n, between the points of the two bodies A and B, where we suppose the forces of the redundant fluid and redundant matter to be concentrated, and erect ordinates having the proportion of those forces. If the law of action be known, even though very imperfectly, we shall see, with one glance, of which kind the movements or tendencies of the bodies will be. Thus, in fig. 5, drawing the line C z, take C p=Ns, Cq=Nn, Cr=Ss, and Ct=Sn, and erect the ordinates Pp, Qq, Rr, and T t. If the electric action be like all the other attractions and repulsions which we are familiarly acquainted with, decreasing with an increase of distance, and