Axiom 3.-A. greater pressure produces a greater moving force, if the time be given.

Prop. 1. Moving forces are not proportional to the masses of the bodies," and the squares of their velocities.

Demonstr.-Let there be two springs, equal, and equally bent, A and B, which, by unbending themselves, push before them two unequal bodies, the spring A pushing before it the greater body.

Now, by axiom 1, the spring a will unbend more slowly than the other; from which it follows, that at every instant of the time which the spring в takes up in unbending itself, the spring a will have unbent itself less than B, or will be more bent than B. Therefore, by axiom 2, the pressure of the spring a will, at any instant of that time, be greater tl:an the pressure of the spring в at that same instant. Hence, by axiom 3, the nascent, or infinitely small moving force, which is produced by the pressure of the spring A, in every infinitely small part of that time, will be greater than that produced by the pressure of the spring B, in the same infinitely small part of the time.

Therefore, the sum of the infinitely small moving forces, that is to say, the whole moving force, which is produced by the spring A, during that time, will be greater than the moving force produced by the spring в in that same time: or the moving force of the greater body will be greater than that of the less, at the instant that the spring B, being now wholly unbent, ceases to act any longer on the body it has pushed before it; and as, after that instant, the spring a, not being yet wholly unbent, continues to act on the greater body, the moving force of the greater body will still continue to increase, and consequently will more and more exceed the moving force of the smaller body. :i

But every one knows, that the products of the masses and squares of the velocities are equal in the two bodies. Therefore the moving forces, which we have proved to be unequal, are not proportional to the products of the masses and squares of the velocities. Q. E. D.

To consider this in a particular example, let us suppose the masses of the two bodies, exposed to the pressure of the springs A and B, to be 4 and 1 respec tively; and let the spring в unbend itself, and thereby give the body 1 its whole moving force in one second of time. Then, at the end of that second, the moving force of the body 4 will already exceed that of the body 1, and will still grow greater during another second of time. For the times are as the square roots of the masses. Also, if the masses be 100 and 1, the moving force of the body 100, will, at the end of the first second of time, be greater than that of the body 1, and will continue to increase during the space of 9 other seconds.

Corol.-When a bent spring, by unbending itself, drives a body before it, the

larger that body is, the greater will be the moving force which it receives from the spring.

Having now clearly proved, that the moving forces are not proportional to the squares of the velocities, Dr. J. proceeds next to demonstrate, that they are proportional to the velocities themselves: and, in order to this, he makes use of no other principles or axioms, than such as are admitted on both sides, or at least have never yet been controverted a priori by either party.

Axiom 4.-Springs of unequal lengths, when bent alike, have equal pressures. We speak here of springs equal in all respects, except the length only; and, by being bent alike, we mean, that they are so compressed, as that the lengths they are now reduced to, are exactly proportional to their natural lengths, or to the lengths they are of when no way compressed.

In this condition, if one be directly opposed to the other, they will mutually - sustain each others pressure, so as to maintain a perfect equilibrium; or, if each be placed separately in a vertical situation, they will sustain equal weights. And in one or the other of these cases, it is evident that they must exercise equal pressures.

Axiom 5.-Equal pressures in equal times produce equal moving forces.

Prop. 2.-Moving forces are proportional to the masses and velocities jointly. Demonstr.-Let there be two springs, of the lengths 1 and 2, but equal in all other respects, and bent alike; and, in unbending themselves, let the spring 1 drive before it a body whose mass is 2; and the spring 2 another body of the

mass 1.

Now, by corol. 2 of his general theorem concerning the action of springs, these two springs will unbend themselves exactly in the same time; and consequently the spring 2 will unbend itself with a velocity double of that of the spring 1; and, by corol, 12 of the same theorem, it will give to the body 1 a velocity double of that which the body 2 will receive from the spring 1.

Also, as the two springs were supposed to be bent alike at first, and the spring 2 unbends itself with a velocity double to that of the spring 1, it is manifest, that during the whole time of their expansion, they will be always bent alike, one to the other.

Therefore, by axiom 4, their pressures will be constantly equal to each other; and hence, by axiom 5, the infinitely small moving forces produced by each of these springs, in every infinitely small part of time, will be equal to each other. Consequently the sums of those infinitely small moving forces, that is, the whole moving forces produced by the two springs, will be equal to each other. And the masses of the two bodies being 2 and 1, and their velocities being 1 and 2 respectively, it is plain, that the moving forces are proportional to the masses and velocities jointly. a. E. D.

As we do not think, that any flaw can be found in either of the demonstrations above laid down; and the axioms, on which they are founded, have never yet been disputed, as far as we know; we presume that the Leibnitian opinion about the measure of moving forces, is incontestably overthrown by the first proposition, and the opposite sentiment is as evidently established by the second.. But if any reader shall be of a different opinion, we must beg leave to propose to his consideration the following experiment, which we hope may justly deserve the name of an experimentum crucis, and, as such, may put a final period to this controversy.

Exper. On a horizontal plane at rest, but moveable with the least force, suppose on a boat in a stagnant water, let there be placed, between two equal bodies, a bent spring, by the unbending of which the two bodies may be pushed contrary ways.

In this case it is evident, that the velocities, which the two bodies receive from the spring, will be exactly equal, and their moving forces will also be exactly equal; and that the plane they move on, and also the boat on which it lies, will have no motion given them either way. Let us call the velocity of each body 1, and the moving force also 1.

Now let us suppose the spring to be bent afresh to the same degree as before, and to be again placed between the two bodies lying at rest; then let the plane, on which the spring and the bodies lie, be carried uniformly forward, in the direction of the length of the spring, with this same velocity 1. In this case it is manifest, that each of the bodies will have the velocity 1, and the moving force 1, both in the direction of the axis of the spring. During this motion, let the spring again unbend, and push the two bodies contrary ways, as before, the one forward, the other backward: then the spring will give to each of these bodies the velocity 1, as before, when the plane was at rest.

By this means the hindmost body, or that which is pushed backward, will have its velocity 1, which it had before by the motion of the plane, now entirely destroyed, and will be absolutely at rest. But the body, which is pushed forward, will now have the velocity 2, namely 1 from the motion of the plane, and 1 from the action of the spring.

Thus far every body agrees in what will be the event of this experiment. But the question is, what will be the moving force of the foremost body, or of that which is pushed forward, and which has the velocity 2; viz. 1 from the motion of the plane, and 1 from the action of the spring. By the Leibnitian doctrine, its moving force must be 4: and, if so, it must have received the moving force 3 from the action of the spring; for it had only the moving force 1 from the motion of the plane.

Let us examine, whether this be possible, or reconcileable to their own doc

trine. Their doctrine is, that equal springs, equally bent, will, by unbending themselves, give equal moving forces to the bodies they act on, whatever those bodies are. We agree to this, not generally indeed, but in the case before us, where the bodies are of equal masses or weights, we agree to it.

Let us therefore imagine the bent spring, which is placed between the two bodies, to be divided transversely into two equal parts. In this case it is plain, that the two halves of the spring may be considered as two entire springs, equal, and equally bent, each of which rests at one end in equilibrio against the other spring, and at the opposite end presses against the body it is to move. Conse quently, by the Leibnitian doctrine, to which, in this particular case, where the bodies are equal, we also agree, the two springs will give equal moving forces to the two bodies.

But the moving force received by the hindmost body from the hinder spring, was undoubtedly the moving force 1: for by that force given it in the direction backward, the moving force 1, which it had before from the motion of the plane in the direction forward, is exactly balanced and destroyed, the body remaining, as was observed before, in absolute rest. Therefore the moving force received by the foremost body, from the foremost spring, was also the moving force 1. And this, added to the other moving force 1, which it had before from the motion of the plane, makes the moving force 2, and not the moving force 4, as the Leibnitian philosophers pretend...

Consequently, that body, which had before the velocity 1, and the moving force 1, and now has the velocity 2, has also the moving force 2: that is, the moving forces are proportional to the velocities.

Observations on Luminous Emanations from Human Bodies, and from Brutes; with some Remarks on Electricity. By the Rev. Henry Miles, D.D. and F.R.S. N° 476, p. 441.

In the late edition of the works of Mr. Boyle, vol. 5, p. 646, is a letter from Mr. Clayton, dated June 23, 1684, at James city in Virginia; in which he gives Mr. Boyle an account of a strange accident, as he calls it, and adds, that he had inclosed the very paper Colonel Digges gave him of it, under his own hand and name, to attest the truth; and that the same was also asserted to him by Madam Digges, his lady, sister to the wife of Major Sewall, and daughter of the Lord Baltimore, to whom this accident happened. This paper came not to hand till after Mr. Boyle's works were printed, and therefore could not be inserted with Mr. Clayton's letter, but having since met with it, the following copy of it is here inserted. A

"There happened in Maryland, about the month of November 1683, to one Mrs. Susanna Sewall, wife to Major Nic. Sewal, of the province aforesaid, a

strange flashing of sparks, seemed to be of fire, in all the wearing apparel she put on, and so continued till Candlemas: and, in the company of several, viz. Captain John Harris, Mr. Edward Braines, Captain Edward Poulson, &c. the said Susanna did send several of her wearing apparel, and, when they were shaken, it would fly out in sparks, and make a noise much like unto bay-leaves when flung into the fire; and one spark fell on Major Sewall's thumb-nail, and there continued at least a minute before it went out, without any heat, all which happened in the company of Wm. Digges."

*"My Lady Baltimore, her mother-in-law, for some time before the death of her son, Cæcilius Calvert, had the like happened to her; which has made Madam Sewall much troubled at what has happened to her.

"They caused Mrs. Susanna Sewall one day to put on, her sister Digges's petticoat, which they had tried beforehand, and would not sparkle; but at night, when Madam Sewall put it off, it would sparkle as the rest of her own garments did."

Bartholin of Copenhagen, in his collection of anatomical histories that are unusual, century 3, hist. 70, which he entitles Mulier Splendens, gives a parallel instance in a noble lady of Verona in Italy, which he says he had from an account of the phenomenon published by Petrus à Castro, a learned physician of the same place, in a small treatise intitled De Igne Lambente.

There is another author, Dr. Simpson, who published a philosophical discourse of fermentation, Anno 1675, who takes notice of light proceeding from animals, on their frication or pectation, as he calls it; and instances in the combing a woman's head, the currying of a horse, and the frication of a cat's back, the last two of which are known to most. According to this gentleman's hypothesis, he would assign the principles of fermentation, which he supposes to be acidum et sulphur, as the cause of these lucid effluvia in animals. But more probably the properties of the effluvia in animal bodies are many of them common with those produced from glass, &c.: such as their being lucid, their snapping, and their not being excited without some degree of friction, and electricity, for a cat's back is strongly electrical when stroked.

In the account of some of the earlier electrical experiments made by Mr. Gray, Phil. Trans, No 366, we are informed, that he electrified several other bodies, besides animal substances, by drawing them between his thumb and fingers; in particular, linen of divers sorts, paper, and fir-shavings, which would not only be attracted to his hand, but attract all small bodies to them, as other electric bodies do. Now, notwithstanding this last circumstance of their attracting as well as being attracted, may it not be questioned, whether, in this

The additional lines are not in Colonel Digges's hand, but seem to be in Mr. Clayton's.-Orig. VOL. IX.

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