LETTER TO SIR CHARLES CAVENDISH.[5]

HONORABLE SIR,

The last weeke I had the honor to receave two letters from you at once, one of the 30 of Dec., the other of the 7^{th} of Jan., w^{ch} I acknowledged, but could not answer in my last. In the first you begin with a difficulty on the principle of Mons^r de Cartes, _that it is all one to move a weight two spaces, or the double of that waight one space_, and so on in other proportions: to w^{ch} you object the difference of swiftnesse, w^{ch} is greater when a waight is moved two spaces than when double waight is moved one space. Certenly de Cartes his meaning was by force the same that mine, namely, a multiplication of the weight of a body in to the swiftnesse wherew^{th} it is moved. So that when I move a pound two foote at the rate of a mile an howre, I do the same as if of 2 poundes I moved one pound a foote at y^e rate of a mile an howre, the other pound another foote at the same rate, not in directū, but parallell to the first pound. As if the wayt A B were moved to C D at the rate of a mile an howre, ’tis all one as if the waight A E were moved to F H at the same rate. Here is all the difference: this swiftnesse or rate of a mile an howre is, in the first case, layd out in the 2 spaces A G, G C, the latter, in the 2 spaces A G, E G. The first case, as like as if a footman should run w^{th} double swiftnesse endwayes, w^{ch} is y^e doubling of swiftnesse in one man: in the other, it is as if you doubled the swiftnesse by doubling the man: for every man has his owne swiftnesse. And so A H is the swiftnesse A G doubled, as well as A D. For that, that Mons^r de Cartes will not have just twice the force requisite to move the same weight twice as fast, I can say nothing. The papers I have of his touching that are in my trunk, w^{ch} hath bene taken by Dunkerkers, and taken againe from them by French, and at length recovered by frends I made: but I shall not have it yet this fortnight. In the meane time I am not in that opinion, but do assure myself, the patient being the same, double force in the agent shall worke upon it double effect.

In the same letter you require a better explication of y^e proportion I gather betweene wayght and swiftnesse: wherein, because you have not my figure, I imagine you have mistaken me very much. And first, you thinke, I suppose, D E equall to A B: w^{ch} I am sure is a mistake. For I put A B for any line you will to expresse a _minutū secundum_. I will, therefore, go over againe the demonstration I sent you before, and see if I can do it cleerer.

Let A B stand for the time knowne wherein the waight D descendeth to E. And let there bee a cylinder of the same matter the waight D consisteth of, and let the altitude of that cylinder be D C: w^{ch} I shew before was the swiftnesse wherew^{th} that cylinder _presseth_, not wherew^{th} it _falleth_. And wee are now to enquire how farre such matter as the cylinder is made of must descend from D, before it attayne a swiftnesse equall to this pressing swiftnesse D C. And I say it must fall to L. For in the time A B it is knowne that the waight in D will fall to E: and it is demonstrated by Gallileo, that when such waight comes to E, it shall be able to go twice the space it hath fallen in the same time. Therefore the waight D being in E, hath velocity to carry him the space D K (w^{ch} I put double to D E) in the same time A B. But I put B F equall to D K. Therefore, in the time A B, the waight’s velocity acquired in E shall be such as to go from B to F without decrease of velocity by the way. Hence I go on to finde in what point the waight in D comes to where it getteth a velocity equall to C D. Therefore, I apply D C to G H, parallel to B F: and then it is, as the time A B to the time A G, so the velocity acquired at the end of the time A B to the velocity acquired at the end of the time A G. For the swiftnesse acquired from time to time (I say, not from place to place, but from time to time) are proportionable to the times wherein they are acquired: w^{ch} is the postulate on w^{ch} Galileo builds all his doctrine. And as A B to A G, so the line B F to the line G H. But, at the end of the time A B, the waight D is by supposition in E, in that degree of velocity as to go B F or D K in the same time A B. The question therefore is, where the waight D shall be at the end of the time A G. For there it hath the velocity of going G H or D C in the same time, because the velocity G H is to the velocity B F as the line G H to the line B F, or as the time of descent A G to the time A B. But, because the spaces of the descent are in double the proportion of the times of descent, make it as B F to G H, that is, D K to D C, so D C to another, D L. The velocity, therefore, acquired in the point of descent E, namely the velocity D K or B F, is to the velocity acquired in the point L, namely, the velocity G H or D C, (w^{ch} is the velocity of the cylinder’s waight), as D K to D L. And therefore in L the waight D has acquired a velocity equal to the velocity of the waight of the cylinder.

In the same letter you desire to knowe, how any mediū, as water, retardeth the motion of a stone that falls into it. To w^{ch} I answer out of that you say afterwards, that nothing can hinder motion but contrary motion: that the motion of the water, when a stone falls into it, is point blanke contrary to the motion of the stone. For the stone by descent causeth so much water to ascend as the bignesse of the stone comes to. For imagine so much water taken out of the place w^{ch} the stone occupies, and layd upon the superficies of the water: it presseth downeward as the stone does, and maketh the water that is below to rise upwards, and this rising upwards is contrary to the descent, and is no other operation than we see in scales, when of two equal bullets in magnitude that w^{ch} is of heavier metal maketh the other to rise. And thus farre goes your letter of Dec. 30.

For the first quære in your second letter, concerning how we see in the time the lucide body contracts itselfe, I have no other solution but that w^{ch} your selfe hath given: w^{ch} is, that the reciprocation is so quicke, that the effect of the first motion lasteth till the next comes, and longer. For by experience we observe that the end of a firebrand swiftely moved about in circle, maketh a circle of fire: w^{ch} could not be, if the impression made at the beginning of the circulation did not last till the end of it. For if the same firebrand be moved slower, there will appear but a peece of a circle, bigger or lesser according to the swiftnesse or slownesse of y^e motion. For the cause of such reciprocation, it is hard to guess what it is. It may well be the reaction of the medium. For though the mediū yeld, yet it resisteth to: for there can be no passion w^{th}out reaction. And if a man could make an hypothesis to salve that contraction of y^e sun, yet such is the nature of naturall thinges, as a cause may be againe demanded of such hypothesis: and never should one come to an end w^{th}out assigning the immediate hand of God. Whereas in mathematicall sciences wee come at last to a definition, w^{ch} is a beginning or principle, made true by pact and consent amongst ourselves. Further, you conceave a difficulty how the medium can be continually driven on, if there be such an alternate contraction. To w^{ch}, first I answer, that the motion forward is propagated to the utmost distance in an instant, and the first push is therefore enough, and in another instant is made the returne back in y^e like manner. And though it were not done in an instant, yet we see by experience in rivers, as in y^e Thames, that the tide goes upward towards London pushed by the water below, and yet at the same instant the water below is going backe to the sea. For seeing it is high-water at Blackwall before ’tis so at Greenwich, the water goes backe from Blackwall when it goes on at Greenwich. And so it would happen, though Blackwall and Greenwich were nerer together then that any quantity given could come betweene.

In my letter from London, speaking of the refraction of a bullet, I thinke I delivered my opinion to be, that a bullet falling out of a thinner medium into a thicker, looseth in the entring nothing but motion perpendicular: but being entred, he looseth proportionably both of one and the other. For suppose a bullet, whose diameter is A B, be in the thiner mediū, and enter at C into the thicker medium. The thicker medium, at the first touch of B in the point C, worketh nothing upon the line A B. And when the diameter A B is entred, suppose halfe way, yet the thicker medium operates laterally but on one halfe of it. So that in the somme there is a losse of velocity perpendicular (to the quantity that the diameter A B requires) without any offence to the motion laterall, but so much of the diameter as is within the thicker mediū is retarded both wayes, and looses of his absolute motion, w^{ch} is compounded of perpendicular and laterall, and that proportionally. Suppose now that a bullet passe from A to D, and receave a peculiar losse of his perpendicular motion by entring at D, so great that he proceed in the perpendicular but halfe so farre, as for example from D to I: and then being in, the thicknesse of the medium take away more of his velocity both perpendicular and laterall, suppose halfe that w^{ch} was left of the perpendicular motion and halfe of his first laterall motion, so that the perpendicular motion is but D K, and the laterall motion D E. Then will the line of refraction be D G. As for that argumentation of Des Cartes, it is, in my opinion, as I have heretofore endeavored to shew you, a mere paralogism.

Lastly, you make this quære, why light hath not at severall inclinations severall swiftnesses as well as a bullet. The bullet itself passeth through the severall media: whereas in the motion of light, the body moved, w^{ch} is the mediū, entreth not into the other medium, but thrusteth it on: and so the parts of that medium thrust on one another, whereby the laterall motion of the thicker medium hath nothing to worke upon, because nothing enters, but stoppes onely and retardes, in oblique _incidence_, that end w^{ch} comes first to it, and thereby causes a refraction the contrary way to that of a bullet, in such manner as I set forth to you in one of my letters from hence concerning the cause of refraction. And this is all I can say for the present to the quæres of y^r two last letters.

I have enquired concerning perspectives after the manner of De Cartes. Mydorgius tells me there is none that goes about them, as a thing too hard to do. And I believe it. For here is one Mons^r de Bosne in towne, that dwells at Bloys, an excellent workman, but by profession a lawier, and is counsellor of Bloys, and a better philosopher in my opinion then De Cartes, and not inferior to him in the analytiques. I have his acquaintance by Pere Mersenne. He tells me he hath tryed De Cartes his way, but cannot do it: and now he workes upon a crooked line of his owne invention. He sayes he shall have made one w^{th}in a moneth after he shall returne to Bloys: after that he will see what he can discover in the heavens himselfe, and then if he discover any new thing he will let his way be publique together w^{th} the effects. This is all the hope I can give you yet. So w^{th} my prayers to God to keepe you in prosperity this troublesome time, I rest

Your most humble and obedient servant TH. HOBBES.

_Paris, Feb. 8, stile no. 1641._

To the Right Honorable Sr CHARLES CAVENDYSSHE present these

/ / / / at Wellinger.

Footnote 5:

Harleian MS. 6796.