To [Thomas Hopkinson?]
According to my Promise I send you in Writing my Observations on your Book. You will be the better able to consider them; which I desire you to do at your Leisure, and to set me right where I am wrong.
I stumble at the Threshold of the Building, and therefore have not read farther. The Author’s Vis Inertiae essential to Matter, upon which the whole Work is founded, I have not been able to comprehend. And I do not think he demonstrates at all clearly (at least to me he does not) that there is really any such Property in Matter.
He says, No. 2. “Let a given Body or Mass of Matter be called A, and let any given Celerity be called C: That Celerity doubled, tripled, &c. or halved, thirded, &c. will be 2C, 3C &c. or 1/2 C, 1/3 C &c. respectively. Also the Body doubled, tripled or halved, thirded; will be 2A, 3A, or 1/2 A, 1/2 A, respectively.” Thus far is clear. But he adds, “Now to move the Body A with the Celerity C, requires a certain Force to be impressed upon it; and to move it with a Celerity as 2C, requires twice that Force to be impressed upon it, &c.” Here I suspect some Mistake creeps in occasioned by the Author’s not distinguishing between a great Force apply’d at once, and a small one continually apply’d, to a Mass of Matter, in order to move it. I think ’tis generally allow’d by the Philosophers, and for aught we know is certainly true, That there is no Mass of Matter how great soever, but may be moved by any Force how small soever (taking Friction out of the Question) and this small Force continued will in Time bring the Mass to move with any Velocity whatsoever. Our Author himself seems to allow this towards the End of the same No. 2 when he is subdividing his Celerities and Forces: For as in continuing the Division to Eternity by his Method of 1/2 C, 1\3 C, 1/4 C, 1\5 C, &c.; you can never come to a Fraction of Celerity that is equal to 0C, or no Celerity at all; so dividing the Force in the same Manner, you can never come to a Fraction of Force that will not produce an equal Fraction of Celerity. Where then is the mighty Vis Inertiae, and what is its Strength when the greatest assignable Mass of Matter will give way to or be moved by the least assignable Force? Suppose two Globes each equal to the Sun and to one another, exactly equipoised in Jove’s Ballance: Suppose no Friction in the Center of Motion in the Beam or elsewhere: If a Musketo then were to light on one of them, would he not give Motion to them both, causing one to descend and the other to rise? If ’tis objected, that the Force of Gravity helps one Globe to descend: I answer, The same Force opposes the other’s Rising: Here is an Equality, that leaves the whole Motion to be produc’d by the Musketo, without whom those Globes would not be moved at all. What then does Vis Inertiae do in this Case? And what other Effect could we expect if there were no such Thing? Surely if it was any Thing more than a Phantom, there might be enough of it in such vast Bodies to annihilate, by its Opposition to Motion, so trifling a Force?
Our Author would have reason’d more clearly, I think, if, as he has us’d the Letter A for a certain Quantity of Matter, and C for a certain Degree of Celerity, he had employ’d one Letter more, and put F (perhaps) for a certain Quantity of Force. This let us suppose to be done; and then, as it is a Maxim that the Force of Bodies in Motion is equal to the Quantity of Matter multiply’d by the Celerity, or F = C x A; and as the Force received by and subsisting in Matter when it is put in Motion, can never exceed the Force given; so if F move A with C, there must needs be required (See No. 3) 2F to move A with 2C; for A moving with 2C would have a Force equal to 2F, which it could not receive from 1F; and this, not because there is such a Thing as Vis Inertiae, for the Case would be the same if that had no Existence; but, because nothing can give more than it hath. And now again, if a Thing can give what it hath; if 1F can to 1A give 1C, which is the same thing as giving it 1F; i.e. if Force apply’d to Matter at Rest, can put it in Motion, and give it equal Force; Where then is Vis Inertiae? If it existed at all in Matter, should we not find the Quantity of its Resistance subtracted from the Force given?
In No. 4. our Author goes on and says, “The Body A requires a certain Force to be impressed on it, to be moved with a Celerity as C, or such a Force is necessary; and therefore it makes a certain Resistance, &c. A Body as 2A, requires twice that Force to be moved with the same Celerity, or it makes twice that Resistance, and so on.” This I think is not true, but that the Body 2A moved by the Force 1F, (tho’ the Eye may judge otherwise of it) does really move with the same Celerity as 1A did when impell’d by the same Force: For 2A is compounded of 1A + 1A; And if each of the 1A’s or each Part of the Compound were made to move with 1C, (as they might be by 2F) then the whole would move with 2C, and not with 1C as our Author Supposes. But 1F apply’d to 2A makes each A move with 1/2 C, and so the Whole moves with 1C, exactly the same as 1A was made to do by 1F before. What is equal Celerity but a Measuring of the same Space by moving Bodies in the same Time? Now if 1A impell’d by 1F measures 100 Yards in a Minute; and in 2A impell’d by 1F, each A measures 50 Yards in a Minute, which added make 100, are not the Celerities as well as the Forces equal? And since Force and Celerity in the same Quantity of Matter are always in Proportion to each other, why should we, when the Quantity of Matter is doubled, allow the Force to continue unimpair’d, and yet suppose one Half of the Celerity to be lost? I wonder the more at our Author’s Mistake in this Point, since in the same No. I find him observing, “We may easily conceive that a Body as 3A, 4A, &c. would make 3 or 4 Bodies equal to once A, each of which would require once the first Force to be moved with the Celerity C.” If then in 3A, each A require once the first Force F to be moved with the Celerity C, would not each move with the Force F, and Celerity C; and consequently the whole be 3A moving with 3F, and 3C? After so distinct an Observation, how could he miss of the Consequence, and imagine that 1C and 3C were the same? Thus as our Author’s Abatement of Celerity in the Case of 2A moved by 1F, is imaginary, so must be his additional Resistance. And here again I am at a Loss to discover any Effect of the Vis Inertiae.
In No. 6 he tells us, “That all this is likewise certain when taken the contrary way, viz. from Motion to Rest; For the Body A moving with a certain Velocity as C requires a certain Degree of Force or Resistance to stop that Motion, &c. &c.” That is, in other Words, equal Force is necessary to destroy Force. It may be so; but how does that discover a Vis Inertiae? Would not the Effect be the same if there were no such Thing? A Force 1F strikes a Body 1A, and moves it with the Celerity 1C, i.e. with the Force 1F. It requires, even according to our Author, only an opposing 1F to stop it. But ought it not, (if there were a Vis Inertiae) to have not only the Force 1F, but an additional Force equal to the Force of Vis Inertiae, that obstinate Power, by which a Body endeavours with all its Might to continue in its present State, whether of Motion or Rest? I say, ought there not to be an opposing Force equal to the Sum of these? The Truth however is, that there is no Body how large soever, moving with any Velocity how great soever, but may be stopped by any opposing Force how small soever, continually apply’d. At least all our modern Philosophers agree to tell us so.
Let me turn the Thing in what Light I please, I cannot discover the Vis Inertiae nor any Effect of it. Tis allowed by all that a Body 1A, moving with a Velocity 1C, and a Force 1F, striking another Body 1A at Rest, they will afterwards move on together, each with 1/2 C, and 1/2 F; which, as I said before, is equal in the Whole to 1C and 1F. If Vis Inertiae as in this Case neither abates the Force nor the Velocity of Bodies, What does it, or how does it discover itself?
I imagine I may venture to conclude my Observations on this Piece, almost in the Words of the Author, “That if the Doctrines of the Immateriality of the Soul, and the Existence of God, and of Divine Providence are demonstrable from no plainer Principles, the Deist hath a desperate Cause in Hand.” I oppose my Theist to his Atheist, because I think they are diametrically opposite and not near of kin, as Mr. Whitefield seems to suppose where (in his Journal) he tells us, Mr. B. was a Deist, I had almost said an Atheist. That is, Chalk, I had almost said Charcoal.
Shall I hazard a Thought to you that for aught I know is new, viz. If God was before all Things, and fill’d all Space; then, when he form’d what we call Matter, he must have done it out of his own Thinking immaterial Substance. The same, tho’ he had not fill’d all Space; if it be true that Ex nihilo nihil fit. From hence may we not draw this Conclusion, That if any Part of Matter does not at present act and think, ’tis not from an Incapacity in its Nature but from a positive Restraint. I know not yet what other Consequences may follow the admitting of this position and therefore I will not be oblig’d to defend it. [ ] ’tis with some Reluctance that I either [ ] in the metaphysical Way. The great Uncertainty I have found in that Science; the wide Contradictions and endless Disputes it affords; and the horrible Errors I led my self into when a young Man, by drawing a Chain of plain Consequences as I thought them, from true Principles, have given me a Disgust to what I was once extreamly fond of.
The Din of the Market encreases upon me, and that, with frequent Interruptions, has, I find, made me say some things twice over, and I suppose forget some others I intended to say. It has, however, one good Effect, as it obliges me to come to the Relief of your Patience, with Your Humble Servant
October 16, 1746