According to my promise, I send you _in writing_ my observations on your book[18]: 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 inertiæ 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 _such a 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 2 _c_, 3 _c_, &c. or ½ _c_, ⅓ _c_, &c. respectively: also the _body_ doubled, tripled, or halved, thirded, will be 2 _a_, 3 _a_, or ½ _a_, ⅓ _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 2 _c_, requires _twice that force_ to be impressed upon it, &c." Here I suspect some mistake creeps in by the author's not distinguishing between a great force applied at once, or a small one continually applied, to a mass of matter, in order to move it. I think it is generally allowed 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 ½ _c_, ⅓ _c_, ¼ _c_, ⅕ _c_, &c. you can never come to a fraction of velocity that is equal to 0 _c_, 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 inertiæ, 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, equal to the sun and to one another, exactly equipoised in Jove's balance; suppose no friction in the centre 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 it is 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 produced by the musketo, without whom those globes would not be moved at all.--What then does vis inertiæ do in this case? and what other effect could we expect _if there were no such thing_? Surely if it were 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?