Our author would have reasoned more clearly, I think, if, as he has used the letter _a_ for a certain quantity of matter, and _c_ for a certain quantity of celerity, he had employed 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 multiplied 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_ moves _a_ with _c_, there must needs be required 2 _f_ to move _a_ with 2 _c_; for _a_ moving with 2 _c_ would have a force equal to 2 _f_, which it could not receive from 1 _f_; and this, not because there is such a thing as vis inertiæ, for the case would be the same _if that had no existence_; but because nothing _can_ give more than it has, if 1 _f_ can to 1 _a_ give 1 _c_, which is the same thing as giving it 1 _f_; (i. e. if force applied to matter at rest, can put it in motion, and give it _equal_ force) where then is vis inertiæ? 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 makes a certain resistance, &c. A body as 2 _a_ 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 2 _a_ moved by the force 1 _f_ (though the eye may judge otherwise of it) does really move with the same celerity as it did when impelled by the same force; for 2 _a_ is compounded of 1 _a_ + 1 _a_: and if each of the 1 _a_'s or each part of the compound were made to move with 1 _c_ (as they might be by 2 _f_) then the whole would move with 2 _c_, and not with 1 _c_, as our author supposes. But 1 _f_ applied to 2 _a_, makes each _a_ move with ½ _c_; and so the whole moves with 1 _c_; exactly the same as 1 _a_ was made to do by 1 _f_ before. What is equal celerity but a _measuring the same space by moving bodies in the same time_?--Now if 1 _a_ impelled by 1 _f_ measures 100 yards in a minute; and in 2 _a_ impelled by 1 _f_, each _a_ measures 50 yards in a minute, which added make 100; are not the celerities 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 unimpaired, 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 number I find him observing: "We may easily conceive that a body as 3 _a_, 4 _a_, &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 3 _a_, each _a_ requires 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 3 _a_ moving with 3 _f_ and 3 _c?_ After so distinct an observation, how could he miss of the consequence, and imagine that 1 _c_ and 3 _c_ were the same? Thus as our author's abatement of celerity in the case of 2 _a_ moved by 1 _f_ is imaginary, so must be his additional resistance.--And here again, I am at a loss to discover any effect of the vis inertiæ.