Besides the already mentioned difficulties, even the most ordinary trivial occurrents, if we contemplate them in the theory, wisl as much puzzle.us, as any of the former. Under this head I'll add three things concerning the motion of a wheel, and conclude this branch of my subject.
§. I. First then in the abstract consideration, it seems impossible that a wheel should move: I mean not the progressive, but that motion which is merely on its own centre. And were it not for the information of experience, it's most likely that philosophy had long ago concluded it impossible: for let's suppose the wheel to be divided according to the alphabet. In motion then there is a change of place, and in the motion of a wheel there is a succession of one part to another in the same place; so that it seems unconceivable that A. should move until B. hath left his place: for A. cannot move, but it must acquire some place or other. It can acquire none but what was B's, which we suppose to be most immediate to it. The same space cannot contain them both. And therefore B. must leave its place, before A. can have it; yea, and the nature of succession requires it. but now B. cannot move, but into the place of C.; and C. must be out, before B. can come in.: so that the motion of C. will be prerequired likewise to the motion of A.; and so onward till it comes to Z. Upon the same accounts Z. will not be able to move, till A. Moves, being the part next to it: neither will A. be able to move (as hath been shown) till Z. hath. And so the motion of every part will be pre-required to itself. Neither can one evade, by saying, that all the parts move at once. For (1.) We cannot conceive in a succession but that something should be first, and that motion should begin somewhere. (2.) If the parts may all change places with one another at the same time without any respect of priority and posteriority to each others motion: why then may not a company of bullets closely crowded together in a box, as well move together by a like mutual and simultaneous exchange? Doubtless the reason of this ineptitude to motion in this position is, that they cannot give way one to another, and motion can nowhere begin because of the plenitude. The case is just the same in the instance before us; and therefore we need go no further for an evidence of its inconceivableness. But yet to give it one ouch more according to the Peripiatetic niceness, which says, that one part enters in the same instant that the other goes out; I'll add this in brief: in the instant that B. leaves its place, it's in it, or not: if so; then A. cannot be in it in the same instant without a penetration. If not; then it cannot be said to leave it in that instant, but to have left it before. These difficulties, which pinch so in this obvious experiment, stand in their full force against all motion on the hypothesis of absolute plenitude. Nor yet have the defenders hereof need to take notice of them, because they equally press a most sensible truth. Neither is it fair, that the opposite opinion of interspersed vacuities should be rejected as absurd upon the account of some inextricable perplexities which attend it. Therefore let them both have fair play; and whichsoever doth with most ease and congruity solve the phenomena, that shall have my vote for the most philosophic hypiothesis.
§. 2. It's a difficulty no less desperatethan the former, that the parts vicine to the centre, which it may be pass not over the hundredth part of space which those do of the extreme circumference, should describe their narrower circle but in equal time with those other, that trace so great a round if they move but in the same degree of velocity; here is then an equality in time and motion, and yet a vast inequality in the acquired space. A thing which seems flatly impossible: for is it conceivable, that of two bodies setting forth together, and continuing their motion in the same swiftness, the one should so far out-go its fellow, as to move ten mile an hour, while the other moves but a furlong? If so, 'twill be no wonder, that the race is not to the swift, and the furthest way about may well be the nearest way home. There is but one way that can be attempted to untie this knot; which is, by saying, that the remoter and more out-side parts move more swiftly than the central ones. But this likewise is as unconceivable as what it would avoid: for suppose a right line drawn from the centre to the circumference, and it cannot be apprehended, but that the line should be inflected, if some parts of it move faster than others. I say if we do abstractedly from experience contemplate it in the theory, it is hard to conceive, but that one part moving, while the other rests, or at least moves slower (which is as rest to a swifter motion) should change its distance from it, and the respect, which it had to it; which one would think should cause an incurvation in the line.
§. 3. Let there be two wheels fixed on the same axle in diameter ten inches apiece. Between them let there be a little wheel, of two inches diameter, fixed on the same axle. Let them be moved together on a plane, the great ones on the ground suppose, and the little one on a table (for because of its parvitude it cannot reach to the same floor with them) and you'll find that the little wheel will move over the same space in equal time, with equal arculations, with the great ones, and describe as long a line. Now this seems big of repugnancies, though sense itself suffragate to its truth: for since every part of the greater wheels make a proportionable part of the line, as do the parts of the little one, and the parts of those so much exceeding in multitude the parts of this: it will seem necessary that the line made by the greater wheels should have as many parts more than the line made by the less, as the wheels themselves have in circumference, and so the line would be as much longer as the wheels are bigger: so that one of these absurdities seems unavoidable, either that more parts of the greater wheels go to the making one part of their lines, which will infer a penetration of dimensions; or that the little wheel hath as many parts as the great ones, though five times in diameter exceeded by them, since the lines they describe are of equal length; or the less wheel's line will have fewer parts than the others, though of equal extent with them, since it can have no more parts than the less circle, nor they fewer than the greater. What offers have been made towards the resolving this difficulty, by the ingenious Tacquett and others, and with what success; will be considered in the appendix; to which, that I may pursue other matters, I remit the inquisitive reader.
Should I have enlarged on this subject to the taking in of all things that claim a share in't, it may be few things would have been left unspoken to, but the Creed. Philosophy would not have engrossed our pen, but we must have been forced to anger the intelligences of higher orbs. But intending only a glance at this rugged theme, I shall forbear to insist more on it, though the consideration of the mysteries of motion, gravity, light, colours, vision, sound, and infinite such like (things obvious, yet unknown) might have been plentiful subject. I come now to trace some of the causes of our ignorance and intellectual weakness: and among so many it's almost as great a wonder as any of the former; that we can say, we know.