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But many particulars must be adverted to, before we can ascertain whether that water can be so applied, as to produce the greatest effect possible.
We shall, for the present, lose sight of the water entirely, and, for the sake of illustration, we shall suppose that a number of equal weights could, by some magical powers, be hooked upon the wheel at a cer, tain place as it turns round, and taken off again in the same way below.
On this supposition we shall easily perceive, that the same weight will produce a much more powerful effect upon one part of the wheel, than upon another part of it. Let A, B, C, D. fig. 1. represent a wheel moveable upon its pivot P; and let the several dots upon one side of it, represent a pumber of equal weights, affixed in the manner above mentioned to one side of the wheel. I would observe:
In the first place, that the weights at A, and C, .can have no tendency whatever to produce any motion in the wheel ; because the one being perpendicularly above the pivot, and the other acting perpendicularly below it, they can have no tendency to move it to either side.
Each of the weights a, and b, however, will have a tendency to move the wheel in a certain degree ; because they are placed a little towards one side of the center; but their moving power will still be small, because they act only upon a radius of small length when compared with that at B. Mathematicians have long ago ascertained, that the power of any given weight, acting on a lever, is always in proportion to the length of that lever ; so that, suppo
sing the length of the lever P B to be four, and the distance P p one, the power of one pound weight, appended at B, will be as four, while that at a or b will be only as one; so that one pound at Bhas an equal force as four at a or b. By a similar mode of investigation, we should find that the weights went on in the same rate, from nothing at A or C, to sixteen at B; or, in other words, the aggregate power of the whole weights, if thus af pended, would be only one fourth part nearly, of what that whole aggregate weight would be, if it could all be applied at the point B only, and to no other part of the wheel.
By this mode of reasoning we are led to perceive, that if, instead of making the water fall down an inclined plain, E B, as it is usual to make it'act by its impetus, we should lead it forward in the direction E A, till it came to a, where it was emptied into a bucket, in order to make the water act only by its dead weight, we should still lose, in this way, a considerable part of the possible power of the water, even if the buckets fhould be so contrived as to lose none of it in the course of its descent; a circumstance that can never be obviated where fixed buckets, of any construction, are employed upon a wheel of large diameter. This is so obvious as to require no illustration. Therefore, where buckets are fixed upon the wheel, the difference of power between buckets appended at equal distances from each other on the wheel, or of one bucket constantly acting at C, equal in weight to the whole, becomes much greater than the proportion here assigned.
If, with a view to obviate this inconvenience, we should think of encreasing the diameter of the great wheel, so as to make the top of it rise higher than the level of the water course, as represented by the dotted lines, the evil would be remedied, in as far as respects the upper part of the wheel ; but still it operates with the same force in as far as respects the lower part of the wheel. Where this augmentation of the diameter of the wheel is even practicable therefore, by reason of the moderate height of the fall, there still must be a very great waste of water when thus applied but where the height of the fall is very great, as from fifty feet and upward, as no wheel could be made of a diameter nearly equal to this, the loss of power that is thus incurred can scarcely admit of a calculation.
From these few obvious considerations it is evident, that if we ever hope to derive the full power of a small stream of water, falling from a very grea. height, we must abandon the idea of making that water act directly on a wheel itself, and make that power be applied to the wheel, by the intervention of some other contrivance better adapted to the purpose than a single wheel in any situation ever can be.
One would suppose, that, when an apparatus of that sort had been discovered, which was equally simple in its construction as economical in its application, it would have been at once universally adopted. But our reasoning is here fallacious; and experience
proves, that though man is eager to seize advantageous improvements when they are pointed out to him, his mind is exceedingly slow at applying the powers that are familiar to him to other purposes than those to which he has seen them applied. In proof of this, I have only to observe, that the following coatrivance for raising a great weight, by means of a very small current of water, has been known to every student of physics for more than a century past, and has never, that I have heard of, been once employed for the purpose of turning machinery, or mill work of any kind ; though it is perfectly well calculated to obviate all the difficulties above stated, and to give to water, falling from a great heigbt, all the effect of which it is susceptible ‘as a moving power.
Let a small wheel A, fig. 2. be fixed so as to turn upon a pivot at the height of the fall of water D, C; and another wheel, exactly similar to it B, at the level of the bottom, from whence the water has a free exit; and let an endless chain be passed over these two wheels, to which is fixed a number of buckets in the position indicated in the figure. In this way no limits can be set to the length of the chain. Let the fall be fifty feet or a hundred, or five hundred feet if you will, there is nothing impossible in thus connecting the whole, and of thus deriving the full benefit of the entire weight of the whole water, without any dimin ution : for not one drop of water can be spilled in descending from the highest to the lowest part of the apparatus.
Let us, for the sake of illustration, suppose, that a stream of water could be commanded, so small as that it ran only a pound weight in a second of time, having a fall of fifty feet, and that the whole of this water was received into the bucket at the top, so as, by its gravity, to produce a rotatory motion of such
velocity as that the chain made one revolution in five minutes. On these data, let me ask what would be its force as a moving power?
Say, the half of five minutes, is two minutes and a half. In two minutes and a half there are 150 seconds; and consequently the full buckets, on one side, would, at all times, exceed the empty ones on the opposite side by 150 pounds; of course, even this small stream would act with a power equal to 150 pounds upon any machinery to which it was applied. But an ordinary mill stream, instead of one pound in a second, discharges nearly a bundred pounds weight of water in the same time. With such a stream, the power
of a machine on this construction would be equal to 15,000 pounds,-a power that no strength of machinery could withstand. Where such a stream therefore could be commanded, with such a fall, it might be subdivided into a great many smaller ones, each of which would have power sufficient to turn a mill. If the height were a hundred feet, the power of the same stream would be doubled ; and so on for any greater height.
Nothing can be more simple than the applying this power, so obtained, to the moving of machinery. It is only to place a vertical wheel, corresponding to the water wheel of an ordinary mill, at one side of this moveable chain, having upon it, instead of fat float boards, firm pins, or teeth, fixed in it at regular distances, to be laid hold of by others corresponding to them, made by the pins that connect the links of the chain; so that, in proportion as the chain moves, the