Water-Wheel in the common acceptation of the term, is an instrument by which the moving force of water is employed to communicate motion to machinery; there is, however, another class of water-wheels, commonly called paddles, in which the water is employed as a stationary resisting force. The last mentioned class is described under the head of Steam-Vessels, in which it forms the most conspicuous feature. Under the present section we therefore confine our notice to the first-mentioned class of water-wheels, of which there are three distinct kinds, namely, the undershot, the overshot, and the breast-wheel. (There is usually described in books upon the subject, a fourth kind, called the horizontal wheel; but it is so disadvantageous an arrangement, compared to the three first mentioned kinds, that we shall exclude it from our description.

The undershot water-wheel is that commonly used in rivers and streams, and is by far the most ancient kind; it requires no other fall or inclination of the stream than may be sufficient to produce a rapid progressive motion on it; and as it acts chiefly by the momentum of the water, - its positive weight being scarcely called into action, - it is only fit to be used where there is a profusion of water always in motion. This wheel has, however, the advantage of being the cheapest of all water-wheels, and is more applicable to rivers in their natural state than any other form. It likewise works equally well whether the water acts upon the one or the other side of its float-boards; which renders it particularly applicable to tide rivers, where the current changes from one direction to the opposite one at ebb and flood. There are, however, some practical disadvantages attending this form of wheel, when made of small diameter, or the increase of water causes a large wheel to be immersed too deeply. In either case the effect is similar.

Let us first suppose that the wheel delineated beneath, is immersed in water up to the dotted line a b; the float-board b would press downward upon the water, while that at a, on the opposite side, would press the water upward; now these two resisting forces combined, together with the unavoidable friction of the machinery, would almost neutralize the whole force that might be derived from the current, if the water line was above the dotted line c d. Now in the other case of a wheel of small diameter, such as we will suppose the dotted circle to represent, and the floats fixed radially around it, in the same manner and at the same distances apart as in the large wheel, it will be evident that a less numher of floats will be submerged or exposed to the action of the current; consequently, they will assume the same unfavourable position as has been described, by the deep immersion of the large wheel; and that, were the small wheel immersed up to the line a b, which is even with its axis, it would not move at all, as the force or weight of water on each side would be exactly balanced.

Persons but little skilled in the principles of mechanics, have attempted to gain an advantage, by placing the float-boards tangentially to the circle, so that the floats shall leave the water edgeways, and not lift it up at all, as in the one we have figured; omitting to notice, or give due weight to the fact, that the floats which are entering the water on the opposite side of such a wheel are, in consequence, posited so as to strike against the water with their broad sides, which thereby counterbalance the advantage gained on the other; and we submit to the consideration of those mechanics who prefer the tangential to the radial position of the floats, that it is less destructive to the wheel and all the mechanism to which it may be connected, to receive two equal concussions of small force on opposite resisting sides of the wheel, than one concussion of double the force upon only one side of the wheel; the direct tendency, it appears to us, is to break the arms of the wheel, close to the axis.

Whenever the weight and motion of water can be made use of as well as its momentum, much greater effects can be produced than the last described machine is capable of, and with a much less lavish expenditure of the fluid, for then its utmost powers of action are brought into play at once; and accordingly, those water-wheels that are distinguished by the nameof breast-wheels, and overshot wheels, will produce much greater power, with a much less supply of water, than the undershot wheel already described. Both these wheels, however, require a considerable fall in the stream upon which they are placed, and consequently destroy it for the purposes of navigation, unless that ingenious hydraulic contrivance, the Canal Lock, be resorted to, by means of which barges or vessels of any magnitude may be transported from one level to another without difficulty, and with very little loss of time. The over-shot water-wheel, which of all others gives the greatest power with the least expense of water, requires a fall in the stream equal to rather more than its own diameter; therefore it is customary to give this description of wheel a greater length in proportion to its height than is given to any other, - by which an equality of power is obtained.

In the construction of the over-shot wheel a hollow cylinder or drum that is impervious to water, is first prepared, and hung upon a proper central axis. A number of narrow troughs or cells, generally formed of thin plates of metal, extending from one end of the drum to the other, are next fixed round the outside of the wheel, so as to give a transverse section through the middle of the wheel the appearance shown in the preceding figure. The water is conducted by a level trough of the same width as the wheel, over its top, and is thence discharged into the buckets or cells placed round the wheel to receive it; from the particular form of these buckets, they retain the water thus thrown into them, until by their motion they descend towards the point when, their mouths being turned downwards, they discharge their contents into the tail-stream, where the water runs to waste. The buckets on the opposite side of the wheel, ascend with their mouths empty, until they arrive under the end of the water-trough, to be refilled, where there is a pen-stock or sluice, for regulating the quantity of water and preventing waste; since, if the water was permitted to flow too rapidly, it would splash out of the buckets instead of filling them, and Would run down over the surface of the wheel, without producing its proper effect.