MECHANICAL POWERS, such machines as are used for raising greater weights, or overcoming greater resis tances, than could be effected by the natural strength without them ; the power or strength being applied to one part of the machine, and another part of the Machine applied to the weight or resistance. In treating of each of which, two principal problems ought to be resolved.
The first is, to determine the proportion which the power and weight ought to have to each other, that they may just sustain one another, or be in equilibrio.
The second is, to determine what ought to be the propor dun of the power and weight to each other in a given machine, that it may produce the greatest effect possible, in a given time.
As to the first problem, this general rule holds in all powers : suppose the engine to move, and reduce the velocities of the power and weight to the respective directions in which they act; lind the proportions of these velocities; then, if' the power be to the weight as the velocity of the weight is to the velocity of the power, —or, which Amounts to the same thing, if' the power multiplied by its velocity, gives the same product as the weight multiplied by its velocity,—this is the case wherein the power and weight sustain each other, and are in equilibrio; so that in this ease the one would not pre vail over the other, it' the engine were at rest ; and if in motion, it would continue to proceed uniformly, were it not for the friction of its parts, and other resistances.
The second general problem in mechanics is, to determine the proportion which the power and weight ought to bear to each other, that when the power prevails, and the machine is in !notion, the greatest effect possible may be produced by it in a given time. it is manifest, that this is an inquiry of the
greatest importance, though few have treated of it. When the power is only a little greater than that which is sufficient to sustain the the motion is too slow; and though greater weight is raised in this case, it is not sufficient to compensate the loss of time. When the weight is much less than that which the power is able to sustain, it is raised in less time ; and this may happen not to be sufficient to pensate the loss arising from the smallness of the load. It ought, therefore. to be determined when the product of the weight, multiplied by its velocity, is the greatest possible; for this product measures the effect of the engine in a given time, which is always the greater in proportion as the weight which is raised is greater, and as the velocity with which it is raised is greater.
The simple machines by which power is gained are six in number, viz., the leper, the wheel and axle, or axis in peritrochio, the pulley (or rather system of pulleys), the inclined plane, the wedge, and the screw. Of these, all sorts of mechanical engines consist ; and in treating of them, so as to settle their theory, we must consider them as mechanically exact, and moving without friction. For the properties and applications of the mechanical powers, see LEVER, PLANE