Volume 183001

Mechanics / By Henry Kater and Dionysius Lardner.

  • Henry Kater
Date:
1830
Catalogue details

Licence: Public Domain Mark

Credit: Mechanics / By Henry Kater and Dionysius Lardner. Source: Wellcome Collection.

    188/408 page 162
    are explained on different principles. Itis true that, in this case, a very small power may elevate a very great weight; but nevertheless, in so doing, whatever be the machine used, the total expenditure of power, in raising the weight through any height, is never less than that which would be expended if the power were immediately applied to the weight without the intervention of any machine. This circumstance arises from an universal property of machines by which the velocity of the weight is always less than that of the power, in exactly the same proportion as the power itself is less than the weight; so that when a certain power is applied to elevate a weight, the rate at which the elevation is effected is always slow in the same proportion as the weight is great. From a due consideration of this remarkable law, it will easily be un- derstood, that a machine can never diminish the total ex- penditure of power necessary to raise any weight or to overcome any resistance. In such cases, all that a machine ever does or ever can do, is to enable the power to be ex- pended at a slow rate, and in a more advantageous direction than if it were immediately applied to the weight or the resistance. Let us suppose that P is a power amounting to an ounce, and that W is a weight amounting to 50 ounces, and that P elevates W by means of a machine. In virtue of the property already stated, it follows, that while P moves through 50 feet, W will be moved through 1 foot ; but in moving P through 50 feet, 50 distinct efforts are made, by each of which 1 ounce is moved through 1 foot, and by which collectively 50 distinct ounces might be successively raised through 1 foot. But the weight W is 50 ounees, and has been raised through 1 foot ; from whence it appears, that the expenditure of power is equal to that which would be necessary to raise the weight with- out the intervention of any machine. This important principle may be presented under an- other aspect, which will perhaps render it more appa- rent. Suppose the weight W were actually divided into 50 equal parts, or suppose it were a vessel of liquid
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