When work is expended in overcoming the resistance to acceleration, i.e., the inertia of a body, we have its equivalent in additional kinetic energy. When it is expended against gravity, as in raising a weight or bendin.o. a spring, we have it stored up in a dormant form as potential energy. Sec FORCE. Mien it is expended in overcoming fric tion, there appears at first sight to be no equivalent—but the comparatively recent researches of Joule (q.v.) and others have satisfactorily accounted for its disappearance, by proving its quantitative transformation usually into heat, sometimes into other forms of molecular energy. But to pursue this point would lead us again to questions already treated at sonic length in the article FORCE. There is one remark, however, which it is important to make. In compressing a gas, in the receiver of an air-gun for instance, we can never recover as useful effect all the work expended. The reason is that a gas is heated by compression, so that part of the work spent is converted into this heat, con ducted through the metal, and by the principle of dissipation of energy lost, at least in part, to man. Had we a gas which could not be heated by compression (take the imper fect analogy of a space filled with fine spiral springs), we should recover, by allowing it to expand, all the work expended in the compression.
One other remark remains to be made. It will be noticed that Newton speaks of the action of an agent as the product of the agent and the component velocity of its point of application. This is what we now call rate of doing work, or horse-power. Watt esti
mated a horse-power at 33,000 foot-pounds per minute, or 550 foot-pounds per second. This is probably too high; but it is constantly employed in engineering calculations. A. curious quantity, sometimes employed as regards steam-engines, especially those employed for pumping mines, is the duty, which is measured by the number of foot pounds of work done by a hundred-weight of coals supplied to the furnace. A similar mode of comparison is now applied to steam-engines for agricultural purposes, etc.
The quantity of work which can be got out of any machine, human, annual, or other, depends in many cases on the rate at which it is done, or the horse-power actually exerted. An average man can easily work at the rate of a horse-power for a few minutes at a time; but if he were to work at no other rate, he would do very little work in a day. Various singular investigations have been made, both theoretically and experimentally, as to the most profitable rate of doing work, and their results are highly interesting. But to discuss them properly would require more space than we can afford.
• The above table, due to Poncelet, gives at least approximate notions of the horse power employed, and the whole work done, in a working day, by men' and animals variously applying their exertions.