universe, and enables one of these to be measured by another. One branch of the "correlation of physical forces," as it was termed by Grove, was the relation between mechanical power and heat, and the convertibility of each into the other, which, under the name of "Thermodynamics," has become one of the most important branches of practical science. Joule's first experiments clearly proved that each of these forms of energy was convertible into the other; but some discrepancies arose in determining the exact equivalent of each. His subsequent researches, however, clearly demonstrated the true relation between both. Taking as the unit of heat the amount which would be necessary to raise 1 lb. of water 1 deg. of Fahrenheit's scale (now called "the English thermal unit"), he proved that this unit was equivalent to the mechanical power which would be required to raise 772 lb. 1 foot, or to raise 1 lb. 772 ft. perpendicularly against the force of gravity. The heat-unit--the pound-degree--which I will distinguish by the Greek letter [theta], is a compound unit of mass and temperature; the second--the foot-pound = f.p.--a compound unit of mass and space. This equation, called "Joule's equivalent," or 1 thermal unit = 772 foot-pounds, is the foundation and the corner-stone of thermodynamics. It is essential to understand the meaning of this equation. It expresses the maximum effect of the given cause, viz., that if _all_ the heat were converted into power, or _all_ the power were converted into heat, 1 thermal unit would produce 772 foot-pounds, or 772 foot-pounds would raise 1 lb. of water 1 deg. Fahr. But there is never a complete conversion of any form of energy. Common solid coal may be partly converted into gases in a retort; but some of the carbon remains unchanged, and more is dissipated but not lost. In the same way, if I take five sovereigns to Paris and convert them into francs, and return to London and convert the francs into shillings, I shall not have 100 shillings, but only perhaps 95 shillings. But the five shillings have not been lost; three of them remain in the French _change de monnaies_, and two of them in the English exchange office. I may have forfeited something, but the world has forfeited nothing. There remains in it exactly the same number of sovereigns, francs, and shillings as there was before I set out on my travels. Nothing has been lost, but some of my money has been "dissipated;" and the analogous case, "the dissipation of energy," has formed the subject of more than one learned essay.