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° 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° 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