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.

Before the invention of the steam-engine, the only powers employed in mechanics were those of wind and water mills, and animal power.  In the first two, no conversion of one force into another took place; they were mere kinematic devices for employing the mechanical force already existing in the gale of wind and the head of water.  With regard to the power developed by man and other animals, we had in them examples of most efficient heat-engines, converting into power a large percentage of the fuel burnt in the lungs.  But animal power is small in amount, and it is expensive for two reasons—­first, because the agents require long intervals of rest, during which they still burn fuel; and next, because the fuel they require is very expensive.  A pound of bread or beef, or oats or beans, costs a great deal more than a pound of coal; while it does not, by its combustion, generate nearly so much heat.  The steam-engine, therefore, took the place of animal power, and for a long time stood alone; and nearly all the motive power derived from heat is still produced by the mechanism which Watt brought to such great efficiency in so short a time.

Now the practical question for all designers and employers of heat-engines is to determine how the greatest quantity of motive force can be developed from the heat evolved from a given kind of fuel; and coal being the cheapest of all, we will see what are the results obtainable from it by the steam-engine.  In this we have three efficiencies to consider—­those of the furnace, the boiler, and the cylinder.