In nearly all commercial heat engines the heat is converted into the energy of movement (kinetic energy) by using some body such as water vapour, gas, or air as an intermediary agent. We do not, however, know at present how to transform heat into mechanical work without losing a greater part of it in the process. Even in the most perfect heat engines at least 70% of the heat is lost, only about 30% being converted into mechanical energy. This is as yet the most perfect result which engineers have obtained even with the most elaborate precautions. As a rule the loss is greater; for instance, many good machines which we consider efficient burn one kilogramme of coal, giving out 8000 calories, equivalent to 3,400,000 kilogramme-metres, and transform only about 400,000 kilogramme-metres into work, the rest, forming nearly 80%, is lost. It has been the aim of engineers for many years past to reduce this extravagant waste by every means possible, and the very fact that such a waste exists, clearly shows that our vaunted engines are hopelessly wrong in their principle. There is reason, however, to hope that one day we may, by converting the chemical energy of coal direct into electricity, and thereby avoiding the wasteful heat altogether, reclaim at least 80% of the latent energy which nature has so bountifully supplied to us. It can be shown mathematically that the ratio of the quantity of heat actually converted into work to the total heat used by an engine depends on the temperature at which the heat was absorbed and on the temperature at which the waste heat was discharged. For instance, in a gas engine the efficiency depends on the temperature of the gases directly after the explosion, and on the temperature of the exhaust gases after the work has been done. The exact relation is as follows: the above stated ratio, which is called the theoretical or thermal efficiency, is equal to the difference between the temperature of the hot gases immediately after explosion, and the temperature of the gases of the exhaust divided by the temperature of the hot gases after explosion. This somewhat cumbrous statement may be expressed more clearly in algebraic symbols— W T_{2} - T_{1} — = ————————————— H T_{2} where W is the amount of work done by an engine supplied with a quantity of heat, H, and T_{2} is the temperature of the heated gases which expand doing work, and are thereby cooled to the temperature T_{1}, at which they are exhausted. It is therefore evident, that to make an engine work perfectly efficiently we must obtain an amount of work from it exactly equivalent to the heat put in. That is to say, W must equal H in the above equation. We therefore have the efficiency of such a perfect engine T_{2} - T_{1} W = ————————————— = — = 1. T_{2} H