of temperature. In every heat-engine, therefore, there must be a fall
from a higher to a lower temperature; otherwise no work would be done.
If the water in the condenser of a steam-engine were as hot as that in
the boiler, there would be equal pressure on both sides of the piston,
and consequently the engine would remain at rest. Now, the greater the
fall, the greater the power developed; for a smaller proportion of the
heat remains as heat. If we call the higher temperature T and the
lower T' on the absolute scale, T - T' is the difference; and the
ratio of this to the higher temperature is called the "efficiency."
This is the foundation of the formula we meet so often: E = (T - T')/T.
A perfect heat-engine would, therefore, be one in which the
temperature of the absolute zero would be attained, for (T - O)/T = 1.
This low temperature, however, has never been reached, and in all
practical cases we are confined within much narrower limits. Taking
the case of the condensing engine, the limits were 312° to 102°, or
773° and 563° absolute, respectively. The equation then becomes
(773 - 563)/773 = 210/773 or (say) 27 per cent. With non-condensing
engines, the temperatures may be taken as 312° and 212°, or 773° and
673° absolute respectively. The equation then becomes (773 - 673)/773
= 100/773, or nearly 13 per cent. The practical efficiencies are not
nearly this, but they are in about the same ratio--27/13. If, then, we
multiply the theoretical efficiencies by 0.37, we get the practical
efficiencies, say 10 per cent. and 5 per cent.; and it is in the
former sense that M. Witz calculated the efficiency of the
steam-engine at 35 per cent.--a statement which, I own, puzzled me a
little when I first met it. These efficiencies do not take any account
of loss of heat before the boiler. In the case of the gas-engine, the
question is much more complicated on account of the large clearance
space and the early opening of the exhaust. The highest temperature
has been calculated by the American observers at 3,443° absolute, and