I have all along spoken of efficiency as a percentage of the total quantity of heat evolved by the fuel; and this is, in the eyes of a manufacturer, the essential question.  Other things being equal, that engine is the most economical which requires the smallest quantity of coal or of gas.  But men of science often employ the term efficiency in another sense, which I will explain.  If I wind a clock, I have spent a certain amount of energy lifting the weight.  This is called “energy of position;” and it is returned by the fall of the weight to its original level.  In the same way if I heat air or water, I communicate to it energy of heat, which remains potential as long as the temperature does not fall, but which can be spent again by a decrease 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 deg. to 102 deg., or 773 deg. and 563 deg. 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 deg. and 212 deg., or 773 deg. and 673 deg. 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 deg. absolute, and the observed temperature of the exhaust gases was 1,229 deg..  The fraction then becomes (3443 — 1229)/3443 = 64 per cent.  If we multiply this by 0.37, as we did in the case of the steam-engine, we get 23.7 per cent., or approximately the same as that arrived at by direct experience.  Indeed, if the consumption is, as sometimes stated, less than 18 feet, the two percentages would be exactly the same.  I do not put this forward as scientifically true; but the coincidence is at least striking.