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.

First, with respect to the furnace. The object is to combine the carbon and the hydrogen of the coal with a sufficient quantity of the oxygen of the air to effect complete combustion into carbonic acid and water. In order to do this, we have to use a quantity of air much larger than is theoretically necessary, and also to heat an amount of inert nitrogen five times greater than the necessary oxygen; and we are therefore obliged to create a draught which carries away to the chimney a considerable portion of the heat developed. The combustion, moreover, is never perfect; and some heat is lost by conduction and radiation. The principal loss is by hot gases escaping from the flues to the chimney. Even with well-set boilers, the temperature in the chimney varies from 400° to 600° Fahr. Taking the mean of 500°, this would represent a large proportion of the total heat, even if the combustion were perfect; for, as a general rule, the supply of air to a furnace is double that which is theoretically necessary.

For our present purpose, it will be sufficient to see how much the whole loss is, without dividing it under the several heads of "imperfect combustion," "radiation," and "convection," by the heated gases passing to the chimney.

With a very good boiler and furnace each pound of coal evaporates 10 pounds of water from 62° Fahr., changing it into steam of 65 lb. pressure at a temperature of 312°, or 250° above that of the water from which it is generated. Besides these 250°, each pound of steam contains 894 units of latent heat, or 1,144 units in all. A very good condensing engine will work with 2.2 lb. of coal and 22 lb. of steam per horse power per hour. Now. 1 lb. of good coal will, by its combustion, produce 14,000 heat-units; and the 2.2 lb. of coal multiplied by 14,000 represent 30,800 θ. Of these we find in the boiler 22 × 1,144, or 25,168 units, or about 81½ per cent., of the whole heat of combustion; so that the difference (5,632 units, or 18½ per cent.) has been lost by imperfect combustion, radiation, or convection. The water required for condensing this quantity of steam is 550 lb.; and, taking the temperature in the hot well as 102°, 550 lb. have been raised 40° from 62°. Thus we account for 550 × 40 = 22,000, or (say) 71½ per cent. still remaining as heat. If we add this 71½ per cent. to 18½ per cent. we have 90 per cent., and there remain only 10 per cent. of the heat that can possibly have been converted into power.

But some of this has been lost by radiation from steam-pipes, cylinder, etc. Allowing but 1 per cent. for this, we have only 9 per cent. as the efficiency of a really good condensing engine. This estimate agrees very closely with the actual result; for the 2.2 lb. of coal would develop 30,800 θ; and this, multiplied by Joule's equivalent, amounts to nearly 24 millions of foot-pounds. As 1 horse power is a little less than 2 million foot-pounds per hour, only one-twelfth, or a little more than 8 per cent. of the total heat is converted; so that whether we look at the total quantity of heat which we show unconverted, or the total heat converted, we find that each supplements and corroborates the other. If we take the efficiency of the engine alone, without considering the loss caused by the boiler, we find that the 25,168 θ which entered the boiler should have given 19,429,696 foot-pounds; so that the 2 millions given by the engine represent about 10 per cent. of the heat which has left the boiler. The foregoing figures refer to large stationary or marine engines, with first-rate boilers.

When, however, we come to high-pressure engines of the best type, the consumption of coal is twice as much; and for those of any ordinary type it is usual to calculate 1 cubic foot, or 62½ lb., of water evaporated per horse power. This would reduce the efficiency to about 6 per cent. for the best, and 3 per cent. for the ordinary non-condensing engines; and if to this we add the inefficiency of some boilers, it is certain that many small engines do not convert into power more than 2 per cent. of the potential energy contained in the coal.

At one time the steam-engine was threatened with serious rivalry by the hot-air engine. About the year 1816 the Rev. Mr. Stirling, a Scotch clergyman, invented one which a member of this Institute (Mr. George Anderson) remembers to have seen still at work at Dundee. The principle of it was that a quantity of air under pressure was moved by a mass, called a "displacer," from the cold to the hot end of a large vessel which was heated by a fire beneath and cooled by a current of water above. The same air was alternately heated and cooled, expanded and contracted; and by the difference of pressure moved the piston in a working cylinder. In this arrangement the furnace was inefficient. As only a small portion of heat reached the compressed air, the loss by radiation was very great, and the wear and tear exceedingly heavy. This system, with some modifications, was revived by Rankine, Ericsson, Laubereau, Ryder, Buckett, and Bailey. Siemens employed a similar system, only substituting steam for air.

Another system, originally proposed by Sir George Cayley, consisted in compressing by a pump cold air which was subsequently passed partly through a furnace, and, expanding, moved a larger piston at the same pressure; and the difference of the areas of the pistons multiplied by the pressure common to both represented the indicated power. This principle was subsequently developed by a very able mechanic, Mr. Wenham; but his engine never came much into favor. The only hot-air engines at present in use are Ryder's, Buckett's, and Bailey's, employed to a limited extent for small powers. I have not said anything of the thermal principles involved in the construction of these engines, as they are precisely the same as those affecting the subject of the present paper.