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 deg. to 600 deg.  Fahr.  Taking the mean of 500 deg., 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 deg.  Fahr., changing it into steam of 65 lb. pressure at a temperature of 312 deg., or 250 deg. above that of the water from which it is generated.  Besides these 250 deg., 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[theta].  Of these we find in the boiler 22 x 1,144, or 25,168 units, or about 811/2 per cent., of the whole heat of combustion; so that the difference (5,632 units, or 181/2 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 deg., 550 lb. have been raised 40 deg. from 62 deg..  Thus we account for 550 x 40 = 22,000, or (say) 711/2 per cent. still remaining as heat.  If we add this 711/2 per cent. to 181/2 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[theta]; 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,