14,544 units
T = 520 deg. + ------------------ = 5,150 deg. absolute.
13.2 lb.  X 0.238

The lower temperature, t, we may take as that of the feed water, say at 100 deg. or 560 deg. absolute, for by means of artificial draught and sufficiently extending the heating surface, the temperature of the smoke may be reduced to very nearly that of the feed water.  Under such circumstances the proportion of heat which can be realized is

5,150 deg. — 560 deg.
= --------------- = 0.891;
5,150 deg.

that is to say, under the extremely favorable if not impracticable conditions assumed, there must be a loss of 11 per cent.  Next, to give a numerical value to the potential energy, H, to be derived from a pound of carbon, calculating from absolute zero, the specific heat of carbon being 0.25, and absolute temperature of air 520 deg.: 

Units.
1 lb. of carbon X 0.25 X 520 = 130
12.2 of air X 0.238 X 520 = 1,485
Heat of combustion = 14,544
------
16,159
Deduct heat equivalent to work of \
displacing atmosphere by products of }
combustion raised from 60 deg. to 100 deg., } 32
or from 149.8 cubic feet to 161.3 }
cubic feet, /
------
Total units of heat available 16,127

Equal to 16.69 lb. of water evaporated from and at 212 deg..  Hence the greatest possible evaporation from and at 212 deg. from a lb. of carbon—­

16,159 u.  X 0.891 — 32 u. 
W = --------------------------- = 14.87 lb.
966 u.

I will now take a definite case, and compare the potential energy of a certain kind of fuel with the results actually obtained.  For this purpose the boiler of the eight-horse portable engine, which gained the first prize at the Cardiff show of the Royal Agricultural Society in 1872, will serve very well, because the trials, all the details of which are set forth very fully in vol. ix. of the Journal of the Society, were carried out with great care and skill by Sir Frederick Bramwell and the late Mr. Menelaus; indeed, the only fact left undetermined was the temperature of the furnace, an omission due to the want of a trustworthy pyrometer, a want which has not been satisfied to this day.[2]

[Footnote 2:  In the fifty-second volume of the Proceedings (1887-78), page 154, will be found a remarkable experiment on the evaporative power of a vertical boiler with internal circulating pipes.  The experiment was conducted by Sir Frederick Bramwell and Dr. Russell, and is remarkable in this respect, that the quantity of air admitted to the fuel, the loss by convection and radiation, and the composition of the smoke were determined.  The facts observed were as follows: 

Steam pressure 53 lb................................... = 300.6 deg.  F.
lb. 
Fuel--Water in coke and wood...........................    26.08