187 
introduced. Practical experiments have shown that the 
determinations made with litharge are always (about one- 
ninth) short of the truth. An elementary organic analysis 
is a much more correct method of finding the calorific 
values. 
The theoretical value of fuel, more particularly of coal, 
with reference to the number of pounds of water which 
1 lb. of fuel win convert into steam being given by the 
formula x ^ x, in which C is 
the quantity of carbon obtained from an analysis of the 
fuel in question, H the quantity of hydrogen, and h the 
amount of this hydrogen, which corresponds to the oxygen 
contained in the fuel, these, multiplied by their heating 
powers, 13,268 and 62,470 respectively, (obtained from the 
accurate experiments of Dulong), and divided by the latent 
heat of steam, indicate the number of lbs. of water that can 
be converted into steam by 1 lb. of coal. It is, however, 
frequently more convenient to have this number converted 
into an expression of mechanical force, which can be accom- 
plished thus. Let w represent the quantity of water of 
which (u) lbs. are evaporated by 1 lb. of coal, then w 
u X 965.7 X 782 = ^ the actual duty obtained by a lb. of 
coal, namely, the number of lbs. of water raised by it to 
the height of one foot. This formula is founded on the 
fact that (u) lbs. of water, multiplied by 965.7, or the 
co-efficient for the latent heat of steam at 212° as obtained 
by Regnault, indicates the number of lbs. of water which 
would be raised 1° Fahrenheit, and the number 782 arises 
from experiments on the mechanical force denoted by the 
elevation of 1 lb. of water 1° Fahrenheit : that force, 
according to the careful experiments of Mr. Joule, on the 
friction of oil, water, and mercury, being equal to 782 lbs. 
raised to the height of one foot. 
But in ascertaining the relative value of a fuel, we must 
