170 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
Foot-pounds. 
. 119,669 
Efficiency = g 47>245 = 0-1413 
Efficiency computed in the last article 0-2189 
Difference= loss of Efficiency by incomplete expansion . 0*0776 
„ . ,. „ . V G 24-60 „ , 
Ratio ol Expansion =^^=3-07 nearly. 
If the power of the same engine be now computed by the tables and formulae pub- 
lished in the 20th volume of the Transactions of the Royal Society of Edinburgh, 
which were calculated on the supposition that steam is sensibly a perfect gas, the 
following results are obtained: — 
24'60 
Ratio of expansion, q 7 ^^ = 2"921 =s in tables. 
Foot-pounds. 
u Action at full pressure ” (PjVj in tables) ..... 63,633 
“Coefficient of Gross Action ” (Z in tables) for the ex- 
pansion 2-921 T98 
Gross Action (P^Z) 1 25,993 ft. lb. 
Deduct for back-pressure of liquefaction P 3 V G = 153*34 x 24*6 . 3,772 ft. lb. 
Power developed per pound of steam . . 122,221 ft. lb. 
This result is too large by about one forty-seventh part; a difference to be ascribed 
chiefly to the error of treating steam as a perfect gas. This difference, however, is not 
of material consequence in computing theoretically the power of a steam-engine, 
being less than the amount of error usually to be expected in such calculations. 
(48.) My object in entering thus minutely into the theory of the efficiency of vapour- 
engines is, not so much to provide new formulae for practical use, as to illustrate the 
details of the mechanical action of heat under varied and complicated circumstances, 
and to show with precision the nature and influence of the circumstances which 
prevent the production, by steam-engines, of the absolute maximum of efficiency 
corresponding to the temperatures between which they work. 
To illustrate the results of these calculations with respect to the consumption of 
coal, let it be assumed, as in article (33.), that each pound of coal consumed in the 
furnace communicates to the water, or air, or other elastic substance which performs 
the work, an amount of heat equivalent to 6,000,000 foot-pounds, which corresponds 
to a power of evaporating, in round numbers, about seven times its weight of 
water. Then the following calculation shows the theoretical indicated duty of one 
pound of such coal, when the limits of working temperature are 140° and 40° Centi- 
grade, at the absolute maximum of theoretical efficiency, and at the reduced efficiency 
computed in the preceding article, on the supposition that the expansive working 
ceases at the atmospheric pressure. 
