On the Expenditure of Heat in the Hot-air Engine. 353 
Whence for the total consumption, 
(T—oy=(T-0—N(4) ” 
Since we have all along regarded T as equal to 450°, @ to 491°, 
and @ to 60°, T'+6 will be =941°, and N=791°-663. Hence 
finally, while these suppositions remain, E 
ast | 
7 
(T—0"y7=(941° ~791° 633 ( -) ys 
From this formula, making y =1-36, as before, we shall have, 
for the case of equal supply and working cylinders, 
186-55 MK, =137:17 MK 3=32'59 MK,, , 
which is a larger result than was obtained in the former article, 
while the effect of final expansion was disregarded. Supposing, 
as before, that the cylinder will contain 70 lbs. of air, the entire 
consumption of heat would be sufficient to raise a pound of water 
70 X32°-59 =2281°, or to convert nearly two pounds of water 
into steam at 212°. The power of this steam, computed as in 
the former article, would be sufficient to raise 115000 Ibs. one 
foot, or 19100 through the six foot stroke. But, as we have seen 
that the air engine will raise, on the present supposition, 56400 
lbs. six feet with the same expenditure, the expansion is in favor 
of air in the ratio 1 : 2-95. 
Supposing the cut-off at 3, the mean pressure will rise to 
116600 Ibs., being an increase of more than 100 per cent., while 
the expenditure of heat will be increased but about 60 per cent. 
The steam which this heat would generate, would raise 30500 
lbs. through the six-foot stroke, showing an advantage in favor of 
air,as 1: 3-80. But if the steam is allowed to expand to the 
oa extent as the air, the advantage will be reduced to the ratio, 
: 2°80. 
A supply cylinder equal to the working cylinder, however, is 
too large foreconomy. This is aconsequence of the loss of heat 
by expansion, in escaping, spoken of in the commencement of this 
article; and it could not be true if the regenerators were capable 
of arresting the heat remaining unexpended at the close of the 
Stroke, to the extent anticipated by the inventor. ‘Taking the 
proportions of Ericsson’s cylinders, we shall have, for a ¥ eut-off, 
186 units of heat consumed to every unit-weight or pound of air. 
ut as the air is now but 3 of what was before supposed, our mul- 
tiplier will now be 47 instead of 70. On completing the calcula- 
tion, we find that heat enough will be expended, to raise, by 
means of steam at 212°, 12830 lbs. six feet. But the air engine, 
in this case, will raise 77660 lbs.,* to the same height with the 
same expenditure of heat; so that, here, the advantage is in favor 
* Stated incorrectly seventy-fowr thousand pounds, in the former article, 
Seconp Serizs, Vol. XVI, No. 48.—Nov., 1853. 45 
