220 On the Expenditure of Heat in the Hot-air Engine. 
on this subject, would of course expect that the next charge of 
air from the reservoir, taking up these 422°, would, in like man- 
ner as the former, lift the piston completely up, exerting precisely 
the same pressure as before, and filling the cylinder once more 
with air at the temperature of 450°. And they would expect to 
see this operation again and again repeated; so that, accidental 
losses being excluded by the supposition, the furnace would be 
unnecessay. And indeed, the only use of the furnace in the prac- 
tical case, would, in their view, be, to repair the waste of heat 
resulting from imperfect insulation, from leakage, and from the 
necessary incompleteness of transfer in the regenerator. Such per- 
sons would therefore be probably surprised to find, that the second 
charge would not maintain the temperature of 450° to the end of 
the stroke, that the third charge would fall off in temperature still 
more than the second, and so on till the regenerator should be 
completely cooled down. But what woufd perhaps occasion even 
greater surprise than this, would be the fact, that, if a secon 
charge of air should be drawn through the same regenerator not 
from the reservoir, but from the supply cylinder directly, the 
machine not now being self-acting, but being moved by som 
external force, this second charge, at the end of the stroke would 
have the full temperature of 450°, and (the other suppositions 
remaining,) would, in escaping, deposit its 422° of acquired heat 
in the regenerator ; which would again heat the next charge to 
450°, and so on ad infinitum. To this paradox the old philosophy 
furnished no key. The initial and final densities and bulks of 
the air in both cases are identical; and in both cases the same 
amount of matter is exposed for the same time to the same source 
of heat. But the second process is attended with no dimimution 
of the stock of heat originally supposed to be in the regenerator, 
while the first is rapidly exhaustive. How shall the difference be 
accounted for? 
