On the Expenditure of Heat in the Hot-air Engine. 223 
heat which it receives will be faithfully returned again as it 
escapes. It is now heated without undergoing enlargement of 
bulk, and it absorbs neither more nor less heat than the denser 
charge would absorb, were it heated just as many degrees by the 
thermometer, without being permitted to expand—without being 
allowed, that is, to do any work, for heat, it is now well settled* 
will no more perform its labor gratis, than any other known 
wer. 
The expenditure of heat, therefore, absolutely necessary to the 
working of one of Ericsson’s engines, in which the supply and 
working cylinders are equal, and no cut-off is used, in which no 
heat is consumed but in working, and in which the air is cooled, 
between the supply and working cylinders, down to the weather 
temperature, assumed at 60° F., will be in a general expression, 
(T - 6) (y—1) MK, 
In which T is the temperature of the air in the working cylinder, 
6, that of the weather, 7, the ratio of the specific heat of air at 
constant pressure to that at constant volume, M the mass of air 
heated ; and K,, the symbol employed by Mr. Rankine to express 
the mechanical equivalent of the specific heat of air at constant 
volume.* 
But as, in point of fact, the temperature of the reservoir is not 
kept down to that of the weather, but is a value, say &, dye to 
compression in the supply cylinder, so the change of temperature 
in passing into the working cylinder is less; being 'T —6’, instead 
of 'T'—6. Hence, the heat expended in working will be really, 
expressed in mechanical equivalents, 
(T—#) (y—1) MK, (II) 
An engine of this kind would be immensely powerful, but for 
the fact that a large amount of the heat which it thus consumes 
is employed in compressing air to feed itself. If the compressed 
air were allowed to expand against the piston, without receiving 
any additional heat, it is capable of exerting precisely as much 
power as has been employed in compressing it ; SO that, if this 
power could be all effectually applied, it would be just adequate to 
the compression of a new charge, and both power and resistance 
might be accounted zero. But it must not hence be inferred that 
all the heat derived from the furnace, and consumed in working, 
is therefore converted into available power ; for just in proportion 
as the air remains heated above the temperature of the weather, 
at the close of the stroke, in the same proportion it is impossible 
for the heat developed by compression to reéxpend itself in ex- 
pansion ; and to that extent it must prove a dead loss, unless 
can be saved by the regenerator. 
* We refer this symbol here, however, to the degree Fah, and not the degree 
