166 Prof. Barnard on the comparative Expenditure of Heat 
Suppose a column of atmospheric air, 
whose altitude is equal to A B, to be con- 
fined in a cylinder by a piston ei Siege of 
moving without friction. Let the pres- 
sure it exerts upon the piston at the tem- 
perature S° be represented by the ordi- 
F. Let it expand with unvary- 
ing temperature until the piston reaches a 
the point C, and let the ordinate CG represent the pressure at 
that time. ‘Let it now expand without receiving or imparting 
heat, from C to D, during which time the temperature falls to T°, 
and the pressure to D H. Let it now undergo compression, main- 
taining the invariable temperature T°, until the piston reaches 
E, a point such that the further compression, (without gain or 
loss of heat,) to the original volume, A B, shall restore the original 
pcre ty S°, and pressure, BF. It is evident that the area, 
G B ; : 



during the expansion, and the area, F K H DB will represent the 
force required to restore the air to its original state. Hence, the 
differential area, F GH K, will be vis measure of the amount of 
heat converted into available force. 
Represent the original volume of the air, AB, by V’, and the 
volume AC by V”; also AD by V, and AE b ve V gs Put # fot 
the original temperature, S°, reckoned from the absolute zero 
(taken at 459° below 0° F.), and 7, for the temperature T°; sim- 
ilarly reckoned, Then, according ‘to Poisson’s formula for tem 
peratures as affected by expansion or compression, . 
1, (vy SiofWAFea: MMM 
is w) , and also — ae ;. OF ee 
tuting for p its value from Poisson’s formula for pressure undet 
these circumstances, viz. : 
Beets) 
where P” represents the pressure corresponding to V”. Hence 
the area in question is expressed by the formula, 
pry” we y-1 
1- {| — ‘ 
i ar C ) 
And, in ae manner, P’ representing the pressure corresponding 
ww YY" the a a FKEB, which measures the force expended e 
the final somipkelsiin, is expressed by 
* Since the surrounding medium—the atmosphere, for instance--aids the 
pression as Genki ta it opppooes tha Gepannden: at seek tee get? 
