Mechanical Theory of Heat to the Steam Engine. 367 
If we multiply this quantity by the space described by the 
surface of the pees up to the same moment, namely (e—«) v’, 
we obtain for the first part of the work, the expression: 
(31.) W,=mB,.— —o'(e-s)b. 
The law according to which the pressure varies during the ex- 
pression which now follows, is also given by equation (29). Let 
the variable volume at any moment be denoted by v, and the 
corresponding pressure by p, and we have 
band me — 6. 
We must substitute this expression in the integral J pdv and 
and then execute the integration from v=ev' to v=v' by which 
means we obtain as the second part of the work 
i 
(32.) W,=mB.log~ —v'(1—e) 6. 
tain the expression in the same form. 
