MOTIVE POWER OF HEAT. 149 



method of determining the amount of mechanical 

 effect to be obtained from any given thermal 

 agency. As, however, it is merely the area of the 

 figure which it is required to determine, it will not 

 be necessary to be able to describe each of the 

 curves A^PA^, A^P'A, but it will be sufficient to 

 know the difference of the abscissas corresponding 

 to any equal ordinates in the two; and the follow- 

 ing analytical method of completing the problem 

 is the most convenient for leading to the actual 

 numerical results. 



20. Draw any line PP' parallel to OX, meeting 

 the curvilinear sides of the quadrilateral in P and 

 P'. Let denote the length of this line, and p 

 its distance from OX. The area of the figure, 

 according to the integral calculus, will be denoted 

 by the expression 



/>*, 



e/P 3 



where p l and p 9 (the limits of integration indicated 

 according to Fourier's notation) denote the lines 

 OA and N t A 3 , which represent respectively the 

 pressures during the first and third operations. 

 Now, by referring to the construction described 

 above, we see that is the difference of the volumes 

 below the piston at corresponding instants of the 

 second and fourth operations, or instants at which 



