348 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF 
following graphical method of representing the mechanical effect developed in the 
several operations, taken from Mons. CLAPEYRON’s paper, is extremely convenient. 
17. LetO X and O Y be two lines , 
at right angles to one another. Along 
O X measure off distances O N,, N N,, 
N.N;, N; O, respectively proportional 
to the spaces described by the piston 
during the four successive operations 
described above; and, with reference 
to these four operations respectively, 
let the following constructions be 
made :— 
(1.) Along O Y measure a length O A, to represent the pressure of the satu- 
rated vapour at the temperature S; and draw A A, parallel to O X, and let it meet 
an ordinate through N,, in Ao. 
(2.) Draw a curve A,P A such that, if ON represent, at any instant during 
the second operation, the distance of the piston from its primitive position, N P 
shall represent the pressure of the vapour at the same instant. 
(3.) Through A, draw A, A; parallel to O X, and let it meet an ordinate 
through N; in As. 
(4.) Draw the curve A; A such that the abscissa and ordinate of any point in 
it may represent respectively the distances of the piston from its primitive posi- 
tion, and the pressure of the vapour, at some instant during the fourth operation. 
The last point of this curve must, according to Carnot’s fundamental principle, 
coincide with A, since the piston is, at the end of the cycle of operations, again 
in its primitive position, and the pressure of the vapour is the same as it was at 
the beginning. 
18. Let us now suppose that the lengths, ON,, N, N,, N.N;, and N30, repre- 
sent numerically the volumes of the spaces moved through by the piston during 
the successive operations. It follows that the mechanical effect obtained during 
the first operation will be numerically represented by the area A A, N,O; that is, 
the number of superficial units in this area will be equal to the number of “ foot- 
pounds ”’ of work performed by the ascending piston during the first operation. 
The work performed by the piston during the second operation will be similarly 
represented by the area A, A, N,N;. Again, during the third operation a certain 
amount of work is spent on the piston, which will be represented by the area 
A, A;N;N,; and lastly, during the fourth operation, work is spent in pushing the 
piston to an amount represented by the area A; AO N3. | 
19. Hence the mechanical effect (represented by the area O A A, A, N.) which 
was obtained during the first and second operations, exceeds the work (repre- 
sented by N, A, A; AO) spent during the third and fourth, by an amount repre- 
sented by the area of the quadrilateral figure AA, A, A;; and, consequently, it 




