.548 



PROFESSOR WILLIAM THOMSON'S ACCOUNT OF 



N: 



following gi'aphical method of representing the mechanical effect developed in the 

 several operations, taken from Mons. Clapeyron's paper, is extremely convenient. 



17. Let X and Y be two lines 

 at right angles to one another. Along 

 X measure off distances N,, N N., 

 N. Nj, N3 0, 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 Y measure a length A, to represent the pressure of the satu- 

 rated vapour at the temperature S ; and draw A A, parallel to X, and let it meet 

 an ordinate through Ni, in Aj. 



(2.) Draw a curve Ai P A such that, if N 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 Ao A3 parallel to X, and let it meet an ordinate 

 through N3 in A3. 



(4.) Draw the curve A3 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 pressm-e of the vapour, at some instant during the fourth operation. 

 The last point of this cm-ve 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, N„ Ni N.,, N2N3, and N3O, repre- 

 sent numerically the volumes of the spacer moved through by the piston during 

 the successive operations. It follows that the mechanical effect obtained during 

 the first operation will be numerically rejn'esented by the area A Ai Ni ; 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 Ai A.. No Ni. Again, during the third operation a certain 

 amount of work is spent on the piston, which will be represented by the area 

 A2 A3 N3 N2 ; and lastly, during the fourth operation, work is spent in pushing the 

 piston to an amount represented by the area A3 A O N3. 



19. Hence the mechanical effect (represented by the area A Ai Ao N,) which 

 was obtained during the first and second operations, exceeds the work (repre- 

 sented by N2 Aj A3 A 0) spent during the third and fom-th, by an amount repre- 

 sented by the area of the quadrilateral figure AAi As A3 ; and, consequently, it 



