IN LOWERING THE FREEZING POINT OF WATER. 579 



Process 4. Remove the cylinder from the lake at — 1°, and place its bottom 

 again on the non-conducing stand. Move the piston back to the position it occu- 

 pied at the commencement of Process 1 . The temperature and pressure, during 

 this process, must vary with one another, as they did in Process 2. Also, since 

 as much heat has been given out as was taken in ; and since the volume is the 

 same as at the commencement of Process 1 , the physical state of the mass con- 

 tained in the cylinder must be now in every respect the same as it was at that 

 time. 



By representing graphically in a diagram the various volumes and corre- 

 sponding pressures, at all the stages of the four processes which have just been 

 laid down, we shall arrive, in a simple and easy manner, at the quantity of work 

 which is developed in one complete stroke by the heat which is transferred during 

 that stroke from the lake at 0^ to the lake at ~ r . For this purpose, let E be 

 the position of the piston at the beginning of Process 1 ; and let some distance, 

 such as E G, represent its 



stroke in feet, its area be- g- m, 3 h 



ing made a square foot, 

 so that the numbers ex- 

 pressing, in feet, distances 

 along E G may also ex- 

 press, in cubic feet, the 



/ 



changes in the contents of a g f he 



the cylinder produced by 



the motion of the piston. Now, when 1-087 cubic feet of ice are melted, 

 one cubic foot of water is formed. Hence, if E F be taken equal to -087 feet, 

 F will be the position of the piston when one cubic foot of water has been melted 

 from ice, that is, the position at the end of Process 1 , the bottom of the cylinder 

 being at a point A distant from F by rather more than a foot. Let ef be parallel 

 to E F, and let E e represent one atmosphere of pressure ; that is, let the units of 

 length for the vertical ordinates be taken such that the number of them in E e 

 may be equal to the number which expresses an atmosphere of pressure. Also 

 let gh be parallel to EF, and let/m represent the increase of pressure produced 

 during Process 2. Then the straight lines ef and g h will be the lines of pressure 

 for Processes 1 and 2 ; and for the other two processes, the lines of pressure will 

 be some curves which would extremely nearly coincide with the straight lines /^ 

 and h e. For want of experimental data, the nature of these two curves cannot 

 be precisely determined ; but, for our present purpose, it is not necessary that 

 they should be so, as we merely require to find the area of the figure efgh, which 

 represents the work developed by the engine during one complete stroke, and this 

 can readily be obtained with sufficient accuracy. For, even though we should 



VOL. XVl. PART V. 7 L 



