Theory 0/ Heat to the Steam-engina^lQ v 



and integrating this equation, we have tj ^ 



1 



257 



S^ki 



U' 



. » A ■ 



W = mwjo — m,WjjOi + -j-[mir| — mr + Mc(l\— T)], (IX) 



whence, the magnitudes mr and mu being already known from 

 former equations, W may be calculated. 



I have also made this calculation for the above special c^s^V, 



W . "''' 



and given the values of ^, i. e. of the work done during expan- 

 sion by the unit of mass, in the following Table. A kilogramme 

 is chosen as unit of mass, and a kilogramme-metre as unit of work. 



For -j-j the value 423*55, as found by Joule, is employed*. 



For the sake of comparison with the numbers in the Table, it 

 may be well to state that when 1 kilogramme of water is eva- 

 porated at the temperature of 150°, and under the corresponding 

 pressure, the quantity of work done by the vapour during its 

 formation in overcoming the eternal coujiter-pressura has the 

 value 18700. oL ot it^irbf al wii^lu/ Tti- 



■JiBik i 



18. We proceed now to the consideration of the steam-engine 

 itself. 



In the adj oining figure, 

 which is intended merely 

 to facilitate our oversight 

 of the whole series of 

 operations involved in the 

 working of a common 

 steam-engine, A repre- 

 sents the boiler whose 

 contents are maintained 

 by the source of heat 

 at a constant tempera- 

 ture Tp A part of the 

 steam passes from the 

 boiler to the cylinder B 

 and raises the piston a 

 certain height. The cylinder and boiler are next disconnected, and 



* — - is the equivalent of work for the unit of heat ; and the above num- 

 ber denotes, therefore, that the quantity of heat which can raise a kilo- 

 gramme of water from 0° to 1° C, when converted into mechanical work, 

 gives an amount equal to 42355 kilogramme-metres. 



Phil. Mag, S. 4. Vol. 12. No. 79. Oct. 1856. S 



