Theory of Heat to the Steam-engine, 21-5 



at a higher temperature than it formerly had ; and steam-engines 

 without condensers receive water in the hquid, and expel it in 

 the gaseous form. Strictly, therefore, the complete circular pro- 

 cess is not fulfilled in these cases ; nevertheless we may always 

 conceive a second machine appended to the given one which 

 shall receive the matter from the first, reduce it in some manner 

 to its original condition, and then expel it. Both machines may 

 then be regarded as constituting one and the same machine, 

 which will fulfil the above condition. In many cases this addi- 

 tion may be made without introducing greater complexity into 

 the investigation. For example, a steam-engine with a condenser 

 at a temperature of 100° C. may be substituted for a machine 

 without a condenser, provided we assume the latter to be fed 

 with water at 100"" C. 



Hence, if we assume that machines which do not fulfil the 

 above condition are theoretically completed in the above manner, 

 we may apply the theorems concerning the circular process to 

 all thermo- dynamic machines, and thereby arrive at conclusions 

 which are quite independent of the nature of the processes 

 executed by the several machines. 



7. In my former memoir I have represented the two funda- 

 mental theorems which hold good in every circular process by 

 the following equations : — . , ^ ,, . ,,. 



. msiimUnm i'» f^ = - N, ... . . ^>^^y -''t ^ 



wherein the letters have the same signification as tefore, viz.— ■ V^ 



A is the equivalent of heat for the unit of work. 



W represents the external work performed during the circular 

 process. 



Q signifies the heat imparted to the changeable body during 

 a circular process, and </Q an element of the same, whereby any 

 heat withdrawn from the body is to be considered as an imparted 

 negative quantity of heat. The integral in the second equation 

 is extended over the whole quantity Q. 



T is a function of the temperature which the changing matter 

 has at the moment when it receives the element of heat ^Q ; or 

 should the temperature of difl*erent parts of the body be different, 

 a function of the temperature of the part which receives dQ,. 

 With respect to the form of the function T, I have shown in my 

 former memoir that it is probably the temperature itself reckoned 

 from a point which may be determined from the reciprocal value 

 of the coefficient of expansion of an ideal gas, and which must 

 be in the neighbourhood of —273° C. ; so that if t represents 



