Theory of Heat to the Steam-engine. 249 



nishes the amount of work, — a conclusion which results easily 

 from a direct consideration of the subject. 



The equation (2) leads to the value of the amount of work in 

 a manner opposite to that usually followed. The amounts of 

 work done in the several operations are not separately deter- 

 mined and then added togetlier, but, instead of this, the maxi- 

 mum of work is first found, and the losses occasioned by the 

 several imperfections of the process are subsequently deducted 

 from it. 



If, with respect to the communication of heat, we introduce a 

 still more limited condition, and assume that the whole quantity 

 of heat Q^ is also imparted to the body at a constant tempera- 

 ture Ti, then the integration which embraces this quantity of 

 heat may also be executed, and gives 



Qj 



whereby the equation (3) for the maximum of work assumes the 

 form O T _T 



w=J-li^. (4) 



In this special form the equation has already been deduced by 

 William Thomson and Rankine from a combination of Carnot's 

 theorem, as modified by me, and the theorem of the equivalence 

 of heat and work*. 



10. Before we proceed, from these considerations which apply 

 to all thermo-dynamic engines, to treat of the steam-engine, 

 we must first premise something concerning the deportment of 

 vapours at a maximum density. 



In a memoir of mine,, published as early as 1850, ''On the 

 Moving Force of Heat," &c., I have already established the 

 equations which show the application of the two fundamental 

 theorems of the mechanical theory of heat to vapours at a maxi- 

 mum density, and I have there employed these equations in de- 

 ducing several consequences. But as in my last memoir, " On 

 a modified Form of the Second Fundamental Theorem of the 

 Mechanical Theory of Heat," I proposed a somewhat difierent 

 mode of treating the whole subject, it appears preferable to me 

 to assume the last memoir only as known. I shall therefore 

 deduce those equations once more, in a diff*erent manner, by 

 means of the results established in my last memoir. 



It was there assumed^ in order to apply the general equations 

 which were first established to a somewhat more special case, 

 that the only foreign force, acting upon the changing material, 

 which required consideration in determining the external work, 



* Phil. Mag. July 1851. 



