y^msii^mWheory of Heat to the Steam-engine. 261 



By employing this expression, therefore, we obtain an equation 

 the right-hand side of which contains only known quantities ; 

 for the masses mj and M, and the temperatures Tj, T^, and Tq, 

 are assumed to be. immediately given, and the magnitudes r, p, 



and -^ are supposed to be known functions of the temperature. 

 cc J. 



21. If in the equation (X) we set T2=Ti, we find the amount 

 of work, for the case that the machine works without expansion, 

 to be 



W' = miMi(;?i— jt?o) (23) 



If, on the contrary, we suppose the expansion to be continued 

 until the vapour sinks from the temperature of the boiler to that of 

 the condenser, — which case cannot of course be strictly realized, 

 but rather forms a limit which it is desirable to approach as 

 much as possible, — we have only to set T2=Tq, when we obtain 



W'=l[m,»-,-moro+Mc(T,-T<,)]. . . (34) 



Eliminating mQVQ by means of the equation before given, in 

 which we must also set T2=To, we have 



W'= l[m,r,?!^« + Mc(T.-To+T„log^)]*. (XI) 



22. If to the foregoing equation we give the form 



W' = m,.,.^^° + M.(T,-T„).l(l+ ^^jog|e), (25) 



then the two products Mc(Tj — Tq) and myVi which appear therein 

 together represent the quantity of heat furnished by the source 

 of heat during a circular process. For the first is the quantity 

 of heat which is necessary to raise the temperature of the liquid 

 mass M, coming from the condenser, from Tq to Tj ; and the 



* The above equations, representing the amount of work under the two 

 simphfying conditions introduced at the close of § 19, were developed by 

 me some time ago, and publicly communicated in my lectures at the Berlin 

 University as early as the summer of 1854. Afterwards, on the appearance, 

 in 1855, of the Philosophical Transactions for the year 1854, 1 found therein 

 a memoir of Rankine's, "On the Geometrical Representation of the Expan- 

 sive Action of Heat, and the Theory of Thermo-dynamic Engines," and 

 was surprised to find that at about the same time Rankine, quite indepen- 

 dently, and in a different manner, arrived at equations which almost en- 

 tirely agreed with mine, not only in their essential contents, but even in 

 their forms ; with this exception only, that Rankine did not consider, that, 

 when entering the cylinder, a quantity of liquid is mixed with the vapour. 

 By the earlier publication of this memoir I lost, of course, all claim to 

 priority with respect to this part of my investigations; nevertheless the 

 agreement was so far satisfactory as to furnish me with a guarantee for the 

 accuracy of the method I had employed. 



