140 



dition,) there in also a transference from a cold body to a hot body 

 of a quantity of heat bearing to the quantity created a definite pro- 

 portion depending on the temperatures of the two bodies. 



II. When heat is created by any unreversible process (such as 

 friction,) there is a dissipation of mechanical energy, and a full 

 restoration of it to its primitive condition is impossible. 



III. When heat is diffused by conduction, there is a dissipation 

 of mechanical energy, and perfect restoration is impossible. 



IV. When radiant heat or light is absorbed, otherwise than in 

 vegetation, or in chemical action, there is a dissipation of mechanical 

 energy, and perfect restoration is impossible. 



In connection with the second proposition, the question, How far 

 is the loss of power experienced by steam in rushing through narrow 

 steam-pipes compensated, as regards the economy of the engine, by 

 the heat (containing an exact equivalent of mechanical energy) 

 created by the friction P — is considered ; and the following conclu- 

 sion is arrived at : — 



Let S denote the temperature of the steam, (which is nearly the 

 same in the boiler and steam-pipe, and in the cylinder till the ex- 

 pansion within it commences) ; T the temperature of the condenser ; 

 fi the value of Carnot's function for any temperature, t ; and R the 

 value of 



«' m 



dt. 



Then (1— R)w; expresses the greatest amount of mechanical effect 



that can be economised, in the circumstances, from a quantity - nj 



J 



of heat produced by the expenditure of a quantity, w, of work in 

 friction, whether of the steam in the pipes and entrance-ports, or of 

 any solids or fluids in motion in any part of the engine; and the 

 remainder, R w, is absolutely and irrecoverably wasted, unless some 

 use is made of the heat discharged from the condenser. The value 

 of 1 — R has been shewn to be not more than about one-fourth for 

 the best steam-engines, and we may infer that in them at least three- 

 fourths of the work spent in any kind of friction is utterly wasted. 



In connection with the third proposition, the quantity of work 

 that could be got by equalising the temperature of all parts of a solid 

 body possessing initially a given non-uniform distribution of heat, if 

 this could be doiie by means of perfect thermo-dynamic engines 



