63 



Expenditure of steam per unit of time, — 



E 

 y^ — — - — . 



A numerical example is added of the solution of this problem of 

 economy. 



The next portion of this paper relates to the proportion of heat 

 converted into expansive power by machines. 



A machine working by expansive power consists essentially of a 

 portion of some substance which alternately expands and contracts 

 under the influence of heat ; receiving heat and expanding at a 

 higher temperature ; emitting heat and contracting at a lower. 



The quantity of heat emitted is less than the quantity received, 

 the difference being transformed into expansive power. To make 

 the proportion of heat thus transformed a maximum, the tempera- 

 tures of reception and emission should each be a constant quantity, 

 so that none of the heat received or emitted may be employed in 

 producing changes of temperature. The temperature must be raised 

 and lowered by compression and expansion only. 



Carnot was the first to assert the law, that when a machine works 

 under these conditions, the ratio of the power evolved to the heat 

 originally received, is a function of the temperatures of reception and 

 emission only, and independent of the nature of the working substance. 

 But his investigation not being founded on the principle of the 

 mutual conversion of heat and power, involves the fallacy that power 

 can be produced out of nothing. 



The merit of combining Carnot's law with that of the converti- 

 bility of heat and power, belongs to M. Clausius and Professor 

 William Thomson. 



The author, having applied to this question the principles laid 

 down in the introduction and first section of his paper on the Mechani- 

 cal Action of Heat, has arrived at the following conclusions : — 



First. — Carnot's law is not an independent principle in the theory 

 of heat, but is deducible as a consequence from the equations of the 

 mutual conversion of heat and expansive power given in the first 

 section. 



Secondly. — The maximum value of the ratio of the quantity of 



