Mr. W. J. M. Rankine on the Mechanical Action of Heat. 249 



construction, are not intended as estimates of their average 

 amount, nor of their amount in any particular case, but are 

 merely assumed in order to illustrate by a numerical example the 

 rules laid down in the preceding article. It is of course the 

 business of the engineer to ascertain those data with reference 

 to the special situation and circumstances of the proposed work ; 

 and having done so, the method explained in this paper will 

 enable him to determine the dimensions and ratio of expansion 

 which ought to be adopted for the engine, in order that it may 

 effect its duty with the greatest possible oeconomy. 



Section V. 0?i the CEconomy of Heat in Expansive Machines*. 



(39.) A machine working by expansive power consists essen- 

 tially of a portion of some substance to which heat is commu- 

 nicated, so as to expand it, at a higher temperature, being 

 abstracted from it, so as to condense it to its original volume at 

 a lower temperature. The quantity of heat given out by the sub- 

 stance is less than the quantity received; the difference disap- 

 pearing as heat to appear in the form of expansive power. 



The heat originally received by the working body may act in 

 two ways; to raise its temperature, and to expand it. The heat 

 given out may also act in two ways; to lower the temperature, 

 and to contract the body. Now as the conversion of heat into 

 expansive power arises from changes of volume only, and not 

 from changes of temperature, it is obvious that the proportion of 

 the heat received which is converted into expansive power will 

 be the greatest possible, when the reception of heat, and its 

 emission, each take place at a constant temperature. 



(■40.) Carnot was the first to assert the law, that the ratio of 

 the maximum mechanical effect to the whole heat expended in an 

 expansive machine is a function solely of the two temperatures at 

 which the heat is respectively received and emitted, and is inde- 

 pendent of the nature of the working substance. But his investi- 

 gations not being based on the principle of the dynamical con- 

 vertibility of heat, involve the fallacy that power can be produced 

 out of nothing. 



(41.) The merit of combining Carnot' s law, as it is termed, 

 with that of the convertibility of heat and power, belongs to 

 M. Clausius and Professor William Thomson ; and in the shape 

 into which they have brought it, it may be stated thus : — 



The maximum proportion of heat converted into expansive power 

 by any machine is a function solely of the temperatures at which 



* Read to the Royal Society of Edinburgh, April 21, 1851. 

 Phil. Mag. S. 4. Vol. 7. No. 45. April 1854. S 



