120 THE POPULAR SCIENCE MONTHLY^ 



the heat which, it employs. Waiving the too subtile question of 

 the nature of heat, he devoted himself principally to fixing the 

 conditions under which a maximum of work is yielded with a 

 given quantity of heat. Guided by the purely philosophical idea 

 of the equivalence of the work expended and the work produced, 

 in perfect mechanics, he affirmed the analogous principle that 

 the possible work is proportional to the quantity of heat employed 

 and to certain functions of the temperatures of the vapor on com- 

 ing in and going out. Carnot's annunciation of his theory was 

 defective in that it took no notice of the fact that the hot body 

 gives out more heat than the cold one receives from it, and that it 

 regarded as equal the amount of heat received upon one isother- 

 mal side of a cycle and that emitted from the other side ; a prin- 

 ciple that may hold good for infinitely small cycles, but not for 

 larger ones, in which a difference exists between the thermic quan- 

 tities proportioned to the size of the cycle. This error and the 

 true condition as pointed out by Clausius are defined by Prof. 

 Rankine, who says, in his paper " On the Economy of Heat in Ex- 

 pansive Machines " : " Carnot was the first to assert the law that 

 the ratio of the maximum mechanical effect to the whole heat ex- 

 pended in an expansive machine is a function solely of the two 

 temperatures at which the heat is respectively received and emit- 

 ted, and is independent of the nature of the working substance. 

 But his investigations, not being based on the principle of the 

 dynamic convertibility of heat, involve the fallacy that power can 

 be produced out of nothing. The merit of combining Carnot's law, 

 as it is termed, with that of the convertibility of heat and power, 

 belongs to Mr. Clausius and Prof. William Thomson ; and, in the 

 shape in 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 heat 

 is received and emitted by the working substance, which function 

 for each pair of temperatures is the same for all substances in na- 

 ture." The law as thus modified and newly expressed might, as M. 

 Langlois remarks, be designated as the equation of Clausius. But 

 Clausius himself, acknowledging the influence which the French- 

 man's ideas had exercised upon him, called it the theorem of Car- 

 not. The second volume of the " Mechanical Theory of Heat " is 

 almost wholly devoted to applications to electrical phenomena. 



The reviewer in " Nature " of the English translation of this 

 work says that the method of treatment pursued in it left hardly 

 anything to be desired, " even from the point of view of a student 

 previously ignorant of the subject. The reader is nowhere per- 

 plexed by uncouth symbols or analytical operations beyond those 

 which are familiar to all acquainted with the principles of the dif- 

 ferential and integral calculus. At the same time, . . . the reader is 



