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SCIENCE 



[N. S. Vol. XXXVI. No. 924 



were not the case, it would be theoretically 

 possible, by employing the most efficient to 

 drive the least efficient reversible engine 

 backwards, to restore to the source all the 

 heat taken from it, and to obtain a balance 

 of useful work without the consumption of 

 fuel; a result sufficiently improbable to 

 serve as the basis of a formal proof. Car- 

 not thus deduces his famous principle, 

 which he states as follows: "The motive 

 power obtainable from heat is independent 

 of the agents set at work to realize it. Its 

 quantity is fixed solely by the tempera- 

 tures between ivhich in the limit the trans- 

 fer of heat takes place." 



Objection is commonly taken to Carnot's 

 proof, on the ground that the combination 

 which he imagines might produce a bal- 

 ance of useful work without infringing the 

 principle of conservation of energy, or 

 constituting what we now understand as 

 perpetual motion of the ordinary kind in 

 mechanics. It has become the fashion to 

 introduce the conservation of energy in 

 the course of the proof, and to make a 

 final appeal to some additional axiom. 

 Any proof of this kind must always be to 

 some extent a matter of taste; but since 

 Carnot's principle can not be deduced from 

 the conservation of energy alone, it seems 

 a pity to complicate the proof by appeal- 

 ing to it. For the particular object in 

 view, the absurdity of a heat engine work- 

 ing without fuel appears to afford the most 

 appropriate improbability which could be 

 invoked. The final appeal must be to ex- 

 periment in any case. At the present time 

 the experimental verification of Carnot's 

 principle in its widest application so far 

 outweighs the validity of any deductive 

 proof, that we might well rest content with 

 the logic that satisfied Carnot instead of 

 confusing the issue by disputing his rea- 

 soning. 



Carnot himself proceeded to test his prin- 



ciple in every possible way by comparison 

 with experiment as far as the scanty data 

 available in his time would permit. He 

 also made several important deductions 

 from it, which were contrary to received 

 opinion at the time, but have since been 

 accurately verified. He appears to have 

 worked out these results analytically in the 

 first instance, as indicated by his footnotes, 

 and to have translated his equations into 

 words in the text for the benefit of his non- 

 mathematical readers. In consequence of 

 this, some of the most important conclu- 

 sions appear to have been overlooked or 

 attributed to others. Owing to want of ex- 

 act knowledge of the properties of sub- 

 stances over extended ranges of tempera- 

 ture, he was unable to apply his principle 

 directly in the general form for any tem- 

 perature limits. "We still labor to a less 

 extent under the same disability at the 

 present day. He showed, however, that a 

 great simplification was effected in its 

 application by considering a cycle of in- 

 finitesimal range at any temperature t. In 

 this simple case the principle is equivalent 

 to the assertion that the work obtainable 

 from a unit of heat per degree fall (or per 

 degree range of the cycle) at a temperature 

 t, is some function F't of the temperature 

 (generally known as Carnot's function), 

 which must be the same for all substances 

 at the same temperature. From the rough 

 data then available for the properties of 

 steam, alcohol and air, he was able to cal- 

 culate the numerical values of this func- 

 tion in kilogrammeters of work per kiloca- 

 lorie of heat at various temperatures be- 

 tween 0° and 100° C, and to show that it 

 was probablj' the same for different sub- 

 stances at the same temperature within the 

 limits of experimental error. For the vapor 

 of alcohol at its boiling point, 78°. 7 C, he 

 found the value F't = 1.230 kilogram- 

 meter per kilocalorie per degree fall. For 



