September =;. 



19 1 2] 



NATURE 



ing^ at the outset the importance ot fundamental facts 

 which are too often obscured in the prevailing method 

 of treatment. 



The explanation of the development of heat by fric- 

 tion was one of the earliest difficulties encountered by 

 the caloric theory. One explanation, maintained by 

 Cavendish and others,, was simply that caloric was 

 generated dc novo by friction in much the same way 

 as electricity. Another explanation, more commonly 

 adopted, was that the fragments of solid, abraded in 

 such operations as boring cannon, had a smaller 

 capacitv for heat than the original material. Caloric 

 already existing in the substance was regarded as 

 being 'squeezed or ground out of it without any fresh 

 caloric being actually generated. The probability of 

 the second explanation was negatived by the celebrated 

 experiments of Rumford and Davy, who concluded 

 that friction did not diminish the capacities of bodies 

 for heat, and that it could not be a material substance 

 because the supply obtainable by friction appeared to be 

 inexhaustible. Rumford also showed that no increase 

 of weight in a body when heated could be detected by 

 the most delicate apparatus available in his time. 

 Caloric evidently did not possess to any marked 

 extent the properties of an ordinary ponderable fluid ; 

 but, if it had any real existence and was not merely 

 a convenient mathematical fiction, it must be some- 

 thing of the same nature as the electric fluids, which 

 had already played so useful a part in the description 

 of phenomena, although their actual existence as 

 physical entities had not then been demonstrated. 

 Heat, as Rumford and Davy maintained, might be 

 merely a mode of motion or a vibration of the ultimate 

 particles of matter, but the idea in this form was too 

 vague to serve as a basis of measurement or calcula- 

 tion. The simple conception of caloric, as a measur- 

 able quantity of something, sufficed for many pur- 

 poses, and led in the hands of Laplace and others to 

 correct results for the ratio of the specific heats, the 

 adiabatic equation of gases, and other fundamental 

 points of theory, though many problems in the rela- 

 tions of heat and work remained obscure. 



The greatest contribution of the caloric theory to 

 thermodynamics was the production of Carnot's im- 

 mortal " Reflections on the Motive Power of Heat." 

 It is one of the most remarkable illustrations of the 

 undeserved discredit into which the caloric theory has 

 fallen, that this work, the very foundation of modern 

 thermodynamics, should still be misrepresented, and 

 its logic assailed, on the ground that much of the 

 reasoning is expressed in the language of the caloric 

 theory. In justice to Carnot, even at the risk of 

 wearying you with an oft-told tale, I cannot refrain 

 from'taking this opportunity of reviewing the essential 

 points of his reasoning, because it affords incidentally 

 the best introduction to the conception of caloric, and 

 explains how a quantity of caloric is to be measured. 



.\t the time when Carnot wrote, the industrial im- 

 portance of the steam-engine was already established, 

 and the economy gained by expansive working was 

 generally appreciated. The air-engine, and a primi- 

 tive form of the internal-combustion engine, had 

 recently been invented. On account of the high value 

 of the latent heat of steam, it was confidently expected 

 that more work might be obtained from a given quan- 

 tity of heat or fuel by employing some other working 

 substance, such as alcohol or ether, in place of steam. 

 Carnot set himself to investigate the conditions under 

 which motive-power was obtainable from heat, how 

 the efficiency was limited, and whether other agents 

 were preferable to steam. These were questions of 

 immediate practical importance to the engineer, but 

 the answer which Carnot found embraces the whole 

 range of science in its ever-widening scope. 



In discussing the production of work from heat it 



NO. 2236, VOL. go] 



is necessary, as Carnot points out, to consider a com- 

 plete series' or cycle of operations in which the work- 

 ing substance, and all parts of the engine, are restored 

 on completion of the cycle to their initial state. 

 Nothing but heat, or its equivalent fuel, may be 

 supplied to the engine. Otherwise part of the motive 

 power obtained might be due, not to heat alone, but 

 to some change in the working substance, or in the 

 disposition of the mechanism. Carnot here assumes 

 the fundamental axiom of the cycle, which he states 

 as follows : — " When a body has undergone any 

 changes, and, after a certain number of transforma- 

 tions, it is brought back identically to its original state, 

 considered relatively to density, temperature, and mode 

 of aggregation, it must contain the same quantity of 

 heat as it contained originally." This does not limit 

 the practical application of the theory, because all 

 machines repeat a regular series of operations, which 

 may be reduced in theory to an equivalent cycle in 

 which everything is restored to its initial state. 



The most essential feature of the working of all 

 heat-engines, considered apart from details of 

 mechanism, is the production of motive power by 

 alternate expansion or contraction, or heating and 

 cooling of the working substance. This necessitates 

 the existence of a difference of temperature, produced 

 by combustion or otherwise, between tvifo bodies, such 

 as the boiler and condenser of a steam-engine, which 

 may be regarded as the source and sink of heat respec- 

 tively. Wherever a difference of temperature exists, it 

 may be made a source of motive-power, and con- 

 versely, without difference of temperature, no motive- 

 power can be obtained from heat by a cyclical or con- 

 tinuous process. From this consideration Carnot 

 deduces the simple and sufficient rule for obtaining 

 the maximum effect: — "In order to realise the maxi- 

 mum effect, it is necessary that, in the process 

 employed, there should not be any direct interchange 

 of heat between bodies at sensibly different tempera- 

 tures." Direct transference of heat between bodies 

 at sensibly different temperatures would be equivalent 

 to wasting a difference of temperature which might 

 have been utilised for the production of motive-power. 

 Equality of temperature is here assumed as the limit- 

 ing condition of thermal equilibrium, such that an 

 infinitesimal difference of temperature will suffice to 

 determine the flow of heat in either direction. .-\n 

 engine satisfying Carnot's rule will be reversible so far 

 as the thermal operations are concerned. Carnot 

 makes use of this property of reversibility in deducing 

 his formal proof that an engine of this type possesses 

 the maximum efficiency. If in the usual or direct 

 method of working such an engine takes a quantity 

 of heat O from the source, rejects heat to the con- 

 denser, and gives a balance of useful work ^^ per 

 cycle, when the engine is reversed and supplied with 

 rnotive-power W per cycle it will in the limit take the 

 same quantity of heat from the condenser as it pre- 

 viously rejected, and return to the source the same 

 quantity of heat Q as it took from it when working 

 direct. ' All such engines must have the same 

 efficiency (measured by the ratio W/Q of the work 

 done to 'the heat taken from the source) whatever the 

 working substance, provided that they work between 

 the same temperature limits. For, if this were not 

 the case, it would be theoretically possible, bv em- 

 ploying 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 sufiicientlv improbable to serve as the basis of 

 a formal proof^ Carnot thus deduces his famous 

 principle, which he states as follows :— " The motive 

 poxfer obtainable from heat is independent of the 

 a^^ents set at ii'ork to realise it. Its quantity is fixed 



