September 13, 1912] 



SCIENCE 



323 



from heat, how the efSciency was limited, 

 and whether other agents were preferable 

 to steam. These were questions of immedi- 

 ate practical importance to the engineer, 

 but the answer which Carnot found em- 

 braces the whole range of science in its 

 ever widening scope. 



In discussing the production of work 

 from heat it is necessary, as Carnot points 

 out, to consider a complete series or cycle 

 of operations in which the working sub- 

 stance, and all parts of the engine are re- 

 stored 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 me- 

 chanism. Carnot here assumes the funda- 

 mental axiom of the cycle, which he states 

 as follows: "When a body has %i,ndergone 

 any changes, and, after a certain number 

 of transformations, is brought back identic- 

 ally to its original state, considered rela- 

 tively 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 applica- 

 tion of the theory, because all machines re- 

 peat 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 work- 

 ing of all heat-engines, considered apart 

 from details of mechanism, is the produc- 

 tion of motive power by alternate expan- 

 sion or contraction, or heating and cooling 

 of the working substance. This necessi- 

 tates the existence of a difference of tem- 

 perature, produced by combustion or 

 otherwise, between two bodies, such as the 

 boiler and condenser of a steam engine, 

 which may be regarded as the source and 



sink of heat respectively. Wherever a dif- 

 ference 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 continuous process. From 

 this consideration Carnot deduces the 

 simple and sufficient rule for obtaining the 

 maximum effect: "In order to realize the 

 maximum effect, it is necessary that, in the 

 process employed, there should not be any 

 direct interchange of heat between bodies 

 at sensibly different temperatures." Di- 

 rect transference of heat between bodies at 

 sensibly different temperatures would be 

 equivalent to wasting a difference of tem- 

 perature which might have been utilized 

 for the production of motive power. 

 Equality of temperature is here assumed as 

 the limiting condition of thermal equilib- 

 rium, such that an infinitesimal difference 

 of temperature will suffice to determine the 

 flow of heat in either direction. An engine 

 satisfying Carnot 's rule will be reversible 

 so far as the thermal operations are con- 

 cerned. 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 Q from the source, 

 rejects heat to the condenser, and gives a 

 balance of useful work W per cycle, when 

 the engine is reversed and supplied with 

 motive power W per cycle it will in the 

 limit take the same quantity of heat from 

 the condenser as it previously rejected, 

 and return ti 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 



