69 



effect may be obtained by the descent of water let down by a water- 

 wheel, and by spending labouring force in turning the wheel back- 

 wards, or in working a pump, water may be elevated to a higher 

 level. The amount of mechanical effect to be obtained by the trans- 

 mission of a given quantity of heat, through the medium of any kind 

 of engine in which the ceconomy is perfect, will depend, as Carnot 

 demonstrates, not on the specific nature of the substance employed 

 as the medium of transmission of heat in the engine, but solely on 

 the interval between the temperatures of the two bodies between 

 which the heat is transferred. 



Carnot examines in detail the ideal construction of an air-engine 

 and of a steam-engine, in which, besides the condition of perfect 

 ceconomy being satisfied, the machine is so arranged, that at the close 

 of a complete operation the substance (air in one case and water in 

 the other) employed is restored to precisely the same physical con- 

 dition as at the commencement. He thus shows on what elements, 

 capable of experimental determination, either with reference to air, or 

 with reference to a liquid and its vapour, the absolute amount of 

 mechanical effect due to the transmission of a unit of heat from a 

 hot body to a cold body, through any given interval of the thermo- 

 metry scale, may be ascertained. In M. Clapeyron's paper various 

 experimental data, confessedly very imperfect, are brought forward, 

 and the amounts of mechanical effect due to a unit of heat descend- 

 ing a degree of the air-thermometer, in various parts of the scale, 

 are calculated from them, according to Carnot's expressions. The 

 results so obtained indicate very decidedly, that what we may with 

 much propriety call the value of a degree (estimated by the mecha- 

 nical effect to be obtained from the descent of a unit of heat through 

 it) of the air- thermometer depends on the part of the scale in which 

 it is taken, being less for high than for low temperatures*. 



The characteristic property of the scale which I now propose is, 

 that all degrees have the same value ; that is, that a unit of heat 

 descending from a body A at the temperature T° of this scale, to a 

 body B at the temperature (T — 1)°, would give out the same me- 

 chanical effect, whatever be the number T. This may justly be 

 termed an absolute scale, since its characteristic is quite independent 

 of the physical properties of any specific substance. 



To compare this scale with that of the air-thermometer, the values 

 (according to the principle of estimation stated above) of degrees of 

 the air-thermometer must be known. Now an expression, obtained 

 by Carnot from the consideration of his ideal steam-engine, enables 



* This is what we might anticipate, when we reflect that infinite cold 

 must correspond to a finite number of degrees of the air-thermometer below 

 zero ; since, if we push the strict principle of graduation, stated above, suf- 

 ficiently far, we should arrive at a point corresponding to the volume of 



air being reduced to nothing, which would be marked as — 273° ( — , 



"366 

 if 366 be the coefficient of expansion) of the scale ; and therefore — 273° 

 of the air-thermometer is a point which cannot be reached at any finite 

 temperature, however low. 



