202 



If H be taken infinitely small, the latter expression becomes 



Hence, if /mt denote the mechanical effect due to the descent of one 

 unit of heat from A at the temperature < + r to B at the tempera- 

 ture t, we have 



dp 



The value of /m (" Carnot's coefficient"), which is independent of the 

 nature of the liquid or gas employed, may be determined for an as- 

 signed temperature, by means of observations upon any gas, or any 

 liquid and its vapour. The most complete series of experiments 

 from which the values of //, at diffei'ent temperatures may be deduced, 

 are those by means of which Regnault has determined the latent 

 heat of a given weight, and the pressure, of saturated steam, at all 

 temperatui-es between 0° and 230°. Besides these data, however, 

 the density of saturated vapour must be given, in order that k, the 

 latent heat of a unit of volume, may be calculated from Eegnault's 

 determination of the latent heat of a given weight. Between the 

 limits of 0°and 100°, it is probable, from various experiments which 

 have been made, that the density of vapour follows very closely the 

 simple laws which are so accurately verified by the ordinary gases ;* 

 and thus it may be calculated from Eegnault's table, giving the pres- 

 sure at any temperature within those limits. Nothing as yet is 

 known with accuracy as to the density of saturated steam between 

 100° and 230°, and we must be contented at present to estimate it 

 by calculation from Regnault's table of pressures ; although, when 

 accurate experimental researches on the subject shall have been made, 

 considerable deviations from the laws of Boyle and Dalton may be 

 found. 



Such are the experimental data on which the calculation of the 

 mean values of /m, for the successive degrees of the air-thermometer 

 from 0° to 230°, at present laid before the Royal Society, is founded. 



* This is well established by experiment, within the ordinary atmospheric 

 limits, in Regnault's Etudes Metcorologiques, in the Annaks de Chimie. 



