666 PROFESSOR WILLIAM THOMSON'S ACCOUNT OF 



plete to the extent of accuracy of the observations.* The considerable discrepancy 

 presented by Carnot's result, deduced from experiments on air, is not to be 

 wondered at when we consider the very uncertain nature of his data. 



45. The fact of the gradual decrease of /x, through a very extensive range of 

 temperature, being indicated both by Regnault's continuous series of experiments, 

 and by the very varied experiments on different media, and in different branches 

 of Physical Science, must be considered as a striking verification of the theory. 



II. On the Heat developed by the compression of Air. 



46. Let a mass of air, occupying initially a given volume V, under a pres- 

 sure P, at a temperature t, be compressed to a less volume V, and allowed to 

 part with heat until it sinks to its primitive temperature t. The quantity of heat 

 which is evolved may be determined, according to Carnot's theory, when the 

 particular value of yu, corresponding to the temperature t, is known. For, by 

 equation ^ 30, equation (6), we have 



^dg^Ep„ v„ 

 dv itt ' 



where d q is the quantity of heat absorbed, when the volume is allowed to in- 

 crease from y to y + d V ; or the quantity evolved by the reverse operation. 

 Hence we deduce 



rf E^^^JLo ^ . . . . (8), 



Now, - '^° °° is constant, since the temperature remains unchanged ; and 



therefore, we may at once integrate the second number. By taking it between 

 the limits V and V, we thus find 



Q=^ log ^ .... (9), 



where Q denotes the required amount of heat, evolved by the compression 

 from V to v. This expression may be modified by employing the equations 

 PV=P' V'=y>„ v„ (1 + E «) ; and we thus obtain 



EPV V EPV- V 



^^-fTill-We '°g V^= (Kl + E /) ^°S Y' (10) 



* A still closer agreement must be expected, when more accurate experimental data are afforded 

 with reference to the otlier media. Mons. Regnault informs me that he is engaged in completing 

 some researches, from which we may expect, possibly before the end of tlie present year, to be fur- 

 nished with all tlic data for five or six different liquids which we possess at present for water. It 

 is therefore to be hoped that, before long, a most important test of the validity of Carnot's theory 

 will be afforded. 



V 

 t The Napierian logarithm of— is here understood. 



