CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 557 
The values of this integral may be practically obtained, in the most con- 
venient manner, by first determining, from observation, the mean values of « 
for the successive degrees of the thermometric scale, and then adding the values 
for all the degrees within the limits of the extreme temperatures S and T.* 
32. The complete theoretical investigation of the motive power of heat is thus 
reduced to the experimental determination of the coefficient «; and may be con- 
sidered as perfect, when, by any series of experimental researches whatever, we 
can find a value of » for every temperature within practical limits. The special 
character of the experimental researches, whether with reference to gases, or with 
reference to vapours, necessary and sufficient for this object, is defined and re- 
stricted in the most precise manner, by the expressions (6) for 4, given above. 
33. The object of ReGNAuLT’s great work, referred to in the title of this 
paper, is the experimental determination of the various physical elements of the 
steam-engine ; and when it is complete, it will furnish all the data necessary for 
the calculation of ». The valuable researches already published in a first part of 
that work, make known the latent heat of a given weight, and the pressure, of 
saturated steam for all temperatures between 0° and 230° cent. of the air-thermo- 
meter. Besides these data, however, the density of saturated vapour must be 
known, in order that &, the latent heat of a unit of volume, may be calculated from 
REGNAULT’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 
ReEGNAULT’s table giving the pressure 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 re- 
searches on the subject shall have been made, considerable deviations from the 
laws of Boye and Daron, on which this calculation is founded, may be disco- 
vered. 
* The results of these investigations are exhibited in Tables I. and II. below. 
+ It is, comparatively speaking, of little consequence to know pecmnately the value of o, for the 
factor (l—c) of the expression for yw, since it is so small (being less than 7755 for all temperatures 
between 0° and 100°) that, unless all the data are known with more accuracy than we can count 
dp 
upon at present, we might neglect it altogether, and take ai simply, as the expression for 4, with- 

out committing any error of important magnitude. 
{ This is well established, within the ordinary atmospheric limits, in Reanavu.t’s Etudes Mé- 
téorologiques, in the Annales de Chimie, vol. xv., 1846. 
VOL. XVI. PART V. . 7E 
