47 
Steam Engine. 
m+lx m'+lx sX'-r 
1. For water, = <? -e 4-<? 
m-\-lx 7n'+lx sx-r s'x^-r' 
— alcohol, y—e + e -he -A. 
Where y represents the height of the column of mercury 
which measures the expansive force, x the corresponding 
degrees of Reaumur’s thermometer, and the other letters 
certain values which are assigned to tliem in the investi- 
gation. 
But M. Prony, in the 2d volume of his Architec-‘ 
ture HydrauliquCy has thrown these equations into a rather 
more convenient form, though analogous to those of Bet- 
tancourt. His formula for the vapour of water is this, 
y—m 
f^;r^f-hrrm riv-^. 
The method which he followed consisted in satisfying the 
results between 0° and 8Qo, by means of the two first 
terms, and to interpolate by means of the other two, the 
differences between the observed values, and those com- 
puted by the two first terms, from 80® up to 110°. In 
this manner he succeeded to express so exactly the obser- 
vations in their whole extent, that the curves of the cal- 
culus and the experiments Avere only distinguishable the 
one from the other by such little anomalies, as were mani- 
festly the effect of some trilling though inevitable errors 
in the observations, and in the graduations of the scales in 
the apparatus. He afterwards employed an equation of 
three terms, giving to the different coefficients the follow- 
ing values : 
- log;, —0-0692259 
- - log. =0-0202661 
- “ =^120736 
- log. -7-8601007 
- log. =1-9369271 
- - log. m,,^=F9369248 
Substituting these several values in the equation 
y^m. 
r, = 1-172805 
= 1-047773 
= 1-028189 
•m^ = — 0-00000072460407 
= -fO'8648 188803 
= —0-8648181057 
