45 
Steam Ejigine. 
to lower the temperature of the water to the freezing point, 
and then, having extracted all the air from the boiler by 
means of the air-pump, the difference between the columns 
of mercury in the two branches of the barometer shewed 
the measure of the elastic force of the vapour arising from 
the water in that temperature. Then lighting the fire be- 
low the boiler, he gradually raised the temperature of the 
water from 0 to 110^ of Reaumur’s thermometer, that is, 
from 32^ to279T of Fahrenheit’s thermometer; and for 
each degree of elevation in the temperature he observed 
the height of the mercurial column which measured the 
elasticity or pressure of the vapour. 
These experiments were repeated various times and 
with different quantities of winter in the vessel ; their re- 
sults w^ere arranged in different columns for the sake of 
comparison, and it appeared that the pressures for different 
temperatures agreed very nearly, however much the quan- 
tity of fluid in the vessel wiis varied. It was also seen 
that the increase in the expansive force of the vapour is 
at first very slow ; but increases gradually unto the higli- 
er temperatures, where the increase becomes very rapid, 
as will be obvious from an examination of the tables in 
some of the following pages. 
To express the relation between the degrees of tempe- 
rature of the vapour and its elastic force, this philosopher 
employs a method suggested by M, Prony, which con- 
sists in imagining the heights of the columns of merciiry 
measuring the expansive force to represent the ordinates 
of a curve, and the degrees of heat the corresponding ab- 
scissse of that curve ; making the ordinates equal to the 
sum of several logarithmic ones which contain two inde- 
terminates, and ascertaining these quantities in such man-* 
ner that the curve may agree with a tolerable number of 
observations taken throughout the wfliole extent of the 
change of temperature, from the lowest to the highest ex- 
treme of the experiments. Then a formula or equation 
