46 
Steam Engine, 
to a curve is investigated, and when the curve correspond- 
ing to that equation is constructed, if it coincide (with the 
exception of a few trifling anomalies) with the curve con- 
structed by the results of the experiments, the formula may 
be looked upon as correct, and furnishing a true analyti- 
cal representation of the phenomena. This was done by 
M. Bettancourt, and the curve constructed from this equar 
tion has a point of inflexion at about the 102 ° of Reau- 
mur,^ as it ought to have, because the second differences 
of the barometrical measures of the elastic force became 
negative at that temperature. 
In a similar manner M. Bett ancourt made experi- 
ments on the strength of the vapour from alcohol of spirit 
of wine ; constructing the curve and deducing the requi- 
site analytical formula. This curve had likewise a point 
of inflexion at about 880 of Reaumur, the second differen- 
ces in the table of barometrical measures becoming then 
negative. From a comparison of the experiments on the 
vapour of water with those on the vapour of alcohol, a re- 
markable conclusion was derived : for it appeared that, af- 
ter the first 20 ® of Reaumur, the strength of the vapour of 
spirit of wine was to that of the vapour of water, nearly in 
the same constant ratio of 23 to 10, or 7 to 3, for any one 
and the same degree of heat Thus, at the temperature 
of 40® of Reaumur, the strength of the steam of water is 
measured by 2-9711 Paris inches in the barometer, and 
that of vapour of alcohol by 6*9770, the latter being about 
2 t times the former. 
The equations to the curve of temperature and 
pressure, denoting the relation between the abscissae and 
ordinates, or between the temperature and the elasticity of 
the vapour, as given by M. Bettancourt, were of the foU 
lowing form. 
* To convert Reau. into Fab. miiltiply Reau. by 9, divide by 4 : add 
X9 
U the quotient 32 and the sum is Fab. Reaum. ~ + 32=rFah‘ 
