86 
MR. J. J. WATERSTON ON DENSITY IN SATURATED VAPOURS. 
It will be observed from the Chart, that the observations on the vapour of water 
below 80° show a small excess of density above what is required by the line drawn 
through those at higher temperatures, and the contour of their projection is a 
curve convex to the axis, and very nearly the same as would be caused by the pres- 
sure of a very minute quantity of air ; but the character of the late experiments of 
M. Regnault and Magnus forbid this mode of explaining the slight divergence. It 
is probable that it is connected with the change of condition that takes place at 32°, 
and the effects of which may be sensible up to 80° or 90°. 
It is a curious circumstance that the law of expansibility of water also becomes 
disturbed at about the same temperature. As this has not been remarked, I have 
given the proof of it by projecting M. Despretz’s observations* on the Chart. If 
the volume is made ordinate to the square root of the G temperature as abscissa, 
these observations above 25° Centigrade or 77° Fahr., trace out in the most exact 
manner a conic parabola. The equation is 
a{v—^) = {^/t-<py, (4.) 
in which v is the volume of the G temperature t in terms of its volume unity at 39°‘2 
Fahr., or 4° Centigrade (its point of maximum density), a=352'38, ^=‘99872, and 
^=21-977 or ?>"=483°. 
In the Chart I have made \/v—6 the ordinate, and sjl the abscissa. The proof 
of the position is, that in this mode of projection the observations range themselves 
exactly in a straight line from about 77° upwards -f, and that below this temperature 
there is both less decrement of volume and less decrement of density than is required 
by the law that is followed above that temperature. Other liquids appear to follow 
the same rule of expansion, but the range of the observations is too small as yet to 
found upon them any general conclusion. 
If these equations for the expansion of water and the density of its vapour hold good 
at high temperatures, they would have a common density at 11 08° Fahr., its amount 
being jr^. 
The equation for the density of steam, at any G temperature under this, in terms of 
the density of water unity at 39’2, is 
19-492 
22-2745 
M. Cagniard de la Tour observed the sudden conversion of water into steam at a 
much lower temperature, but his observations are at variance with the laws of 
Marriotte and Dalton, and Gay-Lussac ; and although a slight divergence from 
these laws has been discovered by M. Regnault, it is quite in the opposite direction 
to that which M. Cagniard de la Tour’s observations require. 
* Ann. de Chem. vol. Ixx. 
t If these ordinates are projected to ordinates =t instead of t, the line is a distinct and regular, though 
flat, curve convex to axis. This, if confirmed at high temperatures, 'will prove that the density of liquids as 
well as vapours has reference to the zero of gaseous tension. 
