FREE AND PERFECTLY ELASTIC MOLECULES IN A STATE OF MOTION. 43 
Each point in the positive quarter of the co-ordinate axes represents a medium of 
a given density and temperature or vis viva; the sixth power of the ordinate x 
represents its density, and the square of its abscissa y its vis viva. Thus, x Cl y 9 - = e is 
the expression for the tension or elastic force of a medium whose point on this chart 
(as it may be called) is defined in position by the co-ordinates x, y. 
If e is supposed constant, x, y to vary, their locus traces out a hyperbolic curve 
(such as NPt) whose equation is x G y z = e. It is a curve of constant pressure, of which 
kind is STPC for one atmosphere drawn on the accompanying large chart of vapours 
(Plate 1). The sine of the inclination of its tangent to the axis of y is ^ xjy. Any gas 
expanding or contracting under a constant pressure traces out a curve of this kind 
with its varying density and vis viva. 
It is remarkable that if the points corresponding to the density and vis viva of a 
vapour in contact with its generating liquid are laid down on this chart (fig. 3), they 
range themselves in a straight line, such as TP, that issues from some point advanced 
on the axis QC. As this fact applies to all vapours that have been experimented 
upon, it seems to point to the true physical law of their equilibrium with the liquid. 
On the accompanying chart of vapours I have projected the points of several sets of 
experiments. It may be viewed as a portion of the fig. 3 enlarged, the point Q, 
or origin of co-ordinates, being about 40 inches to the left of the outer margin. 
The following details will be sufficient, with the chart, to enable any one to satisfy 
himself of the truth, and, if he pleases, to construct the formula of any new vapour by 
means of two simple experiments on its tension. 
In vapours, as well as gases, the pressure or tension being equal to the product of 
the absolute temperature or (t -fi 461) by the density, to find the latter we have only 
to divide the tabular tension (in inches of mercury) opposite f Falir. scale by the 
former. The sixth root of the quotient is the value of x, and the square root of 
(t + 461) is the corresponding value of y. In the accompanying chart I have 
projected several sets of tables of pressures in this way. The unit value of x is 
i lOx/To inches long, and the unit value of y, or square root of absolute temperature, 
is - 6 -ths of an inch in length. 
It will be remarked how nearly the experiments of Southern and the French 
Academy on steam range themselves in one line. To observe this more distinctly I 
have drawn the straight line SF through Southern’s pressure at 212°, and the 
French Academy s observation at 429’4. The divergence at the four lowermost 
experiments of Southern is more apparent than real, the greatest difference being 
equivalent to oidy yj^ths of an inch of mercury. 
The general equation for a straight line Tit (fig. 3) is x = (y — G) tan H, in which 
G = QT and H = ETC. Each vapour being represented by such a line with two 
constants G and H, to find these constants, which may be done by two experiments 
on any one vapour, let e 0 be the tension at t 0 temperature Fahr., and <q the 
tension at t L temperature; then since y 0 2 = 461 -f f 0 and y 0 ~x 0 G = c v , we have 
