that connects the Volume of a Liquid with its Temperature. 411 
throughout, and relations of paralellism appear ; also several radiate 
from the same point in the axis of temperature, showing that, as a 
general law, vapours in contact with their generating liquids have, at 
the same temperature, or at the same constant difference of temperature, 
densities that have a constant ratio. 
Note B. § 2.—This mode of graphical analysis seems a natural 
mode of operating when a law of nature has to be unmasked. If the 
proportionate differentials of volume had been laid off as ordinates, 
not to the temperature, but to the volume, the result would be the 
logarithmic curve, which might not be so easy to recognize with only 
a few points to lead from. We must be guided in the selection of 
the coordinate axis by the causal relation of dependent phenomena. 
Heat being, as it were, the instrument of action in molecular physics, 
claims the preference as a standard by which to measure the propor- 
tionate differentials, and to which other variables may be referred to 
as coordinate axis. As an example, the’following is the analysis of 
the law of saturated vapours by this process. 
The vapour-tensions being divided respectively by the correspond- 
ing temperatures reckoned from the zero of gaseous tension, the quo- 
tients represent densities of saturated vapour. Setting off these quo- 
tients as ordinates to the temperatures, we next draw the curve, and 
equalize the irregularities as far as possible; then take off the ordi- 
nates of the finished curve at equal intervals of temperature, say 10° 
or 5°; next take the differences of adjacent ordinates and divide each 
by the intermediate ordinate. These quotients, 7 are to be laid 
off as ordinates to the temperatures. The points appear to range in 
a conic hyperbola, having the axis of temperature as an asymptote. 
This conjecture is to be tested by laying off the inverse of these 
quotients as ordinates to the temperatures. The conjecture is con- 
firmed by the points ranging in a straight line which cuts the axis 
at a certain temperature g. Hence (t—g)f= Gr) tod eee Gis 
FO D hidit wey 
1 1 
The integration of this gives D=(t—g)f x = in which H=(t—g)f 
when D= unity; or let A4/=H, then Df= (2) Comparing the 
value of f in different vapours, it is found to be constant for all and 
equal to 4. 
As another example, but unconnected with heat, we may inquire 
as to the possibility of ascertaining the law of gravitation from the 
changes in the moon’s apparent size and motion, its actual distance 
_ and the earth’s radius being supposed unknown, but assuming that 
the difficulty caused by an unknown parallax and augmentation of 
diameter might be evaded by taking lunar distances at equal altitudes 
on both sides of the meridian. 
By observations on consecutive nights, while the diameter is in- 
creasing or diminishing at the maximum rate, we might obtain two 
