404 Mr. J.J. Waterston on a Law of Liquid Expansion 
It is not absolutely necessary to correct the temperatures in 
order to recognize these laws of density, and for practical pur- 
poses may not be required; but it seems best to accustom our- 
selves to do so, in order to be prepared for the recognition of 
any other relations of harmony that may exist in the thermo- 
molecular physics of different bodies. 
§ 6. Water is, as might be expected, an exception to the law 
of liquid density, as itis to the law of capillarity and compressi- 
bility (see papers by M. Grassi and M. Simon in the Annales 
de Chimie). Ihave traced its curve of expansion by observations 
in sealed tubes up to 210° C. air-thermometer (see Note E), and 
projected the densities to the value of p required by its vapour- 
gradient ; also those of M. Despretz from 0° to 100° C.; but 
they do not conform to the line required at any point of its 
range even at the highest temperature. These abnormal features 
in this first of liquids have had a prejudicial effect on the pro- 
gress of science in this department. There is no other liqmidas 
yet found with such point of maximum density that remains a 
liquid under its maximum ; yet such a point seems invariably to 
be sought for. M. Muncke and M. Pierre have bestowed much 
unavailing labour on this question. (See Note F.) 
§ 7. To determine the constants of these two equations for 
the density of the liquid and of its vapour, not more than four 
exact observations are strictly required; two of the vapour, and 
two of the liquid. 
If the series of observations on the dilatation of a liquid extend 
over a considerable range of temperature, and have had their 
inequalities equalized by graphical processes equivalent to weigh- 
ing by the method of least squares, the three constants of the 
equation may be directly determined. 
Thus let fo, 4, ¢ be the three temperatures, and v9, 0), vg the 
corresponding volumes observed, to find p and & we have 
=; 
———}__9___ = ___#__0___ 
y-@y @y-Qy 
which may be solved by trial and error. But few observations 
as yet published will stand this test, the range of temperature 
being too small, and the irregularities proportionably too great. 
§ 8. A simple and satisfactory way to test both of these laws 
of density by published observ ations, is to take two of the vapour- 
tensions not far from the boiling-point and compute the value 
of A. Ex. gr., let eo, e, be the two observations of the pressure 
of vapour in contact with its generating liquid; To, T, the cor- 
responding temperatures by air-thermometer reckoned from the 
