1817.) On the Laws of the Dilatation of Liquids. 363 
ARTICLE VI. 
Researches respecting the Laws of the Dilatation of Liquids at all 
Temperatures. By M. Biot. 
(Read to the Societé d’Arcueil, Aug. 8, 1813.) 
Tue knowledge of the laws of the dilatation of liquids is neces- 
sary in numerous chemical and physical investigations. We must 
be acquainted with the dilatations of water to reduce the specific 
gravities observed in this liquid to comparable terms. We must be 
acquainted with those of alcohol to determine its density at different 
temperatures, or to make use of the thermometers in which that 
substance is employed. If we endeavour to compare theoretically 
the dilatability of different liquids with each other, and to combine 
their greater or smaller dilatations with their tendency to boil or be- 
come solid at lower or higher temperatures, we shall find it impos- 
sible to do it generally, or even to form precise notions on the sub- 
ject, until we have expressed the dilatations by general formulas 
which represent them at all temperatures, and which lay before us 
the peculiarities of each liquid which we wish to examine. 
Such is the object of this essay. 1 shall show that for all liquids 
whose dilatations have been hitherto examined the rate of the dila- 
tation may be represented at every temperature by an expression 
of this form :— 
RJ=at+bllh+ct, 
in which ¢ denotes the temperature in degrees of the mercurial 
thermometer, and a, l, c, constant coefficients which depend upon 
the nature of the liquid. I suppose here that 9, is the true dilatation 
for unity of volume reckoned from the temperature of freezing 
water; but it is easy to see that the apparent dilatation follows 
similar laws; for if we represent the apparent dilatation by A,, and 
denote by K the cubic dilatation of the vessel in which we observe 
the liquid,* we have in general 
4,=%—Kz, 
at least if we neglect the square of the coefficient K, which may be 
tok always done, as the dilatation of solid bodies is extremely 
small, 
Let us suppose that the primitive volume of the liquid, being 1 
when ¢ = 0, occupies at + ¢ degrees a number of divisions, X, in 
the vessel whose cubic dilatation is K. ‘This number of divisions 
will correspond with a greater capacity than when ¢ was equal to o. 
It will correspond to the capacity 
* What I mean by cubic dilatation here is the triple of the linear dilatation. 
