364 Researches respecting the Laws of the [May; 
Ke 2), 
Xfl+kKe+ = ie 
and as by supposition it is equal to 1 + 9,, since 9, is the true dila- 
tation for unity of volume, we have 
Kore Ki + wel a1 +2. 
This gives us 
X= 
1+% PE ANN arts teak 49 
ly Kir ee 1+Ki+ Ke" 
The first term of this expression is the primitive volume at 0°; the 
second is the apparent dilatation A,. We have, therefore, 
K? 72 
ha Bye 
Ripper Bie : 
+Kt 
Ais 
The term affected by 2 is absolutely insensible in the most exact 
observations on the dilatations of liquids made in glass vessels be- 
tween the temperatures of — 15° and + 100°. If we neglect it, 
we have 
Wire 
Py Ree 
a value which, neglecting the square of K, and the product of K 
by 3,, becomes 
i= 
A,=%—K4 
as we have supposed above. 
To establish the preceding law, and determine the coefficients 
a, b,c, relatively to different liquids, J shall make use of a set of. 
experiments made with great care by Deluc on the dilatation of 
nine liquids, with which he had constructed thermometers, which 
he regulated in freezing water and boiling water, marking 0° at the 
first point, and 80° at the second, and dividing the interval into 80 
equal parts.* It is true that some of the substances which he em- 
ployed boil in the open air at temperatures below that of boiling 
water; but this was not the case in his thermometers, because he 
had perfectly freed them from air. Rectified alcohol, which boils 
in the open air at about 165°, when freed from air, and inclosed in 
a close tube, may be heated to 212° without boiling, and it con- 
nues still to acquire heat and to dilate even at that point and beyond 
it. It is easy to see the reason of this phenomenon from Dalton’s 
theory of the formation of vapours; but here I shall satisfy myself 
with considering it as a fact. The following table exhibits Deluc’s - 
experiments :— 
* Recherches sar les Modifications de l’Atmosphere, tom. ie 
5 
