440 Researches respecting the Laws of the [JunE, 
dilatable metals, it would be necessary to preserve the term propor- 
tional to K* T°, which we neglected at the beginning of this me- 
moir. Experiment only can show if it becomes sensible. 
To have the absolute values of K and K’ by the same process, we 
must know the true dilatation 2, of the liquid which we employ. 
We will obtain it by observing this dilatation in a vessel which is 
not dilatable ; and it is easy to construct one possessed of this pro- 
perty, namely, which compensates itself, when we know the diffe- 
rence of the dilatation of the metals. 
I conceive that this process will afford an exact and simple 
method of comparing the dilatation of mercury with that of the 
metals ; which is the only thing that remains to be done to enable 
us to bring all the dilatations to the air thermometer, which is the 
most perfect of all; for the absolute dilatations of the metals ap- 
pear perfectly known from the experiments of Lavoisier and La- 
place, io the exactness of which it is difficult to conceive that any 
thing can be added. 
If we adopt them, they will furnish us with the means of calcu- 
lating tbe true dilatations of the liquids when we know their appa- 
rent dilatation in vessels of known dilatability. To find the law of 
these last relative to a given liquid, we must begin by constructing 
a thermometer with it, and hermetically sealing it. It must then 
be compared with the mercurial thermometer. The coefficients A, 
B, and C, will be determined by three of these observations, and 
we will see if all the others are comprehended within the same law. 
It will only remain to determine a single value of the absolute dila- 
tation between two known temperatures, which will be done by 
weighing; and with these data calculation will enable us to deter- 
mine the true or apparent volume of the liquid at any temperature 
whatever. 
Additions to the preceding Memoir. 
(Read Aug. 13, 1813.) 
The relations which I have established in the preceding memoir 
between the dilatations of different liquids and the degrees of the 
mercurial thermometer, are independent of every hypothesis. They 
enable us to determine by calculation the volume of each liquid at 
a temperature given by the thermometer ; or reciprocally to calcu- 
Jate the temperature, the volume being given. ‘This is all that ob- 
servation requires. 
The dilatation of mercury in glass is taken for a type, to which 
all the others are referred. .We may equally refer the variable 
volume to any other dilatation. Its absolute values would remain 
the same; but the form of the function expressing it would change. 
This is what Mr. Dalton has done in his Philosophical Chemistry. 
This skilful philosopher having remarked that the dilatations of 
water increase nearly as the squares of the temperatures, reckoning 
from the maximum of condensation, conceives that the same thing 
ought to hold with all other liquids, whose composition remains 
