374 Researches respecting the Laws of the [May, 
says, likewise, that at the time of this phenomenon the water ther- 
mometer was about half a degree below zero on its own scale. We 
find by our formula — 0:35°, This maximum, however, is only 
apparent, and requires a correction in order to obtain the real 
maximum. The experiment was made with distilled water freed 
from air. Common water, containing air, probably dilates in pro- 
portions a little different. 
I shall now deduce from these results the true and absolute dila- 
tations of the liquids observed by Deluc. In the first place I shall 
remark, that the thermometrical observations which we have em- 
ployed are, in all probability, not exempt from small inaccuracies. 
Deluc, in the work in which these experiments occur, treats at 
great length on the construction of the thermometer; but he takes 
no notice of the necessity of plunging both the bulb and the liquid 
column into the medium the temperature of which we wish to 
communicate. The same thing ought to be done in observing the 
intermediate temperatures between the fixed points. If these pre- 
cautions were neglected by Deluc, which however is not probable, 
all the numbers observed by this philosopher are affected by a sinall 
error equal to the dilatation of the liquid portion contained in the 
tube of his thermometers at each of the temperatures at which he 
made an observation, On that account it would be interesting that 
an exact philosopher would repeat these experiments again, to give 
them all the precision of which they are capable. 
After this remark I set out from the formulas which we have esta- 
blished, and I shall endeavour to deduce from them the true and 
absolute dilatations. 
This is easily done. ‘To regulate the thermometers, Delue put 
them first in melting snow, and then in boiling water. He marked 
in each of these two cases the extremity of the liquid column, and 
he divided the interval between them into 80 equal parts, Of con- 
sequence, the apparent and absolute dilatation of the liquid em- - 
ployed, being denoted by D, this dilatation determines the extent 
of the 80°. Hence knowing D,, that is to say, the number of 
degrees of the same thermometer corresponding to the temperature 
T, we can easily deduce from that the apparent dilatation A; ; for 
we shall have proportionally 
D 
A, = 80. iD 
But if we call the true and absolute dilatation 3,, by which is meant 
the dilatation that would be perceived in a vessel which does not 
itself dilate, we have seen that it may be calculated from the appa- 
rent dilatation, and that we have in general 
= KT + {14+ KTR A, 
K being the cubic dilatation of the matter of the vessel, in which 
the apparent dilatation A, is observed; therefore if we put here, 
instead of 4;, its value, a function of D, we obtain 
