1819.] and on the Laws of the Communication of Heat. 117 
The corresponding temperature of the air thermometer was 
calculated by a method analogous to that which we kave con- 
stantly employed in our experiments on the dilatation of gases. 
The numbers given in the preceding table are the means of four 
results, which do not differ from each other a single degree. 
Before going further, we shall make a remark of considerable 
importance. If we calculate the temperatures of an air ther- 
mometer by the augmentation of volume which the same mass 
of this fluid experiences under a constant pressure, we obtain 
exactly the same results as when we deduce them from the 
measure of the change of elasticity, the volume remaining the 
same. This result proves evidently that the law of Mariotte 
never ceases to be exact, whatever be the temperature. ’ 
From the beautiful observation of Gay-Lussac, that all elastic 
fluids undergo exactly the same dilatation from 0° to 100°, it 
was very probable that the same uniformity would be observed at 
high temperatures, and that the preceding numbers for air would 
apply to all gases. Yet that nothing might be left uncertain 
relating to a subject of such importance, we made an experiment 
on bidiciren gas, which, as is known, differs the most from 
the others in its physical properties. The result was included 
between the extremes of those which we had obtained for air.* 
We may, therefore, consider it as established that all the gases 
dilate absolutely in the same manner and the same quantity by 
equal changes of temperature. 
The determinations which we have just stated would be suffi- 
cient, if it were required only to know the volume of a gas at 
any temperature. whatever of the mercurial thermometer, or 
reciprocally ; but the object which we had in view of comparing 
the respective dilatations of mercury and air is not yet completely 
attained. For all liquid thermometers indicate merely the 
difference of the expansion of the fluid, and of the vessel which 
contains them. But this difference cannot bear the same ratio 
with the absolute expansion of the liquid, excepting in the single 
case when the increments of volume of the two bodies follow 
exactly the same law. If, for example, the matter of the vessel 
dilated itself, according to a less rapid law than the liquid which 
it contains, it is evident that the thermometer would appear to 
rise’ even when the dilatation of the liquid was uniform. On the 
opposite supposition, there would take place a partial and unequal 
compensation, which would equally disturb the accuracy of the 
comparison. It was, therefore, indispensable to endeavour to 
ascertain the variation which the absolute dilatation of one of 
the two bodies constituting the mercurial thermometer expe- 
riences at elevated temperatures. 
When we consider all the difficulties inherent in the measure- 
* The yolume of hydrogen being 1 at zero, we found it equal to 2°1003 at the 
temperature of 300°, of the mercurial thermometer, The extremes of the yolume 
occupied by air, in the same circumstances, are 2-0948 and 2°1027. 
