1819.] and on the Laws of the Communication of Heat. 169 
1. That mercury and all other liquids dilate as the squares of 
their temperatures, setting out from the maximum density of 
each. ; 
2. That the gases dilate in a geometrical progression for 
increments of temperature in an arithmetical progression. 
_8. That the capacity of bodies remains constant under the 
same volume. 
4. That during the whole time of the cooling of bodies in air, 
the temperatures decrease in a geometrical proportion, while the 
times follow an arithmetical progression. 
‘All these laws are very accurately verified in Mr. Dalton’s 
thermometer for the temperatures near those in which the new 
scale coincides with the old; and if the same agreement were 
observed at all temperatures, the union of these laws would 
undoubtedly form one of the most important acquisitions of 
modern physics. But unfortunately this agreement is very far 
from taking place in very low or very high temperatures, as we 
shall now show. 
In setting out from the first two laws, we should find, by a 
very simple calculation, that a volume of air, represented by 1000, 
at the temperature of freezing water, would be reduced to 692 
at the point of the congelation of mercury. We found by our 
experiments, that its volume would be 850. At the temperature 
of 256° on the air thermometer, the common mercurial thermc- 
meter ought to mark 282° according to Mr. Dalton, while in 
reality it only indicates 261°. 
Such differences cannot be ascribed to errors of observation. 
They would be much greater if we went to higher temperatures. 
It is easy to see that by applying to our determinations the prin- 
ciples of Mr. Dalton, we should find by the absolute dilataticns 
of mercury, that what he calls the real temperature would be 
much superior to that indicated by the common thermometer. 
But this would produce an effect precisely contrary to what Mr. 
Dalton had in view, which was to lower the indications of this 
last instrument in high temperatures. 
The third law does not appear better founded; for we have 
shown that the capacity increases about a tenth in several bodies 
_ whose volume does not vary one hundredth part. And if we 
estimated the capacities by the scale of which we have just 
spoken, this law would deviate still further from the truth. 
In fine, to prove, in a few words, that the fourth proposition of 
Mr. Dalton is likewise contradicted by experience, it is sufficient 
to say, that the law of cooling in the air is not the same for all 
bodies ; and that, therefore, no thermometric scale can satisfy 
the condition of rendering for all bodies the loss of heat propor- 
tional to the excess of temperature. 
Though the propositions which we have just discussed do not 
attain the object which Mr. Dalton had in view, they prove at 
keast thatlong ago the insufficiency of the eommon doctrine had 
