442 Researches respecting the Laws of the (June, 
There is likewise another value of a’, but it is not admissible, 
because it would make T diminish when ¢ increases. By substi- 
tuting these values in the general expression of ‘T, we obtain 
T=t+i8? + H,0 
This formula gives the correspondence of the mercurial thermo- 
meter with the ideal thermometer of Dalton. Accordingly the re- 
sults deduced from it are the same as those which that skilful philo- 
sopher has given in his Tables of Temperature, p. 14. The first 
column of that table contains the number of degrees indicated by 
the ideal thermometer, which Mr. Dalton calls true temperature, 
The corresponding values of T form the third column of Mr. 
Dalton’s table, supposing the degrees of Reaumur which we have 
employed to be converted into degrees of Fahrenheit. The next 
column gives the same degrees T affected by the dilatation of the 
glass. The point of the thermometric scale between 0° and 80° at 
which T differs most from ¢ answers to ¢ = 40°, which gives T = 
34°. Hence at that point ¢ differs 6° from T. Mr. Dalton finds 
for this difference 5°3°, probably on account of small fractions which 
we neglected in resolving the value of a’ by approximation ; and 
perhaps likewise because Mr. Dalton has established his calculations 
in a different manner, though from the same principles as we have 
done. 
Now that this hypothesis is reduced to its simplest terms, a reflec- 
tion naturally suggests itself, and it is this: that when considered 
in itself, it is extremely improbable, because it gives to mercury and 
all liquids a true maximum of condensation fixed at their point of 
congelation. The annunciation of the hypothesis leading to an 
expression of this form : 
T=@i+tve 
T has necessarily a maximum when 
a 
op 
= 
For if we make 
a’ 
b= gyrtk we 
which supposes us to reckon the temperatures 7’ setting out from 
a’ 
= a ewe 
we find 
a’? 
T=-—-7 + 
from which we see that the values of T are the smallest possible 
when ?’ is null, and continually increase from that term, at least if 
I’ be positive. For mercury, for example, we shall have 
I 
ai? 
ay = 82 
Consequently 
