372 Researches respecting the Laws of the [May, 
this term is negative, as we shall see immediately. The following 
table exhibits the comparison of experiment with the formula :— 
Mercurial Weak alcohol thermometer. 
Liquid. therm. 
T Calculated. | Observed. { Difference, 
80 80°00 80°0 0°00 
70 63°24 62°9 —0°34 
A mixture 60 47°99 47°7 —0°29 
of one part; 50 34°40 34°4 0°00 
alcohol and 40 22°72 23°0 +0:28 
three parts 30 13°21 13°5 +0°29 
water. 20 6°10 671 0°00 
10 1°61 1°4 * —0°21 
0 0°00 0°0 0°00 
Here the law of dilatation is very different from what it was in 
pure alcohol, and the difference between the two thermometers is 
also much more considerable. Here there is a maximum of con- 
densation ; for the equation which is obtained when D, is a 
maximum is 
0 = 0:010333 + 0:0310554 T — 0°000118333 T? 
the roots of which are 
T’ = — 0:383°; T” = + 263° 
The first of these only is admissible. It gives a maximum of 
condensation at one third of a degree of Reaumur below zero. If 
we substitute this value of 'T’ in D,, we obtain D; = — 0:0017°; 
that is to say, that at the instant of this maximum the thermometer 
filled with the mixture of alcohol and water ought to be sensibly at 
O of its own scale. Accordingly, if we cool it down further, we 
will see it rising above that point. This maximum is indicated by 
the weak dilatation of the mixture, which according to observations 
was only at 0°1° on its own scale when the mercurial thermometer 
was at + 5°, According to the formula, it ought then to be at 
+ 04°. The error is of that kind which may be ascribed to errors 
of observation. 
We come now to examine the law of dilatation in the thermo- 
meter filled with pure water freed from air. In this case the 
formula is , 
D, = — 0:1600 T + 0:01850 T? — 0:00005 T°, 
Here the term proportional to the temperature is negative. 
* M, Biot, inanote, observes that this figure in Deluc’s book is illegible ; but 
that h® eonceives it to be 5. Inmy copy (p. 326), the 4to, edition of Geneva, 
1772, it is very legible, and undoubtedly 4,—T, 
5 
