1817.] Dilatation of Liquids at all Temperatures. 378 
Among the liquids examined, water is the only one which exhibits: 
this circumstance, Hence we ought to expect that its dilatations 
would differ much from those of mercury. The following table 
shows that this is the case :— 
Mercurial Water thermometer, 
Liquid. therm, 
T Calculated. | Observed. | Difference. 
80 80°0 80°0 00 
70 62°3 62:0 | —0°3 
60 46-2 45:3.) |. Los 
50 32°0 32-0 0:0 
40 20°0 205 | +05 
Water. | 39 10°5 11-2 | +07 
20 3°8 al | +0°3 
10 0-2 0-2 0-0 
This thermometer is certainly the most irregular of all; and this 
is peculiar to water, as Deluc has several times observed in his 
work. Yet we see that the observations oscillate round the formula 
within very narrow limits. If we had only these observations to 
consider, we might make them agree a little better with the formula, 
by introducing a considerable change in the coefficients. But in 
that case we would not represent so well other phenomena which 
we shall notice immediately. Besides, the deviations observed are 
such as may very well be ascribed to the observations themselves. 
Here we have again a maximum of condensation, and it occurs 
at a more elevated temperature than in the preceding experiments. 
The equation which determines it is 
0 = — 0°16 + 0:037 T — 0:00015 T? 
the roots of which are 
T’ = + 4:402°; T” = + 251 
The first is that which makes D, a minimum, and which conse- 
uently indicates a maximum of condensation. Deluc says that 
this maximum appeared to him to correspond nearly with the tem- 
perature of + 4°, which differs very little from our calculus.* He 
* I cannot here avoid noticing the impropriety of drawing such conclusions 
from mathematical formulas, entirely empyrical, and founded merely on obser- 
vations. They may be employed with advantage to facilitate the application of 
experimental results, This constitutes the real value of the present paper. But 
to attempt to deduce from them the temperature at which the density of water is 
@ maximum, as Biot does here, is an abuse of mathematics which ought to he 
carefully gnarded against. We cannot discover a new fact by mathematics; but 
merely demonstrate those found out by other means.—T, 
