434 Researches respecting the Laws of the [ June, 
wish to take as an example. This may be done by means of the 
formula 
NEES te Std Saat oP 
We obtain from it the following comparisons, in which unity of 
volume is the volume of water at 0. 
_ _|Ditto of the) Real dilatation from the temperature 
Degrees of the mercurial|water therm, of freezing water, 
thermometer. calculated 
D, Calculated. | Observed. | Difference. 
32 F or OO0OR 0:00 0°00000} 0:00000; 0:00000 
AO .e.e0+ 3°56 |— 0°3373)}—90:00007|—0°00012)| + 0:00005 
EIU saNe sispaie 8:00 |— 0°1220}+0°00019} + 0°00014)—0°00005 
70 ......16°39 |+ 2°3340)+0°00184/ + 0°00188 +0:'00004 
95 ......28°00 |+ 8°9264|+0:00581}+ 0°00583) + 0°00002 
100 ......30°22 |+10°6818)+0:°00685 +.0°00684| —0-00001 
fil Stas hii» al 5 LEE Sa NER RE Rn a etal ae A 
We see that the formula is as exact as the observations themselves. 
The differences never occur but in the hundred thousandths. Thus 
these experiments which required so much delicacy, as the authors 
of them testify, might have been ascertained by calculation, as we 
have done from the thermometric observations of Deluc combined 
with a single measure of the absolute dilatation of water. If we 
reduce the coefficients of 3, into numbers, we obtain the following 
results for any temperature T expressed in degrees of Reaumur :— 
Degrees of the water thermometer on its own scale :— 
D, = — 0°16 T + 0:0185 T? — 0:00005 fi 
Apparent dilatation of water in glass :— 
A,= —0°000087718 T + 0°0000101424 T? — 0:000000027412 T° 
True dilatation :— 
3. = — 0°000054878 T + 00000101395 T?—0-000000027080 T° 
I neglect the term T*, which is equal to 9 preceded by 12 zeros 
all decimal. It would only amount to ,,4,,, of the primitive 
volume even at 80°. We must not forget that the law of the dila- 
tation changes when other substances are dissolved in water. 
The value of 4, is susceptible of a minimum, which will give us 
the absolute condensation of pure water. The equation which de- 
termines this minimum is 
0 = — 0000054878 + 0:000020279 T — 0:00000008124 T* 
If we resolve this equation in the usual manner, and take only 
the smallest root, we obtain T = 2°736° Reaumur, or 38°16° Fahr. 
Gilpin and Blagden, according to Dr. Thomson, placed the true 
maximum at 39°; and Dr. Hope, from the motion of water in 
vessels furnished with thermometers, placed it at 38° Fahr. Some 
