1817.) On the Laws of the Dilatation of Liquids. 431 
Articte III. 
Researches respecting the Laws of the Dilatation of Liquids at all 
Temperatures. By M. Biot. 
(Concluded from p. 377.) 
WE can compare our results advantageously with those of Blag- 
den and Gilpin, because their alcohol was weighed at temperatures 
much inferior to the boiling point of alcohol. To do this we must 
calculate the values of the true dilatation 3, for different tempera- 
tures included in their experiments. This may be done by means 
of the formula 
= KT +5 §AT+ BT + CT} S14 KT} 
We thus obtain the following comparisons :— 
Ditto of the |Truedilatationfrom the freezing point 
Degrees of the mercurial) alcohol therm, 
thermometer. calculated 
T Calculated. | Observed. | Difference. 
T 
s2° F or 0 .R 0°000 0:00000 | 0:00000} 0:00000 
50 ...... 8 6°409 0°01008 | 0°01000 |—0-00008 
BD, tne.» «e 16°B9 13°939 0:02191 | 0°02175 |—0-00016 
95»... 28 23°753 0:03733 | 0°03737 |+0°00004 
BOD .. aici is - 30°22 25°808 0°04056 | 0°04053 |—0-00003 
* ‘The agreement of this result is surely as perfect as could be hoped 
for ; and the deviations may just as well be ascribed to the experi- 
ments as to the calculation. In reducing the coefficients of 3, and 
A, into numbers, we shall have the following results for any tem- 
perature T expressed in degrees of Reaumur’s thermometer. 
Degrees of the alcohol thermometer on its own scale :— 
D, = 0°784 T + 0:00208 T* + 0:00000775 T° 
Apparent dilatation from 0 in glass vessels :— 
A; = 000120085 T + 0:00000318593 T? + 0:00000001187 T* 
True dilatation :-— 
3, = 0°00123369 T + 0:00000322537 T* + 0:00000001198 ft 
In the true dilatation I suppress the term containing T*, the co~ 
efficient of which is 4 preceded by 12 zeros before the decimal 
point. It is evident that an error only amounting to +¢y4sq9 on the 
whole dilatation to 80° would not enable us to introduce this term. 
We must not forget that these formulas apply only to very strong 
alcohol; for we have seen that the dilatation of this liquid follows a 
