1817. Dilatation of Liguids at all Temperatures. 371 
mometer stands at 89°463° below zero. But setting out from this 
term, and proceeding to 80° above or below zero, the rate of the 
two thermometers would be nearly proportional; for the term T’, 
which alone alters the exactness of this proportionality, will not 
amount to four degrees in the extreme case when T’ = + 80°. 
Such, then, is the greatest agreement which can ever exist between 
the alcohol and mercurial thermometers, supposing them prolonged 
indefinitely below zero. ha 
Let us now consider the mixtures of alcohcl and water. When 
the proportion of water is inconsiderable, the affinity of the alcohol 
for it will keep it long fluid, and oppose all retrogradation. This is 
proved by the observations made with the thermometer filled witha . 
mixture of equal parts of alcohol and water. The formula in that 
case is 
D, = 0705333 T + 0:00275 T? + 0-000011667 T? 
The calculations from this formula compared with experiment 
give us the following table :— 
Mercurial Weak alcohoi thermometer. 
Liquid. therm, 
T Calculated. | Observed. | Difference. 
80 80°00 80°0 0:00 
79 66°85 66°7 += 0:15 
A mixture 60 54°74 54°8 +0°06 
ofonepart! 50 43°60 43°6 0:00 
alechol 40 33°36 33°3 — 0°06 
and one 30 23°96 23°9 | —0:06 
partwater.| 20 15°30 15°3 0:00 
10 7°33 71 — 0°23 
0 0°00 0:0 0:00 
We see that the law of dilatation is very well represented by the 
formula. ‘The proportion of water is not sufficient to communicate 
its own retrograde motion to the alcohol; for the equation, when 
D, is a maximum, is 
0 = 0705333 + 0°:0055 T + 0:000035 T? 
the two roots of which are imaginary. 
But when we increase the proportion of water, the influence of 
that liquid becomes sensible. This is proved by the thermometer 
filled with a mixture of one part alcohol and three parts water. In 
that case the formula is 
D, = 0°010333 T + 0:0155277 T* — 0:000039444 T° 
Here the term proportional to the temperatures is almost insen- 
sible. It would only give 0-8° at the temperature of 80°. ‘This is 
the result of the influence of water; for in the case of pure water 
Dag 
