370 Researches respecting the Laws of the [May, 
smaller proportion does not produce this effect. This happens with 
mixtures of water and alcohol, as will be seen hereafter. 
I proceed to highly rectified alcohol. The alcohol used. by Deluc 
was sufficiently strong to set fire to gunpowder, over which it was 
burned. This is the way in which Deluc characterizes it. He 
found that, though not quite so strong, provided the proportion of 
water in it was small, the same results nearly were obtained. The 
following is the formula for this alcohol :— 
D; = 0°754 T + 0:00208 T? + 000000775 T® 
Its agreement with observation will be seen by the following 
table :— 
Mercurial Alcohol thermometer, 
Liquid. therm, : 
T Calculated. | Observed. | Difference, 
sO 80:00 80:0 0°00 
“0 67°73 67°38 +0:07 
60 56°20 56°2 0:00 
| 50 45°37. | 45:3 | —0-07 
| 40 35°09 35°1 +0°01 
|. 30 25°60 | 25°6 0:00 
20 16°57 16°5 — 0°07 
10 8°05 7-9 —0-16 
0 0:00 0-0 0:00 
—10 764} 7-7 +006 
We see that the calculated quantities agree with those observed, 
and this holds below zero as well as above it. The law of the 
dilatation of this alcohol does not indicate a retrogradation. For 
supposing D,a maximum, we obtain the following equation :— 
0 = 0:784 + 0°00416 T + 0:00002325 T? 
the two roots of which are imaginary. 
The value of D, given by our formula will be very convenient 
for determining the correspondence of the mercurial and alcohol. 
thermometers. We see that such a calculation is indispensable ; for: 
there is still a great difference between the two thermometers, 
though they agree at the freezing and boiling points. The difference 
becomes less if the alcohol thermometer is regulated on that of mer- 
cury at low temperatures. [f we make T = (T) + 'T’, and deter- 
mine (T) so as to make the square of T’ to disappear from D, we 
obtain (T) = — 89°163° Reaumur. Then the value of D, becomes 
D,; = — 58°981° + 1°34218 T’ + 0:00000775 T”? 
The alcohol thermometer, then, would stand at — 58-981° on its 
own scale when ‘I’ is null ; that is to say, when the mercurial ther- 
