376 Researches respecting the Laws of the — [May, 
their precision may supply their want of extension. Besides, this 
will be a method of verifying our formulas, as we shall deduce them 
from values which philosophers may hereafter verity by direct expe- 
riments. 
I shall begin with alcohol. By comparing the weights of the 
same volume of liquid observed by Gilpin and Blagden for 30°, 35°, 
and 40° Fahrenheit, 1 have deduced by interpolation the weight of 
the same volume for 32° which corresponds with 0 of our thermo~ 
meter. Then comparing that result with the weights observed at 
50°, 70°, 95°, and 100° of Fahrenheit, [ deduced from them the 
volumes at these different temperatures, taking the volume at 32° 
for unity. Thus I obtained the following results :-— 
Dilatation from 
Degrees of the mercurial| Volume of alco- the heat of 
thermometer. hol observed. | freezing water. 
oy 
32° F or oO R 1:000000 0°000000 
BOW is alas! 8200 1:010003 0°010003 
AO laare se sis 16°89 1021750 0°021750 
95. 222.2. 28°00 1:037569 0°037569 
LOO) ecstetetcts 30°22 1°040525 0°040525 
To deduce from these results the total dilatation D from 0 to 
80° R., I shall employ the last two observations, and I shall regard 
them as values of 3, given. Then in the equation 
3} =KT4D SAT+BT? + CT341+KTt 
r 80 
every thing is known except D. We may, therefore, deduce it 
from that equation. In the first place, by calculating D, and KT 
we find 
T = 28:000; AT + BT? + CT? =22°753; K T = 0°00091952 
T — 32-999; AT + BT? + CT? =25'808; KT = 0:00099248 
Then from observations we have 
T=28'000} 2) =0°0373693 3) —KT =0°036449; ~ 
A ee 
TaKT =0°036416 
‘we 
T=82°222; 3,=0-040525; 2, —KT=0'039533; *——— =0°039494 
By substituting these values in the formula we obtain two equations : 
The first of these equations gives 
D = 0122649; 
- 
80 
The second gives 
D = 0122424 
