482 Researches respecting the Laws of the (Jone, 
different law when it contains a great proportion of water. By 
means of these formulas we may employ indifferently either mer- 
curial or alcohol thermometers. We may likewise employ them to 
reduce to the same temperature weights taken in alcohol. 
I shall now make the same calculations for water. By comparing 
the weights of the same volume of water observed by Gilpin and 
Blagden at 35°, 40°, and 45° of Fahrenheit, I deduce by interpo- 
lation the weight of the same volume at 32° Fahrenheit which cor- 
responds with O of our scale. Then comparing this result with the 
weights observed by the same philosophers at 40°, 50°, 70°, 95°, 
and 100°, I deduced the relation of the volumes at these tempera- 
tures, considering the primitive volume at 32° as unity. Thus I 
obtained the following results :— 
True dilatation of 
Degrees of the mercurial] True yolume of | ditto from the 
thermometer, water observed.| freezing point 
(ig 
32 F or O R} 1:00000 000000 
AO ...... 3°56 | 0:99988 — 000012 
BO. Sees SOO | FO00Ts +0°00014 
JO .sse0- 16°39} 1:00188 +0°00188 
95 ..0e0e- 28°00 | 1°00583 +0:00583 
100 ....... 32°22 | 1°00684 +0:00684 
To deduce from these results the dilatation D from 0 to 80 
Reaumur, I shall employ the last two observations as I did for aleo- 
hol. Ishall consider them as given values of 2,3 and since we can 
calculate D, for the same temperatures from the water thermometer, 
we shall deduce D from the formula 
_k D {1+ KT} 
oy _ Kk TF + ols IWiSOl dee o, 
We find in the first place 
T = 28:000; D, = 8°9264; K T = 0°000919 
T = 32°222; D, = 10°6818; K T = 0:000902 
From observation we have i 
T=28-000; 2, = 0-005829; 3, KT =0-001910; “*—*~ =0-004050 
T = 32-992; 3, = 0:0068409 ; 3, — KT = 0:0058485 ; EE 
= 0:0058427 
By substituting these values in the formula we obtain the two fol- 
lowing equations :— 
0004905 = =" p; o-005s127 = “= D 
We see here that the smallness of D, renders the determination 
