172 Hassier’s Experiments on the Expansion of Water. 
room set apart for the purpose, instead of ‘being forced, unstable 
and therefore doubtful, as in all cases of production of artifici 
transient temperatures, is such as to afford a more than usual 
check upon the aceuracy of any part of it, and a more than usual 
confidence in the equilibrium of the temperatures averre 
In this method of observation, it follows that the actual tem- 
peratures and the corresponding weights succeed one another ir- 
regularly. The first thing to be done, then, was to group the 
resulting weights, degree “by degree, and thus repare them for 
their arithmetical means. ‘Their preparation resulted in a synop- 
tical table, in which the average weights corresponding to frac- 
tions of almost every degree of Fahrenheit between 35° and 86° 
found a place. This synopsis was then converted into another, 
where the temperature was given in whole degrees, and the 
weights corresponding found by taking proportional parts of the 
actual weights observed for the said fractions. Then, in order to 
cover the irregularities of result existing as between degree and 
degree, and to ensure a sufficient generalization, these last ascel~ 
tained weights were tabulated from five to five degrees, com- 
mencing with 40° , which is so near the density of maximum 
density as to allow of being assumed for it. In fact, the actual 
difference of weight observed between 39°:4 and 40°-4 is only 
2-4 grains on a weight of nearly 228000 grains, or somewhat 
more than the ;55.555 par 
The differences of the weights in this last tabulation, divided 
by 5, and thus reduced to a rate per degree for every five degrees, 
presented a quite harmonious diverging series; the second differ- 
ences were nearly constant, and the plus and pene third differ- 
s 
77) 
Qu 
=4 
wa 
i) 
a4 
= 
o 
Qu 
is) 
or 
ta) 
<4 
OT 
= 
bee 
mh 
= 
a 
jor 
ie*) 
GQ 
g 
n 
~- 
° 
oF 
= 
oO 
~» 
an] 
oO 
4 
a 
9°) 
oo 
° 
<< 
ror) 
st 
’ 
ing table 
oe Weights calculated. | Weights observed. Proportional Ditferences._| 
40° 3:3 27843°3 Ge = 
45° 837°3 Oo - 
50° 8113 815-4 — 0000014 
55° 765-3 766— — 0000003 
60° 699°8 695°3 000018 
65° 6133 6043 0000040 
70° 5073 5018 +0-000024 
75° 3813 871-5 +0:000043 
80° 235°3 230°5 0000021 
85° 227069-3 2210765 0000032 
What remained, then, was to convert the said calculated we 
th 
into decimal parts of unity taken as the maximum density 
* 
