406 Mr. J. J. Waterston on a Law of Liquid Expansion 
This value of A being derived from French measures, is to be 
applied to F to find us which thus comes out 1:4284. 
The following are MM. Dulong and Petit’s volumes of mer- 
cury computed with this index :— 
Temp. Inverse of volumes 
Cent. Volumes. raisedtothe power _ First Second 
Air. 1 1.4984. differences. _ differences. 
0 1:000000 —'1-000000 aie 
100 1:0180180 "974815 025213 ‘000028 
200 1:0368664 "94.9602 025236 "000023 
300 = 1:0566037 "924366 
The second differences indicate a slight convexity in the line 
upwards. This shows that : requires augmentation. The fol- 
lowing is the result of computing the same observations with 
t = 1-489 :— | 
' First diff. Second diff. 
CE MMEH LS 0 opie a 
100 973760 | 000001 
200 947521 aoeen 000005 
300 —--921287 
To find y, we have 1—0:947521 : 200°: : 1: 3811°05=y, 
8811:05—¢ 1 a, 1 fees in 
and | ae 3811-05 =A=-,or(3811 05 —#)v'4°9 = 3811-05. 
This expresses MM. Dulong and Petit’s observations with a 
difference at 100° amounting to +,4,5th of a degree, and at 300° 
the difference is =,th of a degree. 
$11. To bring the D of the vapour formula to the same 
standard as the A of the liquid formula, it is requisite to change 
the value of / in the one and & in the other, so that the weight 
in grains of a cubic inch of either may be indicated. | 
Let n='0216216 = weight in grains of a cubic inch of hy- 
drogen at the ‘temperature 0° C. and pressure 760 
millims. 
5= vapour-density of the body on the hydrogen scale. 
T= temperature (reckoned from the zero of gaseous ten- 
sion) at which the pressure of the saturated vapour 
is 760 millims. 
f= required factor 
TGA BBO i, 2 
ion hae 
