408 Mr.J. J. Waterston on a Law of Liquid Expansion 
Computed 
temp. minus 
(=) 35392 observed 
V temp. 
(1) 33-46 + 0:47 = 33-93 108714 87890 = +0°21° 
(2) 47:524+0°51=48-:03  1:05356 —-83140 0 
(3) 50°33+0°5]=50°84 1:05676 82248 —0:19 
(4) 56:26+0:50=56:76 1064.16 980245 —O0°25 
(5) 60:41 +0°48=60°89 1:06989 "78736 +0°03 
(6) 73°70+0°38=74:'08 1:08780 74238 0 
(7) 76°73+0°35=77:08 1:09168 ‘73310 = —0°27 
The computed densities (87890, &c.) set off as ordinates to 
the temperatures, show atrend without any appearance of curva- 
ture. The straight line seems to pass exactly through the points 
of the second and fifth and sixth. Assuming it to pass through 
the second and sixth, we have 
83140 —°74238 = -08902 : 74°08 — 48°'03 = 26°05 : : *74238 : 217°24, 
and 74°08 + 217:24=291°32=y. This line gives unity volume 
at —1°-30, hence k=292°62=y—t when volume equal unity, 
and the equation is (291°°32 — t)v99 = 29262. The differences 
between the observed temperatures and those computed from the 
observed volumes by this equation are given in the last column. 
§ 14, This equation answers well to the observations of M. 
Pierre above 10°; also to those of M. Muncke (St. Peters- 
burgh Memoirs) above the same temperature; but in both the 
trend of the points below this lies in a line inclined to that of 
the equation. The divergence is the greatest in M. Pierre’s. In 
neither is it a general convexity, but distinctly the contour shows 
two lines diverging from about 15° to 20° C. This is most 
distinct in M. Muncke’s observations. I have computed them 
by the above equation, and tabulated the differences between the 
observed and computed temperatures, which are set off in Pl. VI. 
fig.3asordinatesto the temperatures on ten times the natural scale. 
Above these, in fig. 2, M. Pierre’s differences are set off to the 
same scale, and in fig. 4 the differences in my series of observa- 
tions on alcohol, described in the paper above referred to as being 
in the archives of the Royal Society. This alcohol was not 
absolute ; it had 19 per cent. water, and the index of its power 
derived from its line of vapour-density was 3°60; also y=290°89, 
k=209°81, and its equation (the volume being reckoned as unity 
at the boiling point) } 
(2909-89 —#) v3=209°81 C. A. G. 
§ 15. The deflection in M. Pierre and M. Muncke’s observa- 
. sions, it will be remarked, occurs in those below atmospheric tem- 
C. C. A. Ne 
