414 Mr. J.J. Waterston on a Law of Liquid Expansion. 
The following is an extract from note-book of the experiments :— 
“The observations on pure distilled water could only be made up 
to 305° F., in consequence of the glass being corroded and becoming 
opake above that temperature. At the higher temperatures, five 
tubes were employed with water having 3, of carbonate of soda in 
solution. ‘Two only of these five were sufficiently transparent up 
to 413°. But on examining them next day, ;1,th of the volume of 
liquid was absorbed. This allowed for. 
«« The expansion of the solution rather less than pure water. The 
corrosion of the glass began immediately above the surface of the 
liquid. ‘The vapour was computed from formula, assuming the law 
of vapour-density maintained.” 
Note F. § 6.—M. Muncke and M. Pierre have employed the general 
formula 1+ A,=1-+ax+ba’?+ ca’, &c. to represent their observa- 
tions, and have computed the constants for eachseries. They have 
also sought, by means of the roots of this equation, to find points of 
maximum density of each liquid beyond the range of their observa- 
tions. Thus M. Pierre, at p. 358, vol. xv. Ann. de Chim., expresses 
himself as follows :— ‘‘ ... . puisque l’équation ee. =0, dont 
2 
les racines doivent donner la température de ce maximum, a ses deux 
racines imaginaires.” 
I have traced graphically the curve of the equation and of the ob- 
servations, and find that its course through them is similar to fig. 8, 
interlacing at the fixed points, and departing altogether from the line 
of observation beyond the extreme points to which it is bound down. 
The positive and negative differences at the loops sometimes amount 
to 4 degree. A conic section may be drawn to represent almost per- 
fectly a series of observations if the range is not great. The hyperbola 
answers well, and can be simply applied as the increasing rate of ex- 
pansion adapts itself to the curve, referred to an asymptote parallel 
to the axis of temperature. 
Note G. § 15.—The value } 3-98 is taken from Regnault’s ob- 
Pp 
servations on the tension of its vapour at 0° and 20°C. The obser- 
vations at 0° and 30° represent =3°25. Dalton’s observation on 
Pp 
the vapour give it equal to 3:2108, which is probably the most cor- 
rect, as / is thus represented to be the same for sulphuric ether and 
water, their lines of vapour-density being parallel. 
Note H. § 16.—Ina paper on Capillarity in the Philosophical Ma- 
gazine for January 1858, the proofs are given in detail of a law that 
connects molecular volume with capillarity and latent heat. It is ex- 
pressed by the equation mF, in which m is the cube root of the mo- 
lecular volume of aliquid, p the height of the same in a capillary tube 
of constant bore, and L the latent heat of the vapour of the same, all 
