402 Mr. J.J. Waterston on a Law of Liquid Expansion 
§ 2. The curves of expansion, drawn to a large and distinct 
scale, were examined by the following graphical process :—At 
four or five points nearly equidistant, tangents were drawn 
(carefully judging of the direction to be given to the straight 
edge by the sweep of the curve to the right and left of the point 
of contact). Thus were obtained several values of the quotient 
of the differential of volume by the volume or proportionate dif- 
d 
ferentials for constant element of temperature EA . These 
were set off as ordinates to the temperatures, and the curve 
drawn through the points appeared to be the common equilateral 
hyperbola, havin g one asymptote coinciding with the axis of tem- 
perature and the other perpendicular to it, and intersecting it at 
a temperature [y] that evidently was above the transition- -point. 
If this were the case, the product of the coordinates to each point 
of the curve, reckoning from the point y as origin, ought to be 
constant [=p]; and accordingly it was found that when the 
inverse of the quotients were projected as ordinates to the tem- 
peratures, the points ranged in a straight line, which being pro- 
duced, cut the axis in the pomt y. The differential equation is 
thus 
dv y—t 
He Uo ag 
the integration of which is 
+ k 
v=4 —— 
y— 
in which k=(y—z) when v=1. (See Note B.) 
§ 3. There is a relation between this expression and that for 
saturated vapour-density which ‘seems to prove that it is not em- 
pirical, but the true exponent of the physical condition of the 
molecules of a body in the liquid state. The following is a state- 
ment of it. 
In the papers above referred to, there will be found an account — 
of the law of saturated vapour-density, and the proofs on which 
it rests. It is expressed by the equation 
so soma 
If we put A= 2 the law of liquid density is 
Bata" L 
(ayaa 
On comparing the constants for different liquids, I find as a 
general rule that the quotient is a constant quantity [KE]. 
