If we denote the critical volume, pressure and temperature by Vk, **Pk** and Tk, then it may be shown, either by considering the characteristic equation as a perfect cube in v or by using the relations that dp/dv=o, d 2 p/dv 2 =o at the critical point, that Vk = 3b, **Pk**= a/27b2, T ic = 8a/27b.

From the relation between the critical constants **Pk** Vk/Tk = 37 R or T k /P k = 3 .

Whose coefficients are connected by a relation of the form pocr+plcr_1+...-i-**pkcr-k**= o, where po,pi, ï¿½ ..**pk** are independent of x and of r.

For if the liquid of density a rises to the height h and of density p to the height k, and po denotes the atmospheric pressure, the pressure in the liquid at the level of the surface of separation will be ah+Po and **pk** +po, and these being equal we have Uh = **pk**.

These equations can be made to represent the state of convective equilibrium of the atmosphere, depending on the gas-equation p = **pk** =RA (6) where 0 denotes the absolute temperature; and then d9 d p R dz - dz (p) n+ 1' so that the temperature-gradient deldz is constant, as in convective equilibrium in (I I).