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).

= loge(P2891) =2.3 logio(p2/p1) (io) In the **convective** equilibrium of the atmosphere, the air is supposed to change in density and pressure without exchange of heat by conduction; and then PIN = (e/e0) n+1, d5 -(n-{--I) P -(n+I)R ' y - where is the ratio of the specific heat at constant pressure and constant volume.

In the more general case of the **convective** equilibrium of a spherical atmosphere surrounding the earth, of radius a, (1-1?-=(n+ I) Po --a 2 dr, (12) gravity varying inversely as the square of the distance r from the centre; so that, k = po/po, denoting the height of the homogeneous atmosphere at the surface, 0 is given by (n+I)k(I -9/6 0) =a(I -a/r), (13) or if c denotes the distance where 0=o, 0 _a (14) 0 r c -a' When the compressibility of water is taken into account in a deep ocean, an experimental law must be employed, such as p - po=k(P - Po), or P/po=I+(p-p0)/A, A=kpo, (15) so that A is the pressure due to a head k of the liquid at density under atmospheric pressure po; and it is the gauge pressure required on this law to double the density.

This is the law of **convective** equilibrium.

**Convective** equilibrium, which depends upon it, gives far too steep a temperature gradient, for it yields a temperature of 6000° only 200 m.