| p = μ | zn+1 | = | ρz | = | ρ | ( | ρ | ) | 1/n | , |
| n + 1 | n + 1 | n + 1 | μ |
(5)
supposing p and ρ to vanish together.
These equations can be made to represent the state of convective equilibrium of the atmosphere, depending on the gas-equation
p = ρk = R ρθ,
(6)
where θ denotes the absolute temperature; and then
| R | dθ | = | d | ( | p | ) = | 1 | , |
| dz | dz | ρ | n + 1 |
(7)
so that the temperature-gradient dθ/dz is constant, as in convective equilibrium in (11).