or, neglecting second-order terms
where ( ) is the speed of sound.
Also note that the static stability satisfies the following relation:
Eqs.(8) and (9) may now be used to write eq.(6) as:
where ( = ) is the buoyancy force and the full momentum equation becomes:
The conservation of dry entropy may be written as:
or
where is the Brunt-Väisälä frequency.