In the absence of the viscous, diffusive and conductive processes (and radiation) the basic equations (1.1) to (1.4) become
and if we also neglect the net forcing by tide generating forces
Eqs. (4.2) and (4.3) imply that S and 
(and hence 
)
are conserved following a fluid parcel (as in the analysis of
Sec. 2.3).
This immediately implies that
and (4.1) can be expressed as
