A fluid stably stratified by a salinity gradient and enclosed between two vertical
boundaries can become unstable when it is subjected to a temperature difference
between the walls. The linear stability of such a fluid in a vertical slot is investigated.
Errors in earlier results are found, confirming recent results of Young & Rosner
(1998). Four different asymptotic regimes on the stability boundary are identified.
One of these, the limit of a strong salinity gradient, has previously been analysed. The
analyses of the separate asymptotic limits of weak salinity gradient, large temperature
difference and small wavenumber are also given. These four cases make up much of
the total boundary between stability and instability for double-diffusive instabilities in
a vertical slot, and so most of this boundary can be mapped out for general Prandtl
numbers and salt/heat diffusivity ratios using these results.