= Haline contraction coefficient
The <haline contraction coefficient> measures the fractional increase of <mass density> with <salinity> at fixed <temperature> and <pressure>:
$$
\beta=\frac1\rho\left(\frac{\partial\rho}{\partial S}\right)_{T,p}.
$$
Its units depend on the salinity variable $S$: a dimensionless mass fraction and a value in grams per kilogram require different numerical coefficients.
For small changes, $\delta\rho/\rho\simeq-\alpha\,\delta T+\beta\,\delta S$, with thermal expansion coefficient $\alpha$. This formula separates two competing buoyancy contributions. In <thermosolutal convection>, their combination determines the static density gradient, while unequal diffusion rates determine whether that apparently stable gradient can nevertheless become unstable.
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