  We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$)
for the spontaneous magnetisation, susceptibility and specific heat of the
spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and
3. We determine the location of the physical critical point and non-physical
singularities. The number of non-physical singularities closer to the origin
than the physical critical point grows quite rapidly with $S$. The critical
exponents at the singularities which are closest to the origin and for which we
have reasonably accurate estimates are independent of $S$. Due to the many
non-physical singularities, the estimates for the physical critical point and
exponents are poor for higher values of $S$, though consistent with
universality.
