  The finite-lattice method of series expansions has been combined with a new
extrapolation procedure to extend the low-temperature series for the specific
heat, spontaneous magnetisation and susceptibility of the spin-1 Ising model on
the square lattice. The extended series were derived by directly calculating
the series to order 99 (in the variable $u=\exp[-J/k_B T])$ and using the new
extrapolation procedure to calculate an additional 13--14 terms.
