  In this simple paper, we exhibit a Schur partition giving rise to a
triangle-free linear colouring of $K_{1697}$ in 7 colours. Thus we show that
the Schur number $S(7) \ge 1696$ and the multicolour Ramsey number $R_{7}(3)
\ge 1698$.
  We also demonstrate a specific partition of the closed integer interval $[1,
376]$ which, through repeated use of a specific construction, allows us to
conclude that $S(k+5) \ge 376.S(k)+160$ for any positive integer $k$. The
existence of this partition, with its specific properties, implies that
$\lim_{\substack{r \rightarrow \infty}} R{_r}(3)^{1/r} > 3.273$.
