Corollary

Let S be an $\alpha$-chain of roots, and $\gamma$ the origin of S. The length of S is $-n(\gamma, \alpha)$; it is equal to 0, 1, 2 or 3.

The first assertion follows from Prop. 9, (iii), applied to $\beta = \gamma$, and using the fact that $q = 0$.

On the other hand, since $\gamma$ is not proportional to $\alpha$, the list given at the beginning of this no. shows that $|n(\gamma, \alpha)| \leq 3$, hence the corollary.