Exercise 5, § 1

Let R be an irreducible root system. For any $\beta \in R$, 16\gamma(R) = (\sum_{\alpha \in R} n(\alpha, \beta)^2)(\sum_{\alpha \in R} n(\beta, \alpha)^2)

and consequently $\gamma(R) = \gamma(\lambda R)$ for any non-zero scalar $\lambda$. (Use formulas (17) and (19) of no. 12.)