  Let $\mathcal{A}$ be a Weyl arrangement in an $\ell$-dimensional Euclidean
space. The freeness of restrictions of $\mathcal{A}$ was first settled by a
case-by-case method by Orlik and the second author (1993), and later by a
uniform argument by Douglass (1999). Prior to this, Orlik and Solomon (1983)
had completely determined the exponents of these arrangements by exhaustion. A
classical result due to Orlik, Solomon and the second author (1986), asserts
that the exponents of any $A_1$ restriction, i.e., the restriction of
$\mathcal{A}$ to a hyperplane, are given by $\{m_1,\ldots, m_{\ell-1}\}$, where
$\exp(\mathcal{A})=\{m_1,\ldots, m_{\ell}\}$ with $m_1 \le \cdots\le m_{\ell}$.
As a next step towards conceptual understanding of the restriction exponents we
will investigate the $A_1^2$ restrictions, i.e., the restrictions of
$\mathcal{A}$ to the subspaces of type $A_1^2$. In this paper, we give a
combinatorial description of the exponents and describe bases for the modules
of derivations of the $A_1^2$ restrictions in terms of the classical notion of
related roots by Kostant (1955).
