Many Multiplet

The velocity shift, v_j,of transition j due to a small relative variation in $\alpha$, $\nabla \alpha/\alpha \ll 1$, is determined by the q-coefficient for that transition,

(1)

\begin{align} \omega_{z,j} = \omega_{0,j}+q_j \left [ (\alpha_z/\alpha_0)^2 -1 \right ] \end{align}