The differential cross section for the elastic magnetic scattering by an ion with both spin and orbital angular momentum is expressed in the same form as for the `spin-only' case, the spin operator being effectively replaced in the general case by an operator Q. Following Johnston an expression for the matrix elements of Q is given in terms of one set of radial integrals instead of the two sets introduced by Trammell. An explicit proof is given of the equivalence of the calculations of the cross section by Johnston and by Trammell.