In ternary alloys based on the solution of a third metal in binary close-packed hexagonal 3/2 electron compounds ($\zeta$-phases) it is observed that the axial ratio of the structure is essentially constant at a constant value of the valency electron concentration. From determinations of the lattice spacings of solid solutions of manganese, iron and nickel in the gold-tin $\zeta$-phase, and of manganese in the silver-tin $\zeta$-phase, the effective contributions of electrons to the conduction band of the alloys by the transition metal have been deduced. The maximum effective contributions made by iron and nickel are respectively 1 and 0.8 electron per atom; in both cases the effective valency decreases both with increase in electron: atom ratio and with increase in transition metal content. The maximum effective contribution of manganese is two electrons per atom in gold-tin-manganese alloys, and approximately 1.8 in silver-tin-manganese alloys. Again the values decrease with increasing electron: atom ratio and increasing manganese content. The results are discussed in terms of the existence of virtual bound 3d states associated with the transition metal. Considered together with previous results obtained on solutions of transition metals in the copper-germanium $\zeta$-phase, they demonstrate the dependence of the effective valencies of transition metals in solid solution in noble metal alloys on the exact nature of the environment of the dissolved atoms.