Fourth-order charge renormalization in spin-zero electrodynamics

The discrepancy between two recent calculations of the divergent part of ${Z}_{3}$ in scalar electrodynamics is resolved. It is shown that in both approaches certain improper operations have been performed on linearly divergent diagrams. The terms which are necessary to correct each of these two calculations are determined and the results thereby brought into agreement. It is found that while the corrections happen to cancel in Sinclair's approach, there is a nonvanishing contribution to the earlier result of the present authors.