It is shown that for S-S atomic transitions the Schwinger variational principle with sufficiently flexible one-state functions does not take account of long-range polarization effects, even though the Schwinger formalism explicitly contains long-range terms. The plane-wave (1,1) Pade approximant to an S to S transition in general exhibits long-range behaviour. However since this approximant is obtained by applying the Schwinger principle to rather restricted one-state trial functions its accuracy must be called into question.