Professor T. W Chaundy has published two papers on the above subject in Vols. 22 and 25 of the Proceedings of the London Mathematical Society. He discusses the condition necessary that a single infinitude of n-sided polygons may be inscribed in a circle S and circumscribed to another circle S′, basing his discussion on the theory of elliptic functions. A treatment of the topic, within the scope of elementary mathematics, is indicated in this note.