“The Kiss Precise”

IN NATTJBE of June 20 last, we published some verses by Prof. F. Soddy under this title. Shortly afterwards, Mr. E. B. Wedmore sent two verses generalizing Prof. Soddy's equations for the circle and the sphere to space of n-dimensions, and more recently Mr. C. C. Mason has submitted a verse on similar lines. Prof. Soddy informs us that he received a verse (dated July 17, 1936) from Mr. Thorold Gosset, of 136 Chesterton Road, Cambridge, generalizing his equations, and, in response to his request, Mr. Gosset furnished a formal proof of the proposition later in the same month. Mr. Gosset seems to have extended the geometry of all the semi-regular figures to n-dimensions in a lengthy paper some forty years ago, but it remained unpublished, except for a few results which appeared without proofs in the Messenger of Mathematics. The existence of these figures has recently been rediscovered, some in Holland, some in England, and a paper by Dr. Coxeter on the subject has been published by the Royal Society, so that all are now known. Prof. Soddy's development of “The Kiss Precise” and “The Hexlet” appears elsewhere in this issue (p. 77). Dr. F. Morley has also recently furnished a formal proof of the hexlet, which is printed on p. 72. Mr. Gosset's fourth verse to the “Kiss Precise” is appended: