In a letter having the title “Classification and Mathematics,” which appeared in Nature of May 28th, it was suggested that models of spaces and correspondences might usefully be employed in elementary mathematics. The present paper is restricted to the consideration of some simple one-toone correspondences.

It will be taken tor granted that, in order to arrive at any functional dependence or one-to-one correspondence of things, a classification and crossclassification is necessary. For example, the correspondence of English and French words tabulated in an English-French dictionary might be given as an illustration of a function (cf. Oliver Lodge, Easy Mathematics, 1905, p. 164). Here the words are divided into two classes, English and French, and are crossclassified by meaning.