In an article on models of functions in the October (1908) number of the Gazette it was suggested that some knowledge of one-to-one correspondence of operands ought to be acquired by means of models before going on to the correspondence of operands to functions, and of functions to functions. In particular, it is easy and of importance to make models of some of the roots of one. It is needless to say that the order of subjects actually adopted in schools is widely different from that here suggested. It is usual to begin with the addition and multiplication of numbers, that is, with a particular kind of correspondence not of operands but of functions. Even the words function and correspondence are not met with until a comparatively late stage, and the fact is ignored that the numbers 2, 3, 4, etc., are functions, though not one-to-one functions.

Describe a circle ABC (Figs. 1 and 2). Draw two chords AB, BC intersecting within it. Describe eight circles (a, a′ b, b′, etc.), each of which touches ABC and the chords AD, BC; construct a triangle by joining any three of the points of intersections of ABC and the two chords; then the chords of contact and the line of centres of two circles taken in suitable pairs out of the eight circles are concurrent, the point of concurrence being equidistant from the three sides of the triangle.