So-called “standard form.”

Method I have used with success as regards clearness and accuracy. (I believe this is Mr. Pendlebury’s arrangement.)

Ride. Put singles (or units) figure of multiplier under the last figure of multiplicand.

Arguments in favour of this second plan :

Instead of such a mechanical rule as Mr. Borchardt’s (p. 69, Borchardt’s ,Arithmetical Types and Examples), we get the continued use of the sound and fundamental rule of “putting each first figure of a partial product underneath the figure to which that partial product is due.” And this also corresponds to the method of algebraic multiplication.

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.

Writers on mensuration do not seem to call attention to the convenience of quadrature-formulae for determining positions of centres of gravity, magnitudes of moments of inertia, etc.