RITHMS.) Elementary Series.—Amongstthose inheritances from me diaeval arithmetic which found their way into the early textbooks in algebra, was the topic of progressions. This term usually cov ered the rules for the summation of simple types of arithmetical and geometric series, and sometimes a brief discussion of harmonic series. With the improved symbolism came the formulae relating to these sequences, and in recent years the special name pro gression has tended to give place to series. The subject, together with the related Binomial Theorem, is sufficiently treated in cur rent textbooks. (See SERIES; NUMBER SEQUENCES; LIMIT; BI NOMIAL FORMULA.) Elementary algebra contains many practical applications of equations, and modern textbooks are using these to supplement or replace the less valuable inheritances. It would be unfortunate if any attempt should be made to abolish all of this traditional material; it could never have held its place through the centuries if it had not possessed such an interest for young people as to insure the degree of permanence which we see. It has often been from the study of the interesting but impractical that the most practical mathematicians as well as the leaders in pure mathe matics have been made. The most important application of ele mentary algebra is found in the formula. This is the part of alge bra which the pupil will use most frequently in science, in mensura tion, in technical work of all kinds, and in such parts of more ad vanced mathematics as series, determinants, trigonometry, analytic geometry, and the calculus. To the formula, therefore, it is de sirable that increased attention should be given.