14 FEBRUARY 1903, Page 25

Short. Cuts and By - Ways in Arithmetic. By Cecil Burch. (Blackie

and Son. 2s.)—Some of the processes here described are familiar to most educated people. Such is the "casting out of the nines," often used as a test of the correctness of long arithmetical operations. Others are less known. Indeed, it would be safe to say that much of Mr. Burch's book will be new to all but arithmetieal experts. He gives an interesting illustra- tion of the usefulness of one of the processes,—viz., that when he was working in the Egyptian Treasury he saved much time and labour by using a short process of dividing by thirty-nine. The LE is one-thirty-ninth part greater than X, and therefore the amount of LE had to be increased by this fraction to represent it in English currency.