THESE books are too well known to mathematical teachers to need detailed notice from us. Both are very good, and stand in the first rank among the scores of arithmetics published in England. The explanations, arrangement and examples, especially in the former book, are generally very good. We will venture, however, to suggest two or three changes to the authors, which we think would render the book better still, and which our experience would make us wish to see universally adopted. The rule for multiplication of decimals given in these books is the old one of counting the decimal places. We think this becomes a rule of thumb. The method ought to be the same as that in multiplication of integers; and it is at once seen by the pupil that as in multiplying by tens and hundreds, the figures are shifted to the left; so in multiplying by tenths and hundredths, they are shifted to the right. The decimal point is brought down straight, and each line in the working has its meaning; as in the example, multiply 712.35 by 15.807:— The Science of Arithmetic. By James Cornwell, and Joshua G. Fitch, M.A. Thirteenth Edition. (Simpkin, Marshall, and Co., 1870.) The School Arithmetic. By the same authors. Eleventh Edition. (Simpkin, Marshall, and Co., 1871.)