In deciding what subjects to include the authors have been guided throughout by the desire to make the book directly useful in business offices, particularly to persons working in accounting and in the various lines of finance. There are many school texts on commercial arithmetic, but they are necessarily too rudi mentary to be of much aid to readers of mature experience. N 0 space has been given here to a consideration of the elementary and fundamental processes of mathematics. The effort has been, instead, to present material of more advanced nature which has not been generally available. This material falls into three general classes. The earlier chapters explain in considerable detail a number of short processes and practical suggestions that may be applied in routine computations of any sort. Particular attention has been given to the matter of adequate checks upon calculations.