PREFACE. THE present reissue, revised and considerably enlarged, of the "First Book of Arithmetic" of the Irish National Series, has been prepared to meet a generally expressed wish for an edition of this popular text-book suited to middle-class schools, and brought up to the standard or the present advanced system of instruction in arithmetic required for the various public and competitive examinations which are now becoming so general. Part I. is a republication of the original work of the Commissioners, which the Editor has not felt himself at liberty to alter; but he has introduced, as far as the restrictions of a stereotyped work would permit, examples, under the several rules, of new methods and illustrative processes wherever the old ones appeared to be antiquated or defective. Among them may be mentioned some simple and easy forms of proof of the operations in the four elementary rules, several fully worked out models in Compound Multiplication and Practice, and a new method of teaching Long Division, by which this rule, so difficult to beginners, will, it is believed, be found to be much simplified. The new matter, which commences with Part II., comprises a complete course of Vulgar and Decimal Fractions for advanced pupils, and a short, but it is hoped sufficiently full explanation of the "Unitary System," or method of working arithmetic without rules, which is now very generally superseding, in our best schools, the cumbrous and logical methods of our ordinary text-books. At the end will be found several examples of Examination Papers in Arithmetic, set during the last few years by the principal Examining Bodies in this country, including the College of Preceptors, the London University, the Civil Service Commissioners, and the Examiners for the Oxford and Cambridge Local Examinations. It is believed that none of them will be found beyond the capacity of any one who has gone fairly through the previous portion of the work. NOTE TO NEW EDITION. THE Cumbrous process of reducing Fractions to a Common Denominator, by cross-multiplication, given in the original work of the Irish Board (pp. 69 et seq.), is now seldom used: although it is still adhered to by some Teachers, owing to its dispensing with the preliminary operation of finding the L. C. M. In the Second Course of Fractions added by the Editor, new and better methods have been introduced; and he recommends Teachers to pass at once to this course, when the Pupil has reached the stage of Fractions, going back to the earlier course for additional examples for practice, if necessary. Teachers differ, and will always differ, as to the stage when Fractions should be taken up. Some begin it after Practice, others before it; but there is nothing in the order of the Rules (which are independent of each other) to prevent it from being taken up at any stage. The Unitary System" dispenses with all rules after Fractions (excepting such outlying subjects as Involution, Evolution, &c.); and although the Editor is not insensible to the advantage of a mastery of several methods for attaining the same result, he believes that no system can compare with the Unitary Method as an intellectual discipline for training the Pupil to the habit of attacking arithmetical problems of every class with intelligence and confidence. 66 |