NOTICE.

THIS VOLUME, while intended as a sequel to the Introduction to Arithmetic in CHAMBERS'S EDUCATIONAL COURSE, forms also an independent treatise, conducting the pupil from the first steps in the science of numbers to that stage where it becomes necessary to adopt the more general symbols of Algebra. Constructed with reference to the Introduction to Arithmetic on the one hand, and to the Elements of Algebra on the other, a uniformity of system has been observed, which will not only facilitate the progress of the student who follows a complete course, but impart to him a conception of the science more perfect and permanent than could otherwise be attained.

In the arrangement of the work, a more strictly sequential method has been adopted than is to be found in kindred treatises; and while most of the usual rules are retained, others have been introduced which bear more directly upon the business requirements of the present day. In the expression of the rules, simplicity and conciseness have been observed, allowing the pupil to be instructed in details by the methods of solution and explanations which follow, and which in each case should be thoroughly mastered before proceeding to the exercises, as the prime aim throughout has been to inculcate principles rather than empirical formulæ. In the exercises, everything like puzzle and paradox has been avoided, and such a gradation and variety given, as may

at once train the reasoning faculties of the learner, and accustom him to forms and subjects that are likely to present themselves in active life. Series of miscellaneous exercises have been inserted at certain stages; and where these can be readily solved, the pupil may safely proceed to the next stage; but where any difficulty is experienced, it may be inferred that some of the previous principles have been imperfectly understood, and therefore demand revision.

This volume, which forms the second of the Arithmetical and Commercial series of the Course, has been followed by a treatise on BOOK-KEEPING, and a volume of COMMERCIAL TABLES, containing such mercantile information as may render it an acceptable guide to the Warehouse and Counting-room.