PRE FACE. The design of the following work is to afford to Teachers a book for the use of the upper classes in Elementary Schools, by means of which they can supply a sufficient number of suitable examples for practice in any rule, after having explained and illustrated its principles on the black board. The book is, therefore, chiefly intended for the individual and independent working of the scholars of a class, and for Home Lessons. As it is intended for Elementary Schools, those rules which are of most use in the common business of life are principally attended to; and in place of exercises which, though important to a few, are of very little practical advantage to the many, the most useful problems of Mensuration are substituted. A knowledge of this subject is, in general, much valued by the working classes. Much attention has been given to the method of working problems by decimals, which would prove the best preparation to calculations on the Decimal Coinage, should such be introduced. As improvements on ordinary processes, the attention of Teachers is invited to the method of working questions in Compound Interest, and of extracting the Cube Root. As a thorough comprehension of Vulgar Fractions is highly expedient, easy preparatory questions are prefixed to each of the rules to be solved mentally, or with little aid from the slate. Teachers will find great advantage in accustoming their pupils to work all problems by first principles, as it is termed, and thus will lay a much firmer foundation for solid knowledge in Arithmetic than by merely teaching dogmatic rules. Rules, however, are not to be despised when the principles upon which they are founded are perfectly understood. The Miscellaneous Examples are chiefly selected from the Examination Papers published in the Minutes. 8 times 9 times 10 times 11 times 8 9 I are 10 1 are 11 2 16 2 18 2 26 2 22 3 24 3 27 3 30 3 33 4 32 4 36 4 40 4 44 5 40 5 45 5 50 5 55 6 48 54 66 7 7 63 7 70 7 77 8 6+ 8 72 8 80 8 88 9 72 9 81 9 9 99 10 80 10 90 / 10 100 10 110 11 88 11 99 11 110 11 121 12 96 12 108 | 12 120 | 12 132 12 times 1 are 12 2 24 3 36 4 48 5 60 6 72 7 84 8 96 9 108 10 120 11 132 12 144 56 90 B |