WHEN numbers are applied to things, the measure or value of which is expressed by different denominations, they lose their abstract character, and become subject to restrictions, imposed upon them by the denomination to which they are applied. Thus, when we say six cents, ten days, or three inches, we have not only the idea of number, but also the idea of a certain value or measure, which subjects the number in connection with it to certain limitations. And, when used in such connections, we call numbers denominate. Thus in 6 £. 4s. 7 d. the numbers 6, 4, and 7 are denominate numbers, so called, because they are applied to express each a particular denomination.

When now we have several numbers of different denominations, which we wish to add together, we call the process by which this is done Compound Addition; which we define by saying,

That it consists in adding together two or more numbers of different denominations to find the sum total.

RULE.

Write all the given numbers of the same denomination under each other; as dollars under dollars, cents under cents, &c. Then add together the numbers of the lowest denomination and divide the sum by the number which it takes of that denomination to make one of the denomination next above it, and set the remainder directly under the column that has been added. Carry the quotient to the column of the next denomination, and add as before, dividing by the number which it takes of this denomination to make one of the denomination next above it, setting down the remainder and carrying the quotient as before, and thus proceed till the column of the highest denomination is added, under which place its whole sum, and the numbers expressing the several denominations will be the sum total required.

NOTE. As half a mile is equal to 4 furlongs, we add them to the 1 furlong, which make 5 furlongs. And as half a foot is equal to 6 inches, we add them to the 7 inches, which make 13 inches; and these are equal to 1 foot 1 inch. By the same method, we obtain the result in the 14th and 17th questions.

NOTE.

We divide the sum of the signs, in these questions, by 12, and write down the remainder, because it is Circular Motion.