If it be required to have the answer in a particular kind of money, weight, measure, &c., such as £ s. d., cwt., gallon, pint, &c., introduce (without varying the original mode of stating), successively, as many of the intermedate steps of such sorts, as you are acquainted with; viz.: £ = 20; 1s. = 12d., or 12d. = 1s.; 20s. 1£.

17. If the duty on 1 lb. of feathers is 3d. what is the duty on 472 lbs.?

In the present example, it is supposed, that for 472 lbs. the answer will be in £ instead of pence; the question is therefore expressed in higher amount; and such gradations of coin have been progressively introduced, so as to leave the link between the two lengthened columns perfect, finishing with the same as x,

C

or £, the kind wanted. The reading is simple: How many £ for 472 lbs., if 1 lb. = 3d., 12d. 1 shilling, and 20 shillings = £1. The rest as usual.

The same example may also, with a little practice, be stated without having recourse to intermediate steps, thus:

18. If 3 lbs. of tea cost 14s. and 4d. what

This example is the reverse of the former; as 2 oz. will not amount to shillings, the question has been stated in pence, and the intermediate sorts have been linked together in the columns.

In the stating, the 14s. and 4d. have been changed into 143s. After having multiplied the (integer) 14, by the denominator, and added the (numerator) 1, making 43; it has been transposed, the numbers cancelled, &c.

The same as before, with the additional arranging of the fractional number 7 at the left, and the transposition of the (denominator) 6, to the right.

19. If 27 pieces of timber cost £14 17s. what

17 shillings are of a £. The integer 14 having been multiplied by the denominator 20, and 17 added, amounting to 297; the whole has been crossed, and the 20 transposed. The rest as usual.

D.

CANCELLING OR SHORTENING OF NUMBERS.

THE mode of cancelling or shortening opposite numbers, requires no farther illustration than what has been already given. There is no absolute rule as to how often, and in what order,

a number is to be shortened, and by what divisor. The following points, however, inust be attended to:

1. No number is to be cancelled in one column without cancelling or reducing a number in the opposite one, and by the same divisor; the numbers to be cancelled may be taken from any part of the column. It is understood that the whole quantity, and not part of the number, can be cancelled or reduced; thus, in 25 and 27, the 2 of 25 and the 2 of 27, are not to be cancelled, though these figures be alike; cyphers can be cancelled.

2. The divisor must be a perfect divisor and leave no remainder; thus, 3 dividing 5 would leave 2; nor could 3 divide 10, 11, 14, &c.; but 3 would divide 6, 15, &c. So would 8 divide 16 and 144.

3. When numbers are to be transposed, such as a denominator 6, to the left, and a similar denominator from the left to the right, they are cancelled at once.