20. The line of defence in a certain polygon being 236 yards, and that part of it which is terminated by the curtain and shoulder being 146 yards 1 foot 4 inches; what then was the length of the face of the bastion? Ans. 89 yds 1 ft 8 in.

COMPOUND MULTIPLICATION.

COMPOUND MULTIPLICATION shows how to find the amount of any given number of different denominations repeated a certain proposed number of times; which is performed by the following rule.

SET the multiplier under the lowest number of the multiplicand, and draw a line below it.-Multiply the number in the lowest denomination by the multiplier, and find how many units of the next higher denomination are contained in the product, setting down what remains. In like manner, multiply the number in the next denomination, and to the product carry or add the units, before found, and find how many units of the next higher denomination are in this amount,

amount, which carry in like manner to the next product, setting down the overplus.-Proceed thus to the highest denomination proposed: so shall the last product, with the several remainders, taken as one compound number, be the whole amount required.-The method of Proof, and the reason of the Rule, are the same as in Simple Multiplication.

EXAMPLES OF MONEY.

1. To find the amount of 8lb of Tea, at 5s 84d per lb.

I. If the multiplier exceed 12, multiply successively by its component parts, instead of the whole number at once.

Ex. 5. 63 gallons of Oil, at 2s 3d per gall.

Ans. 7 1

6. 70 barrels of Ale, at 17 43 per barrel Ans. 84 0 7. 84 quarters of Oats, at 1/ 12s 8d per qr.Ans. 137 4 8. 96 quarters of Barley,at 11 38 4d per qr.Ans. 112 0 9. 120 days' Wages, at 5s 9d per day. Ans. 34 10

10. 144 reams of Paper, at 138 4d per ream. Ans. 96 0

S d

II. If the multiplier cannot be exactly produced by the multiplication of simple numbers. take the nearest number to it, either greater or less. which can be so produced, and multiply by its parts, as before. Then multiply the given multiplicand by the difference between this assumed number and the multiplier, and add the product to that before found, when the assumed number is less than the multiplier, but subtract the same when it is greater.

2. 29 quarters of Corn, at 21 5s 31d per qr.Ans.
3. 53 loads of Hay at 3/15s 2d per load. Ans. 199
4. 79 bushels of Wheat,at 11s 53d per bus. Ans.
5. 97 casks of Beer, at 12s 2d per cask. Ans.
6. 114 stone of Meat, at 15s 3d per stone. Ans.

65

s d 12 101

3 10

45

59

6 101 0 2

87

571

COMPOUND DIVISION teaches how to divide a number of several denominations by any given number, or into any number of equal parts; as follows:

PLACE the divisor on the left of the dividend, as in Simple Division.-Begin at the left-hand, and divide the number of the highest denomination by the divisor, setting down the quotient in its proper place. If there be any remainder after this division, reduce it to the next lower denomination, which add to the number, if any, belonging to that denomination, and divide the sum by the divisor.-Set down again this quotient, reduce its remainder to the next lower denomination again, and so on through all the denominations to the last.

1. If the divisor exceed 12, find what simple numbers, multiplied together, will produce it, and divide by them separately, as in Simple Division, as below.

EXAMPLES.

1. What is Cheese per cwt, if 16 cwt cost 25l 14s 8d?

1 S d

4) 25 14 8

II. If the divisor cannot be produced by the multiplication of small numbers, divide by the whole divisor at once, after the manner of Long Division, as follows.