(6) By God's blessing upon a merchant's industry, in ten years' time he found himself possessed of 13,000l. It appeared from his books, that the last three years he had cleared 8731. a-year: the three preceding but 586l. ayear, and before that but 3641. a-year. What was the state of his fortune at every year's end that he continued in trade, and what had he to begin with?

(7) A robbery being committed on the highway, there was assessed on a certain hundred, in the county of S., the sum of 3731. 14s. 8d. The four parishes paid 371. 16s. 4d. each, the four hamlets 281. 3s. 10d. each, the four townships 19 guineas each. What was the deficiency?

(8) At Leicester and several other places they weigh their coals by a machine, in the nature of a steel-yard, waggon and all; three of these draughts together amount to 137 cwt. 2 qrs. 10 lb. and the tare or weight of the waggon was 13 cwt. I qr. How many coals had the customer to pay for?

(9) A person dying left his widow 1780l. and 1250l. to each of his four children, 30 guineas a piece to 15 of his poor relations, and 150l. to charities; he had been 25 years in trade, and at an average had cleared 126l. a-year. What had he to begin with?

(10) Suppose a gentleman's income is 500l. per annum, and he expends daily 19s. 11d. What does he lay up at the year's end?

(11) If a gentleman expend daily 11. 12s. 6d. and at the year's end lay up 2941. 12s. 6d. I demand his yearly

income.

(12) The remainder of a division sum is 20, the quotient 423; the divisor is the sum of both, and 19 more. What was the number to be divided ?

(13) Suppose that for a quarter's rent I paid in money seven guineas and sixpence, and was allowed for small repairs 18s. 6d. and for the king's tax 8s. 9d. What did my tenement go at a-year?

(14) A person dying left his widow the use of 5000l. To a charity he bequeathed 8467. 10s. To each of his three nephews 1230l. To each of his four nieces 10501. To 20 poor house-keepers five guineas each, and 200 guineas to his executor. What must he have died possessed of?

(15) A gentleman gave his daughter to her portion a scrutoir, in which were twelve drawers; in each of these were six divisions, and in each division there were 100l. a moidore, and half-a-guinea. What was the young lady's fortune?

QUESTIONS for Exercise at leisure Hours.

(16) The silk mill at Derby contains 26586 wheels, and 97746 movements, which wind off or throw 73726 yards of silk every time the great water-wheel, which gives motion to all the rest, goes about, which is three times in a minute. The question is, how many yards of silk may be thrown by this machine in a day, reckoning ten hours to a day's work? and how many in the compass of a year, deducting for Sundays and great holidays, 63 days; provided no part of it stands

still?

(17) Trajan's bridge over the Danube is said to have had 20 piers to support the arches, every pier being 60 feet thick, and some of them were 150 feet above the bed of the river; they were also 170 feet asunder. Pray what was the width of the river in that place? and how much did it exceed the length of Westminster bridge, which is about 1200 feet from shore to shore, and is supported by 11 piers, making the number of arches 12?

(18) There are two numbers, the less is 187, their difference 34. Required the square of their product, ditto of their sum, and difference and sum of those squares.

(19) There are two numbers, the greater of them is 73 times 109; and their difference 17 times 28. I demand their sum and product.

(20) In the partition of lands in an American settlement, A. had 757 acres allotted to him; B. had 2104 acres; C. 16410; D. 12881; E. 11008; F. 9813; H. 13800; and 1. 8818 acres. Now, how many acres did the settlement contain, since the allotments made as above want 416 acres of one-fifth of the whole?

(21) How many different ways can four common dice come up at one throw?-Note, One may come up siz ways.

(22) In a company S. had 31. 17s. 2d. more than T. who had six guineas less than R. who had within 16s. 8d. of as much as W. who was known to have 100 guineas, wanting ten marks of 13s. 4d. each. What money had they among them?

When the divisor consists of the same figure in all the places; that is, all 9's or all 7's, &c. annex as many ciphers to unit or 1 as there are 9's or 7's, &c. in the given divisor, for a new divisor; and, if the repeating figure be 9, divide the dividend by that divisor, and do the same with the quotient, till you get 0 for an integral quotient; then add all the overplusses together, and divide that sum by the given divisor, the overplus thence arising is that required; and the sum of all the integral quotients is the quotient required. For any other figure, divide nine times the dividend so, and the integral quotient by the repeating figure. This gives the true integral quotient; and if the ninth part of the first overplus be added to the second, repeated as the given figure, the sum will be the true overplus.

D

X. COMPOUND DIVISION

TEACHETH to divide, by one common divisor, either a simple or compound number into any proposed number of equal parts, whereof each shall be a compound number.

Case 1. When the divisor does not exceed 12.
RULE.

1. Place the divisor and dividend as integers. 2. Write their quotas under each respective dividend. 3. But if there be a remainder after dividing any of the denominations except the least, you must find how many of the next lower denomination it is equal to, by multiplying it by as many of the next less as make one of that, which add to the next, if any, and divide as before.

(3) 8)171 11 4 (4) 9)317 06 (5) 11)6*6 11

(6) Bought 3 cwt. of cheese, for which I gave 71. 11s. 6d. At what rate did I give per cwt.?

(7) If 10 dozen of candles cost 31. 17s. Id. what costs one dozen?

(8) Suppose I give my servant fourteen guineas per year, what do his monthly wages come to ?

Case 2. When the divisor exceeds 12, and is such a number that any two figures in the Multiplication Table being multiplied together, will produce it.

RULE.

Divide by component parts, as in Sect. V. Case 4.

EXAMPLES.

(9) Divide 451, 12s. 8d. into 16 equal parts. (10) Divide 31. 13s. equally amongst 24 persons. (11) What is cloth per yard, when 36 yards cost 641. 19s. ? (12) What is tobacco per cwt. if 42 cwt. cost 190l. 4s. 6d.? (13) Bought 48 yards of broad cloth for 371. 14s. 8d. I desire

to know at what rate I gave per yard?

(14) Suppose a man spends 781. 16s. 8d. in eight months' time, what is that per week?

(15) A prize of 45671. Os. 10d. is to be equally divided amongst

55 persons. What is each man's share? (16) What is tea per cwt, when 63 cwt. cost 2641. 12s.? (17) If 72 oz. of silver cost 18 guineas, what is it per oz.? (18) Suppose I have 81 cwt. of cheese, which cost me 1211.

12s. 6d. at what rate did I buy per cwt. ?

(19) Divide 174l. Is. 8d. equally amongst 120 sailors.

Case 3. When the divisor cannot be produced by the multiplication of two small numbers, divide as in Sect. IV. Case 2.

EXAMPLES.

(20) Divide 2141. 17s. 9 d. equally among 17 persons. (21) Divide 470l. amongst 145 people.

The following EXAMPLES require three DIVISIONS:

(22) I gave 30l. 2s. for 112 yards of cambric. At what rate

was that per yard?

(23) Divide 10091. equally amongst 350 persons.

(24) Suppose the clothing of 224 charity children comes to

6101. 8s. what is the expense of each?

(25) Divide 14261. equally among 640 persons.

Case 4. If the given quantity, or divisor, consist of,,

or .

RULE.

Multiply the given quantity by 4, adding to the product 1 for, 2 for, 34; and it will give the divisor, which divide with, as before; and the quotient multiplied by 4 will give the answer.