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21. Said Harry to Dick, my purse and money are worth 34 guin. eas, but the money is worth eleven times as much as the purse; pray how much money is there in it ?

Ans. £4 3s. 5d.

22. It of a yard cost of a £, what will it of a yard cost ?**

As : : : : x1==1f£ Answer. Or, : : : : $X4X1-3f£=£1 78. 137d.

23 There is a cistern, having four cocks; the first will empty it in ten minutes; the second io 25 minutes; the third in 40, and the fourth in 80 minutes; in what time will all four, running together empty it? S202 Cist

. - Min. Cist. Min. Cist. Min. As

:1:: 60: 40

45

60X4
80

that is : 60 ::1: 51.
4

45

6 3

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111 Cist.

24. If the earth revolves 366 times in 365 days, in what time does it perform cne revolution ?

Ans. 23h. 56' 3' 56''+=1 Sidereal day.t

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25. If the earth makes one complete revolution in 23h. 56' 3"+, in what time does it pass through one degree ?

Ans. 3' 55" 20".

26. If the earth performs its diurnal revolution in a solar day, or 24 hours; in wbat time does it move one degree?

Ans. 4'.

* If the first term of the statement be a Vulgar Fraction, whether the other terms are or not, after the first and third terms are reduced to the same denomination, invert the first term as in division of Vulgar Fractions, and the product of the three terms will of course be the answer.

The student should work the questions in Vulgar, or Decimal Fractions, according as the rules for fractions require.

+ A sidereal day is the space of time which happens between the departure of a star from, and its return to the same meridian again.

The solar day is that space of time which intervenes between the sun's departing from any one meridian, and its return to the same again.

27. If yd. cost $}, what will 404 yds. come to?

Ans. $59 6c. 2fm.

28. At $35 per cwt. what will 93 lb. come to?

Ans. 31c. 3m.

29. A conduit has a cock, which will fill a cistern in •2 of an hour ; this cistern has 3 cocks, the first will empty it in 1.25 hour, the second in .625 of an hour, and the third in 5 hour. Jo what time will the cistern be filled, if all four run together?

Ans, ih. 400.

30. In a certain school, alth of the pupils study Greek, i' study Latin, f study Arithmetick, 4 read and write, and 20 attend to other things ; what is the number of pupils ?

+4+3, then 205 and : 20 : : 18 : 100 Ans.

GENERAL METHOD OF MAKING TAXES.

RULE. In the first place an inventory of the value of all the estates, both real and personal, and the number of polls for which each person is rateable, must be taken in separate columns : the most concise way is then to make the total value of the inventory the first term, the tax to be assessed the second, and $1 the third, and the quotient will show the value on the dollar: 2dly, make a table, by multiplying the value on the dollar by 1, 2, 3, 4, &c.-3dly, From the inventory take the real and personal estates of each man, and find them separately in the table, which will shew you each man's proportional share of the tax for real and personal estates.

Note. If any part of the tax is averaged on the polls, or otherwise, before stating, to find the value on the dollar, you must dedact the sum of the average tax from the whole sum to be assessed; for which av. erage you must have a separate column, as well as for the real and personal estates.

236. What method would you pursue sare you to undertake the assessing of town tares ?

EXAMPLES.

1. Sappose the General Court should grant a tax of $500000, of which the town of Portsmouth is to pay $5312 50c. and, of which the polls, being 1550, are to pay $1 25c. each ; The town's inventory amounts to $450000, what will it be on the dollar, and what is A's tax, whose estate (as by the inventory) is as follows, viz. real $1376, personal $1149, and he has 3 polls ? Pol. $ c.

Pol. First, As 1 : 1 25 : : 1550 : 1937 50 the average part of the tax to be deducted from $5312 50c. and there will remain $3375.

$ $ 郑 $ Secondly, As 450000 : 3375 : : 1 : 73m. op the dollar.

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TABLE.

$ $ C. m. 1 is 0 0 1 2-0 1 5 3-0 2 21 4-0 3 0 5-0 3 73 6-0 4 5 7-0 5 21

6 0 9_0

6 77 10-07 5

C.
20 is 0 15 0
30-0 22 6
400 30 0
50-037 5
60—0 45 0
70-0 52 5
8040 600
90_0 67 5
100-075

$ $ C. 200 is 1 50 300--2 25 400-300 500-3 75 600—4 50 700-5 25 800-6 00 900-6 75 1000-7 50

$7 50c.

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Now to find what A's rate will be, Real. Personal. Polls. Total.

His real estate being $1376, we$ c. m. $ c. m. $ c. m. $ c. m. find by this table, that $1000 10 32 08 61 72 3 75 22 68 77 is that $300 is

2 25 that $70 is

52 5m. and that $6 is

4.5 For his real estate $10 32

In like manner we find bis tax for personal estate to be

$8 61 77

+$1032=$22 68c.73m. His 3 polls, at $1 25c. eacb are 3 75

or, $22 69c. Ans.

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2. Suppose a tax of $755 be laid on a town, and the inventory of all the estates in town amounts to $9345, what must A. pay, whose estate is $149!

Ans. $12 038 nearly.

RULE OF THREE DIRECT.

The RULE OF THREE DIRECT teaches, by having three numbers given, to find a fourth, which shall have the same ratio to the second, as the third has to the first.

RULE.

1. Slate the question by making that number, which asks the question,* the third term, that which is of the same name or kind, the first term ; and that which is of the same name or kind with the answer, the second term.

2. Multiply the second and third terms together, and divide the product by the first term, and the quotient will be the fourth term, or

The notes under the general rule are applicable to this rule.

wer.

EXAMPLES.

1. If 3 bushels of corn be worth $1.80, what is the value of 12 bushels ?

bu. $ c. bu.
3 : 1.80 :: 12

12

3)2160

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$7.20 Aps. In this example, 12 bushels asks the question, and is made the third term ; 3 bushels being of the same name, is made the first term; and $1.80 being of the same name with the answer, is made the second term. Here the third term is greater than the first, and the question evidently requires the fourth term or answer to be greater than the second; therefore, the question belongs to the Rule of Three Direct.

2. If 6 lbs. sugar cost 10s. what will 33 lbs. cost at the same rate ?

Aps. £2 15s.

* The term which asks or moves the question has generally some words like these be fore it, viz. What will? What cost? How many? How far ? How much? How

long ? &c.

237. What is the method of operation in the Rule of Three Direct.

RULE OF THREE INVERSE;

OR,
RECIPROCAL PROPORTION.

THE RULE OF THREE INVERSE teaches, by having three numbers given, to tind a fourth, which shall have the same ratio to the second, as the first has to the third.

RULE.-State and reduce the terms as in the Rule of Three Direct; then multiply the first and second terms together, and divide the product by the third, the quotient will be the fourth term, or answer.

EXAMPLES

m.

m.

1. If 6 men can do a piece of work in 18 days, in what time can 12 men do it ?

d. 6 : 18 : : 12 In this example, the third term is greater than 6

the first, yet it is evident, that the question re

quires the fourth term or answer to be less than 12)108 the second; therefore, this question belongs to

the Rule of Three Inverse. 9 days Aos.

2. If a man perform a journey in 15 days, when the day is 12 hours long, io how many days will he do it, when thc day is but 10 hours ?

Ans. 18 days.

THE DOUBLE RULE OF THREE.

THE DOUBLE RULE OF THREE, or COMPOUND PROPORTION, is the method of resolving such questions as require two or more operations by Simple Proportion.

It always consists of an odd number of terms given, as five, seven, &c. These terms are distinguished into terms of supposition, and terms of demand ; the number of the former always exceeding that of the latter by one, which is of the same name or kind with the answer or term required.

238. How do you proceed in the Rule of Three Inverse ?. -239. What is Compound Proportion, or the Double Rule of Three ?- -240, How is it distinguished from Sim. ple Proportion ?

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