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14. If the distance from Newburyport to York be 31 miles; I demand how many times a wheel, whose circumference is 15 feet will turn round in performing the journey?

Ans. 10560 times.

15. What will 371⁄2 gross of buttons come to at 13 cents per dozen?

Ans. $58 50c.

16. If of a ship cost $1163 what is the whole worth?

Ans. $2658 28c. 5m.

17. A merchant bought 9 packages of cloth, at 3 guineas for 7 yards: each package contained 8 parcels, each parcel 12 pieces, and each piece 20 yards; how many dollars came the whole to, and how many per yard?

Yds. guin pack.

As 73

$

9: 34560 Ans. for the whole cost.

yds. guin. yd. $

As 7 3 1: 2 Ans. per yard.

18. A merchant bought 49 tuns of wine for $910; freight cost $90; duties $10; cellar $31 67c.; other charges $50 and he would gain $185 by the bargain; what must I give him for 23 tuns?

Tuns. $ $ $$ C. $ $

Tuns. $

As 49 910+90+40+31 67+50+185 : : 23: 613 33c. Ans.

19. The earth being 360 degrees in circumference, turns round on its axis in 24 hours; how far does it turn in one minute, in the 43d parallel of latitude; the degree of longitude, in this latitude, being about 51 statute miles?

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20. If a staff, 4 feet long, cast a shade (on level ground) 7 feet, what is the height of that steeple, whose shade, at the same time measures 198 feet ?**

F. sh. F. hei. F. sh. F. hei.
As 7 4 198 113 Ans.

As the rays of light from the sun may be considered parallel, the lengths of the shadows must be proportioned to the heights of the objects. Hence the reason of the statement of this question.

21. Said Harry to Dick, my purse and money are worth 3 guineas, 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. If 3 of a yard cost of a £, what will of a yard cost ?*

5

5

8

As ::: 7 : 1×7 ÷ 3 =??£ Answer. Or, 3×× √=£= £1 78. 133d.

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

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

Ans. 23h. 56′ 3′′ 56"" +1 Sidereal day.t

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 what 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 40 yds come to?

come

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

Ans. $59 6c. 24m.

Ans. 31c. 3m.

2 of an hour; hour, the se

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

Ans. 1h. 40m.

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

+++ =8%, then 20

and 20:18 100 Ans.

GENERAL METHOD OF MAKING TAXES.

RULE. In the first place an inventory of the value of all the es-tates, 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 deduct the sum of the average tax from the whole sum to be assessed; for which average you must have a separate column, as well as for the real and personal estates.

236. What method would you pursue were you to undertake the assessing of town taxes?

EXAMPLES.

1. Suppose 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. $ C.

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.

$

$

$

Secondly, As 450000 : 3375 :: 1: 74m. on the dollar.

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

His real estate being $1376, we $c. m. find by this table, that $1000 10 32

is

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$7 50c.
2 25

52 5m.
4 5

For his real estate $10 32

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

His 3 polls, at $1 25c. each are

Total.

0

$ c. m. $c. m. 8 61 73 75

c. m.

22 68 7

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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. $12.127.

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. State 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 answer.

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

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

9)2160

$7.20 Ans.

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? Ans. £2 15s.

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

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

How

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