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Dollar Table, from one dollar Cent Table, from one to ninety

to eighteen.

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$10 1

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30

3

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4

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40

4

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50

5

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60 6

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To make the tax by the help of the tables.

1. Required A. Bs': tax his rateable estate being $8.50 cts.

$8.00 cts. rateable estate pays $80.00 cts. tax.

50 cts. rateable estate pays 5,00

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In the same manner take each man's tax from

the tables, and their several proportions will be ás follows.

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NOTE. It must be remembered that no one set of tables will answer for any two different taxes, unless the sum of the two different taxes are alike. Example second.

1. Suppose the estates in the preceding inventory are taxed in a further sum of 19 dollars; I demand the proportion to each man, according to their several rateable estates.

To find what one dollar pays.

Say if 22 dolls. 50 cents pay 19 dollars; what will 1 dollar pay?

D. cts. D.

D. cts. m.

As 22.50 19: 184 4 Ans.

To find what 1 cent will pay.

Say if 22 dolls. 50 cents pay 19 dollars, what will

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Dollar table, from one dollar Cent Table, from one cent to

to eighteen.

ninety.

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cent pays.

·00.8

66

46

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To make the second tax list.

1. From the last tables it is required to take A. Bs' tax. His rateable estate is $8.50.

8 dollars pay $6.75·2

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Proceed in like manner to find each man's tax, and their several proportions will stand as in the annexed list.

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NOTE. In assessing taxes, the law allows the assessor to assess a certain sum, over and above the necessary sum to be raised; or else the tax would not be large enough when there are remainders, which is almost always the case.

INVERSE PROPORTION.

DEFINITION.-Inverse proportion teaches by having three numbers given to find a fourth, that shall have the same proportion to the third, as the first has to the second; when more requires less, the proportion is Inverse; when less requires more, the proportion is also Inverse; more requires less, when the third term is larger than the first, and the sense of the question requires the fourth to be less than the second; less requires more when the third term is smaller than the first, and the sense of the question requires the fourth to be greater than the second.

RULE. Make that number which asks the question the third term; that, which is of the same name, the first term; and the other remaining number must be the middle term; multiply the first and second terms together, and divide the product by the third; the quotient will be the answer requir ed.*

Examples.

1. If 8 men can build a tower in 12 days; I demand how long it would take them, if 4 more were added to their number?

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*I have followed the same method in Inverse proportion as I did in direct proportion; that is, I have done the sums in decimals and then the other way.

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NOTE. In this example it is evident that 12 men would do the work quicker than 8, therefore more requires less; more men, require less time.

The same question done the other way.

Ans. 8 days.

2. There is a piece of land 16.5 rods long; I demand the width to make an acre, allowing 20 links Ans. 9.696 rds.

to a rod.

The same question done the other way.

Ans. 9. rds. 13† lin.

3. A ship at sea is provided with bread and water sufficient to supply 20 men 9 months, 30 days to a month; but finding a wreck in which were 3 men and 3 boys, to whom they were willing to communicate relief: I demand the time they all can draw their allowance, allowing 2 boys equal to a man. Ans. 7.346 mo.

The same question done the other way.

Ans. 7 months 10 days.

4. There is a piece of land that is 10 rds. 10 links in width; I demand the length to make an acre, allowing 20 links to a rod.

Ans. 15.238 rds.

The same question done the other way.

Ans. 15 rds. 4t links.

5. How much in length of that which is 5 rods

wide will make an acre?

The same question done the other way.

Ans. 32 rds.

Ans. 32 rds.

6. How much carpeting, that is 1.5 yds. wide will cover a floor that is 7.5 yds. long, and 5 yds. wide? Ans. 25 yds.

The same question done the other way.

Ans. 25 yds.

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