42. If a tax of 30,000 dollars be laid on a town in which the ratable property is estimated at 9,000,000 dollars, what will be the tax of one of the citizens whose ratable estate is reckoned at 750 dollars?

D.

D. D. cts.

D. As 9,000,000 30,000.: 750 : 2:50.Ans.* 43. How far are the inhabitants on the equator carried in a minute, allowing the earth to make one revolution in 24 hours; and allowing a degree to contain 69 miles?

The earth being divided into 360 degrees, allowing 69 miles to a degree, makes the distance round it to be 25020 miles;-the number of minutes in 24 hours is 1440. Ans. 17 miles, 3 fur.

44. There is a cistern having 4 spouts; the first will empty in 15 minutes, the second in thirty minutes, the third in 45 minutes, and the fourth in 60 minutes: in what time would the cistern be emptied, if they were all running together? As 15: 1: 30 : 1 : : 90 : 3 45: 1: : 90 : 2

60

: £0 : 6

: 1 : ; 90: 11

cisterns. cist.

12/

min. min. sec.

Then, decimally, as 12.5: 1: : 90 : 7.12 Ans.

*In making taxes in a due proportion, according to the value of each man's ratable estate, proceed in the following manner. Make the amount of ratable property the first term; make the sum to be raised the second term; and one dollar the third term; and the number arising from this operation will be the amount to be raised on the dollar. From this, make a tax table from one dollar to 30, or any amount necessary. In the same manner find what is to be paid on a cent of ratable estate; and from this, make a table from 1 to 99 cents; then, from these tables, take each man's tax. Thus, if the tax were 75 cents on the dollar, and you would know what a portion of property pays, that is rated at $28,80, the tables will show the amount to be $21, for the dollars, and 60 cts., for the cents. In estimating property for making taxes, it is customary to rate it much lower than its real value.

45. If a ship's company of 15 persons have a quantity of bread, sufficient to afford to each one 8 ounces per day, during a voyage at sea, what ought to be their allowance, under the same circumstances, if 5 persons be added to their number? Ans. 6 ounces.

Note.-As the Rule of Three in Vulgar and Decimal Fractions require the same statements as in whole numbers, and is performed by multiplication and division. after the same manner of other sums in the Rule of Three, it is deemed unnecessary to give any examples. When the pupil understands Fractions and the Rule of Three, he will find no difficulty with the Rule of Three in Fractions.

Q. 1. What is the Rule of Three sometimes called? 2. What does it teach?

3. Which of the terms must be set in the third place? 4. How do you ascertain which ought to be the first term, and which is the second?

5. If the third term consist of different denominations, what do you do with them?

6. What do you do if the first and second terms are of different denominations?

7. After stating the sum, and reducing, when neces sary, the terms to similar denominations, how do you proceed to do the sum?

8. How are sums in the Single Rule of Three proved?

DOUBLE RULE OF THREE. The Double Rule of Three is that in which five or more terms are given to find another term sought.

RULE.

Set the term which is of the same denomination as the term sought, in the third place; then consider each pair of similar terms separately, and this third one, as making the terms of a statement in the Single Rule of Three, setting the similar terms in the first or second places, according to the rule of the Single Rule of Three. After stating the question in this manner, and reducing,

if necessary, the similar terms to similar denominations, then multiply the terms in the second and third places together for a dividend, and the terms in the first place together for a divisor-the quotient, after dividing, will be the term sought.

Sums in this rule may also be done by two or more statements in the Single Rule of Three.

PROOF.

By inverting the statement, or, more easily, by two statements in the Single Rule of Three.

EXAMPLES.

1. If 8 men, in 16 days, can earn 96 dollars, how much can 12 men earn in 26 days?

men 8 : 12

: :

} $96

2. If $100 gain $6 in 12 months, what will $400 gain in 9 months?

As 100 : months

6:

$400

12 : 9 : :

1200 54

400 X

1200) 216100

$18 Answer.

3. If 16 men can dig a trench 54 yards in length in 6 days, how many men will be necessary to complete one 135 yards in length, in 8 days?

By two statements in the Single Rule of Three.

as 8 : 6 ::

4. If $100 in one year gain $5 interest, what will be the interest of $750 for 7 years? Ans. $262.50. 5. If 9 persons expend $120 in 8 months, how much will 24 persons spend in 16 months at the same rate? Ans. $640.

6. If 54 dollars be the wages of 8 men for 14 days, what must be the wages of 28 men for 20 days at the same rate? Ans. $270.

7. If a horse travel 130 miles in 3 days, when the days are 12 hours in length, in how many days of 10 hours each can he travel 360 miles? Ans. 98 days.

8. If 60 bushels of corn can serve 7 horses 28 days, how many days will 47 bushels serve 6 horses?

Ans. 253 days. 9. If a barrel of beer serve 7 persons for 12 days, how many barrels will be sufficient for 14 persons for a year, or 365 days? Ans. 60 barrels.

10. If 8 men spend. 32 dollars in 13 weeks, what will 24 men spend in 52 weeks? Ans. $384. Q. 1. How many terms are generally given in the Double Rule of Three?

2. Which of the terms must be set in the third place? 3. How do you ascertain which of the other terms should be placed in the first, and which in the second place?

4. Which of the terms do you multiply together for a dividend?

5. How do you form a divisor?

6. How do you proceed when the terms consist of different denominations?

7. How is a sum in the Double Rule of Three proved?

Promiscuous questions in Simple and Compoun Proportion.

1. What can you buy 15 tons of hay for, if 3 tons cost $36? Ans. $180. 2. "William's income is $1500 a year, and his daily expenses are $2.50; how much will he have saved t the year's end? Ans. $587,50.

3 If 7 men can reap 84 acres of wheat in 12 days; how many can reap 100 acres in 5 days? Ans. 20 men. 4. If a horse will trot in a gig 8 miles in an hour, how far will he trot at the same rate, in 34 hours? Aus. 28 miles. 5. A merchant bought 5 pieces of muslin, cach containing 26 yards, at 11 cents a yard; what did they amount to? Ans. $14.30. 6. Ifa family of 8 persons, in 24 months, spend $480, how much would 16 persons spend in 8 months? Ans. $320. 7. A merchant, owning of a vessel, sells of his share for $500; what was the whole vessel worth? 3 of 3==; then, as of the vessel is $500, is $250, and, or the whole vessel, is 5X250-$1250. Or thus; of : 1 : : 500 $1250. Ans., as before.

8. If 1 lb. indigo cost $3.84, what will 49,2 lbs. cost at the same rate? Ans. $125,952. 9. If 112 acres of meadow be mowed over by 16 men, in 7 days; how many acres can 24 men mow over, in 19 days? Ans. 456 acres. 10. If 8 cwt. of iron can be carried 128 miles for $12.80, what will be the expense of carrying 4 cwt. 32 miles? Ans. $1.60. 11. A merchant bought a bale of cloth, containing 375 yds. at 3.12 a yard; what did the whole amount to? Ans. $1171.87,5. 12. A mother allows her daughter, at a boarding school, 3 cents a day for spending money; how much will that amount to in a year? Ans. $10.95. 13. Suppose the wages of 6 persons for 21 weeks be 288 dollars, what must 14 persons receive for 46 weeks? Ans. $1472.